2,218 research outputs found
Parallels between control PDE's (Partial Differential Equations) and systems of ODE's (Ordinary Differential Equations)
System theorists understand that the same mathematical objects which determine controllability for nonlinear control systems of ordinary differential equations (ODEs) also determine hypoellipticity for linear partial differentail equations (PDEs). Moreover, almost any study of ODE systems begins with linear systems. It is remarkable that Hormander's paper on hypoellipticity of second order linear p.d.e.'s starts with equations due to Kolmogorov, which are shown to be analogous to the linear PDEs. Eigenvalue placement by state feedback for a controllable linear system can be paralleled for a Kolmogorov equation if an appropriate type of feedback is introduced. Results concerning transformations of nonlinear systems to linear systems are similar to results for transforming a linear PDE to a Kolmogorov equation
Canonical coordinates for partial differential equations
Necessary and sufficient conditions are found under which operators of the form Sigma(m, j=1) X(2)sub j + X sub 0 can be made constant coefficient. In addition, necessary and sufficient conditions are derived which classify those linear partial differential operators that can be moved to the Kolmogorov type
Spatial dispersion in Casimir forces: A brief review
We present the basic principles of non-local optics in connection with the
calculation of the Casimir force between half-spaces and thin films.
At currently accessible distances , non-local corrections amount to about
half a percent, but they increase roughly as 1/L at smaller separations. Self
consistent models lead to corrections with the opposite sign as models with
abrupt surfaces.Comment: Proceedings of QFEXT05, Barcelona, Sept. 5-9, 200
Casimir-like tunneling-induced electronic forces
We study the quantum forces that act between two nearby conductors due to
electronic tunneling. We derive an expression for these forces by calculating
the flux of momentum arising from the overlap of evanescent electronic fields.
Our result is written in terms of the electronic reflection amplitudes of the
conductors and it has the same structure as Lifshitz's formula for the
electromagnetically mediated Casimir forces. We evaluate the tunneling force
between two semiinfinite conductors and between two thin films separated by an
insulating gap. We discuss some applications of our results.Comment: 8 pages, 3 figs, submitted to Proc. of QFEXT'05, to be published in
J. Phys.
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