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At least 1,009 records · Page 56Linked to original sources

arXiv1998

Quantum chaos with non-periodic, complex orbits in the Resonant Tunneling Diode

We show that a special type of orbits, which are non-periodic and complex, 'Saddle Orbits' (SOs) describe accurately the quantal and experimental current oscillations in the Resonant Tunneling Diode in tilted fields. This is the first demonstration that one needs to abandon the periodic orbits (POs) paradigm in favour of this new and peculiar type of orbit. The SOs solve the puzzle of broad regions of experimental oscillations where we find no real or complex PO that can explain the data. The SOs succeeds in regimes involving several non-isolated POs, where PO formulas fail.

chao-dyn↗

arXiv1998

Universal scaling exponents in shell models of turbulence: Viscous effects are finite-size corrections to scaling

In a series of recent works it was proposed that shell models of turbulence exhibit inertial range scaling exponents that depend on the nature of the dissipative mechanism. If true, and if one could imply a similar phenomenon to Navier-Stokes turbulence, this finding would cast strong doubts on the universality of scaling in turbulence. In this Letter we propose that these ``nonuniversalities'' are just corrections to scaling that disappear when the Reynolds number goes to infinity.

chao-dyn↗

arXiv1999

Quantum Lévy Processes and Fractional Kinetics

Exotic stochastic processes are shown to emerge in the quantum evolution of complex systems. Using influence function techniques, we consider the dynamics of a system coupled to a chaotic subsystem described through random matrix theory. We find that the reduced density matrix can display dynamics given by Lévy stable laws. The classical limit of these dynamics can be related to fractional kinetic equations. In particular we derive a fractional extension of Kramers equation.

chao-dyn↗

arXiv1999

Phase Ordering and Onset of Collective Behavior in Chaotic Coupled Map Lattices

The phase ordering properties of lattices of band-chaotic maps coupled diffusively with some coupling strength $g$ are studied in order to determine the limit value $g_e$ beyond which multistability disappears and non-trivial collective behavior is observed. The persistence of equivalent discrete spin variables and the characteristic length of the patterns observed scale algebraically with time during phase ordering. The associated exponents vary continuously with $g$ but remain proportional to each other, with a ratio close to that of the time-dependent Ginzburg-Landau equation. The corresponding individual values seem to be recovered in the space-continuous limit.

cond-mat.dis-nn↗

arXiv1999

Theoretical Model for the Kramers-Moyal Description of Turbulence Cascades

We derive the Kramers-Moyal equation for the conditional probability density of velocity increments from the theoretical model recently proposed by V.Yakhot [Phys.Rev.E {\bf 57}, 1737 (1998)] in the limit of high Reynolds number limit. We show that the higher order (n>=3) Kramers-Moyal coefficients tends to zero and the velocity increments are evolved by the Fokker-Planck operator. Our result is compatible with the phenomenological descriptions by R.Friedrich and J.Peinke [Phys.Rev.Lett. {\bf 78}, 863 (1997)].

cond-mat↗

arXiv1999

Smooth-filamental transition of active tracer fields stirred by chaotic advection

The spatial distribution of interacting chemical fields is investigated in the non-diffusive limit. The evolution of fluid parcels is described by independent dynamical systems driven by chaotic advection. The distribution can be filamental or smooth depending on the relative strength of the dispersion due to chaotic advection and the stability of the chemical dynamics. We give the condition for the smooth-filamental transition and relate the Hölder exponent of the filamental structure to the Lyapunov exponents. Theoretical findings are illustrated by numerical experiments.

chao-dyn↗

arXiv1998

Excitation spectrum of Andreev billiards with a mixed phase space

We present a semiclassical theory for the excitation spectrum of a ballistic quantum dot weakly coupled to a superconductor, for the generic situation that the classical motion gives rise to a phase space containing islands of regularity in a chaotic sea. The density of low-energy excitations is determined by quantum energy scales that are related in a simple way to the morphology of the mixed phase space. An exact quantum mechanical computation for the annular billiard shows good agreement with the semiclassical predictions, in particular for the reduction of the excitation gap when the coupling to the regular regions is maximal.

cond-mat.mes-hall↗

arXiv1999

Periodic Orbit Quantization of Mixed Regular Chaotic Systems

A general technique for the periodic orbit quantization of systems with near-integrable to mixed regular-chaotic dynamics is introduced. A small set of periodic orbits is sufficient for the construction of the semiclassical recurrence function up to, in principle, infinite length. As in our recent work the recurrence signal is inverted by means of a high resolution spectral analyzer (harmonic inversion) to obtain the semiclassical eigenenergies. The method is demonstrated for the hydrogen atom in a magnetic field. To our knowledge this is the first successful application of periodic orbit quantization in the deep mixed regular-chaotic regime.

chao-dyn↗

arXiv1998

Kolmogorov equation in fully developed turbulence

The Kolmogorov equation with a forcing term is compared to experimental measurements, in low temperature helium gas, in a range of microscale Reynolds numbers $R_λ$ between 120 and 1200. We show that the relation is accurately verified by the experiment (i.e. within +/- 3 % relative error, over ranges of scales extending up to three decades). Two scales are extracted from the analysis, and revealed experimentally, one characterizing the external forcing, and the other, varying as $R_λ^{-3/5}$, defining the position of the maximum of the function $- S_{3}(r)/r$, and for which a physical interpretation is offered.

