arXiv subjects

G. Oshanin

Publications and source records attributed to G. Oshanin.

At least 37 records · Page 2Linked to original sources

arXiv2014

Microscopic theory for negative differential mobility in crowded environments

We study the behavior of the stationary velocity of a driven particle in an environment of mobile hard-core obstacles. Based on a lattice gas model, we demonstrate analytically that the drift velocity can exhibit a nonmonotonic dependence on the applied force, and show quantitatively that such negative differential mobility (NDM), observed in various physical contexts, is controlled by both the density and diffusion time scale of obstacles. Our study unifies recent numerical and analytical results obtained in specific regimes, and makes it possible to determine analytically the region of the full parameter space where NDM occurs. These results suggest that NDM could be a generic feature of biased (or active) transport in crowded environments.

cond-mat.stat-mech↗

arXiv2013

Trajectory-to-trajectory fluctuations in first-passage phenomena in bounded domains

We study the statistics of the first passage of a random walker to absorbing subsets of the boundary of compact domains in different spatial dimensions. We describe a novel diagnostic method to quantify the trajectory-to-trajectory fluctuations of the first passage, based on the distribution of the so-called uniformity index $ω$, measuring the similarity of the first passage times of two independent walkers starting at the same location. We show that the characteristic shape of $P(ω)$ exhibits a transition from unimodal to bimodal, depending on the starting point of the trajectories. From the study of different geometries in one, two and three dimensions, we conclude that this transition is a generic property of first passage phenomena in bounded domains. Our results show that, in general, the Mean First Passage Time (MFPT) is a meaningful characteristic measure of the first passage behaviour only when the Brownian walkers start sufficiently far from the absorbing boundary. Strikingly, in the opposite case, the first passage statistics exhibit large trajectory-to-trajectory fluctuations and the MFPT is not representative of the actual behaviour.

cond-mat.stat-mech↗

arXiv2013

Fluctuations and correlations of a driven tracer in a hard-core lattice gas

We consider a driven tracer particle (TP) in a bath of hard-core particles undergoing continuous exchanges with a reservoir. We develop an analytical framework which allows us to go beyond the standard force-velocity relation used for this minimal model of active microrheology and quantitatively analyze, for any density of the bath particles, the fluctuations of the TP position and their correlations with the occupation number of the bath particles. We obtain an exact Einstein-type relation which links these fluctuations in the absence of a driving force and the bath particles density profiles in the linear driving regime. For the one-dimensional case we also provide an approximate but very accurate explicit expression for the variance of the TP position and show that it can be a non-monotoneous function of the bath particles density: counter-intuitively, an increase of the density may increase the dispersion of the TP position. We show that this non trivial behavior, which could in principle be observed in active microrheology experiments, is induced by subtle cross-correlations quantified by our approach.

cond-mat.stat-mech↗

arXiv2013

Active transport in dense diffusive single-file systems

We study a minimal model of active transport in crowded single-file environments which generalises the emblematic model of single file diffusion to the case when the tracer particle (TP) performs either an autonomous directed motion or is biased by an external force, while all other particles of the environment (bath) perform unbiased diffusions. We derive explicit expressions, valid in the limit of high density of bath particles, of the full distribution $P_n(X)$ of the TP position and of all its cumulants, for arbitrary values of the bias $f$ and for any time $n$. Our analysis reveals striking features, such as the anomalous scaling $\propto\sqrt{n}$ of all cumulants, the equality of cumulants of the same parity characteristic of a Skellam distribution and a convergence to a Gaussian distribution in spite of asymmetric density profiles of bath particles. Altogether, our results provide the full statistics of the TP position, and set the basis for a refined analysis of real trajectories of active particles in crowded single-file environments.

