Related papers: On singular behaviour in a plane linear elastostat…
Integral expressions are determined for the elastic displacement and stress fields due to stationary or moving dislocation loops in three dimensional, not necessarily isotropic, finite samples. A line integral representation is found for…
Examples of dynamical systems proposed by Z. Artstein and C. M. Dafermos admit non-unique solutions that track a one parameter family of closed circular orbits contiguous at a single point. Switching between orbits at this single point…
Some remarkable generic properties, related to isostaticity and potential energy minimization, of equilibrium configurations of assemblies of rigid, frictionless grains are studied. Isostaticity -the uniqueness of the forces, once the list…
A two-fold singularity is a point on a discontinuity surface of a piecewise-smooth vector field at which the vector field is tangent to the surface on both sides. Due to the double tangency, forward evolution from a two-fold is typically…
The phase-field crystal model in its amplitude equation approximation is shown to provide an accurate description of the deformation field in defected crystalline structures, as well as of dislocation motion. We analyze in detail the…
Integral expressions are determined for the elastic displacement and stress fields due to stationary or moving dislocation loops in finite samples. These general expressions are valid for anisotropic media as well. Specifically for the…
We consider Cauchy's equation of motion for hyperelastic materials. The solution of this nonlinear initial-boundary value problem is the vector field which discribes the displacement which a particle of this material perceives when exposed…
TeVeS uses a dynamical vector field with timelike unit norm constraint to specify a preferred local frame. When matter moves slowly in this frame - the so-called quasi-static regime - Modified Newtonian Dynamics (MoND) results. Theories…
Vector displacements expressed in spherical coordinates are proposed. They correspond to electromagnetic fields in vacuum that globally rotate about an axis and display many circular patterns on the surface of a sphere. The fields basically…
We determine the equilibria of a rigid loop in the plane, subject to the constraints of fixed length and fixed enclosed area. Rigidity is characterized by an energy functional quadratic in the curvature of the loop. We find that the area…
Non-smooth vector fields does not have necessarily the property of uniqueness of solution passing through a point and this is responsible to enrich the behavior of the system. Even on the plane non-smooth vector fields can be chaotic, a…
In this paper we contribute to qualitative and geometric analysis of planar piecewise smooth vector fields, which consist of two smooth vector fields separated by the straight line $y=0$ and sharing the origin as a non-degenerate…
Vector fields can arise in the cosmological context in different ways, and we discuss both abelian and nonabelian sector. In the abelian sector vector fields of the geometrical origin (from dimensional reduction and Einstein-Eddington…
Theories of low-energy Lorentz violation by a fixed-norm "aether" vector field with two-derivative kinetic terms have a globally bounded Hamiltonian and are perturbatively stable only if the vector is timelike and the kinetic term in the…
Uniqueness of solutions in the linear theory of non-singular dislocations, studied as a special case of plasticity theory, is examined. The status of the classical, singular Volterra dislocation problem as a limit of plasticity problems is…
In this paper we present some basic uniqueness results for evolutive equations under density constraints. First, we develop a rigorous proof of a well-known result (among specialists) in the case where the spontaneous velocity field…
Einstein-like Lagrangian field theory is developed to describe elastic solid containing dislocations with finite-sized core. The framework of the Riemann-Cartan geometry in three dimensions is used, and the core self-energy is expressed by…
How do the global properties of a Lorentzian manifold change when endowed with a vector field? This interesting question is tackled in this paper within the framework of Einstein-Aether (EA) theory which has the most general…
Spontaneous Lorentz violation models of antisymmetric tensor field are known to possess singular Hamiltonian on the vacuum manifold, leading to unresolvable pathologies that render such theories unfit for cosmological studies. In this work,…
The equations of stress equilibrium and strain compatibility/incompatibility are discussed for fields with point singularities in a planar domain. The sufficiency (or insufficiency) of the smooth maps, obtained by restricting the singular…