Prevalence and structure of adding machines for cellular automata

Consider the collection of left permutive cellular automata Φ with no memory, defined on the space S of all doubly infinite sequences from a finite alphabet. There exists , a dense subset of S, such that is topologically conjugate to an odometer for all so long as Φm is not the identity map for any m. Moreover, Φ generates the same odometer for all . The set is a dense Gδ subset with full measure of a particular subspace of S.     

Deterministic automata simulation, universality and minimality

Finite automata have been recently used as alternative, discrete models in theoretical physics, especially in problems related to the dichotomy between endophysical/intrinsic and exophysical/ extrinsic perception (see, for instance [3, 6, 18–21]). These studies deal with Moore experiments; the main result states that it is impossible to determine the initial state of an automaton, and, consequently, a discrete model of Heisenberg uncertainty has been suggested. For this aim the classical theory of finite automata — which considers automata with initial states — is not adequate, and a new approach is necessary. A study of finite deterministic automata without initial states is exactly the aim of this paper. We will define and investigate the complexity of various types of simulations between automata. Minimal automata will be constructed and proven to be unique up to an isomorphism. We will build our results on an extension of Myhill-Nerode technique; all constructions will make use of “automata responses” to simple experiments only, i.e., no information about the internal machinery will be considered available.     

Modeling the optimal ethnic composition of an adult stem cell registry

For patients suffering from a blood related disease, a stem cell transplant represents the best, and sometimes the only, possible treatment. Registries have been created throughout the world to match patients with stem cell donors. Canada's adult registry, OneMatch, was formed to meet the needs of Canadian patients. However, only 20–30 percent of unrelated adult stem cell transplants in Canada are sourced from Canadian donors. Self-sufficiency has proven difficult for OneMatch, in part, because the Canadian registry is dwarfed by other international registries with similar donor populations.In this paper, we present a study to evaluate changes the Canadian registry designed to promote ethnic diversity while meeting the needs of the Canadian patient population. We formulate the composition problem as a linear optimization model and solve it using a combination of exact and heuristic methods for a registry of 1 M donors.We conclude that when registry size is constrained, there are advantages to increasing ethnic diversity over self-sufficiency. However, results show that some communities cannot be easily accommodated within an adult registry of a fixed size. Thus, our results highlight the need for stem cells derived from cord blood for hard to match populations.     

A cellular automaton technique for modelling of a binary dendritic growth with convection

A two-dimensional model for the simulation of a binary dendritic growth with convection has been developed in order to investigate the effects of convection on dendritic morphologies. The model is based on a cellular automaton (CA) technique for the calculation of the evolution of solid/liquid (s/l) interface. The dynamics of the interface controlled by temperature, solute diffusion and Gibbs–Thomson effects, is coupled with the continuum model for energy, solute and momentum transfer with liquid convection. The solid fraction is calculated by a governing equation, instead of some approximate methods such as lever rule method [A. Jacot, M. Rappaz, Acta Mater. 50 (2002) 1909–1926.] or interface velocity method [L. Nastac, Acta Mater. 47 (1999) 4253; L. Beltran-Sanchez, D.M. Stefanescu, Mat. and Mat. Trans. A 26 (2003) 367.]. For the dendritic growth without convection, mesh independency of simulation results is achieved. The simulated steady-state tip velocity are compared with the predicted values of LGK theory [Lipton, M.E. Glicksmanm, W. Kurz, Metall. Trans. 18(A) (1987) 341.] as a function of melt undercooling, which shows good agreement. The growth of dendrite arms in a forced convection has been investigated. It was found that the dendritic growth in the upstream direction was amplified, due to larger solute gradient in the liquid ahead of the s/l interface caused by melt convection. In the isothermal environment, the calculated results under very fine mesh are in good agreement with the Oseen–Ivanstov solution for the concentration-driven growth in a forced flow.     

Modeling dendritic solidification of Al–3%Cu using cellular automaton and phase-field methods

We compared a cellular automaton (CA)–finite element (FE) model and a phase-field (PF)–FE model to simulate equiaxed dendritic growth during the solidification of cubic crystals. The equations of mass and heat transports were solved in the CA–FE model to calculate the temperature field, solute concentration, and the dendritic growth morphology. In the PF–FE model, a PF variable was used to identify solid and liquid phases and another PF variable was considered to determine the evolution of solute concentration. Application to Al–3.0 wt.% Cu alloy illustrates the capability of both CA–FE and PF–FE models in modeling multiple arbitrarily-oriented dendrites in growth of cubic crystals. Simulation results from both models showed quantitatively good agreement with the analytical model developed by Lipton–Glicksman–Kurz (LGK) in the tip growth velocity and the tip equilibrium liquid concentration at a given melt undercooling. The dendrite morphology and computational time obtained from the CA–FE model are compared to those of the PF–FE model and the distinct advantages of both methods are discussed.     

