scholarly journals The inactive–active phase transition in the noisy additive (exclusive-or) probabilistic cellular automaton

2015 ◽  
Vol 27 (02) ◽  
pp. 1650016 ◽  
Author(s):  
J. Ricardo G. Mendonça
Keyword(s):  
Phase Transition ◽  
Cellular Automaton ◽  
Critical Behavior ◽  
Transition Probabilities ◽  
Mean Field ◽  
Active Phase ◽  
Mean Field Equations ◽  
Probabilistic Cellular Automaton ◽  
The Mean ◽  
Exclusive Or

We investigate the inactive–active phase transition in an array of additive (exclusive-or) cellular automata (CA) under noise. The model is closely related with the Domany-Kinzel (DK) probabilistic cellular automaton (PCA), for which there are rigorous as well as numerical estimates on the transition probabilities. Here, we characterize the critical behavior of the noisy additive cellular automaton by mean field analysis and finite-size scaling and show that its phase transition belongs to the directed percolation universality class of critical behavior. As a by-product of our analysis, we argue that the critical behavior of the noisy elementary CA 90 and 102 (in Wolfram’s enumeration scheme) must be the same. We also perform an empirical investigation of the mean field equations to assess their quality and find that away from the critical point (but not necessarily very far away) the mean field approximations provide a reasonably good description of the dynamics of the PCA.

Critical Behavior of Gd5Si2Ge1.9Ga0.1 near the Ferromagnetic-Paramagnetic Phase Transition

2013 ◽  
Vol 873 ◽  
pp. 855-860 ◽  
Author(s):  
Zeng Ru Zhao ◽  
Gao Feng Wang ◽  
Xue Feng Zhang
Keyword(s):  
Phase Transition ◽  
Critical Behavior ◽  
Scaling Law ◽  
Mean Field Theory ◽  
Mean Field ◽  
Entropy Change ◽  
Paramagnetic Phase ◽  
Range Type ◽  
Fisher Model ◽  
The Mean

The critical behavior near the ferromagnetic-paramagnetic phase transition in Gd5Si2Ge1.9Ga0.1 has been investigated using a method based on the field dependence of isothermal entropy change. The reliability of the critical exponents determined in such a way has been examined through various techniques, like constructing the modified Arrott plot, applying the scaling law on the isothermal magnetization curves, and comparing the values with those obtained from the Kouvel-Fisher model. The resulting values of the exponents were estimated to be = 0.45(2), = 1.31(5), = 3.9(2) and = 0.69(1), close to the values predicted by the mean field theory. Hence, we concluded that the exchange interaction is of long-range type.

CRITICAL BEHAVIOR OF A PROBABILISTIC LOCAL AND NONLOCAL SITE-EXCHANGE CELLULAR AUTOMATON

1994 ◽  
Vol 05 (03) ◽  
pp. 537-545 ◽  
Author(s):  
N. BOCCARA ◽  
J. NASSER ◽  
M. ROGER
Keyword(s):  
Cellular Automaton ◽  
Critical Behavior ◽  
Exchange Process ◽  
Mean Field ◽  
One Dimensional ◽  
Probabilistic Cellular Automaton ◽  
Site Exchange ◽  
Two Parameters ◽  
Automata Network ◽  
Dimensional Range

We study the critical behavior of a probabilistic automata network whose local rule consists of two subrules. The first one, applied synchronously, is a probabilistic one-dimensional range-one cellular automaton rule. The second, applied sequentially, exchanges the values of a pair of sites. According to whether the two sites are first-neighbors or not, the exchange is said to be local or nonlocal. The evolution of the system depends upon two parameters, the probability p characterizing the probabilistic cellular automaton, and the degree of mixing m resulting from the exchange process. Depending upon the values of these parameters, the system exhibits a bifurcation similar to a second order phase transition characterized by a nonnegative order parameter, whose role is played by the stationary density of occupied sites. When m is very large, the correlations created by the application of the probabilistic cellular automaton rule are destroyed, and, as expected, the behavior of the system is then correctly predicted by a mean-field-type approximation. According to whether the exchange of the site values is local or nonlocal, the critical behavior is qualitatively different as m varies.

