Related papers: Stochastic Turing pattern formation in a model wit…
In this work we investigate the effect of density dependent nonlinear diffusion on pattern formation in the Brusselator system. Through linear stability analysis of the basic solution we determine the Turing and the oscillatory instability…
We study the impact of stochastic perturbations to deterministic dynamical systems using the formalism of the Ruelle response theory and explore how stochastic noise can be used to explore the properties of the underlying deterministic…
In this paper, we study a stochastically driven non-equilibrium quantum system where the driving protocols consist of hopping and waiting processes. The waiting times between two hopping processes satisfy a heavy-tailed distribution. By…
We consider reaction-diffusion equations that are stochastically forced by a small multiplicative noise term. We show that spectrally stable travelling wave solutions to the deterministic system retain their orbital stability if the…
A method is developed to estimate the properties of a global hydrodynamic instability in turbulent flows from measurement data of the limit-cycle oscillations. For this purpose, the flow dynamics are separated in deterministic contributions…
We study the dynamics of covariances in a chain of harmonic oscillators with conservative noise in contact with two stochastic Langevin heat baths. The noise amounts to random collisions between nearest-neighbour oscillators that exchange…
The purpose of this paper is to examine the Lagrangian stochastic modeling of the fluid velocity seen by inertial particles in a nonhomogeneous turbulent flow. A new Langevin-type model, compatible with the transport equation of the drift…
A coupled system of nonlinear mixed-type equations modeling early stages of angiogenesis is analyzed in a bounded domain. The system consists of stochastic differential equations describing the movement of the positions of the tip and stalk…
We investigate a stochastic version of a simple enzymatic reaction which follows the generic Michaelis-Menten kinetics. At sufficiently high concentrations of reacting species, the molecular fluctuations can be approximated as a realization…
For a wide class of stochastic athermal systems, we derive Langevin-like equations driven by non-Gaussian noise, starting from master equations and developing a new asymptotic expansion. We found an explicit condition whereby the…
Macroscopic traffic flow is stochastic, but the physics-informed deep learning methods currently used in transportation literature embed deterministic PDEs and produce point-valued outputs; the stochasticity of the governing dynamics plays…
We analyze diffusion-driven (Turing) instability of a reaction-diffusion system. The innovation is that we replace the traditional Laplacian diffusion operator with a combination of the fourth order bi-Laplacian operator and the second…
Stochastic differential equations of Langevin-diffusion form have received significant attention, thanks to their foundational role in both Bayesian sampling algorithms and optimization in machine learning. In the latter, they serve as a…
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…
We present a new time-dependent Density Functional approach to study the relaxational dynamics of an assembly of interacting particles subject to thermal noise. Starting from the Langevin stochastic equations of motion for the velocities of…
This work presents algebraic closure models associated with advective transport and nonlinear reactions in a Reynolds-averaged Navier-Stokes context for a system of species subject to binary reactions and transport by advection and…
This study delves into the connection between machine learning and lattice field theory by linking generative diffusion models (DMs) with stochastic quantization, from a stochastic differential equation perspective. We show that DMs can be…
We consider a two dimensional Turing like system with two diffusing species which interact with each other. Considering the species to be charged, we include the effect of an electric field along a given direction which can lead to a drift…
We investigate Turing pattern formation in a stochastic reaction-diffusion model defined on $N$ lattice sites, where each lattice site is associated with a reaction vessel of volume $\Omega$. We focus on a regime where spatial discreteness…
This paper studies a stochastic model that describes the evolution of vehicle densities in a road network. It is consistent with the class of (deterministic) kinematic wave models, which describe traffic flows on the basis of conservation…