Related papers: Diffusion rate of windtree models and Lyapunov exp…
The Lyapunov spectrum describes the exponential growth, or decay, of infinitesimal phase-space perturbations. The perturbation associated with the maximum Lyapunov exponent is strongly localized in space, and only a small fraction of all…
We introduce a new approach to evaluate the largest Lyapunov exponent of a family of nonnegative matrices. The method is based on using special positive homogeneous functionals on $R^{d}_+,$ which gives iterative lower and upper bounds for…
We construct diffusions with values in the nonnegative orthant, normal reflection along each of the axes, and two pairs of local drift/variance characteristics assigned according to rank; one of the variances is allowed to vanish, but not…
By using the Zubarev nonequilibrium statistical operator method, and the Liouville equation with fractional derivatives, a generalized diffusion equation with fractional derivatives is obtained within the Renyi statistics. Averaging in…
Recent studies have shown that in the presence of noise both fronts propagating into a metastable state and so-called pushed fronts propagating into an unstable state, exhibit diffusive wandering about the average position. In this paper we…
This work analyzes the turbulent velocity distribution in proximity of the wall using the finite-scale Lyapunov theory just presented in previous works. This theory is here applied to the steady boundary layer under the hypothesis of…
We consider a point particle moving in a random distribution of obstacles described by a potential barrier. We show that, in a weak-coupling regime, under a diffusion limit suggested by the potential itself, the probability distribution of…
We consider multitype Markovian branching processes evolving in a Markovian random environment. To determine whether or not the branching process becomes extinct almost surely is akin to computing the maximal Lyapunov exponent of a sequence…
This work evaluates the magnitude of the turbulent energy cascade in terms of forward and backward scattering by modeling the "stretch and fold" mechanism through a drift-free Hanggi-Klimontovich stochastic process. Mapping this dynamics…
Dynamics of the driven Frenkel-Kontorova model with asymmetric deformable substrate potential is examined by analyzing response function, the largest Lyapunov exponent and Poincar\'{e} sections for two neighboring particles. The obtained…
The transport of an infinitely thin, hard rod in a random, dense array of point obstacles is investigated by molecular dynamics simulations. Our model mimics the sterically hindered dynamics in dense needle liquids. The center-of-mass…
This paper deals with the problem of analytically computing the largest Lyapunov exponent for many degrees of freedom Hamiltonian systems. This aim is succesfully reached within a theoretical framework that makes use of a geometrization of…
From extensive numerical simulations, we find that periodic polygonal billiard channels with angles which are irrational multiples of pi generically exhibit normal diffusion (linear growth of the mean squared displacement) when they have a…
We discuss the role played by the Lyapunov exponents in the dynamics of Zhang's model of Self-Organized Criticality. We show that a large part of the spectrum (slowest modes) is associated with the energy transpor in the lattice. In…
In this work we study the transition from normal to anomalous diffusion of Brownian particles on disordered potentials. The potential model consists of a series of "potential hills" (defined on unit cell of constant length) whose heights…
The Hamiltonian dynamics of classical planar Heisenberg model is numerically investigated in two and three dimensions. By considering the dynamics as a geodesic flow on a suitable Riemannian manifold, it is possible to analytically estimate…
Uniform fluid flow distribution in a symmetric volume can be realized through a symmetric branched tree. It is shown here, however, that the flow partitioning can be highly sensitive to deviations from exact symmetry if inertial effects are…
For a smooth expanding circle map, we show that the empirical distribution of Lyapunov exponents of periodic points of any fixed period is close to normal, with an error that decreases as the period grows. This establishes a version of the…
We consider elliptic diffusion problems with a random anisotropic diffusion coefficient, where, in a notable direction given by a random vector field, the diffusion strength differs from the diffusion strength perpendicular to this notable…
In this paper, we estimate the largest Lyapunov exponent for open billiards in the plane. We show that the largest Lyapunov exponent is differentiable with respect to a billiard deformation.