Solution of the mean field equations for spontaneous fission

1987 ◽  
Vol 35 (3) ◽  
pp. 1007-1027 ◽  
Author(s):  
G. Puddu ◽  
J. W. Negele
Keyword(s):  
Spontaneous Fission ◽  
Mean Field ◽  
Field Equations ◽  
Mean Field Equations ◽  
The Mean

scholarly journals Phase diagram of the selfinteracting particle­-antiparticle boson system

2021 ◽  
Vol 29 (1) ◽  
pp. 5-14
Author(s):  
D. Anchishkin ◽  
V. Gnatovskyy ◽  
D. Zhuravel ◽  
V. Karpenko
Keyword(s):  
Phase Transition ◽  
Phase Diagram ◽  
Phase Diagrams ◽  
Canonical Ensemble ◽  
Bose Condensate ◽  
Mean Field ◽  
Thermodynamic Quantities ◽  
Boson System ◽  
The Mean

A system of interacting relativistic bosons at finite temperatures and isospin densities is studied within the framework of the Skyrme­like mean­field model. The mean field contains both attractive and repulsive terms. The consideration is taken within the framework of the Canonical Ensemble and the isospin­density dependencies of thermodynamic quantities is obtained, in particular as the phase diagrams. It is shown that in such a system, in addition to the formation of a Bose­Einstein condensate, a liquid­gas phase transition is possible. We prove that the multi­boson system develops the Bose condensate for particles of high­density component only.

scholarly journals Insensitivity of the mean field limit of loss systems under SQ(d) routeing

2019 ◽  
Vol 51 (4) ◽  
pp. 1027-1066
Author(s):  
Thirupathaiah Vasantam ◽  
Arpan Mukhopadhyay ◽  
Ravi R. Mazumdar
Keyword(s):  
Fixed Point ◽  
Service Time ◽  
Mean Field ◽  
Service Time Distribution ◽  
Field Limit ◽  
Mean Field Limit ◽  
Mean Field Equations ◽  
The Mean ◽  
Loss Systems ◽  
Exponential Case

AbstractIn this paper, we study a large multi-server loss model under the SQ(d) routeing scheme when the service time distributions are general with finite mean. Previous works have addressed the exponential service time case when the number of servers goes to infinity, giving rise to a mean field model. The fixed point of the limiting mean field equations (MFEs) was seen to be insensitive to the service time distribution in simulations, but no proof was available. While insensitivity is well known for loss systems, the models, even with state-dependent inputs, belong to the class of linear Markov models. In the context of SQ(d) routeing, the resulting model belongs to the class of nonlinear Markov processes (processes whose generator itself depends on the distribution) for which traditional arguments do not directly apply. Showing insensitivity to the general service time distributions has thus remained an open problem. Obtaining the MFEs in this case poses a challenge due to the resulting Markov description of the system being in positive orthant as opposed to a finite chain in the exponential case. In this paper, we first obtain the MFEs and then show that the MFEs have a unique fixed point that coincides with the fixed point in the exponential case, thus establishing insensitivity. The approach is via a measure-valued Markov process representation and the martingale problem to establish the mean field limit.

FLUCTUATION EFFECTS IN A CLASS OF SYSTEMS WITH TWO ORDER PARAMETERS

1993 ◽  
Vol 07 (27) ◽  
pp. 1725-1731 ◽  
Author(s):  
L. DE CESARE ◽  
I. RABUFFO ◽  
D.I. UZUNOV
Keyword(s):  
Phase Transition ◽  
Renormalization Group ◽  
Phase Transitions ◽  
Order Phase Transition ◽  
Mean Field ◽  
Ising Models ◽  
Order Parameters ◽  
The Mean ◽  
Fluctuation Effects ◽  
Second Order Phase Transition

The phase transitions described by coupled spin -1/2 Ising models are investigated with the help of the mean field and the renormalization group theories. Results for the type of possible phase transitions and their fluctuation properties are presented. A fluctuation-induced second-order phase transition is predicted.

Complex Scheduling with Potts Neural Networks

1992 ◽  
Vol 4 (6) ◽  
pp. 805-831 ◽  
Author(s):  
Lars Gislén ◽  
Carsten Peterson ◽  
Bo Söderberg
Keyword(s):  
Neural Network ◽  
Phase Transition ◽  
School System ◽  
Mean Field ◽  
Programming Approach ◽  
Scheduling Problems ◽  
Problem Complexity ◽  
Field Equations ◽  
High Quality ◽  
Mean Field Equations

In a recent paper (Gislén et al. 1989) a convenient encoding and an efficient mean field algorithm for solving scheduling problems using a Potts neural network was developed and numerically explored on simplified and synthetic problems. In this work the approach is extended to realistic applications both with respect to problem complexity and size. This extension requires among other things the interaction of Potts neurons with different number of components. We analyze the corresponding linearized mean field equations with respect to estimating the phase transition temperature. Also a brief comparison with the linear programming approach is given. Testbeds consisting of generated problems within the Swedish high school system are solved efficiently with high quality solutions as results.

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