Related papers: Stochastic heat flow by moments
Simulations of strongly stratified turbulence often exhibit coherent large-scale structures called vertically sheared horizontal flows (VSHFs). VSHFs emerge in both two-dimensional (2D) and three-dimensional (3D) stratified turbulence with…
We prove the hydrodynamic limit for a one-dimensional harmonic chain of interacting atoms with a random flip of the momentum sign. The system is open: at the left boundary it is attached to a heat bath at temperature $T_-$, while at the…
The scaling laws which relate the peak temperature $T_M$ and volumetric heating rate $E_H$ to the pressure $P$ and length $L$ for static coronal loops were established over 40 years ago; they have proved to be of immense value in a wide…
We consider a family of nonlinear stochastic heat equations of the form $\partial_t u=\mathcal{L}u + \sigma(u)\dot{W}$, where $\dot{W}$ denotes space-time white noise, $\mathcal{L}$ the generator of a symmetric L\'evy process on $\R$, and…
A Cahn-Hilliard equation with stochastic multiplicative noise and a random convection term is considered. The model describes isothermal phase-separation occurring in a moving fluid, and accounts for the randomness appearing at the…
Self-consistent field theory (SCFT) is one of the most widely-used framework in studying the equilibrium phase behaviors of inhomogenous polymers. For liquid crystalline polymeric systems, the main numerical challenges of solving SCFT…
Superfluid helium-4 (He II) is a widely adopted coolant in scientific and engineering applications owing to its exceptional heat transfer capabilities. However, boiling can spontaneously occur on a heating surface in He II when the heat…
The solution of Kardar-Parisi-Zhang equation (KPZ equation) is solved formally via Cole-Hopf transformation $h=\log u$, where $u$ is the solution of multiplicative stochastic heat equation(SHE). In earlier works by Chatterjee and Dunlap,…
The Smoothed Particle Hydrodynamics (SPH) is a particle-based, Lagrangian method for fluid-flow simulations. In this work, fundamental concepts of this method are first briefly recalled. Then, the ability to accurately model granular…
We explore the small mass limit of a stochastic wave equation (SWE) driven by cylindrical $\alpha$-stable noise, where $\alpha\in (1,2)$, and prove that it converges to a stochastic heat equation. We establish its well-posedness, and in…
Generalizing an idea of Davie and Gaines (2001), we present a method for the simulation of fully discrete samples of the solution to the stochastic heat equation on an interval. We provide a condition for the validity of the approximation,…
We consider a porous mediaum flow in which the gas is initially distributed in the exterior of an empty region (a hole) and study the final stage of the hole-filling process. Hole-filling is asymptotically described by a self-similar…
A fluid flow is described by fictitious particles hopping on homogeneously distributed nodes with a given finite set of discrete velocities. We emphasize that the existence of a fictitious particle having a discrete velocity among the set…
Quantum-Induced Stochastic Dynamics arises from the coupling between a classical system and a quantum environment. Unlike standard thermal reservoirs, this environment acts as a dynamic bath, capable of simultaneously exchanging heat and…
There have been many attempts to derive continuum models for dense granular flow, but a general theory is still lacking. Here, we start with Mohr-Coulomb plasticity for quasi-2D granular materials to calculate (average) stresses and slip…
We study the stochastic heat equation (SHE) $\partial_t u = \frac12 \Delta u + \beta u \xi$ driven by a multiplicative L\'evy noise $\xi$ with positive jumps and amplitude $\beta>0$, in arbitrary dimension $d\geq 1$. We prove the existence…
The long time dynamics of large particles trapped in two inhomogeneous turbulent shear flows is studied experimentally. Both flows present a common feature, a shear region that separates two colliding circulations, but with different…
In the steady Couette flow of a granular gas the sign of the heat flux gradient is governed by the competition between viscous heating and inelastic cooling. We show from the Boltzmann equation for inelastic Maxwell particles that a special…
This study presents a probabilistic surrogate model for localized wildfire spread based on a conditional flow matching algorithm. The approach models fire progression as a stochastic process by learning the conditional distribution of fire…
Currently existing energy-stable parametric finite element methods for surface diffusion flow and other flows are usually limited to first-order accuracy in time. Designing a high-order algorithm for geometric flows that can also be…