Assessing cellular automata model behaviour using a sensitivity analysis approach

A segment derived patch-based logistic cellular automata for urban growth modeling with heuristic rules

Time is a fundamental dimension in urban dynamics, but the effect of various definitions of time on urban growth models has rarely been evaluated. In urban growth models such as cellular automata (CA), time has typically been defined as a sequence of discrete time steps. However, most urban growth processes such as land‐use changes are asynchronous. The aim of this study is to examine the effect of various temporal dynamics scenarios on urban growth simulation, in terms of urban land‐use planning, and to introduce an asynchronous parcel‐based cellular automata (AParCA) model. In this study, eight different scenarios were generated to investigate the impact of temporal dynamics on CA‐based urban growth models, and their outputs were evaluated using various urban planning indicators. The obtained results show that different degrees of temporal dynamics lead to various patterns appearing in urban growth CA models, and the application of asynchronous (event‐driven) CA models achieves better simulation results than synchronous models.

For urban growth modeling, assessment metrics derived from cell-by-cell comparisons are mainly related to the size of the study area and the urban growth rate. Non-urban areas always occupy an important part of the city to which cellular automata (CA) models do not contribute much, so the simulation accuracy is often exaggerated when this part is included. To enable comparing simulation results across models, regions, and time, we developed an improved equivalent area-based assessment (EQASS) method using cell-by-cell comparison metrics. As against existing assessment methods, EQASS is computed by including the same area of urban and suburban areas (i.e., equivalent areas). EQASS was tested in three Chinese coastal cities using a heuristic CA model and two spatial statistical CA models to simulate urban growth. The results show that EQASS can exclude correct rejections that are not attributable to CA models; these correct rejections have a significant impact on the model assessment. The improved assessment can better evaluate the performance of CA models across regions and over time than the conventional assessment method that accounts for the full study area. This study extends the simulation assessment method and provides a good solution for selecting the best CA model from many candidate models.

As an integrated kind of railway signal-control pattern, the four-aspect fixed autoblock system has been used in many train control systems. This paper takes the four-aspect fixed autoblock system as the research object and proposes the cellular automata model of the fixed autoblock system based on the existing theoretical researches on different train systems and traffic systems by means of the analytical study of the classical cellular automata model. The CA (cellular automata) models combine complexity of passenger railway line with the theory of cellular automata and introduce some new CA models into the existing control systems. After analyzing the relevant simulation results, we study thoroughly and obtain efficiently the needed data for the variation of the section carrying capacity, the average train delay and the train speed which have been affected by redundant time on the operation of passenger trains with different speeds.

There has been a growing interest from academia and industry in developing circuits and systems for edge computing and quality control tasks in food production lines, where image-processing is frequently required. This paper outlines the required considerations for designing a fruit classification system based on image-processing using Cellular Automata (CA) models and integrating it into reconfigurable hardware (HW) such as Field Programmable Gate Arrays (FPGAs). Parallel processing in CA requires numerous processing elements to be implemented and mapping CA models to HW generally comes with limitations. Homogeneous CA arrays are easier to design and implement in HW but can be resource-demanding. To fill this gap, this study explores different alternatives for the HW implementation of CA models, particularly trading computational-parallelism for a more optimized use of the available HW resources. We conducted experimental tests of the designed HW system using the Digilent Nexys development board, and the operation was validated against software-based benchmarks for image-processing, particularly concerning edge-detection. The presented study provides a broader range of design solutions for the HW implementation of two-dimensional CA models and a better understanding of their advantages and disadvantages. The results show that solutions focusing on instruction-parallelism add some complexity to the conception and require more design effort, compared to homogeneous CA models composed of identical cells. However, the instruction-parallel design solutions can significantly improve the HW resource utilization, especially when implementing computationally intensive CA rules in FPGAs.

Modeling urban growth using spatially heterogeneous cellular automata models: Comparison of spatial lag, spatial error and GWR

