相关论文: Sharp moment and upper tail asymptotics for the cr…

We consider the supercritical bond percolation on $\mathbb Z^d$ and study the graph distance on the percolation graph called the chemical distance. It is well-known that there exists a deterministic constant $\mu(x)$ such that the chemical…

The motion of rarefied gases for uniform shear flow at the kinetic level is governed by the spatially homogeneous Boltzmann equation with a deformation force. In the paper we study the corresponding Cauchy problem with initial data of…

We consider the energy supercritical harmonic heat flow from $\mathbb{R}^d$ into the $d$-sphere $\mathbb{S}^d$ with $d \geq 7$. Under an additional assumption of 1-corotational symmetry, the problem reduces to the one dimensional semilinear…

We establish sharp upper and lower bounds of Gaussian type for the heat kernel in the metric measure space satisfying $\RCD(0,N)$ ( equivalently, $\RCD^\ast(0,N)$) condition with $N\in \mathbb{N}\setminus\{1\}$ and having maximum volume…

On doubling metric measure spaces endowed with a strongly local regular Dirichlet form, we show some characterisations of pointwise upper bounds of the heat kernel in terms of global scale-invariant inequalities that correspond respectively…

We consider the $(1+1)$-dimensional stochastic heat equation (SHE) with multiplicative white noise and the Cole-Hopf solution of the Kardar-Parisi-Zhang (KPZ) equation. We show an exact way of computing the Lyapunov exponents of the SHE for…

Let $(E, \| \cdot\|)$ be a Banach space such that, for some $q\geq 2$, the function $x\mapsto \|x\|^q$ is of $C^2$ class and its first and second Fr\'{e}chet derivatives are bounded by some constant multiples of $(q-1)$-th power of the norm…

Continuing our investigation into the numerical properties of the Hierarchical Reference Theory, we study the square well fluid of range lambda from slightly above unity up to 3.6. After briefly touching upon the core condition and the…

An exhaustive numerical investigation of the growth of magnetic films in confined $(d+1)$-dimensional stripped geometries ($d=1,2$) is carried out by means of extensive Monte Carlo simulations. Thin films in contact with a thermal bath are…

The Su-Schrieffer-Heeger (SSH) model perhaps is the easiest and the most basic model for topological excitations. Many variations and extensions of the SSH model have been proposed and explored to better understand both fundamental and…

This paper concerns the time growth of the highest-order energy of the systems of incompressible isotropic elastodynamics in two space dimensions. The global well-posedness of smooth solutions near equilibrium was first obtained by Lei [31]…

Part II of the present work concerns modeling and analyzing the experimental data obtained in Part I. A computational fluid dynamics (CFD) model of two-dimensional conductive heat transfer and thermocapillary-driven convection is developed.…

Specific heat measurements from 2 to 300 K of hydrogenated amorphous silicon prepared by hot-wire chemical vapor deposition show a large excess specific heat at low temperature, significantly larger than the Debye specific heat calculated…

We consider the stochastic evolution of a 1+1-dimensional interface (or polymer) in presence of a substrate. This stochastic process is a dynamical version of the homogeneous pinning model. We start from a configuration far from…

A particle-hole symmetry protected 2D non-Hermitian Su-Schrieffer-Heeger (SSH) model is investigated. This version differs from the usual Hermitian version by the inclusion of gain and/or loss terms which are represented by complex on-site…

We consider fractional stochastic heat equations of the form $\frac{\partial u_t(x)}{\partial t} = -(-\Delta)^{\alpha/2} u_t(x)+\lambda \sigma (u_t(x)) \dot F(t,\, x)$. Here $\dot F$ denotes the noise term. Under suitable assumptions, we…

The possibility of superconductivity (SC) in the 2D Hubbard model (2DH) was investigated by means of the variational Monte Carlo method. The energy gain of the d-wave SC state, obtained as the difference of the minimum energy with a finite…

In this paper, we study the spatially homogeneous inelastic Boltzmann equation for the angular cutoff pseudo-Maxwell molecules with an additional term of linear deformation. We establish the existence of non-Maxwellian self-similar profiles…

We consider a completely resonant nonlinear Schr\"odinger equation on the $d$-dimensional torus, for any $d\geq 1$, with polynomial nonlinearity of any degree $2p+1$, $p\geq1$, which is gauge and translation invariant. We study the…

We present results about large deviations and laws of large numbers for various polymer related quantities. In a completely general setting and strictly positive temperature, we present results about large deviations for directed polymers…