TY  - GEN
A1  - Grebenkov, Denis S.
A1  - Metzler, Ralf
A1  - Oshanin, Gleb
T1  - Distribution of first-reaction times with target regions on boundaries of shell-like domains
T2  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2  - We study the probability density function (PDF) of the first-reaction times between a diffusive ligand and a membrane-bound, immobile imperfect target region in a restricted 'onion-shell' geometry bounded by two nested membranes of arbitrary shapes. For such a setting, encountered in diverse molecular signal transduction pathways or in the narrow escape problem with additional steric constraints, we derive an exact spectral form of the PDF, as well as present its approximate form calculated by help of the so-called self-consistent approximation. For a particular case when the nested domains are concentric spheres, we get a fully explicit form of the approximated PDF, assess the accuracy of this approximation, and discuss various facets of the obtained distributions. Our results can be straightforwardly applied to describe the PDF of the terminal reaction event in multi-stage signal transduction processes.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1255 
KW  - diffusion
KW  - first-passage time
KW  - first-reaction time
KW  - shell-like geometries
KW  - approximate methods
Y1  - 2022
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-557542
SN  - 1866-8372
SP  - 1
EP  - 23
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Grebenkov, Denis S.
A1  - Metzler, Ralf
A1  - Oshanin, Gleb
T1  - Distribution of first-reaction times with target regions on boundaries of shell-like domains
JF  - New Journal of Physics (NJP)
N2  - We study the probability density function (PDF) of the first-reaction times between a diffusive ligand and a membrane-bound, immobile imperfect target region in a restricted 'onion-shell' geometry bounded by two nested membranes of arbitrary shapes. For such a setting, encountered in diverse molecular signal transduction pathways or in the narrow escape problem with additional steric constraints, we derive an exact spectral form of the PDF, as well as present its approximate form calculated by help of the so-called self-consistent approximation. For a particular case when the nested domains are concentric spheres, we get a fully explicit form of the approximated PDF, assess the accuracy of this approximation, and discuss various facets of the obtained distributions. Our results can be straightforwardly applied to describe the PDF of the terminal reaction event in multi-stage signal transduction processes.
KW  - diffusion
KW  - first-passage time
KW  - first-reaction time
KW  - shell-like geometries
KW  - approximate methods
Y1  - 2021
U6  - https://doi.org/10.1088/1367-2630/ac4282
SN  - 1367-2630
VL  - 2021
SP  - 1
EP  - 23
PB  - IOP Publishing
CY  - London
ET  - 23
ER  - 
TY  - THES
A1  - Hennig, Theresa
T1  - Uranium migration in the Opalinus Clay quantified on the host rock scale with reactive transport simulations
T1  - Uranmigration im Opalinuston quantifiziert für die Wirtsgesteinsskala mit reaktiven Transportsimulationen
N2  - Humankind and their environment need to be protected from the harmful effects of spent nuclear fuel, and therefore disposal in deep geological formations is favoured worldwide. Suitability of potential host rocks is evaluated, among others, by the retention capacity with respect to radionuclides. Safety assessments are based on the quantification of radionuclide migration lengths with numerical simulations as experiments cannot cover the required temporal (1 Ma) and spatial scales (>100 m). 

Aim of the present thesis is to assess the migration of uranium, a geochemically complex radionuclide, in the potential host rock Opalinus Clay. Radionuclide migration in clay formations is governed by diffusion due to their low permeability and retarded by sorption. Both processes highly depend on pore water geochemistry and mineralogy that vary between different facies. Diffusion is quantified with the single-component (SC) approach using one diffusion coefficient for all species and the process-based multi-component (MC) option. With this, each species is assigned its own diffusion coefficient and the interaction with the diffuse double layer is taken into account. Sorption is integrated via a bottom-up approach using mechanistic surface complexation models and cation exchange. Therefore, reactive transport simulations are conducted with the geochemical code PHREEQC to quantify uranium migration, i.e. diffusion and sorption, as a function of mineralogical and geochemical heterogeneities on the host rock scale.

Sorption processes are facies dependent. Migration lengths vary between the Opalinus Clay facies by up to 10 m. Thereby, the geochemistry of the pore water, in particular the partial pressure of carbon dioxide (pCO2), is more decisive for the sorption capacity than the amount of clay minerals. Nevertheless, higher clay mineral quantities compensate geochemical variations. Consequently, sorption processes must be quantified as a function of pore water geochemistry in contact with the mineral assemblage. 

Uranium diffusion in the Opalinus Clay is facies independent. Speciation is dominated by aqueous ternary complexes of U(VI) with calcium and carbonate. Differences in the migration lengths between SC and MC diffusion are with +/-5 m negligible. Further, the application of the MC approach highly depends on the quality and availability of the underlying data. Therefore, diffusion processes can be adequately quantified with the SC approach using experimentally determined diffusion coefficients.

The hydrogeological system governs pore water geochemistry within the formation rather than the mineralogy. Diffusive exchange with the adjacent aquifers established geochemical gradients over geological time scales that can enhance migration by up to 25 m. Consequently, uranium sorption processes must be quantified following the identified priority: pCO2 > hydrogeology > mineralogy.  

The presented research provides a workflow and orientation for other potential disposal sites with similar pore water geochemistry due to the identified mechanisms and dependencies. With a maximum migration length of 70 m, the retention capacity of the Opalinus Clay with respect to uranium is sufficient to fulfill the German legal minimum requirement of a thickness of at least 100 m.
