Hardware Design Strategies Oriented to Edge Computing and AgriFood Electronics for Image Processing using Cellular Automata

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.

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.

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

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.

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.

For traffic flow models, calibration and validation are essential. Cellular automaton (CA) models are a special class of models, describing the movement of vehicles in discretised space and time. However, the previous work on calibration and validation does not discuss CA models systematically. This study calibrates and validates a stochastic CA model. The authors use a simple CA model, which only has two important parameters to be calibrated. The methodology for optimisation is to minimise the relative root mean square error between two properties: the averaged velocity and the variation of velocities in a platoon at a given density. Three different sites are used as cases to show the methodology, for which different types of data (video trajectories or GPS data) are available. The authors find that the best model parameters vary for the different locations. This may result from various driving strategies and potential tendencies. Thus, it is concluded that for CA models, various traffic flow phenomena need to be simulated by various parameters.

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.

Study of microstructure evolution of magnesium alloy cylindrical part with longitudinal inner ribs during hot flow forming by coupling ANN-modified CA and FEA

Dendrite is among the most frequently observed structures during the solidification process. Different dendrite morphologies caused by environmental conditions can affect the physical properties of materials. The formation of snowflakes can generate various morphologies under different conditions, and is used in this work as an example. Simulation technologies provide insight into the correlation between a resulting morphology and its impact parameter, including the phase-field method (PF) and cellular automaton (CA). The PF method is derived from thermodynamic functions and kinetic equations, while the CA model is established by interaction rules between subsystems. It is difficult to solve the PF method due to the coupled differential equations, wherein the actual physical parameters are included. The CA model is conceptually simple and computationally efficient; however, the physical meaning of the parameters is absent. In this work, an example of snowflake formation is considered by PF with all the impact factors defined first, and then parameters in CA are searched by iterations to approximate the result, i.e., latent heat and the anisotropic coefficient in the PF method correspond to the initial distribution and the environmental effect in the CA model. In addition, the discrete time of each iteration in the CA model is identified according to the dendritic growth speed of these two models. A systematic identification process for the CA parameters’ physical meaning is demonstrated by the comparison with the PF method, and an approximate simulation of the PF method can be obtained simply by the CA model. The combination of the PF method and the CA model can be used to investigate the influence of environmental factors on dendritic morphology.

Assessing cellular automata model behaviour using a sensitivity analysis approach

The diffusion of chloride ions is one of the main factors that arouses steel corrosion in concrete. In this paper, a two-dimension cellular automaton (CA) model was developed to simulate the diffusion process of chloride ions in concrete. The evolution rules of the proposed CA model were validated by comparing with the Fick’s second laws (FSL), and the distinctions between the CA model and the FSL were discussed pertaining to calculation methods and substantive characteristics of chloride ion penetration in concrete. Further, an improved CA model is proposed, called the JPCA model, which considers the jump probabilities of chloride ions varying with diffusion times and depths. The numerical simulations demonstrate that the computation results on the basis of the JPCA model are closer to the experimental data than those derived from the FSL. The JPCA model proposed in this paper provides a new way to study concrete suffering from chloride ion penetration.

Investigation on dynamic recrystallization using a modified cellular automaton

Under the background of the ecological civilization era, rapidly obtaining coal mining information, timely assessing the ecological environmental impacts, and drafting different management and protection measures in advance to enhance the capacity of green mine construction have become the urgent technical problems to be solved at present. Simulating and analyzing mining subsidence is the foundation for a land reclamation plan. The Cellular Automata (CA) model provides a new tool for simulating the evolution of mining subsidence. This paper takes a mine in East China as a research area, analyses the methods and measures for developing a model of mining subsidence based on the theories of CA and mining technology, then discusses the results of simulation from different aspects. Through comparative analysis, it can be found that the predicted result is well consonant with the observation data. The CA model can simulate complex systems. The system of mining subsidence evolution CA is developed with the support of ArcGIS and Python, which can help to realize data management, visualization, and spatial analysis. The dynamic evolution of subsidence provides a basis for constructing a reclamation program. The research results show that the research methods and techniques adopted in this paper are feasible for the dynamic mining subsidence, and the work will continue to do in the future to help the construction of ecological civilization in mining areas.