Modelling the neutrino in terms of Cosserat elasticity
Olga Chervova, Dmitri Vassiliev
备注：
Submitted to the Proceedings of the Twelfth Marcel Grossmann Meeting
发表信息：
Proceedings of the Twelfth Marcel Grossmann Meeting on General Relativity (in 3 volumes, editors Thibault Damour and Robert Jantzen, series editor Remo Ruffini), World Scientific, 2012, part C, p. 2398-2400
The paper deals with the Weyl equation which is the massless Dirac equation. We study the Weyl equation in the stationary setting, i.e. when the the spinor field oscillates harmonically in time. We suggest a new geometric interpretation of the stationary Weyl equation, one which does not require the use of spinors, Pauli matrices or covariant differentiation. We think of our 3-dimensional space as an elastic continuum and assume that material points of this continuum can experience no displacements, only rotations. This framework is a special case of the Cosserat theory of elasticity. Rotations of material points of the space continuum are described mathematically by attaching to each geometric point an orthonormal basis which gives a field of orthonormal bases called the coframe. As the dynamical variables (unknowns) of our theory we choose the coframe and a density. We choose a particular potential energy which is conformally invariant and then incorporate time into our action in the standard Newtonian way, by subtracting kinetic energy. The main result of our paper is the theorem stating that in the stationary setting our model is equivalent to a pair of Weyl equations. The crucial element of the proof is the observation that our Lagrangian admits a factorisation.
A structure-preserving discretisation of SO(3)-rotation fields for finite Cosserat micropolar elasticity
University of Luxembourg（卢森堡大学）；University of Exeter（埃克塞特大学）；Technische Universität Berlin（柏林工业大学）；Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）；Technische Universität Dortmund（多特蒙德工业大学）
Cosserat micropolar and couple-stress elasticity models of flexomagnetism at finite deformations
University of Luxembourg（卢森堡大学）；University of Exeter（埃克塞特大学）；Universitat Politècnica de Catalunya (UPC)（加泰罗尼亚理工大学）；Institut de Matemàtiques de la UPC-BarcelonaTech (IMTech)（UPC-巴塞罗那科技数学研究所）；University of Galway（高威大学）
A constrained Cosserat shell model up to order $O(h^5)$: Modelling, existence of minimizers, relations to classical shell models and scaling invariance of the bending tensor
The mathematical foundations of general relativity revisited
本文的目的是第一次提出一个初步的总结，通过应用偏微分方程和李伪群的形式理论，以重温广义相对论的数学基础所获得的一些最近的结果。为了说明我们将提供的三个基本结果，还将考虑其他工程实例（控制理论、弹性理论、电磁学）。因此，本文分为三个部分，对应于不同的形式化方法。1)Cartan VS VESSIOT：根据“Vessiot结构方程“出现在“Riemann张量“中的二次项不能等同于李群的著名“Cartan结构方程“中出现的二次项，对于“Weyl张量“也可以做类似的评论。特别是，“曲率+挠率”（Cartan）不能被认为是“仅曲率”（Vessiot）的推广。粗略地说，嘉当和追随者还没有能够“商下降到基流形“，结果只获得了斯宾塞在1970年通过“非线性斯宾塞序列”，但在一种方式完全不同的一个其次是维西奥在1903年为同一目的，仍然被忽视。2)珍妮特VS斯宾塞：“Ricci张量“只依赖于非线性变换（Cartan在1922年称之为“elations“），它描述了外尔群（庞加莱子群的10个参数+ 1个伸缩）和时空共形群（15个参数）之间存在的“差异“。它可以通过正则分裂来定义，也就是说，不使用导致黎曼张量的标准收缩或迹的指数。同时，我们将得到Riemann张量和Weyl张量的分支数，而不需要任何关于指数交换的组合论论证。因此，共形Killing系统的Spencer序列及其形式伴随完全描述了Cosse…
A coupled geometric surface and surface reaction-diffusion framework for modelling nuclear mechanics during confined cell migration
Université Côte d’Azur（蔚蓝海岸大学）；CNRS, Laboratoire Jean-Alexandre Dieudonné（法国国家科学研究中心让·亚历山大·迪厄多内实验室）；Université Paris Cité（巴黎西岱大学）；CNRS, Epigenetics and Cell Fate（法国国家科学研究中心表观遗传与细胞命运研究组）；University of British Columbia（不列颠哥伦比亚大学）；University of Zimbabwe（津巴布韦大学）；University of Pretoria（比勒陀利亚大学）；University of Johannesburg（约翰内斯堡大学）；Institut Universitaire de France（法兰西学院）
