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Etalon boundary-value problem technique for three-dimensional diffraction problems

ELECTROMAGNETICS 2000年第1期20卷 55-63页

作者： Bass, FG Slepyan, AY Slepyan, GY Bar Ilan Univ Dept Phys IL-52900 Ramat Gan Israel

The etalon boundary-value problem technique for approximately solving three-dimensional diffraction problems has been suggested. On etalon boundary-value problems, we use two-dimensional problems which are capable of exact solutions (for example, by the Wiener-Hopf technique). The field sought along one of the coordinate axes is taken to be locally coincident with that in the corresponding etalon problem. The amplitude coefficient (constant for the etalon problem) is assumed to be varying and is determined by substituting the above-mentioned solution representation into wave equations. Applications of the approach developed for the problem of electromagnetic-wave coastal refraction for a coast with a curved (random) coastal line and for the problem of wave diffraction by a perfectly conducting half-plane with a curvilinear edge have been considered.

关键词： boundary value problems -- numerical solutions OPTICAL diffraction ELECTROMAGNETIC wave scattering

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Analysis of a Galerkin finite element method on a Bakhvalov-Shishkin mesh for a linear convection-diffusion problem

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IMA JOURNAL OF numerical ANALYSIS 2000年第4期20卷 621-632页

作者： Linss, T Tech Univ Dresden Inst Numer Math D-01062 Dresden Germany

We consider a Galerkin finite element method that uses piecewise bilinears on a modified Shishkin mesh for a model singularly perturbed convection-diffusion problem on the unit square. The method is shown to be convergent, uniformly in the perturbation parameter epsilon, of order N-1 in a global energy norm, provided only that epsilon less than or equal to N-1, where O(N-2) mesh points are used. Thus on the new mesh the method yields more accurate results than on Shishkin's original piecewise uniform mesh, where it is convergent of order N-1 In N. numerical experiments support our theoretical results.

关键词： FINITE element method GALERKIN methods boundary value problems -- numerical solutions PERTURBATION (Mathematics) STOCHASTIC convergence

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FRICTION FACTOR CORRELATIONS FOR COMPRESSIBLE GASEOUS FLOW IN A CONCENTRIC MICRO ANNULAR TUBE

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numerical HEAT TRANSFER PART A-APPLICATIONS 2012年第3期61卷 163-179页

作者： Hong, Chungpyo Asako, Yutaka Suzuki, Koichi Faghri, Mohammad Tokyo Univ Sci Dept Mech Engn Noda Chiba 2788510 Japan Tokyo Metropolitan Univ Dept Mech Engn Tokyo 158 Japan Univ Rhode Isl Dept Mech Ind & Syst Engn Kingston RI 02881 USA

Compressible momentum and energy equations were solved numerically for concentric micro annular tubes with slip velocity and temperature jump wall boundary conditions. The results were expressed in the form of the product of friction factor and Reynolds number (***) for a quasi-fully developed condition and for the ranges of Re < 1000 and Ma < 1. The numerical methodology was based on the Arbitrary-Lagrangian-Eulerian (ALE) method. The outer tube radius ranged from 5 to 40 mu m with radius ratios of 0.2, 0.5, and 0.8. The length to hydraulic diameter ratio was more than 100. The stagnation pressure was chosen in such a way that the exit Mach number ranged from 0.1 to 1.0, and the outlet pressure was fixed at the atmospheric pressure. For the case of incompressible slip flow, *** is calculated as a function of radius ratio and Knudsen number. For high speed flows, the values of *** for compressible slip flow were higher than those for incompressible slip flow due to compressibility effects. Also, *** correlation for compressible slip flow was obtained from compressible no-slip flow and incompressible slip flow as a function of Mach and Knudsen numbers and radius ratio. In addition, a correlation for microchannel, microtube, and micro annular tube was obtained from the authors' previous work.

关键词： boundary value problems -- numerical solutions FRICTION GAS flow TUBES TEMPERATURE effect RAYLEIGH number ATMOSPHERIC pressure COMPRESSIBILITY MOMENTUM (Mechanics)

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Rovibronic bands of the (A)over-tilde←(X)over-tilde transition of CH₃OO and CD₃OO detected with cavity ringdown absorption near 1.2-1.4 μm

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JOURNAL OF CHEMICAL PHYSICS 2007年第4期127卷 044311-044311页

作者： Chung, Chao-Yu Cheng, Chi-Wen Lee, Yuan-Pern Liao, Hsin-Yi Sharp, Erin N. Rupper, Patrick Miller, Terry A. Natl Chiao Tung Univ Dept Appl Chem Hsinchu 30010 Taiwan Acad Sinica Inst Atom & Mol Sci Taipei 10617 Taiwan Natl Taipei Univ Educ Dept Sci Educ Taipei 10659 Taiwan Ohio State Univ Dept Chem Laser Spect Facil Columbus OH 43210 USA

