The Spine of the Cosmic Web

We present the SpineWeb framework for the topological analysis of the Cosmic Web and the identification of its walls, filaments and cluster nodes. Based on the watershed segmentation of the cosmic density field, the SpineWeb method invokes the local adjacency properties of the boundaries between the watershed basins to trace the critical points in the density field and the separatrices defined by them. The separatrices are classified into walls and the spine, the network of filaments and nodes in the matter distribution. Testing the method with a heuristic Voronoi model yields outstanding results. Following the discussion of the test results, we apply the SpineWeb method to a set of cosmological N-body simulations. The latter illustrates the potential for studying the structure and dynamics of the Cosmic Web.Comment: Accepted for publication HIGH-RES version: http://skysrv.pha.jhu.edu/~miguel/SpineWeb

Random lattice particle modeling of fracture processes in cementitious materials

The capability of representing fracture processes in non-homogeneous media is of great interest among the scientific community for at least two reasons: the first one stems from the fact that the use of composite materials is ubiquitous within structural applications, since the advantages of the constituents can be exploited to improve material performance; the second consists of the need to assess the non-linear post-peak behavior of such structures to properly determine margins of safety with respect to strong excitations (e.g. earthquakes, blast or impact loadings). Different kinds of theories and methodologies have been developed in the last century in order to model such phenomena, starting from linear elastic equivalent methods, then moving to plastic theories and fracture mechanics. Among the different modeling techniques available, in recent years lattice models have established themselves as a powerful tool for simulating failure modes and crack paths in heterogeneous materials. The basic idea dates back to the pioneeristic work of Hrennikoff: a continuum medium can be modeled through the interaction of unidimensional elements (e.g. springs or beams) spatially arranged in different ways. The set of nodes that interconnect the elements can be regularly or irregularly placed inside the domain, leading to regular or random lattices. It has been shown that lattices with regular geometry can strongly bias the direction of cracking, leading to incorrect results. A variety of lattice models have been developed. Such models have seen a wide field of applications, ranging from aerodynamics (using Lattice-Boltzman models) to heat transfer, crystallography and many others. Every material used in civil and infrastructure engineering is constituted of different phases. This is due to the fact that the different features of different elements are usually coupled in order to obtain greater advantages with respect to the original constituents. Even structural steel, which is usually thought of as a homogeneous continuum-type medium, includes carbon particles that can be seen as inhomogeneities at the microscopic level. The mechanical behavior of concrete, which is the main object of the present work, is strongly affected not only by the presence of inclusions (i.e. the aggregates pieces) but also by their arrangement. For this reason, the explicit, statistical representation of their presence is of great interest in the simulations of concrete behavior. Lattice models can directly account for the presence of different phases, and so are advantageous from this perspective. The definition of such models, their implementation in a computer program, together with validation on laboratory tests will be presented. The present work will briefly review the state of the art and the basic principles of these models, starting from the geometrical and computing tools needed to build the simulations. The implementation of this technique in the Matlab environment will be presented, highlighting the theoretical background. The numerical results will be validated based on two complementary experimental campaigns,which focused on the meso- and macro-scales of concrete. Whereas the aim of this work is the representation of the quasi-brittle fracture processes in cementitious materials such as concrete, the discussed approach is general, and therefore valid for the representation of damage and crack growth in a variety of different materials

Decentralized Resource Allocation through Constrained Centroidal Voronoi Tessellations

The advancements in the fields of microelectronics facilitate incorporating team elements like coordination into engineering systems through advanced computing power. Such incorporation is useful since many engineering systems can be characterized as a collection of interacting subsystems each having access to local information, making local decisions, interacting with neighbors, and seeking to optimize local objectives that may well conflict with other subsystems, while also trying to optimize certain global objective. In this dissertation, we take advantage of such technological advancements to explore the problem of resource allocation through different aspects of the decentralized architecture like information structure in a team. Introduced in 1968 as a toy example in the field of team decision theory to demonstrate the significance of information structure within a team, the Witsenhausen counterexample remained unsolved until the analytical person-by-person optimal solution was developed within the past decade. We develop a numerical method to implement the optimal laws and show that our laws coincide with the optimal affine laws. For the region where the optimal laws are non-linear, we show that our laws result in the lowest costs when compared with previously reported costs. Recognizing that, in the framework of team decision theory, the difficulties arising from the non-classical information structure within a team currently limit its applicability in real-world applications, we move on to investigating Centroidal Voronoi Tessellations (CVTs) to solve the resource allocation problem. In one-dimensional spaces, a line communication network is sufficient to obtain CVTs in a decentralized manner, while being scalable to any number of agents in the team. We first solve the static resource allocation problem where the amount of resource is fixed. Using such static allocation solution as an initialization step, we solve the dynamic resource allocation problem in a truly decentralized manner. Furthermore, we allow for flexibility in agents\u27 embedding their local preferences through what we call a civility model. We end the dissertation by revisiting the application of Demand-response in smart grids and demonstrate the developed decentralized dynamic resource allocation method to solve the problem of power allocation in a group of building loads

