Cellular Automata Model Research Articles

Parameter estimation for cellular automata

Abstract Self-organizing complex systems can be modeled using cellular automaton models. However, the parametrization of these models is crucial and significantly determines the resulting structural pattern. In this research, we introduce and successfully apply a sound statistical method to estimate these parameters. The decisive difference to earlier applications of such approaches is that, in our case, both the CA rules and the resulting patterns are discrete. The method is based on constructing Gaussian likelihoods using characteristics of the structures, such as the mean particle size. We show that our approach is robust for the method parameters, domain size of patterns, or CA iterations.

Extended Pedestrian Evacuation Model Considering Multiple Evacuation Behaviors

A variety of behaviors can exist in pedestrian evacuation, altruistic, competitive, indifferent, and so forth. Understanding the psychological state of pedestrians and the various evacuation behaviors that arise is important because it plays a critical role in understanding the entire evacuation process. In this paper, an extended cellular automata model is developed to study the different behaviors of pedestrians in evacuation. Pedestrians are classified by psychological and physical heterogeneity, including helpful pedestrians, aggressive pedestrians, apathetic pedestrians, and vulnerable pedestrians. In this model, pedestrians are affected by static fields, dynamic fields, helper fields, and attack fields. In addition, the pedestrian view is affected by the density and position of movement of surrounding pedestrians. And, pedestrian movement, small group movement, helping behavior, aggressive behavior, and apathetic behavior are also considered simultaneously. Numerical simulations were conducted to discuss the pedestrian evacuation problem under multiple behaviors, and the effects of helping behavior, the number of attackers, attack force, pedestrian density, and apathetic behavior on the evacuation process were analyzed in detail. The results of the study can provide reference and guidance for the development of pedestrian evacuation strategies in the presence of helping, aggressive behavior events, and reducing casualties.

Investigation of Spatio-Temporal Simulation of Mining Subsidence and Its Determinants Utilizing the RF-CA Model

It is important to carry out timely scientific assessments of surface subsidence in coal resource cities for ecological environmental protection. Traditional subsidence simulation methods cannot quantitatively describe the driving factors that contribute to or ignore the dynamic connections of subsidence across time and space. Thus, a novel spatio-temporal subsidence simulation model is proposed that couples random forest (RF) and cellular automaton (CA) models, which are used to quantify the contributions of driving factors and simulate the spatio-temporal dynamic changes in subsidence. The RF algorithm is first utilized to clarify the contributions of the driving factors to subsidence and to formulate transformation rules for simulation. Then, a spatio-temporal simulation of subsidence is accomplished by combining it with the CA model. Finally, the method is validated based on the Yongcheng coalfield. The results show that the depth–thickness ratio (0.242), distance to the working face (0.159), distance to buildings (0.150), and lithology (0.147) play main roles in the development of subsidence. Meanwhile, the model can effectively simulate the spatio-temporal changes in mining subsidence. The simulation results were evaluated using 2021 subsidence data as the basis data; the simulation’s overall accuracy (OA) was 0.83, and the Kappa coefficient (KC) was 0.71. This method can obtain a more realistic representation of the spatio-temporal distribution of subsidence while considering the driving factors, which provides technological support for land-use planning and ecological and environmental protection in coal resource cities.

Predictive modeling of land cover changes in round-1 smart cities of India using cellular automata and GIS

The present study dealt with the Land Use Land Cover (LULC) and built-up dynamics for four round-1 smart cities within a period of 20 years (2001–2021) using satellite-based remote sensing and Geographic Information System (GIS) techniques. The study also presented predictive aspects of built-up dynamics by the year 2031. Various layers contribute to urban growth viz. slope, population density, distance to Central Business District (CBD), major roads, and drainage were analyzed and prepared. The Cellular Automata (CA) model was applied using the previous years’ layers and the thematic ones to predict the spatial extent of the year 2031. Thresholds for all thematic layers based on spatial proximity were selected for various classes of these factors. Built-up change rate for all the four round-1 smart cities viz. Ahmedabad (the year 2001 ~ 183.79 km2, the year 2021 ~ 252.3 km2), Chennai (the year 2001 ~ 102.45 km2, the year 2021 ~ 137.07 km2), Jaipur (the year 2001 ~ 132.73 km2, the year 2021 ~ 221.71 km2) and Surat (the year 2001 ~ 97.73 km2, the year 2021 ~ 158.79 km2) has shown a dynamic growth from 2001–2021. The study also revealed transition states of land cover classes between 2021 and 2031. The comparison between actual and simulated changes for the year 2021 showed the model’s accuracy assessment. The estimates also revealed a continuous increment in the impervious state of the urban surface due to urban expansion. Thus, satellite image-based LULC classification, built-up mapping, and model-based prediction could be utilized for planning infrastructure development.

