Excitable Delaunay triangulations

In an excitable Delaunay triangulation every node takes three states (resting, excited and refractory) and updates its state in discrete time depending on a ratio of excited neighbours. All nodes update their states in parallel. By varying excitability of nodes we produce a range of phenomena, including reflection of excitation wave from edge of triangulation, backfire of excitation, branching clusters of excitation and localized excitation domains. Our findings contribute to studies of propagating perturbations and waves in non-crystalline substrates

Vesicle computers: Approximating Voronoi diagram on Voronoi automata

Irregular arrangements of vesicles filled with excitable and precipitating chemical systems are imitated by Voronoi automata --- finite-state machines defined on a planar Voronoi diagram. Every Voronoi cell takes four states: resting, excited, refractory and precipitate. A resting cell excites if it has at least one excited neighbour; the cell precipitates if a ratio of excited cells in its neighbourhood to its number of neighbours exceed certain threshold. To approximate a Voronoi diagram on Voronoi automata we project a planar set onto automaton lattice, thus cells corresponding to data-points are excited. Excitation waves propagate across the Voronoi automaton, interact with each other and form precipitate in result of the interaction. Configuration of precipitate represents edges of approximated Voronoi diagram. We discover relation between quality of Voronoi diagram approximation and precipitation threshold, and demonstrate feasibility of our model in approximation Voronoi diagram of arbitrary-shaped objects and a skeleton of a planar shape.Comment: Chaos, Solitons & Fractals (2011), in pres

Structural and entropic insights into the nature of the random-close-packing limit

Disordered packings of equal sized spheres cannot be generated above the limiting density (fraction of volume occupied by the spheres) of ??0.64 without introducing some partial crystallization. The nature of this “random-close-packing” limit (RCP) is investigated by using both geometrical and statistical mechanics tools applied to a large set of experiments and numerical simulations of equal-sized sphere packings. The study of the Delaunay simplexes decomposition reveals that the fraction of “quasiperfect tetrahedra” grows with the density up to a saturation fraction of ?30% reached at the RCP limit. At this limit the fraction of aggregate “polytetrahedral” structures (made of quasiperfect tetrahedra which share a common triangular face) reaches it maximal extension involving all the spheres. Above the RCP limit the polytetrahedral structure gets rapidly disassembled. The entropy of the disordered packings, calculated from the study of the local volume fluctuations, decreases uniformly and vanishes at the (extrapolated) limit ?K?0.66. Before such limit, and precisely in the range of densities between 0.646 and 0.66, a phase separated mixture of disordered and crystalline phases is observed

Pore configuration landscape of granular crystallization

Uncovering grain-scale mechanisms that underlie the disorder–order transition in assemblies of dissipative, athermal particles is a fundamental problem with technological relevance. To date, the study of granular crystallization has mainly focussed on the symmetry of crystalline patterns while their emergence and growth from irregular clusters of grains remains largely unexplored. Here crystallization of three-dimensional packings of frictional spheres is studied at the grain-scale using X-ray tomography and persistent homology. The latter produces a map of the topological configurations of grains within static partially crystallized packings. Using numerical simulations, we show that similar maps are measured dynamically during the melting of a perfect crystal. This map encodes new information on the formation process of tetrahedral and octahedral pores, the building blocks of perfect crystals. Four key formation mechanisms of these pores reproduce the main changes of the map during crystallization and provide continuous deformation pathways representative of the crystallization dynamics.N.F. would like to acknowledge the support by the Australian Research Council’s Discovery Early Career Research Award (DE160100742). V.R. would like to acknowledge the support by the Australian Research Council’s Future Fellowship FT140100604. Y.H. acknowledges the support by JST CREST Mathematics (15656429) and JST Materials research by Information Integration Initiative. H.T. would like to acknowledge the support by JSPS KAKENHI Grant Number 16J03138

High-Performance Computing of Flow, Diffusion, and Hydrodynamic Dispersion in Random Sphere Packings

