Narrow Results

Coupled map lattices are a popular and computationally simpler model of pattern formation in nonlinear systems. In this work, we investigate three-site interactions with linear multiplicative coupling in one-dimensional coupled logistic maps that cannot be decomposed into pairwise interactions. We observe the transition to synchronization and the transition to long-range order in space. We coarse-grain the phase space in regions and denote them by spin values. We use two quantifiers the flip rate $F(t)$ that quantify departure from expected band-periodicity as an order parameter. We also study a non-Markovian quantity, known as persistence $P(t)$ to study dynamic phase transitions. Following transitions are observed. (a) Transition to two band attractor state: At this transition $F(t)$ as well as $P(t)$ shows a power-law decay in the range of coupling parameters. Here all sites reach one of the bands. The $F(t)$ as well as $P(t)$ decays as power-law with the decay exponent ${\delta }_1=0.46$ and ${\eta }_1=0.28$, respectively. (b) The transition from a fluctuating chaotic state to a homogeneous synchronized fixed point: Here both the quantifiers $F(t)$ and $P(t)$ show power-law decay with decay exponent ${\delta }_2=1$ and ${\eta }_2=0.11$, respectively. We compare the transitions with the case, where pairwise interactions are also present. The spatiotemporal evolution is analyzed as the coupling parameter is varied.

The contribution of depolarizing electric fields and internal stress fields to the thermodynamics of phase transitions in a ferroelectric–dielectric composite material has been found. This contribution leads to renormalization $\alpha$ and $\beta$ coefficients in the decomposition into a series of the order parameters for thermodynamic potential. It has been established that electric fields always decrease the phase transition temperature. The internal stresses can both increase or decrease the temperature of a first-order phase transition and the width of temperature hysteresis. In the case of the first-order transitions, internal stresses can cause a change in the order of phase transition with appropriate material parameters.

The FORTRAN code for the three-dimensional Ising model is optimized on the Floating Point Computing M64/60 computer system and a good cost-effectiveness (dollar/MFLIP) rate is achieved.

A computer program that performs the microcanonical algorithm for the four-dimensional Ising model in standard FORTRAN-77 is described. A new spin data structure, of wide applicability, is introduced to accomplish this efficiently. Some timings on Class VI/VII supercomputers are given.

This paper explores the phase transitions of the EXPSPACE-complete problems, which mainly focus on the conformant planning problems. The research presents two conformant planning algorithms—CONFORMANT PLAN-NONEXISTENCE algorithm and CONFORMANT PLAN-EXISTENCE algorithm. By analyzing the features of the two algorithms, the phase transition area of the conformant planning problems is obtained. If the number of the operators isn't greater than θ_ub, the CONFORMANT PLAN-NONEXISTENCE algorithm can prove that nearly all the conformant planning instances have no solution. If the number of the operators isn't lower than θ_lb, the CONFORMANT PLAN-EXISTENCE algorithm can prove that nearly all the conformant planning instances have solutions. The results of the experiments show that there exist phase transitions from a region where almost all the conformant planning instances have no solution to a region where almost all the conformant planning instances have solutions.

We consider the free energy of a mean-field quantum spin glass described by a $p$-spin interaction and a transversal magnetic field. Recent rigorous results for the case $p=\infty$, i.e. the quantum random energy model (QREM), are reviewed. We show that the free energy of the $p$-spin model converges in a joint thermodynamic and $p\to \infty$ limit to the free energy of the QREM.

The Monte Carlo simulation of Bonabeau, Theraulaz and Deneubourg is reinvestigated. The phase transition between an egalitarian and an hierarchical society found was due to an instability when the past fights are not forgotten fast enough. Their model is also changed to include pair-specific memories, which again favor egalitarian societies.

We discuss the Lotka–Volterra dynamics of two populations, preys and predators, in the case when the predators posses a genetic information. The genetic information is inherited according to the rules of the Penna model of genetic evolution. Each individual of the predator population is uniquely determined by sex, genotype and phenotype. In our case, the genes are represented by 8-bit integers and the phenotypes are defined with the help of the 8-state Potts model Hamiltonian. We showed that during time evolution, the population of the predators can experience a series of dynamical phase transitions which are connected with the different types of the dominant phenotypes present in the population.

We introduce the basic theory of quantization of radiation field in quantum physics and explain how it relates to the theory of recursive functions in computer science. We outline the basic differences between quantum mechanics (QM) and quantum field theory (QFT) and explain why QFT is better suited for a computational paradigm — based on algorithmic requirement, countably infinite degrees of freedom and the creation of macroscopic output objects. The quanta of the radiation field correspond to the non-negative integers and the harmonic oscillator spectra correspond to the recursive computation — with the creation and annihilation operators, respectively, playing the same role as the successor and predecessor in computability theory. Accordingly, this approach relates the classical computational model and the quantum physical model more directly than the Turing machine approach used earlier. Also, the application of Lambda calculus formalism and the associated denotational semantics (that is widely used in the classical computational paradigm involving recursive functions) for applications to computational paradigm based on quantum field theory is described. Finally, we explain where QFT and conventional paradigm depart from each other, and examine the concept of fixed points, phase transitions, programmability, emergent computation and related open problems.

