Related papers: Geometric Analysis of Hyper-Stresses
Jet manifolds and vector bundles allow one to employ tools of differential geometry to study differential equations, for example those arising as equations of motions in physics. They are necessary for a geometrical formulation of…
Viscoelastic fluids are a class of fluids that exhibit both viscous and elastic nature. Modelling such fluids requires constitutive equations for the stress, and choosing the most appropriate constitutive relationship can be difficult. We…
This article offers a new perspective for the mechanics of solids using moving Cartan's frame, specifically discussing a mixed variational principle in non-linear elasticity. We treat quantities defined on the co-tangent bundles of…
We initiate the study of convex geometry over ordered hyperfields. We define convex sets and halfspaces over ordered hyperfields, presenting structure theorems over hyperfields arising as quotients of fields. We prove hyperfield analogues…
Heterotic backgrounds with torsion preserving minimal supersymmetry in four dimensions can be obtained as orbifolds of principal $T^{2}$ bundles over $K3$. We consider a worldsheet description of these backgrounds as gauged linear…
Surface stress, also known as surface tension, is a fundamental material property of any interface. However, measurements of solid surface stress in traditional engineering materials, such as metals and oxides, have proven to be very…
Gravitational vector degrees of freedom typically arise in many examples of modified gravity models. We start to systematically explore their role in these scenarios, studying the effects of coupling gravitational vector and scalar degrees…
We investigate the existence of coordinate transformations which bring a given vector field on a manifold equipped with an involutive distribution into the form of a second-order differential equation field with parameters. We define…
Vacuum expectation value of the stress-energy-momentum tensor for scalar and spinor fields is obtainted on the homogeneous space with $G$-invariant metrics using the orbits of coadjoint representation of Lie group and the generalized…
In this work, we introduce two novel reformulations of a recent weakly hyperbolic model for two-phase flow with surface tension. In the model, the tracking of phase boundaries is achieved by using a vector interface field, rather than a…
Modelling the large deformation of hyperelastic solids under plane stress conditions for arbitrary compressible and nearly incompressible material models is challenging. This is in contrast to the case of full incompressibility where the…
A natural explicit condition is given ensuring that an action of the multiplicative monoid of non-negative reals on a manifold F comes from homotheties of a vector bundle structure on F, or, equivalently, from an Euler vector field. This is…
A family of Virtual Element Methods for the 2D Navier-Stokes equations is proposed and analysed. The schemes provide a discrete velocity field which is point-wise divergence-free. A rigorous error analysis is developed, showing that the…
The components of the renormalized quantum stress tensor for a massive vector field in the spacetime of a pointlike global monopole are determined analytically in the Schwinger-DeWitt approximation. The general results are employed to…
Recall that a vector field on an n-dimensional differentiable manifold M is a mapping X defined on M with values in the tangent bundle TM that assigns to each point $x\in M$ a vector X(x) in the tangent space $T_x M$. A vector field may be…
The spatial variability of stress fields resulting from polycrystalline aggregate calculations involving random grain geometry and crystal orientations is investigated. A periodogram-based method is proposed to identify the properties of…
We consider the dynamics of an elastic continuum under large deformation but small strain. Such systems can be described by the equations of geometrically nonlinear elastodynamics in combination with the St. Venant-Kirchhoff material law.…
We consider the dynamics of vector fields on three-manifolds which are constrained to lie within a plane field, such as occurs in nonholonomic dynamics. On compact manifolds, such vector fields force dynamics beyond that of a gradient flow,…
The dynamics of the Reynolds stress tensor for turbulent flows is described with an evolution equation coupling both geometric effects and turbulent source terms. The effects of the mean flow geometry are shown up when the source terms are…
A family of holomorphic vector bundles is constructed on a complex manifold $X$. The space of the holomorphic sections of these bundles are calculated in certain cases. As an application, if $X$ is an $N$-dimensional compact K\"ahler…