cond-mat.stat-mech↗

arXiv2013

On the non-equivalence of two standard random walks

We focus on two models of nearest-neighbour random walks on d-dimensional regular hyper-cubic lattices that are usually assumed to be identical - the discrete-time Polya walk, in which the walker steps at each integer moment of time, and the Montroll-Weiss continuous-time random walk in which the time intervals between successive steps are independent, exponentially and identically distributed random variables with mean 1. We show that while for symmetric random walks both models indeed lead to identical behaviour in the long time limit, when there is an external bias they lead to markedly different behaviour.

cond-mat.stat-mech↗

arXiv2012

Distribution of Schmidt-like eigenvalues for Gaussian Ensembles of the Random Matrix Theory

We analyze the form of the probability distribution function P_{n}^{(β)}(w) of the Schmidt-like random variable w = x_1^2/(\sum_{j=1}^n x^{2}_j/n), where x_j are the eigenvalues of a given n \times n β-Gaussian random matrix, βbeing the Dyson symmetry index. This variable, by definition, can be considered as a measure of how any individual eigenvalue deviates from the arithmetic mean value of all eigenvalues of a given random matrix, and its distribution is calculated with respect to the ensemble of such β-Gaussian random matrices. We show that in the asymptotic limit n \to \infty and for arbitrary βthe distribution P_{n}^{(β)}(w) converges to the Marčenko-Pastur form, i.e., is defined as P_{n}^{(β)}(w) \sim \sqrt{(4 - w)/w} for w \in [0,4] and equals zero outside of the support. Furthermore, for Gaussian unitary (β= 2) ensembles we present exact explicit expressions for P_{n}^{(β=2)}(w) which are valid for arbitrary n and analyze their behavior.

cond-mat.dis-nn↗

arXiv2012

Precursor films in wetting phenomena

The spontaneous spreading of non-volatile liquid droplets on solid substrates poses a classic problem in the context of wetting phenomena. It is well known that the spreading of a macroscopic droplet is in many cases accompanied by a thin film of macroscopic lateral extent, the so-called precursor film, which emanates from the three-phase contact line region and spreads ahead of the latter with a much higher speed. Such films have been usually associated with liquid-on-solid systems, but in the last decade similar films have been reported to occur in solid-on-solid systems. While the situations in which the thickness of such films is of mesoscopic size are rather well understood, an intriguing and yet to be fully understood aspect is the spreading of microscopic, i.e., molecularly thin films. Here we review the available experimental observations of such films in various liquid-on-solid and solid-on-solid systems, as well as the corresponding theoretical models and studies aimed at understanding their formation and spreading dynamics. Recent developments and perspectives for future research are discussed.

cond-mat.soft↗

arXiv2011

Symmetry breaking between statistically equivalent, independent channels in a few-channel chaotic scattering

We study the distribution function $P(ω)$ of the random variable $ω= τ_1/(τ_1 + ... + τ_N)$, where $τ_k$'s are the partial Wigner delay times for chaotic scattering in a disordered system with $N$ independent, statistically equivalent channels. In this case, $τ_k$'s are i.i.d. random variables with a distribution $Ψ(τ)$ characterized by a "fat" power-law intermediate tail $\sim 1/τ^{1 + μ}$, truncated by an exponential (or a log-normal) function of $τ$. For $N = 2$ and N=3, we observe a surprisingly rich behavior of $P(ω)$ revealing a breakdown of the symmetry between identical independent channels. For N=2, numerical simulations of the quasi one-dimensional Anderson model confirm our findings.

cond-mat.dis-nn↗

arXiv2011

Proportionate vs disproportionate distribution of wealth of two individuals in a tempered Paretian ensemble

We study the distribution P(ω) of the random variable ω= x_1/(x_1 + x_2), where x_1 and x_2 are the wealths of two individuals selected at random from the same tempered Paretian ensemble characterized by the distribution Ψ(x) \sim ϕ(x)/x^{1 + α}, where α> 0 is the Pareto index and $ϕ(x)$ is the cut-off function. We consider two forms of ϕ(x): a bounded function ϕ(x) = 1 for L \leq x \leq H, and zero otherwise, and a smooth exponential function ϕ(x) = \exp(-L/x - x/H). In both cases Ψ(x) has moments of arbitrary order. We show that, for α> 1, P(ω) always has a unimodal form and is peaked at ω= 1/2, so that most probably x_1 \approx x_2. For 0 < α< 1 we observe a more complicated behavior which depends on the value of δ= L/H. In particular, for δ< δ_c - a certain threshold value - P(ω) has a three-modal (for a bounded ϕ(x)) and a bimodal M-shape (for an exponential ϕ(x)) form which signifies that in such ensembles the wealths x_1 and x_2 are disproportionately different.

