@article{GrebenkovMetzlerOshanin2021, author = {Grebenkov, Denis S. and Metzler, Ralf and Oshanin, Gleb}, title = {A molecular relay race: sequential first-passage events to the terminal reaction centre in a cascade of diffusion controlled processes}, series = {New Journal of Physics (NJP)}, volume = {23}, journal = {New Journal of Physics (NJP)}, publisher = {IOP - Institute of Physics Publishing}, address = {Bristol}, issn = {1367-2630}, doi = {10.1088/1367-2630/ac1e42}, pages = {18}, year = {2021}, abstract = {We consider a sequential cascade of molecular first-reaction events towards a terminal reaction centre in which each reaction step is controlled by diffusive motion of the particles. The model studied here represents a typical reaction setting encountered in diverse molecular biology systems, in which, e.g. a signal transduction proceeds via a series of consecutive 'messengers': the first messenger has to find its respective immobile target site triggering a launch of the second messenger, the second messenger seeks its own target site and provokes a launch of the third messenger and so on, resembling a relay race in human competitions. For such a molecular relay race taking place in infinite one-, two- and three-dimensional systems, we find exact expressions for the probability density function of the time instant of the terminal reaction event, conditioned on preceding successful reaction events on an ordered array of target sites. The obtained expressions pertain to the most general conditions: number of intermediate stages and the corresponding diffusion coefficients, the sizes of the target sites, the distances between them, as well as their reactivities are arbitrary.}, language = {en} } @misc{GrebenkovMetzlerOshanin2021, author = {Grebenkov, Denis S. and Metzler, Ralf and Oshanin, Gleb}, title = {A molecular relay race: sequential first-passage events to the terminal reaction centre in a cascade of diffusion controlled processes}, series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, journal = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, issn = {1866-8372}, doi = {10.25932/publishup-52194}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-521942}, pages = {20}, year = {2021}, abstract = {We consider a sequential cascade of molecular first-reaction events towards a terminal reaction centre in which each reaction step is controlled by diffusive motion of the particles. The model studied here represents a typical reaction setting encountered in diverse molecular biology systems, in which, e.g. a signal transduction proceeds via a series of consecutive 'messengers': the first messenger has to find its respective immobile target site triggering a launch of the second messenger, the second messenger seeks its own target site and provokes a launch of the third messenger and so on, resembling a relay race in human competitions. For such a molecular relay race taking place in infinite one-, two- and three-dimensional systems, we find exact expressions for the probability density function of the time instant of the terminal reaction event, conditioned on preceding successful reaction events on an ordered array of target sites. The obtained expressions pertain to the most general conditions: number of intermediate stages and the corresponding diffusion coefficients, the sizes of the target sites, the distances between them, as well as their reactivities are arbitrary.}, language = {en} } @article{SeissAlbersSremčevićetal.2019, author = {Seiß, Martin and Albers, Nicole and Sremčević, Miodrag and Schmidt, J{\"u}rgen and Salo, Heikki and Seiler, Michael and Hoffmann, Holger and Spahn, Frank}, title = {Hydrodynamic Simulations of Moonlet-induced Propellers in Saturn's Rings}, series = {The astronomical journal}, volume = {157}, journal = {The astronomical journal}, number = {1}, publisher = {IOP Publishing Ltd.}, address = {Bristol}, issn = {0004-6256}, doi = {10.3847/1538-3881/aaed44}, pages = {11}, year = {2019}, abstract = {One of the biggest successes of the Cassini mission is the detection of small moons (moonlets) embedded in Saturns rings that cause S-shaped density structures in their close vicinity, called propellers. Here, we present isothermal hydrodynamic simulations of moonlet-induced propellers in Saturn's A ring that denote a further development of the original model. We find excellent agreement between these new hydrodynamic and corresponding N-body simulations. Furthermore, the hydrodynamic simulations confirm the predicted scaling laws and the analytical solution for the density in the propeller gaps. Finally, this mean field approach allows us to simulate the pattern of the giant propeller Bl{\´e}riot, which is too large to be modeled by direct N-body simulations. Our results are compared to two stellar occultation observations by the Cassini Ultraviolet Imaging Spectrometer (UVIS), which intersect the propeller Bl{\´e}riot. Best fits to the UVIS optical depth profiles are achieved for a Hill radius of 590 m, which implies a moonlet diameter of about 860 m. Furthermore, the model favors a kinematic shear viscosity of the surrounding ring material of ν0 = 340 cm2 s-1, a dispersion velocity in the range of 0.3 cm s-1 < c0 < 1.5 cm s-1, and a fairly high bulk viscosity 7 < ξ0/ν0 < 17. These large transport values might be overestimated by our isothermal ring model and should be reviewed by an extended model including thermal fluctuations.}, language = {en} } @article{AbdallaAharonianBenkhalietal.2019, author = {Abdalla, Hassan E. and Aharonian, Felix A. and Benkhali, F. Ait and Ang{\"u}ner, Ekrem Oǧuzhan and Arakawa, M. and Arcaro, C. and Armand, C. and Arrieta, M. and Backes, M. and Barnard, M. and Becherini, Y. and Tjus, J. Becker and Berge, D. and Bernloehr, K. and Blackwell, R. and Bottcher, M. and Boisson, C. and Bolmont, J. and Bonnefoy, S. and Bordas, Pol and Bregeon, J. and Brun, F. and Brun, P. and Bryan, M. and Buechele, M. and Bulik, T. and Bylund, T. and Capasso, M. and Caroff, S. and Carosi, A. and Casanova, Sabrina and Cerruti, M. and Chakraborty, N. and Chand, T. and Chandra, S. and Chaves, R. C. G. and Chen, A. and Colafrancesco, S. and Condon, B. and Davids, I. D. and Deil, C. and Devin, J. and deWilt, P. and Dirson, L. and Djannati-Atai, A. and Dmytriiev, A. and Donath, A. and Doroshenko, V and Dyks, J. and Egberts, Kathrin and Emery, G. and Ernenwein, J-P and Eschbach, S. and Fegan, S. and Fiasson, A. and Fontaine, G. and Funk, S. and Fuessling, M. and Gabici, S. and Gallant, Y. A. and Gate, F. and Giavitto, G. and Glawion, D. and Glicenstein, J. F. and Gottschall, D. and Grondin, M-H and Hahn, J. and Haupt, M. and Heinzelmann, G. and Henri, G. and Hermann, G. and Hinton, James Anthony and Hofmann, W. and Hoischen, Clemens and Holch, Tim Lukas and Holler, M. and Horns, D. and Huber, D. and Iwasaki, H. and Jacholkowska, A. and Jamrozy, M. and Jankowsky, D. and Jankowsky, F. and Jouvin, L. and Jung-Richardt, I and Kastendieck, M. A. and Katarzynski, K. and Katsuragawa, M. and Katz, U. and Kerszberg, D. and Khangulyan, D. and Khelifi, B. and King, J. and Klepser, S. and Kluzniak, W. and Komin, Nu and Kosack, K. and Kraus, M. and Lamanna, G. and Lau, J. and Lefaucheur, J. and Lemiere, A. and Lemoine-Goumard, M. and Lenain, J-P and Leser, Eva and Lohse, T. and Lopez-Coto, R. and Lypova, I and Malyshev, D. and Marandon, V and Marcowith, Alexandre and Mariaud, C. and Marti-Devesa, G. and Marx, R. and Maurin, G. and Meintjes, P. J. and Mitchell, A. M. W. and Moderski, R. and Mohamed, M. and Mohrmann, L. and Moore, C. and Moulin, Emmanuel and Murach, T. and Nakashima, S. and de Naurois, M. and Ndiyavala, H. and Niederwanger, F. and Niemiec, J. and Oakes, L. and Odaka, H. and Ohm, S. and Ostrowski, M. and Oya, I and Panter, M. and Parsons, R. D. and Perennes, C. and Petrucci, P-O and Peyaud, B. and Piel, Q. and Pita, S. and Poireau, V and Noel, A. Priyana and Prokhorov, D. A. and Prokoph, H. and Puehlhofer, G. and Punch, M. and Quirrenbach, A. and Raab, S. and Rauth, R. and Reimer, A. and Reimer, O. and Renaud, M. and Rieger, F. and Rinchiuso, L. and Romoli, C. and Rowell, G. and Rudak, B. and Ruiz-Velasco, E. and Sahakian, V and Saito, S. and Sanchez, David M. and Santangelo, Andrea and Sasaki, M. and Schlickeiser, R. and Schussler, F. and Schulz, A. and Schutte, H. and Schwanke, U. and Schwemmer, S. and Seglar-Arroyo, M. and Senniappan, M. and Seyffert, A. S. and Shafi, N. and Shilon, I and Shiningayamwe, K. and Simoni, R. and Sinha, A. and Sol, H. and Specovius, A. and Spir-Jacob, M. and Stawarz, L. and Steenkamp, R. and Stegmann, Christian and Steppa, Constantin Beverly and Takahashi, T. and Tavernet, J-P and Tavernier, T. and Taylor, A. M. and Terrier, R. and Tibaldo, L. and Tiziani, D. and Tluczykont, M. and Trichard, C. and Tsirou, M. and Tsuji, N. and Tuffs, R. and Uchiyama, Y. and van der Walt, D. J. and van Eldik, C. and van Rensburg, C. and van Soelen, B. and Vasileiadis, G. and Veh, J. and Venter, C. and Vincent, P. and Vink, J. and Voisin, F. and Voelk, H. J. and Vuillaume, T. and Wadiasingh, Z. and Wagner, S. J. and Wagner, R. M. and White, R. and Wierzcholska, A. and Yang, R. and Yoneda, H. and Zaborov, D. and Zacharias, M. and Zanin, R. and Zdziarski, A. A. and Zech, Alraune and Zefi, F. and Ziegler, A. and Zorn, J. and Zywucka, N.}, title = {Particle transport within the pulsar wind nebula HESS J1825-137}, series = {Astronomy and astrophysics : an international weekly journal}, volume = {621}, journal = {Astronomy and astrophysics : an international weekly journal}, publisher = {EDP Sciences}, address = {Les Ulis}, organization = {HESS Collaboration}, issn = {1432-0746}, doi = {10.1051/0004-6361/201834335}, pages = {18}, year = {2019}, abstract = {Context. We present a detailed view of the pulsar wind nebula (PWN) HESS J1825-137. We aim to constrain the mechanisms dominating the particle transport within the nebula, accounting for its anomalously large size and spectral characteristics. Aims. The nebula was studied using a deep exposure from over 12 years of H.E.S.S. I operation, together with data from H.E.S.S. II that improve the low-energy sensitivity. Enhanced energy-dependent morphological and spatially resolved spectral analyses probe the very high energy (VHE, E > 0.1 TeV) gamma-ray properties of the nebula. Methods. The nebula emission is revealed to extend out to 1.5 degrees from the pulsar, similar to 1.5 times farther than previously seen, making HESS J1825-137, with an intrinsic diameter of similar to 100 pc, potentially the largest gamma-ray PWN currently known. Characterising the strongly energy-dependent morphology of the nebula enables us to constrain the particle transport mechanisms. A dependence of the nebula extent with energy of R proportional to E alpha with alpha = -0.29 +/- 0.04(stat) +/- 0.05(sys) disfavours a pure diffusion scenario for particle transport within the nebula. The total gamma-ray flux of the nebula above 1 TeV is found to be (1.12 +/- 0.03(stat) +/- 0.25(sys)) +/- 10(-11) cm(-2) s(-1), corresponding to similar to 64\% of the flux of the Crab nebula. Results. HESS J1825-137 is a PWN with clearly energy-dependent morphology at VHE gamma-ray energies. This source is used as a laboratory to investigate particle transport within intermediate-age PWNe. Based on deep observations of this highly spatially extended PWN, we produce a spectral map of the region that provides insights into the spectral variation within the nebula.}, language = {en} } @article{SposiniChechkinMetzler2018, author = {Sposini, Vittoria and Chechkin, Aleksei V. and Metzler, Ralf}, title = {First passage statistics for diffusing diffusivity}, series = {Journal of physics : A, Mathematical and theoretical}, volume = {52}, journal = {Journal of physics : A, Mathematical and theoretical}, number = {4}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {1751-8113}, doi = {10.1088/1751-8121/aaf6ff}, pages = {11}, year = {2018}, abstract = {A rapidly increasing number of systems is identified in which the stochastic motion of tracer particles follows the Brownian law < r(2)(t)> similar or equal to Dt yet the distribution of particle displacements is strongly non-Gaussian. A central approach to describe this effect is the diffusing diffusivity (DD) model in which the diffusion coefficient itself is a stochastic quantity, mimicking heterogeneities of the environment encountered by the tracer particle on its path. We here quantify in terms of analytical and numerical approaches the first passage behaviour of the DD model. We observe significant modifications compared to Brownian-Gaussian diffusion, in particular that the DD model may have a faster first passage dynamics. Moreover we find a universal crossover point of the survival probability independent of the initial condition.}, language = {en} } @article{GrebenkovSposiniMetzleretal.2020, author = {Grebenkov, Denis S. and Sposini, Vittoria and Metzler, Ralf and Oshanin, Gleb and Seno, Flavio}, title = {Exact distributions of the maximum and range of random diffusivity processes}, series = {New Journal of Physics}, volume = {23}, journal = {New Journal of Physics}, publisher = {Dt. Physikalische Ges.}, address = {Bad Honnef}, issn = {1367-2630}, doi = {10.1088/1367-2630/abd313}, pages = {23}, year = {2020}, abstract = {We study the extremal properties of a stochastic process xt defined by the Langevin equation ẋₜ =√2Dₜ ξₜ, in which ξt is a Gaussian white noise with zero mean and Dₜ is a stochastic'diffusivity', defined as a functional of independent Brownian motion Bₜ.We focus on threechoices for the random diffusivity Dₜ: cut-off Brownian motion, Dₜt ∼ Θ(Bₜ), where Θ(x) is the Heaviside step function; geometric Brownian motion, Dₜ ∼ exp(-Bₜ); and a superdiffusive process based on squared Brownian motion, Dₜ ∼ B²ₜ. For these cases we derive exact expressions for the probability density functions of the maximal positive displacement and of the range of the process xₜ on the time interval ₜ ∈ (0, T).We discuss the asymptotic behaviours of the associated probability density functions, compare these against the behaviour of the corresponding properties of standard Brownian motion with constant diffusivity (Dₜ = D0) and also analyse the typical behaviour of the probability density functions which is observed for a majority of realisations of the stochastic diffusivity process.