Related papers: Calculation of Dynamical Response Functions Using …
In this expository note we highlight the correlation function method as a unified approach in proving both hydrodynamic limits and fluctuation limits for reaction diffusion particle systems. For simplicity we focus on the case when the…
The aim of this review is to provide a concise overview of some of the generic approaches that have been developed to deal with the statistical description of large systems of interacting dissipative 'units'. The latter notion includes,…
Stochastic line integrals provide a useful tool for quantitatively characterizing irreversibility and detailed balance violation in noise-driven dynamical systems. A particular realization is the stochastic area, recently studied in coupled…
In this work, we consider systems that are subjected to intermittent instabilities due to external stochastic excitation. These intermittent instabilities, though rare, have a large impact on the probabilistic response of the system and…
Using Mathematica 3.0, the Schroedinger equation for bound states is solved. The method of solution is based on a numerical integration procedure together with convexity arguments and the nodal theorem for wave functions. The interaction…
In this paper we study a Markovian two-dimensional bounded-variation stochastic control problem whose state process consists of a diffusive mean-reverting component and of a purely controlled one. The main problem's characteristic lies in…
Returning a system to a desired state under a force field involves a thermodynamic cost, i.e., {\it work}. This cost fluctuates for a small-scale system from one experimental realization to another. We introduce a general framework to…
We present a general setting in which the formula describing the linear response of the physical measure of a perturbed system can be obtained. In this general setting we obtain an algorithm to rigorously compute the linear response. We…
In this work we study the dynamic behaviour of compound shells of revolution partially filled with an ideal incompressible fluid based on boundary-value problems. New analytical mathematical model with corresponding discrete scheme for the…
In order to understand the impact of random influences at physical boundary on the evolution of multiscale systems, a stochastic partial differential equation model under a fast random dynamical boundary condition is investigated. The…
We introduce the model of inelastic hard spheres with random restitution coefficient $\alpha$, in order to account for the fact that, in a vertically shaken granular system interacting elastically with the vibrating boundary, the energy…
Linearizing the appropriate kinetic equation we derive general response functions including selfconsistent mean fields or density functionals and collisional dissipative contributions. The latter ones are considered in relaxation time…
We study the well-posedness of a nonlinear reaction diffusion partial differential equation system on the half-line coupled with a stochastic dynamical boundary condition, a random system arising from the description of the chemical…
An accurate force calculation with the Poisson-Boltzmann equation is challenging, as it requires the electric field on the molecular surface. Here, we present a calculation of the electric field on the solute-solvent interface that is exact…
Traditional models of wormlike chains in shear flows at finite temperature approximate the equation of motion via finite difference discretization (bead and rod models). We introduce here a new method based on a spectral representation in…
The solution of a (stochastic) differential equation can be locally approximated by a (stochastic) expansion. If the vector field of the differential equation is a polynomial, the corresponding expansion is a linear combination of iterated…
In this paper we present a fully deterministic method for the numerical solution to the Boltzmann equation of rarefied gas dynamics in a bounded domain for multi-scale problems. Periodic, specular reflection and diffusive boundary…
Recently, the problem of boundary stabilization and estimation for unstable linear constant-coefficient reaction-diffusion equation on n-balls (in particular, disks and spheres) has been solved by means of the backstepping method. However,…
The unique fluctuation-dissipation theorem for equilibrium stands in contrast with the wide variety of nonequilibrium linear response formulae. Their most traditional approach is "analytic", which, in the absence of detailed balance,…
In the presence of multiscale dynamics in a reaction network, direct simulation methods become inefficient as they can only advance the system on the smallest scale. This work presents stochastic averaging techniques to accelerate…