@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} } @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} } @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} } @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{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{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{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} } @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} }