}, language = {en} } @misc{GrebenkovSposiniMetzleretal.2020, author = {Grebenkov, Denis S. and Sposini, Vittoria and Metzler, Ralf and Oshanin, Gleb and Seno, Flavio}, title = {Exact distributions of the maximum and range of random diffusivity processes}, series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, journal = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, number = {1142}, issn = {1866-8372}, doi = {10.25932/publishup-50397}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-503976}, pages = {24}, year = {2020}, abstract = {We study the extremal properties of a stochastic process xt defined by the Langevin equation ẋₜ =√2Dₜ ξₜ, in which ξt is a Gaussian white noise with zero mean and Dₜ is a stochastic'diffusivity', defined as a functional of independent Brownian motion Bₜ.We focus on threechoices for the random diffusivity Dₜ: cut-off Brownian motion, Dₜt ∼ Θ(Bₜ), where Θ(x) is the Heaviside step function; geometric Brownian motion, Dₜ ∼ exp(-Bₜ); and a superdiffusive process based on squared Brownian motion, Dₜ ∼ B²ₜ. For these cases we derive exact expressions for the probability density functions of the maximal positive displacement and of the range of the process xₜ on the time interval ₜ ∈ (0, T).We discuss the asymptotic behaviours of the associated probability density functions, compare these against the behaviour of the corresponding properties of standard Brownian motion with constant diffusivity (Dₜ = D0) and also analyse the typical behaviour of the probability density functions which is observed for a majority of realisations of the stochastic diffusivity process.}, language = {en} } @article{GraetzSeissSchmidtetal.2019, author = {Gr{\"a}tz, Fabio M. and Seiß, Martin and Schmidt, J{\"u}rgen and Colwell, Joshua and Spahn, Frank}, title = {Sharp Gap Edges in Dense Planetary Rings}, series = {The astrophysical journal : an international review of spectroscopy and astronomical physics}, volume = {872}, journal = {The astrophysical journal : an international review of spectroscopy and astronomical physics}, number = {2}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {0004-637X}, doi = {10.3847/1538-4357/ab007e}, pages = {11}, year = {2019}, abstract = {One of the most intriguing facets of Saturn's rings are the sharp edges of gaps in the rings where the surface density abruptly drops to zero. This is despite of the fact that the range over which a moon transfers angular momentum onto the ring material is much larger. Recent UVIS-scans of the edges of the Encke and Keeler gap show that this drop occurs over a range approximately equal to the rings' thickness. Borderies et al. show that this striking feature is likely related to the local reversal of the usually outward directed viscous transport of angular momentum in strongly perturbed regions. In this article we revise the Borderies et al. model using a granular flow model to define the shear and bulk viscosities, ν and ζ, and incorporate the angular momentum flux reversal effect into the axisymmetric diffusion model we developed for gaps in dense planetary rings. Finally, we apply our model to the Encke and Keeler division in order to estimate the shear and bulk viscosities in the vicinity of both gaps}, language = {en} } @misc{ThapaWyłomańskaSikoraetal.2021, author = {Thapa, Samudrajit and Wyłomańska, Agnieszka and Sikora, Grzegorz and Wagner, Caroline E. and Krapf, Diego and Kantz, Holger and Chechkin, Aleksei V. and Metzler, Ralf}, title = {Leveraging large-deviation statistics to decipher the stochastic properties of measured trajectories}, series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, journal = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, number = {1118}, issn = {1866-8372}, doi = {10.25932/publishup-49349}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-493494}, pages = {24}, year = {2021}, abstract = {Extensive time-series encoding the position of particles such as viruses, vesicles, or individualproteins are routinely garnered insingle-particle tracking experiments or supercomputing studies.They contain vital clues on how viruses spread or drugs may be delivered in biological cells.Similar time-series are being recorded of stock values in financial markets and of climate data.Such time-series are most typically evaluated in terms of time-averaged mean-squareddisplacements (TAMSDs), which remain random variables for finite measurement times. Theirstatistical properties are different for differentphysical stochastic processes, thus allowing us toextract valuable information on the stochastic process itself. To exploit the full potential of thestatistical information encoded in measured time-series we here propose an easy-to-implementand computationally inexpensive new methodology, based on deviations of the TAMSD from itsensemble average counterpart. Specifically, we use the upper bound of these deviations forBrownian motion (BM) to check the applicability of this approach to simulated and real data sets.By comparing the probability of deviations fordifferent data sets, we demonstrate how thetheoretical bound for BM reveals additional information about observed stochastic processes. Weapply the large-deviation method to data sets of tracer beads tracked in aqueous solution, tracerbeads measured in mucin hydrogels, and of geographic surface temperature anomalies. Ouranalysis shows how the large-deviation properties can be efficiently used as a simple yet effectiveroutine test to reject the BM hypothesis and unveil relevant information on statistical propertiessuch as ergodicity breaking and short-time correlations.}, language = {en} } @article{ThapaWyłomańskaSikoraetal.2021, author = {Thapa, Samudrajit and Wyłomańska, Agnieszka and Sikora, Grzegorz and Wagner, Caroline E. and Krapf, Diego and Kantz, Holger and Chechkin, Aleksei V. and Metzler, Ralf}, title = {Leveraging large-deviation statistics to decipher the stochastic properties of measured trajectories}, series = {New Journal of Physics}, volume = {23}, journal = {New Journal of Physics}, publisher = {Dt. Physikalische Ges. ; IOP}, address = {Bad Honnef ; London}, issn = {1367-2630}, doi = {10.1088/1367-2630/abd50e}, pages = {22}, year = {2021}, abstract = {Extensive time-series encoding the position of particles such as viruses, vesicles, or individualproteins are routinely garnered insingle-particle tracking experiments or supercomputing studies.They contain vital clues on how viruses spread or drugs may be delivered in biological cells.Similar time-series are being recorded of stock values in financial markets and of climate data.Such time-series are most typically evaluated in terms of time-averaged mean-squareddisplacements (TAMSDs), which remain random variables for finite measurement times. Theirstatistical properties are different for differentphysical stochastic processes, thus allowing us toextract valuable information on the stochastic process itself. To exploit the full potential of thestatistical information encoded in measured time-series we here propose an easy-to-implementand computationally inexpensive new methodology, based on deviations of the TAMSD from itsensemble average counterpart. Specifically, we use the upper bound of these deviations forBrownian motion (BM) to check the applicability of this approach to simulated and real data sets.By comparing the probability of deviations fordifferent data sets, we demonstrate how thetheoretical bound for BM reveals additional information about observed stochastic processes. Weapply the large-deviation method to data sets of tracer beads tracked in aqueous solution, tracerbeads measured in mucin hydrogels, and of geographic surface temperature anomalies. Ouranalysis shows how the large-deviation properties can be efficiently used as a simple yet effectiveroutine test to reject the BM hypothesis and unveil relevant information on statistical propertiessuch as ergodicity breaking and short-time correlations.}, language = {en} } @phdthesis{Šustr2020, author = {Šustr, David}, title = {Molecular diffusion in polyelectrolyte multilayers}, doi = {10.25932/publishup-48903}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-489038}, school = {Universit{\"a}t Potsdam}, pages = {106}, year = {2020}, abstract = {Research on novel and advanced biomaterials is an indispensable step towards their applications in desirable fields such as tissue engineering, regenerative medicine, cell culture, or biotechnology. The work presented here focuses on such a promising material: polyelectrolyte multilayer (PEM) composed of hyaluronic acid (HA) and poly(L-lysine) (PLL). This gel-like polymer surface coating is able to accumulate (bio-)molecules such as proteins or drugs and release them in a controlled manner. It serves as a mimic of the extracellular matrix (ECM) in composition and intrinsic properties. These qualities make the HA/PLL multilayers a promising candidate for multiple bio-applications such as those mentioned above. The work presented aims at the development of a straightforward approach for assessment of multi-fractional diffusion in multilayers (first part) and at control of local molecular transport into or from the multilayers by laser light trigger (second part). The mechanism of the loading and release is governed by the interaction of bioactives with the multilayer constituents and by the diffusion phenomenon overall. The diffusion of a molecule in HA/PLL multilayers shows multiple fractions of different diffusion rate. Approaches, that are able to assess the mobility of molecules in such a complex system, are limited. This shortcoming motivated the design of a novel evaluation tool presented here. The tool employs a simulation-based approach for evaluation of the data acquired by fluorescence recovery after photobleaching (FRAP) method. In this approach, possible fluorescence recovery scenarios are primarily simulated and afterwards compared with the data acquired while optimizing parameters of a model until a sufficient match is achieved. Fluorescent latex particles of different sizes and fluorescein in an aqueous medium are utilized as test samples validating the analysis results. The diffusion of protein cytochrome c in HA/PLL multilayers is evaluated as well. This tool significantly broadens the possibilities of analysis of spatiotemporal FRAP data, which originate from multi-fractional diffusion, while striving to be widely applicable. This tool has the potential to elucidate the mechanisms of molecular transport and empower rational engineering of the drug release systems. The second part of the work focuses on the fabrication of such a spatiotemporarily-controlled drug release system employing the HA/PLL multilayer. This release system comprises different layers of various functionalities that together form a sandwich structure. The bottom layer, which serves as a reservoir, is formed by HA/PLL PEM deposited on a planar glass substrate. On top of the PEM, a layer of so-called hybrids is deposited. The hybrids consist of thermoresponsive poly(N-isopropylacrylamide) (PNIPAM) -based hydrogel microparticles with surface-attached gold nanorods. The layer of hybrids is intended to serve as a gate that controls the local molecular transport through the PEM-solution-interface. The possibility of stimulating the molecular transport by near-infrared (NIR) laser irradiation is being explored. From several tested approaches for the deposition of hybrids onto the PEM surface, the drying-based approach was identified as optimal. Experiments, that examine the functionality of the fabricated sandwich at elevated temperature, document the reversible volume phase transition of the PEM-attached hybrids while sustaining the sandwich stability. Further, the gold nanorods were shown to effectively absorb light radiation in the tissue- and cell-friendly NIR spectral region while transducing the energy of light into heat. The rapid and reversible shrinkage of the PEM-attached hybrids was thereby achieved. Finally, dextran was employed as a model transport molecule. It loads into the PEM reservoir in a few seconds with the partition constant of 2.4, while it spontaneously releases in a slower, sustained manner. The local laser irradiation of the sandwich, which contains the fluorescein isothiocyanate tagged dextran, leads to a gradual reduction of fluorescence intensity in the irradiated region. The release system fabricated employs renowned photoresponsivity of the hybrids in an innovative setting. The results of the research are a step towards a spatially-controlled on-demand drug release system that paves the way to spatiotemporally controlled drug release. The approaches developed in this work have the potential to elucidate the molecular dynamics in ECM and to foster engineering of multilayers with properties tuned to mimic the ECM. The work aims at spatiotemporal control over the diffusion of bioactives and their presentation to the cells.