arXiv subjects

J. Klafter

Publications and source records attributed to J. Klafter.

34 records · Page 2Linked to original sources

arXiv2003

Molecular motor with a build-in escapement device

We study dynamics of a classical particle in a one-dimensional potential, which is composed of two periodic components, that are time-independent, have equal amplitudes and periodicities. One of them is externally driven by a random force and thus performs a diffusive-type motion with respect to the other. We demonstrate that here, under certain conditions, the particle may move unidirectionally with a constant velocity, despite the fact that the random force averages out to zero. We show that the physical mechanism underlying such a phenomenon resembles the work of an escapement-type device in watches; upon reaching certain level, random fluctuations exercise a locking function creating the points of irreversibility in particle's trajectories such that the particle gets uncompensated displacements. Repeated (randomly) in each cycle, this process ultimately results in a random ballistic-type motion. In the overdamped limit, we work out simple analytical estimates for the particle's terminal velocity. Our analytical results are in a very good agreement with the Monte Carlo data.

cond-mat.stat-mech↗

arXiv2003

On the joint residence time of N independent two-dimensional Brownian motions

We study the behavior of several joint residence times of N independent Brownian particles in a disc of radius $R$ in two dimensions. We consider: (i) the time T_N(t) spent by all N particles simultaneously in the disc within the time interval [0,t]; (ii) the time T_N^{(m)}(t) which at least m out of N particles spend together in the disc within the time interval [0,t]; and (iii) the time {\tilde T}_N^{(m)}(t) which exactly m out of N particles spend together in the disc within the time interval [0,t]. We obtain very simple exact expressions for the expectations of these three residence times in the limit t\to\infty.

cond-mat.stat-mech↗

arXiv2003

Catalytic reactions with bulk-mediated excursions: Mixing fails to restore chemical equilibrium

In this paper we analyze the effect of the bulk-mediated excursions (BME) of reactive species on the long-time behavior of the catalytic Langmuir-Hinshelwood-like A + B \to 0 reactions in systems in which a catalytic plane (CP) is in contact with liquid phase, containg concentrations of reactive particles. Such BME result from repeated particles desorption from the CP, subsequent diffusion in the liquid phase and eventual readsorption on the CP away from the intial detachment point. This process which leads to an effective superdiffusive transport along the CP. We consider both "batch" reactions, in which all particles of reactive species were initially adsorbed onto the CP, and reactions followed by a steady inflow of particles onto the CP. We show that for "batch" reactions the BME provide an effective mixing channel and here the mean-field-type behavior emerges. On contrary, for reaction followed by a steady inflow of particles, we observe essential departures from the mean-field behavior and find that the mixing effect of the BME is insufficient to restore chemical equilibrium. We show that a steady-state is established as t \to \infty, in which the limiting value of the mean coverages of the CP depends on the particles' diffusion coefficient in the bulk liquid phase and the spatial distributions of adsorbed particles are strongly correlated. Moreover, we show that the relaxation to such a steady-state is described by a power-law function of time, in contrast to the exponential time-dependence describing the approach to equilibrium in perfectly stirred systems.

cond-mat.stat-mech↗

arXiv2003

Fractional Diffusion Equation for a Power-Law-Truncated Levy Process

Truncated Levy flights are stochastic processes which display a crossover from a heavy-tailed Levy behavior to a faster decaying probability distribution function (pdf). Putting less weight on long flights overcomes the divergence of the Levy distribution second moment. We introduce a fractional generalization of the diffusion equation, whose solution defines a process in which a Levy flight of exponent alpha is truncated by a power-law of exponent 5 - alpha. A closed form for the characteristic function of the process is derived. The pdf of the displacement slowly converges to a Gaussian in its central part showing however a power law far tail. Possible applications are discussed.

