Dispersion relation

About: Dispersion relation is a research topic. Over the lifetime, 21482 publications have been published within this topic receiving 383295 citations.

Long-Range Surface-Plasma Waves on Very Thin Metal Films

Abstract: The dispersion equation of injected surface-plasma waves that propagate on thin metal films has been solved as a function of the film thickness, and splitting of the modes into two branches is observed. For one branch the imaginary part of the propagation constant goes to zero as the thickness of the metal decreases. Reflectivity calculations agree with this result, which predicts that one can obtain propagation distances that are more than 1 order of magnitude larger than observed before.

Causality and the Dispersion Relation: Logical Foundations

Abstract: "Strict causality" is the assumption that no signal whatsoever can be transmitted over a space-like interval in space-time, or that no signal can travel faster than the velocity of light in vacuo. In this paper a rigorous proof is given of the logical equivalence of strict causality ("no output before the input") and the validity of a dispersion relation, e.g., the relation expressing the real part of a generalized scattering amplitude as an integral involving the imaginary part. This proof applies to a general linear system with a time-independent connection between the output and a freely variable input and has the advantage over previous work that no tacit assumptions are made about the analytic behavior or single-valuedness of the amplitude, but, on the contrary, strict causality is shown to imply that the generalized scattering amplitude is analytic in the upper half of the complex frequency plane. The dispersion relations are given first as a relation between the real and imaginary parts of the generalized scattering amplitude and then in terms of the complex phase shift.

Absolute and convective instabilities in free shear layers

Abstract: The absolute or convective character of inviscid instabilities in parallel shear flows can be determined by examining the branch-point singularities of the dispersion relation for complex frequencies and wavenumbers. According to a criterion developed in the study of plasma instabilities, a flow is convectively unstable when the branch-point singularities are in the lower half complex-frequency plane. These concepts are applied to a family of free shear layers with varying velocity ratio their average velocity. It is demonstrated that spatially growing waves can only be observed if the mixing layer is convectively unstable, i.e. when the velocity ratio is smaller than Rt = 1.315. When the velocity ratio is larger than Rt, the instability develops temporally. Finally, the implications of these concepts are discussed also for wakes and hot jets.