arXiv subjects

S. B. Yuste

Publications and source records attributed to S. B. Yuste.

At least 37 records · Page 2Linked to original sources

arXiv2013

Exploration and Trapping of Mortal Random Walkers

Exploration and trapping properties of random walkers that may evanesce at any time as they walk have seen very little treatment in the literature, and yet a finite lifetime is a frequent occurrence, and its effects on a number of random walk properties may be profound. For instance, whereas the average number of distinct sites visited by an immortal walker grows with time without bound, that of a mortal walker may, depending on dimensionality and rate of evanescence, remain finite or keep growing with the passage of time. This number can in turn be used to calculate other classic quantities such as the survival probability of a target surrounded by diffusing traps. If the traps are immortal, the survival probability will vanish with increasing time. However, if the traps are evanescent, the target may be spared a certain death. We analytically calculate a number of basic and broadly used quantities for evanescent random walkers.

cond-mat.stat-mech↗

arXiv2012

Survival probability of an immobile target in a sea of evanescent diffusive or subdiffusive traps: a fractional equation approach

We calculate the survival probability of an immobile target surrounded by a sea of uncorrelated diffusive or subdiffusive evanescent traps, i.e., traps that disappear in the course of their motion. Our calculation is based on a fractional reaction-subdiffusion equation derived from a continuous time random walk model of the system. Contrary to an earlier method valid only in one dimension (d=1), the equation is applicable in any Euclidean dimension d and elucidates the interplay between anomalous subdiffusive transport, the irreversible evanescence reaction and the dimension in which both the traps and the target are embedded. Explicit results for the survival probability of the target are obtained for a density ρ(t) of traps which decays (i) exponentially and (ii) as a power law. In the former case, the target has a finite asymptotic survival probability in all integer dimensions, whereas in the latter case there are several regimes where the values of the decay exponent for ρ(t) and the anomalous diffusion exponent of the traps determine whether or not the target has a chance of eternal survival in one, two and three dimensions.

cond-mat.stat-mech↗

arXiv2012

Rational-function approximation for fluids interacting via piece-wise constant potentials

The structural properties of fluids whose molecules interact via potentials with a hard-core plus n piece-wise constant sections of different widths and heights are derived using a (semi-analytical) rational-function approximation method. The results are illustrated for the cases of a square-shoulder plus square-well potential and a shifted square-well potential and compared both with simulation data and with those that follow from the (numerical) solutions of the Percus-Yevick integral equation.

cond-mat.soft↗

arXiv2011

Asymptotic solutions of decoupled continuous-time random walks with superheavy-tailed waiting time and heavy-tailed jump length distributions

We study the long-time behavior of decoupled continuous-time random walks characterized by superheavy-tailed distributions of waiting times and symmetric heavy-tailed distributions of jump lengths. Our main quantity of interest is the limiting probability density of the position of the walker multiplied by a scaling function of time. We show that the probability density of the scaled walker position converges in the long-time limit to a non-degenerate one only if the scaling function behaves in a certain way. This function as well as the limiting probability density are determined in explicit form. Also, we express the limiting probability density which has heavy tails in terms of the Fox $H$-function and find its behavior for small and large distances.

cond-mat.stat-mech↗

arXiv2011

Structure of the square-shoulder fluid

The structural properties of square-shoulder fluids are derived from the use of the rational function approximation method. The computation of both the radial distribution function and the static structure factor involves mostly analytical steps, requiring only the numerical solution of a single transcendental equation. The comparison with available simulation data and with numerical solutions of the Percus-Yevick and hypernetted-chain integral equations shows that the present approximation represents an improvement over the Percus-Yevick theory for this system and a reasonable compromise between accuracy and simplicity.

cond-mat.stat-mech↗

arXiv2010

Application of Fractional Calculus to Reaction-Subdiffusion Processes and Morphogen Gradient Formation

