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For a d-dimensional cellular automaton with d $\ge$ 1 we introduce a rescaled entropy which estimates the growth rate of the entropy at small scales by generalizing previous approaches [1, 9]. We also define a notion of Lyapunov exponent and proves a Ruelle inequality as already established for d = 1 in [16, 15]. Finally we generalize the entropy formula for 1-dimensional permutative cellular automata [18] to the rescaled entropy in higher dimensions. This last result extends recent works [17] of Shinoda and Tsukamoto dealing with the metric mean dimensions of two-dimensional symbolic dynamics., Some inaccuracies in Section 4 and 5 corrected

In physics, a topological insulator is a material that simultaneously exhibits the properties of a conductor on the surface and an insulator in the bulk. An abstract model of a twodimensional topological insulator is described in terms of tricolour cellular automata and excitations of a topological insulator are classified.

Cellular automata are interacting classical bits that display diverse emergent behaviors, from fractals to random-number generators to Turing-complete computation. We discover that quantum cellular automata (QCA) can exhibit complexity in the sense of the complexity science that describes biology, sociology, and economics. QCA exhibit complexity when evolving under "Goldilocks rules" that we define by balancing activity and stasis. Our Goldilocks rules generate robust dynamical features (entangled breathers), network structure and dynamics consistent with complexity, and persistent entropy fluctuations. Present-day experimental platforms -- Rydberg arrays, trapped ions, and superconducting qubits -- can implement our Goldilocks protocols, making testable the link between complexity science and quantum computation exposed by our QCA., Comment: 24 pages, 10 figures

We present a one dimensional reversible block cellular automaton, where the time evolution is dictated by a period 3 cycle of update rules. At each time step a subset of the cells is updated using a four site rule with two control bits and two action bits. The model displays rich dynamics. There are three types of stable particles, left movers, right movers and "frozen" bound states that only move as an effect of scattering with the left and right movers. Multi-particle scattering in the system is factorized. We embed the model into the canonical framework of Yang-Baxter integrability by rigorously proving the existence of a commuting set of diagonal-to-diagonal transfer matrices. The construction involves a new type of Lax operator., 16 pages, v2: references added

To study the corrosion process and the pit interactions of multi-pit corrosion covered by an anticorrosive coating, we present a three-dimensional cellular automata model that is efficient of modeling multi-pit corrosion The spatial separation of anodic and cathodic semireactions results in the interaction of pits. Through the corrosion simulation of different number of pits, when there are more than one pits, some pits grow much faster than single-pit case, while some other pits filled with basic ions may stop growing for a long time. Therefore, the heterogeneous distribution of pH in multi-pit corrosion can be observed in the simulation results, and they are shown to be consistent with experimental studies. Specially, the concentration of basic ions in some areas can be seen both from the modal and the experimental results. The permeability of breakdown anticorrosive coating is considered in the model, and the results show that it plays an important role in the corrosion process.

As the COVID-19 pandemic continues to ravage the world, it is critical to assess the COVID-19 risk timely on multi-scale. To implement it and evaluate the public health policies, we develop a machine learning assisted framework to predict epidemic dynamics from the reported infection data. It contains a county-level spatio-temporal epidemiological model, which combines spatial cellular automata (CA) with time sensitive-undiagnosed-infected-removed (SUIR) model, and is compatible with the existing risk prediction models. The CA-SUIR model shows the multi-scale risk to the public and reveals the transmission modes of coronavirus in different scenarios. Through transfer learning, this new toolbox is used to predict the prevalence of multi-scale COVID-19 in all 412 counties in Germany. A t-day-ahead risk forecast as well as assessment of the non-pharmaceutical intervention policies is presented. We analyzed the situation at Christmas of 2020, and found that the most serious death toll could be 34.5. However, effective policy could control it below 21thousand, which provides a quantitative basis for evaluating the public policies implemented by the government. Such intervening evaluation process would help to improve public health policies and restart the economy appropriately in pandemics.

In order to study the mixed traffic of non-motor vehicles and pedestrians at urban intersections, a two-dimensional cellular automata model was established by analyzing the movement characteristics of non-motor vehicles and pedestrians, which included the field, cellular space, attributes, and forward decision-making of pedestrians and non-motor vehicles. This model can reflect the interweaving and interference behavior of non-motor vehicles and pedestrians in the time window of the intersection, and describe the behavior characteristics of non-motor vehicles and pedestrians in different stages of crossing the intersection.

