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Generalized Langevin dynamics (GLD) arise in the modeling of a number of systems, ranging from structured fluids that exhibit a viscoelastic mechanical response, to biological systems, and other media that exhibit anomalous diffusive…
For a model nonlinear dynamical system, we show how one may obtain its bifurcation behavior by introducing noise into the dynamics and then studying the resulting Langevin dynamics in the weak-noise limit. A suitable quantity to capture the…
The modelling of symmetric rigid dumbbell particles suspended in a Newtonian fluid, as a model of a rigid-rod polymeric solution, has been accomplished exclusively through the diffusion equation, which has been detailed elegantly by Bird et…
The friction coefficient of a particle can depend on its position as it does when the particle is near a wall. We formulate the dynamics of particles with such state-dependent friction coefficients in terms of a general Langevin equation…
Generalized Langevin equation for characteristic functional of many-electron system dynamically interacting with a thermostat and besides subjected to external perturbation and observation is derived and formulated in terms of one-particle…
The Langevin formulation of a number of well-known stochastic processes involves multiplicative noise. In this work we present a systematic mapping of a process with multiplicative noise to a related process with additive noise, which may…
We study the convergence to equilibrium of an underdamped Langevin equation that is controlled by a linear feedback force. Specifically, we are interested in sampling the possibly multimodal invariant probability distribution of a Langevin…
We show the relation between processes which are modeled by a Langevin equation with multiplicative noise and infinite ergodic theory. We concentrate on a spatially dependent diffusion coefficient that behaves as ${D(x)}\sim…
We study the effects of noise on stationary pulse solutions (bumps) in spatially extended neural fields. The dynamics of a neural field is described by an integrodifferential equation whose integral term characterizes synaptic interactions…
Many complex systems are described by Langevin-type equations in which the noise exhibits long-range correlations and couples to the system in a state-dependent, multiplicative manner, leading to heterogeneous non-Markovian diffusion. Here,…
The diffusion of colloids inside an active system-e.g. within a living cell or the dynamics of active particles itself (e.g. self-propelled particles) can be modeled through overdamped Langevin equation which contains an additional noise…
We study the stochastic dynamics of a two-dimensional magnetic moment embedded in a three-dimensional environment, described by means of the stochastic Landau-Lifshitz-Gilbert (sLLG) equation. We define a covariant generalization of this…
Stochastic fluid dynamics governs the long time tails of hydrodynamic correlation functions, and the critical slowing down of relaxation phenomena in the vicinity of a critical point in the phase diagram. In this work we study the role of…
The ad-atom dynamic equation, a Langevin type equation is analyzed and solved using some non-linear analytical and numerical tools. We noticeably show that the effect of the surface acoustic wave is to induce an effective potential that…
We review equilibrium properties for the dynamics of a single particle evolving in a visco--elastic medium under the effect of hydrodynamic backflow which includes added mass and Basset force. Arbitrary equilibrium forces acting upon the…
We investigate modifications of a stochastic polymer picture through a shift in the boundary between the system and an external environment. A conventional bead-and-spring model serving as the coarse-graining model is given by the Langevin…
Electronic friction and Langevin dynamics is a popular mixed quantum-classical method for simulating the nonadiabatic dynamics of molecules interacting with metal surfaces, as it can be computationally more efficient than fully quantum…
We develop a general approach for studying the cumulative probability distribution function of localized objects (particles) whose dynamics is governed by the first-order Langevin equation driven by superheavy-tailed noise. Solving the…
We study a stochastic nonlocal PDE, arising in the context of modelling spatially distributed neural activity, which is capable of sustaining stationary and moving spatially-localized ``activity bumps''. This system is known to undergo a…
We present a path integral formalism to compute potentials for nonequilibrium steady states, reached by a multiplicative stochastic dynamics. We develop a weak-noise expansion, which allows the explicit evaluation of the potential in…