TY - THES
A1 - Klumpp, Stefan
T1 - Movements of molecular motors : diffusion and directed walks
N2 - Bewegungen von prozessiven molekularen Motoren des Zytoskeletts sind durch ein Wechselspiel von gerichteter Bewegung entlang von Filamenten und Diffusion in der umgebenden Lösung gekennzeichnet. Diese eigentümlichen 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 Transportphänomene untersucht: (i) Random Walks von einzelnen Motoren in Kompartimenten verschiedener Geometrien, (ii) stationäre Konzentrationsprofile, die sich in geschlossenen Kompartimenten infolge dieser Bewegungen einstellen, (iii) randinduzierte Phasenübergänge in offenen röhrenartigen Kompartimenten, die an Motorenreservoirs gekoppelt sind, und (iv) der Einfluß von kooperativen Effekten bei der Motor-Filament-Bindung auf die Bewegung. Alle diese Phänomene sind experimentell zugänglich, und mögliche experimentelle Realisierungen werden diskutiert.
N2 - Movements of processive cytoskeletal motors are characterized by an interplay between directed motion along filament and diffusion in the surrounding solution. In the present work, these peculiar movements are studied by modeling them as random walks on a lattice. An additional subject of our studies is the effect of motor-motor interactions on these movements. In detail, four transport phenomena are studied: (i) Random walks of single motors in compartments of various geometries, (ii) stationary concentration profiles which build up as a result of these movements in closed compartments, (iii) boundary-induced phase transitions in open tube-like compartments coupled to reservoirs of motors, and (iv) the influence of cooperative effects in motor-filament binding on the movements. All these phenomena are experimentally accessible and possible experimental realizations are discussed.
KW - molekulare Motoren
KW - aktive Prozesse
KW - Diffusion
KW - Random Walks
KW - Gittermodelle
KW - Phasenübergänge
KW - Staus
KW - kooperative Phänomene
KW - molecular motors
KW - active processes
KW - diffusion
KW - random walks
KW - lattice models
KW - phase transitions
KW - traffic jams
KW - cooperative phenomena
Y1 - 2003
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-0000806
ER -
TY - JOUR
A1 - Palyulin, Vladimir V.
A1 - Chechkin, Aleksei V.
A1 - Metzler, Ralf
T1 - Space-fractional Fokker-Planck equation and optimization of random search processes in the presence of an external bias
JF - Journal of statistical mechanics: theory and experiment
N2 - 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.
KW - driven diffusive systems (theory)
KW - fluctuations (theory)
KW - stochastic processes (theory)
KW - diffusion
Y1 - 2014
U6 - http://dx.doi.org/10.1088/1742-5468/2014/11/P11031
SN - 1742-5468 (print)
PB - IOP Publ. Ltd.
CY - Bristol
ER -
TY - JOUR
A1 - Chechkin, Aleksei V.
A1 - Lenz, F.
A1 - Klages, Rainer
T1 - Normal and anomalous fluctuation relations for gaussian stochastic dynamics
JF - Journal of statistical mechanics: theory and experiment
N2 - 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.
KW - stochastic particle dynamics (theory)
KW - fluctuations (theory)
KW - stochastic processes (theory)
KW - diffusion
Y1 - 2012
U6 - http://dx.doi.org/10.1088/1742-5468/2012/11/L11001
SN - 1742-5468 (print)
IS - 4
PB - IOP Publ. Ltd.
CY - Bristol
ER -
TY - JOUR
A1 - Magdziarz, Marcin
A1 - Metzler, Ralf
A1 - Szczotka, Wladyslaw
A1 - Zebrowski, Piotr
T1 - Correlated continuous-time random walks-scaling limits and Langevin picture
JF - Journal of statistical mechanics: theory and experiment
N2 - 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.
KW - stochastic processes (theory)
KW - diffusion
Y1 - 2012
U6 - http://dx.doi.org/10.1088/1742-5468/2012/04/P04010
SN - 1742-5468 (print)
PB - IOP Publ. Ltd.
CY - Bristol
ER -
TY - JOUR
A1 - Palyulin, Vladimir V.
A1 - Metzler, Ralf
T1 - How a finite potential barrier decreases the mean first-passage time
JF - Journal of statistical mechanics: theory and experiment
N2 - 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.
KW - diffusion
Y1 - 2012
U6 - http://dx.doi.org/10.1088/1742-5468/2012/03/L03001
SN - 1742-5468 (print)
IS - 1
PB - IOP Publ. Ltd.
CY - Bristol
ER -
TY - JOUR
A1 - Cherstvy, Andrey G.
A1 - Vinod, Deepak
A1 - Aghion, Erez
A1 - Chechkin, Aleksei V.
A1 - Metzler, Ralf
T1 - Time averaging, ageing and delay analysis of financial time series
JF - New journal of physics
N2 - 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.
KW - time averaging
KW - diffusion
KW - geometric Brownian motion
KW - financial time series
Y1 - 2017
U6 - http://dx.doi.org/10.1088/1367-2630/aa7199
SN - 1367-2630
VL - 19
SP - 1
EP - 11
PB - IOP
CY - London
ER -
TY - GEN
A1 - Cherstvy, Andrey G.
A1 - Vinod, Deepak
A1 - Aghion, Erez
A1 - Chechkin, Aleksei V.
A1 - Metzler, Ralf
T1 - Time averaging, ageing and delay analysis of financial time series
N2 - 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.
T3 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 347
KW - diffusion
KW - financial time series
KW - geometric Brownian motion
KW - time averaging
Y1 - 2017
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-400541
ER -
TY - JOUR
A1 - Shin, Jaeoh
A1 - Cherstvy, Andrey G.
A1 - Kim, Won Kyu
A1 - Metzler, Ralf
T1 - Facilitation of polymer looping and giant polymer diffusivity in crowded solutions of active particles
JF - New journal of physics : the open-access journal for physics
N2 - 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.
KW - diffusion
KW - active transport
KW - polymers
Y1 - 2015
U6 - http://dx.doi.org/10.1088/1367-2630/17/11/113008
SN - 1367-2630 (print)
VL - 17
PB - IOP Publ. Ltd.
CY - Bristol
ER -
TY - JOUR
A1 - Cherstvy, Andrey G.
A1 - Metzler, Ralf
T1 - Ergodicity breaking, ageing, and confinement in generalized diffusion processes with position and time dependent diffusivity
JF - Journal of statistical mechanics: theory and experiment
N2 - 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.
KW - diffusion
Y1 - 2015
U6 - http://dx.doi.org/10.1088/1742-5468/2015/05/P05010
SN - 1742-5468 (print)
PB - IOP Publ. Ltd.
CY - Bristol
ER -
TY - JOUR
A1 - Chen, Xuhui
A1 - Pohl, Martin
A1 - Böttcher, Markus
T1 - Particle diffusion and localized acceleration in inhomogeneous AGN jets - I. Steady-state spectra
JF - Monthly notices of the Royal Astronomical Society
N2 - 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.
KW - acceleration of particles
KW - diffusion
KW - radiation mechanisms: non-thermal
KW - galaxies:active
KW - galaxies: jets
Y1 - 2015
U6 - http://dx.doi.org/10.1093/mnras/stu2438
SN - 0035-8711 (print)
SN - 1365-2966 (online)
VL - 447
IS - 1
SP - 530
EP - 544
PB - Oxford Univ. Press
CY - Oxford
ER -