CMOS technology has reached its physical scaling limits, power consumption limits, and hence CMOS technology has to be replaced by other emerging technologies. Quantum-Dot Cellular Automata (QCA) has proven to be a better solution since it offers better scaling and low power consumption for processing digital signals. However, due to a lack of optimization support improvements, dynamical QCA paradigms require multi-layer designs and increased computations. Hence in this paper, a reconfigurable logic gate based on QCA paradigms is proposed. The design utilizes training of memory cells associated with QCA paradigms and hence can be switched between AND, OR, and MUX logic circuit designs dynamically. Compared to traditional dynamical QCA, the model is designed on a single-layer substrate with a minimum number of cells and size.

In an intelligent networked environment, both the car and the road are more intelligent, and the information interaction between the vehicle and the roadside equipment is more frequent, the vehicle has a greater advantage in information acquisition, processing, decision-making and standardized driving compared to ordinary manual driving vehicles. The study of mixed traffic flow between intelligent networked vehicles and ordinary vehicles in the intelligent networked environment is of great significance to improve the operational efficiency of traffic flow and road capacity. In this paper, we build simulation scenarios in Vissim based on the meta cellular automaton traffic flow model and the Wiedemann model, conduct simulation experiments on the mixed traffic flow of intelligent networked vehicles and ordinary vehicles, and study and analyse the influence of the change in the proportion of intelligent networked vehicles on the flow, density, speed and other characteristics of the traffic flow. The results show that when the proportion of intelligent networked vehicles in the traffic flow is 40% to 80%, with the increase in the proportion of intelligent networked vehicles, the operating speed of the traffic flow, the density of the traffic flow has been improved to varying degrees, and the road passable flow has also been improved.

This article presents the results of the adapted complex methodology operation for the time series dynamics estimating, its features are in the joint use of both classical and new “nonlinear” statistics. The methods proposed and tested by the author are presented in the form of a pre-estimating and estimating model for assessing the grain yields time series trend stability in the Volgograd region (1930–2019) and obtaining a forecasting. The following methods of nonlinear dynamics were tested: the Hurst normalized range method, phase-plane analysis, and a linear cellular automaton. The results of analysis and forecasting on real yield data are presented in the form of the agro-economic system modeling lower level values, which in turn are input data for models of the upper level - the agro-economic system management level.

Computer simulations of steel microstructural development provide a powerful tool, which can form the basis of mechanical property predictions. However, in order to create detailed understanding of the factors affecting the properties, the model should predict microstructural evolution during cooling. The present study compares the results of cellular automata simulations with experimental data for two distinct austenite conditions, recrystallized and deformed. Detailed microstructural features were studied using a laser scanning confocal microscope, FESEM and FESEM-EBSD. The two-dimensional cellular automata (CA) model for simulating the formation of lath martensite was parameterized using fitted Johnson-Mehl-Avrami-Kolmogorov and Koistinen-Marburger equations. The parent austenite microstructure for the CA model was determined from the final martensitic microstructure using austenite grain reconstructions based on the use of MATLAB software and the MTEX toolbox. The results of this cellular automata simulation can be used to estimate the shapes and sizes of martensite blocks, which offers new possibilities for the qualitative estimation of the mechanical properties of high-strength steels formed from recrystallized or deformed austenite.

In this paper, we study the characterization of uniform cellular automata with the restricted vertical neighborhood and hybrid cellular automata with both restricted vertical neighborhood and Von Neumann Neighborhood using reflecting boundary condition over the eld ℤ2. The transition rule matrix for uniform and hybrid cellular automata with reflecting boundary condition is obtained and also reversibility of the uniform cellular automata is studied.

