Emergence of self-replicating structures in a cellular automata space

Numerical simulation of the debris-flow process is commonly based on the shallow water equations. However, as a two-phase anisotropic mixture, debris flows display complex rheological behavior, making it difficult to model or to simulate these using standard approaches. In this paper, an improved cellular automaton (CA) model is developed for simulating the extent of debris-flow run-out. The CA model consists of three essential components: cellular space, lattice relation, and transition function. A two-dimensional rectangular cellular space is generated from mesh grid in the digital terrain model data, and the Moore neighborhood type is selected as the lattice relation. We also use a transition function based on a Monte Carlo iteration algorithm to automatically search the flow direction and flow routine. Specifically, this new transition function combines the topography function and persistence function (due to the flow inertia), and is advanced in its ability to avoid certain illogical lateral spreading due to abrupt changes in topography. In addition, in contrast to previous studies, in the present work, we regressed the persistence function from a well-documented flume experiment, rather than using a manipulated constant value as described in earlier empirical studies. Our results show that the debris-flow persistence function is closely related to the channel slope. It approximates the law of cosines at a steep slope and Gamma law at a gentle slope. To illustrate the performance of the improved CA model, we selected the 2010 Yohutagawa debris-flow event in Japan as a case study. Our results show that the simulated deposition perimeter pattern and run-out distance are in high accordance with the data from in situ investigation.

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.

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.

This paper present a hardware implementation in a FPGA circuit of an efficient pseudo-random number generator based on cellular automata. We demonstrate in this paper how microscopic (local) interactions influence the overall macroscopic (global) behavior of the whole system. We highlight the possibility to build the evolutionary systems on such a simple mathematical model as a cellular automata space by introducing the rules of evolution of individuals, their interaction, and their robustness to variations of the model. A regular, modular, and cascadable hardware implementation of the generator has been implemented, which is efficient in terms of VLSI technology. The design has been specified in VHDL targeted on a XC3S400 based FPGA and verified for functional correctness by software simulation

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

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.

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.

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.

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.

The checkerboard update Glauber model for the one-dimensional Ising model is mapped onto a cellular automata model. This cellular automata model is found to be a special case of the well known (two-state) triangular cellular automata model. The author shows, therefore, that there exists a subspace of the full parameter space of the triangular cellular automata that obeys detailed balance. Using this result the shows that there are no phase transitions within the interior of the cubical parameter space of the triangular cellular automata model. He identifies a new line of critical points for the triangular cellular automata. This critical line is associated with the zero-temperature critical line of the one-dimensional Ising antiferromagnet in an external field. The critical properties of the checkerboard Glauber model are studied and are found to be identical to those of the single-spin update model. In addition, the correlations in the checkerboard Glauber model are found to exhibit a null-cone structure, similar to that found in relativity theory. This null-cone, which originates in the constraints imposed by the checkerboard update procedure, is found to be a general property of the triangular cellular automata model.

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.

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.

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.

Problem solving during artificial selection of self-replicating loops