Cellular Automata Simulation Research Articles

Analytical and cellular automaton approach to a generalized SEIR model for infection spread in an open crowded space

We formulate a generalized susceptible exposed infectious recovered (SEIR) model on a graph, describing the population dynamics of an open crowded place with an arbitrary topology. As a sample calculation, we discuss three simple cases, both analytically, and numerically, by means of a cellular automata simulation of the individual dynamics in the system. As a result, we provide the infection ratio in the system as a function of controllable parameters, which allows for quantifying how acting on the human behavior may effectively lower the disease spread throughout the system.

(Invited) On the Intergranular Corrosion in Non-stationary Conditions: Experimental Approach and Modeling by Cellular Automata

Intergranular corrosion can affect stainless steels even if they are in a non-sensitized state. This is the case when the corrosive medium is particularly oxidizing such as in hot and concentrated nitric acid [1]. Intergranular corrosion is characterized by the formation of triangular grooves at the level of the grain boundaries. Their progression leads to the detachment of grains with a certain periodicity. This corrosion type is quite well described and modeled by different techniques when the medium remains the same [2-3]. Nevertheless, the medium may vary in some industrial chemical processes. Therefore, this work has investigated the impact of non-stationary conditions on the evolution of the intergranular corrosion.The intergranular corrosion kinetics of a 310L stainless steel was first studied in nitric acid with different levels of VO2 + concentrations in stationary conditions. Then non-stationary experiments were performed by varying the concentration of VO2 + as a function of time by periods. The corrosion kinetics was characterized by the evolution of the mass loss of the samples and of the geometry of the grooves (angle and depth) optically measured on cross sections.Numerical simulations were also performed by cellular automata [3]. A hexagonal close-packed (HCP) grid was chosen for the simulations. A realistic 3D granular structure of the stainless steel was modeled with a Voronoi algorithm. Two corrosion probabilities (for the grains and the grain boundaries) were adequately chosen for driving the time evolution in each conditions. These probabilities were kept constant in stationary conditions and varied with time by periods in non-stationary conditions. The simulated mass loss and the surface morphology reflects the same pattern of the experiments.In stationary conditions, the corrosion reaches a steady state after a transient period corresponding to the detachment of the first layer of grains: the corrosion rate and the specific surface in contact with the solution (increased by the formation of grooves) becomes constant. The characteristics of the steady state are directly dependent on the concentration of VO2 +. In non-stationary conditions, it appears that the characteristics of the intergranular corrosion (mass loss and geometry of the grooves) at a given period are influenced by the characteristics reached after the previous period (in other chemical conditions). This influence is only transient during a time corresponding approximately to the duration necessary to the consumption of a layer of grains.[1] Fauvet, P., Corrosion issues in nuclear fuel reprocessing plants. Nuclear corrosion science and engineering. D. Feron, Woodhead Publishing. 22 (2012) 679-728.[2] B.Gwinner et al., Towards a reliable determination of the intergranular corrosion rate of austenitic stainless steel in oxidizing media. Corrosion Science 107 (2016) 60-75.[3] D.Di Caprio et al., 3D cellular automata simulations of intra and intergranular corrosion. Corrosion Science 112 (2016) 438-450.

Implementation of nucleation in cellular automaton simulation of microstructural evolution during additive manufacturing of Al alloys

Abstract In this work, a new approach is developed to integrate a particle-based (seed crystals) nucleation mechanism into the Cellular Automata (CA) simulation of powder-bed laser beam melting. The model aims to reflect two features observed in the microstructures of additively manufactured Al alloys: the fusion boundary nucleation which violates the principle of common bulk nucleation favored under high solidification rates and low thermal gradients, and the epitaxial growth at the melt-pool bottom as observed in the microstructure of AlSi10Mg alloy. Based on the proposed nucleation model, a CA cell will accommodate a nucleus after a few physics-based nomination and activation criteria have been passed. The fusion boundary nucleation can be reproduced by the model with a nomination criterion that restricts nucleation to the CA cells having a maximum experienced temperature below the particle dissolution temperature. However, the second observed feature needs an additional criterion to incorporate the nucleation incubation time. This is interpreted through the competition between the epitaxial growth and the nucleation which results in different behaviors at different melt-pool regions. Accordingly, the model offers high flexibility in calibration based on the growth and nucleation kinetics. The set of parameters used for AlSi10Mg are capable to deliver a similar microstructure and texture compared to the experiments. Moreover, a very high nucleation density along with a lower nucleation incubation time can lead to the bimodal grain structure observed in Sc-modified aluminum alloys.