N2  - Zum Schutz von Mensch und Umwelt vor den schädlichen Auswirkungen abgebrannter Brennelemente, wird weltweit die Endlagerung in tiefen geologischen Formationen favorisiert. Daher ist das Rückhaltevermögen potenzieller Wirtsgesteine gegenüber Radionukliden ein wichtiges Kriterium. Sicherheitsbewertungen basieren auf der Quantifizierung der Migration mit numerischen Simulationen, da Experimente die erforderlichen zeitlichen (1 Ma) und räumlichen Skalen (>100 m) nicht abdecken können. 

Ziel der Dissertation ist es, die Migration des geochemisch komplexen Radionuklids Uran im potenziellen Wirtsgestein Opalinuston zu bewerten. In Tonformationen wird die Radionuklidmigration aufgrund der geringen Durchlässigkeit von Diffusion bestimmt und durch Sorption verzögert. Beide Prozesse hängen stark von der Porenwassergeochemie und Mineralogie ab, die zwischen verschiedenen Fazies variieren. Die Diffusion wird mit dem Einkomponenten- (SC) und Mehrkomponentenansatz (MC) quantifiziert. Nach dem SC-Ansatz wird ein Diffusionskoeffizient für alle Spezies verwendet, wohingegen mit der MC-Option individuelle Werte zugewiesen und die Interaktion mit der diffusen Doppelschicht berücksichtigt wird. Die Sorption ist mit Hilfe mechanistischer Oberflächenkomplexierungsmodelle und Kationenaustausch integriert. Die Durchführung reaktiver Transportsimulationen mit dem Code PHREEQC ermöglicht die Quantifizierung der Uranmigration, d. h. Diffusion und Sorption, in Abhängigkeit der Mineralogie und Porenwassergeochemie für die Wirtsgesteinsskala.

Sorptionsprozesse sind faziesabhängig. Die Migrationslängen variieren um bis zu 10 m zwischen den Fazies aufgrund von Unterschieden in der Porenwassergeochemie. Dabei ist insbesondere der Partialdruck des Kohlendioxids (pCO2) entscheidender für die Sorptionskapazität als die Menge an Tonmineralen. Allerdings kompensieren höhere Tonmineralmengen geochemische Schwankungen. Folglich müssen Sorptionsprozesse in Abhängigkeit der Porenwassergeochemie quantifiziert werden. 

Urandiffusion ist faziesunabhängig. Die Speziation wird durch aquatische ternäre Komplexe von U(VI) mit Kalzium und Karbonat dominiert. Die Unterschiede in den Migrationslängen zwischen SC- und MC-Diffusion sind mit +/-5 m vernachlässigbar. Die Anwendung des MC-Ansatzes hängt stark von der Qualität und Verfügbarkeit der zugrunde liegenden Daten ab. Diffusionsprozesse können also mit dem SC-Ansatz unter Verwendung experimentell ermittelter Diffusionskoeffizienten quantifiziert werden.

Haupteinflussfaktor auf die Porenwassergeochemie ist das hydrogeologische System und nicht die Mineralogie. Der diffusive Austausch mit den angrenzenden Aquiferen hat über geologische Zeiträume geochemische Gradienten geschaffen, die die Migration um bis zu 25 m verlängern können. Folglich müssen Sorptionsprozesse nach der identifizierten Priorität quantifiziert werden: pCO2 > Hydrogeologie > Mineralogie.  

Die ermittelten Abhängigkeiten dienen als Orientierung für andere potenzielle Endlagerstandorte mit ähnlicher Porenwassergeochemie. Mit einer maximalen Migration von 70 m reicht das Rückhaltevermögen des Opalinustons gegenüber Uran aus, um die deutsche gesetzliche Mindestanforderung von 100 m Mächtigkeit zu erfüllen.
KW  - uranium
KW  - Opalinus Clay
KW  - PHREEQC
KW  - diffusion
KW  - sorption
KW  - nuclear waste disposal
KW  - reactive transport simulation
KW  - host rock scale
KW  - Opalinuston
KW  - PHREEQC
KW  - Diffusion
KW  - Wirtsgesteinsskala
KW  - Endlagerung nuklearer Abfälle
KW  - reaktive Transportsimulation
KW  - Sorption
KW  - Uran
Y1  - 2022
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-552700
ER  - 
TY  - GEN
A1  - Makwana, Kirit D.
A1  - Yan, Huirong
T1  - Properties of magnetohydrodynamic modes in compressively driven plasma turbulence
T2  - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2  - We study properties of magnetohydrodynamic (MHD) eigenmodes by decomposing the data of MHD simulations into linear MHD modes-namely, the Alfven, slow magnetosonic, and fast magnetosonic modes. We drive turbulence with a mixture of solenoidal and compressive driving while varying the Alfven Mach number (M-A), plasma beta, and the sonic Mach number from subsonic to transsonic. We find that the proportion of fast and slow modes in the mode mixture increases with increasing compressive forcing. This proportion of the magnetosonic modes can also become the dominant fraction in the mode mixture. The anisotropy of the modes is analyzed by means of their structure functions. The Alfven-mode anisotropy is consistent with the Goldreich-Sridhar theory. We find a transition from weak to strong Alfvenic turbulence as we go from low to high M-A. The slow-mode properties are similar to the Alfven mode. On the other hand, the isotropic nature of fast modes is verified in the cases where the fast mode is a significant fraction of the mode mixture. The fast-mode behavior does not show any transition in going from low to high M-A. We find indications that there is some interaction between the different modes, and the properties of the dominant mode can affect the properties of the weaker modes. This work identifies the conditions under which magnetosonic modes can be a major fraction of turbulent astrophysical plasmas, including the regime of weak turbulence. Important astrophysical implications for cosmic-ray transport and magnetic reconnection are discussed.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1225 
KW  - mhd turbulence
KW  - star formation
KW  - simulations
KW  - Anisotropy
KW  - diffusion
Y1  - 2022
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-531607
SN  - 1866-8372
VL  - 10
IS  - 3
PB  - American Physical Society (APS)
CY  - College Park
ER  - 
TY  - JOUR
A1  - Grätz, Fabio M.
