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The response to a localized force provides a sensitive test for different models of stress transmission in granular solids. The elasto-plastic models traditionally used by engineers have been challenged by theoretical and experimental…

Soft Condensed Matter · Physics 2009-11-13 C. Goldenberg , I. Goldhirsch

We consider the mixed ray transform of tensor fields on a three-dimensional compact simple Riemannian manifold with boundary. We prove the injectivity of the transform, up to natural obstructions, and establish stability estimates for the…

Differential Geometry · Mathematics 2020-08-19 Maarten V. de Hoop , Teemu Saksala , Gunther Uhlmann , Jian Zhai

Using Green's theorem we reduce the variation of the total mean curvature of a smooth surface in the Euclidean 3-space to a line integral of a special vector field and obtain the following well-known theorem as an immediate consequence: the…

Differential Geometry · Mathematics 2009-10-10 Victor Alexandrov

An exact, plane wave solution of the gravitational field equations is investigated. The source stress tensor is represented by an anisotropic null fluid with energy flux to which the energy density $\rho$ and all pressures are finite…

General Relativity and Quantum Cosmology · Physics 2017-01-03 Hristu Culetu

The interplay between gravitational and dispersive forces in a multi-streamed medium leads to an effect which is exposed in the present note as the genuine driving force of stabilization of large-scale structure. The conception of `adhesive…

Astrophysics · Physics 2009-09-25 Thomas Buchert

In the context of elasticity theory, rigidity theorems allow to derive global properties of a deformation from local ones. This paper presents a new asymptotic version of rigidity, applicable to elastic bodies with sufficiently stiff…

Analysis of PDEs · Mathematics 2019-09-04 Fabian Christowiak , Carolin Kreisbeck

We study a smooth cosmological solution within a generalized 5D standing wave braneworld modeled by gravity and a phantom scalar field. In this model the 3-brane is anisotropically warped along its spatial dimensions and contains a novel…

It has been shown that the extension of the elasticity theory in more than three dimensions allows a description of space-time as a properly stressed medium, even recovering the Minkowski metric in the case of uniaxial stress. The…

General Relativity and Quantum Cosmology · Physics 2008-02-03 A. Tartaglia

We consider inertial waves propagating in a fluid contained in a non-axisymmetric three-dimensional rotating cavity. We focus on the particular case of a fluid enclosed inside a truncated cone or frustum, which is the volume that lies…

Fluid Dynamics · Physics 2024-01-11 Benjamin Favier , Stéphane Le Dizès

We study elastic shear waves of small but finite amplitude, composed of an anti-plane shear motion and a general in-plane motion. We use a multiple scales expansion to derive an asymptotic system of coupled nonlinear equations describing…

Soft Condensed Matter · Physics 2019-06-20 Michel Destrade , Edvige Pucci , Giuseppe Saccomandi

In this paper, we establish a general setup for studying incidence-preserving motions of projective geometric configurations of points and lines via a "projective rigidity matrix". The spaces of infinitesimal motions of a point-line…

This paper lays the foundations for a nonlinear theory of differential geometry that is developed in a subsequent paper which is based on Colombeau algebras of tensor distributions on manifolds. We adopt a new approach and construct a…

Functional Analysis · Mathematics 2019-10-14 Eduard A. Nigsch , James A. Vickers

A two-dimensional (2D) dislocation continuum theory is being introduced. The present theory adds elastic rotation, dislocation density, and background stress to the classical energy density of elasticity. This theory contains four material…

Mesoscale and Nanoscale Physics · Physics 2015-10-15 Markus Lazar

Recent equations of motion for the large deflections of a cantilevered elastic beam are analyzed. In the traditional theory of beam (and plate) large deflections, nonlinear restoring forces are due to the effect of stretching on bending;…

Analysis of PDEs · Mathematics 2021-04-06 Maria Deliyianni , Justin T. Webster

In the spirit of Germain the most general objective stored elastic energy for a second gradient material is deduced using a literature result of Fortun\'e & Vall\'ee. Linear isotropic constitutive relations for stress and hyperstress in…

Mathematical Physics · Physics 2010-08-18 F. dell'Isola , G. Sciarra , S. Vidoli

Modelling two-dimensional chiral materials is a challenging problem in continuum mechanics because three-dimensional theories reduced to isotropic two-dimensional problems become non-chiral. Various approaches have been suggested to…

Mathematical Physics · Physics 2018-05-01 Sebastian Bahamonde , Christian G. Boehmer , Patrizio Neff

Usual introductions of the concept of motion are not well adapted to a subsequent, strictly tensorial, theory of elasticity. The consideration of arbitrary coordinate systems for the representation of both, the points in the laboratory, and…

Materials Science · Physics 2009-07-18 Albert Tarantola

A comprehensive study has been undertaken on the dimensional swelling of graphene-reinforced elastomers in liquids. Anisotropic swelling was observed for samples reinforced with graphene nanoplatelets (GNPs), induced by the in-plane…

Applied Physics · Physics 2020-03-25 Mufeng Liu , Suhao Li , Ian A. Kinloch , Robert J. Young , Dimitrios G. Papageorgiou

We investigate the two-dimensional elastostatic inclusion problem in an unbounded medium. Building on the recent developments for rigid inclusions \cite{Mattei:2021:EAS} and conductivity inclusions \cite{Jung:2021:SEL}, we extend these…

Analysis of PDEs · Mathematics 2025-10-08 Daehee Cho , Doosung Choi , Mikyoung Lim

It is hard to imagine curved spacetimes of General Relativity. A simple but powerful way how to achieve this is visualizing them via embedding diagrams of both ordinary geometry and optical reference geometry. They facilitate to gain an…

Astrophysics · Physics 2016-11-15 Stanislav Hledik , Zdenek Stuchlik , Alois Cipko