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At least 1,171 records · Page 65Linked to original sources

arXiv1999

Spectra and statistics of velocity and temperature fluctuations in turbulent convection

Direct measurements of the velocity in turbulent convection of $SF_6$ near its gas-liquid critical point by light scattering on the critical density fluctuations were conducted. The temperature, velocity and cross frequency power spectra in a wide range of the Rayleigh and Prandtl numbers show scaling behaviour with indices, which are rather close to the Bolgiano-Obukhov scaling in the wavenumber domain. The statistics of the velocity fluctuations remains Gaussian up to the Reynolds numbers $10^5$.

chao-dyn↗

arXiv1999

Semiclassical theory of the emission properties of wave-chaotic resonant cavities

We develop a perturbation theory for the lifetime and emission intensity for isolated resonances in asymmetric resonant cavities. The inverse lifetime $Γ$ and the emission intensity $I(θ)$ in the open system are expressed in terms of matrix elements of operators evaluated with eigenmodes of the closed resonator. These matrix elements are calculated in a semiclassical approximation which allows us to represent $Γ$ and $I(θ)$ as sums over the contributions of rays which escape the resonator by refraction.

cond-mat.mes-hall↗

arXiv1999

Hydrodynamics of the Kuramoto-Sivashinsky Equation in Two Dimensions

The large scale properties of spatiotemporal chaos in the 2d Kuramoto-Sivashinsky equation are studied using an explicit coarse graining scheme. A set of intermediate equations are obtained. They describe interactions between the small scale (e.g., cellular) structures and the hydrodynamic degrees of freedom. Possible forms of the effective large scale hydrodynamics are constructed and examined. Although a number of different universality classes are allowed by symmetry, numerical results support the simplest scenario, that being the KPZ universality class.

cond-mat.soft↗

arXiv1999

Information-Theoretic Limits of Control

Fundamental limits on the controllability of physical systems are discussed in the light of information theory. It is shown that the second law of thermodynamics, when generalized to include information, sets absolute limits to the minimum amount of dissipation required by open-loop control. In addition, an information-theoretic analysis of closed-loop control shows feedback control to be essentially a zero sum game: each bit of information gathered directly from a dynamical systems by a control device can serve to decrease the entropy of that system by at most one bit additional to the reduction of entropy attainable without such information (open-loop control). Consequences for the control of discrete binary systems and chaotic systems are discussed.

chao-dyn↗

arXiv1999

From Generalized Synchrony to Topological Decoherence: Emergent Sets in Coupled Chaotic Systems

We consider the evolution of the unstable periodic orbit structure of coupled chaotic systems. This involves the creation of a complicated set outside of the synchronization manifold (the emergent set). We quantitatively identify a critical transition point in its development (the decoherence transition). For asymmetric systems we also describe a migration of unstable periodic orbits that is of central importance in understanding these systems. Our framework provides an experimentally measurable transition, even in situations where previously described bifurcation structures are inapplicable.

chao-dyn↗

arXiv1999

Correlations in the Adiabatic Response of Chaotic Systems

Adiabatic variation of the parameters of a chaotic system results in a fluctuating reaction force. In the leading order in the adiabaticity parameter, a dissipative force, that is present in classical mechanics was found to vanish in quantum mechanics. On the time scale t, this force is proportional to I(t), the integral of the force-force correlation function over time t. In order to understand the crossover between the classical and the quantum mechanical behavior we calculated I(t) in random matrix theory. We found that for systems belonging to the Gaussian unitary ensemble this crossover takes place at a characteristic time (proportional to the Heisenberg time) and for longer times I(t) practically vanishes, resulting in vanishing dissipation. For systems belonging to the Gaussian orthogonal ensemble I(t) drops like 1/t and there is no such characteristic time. I(t) is calculated for various models and the relation to experiment is discussed.

chao-dyn↗

arXiv1999

Finite thermal conductivity in 1d lattices

We discuss the thermal conductivity of a chain of coupled rotators, showing that it is the first example of a 1d nonlinear lattice exhibiting normal transport properties in the absence of an on-site potential. Numerical estimates obtained by simulating a chain in contact with two thermal baths at different temperatures are found to be consistent with those ones based on linear response theory. The dynamics of the Fourier modes provides direct evidence of energy diffusion. The finiteness of the conductivity is traced back to the occurrence of phase-jumps. Our conclusions are confirmed by the analysis of two variants of this model.

chao-dyn↗

arXiv1999

Universality and saturation of intermittency in passive scalar turbulence

The statistical properties of a scalar field advected by the non-intermittent Navier-Stokes flow arising from a two-dimensional inverse energy cascade are investigated. The universality properties of the scalar field are directly probed by comparing the results obtained with two different types of injection mechanisms. Scaling properties are shown to be universal, even though anisotropies injected at large scales persist down to the smallest scales and local isotropy is not fully restored. Scalar statistics is strongly intermittent and scaling exponents saturate to a constant for sufficiently high orders. This is observed also for the advection by a velocity field rapidly changing in time, pointing to the genericity of the phenomenon. The persistence of anisotropies and the saturation are both statistical signatures of the ramp-and-cliff structures observed in the scalar field.

