Cellular Automata Simulation Research Articles

Research of vehicle flow based on cellular automaton in different safety parameters

In this paper, the cellular automaton model is put forward to evaluate the effect of the different drivers’ psychology in the two-lane highway. Each value of safety parameter βji, used to reflect the jth vehicle driver’s psychology in the ith lane, represents his or her cautious or risky preference. Assuming that βji follows normal distribution, whose mathematical expectation is β, we generate a stochastic safety coefficient for each driver in the simulation area. Based on different values of β, the vehicle flow and density are contrasted under some different traffic rules such as driving on the right, free overtaking and non-overtaking with low speed limitation. Through the cellular automaton simulation, the results demonstrate that safety parameter has less influence on the traffic flow under the lightest and heaviest traffic. Meanwhile, non-overtaking with the lowest speed limitation can increase the traffic flow in the light traffic. Free overtaking can improve the usage of the highway. With the increase of vehicle, non-overtaking with the lowest speed limitation will be of benefit to improving the traffic flow.

Cellular automata simulation of saltwater intrusion in coastal aquifer

The wasteful consumption of freshwater in heavily populated coastal areas usually consist the basic reason for the intrusion of saltwater into the coastal aquifers. In order to avoid such catastrophic scenarios, their prediction is of utter significance. Underground water systems are highly complex and the water flow is extremely dynamic, thus making the prediction of this phenomenon a difficult task. For this reason, a two dimensional Cellular Automaton (CA) was designed enabling both the qualitative and quantitative simulation and illustration of the saltwater intrusion into an unconfined coastal aquifer. The presented results ensure the robustness of the proposed CA model taking full advantage of its inherent parallelism and local connectivity.

Epidemiological modeling with a population density map-based cellular automata simulation system

We present a new numerical, two-dimensional cellular automata framework for simulation of the spread of an infectious disease in a region with non-homogenous spatial population distribution. For the simulation the real map of the population density in Poland is used, where the sources of the infection are located. Presented model is a combination of SEIR and IBM models complemented with additional factors like variable population density, death, birth and some stochastic parameters to reflect the more realistic population dynamics. In proposed model the states of individuals are tracked through time like in IBM model and the evolution of the whole system is described by SEIR transition function which determines how cells interact with their neighbours, influencing global behavior of the system. Presented model requires less complicated input than IBM models and is less expensive computationally. We explore influenza as the contagious disease in our map-based simulation. The results of the simulation show the spreading-rate of the disease and can be used to describe possible actions for preventing pandemic.

Cellular automata simulations of grain growth in the presence of second-phase particles

In this article, we studied the grain growth kinetics in the presence of second-phase particles by using a 2D cellular automata (CA) model with deterministic rules. The curvature-driven grain growth mechanism was adopted in the CA model and an expanded method for the computation of curvature along a grain boundary was used. Simulations in real time and space were performed for various particle sizes, volume fractions of particles, and initial grain sizes, and their effects on the microstructure evolution and final limiting grain size were discussed. A modified Zener relation was proposed to predict the limiting grain size by introducing two items: one describes the effect of initial grain size and the other describes the effect of the ratio of initial grain size to particle size. The proposed relation shows a good fit to the simulated limiting grain sizes for different cases.

A Self-Critique of Self-Organized Criticality in Astrophysics

AbstractThe concept of “self-organized criticality” (SOC) was originally proposed as an explanation of 1/f-noise by Bak, Tang, and Wiesenfeld (1987), but turned out to have a far broader significance for scale-free nonlinear energy dissipation processes occurring in the entire universe. Over the last 30 years, an inspiring cross-fertilization from complexity theory to solar and astrophysics took place, where the SOC concept was initially applied to solar flares, stellar flares, and magnetospheric substorms, and later extended to the radiation belt, the heliosphere, lunar craters, the asteroid belt, the Saturn ring, pulsar glitches, soft X-ray repeaters, blazars, black-hole objects, cosmic rays, and boson clouds. The application of SOC concepts has been performed by numerical cellular automaton simulations, by analytical calculations of statistical (powerlaw-like) distributions based on physical scaling laws, and by observational tests of theoretically predicted size distributions and waiting time distributions. Attempts have been undertaken to import physical models into numerical SOC toy models. The novel applications stimulated also vigorous debates about the discrimination between SOC-related and non-SOC processes, such as phase transitions, turbulence, random-walk diffusion, percolation, branching processes, network theory, chaos theory, fractality, multi-scale, and other complexity phenomena. We review SOC models applied to astrophysical observations, attempt to describe what physics can be captured by SOC models, and offer a critique of weaknesses and strengths in existing SOC models.