A1  - Seiss, Martin
A1  - Spahn, Frank
T1  - Formation of moon-induced gaps in dense planetary rings
BT  - application to the rings of saturn
JF  - The astrophysical journal : an international review of spectroscopy and astronomical physics
N2  - We develop an axisymmetric diffusion model to describe radial density profiles in the vicinity of tiny moons embedded in planetary rings. Our diffusion model accounts for the gravitational scattering of the ring particles by an embedded moon and for the viscous diffusion of the ring matter back into the gap. With test particle simulations, we show that the scattering of the ring particles passing the moon is larger for small impact parameters than estimated by Goldreich & Tremaine and Namouni. This is significant for modeling the Keeler gap. We apply our model to the gaps of the moons Pan and Daphnis embedded in the outer A ring of Saturn with the aim to estimate the shear viscosity of the ring in the vicinity of the Encke and Keeler gap. In addition, we analyze whether tiny icy moons whose dimensions lie below Cassini's resolution capabilities would be able to explain the gap structure of the C ring and the Cassini division.
KW  - diffusion
KW  - planets and satellites: rings
KW  - scattering
Y1  - 2018
U6  - https://doi.org/10.3847/1538-4357/aace00
SN  - 0004-637X
SN  - 1538-4357
VL  - 862
IS  - 2
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  - 
TY  - JOUR
A1  - Grebenkov, Denis S.
A1  - Metzler, Ralf
A1  - Oshanin, Gleb
T1  - A molecular relay race: sequential first-passage events to the terminal reaction centre in a cascade of diffusion controlled processes
JF  - New Journal of Physics (NJP)
N2  - 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.
KW  - diffusion
KW  - reaction cascade
KW  - first passage time
Y1  - 2021
U6  - https://doi.org/10.1088/1367-2630/ac1e42
SN  - 1367-2630
VL  - 23
PB  - IOP - Institute of Physics Publishing
CY  - Bristol
ER  - 
TY  - GEN
A1  - Grebenkov, Denis S.
A1  - Metzler, Ralf
A1  - Oshanin, Gleb
T1  - A molecular relay race: sequential first-passage events to the terminal reaction centre in a cascade of diffusion controlled processes
T2  - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2  - 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.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1159 
KW  - diffusion
KW  - reaction cascade
KW  - first passage time
Y1  - 2021
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-521942
SN  - 1866-8372
ER  - 
TY  - JOUR
A1  - Seiß, Martin
A1  - Albers, Nicole
A1  - Sremčević, Miodrag
A1  - Schmidt, Jürgen
A1  - Salo, Heikki
A1  - Seiler, Michael
A1  - Hoffmann, Holger
A1  - Spahn, Frank
T1  - Hydrodynamic Simulations of Moonlet-induced Propellers in Saturn's Rings
BT  - Application to Bleriot
JF  - The astronomical journal
N2  - 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 Blériot, 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 Blériot. 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.
KW  - diffusion
KW  - hydrodynamics
KW  - planets and satellites: rings
Y1  - 2018
U6  - https://doi.org/10.3847/1538-3881/aaed44
SN  - 0004-6256
SN  - 1538-3881
VL  - 157
IS  - 1
PB  - IOP Publishing Ltd.
CY  - Bristol
ER  - 
TY  - JOUR
A1  - Abdalla, Hassan E.
A1  - Aharonian, Felix A.
A1  - Benkhali, F. Ait
A1  - Angüner, Ekrem Oǧuzhan
A1  - Arakawa, M.
A1  - Arcaro, C.
A1  - Armand, C.
A1  - Arrieta, M.
A1  - Backes, M.
A1  - Barnard, M.
A1  - Becherini, Y.
A1  - Tjus, J. Becker
A1  - Berge, D.
A1  - Bernloehr, K.
A1  - Blackwell, R.
A1  - Bottcher, M.
A1  - Boisson, C.
A1  - Bolmont, J.
A1  - Bonnefoy, S.
A1  - Bordas, Pol
A1  - Bregeon, J.
A1  - Brun, F.
A1  - Brun, P.
A1  - Bryan, M.
A1  - Buechele, M.
A1  - Bulik, T.
A1  - Bylund, T.
A1  - Capasso, M.
A1  - Caroff, S.
A1  - Carosi, A.
A1  - Casanova, Sabrina
A1  - Cerruti, M.
A1  - Chakraborty, N.
A1  - Chand, T.
A1  - Chandra, S.
A1  - Chaves, R. C. G.
A1  - Chen, A.
A1  - Colafrancesco, S.
A1  - Condon, B.
A1  - Davids, I. D.