q-fin.GN↗

arXiv2011

First passages for a search by a swarm of independent random searchers

In this paper we study some aspects of search for an immobile target by a swarm of N non-communicating, randomly moving searchers (numbered by the index k, k = 1, 2,..., N), which all start their random motion simultaneously at the same point in space. For each realization of the search process, we record the unordered set of time moments \{τ_k\}, where τ_k is the time of the first passage of the k-th searcher to the location of the target. Clearly, τ_k's are independent, identically distributed random variables with the same distribution function Ψ(τ). We evaluate then the distribution P(ω) of the random variable ω\sim τ_1/barτ, where barτ = N^{-1} \sum_{k=1}^N τ_k is the ensemble-averaged realization-dependent first passage time. We show that P(ω) exhibits quite a non-trivial and sometimes a counterintuitive behaviour. We demonstrate that in some well-studied cases e.g., Brownian motion in finite d-dimensional domains) the \textit{mean} first passage time is not a robust measure of the search efficiency, despite the fact that Ψ(τ) has moments of arbitrary order. This implies, in particular, that even in this simplest case (not saying about complex systems and/or anomalous diffusion) first passage data extracted from a single particle tracking should be regarded with an appropriate caution because of the significant sample-to-sample fluctuations.

cond-mat.stat-mech↗

arXiv2010

Narrow-escape times for diffusion in microdomains with a particle-surface affinity: Mean-field results

We analyze the mean time t_{app} that a randomly moving particle spends in a bounded domain (sphere) before it escapes through a small window in the domain's boundary. A particle is assumed to diffuse freely in the bulk until it approaches the surface of the domain where it becomes weakly adsorbed, and then wanders diffusively along the boundary for a random time until it desorbs back to the bulk, and etc. Using a mean-field approximation, we define t_{app} analytically as a function of the bulk and surface diffusion coefficients, the mean time it spends in the bulk between two consecutive arrivals to the surface and the mean time it wanders on the surface within a single round of the surface diffusion.

cond-mat.soft↗

arXiv2009

Post-Tanner spreading of nematic droplets

The quasistationary spreading of a circular liquid drop on a solid substrate typically obeys the so-called Tanner law, with the instantaneous base radius R(t) growing with time as R ~ t^{1/10} -- an effect of the dominant role of capillary forces for a small-sized droplet. However, for droplets of nematic liquid crystals, a faster spreading law sets in at long times, so that R ~ t^alpha with alpha significantly larger than the Tanner exponent 1/10. In the framework of the thin film model (or lubrication approximation), we describe this "acceleration" as a transition to a qualitatively different spreading regime driven by a strong substrate-liquid interaction specific to nematics (antagonistic anchoring at the interfaces). The numerical solution of the thin film equation agrees well with the available experimental data for nematics, even though the non-Newtonian rheology has yet to be taken into account. Thus we complement the theory of spreading with a post-Tanner stage, noting that the spreading process can be expected to cross over from the usual capillarity-dominated stage to a regime where the whole reservoir becomes a diffusive film in the sense of Derjaguin.