The problem of land value betterment: a simplified agent-based test

In this paper, we employ behaviour-driven cellular automata as a simplified agent-based modelling approach to test the seminal Coase theorem, with a policy focus on the land value betterment effect of urban infrastructure provision. Four prototypical development regimes are identified from international practice: (1) the private developer-oriented Metroland model dating back to the suburbanisation of London in the nineteenth century England; (2) the private household-led special district model, which can be observed in many contemporary US suburbs; (3) the public planning-regulated model, as featured in most post-war European welfare state countries, including the present-day UK; (4) the public state-as-developer model, which characterises what has been taking place in China. A repeated analysis of variance (ANOVA) based on the results of a large number of cellular automata simulations suggests no significant difference between models I and II in terms of their welfare outcomes measured by aggregate utility. However, models III and IV are both found to generate significantly less welfare than models I and II, under strict assumptions of zero transaction costs, perfect information, perfect capital markets and perfect competition.

A solution to the problem of the mesh anisotropy in cellular automata simulations of grain growth

Cellular automata modeling is a powerful tool used for simulating complex grain growth phenomena. However, a computational mesh may give rise to artificial anisotropy, which is a highly undesirable calculational problem. To eliminate this drawback of the approach, we have introduced two new corrections into a two-dimensional cellular automata algorithm for grain growth. The two-dimensional cellular automata model built in the framework of the approach developed by Rappaz and Gandin is based on a combination of the cellular automata and finite difference methods. The simulation results obtained for the cases of single grain growth and evolution of polycrystalline structure during solidification of alloys have demonstrated that the proposed corrections enable the mesh anisotropy problem to be solved.

Dynamic Simulation of 1D Cellular Automata in the Active aTAM.

The Active aTAM is a tile based model for self-assembly where tiles are able to transfer signals and change identities according to the signals received. We extend Active aTAM to include deactivation signals and thereby allow detachment of tiles. We show that the model allows a dynamic simulation of cellular automata with assemblies that do not record the entire computational history but only the current updates of the states, and thus provide a way for (a) algorithmic dynamical structural changes in the assembly and (b) reusable space in self-assembly. The simulation is such that at a given location the sequence of tiles that attach and detach corresponds precisely to the sequence of states the synchronous cellular automaton generates at that location.

Stochastic cellular automata simulation of oscillations and autowaves in reaction-diffusion systems

In this paper, the investigations on stochastic cellular automata models of stable oscillations and autowaves in active media are summarized to formulate a concept of stochastic cellular automaton (CA) corresponding to asynchronous CAs with probabilistic transition rules. A formal description of a stochastic CA and a stochastic CA model is given. The properties and methods of synthesis of CA models for a specified set of elementary physical and chemical transformations are described. Some possibilities of simulating autowave and oscillatory processes are demonstrated using, as an example, a carbon monoxide oxidation reaction on a platinum catalyst with surface restructuring. The CA-simulation has made it possible to reveal the range of reaction parameter values with stable oscillations of reagent concentrations and to observe autowaves on the platinum surface. Special attention is given to providing a highly efficient parallel implementation of the stochastic CA algorithm. For this, the asynchronous mode must be preliminarily transformed to a block-synchronous one. Its equivalence to the asynchronous mode is justified. This is done for the CA reaction model by a comparative statistical analysis of the simulation results.

Analysis of behaviour transitions in tumour growth using a cellular automaton simulation.

The authors used computational biology as an approach for analysing the emergent dynamics of tumour growth at cellular level. They applied cellular automata for modelling the behaviour of cells when the main cancer cell hallmarks are present. Their model is oriented to mimic the development of multicellular spheroids of tumour cells. In their modelling, cells have a genome associated with the different cancer hallmarks, indicating if those are acquired as a consequence of mutations. The presence of the cancer hallmarks defines cell states and cell mitotic behaviours. These hallmarks are associated with a series of parameters, and depending on their values and the activation of the hallmarks in each of the cells, the system can evolve to different dynamics. With the simulation tool the authors performed an analysis of the first phases of cancer growth, using different and alternative strategies: firstly, studying the evolution of cancer cells and hallmarks in different representative situations regarding initial conditions and parameters, analysing the relative importance of the hallmarks for tumour progression; secondly, being the focus of this work, inspecting the behaviour transitions when the cancer cells are killed with a given probability during the cellular system progression.

