Full Iterative Solution of the Two-Dimensional Master Equation for Thermal Unimolecular Reactions

1996 ◽  
Vol 100 (17) ◽  
pp. 7090-7096 ◽  
Author(s):  
Stephen J. Jeffrey ◽  
Kevin E. Gates ◽  
Sean C. Smith
Keyword(s):  
Master Equation ◽  
Iterative Solution ◽  
Two Dimensional ◽  
Unimolecular Reactions

The magneto-hydrodynamic boundary layer in the two-dimensional steady flow past a semi-infinite flat plate II. The Falkner-Skan problem

1963 ◽  
Vol 273 (1355) ◽  
pp. 509-517 ◽  
Keyword(s):  
Flat Plate ◽  
Iterative Procedure ◽  
Hypergeometric Functions ◽  
Close Agreement ◽  
Adverse Pressure Gradient ◽  
Iterative Solution ◽  
Two Dimensional ◽  
Confluent Hypergeometric Functions ◽  
First Case ◽  
Hydrodynamic Boundary Layer

The problem investigated is the flow of a viscous liquid past a semi-infinite flat plate against an adverse pressure gradient. The method used is an iterative method suggested in a paper by Weyl. To start the iterative procedure a function is chosen which satisfies some of the boundary conditions and by using this function the first iterative solution has been obtained analytically in terms of confluent hypergeometric functions. Two different starting functions have been considered. In the first case it has been found possible to compare the results obtained with the well-known Hartree numerical solution and even at the first iteration close agreement is achieved. In the second case, the first iterative solution behaves correctly at infinity but the agreement with Hartree ’s solution is not as good as it is in the first case.

SUPERCONFORMAL CONSTRUCTIONS ON TWO-DIMENSIONAL SIMPLICIAL COMPLEXES

1992 ◽  
Vol 07 (13) ◽  
pp. 3065-3082 ◽  
Author(s):  
M. B. HALPERN ◽  
N. A. OBERS
Keyword(s):  
Master Equation ◽  
Central Charge ◽  
Simplicial Complexes ◽  
Large Set ◽  
Two Dimensional ◽  
Infinite Class ◽  
Generic Construction

The superconformal master equation contains a large set of solvable fermionic constructions which live on an infinite class of 2-dimensional simplicial complexes. All the constructions have rational central charge, and irrational conformal weights are expected in the generic construction.

scholarly journals The Cylindrical Wave Approach for the Electromagnetic Scattering by Targets behind a Wall

Electronics ◽  
2019 ◽  
Vol 8 (11) ◽  
pp. 1262 ◽  
Author(s):  
Cristina Ponti ◽  
Giuseppe Schettini
Keyword(s):  
Electromagnetic Scattering ◽  
Circular Cross Section ◽  
Iterative Solution ◽  
Cylindrical Wave ◽  
Two Dimensional ◽  
Wave Excitation ◽  
Cylindrical Waves ◽  
Wave Approach ◽  
Scattered Fields ◽  
Final System

An overview of the cylindrical wave approach in the modeling of through-wall radar problems with targets hidden behind a dielectric wall is reported. The cylindrical wave approach is a technique for the solution of the two-dimensional scattering by buried circular cross-section cylinders in a semi-analytical way, through expansion of the scattered fields into cylindrical waves. In a through-wall radar application, the scattering environment is made by a dielectric layer between two semi-infinite half-spaces filled by air. For this layout, two possible implementations of the cylindrical wave approach have been developed in the case of plane-wave excitation. The first was an iterative scheme with multiple-reflection scattered fields, and the second was a fast and non-iterative solution, through suitable basis functions (i.e., reflected and transmitted cylindrical waves). Such waves take into account all the interactions of the source field with the interfaces bounding the dielectric layers and the targets. The non-iterative approach was also extended for excitation from the radiated field by a line source. A final system was derived for the computation of the scattered field by PEC or dielectric targets. Numerical results show the potentialities of the cylindrical wave approach in the modeling of through-wall radar, in particular in the evaluation of the scattered fields by human targets in a building’s interior, modeled with a two-dimensional approach.

An Approximate Solution to Radiative Transfer in Two-Dimensional Rectangular Enclosures

1997 ◽  
Vol 119 (4) ◽  
pp. 738-745 ◽  
Author(s):  
J. B. Pessoa-Filho ◽  
S. T. Thynell
Keyword(s):  
Radiative Transfer ◽  
Iterative Solution ◽  
Anisotropic Scattering ◽  
Solution Procedure ◽  
Two Dimensional ◽  
Scattering Media ◽  
Discontinuous Nature ◽  
Selection Of ◽  
Iterative Solution Procedure ◽  
Numerical Approaches

The application of a new approximate technique for treating radiative transfer in absorbing, emitting, anisotropically scattering media in two-dimensional rectangular enclosures is presented. In its development the discontinuous nature of the radiation intensity, stability of the iterative solution procedure, and selection of quadrature points have been addressed. As a result, false scattering is eliminated. The spatial discretization can be formed without considering the chosen discrete directions, permitting a complete compatibility with the discretization of the conservation equations of mass, momentum, and energy. The effects of anisotropic scattering, wall emission, and gray-diffuse surfaces are considered for comparison with results available in the literature. The computed numerical results are in excellent agreement with those obtained by other numerical approaches.

Diffusive transport across irregular and fractal walls

1993 ◽  
Vol 442 (1916) ◽  
pp. 571-583 ◽  
Keyword(s):  
Fractal Geometry ◽  
Numerical Procedure ◽  
Iterative Solution ◽  
Diffusive Transport ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Total Rate ◽  
Nonlinear Algebraic Equations ◽  
Total Transport ◽  
Self Similar

Diffusive transport of heat, mass, and momentum across walls with irregular and fractal geometry is discussed. A configuration is considered in detail, in which the transported variable diffuses across a two-dimensional periodic irregular wall toward an overlying plane wall, while the value of the variable over each wall is maintained at a constant value. Several families of self-similar wall geometries with increasingly finer structure, eventually leading to fractal shapes, are considered in detail using an efficient numerical method that is based on conformal mapping. The numerical procedure involves the iterative solution of a large system of nonlinear algebraic equations. Computed patterns of iso-scalar contours reveal the precise effect of the shape, size, and total length of boundary irregularities on the local and total transport rates, and illustrate the enhancement in transport efficacy with wall refinement. The total rate of transport across walls with self-similar irregularities is shown to be remarkably close to that across walls with random irregularities of same roughness height.

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