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R Klages

Publications and source records attributed to R Klages.

8 recordsLinked to original sources
PubMed2002

Fractal structures of normal and anomalous diffusion in nonlinear nonhyperbolic dynamical systems.

A paradigmatic nonhyperbolic dynamical system exhibiting deterministic diffusion is the smooth nonlinear climbing sine map. We find that this map generates fractal hierarchies of normal and anomalous diffusive regions as functions of the control parameter. The measure of these self-similar sets is positive, parameter dependent, and in case of normal diffusion it shows a fractal diffusion coefficient. By using a Green-Kubo formula we link these fractal structures to the nonlinear microscopic dynamics in terms of fractal Takagi-like functions.

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PubMed2002

Comment on "Analysis of chaotic motion and its shape dependence in a generalized piecewise linear map".

Rajagopalan and Sabir [Phys. Rev. E 63, 057201 (2001)] recently discussed deterministic diffusion in a piecewise linear map using an approach developed by Fujisaka et al. We first show that they rederived the random walk formula for the diffusion coefficient, which is known to be the exact result for maps of Bernoulli-type since the work of Fujisaka and Grossmann [Z. Phys. B: Condens. Matter 48, 261 (1982)]. However, this correct solution is at variance to the diffusion coefficient curve presented in their paper. Referring to another existing approach based on Markov partitions, we answer the question posed by the authors regarding solutions for more general parameter values by recalling the finding of a fractal diffusion coefficient. We finally argue that their model is not suitable for studying intermittent behavior, in contrast to what was suggested in their paper.

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PubMed2002

Suppression and enhancement of diffusion in disordered dynamical systems.

The impact of quenched disorder on deterministic diffusion in chaotic dynamical systems is studied. As a simple example, we consider piecewise linear maps on the line. In computer simulations we find a complex scenario of multiple suppression and enhancement of normal diffusion, under variation of the perturbation strength. These results are explained by a theoretical approximation, showing that the oscillations emerge as a direct consequence of the unperturbed diffusion coefficient, which is known to be a fractal function of a control parameter.

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PubMed2002

Lyapunov instability for a periodic Lorentz gas thermostated by deterministic scattering.

In recent work a deterministic and time-reversible boundary thermostat called thermostating by deterministic scattering was introduced for the periodic Lorentz gas [Phys. Rev. Lett. 84, 4268 (2000)]. Here we assess the nonlinear properties of this dynamical system by numerically calculating its Lyapunov exponents. Based on a revised method for computing Lyapunov exponents, which employs periodic orthonormalization with a constraint, we present results for the Lyapunov exponents and related quantities in equilibrium and nonequilibrium. Finally, we check whether we obtain the same relations between quantities characterizing the microscopic chaotic dynamics and quantities characterizing macroscopic transport as obtained for conventional deterministic and time-reversible bulk thermostats.

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PubMed2000

Thermostating by deterministic scattering: construction of nonequilibrium steady states

We present a novel approach for constructing nonequilibrium steady states. It is based on a deterministic and time-reversible mechanism for dissipating energy from a subsystem into a thermal reservoir. The key idea is to thermalize a moving particle by appropriately modeling its microscopic collision rules with a boundary mimicking a thermal reservoir with arbitrarily many degrees of freedom. We demonstrate our method for the periodic Lorentz gas with an external electric field. By applying our thermostat we do not find an ergodic breakdown with increasing field strength.

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PubMed1999

Simple deterministic dynamical systems with fractal diffusion coefficients.

We analyze a simple model of deterministic diffusion. The model consists of a one-dimensional array of scatterers with moving point particles. The particles move from one scatterer to the next according to a piecewise linear, expanding, deterministic map on unit intervals. The microscopic chaotic scattering process of the map can be changed by a control parameter. The macroscopic diffusion coefficient for the moving particles is well defined and depends upon the control parameter. We calculate the diffusion coefficent and the largest eigenmodes of the system by using Markov partitions and by solving the eigenvalue problems of respective topological transition matrices. For different boundary conditions we find that the largest eigenmodes of the map match the ones of the simple phenomenological diffusion equation. Our main result is that the diffusion coefficient exhibits a fractal structure as a function of the control parameter. We provide qualitative and quantitative arguments to explain features of this fractal structure.

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PubMed1999

Thermostating by deterministic scattering: heat and shear flow.

We apply a recently proposed thermostating mechanism to an interacting many-particle system where the bulk particles are moving according to Hamiltonian dynamics. At the boundaries the system is thermalized by deterministic and time-reversible scattering. We first show how this scattering mechanism can be related to stochastic boundary conditions. We subsequently simulate thermal conduction and shear flow for a hard disk fluid. By comparing the transport coefficients obtained from computer simulations to theoretical results we find that this thermostating mechanism yields well-defined nonequilibrium steady states in the range of linear response. Furthermore, the conjectured identity between thermodynamic entropy production and exponential phase-space contraction rates is investigated from the standpoint of our formalism. We find that, in general, these quantities do not agree.

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