International Journal of Modern Physics C

We present the evolutionary algorithm that evolves the population of numerical solutions of the variational problem. The evolved solutions are model-independent, smooth, can have a predefined shape (if needed), and satisfy boundary or any other additional conditions (if imposed). To exemplify the performance of the proposed algorithm, we show how to solve the variational problem of searching for the spatially modulated distribution of the field of order parameter that gives a minimum to the Landau-type thermodynamic potential in the theory of ferroelectrics with incommensurate phases.

We investigate expressiveness, a parameter of one-dimensional cellular automata, in the context of simulated biological systems. The development of elementary cellular automata is interpreted in terms of biological systems, and biologically inspired parameters for biodiversity are applied to the configurations of cellular automata. This paper contains a survey of the Elementary Cellular Automata in terms of their expressiveness and an evaluation whether expressiveness is a meaningful term in the context of simulated biology.

A coarse-grained cellular automaton is proposed to simulate traffic systems. There, cells represent road sections. A cell can be in two states: jammed or passable. Numerical calculations are performed for a piece of square lattice with open boundary conditions, for the same piece with some cells removed and for a map of a small city. The results indicate the presence of a phase transition in the parameter space, between two macroscopic phases: passable and jammed. The results are supplemented by exact calculations of the stationary probabilities of states for the related Kripke structure constructed for the traffic system. There, the symmetry-based reduction of the state space allows to partially reduce the computational limitations of the numerical method.

We investigate two homogeneous networks: the Watts–Strogatz network with mean degree ⟨k⟩ = 4 and the Erdös–Rényi network with ⟨k⟩ = 10. In both kinds of networks, the clustering coefficient C is a tunable control parameter. The network is an area of two competing contact processes, where nodes can be in two states, S or D. A node S becomes D with probability 1 if at least two its mutually linked neighbors are D. A node D becomes S with a given probability p if at least one of its neighbors is S. The competition between the processes is described by a phase diagram, where the critical probability p_c depends on the clustering coefficient C. For p > p_c the rate of state S increases in time, seemingly to dominate in the whole system. Below p_c, the majority of nodes is in the D-state. The numerical results indicate that for the Watts–Strogatz network the D-process is activated at the finite value of the clustering coefficient C, close to 0.3. On the contrary, for the Erdös–Rényi network the transition is observed at the whole investigated range of C.

In real communication systems, each node has a finite queue length to store packets due to physical constraints. In this paper, we propose a queue resource allocation strategy for traffic dynamics in scale-free networks. With a finite resource of queue, the allocation of queue length on node i is based on B_i, where B_i is the generalized betweenness centrality of node i. The overall traffic capacity of a network system can be evaluated by the critical packet generating rate (R_c). Through the use of the proposed queue allocation scheme for the shortest path protocol and efficient routing protocol, our strategy performs better than the uniform queue length allocation strategy, which is demonstrated by a larger value of the critical generating rate. We also give a method to estimate the network traffic capacity theoretically.

The investigation on the connection between: (1) closed Newton–Cotes formulae of high-order, (2) trigonometrically-fitted differential schemes and (3) symplectic integrators is presented in this paper. In the last decades, several one step symplectic methods were obtained based on symplectic geometry (see the appropriate literature). The investigation on multistep symplectic integrators is poor. In the present paper: (1) we study a trigonometrically-fitted high-order closed Newton–Cotes formula, (2) we investigate the necessary conditions in a general eight-step differential method to be presented as symplectic multilayer integrator, (3) we present a comparative error analysis in order to show the theoretical superiority of the present method, (4) we apply it to solve the resonance problem of the radial Schrödinger equation. Finally, remarks and conclusions on the efficiency of the new developed method are given which are based on the theoretical and numerical results.

Self-reproduction on asynchronous cellular automata (ACAs) has attracted wide attention due to the evident artifacts induced by synchronous updating. Asynchronous updating, which allows cells to undergo transitions independently at random times, might be more compatible with the natural processes occurring at micro-scale, but the dark side of the coin is the increment in the complexity of an ACA in order to accomplish stable self-reproduction. This paper proposes a novel model of self-timed cellular automata (STCAs), a special type of ACAs, where unsheathed loops are able to duplicate themselves reliably in parallel. The removal of sheath cannot only allow various loops with more flexible and compact structures to replicate themselves, but also reduce the number of cell states of the STCA as compared to the previous model adopting sheathed loops [Y. Takada, T. Isokawa, F. Peper and N. Matsui, Physica D227, 26 (2007)]. The lack of sheath, on the other hand, often tends to cause much more complicated interactions among loops, when all of them struggle independently to stretch out their constructing arms at the same time. In particular, such intense collisions may even cause the emergence of a mess of twisted constructing arms in the cellular space. By using a simple and natural method, our self-reproducing loops (SRLs) are able to retract their arms successively, thereby disentangling from the mess successfully.

We investigate the phase transitions and the Korteweg-de Vries (KdV) equation in the density difference lattice hydrodynamic (DDLM) model, which shows a close connection with the gas-kinetic-based model and the microscopic car following model. The KdV equation near the neutral stability line is derived and the corresponding soliton solution describing the density waves is obtained. Numerical simulations are conducted in two aspects. On the one hand, under periodic conditions perturbations are applied to demonstrate the nonlinear analysis result. On the other hand, the open boundary condition with random fluctuations is designed to explore the empirical congested traffic patterns. The phase transitions among the free traffic (FT), widening synchronized flow pattern (WSP), moving localized cluster (MLC), oscillatory congested traffic (OCT) and homogeneous congested traffic (HCT) occur by varying the amplitude of the fluctuations. To our knowledge, it is the first research showing that the lattice hydrodynamic model could reproduce so many congested traffic patterns.