chao-dyn↗

arXiv1999

Chaotic Transport and Current Reversal in Deterministic Ratchets

We address the problem of the classical deterministic dynamics of a particle in a periodic asymmetric potential of the ratchet type. We take into account the inertial term in order to understand the role of the chaotic dynamics in the transport properties. By a comparison between the bifurcation diagram and the current, we identify the origin of the current reversal as a bifurcation from a chaotic to a periodic regime. Close to this bifurcation, we observed trajectories revealing intermittent chaos and anomalous deterministic diffusion.

chao-dyn↗

arXiv2000

Dynamical Anomalies and Intermittency in Burgers Turbulence

We analyze the field theory of fully developed Burgers turbulence. Its key elements are shock fields, which characterize the singularity statistics of the velocity field. The shock fields enter an operator product expansion describing intermittency. The latter is found to be constrained by dynamical anomalies expressing finite dissipation in the inviscid limit. The link between dynamical anomalies and intermittency is argued to be important in a wider context of turbulence.

cond-mat↗

arXiv1999

Quantization of a billiard model for interacting particles

We consider a billiard model of a self-bound, interacting three-body system in two spatial dimensions. Numerical studies show that the classical dynamics is chaotic. The corresponding quantum system displays spectral fluctuations that exhibit small deviations from random matrix theory predictions. These can be understood in terms of scarring caused by a 1-parameter family of orbits inside the collinear manifold.

chao-dyn↗

arXiv1999

Momentum conservation implies anomalous energy transport in 1d classical lattices

Under quite general conditions, we prove that for classical many-body lattice Hamiltonians in one dimension (1D) total momentum conservation implies anomalous conductivity in the sense of the divergence of the Kubo expression for the coefficient of thermal conductivity, $κ$. Our results provide rigorous confirmation and explanation of many of the existing ``surprising'' numerical studies of anomalous conductivity in 1D classical lattices, including the celebrated Fermi-Pasta-Ulam problem.

chao-dyn↗

arXiv1999

Impurity-induced stabilization of solitons in arrays of parametrically driven nonlinear oscillators

Chains of parametrically driven, damped pendula are known to support soliton-like clusters of in-phase motion which become unstable and seed spatiotemporal chaos for sufficiently large driving amplitudes. We show that the pinning of the soliton on a "long" impurity (a longer pendulum) expands dramatically its stability region whereas "short" defects simply repel solitons producing effective partition of the chain. We also show that defects may spontaneously nucleate solitons.

patt-sol↗

arXiv2000

Singularity theory study of overdetermination in models for L-H transitions

Two dynamical models that have been proposed to describe transitions between low and high confinement states (L-H transitions) in confined plasmas are analysed using singularity theory and stability theory. It is shown that the stationary-state bifurcation sets have qualitative properties identical to standard normal forms for the pitchfork and transcritical bifurcations. The analysis yields the codimension of the highest-order singularities, from which we find that the unperturbed systems are overdetermined bifurcation problems and derive appropriate universal unfoldings. Questions of mutual equivalence and the character of the state transitions are addressed.

math-ph↗

arXiv1999

Quantum Resonances of Kicked Rotor and SU(q) group

The quantum kicked rotor (QKR) map is embedded into a continuous unitary transformation generated by a time-independent quasi-Hamiltonian. In some vicinity of a quantum resonance of order $q$, we relate the problem to the {\it regular} motion along a circle in a $(q^2-1)$-component inhomogeneous "magnetic" field of a quantum particle with $q$ intrinsic degrees of freedom described by the $SU(q)$ group. This motion is in parallel with the classical phase oscillations near a non-linear resonance.

chao-dyn↗

arXiv1999

The Statistics of Chaotic Tunnelling

We discuss the statistics of tunnelling rates in the presence of chaotic classical dynamics. This applies to resonance widths in chaotic metastable wells and to tunnelling splittings in chaotic symmetric double wells. The theory is based on using the properties of a semiclassical tunnelling operator together with random matrix theory arguments about wave function overlaps. The resulting distribution depends on the stability of a specific tunnelling orbit and is therefore not universal. However it does reduce to the universal Porter-Thomas form as the orbit becomes very unstable. For some choices of system parameters there are systematic deviations which we explain in terms of scarring of certain real periodic orbits. The theory is tested in a model symmetric double well problem and possible experimental realisations are discussed.

chao-dyn↗

arXiv1998

Thermostatting by deterministic scattering

We present a mechanism for thermalizing a moving particle by microscopic deterministic scattering. As an example, we consider the periodic Lorentz gas. We modify the collision rules by including energy transfer between particle and scatterer such that the scatterer mimics a thermal reservoir with arbitrarily many degrees of freedom. The complete system is deterministic, time-reversible, and provides a microcanonical density in equilibrium. In the limit of the disk representing infinitely many degrees of freedom and by applying an electric field the system goes into a nonequilibrium steady state.

chao-dyn↗

arXiv1999

Quantized Orbits and Resonant Transport

A tight binding representation of the kicked Harper model is used to obtain an integrable semiclassical Hamiltonian consisting of degenerate "quantized" orbits. New orbits appear when renormalized Harper parameters cross integer multiples of $π/2$. Commensurability relations between the orbit frequencies are shown to correlate with the emergence of accelerator modes in the classical phase space of the original kicked problem. The signature of this resonant transport is seen in both classical and quantum behavior. An important feature of our analysis is the emergence of a natural scaling relating classical and quantum couplings which is necessary for establishing correspondence.

chao-dyn↗