Stability of streamwise vortices

A brief overview of some theoretical and computational studies of the stability of streamwise vortices is given. The local induction model and classical hydrodynamic vortex stability theories are discussed in some detail. The importance of the three-dimensionality of the mean velocity profile to the results of stability calculations is discussed briefly. The mean velocity profile is provided by employing the similarity solution of Donaldson and Sullivan. The global method of Bridges and Morris was chosen for the spatial stability calculations for the nonlinear eigenvalue problem. In order to test the numerical method, a second order accurate central difference scheme was used to obtain the coefficient matrices. It was shown that a second order finite difference method lacks the required accuracy for global eigenvalue calculations. Finally the problem was formulated using spectral methods and a truncated Chebyshev series

It Takes More Than an Apple a Day

http://dx.doi.org/10.1126/science.337.6101.146

Scanned Imaging Techniques for Surface NDE

A phase sensitive laser probe in which the focussed spot is small, as compared with the acoustic wavelength, is capable of measuring the complex distributions of a SAW field along prescribed scan lines. Using the probe, it is possible, on a defect free sample, to measure the SAW velocity surface with an accuracy of a few parts in 105. Such accuracy suggests that the technique is sufficiently sensitive to detect small changes in surface characteristics; the presence of a defect is revealed by perturbations in the relationship between various scans. The scattered radiation patterns from a surface crack irradiated by acoustic surface waves can be utilised to determine the defect size and location with improved accuracy. Results on deliberate and real cracks are presented

Analycity and smoothing effect for the coupled system of equations of Korteweg - de Vries type with a single point singularity

We study that a solution of the initial value problem associated for the coupled system of equations of Korteweg - de Vries type which appears as a model to describe the strong interaction of weakly nonlinear long waves, has analyticity in time and smoothing effect up to real analyticity if the initial data only has a single point singularity at $x=0.

Entropy Encoding, Hilbert Space and Karhunen-Loeve Transforms

By introducing Hilbert space and operators, we show how probabilities, approximations and entropy encoding from signal and image processing allow precise formulas and quantitative estimates. Our main results yield orthogonal bases which optimize distinct measures of data encoding.Comment: 25 pages, 1 figur

On the origin of ambiguity in efficient communication

This article studies the emergence of ambiguity in communication through the concept of logical irreversibility and within the framework of Shannon's information theory. This leads us to a precise and general expression of the intuition behind Zipf's vocabulary balance in terms of a symmetry equation between the complexities of the coding and the decoding processes that imposes an unavoidable amount of logical uncertainty in natural communication. Accordingly, the emergence of irreversible computations is required if the complexities of the coding and the decoding processes are balanced in a symmetric scenario, which means that the emergence of ambiguous codes is a necessary condition for natural communication to succeed.Comment: 28 pages, 2 figure

Rapid Quantification of Molecular Diversity for Selective Database Acquisition

There is an increasing need to expand the structural diversity of the molecules investigated in lead-discovery programs. One way in which this can be achieved is by acquiring external datasets that will enhance an existing database. This paper describes a rapid procedure for the selection of external datasets using a measure of structural diversity that is calculated from sums of pairwise intermolecular structural similarities

Entropic bounds on coding for noisy quantum channels

In analogy with its classical counterpart, a noisy quantum channel is characterized by a loss, a quantity that depends on the channel input and the quantum operation performed by the channel. The loss reflects the transmission quality: if the loss is zero, quantum information can be perfectly transmitted at a rate measured by the quantum source entropy. By using block coding based on sequences of n entangled symbols, the average loss (defined as the overall loss of the joint n-symbol channel divided by n, when n tends to infinity) can be made lower than the loss for a single use of the channel. In this context, we examine several upper bounds on the rate at which quantum information can be transmitted reliably via a noisy channel, that is, with an asymptotically vanishing average loss while the one-symbol loss of the channel is non-zero. These bounds on the channel capacity rely on the entropic Singleton bound on quantum error-correcting codes [Phys. Rev. A 56, 1721 (1997)]. Finally, we analyze the Singleton bounds when the noisy quantum channel is supplemented with a classical auxiliary channel.Comment: 20 pages RevTeX, 10 Postscript figures. Expanded Section II, added 1 figure, changed title. To appear in Phys. Rev. A (May 98

On the possible role of elemental carbon in the formation of reduced chondrules

Recent experiments have been designed to produce chondrule textures via flash melting while simultaneously studying the nature of chondrule precursors. However, these experiments have only been concerned with silicate starting material. This is a preliminary report concerning what effects elemental carbon, when added to the silicate starting material, has on the origin of chondrules produced by flash melting