Kinetic Modeling of West Nile Virus Fusion Indicates an Off-Pathway State.

West Nile virus (WNV) is a prominent mosquito-borne flavivirus that causes febrile illness in humans. To infect host cells, WNV virions first bind to plasma membrane receptors, then initiate membrane fusion following endocytosis. The viral transmembrane E protein, triggered by endosomal pH, catalyzes fusion while undergoing a dimer-to-trimer transition. Previously, single-particle WNV fusion data was interrogated with a stochastic cellular automaton simulation, which modeled the E proteins during the fusion process. The results supported a linear fusion mechanism, with E protein trimerization being rate-limiting. Here, we present corrections to the previous simulation, and apply them to the WNV fusion data. We observe that a linear mechanism is no longer sufficient to fit the data. Instead, an off-pathway state is necessary; these results are corroborated by per virus chemical kinetics modeling. When compared with a similar Zika virus fusion model, this suggests that off-pathway fusion mechanisms may characterize flaviviruses more broadly.

Diffusion of Innovations in Middle Eastern versus Western Markets: A Mathematical Computation Cellular Automata Simulation Model

Simulation modelling has gained ground over the years since it can provide various scenarios applied to any scientific area. In this study, a stochastic cellular automata model is proposed, in which agents fall into three distinct categories (adopters, non-adopters and denials). Based on Hofstede’s cultural dimension individualism, we characterize three major international markets, as perfectly clustered (collective) to perfectly random (individualistic). We investigate innovation diffusion speed, in each network topology. At each time step, the decision of non-adopters to purchase innovative products, is affected by their immediate neighborhood (von Neumman). The speed of diffusion is evaluated using time at which sales reach 50% of market. Effects of simulation parameters on speed of diffusion, are assessed using a log-normal accelerated failure time model. Results demonstrate that diffusion of innovative products accelerates when innovators of a virtual economic system are placed according to a random network and when amount of innovators and imitators in the economic system increases. Slower innovative products’ diffusion process is a result of a large amount of denials and of how imitators are placed in the in the virtual economic system. Diffusion in small-world virtual economic systems lead to small time inflexion points very close to those of a random networked market.

Modeling Human Evacuating Behavior in Limited Space Based on Cellular Automata Model

The study of evacuation for buildings with limited space is an important part of improving evacuation efficiency and preventing stampedes. A building evacuation model was proposed based on cellular automata simulation considering different crowd states. Different flow sizes under layout environments with the same facilities as well as evacuation efficiency, bottleneck area density, and escape routes choice under the orderly and disorderly distribution conditions have also been analyzed. The results show that the initial disorderly distribution state is superior to the orderly distribution state in terms of the evacuation efficiency index. The former provides evacuees with maximum room for the corridor and the exit, with the overall evacuation density being lower than that of the latter. Evacuation along the central corridor provides more room compared to that of the two flanks, which explains why evacuees prefer to occupy the central area when space is limited, and this is detrimental to the moving capacity.

Degradation Simulation of Poly Lactic Acid in Vitro Using the Genetic Algorithm.