cond-mat↗

arXiv2003

From deterministic dynamics to kinetic phenomena

We investigate a one-dimenisonal Hamiltonian system that describes a system of particles interacting through short-range repulsive potentials. Depending on the particle mean energy, $ε$, the system demonstrates a spectrum of kinetic regimes, characterized by their transport properties ranging from ballistic motion to localized oscillations through anomalous diffusion regimes. We etsablish relationships between the observed kinetic regimes and the "thermodynamic" states of the system. The nature of heat conduction in the proposed model is discussed.

cond-mat.stat-mech↗

arXiv2003

Single Stranded DNA Translocation Through A Nanopore: A Master Equation Approach

We study voltage driven translocation of a single stranded (ss) DNA through a membrane channel. Our model, based on a master equation (ME) approach, investigates the probability density function (pdf) of the translocation times, and shows that it can be either double or mono-peaked, depending on the system parameters. We show that the most probable translocation time is proportional to the polymer length, and inversely proportional to the first or second power of the voltage, depending on the initial conditions. The model recovers experimental observations on hetro-polymers when using their properties inside the pore, such as stiffness and polymer-pore interaction.

cond-mat.stat-mech↗

arXiv2003

A New Look at Dynamic Force Spectroscopy of Adhesion Bonds

Dynamic force spectroscopy of single molecules is described by a model which predicts a distribution of rupture forces, the corresponding mean rupture force and variance, all amenable to experimental tests. The distribution has a pronounced asymmetry which has recently been observed experimentally. The mean rupture force follows a lnV to the power of 2/3 dependence on the pulling velocity V and differs from earlier predictions.Interestingly, at low pulling velocities a rebinding process is obtained whose signature is an intermittent behavior of the spring force which delays the rupture. An extension to include conformational changes of the adhesion complex is proposed which leads to the possibility of bimodal distributions of rupture forces.

cond-mat.soft↗

arXiv2003

Manipulations of individual molecules by scanning probe microscopy

In this Letter we suggest a new method of manipulating individual molecules with scanning probes using a "pick-up-and put-down" mode. We demonstrate that the number of molecules picked up by the tip and deposited in a different location can be controlled by adjusting the pulling velocity of the tip and the distance of closest approach of the tip to the surface.

cond-mat.soft↗

arXiv2003

Dynamical heat channels

We consider heat conduction in a 1D dynamical channel. The channel consists of a group of noninteracting particles, which move between two heat baths according to some dynamical process. We show that the essential thermodynamic properties of the heat channel can be evaluated from the diffusion properties of the underlying particles. Emphasis is put on the conduction under anomalous diffusion conditions. \\{\bf PACS number}: 05.40.+j, 05.45.ac, 05.60.cd

cond-mat.stat-mech↗

arXiv2003

Fractional Fokker-Planck Equation for Ultraslow Kinetics

Several classes of physical systems exhibit ultraslow diffusion for which the mean squared displacement at long times grows as a power of the logarithm of time ("strong anomaly") and share the interesting property that the probability distribution of particle's position at long times is a double-sided exponential. We show that such behaviors can be adequately described by a distributed-order fractional Fokker-Planck equations with a power-law weighting-function. We discuss the equations and the properties of their solutions, and connect this description with a scheme based on continuous-time random walks.

cond-mat.stat-mech↗

arXiv2002

The dynamical foundation of fractal stream chemistry: The origin of extremely long retention times

We present a physical model to explain the behavior of long-term, time series measurements of chloride, a natural passive tracer, in rainfall and runoff in catchments [Kirchner et al., Nature 403(524), 2000]. A spectral analysis of the data shows the chloride concentrations in rainfall to have a white noise spectrum, while in streamflow, the spectrum exhibits a fractal $1/f$ scaling. The empirically derived distribution of tracer travel times $h(t)$ follows a power-law, indicating low-level contaminant delivery to streams for a very long time. Our transport model is based on a continuous time random walk (CTRW) with an event time distribution governed by $ψ(t)\sim A_βt^{-1-β}$. The CTRW using this power-law $ψ(t)$ (with $0<β<1$) is interchangeable with the time-fractional advection-dispersion equation (FADE) and has accounted for the universal phenomenon of anomalous transport in a broad range of disordered and complex systems. In the current application, the events can be realized as transit times on portions of the catchment network. The travel time distribution is the first passage time distribution $F(t; l)$ at a distance $l$ from a pulse input (at $t=0$) at the origin. We show that the empirical $h(t)$ is the catchment areal composite of $F(t; l)$ and that the fractal $1/f$ spectral response found in many catchments is an example of the larger class of transport phenomena cited above. The physical basis of $ψ(t)$, which determines $F(t; l)$, is the origin of the extremely long chemical retention times in catchments.