cond-mat.soft↗

arXiv2009

Survival of an evasive prey

We study the survival of a prey that is hunted by N predators. The predators perform independent random walks on a square lattice with V sites and start a direct chase whenever the prey appears within their sighting range. The prey is caught when a predator jumps to the site occupied by the prey. We analyze the efficacy of a lazy, minimal-effort evasion strategy according to which the prey tries to avoid encounters with the predators by making a hop only when any of the predators appears within its sighting range; otherwise the prey stays still. We show that if the sighting range of such a lazy prey is equal to 1 lattice spacing, at least 3 predators are needed in order to catch the prey on a square lattice. In this situation, we establish a simple asymptotic relation ln(Pev)(t) \sim (N/V)2ln(Pimm(t)) between the survival probabilities of an evasive and an immobile prey. Hence, when the density of the predators is low N/V<<1, the lazy evasion strategy leads to the spectacular increase of the survival probability. We also argue that a short-sighting prey (its sighting range is smaller than the sighting range of the predators) undergoes an effective superdiffusive motion, as a result of its encounters with the predators, whereas a far-sighting prey performs a diffusive-type motion.

cond-mat.stat-mech↗

arXiv2009

Finding passwords by random walks: How long does it take?

We compare an efficiency of a deterministic "lawnmower" and random search strategies for finding a prescribed sequence of letters (a password) of length M in which all letters are taken from the same Q-ary alphabet. We show that at best a random search takes two times longer than a "lawnmower" search.

cs.CR↗

arXiv2009

Confinement effects on diffusiophoretic self-propellers

We study theoretically the effects of spatial confinement on the phoretic motion of a dissolved particle driven by composition gradients generated by chemical reactions of its solvent, which are active only on certain parts of the particle surface. We show that the presence of confining walls increases in a similar way both the composition gradients and the viscous friction, and the overall result of these competing effects is an increase in the phoretic velocity of the particle. For the case of steric repulsion only between the particle and the product molecules of the chemical reactions, the absolute value of the velocity remains nonetheless rather small.

cond-mat.soft↗

arXiv2008

Exact asymptotics for non-radiative migration-accelerated energy transfer in one-dimensional systems

We study direct energy transfer by multipolar or exchange interactions between diffusive excited donor and diffusive unexcited acceptors. Extending over the case of long-range transfer of an excitation energy a non-perturbative approach by Bray and Blythe [Phys. Rev. Lett. 89, 150601 (2002)], originally developed for contact diffusion-controlled reactions, we determine exactly long-time asymptotics of the donor decay function in one-dimensional systems.

cond-mat.stat-mech↗

arXiv2008

Helix or Coil? Fate of a Melting Heteropolymer

We determine the probability that a partially melted heteropolymer at the melting temperature will either melt completely or return to a helix state. This system is equivalent to the splitting probability for a diffusing particle on a finite interval that moves according to the Sinai model. When the initial fraction of melted polymer is f, the melting probability fluctuates between different realizations of monomer sequences on the polymer. For a fixed value of f, the melting probability distribution changes from unimodal to a bimodal as the strength of the disorder is increased.

cond-mat.stat-mech↗

arXiv2008

Survival probability of a particle in a sea of mobile traps: A tale of tails

We study the long-time tails of the survival probability $P(t)$ of an $A$ particle diffusing in $d$-dimensional media in the presence of a concentration $ρ$ of traps $B$ that move sub-diffusively, such that the mean square displacement of each trap grows as $t^γ$ with $0\leq γ\leq 1$. Starting from a continuous time random walk (CTRW) description of the motion of the particle and of the traps, we derive lower and upper bounds for $P(t)$ and show that for $γ\leq 2/(d+2)$ these bounds coincide asymptotically, thus determining asymptotically exact results. The asymptotic decay law in this regime is exactly that obtained for immobile traps. This means that for sufficiently subdiffusive traps, the moving $A$ particle sees the traps as essentially immobile, and Lifshitz or trapping tails remain unchanged. For $γ> 2/(d+2)$ and $d\leq 2$ the upper and lower bounds again coincide, leading to a decay law equal to that of a stationary particle. Thus, in this regime the moving traps see the particle as essentially immobile. For $d>2$, however, the upper and lower bounds in this $γ$ regime no longer coincide and the decay law for the survival probability of the $A$ particle remains ambiguous.

cond-mat.stat-mech↗