Rigorous Boundary Conditions Research Articles

Self‐consistent numerical model for analyzing thermal layering of liquid mixtures of hydrogen isotopes inside a spherical inertial confinement fusion target

A self‐consistent numerical model has been developed to describe the thermally induced behavior of a liquid layer of hydrogen isotopes inside a spherical inertial confinement fusion (ICF) target and to calculate the far‐field temperature gradient which will sustain a uniform liquid layer. This method is much faster than the trial‐and‐error method previously employed. The governing equations are the equations of continuity, momentum, energy, mass diffusion–convection, and conservation of the individual isotopic species. Ordinary and thermal diffusion equations for the diffusion of fluxes of the species are included. These coupled equations are solved by a finite‐difference method using upwind schemes, variable mesh, and rigorous boundary conditions. The solution methodology unique to the present problem is discussed in detail. In particular, the significance of the surface tension gradient driven flows (also called as Marangoni flows) in forming uniform liquid layers inside ICF targets is demonstrated. Usi...

A novel reactor for large-area epitaxial solar cell materials

Abstract A novel vertical stagnation flow organometallic vapor phase epitaxy reactor was designed and fabricated for the growth of GaAs and AlGaAs for solar cell applications. The reactor had an inverted configuration to eliminate recirculation problems. The susceptor and gas inlet nozzle were closely spaced (about 1 cm) in order to achieve improvements in deposition efficiency, layer uniformity and abruptness of interfaces. A specially designed water-cooled inlet nozzle was used to maintain the nozzle surface at relatively low temperatures under all operating conditions. A computer model was formulated to study the various thermal processes in this reactor. The model used rigorous thermal boundary conditions which included thermal radiation effects. Simulated and experimental nozzle temperatures were compared for different susceptor temperatures, susceptor-nozzle distances, gas flow rates and reactor pressures. The maximum nozzle temperature was about 100 °C, which is sufficiently low to prevent premature decomposition of the reactants on its surface.

Magnetic field distribution in large two-dimensional Josephson junctions

Asymptotic approach to the theory of large ( a \ll \lambda_{J} ) two-dimensional Josephson junction is developed. As a result, the usual dc sine-Gordon equation for the rapidly changing Josephson phase difference φ is reduced to the much more simple hydrodynamic-type equations div\{A(k)\rightarrow{k}\} = 0 , curl \rightarrow{k} = 0 , for the slowly changing wave vector \rightarrow{k} (A is a simple function of k ). The reduced equations are applied for analysis of a square-shaped Josephson junction and are solved using the rigorous boundary conditions. The obtained dependence of the junction critical current on the applied magnetic field is discussed and compared with the recent experimental data.

The thermodynamic driving force in mutual diffusion of hard spheres

The derivation of mutual translational diffusion coefficients from irreversible thermodynamics is shown to be ambiguous. The rather different results of Batchelor on the one hand and Berne and Pecora on the other follow from fundamentally different assumptions regarding the thermodynamic driving force that exactly balances the actual hydrodynamic friction force on the solute. The thermodynamic driving force of Batchelor (Vμ2)T,p/(1 - φ2), which was obtained by a generalization of Einstein's argument, is favored by recent experimental data on a model hard sphere system. It is argued that the driving force in N-particle statistical thermodynamic theories should likewise contain a factor of (1 - φ2)−1, which has not previously been applied. Incorporation of such a factor would exactly cancel the backflow correction factor (1 - φ2) suggested by Phillies (to maintain zero volume flux). Thus, the completely uncorrected N-particle theories should converge to Batchelor's result with increasingly accurate treatment of the hydrodynamic interactions, as is found to be the case, due to cancelling errors of omission. The constraint of zero velocity of approach at contact, which is predicted to hold for a rigorous stick boundary condition for the solvent fluid on a smooth hard spherical solute surface, is not obeyed by the experimental model system, and would not be expected to hold for that particular surface in any case.

Optics of Polaritons in Bounded Media

Using a simple polarization picture of a medium in which there is spatial dispersion and using the integral equation method of Ewald-Oseen, some rigorous results are obtained for the optics of a bounded spatially dispersive medium. In particular, an extinction theorem for polaritons, and rigorous additional boundary conditions are obtained. The normal-incidence propagation of transverse modes for an isotropic crystal bounded by a plane is analyzed. The rigorous boundary conditions obtained by this method, in general, do not agree with other popular choices, based upon the same constitutive relations.

Buckling of clamped oval cylindrical shells under axial loads

Abstract : The effect of clamped boundary conditions on the elastic buckling of finite, oval cylindrical shells under axial compression is investigated. In the development of the problem, a rather accurate representation of the prebuckling state is employed. The rigorous boundary conditions are enforced on both the prebuckling and buckling solutions. The stability equations are solved by the Fourier method in conjunction with the use of a higher order difference technique. Noticeable deviations between the results of the present analysis and those established for infinitely long shells were observed, particularly for moderate-to-large out-of-roundness. (Author)

High injection theories of the p− n junction in the charge neutrality approximation

Abstract A survey is presented of the basic equations underlying the transport in p−n junctions and transistors, with particular emphasis on the restrictions under which various approximate relations are valid. The ambipolar aspect of the equations for all injection levels is stressed. The most general recombination processes have been considered and are incorporated in the analysis. Boundary conditions have been derived in terms of the junction voltage and in terms of the externally applied voltage, accounting for the voltage drops in the bulk region. It is shown that the “p−n product method” as applied in the usual way, in which the difference of the quasi-Fermi levels is equated to the junction voltage, is incorrect, and violates normal semiconductor relationships. To derive variational boundary conditions valid for a.c. applications, the complete d.c. expressions as given by F letcher must be considered. The d.c. problem is solved for all injection levels taking into account the decrease in emitter efficiency with applied voltage, the voltage drop in the bulk regions and more rigorous boundary conditions than employed hitherto. The problems associated with an analytic solution to the a.c. admittance of a p−n junction operating under moderately high injection levels are discussed and the impossibility of a solution in terms of known functions is indicated. For high injection, frequency dependent boundary conditions in terms of the applied voltage are derived and a closed form solution for the high frequency admittance is established.