It is a well known fact that subdiffusion equations in terms of fractional derivatives can be obtained from Continuous Time Random Walk (CTRW) models with long-tailed waiting time distributions. Over the last years various authors have shown that extensions of such CTRW models incorporating reactive processes to the mesoscopic transport equations may lead to non-intuitive reaction-subdiffusion equations. In particular, one such equation has been recently derived for a subdiffusive random walker subject to a linear (first-order) death process. We take this equation as a starting point to study the developmental biology key problem of morphogen gradient formation, both for the uniform case where the morphogen degradation rate coefficient (reactivity) is constant and for the non-uniform case (position-dependent reactivity). In the uniform case we obtain exponentially decreasing stationary concentration profiles and we study their robustness with respect to perturbations in the incoming morphogen flux. In the non-uniform case we find a rich phenomenology at the level of the stationary profiles. We conclude that the analytic form of the long-time morphogen concentration profiles is very sensitive to the spatial dependence of the reactivity and the specific value of the anomalous diffusion coefficient.

physics.bio-ph↗

arXiv2009

Reaction-subdiffusion and reaction-superdiffusion equations for evanescent particles performing continuous time random walks

Starting from a continuous time random walk (CTRW) model of particles that may evanesce as they walk, our goal is to arrive at macroscopic integro-differential equations for the probability density for a particle to be found at point r at time t given that it started its walk from r_0 at time t=0. The passage from the CTRW to an integro-differential equation is well understood when the particles are not evanescent. Depending on the distribution of stepping times and distances, one arrives at standard macroscopic equations that may be "normal" (diffusion) or "anomalous" (subdiffusion and/or superdiffusion). The macroscopic description becomes considerably more complicated and not particularly intuitive if the particles can die during their walk. While such equations have been derived for specific cases, e.g., for location-independent exponential evanescence, we present a more general derivation valid under less stringent constraints than those found in the current literature.

cond-mat.stat-mech↗

arXiv2009

Coagulation reaction in low dimensions: Revisiting subdiffusive A+A reactions in one dimension

We present a theory for the coagulation reaction A+A -> A for particles moving subdiffusively in one dimension. Our theory is tested against numerical simulations of the concentration of $A$ particles as a function of time (``anomalous kinetics'') and of the interparticle distribution function as a function of interparticle distance and time. We find that the theory captures the correct behavior asymptotically and also at early times, and that it does so whether the particles are nearly diffusive or very subdiffusive. We find that, as in the normal diffusion problem, an interparticle gap responsible for the anomalous kinetics develops and grows with time. This corrects an earlier claim to the contrary on our part.

cond-mat.stat-mech↗

arXiv2009

Contact values for disparate-size hard-sphere mixtures

A universality ansatz for the contact values of a multicomponent mixture of additive hard spheres is used to propose new formulae for the case of disparate-size binary mixtures. A comparison with simulation data and with a recent proposal by Alawneh and Henderson for binary mixtures shows reasonably good agreement with the predictions for the contact values of the large-large radial distribution functions. A discussion on the usefulness and limitations of the new proposals is also presented.

cond-mat.soft↗

arXiv2009

Mean Field Model of Coagulation and Annihilation Reactions in a Medium of Quenched Traps: Subdiffusion

We present a mean field model for coagulation ($A+A\to A$) and annihilation ($A+A\to 0$) reactions on lattices of traps with a distribution of depths reflected in a distribution of mean escape times. The escape time from each trap is exponentially distributed about the mean for that trap, and the distribution of mean escape times is a power law. Even in the absence of reactions, the distribution of particles over sites changes with time as particles are caught in ever deeper traps, that is, the distribution exhibits aging. Our main goal is to explore whether the reactions lead to further (time dependent) changes in this distribution.

cond-mat.stat-mech↗

arXiv2008

Simple equation of state for hard disks on the hyperbolic plane

A simple equation of state for hard disks on the hyperbolic plane is proposed. It yields the exact second virial coefficient and contains a pole at the highest possible packing. A comparison with another very recent theoretical proposal and simulation data is presented.

cond-mat.soft↗

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↗

arXiv2007

Alternative Approaches to the Equilibrium Properties of Hard-Sphere Liquids

An overview of some analytical approaches to the computation of the structural and thermodynamic properties of single component and multicomponent hard-sphere fluids is provided. For the structural properties, they yield a thermodynamically consistent formulation, thus improving and extending the known analytical results of the Percus-Yevick theory. Approximate expressions for the contact values of the radial distribution functions and the corresponding analytical equations of state are also discussed. Extensions of this methodology to related systems, such as sticky hard spheres and square-well fluids, as well as its use in connection with the perturbation theory of fluids are briefly addressed.

