scholarly journals Asymptotic Solutions and Estimations of Some Three-dimensional Problems for Bodies Weakened by Plane Crack Systems

2011 ◽  
Vol 10 ◽  
pp. 918-923
Author(s):  
B.V. Sobol
Keyword(s):  
Three Dimensional ◽  
Asymptotic Solutions ◽  
Plane Crack

Forced convection in three-dimensional flows: II. Asymptotic solutions for mobile interfaces

AIChE Journal ◽  
1970 ◽  
Vol 16 (5) ◽  
pp. 771-786 ◽  
Author(s):  
W. E. Stewart ◽  
J. B. Angelo ◽  
E. N. Lightfoot
Keyword(s):  
Forced Convection ◽  
Three Dimensional ◽  
Asymptotic Solutions ◽  
Mobile Interfaces

Exact solutions of the three-dimensional scalar wave equation and Maxwell's equations from the approximate solutions in the wave zone through the use of the Radon transform

1989 ◽  
Vol 422 (1863) ◽  
pp. 351-365 ◽  
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Radon Transform ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Three Dimensional ◽  
Asymptotic Solutions ◽  
Scalar Wave ◽  
Wave Zone ◽  
One Dimensional

In our earlier paper we have shown that the solutions of both the three-dimensional scalar wave equation, which is also the three-dimensional acoustic equation, and Maxwell’s equations have forms in the wave zone, which, except for a factor 1/ r , represent one-dimensional wave motions along straight lines through the origin. We also showed that it is possible to reconstruct the exact solutions from the asymptotic forms. Thus we could prescribe the solutions in the wave zone and obtain the exact solutions that would lead to them. In the present paper we show how the exact solutions can be obtained from the asymptotic solutions and conversely, through the use of a refined Radon transform, which we introduced in a previous paper. We have thus obtained a way of obtaining the exact three-dimensional solutions from the essentially one-dimensional solutions of the asymp­totic form entirely in terms of transforms. This is an alternative way to obtaining exact solutions in terms of initial values through the use of Riemann functions. The exact solutions that we obtain through the use of the Radon transform are causal and therefore physical solutions. That is, these solutions for time t > 0 could have been obtained from the initial value problem by prescribing the solution and its time-derivative, in the acoustic case, and the electric and magnetic fields, in the case of Maxwell’s equations, at time t = 0. The role of time in the relation between the exact solutions and in the asymptotic solutions is made very explicit in the present paper.

Investigation of plane crack growth in a three-dimensional body

1994 ◽  
Vol 29 (5) ◽  
pp. 485-489
Author(s):  
O. E. Andreikiv ◽  
O. I. Darchuk
Keyword(s):  
Crack Growth ◽  
Three Dimensional ◽  
Plane Crack

A flow in the depth of infinite annular cylindrical cavity

2012 ◽  
Vol 711 ◽  
pp. 667-680 ◽  
Author(s):  
Vladimir Shtern
Keyword(s):  
Eigenvalue Problem ◽  
Viscous Fluid ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Cylindrical Cavity ◽  
Axisymmetric Flow ◽  
Three Dimensional ◽  
Asymptotic Solutions

AbstractThe paper describes an asymptotic flow of a viscous fluid in an infinite annular cylindrical cavity as the distance from the flow source tends to infinity. If the driving flow near the source is axisymmetric then the asymptotic pattern is cellular; otherwise it is typically not. Boundary conditions are derived to match the asymptotic axisymmetric flow with that near the source. For a narrow cavity, the asymptotic solutions for the axisymmetric and three-dimensional flows are obtained analytically. For any gap, the flow is described by a numerical solution of an eigenvalue problem. The least decaying mode corresponds to azimuthal wavenumber $m= 1$.

Stability of viscous flow over concave cylindrical surfaces

1950 ◽  
Vol 203 (1073) ◽  
pp. 253-265 ◽  
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Finite Number ◽  
Viscous Flow ◽  
Critical Condition ◽  
Three Dimensional ◽  
Steady States ◽  
Asymptotic Solutions ◽  
Radius Of Curvature ◽  
The Stability

The stability for three-dimensional disturbances of viscous flow over concave cylindrical surfaces is investigated by the method of asymptotic solutions. The results confirm Görtler’s conclusions that these disturbances can only take place on concave surfaces, and that in the critical condition that the parameter R δ (δ/ r ) ½ remains constant, where R δ is Reynolds number and δ/r is the ratio of the thickness of the boundary layer to the radius of curvature. Additionally, it is found that there are many steady states, and the values R δ (δ/ r ) ½ are evaluated for the first two states. For a fixed Rδ(δ / r ) ½ there is a finite number of steady states.

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