We have recorded several rovibronic bands of CH3OO and CD3OO in their (A) over tilde <-(K) over tilde transitions in the range of 1.18-1.40 mu m with the cavity ringdown technique. While the electronic origins for these species have been reported previously, many newly observed rovibronic bands are described here. The experimental vibrational frequencies (given as nu in the unit cm(-1) in this paper) for the COO bending (nu(8)) and COO symmetric stretching (nu(7)) modes in the (A) over tilde state are 378 and 887 cm(-1) for CH3OO, and 348 and 824 cm(-1) for CD3OO, respectively. In addition, two other vibrational frequencies were observed for the (A) over tilde state of CD3OO, namely, nu(5) (954 cm(-1)) and nu(6) (971 cm(-1)). These experimental vibrational frequencies for the A state of both CH3OO and CD3OO are in good agreement with predictions from quantum-chemical calculations at the UB3LYP/aug-cc-pVTZ level. The enhanced activity of the nu(5) vibrational mode in CD3OO is rationalized by mode mixing with the nu(7) mode, as supported by calculations of multidimensional Franck-Condon factors. In addition, many hot bands involving the methyl torsional mode (nu(12)) are observed for both normal and deuterated methyl peroxy. These bands include the "typical" sequence transitions and some "atypical" ones due to the nature of the eigenvalues and eigenfunctions which are a consequence of the low, but very different, torsional barriers in the (X) over tilde and (A) over tilde states. In addition, the 12(2)(2) band in CH3OO and the 12(3)(3) band in CD3OO show quite different structures than the origin bands, an effect which results from tunneling splittings comparable to the rotational contour. (C) 2007 American Institute of Physics.

关键词： boundary value problems -- numerical solutions ANGULAR momentum (Nuclear physics) APPROXIMATION theory ELECTRON mobility EIGENvalueS

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On bifurcation of solutions of the Yamabe problem in product manifolds

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ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE 2012年第2期29卷 261-277页

作者： de Lima, L. L. Piccione, P. Zedda, M. Univ Sao Paulo Dept Matemat BR-05508 Sao Paulo Brazil Univ Fed Ceara Dept Matemat Fortaleza Ceara Brazil Univ Cagliari I-09124 Cagliari Italy

We study local rigidity and multiplicity of constant scalar curvature metrics in arbitrary products of compact manifolds. Using (equivariant) bifurcation theory we determine the existence of infinitely many metrics that are accumulation points of pairwise non-homothetic solutions of the Yamabe problem. Using local rigidity and some compactness results for solutions of the Yamabe problem, we also exhibit new examples of conformal classes (with positive Yamabe constant) for which uniqueness holds. (C) 2011 Elsevier Masson SAS. All rights reserved.

关键词： BIFURCATION theory boundary value problems -- numerical solutions MANIFOLDS (Mathematics) MATHEMATICAL constants EXISTENCE theorems COMPACT spaces (Topology)

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Identification of the Cooling Condition in 2-D and 3-D Continuous Casting Processes

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numerical HEAT TRANSFER PART B-FUNDAMENTALS 2009年第2期55卷 155-176页

作者： Slota, Damian Silesian Tech Univ Inst Math PL-44100 Gliwice Poland

In this article, the reconstruction of the function describing the boundary conditions along the primary and secondary cooling zones in the 2-D and 3-D continuous casting processes of pure metal is presented. The process is modeled by the inverse Stefan problem, where additional information consists of temperature measurements at selected points of the domain. In numerical calculations, Tikhonov's regularization, a genetic algorithm, and an alternating phase truncation method are used. The featured examples of calculations show very good approximation of the exact solution. The influence of the number and accuracy of measurements are also investigated.

关键词： CONTINUOUS casting THERMOPHYSICAL properties GENETIC algorithms RESEARCH THERMAL conductivity measurement boundary value problems -- numerical solutions SOLIDIFICATION

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On the Global Relation and the Dirichlet-to-Neumann Correspondence

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STUDIES IN APPLIED MATHEMATICS 2011年第1期126卷 75-102页

作者： Dassios, G. Doschoris, M. Univ Patras Dept Chem Engn Div Appl Math GR-26504 Patras Greece

The recently developed Fokas method for solving two-dimensional boundary value problems (BVP) via the use of global relations is utilized to solve axisymmetric problems in three dimensions. In particular, novel integral representations for the interior and exterior Dirichlet and Neumann problems for the sphere are derived, which recover and improve the already known solutions of these problems. The BVPs considered in this paper can be classically solved using either the finite Legendre transform or the Mellin-sine transform (which can be derived from the classical Mellin transform in a way similar to the way that the sine transform can be derived from the Fourier transform). The Legendre transform representation is uniformly convergent at the boundary, but it involves a series that is not useful for many applications. The Mellin-sine transform involves of course an integral but it is not uniformly convergent at the boundary. In this paper: (a) The Legendre transform representation is rederived in a simpler approach using algebraic manipulations instead of solving ODEs. (b) An integral representation, different that the Mellin-sine transform representation is derived which is uniformly convergent at the boundary. Furthermore, the derivation of the Fokas approach involves only algebraic manipulations, instead of solving an ordinary differential equation.

