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At least 307 records · Page 17Linked to original sources

arXiv1997

Slow modes in passive advection

The anomalous scaling in the Kraichnan model of advection of the passive scalar by a random velocity field with non-smooth spatial behavior is traced down to the presence of slow resonance-type collective modes of the stochastic evolution of fluid trajectories. We show that the slow modes are organized into infinite multiplets of descendants of the primary conserved modes. Their presence is linked to the non-deterministic behavior of the Lagrangian trajectories at high Reynolds numbers caused by the sensitive dependence on initial conditions within the viscous range where the velocity fields are more regular. Revisiting the Kraichnan model with smooth velocities we describe the explicit solution for the stationary state of the scalar. The properties of the probability distribution function of the smeared scalar in this state are related to a quantum mechanical problem involving the Calogero-Sutherland Hamiltonian with a potential.

cond-mat↗

arXiv1999

Density-dependent diffusion in the periodic Lorentz gas

We study the deterministic diffusion coefficient of the two-dimensional periodic Lorentz gas as a function of the density of scatterers. Results obtained from computer simulations are compared to the analytical approximation of Machta and Zwanzig [Phys.Rev.Lett. 50, 1959 (1983)] showing that their argument is only correct in the limit of high densities. We discuss how the Machta-Zwanzig argument, which is based on treating diffusion as a Markovian hopping process on a lattice, can be corrected systematically by including microscopic correlations. We furthermore show that, on a fine scale, the diffusion coefficient is a non-trivial function of the density. We finally argue that, on a coarse scale and for lower densities, the diffusion coefficient exhibits a Boltzmann-like behavior, whereas for very high densities it crosses over to a regime which can be understood qualitatively by the Machta-Zwanzig approximation.

chao-dyn↗

arXiv1998

The dynamics of a low-order coupled ocean-atmosphere model

A system of five ordinary differential equations is studied which combines the Lorenz-84 model for the atmosphere and a box model for the ocean. The behaviour of this system is studied as a function of the coupling parameters. For most parameter values, the dynamics of the atmosphere model is dominant. For a range of parameter values, competing attractors exist. The Kaplan-Yorke dimension and the correlation dimension of the chaotic attractor are numerically calculated and compared to the values found in the uncoupled Lorenz model. In the transition from periodic behaviour to chaos intermittency is observed. The intermittent behaviour occurs near a Neimark-Sacker bifurcation at which a periodic solution loses its stability. The length of the periodic intervals is governed by the time scale of the ocean component. Thus, in this regime the ocean model has a considerable influence on the dynamics of the coupled system.

chao-dyn↗

arXiv1999

How Events Come Into Being: EEQT, Particle Tracks, Quantum Chaos, and Tunneling Time

In sections 1 and 2 we review Event Enhanced Quantum Theory (EEQT). In section 3 we discuss applications of EEQT to tunneling time, and compare its quantitative predictions with other approaches, in particular with Büttiker-Larmor and Bohm trajectory approach. In section 4 we discuss quantum chaos and quantum fractals resulting from simultaneous continuous monitoring of several non-commuting observables. In particular we show self-similar, non-linear, iterated function system-type, patterns arising from quantum jumps and from the associated Markov operator. Concluding remarks pointing to possible future development of EEQT are given in section 5.

quant-ph↗

arXiv1996

Chaos in Static Axisymmetric Spacetimes I : Vacuum Case

We study the motion of test particle in static axisymmetric vacuum spacetimes and discuss two criteria for strong chaos to occur: (1) a local instability measured by the Weyl curvature, and (2) a tangle of a homoclinic orbit, which is closely related to an unstable periodic orbit in general relativity. We analyze several static axisymmetric spacetimes and find that the first criterion is a sufficient condition for chaos, at least qualitatively. Although some test particles which do not satisfy the first criterion show chaotic behavior in some spacetimes, these can be accounted for the second criterion.

gr-qc↗

arXiv1995

Quantum Surface of Section Method: Demonstration of semiclassical Berry-Robnik energy level spacing distribution in a generic 2-dim Hamiltonian system

The recently developed quantum surface of section method is applied to a search for extremely high-lying energy levels in a simple but generic Hamiltonian system between integrability and chaos, namely the semiseparable 2-dim oscillator. Using the stretch of 13,445 consecutive levels with the sequential number around $1.8\cdot 10^7$ (eighteen million) we have clearly demonstrated the validity of the semiclassical Berry-Robnik level spacing distribution while at 1000 times smaller sequential quantum numbers we find the very persistent quasi universal phenomenon of power-law level repulsion which is globally very well described by the Brody distribution.

chao-dyn↗

arXiv1996

Reflection Symmetric Ballistic Microstructures: Quantum Transport Properties

We show that reflection symmetry has a strong influence on quantum transport properties. Using a random S-matrix theory approach, we derive the weak-localization correction, the magnitude of the conductance fluctuations, and the distribution of the conductance for three classes of reflection symmetry relevant for experimental ballistic microstructures. The S-matrix ensembles used fall within the general classification scheme introduced by Dyson, but because the conductance couples blocks of the S-matrix of different parity, the resulting conductance properties are highly non-trivial.

cond-mat↗

arXiv1995

Nuclear Mass Dependence of Chaotic Dynamics in Ginocchio Model

The chaotic dynamics in nuclear collective motion is studied in the framework of a schematic shell model which has only monopole and quadrupole degrees of freedom. The model is shown to reproduce the experimentally observed global trend toward less chaotic motion in heavier nuclei. The relation between current approach and the earlier studies with bosonic models is discussed.