Gamma titanium aluminide (γ-TiAl) based alloys are very interesting materials for structural applications at elevated temperatures owing to the combination of high specific strength, good oxidation, creep and fatigue resistance. However, their relatively poor ductility and fracture toughness remain important obstacles for their industrial applications in engineering components. The mechanical properties of these alloys, namely the poor room temperature ductility, as well as the yield stress, creep and fracture resistance, can be significantly improved by controlling the microstructure. These alloys undergo solid state phase transformations upon cooling from the high temperature α phase, which results in formation of different types of microstructures depending on the cooling conditions and the alloy composition. Low and moderate cooling rates lead to the precipitation of the γ phase as parallel plates within the α matrix, followed by the α → α2 ordering reaction. As a result of this transformation, the characteristic lamellar structure of TiAl is produced. Rapid cooling leads to a massive transformation from α to γ. It has been shown that the massive microstructure can be used as a precursor to obtain a refined microstructure through a subsequent tempering in the α + γ phase field. However, obtaining a fully massive microstructure at all depths in a component can be difficult to achieve. Numerical simulation of microstructure formation can be used as a tool to anticipate the microstructure distribution in a component depending on the local chemistry and cooling conditions. The main objective of this work was to develop microstructure models describing the formation of the massive and lamellar microstructures. Two distinct modeling approaches have been used. The first approach is a deterministic model having for objective to predict the microstructure distribution in a cast and heat treated component. The model was designed to be integrated into a FEM or FDM heat flow solver in order to calculate microstructural quantities such as the proportion of phases and lamellar spacings at each nodal point of the mesh. The modeling approach is based on a combination of nucleation and growth laws which take into account the specific mechanisms of each phase transformation. Nucleation of massive and lamellar γ is described with classical nucleation theory, accounting for the fact that nuclei are formed predominantly at α/α grain boundaries. Growth of the massive γ grains is based on theory for interface-controlled reactions. A modified Zener model is used to calculate the thickening rate of the lamellar γ precipitates. The model incorporates the effect of particle impingement and coverage of the nucleation sites by the growing phases. The driving pressures of the phase transformations are obtained from Thermo-Calc based on the actual temperature and matrix composition. The deterministic approach was used to calculate CCT diagrams and lamellar spacings, which showed to be in good agreement with experimental data obtained from dedicated heat treatment experiments and from the literature. The model permitted investigating the influence of cooling rate, alloy chemistry and average α grain size upon the amount of massive γ and the average thickness and spacing of the lamellae. In particular, it indicated that the Al depletion of the α phase during lamellar precipitation seems to play an important role in the suppression of the massive transformation at moderate cooling rate and in the large lamellar spacings observed at low cooling rate. It was also found that Nb additions enhance the formation of massive γ by lowering the lamellar transformation temperature, increasing the T0 temperature and slowing down the lamellar growth due to the low diffusivity of Nb. The second approach was a cellular automaton (CA) model, which was used to describe the formation of the lamellar microstructure on the scale of a few microns. The objective of this approach was to make a direct description of the growth of a precipitate by an interfacial ledge mechanism, and then to evaluate whether the simplifications made in the deterministic model regarding this mechanism are appropriate. The modelling approach is based on the resolution of the diffusion equations in the α and γ phases. The ledge structure at the α/γ interface is described by introducing different types of cells in the CA grid. The CA model was used to describe the formation of the lamellar microstructure at isothermal conditions and at various cooling rates. The thickening kinetics of the lamellae, the lamellar spacings and the overall kinetics of the transformation were calculated with this approach and were compared with the results obtained with the deterministic model. It was found first that the thickening kinetics of the lamellae calculated with the deterministic model are slower than those calculated with the CA model. It was established that the method used in the deterministic model to account for the growth by a ledge mechanism always leads to a growth exponent of 0.5, which is characteristic of diffusion controlled reactions. In contrast, the CA approach yields growth exponents that are comprised between 0.5 and 1, as it is expected for growth in a mixed diffusion/interface controlled mode. The incorporation of a kinetic undercooling term into the deterministic model was found to be an appropriate correction. A good agreement was finally obtained in terms of lamellar spacings and overall kinetics. The underestimated thickening kinetics of the deterministic model was observed to be partly compensated by a higher nucleation rate at the beginning of the transformation. The overall kinetics of the lamellar transformation calculated with the deterministic model was found to be sufficiently accurate to correctly predict the competition between the lamellar and massive microstructures.

The diversity of human immunodeficiency virus (HIV) in vivo has been reported. In this article, we propose a cellular automata (CA) model describing the interactions between the immune system and HIV, and examine the effect of the diversity of these interactions. The novel aspects of our CA model are that it not only considers four states (HIV, virgin, dead, infect) but also the diversity exhibited by both HIV and T cells. We simulated maximum diversities for these states by simulating CA on a computer. The model revealed that increased diversity had the effect of increasing the HIV population and simulation steps. In addition, we observed that the CA model accurately reflects the occurrence of infection, incubation period, and the development of AIDS. The CA model demonstrated that the diversity of the virus is the major factor affecting the success rate of the escape of HIV from the immune response.