Thermal Environmental Impact of Urban Development Scenarios from a Low Carbon Perspective: A Case Study of Wuhan

Amidst the increasingly escalating global concern regarding climate change, adopting a low-carbon approach has become crucial for charting the future developmental trajectory of urban areas. It also offers a novel angle for cities to avoid high-temperature risks. This paper estimates carbon emissions in Wuhan City from both direct and indirect aspects. Then, the ANN (artificial neural network)–CA (Cellular Automata) model is employed to establish three distinct development scenarios (Ecological Priority, Tight Growth, and Natural Growth) to predict future urban expansion. Additionally, the WRF (Weather Research and Forecasting Model)—UCM (Urban Canopy Model) model is used to investigate the thermal environmental impacts of varying urban development scenarios. This study uses a low-carbon perspective to explore how cities can develop scientifically sound urban strategies to meet climate change challenges and achieve sustainable development goals. The conclusions are as follows: (1) The net carbon emission for Wuhan in 2022 is estimated to be approximately 20.8353 million tonnes. Should the city maintain an average annual emission reduction rate of 10%, the carbon sink capacity of Wuhan would need to be enhanced by 382,200 tonnes by 2060. (2) In the absence of anthropogenic influence, there is a propensity for the urban construction zone of Wuhan to expand primarily towards the southeast and western sectors. (3) The Ecological Priority (EP) and Tight Growth (TG) scenarios are effective in alleviating the urban thermal environment, achieving a reduction of 0.88% and 2.48%, respectively, in the urban heat island index during afternoon hours. In contrast, the Natural Growth (NG) scenario results in a degradation of the urban thermal environment, with a significant increase of over 4% in the urban heat island index during the morning and evening periods. (4) An overabundance of urban green spaces and water bodies could exacerbate the urban heat island effect during the early morning and at night. The findings of this study enhance the comprehension of the climatic implications associated with various urban development paradigms and are instrumental in delineating future trajectories for low-carbon sustainable urban development models.

Cellular automata modelling of leukaemic stem cell dynamics in acute myeloid leukaemia: insights into predictive outcomes and targeted therapies.

Acute myeloid leukaemia (AML) is a haematologic malignancy with high relapse rates in both adults and children. Leukaemic stem cells (LSCs) are central to leukaemopoiesis, treatment response and relapse and frequently associated with measurable residual disease (MRD). However, the dynamics of LSCs within the AML microenvironment is not fully understood. This study utilized three-dimensional cellular automata (CA) modelling to simulate LSC behaviour and treatment response under induction chemotherapy. Our study revealed: (i) a correlation between LSC persistence post-induction chemotherapy and risk of AML relapse; (ii) MRD negativity based on LSC count may not reliably predict outcomes, supporting clinical evidence that patients with MRD-negative status can still be at risk of relapse; (iii) prolonged persistence of LSCs post-chemotherapy without disruption of normal haematopoiesis, aligning with clinical observations of dormant AML clones; (iv) early LSC dynamics post-induction chemotherapy, characterized by stochastic behaviours and movement velocities, are insufficient predictors of long-term prognosis; and (v) a distinct spatiotemporal organization of LSCs in later phases post-induction chemotherapy is correlated with long-term outcomes. Our modelling results provide a theoretical and clinical framework for AML research, and future clinical data validation could refine the utility of CA modelling for oncological studies.

Cross-diffusion waves by cellular automata modeling: Pattern formation in porous media.

