Related papers: Quasilimiting behavior for one-dimensional diffusi…
In this paper, we present an approach to characterising self-similar fast-reaction limits of systems with nonlinear diffusion. For appropriate initial data, in the fast-reaction limit as k tends to infinithy,spatial segregation results in…
The paper presents new simple sharp bounds for transition density functions for time-homogeneous diffusions processes. The bounds are obtained under mild conditions on the drift and diffusion coefficients, extending and substantially…
Suppose that a point-like steady source at $x=0$ injects particles into a half-infinite line. The particles diffuse and die. At long times a non-equilibrium steady state sets in, and we assume that it involves many particles. If the…
We consider two processes that have been used to study gene duplication, Watterson's [Genetics 105 (1983) 745--766] double recessive null model and Lynch and Force's [Genetics 154 (2000) 459--473] subfunctionalization model. Though the…
We introduce a construction to embed a quasiperiodic lattice of obstacles into a single unit cell of a higher-dimensional space, with periodic boundary conditions. This construction transparently shows the existence of channels in these…
A quasi-entropy is constructed for tensors averaged by a density function on $SO(3)$ using the log-determinant of a covariance matrix. It serves as a substitution of the entropy for tensors derived from a constrained minimization that…
Let $(X_t)_{t\geq 0}$ be a regular one-dimensional diffusion that models a biological population. If one assumes that the population goes extinct in finite time it is natural to study the $Q$-process associated to $(X_t)_{t\geq 0}$. This is…
We discuss the diffusion phenomenon in the parabolic and hyperbolic regimes. New effects related to the finite velocity of the diffusion process are predicted, that can partially explain the strange behavior associated to adsorption…
We consider a nonlinear drift-diffusion system for multiple charged species in a porous medium in 2D and 3D with periodic microstructure. The system consists of a transport equation for the concentration of the species and Poisson's…
We study quasi-stationary distributions and quasi-limiting behavior of Markov chains in general reducible state spaces with absorption. We propose a set of assumptions dealing with particular situations where the state space can be…
In a first part, we prove a Lyapunov-type criterion for the $\xi\_1$-positive recurrence of absorbed birth and death processes and provide new results on the domain of attraction of the minimal quasi-stationary distribution. In a second…
Recent results in quantization theory show that the mean-squared expected distortion can reach a rate of convergence of $\mathcal{O}(1/n)$, where $n$ is the sample size [see, e.g., IEEE Trans. Inform. Theory 60 (2014) 7279-7292 or Electron.…
Strong anomalous diffusion, where $\langle |x(t)|^q \rangle \sim t^{q \nu(q)}$ with a nonlinear spectrum $\nu(q) \neq \mbox{const}$, is wide spread and has been found in various nonlinear dynamical systems and experiments on active…
We investigate the long-time behavior of solutions of quasilinear hyperbolic systems with transparent boundary conditions when small source terms are incorporated in the system. Even if the finite-time stability of the system is not…
The Einstein relation describes the response of a diffusing particle to a small constant external force. It states that, as the force tends to zero, the ratio of the limiting velocity to the force magnitude converges to the diffusivity…
The global existence of bounded solutions to reaction-diffusion systems with fractional diffusion in the whole space $\mathbb R^N$ is investigated. The systems are assumed to preserve the non-negativity of initial data and to dissipate…
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…
Statistical properties of the front of a semi-infinite system of single-file diffusion (one dimensional system where particles cannot pass each other, but in-between collisions each one independently follow diffusive motion) are…
In this paper we show that a process modeled by a strongly continuous real-valued semigroup (that has a space convolution operator as infinitesimal generator) cannot satisfy causality. We present and analyze a causal model of diffusion that…
Classical results in the theory of monotone semiflows give sufficient conditions for the generic solution to converge toward an equilibrium or towards the set of equilibria (quasiconvergence). In this paper, we provide new formulations of…