}, language = {en} } @phdthesis{Sposini2020, author = {Sposini, Vittoria}, title = {The random diffusivity approach for diffusion in heterogeneous systems}, doi = {10.25932/publishup-48780}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-487808}, school = {Universit{\"a}t Potsdam}, year = {2020}, abstract = {The two hallmark features of Brownian motion are the linear growth < x2(t)> = 2Ddt of the mean squared displacement (MSD) with diffusion coefficient D in d spatial dimensions, and the Gaussian distribution of displacements. With the increasing complexity of the studied systems deviations from these two central properties have been unveiled over the years. Recently, a large variety of systems have been reported in which the MSD exhibits the linear growth in time of Brownian (Fickian) transport, however, the distribution of displacements is pronouncedly non-Gaussian (Brownian yet non-Gaussian, BNG). A similar behaviour is also observed for viscoelastic-type motion where an anomalous trend of the MSD, i.e., ~ ta, is combined with a priori unexpected non-Gaussian distributions (anomalous yet non-Gaussian, ANG). This kind of behaviour observed in BNG and ANG diffusions has been related to the presence of heterogeneities in the systems and a common approach has been established to address it, that is, the random diffusivity approach. This dissertation explores extensively the field of random diffusivity models. Starting from a chronological description of all the main approaches used as an attempt of describing BNG and ANG diffusion, different mathematical methodologies are defined for the resolution and study of these models. The processes that are reported in this work can be classified in three subcategories, i) randomly-scaled Gaussian processes, ii) superstatistical models and iii) diffusing diffusivity models, all belonging to the more general class of random diffusivity models. Eventually, the study focuses more on BNG diffusion, which is by now well-established and relatively well-understood. Nevertheless, many examples are discussed for the description of ANG diffusion, in order to highlight the possible scenarios which are known so far for the study of this class of processes. The second part of the dissertation deals with the statistical analysis of random diffusivity processes. A general description based on the concept of moment-generating function is initially provided to obtain standard statistical properties of the models. Then, the discussion moves to the study of the power spectral analysis and the first passage statistics for some particular random diffusivity models. A comparison between the results coming from the random diffusivity approach and the ones for standard Brownian motion is discussed. In this way, a deeper physical understanding of the systems described by random diffusivity models is also outlined. To conclude, a discussion based on the possible origins of the heterogeneity is sketched, with the main goal of inferring which kind of systems can actually be described by the random diffusivity approach.}, language = {en} } @article{PohlenzNiedermeier2019, author = {Pohlenz, Philipp and Niedermeier, Frank}, title = {The Bologna Process and the harmonisation of higher education systems in other world regions}, series = {Innovation : the European journal of social sciences}, volume = {32}, journal = {Innovation : the European journal of social sciences}, number = {4}, publisher = {Routledge, Taylor \& Francis Group}, address = {Abingdon}, issn = {1351-1610}, doi = {10.1080/13511610.2019.1637248}, pages = {481 -- 494}, year = {2019}, abstract = {The Bologna Process has inspired harmonisation strategies for higher education systems in other parts of the world. However, developments in other contexts are not much under review in the European debate. The present article describes the case of Southeast Asia and the attempt to promote harmonisation of its higher education systems. It further compares the processes in ASEAN and the European Higher Education Area to then discuss open questions for future comparative research. To do so the authors re-contextualise data from a study in ASEAN against the background of future research needs in the field of higher education harmonisation.}, language = {en} } @misc{WoodfieldHorneGlauertetal.2018, author = {Woodfield, Emma E. and Horne, Richard B. and Glauert, Sarah A. and Menietti, John D. and Shprits, Yuri Y. and Kurth, William S.}, title = {Formation of electron radiation belts at Saturn by Z-mode wave acceleration}, series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, journal = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, number = {1032}, issn = {1866-8372}, doi = {10.25932/publishup-46834}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-468342}, pages = {9}, year = {2018}, abstract = {At Saturn electrons are trapped in the planet's magnetic field and accelerated to relativistic energies to form the radiation belts, but how this dramatic increase in electron energy occurs is still unknown. Until now the mechanism of radial diffusion has been assumed but we show here that in-situ acceleration through wave particle interactions, which initial studies dismissed as ineffectual at Saturn, is in fact a vital part of the energetic particle dynamics there. We present evidence from numerical simulations based on Cassini spacecraft data that a particular plasma wave, known as Z-mode, accelerates electrons to MeV energies inside 4 R-S (1 R-S = 60,330 km) through a Doppler shifted cyclotron resonant interaction. Our results show that the Z-mode waves observed are not oblique as previously assumed and are much better accelerators than O-mode waves, resulting in an electron energy spectrum that closely approaches observed values without any transport effects included.}, language = {en} } @article{GrebenkovMetzlerOshanin2020, author = {Grebenkov, Denis S. and Metzler, Ralf and Oshanin, Gleb}, title = {From single-particle stochastic kinetics to macroscopic reaction rates}, series = {New Journal of Physics}, volume = {22}, journal = {New Journal of Physics}, publisher = {Dt. Physikalische Ges.}, address = {Bad Honnef}, issn = {1367-2630}, doi = {10.1088/1367-2630/abb1de}, pages = {28}, year = {2020}, abstract = {We consider the first-passage problem for N identical independent particles that are initially released uniformly in a finite domain Ω and then diffuse toward a reactive area Γ, which can be part of the outer boundary of Ω or a reaction centre in the interior of Ω. For both cases of perfect and partial reactions, we obtain the explicit formulas for the first two moments of the fastest first-passage time (fFPT), i.e., the time when the first out of the N particles reacts with Γ. Moreover, we investigate the full probability density of the fFPT. We discuss a significant role of the initial condition in the scaling of the average fFPT with the particle number N, namely, a much stronger dependence (1/N and 1/N² for partially and perfectly reactive targets, respectively), in contrast to the well known inverse-logarithmic behaviour found when all particles are released from the same fixed point. We combine analytic solutions with scaling arguments and stochastic simulations to rationalise our results, which open new perspectives for studying the relevance of multiple searchers in various situations of molecular reactions, in particular, in living cells.}, language = {en} } @misc{GrebenkovMetzlerOshanin2020, author = {Grebenkov, Denis S. and Metzler, Ralf and Oshanin, Gleb}, title = {From single-particle stochastic kinetics to macroscopic reaction rates}, series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, journal = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, number = {1018}, issn = {1866-8372}, doi = {10.25932/publishup-48405}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-484059}, pages = {29}, year = {2020}, abstract = {We consider the first-passage problem for N identical independent particles that are initially released uniformly in a finite domain Ω and then diffuse toward a reactive area Γ, which can be part of the outer boundary of Ω or a reaction centre in the interior of Ω. For both cases of perfect and partial reactions, we obtain the explicit formulas for the first two moments of the fastest first-passage time (fFPT), i.e., the time when the first out of the N particles reacts with Γ. Moreover, we investigate the full probability density of the fFPT. We discuss a significant role of the initial condition in the scaling of the average fFPT with the particle number N, namely, a much stronger dependence (1/N and 1/N² for partially and perfectly reactive targets, respectively), in contrast to the well known inverse-logarithmic behaviour found when all particles are released from the same fixed point. We combine analytic solutions with scaling arguments and stochastic simulations to rationalise our results, which open new perspectives for studying the relevance of multiple searchers in various situations of molecular reactions, in particular, in living cells.}, language = {en} } @phdthesis{Graetz2020, author = {Gr{\"a}tz, Fabio M.}, title = {Nonlinear diffusion in granular gases and dense planetary rings}, school = {Universit{\"a}t Potsdam}, pages = {101}, year = {2020}, abstract = {Small moonlets or moons embedded in dense planetary rings create S-shaped density modulations called propellers if their masses are smaller than a certain threshold, alternatively they create a circumferential gap in the disk if the embedded body's mass exceeds this threshold (Spahn and Sremčević, 2000). The gravitational perturber scatters the ring particles, depletes the disk's density, and, thus, clears a gap, whereas counteracting viscous diffusion of the ring material has the tendency to close the created gap, thereby forming a propeller. Propeller objects were predicted by Spahn and Sremčević (2000) and Sremčević et al. (2002) and were later discovered by the Cassini space probe (Tiscareno et al., 2006, Sremčević et al., 2007, Tiscareno et al., 2008, and Tiscareno et al., 2010). The ring moons Pan and Daphnis are massive enough to maintain the circumferential Encke and Keeler gaps in Saturn's A ring and were detected by Showalter (1991) and Porco (2005) in Voyager and Cassini images, respectively. In this thesis, a nonlinear axisymmetric diffusion model is developed to describe radial density profiles of circumferential gaps in planetary rings created by embedded moons (Grätz et al., 2018). The model accounts for the gravitational scattering of the ring particles by the embedded moon and for the counteracting viscous diffusion of the ring matter back into the gap. With test particle simulations it is shown that the scattering of the ring particles passing the moon is larger for small impact parameters than estimated by Goldreich and Tremaine (1980). This is especially significant for the modeling of the Keeler gap. The model is applied to the Encke and Keeler gaps with the aim to estimate the shear viscosity of the ring in their vicinities. In addition, the model is used to analyze whether tiny icy moons whose dimensions lie below Cassini's resolution capabilities would be able to cause the poorly understood gap structure of the C ring and the Cassini Division. One of the most intriguing facets of Saturn's rings are the extremely sharp edges of the Encke and Keeler gaps: UVIS-scans of their gap edges show that the optical depth drops from order unity to zero over a range of far less than 100 m, a spatial scale comparable to the ring's vertical extent. This occurs despite the fact that the range over which a moon transfers angular momentum onto the ring material is much larger. Borderies et al. (1982, 1989) have shown that this striking feature is likely related to the local reversal of the usually outward-directed viscous transport of angular momentum in strongly perturbed regions. We have revised the Borderies et al. (1989) model using a granular flow model to define the shear and bulk viscosities, ν and ζ, in order to incorporate the angular momentum flux reversal effect into the axisymmetric diffusion model for circumferential gaps presented in this thesis (Grätz et al., 2019). The sharp Encke and Keeler gap edges are modeled and conclusions regarding the shear and bulk viscosities of the ring are discussed. Finally, we explore the question of whether the radial density profile of the central and outer A ring, recently measured by Tiscareno and Harris (2018) in the highest resolution to date, and in particular, the sharp outer A ring edge can be modeled consistently from the balance of gravitational scattering by several outer moons and the mass and momentum transport. To this aim, the developed model is extended to account for the inward drifts caused by multiple discrete and overlapping resonances with multiple outer satellites and is then used to hydrodynamically simulate the normalized surface mass density profile of the A ring. This section of the thesis is based on studies by Tajeddine et al. (2017a) who recently discussed the common misconception that the 7:6 resonance with Janus alone maintains the outer A ring edge, showing that the combined effort of several resonances with several outer moons is required to confine the A ring as observed by the Cassini spacecraft.}, language = {en} } @article{WangSenoSokolovetal.2020, author = {Wang, Wei and Seno, Flavio and Sokolov, Igor M. and Chechkin, Aleksei V. and Metzler, Ralf}, title = {Unexpected crossovers in correlated random-diffusivity processes}, series = {New Journal of Physics}, volume = {22}, journal = {New Journal of Physics}, publisher = {Dt. Physikalische Ges.}, address = {Bad Honnef}, issn = {1367-2630}, doi = {10.1088/1367-2630/aba390}, pages = {17}, year = {2020}, abstract = {The passive and active motion of micron-sized tracer particles in crowded liquids and inside living biological cells is ubiquitously characterised by 'viscoelastic' anomalous diffusion, in which the increments of the motion feature long-ranged negative and positive correlations. While viscoelastic anomalous diffusion is typically modelled by a Gaussian process with correlated increments, so-called fractional Gaussian noise, an increasing number of systems are reported, in which viscoelastic anomalous diffusion is paired with non-Gaussian displacement distributions. Following recent advances in Brownian yet non-Gaussian diffusion we here introduce and discuss several possible versions of random-diffusivity models with long-ranged correlations. While all these models show a crossover from non-Gaussian to Gaussian distributions beyond some correlation time, their mean squared displacements exhibit strikingly different behaviours: depending on the model crossovers from anomalous to normal diffusion are observed, as well as a priori unexpected dependencies of the effective diffusion coefficient on the correlation exponent. Our observations of the non-universality of random-diffusivity viscoelastic anomalous diffusion are important for the analysis of experiments and a better understanding of the physical origins of 'viscoelastic yet non-Gaussian' diffusion.