Porous earth materials exhibit large-scale deformation patterns, such as deformation bands, which emerge from complex small-scale interactions. This paper introduces a cross-diffusion framework designed to capture these multiscale, multiphysics phenomena, inspired by the study of multi-species chemical systems. A microphysics-enriched continuum approach is developed to accurately predict the formation and evolution of these patterns. Utilizing a cellular automata algorithm for discretizing the porous network structure, the proposed framework achieves substantial computational efficiency in simulating the pattern formation process. This study focuses particularly on a dynamic regime termed "cross-diffusion wave," an instability in porous media where cross-diffusion plays a significant role-a phenomenon experimentally observed in materials like dry snow. The findings demonstrate that external thermodynamic forces can initiate pattern formation in cross-coupled dynamic systems, with the propagation speed of deformation bands primarily governed by cross-diffusion and a specific cross-reaction coefficient. Owing to the universality of thermodynamic force-flux relationships, this study sheds light on a generic framework for pattern formation in cross-coupled multi-constituent reactive systems.

A cellular automata model for recrystallization annealing of aged GH4169 superalloy and its application

For the forging of GH4169, there are often serious mixed and coarse grains that need to be uniformly refined through a multi-stage annealing process. However, it will need to take a lot of time and cost to explore suitable multi-stage annealing process parameters if we only employ the experimental method. The cellular automata (CA) simulation can reveal the evolution of microstructure during forming and annealing, which can obviously reduce the number of experiments. Therefore, in the study, a CA model to simulate the evolution of grain microstructure, dislocation density and δ phase is established. The results demonstrate that the established CA model can effectively predict the microstructural evolution of GH4169. The correlation coefficient exceeds 0.94. Furthermore, using the CA simulation, an optimized multi-stage annealing parameter of “1000 ℃×3min+1000 ℃-5 min-950 ℃+950 ℃×50min” has been identified, which is also verified by experiments. These findings further verify the accuracy and reliability of the model in simulating microstructural evolution during the annealing process of GH4169 forgings. Eventually, based on the CA simulation, the formation mechanism for the uneven grain growth in the annealed microstructure is revealed. At original deformed grain boundaries, dynamic recrystallization (DRX) grains grow slowly, whereas static recrystallization (SRX) grains at DRX boundaries or δ phase boundaries within original deformed grains grow rapidly.

Investigation of marine corrosion characteristics of 10CrNiCu steel subjected to stress fields using an improved 3D cellular automata modeling

Investigation of marine corrosion characteristics of 10CrNiCu steel subjected to stress fields using an improved 3D cellular automata modeling

Simulation of grain refinement of Al-8Si-0.2 Mg alloy inoculated with Al-Nb-B via an improved cellular automaton model

Simulation of grain refinement of Al-8Si-0.2 Mg alloy inoculated with Al-Nb-B via an improved cellular automaton model

Calibration and validation of a hybrid traffic flow model based on vehicle trajectory data from a field car-following experiment

ABSTRACT The paper focuses on the calibration of the hybrid multi-scale modelling approach that incorporates multiple levels of traffic flow representation. This paper refers to a model already developed in the literature, the Hybrid Cellular Automata (CA) and Cell Transmission Model (CTM). We use vehicle trajectory data collected from a car-following field experiment on a circular road track to explore the calibration of the CA model concerning various cell lengths through two distinct approaches: simulating all vehicles within the closed loop and simulating each vehicle using data obtained from its respective follower. We also evaluate different methods for the CTM calibration with respect to the CA model. The major findings are: (1) the calibrated parameters obtained using the simulated leader approach display greater regularity across different cell lengths; (2) the Constrained Squared Error [CsqE] method for macroscopic calibrations yielded promising results, showcasing the lowest sum of squared errors between fundamental diagrams.

