Local Evolution Rules Research Articles

Bed Separation Formation Mechanism and Water Inrush Evaluation in Coal Seam Mining under a Karst Cave Landform

Understanding the formation mechanism of bed separation in coal seam mining under a karst landform is needed for the prevention and control of roof-separated water damage in such areas. This research used a mine in the northern Guizhou coalfield, China, as a case study, and applied theoretical analysis, numerical simulation, and on-site measurement to develop a circular cave structure model in a key stratum. The dynamic evolution of a separation bed was analyzed from several aspects, including the formation mechanism, development location, the mechanical condition of local karst caves, fracture evolution, and fractal rules. Verification using in situ measurements is presented for the case study mine, and a quantitative evaluation method for water inrush from bed separation and improved fusion weighting is proposed based on a cloud model. The research results indicate the following: (1) Tensile cracks are prone to occur above and below a karst cave, which produce an impact of connectivity on the separated space. (2) When the working face advances to 270 m in coal mining, longitudinal tensile cracks below the karst cave gradually increase and the width of the bed separation crack shrinks to 68.2 m, with a maximum separation layer height of 3.01 m. (3) Based on the cloud model and the improved weighted fusion method, the risk of water inrush in bed separation is judged as “high”. The En of the cloud digital features is 0.0622 and the He is 0.0307, achieving a quantitative evaluation of water inrush in the separation layer that is consistent with on-site practice, and is highly stable and reliable. This study improves the understanding of the development pattern of bed separation and water inrush risk assessment in coal seam mining under a karst cave landform.

An Extended Membrane System Based on Cell-like P Systems and Improved Particle Swarm Optimization for Image Segmentation

An extended membrane system with a dynamic nested membrane structure, which is integrated with the evolution-communication mechanism of a cell-like P system with evolutional symport/antiport rules and active membranes (ECP), and the evolutionary mechanisms of particle swarm optimization (PSO) and improved PSO inspired by starling flock behavior (SPSO), named DSPSO-ECP, is designed and developed to try to break application restrictions of P systems in this paper. The purpose of DSPSO-ECP is to enhance the performance of extended membrane system in solving optimization problems. In the proposed DSPSO-ECP, the updated model of velocity and position of standard PSO, as basic evolution rules, are adopted to evolve objects in elementary membranes. The modified updated model of the velocity of improved SPSO is used as local evolution rules to evolve objects in sub-membranes. A group of sub-membranes for elementary membranes are specially designed to avoid prematurity through membrane creation and dissolution rules with promoter/inhibitor. The exchange and sharing of information between different membranes are achieved by communication rules for objects based on evolutional symport rules of ECP. At last, computational results, which are made on numerical benchmark functions and classic test images, are discussed and analyzed to validate the efficiency of the proposed DSPSO-ECP.

Simulation Approach for Random Diffusion of Chloride in Concrete under Sustained Load with Cellular Automata

Steel bar corrosion caused by chloride is the major reason for concrete structure durability failures in a corrosive environment. An accurate simulation of chloride ion diffusion in concrete is hence critical to durability design, maintenance, and reinforcement of concretes in erosive environments. To accurately simulate actual chloride ion diffusion in concretes, an improved three-dimensional neighborhood type is proposed according to the mechanism of chloride ion diffusion in concrete, and a three-dimensional cellular automaton model (3D CA model) for describing the diffusion process of chloride in concrete is established based on this neighborhood type. The accuracy and correctness of simulation results obtained from the 3D CA model were verified by comparison with Fick’s second law analytical solutions. Based on the 3D CA model, an improved modified 3D CA model is developed (3D RTCA model) which takes into account random chloride ion distribution in concrete, the time dependence of the coefficient of chloride ion diffusion, and the structure stress level effect on chloride ion diffusion. Numerical simulation results reveal that the 3D RTCA model has higher calculation accuracy in predicting long-term concentration of chloride in concretes, and the simulation results are closer to experimental findings than analytical results obtained based on Fick’s second law. Compared with Fick’s second law analytical solutions, the 3D RTCA model can reflect more truly the cross-sectional stress level effect on chloride ion diffusion through simple local evolution rules. Besides, the 3D RTCA model can genuinely describe the randomness and uncertainty of the chloride diffusion process. The 3D RTCA model developed in the current study provides a novel perspective and method to investigate chloride ion diffusion in concrete from structural level.

