Some results on the stability and dynamics of finite difference approximations to nonlinear partial differential equations

A miscellany of results on the nonlinear instability and dynamics of finite difference discretizations of the Burgers and Kortweg de Vries equations is obtained using a variety of phase-plane, functional analytic, and regularity methods. For the semidiscrete (space-discrete, time-continuous) schemes, large-wave-numer instabilities occurring in special exact solutions are investigated, and parameter values for which the semidiscrete scheme is monotone are considered. For fully discrete schemes (space and time discrete), large-wave-number instabilities introduced by various time-stepping schemes such as forward Euler, leapfrog, and Runge–Kutta schemes are analyzed. Also, a time step restriction for the monotonicity of the forward-Euler time-stepping scheme, and regularity of a 4-stage monotone/conservative Runge–Kutta time stepping are investigated. The techniques used here may be employed, in conjunction with bifurcation-theoretic and weakly nonlinear analyses, to analyze the stability of numerical schemes for other nonlinear partial differential equations of both dissipative and dispersive varieties. © 1993 John Wiley & Sons, Inc.     

Influence of alloy composition on the diffusivity-mobility ratio in n-channel inversion layers on ternary semiconductors

An expression is derived for the diffusivity-mobility ratio of the carriers in n-channel inversion layers on semiconductors like the ternary compounds which have strongly non-parabolic energy bands. The dependence of the ratio on alloy composition is also studied under the weak-field limit taking n-channel Hg_1–xCd_x.Te as an example.On leave of absence fromthe Department of Physics, Patna University, Patna, India.     

The soft bremsstrahlung structure function

Low's theorem is used to express the soft-photon structure function in terms of the single- and double-charged particle structure functions. With the simplifying assumption that asymptotically the hadronic particles cluster (in the c.m. frame) in sharp forward and backward cones, we obtain a simple explicit form for this soft bremsstrahlung structure function. The question of scaling is discussed.     

Synthesis of 2,2-dimethyl-5-hydroxy-3-(3-oxobutyl)-7-pentyl-4-chromone

Alkylation and deformylation of 2,2-dimethyl-3-hydroxymethylene-5-hydroxy-7-pentyl-4-chromone occurs in the same step to give the title compound.     

Medium-dependent electron and H atom transfer between 2'-deoxyadenosine and menadione: a magnetic field effect study

The interaction between 2'-deoxyadenosine and the model antitumor drug menadione has been studied in organic solvent and in micellar medium. The aim of the work is to elucidate the mechanism of this drug-nucleoside interaction and to determine the environmental effects. Laser flash photolysis and magnetic field effect are used to detect the transients and their spin states. The results indicate that H atom transfer and electron transfer are the operative mechanisms depending upon the medium.     

Microwave–assisted synthesis of <Emphasis Type="Italic">submicrometer</Emphasis> GaO(OH) and Ga<Subscript>2</Subscript>O<Subscript>3</Subscript> rods

Submicrometer sized gallium oxide hydroxide (GaO(OH)) and gallium oxide (Ga₂O₃) rods have been successfully fabricated on a large scale by refluxing an aqueous solution of Ga(NO₃)₃ and NH₄OH in a simple domestic microwave oven (DMO). The structures, morphologies, compositions and physical properties of the as–synthesized and calcined products have been characterized by powder X-ray diffraction (XRD), transmission electron microscopy (TEM), selected area electron diffraction (SAED), selected area energy dispersive X-ray spectroscopy (SAEDS), thermo gravimetric analysis (TGA), differential scanning calorimetry (DSC), and energy dispersive X-ray (EDX) analysis. TEM images show that submicrometer sized as–synthesized Ga O(OH) rods have diameters of 0.3–0.5 m and lengths of 3.2–3.5 m. The calcined product consists of submicrometer rods with diameters of 0.4–0.5 m and lengths of 5–5.5 m. XRD, EDX and SAED analysis together indicate that the as–synthesized product has an orthorhombic gallium oxide hydroxide (GaO(OH)) crystal structure, and that the calcined product is rhombohedral Ga₂O₃. A possible mechanism for the formation of submicrometer sized GaO(OH) rods is discussed briefly.     

Measurement of nonrandom event-by-event fluctuations of average transverse momentum in square root of (sNN)=200 GeV Au+Au and p+p collisions

Event-by-event fluctuations of the average transverse momentum of produced particles near midrapidity have been measured by the PHENIX Collaboration in square root of (sNN)=200 GeV Au+Au, and p+p collisions at the Relativistic Heavy Ion Collider. The fluctuations are observed to be in excess of the expectation for statistically independent particle emission for all centralities. The excess fluctuations exhibit a dependence on both the centrality of the collision and on the pT range over which the average is calculated. Both the centrality and pT dependence can be well reproduced by a simulation of random particle production with the addition of contributions from hard-scattering processes.     

Atomic force algorithms in density functional theory electronic-structure techniques based on local orbitals

Electronic structure methods based on density-functional theory, pseudopotentials, and local-orbital basis sets offer a hierarchy of techniques for modeling complex condensed-matter systems with a wide range of precisions and computational speeds. We analyze the relationships between the algorithms for atomic forces in this hierarchy of techniques, going from empirical tight-binding through ab initio tight-binding to full ab initio. The analysis gives a unified overview of the force algorithms as applied within techniques based either on diagonalization or on linear-scaling approaches. The use of these force algorithms is illustrated by practical calculations with the CONQUEST code, in which different techniques in the hierarchy are applied in a concerted manner.