Numerical simulation of the unsteady aerodynamic interaction of two plane airfoil cascades

A method for the calculation of unsteady aerodynamic interaction of two plane airfoil cascades that are in relative motion in a subsonic flow of ideal gas is developed. This interaction provides a two-dimensional approximation of the flow in a stage of an axial turbomachine. The method is based on the reduction of the problem to the calculation of the unsteady flow in a single interblade passage of each of the cascades. The calculation uses generalized space-time periodicity relations corresponding to the unsteady process of interest. The calculation is based on the direct numerical integration of the non-stationary gas dynamics equations with the use of the finite difference Godunov-Kolgan-Rodionov scheme of the second approximation order with respect to time and space. The calculation procedure includes the determination of the acoustic fields that are generated by the stage in the incident flow and in the flow behind it. The results of the calculations that illustrate the accuracy of the numerical solution and the capabilities of the method are presented.     

Four species CA model for facing pedestrian traffic at rush hour

A model for the facing pedestrian traffic on a passage with a partition line at rush hour is developed. The model is described by a bi-directional cellular automaton (CA) model with four species. The CA model is not stochastic but deterministic. If the passage is congested and the local density is superior to the threshold, walkers to the east and to the west try to move separately changing their lane as the traffic rule is imposed on pedestrians at a high density. Walkers move freely ignoring the partition line at a low density. The traffic-rule effect at rush hour is taken into account in addition to the excluded-volume effect and bi-directionality. The pedestrian behavior under the traffic rule is clarified.     

3D numerical simulation on fluid-structure interaction of structure subjected to underwater explosion with cavitation

In the underwater-shock environment,cavitation occurs near the structural surface.The dynamic response of fluid-structure interactions is influenced seriously by the cavitation effects.It is also the d...     

Modeling and simulation with operator scaling

Self-similar processes are useful models for natural systems that exhibit scaling. Operator scaling allows a different scale factor in each coordinate. This paper develops practical methods for modeling and simulation. A simulation method is developed for operator scaling Lévy processes, based on a series representation, along with a Gaussian approximation of the small jumps. Several examples are given to illustrate the range of practical applications. A complete characterization of symmetries in two dimensions is given, for any exponent and spectral measure, to inform the choice of these model parameters. The paper concludes with some extensions to general operator self-similar processes.     

The one-dimensional cyclic cellular automaton: A system with deterministic dynamics that emulates an interacting particle system with stochastic dynamics

Consider a cellular automaton defined on where each lattice site may take on one ofN values, referred to as colors. TheN colors are arranged in a cyclic hierarchy, meaning that colork follows colork–1 modN (k=0,...,N–1). Any two colors that are not adjacent in this hierarchy form an inert pair. In this scheme, there is symmetry in theN colors. Initialized the cellular automaton with product measure, and let time pass in discrete units. To get the configuration at timet+1 from the one at timet, each lattice site looks at the colors of its two nearest neighbors, and if it sees the color that follows its own color, then that site changes color to the color that follows; otherwise, that site does not change color. All such updates occur synchronously at timet+1. For each value ofN2, the fundamental question is whether each site in the cellular automaton changes color infinitely often (fluctuation) or only finitely often (fixation). We prove here that ifN4, then fluctuation occurs, and ifN5, then fixation occurs.     

Modeling the depletion of dissolved oxygen due to algal bloom in a lake by taking Holling type-III interaction

In this paper a non-linear mathematical model for depletion of dissolved oxygen due to algal bloom in a lake is proposed and analyzed. The model is formulated by considering four variables namely, cumulative concentration of nutrients, density of algal population, density of detritus and concentration of dissolved oxygen. In the modeling process it is assumed that nutrients are continuously coming with a constant rate to the lake through water runoff from agricultural fields and domestic drainage. The Holling type-III interaction between nutrients and algal population is considered. Equilibrium values have been obtained and their stability analysis has also been performed. Numerical simulations are carried out to explain the mathematical results.     

Three-dimensional cellular automaton simulation of tumour growth in inhomogeneous oxygen environment

Cellular automaton theory has previously been used to study cell growth. In this study, we present a three-dimensional cellular automaton model performing the growth simulation of normal and cancerous cells. The necessary nutrient supply is provided by an artificial arterial tree which is generated by constrained constructive optimization. Spatial oxygen diffusion is approximated again by a cellular automaton model. All results could be illustrated dynamically by three-dimensional volume visualization. Because of the chosen modelling approach, an extension of the model to simulate angiogenic processes is possible.     

A single-copy minimal-time simulation of a torus of automata by a ring of automata

We consider cellular automata on Cayley graphs and we simulate the behavior of a torus of n×m automata (nodes) by a ring of n·m automata (cells). Our simulation technique requires the neighborhood of the nodes to be preserved. We achieve this constraint by copying the contents of nodes on the cells. We consider the problem of minimizing the number of the copies. We prove that it is possible to simulate the behavior of a torus on a ring with a single copy on each cell if and only if n and m satisfy a given condition. In that case we propose a time-optimal algorithm. We thus improve a previous work done by Martin where two copies were requested. When the condition on n and m is not fulfilled one can use the previous algorithm.     