cond-mat.stat-mech↗

arXiv2001

Linear Response in Complex Systems: CTRW and the Fractional Fokker-Planck Equations

We consider the linear response of systems modelled by continuous-time random walks (CTRW) and by fractional Fokker-Planck equations under the influence of time-dependent external fields. We calculate the corresponding response functions explicitely. The CTRW curve exhibits aging, i.e. it is not translationally invariant in the time-domain. This is different from what happens under fractional Fokker-Planck conditions.

cond-mat.stat-mech↗

arXiv2001

Dynamics of Annealed Systems under External Fields: CTRW and the Fractional Fokker-Planck Equations

We consider the linear response of a system modelled by continuous-time random walks (CTRW) to an external field pulse of rectangular shape. We calculate the corresponding response function explicitely and show that it exhibits aging, i.e. that it is not translationally invariant in the time-domain. This result differs from that of systems which behave according to fractional Fokker-Planck equations.

cond-mat.stat-mech↗

arXiv2000

Does strange kinetics imply unusual thermodynamics?

We introduce a fractional Fokker-Planck equation (FFPE) for Levy flights in the presence of an external field. The equation is derived within the framework of the subordination of random processes which leads to Levy flights. It is shown that the coexistence of anomalous transport and a potential displays a regular exponential relaxation towards the Boltzmann equilibrium distribution. The properties of the Levy-flight FFPE derived here are compared with earlier findings for subdiffusive FFPE. The latter is characterized by a non-exponential Mittag-Leffler relaxation to the Boltzmann distribution. In both cases, which describe strange kinetics, the Boltzmann equilibrium is reached and modifications of the Boltzmann thermodynamics are not required.

cond-mat.stat-mech↗

arXiv2000

Generalized model for dynamic percolation

We study the dynamics of a carrier, which performs a biased motion under the influence of an external field E, in an environment which is modeled by dynamic percolation and created by hard-core particles. The particles move randomly on a simple cubic lattice, constrained by hard-core exclusion, and they spontaneously annihilate and re-appear at some prescribed rates. Using decoupling of the third-order correlation functions into the product of the pairwise carrier-particle correlations we determine the density profiles of the "environment" particles, as seen from the stationary moving carrier, and calculate its terminal velocity, V_c, as the function of the applied field and other system parameters. We find that for sufficiently small driving forces the force exerted on the carrier by the "environment" particles shows a viscous-like behavior. An analog Stokes formula for such dynamic percolative environments and the corresponding friction coefficient are derived. We show that the density profile of the environment particles is strongly inhomogeneous: In front of the stationary moving carrier the density is higher than the average density, $ρ_s$, and approaches the average value as an exponential function of the distance from the carrier. Past the carrier the local density is lower than $ρ_s$ and the relaxation towards $ρ_s$ may proceed differently depending on whether the particles number is or is not explicitly conserved.

cond-mat.stat-mech↗

arXiv2000

One-Dimensional Stochastic Lévy-Lorentz Gas

We introduce a Lévy-Lorentz gas in which a light particle is scattered by static point scatterers arranged on a line. We investigate the case where the intervals between scatterers $\{ξ_i \}$ are independent random variables identically distributed according to the probability density function $μ(ξ)\sim ξ^{-(1 + γ)}$. We show that under certain conditions the mean square displacement of the particle obeys $ \ge C t^{3 - γ}$ for $1 < γ< 2$. This behavior is compatible with a renewal Lévy walk scheme. We discuss the importance of rare events in the proper characterization of the diffusion process.

cond-mat.stat-mech↗