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     

Convergence dynamics of 2-dimensional isotropic and anisotropic Bak-Sneppen models

The conventional Hamming distance measurement captures only short-time dynamics of the displacement between uncorrelated random configurations. The minimum difference technique introduced by Tirnakli and Lyra [U. Tirnakli, M.L. Lyra. Int. J. Mod. Phys. C 14 (2003) 805] is used to study short-time and long-time dynamics of the two distinct random configurations of isotropic and anisotropic Bak-Sneppen models on a square lattice. Similar to a 1-dimensional case, the time evolution of the displacement is intermittent. The scaling behavior of the jump activity rate and waiting time distribution reveal the absence of typical spatial-temporal scales in the mechanism of displacement jumps used to quantify convergence dynamics.     

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     

Analytical properties and exact solutions of static plasma equilibrium systems in three dimensions

For static reductions of isotropic and anisotropic magnetohydrodynamics plasma equilibrium models, a complete classification of admitted point symmetries and conservation laws up to first order is presented. It is shown that the symmetry algebra for the isotropic equations is finite-dimensional, whereas anisotropic equations admit infinite symmetries depending on a free function defined on the set of magnetic surfaces. A direct transformation is established between isotropic and anisotropic equations, which provides an efficient way of constructing new exact anisotropic solutions. In particular, axially and helically symmetric anisotropic plasma equilibria arise from classical Grad-Shafranov and JFKO equations.     

Fluctuations and finite-size effect in the Bak-Sneppen model

The self-organized criticality in the nearest-neighbor version of the Bak-Sneppen model is investigated from the event-by-event fluctuations of the mean fitness. The finite-size effect on the evolution of the critical state is shown, and a scaling solution to the gap equation for an infinite one-dimensional lattice is given numerically for the first time. The mean lifetime of avalanches is presented as a function of the gap from the solution. The critical value of the gap and an exponent are calculated from the solution. Received 10 December 2000 and Received in final form 18 January 2001     

Critical properties of the metal-insulator transition in anisotropic systems

We study the three-dimensional Anderson model of localization with anisotropic hopping, i.e., weakly coupled chains and weakly coupled planes. In our extensive numerical study we identify and characterize the metal-insulator transition by means of the transfer-matrix method. The values of the critical disorder obtained are consistent with results of previous studies, including multifractal analysis of the wave functions and energy-level statistics. decreases from its isotropic value with a power law as a function of anisotropy. Using high accuracy data for large system sizes we estimate the critical exponent as . This is in agreement with its value in the isotropic case and in other models of the orthogonal universality class. Received 25 October 1999     

Universal growth laws in liquid crystals far from equilibrium

Universal growth laws were examined experimentally for the transition from an isotropic melt to the liquid-crystalline state as well as the liquid-crystal (LC) to crystal transition for a system, which can be largely super-cooled. For large quench depths the growth exponent of the growth law L(t) ∼tⁿ is given by n=1. On decreasing the quench depth, two phase-ordering processes can be resolved for the isotropic (Iso.)–LC transition, one with a decreasing growth exponent 1<n<1/2 and a long-time process with n=1, independent of quench depth. In the very vicinity of the transition, nucleus growth is described by a single process according to L(t) ∼t^1/2. This behavior is interpreted in terms of an Iso. to blue-phase (BP) to cholesteric (N*) transition. The crystallization from the liquid-crystalline state (monotropic smectic A*) can be super-cooled substantially and follows a linear-growth process L(t)∼t. Received: 3 July 2000 / Accepted: 17 October 2000 / Published online: 10 January 2001     

Metastability Thresholds for Anisotropic Bootstrap Percolation in Three Dimensions

In this paper we analyze several anisotropic bootstrap percolation models in three dimensions. We present the order of magnitude for the metastability thresholds for a fairly general class of models. In our proofs, we use an adaptation of the technique of dimensional reduction. We find that the order of the metastability threshold is generally determined by the ‘easiest growth direction’ in the model. In contrast to anisotropic bootstrap percolation in two dimensions, in three dimensions the order of the metastability threshold for anisotropic bootstrap percolation can be equal to that of isotropic bootstrap percolation.     