}, language = {en} } @misc{WangSenoSokolovetal.2020, author = {Wang, Wei and Seno, Flavio and Sokolov, Igor M. and Chechkin, Aleksei V. and Metzler, Ralf}, title = {Unexpected crossovers in correlated random-diffusivity processes}, number = {1006}, issn = {1866-8372}, doi = {10.25932/publishup-48004}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-480049}, pages = {18}, year = {2020}, abstract = {The passive and active motion of micron-sized tracer particles in crowded liquids and inside living biological cells is ubiquitously characterised by 'viscoelastic' anomalous diffusion, in which the increments of the motion feature long-ranged negative and positive correlations. While viscoelastic anomalous diffusion is typically modelled by a Gaussian process with correlated increments, so-called fractional Gaussian noise, an increasing number of systems are reported, in which viscoelastic anomalous diffusion is paired with non-Gaussian displacement distributions. Following recent advances in Brownian yet non-Gaussian diffusion we here introduce and discuss several possible versions of random-diffusivity models with long-ranged correlations. While all these models show a crossover from non-Gaussian to Gaussian distributions beyond some correlation time, their mean squared displacements exhibit strikingly different behaviours: depending on the model crossovers from anomalous to normal diffusion are observed, as well as a priori unexpected dependencies of the effective diffusion coefficient on the correlation exponent. Our observations of the non-universality of random-diffusivity viscoelastic anomalous diffusion are important for the analysis of experiments and a better understanding of the physical origins of 'viscoelastic yet non-Gaussian' diffusion.}, language = {en} } @article{GranadoAbadMetzleretal.2020, author = {Granado, Felipe Le Vot and Abad, Enrique and Metzler, Ralf and Yuste, Santos B.}, title = {Continuous time random walk in a velocity field}, series = {New Journal of Physics}, volume = {22}, journal = {New Journal of Physics}, publisher = {Dt. Physikalische Ges.}, address = {Bad Honnef}, issn = {1367-2630}, doi = {10.1088/1367-2630/ab9ae2}, pages = {27}, year = {2020}, abstract = {We consider the emerging dynamics of a separable continuous time random walk (CTRW) in the case when the random walker is biased by a velocity field in a uniformly growing domain. Concrete examples for such domains include growing biological cells or lipid vesicles, biofilms and tissues, but also macroscopic systems such as expanding aquifers during rainy periods, or the expanding Universe. The CTRW in this study can be subdiffusive, normal diffusive or superdiffusive, including the particular case of a L{\´e}vy flight. We first consider the case when the velocity field is absent. In the subdiffusive case, we reveal an interesting time dependence of the kurtosis of the particle probability density function. In particular, for a suitable parameter choice, we find that the propagator, which is fat tailed at short times, may cross over to a Gaussian-like propagator. We subsequently incorporate the effect of the velocity field and derive a bi-fractional diffusion-advection equation encoding the time evolution of the particle distribution. We apply this equation to study the mixing kinetics of two diffusing pulses, whose peaks move towards each other under the action of velocity fields acting in opposite directions. This deterministic motion of the peaks, together with the diffusive spreading of each pulse, tends to increase particle mixing, thereby counteracting the peak separation induced by the domain growth. As a result of this competition, different regimes of mixing arise. In the case of L{\´e}vy flights, apart from the non-mixing regime, one has two different mixing regimes in the long-time limit, depending on the exact parameter choice: in one of these regimes, mixing is mainly driven by diffusive spreading, while in the other mixing is controlled by the velocity fields acting on each pulse. Possible implications for encounter-controlled reactions in real systems are discussed.}, language = {en} } @misc{GranadoAbadMetzleretal.2020, author = {Granado, Felipe Le Vot and Abad, Enrique and Metzler, Ralf and Yuste, Santos B.}, title = {Continuous time random walk in a velocity field}, series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, journal = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, number = {1005}, issn = {1866-8372}, doi = {10.25932/publishup-47999}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-479997}, pages = {28}, year = {2020}, abstract = {We consider the emerging dynamics of a separable continuous time random walk (CTRW) in the case when the random walker is biased by a velocity field in a uniformly growing domain. Concrete examples for such domains include growing biological cells or lipid vesicles, biofilms and tissues, but also macroscopic systems such as expanding aquifers during rainy periods, or the expanding Universe. The CTRW in this study can be subdiffusive, normal diffusive or superdiffusive, including the particular case of a L{\´e}vy flight. We first consider the case when the velocity field is absent. In the subdiffusive case, we reveal an interesting time dependence of the kurtosis of the particle probability density function. In particular, for a suitable parameter choice, we find that the propagator, which is fat tailed at short times, may cross over to a Gaussian-like propagator. We subsequently incorporate the effect of the velocity field and derive a bi-fractional diffusion-advection equation encoding the time evolution of the particle distribution. We apply this equation to study the mixing kinetics of two diffusing pulses, whose peaks move towards each other under the action of velocity fields acting in opposite directions. This deterministic motion of the peaks, together with the diffusive spreading of each pulse, tends to increase particle mixing, thereby counteracting the peak separation induced by the domain growth. As a result of this competition, different regimes of mixing arise. In the case of L{\´e}vy flights, apart from the non-mixing regime, one has two different mixing regimes in the long-time limit, depending on the exact parameter choice: in one of these regimes, mixing is mainly driven by diffusive spreading, while in the other mixing is controlled by the velocity fields acting on each pulse. Possible implications for encounter-controlled reactions in real systems are discussed.}, language = {en} } @article{SposiniGrebenkovMetzleretal.2020, author = {Sposini, Vittoria and Grebenkov, Denis S. and Metzler, Ralf and Oshanin, Gleb and Seno, Flavio}, title = {Universal spectral features of different classes of random-diffusivity processes}, series = {New Journal of Physics}, volume = {22}, journal = {New Journal of Physics}, number = {6}, publisher = {Dt. Physikalische Ges.}, address = {Bad Honnef}, issn = {1367-2630}, doi = {10.1088/1367-2630/ab9200}, pages = {26}, year = {2020}, abstract = {Stochastic models based on random diffusivities, such as the diffusing-diffusivity approach, are popular concepts for the description of non-Gaussian diffusion in heterogeneous media. Studies of these models typically focus on the moments and the displacement probability density function. Here we develop the complementary power spectral description for a broad class of random-diffusivity processes. In our approach we cater for typical single particle tracking data in which a small number of trajectories with finite duration are garnered. Apart from the diffusing-diffusivity model we study a range of previously unconsidered random-diffusivity processes, for which we obtain exact forms of the probability density function. These new processes are different versions of jump processes as well as functionals of Brownian motion. The resulting behaviour subtly depends on the specific model details. Thus, the central part of the probability density function may be Gaussian or non-Gaussian, and the tails may assume Gaussian, exponential, log-normal, or even power-law forms. For all these models we derive analytically the moment-generating function for the single-trajectory power spectral density. We establish the generic 1/f²-scaling of the power spectral density as function of frequency in all cases. Moreover, we establish the probability density for the amplitudes of the random power spectral density of individual trajectories. The latter functions reflect the very specific properties of the different random-diffusivity models considered here. Our exact results are in excellent agreement with extensive numerical simulations.}, language = {en} } @misc{SposiniGrebenkovMetzleretal.2020, author = {Sposini, Vittoria and Grebenkov, Denis S. and Metzler, Ralf and Oshanin, Gleb and Seno, Flavio}, title = {Universal spectral features of different classes of random-diffusivity processes}, series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, journal = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, number = {999}, issn = {1866-8372}, doi = {10.25932/publishup-47696}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-476960}, pages = {27}, year = {2020}, abstract = {Stochastic models based on random diffusivities, such as the diffusing-diffusivity approach, are popular concepts for the description of non-Gaussian diffusion in heterogeneous media. Studies of these models typically focus on the moments and the displacement probability density function. Here we develop the complementary power spectral description for a broad class of random-diffusivity processes. In our approach we cater for typical single particle tracking data in which a small number of trajectories with finite duration are garnered. Apart from the diffusing-diffusivity model we study a range of previously unconsidered random-diffusivity processes, for which we obtain exact forms of the probability density function. These new processes are different versions of jump processes as well as functionals of Brownian motion. The resulting behaviour subtly depends on the specific model details. Thus, the central part of the probability density function may be Gaussian or non-Gaussian, and the tails may assume Gaussian, exponential, log-normal, or even power-law forms. For all these models we derive analytically the moment-generating function for the single-trajectory power spectral density. We establish the generic 1/f²-scaling of the power spectral density as function of frequency in all cases. Moreover, we establish the probability density for the amplitudes of the random power spectral density of individual trajectories. The latter functions reflect the very specific properties of the different random-diffusivity models considered here. Our exact results are in excellent agreement with extensive numerical simulations.}, language = {en} } @article{LiMeiXuetal.2020, author = {Li, Yongge and Mei, Ruoxing and Xu, Yong and Kurths, J{\"u}rgen and Duan, Jinqiao and Metzler, Ralf}, title = {Particle dynamics and transport enhancement in a confined channel with position-dependent diffusivity}, series = {New Journal of Physics}, volume = {22}, journal = {New Journal of Physics}, publisher = {Dt. Physikalische Ges.}, address = {Bad Honnef}, issn = {1367-2630}, doi = {10.1088/1367-2630/ab81b9}, pages = {27}, year = {2020}, abstract = {This work focuses on the dynamics of particles in a confined geometry with position-dependent diffusivity, where the confinement is modelled by a periodic channel consisting of unit cells connected by narrow passage ways. We consider three functional forms for the diffusivity, corresponding to the scenarios of a constant (D ₀), as well as a low (D ₘ) and a high (D d) mobility diffusion in cell centre of the longitudinally symmetric cells. Due to the interaction among the diffusivity, channel shape and external force, the system exhibits complex and interesting phenomena. By calculating the probability density function, mean velocity and mean first exit time with the It{\^o} calculus form, we find that in the absence of external forces the diffusivity D d will redistribute particles near the channel wall, while the diffusivity D ₘ will trap them near the cell centre. The superposition of external forces will break their static distributions. Besides, our results demonstrate that for the diffusivity D d, a high dependence on the x coordinate (parallel with the central channel line) will improve the mean velocity of the particles. In contrast, for the diffusivity D ₘ, a weak dependence on the x coordinate will dramatically accelerate the moving speed. In addition, it shows that a large external force can weaken the influences of different diffusivities; inversely, for a small external force, the types of diffusivity affect significantly the particle dynamics. In practice, one can apply these results to achieve a prominent enhancement of the particle transport in two- or three-dimensional channels by modulating the local tracer diffusivity via an engineered gel of varying porosity or by adding a cold tube to cool down the diffusivity along the central line, which may be a relevant effect in engineering applications. Effects of different stochastic calculi in the evaluation of the underlying multiplicative stochastic equation for different physical scenarios are discussed.}, language = {en} } @misc{LiMeiXuetal.2020, author = {Li, Yongge and Mei, Ruoxing and Xu, Yong and Kurths, J{\"u}rgen and Duan, Jinqiao and Metzler, Ralf}, title = {Particle dynamics and transport enhancement in a confined channel with position-dependent diffusivity}, series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, journal = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, number = {974}, issn = {1866-8372}, doi = {10.25932/publishup-47454}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-474542}, pages = {28}, year = {2020}, abstract = {This work focuses on the dynamics of particles in a confined geometry with position-dependent diffusivity, where the confinement is modelled by a periodic channel consisting of unit cells connected by narrow passage ways. We consider three functional forms for the diffusivity, corresponding to the scenarios of a constant (D ₀), as well as a low (D ₘ) and a high (D d) mobility diffusion in cell centre of the longitudinally symmetric cells. Due to the interaction among the diffusivity, channel shape and external force, the system exhibits complex and interesting phenomena. By calculating the probability density function, mean velocity and mean first exit time with the It{\^o} calculus form, we find that in the absence of external forces the diffusivity D d will redistribute particles near the channel wall, while the diffusivity D ₘ will trap them near the cell centre. The superposition of external forces will break their static distributions. Besides, our results demonstrate that for the diffusivity D d, a high dependence on the x coordinate (parallel with the central channel line) will improve the mean velocity of the particles. In contrast, for the diffusivity D ₘ, a weak dependence on the x coordinate will dramatically accelerate the moving speed. In addition, it shows that a large external force can weaken the influences of different diffusivities; inversely, for a small external force, the types of diffusivity affect significantly the particle dynamics. In practice, one can apply these results to achieve a prominent enhancement of the particle transport in two- or three-dimensional channels by modulating the local tracer diffusivity via an engineered gel of varying porosity or by adding a cold tube to cool down the diffusivity along the central line, which may be a relevant effect in engineering applications. Effects of different stochastic calculi in the evaluation of the underlying multiplicative stochastic equation for different physical scenarios are discussed.