Simple form of the stationary distribution for 3D cellular automata in a special case

3D cellular automata can be analyzed by means of finite homogeneous Markov chains. If the automaton is allowed to change only one cell per iteration, and the transition probability depends linearly on the number of ones in the neighborhood, the Markov chain has two attractors at all zeroes and all ones. Otherwise-and this is the case we tackle-the chain is ergodic, thus allowing for the search of stationary distributions. This proves cumbersome in the general case, still, under detailed balance equation, the stationary distribution can be derived in closed form. The probability of a particular state is found to be exponential in the number of zero-one borders within the configuration.     

Effect of external fluctuations on the Fréedericksz transition in an analogue simulator

The influence of multiplicative external fluctuations (noise) on the phenomenological equation describing the Fréedericksz transition has been studied by means of an electronic analogue simulator. Measurements were made of the stationary probability density for a wide range of fluctuation intensities and correlation times, for both dichotomous and Gaussianly distributed noise. For dichotomous forcing, the resultant phase diagrams at particular values of the field intensity parameter were found to be in satisfactory agreement with exact theoretical predictions by Horsthemkeet al. In the (physically more realistic) case of Gaussian fluctuations, for which no theory is currently available, the results obtained were distinctively different. A physically motivated discussion is given to account for the interesting differences and similarities of behavior found for the two types of external noise.     

Subcritical asymptotic behavior in the thermodynamic limit of reversible random polymerization processes

We consider a reversible Markov process as a chemical polymerization model and study the asymptotic behavior (in the thermodynamic limit asN+) of a particular probability distribution on the set ofN-dimensional vectors, thekth component of which is the number ofk-mers. The study establishes the existence of three stages (subcritical, near-critical, and supercritical stages) of polymerization, depending on the value of the strength of the fragmentation reaction. The present paper concentrates on the analysis of the subcritical stage. In the subcritical stages we show that the size of the largest length of polymers of sizeN is of the order logN asN+.     

Self-diffusion in one-dimensional lattice gases in the presence of an external field

We study the motion of a tagged particle in a one-dimensional lattice gas with nearest-neighbor asymmetric jumps, withp (respectively,q),p > q, the probability to jump to the right (left). It was shown in Ref. 6 that the fluctuations in the position of the tagged particle behave normally; (X)²Dt. Here we compute explicitly the diffusion coefficient. We findD=(1-)(p-q). where is the gas density. The result confirms some recent conjectures based on theoretical arguments and computer experiments.Partially supported by NSF grant No. DMR81-14726.Partially supported by CNR.Partially supported by CNPq, grant No. 201682-83.     

Approach to equilibrium in models of a system in contact with a heat bath

We investigate simple model systems in contact with an infinite heat bath. The former consists of a finite number of particles in a bounded region of ^d,d=1,2. The heat baths are infinite particle systems which can penetrate and interact with the system via elastic collisions. Outside the particles move freely and have a Gibbs probability measure prior to entering. We show that starting from almost any initial configuration, the system approaches, ast , the appropriate Gibbs distribution. The combined system plus bath is Bernoulli.Partially supported by NSF Grants PHY 8201708 and DMR 81-14726-02.     

Computer simulation of shock waves in the completely asymmetric simple exclusion process

We study the evolution of the completely asymmetric simple exclusion process in one dimension, with particles moving only to the right, for initial configurations corresponding to average density _– ( ₊) left (right) of the origin, _{– +}. The microscopic shock position is identified by introducing a second-class particle. Results indicate that the shock profile is stable, and that the distribution as seen from the shock positionN(t) tends, as time increases, to a limiting distribution, which is locally close to an equilibrium distribution far from the shock. Moreover , withV=1– _–– ₊, as predicted, and the dispersion ofN(t), ²(t), behaves linearly, for not too small values of ₊– _–, i.e., , whereS is equal, up to a scaling factor, to the valueS _WA predicted in the weakly asymmetric case. For ₊= _– we find agreement with the conjecture .Dedicated to the memory of Paola Calderoni.     

充模过程中熔接痕的改进光滑粒子动力学方法模拟与预测

提出了一种黏弹性流体的改进光滑粒子动力学(SPH)方法以试探性地模拟和预测黏弹性FENE-P熔体充模过程中熔接痕的形态演化. 首先基于SPH方法建立了聚合物流动的宏微观耦合模型, 同时提出了黏弹性流体的改进SPH离散格式. 随后, 通过模拟一些基准算例验证了改进的SPH方法模拟聚合物宏微观耦合问题的有效性及收敛性, 以及所提出的黏弹性温度模型的有效性. 最后, 模拟了环型腔内的充模过程, 试探性地展示了充模过程中微观分子的变形过程. 同时采用顺序热流道技术模拟了多浇口C形腔内的充模过程, 并与其他数值结果做比较. 数值结果表明: 对于大制件多浇口充模过程, 顺序热流道技术能够改善甚至消除充模过程中的熔接痕.     

Zone inhomogeneity with the random asymmetric simple exclusion process in a one-lane system

In this paper we use theoretical analysis and extensive simulations to study zone inhomogeneity with the random asymmetric simple exclusion process (ASEP). In the inhomogeneous zone, the hopping probability is less than 1. Two typical lattice geometries are investigated here. In case A, the lattice includes two equal segments. The hopping probability in the left segment is equal to 1, and in the right segment it is equal to p, which is less than 1. In case B, there are three equal segments in the system; the hopping probabilities in the left and right segments are equal to 1, and in the middle segment it is equal to p, which is less than 1. Through theoretical analysis, we can discover the effect on these systems when p is changed.     

Detection of functional states by the ‘LAMDA’ classification technique: application to a coagulation process in drinking water treatment

The present Note proposes a learning classification methodology to identify functional states on a coagulation process involved in drinking water treatment. In this work, we chose to carry out the supervised control of this process while using the LAMDA (Learning Algorithm for Multivariate Data Analysis) classification technique. The LAMDA classification technique proposes the interactive participation of the expert operator during the learning phase and in the optimisation of the classification. In this work, all information stemming from the environment process as well as expert knowledge has been aggregated and exploited. The application chosen for state identification is the Rocade drinking water treatment plant located at Marrakech, Morocco. To cite this article: B. Lamrini et al., C. R. Physique 6 (2005).     

A metastable hard magnetic phase in the crystallization process of the Fe75Si11B10Nb3Sn1 alloy

A very interesting characteristic of FeSiB based amorphous alloys is its soft magnetic behavior. Most of these alloys remains soft along the crystallization process up to the nucleation of the iron borides. Examples of this are the widely studied Finemet and the FeSiBSn. In this work the crystallization of Fe₇₆Si₁₁B₁₀Nb₃ and Fe₇₅Si₁₁B₁₀Nb₃Sn₁ is studied by means of X-ray diffraction, Mössbauer spectroscopy and coercive magnetic field measurements after one hour isothermal annealing at different temperatures. In the crystallization process of the latter alloy a hard magnetic phase appeared when the samples were annealed above 773 K. The soft magnetic behavior was recovered after annealing at 873 K. The hyperfine parameters as well as the X-ray diffraction patterns are reported.