This thesis is dedicated to the study of mass transport processes (flow, diffusion, and hydrodynamic dispersion) in computer-generated random sphere packings. Periodic and confined packings of hard impermeable spheres were generated using Jodrey–Tory and Monte Carlo procedure-based algorithms, mass transport in the packing void space was simulated using the lattice Boltzmann and random walk particle tracking methods. Simulation codes written in C programming language using MPI library allowed an efficient use of the high-performance computing systems (supercomputers). The first part of this thesis investigates the influence of the cross-sectional geometry of the confined random sphere packings on the hydrodynamic dispersion. Packings with different values of porosity (interstitial void space fraction) generated in containers of circular, quadratic, rectangular, trapezoidal, and irregular (reconstructed) geometries were studied, and resulting pre-asymptotic and close-to-asymptotic hydrodynamic dispersion coefficients were analyzed. It was demonstrated i) a significant impact of the cross-sectional geometry and porosity on the hydrodynamic dispersion coefficients, and ii) reduction of the symmetry of the cross section results in longer times to reach close-to-asymptotic values and larger absolute values of the hydrodynamic dispersion coefficients. In case of reconstructed geometry, good agreement with experimental data was found. In the second part of this thesis i) length scales of heterogeneity persistent in unconfined and confined sphere packings were analyzed and correlated with a time behavior of the hydrodynamic dispersion coefficients; close-to-asymptotic values of the dispersion coefficients (expressed in terms of plate height) were successfully fitted to the generalized Giddings equation; ii) influence of the packing microstructural disorder on the effective diffusion and hydrodynamic dispersion coefficients was investigated and clear qualitative corellation with geometrical descriptors (which are based on Delaunay and Voronoi spatial tessellations) was demonstrated

A Collective Dynamics-based Method for Initial Pebble Packing

ABSTRACT In the simulation of pebble flow in Pebble Bed Reactors (PBR), high-fidelity methods, such as Discrete Element Methods (DEM) and Computational Fluid Dynamics (CFD) methods, are usually employed to simulate the dynamic process of pebbles circulation, accounting for the pebble-to-pebble, pebble-to-reflector wall and pebble-to-fluid interactions. To obtain a realistic model of pebble distribution around dynamic equilibrium state of pebble flow, the simulation based on high-fidelity methods normally resists brute force computation. However, if an initial dense packing of pebbles can be provided, which is close to realistic packing at equilibrium state and can be easily implemented without much computational effort, the long time high-fidelity simulation can be considerably more efficient and take much less time to reach dynamic equilibrium state. In this paper, a collective arrangement method based on a dynamics model is developed to generate an initial pebble distribution at a quasi-equilibrium state. In the new method, pebble positions are generated firstly by a fast sequential process in the full core allowing overlapping, and then a simplified normal contact force model is adopted in the initialization for eliminating the pebble overlap. The adopted model provides an adaptive way to account for the situations in which multiple pebbles are overlapped and different contact forces should be applied for different ratios of overlapping depth and sphere size, thus speeding up the initialization without loss of reliability and making the approach feasible for variable size sphere packing. Moreover, an intermittent vibration function, as an optional process, can be provided to further densify the packing depending on different applications. Comparisons with other existing random packing methods for initialization are made. It is shown that the developed method not only exhibits unique significance and good computation efficiency in speeding up the pebble flow simulation, but also presents desirable potential in other applications as a general packing algorithm for packing uniform-or variable-size spheres in a large container

