Shock wave diffraction over a 90 degree sharp corner — Posters presented at 18th ISSW

A special poster session was run during the 18th International Symposium on Shock Waves, held on July 21 – 26, 1991, in Sendai, Japan. The purpose of this session was to compare various CFD schemes which are useful for simulating shock wave phenomena. A 2-D planar shock wave diffraction over a 90 degree sharp corner was selected as a bench mark problem. The problem specification and the output format are described below. Experimental outputs for the close flow conditions to the computational ones were also called for. Twenty six poster presentations were made at this session and the majority of the posters reflected a standard of excellence that warrants publication in the Shock Waves journal. Therefore these results are reproduced here. However, since there is a limit on the available page numbers, it was not possible to publish all the posters that were presented at the special poster session. We express our sincere thanks to all the participants in this session.     

A preconditioned domain decomposition algorithm for the solution of the elliptic Neumann problem

A new preconditioned conjugate gradient (PCG)-based domain decomposition method is given for the solution of linear equations arising in the finite element method applied to the elliptic Neumann problem. The novelty of the proposed method is in the recommended preconditioner which is constructed by using cyclic matrix. The resulting preconditioned algorithms are well suited to parallel computation.     

Dislocation unpinning model of acoustic emission from alkali halide crystals

The present paper reports the dislocation unpinning model of acoustic emission (AE) from alkali halide crystals. Equations are derived for the strain dependence of the transient AE pulse rate, peak value of the AE pulse rate and the total number of AE pulse emitted. It is found that the AE pulse rate should be maximum for a particular strain of the crystals. The peak value of the AE pulse rate should depend on the volume and strain rate of the crystals, and also on the pinning time of dislocations. Since the pinning time of dislocations decreases with increasing strain rate, the AE pulse rate should be weakly dependent on the strain rate of the crystals. The total number of AE should increase linearly with deformation and then it should attain a saturation value for the large deformation. By measuring the strain dependence of the AE pulse rate at a fixed strain rate, the time constantτ _s for surface annihilation of dislocations and the pinning timeτ _p of the dislocations can be determined. A good agreement is found between the theoretical and experimental results related to the AE from alkali halide crystals.     

Photoreflectance investigations of AlGaN/GaN heterostructures with a two dimensional electron gas

Undoped AlGaN/GaN heterostructures with different content and thickness of AlGaN layer are investigated by photoreflectance (PR) spectroscopy. We have observed PR resonances related to an absorption in both GaN and AlGaN layers. The character of these resonances has been analyzed, and PR lines associated with excitonic and band-to-band absorption in the GaN layer and band-to-band absorption in the AlGaN layer have been identified. The transition related to band-to-band absorption possesses characteristic Franz–Keldysh oscillations (FKOs) associated with a built-in electric field. The electric field in the AlGaN layer obtained on the basis of the analysis of FKOs has been found to be in the range of 244–341 kV/cm. The value of the field has been found to decrease with the increase in AlGaN thickness and to increase with the increase in Al concentration. The surface potential for AlGaN layers has been found to increase with the increase in Al mole fraction and has been estimated to be in the range of 1.0–1.7 eV.     

Fluctuations of an Evaporating Black Hole from Back Reaction of Its Hawking Radiation: Questioning a Premise in Earlier Work

This paper delineates the first steps in a systematic quantitative study of the spacetime fluctuations induced by quantum fields in an evaporating black hole. We explain how the stochastic gravity formalism can be a useful tool for that purpose within a low-energy effective field theory approach to quantum gravity. As an explicit example we apply it to the study of the spherically-symmetric sector of metric perturbations around an evaporating black hole background geometry. For macroscopic black holes we find that those fluctuations grow and eventually become important when considering sufficiently long periods of time (of the order of the evaporation time), but well before the Planckian regime is reached. In addition, the assumption of a simple correlation between the fluctuations of the energy flux crossing the horizon and far from it, which was made in earlier work on spherically-symmetric induced fluctuations, is carefully analyzed and found to be invalid. Our analysis suggests the existence of an infinite amplitude for the fluctuations of the horizon as a three-dimensional hypersurface. We emphasize the need for understanding and designing operational ways of probing quantum metric fluctuations near the horizon and extracting physically meaningful information. Dedicated to Rafael Sorkin on the occasion of his 60th birthday.     

Synthesis of 5-azaadenine derivatives from N-(1,2,4-triazol-5-yl)amidines

A method is proposed for the synthesis of N-substituted 5-azaadenines. The condensation of N-(1,2,4-triazol-5-yl)amidines with trichloroacetonitrile gives trichloromethyl derivatives of 1,2,4-triazolo[1,5-a]-1,3,5-triazines, which are converted by the action of primary or secondary amines into N-alkylamino- or N,N-dialkylamino-1,2,4-triazolo-[1,5-a]-1,3,5-triazines (5-azaadenines).Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 1, pp. 241–243, January, 1991.     

Asymptotics of Dirichlet Spectrum on Some Class of Noncompact Domains

We investigate the asymptotic behaviour of the counting function of Dirichlet eigenvalues on some class of noncompact manifolds. We prove that in cases when the volume or the perimeter (the volume of the boundary) of the manifold is infinite, some additional (nonclassical) terms appear in the precise asymptotics. The coefficients at the classical terms in those are regularized in some special way volume (resp. perimeter) of the manifold.     

Note on a conjecture of toft

A conjecture of Toft [17] asserts that any 4-critical graph (or equivalently, every 4-chromatic graph) contains a fully odd subdivision ofK ₄. We show that if a graphG has a degree three nodev such thatG-v is 3-colourable, then eitherG is 3-colourable or it contains a fully oddK ₄. This resolves Toft's conjecture in the special case where a 4-critical graph has a degree three node, which is in turn used to prove the conjecture for line-graphs. The proof is constructive and yields a polynomial algorithm which given a 3-degenerate graph either finds a 3-colouring or exhibits a subgraph that is a fully odd subdivision ofK ₄. (A graph is 3-degenerate if every subgraph has some node of degree at most three.)