Propagation and ignition of fast gasless detonation waves of phase or chemical transformation in condensed matter

Fast self sustained waves of chemical or phase transformations, observed in several contexts in condensed matter effectively result in “gasless detonation". The phenomenon is modelled by coupling the reaction diffusion equation, describing chemical or phase transformations, and the wave equation, describing elastic perturbations. The coupling considered in this work involves (i) a dependence of the sound velocity on the chemical (phase) field, and (ii) the destruction of the initial chemical equilibrium when the strain exceeds a critical value (strain induced phase transition). Both the case of an initially unstable state (first order kinetics) and metastable state (second order kinetics) are considered. An exhaustive analytic and numerical study of travelling waves reveals the existence of supersonic modes of transformations. The practically important problem of ignition of fast waves by mechanical perturbation is investigated. With the present model, the critical strain necessary to ignite gasless detonation by local perturbations is determined. Received 18 November 1999     

Detonation type waves in phase (chemical) transformation processes in condensed matter

Fast self sustained waves (autowaves) associated with chemical or phase transformations are observed in many situations in condensed matter. They are governed neither by diffusion of matter or heat (as in combustion processes) nor by a travelling shock wave (as in gaseous detonation). Instead, they result from a coupling between phase transformation and the stress field, and may be classified as gasless detonation autowaves in solids. We propose a simple model to describe these regimes. The model rests on the classical equations of elastic deformations in a 1-dimensional solid bar, with the extra assumption that the phase (chemical) transformation induces a change of the sound velocity. The transformations are assumed to occur through a chain branched mechanism, which starts when the mechanical stress exceeds a given threshold. Our investigation shows that supersonic autowaves exist in this model. In the absence of diffusion (dissipation factor, losses), a continuum of travelling wave solutions is found. In the presence of diffusion, a steady state supersonic wave solution is found, along with a slower wave controlled by diffusion. Received 15 October 1998     

Influence of heat bath on the heat conductivity in disordered anharmonic chain

We study heat conduction in a one-dimensional disordered anharmonic chain with arbitrary heat bath by using extended Ford, Kac and Mazur (FKM) formulation, which satisfy the fluctuation-dissipation theorem. A simple formal expression for the heat conductivity κ is obtained, from which the asymptotic system-size (N) dependence is extracted. It shows κ∼N^α. As a special case we give the expression that κ∼N^1/2 for free boundaries, and κ∼ N^-1/2 for fixed boundaries, from which we can get the conclusion that the momentum conservation is a key factor of the anomalous heat conduction. Comparing with different ∇T, the heat conductivity shows large difference between the linear system and the nonlinear system.     

Weak chaos and metastability in a symplectic system of many long-range-coupled standard maps

We introduce, and numerically study, a system of N symplectically and globally coupled standard maps localized in a d=1 lattice array. The global coupling is modulated through a factor r^-α, being r the distance between maps. Thus, interactions are long-range (nonintegrable) when 0≤α≤1, and short-range (integrable) when α>1. We verify that the largest Lyapunov exponent λ_M scales as λ_M ∝ N^-κ(α), where κ(α) is positive when interactions are long-range, yielding weak chaos in the thermodynamic limit N↦∞ (hence λ_M→0). In the short-range case, κ(α) appears to vanish, and the behaviour corresponds to strong chaos. We show that, for certain values of the control parameters of the system, long-lasting metastable states can be present. Their duration t_c scales as t_c ∝N^β(α), where β(α) appears to be numerically in agreement with the following behavior: β>0 for 0 ≤α< 1, and zero for α≥1. These results are consistent with features typically found in nonextensive statistical mechanics. Moreover, they exhibit strong similarity between the present discrete-time system, and the α-XY Hamiltonian ferromagnetic model.     

Heat and fluctuations from order to chaos

The Heat theorem reveals the second law of equilibrium Thermodynamics (i.e. existence of Entropy) as a manifestation of a general property of Hamiltonian Mechanics and of the Ergodic Hypothesis, valid for 1 as well as 10²³ degrees of freedom systems, i.e. for simple as well as very complex systems, and reflecting the Hamiltonian nature of the microscopic motion. In Nonequilibrium Thermodynamics theorems of comparable generality do not seem to be available. Yet it is possible to find general, model independent, properties valid even for simple chaotic systems (i.e. the hyperbolic ones), which acquire special interest for large systems: the Chaotic Hypothesis leads to the Fluctuation Theorem which provides general properties of certain very large fluctuations and reflects the time-reversal symmetry. Implications on Fluids and Quantum systems are briefly hinted. The physical meaning of the Chaotic Hypothesis, of SRB distributions and of the Fluctuation Theorem is discussed in the context of their interpretation and relevance in terms of Coarse Grained Partitions of phase space. This review is written taking some care that each section and appendix is readable either independently of the rest or with only few cross references.     

