Related papers: Thermodynamic formalism for Lorenz maps

We derive the general analytical solution of the viscous hydrodynamic equations for an ultrarelativistic gas of hard spheres undergoing Bjorken expansion, taking into account effects from particle number conservation, and use it to…

Thermodynamic properties of matter are conveniently expressed as functional relations between variables known as equations of state. Here we experimentally determine the compressibility, density and pressure equations of state for an…

Given an one-dimensional Lorenz-like expanding map we prove that the condition\linebreak $P_{top}(\phi,\partial \mathcal{P},\ell)<P_{top}(\phi,\ell)$ (see, subsection 2.4 for definition), introduced by Buzzi and Sarig in [1] is satisfied…

For a smooth manifold of any dimension greater than one, we present an open set of smooth endomorphisms such that any of them has a transitive attractor with a non-empty interior. These maps are $m$-fold non-branched coverings, $m \ge 3$.…

We analyze in the context of geometrothermodynamics a Legendre invariant metric structure in the equilibrium space of an ideal gas. We introduce the concept of thermodynamic geodesic as a succession of points, each corresponding to a state…

We classify the measure theoretic attractors of general C^3 unimodal maps with quadratic critical points. The main ingredient is the decay of geometry.

In this paper, plane polynomial systems having a singular point attracting all orbits in positive time are classified up to topological equivalence. This is done by assigning a combinatorial invariant to the system (a so-called "feasible…

The localization tensor is a measure of distinguishability between insulators and metals. This tensor is related to the quantum metric tensor associated with the occupied bands in momentum space. In two dimensions and in the thermodynamic…

We introduce the first simple mechanical system that shows fully realistic transport behavior while still being exactly solvable at the level of equilibrium statistical mechanics. The system under consideration is a Lorentz gas with fixed…

Let $\mathcal{L}$ be a measured geodesic lamination on a complete hyperbolic surface of finite area. Assuming $\mathcal{L}$ is not a multicurve, our main result establishes the existence of a geodesic ray which has finite intersection…

A dynamical system is called contractive if any two solutions approach one another at an exponential rate. More precisely, the dynamics contracts lines at an exponential rate. This property implies highly ordered asymptotic behavior…

We study the attractor of Iterated Function Systems composed of infinitely many affine, homogeneous maps. In the special case of second generation IFS, defined herein, we conjecture that the attractor consists of a finite number of…

Pursuing our work in [18], [17], [20], [5], we consider in this article the two-dimensional thermohydraulics equations. We discretize these equations in time using the implicit Euler scheme and we prove that the global attractors generated…

The hydrodynamic attractors paradigm aims to explain the applicability of hydrodynamics after a very short timescale in ultra-relativistic nuclear collisions at RHIC and LHC in terms of the emergence of universal behavior across different…

Closure seems to be something rheologists would prefer to avoid. Here, the story of closure is told in such a way that one should enduringly forget any improper undertone of "uncontrolled approximation" or "necessary evil" which might…

The purpose of this paper is finding the essential attributes underlying the convexity theorems for momentum maps. It is shown that they are of topological nature; more specifically, we show that convexity follows if the map is open onto…

We propose a formalism which uses boundary conditions imposed on the Luttinger liquid (LL) to describe the transport properties of a LL coupled to reservoirs. The various boundary conditions completely determine linear transport in the…

We introduce a new model for quasi one-dimensional materials, motivated by intriguing but not yet well-understood experiments that have shown two-dimensional polymer films to be promising materials for thermoelectric devices. We consider a…

A well-known theorem of J.E. Hutchinson states that if an iterated function system consists of similarity transformations and satisfies the open set condition then its attractor supports a self-similar measure with Hausdorff dimension equal…

We prove that given a computable metric space and two computable measures, the set of points that have high universal uniform test scores with respect to the first measure will have a lower bound with respect to the second measure. This…