A1  - Deil, C.
A1  - Devin, J.
A1  - deWilt, P.
A1  - Dirson, L.
A1  - Djannati-Atai, A.
A1  - Dmytriiev, A.
A1  - Donath, A.
A1  - Doroshenko, V
A1  - Dyks, J.
A1  - Egberts, Kathrin
A1  - Emery, G.
A1  - Ernenwein, J-P
A1  - Eschbach, S.
A1  - Fegan, S.
A1  - Fiasson, A.
A1  - Fontaine, G.
A1  - Funk, S.
A1  - Fuessling, M.
A1  - Gabici, S.
A1  - Gallant, Y. A.
A1  - Gate, F.
A1  - Giavitto, G.
A1  - Glawion, D.
A1  - Glicenstein, J. F.
A1  - Gottschall, D.
A1  - Grondin, M-H
A1  - Hahn, J.
A1  - Haupt, M.
A1  - Heinzelmann, G.
A1  - Henri, G.
A1  - Hermann, G.
A1  - Hinton, James Anthony
A1  - Hofmann, W.
A1  - Hoischen, Clemens
A1  - Holch, Tim Lukas
A1  - Holler, M.
A1  - Horns, D.
A1  - Huber, D.
A1  - Iwasaki, H.
A1  - Jacholkowska, A.
A1  - Jamrozy, M.
A1  - Jankowsky, D.
A1  - Jankowsky, F.
A1  - Jouvin, L.
A1  - Jung-Richardt, I
A1  - Kastendieck, M. A.
A1  - Katarzynski, K.
A1  - Katsuragawa, M.
A1  - Katz, U.
A1  - Kerszberg, D.
A1  - Khangulyan, D.
A1  - Khelifi, B.
A1  - King, J.
A1  - Klepser, S.
A1  - Kluzniak, W.
A1  - Komin, Nu
A1  - Kosack, K.
A1  - Kraus, M.
A1  - Lamanna, G.
A1  - Lau, J.
A1  - Lefaucheur, J.
A1  - Lemiere, A.
A1  - Lemoine-Goumard, M.
A1  - Lenain, J-P
A1  - Leser, Eva
A1  - Lohse, T.
A1  - Lopez-Coto, R.
A1  - Lypova, I
A1  - Malyshev, D.
A1  - Marandon, V
A1  - Marcowith, Alexandre
A1  - Mariaud, C.
A1  - Marti-Devesa, G.
A1  - Marx, R.
A1  - Maurin, G.
A1  - Meintjes, P. J.
A1  - Mitchell, A. M. W.
A1  - Moderski, R.
A1  - Mohamed, M.
A1  - Mohrmann, L.
A1  - Moore, C.
A1  - Moulin, Emmanuel
A1  - Murach, T.
A1  - Nakashima, S.
A1  - de Naurois, M.
A1  - Ndiyavala, H.
A1  - Niederwanger, F.
A1  - Niemiec, J.
A1  - Oakes, L.
A1  - Odaka, H.
A1  - Ohm, S.
A1  - Ostrowski, M.
A1  - Oya, I
A1  - Panter, M.
A1  - Parsons, R. D.
A1  - Perennes, C.
A1  - Petrucci, P-O
A1  - Peyaud, B.
A1  - Piel, Q.
A1  - Pita, S.
A1  - Poireau, V
A1  - Noel, A. Priyana
A1  - Prokhorov, D. A.
A1  - Prokoph, H.
A1  - Puehlhofer, G.
A1  - Punch, M.
A1  - Quirrenbach, A.
A1  - Raab, S.
A1  - Rauth, R.
A1  - Reimer, A.
A1  - Reimer, O.
A1  - Renaud, M.
A1  - Rieger, F.
A1  - Rinchiuso, L.
A1  - Romoli, C.
A1  - Rowell, G.
A1  - Rudak, B.
A1  - Ruiz-Velasco, E.
A1  - Sahakian, V
A1  - Saito, S.
A1  - Sanchez, David M.
A1  - Santangelo, Andrea
A1  - Sasaki, M.
A1  - Schlickeiser, R.
A1  - Schussler, F.
A1  - Schulz, A.
A1  - Schutte, H.
A1  - Schwanke, U.
A1  - Schwemmer, S.
A1  - Seglar-Arroyo, M.
A1  - Senniappan, M.
A1  - Seyffert, A. S.
A1  - Shafi, N.
A1  - Shilon, I
A1  - Shiningayamwe, K.
A1  - Simoni, R.
A1  - Sinha, A.
A1  - Sol, H.
A1  - Specovius, A.
A1  - Spir-Jacob, M.
A1  - Stawarz, L.
A1  - Steenkamp, R.
A1  - Stegmann, Christian
A1  - Steppa, Constantin Beverly
A1  - Takahashi, T.
A1  - Tavernet, J-P
A1  - Tavernier, T.
A1  - Taylor, A. M.
A1  - Terrier, R.
A1  - Tibaldo, L.
A1  - Tiziani, D.
A1  - Tluczykont, M.
A1  - Trichard, C.
A1  - Tsirou, M.
A1  - Tsuji, N.
A1  - Tuffs, R.
A1  - Uchiyama, Y.
A1  - van der Walt, D. J.
A1  - van Eldik, C.
A1  - van Rensburg, C.
A1  - van Soelen, B.
A1  - Vasileiadis, G.
A1  - Veh, J.
A1  - Venter, C.
A1  - Vincent, P.
