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Joseph Klafter

Publications and source records attributed to Joseph Klafter.

At least 19 recordsLinked to original sources
arXiv2013

Generalized Elastic Model: Fractional Langevin Description, Fluctuation Relation, and Linear Response

The Generalized Elastic Model is a linear stochastic model which accounts for the behaviour of many physical systems in nature, ranging from polymeric chains to single-file systems. If an external perturbation is exerted \emph{only} on a single point $\vec{x}^\star$ (\emph{tagged probe}), it propagates throughout the entire system. Within the fractional Langevin equation framework, we study the effect of such a perturbation, in cases of a constant force applied. We report most of the results arising from our previous analysis and, in the present work, we show that the Fox $H$-functions formalism provides a compact, elegant and useful tool for the study of the scaling properties of any observable. In particular we show how the generalized Kubo fluctuation relations can be expressed in terms of $H$-functions.

cond-mat.stat-mech↗
arXiv2012

A Test for Determining a Subdiffusive Model in Ergodic Systems from Single Trajectories

Experiments on particles' motion in living cells show that it is often subdiffusive. This subdiffusion may be due to trapping, percolation-like structures, or viscoelatic behavior of the medium. While the models based on trapping (leading to continuous-time random walks) can easily be distinguished from the rest by testing their non-ergodicity, the latter two cases are harder to distinguish. We propose a statistical test for distinguishing between these two based on the space-filling properties of trajectories, and prove its feasibility and specificity using synthetic data. We moreover present a flow-chart for making a decision on a type of subdiffusion for a broader class of models.

cond-mat.dis-nn↗
arXiv2012

Generalized Elastic Model: thermal vs non-thermal initial conditions. Universal scaling, roughening, ageing and ergodicity

We study correlation properties of the generalized elastic model which accounts for the dynamics of polymers, membranes, surfaces and fluctuating interfaces, among others. We develop a theoretical framework which leads to the emergence of universal scaling laws for systems starting from thermal (equilibrium) or non-thermal (non-equilibrium) initial conditions. Our analysis incorporates and broadens previous results such as observables' double scaling regimes, (super)roughening and anomalous diffusion, and furnishes a new scaling behavior for correlation functions at small times (long distances). We discuss ageing and ergodic properties of the generalized elastic model in non-equilibrium conditions, providing a comparison with the situation occurring in continuous time random walk. Our analysis also allows to assess which observable is able to distinguish whether the system is in or far from equilibrium conditions in an experimental set-up.

cond-mat.stat-mech↗
arXiv2012

Correlations in a Generalized Elastic Model: Fractional Langevin Equation Approach

The Generalized Elastic Model (GEM) provides the evolution equation which governs the stochastic motion of several many-body systems in nature, such as polymers, membranes, growing interfaces. On the other hand a probe (\emph{tracer}) particle in these systems performs a fractional Brownian motion due to the spatial interactions with the other system's components. The tracer's anomalous dynamics can be described by a Fractional Langevin Equation (FLE) with a space-time correlated noise. We demonstrate that the description given in terms of GEM coincides with that furnished by the relative FLE, by showing that the correlation functions of the stochastic field obtained within the FLE framework agree to the corresponding quantities calculated from the GEM. Furthermore we show that the Fox $H$-function formalism appears to be very convenient to describe the correlation properties within the FLE approach.

cond-mat.stat-mech↗
arXiv2012

Unusual Response to a Localized Perturbation in a Generalized Elastic Model

The generalized elastic model encompasses several physical systems such as polymers, membranes, single file systems, fluctuating surfaces and rough interfaces. We consider the case of an applied localized potential, namely an external force acting only on a single (tagged) probe, leaving the rest of the system unaffected. We derive the fractional Langevin equation for the tagged probe, as well as for a generic (untagged) probe, where the force is not directly applied. Within the framework of the fluctuation-dissipation relations, we discuss the unexpected physical scenarios arising when the force is constant and time periodic, whether or not the hydrodynamic interactions are included in the model. For short times, in case of the constant force, we show that the average drift is linear in time for long range hydrodynamic interactions and behaves ballistically or exponentially for local hydrodynamic interactions. Moreover, it can be opposite to the direction of external disturbance for some values of the model's parameters. When the force is time periodic, the effects are macroscopic: the system splits into two distinct spatial regions whose size is proportional to the value of the applied frequency. These two regions are characterized by different amplitudes and phase shifts in the response dynamics.