Computer simulation using a degradation model is the most effective method to investigate the degradation behaviors of poly lactic acid (PLA). Various kinetic parameters are introduced into numerous degradation models to achieve the best simulation result. Nevertheless, massive possibilities of different parameter combinations limit the application of the enumeration algorithm, while the nonlinear relationship between the kinetic parameters and the degradation behaviors of PLA indicates that the ordinary parameter search algorithms cannot do well in the parameter optimization. A genetic algorithm (GA) with a small population size is proposed and utilized to optimize the kinetic parameters of the cellular automaton (CA) simulation in the present work. The optimal result indicates that the presented GA can realize the parameter optimization of the CA degradation model. The elitist tournament selection operation can speed up the optimization process. The algorithm can be executed as a single-stage algorithm alone or applied as a multistage algorithm according to various solution objects and corresponding fitness functions. Moreover, the algorithm can be hybridized with other traditional search methods such as binary search or local enumeration search to achieve a balance between accuracy and search speed.

Cellular automaton simulation of the quantum war of attrition game

The quantum war of attrition game is studied in this work via spatial numerical simulation. It is found that the implemented simulation converges to the Pareto optimal solution, i.e. no fighting at all, when the resign times of the players are entangled with higher factor, whereas larger resign times would be got with weak entanglement. This finding is shown to apply also in a fiercer war game, the war of extermination, in which game the non-entangled (or classical) simulation leads to very high resign times and consequently to very high negative payoffs.

Mathematical modeling and cellular automata simulation of infectious disease dynamics: Applications to the understanding of herd immunity.

The complexity associated with an epidemic defies any quantitatively reliable predictive theoretical scheme. Here, we pursue a generalized mathematical model and cellular automata simulations to study the dynamics of infectious diseases and apply it in the context of the COVID-19 spread. Our model is inspired by the theory of coupled chemical reactions to treat multiple parallel reaction pathways. We essentially ask the question: how hard could the time evolution toward the desired herd immunity (HI) be on the lives of people? We demonstrate that the answer to this question requires the study of two implicit functions, which are determined by several rate constants, which are time-dependent themselves. Implementation of different strategies to counter the spread of the disease requires a certain degree of a quantitative understanding of the time-dependence of the outcome. Here, we compartmentalize the susceptible population into two categories, (i) vulnerables and (ii) resilients (including asymptomatic carriers), and study the dynamical evolution of the disease progression. We obtain the relative fatality of these two sub-categories as a function of the percentages of the vulnerable and resilient population and the complex dependence on the rate of attainment of herd immunity. We attempt to study and quantify possible adverse effects of the progression rate of the epidemic on the recovery rates of vulnerables, in the course of attaining HI. We find the important result that slower attainment of the HI is relatively less fatal. However, slower progress toward HI could be complicated by many intervening factors.

Monitoring land use changes and its future prospects using cellular automata simulation and artificial neural network for Ahmedabad city, India

The urban sprawl is one of the potential threat for sustainable development. The present study has been carried out on Ahmedabad Municipal Corporation (AMC) area including Ahmedabad city to monitor the urban sprawl from 1976 to 2017. Normalized Difference Vegetation Index, Normalized Difference Built-Up Index, and Built-Up Index are applied to monitor the urban land use change by using multi-temporal and multi-date remote sensing satellite data from Landsat. The future scenario of urban land use prediction of AMC has been modelled by the use of cellular automata (CA) and artificial neural network (ANN) with GIS techniques. The results of land use monitoring indicate that the built-up area has increased by 156.93 km2 whereas, agricultural land, open spaces, urban vegetation, and water bodies have decreased during the last 4-decades from 1976 to 2017. Moreover, the results of CA simulation reveals that the built-up will continue to increase in the future at the cost of other classes. The decadal built-up growth was 2.58 km2 during the earlier period and it was the highest (5.98 km2) during the decade of 2007–2017. The validation of results related to CA–ANN has been measured by the Kappa coefficient in which the obtained values of Kappa local, Kappa histogram and Kappa overall were 0.92, 0.75, and 0.69 respectively and the measured percentage of correctness was 78.63%. The predicted urban land use growth reveals that the built-up would cover the maximum part of the AMC area by 2027 provided that the present land use trend, demographic growth, and commercial development does not show any major change. Therefore, the study pertaining to LULC change and its future prediction will be highly helpful for urban planners and administrators to prepare a sustainable city planning for the Ahmedabad city and its surroundings.