nucl-th↗

arXiv1996

Anomalous Scaling in the N-Point Functions of Passive Scalar

A recent analysis of the 4-point correlation function of the passive scalar advected by a time-decorrelated random flow is extended to the N-point case. It is shown that all stationary-state inertial-range correlations are dominated by homogeneous zero modes of singular operators describing their evolution. We compute analytically the zero modes governing the N-point structure functions and the anomalous dimensions corresponding to them to the linear order in the scaling exponent of the 2-point function of the advecting velocity field. The implications of these calculations for the dissipation correlations are discussed.

chao-dyn↗

arXiv1995

Scale Anomaly and Quantum Chaos in the Billiards with Pointlike Scatterers

We argue that the random-matrix like energy spectra found in pseudointegrable billiards with pointlike scatterers are related to the quantum violation of scale invariance of classical analogue system. It is shown that the behavior of the running coupling constant explains the key characteristics of the level statistics of pseudointegrable billiards.

hep-th↗

arXiv1997

Solitons and diffusive modes in the noiseless Burgers equation: Stability analysis

The noiseless Burgers equation in one spatial dimension is analyzed from the point of view of a diffusive evolution equation in terms of nonlinear soliton modes and linear diffusive modes. The transient evolution of the profile is interpreted as a gas of right hand solitons connected by ramp solutions with superposed linear diffusive modes. This picture is supported by a linear stability analysis of the soliton mode. The spectrum and phase shift of the diffusive modes are determined. In the presence of the soliton the diffusive modes develop a gap in the spectrum and are phase-shifted in accordance with Levinson's theorem. The spectrum also exhibits a zero-frequency translation or Goldstone mode associated with the broken translational symmetry.

cond-mat.stat-mech↗

arXiv1997

Multiscaling in passive scalar advection as stochastic shape dynamics

The Kraichnan rapid advection model is recast as the stochastic dynamics of tracer trajectories. This framework replaces the random fields with a small set of stochastic ordinary differential equations. Multiscaling of correlation functions arises naturally as a consequence of the geometry described by the evolution of N trajectories. Scaling exponents and scaling structures are interpreted as excited states of the evolution operator. The trajectories become nearly deterministic in high dimensions allowing for perturbation theory in this limit. We calculate perturbatively the anomalous exponent of the third and fourth order correlation functions. The fourth order result agrees with previous calculations.

cond-mat.stat-mech↗

arXiv1999

Synchronization and Maximum Lyapunov Exponents of Cellular Automata

We study the synchronization of totalistic one dimensional cellular automata (CA). The CA with a non zero synchronization threshold exhibit complex non periodic space time patterns and conversely. This synchronization transition is related to directed percolation. We study also the maximum Lyapunov exponent for CA, defined in analogy with continuous dynamical systems as the exponential rate of expansion of the linear map induced by the evolution rule of CA, constructed with the aid of the Boolean derivatives. The synchronization threshold is strongly correlated to the maximum Lyapunov exponent and we propose approximate relations between these quantities. The value of this threshold can be used to parametrize the space time complexity of CA.

cond-mat.stat-mech↗

arXiv1999

On The Three Point Velocity Correlation Functions in 2d Forced Turbulence

We present a simple exact formula for the three point velocity correlation functions in two dimensional turbulence which is valid on all scales and which interpolates between the direct and inverse cascade regimes. As expected, these correlation functions are universal in these extreme regimes. We also discuss the effect of anisotropy and friction.

chao-dyn↗

arXiv1999

Frozen spatial chaos induced by boundaries

We show that rather simple but non-trivial boundary conditions could induce the appearance of spatial chaos (that is stationary, stable, but spatially disordered configurations) in extended dynamical systems with very simple dynamics. We exemplify the phenomenon with a nonlinear reaction-diffusion equation in a two-dimensional undulated domain. Concepts from the theory of dynamical systems, and a transverse-single-mode approximation are used to describe the spatially chaotic structures.

chao-dyn↗

arXiv1999

About coherent structures in random shell models for passive scalar advection

A study of anomalous scaling in models of passive scalar advection in terms of singular coherent structures is proposed. The stochastic dynamical system considered is a shell model reformulation of Kraichnan model. We extend the method introduced in \cite{DDG99} to the calculation of self-similar instantons and we show how such objects, being the most singular events, are appropriate to capture asymptotic scaling properties of the scalar field. Preliminary results concerning the statistical weight of fluctuations around these optimal configurations are also presented.

chao-dyn↗

arXiv1999

Quantum Algorithmic Integrability: The Metaphor of Polygonal Billiards

An elementary application of Algorithmic Complexity Theory to the polygonal approximations of curved billiards-integrable and chaotic-unveils the equivalence of this problem to the procedure of quantization of classical systems: the scaling relations for the average complexity of symbolic trajectories are formally the same as those governing the semi-classical limit of quantum systems. Two cases-the circle, and the stadium-are examined in detail, and are presented as paradigms.

chao-dyn↗

arXiv1999

Unstable dimension variability and synchronization of chaotic systems

An aspect of the synchronization dynamics is investigated in this work. We argue analytically and confirm numerically that the chaotic dynamics on the synchronization manifold exhibits unstable dimension variability. Unstable dimension variability is a cause of severe modeling difficulty for physical phenomena, since trajectories obtained from the mathematical model may not be related to trajectories of the actual system. We present and example of unstable dimension variability occurring in a system of two coupled chaotic maps, considering the dynamics in the synchronization manifold and its corresponding transversal direction, where a tongue-like structure is formed. The unstable dimension variability is revealed in the statistical distribution of the finite-time transversal Lyapunov exponent, having both negative and positive values.

chao-dyn↗