Chaos from turbulence: stochastic-chaotic equilibrium in turbulent convection at high Rayleigh numbers

It is shown that the correlation function of the mean wind velocity generated by a turbulent thermal convection (Rayleigh number Ra ～ 10(11)) exhibits exponential decay with a very long correlation time, while the corresponding largest Lyapunov exponent is certainly positive. These results together with the reconstructed phase portrait indicate the possible presence of chaotic component in the examined mean wind. Telegraph approximation is also used to study the relative contribution of the chaotic and stochastic components to the mean wind fluctuations and an equilibrium between these components has been studied in detail.     

Anomalous scaling of a passive scalar in turbulence and in equilibrium

We analyze the multipoint correlation functions of a tracer in an incompressible flow at scales far exceeding the scale L at which fluctuations are generated (quasiequilibrium domain) and compare them with the correlation functions at scales smaller than L (turbulence domain). We demonstrate that scale invariance can be broken in the equilibrium domain and trace this breakdown to the statistical integrals of motion (zero modes) as has been done before for turbulence. Employing the Kraichnan model of short-correlated velocity we identify the new type of zero modes, which break scale invariance and determine an anomalously slow decay of correlations at large scales.     

Ionization waves: from stability to chaos and turbulence

The spatio-temporal dynamics of self-excited ionization waves in a neon glow discharge is experimentally investigated. Various mechanisms leading to ionization waves chaos and turbulence are identified: subharmonics cascade, Ruelle-Takens-Newhouse scenario, and spatio-temporal intermittency. The dynamical states involved in the transition scenarios from stability to chaotic regimes are characterized through both temporal and spatio-temporal analysis by means of the Biorthogonal Decomposition (BD). Received 25 October 2001     

Lattice Boltzmann across scales: from turbulence to DNA translocation

The capability of the lattice Boltzmann (LB) method to describe complex flow behaviour across a wide range of scales of motion is discussed. This capability is illustrated by means of three examples, straddling across over ten decades of fluid motion, from macroscopic turbulence, to microfluidics, all the way down to nanoscopic flows of biological interest. It is pointed out that each of these applications requires extensions of the original LB scheme, beyond the realm of Navier-Stokes hydrodynamics for which the method was originally designed. The main qualitative ideas behind such extensions are discussed and commented on, with special emphasis on their direct ties with modern non-equilibrium statistical mechanics.     

Predictability: a way to characterize complexity

Different aspects of the predictability problem in dynamical systems are reviewed. The deep relation among Lyapunov exponents, Kolmogorov–Sinai entropy, Shannon entropy and algorithmic complexity is discussed. In particular, we emphasize how a characterization of the unpredictability of a system gives a measure of its complexity. Adopting this point of view, we review some developments in the characterization of the predictability of systems showing different kinds of complexity: from low-dimensional systems to high-dimensional ones with spatio-temporal chaos and to fully developed turbulence. A special attention is devoted to finite-time and finite-resolution effects on predictability, which can be accounted with suitable generalization of the standard indicators. The problems involved in systems with intrinsic randomness is discussed, with emphasis on the important problems of distinguishing chaos from noise and of modeling the system. The characterization of irregular behavior in systems with discrete phase space is also considered.     

Transition from spirals to defect-mediated turbulence driven by a doppler instability

A transition from rotating chemical spirals to turbulence is observed in experiments on the Belousov-Zhabotinsky reaction. The transition occurs when the waves near the spiral tip spontaneously break, generating defects. Measurements reveal that this defect-mediated turbulence is caused by the Doppler effect on the traveling waves. The observations are in good accord with numerical simulations and theory.     

Dynamic phase separation: from coarsening to turbulence via structure formation

We investigate some new two-dimensional evolution models belonging to the class of convective Cahn-Hilliard models: (i) a local model with a scalar order parameter, (ii) a nonlocal model with a scalar order parameter, and (iii) a model with a vector order parameter. These models are applicable to phase-separating system where concentration gradients cause hydrodynamic motion due to buoyancy or Marangoni effect. The numerical study of the models shows transition from coarsening, typical of Cahn-Hilliard systems, to spatiotemporally irregular behavior (turbulence), typical of the Kuramoto-Sivashinsky equation, which is obtained in the limit of very strong driving. The transition occurs not in a straightforward way, but through the formation of spatial patterns that emerge for intermediate values of the driving intensity. As in driven one-dimensional models studied before, the mere presence of the driving force, however small, breaks the symmetry between the two separating phases, as well as increases the coarsening rate. With increasing driving, coarsening stops. The dynamics is generally irregular at strong driving, but exhibits specific structural features.     