Self Assembly Problems of Anisotropic Particles in Soft Matter.

Anisotropic building blocks assembled from colloidal particles are attractive building blocks for self-assembled materials because their complex interactions can be exploited to drive self-assembly. In this dissertation we address the self-assembly of anisotropic particles from multiple novel computational and mathematical angles. First, we accelerate algorithms for modeling systems of anisotropic particles via massively parallel GPUs. We provide a scheme for generating statistically robust pseudo-random numbers that enables GPU acceleration of Brownian and dissipative particle dynamics. We also show how rigid body integration can be accelerated on a GPU. Integrating these two algorithms into a GPU-accelerated molecular dynamics code (HOOMD-blue), make a single GPU the ideal computing environment for modeling the self-assembly of anisotropic nanoparticles. Second, we introduce a new mathematical optimization problem, filling, a hybrid of the familiar shape packing and covering problem, which can be used to model shaped particles. We study the rich mathematical structures of the solution space and provide computational methods for finding optimal solutions for polygons and convex polyhedra. We present a sequence of isosymmetric optimal filling solutions for the Platonic solids. We then consider the filling of a hyper-cone in dimensions two to eight and show the solution remains scale-invariant but dependent on dimension. Third, we study the impact of size variation, polydispersity, on the self-assembly of an anisotropic particle, the polymer-tethered nanosphere, into ordered phases. We show that the local nanoparticle packing motif, icosahedral or crystalline, determines the impact of polydispersity on energy of the system and phase transitions. We show how extensions of the Voronoi tessellation can be calculated and applied to characterize such micro-segregated phases. By applying a Voronoi tessellation, we show that properties of the individual domains can be studied as a function of system properties such as temperature and concentration. Last, we consider the thermodynamically driven self-assembly of terminal clusters of particles. We predict that clusters related to spherical codes, a mathematical sequence of points, can be synthesized via self-assembly. These anisotropic clusters can be tuned to different anisotropies via the ratio of sphere diameters and temperature. The method suggests a rich new way for assembling anisotropic building blocks.Ph.D.Applied Physics and Scientific ComputingUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/91576/1/phillicl_1.pd

Modeling and simulation of multi-cellular systems using hybrid FEM/Agent-based approaches

