Related papers: The Mobius disjointness conjecture for distal flow…
Active matter is a new class of material, intrinsically out-of equilibrium with intriguing properties. So far, the recent upsurge of studies has mostly focused on the spontaneous behavior of these systems --in the absence of external…
In this paper, we investigate the embeddings for topological flows. We prove an embedding theorem for discrete topological system. Our results apply to suspension flows via constant function, and for this case we show an embedding theorem…
We introduce a proximal subdifferential and develop a calculus for nonsmooth functions defined on any Riemannian manifold $M$. We give several applications of this theory, concerning: 1) differentiability and geometrical properties of the…
In the first part of this paper we prove that the flow associated to the Burgers equation with a non local term of the form $\partial_x |D|^{\alpha-1} u$ fails to be uniformly continuous from bounded sets of $H^s({\mathbb D})$ to…
We consider bifurcation of critical points from a trivial branch for families of functionals that are invariant under the orthogonal action of a compact Lie group. Based on a recent construction of an equivariant spectral flow by the…
Let $\mathbb{T}$ be the unit circle and $\Gamma \backslash G$ the $3$-dimensional Heisenberg nilmanifold. We prove that a class of skew products on $\mathbb{T} \times \Gamma \backslash G$ are distal, and that the M\"{o}bius function is…
We investigate regularity properties of generalized conjugate functions induced by a general coupling function and the associated generalized proximal mapping. Our main results provide verifiable conditions ensuring local single-valuedness,…
In this paper we consider the multispecies stirring process on the discrete torus. We prove a large deviation principle for the trajectory of the vector of densities of the different species. The technique of proof consists in extending the…
We prove the Effective Bogomolov Conjecture, and so the Bogomolov Conjecture, over a function field of characteristic 0 by proving Zhang's Conjecture about certain invariants of metrized graphs. In the function field case, these conjectures…
This work is concerned with the intricate interplay between node or pore pressures and connection or throat conductivities in flow or pore networks. A setting similar to pore networks is given by fracture networks. Recently, a non-local…
Considering recent results revealing the existence of multi-scale rigid clusters of grains embedded in granular surface flows, i.e. flows down an erodible bed, we describe here the surface flows rheology through a non-local constitutive…
The large-scale collective behavior of biological systems can be characterized by macroscopic transport, which arises from the non-equilibrium microscopic interactions among individual constituents. A prominent example is the formation of…
This paper is focused on the generalized Forchheimer flows for slightly compressible fluids. We prove the existence and uniqueness of the differential system for stationary problem. The technique of semi-discretization in time is used to…
We show continuity of the martingale optimal transport optimisation problem as a functional of its marginals. This is achieved via an estimate on the projection in the nested/causal Wasserstein distance of an arbitrary coupling on to the…
A fundamental question in nonequilibrium statistical physics is whether effective equilibrium behavior can emerge at coarse-grained scales in strongly driven systems. Here, we investigate this question in the context of human mobility by…
We investigate the linear instability of flows that are stable according to Rayleigh's criterion for rotating fluids. Using Taylor-Couette flow as a primary test case, we develop large Reynolds number matched asymptotic expansion theories.…
Given a topological dynamical system $(X,T)$ and an arithmetic function $\boldsymbol{u}\colon\mathbb{N}\to\mathbb{C}$, we study the strong MOMO property (relatively to $\boldsymbol{u}$) which is a strong version of…
The problem of finding bounds of time-averaged characteristics of dynamical systems, such as the bound on the mean energy dissipation rate in a turbulent flow governed by incompressible Navier-Stokes equations, is considered. It is shown…
We show that an appropriately defined fluctuation-dissipation theorem, connecting generalized susceptibilities and time correlation functions, is valid for times shorter than the nucleation time of the metastable state of Markovian systems…
In this paper, we study the stationary states of diffusive dynamics driven out of equilibrium by reservoirs. For a small forcing, the system remains close to equilibrium and the large deviation functional of the density can be computed…