Related papers: Foundations of consistent couple stress theory
We consider a static theory of dislocations with moment stress in an anisotropic or isotropic elastoplastical material as a T(3)-gauge theory. We obtain Yang-Mills type field equations which express the force and the moment equilibrium.…
We study the implications of a change of coordinatization of momentum space for theories with curved momentum space. We of course find that after a passive diffeomorphism the theory yields the same physical predictions, as one would expect…
Solids are distinguished from fluids by their ability to resist shear. In traditional solids, the resistance to shear is associated with the emergence of broken translational symmetry as exhibited by a non-uniform density pattern. In this…
In this paper, we investigate the inherent physical and mathematical character of higher gradient theories, in which the strain or distortion gradients are considered as the fundamental measures of deformation. Contrary to common belief,…
The methods of conformal field theory are used to obtain the series of exact solutions of the fundamental equations of the theory of turbulence. The basic conjecture, proved to be self-consistent ,is the conformal invariance of the inertial…
The notions of consistent pairs and consistent chains of t-structures are introduced. A theorem that two consistent chains of t-structures generate a distributive lattice is proven. The technique developed is then applied to the pairs of…
The behaviour in simple shear of two concentrated and strongly cohesive mineral suspensions showing highly non-monotonic flow curves is described. Two rheometric test modes were employed, controlled stress and controlled shear-rate. In…
Transient stability is crucial to the reliable operation of power systems. Existing theories rely on the simplified electromechanical models, substituting the detailed electromagnetic dynamics of inductor and capacitor with their impedance…
The hysteresis or internal friction in the deformation of crystalline solids stressed cyclically is studied from the viewpoint of collective dislocation dynamics. Stress-controlled simulations of a dislocation dynamics model at various…
Minimal surface problems arise naturally in many soft matter systems whose free energies are dominated by surface or interface energies. Of particular interest are the shapes, stability and mechanical stresses of minimal surfaces spanning…
We propose a dynamical theory of low-temperature shear deformation in amorphous solids. Our analysis is based on molecular-dynamics simulations of a two-dimensional, two-component noncrystalline system. These numerical simulations reveal…
With this paper we extend our studies [1] on polarized beams by distilling tools from the theory of principal bundles. Four major theorems are presented, one which ties invariant fields with the notion of normal form, one which allows one…
In this paper we formulate a geometric theory of thermal stresses. Given a temperature distribution, we associate a Riemannian material manifold to the body, with a metric that explicitly depends on the temperature distribution. A change of…
A new microscopic derivation of the elastic constants of amorphous solids is presented within the framework of nonaffine lattice dynamics, which makes use of a perturbative form of the low-frequency eigenvectors of the dynamical matrix…
We establish that a mode-coupling approximation for the dynamics of multi-component systems obeying Smoluchowski dynamics preserves a subtle yet fundamental property: the matrices of partial density correlation functions are completely…
Following up on purely theoretical work of Bredereck et al. [AAAI 2020], we contribute further theoretical insights into adapting stable two-sided matchings to change. Moreover, we perform extensive empirical studies hinting at numerous…
The relation between the properties of a specific crystallographic site and the properties of the full crystal is discussed by using spherical tensors. The concept of spherical tensors is introduced and the way it transforms under the…
The past decade has witnessed the development of systematic effective theories for dissipative thermal systems. Here, we describe an analogous effective theory framework that applies to the classical stochastic dynamics of nonequilibrium…
We present a framework to take new measurements in nematic systems that contain active elements such as molecular motors. Spatio-temporal fields of stress, traction, velocity, pressure, and forces are estimated jointly from microscopy…
The study of integrability of the mathematical physics equations showed that the differential equations describing real processes are not integrable without additional conditions. This follows from the functional relation that is derived…