484 research outputs found
A complex ray-tracing tool for high-frequency mean-field flow interaction effects in jets
This paper presents a complex ray-tracing tool for the calculation of high-frequency Green’s functions in 3D mean field jet flows. For a generic problem, the ray solution suffers from three main deficiencies: multiplicity of solutions, singularities at caustics, and the determining of complex solutions. The purpose of this paper is to generalize, combine and apply existing stationary media methods to moving media scenarios. Multiplicities are dealt with using an equivalent two-point boundary-value problem, whilst non-uniformities at caustics are corrected using diffraction catastrophes. Complex rays are found using a combination of imaginary perturbations, an assumption of caustic stability, and analytic continuation of the receiver curve. To demonstrate this method, the ray tool is compared against a high-frequency modal solution of Lilley’s equation for an off-axis point source. This solution is representative of high-frequency source positions in real jets and is rich in caustic structures. A full utilization of the ray tool is shown to provide excellent results<br/
The spectral and polarization characteristics of the nonspherically decaying radiation generated by polarization currents with superluminally rotating distribution patterns
We present a theoretical study of the emission from a superluminal
polarization current whose distribution pattern rotates (with an angular
frequency ) and oscillates (with a frequency ) at the same
time, and which comprises both poloidal and toroidal components. This type of
polarization current is found in recent practical machines designed to
investigate superluminal emission. We find that the superluminal motion of the
distribution pattern of the emitting current generates localized
electromagnetic waves that do not decay spherically, i.e. that do not have an
intensity diminishing like with the distance from their
source. The nonspherical decay of the focused wave packets that are emitted by
the polarization currents does not contravene conservation of energy: the
constructive interference of the constituent waves of such propagating caustics
takes place within different solid angles on spheres of different radii ()
centred on the source. For a polarization current whose longitudinal
distribution (over an azimuthal interval of length ) consists of
cycles of a sinusoidal wave train, the nonspherically decaying part of the
emitted radiation contains the frequencies ; i.e. it
contains {\it only} the frequencies involved in the creation and implementation
of the source. This is in contrast to recent studies of the spherically
decaying emission, which was shown to contain much higher frequencies. The
polarization of the emitted radiation is found to be linear for most
configurations of the source.Comment: 19 pages, six figure
Bistatic scattering from a cone frustum
The bistatic scattering from a perfectly conducting cone frustum is investigated using the Geometrical Theory of Diffraction (GTD). The first-order GTD edge-diffraction solution has been extended by correcting for its failure in the specular region off the curved surface and in the rim-caustic regions of the endcaps. The corrections are accomplished by the use of transition functions which are developed and introduced into the diffraction coefficients. Theoretical results are verified in the principal plane by comparison with the moment method solution and experimental measurements. The resulting solution for the scattered fields is accurate, easy to apply, and fast to compute
Self-force via Green functions and worldline integration
A compact object moving in curved spacetime interacts with its own
gravitational field. This leads to both dissipative and conservative
corrections to the motion, which can be interpreted as a self-force acting on
the object. The original formalism describing this self-force relied heavily on
the Green function of the linear differential operator that governs
gravitational perturbations. However, because the global calculation of Green
functions in non-trivial black hole spacetimes has been an open problem until
recently, alternative methods were established to calculate self-force effects
using sophisticated regularization techniques that avoid the computation of the
global Green function. We present a method for calculating the self-force that
employs the global Green function and is therefore closely modeled after the
original self-force expressions. Our quantitative method involves two stages:
(i) numerical approximation of the retarded Green function in the background
spacetime; (ii) evaluation of convolution integrals along the worldline of the
object. This novel approach can be used along arbitrary worldlines, including
those currently inaccessible to more established computational techniques.
Furthermore, it yields geometrical insight into the contributions to
self-interaction from curved geometry (back-scattering) and trapping of null
geodesics. We demonstrate the method on the motion of a scalar charge in
Schwarzschild spacetime. This toy model retains the physical history-dependence
of the self-force but avoids gauge issues and allows us to focus on basic
principles. We compute the self-field and self-force for many worldlines
including accelerated circular orbits, eccentric orbits at the separatrix, and
radial infall. This method, closely modeled after the original formalism,
provides a promising complementary approach to the self-force problem.Comment: 18 pages, 9 figure
Semiclassical Estimates of Electromagnetic Casimir Self-Energies of Spherical and Cylindrical Metallic Shells
The leading semiclassical estimates of the electromagnetic Casimir stresses
on a spherical and a cylindrical metallic shell are within 1% of the field
theoretical values. The electromagnetic Casimir energy for both geometries is
given by two decoupled massless scalars that satisfy conformally covariant
boundary conditions. Surface contributions vanish for smooth metallic
boundaries and the finite electromagnetic Casimir energy in leading
semiclassical approximation is due to quadratic fluctuations about periodic
rays in the interior of the cavity only. Semiclassically the non-vanishing
Casimir energy of a metallic cylindrical shell is almost entirely due to
Fresnel diffraction.Comment: 12 pages, 2 figure
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