Using quantum maps we study the accuracy of semiclassical trace formulas. The role of chaos in improving the semiclassical accuracy, in some systems, is demonstrated quantitatively. However, our study of the standard map cautions that this may not be most general. While studying a sawtooth map we demonstrate the rather remarkable fact that at the level of the time one trace even in the presence...

For the first time we present the consideration of the antiferromagnetic Ising model in case of fully developed chaos and obtain the exact connection between this model and chaotic repellers. We describe the chaotic properties of this statistical mechanical system via the invariants characterizing a fractal set and show that in chaotic region it displays phase transition at positive ”temperatur...

Exact results are derived concerning quasiregularity and diffusion of strong chaos on resonances of the sawtooth map. A chaotic ensemble of well-defined quasiregularity type (the sequence of resonances visited) is generally a fractal set whose main characteristics, the topological entropy and the Hausdorff dimension, are calculated exactly, under some conditions, using a symbolic dynamics. The ...

The sensitivity of the random field Ising model to small random perturbations of the quenched disorder is studied via exact ground states obtained with a maximum-flow algorithm. In one and two space dimensions we find a mild form of chaos, meaning that the overlap of the old, unperturbed ground state and the new one is smaller than 1, but extensive. In three dimensions the rearrangements are ma...

A stochastic variational multiscale method with explicit subgrid modeling is provided for solution of stochastic elliptic equations that arise while modeling diffusion in heterogeneous random media [1]. The exact solution of the governing equations is split into two components: a coarse-scale solution and a subgrid solution. A localized computational model for the subgrid solution is derived. T...

We demonstrate a family of two-dimensional steady viscous flows which have singular continuous (fractal) Fourier spectra. Such flows represent a novel intermediate stage between order and Lagrangian chaos: The motion of individual fluid particles in them is neither entirely correlated nor completely disordered. In the considered setup these flows are presented by the exact solutions of the Navi...

In order to achieve chaotic signal processing, a dedicated chaos processor is required. The chaos processor is composed of two parts: chaos signal generation and chaos signal retrieval (Fig. 1). Chaos signal generation is used to generate chaos signal, while chaos signal retrieval is used to retrieve initial state of received chaos signal. Since chaos signal is analog in nature, with convention...

The stochastic finite element method (SFEM) is employed for solving stochastic onedimension time-dependent differential equations with random coefficients. SFEM is used to have a fixed form of linear algebraic equations for polynomial chaos coefficients of the solution process. Four fixed forms are obtained in the cases of stochastic heat equation with stochastic heat capacity or heat conductiv...

The critical exponents for T → 0 of the two-dimensional Ising spin-glass model with Gaussian couplings are determined with the help of exact ground states for system sizes up to L = 50 and by a Monte Carlo study of a pseudo-ferromagnetic order parameter. We obtain: for the stiffness exponent y(= θ) = −0.281±0.002, for the magnetic exponent δ = 1.48±0.01 and for the chaos exponent ζ = 1.05 ± 0.0...

By applying nonlinear dynamics to the dense storage of information, we demonstrate how a single nonlinear dynamical element can store M items, where M is variable and can be large. This provides the capability for naturally storing data in different bases or in different alphabets and can be used to implement multilevel logic. Further we show how this method of storing information can serve as ...