Related papers: Singularity theory and heat equation
We consider cosmological solutions of string and M-theory compactified to four dimensions by giving a general prescription to construct four-dimensional modular cosmologies with two commuting Killing vectors from vacuum solutions. By…
In this note we consider a heat trace expansion on a manifold with wedge-like singularity. We show that there are two terms in the expansion that contain information about the presence of the singularity, namely the logarithmic term…
The role of singular solutions in some simple quantum mechanical models is studied. The space of the states of two-dimensional quantum harmonic oscillator is shown to be separated into sets of states with different properties.
While not generally a conservation law, any symmetry of the equations of motion implies a useful reduction of any second-order equationto a first-order equation between invariants, whose solutions (first integrals) can then be integrated by…
We investigate uniqueness of solution to the heat equation with a density $\rho$ on complete, non-compact weighted Riemannian manifolds of infinite volume. Our main goal is to identify sufficient conditions under which the solution $u$…
In the semi-classical limit, the quantum mechanics of a stationary beam of counter-streaming relativistic electrons and ions is described by a nonlinear system of finite-temperature Thomas-Fermi equations. In the high temperature / low…
The action for a class of three-dimensional dilaton-gravity theories, with an electromagnetic Maxwell field and a cosmological constant, can be recast in a Brans-Dicke-Maxwell type action, with its free $\omega$ parameter. For a negative…
We study the De Giorgi type conjecture, that is, one dimensional symmetry problem for entire solutions of an two components elliptic system in $\mathbb{R}^n$, for all $n\geq 2$. We prove that, if a solution $(u,v)$ has a linear growth at…
Our earlier results on the temperature inversion properties and the ellipticisation of the finite temperature internal energy on odd spheres are extended to orbifold factors of odd spheres and then to other thermodynamic quantities, in…
Providing students of introductory thermal physics with a plot of the heat capacities of many low density gases as a function of temperature allows them to look for systematic trends. Specifically, large amounts of heat capacity data allow…
We investigate Gevrey order and 1-summability properties of the formal solution of a general heat equation in two variables. In particular, we give necessary and sufficient conditions for the 1-summability of the solution in a given…
We present a class of singularity free exact cosmological solutions of Einstein's equations describing a perfect fluid with heat flow. It is obtained as generalization of the Senovilla class [1] corresponding to incoherent radiation field.…
We find and analyse solutions of Einstein's equations in arbitrary d dimensions and in the presence of a scalar field with a Liouville potential coupled to a Maxwell field. We consider spacetimes of cylindrical symmetry or again subspaces…
In this work we analyze and review cosmological models in which the dynamics of a single scalar field accounts for a unified description of the Dark Matter and Dark Energy sectors, dubbed Unified Dark Matter (UDM) models. In this framework,…
We propose a method for constructing the specific heat for the universe by following standard definitions of classical thermodynamics, in a spatially flat homogeneous and isotropic spacetime. We use cosmography to represent the specific…
Inspired by quantum gravity proposal, we construct a deformed phase space which supports the UV and IR cutoffs. We show that the Liouville theorem is satisfied in the deformed phase space which allows us to formulate the thermodynamics of…
Density functional theory (DFT) has become the most popular approach to electronic structure across disciplines, especially in material and chemical sciences. Last year, at least 30,000 papers used DFT to make useful predictions or give…
We survey rigorous, formal, and numerical results on the formation of point-like singularities (or blow-up) for a wide range of evolution equations. We use a similarity transformation of the original equation with respect to the blow-up…
We study the Stokes phenomenon for the solutions of the 1-dimensional complex heat equation and its generalizations with meromorphic initial data. We use the theory of Borel summability for the description of the Stokes lines, the…
In this paper, we study the Feingold-Peres model as an example, which is a well-known paradigm of quantum chaos. Using semiclassical analysis and numerical simulations, we study the statistical properties of observables in few-body systems…