Cosmic ray diffusion: Report of the Workshop in Cosmic Ray Diffusion Theory

A workshop in cosmic ray diffusion theory was held at Goddard Space Flight Center on May 16-17, 1974. Topics discussed and summarized are: (1) cosmic ray measurements as related to diffusion theory; (2) quasi-linear theory, nonlinear theory, and computer simulation of cosmic ray pitch-angle diffusion; and (3) magnetic field fluctuation measurements as related to diffusion theory

Quasi-linear theory via the cumulant expansion approach

The cumulant expansion technique of Kubo was used to derive an intergro-differential equation for f , the average one particle distribution function for particles being accelerated by electric and magnetic fluctuations of a general nature. For a very restricted class of fluctuations, the f equation degenerates exactly to a differential equation of Fokker-Planck type. Quasi-linear theory, including the adiabatic assumption, is an exact theory for this limited class of fluctuations. For more physically realistic fluctuations, however, quasi-linear theory is at best approximate

The partially averaged field approach to cosmic ray diffusion

The kinetic equation for particles interacting with turbulent fluctuations is derived by a new nonlinear technique which successfully corrects the difficulties associated with quasilinear theory. In this new method the effects of the fluctuations are evaluated along particle orbits which themselves include the effects of a statistically averaged subset of the possible configurations of the turbulence. The new method is illustrated by calculating the pitch angle diffusion coefficient D sub Mu Mu for particles interacting with slab model magnetic turbulence, i.e., magnetic fluctuations linearly polarized transverse to a mean magnetic field. Results are compared with those of quasilinear theory and also with those of Monte Carlo calculations. The major effect of the nonlinear treatment in this illustration is the determination of D sub Mu Mu in the vicinity of 90 deg pitch angles where quasilinear theory breaks down. The spatial diffusion coefficient parallel to a mean magnetic field is evaluated using D sub Mu Mu as calculated by this technique. It is argued that the partially averaged field method is not limited to small amplitude fluctuating fields and is hence not a perturbation theory

A new approach to cosmic ray diffusion theory

An approach is presented for deriving a diffusion equation for charged particles in a static, random magnetic field. The approach differs from the usual, quasi-linear one, in that particle orbits in the average field are replaced by particle orbits in a partially averaged field. In this way the fluctuating component of the field significantly modifies the particle orbits in those cases where the orbits in the average field are unrealistic. The method permits the calculation of a finite value for the pitch angle diffusion coefficient for particles with a pitch angle of 90 rather than the divergent or ambiguous results obtained by quasi-linear theories. Results of the approach are compared with results of computer simulations using Monte Carlo techniques

Applications of numerical codes to space plasma problems

Solar wind, earth's bowshock, and magnetospheric convection and substorms were investigated. Topics discussed include computational physics, multifluid codes, ionospheric irregularities, and modeling laser plasmas

Comment on 4D Lorentz invariance violations in the brane-world

The brane-world scenario offers the possibility for signals to travel outside our visible universe and reenter it. We find the condition for a signal emitted from the brane to return to the brane. We study the propagation of such signals and show that, as seen by a 4D observer, these signals arrive earlier than light traveling along the brane. We also study the horizon problem and find that, while the bulk signals can travel far enough to homogenize the visible universe, it is unlikely that they have a significant effect since they are redshifted in the gravitational field of the bulk black hole.Comment: 21 pages, 6 figures, REVTEX, New section adde

A Comprehensive Trainable Error Model for Sung Music Queries

We propose a model for errors in sung queries, a variant of the hidden Markov model (HMM). This is a solution to the problem of identifying the degree of similarity between a (typically error-laden) sung query and a potential target in a database of musical works, an important problem in the field of music information retrieval. Similarity metrics are a critical component of query-by-humming (QBH) applications which search audio and multimedia databases for strong matches to oral queries. Our model comprehensively expresses the types of error or variation between target and query: cumulative and non-cumulative local errors, transposition, tempo and tempo changes, insertions, deletions and modulation. The model is not only expressive, but automatically trainable, or able to learn and generalize from query examples. We present results of simulations, designed to assess the discriminatory potential of the model, and tests with real sung queries, to demonstrate relevance to real-world applications

Superconductors with Topological Order

We propose a mechanism of superconductivity in which the order of the ground state does not arise from the usual Landau mechanism of spontaneous symmetry breaking but is rather of topological origin. The low-energy effective theory is formulated in terms of emerging gauge fields rather than a local order parameter and the ground state is degenerate on topologically non-trivial manifolds. The simplest example of this mechanism of superconductivty is concretely realized as global superconductivty in Josephson junction arrays.Comment: 4 pages, no figure

Topological Modes in Dual Lattice Models

Lattice gauge theory with gauge group $Z_{P}$ is reconsidered in four dimensions on a simplicial complex $K$. One finds that the dual theory, formulated on the dual block complex $\hat{K}$, contains topological modes which are in correspondence with the cohomology group $H^{2}(\hat{K},Z_{P})$, in addition to the usual dynamical link variables. This is a general phenomenon in all models with single plaquette based actions; the action of the dual theory becomes twisted with a field representing the above cohomology class. A similar observation is made about the dual version of the three dimensional Ising model. The importance of distinct topological sectors is confirmed numerically in the two dimensional Ising model where they are parameterized by $H^{1}(\hat{K},Z_{2})$.Comment: 10 pages, DIAS 94-3

Gauge symmetry breaking on orbifolds

We discuss a new method for gauge symmetry breaking in theories with one extra dimension compactified on the orbifold S^1/Z_2. If we assume that fields and their derivatives can jump at the orbifold fixed points, we can implement a generalized Scherk-Schwarz mechanism that breaks the gauge symmetry. We show that our model with discontinuous fields is equivalent to another with continuous but non periodic fields; in our scheme localized lagrangian terms for bulk fields appear.Comment: 6 pages, 2 figures. Talk given at the XXXVIIth Rencontres de Moriond, "Electroweak interactions and unified theories", Les Arcs, France, 9-16 Mar 2002. Minor changes, one reference adde