Globular to lamellar transition during anomalous eutectic growth

As a typical solidification microstructure, anomalous eutectic is still not known of its growth mechanism. Mullis et al (2018, Acta Mater. 145:186) experimentally showed that the volume faction of anomalous eutectic was not consisted with the predictions by any model invoking partial remelting of primary solidified microstructure. In the present article, the anomalous eutectic microstructure of Ni–Sn alloy solidified from undercooled melts and laser remelting melt pool has been investigated through experiments and cellular automaton (CA) simulations. Computational and experimental results showed that the nucleated α-Ni particulates grew into globular, lamellar or ‘tadpole’ morphology. The ‘tadpole’ morphology, which has a globular ‘head’ and a lamellar ‘tail’, is an intermediate pattern between globular and lamellar morphologies, and would be seen as an evidence of the globular to lamellar transition (GLT). The occurrence of the GLT or not determines that the solidified microstructure is either anomalous eutectic or lamellar eutectic. CA simulations showed that the GLT was mainly influenced by the temperature gradient G and pulling velocity V. For positive G and V, representing the directional solidification at the bottom of melt pool, the GLT prefers to occur at high G and low V; for negative G and V, which refers to the solidification in undercooled melts, the GLT prefers to occur at low absolute value of G and V. The GLT was also experimentally observed under the above two circumstances. The GLT growth mechanism abstained from CA simulations well explains the experimental results.

Cellular automaton model for the simulation of laser cladding profile of metal alloys

Based on the mechanism of laser-powder interaction and droplet forming method, a cellular automaton simulation model of laser cladding layer morphology is introduced. In the model, the influences of thermophysical parameters including specific heat and thermal conductivity are taken into consideration. Meanwhile, the relationships involving laser power, scan speed and powder feed rate and the morphology parameters of the cladding layer are established. Subsequently, in order to verify the applicability and accuracy of the simulation of the cladding layer, single-track experiments of Stellite6, Ni60AA and SUS316, materials with different thermophysical properties, were carried out under different process parameters, respectively. Additionally, the stepwise method is applied to multitrack cladding experiments with different overlap to obtain morphological parameters of different tracks. The morphology of the cladding layer calculated by the model is in good agreement with the experimental results. Both of the relative errors of width and height are less than 5%, and the relative error of the cross-sectional area is less than 9%, which affirms the possibility of the model to predict the cladding morphology of different materials under different process parameters. This research can optimize process parameters and improve the forming quality of laser cladding.

Simulation of hot rolling by cellular automata

This development is focusing on one of the most complex and important production steps of flat rolled products that is the simulation of hot rolling. During hot rolling two phenomena, work hardening and the process of regeneration of microstructure have strong influence for physical properties of aluminium alloys. Dynamic recovery has importance in the dynamic softening beside dynamic recrystallization in aluminium alloys. Hot rolled and newly modified grain structure is influenced by these dynamic phenomena. Hot rolled grain structure goes through significant changes under further production steps like cold rolling and heat treatments. But aside from these intermediate production steps the microstructure that we get after hot rolling has significant effect on mechanical and grains structure of the final flat rolled product. Proper cellular automata simulations of recrystallization and recovery can be the basis for good technology planning practices.