}, language = {en} } @misc{GallegoLlorenteSarahJonesetal.2016, author = {Gallego-Llorente, Marcos and Sarah, Connell and Jones, Eppie R. and Merrett, Deborah C. and Jeon, Y. and Eriksson, Anders and Siska, Veronika and Gamba, Cristina and Meiklejohn, Christopher and Beyer, Robert and Jeon, Sungwon and Cho, Yun Sung and Hofreiter, Michael and Bhak, Jong and Manica, Andrea and Pinhasi, Ron}, title = {The genetics of an early Neolithic pastoralist from the Zagros, Iran}, series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, journal = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, number = {952}, issn = {1866-8372}, doi = {10.25932/publishup-43935}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-439355}, pages = {9}, year = {2016}, abstract = {The agricultural transition profoundly changed human societies. We sequenced and analysed the first genome (1.39x) of an early Neolithic woman from Ganj Dareh, in the Zagros Mountains of Iran, a site with early evidence for an economy based on goat herding, ca. 10,000 BP. We show that Western Iran was inhabited by a population genetically most similar to hunter-gatherers from the Caucasus, but distinct from the Neolithic Anatolian people who later brought food production into Europe. The inhabitants of Ganj Dareh made little direct genetic contribution to modern European populations, suggesting those of the Central Zagros were somewhat isolated from other populations of the Fertile Crescent. Runs of homozygosity are of a similar length to those from Neolithic farmers, and shorter than those of Caucasus and Western Hunter-Gatherers, suggesting that the inhabitants of Ganj Dareh did not undergo the large population bottleneck suffered by their northern neighbours. While some degree of cultural diffusion between Anatolia, Western Iran and other neighbouring regions is possible, the genetic dissimilarity between early Anatolian farmers and the inhabitants of Ganj Dareh supports a model in which Neolithic societies in these areas were distinct.}, language = {en} } @article{CherstvyVinodAghionetal.2017, author = {Cherstvy, Andrey G. and Vinod, Deepak and Aghion, Erez and Chechkin, Aleksei V. and Metzler, Ralf}, title = {Time averaging, ageing and delay analysis of financial time series}, series = {New journal of physics : the open-access journal for physics}, volume = {19}, journal = {New journal of physics : the open-access journal for physics}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {1367-2630}, doi = {10.1088/1367-2630/aa7199}, pages = {135 -- 147}, year = {2017}, abstract = {We introduce three strategies for the analysis of financial time series based on time averaged observables. These comprise the time averaged mean squared displacement (MSD) as well as the ageing and delay time methods for varying fractions of the financial time series. We explore these concepts via statistical analysis of historic time series for several Dow Jones Industrial indices for the period from the 1960s to 2015. Remarkably, we discover a simple universal law for the delay time averaged MSD. The observed features of the financial time series dynamics agree well with our analytical results for the time averaged measurables for geometric Brownian motion, underlying the famed Black-Scholes-Merton model. The concepts we promote here are shown to be useful for financial data analysis and enable one to unveil new universal features of stock market dynamics.}, language = {en} } @article{DalBiancoWischkeZhouetal.2017, author = {Dal Bianco, Andrea and Wischke, Christian and Zhou, Shuo and Lendlein, Andreas}, title = {Controlling surface properties and permeability of polyglycerol network films}, series = {Polymers for advanced technologies}, volume = {28}, journal = {Polymers for advanced technologies}, publisher = {Wiley}, address = {Hoboken}, issn = {1042-7147}, doi = {10.1002/pat.3917}, pages = {1263 -- 1268}, year = {2017}, abstract = {While branched polyglycerol (PG)-based molecules are well established as hydrophilic particles, the capacity of utilizing PG in bulk materials and opportunities arising by their further surface functionalization have only recently been considered. Here we investigated how the mold used in PG network synthesis may affect surface composition and how the permeability of substances through PG can be controlled by altering network structure, i.e. introducing 20mol\% oligoethylene glycol (OEG) bifunctional spacer molecules. Overall, PG-based bulk network materials were shown to be tailorable, hydrophilic, low swelling and relatively stiff polyether-based materials, with low impact of salt onto material properties. Based on these features, but also on the principal capacity of free hydroxyl groups to be used for functionalization reactions, these materials may be an interesting platform for medical and technical applications, e.g. as diffusion-rate controlling membrane in aqueous environment. Copyright (c) 2016 John Wiley \& Sons, Ltd.}, language = {en} } @article{ChenPohlBottcheretal.2016, author = {Chen, Xuhui and Pohl, Martin and Bottcher, Markus and Gao, Shan}, title = {Particle diffusion and localized acceleration in inhomogeneous AGN jets - II. Stochastic variation}, series = {Monthly notices of the Royal Astronomical Society}, volume = {458}, journal = {Monthly notices of the Royal Astronomical Society}, publisher = {Oxford Univ. Press}, address = {Oxford}, issn = {0035-8711}, doi = {10.1093/mnras/stw528}, pages = {3260 -- 3271}, year = {2016}, abstract = {We study the stochastic variation of blazar emission under a 2D spatially resolved leptonic jet model we previously developed. Random events of particle acceleration and injection in small zones within the emission region are assumed to be responsible for flux variations. In addition to producing spectral energy distributions that describe the observed flux of Mrk 421, we further analyse the timing properties of the simulated light curves, such as the power spectral density (PSD) at different bands, flux-flux correlations, aswell as the cross-correlation function between X-rays and TeV gamma-rays. We find spectral breaks in the PSD at a time-scale comparable to the dominant characteristic time-scale in the system, which is usually the predefined decay time-scale of an acceleration event. Cooling imposes a delay, and so PSDs taken at lower energy bands in each emission component (synchrotron or inverse Compton) generally break at longer time-scales. The flux-flux correlation between X-rays and TeV gamma-rays can be either quadratic or linear, depending on whether or not there are large variation of the injection into the particle acceleration process. When the relationship is quadratic, the TeV flares lag the X-ray flares, and the optical and GeV flares are large enough to be comparable to the ones in X-ray. When the relationship is linear, the lags are insignificant, and the optical and GeV flares are small.}, language = {en} } @article{Beta2016, author = {Beta, Carsten}, title = {To turn or not to turn?}, series = {NEW JOURNAL OF PHYSICS}, volume = {18}, journal = {NEW JOURNAL OF PHYSICS}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {1367-2630}, doi = {10.1088/1367-2630/18/5/051003}, pages = {1 -- 17}, year = {2016}, abstract = {Bacteria typically swim in straight runs, interruped by sudden turning events. In particular, some species are limited to a reversal in the swimming direction as the only turning maneuver at their disposal. In a recent article, Grossmann et al (2016 New J. Phys. 18 043009) introduce a theoretical framework to analyze the diffusive properties of active particles following this type of run-and-reverse pattern. Based on a stochastic clock model to mimic the regulatory pathway that triggers reversal events, they show that a run-and-reverse swimmer can optimize its diffusive spreading by tuning the reversal rate according to the level of rotational noise. With their approach, they open up promising new perspectives of how to incorporate the dynamics of intracellular signaling into coarse-grained active particle descriptions.}, language = {en} } @article{SchwarzlGodecOshaninetal.2016, author = {Schwarzl, Maria and Godec, Aljaz and Oshanin, Gleb and Metzler, Ralf}, title = {A single predator charging a herd of prey: effects of self volume and predator-prey decision-making}, series = {Journal of physics : A, Mathematical and theoretical}, volume = {49}, journal = {Journal of physics : A, Mathematical and theoretical}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {1751-8113}, doi = {10.1088/1751-8113/49/22/225601}, pages = {19}, year = {2016}, abstract = {We study the degree of success of a single predator hunting a herd of prey on a two-dimensional square lattice landscape. We explicitly consider the self volume of the prey restraining their dynamics on the lattice. The movement of both predator and prey is chosen to include an intelligent, decision making step based on their respective sighting ranges, the radius in which they can detect the other species (prey cannot recognise each other besides the self volume interaction): after spotting each other the motion of prey and predator turns from a nearest neighbour random walk into directed escape or chase, respectively. We consider a large range of prey densities and sighting ranges and compute the mean first passage time for a predator to catch a prey as well as characterise the effective dynamics of the hunted prey. We find that the prey's sighting range dominates their life expectancy and the predator profits more from a bad eyesight of the prey than from his own good eye sight. We characterise the dynamics in terms of the mean distance between the predator and the nearest prey. It turns out that effectively the dynamics of this distance coordinate can be captured in terms of a simple Ornstein-Uhlenbeck picture. Reducing the many-body problem to a simple two-body problem by imagining predator and nearest prey to be connected by an effective Hookean bond, all features of the model such as prey density and sighting ranges merge into the effective binding constant.}, language = {en} } @article{ProkopovicVikulinaSustretal.2016, author = {Prokopovic, Vladimir Z. and Vikulina, Anna S. and Sustr, David and Duschl, Claus and Volodkin, Dmitry}, title = {Biodegradation-Resistant Multilayers Coated with Gold Nanoparticles. Toward a Tailor-made Artificial Extracellular Matrix}, series = {Journal of colloid and interface science}, volume = {8}, journal = {Journal of colloid and interface science}, publisher = {American Chemical Society}, address = {Washington}, issn = {1944-8244}, doi = {10.1021/acsami.6b10095}, pages = {24345 -- 24349}, year = {2016}, abstract = {Polymer multicomponent coatings such as multilayers mimic an extracellular, matrix (ECM) that attracts significant attention for the use of the multilayers as functional supports for advanced cell culture and tissue engineering. Herein, biodegradation and molecular transport in hyaluronan/polylysine multilayers coated with gold nanoparticles were described. Nanoparticle coating acts as a semipermeable barrier that governs molecular transport into/from the multilayers, and makes them biodegradation-resistant. Model protein lysozyme (mimics of ECM-soluble signals) diffuses into the multilayers as fast- and, slow-diffusing populations existing in an equilibrium,. Such a. composite system may have high potential to be exploited as degradation-resistant drug-delivery platforms suitable for cell-based applications.}, language = {en} } @misc{WeberBahrsAlirezaeizanjanietal.2019, author = {Weber, Ariane and Bahrs, Marco and Alirezaeizanjani, Zahra and Zhang, Xingyu and Beta, Carsten and Zaburdaev, Vasily}, title = {Rectification of Bacterial Diffusion in Microfluidic Labyrinths}, series = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe}, journal = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe}, number = {801}, issn = {1866-8372}, doi = {10.25932/publishup-44122}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-441222}, pages = {11}, year = {2019}, abstract = {In nature as well as in the context of infection and medical applications, bacteria often have to move in highly complex environments such as soil or tissues. Previous studies have shown that bacteria strongly interact with their surroundings and are often guided by confinements. Here, we investigate theoretically how the dispersal of swimming bacteria can be augmented by microfluidic environments and validate our theoretical predictions experimentally. We consider a system of bacteria performing the prototypical run-and-tumble motion inside a labyrinth with square lattice geometry. Narrow channels between the square obstacles limit the possibility of bacteria to reorient during tumbling events to an area where channels cross. Thus, by varying the geometry of the lattice it might be possible to control the dispersal of cells. We present a theoretical model quantifying diffusive spreading of a run-and-tumble random walker in a square lattice. Numerical simulations validate our theoretical predictions for the dependence of the diffusion coefficient on the lattice geometry. We show that bacteria moving in square labyrinths exhibit enhanced dispersal as compared to unconfined cells. Importantly, confinement significantly extends the duration of the phase with strongly non-Gaussian diffusion, when the geometry of channels is imprinted in the density profiles of spreading cells. Finally, in good agreement with our theoretical findings, we observe the predicted behaviors in experiments with E. coli bacteria swimming in a square lattice labyrinth created in amicrofluidic device. Altogether, our comprehensive understanding of bacterial dispersal in a simple two-dimensional labyrinth makes the first step toward the analysis of more complex geometries relevant for real world applications.