六方小面相螺旋在各向异性、表面吸附、界面动力学作用下生长的相场

利用定量相场模型研究了强各向异性、表面吸附率以及界面动力学作用条件下六方Ga N螺旋结构的表面形貌与生长机理.通过引入小面相各向异性的相场修正方程,研究了不同各向异性的稳态螺旋形貌,发现各向异性通过改变台阶尖端的曲率作用影响螺旋生长.弱各向异性下稳态螺距及界面动力学特征相对稳定,各向异性较强时尖端的过饱和度随着各向异性的增强而增大,并使得界面平衡态向着有利于螺旋台阶推进的方向移动.研究了表面吸附率对小面相螺旋生长的作用机理,发现吸附率的增加导致了稳态螺旋间距的降低,通过分析螺旋间距随台阶宽度的变化趋势,发现增强的表面吸附和各向异性强度降低了螺旋间距的收敛性,并且具体分析了收敛性误差;通过探讨界面动力学作用条件下螺旋形貌特征以及螺旋间距变化趋势,发现界面动力学系数通过改变稳态螺旋间距与特征指数因子调控螺旋生长的动力学机理,与各向同性相比小面相螺旋生长表现出较低的界面动力学系数依赖性.     

An equation of state for anisotropic solids under shock loading

An anisotropic equation of state is proposed for accurate extrapolation of high-pressure shock Hugoniot states to other thermodynamics states for shocked single crystals and polycrystalline alloys. The proposed equation of state represents mathematical and physical generalization of the Mie-Grüneisen equation of state for isotropic material and reduces to this equation in the limit of isotropy. Using an anisotropic nonlinear continuum framework and generalized decomposition of a stress tensor [Int. J. Plasticity 24, 140 (2008)], the shock waves propagation along arbitrary directions in anisotropic solids of any symmetry can be examined. The non-associated strength model includes the distortion effect of the yield surface which can be used to describe the anisotropic strength differential effect. A numerical calculation showed that the general pulse shape, Hugoniot Elastic Limits (HELs), and Hugoniot stress levels for aluminum alloy 7010-T6 agree with the experimental data. The results are presented and discussed, and future studies are outlined.     

Conical parametric scattering of a single extraordinary beam in BaTiO3 crystal

In this paper, the parametric scattering of a single extraordinary polarized beam of laser in BaTiO₃ photorefractive crystal has been investigated experimentally and theoretically. The resulting pattern consists of beam fanning, isotropic ring, and anisotropic one. Among all parts of scattering pattern, isotropic ring has not been studied as much as beam fanning and anisotropic ring, and there still are some differences in reports about it. Therefore, the study has mainly focused on this part. In this experimental configuration, isotropic ring is just visible in positive angles although the other parts of parametric scattering pattern can be visible from behind and in front of the crystal. In addition to steady state pattern in forward and backward directions, its transient behavior with the rotation of crystal has been studied. The results of experiments have been analyzed carefully, and their theoretical explanations have been presented based on the standard theory of parametric scattering in photorefractive crystals. It has been shown that this configuration corresponds to the so called parametric B-process scattering.     

Approximate renormalization group calculation of cubic crossover

The cross-over exponent for an anisotropic cubic perturbation is calculated for all n > 1 and d = 3. It is found that the isotropic fixed point is unstable for $\text{n ? 2.3}$.     

Perturbative approach to the Bak-Sneppen model

We study the Bak-Sneppen model in the probabilistic framework of the run time statistics (RTS). This model has attracted a large interest for its simplicity being a prototype for the whole class of models showing self-organized criticality. The dynamics is characterized by a self-organization of almost all the species fitnesses above a nontrivial threshold value, and by a lack of spatial and temporal characteristic scales. This results in avalanches of activity power law distributed. In this Letter we use the RTS approach to compute the value of x(c), the value of the avalanche exponent tau, and the asymptotic distribution of minimal fitnesses.     

LRS Bianchi type I models with anisotropic dark energy and constant deceleration parameter

Locally rotationally symmetric Bianchi type I cosmological models are examined in the presence of dynamically anisotropic dark energy and perfect fluid. We assume that the dark energy (DE) is minimally interacting, has dynamical energy density, anisotropic equation of state parameter (EoS). The conservation of the energy-momentum tensor of the DE is assumed to consist of two separately additive conserved parts. A special law is assumed for the deviation from isotropic EoS, which is consistent with the assumption on the conservation of the energy-momentum tensor of the DE. Exact solutions of Einstein’s field equations are obtained by assuming a special law of variation for the mean Hubble parameter, which yields a constant value of the deceleration parameter. Geometrical and kinematic properties of the models and the behaviour of the anisotropy of the dark energy have been carried out. The models give dynamically anisotropic expansion history for the universe that allows to fine tune the isotropization of the Bianchi metric, hence the CMB anisotropy.     

Different hierarchy of avalanches observed in the bak-sneppen evolution model

A quantity &fmacr; denoting the average fitness of an ecosystem is introduced in the Bak-Sneppen model. Through this quantity, a different hierarchy of avalanches, &fmacr;(0) avalanche, is observed in the evolution of Bak-Sneppen model. An exact gap equation, governing the self-organization of the model, is presented in terms of &fmacr;. It is found that self-organized threshold &fmacr;(c) can be exactly obtained. Two basic exponents of the new avalanche tau, avalanche distribution, and D, avalanche dimension are given through simulations of one- and two-dimensional Bak-Sneppen models. It is suggested that &fmacr; may be a good quantity in determining the emergence of criticality.     

