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 - https://doi.org/10.1088/1742-5468/2012/03/L03001 SN - 1742-5468 IS - 1 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 - https://doi.org/10.1088/1742-5468/2012/04/P04010 SN - 1742-5468 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 - https://doi.org/10.1088/1742-5468/2012/11/L11001 SN - 1742-5468 IS - 4 PB - IOP Publ. Ltd. CY - Bristol 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 - https://doi.org/10.1088/1742-5468/2014/11/P11031 SN - 1742-5468 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 - https://doi.org/10.1088/1742-5468/2015/05/P05010 SN - 1742-5468 PB - IOP Publ. Ltd. CY - Bristol 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 - https://doi.org/10.1088/1367-2630/17/11/113008 SN - 1367-2630 VL - 17 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Prokopovic, Vladimir Z. A1 - Duschl, Claus A1 - Volodkin, Dmitry T1 - Hyaluronic Acid/Poly-l-Lysine Multilayers as Reservoirs for Storage and Release of Small Charged Molecules JF - Macromolecular bioscience N2 - 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. KW - diffusion KW - drug delivery KW - dye KW - release mechanism Y1 - 2015 U6 - https://doi.org/10.1002/mabi.201500093 SN - 1616-5187 SN - 1616-5195 VL - 15 IS - 10 SP - 1357 EP - 1363 PB - Wiley-VCH CY - Weinheim 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 - https://doi.org/10.1093/mnras/stu2438 SN - 0035-8711 SN - 1365-2966 VL - 447 IS - 1 SP - 530 EP - 544 PB - Oxford Univ. Press CY - Oxford ER - TY - JOUR A1 - Beta, Carsten T1 - To turn or not to turn? JF - NEW JOURNAL OF PHYSICS N2 - Bacteria typically swim in straight runs, interruped by sudden turning events. In particular, some species are limited to a reversal in the swimming direction as the only turning maneuver at their disposal. In a recent article, Grossmann et al (2016 New J. Phys. 18 043009) introduce a theoretical framework to analyze the diffusive properties of active particles following this type of run-and-reverse pattern. Based on a stochastic clock model to mimic the regulatory pathway that triggers reversal events, they show that a run-and-reverse swimmer can optimize its diffusive spreading by tuning the reversal rate according to the level of rotational noise. With their approach, they open up promising new perspectives of how to incorporate the dynamics of intracellular signaling into coarse-grained active particle descriptions. KW - bacterial swimming KW - random walks KW - diffusion KW - stochastic models Y1 - 2016 U6 - https://doi.org/10.1088/1367-2630/18/5/051003 SN - 1367-2630 VL - 18 SP - 1 EP - 17 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Schwarzl, Maria A1 - Godec, Aljaz A1 - Oshanin, Gleb A1 - Metzler, Ralf T1 - A single predator charging a herd of prey: effects of self volume and predator-prey decision-making JF - Journal of physics : A, Mathematical and theoretical N2 - We study the degree of success of a single predator hunting a herd of prey on a two-dimensional square lattice landscape. We explicitly consider the self volume of the prey restraining their dynamics on the lattice. The movement of both predator and prey is chosen to include an intelligent, decision making step based on their respective sighting ranges, the radius in which they can detect the other species (prey cannot recognise each other besides the self volume interaction): after spotting each other the motion of prey and predator turns from a nearest neighbour random walk into directed escape or chase, respectively. We consider a large range of prey densities and sighting ranges and compute the mean first passage time for a predator to catch a prey as well as characterise the effective dynamics of the hunted prey. We find that the prey's sighting range dominates their life expectancy and the predator profits more from a bad eyesight of the prey than from his own good eye sight. We characterise the dynamics in terms of the mean distance between the predator and the nearest prey. It turns out that effectively the dynamics of this distance coordinate can be captured in terms of a simple Ornstein–Uhlenbeck picture. Reducing the many-body problem to a simple two-body problem by imagining predator and nearest prey to be connected by an effective Hookean bond, all features of the model such as prey density and sighting ranges merge into the effective binding constant. KW - first passage process KW - diffusion KW - predator-prey model Y1 - 2016 U6 - https://doi.org/10.1088/1751-8113/49/22/225601 SN - 1751-8113 SN - 1751-8121 VL - 49 PB - IOP Publ. Ltd. CY - Bristol ER -