scholarly journals A two-dimensional problem in magnetothermoelasticity with laser pulse under different boundary conditions

2013 ◽  
Vol 8 (8-10) ◽  
pp. 441-459 ◽  
Author(s):  
Sunita Deswal ◽  
Sandeep Singh Sheoran ◽  
Kapil Kumar Kalkal
Keyword(s):  
Laser Pulse ◽  
Boundary Conditions ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Different Boundary Conditions

scholarly journals Inversion of Potential Vorticity Density

2017 ◽  
Vol 74 (3) ◽  
pp. 801-807 ◽  
Author(s):  
Joseph Egger ◽  
Klaus-Peter Hoinka ◽  
Thomas Spengler
Keyword(s):  
Boundary Conditions ◽  
Potential Vorticity ◽  
Potential Temperature ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Absolute Vorticity ◽  
Vertical Vector ◽  
The North ◽  
And Function

Abstract Inversion of potential vorticity density with absolute vorticity and function η is explored in η coordinates. This density is shown to be the component of absolute vorticity associated with the vertical vector of the covariant basis of η coordinates. This implies that inversion of in η coordinates is a two-dimensional problem in hydrostatic flow. Examples of inversions are presented for (θ is potential temperature) and (p is pressure) with satisfactory results for domains covering the North Pole. The role of the boundary conditions is investigated and piecewise inversions are performed as well. The results shed new light on the interpretation of potential vorticity inversions.

scholarly journals CONTINUOUS ABELIAN SANDPILE MODEL IN TWO DIMENSIONAL LATTICE

2011 ◽  
Vol 25 (32) ◽  
pp. 4709-4720 ◽  
Author(s):  
N. AZIMI-TAFRESHI ◽  
E. LOTFI ◽  
S. MOGHIMI-ARAGHI
Keyword(s):  
Boundary Conditions ◽  
Small Mass ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
New Model ◽  
Different Boundary Conditions ◽  
Sandpile Model ◽  
Abelian Sandpile Model ◽  
General Properties ◽  
Abelian Sandpile

We investigate a new version of sandpile model which is very similar to Abelian Sandpile Model (ASM), but the height variables are continuous ones. With the toppling rule we define in our model, we show that the model can be mapped to ASM, so the general properties of the two models are identical. Yet the new model allows us to investigate some problems such as the effect of very small mass on the height probabilities, different boundary conditions, etc.

Contact Problems of Two Dissimilar Anisotropic Elastic Bodies

1998 ◽  
Vol 65 (3) ◽  
pp. 580-587 ◽  
Author(s):  
Chyanbin Hwu ◽  
C. W. Fan
Keyword(s):  
Boundary Conditions ◽  
Contact Region ◽  
Complex Function ◽  
Contact Problems ◽  
Anisotropic Elasticity ◽  
Analytical Continuation ◽  
Two Dimensional ◽  
Different Boundary Conditions ◽  
Elastic Bodies ◽  
Anisotropic Elastic

In this paper, a two-dimensional contact problem of two dissimilar anisotropic elastic bodies is studied. The shapes of the boundaries of these two elastic bodies have been assumed to be approximately straight, but the contact region is not necessary to be small and the contact surface can be nonsmooth. Base upon these assumptions, three different boundary conditions are considered and solved. They are: the contact in the presence of friction, the contact in the absence of friction, and the contact in complete adhesion. By applying the Stroh’s formalism for anisotropic elasticity and the method of analytical continuation for complex function manipulation, general solutions satisfying these different boundary conditions are obtained in analytical forms. When one of the elastic bodies is rigid and the boundary shape of the other elastic body is considered to be fiat, the reduced solutions can be proved to be identical to those presented in the literature for the problems of rigid punches indenting into (or sliding along) the anisotropic elastic halfplane. For the purpose of illustration, examples are also given when the shapes of the boundaries of the elastic bodies are approximated by the parabolic curves.

Higher Order Perturbation Solutions for Electrochemical Machining

1976 ◽  
Vol 4 (2) ◽  
pp. 90-96 ◽  
Author(s):  
Henning Rasmussen
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fourth Order ◽  
Electrochemical Machining ◽  
Higher Order ◽  
Order Perturbation ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Initial Distance ◽  
Perturbation Solutions

The calculation of higher order perturbation solutions is discussed for electrochemical machining and is illustrated for a particular two-dimensional problem, which consists of a plane cathode and an anode whose initial distance from the cathode varies spatially in a sinusoidal manner. Terms up to fourth order are obtained as the solutions to six ordinary coupled differential equations which are solved numerically. Also shown is how the effects of changes in the boundary conditions due to overpotential can be included.

MATRIX TECHNIQUES FOR TWO-DIMENSIONAL O(N) MODELS

2006 ◽  
Vol 21 (11) ◽  
pp. 2297-2320
Author(s):  
MIGUEL AGUADO
Keyword(s):  
Boundary Conditions ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
Different Boundary Conditions

Recently developed matrix techniques, useful in the study of O (N) models on a two-dimensional lattice with different boundary conditions, are reviewed. Their application to perturbative problems is considered for illustration.

Removal of an inconsistency in the theory of diffraction

1952 ◽  
Vol 48 (4) ◽  
pp. 733-741 ◽  
Author(s):  
D. S. Jones
Keyword(s):  
Plane Wave ◽  
Boundary Conditions ◽  
Stationary Phase ◽  
Interior Point ◽  
Final Section ◽  
Solid Angle ◽  
Three Dimensional ◽  
Special Boundary ◽  
Dimensional Problem ◽  
Different Boundary Conditions

AbstractIt is indicated by means of a particular example how an inconsistency arises in one formulation of diffraction problems. It is shown that the inconsistency is removed if different boundary conditions are imposed during the formulation. In the proof it is necessary to determine the contributions to the field from parts of a sphere of radius R at an interior point when the field on the sphere is a plane wave. It is found that, as R → ∞, the part of the sphere near the source which subtends a solid angle of order at the centre contributes the plane wave and that the remainder of the sphere provides a contribution which vanishes in the limit. The demonstration involves the use of the principle of stationary phase for an integral of two variables.In the final section special boundary conditions are given for an exceptional three-dimensional problem.

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