Related papers: Cost of diffusion: nonlinearity and giant fluctuat…
A vibrational model of transport properties of dense fluids assumes that solid-like oscillations of atoms around their temporary equilibrium positions dominate the dynamical picture. The temporary equilibrium positions of atoms do not form…
We present a perturbation theory by extending a prescription due to Feynman for computing the probability density function for the random flight motion. The method can be applied to a wide variety of otherwise difficult circumstances. The…
The bulk nuclear matter produced in heavy ion collisions carries a multitude of conserved quantum numbers: electric charge, baryon number, and strangeness. Therefore, the diffusion processes associated to these conserved charges cannot…
We describe stochastic calculus in the context of processes that are driven by an adapted point process of locally finite intensity and are differentiable between jumps. This includes Markov chains as well as non-Markov processes. By…
In a growing number of strongly disordered and dense systems, the dynamics of a particle pulled by an external force field exhibits super-diffusion. In the context of glass forming systems, super cooled glasses and contamination spreading…
We introduce novel finite element schemes for curve diffusion and elastic flow in arbitrary codimension. The schemes are based on a variational form of a system that includes a specifically chosen tangential motion. We derive optimal $L^2$-…
Current fluctuations in boundary-driven diffusive systems are, in many cases, studied using hydrodynamic theories. Their predictions are then expected to be valid for currents which scale inversely with the system size. To study this…
Recent studies have shown that in the presence of noise both fronts propagating into a metastable state and so-called pushed fronts propagating into an unstable state, exhibit diffusive wandering about the average position. In this paper we…
Point processes often have a natural interpretation with respect to a continuous process. We propose a point process construction that describes arrival time observations in terms of the state of a latent diffusion process. In this…
In this article, we consider a jump diffusion process (X_t), with drift function b, diffusion coefficient sigma and jump coefficient xi^{2}. This process is observed at discrete times t=0,Delta,...,nDelta. The sampling interval Delta tends…
We investigate the long time behavior of a passive particle evolving in a one-dimensional diffusive random environment, with diffusion constant $D$. We consider two cases: (a) The particle is pulled forward by a small external constant…
Motivated by networked systems, stochastic control, optimization, and a wide variety of applications, this work is devoted to systems of switching jump diffusions. Treating such nonlinear systems, we focus on stability issues. First…
We consider fluctuations of the dissipated energy in nonlinear driven diffusive systems subject to bulk dissipation and boundary driving. With this aim, we extend the recently-introduced macroscopic fluctuation theory to nonlinear driven…
An extension of fluctuation-dissipation theorem is used to derive a "speed limit" theorem for nonlinear electronic devices. This speed limit provides a lower bound on the dissipation that is incurred when transferring a given amount of…
Recent experimental and theoretical works have shown that giant fluctuations are present during diffusion in liquid systems. We use linearized fluctuating hydrodynamics to calculate the net mass transfer due to these non equilibrium…
We consider a tracer particle performing a random walk on a two-dimensional lattice in the presence of immobile hard obstacles. Starting from equilibrium, a constant force pulling on the particle is switched on, driving the system to a new…
We study the motion of a particle sliding under the action of an external field on a stochastically fluctuating one-dimensional Edwards-Wilkinson surface. Numerical simulations using the single-step model shows that the mean-square…
It is a well known fact that local scale invariance plays a fundamental role in the theory of derivative pricing. Specific applications of this principle have been used quite often under the name of `change of numeraire', but in recent work…
Random walk has wide applications in many fields, such as machine learning, biology, physics, and chemistry. Random walk can be discrete or continuous in time and space. Asymmetric random walk could be described by drift-diffusion equation.…
A diffusion process for charge distributions in a phase space is examined. The corresponding charge moves in a force field and under an action of a random field. There are the diffusion motions for coordinates and for momenta. In our model,…