The growing of population of a pioneer species may show a unique behavior. Casuarina junghuhniana is reported as a pioneer species, this is because of its tolerance to adverse environment and transform it to become inhabitable for other organism. A comprehensive method involving field observation, the use of mathematical model and computation to understand plants behavior still needs to be developed. This paper is attempting to show a method to build a model for showing unique dispersal behavior of Casuarina junghuhniana. A relatively straightforward use of Fisher’s reaction diffusion equation, cellular automata based modeling and programming can show behavior easier to understand on a grid space. Some assumption must be used to represent the C. junghuhniana dispersal. As it is known that C. junghuhniana can reproduce both vegetatively and generatively, and both were assumed to have different dispersal behavior. Vegetative reproduction using shoots emerging from roots has pattern to spread close to each other. While generative reproduction by seeds which is lightweight has possibility spread further with the help of wind. The total model area of 1km 2 was divided into 300 × 300 cells which represents 1 km 2 area. Cellular automata apply the same rule to each cell and the result was observed from the pattern of cells interaction. A simple program was developed using Python with Jupyter Notebook an interactive computing environment. The number of iteration was limited before observed simulation reached one of area boundaries. The simulation running time was greatly reduced using Graphical Processing Unit (GPU) parallel processing. NUMBA was used as an interface between python and Compute Unified Device Architecture (CUDA), the GPU programming API. The simulation showed behavior of the trees spread downward along the slope. The wind direction simulation with additional data from wind rose available from internet was also demonstrated in the simulation. Modeling dispersal with influence from wind showed more sporadic pattern at further distance from originating parents cluster. The trees in the simulation showed clusters in dispersal pattern when rely more on generative reproduction. When the trees rely on vegetative reproduction by roots shoots, the population showed more like continuous cover. When concerning real 3 dimensional aspect, this simulation still can not distinguish vertical (z axis) aspect. It means two points would be seen as close to each other although they actually have far vertical distance. At this stage, the simulation has not yet been optimized to easily convert input from the wind rose. The wind information still needs to be written as code into the program.

Controlling the thermal condition of a solidification process to obtain a desirable microstructure morphology and then prepare specific materials with excellent mechanical properties or special functions has been attracting many concerns, where the behavior of microstructure morphology transition, especially the columnar-to-equiaxed transition, is one of the most important fundamental issues. This paper introduced a kinetic model for dendrite growth with a large undercooling during a non-equilibrium solidification process using cellular automaton, in which the local thermodynamic equilibrium condition, non-equilibrium partitioned solute, curvature and interface energy anisotropy were considered. The growth rate of dendrite tip was numerically investigated by using the cellular automaton model, and the effects of temperature gradient and cooling rate on the growth rate and morphology features were found. By integrating the simulation results and analytical models, a new microstructure morphology transition criterion for the non-equilibrium solidification depending on the temperature gradient and cooling rate was proposed, in which both the planar-to-columnar and the columnar-to-equiaxed transition were presented.

The new crown pneumonia epidemic has swept the world, panic, anxious, and uneasy emotions flowed into the psychology of everyone. This epidemic not only puts many countries in economic crisis, but may also put some small countries in danger of disappearing forever, and even make it impossible for large-scale people to return home. Therefore, the World Health Organization (WHO) and countries around the world need to join hands and work together to further explore ways to effectively control the epidemic. Analyze the relevant data of the four modes of disease (susceptible persons, latent persons, asymptomatic persons, and recovered persons), establish a differential equation model, and combine the results of question 1 to get the trend of the number of asymptomatic infections (present The trend of first rising and then falling) and specific data (it peaked at about 2733 people on the 42nd day after the outbreak; it dropped to 10 people about 70 days after the outbreak; it decreased to 0 at about 80 days). Then we simulated the distribution of asymptomatic infections based on the data reported by the Beijing Municipal Health Commission and combined with the cellular automaton model: the clustering state appeared in the first 10 days, and it gradually dispersed over time, and the distribution became more distributed after about 50 days. Evenly. Finally, it summarizes the applicable fields of this model in life and effective and accurate suggestions for epidemic prevention and risk reduction.

Cellular automata have found application in the study of discrete dynamic processes of physical reality. The article deals with the evolution of a discrete dynamic cellular system modeled in the Wolfram Mathematica computer environment. A comparative analysis of various variants of the cellular automaton model implementation is given: according to rules 90, 105 and 110. An algorithm for modeling the deformed state of a solid body using rule 110 is proposed. To simulate local structures that simulate stress concentrators, the algorithm is supplemented by generating a sequence of pseudo-random numbers. The simulation results showed that the appearance of stress concentrators corresponds to the transition from deterministic to chaotic behavior of a discrete cellular system. The article also estimates the possibility of using a discrete cellular system to simulate the turbulent motion of an incompressible fluid based on a generalized local balance model. The appearance of turbulence zones can be estimated by changing the pattern of the cellular automaton.