A1  - Vink, J.
A1  - Voisin, F.
A1  - Voelk, H. J.
A1  - Vuillaume, T.
A1  - Wadiasingh, Z.
A1  - Wagner, S. J.
A1  - Wagner, R. M.
A1  - White, R.
A1  - Wierzcholska, A.
A1  - Yang, R.
A1  - Yoneda, H.
A1  - Zaborov, D.
A1  - Zacharias, M.
A1  - Zanin, R.
A1  - Zdziarski, A. A.
A1  - Zech, Alraune
A1  - Zefi, F.
A1  - Ziegler, A.
A1  - Zorn, J.
A1  - Zywucka, N.
T1  - Particle transport within the pulsar wind nebula HESS J1825-137
JF  - Astronomy and astrophysics : an international weekly journal
N2  - 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.
KW  - gamma rays: general
KW  - acceleration of particles
KW  - convection
KW  - diffusion
KW  - pulsars: general
Y1  - 2019
U6  - https://doi.org/10.1051/0004-6361/201834335
SN  - 1432-0746
VL  - 621
PB  - EDP Sciences
CY  - Les Ulis
ER  - 
TY  - JOUR
A1  - Sposini, Vittoria
A1  - Chechkin, Aleksei V.
A1  - Metzler, Ralf
T1  - First passage statistics for diffusing diffusivity
JF  - Journal of physics : A, Mathematical and theoretical
N2  - 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.
KW  - diffusion
KW  - superstatistics
KW  - first passage
Y1  - 2018
U6  - https://doi.org/10.1088/1751-8121/aaf6ff
SN  - 1751-8113
SN  - 1751-8121
VL  - 52
IS  - 4
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  - 
TY  - JOUR
A1  - Grebenkov, Denis S.
A1  - Sposini, Vittoria
A1  - Metzler, Ralf
A1  - Oshanin, Gleb
A1  - Seno, Flavio
T1  - Exact distributions of the maximum and range of random diffusivity processes
JF  - New Journal of Physics
N2  - 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.
KW  - random diffusivity
KW  - extremal values
KW  - maximum and range
KW  - diffusion
KW  - Brownian motion
Y1  - 2021
U6  - https://doi.org/10.1088/1367-2630/abd313
SN  - 1367-2630
VL  - 23
PB  - Dt. Physikalische Ges.
CY  - Bad Honnef
ER  - 
TY  - GEN
A1  - Grebenkov, Denis S.
A1  - Sposini, Vittoria
A1  - Metzler, Ralf
A1  - Oshanin, Gleb
A1  - Seno, Flavio
T1  - Exact distributions of the maximum and range of random diffusivity processes
T2  - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2  - 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.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1142 
KW  - random diffusivity
KW  - extremal values
KW  - maximum and range
KW  - diffusion
KW  - Brownian motion
Y1  - 2021
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-503976
SN  - 1866-8372
IS  - 1142
ER  - 
TY  - JOUR
A1  - Grätz, Fabio M.
A1  - Seiß, Martin
A1  - Schmidt, Jürgen
A1  - Colwell, Joshua
A1  - Spahn, Frank
T1  - Sharp Gap Edges in Dense Planetary Rings
BT  - an Axisymmetric Diffusion Model
JF  - The astrophysical journal : an international review of spectroscopy and astronomical physics
N2  - 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
KW  - celestial mechanics
KW  - diffusion
KW  - hydrodynamics
KW  - planets and satellites: rings
KW  - scattering
Y1  - 2019
U6  - https://doi.org/10.3847/1538-4357/ab007e
SN  - 0004-637X
SN  - 1538-4357
VL  - 872
IS  - 2
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  - 
TY  - GEN
A1  - Thapa, Samudrajit
A1  - Wyłomańska, Agnieszka
A1  - Sikora, Grzegorz
A1  - Wagner, Caroline E.
A1  - Krapf, Diego
A1  - Kantz, Holger
A1  - Chechkin, Aleksei V.
A1  - Metzler, Ralf
T1  - Leveraging large-deviation statistics to decipher the stochastic properties of measured trajectories
T2  - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2  - 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.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1118 
KW  - diffusion
KW  - anomalous diffusion
KW  - large-deviation statistic
KW  - time-averaged mean squared displacement
KW  - Chebyshev inequality
Y1  - 2021
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-493494
SN  - 1866-8372
IS  - 1118
ER  - 
TY  - JOUR
A1  - Thapa, Samudrajit
A1  - Wyłomańska, Agnieszka
A1  - Sikora, Grzegorz
A1  - Wagner, Caroline E.
A1  - Krapf, Diego
A1  - Kantz, Holger
A1  - Chechkin, Aleksei V.
A1  - Metzler, Ralf
T1  - Leveraging large-deviation statistics to decipher the stochastic properties of measured trajectories
JF  - New Journal of Physics
N2  - 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.
KW  - diffusion
KW  - anomalous diffusion
KW  - large-deviation statistic
KW  - time-averaged mean squared displacement
KW  - Chebyshev inequality
Y1  - 2020
U6  - https://doi.org/10.1088/1367-2630/abd50e
SN  - 1367-2630
VL  - 23
PB  - Dt. Physikalische Ges. ; IOP
CY  - Bad Honnef ; London
ER  - 
TY  - THES
A1  - Šustr, David
T1  - Molecular diffusion in polyelectrolyte multilayers
N2  - 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.