cond-mat.stat-mech↗
arXiv2012

Generalized Elastic Model yields Fractional Langevin Equation

Starting from a generalized elastic model which accounts for the stochastic motion of several physical systems such as membranes, (semi)flexible polymers and fluctuating interfaces among others, we derive the fractional Langevin equation (FLE) for a probe particle in such systems, in the case of thermal initial conditions. We show that this FLE is the only one fulfilling the fluctuation-dissipation (FD) relation within a new family of fractional Brownian motion (FBM) equations. The FLE for the time-dependent fluctuations of the donor-acceptor distance in a protein, is shown to be recovered. When the system starts from non-thermal conditions, the corresponding FLE, which does not fulfill FD relation, is derived.

cond-mat.stat-mech↗
arXiv2011

The Unequal Twins - Probability Distributions Aren't Everything

It is the common lore to assume that knowing the equation for the probability distribution function (PDF) of a stochastic model as a function of time tells the whole picture defining all other characteristics of the model. We show that this is not the case by comparing two exactly solvable models of anomalous diffusion due to geometric constraints: The comb model and the random walk on a random walk (RWRW). We show that though the two models have exactly the same PDFs, they differ in other respects, like their first passage time (FPT) distributions, their autocorrelation functions and their aging properties.

cond-mat.stat-mech↗
arXiv2008

Power-Law Distributions: Beyond Paretian Fractality

The notion of fractality, in the context of positive-valued probability distributions, is conventionally associated with the class of Paretian probability laws. In this research we show that the Paretian class is merely one out of six classes of probability laws - all equally entitled to be ordained fractal, all possessing a characteristic power-law structure, and all being the unique fixed points of renormalizations acting on the space of positive-valued probability distributions. These six fractal classes are further shown to be one-dimensional functional projections of underlying fractal Poisson processes governed by: (i) a common elemental power-law structure; and, (ii) an intrinsic scale which can be either linear, harmonic, log-linear, or log-harmonic. This research provides a panoramic and comprehensive view of fractal distributions, backed by a unified theory of their underlying Poissonian fractals.

cond-mat.stat-mech↗
arXiv2007

The advantage of Lévy strategies in intermittent search processes

Search strategies based on random walk processes with long-tailed jump length distributions (Levy walks) on the one hand and intermittent behavior switching between local search and ballistic relocation phases on the other, have been previously shown to be beneficial in stochastic target finding problems. We here study a combination of both mechanisms: an intermittent process with Levy distributed relocations. We demonstrate how Levy distributed relocations reduce oversampling and thus further optimize the intermittent search strategy in the critical situation of rare targets.

cond-mat.stat-mech↗
arXiv2007

Leapover lengths and first passage time statistics for Lévy flights

Exact results for the first passage time and leapover statistics of symmetric and one-sided Levy flights (LFs) are derived. LFs with stable index alpha are shown to have leapover lengths, that are asymptotically power-law distributed with index alpha for one-sided LFs and, surprisingly, with index alpha/2 for symmetric LFs. The first passage time distribution scales like a power-law with index 1/2 as required by the Sparre Andersen theorem for symmetric LFs, whereas one-sided LFs have a narrow distribution of first passage times. The exact analytic results are confirmed by extensive simulations.

cond-mat.stat-mech↗
arXiv2007

Manipulating single enzymes by an external harmonic force

We study a Michaelis-Menten reaction for a single two-state enzyme molecule, whose transition rates between the two conformations are modulated by an harmonically oscillating external force. In particular, we obtain a range of optimal driving frequencies for changing the conformation of the enzyme thereby controlling the enzymatic activity (i.e. product formation). This analysis demonstrates that it is, in principle, possible to obtain information about particular rates within the kinetic scheme.

