Bulk viscosity damping for accelerating convergence of low Mach number Euler solvers

In solution of the Euler equations in the steady state external flows, error or residual waves are blamed for decelerating the convergence. These waves may be damped by adding a bulk viscosity term to the momentum equations. We analyse effects of this term on the linearized differential equations, and study its explicit and implicit implementation in one and two space dimensions. Optimum values of the bulk viscosity damping (BVD) are discussed. After generalization to two space dimensions, its performance both alone and in combination with a soft wall boundary condition and residual smoothing in central differencing codes is reviewed. It is shown that BVD is complementary to them, and acts independently of them. Finally, application of BVD in solution of low Mach number flows is considered, to show how it can strongly stabilize and accelerate these low Mach number computations. Copyright © 2003 John Wiley & Sons, Ltd.     

On non-inflectional solutions of non-uniform elasticae

We study buckled states of non-uniform elasticae and show that solutions having pairs of loops not separated by inflection points appear if and only if there is an (isolated) minimum in the bending stiffness. Such solutions lie on branches disconnected from the trivial solution in the global bifurcation diagram and so we obtain partial information regarding the qualitative structure of the latter.     

Proof of the ionization conjecture in a reduced Hartree-Fock model

Summary The ionization conjecture for atomic models states that the ionization energy and maximal excess charge are bounded by constants independent of the nuclear charge. We prove this for the Hartree-Fock model without the exchange term.Oblatum 3-V-1990Work supported in part by the U.S. National Science Foundation grant DMS-9002416     

Anomalous change in the photoacoustic phase near superconducting transition in YBa2Cu3O7

Photoacoustic amplitude and phase measurements have been carried out near the superconducting transition temperature in the highT _csuperconductor YBa₂Cu₃O₇. In both the samples investigated, the photoacoustic phase undergoes an anomalous step-like decrease aroundT _c≈ 96 K and increases at lower temperatures. A clear temperature hysteresis for the phase change has been noticed. No anomalous variation has been observed in the amplitude values. Neither phase nor amplitude shows any anomaly in a non-superconducting sample of the same composition.     

Evolution of a quasi-neutral shock wave in inhomogeneous semiconductors

It is shown that in a current carrying extrinsic semiconductor, a quasi-neutral wave of carrier concentrations evolves into a shock wave(s). Inhomogeneous distribution of impurities causes either amplification (an absolute instability) or depression of these waves.     

Pyridazines. XLI synthesis of novel pyrido[3,4-d]pyridazine derivatives from 4,5-disubstituted pyridazines

Pyrido[3,4-d]pyridazines 2–5, 21 bearing one, two, or three aryl substituents in the pyridine moiety are shown to be conveniently accessible from 4-aroyl-5-methylpyridazines or 4,5-diaroylpyridazines, respectively, by condensation reactions with appropriate C-N fragments. In addition, the novel pyridazine-annelated pyridones 24, 25 were found to be easily available from ethyl 5-methyl-4-pyridazinecarboxylate.     

Path integrals for the continuous spontaneous localization theory

Path integral expressions are given for the wave function and for the density matrix in a theory which describes state vector reduction. The magnitude of the contribution of each classical path to the propagator is not unity, as in ordinary quantum theory, but depends upon the path.