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Variational Theory (variational + theory)

Distribution by Scientific Domains

Mathematics and Statistics	50%

Selected Abstracts

A new computational method for transient dynamics including the low- and the medium-frequency ranges

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2005
Pierre Ladevèze
Abstract This paper deals with a new computational method for transient dynamic analysis which enables one to cover both the low- and medium-frequency ranges. This is a frequency approach in which the low-frequency part is obtained through a classical technique while the medium-frequency part is handled through the variational theory of complex rays (VTCR) initially introduced for vibrations. Preliminary examples are shown. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Revisiting N -continuous density-functional theory: Chemical reactivity and "Atoms" in "Molecules"

ISRAEL JOURNAL OF CHEMISTRY, Issue 3-4 2003
Morrel H. Cohen
We construct an internally-consistent density-functional theory valid for noninteger electron numbers N by precise definition of a density functional that is continuous in N. In this theory, charge transfer between the atoms of a heteronuclear diatomic molecule, which have been separated adiabatically to infinity, is avoided because the hardness for fractional occupation of a single HOMO spin-orbital is negative. This N -continuous density functional makes possible a variational theory of "atoms" in "molecules" that exactly decomposes the molecular electron density into a sum of contributions from its parts. The parts are treated as though isolated. That theory, in turn, gives a deep foundation to the chemical reactivity theory provided that the hardness of entities with vanishing spin density is positive, as argued to be the case here. This transition from negative to positive hardness closely parallels the transition from the Heitler-London to the Hund-Mulliken picture of molecular bonding. [source]

Evolution completeness of separable solutions of non-linear diffusion equations in bounded domains

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 15 2004
V. A. Galaktionov
Abstract As a basic example, we consider the porous medium equation (m > 1) (1) where , , ,N is a bounded domain with the smooth boundary ,,, and initial data . It is well-known from the 1970s that the PME admits separable solutions , where each ,k , 0 satisfies a non-linear elliptic equation . Existence of at least a countable subset , = {,k} of such non-linear eigenfunctions follows from the Lusternik,Schnirel'man variational theory from the 1930s. The first similarity pattern t,1/(m,1),0(x), where ,0 > 0 in ,, is known to be asymptotically stable as t , , and attracts all nontrivial solutions with u0 , 0 (Aronson and Peletier, 1981). We show that if , is discrete, then it is evolutionary complete, i.e. describes the asymptotics of arbitrary global solutions of the PME. For m = 1 (the heat equation), the evolution completeness follows from the completeness-closure of the orthonormal subset , = {,k} of eigenfunctions of the Laplacian , in L2. The analysis applies to the perturbed PME and to the p -Laplacian equations of second and higher order. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Variational iteration method for solving the space- and time-fractional KdV equation

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 1 2008
Shaher Momani
Abstract This paper presents numerical solutions for the space- and time-fractional Korteweg,de Vries equation (KdV for short) using the variational iteration method. The space- and time-fractional derivatives are described in the Caputo sense. In this method, general Lagrange multipliers are introduced to construct correction functionals for the problems. The multipliers in the functionals can be identified optimally via variational theory. The iteration method, which produces the solutions in terms of convergent series with easily computable components, requiring no linearization or small perturbation. The numerical results show that the approach is easy to implement and accurate when applied to space- and time-fractional KdV equations. The method introduces a promising tool for solving many space,time fractional partial differential equations. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2007 [source]