Relativistic Mean-Field Study to Odd-A Nuclei Far from Stability

Ground state properties of recently discovered odd-A nuclei near the particle-dripline have been investigated in the relativistic mean-field model. Special emphasis is placed on the effect of the spatial component of vector meson fields on ground state properties which is due to breaking of time reversal invariance for odd-A nuclei. Calculations show that its contribution to binding energies, radii and single particle energies is small but cannot be neglected completely for some drip-line nuclei because the last nucleon in them is very weakly bound. Calculated binding energies are in reasonably good agreement with present experimental data and estimated values in mass tables. The structure of newly discovered nuclei is also discussed.     

Hilbert Expansion from the Boltzmann Equation to Relativistic Fluids

We study the local-in-time hydrodynamic limit of the relativistic Boltzmann equation using a Hilbert expansion. More specifically, we prove the existence of local solutions to the relativistic Boltzmann equation that are nearby the local relativistic Maxwellians. The Maxwellians are constructed from a class of solutions to the relativistic Euler equations that includes a large subclass of near-constant, non-vacuum fluid states. In particular, for small Knudsen number, these solutions to the relativistic Boltzmann equation have dynamics that are effectively captured by corresponding solutions to the relativistic Euler equations.     

Trend to Equilibrium of a Degenerate Relativistic Gas

We examine the problem of the trend to equilibrium for a relativistic gas which may follow Fermi–Dirac, Bose–Einsten, classical Boltzmann statistics. We use the relativistic version of the quasiclassical Boltzmann equation for fermions and bosons, the Uehling–Uhlenbeck equation.     

Direct transition from a stable equilibrium to quasiperiodicity in non-smooth systems

The purpose of this Letter is to show how a border-collision bifurcation in a piecewise-smooth dynamical system can produce a direct transition from a stable equilibrium point to a two-dimensional invariant torus. Considering a system of nonautonomous differential equations describing the behavior of a power electronic DC/DC converter, we first determine the chart of dynamical modes and show that there is a region of parameter space in which the system has a single stable equilibrium point. Under variation of the parameters, this equilibrium may collide with a discontinuity boundary between two smooth regions in phase space. When this happens, one can observe a number of different bifurcation scenarios. One scenario is the continuous transformation of the stable equilibrium into a stable period-1 cycle. Another is the transformation of the stable equilibrium into an unstable period-1 cycle with complex conjugate multipliers, and the associated formation of a two-dimensional (ergodic or resonant) torus.     

Heavy ions: Report from Relativistic Heavy Ion Collider

We review selected highlights?from the experiments at the Relativistic Heavy Ion Collider (RHIC) exploring the QCD phase diagram. A wealth of new results appeared recently from RHIC due to major recent upgrades, like for example the ?? suppression in central nucleus?Cnucleus collisions which has been discovered recently in both RHIC and LHC. Furthermore, we discuss RHIC results from the beam energy scan (BES) program aiming to search for a possible critical point and to map out the QCD phase diagram.     

Two-dimensional turbulence: a physicist approach

Much progress has been made on two-dimensional turbulence, these last two decades, but still, a number of fundamental questions remain unanswered. The objective of the present review is to collect and organize the available information on the subject, emphasizing on aspects accessible to experiment, and outlining contributions made on simple flow configurations. Whenever possible, open questions are made explicit. Various subjects are presented: coherent structures, statistical theories, inverse cascade of energy, condensed states, Richardson law, direct cascade of enstrophy, and the inter-play between cascades and coherent structures. The review offers a physicist's view on two-dimensional turbulence in the sense that experimental facts play an important role in the presentation, technical issues are described without much detail, sometimes in an oversimplified form, and physical arguments are given whenever possible. I hope this bias does not jeopardize the interest of the presentation for whoever wishes to visit the fascinating world of Flatland.     

Transition to turbulence in a shear flow

We analyze the properties of a 19-dimensional Galerkin approximation to a parallel shear flow. The laminar flow with a sinusoidal shape is stable for all Reynolds numbers Re. For sufficiently large Re additional stationary flows occur; they are all unstable. The lifetimes of finite amplitude perturbations shows a fractal dependence on amplitude and Reynolds number. These findings are in accord with observations on plane Couette flow and suggest a universality of this transition scenario in shear flows.     

Transition to collisionless ion-temperature-gradient-driven plasma turbulence: a dynamical systems approach

The transition to collisionless ion-temperature-gradient-driven plasma turbulence is considered by applying dynamical systems theory to a model with 10 degrees of freedom. The study of a four-dimensional center manifold predicts a "Dimits shift" of the threshold for turbulence due to the excitation of zonal flows and establishes (for the model) the exact value of that shift.     

Scattering from a long helix: Theory and simulation

We consider here the electromagnetic scattering by a long helical particle made from a thin (in comparison to the wavelength) wire. In contrast to several previous theoretical works, we adopt here the algorithm developed for scattering by a multi-layered fiber. In the present work, the helical particle is considered as a hollow cylinder with a thin non-homogeneous membrane for which periodical boundary conditions are imposed.