Effective one-dimensional description of confined diffusion biased by a transverse gravitational force

Diffusion of point-like non interacting particles in a two-dimensional (2D) channel of varying cross section is considered. The particles are biased by a constant force in the transverse direction. We apply our recurrence mapping procedure, which enables us to derive an effective one-dimensional (1D) evolution equation, governing the 1D density of the particles in the channel. In the limit of stationary flow, we arrive at an extended Fick-Jacobs equation, corrected by an effective diffusion coefficient D(x), depending on the longitudinal coordinate x. Our result is an approximate formula for D(x), involving also influence of the transverse force. Our calculations are verified on the stationary diffusion in a linear cone, which is exactly solvable.Comment: 10 pages, 7 figures, submitted in Phys. Rev.

Healthiness from Duality

Healthiness is a good old question in program logics that dates back to Dijkstra. It asks for an intrinsic characterization of those predicate transformers which arise as the (backward) interpretation of a certain class of programs. There are several results known for healthiness conditions: for deterministic programs, nondeterministic ones, probabilistic ones, etc. Building upon our previous works on so-called state-and-effect triangles, we contribute a unified categorical framework for investigating healthiness conditions. We find the framework to be centered around a dual adjunction induced by a dualizing object, together with our notion of relative Eilenberg-Moore algebra playing fundamental roles too. The latter notion seems interesting in its own right in the context of monads, Lawvere theories and enriched categories.Comment: 13 pages, Extended version with appendices of a paper accepted to LICS 201

Interaction of vortices in superconductors with kappa close to 2^(-1/2)

Using a perturbative approach to the infinitely degenerate Bogomolnyi vortex state for a superconductor with kappa = 2^(-1/2), T -> T_c, we calculate the interaction of vortices in a superconductor with kappa close to 2^(-1/2). We find, numerically and analytically, that depending on the material the interaction potential between the vortices varies with decreasing kappa from purely repulsive (as in a type-II superconductor) to purely attractive (as in a type-I superconductor) in two different ways: either vortices form a bound state and the distance between them changes gradually from infinity to zero, or this transition occurs in a discontinuous way as a result of a competition between minima at infinity and zero. We study the discontinuous transition between the vortex and Meissner states caused by the non-monotonous vortex interaction and calculate the corresponding magnetization jump.Comment: v1:original submit v2:changed formate of images (gave problems to some) v3:corrected fig v4v6 (was -v4v6) orthographic corrections (and U_lat/int) mismatch v4:more small orthographic corrections v5:converted to revtex4 and bibTex v6:Renamed images to submit to pr

Study of information transfer optimization for communication satellites

The results are presented of a study of source coding, modulation/channel coding, and systems techniques for application to teleconferencing over high data rate digital communication satellite links. Simultaneous transmission of video, voice, data, and/or graphics is possible in various teleconferencing modes and one-way, two-way, and broadcast modes are considered. A satellite channel model including filters, limiter, a TWT, detectors, and an optimized equalizer is treated in detail. A complete analysis is presented for one set of system assumptions which exclude nonlinear gain and phase distortion in the TWT. Modulation, demodulation, and channel coding are considered, based on an additive white Gaussian noise channel model which is an idealization of an equalized channel. Source coding with emphasis on video data compression is reviewed, and the experimental facility utilized to test promising techniques is fully described

Comparison of CDMA and FDMA for the MobileStar(sm) system

Spread-spectrum code division multiple access (CDMA) and single channel per carrier frequency division multiple access (FDMA) systems are compared for spectrum efficiency. CDMA is shown to have greater maximum throughput than FDMA for the MobileStar(sm) system which uses digital voice activated carriers and directive circularly polarized satellite antennas

Involutive Categories and Monoids, with a GNS-correspondence

This paper develops the basics of the theory of involutive categories and shows that such categories provide the natural setting in which to describe involutive monoids. It is shown how categories of Eilenberg-Moore algebras of involutive monads are involutive, with conjugation for modules and vector spaces as special case. The core of the so-called Gelfand-Naimark-Segal (GNS) construction is identified as a bijective correspondence between states on involutive monoids and inner products. This correspondence exists in arbritrary involutive categories

Floppy modes and the free energy: Rigidity and connectivity percolation on Bethe Lattices

We show that negative of the number of floppy modes behaves as a free energy for both connectivity and rigidity percolation, and we illustrate this result using Bethe lattices. The rigidity transition on Bethe lattices is found to be first order at a bond concentration close to that predicted by Maxwell constraint counting. We calculate the probability of a bond being on the infinite cluster and also on the overconstrained part of the infinite cluster, and show how a specific heat can be defined as the second derivative of the free energy. We demonstrate that the Bethe lattice solution is equivalent to that of the random bond model, where points are joined randomly (with equal probability at all length scales) to have a given coordination, and then subsequently bonds are randomly removed.Comment: RevTeX 11 pages + epsfig embedded figures. Submitted to Phys. Rev.

It's Hard to Learn How Gravity and Electromagnetism Couple

We construct the most general effective Lagrangian coupling gravity and electromagnetism up to mass dimension 6 by enumerating all possible non-minimal coupling terms respecting both diffeomorphism and gauge invariance. In all, there are only two unique terms after field re-definitions; one is known to arise from loop effects in QED while the other is a parity violating term which may be generated by weak interactions within the standard model of particle physics. We show that neither the cosmological propagation of light nor, contrary to earlier claims, solar system tests of General Relativity are useful probes of these terms. These non-minimal couplings of gravity and electromagnetism may remain a mystery for the foreseeable future.Comment: 9 pages. Minor corrections made. To appear in Phys. Rev.