577 research outputs found

    Tracking uncertainty in a spatially explicit susceptible-infected epidemic model

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    In this paper we conceive an interval-valued continuous cellular automaton for describing the spatio-temporal dynamics of an epidemic, in which the magnitude of the initial outbreak and/or the epidemic properties are only imprecisely known. In contrast to well-established approaches that rely on probability distributions for keeping track of the uncertainty in spatio-temporal models, we resort to an interval representation of uncertainty. Such an approach lowers the amount of computing power that is needed to run model simulations, and reduces the need for data that are indispensable for constructing the probability distributions upon which other paradigms are based

    Simulations for a Class of Two-Dimensional Automata

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    We study the notion of simulation over a class of automata which recognize 2D languages (languages of arrays of letters). This class of two-dimensional On-line Tessellation Automata (2OTA) accepts the same class of languages as the class of tiling systems, considered as the natural extension of classical regular word languages to the 2D case. We prove that simulation over 2OTA implies language inclusion. Even if the existence of a simulation relation between two 2OTA is shown to be an NP-complete problem in time, this is an important result since the inclusion problem is undecidable in general in this class of languages. Then we prove the existence in a given 2OTA of a unique maximal autosimulation relation, computable in polynomial time

    A study of fragmentation processes using a discrete element method

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    We present a model of solids made from polygonal cells connected via beams. We calculate the macroscopic elastic moduli from the beam and cell parameters. This modellisation is particularly suited for the simulation of fragmentation processes. We study the effects of an explosion inside a circular disk and the impact of a projectile and obtain the fragment size distribution. We find that if breaking only happens under tensile forces a layer on the free wall opposed to impact is first ejected. In that case the distribution follows a power-law with an exponent that in most cases is around two.Comment: 16 pages in LaTex format, 17 PostScript figures. Figures are available upon request from the authors. Submitted to Int. J. of Mod. Phys.

    Kinetic and Dynamic Delaunay tetrahedralizations in three dimensions

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    We describe the implementation of algorithms to construct and maintain three-dimensional dynamic Delaunay triangulations with kinetic vertices using a three-simplex data structure. The code is capable of constructing the geometric dual, the Voronoi or Dirichlet tessellation. Initially, a given list of points is triangulated. Time evolution of the triangulation is not only governed by kinetic vertices but also by a changing number of vertices. We use three-dimensional simplex flip algorithms, a stochastic visibility walk algorithm for point location and in addition, we propose a new simple method of deleting vertices from an existing three-dimensional Delaunay triangulation while maintaining the Delaunay property. The dual Dirichlet tessellation can be used to solve differential equations on an irregular grid, to define partitions in cell tissue simulations, for collision detection etc.Comment: 29 pg (preprint), 12 figures, 1 table Title changed (mainly nomenclature), referee suggestions included, typos corrected, bibliography update

    3D cellular automata simulations of intra and intergranular corrosion

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    tA simple model for the effect of intergranular corrosion on overall corrosion processes is investigatedusing a cellular automata approach. The corroding polycrystalline material consists of domains and theirboundaries. The domains represent the monocrystalline cores while their boundaries represent the inter-granular defects. Either, a periodic pattern or randomly generated domains of VoronoĂŻ tessellation areused to represent the polycrystalline structure. The parameters of the model, taking into account thepolycrystalline aspect of corrosion, are the domain density and the corrosion probabilities of metal graincore and grain boundary sites. The corrosion probability for grain boundary is set to a value higher thanit is for the grain core. A complex surface structure appears with a high geometrical roughness whendefects are not too dense. A strong correlation is established between the roughness evolution, the metalcrystalline properties and the corrosion mechanism of metal dissolution. This work concerns simulationsin 3D and extends the previous work limited to 2D simulations

    Single-Shot Decoding of Linear Rate LDPC Quantum Codes With High Performance

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    We construct and analyze a family of low-density parity check (LDPC) quantum codes with a linear encoding rate, distance scaling as nϵ for ϵ>0 and efficient decoding schemes. The code family is based on tessellations of closed, four-dimensional, hyperbolic manifolds, as first suggested by Guth and Lubotzky. The main contribution of this work is the construction of suitable manifolds via finite presentations of Coxeter groups, their linear representations over Galois fields and topological coverings. We establish a lower bound on the encoding rate k/n of 13/72=0.180… and we show that the bound is tight for the examples that we construct. Numerical simulations give evidence that parallelizable decoding schemes of low computational complexity suffice to obtain high performance. These decoding schemes can deal with syndrome noise, so that parity check measurements do not have to be repeated to decode. Our data is consistent with a threshold of around 4% in the phenomenological noise model with syndrome noise in the single-shot regime

    Meso-scale modeling of reaction-diffusion processes using cellular automata

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    A Virtual Grain Structure Representation System for Micromechanics Simulations

