Related papers: Hausdorff dimension and hierarchical system dynami…
We rigorously analyze the low temperature non-equilibrium dynamics of the East model, a special example of a one dimensional oriented kinetically constrained particle model, when the initial distribution is different from the reversible one…
A simple multifractal coarsening model is suggested that can explain the observed dynamical behavior of the fractal dimension in a wide range of coarsening fractal systems. It is assumed that the minority phase (an ensemble of droplets) at…
We are going to introduce a new algebraic, analytic structure that is a kind of generalization of the Hausdorff dimension and measure. We give many examples and study the basic properties and relations of such systems.
We introduce a new simple hierarchically constrained model of slow relaxation. The configurational energy has a simple form as there is no coupling among the spins defining the system; the associated stationary distribution is an…
We prove bounds for the almost sure value of the Hausdorff dimension of the limsup set of a sequence of balls in $\mathbf{R}^d$ whose centres are independent, identically distributed random variables. The formulas obtained involve the rate…
We study the Hausdorff dimension of a measure related to a positive weak solution of a certain partial differential equation in a simply connected domain in the plane. Our work generalizes work of Lewis and coauthors when the measure is $p$…
This paper is concerned with the large deviation principle of the stochastic reaction-diffusion lattice systems defined on the N-dimensional integer set, where the nonlinear drift term is locally Lipschitz continuous with polynomial growth…
It is known that nonergodic directions in a rational billiard form a subset of the unit circle with Hausdorff dimension at most 1/2. Explicit examples realizing the dimension 1/2 are constructed using Diophantine numbers and continued…
A novel formalism, called H-theory, is applied to the problem of statistical equilibrium of a hierarchical complex system with multiple time and length scales. In this approach, the system is formally treated as being composed of a small…
A study of the transport coefficients of a system of elastic hard disks, based on the use of Helfand-Einstein expressions is reported. The self-diffusion, the viscosity, and the heat conductivity are examined with averaging techniques…
For several atomistic models of glass formers, at conditions below their glassy dynamics onset temperatures, ${T_\mathrm{o}}$, we use importance sampling of trajectory space to study the structure, statistics and dynamics of excitations…
Orientational dynamics in a liquid crystalline system near the isotropic-nematic (I-N) phase transition is studied using Molecular Dynamics simulations of the well-known Lebwohl-Lasher (LL) model. As the I-N transition temperature is…
Using a double-well potential as a physical memory, we study with experiments and numerical simulations the energy exchanges during erasure processes, and model quantitatively the cost of fast operation. Within the stochastic thermodynamics…
We consider linear mappings on the $d$-dimensional torus, defined by $T(x) = Ax \pmod 1$, where $A$ is an invertible $d \times d$ integer matrix, with no eigenvalues on the unit circle. In the case $d = 2$ and $\det A = \pm 1$, we give a…
In this paper we consider the probability distribution function of a Gibbs measure supported on a self-conformal set given by an iterated function system (devil's staircase). We use thermodynamic multifractal formalism to calculate the…
By viewing the covers of a fractal as a statistical mechanical system, the exact capacity of a multifractal is computed. The procedure can be extended to any multifractal described by a scaling function to show why the capacity and…
The data generated by long-delayed dynamical systems can be organized in patterns by means of the so-called spatio-temporal representation, uncovering the role of multiple time-scales as independent degrees of freedom. However, their…
The holographic complexity of a 3+1-dimensional Lifshitz spacetime having a scaling symmetry is computed. The change in the holographic complexity between the excited state and the ground state is then obtained. This is then related to the…
We consider stochastic dynamical systems defined by differential equations with a uniform random time delay. The latter equations are shown to be equivalent to deterministic higher-order differential equations: for an $n$-th order equation…
We construct so-called Darboux transformations and solutions of the dynamical Hamiltonian systems with several space variables $\frac{\partial \psi}{\partial t}=\sum_{k=1}^r H_k(t)\frac{\partial \psi}{\partial \zeta_k}\,$ $( H_k(t)=…