Search results for "equation"
showing 10 items of 4219 documents
Figures of equilibrium in close binary systems
1992
The equilibrium configurations of close binary systems are analyzed. The autogravitational, centrifugal and tidal potentials are expanded in Clairaut's coordinates. From the set of the total potential angular terms an integral equations system is derived. The reduction of them to ordinary differential equations and the determination of the boundary conditions allow a formulation of the problem in terms of a single variable.
A strain-difference-based nonlocal elasticity model
2004
Abstract A two-component local/nonlocal constitutive model for (macroscopically) inhomogeneous linear elastic materials (but constant internal length) is proposed, in which the stress is the sum of the local stress and a nonlocal-type stress expressed in terms of the strain difference field, hence identically vanishing in the case of uniform strain. Attention is focused upon the particular case of piecewise homogeneous material. The proposed model is thermodynamically consistent with a suitable free energy potential. It constitutes an improved form of the Vermeer and Brinkgreve [A new effective nonlocal strain measure for softening plasticity. In: Chambon, R., Desrues, J., Vardulakis, I. (E…
Gradient elasticity and nonstandard boundary conditions
2003
Abstract Gradient elasticity for a second gradient model is addressed within a suitable thermodynamic framework apt to account for nonlocality. The pertinent thermodynamic restrictions upon the gradient constitutive equations are derived, which are shown to include, besides the field (differential) stress–strain laws, a set of nonstandard boundary conditions. Consistently with the latter thermodynamic requirements, a surface layer with membrane stresses is envisioned in the strained body, which together with the above nonstandard boundary conditions make the body constitutively insulated (i.e. no long distance energy flows out of the boundary surface due to nonlocality). The total strain en…
Multidomain boundary integral formulation for piezoelectric materials fracture mechanics
2001
Abstract A boundary element method and its numerical implementation for the analysis of piezoelectric materials are presented with the aim to exploit their features in linear electroelastic fracture mechanics. The problem is formulated employing generalized displacements, that is displacements and electric potential, and generalized tractions, that is tractions and electric displacement. The generalized displacements boundary integral equation is obtained by using the closed form of the piezoelasticity fundamental solutions. These are derived through a displacement based modified Lekhnitskii’s functions approach. The multidomain boundary element technique is implemented to achieve the numer…
Itô calculus extended to systems driven by -stable Lévy white noises (a novel clip on the tails of Lévy motion)
2007
Abstract The paper deals with probabilistic characterization of the response of non-linear systems under α -stable Levy white noise input. It is shown that, by properly selecting a clip in the probability density function of the input, the moments of the increments of Levy motion process remain all of the same order ( d t ) , like the increments of the Compound Poisson process. It follows that the Ito calculus extended to Poissonian input, may also be used for α -stable Levy white noise input processes. It is also shown that, when the clip on the tails of the probability of the increments of the Levy motion approaches to infinity, the Einstein–Smoluchowsky equation is restored. Once these c…
3‐D CALCULATION OF ZERO‐COMPONENT FLUX IN THREE‐PHASE THREE‐COLUMN TRANSFORMER
1994
The paper discusses the problem of space distribution of zero‐component magnetic flux generated in three‐column transformer. For 3‐D magnetic field calculation the method of integral equations was used. The numerical calculations were made for physical model of the transformer and compared with experimental results. The accuracy of the calculations of the magnetic field, achieved in the work, proves that the modelling may be used as a computer aided designing tool.
Jacobian of solutions to the conductivity equation in limited view
2022
Abstract The aim of hybrid inverse problems such as Acousto-Electric Tomography or Current Density Imaging is the reconstruction of the electrical conductivity in a domain that can only be accessed from its exterior. In the inversion procedure, the solutions to the conductivity equation play a central role. In particular, it is important that the Jacobian of the solutions is non-vanishing. In the present paper we address a two-dimensional limited view setting, where only a part of the boundary of the domain can be controlled by a non-zero Dirichlet condition, while on the remaining boundary there is a zero Dirichlet condition. For this setting, we propose sufficient conditions on the bounda…
The Calderón problem for the fractional Schrödinger equation
2020
We show global uniqueness in an inverse problem for the fractional Schr\"odinger equation: an unknown potential in a bounded domain is uniquely determined by exterior measurements of solutions. We also show global uniqueness in the partial data problem where the measurements are taken in arbitrary open, possibly disjoint, subsets of the exterior. The results apply in any dimension $\geq 2$ and are based on a strong approximation property of the fractional equation that extends earlier work. This special feature of the nonlocal equation renders the analysis of related inverse problems radically different from the traditional Calder\'on problem.
Finite element approximation of parabolic hemivariational inequalities
1998
In this paper we introduce a finite element approximation for a parabolic hemivariational initial boundary value problem. We prove that the approximate problem is solvable and its solutions converge on subsequences to the solutions of the continuous problem
Influence of Teacher and Family Support on University Student Motivation and Engagement
2021
Although many studies endorse the notion that the way students perceive support influences their engagement, very few have explored the possible mediator role of intention to learn between these variables. The present work provides new evidence to the existing literature because it analyses the work of intention to learn (measured with expectancy–value beliefs and achievement goals) as a mediating motivational variable in the relation between university students’ external support (teacher and family) and their engagement. The Educational Situation Quality Model (MOCSE, its acronym in Spanish) has employed as a theoretical framework to perform this analysis. A sample of 267 Spanish universit…