817 research outputs found
Optimal Focusing for Monochromatic Scalar and Electromagnetic Waves
For monochromatic solutions of D'Alembert's wave equation and Maxwell's
equations, we obtain sharp bounds on the sup norm as a function of the far
field energy. The extremizer in the scalar case is radial. In the case of
Maxwell's equation, the electric field maximizing the value at the origin
follows longitude lines on the sphere at infinity. In dimension the
highest electric field for Maxwell's equation is smaller by a factor 2/3 than
the highest corresponding scalar waves.
The highest electric field densities on the balls occur as .
The density dips to half max at approximately equal to one third the
wavelength. The extremizing fields are identical to those that attain the
maximum field intensity at the origin.Comment: 30 pages, 7 figure
Dispersive Stabilization
Ill posed linear and nonlinear initial value problems may be stabilized, that
it converted to to well posed initial value problems, by the addition of purely
nonscalar linear dispersive terms. This is a stability analog of the Turing
instability. This idea applies to systems of quasilinear Schr\"odinger
equations from nonlinear optics
Diffraction of Bloch Wave Packets for Maxwell's Equations
We study, for times of order 1/h, solutions of Maxwell's equations in an
O(h^2) modulation of an h-periodic medium. The solutions are of slowly varying
amplitude type built on Bloch plane waves with wavelength of order h. We
construct accurate approximate solutions of three scale WKB type. The leading
profile is both transported at the group velocity and dispersed by a
Schr\"odinger equation given by the quadratic approximation of the Bloch
dispersion relation. A weak ray average hypothesis guarantees stability.
Compared to earlier work on scalar wave equations, the generator is no longer
elliptic. Coercivity holds only on the complement of an infinite dimensional
kernel. The system structure requires many innovations
Incoming and disappearing solutions for Maxwell's equations
We prove that in contrast to the free wave equation in there are no
incoming solutions of Maxwell's equations in the form of spherical or modulated
spherical waves. We construct solutions which are corrected by lower order
incoming waves. With their aid, we construct dissipative boundary conditions
and solutions to Maxwell's equations in the exterior of a sphere which decay
exponentially as . They are asymptotically disappearing.
Disappearing solutions which are identically zero for are
constructed which satisfy maximal dissipative boundary conditions which depend
on time . Both types are invisible in scattering theory
A bound on the group velocity for Bloch wave packets
We give a direct proof that the group velocities of
Bloch wave packet solutions of periodic second order
wave equations cannot exceed the maximal speed of propagation of the periodic wave equation
Comparative survey of dynamic analyses of free-piston Stirling engines
Reported dynamics analyses for evaluating the steady-state response and stability of free-piston Stirling engine (FPSE) systems are compared. Various analytical approaches are discussed to provide guidance on their salient features. Recommendations are made in the recommendations remarks for an approach which captures most of the inherent properties of the engine. Such an approach has the potential for yielding results which will closely match practical FPSE-load systems
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