Modeling employees behavior in workplace dynamics

During the past years, Cellular Automata (CAs) have been extensively used for modeling of many complex systems and processes with great success. In this paper, we study a Cellular Automaton (CA) model for the influence of employees’ behavior in a parameterized workplace environment taking into account different behavioral characteristics. In specific, we model employees’ interactions based on their influence radius, the degree of their willingness on adaption of organizational norms and the employee's attitude in general in the under study workplace. The proposed CA model is taking into account employee loyalty, a combined statistic of the employee behavior and her/his insistence and company policies applied to the employees so as to restrain unwanted or impose desirable behavioral patterns in correspondence to the organization norms. Conclusively, the CA model facilitates the presentation and simulation of a workplace with a variety of employee behavioral characteristics and under adaptable company policies. Different workplaces were used to illustrate the simulation of employee behavior with CA model. As a result, the proposed model was practically used on two levels, firstly to estimate the workplace robustness and secondly to illustrate workspace dynamics. Finally, the CA model has been utilized to simulate behavioral patterns at a small enterprise in Greece. In specific, based on the employees answers to detailed surveys the CA model was initialized and then applied to describe the behavioral traits of the under study company employees. Finally, the proposed model, in all the examined cases can be utilized in conjunction with applied employee management techniques to facilitate managerial decisions and forecast the impact of employee behavioral changes and company decisions.     

Modeling and simulation of extrusion of aluminum alloys

The purpose of this work is the modeling and simulation of the material behavior of aluminum alloys during extrusion, cooling and metal forming processes. In particular, the alloys of the 6000 series (Al-Mg-Si) and 7000 series (Al-Zn-Mg) are relevant here. Under the corresponding conditions, their behavior is controlled mainly by dynamic recovery during the extrusion and static recrystallization during cooling. The current material model is based on the role of the energy stored in the material during extrusion as the driving force for microstructural evolution. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling, simulation and optimization in logistics

This text summarizes the PhD thesis defended by the author in March 2009 under the supervision of Pasquale Legato at the University of Calabria, Italy. The thesis is written in English and is available for download at the following URL: . It aims to explore friendly Operations Research tools for modeling and simulation of logistics processes, with particular interest for mathematical programming models combined with stochastic simulation tools. In particular key assignment and scheduling problems that arise in maritime container terminals are explored. Initially it is presented a study on different modeling paradigms devoted to the representation of logistical processes and the formalization of problems with complex scheduling/assignment constraints. Successively an IP model for managing the assignment of a pool of rail-mounted gantry cranes to berthed vessels is proposed. Then, according to a functional integration approach, a second model centered on the intra-ship scheduling of vessel container bulks to the assigned cranes is further formulated. Finally a simulation-based optimization approach is investigated and the effectiveness of recent search methods is evaluated by comparison with a commercial solver.     

Modeling and simulation of extrusion of aluminum alloys

The purpose of this work is the modeling and simulation of the material behavior of aluminum alloys during extrusion, cooling and metal forming processes. In particular, the alloys of the 6000 series (Al-Mg-Si) and 7000 series (Al-Zn-Mg) are relevant here. Under the corresponding conditions, their behavior is controlled mainly by dynamic recovery during the extrusion and static recrystallization during cooling. The current material model is based on the role of the energy stored in the material during extrusion as the driving force for microstructural evolution. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Exact Singularity Subtraction from Boundary Integral Equations in Modeling Vesicles and Red Blood Cells

The study of vesicles, capsules and red blood cells (RBCs) under flow is a field of active research, belonging to the general problematic of fluid/structure interactions. Here, we are interested in modeling vesicles, capsules and RBCs using a boundary integral formulation, and focus on exact singularity subtractions of the kernel of the integral equations in 3D. In order to increase the precision of singular and near-singular integration, we propose here a refinement procedure in the vicinity of the pole of the Green-Oseen kernel. The refinement is performed homogeneously everywhere on the source surface in order to reuse the additional quadrature nodes when calculating boundary integrals in multiple target points. We also introduce a multi-level look-up algorithm in order to select the additional quadrature nodes in vicinity of the pole of the Green-Oseen kernel. The expected convergence rate of the proposed algorithm is of order$\mathcal{O}(1/N^2)$ while the computational complexity is of order$\mathcal{O}$($N^2$ln$N$), where $N$ is the number of degrees of freedom used for surface discretization. Several numerical tests are presented to demonstrate the convergence and the efficiency of the method.     

Modeling and simulation of pollutants transport in rivers

This paper is devoted to mathematical modeling and computer simulation of diffusion and transport of chemicals in rivers. We present one-, two-, and three-dimensional models in terms of time-dependent convection–diffusion–reaction differential equations, further we give the finite difference approximation and appropriate numerical algorithms for these models, and finally we discuss briefly the computer implementation of this methodology in a user friendly software package. To verify the model and the computer code we have used it to study the diffusion and transport of chemicals, in this case NO₃ and PO₄, in two rivers in Western Georgia flowing into the Black Sea. Namely, we considered the river Khobistskali subject to pollution sources Ochkhomuri and Chanistskali river Choga polluted with NO₃.