arXiv math-ph/04060362004-06-18math-phmath.DGmath.MP

Geometry of interactions in complex bodies

Chiara de Fabriitis, Paolo Maria Mariano

备注：: 27 pages

英文摘要：

We analyze geometrical structures necessary to represent bulk and surface interactions of standard and substructural nature in complex bodies. Our attention is mainly focused on the influence of diffuse interfaces on sharp discontinuity surfaces. In analyzing this phenomenon, we prove the covariance of surface balances of standard and substructural interactions.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

The geometry of the space-time and motion of the spinning bodies

In this paper an alternative theory about space-time is given. First some preliminaries about 3-dimensional time and the reasons for its introduction are presented. Alongside the 3-dimensional space (S) the 3-dimensional space of spatial rotations (SR) is considered independently from the 3-dimensional space. Then it is given a model of the universe, based on the Lie groups of real and complex orthogonal 3x3 matrices in this 3+3+3-dimensional space. Special attention is dedicated for introduction and study of the space SxSR, which appears to be isomorphic to SO(3,R)xSO(3,R) or S^3xS^3. The inf…

2015-04-19math-phmath.DGmath.MP

Representation of Material Elements and Geometry of Substructural Interactions

This paper collects some characteristic aspects of the general model-building framework of the mechanics of complex bodies, that are bodies in which the material substructure influences prominently the gross behavior through interactions conjugated with substructural changes. The emphasis in on issues that are foundational in nature: the geometrica description of the material elements, their energetic characterization, the representation of interactions, conditions for the existence of ground states in conservative setting.

2008-02-11math-phmath.MP

Complex Eigenfrequencies of Some Axially Symmetrical Bodies

The complex eigenfrequencies of a perfectly conducting cone, truncated cone, and finite circular cylinder are determined using the time-domain integral equation method and the Prony technique.

2005-10-27math-phmath.MP

Geometry of the Motion of Ideal Fluids and Rigid Bodies

Arnold pointed out that the Euler equation of incompressible ideal hydrodynamics describes geodesics on the group of volume-preserving diffeomorphisms. A simple analogue is the Euler equation for a rigid body, which is the geodesic equation on the rotation group with respect to a metric determined by the moment of inertia. The metric on the group is left-invariant but not right-invariant. We will reduce the geometry of such groups (using techniques popularized by Milnor) to algebra on their tangent space. In particular, the curvature can be expressed as a biquadratic form on the Lie algebra. A…

2009-05-31math-phmath.MP

Complex bodies with memory: linearized setting

The mechanics of complex bodies with memory effects is discussed in linearized setting. The attention is focused on the characterization of free energies in terms of minimum work and maximum recoverable work in the bulk and along a discontinuity surface endowed with its own surface energy, a surface internal to the body. To this aim, use is made of techniques proposed by Del Piero. Consequences of the Clausius-Duhem inequality are investigated for complex bodies with instantaneous linear elastic response.

2008-05-28math-phmath.MP

Mechanics of complex bodies: commentary on the unified modelling of material substructures

Basic issues of the general model-building framework of the mechanics of complex bodies are discussed. Attention is focused on the representation of the material elements, the conditions for the existence of ground states in conservative setting and the interpretation of the nature of the various balance laws occurring.

2008-03-26math-phmath.MP

更多相关论文收起更多论文

Discrete dynamics of complex bodies with substructural dissipation: variational integrators and convergence

For the linearized setting of the dynamics of complex bodies we construct variational integrators and prove their convergence by making use of BV estimates on the rate fields. We allow for peculiar substructural inertia and internal dissipation, all accounted for by a d'Alembert-Lagrange-type principle.

2008-03-11math-phmath.APmath.MP

Ground states in complex bodies

A unified framework for analyzing the existence of ground states in wide classes of elastic complex bodies is presented here. The approach makes use of classical semicontinuity results, Sobolev mappinngs and Cartesian currents. Weak diffeomorphisms are used to represent macroscopic deformations. Sobolev maps and Cartesian currents describe the inner substructure of the material elements. Balance equations for irregular minimizers are derived. A contribution to the debate about the role of the balance of configurational actions follows. After describing a list of possible applications of the ge…

2008-02-11math-phmath.MP

Complementarity problems for two pairs of charged bodies

We consider an interaction of charged bodies under the following simplified conditions: the distribution of charge over each body is stable; the interaction of bodies is governed by electrical forces only. Physically, these assumptions can be treated as the following decomposition of charges: the structure of each body is assumed to be stable due to inner forces (say, quantum forces [1]), which do not influence the interaction of the bodies; the bodies interact due to the classical electrical forces [2] only. In this model, the role of inner forces is to create a specific stable distribution o…

2012-07-05math-phmath.MP

Heat transfer in a complex medium

The heat equation is considered in the complex medium consisting of many small bodies (particles) embedded in a given material. On the surfaces of the small bodies an impedance boundary condition is imposed. An equation for the limiting field is derived when the characteristic size $a$ of the small bodies tends to zero, their total number $\mathcal{N}(a)$ tends to infinity at a suitable rate, and the distance $d = d(a)$ between neighboring small bodies tends to zero: $a << d$, $\lim_{a\to 0}\frac{a}{d(a)}=0$. No periodicity is assumed about the distribution of the small bodies. These results a…

2016-01-09math-phmath.MP

Heat transfer in a medium in which many small particles are embedded

The heat equation is considered in the complex system consisting of many small bodies (particles) embedded in a given material. On the surfaces of the small bodies a Newton-type boundary condition is imposed. An equation for the limiting field is derived when the characteristic size $a$ of the small bodies tends to zero, their total number $\mathcal{N}(a)$ tends to infinity at a suitable rate, and the distance $d = d(a)$ between neighboring small bodies tends to zero $a << d$. No periodicity is assumed about the distribution of the small bodies.

2012-07-03math-phmath.APmath.MP

On de-Sitter geometry in crater statistics

The cumulative size-frequency distributions of impact craters on planetary bodies in the solar system appear to approximate a universal inverse square power-law for small crater radii. In this article, we show how this distribution can be understood easily in terms of geometrical statistics, using a de-Sitter geometry of the configuration space of circles on the Euclidean plane and on the unit sphere. The effect of crater overlap is also considered.

2012-11-15astro-ph.EPgr-qcmath-ph