Spatiotemporal chaos control in two-wave driven systems

Spatiotemporal chaos control is considered by taking a one-dimensional driven/damped nonlinear drift-wave equation as a model. We apply an additional sinusoidal wave to suppress spatiotemporal chaos, and the system becomes a two-sinusoidal-wave driven system (the original driving wave with frequency ω and an additional controlling wave with frequency Ω). Numerical simulations show that when the frequency of the controlling wave is in the proper range, spatiotemporal chaos can be modified into a regular state where the amplitudes of all modes vary periodically with frequency Ω-ω while the phases of all modes evolve quasi-periodically with a running frequency Ω overlapped by a small modulation of frequency Ω-ω. The physical reason for this peculiar phenomenon is attributed to a frequency entrainment in the competition of the two external waves.     

A definition of metastability for Markov processes with detailed balance

A definition of metastable states applicable to arbitrary finite state Markov processes satisfying detailed balance is discussed. In particular, we identify a crucial condition that distinguishes genuine metastable states from other types of slowly decaying modes and which leads to properties similar to those postulated in the restricted ensemble approach [1]. The intuitive physical meaning of this condition is simply that the total equilibrium probability of finding the system in the metastable state is negligible. As a concrete application of our formalism we present preliminary results on a 2D kinetic Ising model.     

Thermal cycles, interface chemistry and optical performance of Mg/SiC multilayers

The interplay between optical performance and the thermally activated interface chemistry of periodic Mg/SiC multilayers designed for application at 30.4 nm are investigated by optical (hard X-ray, soft X-ray and ultraviolet ranges, i.e. from 0.154 to 30.4 nm) reflectivity and X-ray emission spectroscopy. The multilayers are prepared by magnetron sputtering and then annealed up to a temperature of 500 °C. Two clear changes take place in the multilayer upon annealing. At first, between 200 and 300 °C a strong decrease of the reflectivity is observed, due to the development of interfacial roughness following the crystallization of the Mg layers. No interfacial compound is detected. Then, between 350 and 400 °C there is formation of the Mg₂Si magnesium silicide at the interfaces following the reaction between the Mg and SiC layers. This also leads to the almost total loss of reflectivity of the multilayer. Thus, this kind of multilayer is thermally stable only for application requiring no heating above 200 °C.     

局域反馈抑制心脏中的螺旋波和时空混沌

采用LuoRud91模型研究了螺旋波和时空混沌的抑制,提出用局域反馈控制方法抑制螺旋波和时空混沌,采用静止和运动控制器两种控制策略.结果表明:适当选择控制参数,静止控制器的局域反馈方法能很好抑制螺旋波,但不能有效抑制时空混沌;采用运动控制器的局域反馈方法能有效抑制螺旋波和时空混沌,抑制速度与控制器移动的速度有关,在选择适当的控制参数下,螺旋波和时空混沌能在很短的时间内被抑制.     

Suppression of spatiotemporal chaos under a constant electric potential signal

Suppression of spatiotemporal chaos in a one-dimensional nonlinear drift-wave equation driven by a sinusoidal wave is considered. Using a constant electric potential signal we demonstrate numerically that the spatiotemporal chaos can be effectively suppressed if the control parameters are properly chosen. The threshold and the controllable range of the control parameters are given. By establishing the kinetic equation of the system energy we find theoretically that an additional driving term in the energy equation is produced by the control signal and it can lead up to the frequency entrainment. Moreover, when the regular state is reached under the control, the system energy oscillates quasi-periodically, while the additional driving term decays to zero.     

Effect of long range interactions on the growth of compact clusters under deposition

In the paper the role of long range interactions on the growth of a volume conserving surface is studied using the Nonlocal Conserved Kardar-Parisi-Zhang (NCKPZ) equation. It is shown that previous theoretical predictions are inconsistent with an exact one-dimensional result. This serves as a motivation for construction of a Self-Consistent Expansion (SCE) that recovers the exact one-dimensional result, and gives the scaling exponents in higher dimensions as well. A possible application of this result to colloidal systems is discussed.     

Anomalous scaling in the Zhang model

We apply the moment analysis technique to analyze large scale simulations of the Zhang sandpile model. We find that this model shows different scaling behavior depending on the update mechanism used. With the standard parallel updating, the Zhang model violates the finite-size scaling hypothesis, and it also appears to be incompatible with the more general multifractal scaling form. This makes impossible its affiliation to any one of the known universality classes of sandpile models. With sequential updating, it shows scaling for the size and area distribution. The introduction of stochasticity into the toppling rules of the parallel Zhang model leads to a scaling behavior compatible with the Manna universality class. Received 8 August 2000 and Received in final form 4 October 2000     

The short-time critical behaviour of the Ginzburg-Landau model with long-range interaction

