Related papers: Heat trace asymptotics for wedge-like singularity

A computer aided high temperature expansion of the magnetic susceptibility and the magnetic specific heat is presented and demonstrated for frustrated and unfrustrated spin chains. The results are analytic in nature since the calculations…

We examine the local super trace asymptotics for the de Rham complex defined by an arbitrary super connection on the exterior algebra. We show, in contrast to the situation in which the connection in question is the Levi-Civita connection,…

The paper (in French) exemplifies graphically a solution of the heat equation which is a 1-dimensional unfolding of an elliptic umbilic catastrophe. The example is due to James Damon and adapts Thom-Mather's singularity theory to multiscale…

We consider the Casimir-Helmholtz free energy at nonzero temperature $T$ for a circular cylinder and perfectly conducting wedge closed by a cylindrical arc, either perfectly conducting or isorefractive. The energy expression at nonzero…

Let $\mathcal{M}$ be a smooth, closed and connected manifold of dimension $n\in\mathbb{N}$, endowed with a Riemannian metric $g$. Moreover, let $\mathcal{B}$ be an $(n+1)$-dimensional compact manifold with boundary equal to $\mathcal{M}$.…

The singularities prevalent in classical thermodynamics largely stem from the "postulate of equal a priori probabilities" neglecting the physical constraints imposed by computational complexity. This paper introduces Complexity Window…

We present an interpolation method for the specific heat $c_v(T)$, when there is a phase transition with a logarithmic singularity in $c_v$ at a critical temperature $T=T_c$. The method uses the fact that $c_v$ is constrained both by its…

In this paper, we study the heat equation with an irregular spatially dependent thermal conductivity coefficient. We prove that it has a solution in an appropriate very weak sense. Moreover, the uniqueness result and consistency with the…

We study the asymptotic behavior of the heat trace coefficients $a_n$ as n tends to infinity for the scalar Laplacian in the context of locally symmetric spaces. We show that if the Plancherel measure of a noncompact type symmetric space is…

We investigate the heat flow in an open, bounded set $D$ in $\mathbb{R}^2$ with polygonal boundary $\partial D$. We suppose that $D$ contains an open, bounded set $\widetilde{D}$ with polygonal boundary $\partial \widetilde{D}$. The initial…

The heat kernel expansion for a general non--minimal operator on the spaces $C^\infty (\Lambda^k)$ and $C^\infty (\Lambda^{p,q})$ is studied. The coefficients of the heat kernel asymptotics for this operator are expressed in terms of the…

We establish the asymptotics of blowup for nonlinear heat equations with superlinear power nonlinearities in arbitrary dimensions and we estimate the remainders.

We examine the derived heat trace asymptotics in both the real and the complex settings for a generalized Witten perturbation. If the dimension is even, in the real context we show the integral of the local density for the derived heat…

Let $G$ be a connected, real, semisimple Lie group with finite center, and $K$ a maximal compact subgroup of $G$. In this paper, we derive $K$-equivariant asymptotics for heat traces with remainder estimates on compact Riemannian manifolds…

For a pseudodifferential boundary operator A of integer order \nu and class zero (in the Boutet de Monvel calculus) on a compact n-dimensional manifold with boundary, we consider the function Trace(AB^{-s}) where B is an auxiliary system…

We report new results on complex-temperature properties of Ising models. These include studies of the $s=1/2$ model on triangular, honeycomb, kagom\'e, $3 \cdot 12^2$, and $4 \cdot 8^2$ lattices. We elucidate the complex--$T$ phase diagrams…

An updated review [1] of nonextensive statistical mechanics and thermodynamics is colloquially presented. Quite naturally the possibility emerges for using the value of q-1 (entropic nonextensivity) as a simple and efficient manner to…

We give a short proof of a strong version of the short time asymptotic expansion of heat kernels associated to Laplace type operators acting on sections of vector bundles over compact Riemannian manifolds, including exponential decay of the…

In this paper, we extend the results of [1] by proving exponential asymptotic $H^1$-convergence of solutions to a one-dimensional singular heat equation with $L^2$-source term that describe evolution of viscous thin liquid sheets while…

In the present paper, we study a model of a thermoelastic string that is initially heated. We classify all the possible asymptotic states when time tends to infinity of such a model. Actually, we show that whatever the initial data is, a…