q-bio.BM↗
arXiv2007

Closed-form solutions for continuous time random walks on finite chains

Continuous time random walks (CTRW) on finite arbitrarily inhomogeneous chains are studied. By introducing a technique of counting all possible trajectories, we derive closed-form solutions in Laplace space for the Green's function and for the first passage time probability density function (PDF) for nearest neighbor CTRWs in terms of the input waiting time PDFs. These solutions are also the Laplace space solutions of the generalized master equation (GME). Moreover, based on our counting technique, we introduce the adaptor function for expressing higher order propagators (joint PDFs of time-position variables) for CTRWs in terms of Green's functions. Using the derived formulae, an escape problem from a biased chain is considered.

cond-mat.soft↗
arXiv2007

Correctly validating results from single molecule data: the case of stretched exponential decay in the catalytic activity of single lipase B molecules

The question of how to validate and interpret correctly the waiting time probability density functions (WT-PDFs) from single molecule data is addressed. It is shown by simulation that when a stretched exponential WT-PDF, with a stretched exponent alfa and a time scale parameter tau, generates the off periods of a two-state trajectory, a reliable recovery of the input WT-PDF from the trajectory is obtained even when the bin size used to define the trajectory, dt, is much larger than the parameter tau. This holds true as long as the first moment of the WT-PDF is much larger than dt. Our results validate the results in an earlier study of the activity of single Lipase B molecules and disprove recent related critique.

q-bio.SC↗
arXiv2006

Barrier crossing driven by Levy noise: Universality and the Role of Noise Intensity

We study the barrier crossing of a particle driven by white symmetric Levy noise of index $α$ and intensity $DD for three different generic types of potentials: (a) a bistable potential; (b) a metastable potential; and (c) a truncated harmonic potential. For the low noise intensity regime we recover the previously proposed algebraic dependence on $D$ of the characteristic escape time, $T_{\mathrm{esc}}\simeq C(α)/D^{μ(α)}$, where $C(α)$ is a coefficient. It is shown that the exponent $μ(α)$ remains approximately constant, $μ\approx 1$ for $0<α<2$; at $α=2$ the power-law form of $T_{\mathrm{esc}}$ changes into the known exponential dependence on 1/D; it exhibits a divergence-like behavior as $α$ approaches 2. In this regime we observe a monotonous increase of the escape time $T_{\mathrm{esc}}$ with increasing $α$ (keeping the noise intensity $D$ constant). The probability density of the escape time decays exponentially. In addition, for low noise intensities the escape times correspond to barrier crossing by multiple Levy steps. For high noise intensities, the escape time curves collapse for all values of $α$. At intermediate noise intensities, the escape time exhibits non-monotonic dependence on the index $α$, while still retaining the exponential form of the escape time density.

cond-mat.stat-mech↗
arXiv2005

What can one learn from two-state single molecule trajectories?

A time trajectory of an observable that fluctuates between two values (say, on and off), stemming from some unknown multi-substate kinetic scheme, is the output of many single molecule experiments. Here we show that when all successive waiting times along the trajectory are uncorrelated the on and the off waiting time probability density functions (PDFs) contain all the information. By relating the lack of correlation in the trajectory to the topology of kinetic schemes, we can immediately specify those kinetic schemes that are equally consistent with experiment, which means that it is impossible to differentiate between them by any sophisticated analyses of the trajectory. Correlated trajectories, however, contain additional information about the underlying kinetic scheme, and we consider the strategy that one should use to extract it. An example is given on correlations in the activity of individual lipase molecules.

q-bio.SC↗
arXiv2005

Uncorrelated two-state single molecule trajectories from reducible kinetic schemes

Trajectories of on-off events are the output of many single molecule experiments. Usually, one describes the underlying mechanism that generates the trajectory using a kinetic scheme, and by analyzing the trajectory aims at deducing this scheme. In a previous work [O. Flomenbom, J. Klafter, and A. Szabo, submitted (2004)], we showed that when successive events along a trajectory are uncorrelated, all the information in the trajectory is contained in two basic functions, which are the waiting time probability functions (PDFs) of the on state and of the off state. The kinetic schemes that lead to such uncorrelated trajectories were termed reducible. Here we discuss the reasons that lead to reducible schemes. In particular, the topology of reducible schemes is characterized and proven.

q-bio.SC↗