The steady state creep rates of QT600 ductile iron under various temperature are obtained by high temperature creep experiments. And the cellular automata model of creep microstructure evolution of QT600 ductile iron was established based on quantitative analysis of the microstructure. The results of the model are in good agreement with the results of the validation experiments. It’s shown that the cellular automata model is feasible and with high precision to predict the creep law of QT600 ductile iron. The results can provide some technical references for the safety analysis of QT600 ductile iron.

The competition and integration of cultures is an unavoidable trend in the context of globalization, and immigration behavior has significantly accelerated the process of cultural transmission and integration. Cultural change is an evolutionary process in a complex social system. At present, scholars in this field mainly use the complex network model, Axelrod’s cultural communication model, and cellular automata model to simulate the evolution of culture. The process of. Among them, the cellular automaton is a mathematical model with discrete time, space, and variables. Based on the above characteristics of the model, the affected population can be divided into small rectangular units, and time can be divided into units at the same time. Effectively simplified the simulation process.

It seems that everyone has the experience of making sandcastles on the leisure beach. In order to know how to build a beautiful and sturdy beach castle, this article simulates and analyzes the process of sand castles being eroded by water, and obtains some factors that extend the life of sand castles. First, we model the waves. Simplify the waves into a sine wave. Using calculus and fluid mechanics, the water wave impact force on a particle on the sand castle was calculated. Second, we model the sandcastle. Discretizing time, space, and state, we innovatively introduce the concepts of friction and impact into the model, and propose a new Three-dimensional Cellular Automaton model combined with step factors. We consider each gravel or water molecule as a cell, and simultaneously introduce the moving probability and collision probability to describe the moving trend and collision between the gravel cells, respectively. In order to effectively describe the loss of sand castles in the waves, the gravel cells that are in direct contact with the water cells will receive an impact force calculated by the first model. According to the law of large numbers, we use enough cells to simulate the erosion of sandcastles by the waves. It was found that within a certain range, the farther from the ocean and the more the total gravel, the stronger the anti-erosion ability of the sand castle.

The increase of population could leads to residential area availability. This could lead to imbalance between population and available housing and could results in higher population pressure on the available area. Spatial modeling prediction is needed as a prevention step to prevent excessive land cover change in the future. This research aims to analyze residential area carrying capacity and spatial modelling of land cover change of Samarinda in 2006, 2014 and 2020 using Cellular Automata Markov Chain (CAMC) and residential area carrying capacity index. The Cellular Automata Markov Chain (CAMC) results show that there is an expansion of residential area land cover which affected by driving factors that consist of distance from the nearby road, distance from the river, distance from the point of interest (health facility and education facility), slope, and elevation. Residential area land carrying capacity affected by population density, standard needed land area, and residential area extent in Samarinda City. Thus, it is needed to analyze the model to see the available area for residential area development sustainably.

This study proposes a potential-based three-dimensional cellular automata model to describe the route choice behavior of pedestrians while evacuating terraced stands. The model takes into account the pedestrians’ states of sitting, standing, and moving, and the possible transitions on terraced stands. The proposed potential field algorithm reflects the influence on route choice behavior of heterogeneous heights, route distance, pedestrian congestion, and route capacity. Three parameters related to the pedestrians’ behaviors in the spaces with heterogeneous heights are then analyzed to demonstrate the ability of the model to reproduce pedestrian route choice behaviors on terraced stands. Finally, empirical data observed in a terraced stand of a stadium are applied for further validation. The results show that the proposed model performs consistently well with the observed data.

In this study, traffic light management in intersection system was simulated based on cellular automata traffic flow model. Characteristic of vehicles flow is defined according to the NS model. Our model was developed by adding driving behaviours, which are randomly defined in different maximum vehicle speed of mixed flow for two-lane traffic flow without lane-changing. The relation between time duration of traffic light signal and the traffic flow by analyzing vehicle density and averaged speed were investigated. The results show that the time duration of traffic light signal affects the traffic flow. Our model can be used to find the appropriated time duration to handle the traffic and can eventually reduce traffic jam. Additionally. Our result also presents an effect of the driving behaviour on the traffic flow.

