Related papers: Mixing for Time-Changes of Heisenberg Nilflows
A plane turbulent mixing in a shear flow of an ideal homogeneous fluid confined between two relatively close rigid walls is considered. The character of the flow is determined by interaction of vortices arising at the nonlinear stage of the…
We investigate the spectral flow of the integrable non-hermitian Heisenberg spin chain under boundary conditions with complex twist angle. It is shown that the period of the spectral flow is $4\pi$ up to a certain critical imaginary twist,…
We introduce a geometric framework to study Newton's equations on infinite-dimensional configuration spaces of diffeomorphisms and smooth probability densities. It turns out that several important PDEs of hydrodynamical origin can be…
A multicomponent extension of our recent theory of simple fluids [ U.M.B. Marconi and S. Melchionna, Journal of Chemical Physics, 131, 014105 (2009) ] is proposed to describe miscible and immiscible liquid mixtures under inhomogeneous, non…
We show the $L^2$-convergence of continuous time ergodic averages of a product of functions evaluated at return times along polynomials. These averages are the continuous time version of the averages appearing in Furstenberg's proof of…
The celebrated Birkhoff Ergodic Theorem asserts that, for an ergodic map, orbits of almost every point equidistributes when sampled at integer times. This result was generalized by Bourgain to many natural sparse subsets of the integers. On…
This work presents mixed variational flows (MixFlows), a new variational family that consists of a mixture of repeated applications of a map to an initial reference distribution. First, we provide efficient algorithms for i.i.d. sampling,…
We study diffusion and mixing in different linear fluid dynamics models, mainly related to incompressible flows. In this setting, mixing is a purely advective effect which causes a transfer of energy to high frequencies. When diffusion is…
We show that in a rapidly mixing flow with an invariant measure, the time which is needed to hit a given section is related to a sort of conditional dimension of the measure at the section. The result is applied to the geodesic flow of…
We consider smooth locally Hamiltonian flows on compact surfaces of genus $g\geq 2$ to prove their deviation of Birkhoff integrals for smooth observables. Our work generalizes results of Forni and Bufetov which prove the existence of…
Let X be a vector field on a compact connected manifold M. An important question in dynamical systems is to know when a function g:M -> R is a coboundary for the flow generated by X, i.e. when there exists a function f: M->R such that Xf=g.…
We study ergodic and mixing properties of non-autonomous dynamics on the unit circle generated by inner functions fixing the origin.
In this paper we give a criterion for a special flow to be not isomorphic to its inverse which is a refine of a result in \cite{Fr-Ku-Le}. We apply this criterion to special flows $T^f$ built over ergodic interval exchange transformations…
We present the derivation of a new unidirectional model for We present the derivation of a new unidirectional model for unsteady mixed flows in non uniform closed water pipes. We introduce a local reference frame to take into account the…
The Nagel-Schreckenberg model with overtaking strategy (NSOS) is proposed, and numerical simulations are performed for both closed and open boundary conditions. The fundamental diagram, space-time diagram, and spatial-temporal distribution…
In the context of the long-standing issue of mixing in infinite ergodic theory, we introduce the idea of mixing for observables possessing an infinite-volume average. The idea is borrowed from statistical mechanics and appears to be…
By studying the weak closure of multidimensional off-diagonal self-joinings we provide a criterion for non-isomorphism of a flow with its inverse, hence the non-reversibility of a flow. This is applied to special flows over rigid…
Dense amorphous materials exhibit both nonlocal flow cooperativity and pronounced history dependence, yet existing continuum models capture only one of these features at a time. Nonlocal rheologies are intrinsically memoryless, while…
Aligned superhydrophobic surfaces with the same texture orientation reduce drag in the channel and generate secondary flows transverse to the direction of the applied pressure gradient. Here we show that a transverse shear can be easily…
In this work we obtain mixing (and in some cases sharp mixing rates) for a reasonable large class of invertible systems preserving an infinite measure. The examples considered here are the invertible analogue of both Markov and non Markov…