A survey of partial differential equations in geometric design

YesComputer aided geometric design is an area where the improvement of surface generation techniques is an everlasting demand since faster and more accurate geometric models are required. Traditional methods for generating surfaces were initially mainly based upon interpolation algorithms. Recently, partial differential equations (PDE) were introduced as a valuable tool for geometric modelling since they offer a number of features from which these areas can benefit. This work summarises the uses given to PDE surfaces as a surface generation technique togethe

A Model for Multidimensional Delayed Detonations in SN Ia Explosions

We show that a flame tracking/capturing scheme originally developed for deflagration fronts can be used to model thermonuclear detonations in multidimensional explosion simulations of type Ia supernovae. After testing the accuracy of the front model, we present a set of two-dimensional simulations of delayed detonations with a physically motivated off-center deflagration-detonation-transition point. Furthermore, we demonstrate the ability of the front model to reproduce the full range of possible interactions of the detonation with clumps of burned material. This feature is crucial for assessing the viability of the delayed detonation scenario.Comment: 7 pages, accepted by A&

A new ghost cell/level set method for moving boundary problems:application to tumor growth

In this paper, we present a ghost cell/level set method for the evolution of interfaces whose normal velocity depend upon the solutions of linear and nonlinear quasi-steady reaction-diffusion equations with curvature-dependent boundary conditions. Our technique includes a ghost cell method that accurately discretizes normal derivative jump boundary conditions without smearing jumps in the tangential derivative; a new iterative method for solving linear and nonlinear quasi-steady reaction-diffusion equations; an adaptive discretization to compute the curvature and normal vectors; and a new discrete approximation to the Heaviside function. We present numerical examples that demonstrate better than 1.5-order convergence for problems where traditional ghost cell methods either fail to converge or attain at best sub-linear accuracy. We apply our techniques to a model of tumor growth in complex, heterogeneous tissues that consists of a nonlinear nutrient equation and a pressure equation with geometry-dependent jump boundary conditions. We simulate the growth of glioblastoma (an aggressive brain tumor) into a large, 1 cm square of brain tissue that includes heterogeneous nutrient delivery and varied biomechanical characteristics (white matter, gray matter, cerebrospinal fluid, and bone), and we observe growth morphologies that are highly dependent upon the variations of the tissue characteristics—an effect observed in real tumor growth

Anomalous wave structure in magnetized materials described by non-convex equations of state

Agraïments: Institute for Pure and Applied Mathematics (UCLA) 2012 program on "Computational Methods in High Energy Density Plasmas.We analyze the anomalous wave structure appearing in flow dynamics under the influence of magnetic field in materials described by non-ideal equations of state. We consider the system of magnetohydrodynamics equations closed by a general equation of state (EOS) and propose a complete spectral decomposition of the fluxes that allows us to derive an expression of the nonlinearity factor as the mathematical tool to determine the nature of the wave phenomena. We prove that the possible formation of non-classical wave structure is determined by both the thermodynamic properties of the material and the magnetic field as well as its possible rotation. We demonstrate that phase transitions induced by material properties do not necessarily imply the loss of genuine nonlinearity of the wavefields as is the case in classical hydrodynamics. The analytical expression of the nonlinearity factor allows us to determine the specific amount of magnetic field necessary to prevent formation of complex structure induced by phase transition in the material. We illustrate our analytical approach by considering two non-convex EOS that exhibit phase transitions and anomalous behavior in the evolution. We present numerical experiments validating the analysis performed through a set of one-dimensional Riemann problems. In the examples we show how to determine the appropriate amount of magnetic field in the initial conditions of the Riemann problem to transform a thermodynamic composite wave into a simple nonlinear wave

The Irredeemable Debt: On the English Translation of Lacan's First Two Public Seminars

This is an Accepted Manuscript of an article published by Edinburgh University Press in Psychoanalysis and History . The Version of Record is available online at: https://www.euppublishing.com/doi/10.3366/pah.2017.0214Drawing on archival sources and personal recollections, this essay reconstructs the troubled history of the first robust attempt at making the works of the French psychoanalyst Jacques Lacan newly available to an anglophone readership, after his death in 1981. It details how the project was initiated by John Forrester as part of a large-scale initiative to generate translations of both Lacan’s own texts and seminars, and various books written in the Lacanian tradition. If, almost seven years after it was conceived, Forrester’s project only resulted in the publication of English translations of Lacan’s first two public seminars, the essay demonstrates that this was not owing to disagreements over the quality of Forrester’s work, but because of two consecutive sources of resistance. External resistance from publishers first led to the initial project being reduced to the translation of two seminars, whereas internal resistance from Lacan’s son-in-law Jacques-Alain Miller to Forrester’s vision of presenting the seminars with a full scholarly apparatus subsequently brought about delays in its execution