Rarefied Flow Computations Using Nonlinear Model Boltzmann Equations

High resolution finite difference schemes for solving the nonlinear model Boltzmann equations are presented for the computations of rarefied gas flows. The discrete ordinate method is first applied to remove the velocity space dependency of the distribution function which renders the model Boltzmann equation in phase space to a set of hyperbolic conservation laws with source terms in physical space. Then a high order essentially nonoscillatory method due to Harten et al. (J. Comput. Phys. 71, 231, 1987) is adapted and extended to solve them. Explicit methods using operator splitting and implicit methods using the lower-upper factorization are described to treat multidimensional problems. The methods are tested for both steady and unsteady rarefied gas flows to illustrate its potential use. The computed results using model Boltzmann equations are found to compare well both with those using the direct simulation Monte Carlo results in the transitional regime flows and those with the continuum Navier-Stokes calculations in near continuum regime flows.     

Anisotropic transport of charge and complexified duality

Charge transport in two dimensions provides an ideal laboratory for investigating parameter space geometries. The Onsager relations for anisotropic transport in a parity-violating external field endow these spaces with a highly nontrivial complex (and Kähler) structure, which can be given a simple geometrical interpretation. A large class of Coulomb gases exhibiting this structure have a generalized Kramers-Wannier symmetry (complexfield duality) which is contained in the modular group. Knowledge of this symmetry and the degrees of freedom encoded in the Coulomb gas appear to be sufficient to determine the global phase diagram and the renormalization group fixed-point structure, including the critical exponents. This accounts for all the scaling behavior observed so far in the quantum Hall system.     

Study of the gas-phase parameters affecting the silicon-oxide film deposition induced by an ArF laser

A study of the gas-phase parameters involved in ArF laser induced chemical vapour deposition of silicon-oxide thin films is presented. A complete set of experiments has been performed showing the influence of the concentration of the precursor gases, N₂O and SiH₄, and their influence on total and partial pressures on film growth and properties. In this paper we demonstrate the ability of this LCVD method to deposit silicon oxide films of different compositions and densities by appropriate control of gas composition and total pressure. Moreover, a material specific calibration plot comprising data obtained using different preparation techniques is presented, allowing determination of the stoichiometry of SiO _x films by using FTIR spectroscopy independently of the deposition method. For the range of processing conditions examined, the experimental results suggest that chemical processes governing deposition take place mainly in the gas phase.     

Optical detection of NO3 and NO2 in “pure” HNO3 vapor,the liquid-phase decomposition of HNO3

Flowing and static gas-phase samples of HNO₃ in O₂ and N₂ were analyzed by long-path ultraviolet/visible (UV/VIS) spectroscopy to reveal the presence of both NO₂ and NO₃, the concentrations of which were calculated using differential absorption cross sections. NO₂ is produced predominantly by the heterogeneous decomposition of HNO₃, whereas NO₃ is generated in the gas phase by the thermal decomposition of N₂O₅, a product of the self-disproportionation of liquid HNO₃. © 1993 John Wiley & Sons, Inc.     

Boundary-value problems for an elliptic equation with complex coefficients and a certain moment problem

Elliptic systems of two second-order equations, which can be written as a single equation with complex coefficients and a homogeneous operator, are studied. The necessary and sufficient conditions for the connection of traces of a solution are obtained for an arbitrary bounded domain with a smooth boundary. These conditions are formulated in the form of a certain moment problem on the boundary of a domain; they are applied to the study of boundary-value problems. In particular, it is shown that the Dirichlet problem and the Neumann problem are solvable only together. In the case where the domain is a disk, the indicated moment problem is solved together with the Dirichlet problem and the Neumann problem. The third boundary-value problem in a disk is also investigated.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 11, pp. 1476–1483, November, 1993.     

Relativistic quantum defect calculations on the copper isoelectronic sequence

The quantum defect orbital (QDO ) method and its relativistic (RQDO ) counterpart have been employed in this work to compute oscillator strengths for several fine-structure transitions in members of the copper isoelectronic sequence up to Z = 92. The RQDO results are found to be in quite good agreement with the best estimates derived from other sources, whenever the comparison is possible. © 1994 John Wiley & Sons, Inc.