相关论文: Rectifiability of entropy defect measures in a mic…

In this paper we establish asymptotic results for Christoffel functions with respect to measures supported on Jordan curves having a Radon-Nikodym derivative with a jump singularity. We extend the results known for measures supported in the…

Magnetic impurities coupled to both fermionic and bosonic baths or to a fermionic bath with pseudogap density of states, described by the Fermi-Bose Kondo and pseudogap Kondo models, display non-trivial intermediate coupling fixed points…

The notion of metric entropy dimension is introduced to measure the complexity of entropy zero dynamical systems. For measure preserving systems, we define entropy dimension via the dimension of entropy generating sequences. This…

In this work, we investigate the thermal properties of black holes using a new class of generalized entropy functions [K. Ourabah, Class. Quantum Grav., 41, 015010 (2024)]. At the fundamental level, these entropic forms are associated with…

We obtain new entropy rigidity results for $u$-Gibbs measures by showing that whenever a $u$-Gibbs measure of a partially hyperbolic diffeomorphism admits an unstable Margulis family, the unstable Jacobian data of the system must to be…

We introduce a notion of a point-wise entropy of measures (i.e local entropy) called neutralized local entropy, and compare it with the Brin-Katok local entropy. We show that the neutralized local entropy coincides with Brin-Katok local…

This paper investigates an elliptic MEMS-Type equation with Henon and external pressure terms: Delta u = lambda|x|^alpha / u^p + F for x in R^N \ {0}, with u(0)=0 and u>0 for x in R^N \ {0}, where N >= 1, lambda > 0, p > 0, alpha > -2 and F…

We consider the asymptotic behavior of compressible isentropic flow when the initial mass is finite, which is modeled by the compressible Euler equation with frictional damping. It is shown in \cite{HUA} (resp.\cite{GEN}) that any…

An adaptive finite element method is presented for the elastic scattering of a time-harmonic plane wave by a periodic surface. First, the unbounded physical domain is truncated into a bounded computational domain by introducing the…

Temperature dependencies of the impurity magnetic susceptibility, entropy, and heat capacity have been obtained by the method of numerical renormalization group and exact diagonalization for the Kondo model with peaks in the electron…

We consider a constrained minimal energy problem with an external field over noncompact classes of infinite dimensional vector measures on a locally compact space. The components are positive measures (charges) that are constrained from…

In this dissertation, we prove a number of results regarding the conformal method of finding solutions to the Einstein constraint equations. These results include necessary and sufficient conditions for the Lichnerowicz equation to have…

While there are numerous results on minimizers or stable solutions of the Bernoulli problem proving regularity of the free boundary and analyzing singularities, much less in known about critical points of the corresponding energy. Saddle…

We investigate the relaxation problem for the one-dimensional pressureless Euler--Poisson equations with the initial density being a finite Radon measure. The entropy solution of this linearly degenerate hyperbolic system converges to the…

Let $\mu>0$ be a fixed constant, and we prove that minimizers to the following energy functional \begin{align*} E_f(u,\Omega):=\int_{\Omega}|\nabla u|^2+\mu P(\Omega) \end{align*}exist among pairs $(\Omega,u)$ such that $\Omega$ is an…

This work demonstrates that repeated weak measurements together with post-selection can produce sharp dynamical discontinuities in meter observables, even in minimal quantum systems. The discontinuous behavior is governed by the polar angle…

We consider capillarity functionals which measure the perimeter of sets contained in a Euclidean half-space assigning a constant weight $\lambda \in (-1,1)$ to the portion of the boundary that touches the boundary of the half-space.…

We introduce a new concept of dissipative measure-valued martingale solutions to the stochastic compressible Euler equations. These solutions are weak in the probabilistic sense i.e., the probability space and the driving Wiener process are…

Problems with topological uncertainties appear in many fields ranging from nano-device engineering to the design of bridges. In many of such problems, a part of the domains boundaries is subjected to random perturbations making inefficient…

The behavior of the residual (impurity-dominated) resistivity is computed for a material near a two dimensional quantum critical point characterized by a divergent $q=0$ susceptibility. A singular renormalization of the amplitude for…