}, language = {en} } @article{WeberBahrsAlirezaeizanjanietal.2019, author = {Weber, Ariane and Bahrs, Marco and Alirezaeizanjani, Zahra and Zhang, Xingyu and Beta, Carsten and Zaburdaev, Vasily}, title = {Rectification of Bacterial Diffusion in Microfluidic Labyrinths}, series = {Frontiers in Physics}, volume = {7}, journal = {Frontiers in Physics}, publisher = {Frontiers Media}, address = {Lausanne}, issn = {2296-424X}, doi = {10.3389/fphy.2019.00148}, pages = {11}, year = {2019}, abstract = {In nature as well as in the context of infection and medical applications, bacteria often have to move in highly complex environments such as soil or tissues. Previous studies have shown that bacteria strongly interact with their surroundings and are often guided by confinements. Here, we investigate theoretically how the dispersal of swimming bacteria can be augmented by microfluidic environments and validate our theoretical predictions experimentally. We consider a system of bacteria performing the prototypical run-and-tumble motion inside a labyrinth with square lattice geometry. Narrow channels between the square obstacles limit the possibility of bacteria to reorient during tumbling events to an area where channels cross. Thus, by varying the geometry of the lattice it might be possible to control the dispersal of cells. We present a theoretical model quantifying diffusive spreading of a run-and-tumble random walker in a square lattice. Numerical simulations validate our theoretical predictions for the dependence of the diffusion coefficient on the lattice geometry. We show that bacteria moving in square labyrinths exhibit enhanced dispersal as compared to unconfined cells. Importantly, confinement significantly extends the duration of the phase with strongly non-Gaussian diffusion, when the geometry of channels is imprinted in the density profiles of spreading cells. Finally, in good agreement with our theoretical findings, we observe the predicted behaviors in experiments with E. coli bacteria swimming in a square lattice labyrinth created in amicrofluidic device. Altogether, our comprehensive understanding of bacterial dispersal in a simple two-dimensional labyrinth makes the first step toward the analysis of more complex geometries relevant for real world applications.}, language = {en} } @misc{ŚlęzakBurneckiMetzler2019, author = {Ślęzak, Jakub and Burnecki, Krzysztof and Metzler, Ralf}, title = {Random coefficient autoregressive processes describe Brownian yet non-Gaussian diffusion in heterogeneous systems}, series = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe}, journal = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe}, number = {765}, issn = {1866-8372}, doi = {10.25932/publishup-43792}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-437923}, pages = {18}, year = {2019}, abstract = {Many studies on biological and soft matter systems report the joint presence of a linear mean-squared displacement and a non-Gaussian probability density exhibiting, for instance, exponential or stretched-Gaussian tails. This phenomenon is ascribed to the heterogeneity of the medium and is captured by random parameter models such as 'superstatistics' or 'diffusing diffusivity'. Independently, scientists working in the area of time series analysis and statistics have studied a class of discrete-time processes with similar properties, namely, random coefficient autoregressive models. In this work we try to reconcile these two approaches and thus provide a bridge between physical stochastic processes and autoregressive models.Westart from the basic Langevin equation of motion with time-varying damping or diffusion coefficients and establish the link to random coefficient autoregressive processes. By exploring that link we gain access to efficient statistical methods which can help to identify data exhibiting Brownian yet non-Gaussian diffusion.}, language = {en} } @article{ŚlęzakBurneckiMetzler2019, author = {Ślęzak, Jakub and Burnecki, Krzysztof and Metzler, Ralf}, title = {Random coefficient autoregressive processes describe Brownian yet non-Gaussian diffusion in heterogeneous systems}, series = {New Journal of Physics}, volume = {21}, journal = {New Journal of Physics}, publisher = {Deutsche Physikalische Gesellschaft ; IOP, Institute of Physics}, address = {Bad Honnef und London}, issn = {1367-2630}, doi = {10.1088/1367-2630/ab3366}, pages = {18}, year = {2019}, abstract = {Many studies on biological and soft matter systems report the joint presence of a linear mean-squared displacement and a non-Gaussian probability density exhibiting, for instance, exponential or stretched-Gaussian tails. This phenomenon is ascribed to the heterogeneity of the medium and is captured by random parameter models such as 'superstatistics' or 'diffusing diffusivity'. Independently, scientists working in the area of time series analysis and statistics have studied a class of discrete-time processes with similar properties, namely, random coefficient autoregressive models. In this work we try to reconcile these two approaches and thus provide a bridge between physical stochastic processes and autoregressive models.Westart from the basic Langevin equation of motion with time-varying damping or diffusion coefficients and establish the link to random coefficient autoregressive processes. By exploring that link we gain access to efficient statistical methods which can help to identify data exhibiting Brownian yet non-Gaussian diffusion.}, language = {en} } @misc{SposiniMetzlerOshanin2019, author = {Sposini, Vittoria and Metzler, Ralf and Oshanin, Gleb}, title = {Single-trajectory spectral analysis of scaled Brownian motion}, series = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe}, journal = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe}, number = {753}, issn = {1866-8372}, doi = {10.25932/publishup-43652}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-436522}, pages = {16}, year = {2019}, abstract = {Astandard approach to study time-dependent stochastic processes is the power spectral density (PSD), an ensemble-averaged property defined as the Fourier transform of the autocorrelation function of the process in the asymptotic limit of long observation times, T → ∞. In many experimental situations one is able to garner only relatively few stochastic time series of finite T, such that practically neither an ensemble average nor the asymptotic limit T → ∞ can be achieved. To accommodate for a meaningful analysis of such finite-length data we here develop the framework of single-trajectory spectral analysis for one of the standard models of anomalous diffusion, scaled Brownian motion.Wedemonstrate that the frequency dependence of the single-trajectory PSD is exactly the same as for standard Brownian motion, which may lead one to the erroneous conclusion that the observed motion is normal-diffusive. However, a distinctive feature is shown to be provided by the explicit dependence on the measurement time T, and this ageing phenomenon can be used to deduce the anomalous diffusion exponent.Wealso compare our results to the single-trajectory PSD behaviour of another standard anomalous diffusion process, fractional Brownian motion, and work out the commonalities and differences. Our results represent an important step in establishing singletrajectory PSDs as an alternative (or complement) to analyses based on the time-averaged mean squared displacement.}, language = {en} } @article{SposiniMetzlerOshanin2019, author = {Sposini, Vittoria and Metzler, Ralf and Oshanin, Gleb}, title = {Single-trajectory spectral analysis of scaled Brownian motion}, series = {New Journal of Physics}, volume = {21}, journal = {New Journal of Physics}, publisher = {Deutsche Physikalische Gesellschaft ; IOP, Institute of Physics}, address = {Bad Honnef und London}, issn = {1367-2630}, doi = {10.1088/1367-2630/ab2f52}, pages = {16}, year = {2019}, abstract = {Astandard approach to study time-dependent stochastic processes is the power spectral density (PSD), an ensemble-averaged property defined as the Fourier transform of the autocorrelation function of the process in the asymptotic limit of long observation times, T → ∞. In many experimental situations one is able to garner only relatively few stochastic time series of finite T, such that practically neither an ensemble average nor the asymptotic limit T → ∞ can be achieved. To accommodate for a meaningful analysis of such finite-length data we here develop the framework of single-trajectory spectral analysis for one of the standard models of anomalous diffusion, scaled Brownian motion.Wedemonstrate that the frequency dependence of the single-trajectory PSD is exactly the same as for standard Brownian motion, which may lead one to the erroneous conclusion that the observed motion is normal-diffusive. However, a distinctive feature is shown to be provided by the explicit dependence on the measurement time T, and this ageing phenomenon can be used to deduce the anomalous diffusion exponent.Wealso compare our results to the single-trajectory PSD behaviour of another standard anomalous diffusion process, fractional Brownian motion, and work out the commonalities and differences. Our results represent an important step in establishing singletrajectory PSDs as an alternative (or complement) to analyses based on the time-averaged mean squared displacement.}, language = {en} } @misc{ŚlęzakMetzlerMagdziarz2019, author = {Ślęzak, Jakub and Metzler, Ralf and Magdziarz, Marcin}, title = {Codifference can detect ergodicity breaking and non-Gaussianity}, series = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe}, journal = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe}, number = {748}, doi = {10.25932/publishup-43617}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-436178}, pages = {25}, year = {2019}, abstract = {We show that the codifference is a useful tool in studying the ergodicity breaking and non-Gaussianity properties of stochastic time series. While the codifference is a measure of dependence that was previously studied mainly in the context of stable processes, we here extend its range of applicability to random-parameter and diffusing-diffusivity models which are important in contemporary physics, biology and financial engineering. We prove that the codifference detects forms of dependence and ergodicity breaking which are not visible from analysing the covariance and correlation functions. We also discuss a related measure of dispersion, which is a nonlinear analogue of the mean squared displacement.}, language = {en} } @article{ŚlęzakMetzlerMagdziarz2019, author = {Ślęzak, Jakub and Metzler, Ralf and Magdziarz, Marcin}, title = {Codifference can detect ergodicity breaking and non-Gaussianity}, series = {New Journal of Physics}, volume = {21}, journal = {New Journal of Physics}, publisher = {Deutsche Physikalische Gesellschaft}, address = {Bad Honnef}, issn = {1367-2630}, doi = {10.1088/1367-2630/ab13f3}, pages = {25}, year = {2019}, abstract = {We show that the codifference is a useful tool in studying the ergodicity breaking and non-Gaussianity properties of stochastic time series. While the codifference is a measure of dependence that was previously studied mainly in the context of stable processes, we here extend its range of applicability to random-parameter and diffusing-diffusivity models which are important in contemporary physics, biology and financial engineering. We prove that the codifference detects forms of dependence and ergodicity breaking which are not visible from analysing the covariance and correlation functions. We also discuss a related measure of dispersion, which is a nonlinear analogue of the mean squared displacement.}, language = {en} } @misc{ShpritsMeniettiDrozdovetal.2018, author = {Shprits, Yuri Y. and Menietti, J. D. and Drozdov, Alexander and Horne, Richard B. and Woodfield, Emma E. and Groene, J. B. and de Soria-Santacruz, M. and Averkamp, T. F. and Garrett, H. and Paranicas, C. and Gurnett, Don A.}, title = {Strong whistler mode waves observed in the vicinity of Jupiter's moons}, series = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe}, journal = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe}, number = {695}, issn = {1866-8372}, doi = {10.25932/publishup-42627}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-426278}, pages = {6}, year = {2018}, abstract = {Understanding of wave environments is critical for the understanding of how particles are accelerated and lost in space. This study shows that in the vicinity of Europa and Ganymede, that respectively have induced and internal magnetic fields, chorus wave power is significantly increased. The observed enhancements are persistent and exceed median values of wave activity by up to 6 orders of magnitude for Ganymede. Produced waves may have a pronounced effect on the acceleration and loss of particles in the Jovian magnetosphere and other astrophysical objects. The generated waves are capable of significantly modifying the energetic particle environment, accelerating particles to very high energies, or producing depletions in phase space density. Observations of Jupiter's magnetosphere provide a unique opportunity to observe how objects with an internal magnetic field can interact with particles trapped in magnetic fields of larger scale objects.