Moving-boundary problems solved by adaptive radial basis functions

The objective of this paper is to present an alternative approach to the conventional level set methods for solving two-dimensional moving-boundary problems known as the passive transport. Moving boundaries are associated with time-dependent problems and the position of the boundaries need to be determined as a function of time and space. The level set method has become an attractive design tool for tracking, modeling and simulating the motion of free boundaries in fluid mechanics, combustion, computer animation and image processing. Recent research on the numerical method has focused on the idea of using a meshless methodology for the numerical solution of partial differential equations. In the present approach, the moving interface is captured by the level set method at all time with the zero contour of a smooth function known as the level set function. A new approach is used to solve a convective transport equation for advancing the level set function in time. This new approach is based on the asymmetric meshless collocation method and the adaptive greedy algorithm for trial subspaces selection. Numerical simulations are performed to verify the accuracy and stability of the new numerical scheme which is then applied to simulate a bubble that is moving, stretching and circulating in an ambient flow to demonstrate the performance of the new meshless approach. (C) 2010 Elsevier Ltd. All rights reserved

A Fixed-Grid Front-Tracking Algorithm for Solidification Problems. Part I - Method and Validation

A numerical study of directional solidification has been performed using a fixed-grid front- tracking algorithm. The directional solidification of pure tin, as well as the horizontal Bridgman growth of pure succinonitrile, were investigated. In both cases, the growth front was stable and nondendritic, but was significantly distorted by the influence of convection in the melt and, for the Bridgman growth case, by the translation of temperatures at the boundaries which represents furnace movement. Results obtained for the directional soli- dification of pure tin were found to agree reasonably well with experimental and numerical data for temperatures and front locations obtained from the literature. For the Bridgman growth of succinonitrile, the results were compared with detailed experimental data obtained from carefully controlled experiments, and numerical simulations reported in the literature. The predicted interface shapes and melt velocities agree well with experimental results. The predicted front locations exhibit superior agreement to the experimental data than those obtained in the literature using other numerical techniques

Numerical methods in phase-change problems

This paper summarizes the state of the art of the numerical solution of phase-change problems. After describing the governing equations, a review of the existing methods is presented. The emphasis is put mainly on fixed domain techniques, but a brief description of the main front-tracking methods is included. A special section is devoted to the Newton-Raphson resolution with quadratic convergence of the non-linear system of equations

End-to-End Learning of Representations for Asynchronous Event-Based Data

Event cameras are vision sensors that record asynchronous streams of per-pixel brightness changes, referred to as "events". They have appealing advantages over frame-based cameras for computer vision, including high temporal resolution, high dynamic range, and no motion blur. Due to the sparse, non-uniform spatiotemporal layout of the event signal, pattern recognition algorithms typically aggregate events into a grid-based representation and subsequently process it by a standard vision pipeline, e.g., Convolutional Neural Network (CNN). In this work, we introduce a general framework to convert event streams into grid-based representations through a sequence of differentiable operations. Our framework comes with two main advantages: (i) allows learning the input event representation together with the task dedicated network in an end to end manner, and (ii) lays out a taxonomy that unifies the majority of extant event representations in the literature and identifies novel ones. Empirically, we show that our approach to learning the event representation end-to-end yields an improvement of approximately 12% on optical flow estimation and object recognition over state-of-the-art methods.Comment: To appear at ICCV 201

On a viscous critical-stress model of martensitic phase transitions

The solid-to-solid phase transitions that result from shock loading of certain materials, such as the graphite-to-diamond transition and the alpha-epsilon transition in iron, have long been subjects of a substantial theoretical and experimental literature. Recently a model for such transitions was introduced which, based on a CS condition (CS) and without use of fitting parameters, accounts quantitatively for existing observations in a number of systems [Bruno and Vaynblat, Proc. R. Soc. London, Ser. A 457, 2871 (2001)]. While the results of the CS model match the main features of the available experimental data, disagreements in some details between the predictions of this model and experiment, attributable to an ideal character of the CS model, do exist. In this article we present a version of the CS model, the viscous CS model (vCS), as well as a numerical method for its solution. This model and the corresponding solver results in a much improved overall CS modeling capability. The innovations we introduce include: (1) Enhancement of the model by inclusion of viscous phase-transition effects; as well as a numerical solver that allows for a fully rigorous treatment of both, the (2) Rarefaction fans (which had previously been approximated by “rarefaction discontinuities”), and (3) viscous phase-transition effects, that are part of the vCS model. In particular we show that the vCS model accounts accurately for well known “gradual” rises in the alpha-epsilon transition which, in the original CS model, were somewhat crudely approximated as jump discontinuities