关键词： NEUMANN problem RELATION algebras DIRICHLET problem boundary value problems -- numerical solutions DIFFERENTIAL equations -- numerical solutions MELLIN transform STOCHASTIC convergence

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numerical Simulation of Ethanol-Water-NaCl Droplet Evaporation

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INDUSTRIAL & ENGINEERING CHEMISTRY RESEARCH 2010年第12期49卷 5631-5643页

作者： Jiang, Xingmao Ward, Timothy L. van Swol, Frank Brinker, C. Jeffrey Univ New Mexico Dept Chem & Nucl Engn Albuquerque NM 87106 USA Univ New Mexico Ctr Microengineered Mat Albuquerque NM 87106 USA Sandia Natl Labs Albuquerque NM 87185 USA

A quantitative description of droplet evaporation is important to aerosol research for nanofabrication, spray drying, fuel combustion, pollution control, and respiratory medical treatments. Evaporation is a moving-boundary problem with coupled mass and heat transport. An explicit finite-difference methodology and computer code has been developed for simulation of an evolving droplet, property data for size, and profiles for various compositions and temperature. The code accurately predicts the evaporation of pure water and pure ethanol droplets. To understand aerosol-assisted evaporation-induced self-assembly and the formation mechanism for single-crystal NaCl core/hexagonally ordered mesoporous silica shell particles, evaporation of ethanol-water-NaCl droplets in N-2 has been investigated by numerical simulation. The extended universal quasichemical (UNIQUAC) model with a Debye-Huckel term is used to describe the vapor liquid phase equilibrium. For 1-2-mu m-radius droplets with a number density of 10(7)similar to 10(8)/cm(3), it takes only tens of milliseconds to reach phase equilibrium after adiabatic or isothermal evaporation at 25 degrees C in the drying zone. The droplets entering a heating zone can be simply treated like a single-stage flash evaporation at 25 C. For a 1-mu um-radius droplet, after 0.18 ms of evaporation at 100 degrees C in N-2, the NaCl saturation ratio reaches levels as high as 1.3, first at the droplet center, where the initial NaCl nucleation and crystallization happens as a result of relatively quick evaporation and a steep gradient in the concentration of ethanol, an antisolvent for NaCl. NaCl crystallization "consumes" NaCl molecules near the droplet center and quenches the formation of new stable NaCl nuclei, favoring the formation of only one single-crystal NaCl core per droplet. The code provides guidance for the custom engineering of aerosol nanoparticle architectures.

关键词： ETHANOL SALT WATER EVAPORATION (Chemistry) SPRAY drying COMBUSTION boundary value problems -- numerical solutions COMPUTER simulation

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Fast stratified flow over several obstacles, including wings

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IMA JOURNAL OF APPLIED MATHEMATICS 1996年第3期57卷 243-256页

作者： Krutitskii, PA Department of Mathematics Faculty of Physics Moscow State University Moscow 119899 Russia

Fast two-dimensional stratified flow over several obstacles is considered, in particular over thin wings. The problem is reduced to a linear boundary-value problem by a nonlinear substitution. The linear problem is st... 详细信息

关键词： STRATIFIED flow boundary value problems -- numerical solutions POTENTIAL theory (Mathematics) SUBSTITUTIONS (Mathematics) NONLINEAR theories LINEAR systems

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Nanoscale planar field projections of atomic decohesion and slip in crystalline solids. Part I. A crack-tip cohesive zone

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PHILOSOPHICAL MAGAZINE 2007年第12期87卷 1889-1919页

作者： Choi, S. T. Kim, K. -S. Brown Univ Div Engn Providence RI 02912 USA

The field projection method of Hong and Kim ( 2003) to identify the crack-tip cohesive zone constitutive relations in an isotropic elastic solid is extended to a nanoscale planar field projection of a cohesive crack tip on an interface between two anisotropic solids. This formulation is applicable to the elastic field of a cohesive crack tip on an interface or in a homogeneous material for any combination of anisotropies. This method is based on a new orthogonal eigenfunction expansion of the elastic field around an interfacial cohesive crack, as well as on the effective use of interaction J integrals. The nanoscale planar field projection is applied to characterizing a crack-tip cohesive zone naturally arising in the fields of atomistics. The atomistic fields analyzed are obtained from molecular statics simulations of decohesion in a gold single crystal along a [(1) over bar(1) over bar2] direction in a (111) plane, for which the interatomic interactions are described by an embedded atom method potential. The field projection provides cohesive traction, interface separation, and the surface-stress gradient caused by the gradual variation of surface formation within the cohesive zone. Therefore, the cohesive traction and surface energy gradient can be measured as functions of the cohesive zone displacements. The introduction of an atomistic hybrid reference configuration for the deformation analysis has made it possible to complete the field projection and to evaluate the energy release rate of decohesion with high precision. The results of the hybrid analyses of the atomistics and continuum show that there is a nanoscale mechanism of decohesion lattice trapping or hardening caused by the characteristics of non-local atomistic deformations near the crack tip. These characteristics are represented by surface relaxation and the development of surface stresses in the cohesive zone.

关键词： EIGENFUNCTIONS boundary value problems -- numerical solutions SOLID state physics ANISOTROPY CRYSTALLOGRAPHY

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