Related papers: Construction and analysis of sticky reflected diff…
We develop a variational method for constructing positive entropy invariant measures of Lagrangian systems without assuming transversal intersections of stable and unstable manifolds, and without restrictions to the size of non-integrable…
Constrained Markov processes, such as reflecting diffusions, behave as an unconstrained process in the interior of a domain but upon reaching the boundary are controlled in some way so that they do not leave the closure of the domain. In…
The equations of a planar elastica under pressure can be rewritten in a useful form by parametrising the variables in terms of the local orientation angle, $\theta$, instead of the arc length. This ``$\theta$-formulation'' lends itself to a…
In this paper we study the moment generating function and the moments of occupation time functionals of one-dimensional diffusions. Assuming, specifically, that the process lives on $\mathbb{R}$ and starts at~0, we apply Kac's moment…
We introduce numerical methods for simulating the diffusive motion of rigid bodies of arbitrary shape immersed in a viscous fluid. We parameterize the orientation of the bodies using normalized quaternions, which are numerically robust,…
We consider a pseudo-differential equation driven by the fractional $p$-Laplacian with $p\ge 2$ (degenerate case), with a bounded reaction $f$ and Dirichlet type conditions in a smooth domain $\Omega$. By means of barriers, a nonlocal…
We construct a class of one-dimensional diffusion processes on the particles of branching Brownian motion that are symmetric with respect to the limits of random martingale measures. These measures are associated with the extended extremal…
We study the asymptotic behavior of a self-interacting one-dimensional Brownian polymer first introduced by Durrett and Rogers [Probab. Theory Related Fields 92 (1992) 337--349]. The polymer describes a stochastic process with a drift which…
We develop a general boundary calculus for algebraic phases and use it to formulate an intrinsic structural framework for deformation and obstruction phenomena. Structural boundaries are shown to be finitely detectable and canonically…
The stochastic trajectories of molecules in living cells, as well as the dynamics in many other complex systems, often exhibit memory in their path over long periods of time. In addition, these systems can show dynamic heterogeneities due…
Results from a modified Diffusion Limited Aggregation (DLA) model are presented. The modifications of the classical DLA model are in the attachment to the cluster rules and in the scheme of particle generation/killing. In the classical DLA…
This work presents a comprehensive framework for enhanced diffusion modeling in fluid-structure interactions by combining the Immersed Boundary Method (IBM) with stochastic trajectories and high-order spectral boundary conditions. Using…
The classical models for irreversible diffusion-influenced reactions can be derived by introducing absorbing boundary conditions to over-damped continuous Brownian motion (BM) theory. As there is a clear corresponding stochastic process,…
The aim of this paper is to study the behavior of the weighted empirical measures of the decreasing step Euler scheme of a one-dimensional diffusion process having multiple invariant measures. This situation can occur when the drift and the…
We study differential equations with a linear, path dependent drift and discrete delay in the diffusion term driven by a $\gamma$-H\"older rough path for $\gamma > \frac{1}{3}$. We prove well-posedness of these systems and establish a…
Well posedness is established for a family of equations modelling particle populations undergoing delocalised coagulation, advection, inflow and outflow in a externally specified velocity field. Very general particle types are allowed while…
We consider Dirichlet Laplacians on straight strips in R^2 or layers in R^3 with a weak local deformation. First we generalize a result of Bulla et al. to the three-dimensional situation showing that weakly coupled bound states exist if the…
We consider a segmented structure, possibly connected with a continuous medium, as initially homogeneous, where discontinuities arise as localized strains induced by self-equilibrated localized actions. Under this formulation augmented by…
We carry out a comprehensive linear stability analysis of active Brownian particle systems around a constant homogeneous state. These scalar models, being important prototypes for the continuous description of active matter, are…
This paper addresses the asymptotic development of order 2 by the $\Gamma$ -convergence of the Cahn-Hilliard functional with Dirichlet boundary conditions. The Dirichlet data are assumed to be well separated from one of the two wells. In…