Related papers: On the exit-problem for self-interacting diffusion…
This paper presents an improved version of the previously proposed self-consistent drift-diffusion-reaction model correcting for non-physical behavior at longer time scales. To this end a novel boundary condition is employed that takes into…
Diffusion-mediated surface phenomena are crucial for human life and industry, with examples ranging from oxygen capture by lung alveolar surface to heterogeneous catalysis, gene regulation, membrane permeation and filtration processes.…
We consider one-dimensional diffusions, with polynomial drift and diffusion coefficients, so that in particular the motion can be space-inhomogeneous, interacting via one-sided reflections. The prototypical example is the well-known model…
In his seminal work from the 1950s, William Feller classified all one-dimensional diffusions on $-\infty\leq a<b\leq \infty$ in terms of their ability to access the boundary (Feller's test for explosions) and to enter the interior from the…
In the recent literature, the g-subdiffusion equation involving Caputo fractional derivatives with respect to another function has been studied in relation to anomalous diffusions with a continuous transition between different subdiffusive…
The dynamics of an interface between the normal and superconducting phases under nonstationary external conditions is studied within the framework of the time-dependent Ginzburg-Landau equations of superconductivity, modified to include…
We consider a family of initial boundary value problems governed by a fractional diffusion equation with Caputo derivative in time, where the parameter is the Newton heat transfer coefficient linked to the Robin condition on the boundary.…
We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded domain, like the density of the medium or the velocity field…
For an arbitrary diffusion process $X$ with time-homogeneous drift and variance parameters $\mu(x)$ and $\sigma^2(x)$, let $V_\varepsilon$ be $1/\varepsilon$ times the total time $X(t)$ spends in the strip…
Let $U$ be a domain, convex in $x$ and symmetric about the y-axis, which is contained in a centered and oriented rectangle $R$. \linebreak If $\tau_A$ is the first exit time of Brownian motion from $A$ and $A^+=A\cap \{(x,y):x>0\}$, it is…
We derive a variational expression for the correlation time of physical observables in steady-state diffusive systems. As a consequence of this variational expression, we obtain lower bounds on the correlation time, which provide speed…
This paper proves almost-sure convergence for the self-attracting diffusion on the unit sphere $$dX(t)=\sigma dW_{t}(X(t))-a\int_{0}^{t}\nabla_{\mathbb{S}^n}V_{X_s}(X_t) dsdt,\qquad X(0)=x\in\mathbb{S}^n $$ %given by the stochastic…
In this article, we obtain properties of the law associated to the first hitting time of a threshold by a one-dimensional uniformly elliptic diffusion process and to the associated process stopped at the threshold. Our methodology relies on…
We consider a heat problem with discontinuous diffusion coefficientsand discontinuous transmission boundary conditions with a resistancecoefficient. For all compact $(\epsilon,\delta)$-domains $\Omega\subset\mathbb{R}^n$ with a $d$-set…
Finding the mean time it takes for a particle to escape from a meta-stable state due to thermal fluctuations is a fundamental problem in physics, chemistry and biology. For weak thermal noise, the mean escape time is captured by the…
We consider a finite dimensional deterministic dynamical system with a global attractor A with a unique ergodic measure P concentrated on it, which is uniformly parametrized by the mean of the trajectories in a bounded set D containing A.…
We discuss the identification of a time-dependent potential in a time-fractional diffusion model from a boundary measurement taken at a single point. Theoretically, we establish a conditional Lipschitz stability for this inverse problem.…
We consider Langevin equation with dichotomously fluctuating diffusivity, where the diffusion coefficient changes dichotomously in time, in order to study fluctuations of time-averaged observables in temporary heterogeneous diffusion…
We discuss chains of interacting Brownian motions. Their time reversal invariance is broken because of asymmetry in the interaction strength between left and right neighbor. In the limit of a very steep and short range potential one arrives…
We derive an analytical expression for the propagator and the transition path time distribution of a two-dimensional active Brownian particle crossing a parabolic barrier with absorbing boundary conditions at both sides. By taking those of…