N2  - Die Forschung an neuartigen und komplexen Biomaterialien ist unabdingbar für deren Einsatz in begehrten Bereichen wie der Gewebezüchtung, regenerativen Medizin, Zellkultivierung und Biotechnologie. Die hier vorgelegte Arbeit beschäftigt sich eingehend mit einem dieser vielversprechenden Materialien: Polyelektrolytische Multilayers (PEM), die aus Hyaluronsäure (Hyaluronic Acid, HA) und Poly-L-Lysin (PLL) zusammengesetzt sind. Diese gelartige Polymerbeschichtung ermöglicht es, (Bio-) Moleküle wie z.B. Proteine oder Medikamente zu akkumulieren und diese kontrolliert wieder abzugeben. Durch ihre Zusammensetzung und intrinsischen Merkmale können die PEM der Imitation einer Extrazellulären Matrix (ECM) dienen. Diese Eigenschaften machen die HA/PLL-PEM zu einem Anwärter auf verschiedene Bio-Anwendungen, wie den oben genannten. Die vorliegende Arbeit zielt auf die Entwicklung eines Ansatzes zur Einschätzung der multi-fraktionellen Diffusion in Multilayers (1. Teil), und auf die Kontrolle des lokalen molekularen Transports in und aus den Multilayers durch Laser-Stimulation (2. Teil).

Der Aufnahme- und Freisetzungsmechanismus wird bestimmt von der Wechselwirkung zwischen Bioaktiva und den Bestandteilen der Multilayers, sowie allgemein vom Diffusionsprozess. Der Diffusion eines Molekül in HA/PLL-PEM weist unterschiedliche Diffusionsraten einzelner Molekülbestandteile auf. Derzeit existieren nur wenige Ansätze zur Einschätzung der Mobilität von Molekülen in derart komplexen Systemen. Diesem Mangel will die vorliegende Arbeit durch das Design eines neuartigen Evaluations-Instruments abhelfen.
Dieses Instrument bedient sich eines simulationsbasierten Ansatzes zur Evaluation von Daten, die durch die fluorescence recovery after photobleaching (FRAP) -Methode erfasst wurden. Der Ansatz simuliert zunächst mögliche Szenarien der Fluoreszenz-Rückbildung, um diese anschließend mit Messdaten zu vergleichen; dazu werden Modell-Parameter angepasst, um suffiziente Vergleichswerte zu erzielen. Fluoreszierende Latex-Partikel verschiedener Größe und eine Fluoresceinlösung wurden als Kontroll- und Vergleichs-Proben verwendet, um die Ergebnisse zu überprüfen. Zusätzlich wurde die Diffusion des Proteins Cytochrom C in eine HA/PLL-PEM ausgewertet.
Dieses Instrument weitet die Möglichkeiten der Analyse von spatiotemporären FRAP-Daten, die aus der multi-fraktionellen Diffusion stammen, erheblich und gleichzeitig ist es vielseitig einsetzbar. Das Instrument hat das Potential, die Mechanismen des Molekültransports weiter zu erhellen, und eine gezielte Steuerung der Freisetzung medikamentöser Wirkstoffe zu ermöglichen.

Der zweite Teil der Arbeit widmet sich der Erstellung eines Systems zur spatiotemporären Wirkstofffreisetzung, das sich die HA/PLL-PEM zunutze macht. Dieses Freisetzungssystem umfasst verschiedene Lagen mit jeweils unterschiedlichen Funktionsweisen, die zusammen ein „Sandwich“ bilden. Die zugrundeliegende Schicht aus HA/PLL-PEM auf einem planaren Glassubstrat dient als Reservoir. Auf diese PEM ist eine Schicht sogenannter Hybride aufgebracht. Die Hybride bestehen aus thermoresponsiven Poly-N-Isopropylacrylamid (PNIPAM) -basierten Hydrogel-Mikropartikeln auf deren Gold-Nanostäbchen gebunden sind. Die Hybridschicht dient in der räumlichen Kontrolle des lokalen Molekültransports als „Schlupfloch“ an der Schnittstelle von PEM und Lösung. Die Möglichkeit der Stimulation des molekülaren Transports durch Bestrahlung mit einem Nah-Infrarot-Laser (NIR) wird hier untersucht.
Von den mehreren getesteten Ansätzen zur Aufbringung von Hybriden auf die PEM-Oberfläche stellte sich die Trocknung als beste Möglichkeit heraus. Funktionalitätskontrollen des hergestellten Sandwiches bei erhöhter Temperatur ergaben eine reversible Volumenphasenübergang der PEM-gebundenen Hybride, wobei die Sandwich-Struktur erhalten blieb. Weiterhin wurde eine effektive Lichtabsorption durch die Gold-Nanostäbchen in den gewebe- und zellschonenden NIR-Spektrumsbereich gezeigt, wobei die aufgenommene Lichtenergie in Wärme umgewandelt wurde. Dadurch wurde eine schnelle und reversible Schrumpfung der PEM-gebundenen Hybride erreicht.
Zuguterletzt wird Dextran als Modellmolekül für den Transport eingesetzt. Dieses wird in wenigen Sekunden – mit einem Verteilungskoeffizient von 2,4 – in das PEM-Reservoir aufgenommen, während es auf langsamere, anhaltende Weise freigesetzt wird. Die lokale Laser-Bestrahlung des Dextran-FITC-haltigen Sandwiches bewirkte eine schrittweise Reduktion der Fluoreszenz-Intensität in der bestrahlten Region.