Structural characterization and continuous cellular automata simulation of micro structures by focused Ga ion beam induced deposition process

Focused ion beam induced deposition (FIBID) is a high-resolution micro/nano fabrication technique with the injection of precursor gas to produce complex three-dimensional structures, which can be used to construct nanodevices. Due to the complex interaction between precursor gas, incident ions, and the substrate, the morphology of deposition structure dramatically depends on the process parameters. In this paper, based on the Continuous Cellular Automata (CCA) and the extended precursor molecule diffusion model (EPMDM), the effects of different process parameters on the final deposition morphology, are systematically studied. The experimental and theoretical work explores the relationship between the characterization of the deposition structure and process parameters. Considering the variation of diffusion effect intensity, the diffusion coefficient matrix decaying with the structure height is established to calculate the contribution of diffusion effect more precisely, which can also explain the non-uniform growth of deposition structure in the FIBID process. The vacuum surface cells (VSCs) and solid surface cells (SSCs) are recognized for deposition and sputtering respectively in the CCA, so as to trace the dynamic deposition contour, and reproduce the coexistence of deposition and sputtering phenomena. In order to verify the proposed CCA simulation model, micro pillar array and other structures are fabricated by focused Ga ion beam induced C9H16Pt precursor gas. The experimental and simulation results show that the proposed model can well simulate the morphology of deposition structures under a wide range of process parameters of dwell time, refresh time, ion beam current and pixel overlap. Therefore, the model can provide a good prediction method for parameter optimization of focused Ga ion beam induced deposition process.

Game theory model of exit selection in pedestrian evacuation considering visual range and choice firmness**Project supported by the National Natural Science Foundation of China (Grant No. 71904116) and the Fund from the Shanghai Municipal Commission of Science and Technology, China (Grant Nos. 19DZ1209600 and 18DZ1201500).

Exit choice is one of the most important pedestrian behaviors during evacuation. Distance to the exit is a generally recognized factor influencing expected moving time to the exit. Visual range determines how much information a pedestrian can perceive, thus the number of pedestrians within the visual field can be used to estimate waiting time at the exit. Besides, the choice firmness that reflects the degree to which a pedestrian would persist in his/her previous choice of exit is proposed. By integrating game theory into a cellular automata simulation framework, the pedestrian exit choice mechanism is investigated and explicitly modeled in this paper. A systematic analysis of the key factors influencing pedestrian evacuation is conducted, including visual radius and choice firmness of a pedestrian, initial crowd distribution of the room, exit layout as well as exit width. It is found that low choice firmness level can lead to unnatural pedestrian behavior such as wandering, which is adverse to evacuation. The longer the pedestrian’s visual radius, the earlier the pedestrian can determine his/her final selection of the exit. Compared with the scenario where the pedestrians are randomly distributed, pedestrians clustered together in a corner of the room lead to high crowd density and imbalanced use of exits. Furthermore, the exit layout and exit width also have a certain influence on pedestrian evacuation process. The results of this paper may be of benefit to the formulation of behavioral rules in other pedestrian simulation models.

Multi-phase transformation kinetics of HSLA steels during continuous cooling: experiments and cellular automaton (CA) simulation

ABSTRACT Kinetics of multiply ferrite/bainite phase transformation of HSLA steels is investigated by experiments and cellular automaton (CA) simulation. Peak-differentiation method to elucidate the sequential ferrite and bainite phase transformation individually, which is verified by the CA simulation. Such CA modelling executed using classic JMAK theory, but also gives an insight of microstructure evolution of the multi-phase transformation routine on different cooling rate. From that, it enables classic JMAK modelling to capture the detached phase transformation with different growth models and interface-migration mechanisms. Also, we find that the final phase constitution is sensitive to the cooling rate. With increasing the cooling rate, bainite sheaves nucleated at prior austenite boundaries and ferrite/austenite interfaces are significantly facilitated, which seriously inhibits the growth of prior ferrites. The scenario can be interpreted by the CA simulation and the influence of the cooling rate on sequential multi-phase transformation can be also obtained.