}, language = {en} } @misc{MuenchKipfstuhlFreitagetal.2017, author = {M{\"u}nch, Thomas and Kipfstuhl, Sepp and Freitag, Johannes and Meyer, Hanno and Laepple, Thomas}, title = {Constraints on post-depositional isotope modifications in East Antarctic firn from analysing temporal changes of isotope profiles}, series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, journal = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, number = {662}, issn = {1866-8372}, doi = {10.25932/publishup-41876}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-418763}, pages = {14}, year = {2017}, abstract = {The isotopic composition of water in ice sheets is extensively used to infer past climate changes. In low-accumulation regions their interpretation is, however, challenged by poorly constrained effects that may influence the initial isotope signal during and after deposition of the snow. This is reflected in snow-pit isotope data from Kohnen Station, Antarctica, which exhibit a seasonal cycle but also strong interannual variations that contradict local temperature observations. These inconsistencies persist even after averaging many profiles and are thus not explained by local stratigraphic noise. Previous studies have suggested that post-depositional processes may significantly influence the isotopic composition of East Antarctic firn. Here, we investigate the importance of post-depositional processes within the open-porous firn (greater than or similar to 10 cm depth) at Kohnen Station by separating spatial from temporal variability. To this end, we analyse 22 isotope profiles obtained from two snow trenches and examine the temporal isotope modifications by comparing the new data with published trench data extracted 2 years earlier. The initial isotope profiles undergo changes over time due to downward advection, firn diffusion and densification in magnitudes consistent with independent estimates. Beyond that, we find further modifications of the original isotope record to be unlikely or small in magnitude (<< 1 parts per thousand RMSD). These results show that the discrepancy between local temperatures and isotopes most likely originates from spatially coherent processes prior to or during deposition, such as precipitation intermittency or systematic isotope modifications acting on drifting or loose surface snow.}, language = {en} } @misc{MuenchKipfstuhlFreitagetal.2016, author = {M{\"u}nch, Thomas and Kipfstuhl, Sepp and Freitag, Johannes and Meyer, Hanno and Laepple, Thomas}, title = {Regional climate signal vs. local noise}, series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, journal = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, number = {500}, issn = {1866-8372}, doi = {10.25932/publishup-40838}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-408385}, pages = {17}, year = {2016}, abstract = {In low-accumulation regions, the reliability of delta O-18-derived temperature signals from ice cores within the Holocene is unclear, primarily due to the small climate changes relative to the intrinsic noise of the isotopic signal. In order to learn about the representativity of single ice cores and to optimise future ice-core-based climate reconstructions, we studied the stable-water isotope composition of firn at Kohnen Station, Dronning Maud Land, Antarctica. Analysing delta O-18 in two 50m long snow trenches allowed us to create an unprecedented, two-dimensional image characterising the isotopic variations from the centimetre to the 100-metre scale. Our results show seasonal layering of the isotopic composition but also high horizontal isotopic variability caused by local stratigraphic noise. Based on the horizontal and vertical structure of the isotopic variations, we derive a statistical noise model which successfully explains the trench data. The model further allows one to determine an upper bound for the reliability of climate reconstructions conducted in our study region at seasonal to annual resolution, depending on the number and the spacing of the cores taken.}, language = {en} } @phdthesis{Roder2018, author = {Roder, Phillip}, title = {Kombination von Fluoreszenzmikroskopie und Rasterkraftmikroskopie zur Aufkl{\"a}rung physiologischer Prozesse in lebenden Zellen}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-419806}, school = {Universit{\"a}t Potsdam}, pages = {xvi, 113}, year = {2018}, abstract = {Innerhalb dieser Doktorarbeit wurde eine neuartige Mikromanipulationstechnik f{\"u}r die lokale Fl{\"u}ssigkeitsabgabe am komplexen Dr{\"u}sengewebe der Schabe P. americana charakterisiert und f{\"u}r die damit verbundene gezielte Manipulation von einzelnen Zellen in einem Zellkomplex (Gewebe) angewandt. Bei dieser Mikromanipulationstechnik handelt es sich um die seit 2009 bekannte nanofluidische Rasterkraftmikroskopie (FluidFM = fluidic force microscopy). Dabei werden sehr kleine mikrokan{\"a}lige Rasterkraftspitzen bzw. Mikro-/Nanopipetten mit einer {\"O}ffnung zwischen 300 nm und 2 µm verwendet, mit denen es m{\"o}glich ist, sehr kleine Volumina im Pikoliter- bis Femtoliter-Bereich (10-12 L - 10-15 L) gezielt und ortsgenau abzugeben. Das Ziel dieser Arbeit war die Analyse zellul{\"a}rer Prozesse, wie z. B. Zell-Zell-Kommunikation oder Signalweiterleitung, zwischen benachbarten Zellen unter Zuhilfenahme der Fluoreszenzmikroskopie. Mit dieser Methode k{\"o}nnen die Zellen und ihre Bestandteile mittels vorheriger Farbstoffbeladung unter einem Mikroskop mit hohem Kontrast optisch dargestellt werden. Mit Hilfe der Fluoreszenzmikroskopie sollten schlussendlich die zellul{\"a}ren Reaktionen innerhalb des Gewebes nach der lokalen Manipulation visualisiert werden. Zun{\"a}chst wurde die Anwendung des Systems an Luft und w{\"a}ssriger Umgebung beschrieben. In diesem Zusammenhang wurde eine Reinigungs- und Beladungsmethode entwickelt, mit der es m{\"o}glich war, die kostspieligen Mikro-/Nanopipetten zu reinigen und anschließend mehrmals wiederzuverwenden. Hierzu wurde eine alternative Methode getestet, mit der das Diffusionsverhalten von Farbstoffmolek{\"u}len in unterschiedlichen Medien untersucht werden kann. Des Weiteren wurden die Systemparameter optimiert, welche n{\"o}tig sind, um zwischen der Probenoberfl{\"a}che und der Pipette einen guten Pipetten{\"o}ffnungs-abschluss zu erhalten. Dieser Abschluss ist essentiell, damit die abgegebene Fl{\"u}ssigkeit ausschließlich in der Abgaberegion mit der Probe wechselwirkt und die darauffolgenden Reaktionen nur innerhalb des Gewebes erfolgen, da ansonsten die Zell-Zell-Signalweiterleitung zwischen den Zellen nicht eindeutig nachvollzogen werden kann. Diese interzellul{\"a}re Kommunikation wurde anhand zweier sekund{\"a}rer Botenstoffe (Ca2+ und NO) untersucht. Hierbei war es m{\"o}glich einzelne lokale Reaktionen zu detektieren, welche sich {\"u}ber weitere Zellen ausbreiteten. Schlussendlich wurde die Fertigung einer speziellen Injektionspipette beschrieben, welche an zwei biologischen Systemen getestet wurde.}, language = {de} } @article{CherstvyVinodAghionetal.2017, author = {Cherstvy, Andrey G. and Vinod, Deepak and Aghion, Erez and Chechkin, Aleksei V. and Metzler, Ralf}, title = {Time averaging, ageing and delay analysis of financial time series}, series = {New journal of physics}, volume = {19}, journal = {New journal of physics}, publisher = {IOP}, address = {London}, issn = {1367-2630}, doi = {10.1088/1367-2630/aa7199}, pages = {1 -- 11}, year = {2017}, abstract = {We introduce three strategies for the analysis of financial time series based on time averaged observables. These comprise the time averaged mean squared displacement (MSD) as well as the ageing and delay time methods for varying fractions of the financial time series. We explore these concepts via statistical analysis of historic time series for several Dow Jones Industrial indices for the period from the 1960s to 2015. Remarkably, we discover a simple universal law for the delay time averaged MSD. The observed features of the financial time series dynamics agree well with our analytical results for the time averaged measurables for geometric Brownian motion, underlying the famed Black-Scholes-Merton model. The concepts we promote here are shown to be useful for financial data analysis and enable one to unveil new universal features of stock market dynamics.}, language = {en} } @misc{CherstvyVinodAghionetal.2017, author = {Cherstvy, Andrey G. and Vinod, Deepak and Aghion, Erez and Chechkin, Aleksei V. and Metzler, Ralf}, title = {Time averaging, ageing and delay analysis of financial time series}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-400541}, pages = {11}, year = {2017}, abstract = {We introduce three strategies for the analysis of financial time series based on time averaged observables. These comprise the time averaged mean squared displacement (MSD) as well as the ageing and delay time methods for varying fractions of the financial time series. We explore these concepts via statistical analysis of historic time series for several Dow Jones Industrial indices for the period from the 1960s to 2015. Remarkably, we discover a simple universal law for the delay time averaged MSD. The observed features of the financial time series dynamics agree well with our analytical results for the time averaged measurables for geometric Brownian motion, underlying the famed Black-Scholes-Merton model. The concepts we promote here are shown to be useful for financial data analysis and enable one to unveil new universal features of stock market dynamics.}, language = {en} } @article{ChenPohlBoettcher2015, author = {Chen, Xuhui and Pohl, Martin and B{\"o}ttcher, Markus}, title = {Particle diffusion and localized acceleration in inhomogeneous AGN jets - I. Steady-state spectra}, series = {Monthly notices of the Royal Astronomical Society}, volume = {447}, journal = {Monthly notices of the Royal Astronomical Society}, number = {1}, publisher = {Oxford Univ. Press}, address = {Oxford}, issn = {0035-8711}, doi = {10.1093/mnras/stu2438}, pages = {530 -- 544}, year = {2015}, abstract = {We study the acceleration, transport, and emission of particles in relativistic jets. Localized stochastic particle acceleration, spatial diffusion, and synchrotron as well as synchrotron self-Compton (SSC) emission are considered in a leptonic model. To account for inhomogeneity, we use a 2D axisymmetric cylindrical geometry for both relativistic electrons and magnetic field. In this first phase of our work, we focus on steady-state spectra that develop from a time-dependent model. We demonstrate that small isolated acceleration region in a much larger emission volume are sufficient to accelerate particles to high energy. Diffusive escape from these small regions provides a natural explanation for the spectral form of the jet emission. The location of the acceleration regions within the jet is found to affect the cooling break of the spectrum in this diffusive model. Diffusion-caused energy-dependent inhomogeneity in the jets predicts that the SSC spectrum is harder than the synchrotron spectrum. There can also be a spectral hardening towards the high-energy section of the synchrotron spectrum, if particle escape is relatively slow. These two spectral hardening effects indicate that the jet inhomogeneity might be a natural explanation for the unexpected hard. gamma-ray spectra observed in some blazars.}, language = {en} } @article{CherstvyMetzler2015, author = {Cherstvy, Andrey G. and Metzler, Ralf}, title = {Ergodicity breaking, ageing, and confinement in generalized diffusion processes with position and time dependent diffusivity}, series = {Journal of statistical mechanics: theory and experiment}, journal = {Journal of statistical mechanics: theory and experiment}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {1742-5468}, doi = {10.1088/1742-5468/2015/05/P05010}, pages = {20}, year = {2015}, abstract = {We study generalized anomalous diffusion processes whose diffusion coefficient D(x, t) similar to D-0x(alpha)t(beta) depends on both the position x of the test particle and the process time t. This process thus combines the features of scaled Brownian motion and heterogeneous diffusion parent processes. We compute the ensemble and time averaged mean squared displacements of this generalized diffusion process. The scaling exponent of the ensemble averaged mean squared displacement is shown to be the product of the critical exponents of the parent processes, and describes both subdiffusive and superdiffusive systems. We quantify the amplitude fluctuations of the time averaged mean squared displacement as function of the length of the time series and the lag time. In particular, we observe a weak ergodicity breaking of this generalized diffusion process: even in the long time limit the ensemble and time averaged mean squared displacements are strictly disparate. When we start to observe this process some time after its initiation we observe distinct features of ageing. We derive a universal ageing factor for the time averaged mean squared displacement containing all information on the ageing time and the measurement time. External confinement is shown to alter the magnitudes and statistics of the ensemble and time averaged mean squared displacements.}, language = {en} } @article{ProkopovicDuschlVolodkin2015, author = {Prokopovic, Vladimir Z. and Duschl, Claus and Volodkin, Dmitry}, title = {Hyaluronic Acid/Poly-l-Lysine Multilayers as Reservoirs for Storage and Release of Small Charged Molecules}, series = {Macromolecular bioscience}, volume = {15}, journal = {Macromolecular bioscience}, number = {10}, publisher = {Wiley-VCH}, address = {Weinheim}, issn = {1616-5187}, doi = {10.1002/mabi.201500093}, pages = {1357 -- 1363}, year = {2015}, abstract = {Polyelectrolyte multilayer films are nowadays very attractive for bioapplications due to their tunable properties and ability to control cellular response. Here we demonstrate that multilayers made of hyaluronic acid and poly-l-lysine act as high-capacity reservoirs for small charged molecules. Strong accumulation within the film is explained by electrostatically driven binding to free charges of polyelectrolytes. Binding and release mechanisms are discussed based on charge balance and polymer dynamics in the film. Our results show that transport of molecules through the film-solution interface limits the release rate. The multilayers might serve as an effective platform for drug delivery and tissue engineering due to high potential for drug loading and controlled release.