相关论文: Continuum polymer measures corresponding to the cr…
In dimension $d \geq 3$, the directed polymer in a random medium undergoes a phase transition between a free phase and a disorder dominated phase. For the latter, Fisher and Huse have proposed a droplet theory based on the scaling of the…
The cumulants of thermal variables are of general interest in physics due to their extensivity and their correspondence with susceptibilities. They become especially significant near critical points of phase transitions where they diverge…
The statistical mechanics of directed line-like objects, such as directed polymers in an external field, strands of dipoles in both ferro- and electrorheological fluids, and flux lines in high-$T_{\tiny C}$ superconductors bears a close…
The asymptotic behavior of solutions of two dimensional stochastic convective Brinkman-Forchheimer (2D SCBF) equations in unbounded domains is discussed in this work (for example, Poincar\'e domains). We first prove the existence of…
In fluid dynamical simulations in astrophysics, large deformations are common and surface tracking is sometimes necessary. Smoothed Particle Hydrodynamics (SPH) method has been used in many of such simulations. Recently, however, it has…
We give a new proof of the fact that the solutions of the stochastic heat equation, started with non-negative initial conditions, are strictly positive at positive times. The proof uses concentration of measure arguments for discrete…
We consider disordered systems of directed polymer type, for which disorder is so-called marginally relevant. These include the usual (short-range) directed polymer model in dimension (2+1), the long-range directed polymer model with Cauchy…
A polymer-chain network is a collection of interconnected polymer-chains, made themselves of the repetition of a single pattern called a monomer. Our first main result establishes that, for a class of models for polymer-chain networks, the…
This paper provides a systematic investigation of the mathematical structure of path measures and their profound connections to stochastic differential equations (SDEs) through the framework of second-order Hamilton--Jacobi (HJ) equations.…
In finite-dimensional dynamical systems, stochastic stability provides the selection of physical relevant measures from the myriad invariant measures of conservative systems. That this might also apply to infinite-dimensional systems is the…
Describing the dynamics and thermodynamics of amorphous materials near the glass transition is a major challenge in soft-matter physics and polymer engineering. Here, we show that the dependence of the dielectric alpha-relaxation time on…
This paper presents simulations of the 2d model developed by Poth\'erat at al (\emph{J. Fluid Mech}, 2000) for MHD flows between two planes with a strong transverse homogeneous and steady magnetic field, accounting for moderate inertial…
Second-order phase field models have emerged as an attractive option for capturing the advection of interfaces in two-phase flows. Prior to these, state-of-the-art models based on the Cahn-Hilliard equation, which is a fourth-order…
We compute the limit of the moments of the partition function $Z_{N}^{\beta_N} $ of the directed polymer in dimension $d=2$ in the subcritical regime, i.e. when the inverse temperature is scaled as $\beta_N \sim \hat{\beta}…
Starting from our previous work where we have obtained a system of coupled integro-differential equations for acoustic sound waves and phonon density fluctuations in 2D crystals, we derive here the corresponding hydrodynamic equations and…
We provide a moment map interpretation for the coupled K\"ahler-Einstein equations introduced by Hultgren and Witt Nystr\"om, and in the process introduce a more general system of equations, which we call coupled cscK equations. A…
A simple vibrational model of heat transfer in two-dimensional (2D) fluids relates the heat conductivity coefficient to the longitudinal and transverse sound velocities, specific heat, and the mean interatomic separation. This model is…
We consider the numerical approximation of single phase flow in porous media by a mixed finite element method with mass lumping. Our work extends previous results of Wheeler and Yotov, who showed that mass lumping together with an…
For decades, uncertainty quantification techniques based on the spectral approach have been demonstrated to be computationally more efficient than the Monte Carlo method for a wide variety of problems, particularly when the dimensionality…
We investigate a chain of oscillators with anharmonic on-site potentials, with long range interparticle interactions, and coupled both to external and internal stochastic thermal reservoirs of Ornstein-Uhlenbeck type. We develop an integral…