Mean first-passage time of surface-mediated diffusion in spherical domains

We present an exact calculation of the mean first-passage time to a target on the surface of a 2D or 3D spherical domain, for a molecule alternating phases of surface diffusion on the domain boundary and phases of bulk diffusion. The presented approach is based on an integral equation which can be solved analytically. Numerically validated approximation schemes, which provide more tractable expressions of the mean first-passage time are also proposed. In the framework of this minimal model of surface-mediated reactions, we show analytically that the mean reaction time can be minimized as a function of the desorption rate from the surface.Comment: to appear in J. Stat. Phy

Kinetics of active surface-mediated diffusion in spherically symmetric domains

We present an exact calculation of the mean first-passage time to a target on the surface of a 2D or 3D spherical domain, for a molecule alternating phases of surface diffusion on the domain boundary and phases of bulk diffusion. We generalize the results of [J. Stat. Phys. {\bf 142}, 657 (2011)] and consider a biased diffusion in a general annulus with an arbitrary number of regularly spaced targets on a partially reflecting surface. The presented approach is based on an integral equation which can be solved analytically. Numerically validated approximation schemes, which provide more tractable expressions of the mean first-passage time are also proposed. In the framework of this minimal model of surface-mediated reactions, we show analytically that the mean reaction time can be minimized as a function of the desorption rate from the surface.Comment: Published online in J. Stat. Phy

Diffusion and subdiffusion of interacting particles on comb-like structures

We study the dynamics of a tracer particle (TP) on a comb lattice populated by randomly moving hard-core particles in the dense limit. We first consider the case where the TP is constrained to move on the backbone of the comb only, and, in the limit of high density of particles, we present exact analytical results for the cumulants of the TP position, showing a subdiffusive behavior $\sim t^{3/4}$. At longer times, a second regime is observed, where standard diffusion is recovered, with a surprising non analytical dependence of the diffusion coefficient on the particle density. When the TP is allowed to visit the teeth of the comb, based on a mean-field-like Continuous Time Random Walk description, we unveil a rich and complex scenario, with several successive subdiffusive regimes, resulting from the coupling between the inhomogeneous comb geometry and particle interactions. Remarkably, the presence of hard-core interactions speeds up the TP motion along the backbone of the structure in all regimes.Comment: 5 pages, 3 figures + supplemental materia

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.Comment: 7 pages, 3 figure

Mean first-passage times of non-Markovian random walkers in confinement

The first-passage time (FPT), defined as the time a random walker takes to reach a target point in a confining domain, is a key quantity in the theory of stochastic processes. Its importance comes from its crucial role to quantify the efficiency of processes as varied as diffusion-limited reactions, target search processes or spreading of diseases. Most methods to determine the FPT properties in confined domains have been limited to Markovian (memoryless) processes. However, as soon as the random walker interacts with its environment, memory effects can not be neglected. Examples of non Markovian dynamics include single-file diffusion in narrow channels or the motion of a tracer particle either attached to a polymeric chain or diffusing in simple or complex fluids such as nematics \cite{turiv2013effect}, dense soft colloids or viscoelastic solution. Here, we introduce an analytical approach to calculate, in the limit of a large confining volume, the mean FPT of a Gaussian non-Markovian random walker to a target point. The non-Markovian features of the dynamics are encompassed by determining the statistical properties of the trajectory of the random walker in the future of the first-passage event, which are shown to govern the FPT kinetics.This analysis is applicable to a broad range of stochastic processes, possibly correlated at long-times. Our theoretical predictions are confirmed by numerical simulations for several examples of non-Markovian processes including the emblematic case of the Fractional Brownian Motion in one or higher dimensions. These results show, on the basis of Gaussian processes, the importance of memory effects in first-passage statistics of non-Markovian random walkers in confinement.Comment: Submitted version. Supplementary Information can be found on the Nature website : http://www.nature.com/nature/journal/v534/n7607/full/nature18272.htm

Windings of the 2D free Rouse chain

We study long time dynamical properties of a chain of harmonically bound Brownian particles. This chain is allowed to wander everywhere in the plane. We show that the scaling variables for the occupation times T_j, areas A_j and winding angles \theta_j (j=1,...,n labels the particles) take the same general form as in the usual Brownian motion. We also compute the asymptotic joint laws P({T_j}), P({A_j}), P({\theta_j}) and discuss the correlations occuring in those distributions.Comment: Latex, 17 pages, submitted to J. Phys.

Enhanced reaction kinetics in biological cells

The cell cytoskeleton is a striking example of "active" medium driven out-of-equilibrium by ATP hydrolysis. Such activity has been shown recently to have a spectacular impact on the mechanical and rheological properties of the cellular medium, as well as on its transport properties : a generic tracer particle freely diffuses as in a standard equilibrium medium, but also intermittently binds with random interaction times to motor proteins, which perform active ballistic excursions along cytoskeletal filaments. Here, we propose for the first time an analytical model of transport limited reactions in active media, and show quantitatively how active transport can enhance reactivity for large enough tracers like vesicles. We derive analytically the average interaction time with motor proteins which optimizes the reaction rate, and reveal remarkable universal features of the optimal configuration. We discuss why active transport may be beneficial in various biological examples: cell cytoskeleton, membranes and lamellipodia, and tubular structures like axons.Comment: 10 pages, 2 figure

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.Comment: 5 pages, 2 figures + supplemental materia