Related papers: Thermodynamic formalism for contracting Lorenz flo…
It is shown that low Reynolds number fluid flows can cause suspended particles to respond as though they were in an equilibrium system with an effective potential. This general result follows naturally from the fact that different methods…
We propose a general procedure for evaluating, directly from microphysics, the constitutive relations of heat-conducting fluids in regimes of large fluxes of heat. Our choice of hydrodynamic formalism is Carter's two-fluid theory, which…
The recently introduced consistent lattice Boltzmann model with energy conservation [S. Ansumali, I.V. Karlin, Phys. Rev. Lett. 95, 260605 (2005)] is extended to the simulation of thermal flows on standard lattices. The two-dimensional…
We obtain limit theorems (Stable Laws and Central Limit Theorems, both Gaussian and non-Gaussian) and thermodynamic properties for a class of non-uniformly hyperbolic flows: almost Anosov flows, constructed here. The proofs of the limit…
The usable limits of the customary and relaxational filtrational theories are considered. The questions of applicable the locality and local thermodynamical equilibrium principles to depict the nonstationary flows are discussed. The…
We propose a new theory of second-order viscous relativistic hydrodynamics which does not impose any frame conditions on the choice of the hydrodynamic variables. It differs from Mueller-Israel-Stewart theory by including additional…
In this paper we study some aspects of thermodynamic formalism, more specifically topological pressure and, as a consequence, topological entropy for piecewise smooth vector fields, using topological conjugation with shift maps and the…
The thermodynamic formalism, which was first developed for dynamical systems and then applied to discrete Markov processes, turns out to be well suited for continuous time Markov processes as well, provided the definitions are interpreted…
Inspired by work of Besson-Courtois-Gallot, we construct a flow called the natural flow on a non-positively curved Riemannian manifold $M$. As with the natural map, the $k$-Jacobian of the natural flow is directly related to the critical…
We find conditions which guarantee that a given flow on a closed smooth manifold admits a smooth Lyapunov one-form lying in a prescribed de Rham cohomology class. These conditions are formulated in terms of Schwartzman's asymptotic cycles…
We improve the description of $\mathbb{F}$-limits of noncollapsed Ricci flows in the K\"ahler setting. In particular, the singular strata $\mathcal{S}^k$ of such metric flows satisfy $\mathcal{S}^{2j}=\mathcal{S}^{2j+1}$. We also prove an…
We study the topological entropy of the Lagrangian flow restricted to an energy level $E_{L}^{-1}(c) \subset TM$ for $ c >e_0(L)$. We prove that if the flow of the Tonelli Lagrangian $ L: M \to \mathbb{R}$, on a closed manifold of dimension…
We introduce a dynamical energy functional on compact ancient asymptotically Ricci-flat Ricci flows with modest decay using limits of conjugate heat flows. This functional satisfies a steady Ricci breather-type rigidity and provides an…
In this paper we introduce a flow to study the Toda system, which we call {\it Toda flow.} More generally, we introduce a flow of the Liouville systems, formulated as a coupled parabolic system with nonlocal interactions. Finite-time…
Recently, a morphological transition in the velocity distribution of a relativistic gas has been pointed out which shows hallmarks of a critical phenomenon. Here, we provide a general framework which allows for a thermodynamic approach to…
In connection with parametric rescaling of free dynamics of CCR, we introduce a flow on the set of covariance forms and investigate its thermodynamic behavior at low temperature with the conclusion that every free state approaches to a…
We consider a geodesic flow on a compact manifold endowed with a Riemannian (or Finsler, or Lorentz) metric satisfying some generic, explicit conditions. We couple the geodesic flow with a time-dependent potential, driven by an external…
We analyze a volumetric formulation of lattice Boltzmann for compressible thermal fluid flows. The velocity set is chosen with the desired accuracy, based on the Gauss-Hermite quadrature procedure, and tested against controlled problems in…
Despite its importance, there have been few PDE results to investigate Prandtl layers for compressible fluids, in which the thermal boundary layer for the temperature field interacts with the classical velocity Prandtl boundary layer in a…
We compute the continuum thermo-hydrodynamical limit of a new formulation of lattice kinetic equations for thermal compressible flows, recently proposed in [Sbragaglia et al., J. Fluid Mech. 628 299 (2009)]. We show that the hydrodynamical…