Gauges for the Ginzburg-Landau equations of superconductivity

This note is concerned with gauge choices for the time-dependent Ginzburg-Landau equations of superconductivity. The requiations model the state of a superconducting sample in a magnetic field near the critical tempeature. Any two solutions related through a ``gauge transformation`` describe the same state and are physically indistinquishable. This ``gauge invariance`` can be exploited for analtyical and numerical purposes. A new gauge is proposed, which reduces the equations to a particularly attractive form

The EDIBLES survey:VI. Searching for time variations of interstellar absorption features

Context. Interstellar absorption observed toward stellar targets changes slowly over long timescales, mainly due to the proper motion of the background target relative to the intervening clouds, such that over time, different parts of the intervening cloud are probed. On longer timescales, the slowly changing physical and chemical conditions in the cloud can also cause variation. Detecting such time variations thus provides an opportunity to study cloud structure.Aims. We searched for systematic variations in the absorption profiles of the diffuse interstellar bands (DIBs) and interstellar atomic and molecular lines by comparing the high-quality data set from the recent ESO diffuse interstellar bands large exploration survey (EDIBLES) to older archival observations, bridging typical timescales of ~10 yr with a maximum timescale of 22 yr.Methods. For 64 EDIBLES targets, we found adequate archival observations. We selected 31 strong DIBs, seven atomic lines, and five molecular lines to focus our search on. We carefully considered various systematic effects and used a robust Bayesian quantitative test to establish which of these absorption features could display significant variations.Results. While systematic effects greatly complicate our search, we find evidence for variations in the profiles of the λλ4727 and 5780 DIBs in a few sightlines. Toward HD 167264, we find a new Ca I cloud component that appears and becomes stronger after 2008. The same sightline furthermore displays marginal, but systematic changes in the column densities of the atomic lines originating from the main cloud component in the sightline. Similar variations are seen toward HD 147933.Conclusions. Our high-quality spectroscopic observations in combination with archival data show that it is possible to probe interstellar time variations on time scales of typically a decade. Despite the fact that systematic uncertainties as well as the generally somewhat lower quality of older data complicate matters, we can conclude that time variations can be made visible, both in atomic lines and DIB profiles for a few targets, but that generally, these features are stable along many lines of sight. We present this study as an archival baseline for future comparisons, bridging longer periods.<br/

Abstract kinetic equations with positive collision operators

We consider "forward-backward" parabolic equations in the abstract form $Jd \psi / d x + L \psi = 0$, $0< x < \tau \leq \infty$, where $J$ and $L$ are operators in a Hilbert space $H$ such that $J=J^*=J^{-1}$, $L=L^* \geq 0$, and $\ker L = 0$. The following theorem is proved: if the operator $B=JL$ is similar to a self-adjoint operator, then associated half-range boundary problems have unique solutions. We apply this theorem to corresponding nonhomogeneous equations, to the time-independent Fokker-Plank equation $\mu \frac {\partial \psi}{\partial x} (x,\mu) = b(\mu) \frac {\partial^2 \psi}{\partial \mu^2} (x, \mu)$, $0<x<\tau$, $\mu \in \R$, as well as to other parabolic equations of the "forward-backward" type. The abstract kinetic equation $T d \psi/dx = - A \psi (x) + f(x)$, where $T=T^*$ is injective and $A$ satisfies a certain positivity assumption, is considered also.Comment: 20 pages, LaTeX2e, version 2, references have been added, changes in the introductio

Dynamic Ordering and Transverse Depinning of a Driven Elastic String in a Disordered Media

We examine the dynamics of an elastic string interacting with quenched disorder driven perpendicular and parallel to the string. We show that the string is the most disordered at the depinning transition but with increasing drive partial ordering is regained. For low drives the noise power is high and we observe a 1/f^2 noise signature crossing over to a white noise character with low power at higher drives. For the parallel driven moving string there is a finite transverse critical depinning force with the depinning transition occuring by the formation of running kinks.Comment: 4 pages, 4 postscript figure

Long-time behavior of a nuclear reactor

A fundamental problem of reactor physics is the determination of the long-time behavior of the neutron population in a nuclear reactor. In particular, one is interested in the question whether the total neutron density has a purely exponential behavior as t ..-->.. infinity. We formulate this problem as an abstract Cauchy problem, show that the solution is given by a semigroup, and investigate the asymptotic behavior of the semigroup