Simulation of Hot Rolling by Cellular Automata

Our research is focusing to one of the most complex and important production step of flat rolled products that is the simulation of hot rolling. During hot rolling two phenomena as work hardening and the process of regeneration of crystals has strong influence for physical properties of microstructure of aluminium alloys. It needs to be taken into account in case of rolling technology steps and development. When we talk about aluminium the dynamic softening in fact it is dynamic recovery that is followed by dynamic recrystallization. It goes in the same order of magnitude rate. But in steels the recovery has only a minor effect. Hot rolled and newly modified grain structure is influenced by these dynamic phenomena. Hot rolled grain structure goes through significant changes under further production steps like cold rolling and heat treatments. But aside from these intermediate production steps the microstructure that we get after hot rolling has significant effect for mechanical and grains structure of the final flat rolled product. Proper technology planning is essential that for cellular automata simulation method can ensure useable and good solution for the simulation of recrystallization.

Simulation of Hot Rolling by Cellular Automata

Our research is focusing to one of the most complex and important production step of flat rolled products that is the simulation of hot rolling. During hot rolling two phenomena as work hardening and the process of regeneration of crystals has strong influence for physical properties of microstructure of aluminium alloys. It needs to be taken into account in case of rolling technology steps and development. When we talk about aluminium the dynamic softening in fact it is dynamic recovery that is followed by dynamic recrystallization. It goes in the same order of magnitude rate. But in steels the recovery has only a minor effect. Hot rolled and newly modified grain structure is influenced by these dynamic phenomena. Hot rolled grain structure goes through significant changes under further production steps like cold rolling and heat treatments. But aside from these intermediate production steps the microstructure that we get after hot rolling has significant effect for mechanical and grains structure of the final flat rolled product. Proper technology planning is essential that for cellular automata simulation method can ensure useable and good solution for the simulation of recrystallization.

Microstructural Changes During Static Recrystallization of Austenitic Stainless Steel 304L: Cellular Automata Simulation

Static recrystallization and microstructural changes in austenitic stainless steel 304L were studied. The rolling experiments at 200 °C were carried out, and then, annealing treatment was made at temperatures ranging between 500 and 830 °C. A model was also developed to simulate the kinetics of non-isothermal recrystallization within the rolled steel. The distribution of plastic strains during rolling was predicted utilizing an elastic–plastic finite element formulation performed in ABAQUS/Explicit, while the predicted results were used to generate the as-rolled microstructure and to estimate the stored energy. Finally, microstructural–thermal model based on cellular automata was developed to evaluate the rate of static recrystallization within the rolled steel. The comparison between experimental and simulations showed a good consistency. The predictions illustrated that inhomogeneous distribution of plastic strain was produced during multi-pass rolling leading to different rates of recrystallization in the center and the surface regions of the rolled plate. The onset temperature of recrystallization was found about 700 °C, and the activation energies for nucleation and growth for recrystallization were determined as 180 kJ/mol and 240 kJ/mol, respectively. It was found that homogenous nucleation mechanism can be operative in recrystallization of multi-pass rolled steel, i.e., for reduction of 40% or higher.

Develop of a fuel consumption model for hybrid vehicles

Despite extensive work on the fuel consumption of vehicles, the evaluation of hybrid electric vehicles (HEVs) requires a model that can predict fuel consumption second by second. In this paper, a fuel consumption model for hybrid vehicles is developed based on the operation of internal combustion engine (ICE), electric machine (EM) and battery. The fuel consumption model for engine is based on steady-state fuel mapping with a transient correction. EM and battery module (EBM) is introduced to estimate the fuel consumption for different modes of hybrid vehicle. The Argonne National Laboratory (ANL) measurements of different driving cycles including the steady-state cycle, the Urban Dynamometer Driving Schedule (UDDS) cycle, the Highway cycle and the United States 06 (US06) cycle are used to verified the model. With cellular automaton simulation, we study the fuel consumption in traffic flow and show that the fuel consumption can be significantly reduced by hybrid mode. The mean fuel saving is approximately 30% in the traffic flow on a horizontal road. The fuel consumption of traffic flow under uphill, downhill, tailwind and headwind conditions also showes considerable fuel saving. The model can be used to evaluate the fuel economy of HEVs, and provide eco-driving route-choice suggestions for drivers.