cond-mat.stat-mech↗

arXiv2006

Simulations for trapping reactions with subdiffusive traps and subdiffusive particles

While there are many well-known and extensively tested results involving diffusion-limited binary reactions, reactions involving subdiffusive reactant species are far less understood. Subdiffusive motion is characterized by a mean square displacement $ \sim t^γ$ with $0<γ<1$. Recently we calculated the asymptotic survival probability $P(t)$ of a (sub)diffusive particle ($γ^\prime$) surrounded by (sub)diffusive traps ($γ$) in one dimension. These are among the few known results for reactions involving species characterized by different anomalous exponents. Our results were obtained by bounding, above and below, the exact survival probability by two other probabilities that are asymptotically identical (except when $γ^\prime=1$ and $0<γ<2/3$). Using this approach, we were not able to estimate the time of validity of the asymptotic result, nor the way in which the survival probability approaches this regime. Toward this goal, here we present a detailed comparison of the asymptotic results with numerical simulations. In some parameter ranges the asymptotic theory describes the simulation results very well even for relatively short times. However, in other regimes more time is required for the simulation results to approach asymptotic behavior, and we arrive at situations where we are not able to reach asymptotia within our computational means. This is regrettably the case for $γ^\prime=1$ and $0<γ<2/3$, where we are therefore not able to prove or disprove even conjectures about the asymptotic survival probability of the particle.

cond-mat.stat-mech↗

arXiv2006

The target problem with evanescent subdiffusive traps

We calculate the survival probability of a stationary target in one dimension surrounded by diffusive or subdiffusive traps of time-dependent density. The survival probability of a target in the presence of traps of constant density is known to go to zero as a stretched exponential whose specific power is determined by the exponent that characterizes the motion of the traps. A density of traps that grows in time always leads to an asymptotically vanishing survival probability. Trap evanescence leads to a survival probability of the target that may be go to zero or to a finite value indicating a probability of eternal survival, depending on the way in which the traps disappear with time.

cond-mat.soft↗

arXiv2006

Trapping reactions with subdiffusive traps and particles

Reaction dynamics involving subdiffusive species is an interesting topic with only few known results, especially when the motion of different species is characterized by different anomalous diffusion exponents. Here we study the reaction dynamics of a (sub)diffusive particle surrounded by a sea of (sub)diffusive traps in one dimension. Under some reasonable assumptions we find rigorous results for the asymptotic survival probability of the particle in most cases, but have not succeeded in doing so for a particle that diffuses normally while the anomalous diffusion exponent of the traps is smaller than 2/3.

cond-mat.soft↗

arXiv2006

On the radial distribution function of a hard-sphere fluid

Two related approaches, one fairly recent [A. Trokhymchuk et al., J. Chem. Phys. 123, 024501 (2005)] and the other one introduced fifteen years ago [S. B. Yuste and A. Santos, Phys. Rev. A 43, 5418 (1991)], for the derivation of analytical forms of the radial distribution function of a fluid of hard spheres are compared. While they share similar starting philosophy, the first one involves the determination of eleven parameters while the second is a simple extension of the solution of the Percus-Yevick equation. It is found that the {second} approach has a better global accuracy and the further asset of counting already with a successful generalization to mixtures of hard spheres and other related systems.

cond-mat.stat-mech↗

arXiv2005

Trapping reactions with subdiffusive traps and particles characterized by different anomalous diffusion exponents

A number of results for reactions involving subdiffusive species all with the same anomalous exponent gamma have recently appeared in the literature and can often be understood in terms of a subordination principle whereby time t in ordinary diffusion is replaced by t^gamma. However, very few results are known for reactions involving different species characterized by different anomalous diffusion exponents. Here we study the reaction dynamics of a (sub)diffusive particle surrounded by a sea of (sub)diffusive traps in one dimension. We find rigorous results for the asymptotic survival probability of the particle in most cases, with the exception of the case of a particle that diffuses normally while the anomalous diffusion exponent of the traps is smaller than 2/3.

cond-mat.stat-mech↗