Correction for Transition Boundary Conditions to Consider Scattering by a Chiral Infinite Slab

2018 ◽  
Author(s):  
N.G. Tuncel ◽  
A.H. Serbest
Keyword(s):  
Boundary Conditions ◽  
Transition Boundary ◽  
Infinite Slab

Stresses in a Transversely Isotropic Slab Having a Spherical Cavity

1973 ◽  
Vol 40 (3) ◽  
pp. 752-758 ◽  
Author(s):  
A. Atsumi ◽  
S. Itou
Keyword(s):  
Stress Distribution ◽  
Boundary Conditions ◽  
Spherical Cavity ◽  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
Hankel Transform ◽  
Isotropic Slab ◽  
Infinite Slab

This paper deals with the analysis of the stress distribution arising in a transversely isotropic infinite slab with a symmetrically located spherical cavity under all-around tension. Difficulties in satisfying both boundary conditions on the surfaces of the slab and the surface of the cavity are successfully overcome by using the methods of Hankel transform and Schmidt-orthogonormalization. For some practical materials the influence of transverse isotropy upon stress distribution is presented in the form of curves.

Stresses in a Stretched Slab Having a Spherical Cavity

1959 ◽  
Vol 26 (2) ◽  
pp. 235-240
Author(s):  
Chih-Bing Ling
Keyword(s):  
Boundary Conditions ◽  
Stress Function ◽  
Spherical Cavity ◽  
Analytic Solution ◽  
Linear Equations ◽  
Hankel Transform ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Biharmonic Functions ◽  
Infinite Slab

Abstract This paper presents an analytic solution for an infinite slab having a symmetrically located spherical cavity when it is stretched by an all-round tension. The required stress function is constructed by combining linearly two sets of periodic biharmonic functions and a biharmonic integral. The sets of biharmonic functions are derived from two fundamental functions specially built up for the purpose. The arbitrary functions involved in the biharmonic integral are first adjusted to satisfy the boundary conditions on the surfaces of the slab by applying the Hankel transform of zero order. Then the stress function is expanded in spherical co-ordinates and the boundary conditions on the surface of the cavity are satisfied by adjusting the coefficients of superposition attached to the sets of biharmonic functions. The resulting system of linear equations is solved by the method of successive approximations. The solution is finally illustrated by numerical examples for two radii of the cavity.

Transition boundary conditions for simulation of thin chiral slab

1998 ◽  
Vol 34 (12) ◽  
pp. 1211 ◽  
Author(s):  
M.A. Lyalinov ◽  
A.H. Serbest
Keyword(s):  
Boundary Conditions ◽  
Transition Boundary

scholarly journals The temporal evolution of a system in combustion theory

1983 ◽  
Vol 24 (4) ◽  
pp. 473-483 ◽  
Author(s):  
K. K. Tam
Keyword(s):  
Boundary Conditions ◽  
Laplace Transform ◽  
Parabolic Equations ◽  
Numerical Solutions ◽  
Temporal Evolution ◽  
Time Duration ◽  
Numerical Work ◽  
Infinite Slab ◽  
Over Time ◽  
Good Agreement

AbstractA model governing the combustion of a material is considered. The model consists of two non-linear coupled parabolic equations with initial and boundary conditions. An approximation for the rate of reactant consumption is made to enable the system to the treated by laplace transform. Three simple geometries are considered; namely, an infinite slab, an infinite circular and a sphere. The results obtained are then compared with numerical solutions for spme specific values of the parameters. There is good agreement over time duration for which numerical work was performed.

Stationary-state solutions for coupled reaction-diffusion and temperature-conduction equations I. Infinite slab and cylinder with general boundary conditions

1990 ◽  
Vol 430 (1880) ◽  
pp. 459-477 ◽  
Keyword(s):  
Boundary Conditions ◽  
Stationary State ◽  
Reaction Rate ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Laplacian Operator ◽  
Gaseous Species ◽  
Temperature Position ◽  
Infinite Slab ◽  
Coupled Reaction

A simple model for the exothermic oxidation of a solid reactant or reaction in a catalyst bed is considered. A gaseous component, e. g. O 2 , diffuses through a porous medium where it reacts releasing heat. The concentration of the gaseous species in the surrounding reservoir is held constant as is the surrounding (ambient) temperature. Heat transfer within the reaction zone occurs by conduction, leading to an internal temperature-position profile. The reaction rate at any point depends on the local temperature through an Arrhenius rate-law and is first order in the gaseous species concentration. Consumption of the solid is ignored in this paper. Stationary-state solutions are governed by the dimensionless coupled reaction-diffusion equations ∇ 2 v - αλ (1 + v ) exp [ u /(1+ εu )] = 0, ∇ 2 u + λ (1 + v ) exp [ u /(1 + εu )] = 0, where u and v are temperature and concentration respectively, λ, α and ε are parameters and ∇ 2 is the laplacian operator. The boundary conditions considered here are of Robin form: ∂ u /∂ n + μu = 0, ∂ v /∂ u + νv = 0 at x = 1, where μ and ν are the Nusselt and Sherwood (or Biot) numbers. The reaction geometry is restricted to the infinite slab and infinite cylinder for which ∇ 2 = ∂ 2 /∂ x 2 + ( j / x ) ∂/∂ x with j = 0 and 1 respectively. Of particular interest are the dependences of the stationary-state temperature and concentration profiles on the parameter λ and the way in which these dependences are unfolded as α, ε , μ and v are varied. Up to five branches of Stationary-state solutions may be encountered, although this requires σ = μ/v < 1. The development of the temperature-position and reaction-rate-position profiles along the different branches is determined both numerically and analytically.

Use of the Magnetostatic Analogue In Electromagnetic Lens Engineering

1970 ◽  
Vol 28 ◽  
pp. 360-361
Author(s):  
John W. Coleman
Keyword(s):  
Boundary Conditions ◽  
High Performance ◽  
Force Fields ◽  
Optical Design ◽  
Direct Conversion ◽  
Design Engineering ◽  
Design Data ◽  
Scalar Potentials ◽  
Geometric Elements ◽  
At Will

In the design engineering of high performance electromagnetic lenses, the direct conversion of electron optical design data into drawings for reliable hardware is oftentimes difficult, especially in terms of how to mount parts to each other, how to tolerance dimensions, and how to specify finishes. An answer to this is in the use of magnetostatic analytics, corresponding to boundary conditions for the optical design. With such models, the magnetostatic force on a test pole along the axis may be examined, and in this way one may obtain priority listings for holding dimensions, relieving stresses, etc..The development of magnetostatic models most easily proceeds from the derivation of scalar potentials of separate geometric elements. These potentials can then be conbined at will because of the superposition characteristic of conservative force fields.

A digital vocal tract simulator with boundary conditions at lips and glottis

1981 ◽  
Vol 64 (11) ◽  
pp. 18-26 ◽  
Author(s):  
Tetsuya Nomura ◽  
Nobuhiro Miki ◽  
Nobuo Nagai
Keyword(s):  
Boundary Conditions ◽  
Vocal Tract
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