Complex Battery Storage Fire Propagation Translational Forensic Study Using Cellular Automata

The surge in lithium-ion battery (LIB) use, essential for mass-scale renewable energy storage, raises concerns about fire hazards. However, to date, there is a lack of industry-wide understanding of large-scale LIB fire propagation. This paper suggests a translational forensic approach to promote fire safety awareness and introduces the cellular automata (CA) model coupled with the Monte Carlo (MC) approach to address the complex fire propagation simulation within an energy storage system (ESS). The objective is to demonstrate that the CA-MC model can provide a flexible and scalable connection for all levels of battery fire studies. The numerical model is coupled with experimental tests which have been performed to establish the actual timing of fire propagation from a single source. Cellular automata simulation, conducted through hybrid modeling and an applied risk analysis approach to evaluate fire hazards associated with LIBs, offers crucial insights into potential risks. The results demonstrate that, with fire incident initiation at a probability of 0.1 (10%), 33% of batteries will burn, and at a probability of 0.6 (60%) and beyond, the entire battery module will face complete burndown. Achieving full combustion of the entire module will take only approximately 42 timesteps on average, indicating rapid fire propagation. The actual time for a complete fire to occur in the battery module has been estimated to be 304 s per timestep, or 3.5 h total. Using this example, it is shown that the CA-MC approach can be extended to many other aspects of battery fire studies and is ideal as a translational tool, spanning all domains of the LIB industry.

Median U-Turn Intersection Critical Parameter Research and Operational Performance Evaluation

As one of the unconventional intersection designs, the median U-turn (MUT) intersection design has been confirmed to have the potential to improve intersection efficiency and produce lower vehicle delays, and it has been widely applied to many urban networks. Most existing studies have successfully evaluated the operational performance of MUT intersections by analyzing the overall traffic flow, particularly for intersection delay and capacity. However, the impact of the critical parameters and behavior of individual vehicles in MUT intersection operations has not been adequately studied. These limitations cannot provide a complete and objective evaluation of MUT intersections. Therefore, a comprehensive cellular automata model is proposed to simulate vehicle dynamic variations, considering road channelization information and vehicle random movements. This model will be compared to the VISSIM model to validate rationality by using field data, and it shows a good agreement between the simulation results of both models. In addition, sensitive experiments reveal that properly adjusting the elements, including the separation distance, the proportion of left-turn vehicles, and green phase percentage, can improve the operation of MUT intersections to varying degrees. By appropriately improving intersection features and conducting reasonable evaluations, the overall performance and sustainability of the MUT intersections in Xi’an city can be enhanced. Finally, this paper offers a valuable guideline for the evaluation and modeling strategies of MUT intersections.

A modified microscopic cellular automaton model for the simulation of microstructure evolution during solidification/melting of nickel-based superalloys

A modified microscopic cellular automaton model for the simulation of microstructure evolution during solidification/melting of nickel-based superalloys

A Three-Stage Cellular Automata Model of Complex Large Roundabout Traffic Flow, with a Flow-Efficiency- and Safety-Enhancing Strategy.

Intelligent transportation systems (ITSs) present new opportunities for enhanced traffic management by leveraging advanced driving behavior sensors and real-time information exchange via vehicle-based and cloud-vehicle communication technologies. Specifically, onboard sensors can effectively detect whether human-driven vehicles are adhering to traffic management directives. However, the formulation and validation of effective strategies for vehicle implementation rely on accurate driving behavior models and reliable model-based testing; in this paper, we focus on large roundabouts as the research scenario. To address this, we proposed the Three-Stage Cellular Automata (TSCA) model based on empirical observations, dividing the vehicle journey over roundabouts into three stages: entrance, following, and exit. Furthermore, four optimization strategies were developed based on empirical observations and simulation results, using the traffic efficiency, delay time, and dangerous interaction frequency as key evaluation indicators. Numerical tests reveal that dangerous interactions and delays primarily occurred when the roundabout Road Occupancy Rate (ρ) ranged from 0.12 to 0.24, during which times the vehicle speed also decreased rapidly. Among the strategies, the Path Selection Based on Road Occupancy Rate Recognition Strategy (Simulation 4) demonstrated the best overall performance, increasing the traffic efficiency by 15.65% while reducing the delay time, dangerous interactions, and frequency by 6.50%, 28.32%, and 38.03%, respectively. Additionally, the Entrance Facility Optimization Strategy (Simulation 1) reduced the delay time by 6.90%. While space-based optimization strategies had a more moderate overall impact, they significantly improved the local traffic efficiency at the roundabout by approximately 25.04%. Our findings hold significant practical value, particularly with the support of onboard sensors, which can effectively detect non-compliance and provide real-time warnings to guide drivers in adhering to the prescribed traffic management strategies.