This paper demonstrates the use of cellular automata in the study of heat and mass transfer processes, in particular during wood drying. For study, we developed a three-dimensional mathematical model. This model is described by a system of interconnected differential equations. These equations are described in partial time derivatives and coordinates in space. The peculiarity of this work is the possibility of combining a three-dimensional mathematical model and the theory of cellular automata in solving the problem. Usage of the theory of cellular automata requires the presence of a certain number of identical elements of the system. In this case, we propose to present the studied CAD model in the form of cubes of the same size. The paper also describes the relationships between the created cubes. In addition, we give the algorithm of calculations. Based on the described algorithm, we carried out the number of experiments, which prove the possibility of using the theory of cellular automata in solving the problem.

Development and economic growth in an area can cause land cover changes. Penajam Paser Utara Regency, as a new capital candidate, is also predicted to experience in land cover changes. Land cover changes that are not following the land’s potential will cause environmental problems, so it is necessary to predict land cover changes by looking at patterns of land cover changes in the past and the factors that influence it. The purpose of this study is to analyze and predict the land cover change in Penajam Paser Utara Regency in 2031. The method used in this study is modeling using Cellular Automata - Markov. The driving factor of land cover change is used in making prediction models such as distance from the center of activity, distance from the road, distance from the river, elevation, and slope. The prediction land cover changes show that there has been an increase in plantation area and a decrease in forest area, while the development of the built-up area is not visible. The kappa test for predicted land cover showed perfect results. The resulting land cover model can be used to formulate land-use policies.

We study matrix product unitary operators (MPUs) for fermionic one-dimensional (1D) chains. In stark contrast with the case of 1D qudit systems, we show that (i) fermionic MPUs do not necessarily feature a strict causal cone and (ii) not all fermionic Quantum Cellular Automata (QCA) can be represented as fermionic MPUs. We then introduce a natural generalization of the latter, obtained by allowing for an additional operator acting on their auxiliary space. We characterize a family of such generalized MPUs that are locality-preserving, and show that, up to appending inert ancillary fermionic degrees of freedom, any representative of this family is a fermionic QCA and viceversa. Finally, we prove an index theorem for generalized MPUs, recovering the recently derived classification of fermionic QCA in one dimension. As a technical tool for our analysis, we also introduce a graded canonical form for fermionic matrix product states, proving its uniqueness up to similarity transformations., Comment: 35 pages, no figures; v2: minor revision

The article provides a theoretical description of the tensor approach to the software implementation of the cellular automaton model of diffusion. A block-synchronous cellular automaton with a neighborhood of Margolus was chosen as a model. Within the framework of the proposed approach, the rotation of the automaton block clockwise or counterclockwise can be carried out using a special operation on tensors, namely convolution. The approach discussed in this paper allows you to use various frameworks aimed at parallelizing computations to organize scientific calculations on modern powerful graphics adapters.

The authors created a cellular automata model simulating the dynamics of a fire source for rough terrain on a triangular grid, including cases of artificial and natural obstacles. The model can be used as a part of a complex of models describing fire propagation and migration of polluting aerosol and gaseous products of combustion in the atmosphere. It is applicable for predicting a possibility of occurrence, intensity, scenario of fire propagation, as well as assessing its impact on environment and also in decision support systems for the prevention of emergency fire situations. For the model description of real settlement areas, we used a digital model of the territory of the Krasnodar Territory built using geographic information systems.

A method based on cellular automata was established to simulate the solidification process of solder balls used in ball grid array (BGA) packaging technology. For the uniform and constant temperature distribution inside the droplets, the equiaxed crystal morphology and the equiaxed crystal solute field were studied. The simulation results are also shown for solidification process with the BGA tin-lead solder ball prepared by uniform droplet spray (UDS) process under the condition that the cooling rate of is invariable.

