Tensor valuations

张量估值

• 批准号: 197096744
• 负责人: Professor Dr. Klaus Mecke
• 金额: --
• 依托单位: Institut für Theoretische Physik
• 依托单位国家: 德国
• 项目类别: Research Units
• 财政年份: 2011
• 资助国家: 德国
• 起止时间: 2010-12-31 至 2017-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/197096744?language=en
• 关键词: Tensor; valuations

This project aims at a thorough study of integral geometric results and morphological properties of tensorial functionals of various classes of sets. One main focus will be on translative, kinematic and rotational integral geometric formulas for tensor valuations and for not necessarily additive tensor functionals. We will introduce tensor-valued functionals for quite general classes of sets and with respect to different generating measures. This will enable us to apply tensor valuations as morphological measures that are relevant to the physical processes in anisotropic microstructured materials, and for the thermodynamics of ensembles of non-spherical particles. Tensor functionals will play an important role as geometric descriptors in all projects of the proposal. A particular emphasis in this project will be on foundational problems.

本项目旨在深入研究各类集合的张量泛函的积分几何结果和形态性质。一个主要的焦点将是张量赋值的平移、运动学和旋转积分几何公式，以及不一定是加性张量泛函的几何公式。我们将为相当一般的集合类和关于不同的生成测度引入张量值泛函。这将使我们能够应用张量值作为与各向异性微结构材料中的物理过程相关的形态度量，并用于非球形粒子系综的热力学。张量泛函将在提案的所有项目中作为几何描述符发挥重要作用。这个项目的一个特别重点将是基本问题。