Muchas de las propiedades biomecánicas de los organismos multicelulares surgen directamente de las interacciones entre células. Las células de los órganos y tejidos interactúan entre sí y con su entorno de diferentes formas. Debido a este hecho, es fundamental analizar cómo estas interacciones se traducen como propiedades mecánicas a nivel del tejido. Por ejemplo, las adhesiones entre células determinan la rigidez aparente de una capa epitelial. Las interacciones célula-matriz pueden además determinar la formación de muchas estructuras biológicas y su morfología. Estos sistemas multicelulares no se pueden considerar como estructuras estáticas ya que sufren constantes cambios causados por la proliferación, la reorganización o la migración celular. Por lo tanto, es necesario estudiar la dinámica de la célula y las interacciones individuales para comprender plenamente cómo funcionan los fenómenos a escalas superiores, desde el desarrollo de tejidos hasta el crecimiento de tumores.Recientemente, el uso de enfoques basados en agentes se ha vuelto muy popular para modelar sistemas multicelulares. Los modelos basados en agentes representan células como entidades individuales. Estos modelos son especialmente adecuados para estudiar fenómenos biofísicos que ocurren a nivel celular. Aquí las interacciones célula-célula se pueden simular directamente de forma mecanicista. Además, estos modelos capturan realmente bien las heterogeneidades presentes en las estructuras biológicas. Por otra parte, los modelos continuos se utilizan comúnmente en problemas de escalas mayores. A diferencia de los modelos basados en agentes, en estos no representan células como entidades individuales, sino que se definen leyes constitutivas para modelar procesos biológicos, físicos y químicos. Por lo tanto, las propiedades celulares se promedian usando parámetros macroscópicos, y estos modelos a menudo trabajan con la densidad celular en lugar de entidades celulares separadas. En cualquier caso, los modelos continuos presentan una buena escalabilidad y una excelente representación de fenómenos físicos particulares como el transporte masivo y las transmisiones de fuerza en medios continuos.En esta tesis, se exploran las posibilidades que los enfoques híbridos pueden ofrecer para desarrollar nuevos modelos de sistemas multicelulares. Se presentan dos modelos híbridos diferentes que combinan un modelo basado en agentes y un modelo continuo. Ambos enfoques tienen en común que el modelo continuo se resuelve utilizando el método de los elementos finitos. También se muestra, siguiendo este patrón de diseño, cómo resolver varias de las limitaciones intrínsecas de cada tipo individual de modelo.En primer lugar, se presenta un modelo híbrido para simular la mecánica epitelial monocapa. Este modelo se centra en el modelado de las interacciones mecánicas célula-célula y célula-sustrato, pero también en la topología y morfología de los tejidos. Con este enfoque se reproducen tejidos epiteliales proliferativos, movimientos celular colectivo y procesos de migración. El segundo modelo presentado en esta tesis se ha diseñado para simular agregados celulares en entornos tridimensionales. Se estudian las interacciones mecánicas entre células, pero este modelo se centra especialmente en analizar cómo afecta el transporte de oxígeno a las células en un proceso de agrupamiento en 3D.Finalmente, se comparan los resultados de ambos modelos con datos experimentales de otros autores y se discuten los beneficios de combinar diferentes tipos de modelos. Se demuestra que los enfoques híbridos que se proponen en este trabajo son capaces de simular una amplia variedad de sistemas multicelulares. De hecho, son particularmente útiles para estudiar cómo algunos fenómenos emergen de las interacciones celulares individuales a escalas biológicas más grandes.<br /

Vorosweep: a fast generalized crystal growing Voronoi diagram generation algorithm

We propose a new algorithm for generating quickly approximate generalized Voronoi diagrams of point sites associated to arbitrary convex distance metric in the Euclidian plane. This algorithm produces connected cells by emulating the growth of crystals starting at the point sites, in order to reduce the complexity of the diagram. The main practical contribution is the Vorosweep package which is the reference implementation of the algorithm. Experimental results and benchmarks are given to demonstrate the versatility of this approach.WIST 3 grant 1017074 DOMHEX (Dominant Hexahedral Mesh Generation

An integrative computational model for intestinal tissue renewal

Objectives\ud \ud The luminal surface of the gut is lined with a monolayer of epithelial cells that acts as a nutrient absorptive engine and protective barrier. To maintain its integrity and functionality, the epithelium is renewed every few days. Theoretical models are powerful tools that can be used to test hypotheses concerning the regulation of this renewal process, to investigate how its dysfunction can lead to loss of homeostasis and neoplasia, and to identify potential therapeutic interventions. Here we propose a new multiscale model for crypt dynamics that links phenomena occurring at the subcellular, cellular and tissue levels of organisation.\ud \ud Methods\ud \ud At the subcellular level, deterministic models characterise molecular networks, such as cell-cycle control and Wnt signalling. The output of these models determines the behaviour of each epithelial cell in response to intra-, inter- and extracellular cues. The modular nature of the model enables us to easily modify individual assumptions and analyse their effects on the system as a whole.\ud \ud Results\ud \ud We perform virtual microdissection and labelling-index experiments, evaluate the impact of various model extensions, obtain new insight into clonal expansion in the crypt, and compare our predictions with recent mitochondrial DNA mutation data. \ud \ud Conclusions\ud \ud We demonstrate that relaxing the assumption that stem-cell positions are fixed enables clonal expansion and niche succession to occur. We also predict that the presence of extracellular factors near the base of the crypt alone suffices to explain the observed spatial variation in nuclear beta-catenin levels along the crypt axis