The floor field model has been widely used in evacuation simulation research based on cellular automata model. However, conventional methods of setting floor field will lead to highly insufficient utilization of the exit area when people gather on one side of the exit. In this study, an extended cellular automata model with modified floor field is proposed to solve this problem. Additionally, a congestion judgment mechanism is integrated in our model, whereby people can synthetically judge the degree of congestion and distance in front of them to determine whether they need to change another exit to evacuate or not. We contrasted the simulation results of the conventional floor field model, the extended model proposed in this paper, and Pathfinder software in a same scenario. It is demonstrated that this extended model can ameliorate the problem of insufficient utilization of the exit area and the trajectory of pedestrian movement and the crowd shape of pedestrians in front of exit in this new model are more realistic than those of the other two models. The findings have implications for modeling pedestrian evacuation.

Urban boundaries, an essential property of cities, are widely used in many urban studies. However, extracting urban boundaries from satellite images is still a great challenge, especially at a global scale and a fine resolution. In this study, we developed an automatic delineation framework to generate a multi-temporal dataset of global urban boundaries (GUB) using 30 m global artificial impervious area (GAIA) data. First, we delineated an initial urban boundary by filling inner non-urban areas of each city. A kernel density estimation approach and cellular-automata based urban growth modeling were jointly used in this step. Second, we improved the initial urban boundaries around urban fringe areas, using a morphological approach by dilating and eroding the derived urban extent. We implemented this delineation on the Google Earth Engine platform and generated a 30 m resolution global urban boundary dataset in seven representative years (i.e. 1990, 1995, 2000, 2005, 2010, 2015, and 2018). Our extracted urban boundaries show a good agreement with results derived from nighttime light data and human interpretation, and they can well delineate the urban extent of cities when compared with high-resolution Google Earth images. The total area of 65 582 GUBs, each of which exceeds 1 km2, is 809 664 km2 in 2018. The impervious surface areas account for approximately 60% of the total. From 1990 to 2018, the proportion of impervious areas in delineated boundaries increased from 53% to 60%, suggesting a compact urban growth over the past decades. We found that the United States has the highest per capita urban area (i.e. more than 900 m2) among the top 10 most urbanized nations in 2018. This dataset provides a physical boundary of urban areas that can be used to study the impact of urbanization on food security, biodiversity, climate change, and urban health. The GUB dataset can be accessed from http://data.ess.tsinghua.edu.cn.

Our work is performed in the framework of the mathematical model suggested by P.V. Makarov to describe the joint generation and propagation of ordinary stress waves (propagating with the sound speed) and slow deformation waves of the inelastic nature in loaded elastoplastic media. Structural models of block media with weakened regions (faults or deformation sites) are constructed for test calculations on generation and propagation of slow deformation waves in nonlinear dissipative media. The features of propagation of deformation waves are investigated for different fault orientations and implementations of the algorithm of cellular automata for transmitting slow perturbation. The zigzag and diamond nature of propagating fronts of slow deformation disturbances is revealed.

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.

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.

With the increasing number of terror attacks in France, evacuation plans at the Louvre, which receives tens of thousands of visitors every year, has become the key to the safety of visitors. Our goal is to make a reasonable emergency evacuation plan. First, we establish a two-dimensional evacuation model, based on the model, we build a three-dimensional cellular automaton model, which takes the speed of moving up and down the stairs of the occupants, positional attraction and probability of collisions into consideration. Second, we use Pathfinder for simulation. Finally, we find that the exit 1(secondary entrance) should be opened when the visitor density is high, while the exit 3 should be opened when the visitor density is low; and the Passage Richelieu entrance has the greatest influence on evacuation time, and emergency personnel should choose the Pyramid entrance as their emergency entrance.

China is a country with frequent forest fires. Forest fires not only damage the forest ecosystem, cause the loss of forest resources, but also threaten the safety of people’s lives and property. If the spread trend of forest fire can be predicted quickly and accurately after the fire, it will be of great significance and role to put out the fire and reduce the loss and casualties. In this study, based on the in-depth comparison of domestic and foreign commonly used forest fire spread models and related algorithms, the geographic cellular automata is selected as the diffusion algorithm, combined with the revised Wang Zhengfei fire spread model, and the host development method is adopted to achieve the forest fire spread prediction. Through the comparative analysis of the prediction results in the actual cases, the error is within the acceptable range, achieving the expected effect, meeting the requirements of real-time and efficient simulation of forest fire spread, and providing reliable decision support for the management.