An optimal Cellular Automata algorithm for simulating wildfire spread

Raster-based methods for simulating wildfire spread are computationally more efficient than vector-based approaches. In spite of this, their success has been limited by the distortions that affect the fire shapes. This work presents a Cellular Automata (CA) approach that is able to mitigate the problem of distorted fire shapes thanks to a redefinition of the spread velocity, where the equations generally used in vector-based approaches are modified by means of some correction factors. A numerical optimization approach is used to find the optimal values for the correction factors. The results are compared to the ones given by two Cellular Automata simulators from the literature under homogeneous conditions. According to this work, the proposed approach provides better results, in terms of accuracy, at a comparable computational cost. The proposed approach has then been compared to Farsite, a vector-based fire-spread simulator, under realistic slope and wind conditions, producing equivalent results in a reduced computational time.

Grain boundary energy and curvature in Monte Carlo and cellular automata simulations of grain boundary motion

Monte Carlo and cellular automata simulations of grain boundary motion generally suffer from insufficient units of measure. This complicates the comparison of simulations with experiments, the consistent implementation of more than one driving force, and the development of models with predictive capabilities. This paper derives the proportionality constant relating the voxel interaction strength to a boundary energy, derives a formula for the boundary curvature, and uses the Turnbull expression to find the boundary velocity. Providing units of measure for the boundary energy and the boundary curvature allow Monte Carlo simulations and cellular automata simulations, respectively, to be subject to more than one driving force. Using the Turnbull expression to relate a driving pressure to a boundary velocity allows the remaining quantities in cellular automata simulations to be endowed with units of measure. The approach in this paper does not require any calibration of parametric links, but assumes that the voxel interaction strength is a Gaussian function of the distance. The proposed algorithm is implemented in a cellular automata simulation of curvature-driven grain growth.

Cellular automaton simulation of three-dimensional dendrite growth in Al–7Si–Mg ternary aluminum alloys

Due to the extensive applications in the automotive and aerospace industries of Al–7Si–Mg casting alloys, an understanding of their dendrite microstructural formation in three dimensions is of great importance in order to control the desirable microstructure, so as to modify the performance of castings. For this reason, a three-dimensional cellular automaton model (3-D CA) allowing for the prediction of dendrite growth of ternary alloys is presented. The growth kinetics of the solid/liquid (S/L) interface is calculated based on the solutal equilibrium approach. This proposed model introduces a modified decentered octahedron algorithm for neighborhood tracking, in order to eliminate the effects of mesh dependency on dendrite growth. The thermodynamic and kinetic data needed in the simulations are obtained through coupling with the Pandat software package in combination with thermodynamic/kinetic/equilibrium phase diagram calculation databases. The solute interactions between alloying elements are considered in the model. The model was first used to simulate the Al–7Si dendrite, followed by a validation using theoretical predictions. The influence of Mg content on the dendrite growth dynamics and dendrite morphologies was investigated. Also, the model was applied to Al–7Si–0.5Mg dendrite simulation both with and without a consideration of solute interactions between the Si and Mg alloying elements and the effects on dendrite growth process was analyzed using the simulation results. This model was finally used in order to simulate the dendrite growth in different crystallographic orientations in an Al–7Si–0.36Mg ternary alloy during polycrystalline solidification, resulting in a predicted secondary dendrite arm spacing (SDAS) and dendrite volume fraction data that show a reasonable agreement with experimental results. The single dendrite and polycrystalline growth simulations effectively demonstrate the capability of this model in predicting the three-dimensional dendrite microstructure of ternary alloys.

Cellular automaton simulation of ferrite-austenite transformation in low-carbon steels

A two-dimensional (2-D) cellular automaton (CA) model is adopted to simulate ferrite (α)-austenite (γ) transformation in low-carbon steels. In the model, the preferential nucleation sites of austenite, the driving force of phase transformation coupled with thermodynamic parameters, solute partition at the α/γ interface, and carbon diffusion in both the α and γ phases are taken into consideration. The model is able to simulate the ferrite-to- austenite transformation during isothermal heating in the ferrite-austenite two-phase region, and the austenite-to-ferrite transformation during continuous cooling. The influences of cooling rate and α grain size on the final carbon concentration field are investigated. The results show that after isothermal heating at 815°C for 300 s, the carbon concentration in both the α and γ phases reach the respective equilibrium values. The simulated microstructures compare well with the SEM images. After cooling to room temperature, the carbon distribution is more uniform when cooled at 1.2°C/s than at 7°C/s. The carbon distributions for different α grain sizes cooled at 1.2°C/s are similar. The simulation results are used to understand the mechanisms of the experimental phenomena of an enameling steel.