The renormalisation group approach is applied to the study of the short-time critical behaviour of the d-dimensional Ginzburg-Landau model with long-range interaction of the form in momentum space. Firstly the system is quenched from a high temperature to the critical temperature and then relaxes to equilibrium within the model A dynamics. The asymptotic scaling laws and the initial slip exponents and of the order parameter and the response function respectively, are calculated to the second order in . Received 9 June 2000 and Received in final form 2 August 2000     

Controlling chaos by a modified straight-line stabilization method

By adjusting external control signal, rather than some available parameters of the system, we modify the straight-line stabilization method for stabilizing an unstable periodic orbit in a neighborhood of an unstable fixed point formulated by Ling Yang et al., and derive a more simple analytical expression of the external control signal adjustment. Our technique solves the problem that the unstable fixed point is independent of the system parameters, for which the original straight-line stabilization method is not suitable. The method is valid for controlling dissipative chaos, Hamiltonian chaos and hyperchaos, and may be most useful for the systems in which it may be difficult to find an accessible system parameter in some cases. The method is robust under the presence of weak external noise. Received 10 January 2001     

Structure and fragmentation in colloidal artificial molecules and nuclei

Motivated by recent experiments on colloidal systems with competing attractive and repulsive interactions, we simulate a two-dimensional system of colloids with competing interactions that can undergo fragmentation. In the absence of any other confining potential, the colloids can form stable clusters depending on the strength of the short range attractive term. By suddenly changing the strength of one of the interaction terms we find a rich variety of fragmentation behavior which is affected by the existence of “magic” cluster numbers. Such soft matter systems can be used to construct artificial nuclei.     

Non-commutative geometry and irreversibility

A kinetics built upon q-calculus, the calculus of discrete dilatations, is shown to describe diffusion on a hierarchical lattice. The only observable on this ultrametric space is the “quasi-position” whose eigenvalues are the levels of the hierarchy, corresponding to the volume of phase space available to the system at any given time. Motion along the lattice of quasi-positions is irreversible. Received: 24 June 1997 / Revised: 15 September 1997 / Accepted: 6 October 1997     

Damage-spreading in the Bak-Sneppen model without noise

We study the behavior under perturbations in the, recently introduced, Bak-Sneppen model with deterministic updating. We focus our attention on the damage-spreading features and show that the value of the growth exponent for the distance, , coincides with that of the random updating Bak-Sneppen model. Moreover, we generalize this analysis by considering a broader set of initial perturbations for which the value of is preserved. Received: 24 June 1998 / Accepted: 9 July 1998     

Sensitivity to initial conditions in the Bak-Sneppen model of biological evolution

We consider biological evolution as described within the Bak and Sneppen 1993 model. We exhibit, at the self-organized critical state, a power-law sensitivity to the initial conditions, calculate the associated exponent, and relate it to the recently introduced nonextensive thermostatistics. The scenario which here emerges without tuning strongly reminds of that of the tuned onset of chaos in say logistic-like one-dimensional maps. We also calculate the dynamical exponent z. Received: 5 November 1997 / Received in final form: 11 November 1997 / Accepted: 19 November 1997     

Driven lattice gas with nearest-neighbor exclusion: shear-like drive

We study the lattice gas with nearest-neighbor exclusion on the square lattice and Kawasaki (hopping) dynamics, under the influence of a nonuniform drive, via Monte Carlo simulation. The drive, which favors motion along the +x direction and inhibits motion in the opposite direction, varies linearly with y. (The boundaries along the drive direction are periodic, so that the system is not described by an equilibrium Gibbs distribution.) As in the uniformly driven case [R. Dickman, Phys. Rev. E 64, 16124 (2001)], the onset of sublattice ordering occurs at a lower density than in equilibrium, but here an unexpected feature appears: particles migrate out of the high-drive region. For intermediate system sizes (L ≃100), the accumulation of particles is sufficient for the low-drive region to become ordered at a global density of about 0.3. Above this density we observe a surprising reversal in the density profile, with particles accumulating to the high-drive region, due to jamming. For larger systems (L≥200) particles quickly jam in the high-drive region, as occurs under uniform drive, and the accumulation of particles in the low-field region is severely reduced.     

Damage-spreading in the parallel Bak-Sneppen model

We study the behavior under perturbations of the Parallel Bak-Sneppen model (PBS) in 1+1 dimension, which has been shown to belong to the universality class of Directed Percolation (DP) in 1+1 dimensions [#!SD96!#]. We focus our attention on the damage-spreading features of the PBS model with both random and deterministic updating, which are studied and compared to the known results for the extremal Bak-Sneppen model (BS) and for DP. For both random and deterministic updating, we observe a power law growth of the Hamming distance. In addition, we compute analytically the asymptotic plateau reached by the distance after the growing phase. Received: 24 September 1998 / Revised: 17 November 1998 / Accepted: 19 November 1998