arXiv subjects

M. Coppey

Publications and source records attributed to M. Coppey.

10 recordsLinked to original sources

arXiv2005

Averaged residence times of stochastic motions in bounded domains

Two years ago, Blanco and Fournier (Blanco S. and Fournier R., Europhys. Lett. 2003) calculated the mean first exit time of a domain of a particle undergoing a randomly reoriented ballistic motion which starts from the boundary. They showed that it is simply related to the ratio of the volume's domain over its surface. This work was extended by Mazzolo (Mazzolo A., Europhys. Lett. 2004) who studied the case of trajectories which start inside the volume. In this letter, we propose an alternative formulation of the problem which allows us to calculate not only the mean exit time, but also the mean residence time inside a sub-domain. The cases of any combinations of reflecting and absorbing boundary conditions are considered. Lastly, we generalize our results for a wide class of stochastic motions.

cond-mat.stat-mech↗

arXiv2005

Kinetics of diffusion-limited catalytically-activated reactions: An extension of the Wilemski-Fixman approach

We study kinetics of diffusion-limited catalytically-activated $A + B \to B$ reactions taking place in three dimensional systems, in which an annihilation of diffusive $A$ particles by diffusive traps $B$ may happen only if the encounter of an $A$ with any of the $B$s happens within a special catalytic subvolumen, these subvolumens being immobile and uniformly distributed within the reaction bath. Suitably extending the classical approach of Wilemski and Fixman (G. Wilemski and M. Fixman, J. Chem. Phys. \textbf{58}:4009, 1973) to such three-molecular diffusion-limited reactions, we calculate analytically an effective reaction constant and show that it comprises several terms associated with the residence and joint residence times of Brownian paths in finite domains. The effective reaction constant exhibits a non-trivial dependence on the reaction radii, the mean density of catalytic subvolumens and particles' diffusion coefficients. Finally, we discuss the fluctuation-induced kinetic behavior in such systems.

cond-mat.stat-mech↗

arXiv2005

Mean joint residence time of two Brownian particles in a sphere

We calculate the mean joint residence time of two Brownian particles in a sphere, for very general initial conditions. In particular, we focus on the dependence of this residence time as a function of the diffusion coefficients of the two particles. Our results can be useful for describing kinetics of bimolecular diffusion controlled reactions activated by catalytic sites.

cond-mat.soft↗

arXiv2005

Optimal search strategies for hidden targets

What is the fastest way of finding a randomly hidden target? This question of general relevance is of vital importance for foraging animals. Experimental observations reveal that the search behaviour of foragers is generally intermittent: active search phases randomly alternate with phases of fast ballistic motion. In this letter, we study the efficiency of this type of two states search strategies, by calculating analytically the mean first passage time at the target. We model the perception mecanism involved in the active search phase by a diffusive process. In this framework, we show that the search strategy is optimal when the average duration of "motion phases" varies like the power either 3/5 or 2/3 of the average duration of "search phases", depending on the regime. This scaling accounts for experimental data over a wide range of species, which suggests that the kinetics of search trajectories is a determining factor optimized by foragers and that the perception activity is adequately described by a diffusion process.

cond-mat.stat-mech↗

arXiv2005

Kinetics of target site localization of a protein on DNA: a stochastic approach

It is widely recognized that the cleaving rate of a restriction enzyme on target DNA sequences is several orders of magnitude faster than the maximal one calculated from the diffusion--limited theory. It was therefore commonly assumed that the target site interaction of a restriction enzyme with DNA has to occur via two steps: one--dimensional diffusion along a DNA segment, and long--range jumps coming from association/dissociation events. We propose here a stochastic model for this reaction which comprises a series of 1D diffusions of a restriction enzyme on non-specific DNA sequences interrupted by 3D excursions in the solution until the target sequence is reached. This model provides an optimal finding strategy which explains the fast association rate. Modeling the excursions by uncorrelated random jumps, we recover the expression of the mean time required for target site association to occur given by Berg & al. \cite{berg81}, and we explicitly give several physical quantities describing the stochastic pathway of the enzyme. For competitive target sites we calculate two quantities: processivity and preference. By comparing these theoretical expressions to recent experimental data obtained for \textit{Eco}RV--DNA interaction, we quantify: i) the mean residence time per binding event of \textit{Eco}RV on DNA for a representative 1D diffusion coefficient, ii) the average lengths of DNA scanned during the 1D diffusion (during one binding event and during the overall process), iii) the mean time and the mean number of visits needed to go from one target site to the other. Further, we evaluate the dynamics of DNA cleavage with regard to the probability for the restriction enzyme to perform another 1D diffusion on the same DNA substrate following a 3D excursion.

q-bio.SC↗

arXiv2004

Lattice theory of trapping reactions with mobile species

We present a stochastic lattice theory describing the kinetic behavior of trapping reactions $A + B \to B$, in which both the $A$ and $B$ particles perform an independent stochastic motion on a regular hypercubic lattice. Upon an encounter of an $A$ particle with any of the $B$ particles, $A$ is annihilated with a finite probability; finite reaction rate is taken into account by introducing a set of two-state random variables - "gates", imposed on each $B$ particle, such that an open (closed) gate corresponds to a reactive (passive) state. We evaluate here a formal expression describing the time evolution of the $A$ particle survival probability, which generalizes our previous results. We prove that for quite a general class of random motion of the species involved in the reaction process, for infinite or finite number of traps, and for any time $t$, the $A$ particle survival probability is always larger in case when $A$ stays immobile, than in situations when it moves.

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

Pascal Principle for Diffusion-Controlled Trapping Reactions

"All misfortune of man comes from the fact that he does not stay peacefully in his room", has once asserted Blaise Pascal. In the present paper we evoke this statement as the "Pascal principle" in regard to the problem of survival of an "A" particle, which performs a lattice random walk in presence of a concentration of randomly moving traps "B", and gets annihilated upon encounters with any of them. We prove here that at sufficiently large times for both perfect and imperfect trapping reactions, for arbitrary spatial dimension "d" and for a rather general class of random walks, the "A" particle survival probability is less than or equal to the survival probability of an immobile target in the presence of randomly moving traps.

cond-mat.stat-mech↗

arXiv2002

Trapping Reactions with Randomly Moving Traps: Exact Asymptotic Results for Compact Exploration

In a recent Letter Bray and Blythe have shown that the survival probability P(t) of an A particle diffusing with a diffusion coefficient D_A in a 1D system with diffusive traps B is independent of D_A in the asymptotic limit t \to \infty and coincides with the survival probability of an immobile target in the presence of diffusive traps. Here we show that this remarkable behavior has a more general range of validity and holds for systems of an arbitrary dimension d, integer or fractal, provided that the traps are "compactly exploring" the space, i.e. the "fractal" dimension dw of traps' trajectories is greater than d. For the marginal case when dw = d, as exemplified here by conventional diffusion in 2D systems, the decay form is determined up to a numerical factor in the characteristic decay time.

cond-mat.stat-mech↗