An approach to lattice Boltzmann simulation is described, which makes a direct connection between classical kinetic theory and contemporary lattice Boltzmann modeling methods. This approach can lead to greater accuracy, improved numerical stability and significant reductions in computational needs, while giving a new philosophical point of view to lattice Boltzmann calculations for a large range of applications.

Based on the concepts of educational psychology, sociology and statistical physics, a mathematical model for a new type of social learning process that takes place when individuals interact via the Internet is proposed and studied. The noise of the interaction (misunderstandings, lack of well organized participative activities, etc.) dramatically restricts the number of individuals that can be efficiently in mutual contact and drives phase transitions between "ordered states" such as the achievements of the individuals are satisfactory and "disordered states" with negligible achievements.

We present a method for estimating the density of states of a classical statistical model. The algorithm successfully combines the Wang–Landau flat histogram method with the N-fold way in order to improve the efficiency of the original single-spin-flip version. We test our implementation of the Wang–Landau method with the two-dimensional nearest neighbor Ising model for which we determine the tunneling time and the density of states on lattices with sizes up to 50 × 50. Furthermore, we show that our new algorithm performs correctly at right edges of an energy interval over which the density of states is computed. This removes a disadvantage of the original single-spin-flip Wang–Landau method where results showed systematically higher errors in the density of states at right boundaries. In order to demonstrate the improvements made, we compare our data with the detailed numerical tests presented in a study by Wang and Swendsen where the original Wang–Landau method was tested against various other methods, especially the transition matrix Monte Carlo method (TMMC). Finally, we apply our method to a thin Ising film of size 32 × 32 × 6 with antiparallel surface fields. With the density of states obtained from the simulations we calculate canonical averages related to the energy such as internal energy, Gibbs free energy and entropy, but we also sample microcanonical averages during simulations in order to determine canonical averages of the susceptibility, the order parameter and its fourth order cumulant. We compare our results with simulational data obtained from a conventional Monte Carlo algorithm.

We propose and solve a Hamiltonian model for multidimensional epistatic interactions between beneficial mutations. The model gives rise to either a phase transition between two equilibrium states, without any coexistence, or exhibits a state where hybrid species coexist, with gradual passage from one wild type to another. The transition takes place as a function of the tolerance of the environment, which we defined as the amount of noise in the system.

We introduce a consensus model inspired by the Sznajd Model. The updating is synchronous and memory plays a decisive role in making possible the reaching of total consensus. We study the transition between the state with no-consensus to the state with total consensus.

We consider a standard susceptible–infected–susceptible (SIS) model to study the behaviors of steady states of epidemic spreading in small-world networks. Using analytical methods and large scale simulations, we recover the usual epidemic behavior with a critical threshold λ_c below which infectious diseases die out. For the spreading rate λ far above λ_c, it was found that the density of infected individuals ρ as a function of λ has the property ρ≈f(K)(lnλ-lnλ_c).

We investigate the critical features of coupling parameters in the synchronization of the ensemble of identical neural networks with small-world connectivity. An exponential decay form is observed in the extreme case of global coupling among subsystems and full connection in each networks: there exists a maximum and a minimum of the critical coupling intensity for synchronization in this spatially extended system. For partial coupling, we present the primary result about the critical coupling fraction for various linked degree of subnetworks.

A model for opinion formation in a social group, based on the Theory of Social Impact developed by Latané, is studied by means of numerical simulations. Interactions among the members of the group, as well as with a strong leader competing with the mass media, are considered. The model exhibits first-order transitions between two different states of opinion, which are supported by the leader and the mass media, respectively. The social inertia of the group becomes evident when the opinion of the leader changes periodically. In this case two dynamic states are identified: for long periods of time, the group follows the changes of the leader but, decreasing the period, the opinion of the group remains unchanged. This scenery is suitable for the ocurrence of dynamic phase transitions.

A model for the displacement of self-driven organisms is studied by means of extensive computer simulations. Local interactions influenced by noisy communications among organisms, leads to the onset of collective motion at low noise levels. When the noise is increased the system undergoes first-order transitions into disordered states of motion. We have also studied the relaxation process between these states. By fitting the time dependence of the order parameter when the system is annealed from a state below coexistence to another above it, we conclude that the relaxation can be well described by means of a stretched exponential. In this way the characteristic relaxation times are obtained.

We consider the random Erdös–Rényi network with enhanced clusterization and Ising spins s = ±1 at the network nodes. Mutually linked spins interact with energy J. Magnetic properties of the system that are dependent on the clustering coefficient C are investigated with the Monte Carlo heat bath algorithm. For J > 0 the Curie temperature T_c increases from 3.9 to 5.5 when C increases from almost zero to 0.18. These results deviate only slightly from the mean field theory. For J < 0 the spin-glass phase appears below T_SG; this temperature decreases with C, on the contrary to the mean field calculations. The results are interpreted in terms of social systems.

In the magnetic Eden model (MEM), particles have a spin and grow in contact with a thermal bath. Although Ising-like interactions affect the growth dynamics, deposited spins are frozen and not allowed to flip. This paper focuses on recent developments and future prospects, such as spontaneous switching phenomena, critical behavior associated with fractal, wetting, and order-disorder phase transitions, the equilibrium/nonequilibrium correspondence conjecture, as well as dynamical and critical features of the MEM defined on complex network substrates.