Firefly algorithm-based cellular automata for reproducing urban growth and predicting future scenarios

Modeling the deposition of turbidite systems with Cellular Automata numerical simulations: A case study in the Brazilian offshore

The number of bicycle passing events was proposed as a good indicator to evaluate the level of service of bicycle roadways. However, modeling methods that can be used for quantitatively calculating the number of passing events were quite few. The primary objective of this study is to develop a Cellular Automaton (CA) model firstly used for modeling the bicycle passing events and validate the calculation accuracy of the proposed model. Bicycle operating and overtaking rules were developed in the CA model. Field data of passing events were collected on four physically separated bicycle roadways in Nanjing city. The collected data were compared with the prediction results of CA model. It is found that the CA model provides a reasonable accuracy in predicting the number of bicycle passing events. Time-space diagrams analysis shows that bicycle flow is congested and the overall mean speed decreases under high density traffic condition.

Globally, rapid and haphazard urban growth has induced land use land cover (LULC) transformations in cities and their surroundings. The cities located in the Himalayan foothills have experienced tremendous urban growth in recent years. In this context, urban growth modeling integrated with remote sensing and geoinformatics assists to predict the future urban growth pattern. Therefore, the urban growth pattern of Jammu Urban Agglomeration (UA) from 1991 to 2021 is assessed in this paper. Shannon’s entropy index assesses the trend of built-up expansion in Jammu UA. Further, the upcoming urban growth for the year 2031 was predicted by integrating artificial neural network-multi-layer perceptron (ANN-MLP) and cellular automata (CA) model. The results revealed a substantial rise in built-up land cover while fallow land, vegetation, agriculture, and water body land cover decreased during 1991–2021. The occurrence of dispersed growth in Jammu UA was specified by the entropy index. The predicted urban growth pattern for the year 2031 showcased a further escalation in the built-up land cover while other land cover categories continued declining trend. Overall, such an urban growth pattern is unsustainable for Jammu UA, and there is an urgent requirement of urban containment measures.KeywordsUrban growthUrban growth modelingArtificial neural network-multi-layer perceptronCellular automata

In this paper, cellular automata (CA) are viewed as an abstract model for distributed computing. The author argues that the classical CA model must be modified in several important respects to become a relevant model for large-scale MAS. The paper first proposes sequential cellular automata (SCA) and formalizes deterministic and nondeterministic versions of SCA. The author then analyzes differences in possible dynamics between classical parallel CA and various SCA models. The analysis in this paper focuses on one-dimensional parallel and sequential CA with node update rules restricted to simple threshold functions, as arguably the simplest totalistic, yet non-linear (and non-affine) update rules. The author identifies properties of asymptotic dynamics that can be proven to be entirely due to the assumption of perfect synchrony in classical, parallel CA. Finally, the paper discusses what an appropriate CA-based abstraction would be for large-scale distributed computing, insofar as the inter-agent communication models. In that context, the author proposes genuinely asynchronous CA and discusses main differences between genuinely asynchronous CA and various weakly asynchronous sequential CA models found in the literature.

We generalize our recent discrete cellular automata (CA) model of excitable media [Y. B. Chernyak, A. B. Feldman, and R. J. Cohen, Phys. Rev. E 55, 3215 (1997)] to incorporate the effects of inhibitory processes on the propagation of the excitation wave front. In the common two variable reaction-diffusion (RD) models of excitable media, the inhibitory process is described by the $v$ ``controller'' variable responsible for the restoration of the equilibrium state following excitation. In myocardial tissue, the inhibitory effects are mainly due to the inactivation of the fast sodium current. We represent inhibition using a physical model in which the ``source'' contribution of excited elements to the excitation of their neighbors decreases with time as a simple function with a single adjustable parameter (a rate constant). We sought specific solutions of the CA state transition equations and obtained (both analytically and numerically) the dependence of the wave-front speed $c$ on the four model parameters and the wave-front curvature $\ensuremath{\kappa}$. By requiring that the major characteristics of $c(\ensuremath{\kappa})$ in our CA model coincide with those obtained from solutions of a specific RD model, we find a unique set of CA parameter values for a given excitable medium. The basic structure of our CA solutions is remarkably similar to that found in typical RD systems (similar behavior is observed when the analogous model parameters are varied). Most notably, the ``turn-on'' of the inhibitory process is accompanied by the appearance of a solution branch of slow speed, unstable waves. Additionally, when $\ensuremath{\kappa}$ is small, we obtain a family of ``eikonal'' relations $c(\ensuremath{\kappa})$ that are suitable for the kinematic analysis of traveling waves in the CA medium. We compared the solutions of the CA equations to CA simulations for the case of plane waves and circular (target) waves and found excellent agreement. We then studied a spiral wave using the CA model adjusted to a specific RD system and found good correspondence between the shapes of the RD and CA spiral arms in the region away from the tip where kinematic theory applies. Our analysis suggests that only four physical parameters control the behavior of wave fronts in excitable media.

A new cellular automata framework of urban growth modeling by incorporating land use policies and economic development zone planning