Grain refinement by inoculation is widely practised in metal casting, in particular for aluminium alloys. During the last decades several modelling techniques have emerged to quantitatively predict solidification microstructures. The prediction of grain size remains however a challenge due to the complex competition between nucleation and growth, and physical phenomena taking place at very different length scales. Models often address the thermal recalescence and sometimes the suppression of nucleation by the solute boundary layers. The possible clustering tendency of the nucleant particles is however usually not considered, although it can play an important influence on the final grain size. This effect is particularly difficult to quantify because it requires a small-scale approach to describe the clusters, while a large computational domain is needed for grain size statistics. A cellular automaton (CA) model tracking the grain envelopes was developed to address this challenge. The spatial distribution of the nucleant particles and the solute diffusion field in the intergranular liquid were represented directly on the CA grid. Predicted grain sizes were first compared successfully with published experimental and modelling data. An investigation of the role of clustering of nucleant particles was then carried out, which demonstrated the potential of the model to address this topic.

A microscopic cellular automaton combined with macroscopic heat and solute transport was developed to simulate the mutual growth and evolution of austenite and M7C3 carbide grains during Fe-C-Cr ternary alloy solidification process. The diffusion of solute C and Cr are contributed together to the constitutional undercooling, together with curvature undercooling, for obtaining the grain growth rate of austenite and M7C3 carbide. Results show that, the absorption of solute C and Cr by M7C3 grain and rejection by austenite grain promote the two grains’ cooperative growth. Once they approach to each other, the austenite grain quickly overgrows towards the M7C3 grain till finally envelops it. The simulated solidification morphology of the Fe-4wt%C-17wt%Cr alloy, predicted averaged grain size of M7C3 carbides and C and Cr concentration in austenite grains agree with the experimental measurements and solidification path prediction. The predicted average liquid concentration curve fits with the LR, GS and PE prediction at the initial M7C3 precipitation regime and after austenite grains fully enveloping towards the M7C3 grains, returns to overlap the LR, GS and PE prediction curves.

In this study, we developed a cellular automaton (CA) model to simulate the multiphase microstructural evolution of the solidification of Fe-C binary peritectic alloys. Three phases were considered in the model: δ, γ, and liquid (L). To simulate microstructures formed by the peritectic transformation, moving interfaces at δ-γ, δ-L, and γ-L transformations were introduced for diffusion-controlled growth. The coarsening growth of γ grains after solidification of peritectic alloys was modelled using the CA method. Numerical simulations of multi-phase microstructure evolution for hyper-peritectic and hypo-peritectic alloys were performed in two and three dimensions. In these simulations, the nuclei of γ phases were formed at the δ/L interface below the peritectic temperature. After nucleation of the γ phase in hyper-peritectic alloys, the δ phase in the calculation domain disappeared before γ solidification was completed. Conversely, in hypo-peritectic alloys, the L phase disappeared before the δ-γ transformation was complete. Moreover, the coarsening of γ grains occurred for both alloys after the end of the peritectic transformation. These outcomes agree with the fact that the phase transformation of alloys involves the solidification of peritectic alloys. Thus, we confirmed that the proposed model was a valid approach to simulating multi-phase microstructures formed by the solidification of peritectic alloys.

The mesoscopic dendrite growth model in the solidification process of molten steel is established, based on the cellular automata model. To accurately describe the TiN nucleation process, a heterogeneous nucleation model was used to describe the TiN nucleation process. The accuracy of the dendrite growth model is verified by comparing the CA model and Lipton–Glicksman–Kurz (LGK) analytical model. The growth process of TiN precipitates was simulated by dynamic mesh generation. Meanwhile, the influence of grid anisotropy on dendrite growth is greatly weakened by introducing the decentered square algorithm, and the growth of the equiaxed crystal in all directions is simulated. The results show that the calculated results of the model are in good agreement with the volume and morphology of TiN observed in the experiment. Meanwhile, it is found that the smaller TiN will dissolve at the end of solidification, and there will be a re-precipitation. The precipitation time of High-N and High-Ti alloy systems with the same concentration product is basically the same, but the final precipitation solid fraction of TiN inclusions in High-N (small Ti/N) alloy is larger. N element is the decisive factor of TiN precipitation.