An elementary model for fast detonations in tubular charges

The paper is concerned with the experimentally known phenomenon that the detonation velocity of a tubular charge may markedly exceed that of a homogeneous charge of the same explosive. It is shown that the effect may be successfully reproduced using a simple quasi-one-dimensional two-layer model assuming the gas–solid system to be isothermal and the volumetric fraction of the solid phase to be small. In view of a considerable drop of the burned gas pressure/density, compared to the Chapman–Jouguet case, fast detonation may be perceived as a variety of weak (undercompressed) detonation.     

The splash/non-splash boundary upon a dry surface and thin fluid film

On the basis of empirical data, power-law boundary relations are formulated to delineate the splash and non-splash regions on dry surfaces or thin films under isothermal conditions, using the Ohnesorge and Reynolds numbers. Approximation of the relations permits cancellation of fundamental fluid physical constants to give simplified formulas which provide insight into the governing parameters describing splashing and non-splashing behaviors. Thus, for a droplet impinging upon a dry solid surface, the splash/non-splash border is well described by √Ca = 0.35. For a drop impinging upon a thin fluid film, the analytical simplification yields a boundary described by √We = 20. For both expressions, values greater than the numerical value result in splashing.     

Chord length distributions in binary stochastic media in two and three dimensions

Simple models for transport through stochastic media usually assume that the chord lengths of materials are distributed exponentially. Theory predicts that, in a medium consisting of disks/spheres that can interpenetrate, chord lengths in the background material (between the disks/spheres) should exactly follow an exponential. In a medium with impenetrable (non-overlapping) disks/spheres, the distribution is only approximately exponential. This paper demonstrates, through direct numerical simulations, that for randomly distributed disks in 2D and spheres in 3D, with distributions of radii, chord lengths in the background material (between the disks/spheres) are accurately described by exponentials over five orders of magnitude when the material is dilute. The chord lengths inside the disks and spheres are not exponentially distributed, but those distributions can be calculated. A scaling relationship between the mean chord lengths in the two materials is presented for an infinite medium. By knowing the mean properties of the disks/spheres in a medium, this relationship allows one to accurately describe the statistical properties of the background material. The stochastic simulations are validated by this infinite medium relationship. When the fraction of space occupied by the disks or spheres becomes large, the distributions are no longer accurately described by an exponential.     

Infrared negative luminescent devices and higher operating temperature detectors

Infrared LEDs and negative luminescent devices, where less light is emitted than in equilibrium, have been attracting an increasing amount of interest recently. They have a variety of applications, including as a ‘source’ of IR radiation for gas sensing; radiation shielding for, and non-uniformity correction of, high sensitivity staring infrared detectors; and dynamic infrared scene projection. Similarly, infrared (IR) detectors are used in arrays for thermal imaging and, discretely, in applications such as gas sensing. Multi-layer heterostructure epitaxy enables the growth of both types of device using designs in which the electronic processes can be precisely controlled and techniques such as carrier exclusion and extraction can be implemented. This enables detectors to be made which offer good performance at higher than normal operating temperatures, and efficient negative luminescent devices to be made which simulate a range of effective temperatures whilst operating uncooled. In both cases, however, additional performance benefits can be achieved by integrating optical concentrators around the diodes to reduce the volume of semiconductor material, and so minimise the thermally activated generation-recombination processes which compete with radiative mechanisms. The integrated concentrators are in the form of Winston cones, which can be formed using an iterative dry etch process involving methane/hydrogen and oxygen. We present results on negative luminescence in the mid- and long-IR wavebands, from devices made from indium antimonide and mercury cadmium telluride, where the aim is sizes greater than 1 cm×1 cm. We also discuss progress on, and the potential for, operating temperature and/or sensitivity improvement of detectors, where very high-performance imaging is anticipated from systems which require no mechanical cooling.     

On approximation of amenable groups by finite quasigroups

We give an amenability criterion for groups in terms of their approximation by finite quasigroups. Bibliography: 20 titles. Dedicated to A. M. Vershik __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 326, 2005, pp. 48–58.     

Hamiltonian properties of triangular grid graphs

A triangular grid graph is a finite induced subgraph of the infinite graph associated with the two-dimensional triangular grid. In 2000, Reay and Zamfirescu showed that all 2-connected, linearly-convex triangular grid graphs (with the exception of one of them) are hamiltonian. The only exception is a graph D which is the linearly-convex hull of the Star of David. We extend this result to a wider class of locally connected triangular grid graphs. Namely, we prove that all connected, locally connected triangular grid graphs (with the same exception of graph D) are hamiltonian. Moreover, we present a sufficient condition for a connected graph to be fully cycle extendable. We also show that the problem Hamiltonian Cycle is NP-complete for triangular grid graphs.     

Grey radiative transfer in binary statistical media with material temperature coupling: asymptotic limits

Simplified models for the unconditional ensemble-averaged radiation intensity and material energy are developed for radiative transfer in binary statistical media. Asymptotic analysis is used to construct an effective transport model with homogenized opacities in two limits. In the first, the material properties are assumed to have low contrast on average, and is shown to correctly reproduce the well-known atomic mix model in both time-dependent and equilibrium situations. Our analysis successfully resolves an inconsistency previously noted in the literature with the application of the standard definition of the atomic mix limit to radiative transfer in participating random media. In the second limit considered, the materials are assumed to have highly contrasting opacities, yielding a reduced transport model with effective scattering. The existence of these limits requires the mean chunk sizes to be independent of the photon direction and this creates an ambiguity in the interpretation of the models when the underlying stochastic geometry is comprised of alternating one-dimensional slabs. A consistent one-dimensional setting is defined and the asymptotic models are numerically validated over a broad range of physical parameter values.     

Rouquier blocks

This paper investigates the Rouquier blocks of the Hecke algebras of the symmetric groups and the Rouquier blocks of the q-Schur algebras. We first give an algorithm for computing the decomposition numbers of these blocks in the ``abelian defect group case' and then use this algorithm to explicitly compute the decomposition numbers in a Rouquier block. For fields of characteristic zero, or when q=1 these results are known; significantly, our results also hold for fields of positive characteristic with q≠1. We also discuss the Rouquier blocks in the ``non–abelian defect group' case. Finally, we apply these results to show that certain Specht modules are irreducible.