Related papers: Quantitative hydrodynamic limits of the Langevin d…
A thermodynamic analysis of weakly nonlocal non-relativistic fluids is presented under the assumption that an additional scalar field also contributes to the dynamics. The most general evolution of this field and the constitutive relations…
We study charged hydrodynamics in a periodic lattice background. Fluctuations are Bloch waves rather than single momentum Fourier modes. At boundaries of the unit cell where hydrodynamic fluctuations are formally degenerate with their…
Generalized hydrodynamics is a framework to study the large scale dynamics of integrable models, special fine-tuned one-dimensional many-body systems that possess an infinite number of local conserved quantities. Unlike classical models,…
The dynamic entropic repulsion for the Ginzburg-Landau $\nabla\phi$ interface model was discussed in [Deuschel-N. 2007] and the asymptotics of the height of the interface was identified. This paper studies a similar problem for two…
Collisionless regime kinetic models for coherent nonlinear Alfven wave dynamics are studied using fluid moment equations with an approximate closure anzatz. Resonant particle effects are modelled by incorporating an additional term…
Based on the Langevin equation of Brownian motion, we present a simple model that emulates a typical mode in incompressible magnetohydrodynamic turbulence, providing a demonstration of several key properties. The model equation is…
We study Langevin dynamics with noise projected onto the directions orthogonal to an isometric group action. This mathematical model is introduced to shed new light on the effects of symmetry on stochastic gradient descent for…
Boundary conditions for the solid-liquid interface of the solidifying pure melt have been derived. In the derivation the model of Gibbs interface is used. The boundary conditions include both the state quantities of bulk phases are taken at…
In this article we investigate hypocoercivity of Langevin-type dynamics in nonlinear smooth geometries. The main result stating exponential decay to an equilibrium state with explicitly computable rate of convergence is rooted in an…
We formulate a new theory for how caging constraints in glass-forming liquids at a surface or interface are modified and then spatially transferred, in a layer-by-layer bootstrapped manner, into the film interior in the context of the…
We study the underdamped Langevin dynamics with invariant measure $\mu(\,\mathrm{d}x\,\mathrm{d}v)\propto \mathrm{e}^{-U(x)-\lvert v\rvert^2/2}\,\mathrm{d}x\,\mathrm{d}v$. Assume that the position marginal $\mu_x(\,\mathrm{d}x)\propto…
We consider the general physical situation of a quantum system $\H_0$ interacting with a chain of exterior systems $\bigotimes_\N \H$, one after the other, during a small interval of time $h$ and following some Hamiltonian $H$ on $\H_0…
We study the dynamics of elastic interfaces-membranes-immersed in thermally excited fluids. The work contains three components: the development of a numerical method, a purely theoretical approach, and numerical simulation. In developing a…
The linearized Boltzmann equation is considered to describe small spatial perturbations of the homogeneous cooling state. The corresponding macroscopic balance equations for the density, temperature, and flow velocity are derived from it as…
The Lagrangian-Averaged Navier-Stokes-$\alpha$ (LANS-$\alpha$) model, a turbulence closure scheme based on energy-conserving modifications to nonlinear advection, can produce more energetic simulations than standard models, leading to…
The propagation of water waves of finite depth and flat bottom is studied in the case when the depth is not small in comparison to the wavelength. This propagation regime is complementary to the long-wave regime described by the famous KdV…
The discrete Boltzmann equation for both the ideal and a non-ideal fluid is extended by adding Langevin noise terms in order to incorporate the effects of thermal fluctuations. After casting the fluctuating discrete Boltzmann equation in a…
Hydrodynamic interactions between particles confined in a liquid-filled linear channel are known to be screened beyond a distance comparable to the channel width. Using a simple analytical theory and lattice-Boltzmann simulations, we show…
A new phase field model is introduced, which can be viewed as nontrivial generalisation of what is known as the Caginalp model. It involves in particular nonlinear diffusion terms. By formal asymptotic analysis, it is shown that in the…
For a class of interacting particle systems in continuous space, we show that finite-volume approximations of the bulk diffusion matrix converge at an algebraic rate. The models we consider are reversible with respect to the Poisson…