Construction of an Improved English Teaching Model Based on Cellular Automata

In order to improve the effect of college English teaching reform, this paper puts cellular automata English into English teaching simulation and uses the cellular automata model to study the behavior of complex teaching systems. Moreover, this article uses the method of man-machine combination to establish the corresponding dynamic evolution model and design the local evolution rules of the complex system to simulate the English teaching process, including the movement of students and teachers, the interaction of the teaching process, the development of teaching activities, and the processing of teaching resources. In addition, this paper constructs the functional structure of the system and conducts system verification through experimental research. The experimental research results show that the English classroom teaching evaluation system based on the cellular automaton proposed in this article is very effective, and it has a certain role in promoting English teaching.

Rapid Mixing of Dynamic Graphs With Local Evolution Rules

Dynamic graphs arise naturally in many contexts. In peer-to-peer networks, for instance, a participating peer may replace an existing connection with one neighbor by a new connection with a neighbor of that neighbor. Several such local rewiring rules have been proposed to ensure that peer-to-peer networks achieve good connectivity properties (e.g., high expansion) at equilibrium. However, the question of whether there exists such a rule that converges rapidly to equilibrium has remained open. In this paper, we provide an affirmative answer: we exhibit a local rewiring rule that converges to equilibrium after each participating node has undergone only a number of changes that is at most poly-logarithmic in the system size. As a byproduct, we derive new results for random walks on graphs, bounding the spread of their law throughout the transient phase, i.e., prior to mixing. These rely on an extension of Cheeger's inequality, based on generalized isoperimetric constants, and may be of independent interest.

BLOCK TRANSFORMATION OF HYBRID CELLULAR AUTOMATA

By introducing the sequence-block transformation and vector-block transformation, a discussion of symbolic dynamics of hybrid cellular automation (HCA) and hybrid cellular automation with memory (HCAM) is presented in this paper. As the local evolution rules of HCA and HCAM are not uniform, the new uniform cellular automata (CAs) with multiple states can be constructed by specific block transformations. It is proved that the new CA rules are topologically conjugate with the originals. Furthermore, the complex dynamics of the HCA and HCAM rules can be investigated via the new CA rules.

Cellular automata simulation of interactions between metastable corrosion pits on stainless steel

The interactions between metastable corrosion pits on stainless steel are studied by a two-dimensional cellular automata model at a mesoscopic scale. The cellular automata model focuses on a metal/film/electrolyte system, including fifteen kinds of species. A series of local evolution rules for the growth of corrosion pits is performed to simulate the corrosion kinetics processes. The transient current characteristics of the interactions between metastable corrosion pits under different simulation factors including the breakdown time and extent of pit cover are analyzed. The analysis of the pit stability product shows that the simulation results are close to the experimental conclusions.

Mesoscopic Simulation of Diffusion Characteristics in the Corrosion Film

A cellular automata model was used to study the diffusion characteristics in the corrosion film at a mesoscopic scale. The model focused on a metal/film/electrolyte system, including a series of local evolution rules. The effect of diffusion rate on the film growth and metal corrosion was investigated. The result showed that the growth rate of the film followed a power law with the diffusion steps, and the corrosion rate had the same law as that of the film growth in the model with the feedback effect. There existed a diffusing plane in the film, where the concentration of the diffusing species did not depend on time. The diffusion steps were found to have a great influence on the position and species concentration of the diffusing plane.

