Related papers: Measure structured deformations
Dynamics of systems of structured particles consisting of potentially interacting material points is considered in the framework of classical mechanics. Equations of interaction and motion of structured particles have been derived. The…
Solution of the momentum space Schr\"odinger equation in the case of deformed fields is being addressed. In particular it is shown that a complete set of single particle states which includes bound, resonant and complex continuum states may…
Rigidity regulates the integrity and function of many physical and biological systems. This is the first of two papers on the origin of rigidity, wherein we propose that "energetic rigidity," in which all non-trivial deformations raise the…
In the recent development in a various disciplines of physics, it is noted the need for including the deformed versions of the exponential functions. In this paper, we consider the deformations which have two purposes: to have them like…
Modeling coupled processes in fractured porous media -- flow, deformation, fracture mechanics, and thermal/chemical effects -- often relies on mixed dimensional multiphysics formulations. These systems are nonlinear and depend on physical…
We introduce a new measure for the stability of structures, such as the cross-section of the deck of a suspension bridge, subject to a 2D fluid force, such as the lift exerted by a laminar wind. We consider a wide class of possible flows,…
The structure function is a useful quantity to characterize wavefront distortions. We derive expressions for the structure functions of the averaged wavefront phase and slopes. The expressions are valid within the inertial range of…
An technique is extended to estimate some critical exponents without using the expansion over the coupling constant. The data obtained is in a agreement with those found by help of the 2D Onsager method or with recent 3D results. In the…
While determining the stability of an unconstrained elastic structure is a straightforward task, this is not the case for viscoelastic structures. Seemingly elastically stable conformations of viscoelastic structures may gradually creep…
We introduce the concept of index for regular Dirichlet forms by means of energy measures, and discuss its properties. In particular, it is proved that the index of strong local regular Dirichlet forms is identical with the martingale…
We investigate equilibria of charged deformable materials via the minimization of an electroelastic energy. This features the coupling of elastic response and electrostatics by means of a capacitary term, which is naturally defined in…
Symmetry is one of the most general and useful concepts in physics. A theory or a system that has a symmetry is fundamentally constrained by it. The same constraints do not apply when the symmetry is broken. The quantitative determination…
Electronic devices exhibit changes in electrical resistance over time at varying rates, depending on the configuration of certain components. Since measuring overall electrical resistance requires partial disassembly, only a limited number…
The continuum mechanics of line defects representing singularities due to terminating discontinuities of the elastic displacement and its gradient field is developed. The development is intended for application to coupled phase…
Examples are given of q-deformed systems that may be interpreted by the standard rules of quantum theory in terms of new degrees of freedom and supplementary quantum numbers.
Plastic deformation is widely regarded as an intrinsically dissipative phenomenon and its theoretical description is largely phenomenological. We argue instead that plasticity possesses a non-dissipative, symmetry determined backbone:…
We propose a measure of shape which is appropriate for the study of a complicated geometric structure, defined using the topology of neighborhoods of the structure. One aspect of this measure gives a new notion of fractal dimension. We…
Deformations of conventional solids are described via elasticity, a classical field theory whose form is constrained by translational and rotational symmetries. However, flexible metamaterials often contain an additional approximate…
Measuring inconsistency is viewed as an important issue related to handling inconsistencies. Good measures are supposed to satisfy a set of rational properties. However, defining sound properties is sometimes problematic. In this paper, we…
Measures play an important role in the characterisation of various function spaces. In this paper, the structure of density measures will be investigated. These are elements of the dual of the space of essentially bounded func- tions. The…