chao-dyn↗

arXiv1999

Random Roughness of Boundary Increases Turbulent Convection Scaling Exponent

The influence of the boundary layer properties on the heat transport in turbulent thermal convection is experimentally investigated in a cell with a rough bottom plate.It is shown that the standard 2/7 exponent of the convective heat flow dependence on the Rayleigh number, usually observed in cell with smooth boundaries, increases if the roughness has power law distributed asperity heights and the thermal boundary layer thickness is smaller than the maximum asperity size. In contrast a periodic roughness does not influence the heat transportlaw exponent.

chao-dyn↗

arXiv1998

Noiseless Collective Motion out of Noisy Chaos

We consider the effect of microscopic external noise on the collective motion of a globally coupled map in fully desynchronized states. Without the external noise a macroscopic variable shows high-dimensional chaos distinguishable from random motion. With the increase of external noise intensity, the collective motion is successively simplified. The number of effective degrees of freedom in the collective motion is found to decrease as $-\log{σ^2}$ with the external noise variance $σ^2$. It is shown how the microscopic noise can suppress the number of degrees of freedom at a macroscopic level.

chao-dyn↗

arXiv1998

A simplified model for red cell dynamics in small blood vessels

A simple mechanism for the confinement of red cells in the middle of narrow blood vessels is proposed. In the presence of a quadratic shear, red cells deform in such a way to loose fore-aft symmetry and to achieve a fixed orientation with respect to the flow. This leads to a drift away from the vessel walls, when the vessel diameter goes below a critical value depending on the viscoelastic properties and the dimensions of the cell.

chao-dyn↗

arXiv1998

Absence of local thermal equilibrium in two models of heat conduction

A crucial assumption in the conventional description of thermal conduction is the existence of local thermal equilibrium. We test this assumption in two simple models of heat conduction. Our first model is a linear chain of planar spins with nearest neighbour couplings, and the second model is that of a Lorentz gas. We look at the steady state of the system when the two ends are connected to heat baths at temperatures T1 and T2. If T1=T2, the system reaches thermal equilibrium. If T1 is not equal to T2, there is a heat current through the system, but there is no local thermal equilibrium. This is true even in the limit of large system size, when the heat current goes to zero. We argue that this is due to the existence of an infinity of local conservation laws in their dynamics.

cond-mat.stat-mech↗

arXiv1999

Disentangling Scaling Properties in Anisotropic and Inhomogeneous Turbulence

We address scaling in inhomogeneous and anisotropic turbulent flows by decomposing structure functions into their irreducible representation of the SO(3) symmetry group which are designated by $j,m$ indices. Employing simulations of channel flows with Re$_λ\approx 70$ we demonstrate that different components characterized by different $j$ display different scaling exponents, but for a given $j$ these remain the same at different distances from the wall. The $j=0$ exponent agrees extremely well with high Re measurements of the scaling exponents, demonstrating the vitality of the SO(3) decomposition.

chao-dyn↗

arXiv1999

Quantum resonances and decay of a chaotic fractal repeller observed using microwaves

The quantum resonances of classically chaotic n-disk geometries were studied experimentally utilizing thin 2-D microwave geometries. The experiments yield the frequencies and widths of low-lying resonances, which are compared with semiclassical calculations. The longtime or small energy behavior of the wave-vector auto-correlation gives information about the quantum decay rate, which is in good agreement with that obtained from classical scattering theory. The intermediate energy behavior shows non-universal oscillations determined by periodic orbits.

chao-dyn↗

arXiv1998

Asymptotic Statistics of Poincaré Recurrences in Hamiltonian Systems with Divided Phase Space

By different methods we show that for dynamical chaos in the standard map with critical golden curve the Poincaré recurrences P(τ) and correlations C(τ) asymptotically decay in time as P ~ C/τ~ 1/τ^3. It is also explained why this asymptotic behavior starts only at very large times. We argue that the same exponent p=3 should be also valid for a general chaos border.

cond-mat↗

arXiv1999

Evidence for a singularity in ideal magnetohydrodynamics: implications for fast reconnection

Numerical evidence for a finite-time singularity in ideal 3D magnetohydrodynamics (MHD) is presented. The simulations start from two interlocking magnetic flux rings with no initial velocity. The magnetic curvature force causes the flux rings to shrink until they come into contact. This produces a current sheet between them. In the ideal compressible calculations, the evidence for a singularity in a finite time $t_c$ is that the peak current density behaves like $|J|_\infty \sim 1/(t_c-t)$ for a range of sound speeds (or plasma betas). For the incompressible calculations consistency with the compressible calculations is noted and evidence is presented that there is convergence to a self-similar state. In the resistive reconnection calculations the magnetic helicity is nearly conserved and energy is dissipated.

physics.plasm-ph↗

arXiv1999

Transitions to Line-Defect Turbulence in Complex Oscillatory Media

The transition from complex-periodic to chaotic behavior is investigated in oscillatory media supporting spiral waves. We find turbulent regimes characterized by the spontaneous nucleation, proliferation and erratic motion of synchronization defect lines which separate domains of different oscillation phases. The line defect dynamics is controlled by the competition between diffusion, which reduces line length and curvature, and phase-gradient-induced growth. The onset of each type of defect-line turbulence is identified with a non-equilibrium phase transition characterized by non-trivial critical exponents.

chao-dyn↗