Optimal-tuning PID control of adaptive materials for structural efficiency

The objective of this paper was solving the optimization problem of lightweight stiffened structures modelled as a two-dimensional domain in an efficient computational way. The underlying premise was that mass should be distributed in an efficient way, so as to use a minimum amount of material to accomplish the mechanical function. This premise was expressed as a global, multi-objective optimization problem in which stiffness and mass were conflicting objectives. Alternative local evolution rules were implemented to update mass density or Young's modulus at each step of the iterative procedure. The solution of the structural optimization problem was accomplished by a novel automatic procedure consisting of two consecutive stages of control and optimization. In the first stage of Proportional Integral Derivative (PID) control gains were manually selected whereas in the second stage the finding of optimal values of control gains, target, and cost indices was allowed. In this study a bone-like material was adopted and a thin slab was analysed as a sample problem.

Adsorption–desorption kinetics of the monomer–dimer mixture

The kinetics of the monomer–dimer mixtures is formulated in the framework of the kinetic lattice gas model. The so-called local evolution rules are used to derive the hierarchy of coupled differential equations for coverage and other correlators, when processes like adsorption, desorption and diffusion are included. The hierarchy of equation is truncated by using mean-field ( m , n ) closures. Equilibrium properties are analyzed. In particular, adsorption isotherms as a function of the nearest neighbor lateral interaction are presented. The irreversible kinetics are also considered. Temperature-programmed-desorption (TPD) with readsorption is of special interest and this experiment is simulated under different conditions giving different spectra. In these spectra, the influence of adsorbate mobility is analyzed in two dimensions by Monte Carlo simulations.

From thermodynamic cell models to partitioning cellular automata for diffusion in zeolites. I. Structure of the algorithm

In the study of adsorption of simple adsorbates in microporous materials like zeolites, thermodynamic models of small grand-canonical cells with very local interactions [e.g., see K. G. Ayappa, J. Chem. Phys. 111, 4736 (1999)] have been proven to be able to produce thermodynamic properties in very good agreement with the results of experiments and atomistic simulations. In this paper we present in details the structure and implementation of a thermodynamic partitioning cellular automaton (PCA) devised as a dynamical version of thermodynamic cell models and proposed as an easy environment to perform coarse-grained simulations of adsorption/diffusion of simple interacting molecules in microporous materials. Local evolution rules and memory effects are introduced to make our PCA able to complete the static picture provided by thermodynamic cell models with the simulation of transport properties.

Urban growth processes joining cellular automata and multiagent systems. Part 2: computer simulations

The mathematical model of urban dynamics introduced in an earlier paper is applied to a case study in a small region in the southern part of Switzerland. The model mixes the point of view of cellular automata (cellular decomposition of the space, neighbourhood relations among cells, dynamics based on local evolution rules) with the approach to multiagent systems: the dynamics of the urban system are described in terms of decision processes of agents formalized using fuzzy-decision-theory methods. The region chosen for the case study evolves under the pressure of the nearby city of Lugano, owing to several factors: the accessibility of the area from Lugano, the availability of spatial resources for new development, the high level of quality of space, and the high level of congestion of Lugano. Local changes in the master plan from agricultural to residential use are taken into account, by introducing suitable memory variables that keep track of the demand of spatial resources for building in the recent pas...

Local evolution rules and the diffusion equation

A partial differential equation describing the diffusion of a set of interacting particles on a lattice is obtained using the so-called local evolution rules approach. This equation is derived after truncating a hierarchy of partial differential equations using a mean-field ( m, n) closure. Both, the partial differential equations and the diffusion coefficients, are derived in a variety of cases. The description of the noninteracting set of particles is obtained always as a limiting case. The results are compared to those previously obtained by other method.

