Jt Fundamental Notes 1 on Instability Analysis
نویسنده
چکیده
In this special technical report we present fundamental studies on instability analysis. When an electromagnetic wave linearly interacts with an active medium or system, there can occur basically two types of instabilities. One of them, in which the wave grows indefinitely with tin», Is called absolute Instability, and the other, in which the wave grows spatially as it travels, is called convective instability. By conformal mapping of the dispersion equation from a) onto the k plane or vice versa, we have made a detailed analysis of these two types of instabilities. General procedures for analyzing instabilities are summarized. Effects of driving sources and the possible occurrence of branch cuts, in the k plane, of the dispersion equation are also discussed.
منابع مشابه
A pr 1 99 9 The stability of magnetic vortices ∗
We study the linearized stability of n-vortex (n ∈ Z) solutions of the magnetic Ginzburg-Landau (or Abelian Higgs) equations. We prove that the fundamental vortices (n = ±1) are stable for all values of the coupling constant, λ, and we prove that the higher-degree vortices (|n| ≥ 2) are stable for λ < 1, and unstable for λ > 1. This resolves a long-standing conjecture (see, eg, [JT]).
متن کاملThe Stability of Magnetic Vortices
W e study the linearized stability of -vortex ( ) solutions of the magnetic Ginzb urg–Landau (or Abelian Higgs) equations. We prove that the fundamental vortices ( 1) are stable for all values of the coupling constant, , and we prove that the higher -degree vortices ( 2) are stable for 1, and unstable for 1. This resolves a long-standing conjecture (see, eg, [JT]).
متن کاملBerryonic Matter in the Cuprates
A novel form of Jahn-Teller (JT) effect in the cuprates can be reinterpreted as a conventional JT effect on a lattice with a larger unit cell. There is a triplet of instabilities, parametrized by a pseudospin, consisting of a form of the low-temperature tetragonal phase, a charge density wave phase, and a flux phase (orbital antiferromagnet). On a single 4-Cu plaquette, the problem is of E ⊗ (b...
متن کاملFoundations of Mathematics Jt Smith
1. I’ll post outlines such as this at first with the notation “Tentative” on the title line. I’ll revise them after they’re covered in class, and remove that notation. After that, I’ll won’t change them unless I notify you explicitly. Don’t trust hardcopies made before those revisions! 2. Assignment 1 a. Investigate the course Syllabus. b. Turn in to me ASAP a sheet of paper with i. Your e-mail...
متن کاملHeuristics of Instability and Stabilization in Model Selection
In model selection, usually a 'best" predictor is chosen from collection {A(., s)} of predictors where j(., s) is the minimum least squares predictor in a collection U, of predictors. Here s is a complexity parameter; that is, the smaller s, the lower dimensional/smoother the models in U. If L is the data used to derive the sequence {j(.,s)}, the procedure is called unstable if a small change i...
متن کامل