A generic topological framework for physical simulation

This paper presents the use of a topological model to simulate a soft body deformation based on a Mass-Spring System. We provide a generic framework which can integrate any kind of geometrical meshes (hexahedral or tetrahedral elements), using several numerical integration schemes (Euler semi-implicit or implicit). This framework naturally allows topological changes in the simulated object during the animation. Our model is based on the 3D Linear Cell Complex topological model (itself based on a 3D combinatorial map), adding the extra information required for simulation purposes. Moreover, we present some adaptations performed on this data structure to fit our simulation requirements, and to allow efficient cutting or piercing in a 3D object

Generalized liquid crystals: giant fluctuations and the vestigial chiral order of II, OO and TT matter

The physics of nematic liquid crystals has been subject of intensive research since the late 19th century. However, because of the limitations of chemistry the focus has been centered around uni- and biaxial nematics associated with constituents bearing a $D_{\infty h}$ or $D_{2h}$ symmetry respectively. In view of general symmetries, however, these are singularly special since nematic order can in principle involve any point group symmetry. Given the progress in tailoring nano particles with particular shapes and interactions, this vast family of "generalized nematics" might become accessible in the laboratory. Little is known since the order parameter theories associated with the highly symmetric point groups are remarkably complicated, involving tensor order parameters of high rank. Here we show that the generic features of the statistical physics of such systems can be studied in a highly flexible and efficient fashion using a mathematical tool borrowed from high energy physics: discrete non-Abelian gauge theory. Explicitly, we construct a family of lattice gauge models encapsulating nematic ordering of general three dimensional point group symmetries. We find that the most symmetrical "generalized nematics" are subjected to thermal fluctuations of unprecedented severity. As a result, novel forms of fluctuation phenomena become possible. In particular, we demonstrate that a vestigial phase carrying no more than chiral order becomes ubiquitous departing from high point group symmetry chiral building blocks, such as $I$, $O$ and $T$ symmetric matter.Comment: 14 pages, 5 figures; published versio

Digital Tectonics as a Morphogenetic Process

p. 938-948Tectonics is a seminal concept that defines the nature of the relationship between architecture and its structural properties. The changing definition of the symbiotic relationship between structural engineering and architectural design may be considered one of the formative influences on the conceptual evolution of tectonics in different historical periods. Recent developments in the field of morphogenesis, digital media, theories techniques and methods of digital design have contributed a new models of integration between structure, material and form in digital tectonics. The objective of this paper is to propose and define tectonics as a model of morphogenetic process. The paper identifies and presents the manner in which theory and emerging concepts of morphogenesis as well as digital models of design are contributing to this new model. The paper first analyzes the historical evolution of tectonics as a concept and characterizes the emergence of theoretical framework reflected in concepts and terms related to morphogenesis.Oxman, R. (2010). Digital Tectonics as a Morphogenetic Process. Editorial Universitat Politècnica de València. http://hdl.handle.net/10251/695

Spatial Aggregation: Theory and Applications

Visual thinking plays an important role in scientific reasoning. Based on the research in automating diverse reasoning tasks about dynamical systems, nonlinear controllers, kinematic mechanisms, and fluid motion, we have identified a style of visual thinking, imagistic reasoning. Imagistic reasoning organizes computations around image-like, analogue representations so that perceptual and symbolic operations can be brought to bear to infer structure and behavior. Programs incorporating imagistic reasoning have been shown to perform at an expert level in domains that defy current analytic or numerical methods. We have developed a computational paradigm, spatial aggregation, to unify the description of a class of imagistic problem solvers. A program written in this paradigm has the following properties. It takes a continuous field and optional objective functions as input, and produces high-level descriptions of structure, behavior, or control actions. It computes a multi-layer of intermediate representations, called spatial aggregates, by forming equivalence classes and adjacency relations. It employs a small set of generic operators such as aggregation, classification, and localization to perform bidirectional mapping between the information-rich field and successively more abstract spatial aggregates. It uses a data structure, the neighborhood graph, as a common interface to modularize computations. To illustrate our theory, we describe the computational structure of three implemented problem solvers -- KAM, MAPS, and HIPAIR --- in terms of the spatial aggregation generic operators by mixing and matching a library of commonly used routines.Comment: See http://www.jair.org/ for any accompanying file