Non-interacting dimer kinetics in hypercubic lattices

The exact formulation of the kinetic of dimer in hypercubic lattices is developed in the framework of the kinetic lattice gas model. The so-called local evolution rules are used to obtain the hierarchy of equation of motion for the correlation functions where processes like adsorption and desorption are included. The hierarchy of equations are truncated using a mean field ( m, n) closures which allows the analytical treatment of the system. A general expression for non-interacting dimer isotherm and two particle correlation functions are obtained in hypercubic lattices.

Remaining coverage in associative desorption process

In this paper the kinetic of dissociative adsorption of dimers followed by associative desorption is analyzed. The coupled differential equations which describe the kinetics of the process were obtained by applying the so-called local evolution rules. Particular interest presents the irreversible desorption process. In fact, given that desorption proceeds from the reacting nearest-neighbor monomers, a remaining coverage results from those isolated particles when the mobility is neglected, therefore, the resulting configuration can be considered as a jamming state of the system. The exact solution for the remaining coverage is obtained in one-dimensional chain, where the effect of the lateral interactions are also included. The two-dimensional case is analyzed by using Monte Carlo simulation. The equilibrium solutions and the thermal desorption spectra are also studied.

MULTIFRACTAL CHARACTERISTICS OF LINEAR ONE-DIMENSIONAL CELLULAR AUTOMATA

Cellular automata (CA) can be considered as discrete dynamical systems exhibiting a rich intrinsic behavior both in space and time. Starting from disordered initial configurations and according to different local evolution rules, CA can evolve into steady states showing regular or complex space–time structures. These structures have been shown to have fractal and multifractal properties. Here, the multifractal properties of linear one-dimensional cellular automata with complex spatio-temporal behaviors are calculated using discrete wavelets transforms.

Dimer kinetics in a one-dimensional lattice

The kinetics of dimer molecules in a one-dimensional lattice is formulated in the framework of the kinetic lattice gas model. Local evolution rules are used to obtain the hierarchy of equations of motion for correlation functions where processes like adsorption, desorption and surface diffusion are included. By use of mean-field ( m, n) closures, that allow the truncation of the infinite set of coupled differential equations of motion, we obtain the equilibrium properties and the time evolution of the adsorbate as well as the desorption kinetics. The temperature-programmed desorption (TPD) spectra for mobile and immobile adsorbates are obtained as limiting cases. The effect of the diffusion on TPD is also analyzed.

Application of cellular automata to modelling competitive growths of two underwater species Chara aspera and Potamogeton pectinatus in Lake Veluwe

The objective of this research is to explore the relatively new approach, cellular automata (CA), to model the competitive growths and then try to explain the succession process of two underwater species Chara aspera ( C. aspera) and Potamogeton pectinatus ( P. pectinatus) in a eutrophicated lake, the Netherlands. CA constitutes a mathematical system that simulates the dynamics of spatial-temporal patterns in discrete steps according to prescribed local evolution rules. It consists of three main components: a set of cells, cell properties or states, and local evolution rules. Comparing to conventional aggregated-based ecological models formulated by partial differential equations (PDE), CA has more flexibility to implement the individual property differences and local interactions, especially with the facilitation of the object-oriented programming (OOP) techniques. The model results are seen to be both qualitatively and quantitatively in agreement with field observations. Namely, CA is not only applicable to ecohydraulics modelling, but also in some aspects more efficient than PDE based models.

Quantum mechanics of lattice gas automata: boundary conditions and other inhomogeneities

We continue our analysis of the physics of quantum lattice gas automata (QLGA). Previous work has been restricted to periodic or infinite lattices; simulation of more realistic physical situations requires finite sizes and nonperiodic boundary conditions. Furthermore, envisioning a QLGA as a nanoscale computer architecture motivates consideration of inhomogeneities in the `substrate'; this translates into inhomogeneities in the local evolution rules. Concentrating on the one-particle sector of the model, we determine the various boundary conditions and rule inhomogeneities which are consistent with unitary global evolution. We analyse the reflection of plane waves from boundaries, simulate wavepacket refraction across inhomogeneities, and conclude by discussing the extension of these results to multiple particles.