Thermodynamic fluctuations in two-dimensional degenerate antiferromagnetic structures

A model of a two-dimensional antiferromagnet with an arbitrary anisotropic interaction that allows for degeneracy of the ground state is proposed. The lifting of degeneracy by thermodynamic fluctuations and the accompanying effects are studied by a method of self-consistent calculations of Gaussian angular fluctuations that is asymptotically exact at low temperatures. Fluctuations are shown to lead to collinear ordering of the orientations of magnetic sublattices, an effect that initiates long-range orientational order in systems with anisotropic interaction but retains only short-range order in systems with isotropic short-range interaction. The temperature patterns of the orientational correlators are given for the particular cases of dipole and isotropic short-range interaction models. The nature of the Ising-like behavior of the system is discussed for the case of a strong anisotropy of the correlators, which corresponds to quasi-one-dimensional behavior. Zh. éksp. Teor. Fiz. 111, 669–680 (February 1997)     

Elastic interaction between defects in thin and 2D films

Elastic interactions between defects is investigated at the surface of thin layers, a question on which we have given a brief account [P. Peyla et al. Phys. Rev. Lett. 82, 787 (1999)]. Two isotropic defects do not interact in an unlimited medium, regardless of the spatial dimension, a result which can be shown on the basis of the Gauss theorem in electrostatics. Within isotropic elasticity theory, defects interact only (i) if they are, for example, at a surface (or at least if they feel a boundary), or if their action on the material is anisotropic (e.g. they create a non central force distribution, though the material elasticity is isotropic). It is known that two identical isotropic defects on the surface of a semi-infinite material repel each other. The repulsion law behaves as 1/r ³(r = defects separation). We first revisit the Lau-Kohn theory and extend it to anisotropic defects. Anisotropy is found to lead to attraction. We show that in thin films defects may either attract or repel each other depending on the local geometric force distribution caused by the defect. It is shown that the force distribution (or more precisely the forces configuration symmetry) fixes the exponent in the power law 1/r ⁿ (e.g. for a four-fold symmetry n = 4). We discuss the implication of this behaviour in various situations. We treat the interactions in terms of the symmetries associated with the defect. We argue that if the defects are isotropic, then their effective interaction in an unlimited 2D (or a thin film) medium arises from the induced interaction, which behaves as 1/r ⁴ for any defect symmetry. We shall also comment on the contribution to the interaction which arises from flexion of thin films. Received 7 October 2002 Published online 4 June 2003 RID="a" ID="a"e-mail: chaouqi.misbah@ujf-grenoble.fr     

Quantum Correlations in Infinite XY Spin-1/2 Chains and Quantum Phase Transition

We examine the ability of quantum discord (QD) and entanglements (concurrence, EoF and negativity) to detect the critical points associated to quantum phase transitions (QPTs) for XY models, i.e., the isotropic XY model with three-spin interactions at zero temperature, and the anisotropic XY model in a transverse magnetic field h at finite temperatures. For the case of zero temperature, we found that both entanglements and QD can spotlight the critical points of QPTs for these two models. Moreover, QD versus distance M exhibits the long-range behavior of quantum correlation for the anisotropic XY model, while entanglement is short-ranged. For the case of finite temperatures, we found that negativity has the same behaviors with concurrence at or near transition points. Moreover, QD for the anisotropic XY model can increase with temperature even in the absence of a magnetic field.     

Universal crossing probabilities and incipient spanning clusters in directed percolation

Shape-dependent universal crossing probabilities are studied, via Monte Carlo simulations, for bond and site directed percolation on the square lattice in the diagonal direction, at the percolation threshold. In a dynamical interpretation, the crossing probability is the probability that, on a system with size L, an epidemic spreading without immunization remains active at time t. Since the system is strongly anisotropic, the shape dependence in space-time enters through the effective aspect ratio r _eff = ct/L ^z, where c is a non-universal constant and z the anisotropy exponent. A particular attention is paid to the influence of the initial state on the universal behaviour of the crossing probability. Using anisotropic finite-size scaling and generalizing a simple argument given by Aizenman for isotropic percolation, we also obtain the behaviour of the probability to find n incipient spanning clusters on a finite system at time t. The numerical results are in good agreement with the conjecture. Received 10 February 2003 Published online 20 June 2003 RID="a" ID="a"e-mail: turban@lpm.u-nancy.fr RID="b" ID="b"UMR CNRS 7556