Exact solution of axially symmetric Rayleigh scattering transport equation by Laplace transform and Wiener-Hopf technique and new expression ofH l andH r function

1978 ◽  
Vol 57 (2) ◽  
pp. 429-438
Author(s):  
Rabindra Nath Das
Keyword(s):  
Exact Solution ◽  
Laplace Transform ◽  
Transport Equation ◽  
Rayleigh Scattering ◽  
Axially Symmetric

Die Leitfähigkeit eines freien Elektronengases in einem Phononenbad nach der statistischen Thermodynamik irreversibler Prozesse

1963 ◽  
Vol 18 (12) ◽  
pp. 1351-1359
Author(s):  
Rudolf Klein
Keyword(s):  
Laplace Transform ◽  
Transport Equation ◽  
Low Temperatures ◽  
Body Problem ◽  
Complex Conductivity ◽  
Many Body ◽  
Free Electrons ◽  
Diagram Method ◽  
The Laplace Transform ◽  
The Many

The formulation of the many-body problem by MARTIN and SCHWINGER is applied to a system of free electrons interacting with a phonon bath. Simplifying the general expression for the wave vector and frequency dependent complex conductivity to the case of a static dc situation the conductivity is expressed in terms of the LAPLACE transform of an appropriate GREEN'S function. By means of a simple diagram method a transport equation for this function is derived. In the lowest approximation the solution of this equation gives the BLOCH-GRÜNEISEN law for the conductivity of metals at low temperatures.

Flow Mathematic Model and Exact Solution of Swabbing Wells’ Fluid Level Build up

2012 ◽  
Vol 524-527 ◽  
pp. 1418-1422
Author(s):  
Yan Chen ◽  
Xin Hai Wang ◽  
Feng Yang ◽  
Hai Min Xu ◽  
Bo Tao Liu
Keyword(s):  
Exact Solution ◽  
Laplace Transform ◽  
Bessel Function ◽  
Mathematic Model ◽  
Well Bore ◽  
Fluid Level ◽  
Type Curve ◽  
Skin Factor ◽  
Reservoir Flow

The fluid level of swabbing wells with packers or without packers is different from other wells’ when the swabbing wells are stopped swabbing, because the effect of gravity differentiation is obvious, which is used to calculate the sand face pressure. In the homogeny reservoir, flow mathematic model of build-up of fluid swabbing well in circular sealed stratum is built up under considering the well bore effect and skin factor. Then, the non-homogeneous equation’s exact solution in Laplace space of the model are acquired by using theory of Laplace transform and Bessel function ,then the chart of type curve and the matching of type curve are analyzed. Finally, the software of swabbing well’s fluid level build-up is developed which is used to calculate the formation parameters that are fitted the formation parameters calculated with other methods.

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