Comparative Study of Cellular-Automata Diffusion Models

Bandman, Olga

doi:10.1007/3-540-48387-x_41

Cited by 22 publications

(16 citation statements)

References 7 publications

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“…One of the extensively used explicit methods to approximate Equation (1) is the forward time central space finite difference method [38]. This method is based on the replacement of the differential operators by finite differences [24].…”

Section: An Explicit Numerical Scheme To Approximate the Diffusion Eqmentioning

confidence: 99%

An explicit numerical scheme to efficiently simulate molecular diffusion in environments with dynamically changing barriers

Kossow

Rybacki

Millat

et al. 2015

Mathematical and Computer Modelling of Dynamical Systems

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Despite temporal changes in the quantities of molecules, the functioning of cells also depends on their distribution within cells and in their extracellular environment. The dynamics of molecules are often governed by diffusion in heterogeneous environments consisting of dynamically changing impenetrable barriers (excluded volumes). This provides a challenge for efficient simulations of cellular processes with large numbers of molecules. To model the diffusion of molecular mass in consideration of excluded volumes, we here present an explicit numerical scheme that approximates the diffusion equation by using cellular automata. Because this approach represents molecular diffusion at the macroscopic scale, it is more amenable for efficient simulations than comparable microscopic approaches that treat diffusing molecules individually. In contrast to implicit numerical schemes (macroscopic approach), our approach is capable of accounting for excluded volumes, even if those exhibit a dynamic of their own, without increasing computational costs. The presented approach can easily be integrated into certain types of spatio-temporal multiscale models, as demonstrated by an existing model investigating cancer progression. Thereby, it allows to take the spatial effects of a heterogeneous environment on diffusing molecules into account.

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Section: An Explicit Numerical Scheme To Approximate the Diffusion Eqmentioning

confidence: 99%

An explicit numerical scheme to efficiently simulate molecular diffusion in environments with dynamically changing barriers

Kossow

Rybacki

Millat

et al. 2015

Mathematical and Computer Modelling of Dynamical Systems

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“…The diffusion process has to conserve the number of particles (satisfying the conservation law [1]). The classical approach is to sequentially choose a pair of particles and to interchange them [14] or to use random walks [2].…”

Section: Application: Diffusion Of Particlesmentioning

confidence: 99%

A scalable configurable architecture for the massively parallel GCA model

Jendrsczok

Ediger

Hoffmann

2009

International Journal of Parallel, Emergent and Distributed Sys

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The global cellular automata model (GCA) is a massively parallel computation model which extends the classical cellular automata (CA) model with dynamic global neighbours. We present for that model a data parallel architecture which is scalable in the number of parallel pipelines and which uses application specific operators (adapted operators). The instruction set consists of control and RULE instructions. A RULE computes the next cell contents for each cell in the destination object. The machine consists of P pipelines. Each pipeline has an associated primary memory bank and has access to the global memory (real or emulated multiport memory). Therefore each pipeline can execute one cell operation in every clock cycle. The diffusion of particles was used as an example in order to demonstrate the adaptive operators, the machine programming and its performance. Particles which point to each other within a defined neighbourhood search space are interchanged. The pointers are modified in each generation by a pseudo random function. For that application, an application-specific data parallel machine with up to 32 pipelines was synthesised for an Altera field-programmable gate array. In addition, this application was described in the high-level language GCAL. The RULE instruction can also automatically be extracted from the GCAL program leading to the same generated application specific DPA machine.

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“…The main task of computational mathematics is to study the spatial dynamics of a physical medium [1]. However, two alternative approaches have been proposed to solve the problem: traditional partial differential equations and cellular automaton (CA).…”

Section: Introductionmentioning

confidence: 99%

“…However, two alternative approaches have been proposed to solve the problem: traditional partial differential equations and cellular automaton (CA). The kernel of a CA model is the fact that both time and space are initially given in a discrete form [1].…”

Section: Introductionmentioning

confidence: 99%

Effect of Grain Size on the Hydrogen Diffusion Process in Steel Using Cellular Automaton Approach

Yazdipour

Dunne

Pereloma

2012

MSF

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The role of microstructure in susceptibility to hydrogen uptake and property degradation is being evaluated using a number of high strength pipeline steels. To do so, a cellular automaton (CA) model has been used to examine the effect of grain size, as a first step in assessing the influence of microstructure. The simulation results of hydrogen diffusion into microstructures with different grain sizes are presented.

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Comparative Study of Cellular-Automata Diffusion Models

Cited by 22 publications

References 7 publications

An explicit numerical scheme to efficiently simulate molecular diffusion in environments with dynamically changing barriers

An explicit numerical scheme to efficiently simulate molecular diffusion in environments with dynamically changing barriers

A scalable configurable architecture for the massively parallel GCA model

Effect of Grain Size on the Hydrogen Diffusion Process in Steel Using Cellular Automaton Approach

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