Related papers: Probing ergodicity in granular matter
In this paper we discuss how the notion of subgeometric ergodicity in Markov chain theory can be exploited to study stationarity and ergodicity of nonlinear time series models. Subgeometric ergodicity means that the transition probability…
We experimentally investigate the steady states of two granular assemblies differing in their material properties and allowed to exchange volume with each other under external agitation in the vicinity of their jamming transition. We…
We investigate experimentally the statistics of the free volume inside bidimensional granular packings, for two different kinds of grains and two levels of compaction. With the aim to gain new insight into the statistical description of…
We study images of equilibrium (Gibbs) states for a class of non-invertible transformations associated to conformal iterated function systems with overlaps $\mathcal S$. We prove exact dimensionality for these image measures, and find a…
We provide a framework for studying randomly coloured point sets in a locally compact, second-countable space on which a metrisable unimodular group acts continuously and properly. We first construct and describe an appropriate dynamical…
This paper illustrates how the tools of equilibrium statistical mechanics can help to explain a far-from-equilibrium problem: the jamming transition in frictionless granular materials. Edwards ideas consist of proposing a statistical…
Large-eddy simulation developments and validations are presented for an improved simulation of turbulent internal flows. Numerical methods are proposed according to two competing criteria: numerical qualities (precision and spectral…
We study dynamical systems acting on the path space of a stationary (non-simple) Bratteli diagram. For such systems we explicitly describe all ergodic probability measures invariant with respect to the tail equivalence relation (or the…
The histogram method is a powerful non-parametric approach for estimating the probability density function of a continuous variable. But the construction of a histogram, compared to the parametric approaches, demands a large number of…
For a quantum system in a macroscopically large volume $V$, prepared in a pure state and subject to maximally noisy or ergodic unitary dynamics, the reduced density matrix of any sub-system $v\ll V$ is almost surely totally mixed. We show…
The mixedness of a quantum state is usually seen as an adversary to topological quantization of observables. For example, exact quantization of the charge transported in a so-called Thouless adiabatic pump is lifted at any finite…
The main focus of this article is the study of ergodicity of Interacting Particle Systems (IPS). We present a simple lemma showing that scaling time is equivalent to taking the convex combination of the transition matrix of the IPS with the…
Tap density of a granular powder is often linked to the flowability via Carr Index that measures how tight a powder can be packed, under an assumption that more easily packed powders usually flow poorly. Understanding how particles are…
A one dimensional lattice model is formulated to study tapping dynamics and the long time steady distribution in granular media. The dynamics conserves the number of particles in the system, and density changes are associated to the…
This paper is aim to extend Kenneth R. Berg's findings on the maximal entropy theorem and the ergodicity of measure convolution to the case of surjective homomorphisms. We further explores dynamical systems under surjective homomorphism in…
In this short note, we investigate non-invertible stochastic dynamical systems on the unit interval $[0, 1]$. We provide a handy condition for unique ergodicity for systems that are injective in mean. On the other hand, we give concrete…
The dynamics of one dimensional iterative maps in the regime of fully developed chaos is studied in detail. Motivated by the observation of dynamical structures around the unstable fixed point we introduce the geometrical concept of a…
We study random dynamical systems of certain continuous functions on the unit interval. We use bounded variation to provide sufficient conditions for unique ergodicity of these systems. Several classes of examples are provided.
Using confocal microscopy, we measure the packing geometry and interdroplet forces as a function of the osmotic pressure in a 3D emulsion system. We find that the nonlinear elastic response of the pressure with density is not a result of…
We study the dynamics of compositions of a sequence of holomorphic mappings in projective space. We define ergodicity and mixing for non-autonomous dynamical systems, and we construct totally invariant measures for which our sequence…