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    Representing a grain structure within a combined finite element computer aided engineering environment is essential for micromechanics simulations. Methods are required to effectively generate high-fidelity virtual grain structures for accurate studies. A high-fidelity virtual grain structure means a statistically equivalent structure in conjunction with desired grain size distribution features, and must be represented with realistic grain morphology. A family of controlled Poisson Voronoi tessellation (CPVT) models have been developed in this work for systematically generating virtual grain structures with the aforementioned properties. Three tasks have been accomplished in the development of the CPVT models: (i) defining the grain structure’s regularity that specifies the uniformity of a tessellation as well as deriving a control parameter based on the regularity; (ii) modelling the mapping from a grain structure’s regularity to its grain size distribution; and (iii) establishing the relation between a set of physical parameters and a distribution function. A one-gamma distribution function is used to describe a grain size distribution characteristic and a group of four physical parameters are employed to represent the metallographic measurements of a grain size distribution property. Mathematical proofs of the uniqueness of the determination of the distribution parameter from the proposed set of physical parameters have been studied, and an efficient numerical procedure is provided for computing the distribution parameter. Based on the general scheme, two- and three-dimensional CPVT models have been formulated, which respectively define the quantities of regularity and control parameters, and model the mapping between regularity and grain size distribution. For the 2D-CPVT model, statistical tests have been carried out to validate the accuracy and robustness of regularity and grain size distribution control. In addition, micrographs with different grain size distribution features are employed to examine the capability of the 2D-CPVT model to generate virtual grain structures that meet physical measurements. A crystal plasticity finite element (CPFE) simulation of plane strain uniaxial tension has been performed to show the effect of grain size distribution on local strain distribution. For the 3D-CPVT model, a set of CPFE analyses of micro-pillar compression have been run and the effects of both regularity and grain size on deformation responses investigated. Further to this, a multi-zone scheme is proposed for the CPVT models to generate virtual gradient grain structures. In conjunction with the CPVT model that controls the seed generating process within individual zones, the multi-zone CPVT model has been developed by incorporating a novel mechanism of controlling the seed generation for grains spanning different zones. This model has the flexibility of generating various gradient grain structures and the natural morphology for interfacial grains between adjacent zones. Both of the 2D- and 3D-CPVT models are capable of generating a virtual grain structure with a mean grain size gradient for the grain structure domain and grain size distribution control for individual zones. A true gradient grain structure, two simulated gradient grain structure, and a true gradient grain structure with an elongated zone have been used to examine the capability of the multi-zone CPVT model. To facilitate the CPFE analyses of inter-granular crack initiation and evolution using the cohesive zone models, a Voronoi tessellation model with non-zero thickness cohesive zone representation was developed. A grain boundary offsetting algorithm is proposed to efficiently produce the cohesive boundaries for a Voronoi tessellation. The most challenging issue of automatically meshing multiple junctions with quadrilateral elements has been resolved and a rule-based method is presented to perform the automatically partitioning of cohesive zone junctions, including data representation, edge event processing and cut-trim operations. In order to demonstrate the novelty of the proposed cohesive zone modelling and junction partitioning schemes, the CPFE simulations of plane strain uniaxial tension and three point bending have been studied. A software system, VGRAIN, was developed to implement the proposed virtual grain structure modelling methods. Via user-friendly interfaces and the well-organised functional modules a virtual grain structure can be automatically generated to a very large-scale with the desired grain morphology and grain size properties. As a pre-processing grain structure representation system, VGRAIN is also capable of defining crystallographic orientations and mechanical constants for a generated grain structure. A set of additional functions has also been developed for users to study a generated grain structure and verify the feasibility of the generated case for their simulation requirements. A well-built grain structure model in VGRAIN can be easily exported into the commercial FE/CAE platform, e.g. ABAQUS and DEFORM, via script input, whereby the VGRAIN system is seamlessly integrated into CPFE modelling and simulation processing

    A numerical investigation of the jamming transition in traffic flow on diluted planar networks

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    In order to develop a toy model for car's traffic in cities, in this paper we analyze, by means of numerical simulations, the transition among fluid regimes and a congested jammed phase of the flow of "kinetically constrained" hard spheres in planar random networks similar to urban roads. In order to explore as timescales as possible, at a microscopic level we implement an event driven dynamics as the infinite time limit of a class of already existing model (e.g. "Follow the Leader") on an Erdos-Renyi two dimensional graph, the crossroads being accounted by standard Kirchoff density conservations. We define a dynamical order parameter as the ratio among the moving spheres versus the total number and by varying two control parameters (density of the spheres and coordination number of the network) we study the phase transition. At a mesoscopic level it respects an, again suitable adapted, version of the Lighthill-Whitham model, which belongs to the fluid-dynamical approach to the problem. At a macroscopic level the model seems to display a continuous transition from a fluid phase to a jammed phase when varying the density of the spheres (the amount of cars in a city-like scenario) and a discontinuous jump when varying the connectivity of the underlying network.Comment: accepted in Int.J.Mod.Phys.
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