Scattering formulation based on an amplitude-independent variational principle

$(varphi_1, varphi_2)$-variational principle

In this paper we prove that if $X $ is a Banach space, then for every lower semi-continuous bounded below function $f, $ there exists a $left(varphi_1, varphi_2right)$-convex function $g, $ with arbitrarily small norm,  such that $f + g $ attains its strong minimum on $X. $ This result extends some of the  well-known varitional principles as that of Ekeland [On the variational principle,  J. Ma...

An extended variational principle

On the Variational Principle

The variational principle states that if a differentiable functional F attains its minimum at some point zi, then F’(C) = 0; it has proved a valuable tool for studying partial differential equations. This paper shows that if a differentiable function F has a finite lower bound (although it need not attain it), then, for every E > 0, there exists some point u( where 11 F’(uJj* < l , i.e., its de...

Variational formulation of ideal fluid flows according to gauge principle

On the basis of the gauge principle of field theory, a new variational formulation is presented for flows of an ideal fluid. The fluid is defined thermodynamically by mass density and entropy density, and its flow fields are characterized by symmetries of translation and rotation. The rotational transformations are regarded as gauge transformations as well as the translational ones. In addition...

Variational principle for scattering of light by dielectric particles.

S2 I Fig. 1. Cross-sectional view of dye cell showing aluminum rings AL1 and AL2, substrates S1 and S2, the sealing O-rings, and the Swagelok connectors. the entire cell could be repositioned, and another portion of the mirror could be used. In this way a single mirror could continue to be used following several damaging events. The cell, shown in Fig. 1, consists of two 5.08-cm diam, 0.95-cm t...