Related papers: Relating small Feynman and Bjoken $x$
A simplified relativistic kinetic theory for gases with internal degrees of freedom, based on a BGK-type collision term, is considered. First the Boltzmann equation is rewritten in tetrad form and then thermal coefficients are determined to…
We consider a half-order time-fractional diffusion equation in an arbitrary dimension and investigate inverse problems of determining the source term or the diffusion coefficient from spatial data at an arbitrarily fixed time under some…
This paper can be viewed as a sequel to the author's long survey on the Zimmer program \cite{F11} published in 2011. The sequel focuses on recent rapid progress on certain aspects of the program particularly concerning rigidity of Anosov…
Distributed order fractional Langevin-like equations are introduced and applied to describe anomalous diffusion without unique diffusion or scaling exponent. It is shown that these fractional Langevin equations of distributed order can be…
We derive a set of isometric fluctuation relations, which constrain the order parameter fluctuations in finite-size systems at equilibrium and in the presence of a broken symmetry. These relations are exact and should apply generally to…
We introduce a new machinery to study the large time behavior for general classes of Hamilton--Jacobi type equations, which include degenerate parabolic equations and weakly coupled systems. We establish the convergence results by using the…
We provide several characterizations of convergence to unstable equilibria in nonlinear systems. Our current contribution is three-fold. First we present simple algebraic conditions for establishing local convergence of non-trivial…
Following the random approach of Mitake, Siconolfi,Tran and Yamada, we define a Lax--Oleinik formula adapted to evolutive weakly coupled systems of Hamilton--Jacobi equations. It is reminiscent of the corresponding scalar formula, with the…
The fluctuations in nonequilibrium systems are under intense theoretical and experimental investigation. Topical ``fluctuation relations'' describe symmetries of the statistical properties of certain observables, in a variety of models and…
Recently, the research community has been exploring fractional calculus to address problems related to cosmology; in this approach, the gravitational action integral is altered, leading to a modified Friedmann equation, then the resulting…
This note aims at providing a rather informal and hopefully accessible overview of the fairly long and technical work [4]. In that paper, the authors established new global-in-time existence results for admissible solutions of nonlinear…
In this paper, we establish coincidence-like results in the case when the values of the correspondences are not convex. In order to do this, we define a new type of correspondences, namely properly quasi-convex-like. Further, we apply the…
I comment on the interpretation of a recent experiment showing quantum interference in time. It is pointed out that the standard nonrelativistic quantum theory, used by the authors in their analysis, cannot account for the results found,…
As R.Feynman has shown to F. Dyson -- who published it then in 1990 under the name of "Feynman's proof of Maxwell's equations" -- the only interactions compatible with the canonical uncertainty relation (for scalar particles on flat $\R^3$)…
We examine the short and long-time behaviors of time-fractional diffusion equations with variable space-dependent order. More precisely, we describe the time-evolution of the solution to these equations as the time parameter goes either to…
In this article, we study the large time behavior of solutions of first-order Hamilton-Jacobi Equations, set in a bounded domain with nonlinear Neumann boundary conditions, including the case of dynamical boundary conditions. We establish…
We consider minimization problems in the calculus of variations set in a sequence of domains the size of which tends to infinity in certain directions and such that the data only depend on the coordinates in the directions that remain…
Most cosmological models studied today are based on the assumption of homogeneity and isotropy. Observationally one can find evidence that supports these assumptions on very large scales, the strongest being the almost isotropy of the…
This chapter describes the progress made during the past three decades in the finite size scaling analysis of the critical phenomena of the Anderson transition. The scaling theory of localisation and the Anderson model of localisation are…
This short essay traces the conceptual history of micro- and macroscopicity in the context of physical science. By focusing on three distinct episodes spanning five centuries, we show the scientific and philosophical meanings of this…