Fast, Scalable, and Interactive Software for Landau-de Gennes Numerical Modeling of Nematic Topological Defects

Numerical modeling of nematic liquid crystals using the tensorial Landau-de Gennes (LdG) theory provides detailed insights into the structure and energetics of the enormous variety of possible topological defect configurations that may arise when the liquid crystal is in contact with colloidal inclusions or structured boundaries. However, these methods can be computationally expensive, making it challenging to predict (meta)stable configurations involving several colloidal particles, and they are often restricted to system sizes well below the experimental scale. Here we present an open-source software package that exploits the embarrassingly parallel structure of the lattice discretization of the LdG approach. Our implementation, combining CUDA/C++ and OpenMPI, allows users to accelerate simulations using both CPU and GPU resources in either single- or multiple-core configurations. We make use of an efficient minimization algorithm, the Fast Inertial Relaxation Engine (FIRE) method, that is well-suited to large-scale parallelization, requiring little additional memory or computational cost while offering performance competitive with other commonly used methods. In multi-core operation we are able to scale simulations up to supra-micron length scales of experimental relevance, and in single-core operation the simulation package includes a user-friendly GUI environment for rapid prototyping of interfacial features and the multifarious defect states they can promote. To demonstrate this software package, we examine in detail the competition between curvilinear disclinations and point-like hedgehog defects as size scale, material properties, and geometric features are varied. We also study the effects of an interface patterned with an array of topological point-defects.Comment: 16 pages, 6 figures, 1 youtube link. The full catastroph

Report from the MPP Working Group to the NASA Associate Administrator for Space Science and Applications

NASA's Office of Space Science and Applications (OSSA) gave a select group of scientists the opportunity to test and implement their computational algorithms on the Massively Parallel Processor (MPP) located at Goddard Space Flight Center, beginning in late 1985. One year later, the Working Group presented its report, which addressed the following: algorithms, programming languages, architecture, programming environments, the way theory relates, and performance measured. The findings point to a number of demonstrated computational techniques for which the MPP architecture is ideally suited. For example, besides executing much faster on the MPP than on conventional computers, systolic VLSI simulation (where distances are short), lattice simulation, neural network simulation, and image problems were found to be easier to program on the MPP's architecture than on a CYBER 205 or even a VAX. The report also makes technical recommendations covering all aspects of MPP use, and recommendations concerning the future of the MPP and machines based on similar architectures, expansion of the Working Group, and study of the role of future parallel processors for space station, EOS, and the Great Observatories era

Reticulados em problemas de comunicação

Orientadores: Sueli Irene Rodrigues Costa, Vinay Anant VaishampayanTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação CientíficaResumo: O estudo de códigos no contexto de reticulados e outras constelações discretas para aplicações em comunicações é um tópico de interesse na área de teoria da informação. Certas construções de reticulados, como é o caso das Construções A e D, e de outras constelações que não são reticulados, como a Construção C, são utilizadas na decodificação multi-estágio e para quantização vetorial eficiente. Isso motiva a primeira contribuição deste trabalho, que consiste em investigar características da Construção C e propor uma nova construção baseada em códigos lineares, que chamamos de Construção $C^\star,$ analisando suas propriedades (condições para ser reticulado, uniformidade geométrica e distância mínima) e relação com a Construção C. Problemas na área de comunicações envolvendo reticulados podem ser computacionalmente difíceis à medida que a dimensão aumenta, como é o caso de, dado um vetor no espaço real $n-$dimensional, determinar o ponto do reticulado mais próximo a este. A segunda contribuição deste trabalho é a análise desse problema restrito a um sistema distribuído, ou seja, onde o vetor a ser decodificado possui cada uma de suas coordenadas disponíveis em um nó distinto desse sistema. Nessa investigação, encontramos uma solução aproximada para duas e três dimensões considerando a partição de Babai e também estudamos o custo de comunicação envolvidoAbstract: The study of codes in the context of lattices and other discrete constellations for applications in communications is a topic of interest in the area of information theory. Some lattice constructions, such as the known Constructions A and D, and other special nonlattice constellations, as Construction C, are used in multi-stage decoding and efficient vector quantization. This motivates the first contribution of this work, which is to investigate characteristics of Construction C and to propose a new construction based on linear codes that we called Construction $C^\star,$ analyzing its properties (latticeness, geometric uniformity and minimum distance) and relations with Construction C. Communication problems related to lattices can be computationally hard when the dimension increases, as it is the case of, given a real vector in the $n-$dimensional space, determine the closest lattice point to it. The second contribution of this work is the analysis of this problem restricted to a distributed system, i.e., where the vector to be decoded has each coordinate available in a separated node in this system. In this investigation, we find the approximate solution for two and three dimensions considering the Babai partition and study the communication cost involvedDoutoradoMatematica AplicadaDoutora em Matemática Aplicada140797/2017-3CNPQCAPE

A Framework for Developing Real-Time OLAP algorithm using Multi-core processing and GPU: Heterogeneous Computing

The overwhelmingly increasing amount of stored data has spurred researchers seeking different methods in order to optimally take advantage of it which mostly have faced a response time problem as a result of this enormous size of data. Most of solutions have suggested materialization as a favourite solution. However, such a solution cannot attain Real- Time answers anyhow. In this paper we propose a framework illustrating the barriers and suggested solutions in the way of achieving Real-Time OLAP answers that are significantly used in decision support systems and data warehouses

Nomographic Functions: Efficient Computation in Clustered Gaussian Sensor Networks

In this paper, a clustered wireless sensor network is considered that is modeled as a set of coupled Gaussian multiple-access channels. The objective of the network is not to reconstruct individual sensor readings at designated fusion centers but rather to reliably compute some functions thereof. Our particular attention is on real-valued functions that can be represented as a post-processed sum of pre-processed sensor readings. Such functions are called nomographic functions and their special structure permits the utilization of the interference property of the Gaussian multiple-access channel to reliably compute many linear and nonlinear functions at significantly higher rates than those achievable with standard schemes that combat interference. Motivated by this observation, a computation scheme is proposed that combines a suitable data pre- and post-processing strategy with a nested lattice code designed to protect the sum of pre-processed sensor readings against the channel noise. After analyzing its computation rate performance, it is shown that at the cost of a reduced rate, the scheme can be extended to compute every continuous function of the sensor readings in a finite succession of steps, where in each step a different nomographic function is computed. This demonstrates the fundamental role of nomographic representations.Comment: to appear in IEEE Transactions on Wireless Communication