Das hier vorgestellte Molekül-Freisetzungssystem verwendet die vielzitierte Photoresponsivität von Hybriden auf neuartige Weise. Die Ergebnisse der Untersuchung bedeuten einen Fortschritt in Richtung eines räumlich kontrollierten, nach Bedarf steuerbaren Freisetzungs-Systems, das wiederum den Weg zu einer spatiotemporären Kontrollierbarkeit der Wirkstoff-Freisetzung bereiten könnte.

Die in dieser Arbeit entwickelten Ansätze ermöglichen ein besseres Verständnis der Dynamik in der ECM, sowie die Entwicklung ECM-ähnlicher Multilayers. Die Arbeit hat die spatiotemporäre Kontrolle der Diffusion von bioaktiven Stoffen und deren Präsentation gegenüber Zellen zum Ziel.
T2  - Molekulare Diffusion in Polyelektrolyt-Multischichten
KW  - polyelectrolyte multilayers
KW  - diffusion
KW  - simulation
KW  - FRAP
KW  - microgel
KW  - drug release
KW  - PNIPAM
KW  - IR laser
KW  - assessment of the diffusion
KW  - mulifractional diffusion
KW  - spatially and temporally controlled drug release
KW  - ordering of particles on the surface
KW  - close packing
KW  - dichteste Packung
KW  - Diffusion
KW  - Einschätzung der Diffusion
KW  - Wirkstoff-Freisetzun
KW  - Mikrogel
KW  - multi-fraktionelle Diffusion
KW  - Ordnung der Partikel auf der Oberfläche
KW  - Polyelektrolyt-Multischichten
KW  - Simulation
KW  - räumlich und zeitlich kontrollierte Wirkstoff-Freisetzung
KW  - FRAP
KW  - IR laser
KW  - PNIPAM
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-489038
ER  - 
TY  - THES
A1  - Sposini, Vittoria
T1  - The random diffusivity approach for diffusion in heterogeneous systems
N2  - 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., <x2(t)> ~ 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.
N2  - Die zwei grundlegenden Eigenschaften der Brownschen Molekularbewegung sind das lineare Wachstum < x2(t)> =  2Ddt der mittleren quadratischen Verschiebung (mean squared displacement, MSD) mit dem Diffusionskoeffizienten D in Dimension d und die Gauß Verteilung der räumlichen Verschiebung. Durch die zunehmende Komplexität der untersuchten Systeme wurden in den letzten Jahren Abweichungen von diesen zwei grundlegenden Eigenschaften gefunden. Hierbei, wurde über eine große Anzahl von Systemen berichtet, in welchen die MSD das lineare Wachstum der Brownschen Bewegung (Ficksches Gesetzt) zeigt, jedoch die Verteilung der Verschiebung nicht einer Gaußverteilung folgt (Brownian yet non-Gaussian, BNG). Auch in viskoelastischen Systemen Bewegung wurde ein analoges Verhalten beobachtet. Hier ist ein anomales Verhalten des MSD, <x2(t)> ~ ta, in Verbindung mit einer a priori unerwarteten nicht gaußchen Verteilung (anomalous yet non-Gaussian, ANG). Dieses Verhalten, welches sowohl in BNG- als auch in ANG-Diffusion beobachtet wird, ist auf eine Heterogenität in den Systemen zurückzuführen. Um diese Systeme zu beschreiben, wurde ein einheitlicher Ansatz, basierend auf den Konzept der zufälligen Diffusivität, entwickelt. 
Die vorliegende Dissertation widmet sich ausführlich Modellen mit zufälligen Diffusivität. Ausgehend von einem chronologischen Überblick der grundlegenden Ansätze der Beschreibung der BNG- und ANG-Diffusion werden mathematische Methoden entwickelt, um die verschiedenen Modelle zu untersuchen. Die in dieser Arbeit diskutierten Prozesse können in drei Kategorien unterteil werden: i) randomly-scaled Gaussian processes, ii) superstatistical models und iii) diffusing diffusivity models, welche alle zu den allgemeinen Modellen mit zufälligen Diffusivität gehören. Der Hauptteil dieser Arbeit ist die Untersuchung auf die BNG Diffusion, welche inzwischen relativ gut verstanden ist. Dennoch werden auch viele Beispiele für die Beschreibung von ANG-Diffusion diskutiert, um die Möglichkeiten der Analyse solcher Prozesse aufzuzeigen. 
Der zweite Teil der Dissertation widmet sich der statistischen Analyse von Modellen mit zufälligen Diffusivität. Eine allgemeine Beschreibung basierend auf dem Konzept der momenterzeugenden Funktion wurde zuerst herangezogen, um grundsätzliche statistische Eigenschaften der Modelle zu erhalten. Anschließend konzentriert sich die Diskussion auf die Analyse der spektralen Leistungsdichte und der first passage Statistik für einige spezielle Modelle mit zufälligen Diffusivität. Diese Ergebnisse werden mit jenen der normalen Brownschen Molekularbewegung verglichen. Dadurch wird ein tiefergehendes physikalisches Verständnis über die Systeme erlangt, welche durch ein Modell mit zufälligen Diffusivität beschrieben werden. Abschließend, zeigt eine Diskussion mögliche Ursachen für die Heterogenität auf, mit dem Ziel darzustellen, welche Arten von Systemen durch den Zufalls-Diffusivitäts-Ansatz beschrieben werden können.