Dynamic triangulations for efficient 3D simulation of granular materials

Granular materials are omnipresent in many fields ranging from civil engineering to food, mining and pharmaceutical industries. Often considered a fourth state of matter, they exhibit specific phenomena such as segregation, arching effects, pattern formation, etc. Due to its potential capability of realistically rendering these behaviors, the Distinct Element Method (DEM) is a very enticing simulation technique. Indeed it makes it possible to analyze and observe phenomena that are barely if at all accessible experimentally. DEM works by tracking every particle in the system individually, maintaining for each a trajectory influenced by external factors such as gravitation or contacts with boundary objects and by the interactions with other grains. The mathematical problem of identifying pairs of grains that interact and locating precisely where the contact occurs is highly dependent on the shape of the grains. We focus in this thesis on 3D spherical grains and use dynamic weighted Delaunay triangulations to track the collisions. The triangulation is built on the centers of the grains and evolves to follow their motion. We prove that all potentially colliding pairs of spheres are adjacent in the triangulation. As there are 6n to 8n edges for n spheres in most practical cases, the complexity of the collision detection becomes linear instead of quadratic in the number of particles, with a small overhead in maintaining the triangulation with efficient local operations. For the physical problem of realistically rendering the collision in a numerical contact model suitable for computer simulation, we have used widely accepted theories such as the viscoelastic model of Cundall, but have also tested some recent, more sophisticated developments in the field. The collision detection and contact models have been implemented in a modular DEM simulation code with advanced features in data structures storing the triangulation, in numerical robustness of the geometric computations, and in parallel processing on shared memory computers. Optimal packing of powders is important in many industrial processes, yet no theoretical result exists when dealing with grains of different sizes. We have performed simulations of such cases and could compare our results with experimental data. Preliminary results have been obtained regarding the relation between the size and proportion of grains and the density of the packing. Other simulations have also been performed, such as the granular flow through an hourglass. As no efficient simulation method is currently known for non-spherical 3D grains, we propose an intermediate approach of gluing spheres together into arbitrary shaped clusters and show some examples based on this approach

LIPIcs, Volume 258, SoCG 2023, Complete Volume

LIPIcs, Volume 258, SoCG 2023, Complete Volum

On the behavior of spherical and non-spherical grain assemblies, its modeling and numerical simulation

This thesis deals with the numerical modeling and simulation of granular media with large populations of non-spherical particles. Granular media are highly pervasive in nature and play an important role in technology. They are present in fields as diverse as civil engineering, food processing, and the pharmaceutical industry. For the physicist, they raise many challenging questions. They can behave like solids, as well as liquids or even gases and at times as none of these. Indeed, phenomena like granular segregation, arching effects or pattern formation are specific to granular media, hence often they are considered as a fourth state of matter. Around the turn of the century, the increasing availability of large computers made it possible to start investigating granular matter by using numerical modeling and simulation. Most numerical models were originally designed to handle spherical particles. However, making it possible to process non-spherical particles has turned out to be of utmost importance. Indeed, it is such grains that one finds in nature and many important phenomena cannot be reproduced just using spherical grains. This is the motivation for the research of the present thesis. Subjects in several fields are involved. The geometrical modeling of the particles and the simulation methods require discrete geometry results. A wide range of particle shapes is proposed. Those shapes, spheropolyhedra, are Minkowski sums of polyhedra and spheres and can be seen as smoothed polyhedra. Next, a contact detection algorithm is proposed that uses triangulations. This algorithm is a generalization of a method already available for spheres. It turns out that this algorithm relies on a positive answer to an open problem of computational geometry, the connectivity of the flip-graph of all triangulations. In this thesis it has been shown that the flip-graph of regular triangulations that share a same vertex set is connected. The modeling of contacts requires physics. Again the contact model we propose is based on the existing molecular dynamics model for contacts between spheres. Those models turn out to be easily generalizable to smoothed polyhedra, which further motivates this choice of particle shape. The implementation of those methods requires computer science. An implementation of this simulation methods for granular media composed of non-spherical particles was carried out based on the existing C++ code by J.-A. Ferrez that originally handled spherical particles. The resulting simulation code was used to gain insight into the behavior of granular matter. Three experiments are presented that have been numerically carried out with our models. The first of these experiments deals with the flowability (i. e. the ability to flow) of powders. The flowability of bidisperse bead assemblies was found to depend only on their mass-average diameters. Next, an experiment of vibrating rods inside a cylindrical container shows that under appropriate conditions they will order vertically. Finally, experiments investigating the shape segregation of sheres and spherotetrahedra are perfomed. Unexpectedly they are found to mix