相关论文: The one-dimensional equilibrium shape of a crystal
This paper discusses an ordinary homogeneous differential equation of the second order with constant real-valued coefficients. The solution of this equation has to satisfy additional conditions. The first of the conditions stems from the…
We consider the equilibria of point particles under the action of two body central forces in which there are both repulsive and attractive interactions, often known as central configurations, with diverse applications in physics, in…
We review the circumstances under which test particles can be localized around a spacetime section \Sigma_0 smoothly contained within a codimension-1 embedding space M. If such a confinement is possible, \Sigma_0 is said to be totally…
The low-temperature phase diagram of parahydrogen in one dimension is studied by quantum Monte Carlo simulations, whose results are interpreted within the framework of Luttinger liquid theory. We show that, contrary to what was claimed in a…
The classical one-phase Stefan problem (without surface tension) allows for a continuum of steady state solutions, given by an arbitrary (but sufficiently smooth) domain together with zero temperature. We prove global-in-time stability of…
In this paper we prove that solutions to several shape optimization problems in the plane, with a convexity constraint on the admissible domains, are polygons. The main terms of the shape functionals we consider are either E f ($\Omega$),…
A novel approach is introduced to a very widely occurring problem, providing a complete, explicit resolution of it: minimisation of a convex quadratic under a general quadratic, equality or inequality, constraint. Completeness comes via…
Symmetry equations are obtained for the rigidity matrices associated with various forms of infinitesimal flexibility for an idealised bond-node crystal framework $\C$ in $\bR^d$. These equations are used to derive symmetry-adapted…
There is increasing evidence that the universe may have a small cosmological constant. We suggest a scheme for naturally generating a small cosmological constant. Our idea requires the presence of a discrete accidental symmetry which is…
We analyze the d-dimensional Blume-Emery-Griffiths model in the disordered region of parameters and we show that its free energy can be explicitly written in term of a series which is absolutely convergent at any temperature in an unbounded…
We deduce Levinson\'{}s theorem in non-relativistic quantum mechanics in one dimension as a sum rule for the spectral density constructed from asymptotic data. We assume a self-adjoint hamiltonian which guarantees completeness; the…
Equilibrium mapping techniques for nonaligning self-propelled particles have made it possible to predict the density profile of an active ideal gas in a wide variety of external potentials, however they fail when the self-propulsion is very…
The macroscopic properties of compact stars in modified gravity theories can be significantly different from the general relativistic (GR) predictions. Within the gravitational context of scalar-tensor theories, with a scalar field $\phi$…
Out of equilibrium states in glasses and crystals have been a major topic of research in condensed-matter physics for many years, and the idea of time crystals has triggered a flurry of new research. Here, we provide the first description…
In dimensions one to three, the fundamental solution to the free wave equation is positive. Therefore, there exists a simple positivity criterion for solutions. We use this to obtain large global solutions to two well-studied…
Let $g$ be a locally Lipschitz continuous real valued function which satisfies the Keller-Osserman condition and is convex at infinity, then any large solution of $-\Delta u+g(u)=0$ in a ball is radially symmetric.
A one-dimensional long-range model of classical rotators with an extended degree of complexity, as compared to paradigmatic long-range systems, is introduced and studied. Working at constant density, in the thermodynamic limit one can prove…
The aim of this chapter is to present an introduction and also an overview of some of the most relevant results concerning positivity energy theorems in General Relativity. These theorems provide the answer to a long standing problem that…
A technique to reconstruct one-dimensional, reflectionless potentials and the associated quantum wave functions starting from a finite number of known energy spectra is discussed. The method is demonstrated using spectra that scale like the…
This article presents some qualitative results for entire solutions of the fully nonlinear elliptic equations of Allen Cahn type . Precisely under some additional assumptions on the forcing term, if the solution is bounded and converges…