Exact Solutions of the Space Charge Equation Using the Hodograph Method

In this paper we show that a hodograph method first introducedby Budd & Wheeler (1987) to develop a new numerical algorithmto solve the space charge equation •()=0 can be employedto derive all the known exact solutions, which have recentlybeen found by Smith (1988). All these solutions are shown tobe separable solutions of the equations resulting from the applicationof the hodograph transformation. We also briefly describe thisnew numerical method and use one of the exact solutions to demonstrateits accuracy.     

Linear fractional composition operators on H2

If ? is an analytic function mapping the unit diskD into itself, the composition operatorC _? is the operator onH ² given byC _?f=fo?. The structure of the composition operatorC _? is usually complex, even if the function ? is fairly simple. In this paper, we consider composition operators whose symbol ? is a linear fractional transformation mapping the disk into itself. That is, we will assume throughout that $$\varphi \left( z \right) = \frac{{az + b}}{{cz + d}}$$ for some complex numbersa, b, c, d such that ? maps the unit diskD into itself. For this restricted class of examples, we address some of the basic questions of interest to operator theorists, including the computation of the adjoint.     

A method to account for acoustic microstreaming when predicting bubble growth rates produced by rectified diffusion

A reinterpretation of existing theory for rectified diffusion, the process by which bubbles in a sound field may grow in radius, is presented in order to quantitate the effect of acoustic microstreaming on bubble growth rates. The 1/t term in the growth rate equation is defined as the "decay term" and t as the "decay time," the time required for the gas concentration in the liquid contacting the bubble to rise (or fall) from its initial to its final value. In the absence of microstreaming, t is the duration of sonification. In the presence of microstreaming, t may be calculated from the streaming velocity and the bubble radius. A comparison between theory and the experimental results of Eller [A. Eller, J. Acoust. Soc. Am. 46, 1246-1250 (1969)] and of Gould [R.K. Gould, J. Acoust. Soc. Am. 56, 1740-1746 (1974)] shows reasonable agreement in the low kHz range. Theoretical results in the frequency range of 1-10 MHz at 1 and 4 bar are also presented.     

Does iron inhibit cryptoendolithic microbial communities?

Photosynthetic activity of three cryptoendolithic microbial communities was studied under controlled conditions in the laboratory. In two of these communities, the dominant organisms were lichens, collected from Linnaeus Terrace and from Battleship Promontory. The third community, dominated by cyanobacteria, was collected from Battleship Promontory. Both sites are in the ice-free valleys of southern Victoria Land. Previous efforts have shown how physical conditions can influence metabolic activity in endolithic communities (Kappen and Friedmann 1983; Kappen, Friedmann, and Garty 1981; Vestal, Federle, and Friedmann 1984). Biological activity can also be strongly influenced by the chemical environment. Inorganic nutrients such as nitrate, ammonia, and phosphate are often limiting factors, so their effects on photosynthetic carbon-14 bicarbonate incorporation were investigated. Iron and manganese are two metals present in Linnaeus Terrace and Battleship Promontory sandstones, and their effects on photosynthesis were also studied. The results may add to our understanding of biogeochemical interactions within this unique microbial community.     

An intermediate phase with slow decay of correlations in one dimensional 1/|x−y|2 percolation,Ising and Potts models

We rigorously establish the existence of an intermediate ordered phase in one-dimensional 1/|x–y|² percolation, Ising and Potts models. The Ising model truncated two-point function has a power law decay exponent which ranges from its low (and high) temperature value of two down to zero as the inverse temperature and nearest neighbor coupling vary. Similar results are obtained for percolation and Potts models.Alfred P. Sloan Research Fellow. Research supported in part by NSF Grants No. PHY-8706420 and PHY-8645122Research supported in part by NSF Grant No. DMS-8514834 and AFOSR Contract F49620-86-C0130 at the Arizona Center for Math. Sciences     

Analyticity properties of the surface free energy of the Ising model

For an Ising ferromagnet with nearest-neighbour interactions of strengthK and surface magnetic fieldh, the surface free energy in the presence of a positively (or negatively) magnetized zero-field bulk phase is shown to be analytic inh for Reh<K–/, where =2.96 ... and is the inverse temperature. This puts the lower boundK–/ on the values ofh at which wetting and layering transitions can take place.     

Sensitivity of hydrodynamic system of the Obukhov type

The paper deals with the regime of advanced Bénard instabilities (described usually by the Lorenz system) in a more general system formulated firstly by Obukhov. It has been shown that triplet co-operation leads to characteristic courses where some new regularities occur.     

Influence of metastable-metastable collisions on electron distribution function in afterglow

The time dependence of the electron distribution function in helium afterglow, for pressures of 60–260 Pa, is calculated for the case in which metastable-metastable reactions are present. The time variation of the shape of the distribution function shows that careful consideration must be made of the time derivative of the distribution function in the Boltzmann equation for the calculation of the rate constant of such reactions from experimentally determined distribution function.     

Softening during and after the hot deformation of the AISI 321 steel with respect to practical applications

The softening processes during and after the hot deformation (850–1180 C) in AISI 321 stainless steel were studied with respect to true strains _D and true strain rates . The analysis of deformation curves indicates the occurrence of dynamic recrystallization for values of Zener-Hollomon parameterZ10¹⁵ s^–1. The retardation of static recrystallization by fine Ti(N, C) precipitates is documented by microstructure studies and by variations of annealing conditions.     

Proton-proton correlations at small relative momentum in neon-nucleus collisions at E/A=400 and 800 MeV

Proton-proton small angle correlations have been measured in neon-nucleus collisions, using the 4 pi detector Diogene, at 400 and 800 MeV per nucleon incident energies. Values of the size of the emitting region are obtained by comparison with the Koonin formula, taking into account the biases of the apparatus. The dependence of the density on target mass and incident energy is also analysed.