}, language = {en} } @article{ShinCherstvyKimetal.2015, author = {Shin, Jaeoh and Cherstvy, Andrey G. and Kim, Won Kyu and Metzler, Ralf}, title = {Facilitation of polymer looping and giant polymer diffusivity in crowded solutions of active particles}, series = {New journal of physics : the open-access journal for physics}, volume = {17}, journal = {New journal of physics : the open-access journal for physics}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {1367-2630}, doi = {10.1088/1367-2630/17/11/113008}, pages = {12}, year = {2015}, abstract = {We study the dynamics of polymer chains in a bath of self-propelled particles (SPP) by extensive Langevin dynamics simulations in a two-dimensional model system. Specifically, we analyse the polymer looping properties versus the SPP activity and investigate how the presence of the active particles alters the chain conformational statistics. We find that SPPs tend to extend flexible polymer chains, while they rather compactify stiffer semiflexible polymers, in agreement with previous results. Here we show that higher activities of SPPs yield a higher effective temperature of the bath and thus facilitate the looping kinetics of a passive polymer chain. We explicitly compute the looping probability and looping time in a wide range of the model parameters. We also analyse the motion of a monomeric tracer particle and the polymer's centre of mass in the presence of the active particles in terms of the time averaged mean squared displacement, revealing a giant diffusivity enhancement for the polymer chain via SPP pooling. Our results are applicable to rationalising the dimensions and looping kinetics of biopolymers at constantly fluctuating and often actively driven conditions inside biological cells or in suspensions of active colloidal particles or bacteria cells.}, language = {en} } @article{PalyulinChechkinMetzler2014, author = {Palyulin, Vladimir V. and Chechkin, Aleksei V. and Metzler, Ralf}, title = {Space-fractional Fokker-Planck equation and optimization of random search processes in the presence of an external bias}, series = {Journal of statistical mechanics: theory and experiment}, journal = {Journal of statistical mechanics: theory and experiment}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {1742-5468}, doi = {10.1088/1742-5468/2014/11/P11031}, pages = {32}, year = {2014}, abstract = {Based on the space-fractional Fokker-Planck equation with a delta-sink term, we study the efficiency of random search processes based on Levy flights with power-law distributed jump lengths in the presence of an external drift, for instance, an underwater current, an airflow, or simply the preference of the searcher based on prior experience. While Levy flights turn out to be efficient search processes when the target is upstream relative to the starting point, in the downstream scenario, regular Brownian motion turns out to be advantageous. This is caused by the occurrence of leapovers of Levy flights, due to which Levy flights typically overshoot a point or small interval. Studying the solution of the fractional Fokker-Planck equation, we establish criteria when the combination of the external stream and the initial distance between the starting point and the target favours Levy flights over the regular Brownian search. Contrary to the common belief that Levy flights with a Levy index alpha = 1 (i.e. Cauchy flights) are optimal for sparse targets, we find that the optimal value for alpha may range in the entire interval (1, 2) and explicitly include Brownian motion as the most efficient search strategy overall.}, language = {en} } @article{PalyulinMetzler2012, author = {Palyulin, Vladimir V. and Metzler, Ralf}, title = {How a finite potential barrier decreases the mean first-passage time}, series = {Journal of statistical mechanics: theory and experiment}, journal = {Journal of statistical mechanics: theory and experiment}, number = {1}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {1742-5468}, doi = {10.1088/1742-5468/2012/03/L03001}, pages = {10}, year = {2012}, abstract = {We consider the mean first-passage time of a random walker moving in a potential landscape on a finite interval, the starting and end points being at different potentials. From analytical calculations and Monte Carlo simulations we demonstrate that the mean first-passage time for a piecewise linear curve between these two points is minimized by the introduction of a potential barrier. Due to thermal fluctuations, this barrier may be crossed. It turns out that the corresponding expense for this activation is less severe than the gain from an increased slope towards the end point. In particular, the resulting mean first-passage time is shorter than for a linear potential drop between the two points.}, language = {en} } @article{MagdziarzMetzlerSzczotkaetal.2012, author = {Magdziarz, Marcin and Metzler, Ralf and Szczotka, Wladyslaw and Zebrowski, Piotr}, title = {Correlated continuous-time random walks-scaling limits and Langevin picture}, series = {Journal of statistical mechanics: theory and experiment}, journal = {Journal of statistical mechanics: theory and experiment}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {1742-5468}, doi = {10.1088/1742-5468/2012/04/P04010}, pages = {18}, year = {2012}, abstract = {In this paper we analyze correlated continuous-time random walks introduced recently by Tejedor and Metzler (2010 J. Phys. A: Math. Theor. 43 082002). We obtain the Langevin equations associated with this process and the corresponding scaling limits of their solutions. We prove that the limit processes are self-similar and display anomalous dynamics. Moreover, we extend the model to include external forces. Our results are confirmed by Monte Carlo simulations.}, language = {en} } @article{ChechkinLenzKlages2012, author = {Chechkin, Aleksei V. and Lenz, F. and Klages, Rainer}, title = {Normal and anomalous fluctuation relations for gaussian stochastic dynamics}, series = {Journal of statistical mechanics: theory and experiment}, journal = {Journal of statistical mechanics: theory and experiment}, number = {4}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {1742-5468}, doi = {10.1088/1742-5468/2012/11/L11001}, pages = {12}, year = {2012}, abstract = {We study transient work fluctuation relations (FRs) for Gaussian stochastic systems generating anomalous diffusion. For this purpose we use a Langevin approach by employing two different types of additive noise: (i) internal noise where the fluctuation dissipation relation of the second kind (FDR II) holds, and (ii) external noise without FDR II. For internal noise we demonstrate that the existence of FDR II implies the existence of the fluctuation dissipation relation of the first kind (FDR I), which in turn leads to conventional (normal) forms of transient work FRs. For systems driven by external noise we obtain violations of normal FRs, which we call anomalous FRs. We derive them in the long-time limit and demonstrate the existence of logarithmic factors in FRs for intermediate times. We also outline possible experimental verifications.}, language = {en} } @book{SchmiedgenRhinowKoeppenetal.2015, author = {Schmiedgen, Jan and Rhinow, Holger and K{\"o}ppen, Eva and Meinel, Christoph}, title = {Parts without a whole?}, number = {97}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, isbn = {978-3-86956-334-3}, issn = {1613-5652}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-79969}, publisher = {Universit{\"a}t Potsdam}, pages = {143}, year = {2015}, abstract = {This explorative study gives a descriptive overview of what organizations do and experience when they say they practice design thinking. It looks at how the concept has been appropriated in organizations and also describes patterns of design thinking adoption. The authors use a mixed-method research design fed by two sources: questionnaire data and semi-structured personal expert interviews. The study proceeds in six parts: (1) design thinking¹s entry points into organizations; (2) understandings of the descriptor; (3) its fields of application and organizational localization; (4) its perceived impact; (5) reasons for its discontinuation or failure; and (6) attempts to measure its success. In conclusion the report challenges managers to be more conscious of their current design thinking practice. The authors suggest a co-evolution of the concept¹s introduction with innovation capability building and the respective changes in leadership approaches. It is argued that this might help in unfolding design thinking¹s hidden potentials as well as preventing unintended side-effects such as discontented teams or the dwindling authority of managers.}, language = {en} } @misc{Ansel2015, type = {Master Thesis}, author = {Ansel, Simon}, title = {Die Diffusion von Innovationen in deutschen Kommunen}, issn = {2190-4561}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-80370}, school = {Universit{\"a}t Potsdam}, pages = {IV, 67}, year = {2015}, abstract = {Die fortschreitende Diffusion von E-Government ist ein Ph{\"a}nomen, dem in der internationa-len Forschungsliteratur bereits viel Aufmerksamkeit zu Teil wurde. Erstaunlich wenige Studien widmen sich bislang jedoch dezidiert dem Faktor Interdependenz, der eigentlichen Ursache von Diffusionsprozessen. In dieser Arbeit werden Interdependenzbeziehungen anhand dreier spezifischer Mechanismen der Diffusion, namentlich „Nachahmung", „Wettbewerb" und „Lernen", untersucht. Auf Basis einer empirischen Analyse mit Daten zur Einf{\"u}hrung von E-Government-Komponenten in 183 deutschen St{\"a}dten {\"u}ber den Zeitraum von 1995 bis 2014 konnte ein Einfluss der Mechanismen „Nachahmung" und „Lernen" auf das Innovationsverhalten von Kommunen festgestellt werden. F{\"u}r das Vorliegen von Wettbe-werbsdynamiken ließen sich demgegen{\"u}ber keine Anhaltspunkte finden. F{\"u}r zuk{\"u}nftige Forschungen zur Diffusion von Innovationen wird angeregt, verst{\"a}rkt an die mechanismen- und prozessbasierte Perspektive von Diffusion als theoretischem Rahmenkonzept anzukn{\"u}pfen.}, language = {de} } @phdthesis{Mulansky2012, author = {Mulansky, Mario}, title = {Chaotic diffusion in nonlinear Hamiltonian systems}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-63180}, school = {Universit{\"a}t Potsdam}, year = {2012}, abstract = {This work investigates diffusion in nonlinear Hamiltonian systems. The diffusion, more precisely subdiffusion, in such systems is induced by the intrinsic chaotic behavior of trajectories and thus is called chaotic diffusion''. Its properties are studied on the example of one- or two-dimensional lattices of harmonic or nonlinear oscillators with nearest neighbor couplings. The fundamental observation is the spreading of energy for localized initial conditions. Methods of quantifying this spreading behavior are presented, including a new quantity called excitation time. This new quantity allows for a more precise analysis of the spreading than traditional methods. Furthermore, the nonlinear diffusion equation is introduced as a phenomenologic description of the spreading process and a number of predictions on the density dependence of the spreading are drawn from this equation. Two mathematical techniques for analyzing nonlinear Hamiltonian systems are introduced. The first one is based on a scaling analysis of the Hamiltonian equations and the results are related to similar scaling properties of the NDE. From this relation, exact spreading predictions are deduced. Secondly, the microscopic dynamics at the edge of spreading states are thoroughly analyzed, which again suggests a scaling behavior that can be related to the NDE. Such a microscopic treatment of chaotically spreading states in nonlinear Hamiltonian systems has not been done before and the results present a new technique of connecting microscopic dynamics with macroscopic descriptions like the nonlinear diffusion equation. All theoretical results are supported by heavy numerical simulations, partly obtained on one of Europe's fastest supercomputers located in Bologna, Italy. In the end, the highly interesting case of harmonic oscillators with random frequencies and nonlinear coupling is studied, which resembles to some extent the famous Discrete Anderson Nonlinear Schroedinger Equation. For this model, a deviation from the widely believed power-law spreading is observed in numerical experiments. Some ideas on a theoretical explanation for this deviation are presented, but a conclusive theory could not be found due to the complicated phase space structure in this case. Nevertheless, it is hoped that the techniques and results presented in this work will help to eventually understand this controversely discussed case as well.}, language = {en} } @phdthesis{Klumpp2003, author = {Klumpp, Stefan}, title = {Movements of molecular motors : diffusion and directed walks}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-0000806}, school = {Universit{\"a}t Potsdam}, year = {2003}, abstract = {Bewegungen von prozessiven molekularen Motoren des Zytoskeletts sind durch ein Wechselspiel von gerichteter Bewegung entlang von Filamenten und Diffusion in der umgebenden L{\"o}sung gekennzeichnet. Diese eigent{\"u}mlichen Bewegungen werden in der vorliegenden Arbeit untersucht, indem sie als Random Walks auf einem Gitter modelliert werden. Ein weiterer Gegenstand der Untersuchung sind Effekte von Wechselwirkungen zwischen den Motoren auf diese Bewegungen. Im einzelnen werden vier Transportph{\"a}nomene untersucht: (i) Random Walks von einzelnen Motoren in Kompartimenten verschiedener Geometrien, (ii) station{\"a}re Konzentrationsprofile, die sich in geschlossenen Kompartimenten infolge dieser Bewegungen einstellen, (iii) randinduzierte Phasen{\"u}berg{\"a}nge in offenen r{\"o}hrenartigen Kompartimenten, die an Motorenreservoirs gekoppelt sind, und (iv) der Einfluß von kooperativen Effekten bei der Motor-Filament-Bindung auf die Bewegung. Alle diese Ph{\"a}nomene sind experimentell zug{\"a}nglich, und m{\"o}gliche experimentelle Realisierungen werden diskutiert.}, language = {en} }