A cellular automata modelling approach for grain growth topological evolution process of ternary cathode materials combined with deep neural networks

Ternary cathode materials are pivotal in high-performance battery technologies, with grain size influencing their electrochemical performance. However, the absence of real-time grain size inspection during material preparation poses challenges in maintaining the consistent quality of ternary cathode materials. To address this, this paper proposes a novel method employing cell automata to model the topological evolution of grain growth in these materials, integrated with deep neural networks (DNN). The grain growth process is divided into two stages: heating and constant temperature. In the heating stage, varying heating rates and plateau temperatures serve as DNN inputs, yielding the primary grain distribution for the cell automata model in the constant temperature stage. Based on cell automata, the grain growth model links the grain growth rate to the grain size distribution in the constant temperature stage. A surface energy constraint rule, based on local curvature and grain boundary surface tension, governs growth rates. The grain boundary growth ratio is also used to create a grain ID transition variable, dictating grain ID conversion in the model. This approach accurately simulates the dynamic evolution of polycrystalline grain size and morphology. Simulation results show that this method effectively models grain growth in ternary cathode materials, offering insights for optimising the sintering process and improving material quality.

Fire-Image-DenseNet (FIDN) for predicting wildfire burnt area using remote sensing data

Predicting the extent of massive wildfires once ignited is essential to reduce the subsequent socioeconomic losses and environmental damage, but challenging because of the complexity of fire behavior. Existing physics-based models are limited in predicting large or long-duration wildfire events. Here, we develop a deep-learning-based predictive model, Fire-Image-DenseNet (FIDN), that uses spatial features derived from both near real-time and reanalysis data on the environmental and meteorological drivers of wildfire. We trained and tested this model using more than 300 individual wildfires that occurred between 2012 and 2019 in the western US. In contrast to existing models, the performance of FIDN does not degrade with fire size or duration. Furthermore, it predicts final burnt area accurately even in very heterogeneous landscapes in terms of fuel density and flammability. The FIDN model showed higher accuracy, with a mean squared error (MSE) about 82% and 67% lower than those of the predictive models based on cellular automata (CA) and the minimum travel time (MTT) approaches, respectively. Its structural similarity index measure (SSIM) averages 97%, outperforming the CA and FlamMap MTT models by 6% and 2%, respectively. Additionally, FIDN is approximately three orders of magnitude faster than both CA and MTT models. The enhanced computational efficiency and accuracy advancements offer vital insights for strategic planning and resource allocation for firefighting operations.

Estimation of Potential Impact of Land Use Change on Sediment Yield From a Small Tropical Watershed Using the TREX Erosion Model

ABSTRACTAnalysis of the influence of changes in land use on the sediment yield from watersheds provides crucial inputs that aid the development of appropriate strategies for the sustainable management of consequent land degradation. Event‐based hydrologic models can be used for performing such analysis, as long‐term hydrological datasets are not available for most of the rivers in developing countries like India. In this study, an event‐based Two‐Dimensional Runoff, Erosion, and Export (TREX) model was used to simulate the soil erosion process in Moozhy, an ungauged watershed in the Karamana River basin in Thiruvananthapuram District, Kerala State, India. Rainfall, streamflow, and sediment concentration data corresponding to three isolated storm events were used to calibrate and validate the model. The performance of the model was assessed using four statistical measures, namely, Percent bias (PBIAS), Nash‐Sutcliffe Efficiency Coefficient (NSEC), Coefficient of determination (R2) and RMSE‐observations standard deviation ratio (RSR). The values of PBIAS varied between 46% and 49%, indicating satisfactory performance of the model. Also, from the values of NSEC and RSR, it can be concluded that the TREX model yields acceptable results. For a rainfall event that occurred on the 17 September 2017, the simulated values showed that about 1054 t of suspended sediments are transported from the watershed to the stream channels, and about 1020 t is carried out of the Moozhy watershed. Only a very small amount of sediment is left in the channel at the end of the simulation. About 34 t of sediment is deposited in the channel bed, about 0.04 t remains in suspension, and the balance 0.04 t remains in suspension as a suspended load. About 3% of the total sediment entering the reach of the stream considered in this study is deposited on the riverbed. The major component of the settled sediments is silt; about 12% of the total silt size fraction entering the stream settles on the river bed. Future scenarios of land use in the watershed were modelled using a hybrid Artificial Neural Network (ANN) and Cellular Automata (CA) model. These were used for simulating sediment discharge using the TREX erosion model. The predicted land use scenarios were used to investigate both short‐term (2025 and 2029) and long‐term (2037, 2045, and 2053) variations in sediment discharge. The sediment yield for the storm event that occurred on 17 September 2017 was used to benchmark the variation in sediment yield under the predicted land use scenarios. Results indicate that the peak runoff and the runoff volume are expected to increase by about 29% and 22% respectively in the period from 2005 to 2053. The expected increase in the volume of sediments in this period is about 50%; the peak sediment concentration is likely to increase by about 56%. The study highlights the threats of likely increase in soil erosion and consequent land degradation posed by unscientific changes in land use caused by urbanisation and calls for proper management interventions to address the problem.