N2  - Las dos características distintivas del movimiento Browniano son el crecimiento lineal  < x2(t)> =  2Ddt del desplazamiento cuadrático medio (mean squared displacement}, MSD) con el coeficiente de difusión D en dimensiones espaciales d, y la distribución Gaussiana de los desplazamientos. Con los continuos avances en tecnologías experimentales y potencia de cálculo, se logra estudiar con mayor detalle sistemas cada vez más complejos y algunos sistemas revelan desviaciones de estas dos propiedades centrales. En los últimos años se ha observado una gran variedad de sistemas en los que el MSD presenta un crecimiento lineal en el tiempo (típico del transporte Browniano), no obstante, la distribución de los desplazamientos es pronunciadamente no Gaussiana (Brownian yet non-Gaussian diffusion}, BNG). Un comportamiento similar se observa asimismo en el caso del movimiento de tipo viscoelástico, en el que se combina una tendencia anómala del MSD, es decir, <x2(t)> ~ ta, con a, con distribuciones inesperadamente no Gaussianas (Anomalous yet non-Gaussian diffusion, ANG).  Este tipo de comportamiento observado en las difusiones BNG y ANG se ha relacionado con la presencia de heterogeneidades en los sistemas y se ha establecido un enfoque común para abordarlo: el enfoque de difusividad aleatoria. 
En la primera parte de esta disertación se explora extensamente el área de los modelos de difusividad aleatoria. A través de una descripción cronológica de los principales enfoques utilizados para caracterizar las difusiones BNG y ANG, se definen diferentes metodologías matemáticas para la resolución y el estudio de estos modelos. Los procesos expuestos en este trabajo, pertenecientes a la clase más general de modelos de difusividad aleatoria, pueden clasificarse en tres subcategorías: i) randomly-scaled Gaussian processes, ii) superstatistical models y iii) diffusing diffusivity models. Fundamentalmente el enfoque de este trabajo se centra en la difusión BNG, bien establecida y ampliamente estudiada en los últimos años. No obstante, múltiples ejemplos son examinados para la descripción de la difusión ANG, a fin de remarcar los diferentes modelos de estudio disponibles hasta el momento. 
En la segunda parte de la disertación se desarolla el análisis estadístico de los procesos de difusividad aleatoria. Inicialmente se expone una descripción general basada en el concepto de la función generadora de momentos para obtener las propiedades estadísticas estándar de los modelos. A continuación, la discusión aborda el estudio de la densidad espectral de potencia y la estadística del tiempo de primer paso para algunos modelos de difusividad aleatoria. Adicionalmente, los resultados del método de difusividad aleatoria se comparan junto a los de movimiento browniano estándar. Como resultado, se obtiene una mayor comprensión física de los sistemas descritos por los modelos de difusividad aleatoria. 
Para concluir, se presenta una discusión acerca de los posibles orígenes de la heterogeneidad, con el objetivo principal de inferir qué tipo de sistemas pueden describirse apropiadamente según el enfoque de la difusividad aleatoria.
KW  - diffusion
KW  - non-gaussianity
KW  - random diffusivity
KW  - power spectral analysis
KW  - first passage
KW  - Diffusion
KW  - zufälligen Diffusivität
KW  - spektrale Leistungsdichte
KW  - first passage
KW  - Heterogenität
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-487808
ER  - 
TY  - JOUR
A1  - Pohlenz, Philipp
A1  - Niedermeier, Frank
T1  - The Bologna Process and the harmonisation of higher education systems in other world regions
BT  - a case from Southeast Asia
JF  - Innovation : the European journal of social sciences
N2  - 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.
KW  - ASEAN
KW  - Bologna Process
KW  - European Higher Education Area
KW  - higher education
KW  - quality assurance
KW  - harmonisation
KW  - regionalisation
KW  - diffusion
KW  - mobility
Y1  - 2019
U6  - https://doi.org/10.1080/13511610.2019.1637248
SN  - 1351-1610
SN  - 1469-8412
VL  - 32
IS  - 4
SP  - 481
EP  - 494
PB  - Routledge, Taylor & Francis Group
CY  - Abingdon
ER  - 
TY  - GEN
A1  - Woodfield, Emma E.
A1  - Horne, Richard B.
A1  - Glauert, Sarah A.
A1  - Menietti, John D.
A1  - Shprits, Yuri
A1  - Kurth, William S.
T1  - Formation of electron radiation belts at Saturn by Z-mode wave acceleration
T2  - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2  - 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.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1032 
KW  - astrophysical plasmas
KW  - giant planets
KW  - magnetospheric physics
KW  - diffusion
KW  - pitch angle
KW  - plasma
KW  - radio
KW  - region
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-468342
SN  - 1866-8372
IS  - 1032
ER  - 
TY  - JOUR
A1  - Grebenkov, Denis S.
A1  - Metzler, Ralf
A1  - Oshanin, Gleb
T1  - From single-particle stochastic kinetics to macroscopic reaction rates
BT  - fastest first-passage time of N random walkers
JF  - New Journal of Physics
N2  - 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.
KW  - diffusion
KW  - first-passage
KW  - fastest first-passage time of N walkers
Y1  - 2020
U6  - https://doi.org/10.1088/1367-2630/abb1de
SN  - 1367-2630
VL  - 22
PB  - Dt. Physikalische Ges.
CY  - Bad Honnef
ER  -