Robot Guided Crowd Evacuation

The congregation of crowd undoubtedly constitutes an important risk factor, which may endanger the safety of the gathered people. The solution reported against this significant threat to citizens safety is to consider careful planning and measures. Thereupon, in this paper, we address the crowd evacuation problem by suggesting an innovative technological solution, namely, the use of mobile robot agents. The contribution of the proposed evacuation system is twofold: (i) it proposes an accurate Cellular Automaton simulation model capable of assessing the human behavior during emergency situations and (ii) it takes advantage of the simulation output to provide sufficient information to the mobile robotic guide, which in turn approaches and redirects a group of people towards a less congestive exit at a time. A custom-made mobile robotic platform was accordingly designed and developed. Last, the performance of the proposed robot guided evacuation model has been examined in real-world scenarios exhibiting significant performance improvement during the crucial first response time window.

Simulation of Isothermal Austenitization in Banded Pearlite Steels by Cellular Automaton

The austenitization of steels can occur in a wide variety of initial microstructures. In this study we addressed the transformation of banded pearlite steels. Banded pearlite initial structures similar to the real ones were created. In these structures the entire transformation process was simulated whose part processes are nucleation and grain growth. The nucleation is described by a free energy based model, and the Fick II. diffusion equation by using Finite Difference Method describes the grain growth. These models have been coupled in cellular automata simulations.

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.

Two dimensional cellular automata simulation of grain growth during solidification and recrystallization

A two dimensional cellular automata model has been developed to simulate and to study grain growth behavior during solidification and recrystallization processes, including predicting mechanical properties of metallic materials or investigating mechanical defects. Using the algorithm implemented, grain growth in model materials (nickel-based and titanium alloys) has been calculated in different thermal fields.

Microenvironment-enhanced invasive tumor growth via cellular automaton simulations

Emergence of invasive and metastatic behavior in malignant tumors can often lead to fatal outcomes for patients. The collective malignant tumor behavior resulting from the complex tumor-host interactions and the interactions between the tumor cells are currently poorly understood. Progress towards such an understanding necessarily requires an interdisciplinary and collaborative effort. In this paper, we review a state-of-art simulation technique, i.e., a cellular automaton (CA) model which has been developed by the authors over the past few years to investigate microenvironment-enhanced invasive growth of avascular solid tumors. This CA model incorporates a variety of microscopic-scale tumor-host interactions, including the degradation of the extracellular matrix by the malignant cells, nutrient-driven cell migration, pressure build-up due to the deformation of the microenvironment by the growing tumor and its effect on the local tumor-host interface stability. Moreover, the effects of cell-cell adhesion on tumor growth are also explicitly taken into account. A number of bench-mark collective invasion behaviors have been successfully reproduced via the CA model, including the emergence of elongated invasion branches characterized by homotype attraction and least resistance path, development of rough tumor surface in a high-pressure confined environment, as well as reduced invasion due to strong cell-cell adhesion. Such simulated bench-mark behaviors strongly indicate the validity and predictive power of the CA model. In addition, the CA model allows one to investigate the role of various different microenvironment factors in the progression of the neoplasm, in particular, the promotion and enhancement of tumor malignancy. As an example, a “phase diagram” that summarizes the dependency of tumor invasive behavior on extracellular matrix (ECM) rigidity (density) and strength of cell-cell adhesion is constructed based on comprehensive simulations. In this simple phase diagram, a clear transition from non-invasive to invasive behaviors of the tumor can be achieved by increasing ECM rigidity and/or decreasing the strength of cell-cell adhesion. This model, when properly combined with clinical data, in principle enables one to broaden the conclusions drawn from existing medical data, suggest new experiments, test hypotheses, predict behavior in experimentally unobservable situations, be employed for early detection and prognosis, and to suggest optimized treatment strategy for individual patient.

An Improved Cellular Automata for Wildfire Spread

Despite being computationally more efficient than vector-based approaches, the use of raster-based techniques for simulating wildfire spread has been limited by the distortions that affect the fire shapes. This work presents a Cellular Automata approach that is able to mitigate this problem with a redefinition of the spread velocity, where the equations generally used in vector-based approaches are modified by means of a number of correction factors. A numerical optimization approach is used to find the optimal values for the correction factors. The results are compared to the ones given by two well-known Cellular Automata simulators. According to this work, the proposed approach provides better results, at a comparable computational cost.