The Impact of Dependent Behavior on the Design of Classroom Evacuation Exits for Intellectually Disabled Students

The increasing demand for special education in architectural design highlights the urgent need to ensure the safe evacuation of students with intellectual disabilities. However, current research on classroom evacuation for these students remains limited, particularly concerning critical factors, such as the number, location, and distance of exits. This study investigated the impact of dependent behavior on classroom exit design for students with intellectual disabilities by developing a Cellular Automaton (CA) model based on their behavioral characteristics. Simulated evacuation scenarios, considering and disregarding dependent behaviors, were analyzed to assess their effects on the number and positioning of exits, and a predictive model was implemented to establish the relationship between exit spacing and evacuation time. The results indicated that the dependent behavior significantly reduced evacuation efficiency and substantially affected classroom exit design. Considering the dependent behavior, this study demonstrated that setting two exits reduced the average evacuation time for students with intellectual disabilities by 12.99%, with further reductions achieved by placing the exits at the rear rather than at the sides or front of the classroom. The research also revealed that under the influence of dependent behavior, the average evacuation time initially decreased and then increased as the distance between exits increased. As one of the few studies addressing evacuation issues for students and the first to incorporate dependent behavior into the evacuation model, this study provides valuable recommendations for classroom designs that balance evacuation safety and daily usability. It offers essential data to inform architectural designs for classrooms serving students with intellectual disabilities and serves as a reference for future educational building design standards and regulations.

Top 10+1 indicators for assessing forest ecosystem conditions: A five-decade fragmentation analysis

Globally, land use change has consistently resulted in greater losses than gains in aboveground biomass (AGB). Forest fragmentation is a primary driver of biodiversity loss and the depletion of natural capital. Measuring landscape characteristics and analyzing changes in forest landscape patterns are essential for accounting for the contributions of forest ecosystems to the economy and human well-being. This study predicts national forest distribution for 2036 and 2054 using a Cellular Automata (CA) system and assesses ecosystem conditions through landscape metrics at the patch, class, and landscape levels. We calculated 130 metrics and applied a Variance Threshold method to remove features with low variance, testing different thresholds. The first filtered-out metrics were further analysed through Principal Component Analysis combined with a Feature Importance technique to select and rank the top 10 indicators: effective mesh size, splitting index, mean radius of gyration, largest patch index, mean core area, core area percentage, Simpson's evenness index, mutual information, Simpson's diversity index, and mean contiguity index. The eleventh selected indicator is the AGB density, a structural measurement for ecosystem condition and a proxy for forest carbon storage and sequestration assessments. From 2000 to 2018, the national AGB forest carbon stock decreased from 131.5 to 91.3 Megatons (Mt) with expected values for 2036 and 2054 being 71.8 and 55.3 Mt., respectively. Landscape measurements quantitatively describe forest dynamics, providing insights into the structure, configuration, and changes characterizing landscape evolution. This research underscores the capability of CA models to map large-scale forest resources and predict future development scenarios, offering useful information for conservation and environmental management decisions. Additionally, it provides measurements to support Ecosystem Accounting by assessing forest extent and indicators of its conditions.