Exact solution of the transport equation for radiative transfer with scattering albedo ?O < 1 using the Laplace transform and the Wiener-Hopf technique and an expression ofH-function

1979 ◽  
Vol 60 (1) ◽  
pp. 49-58 ◽  
Author(s):  
Rabindra Nath Das
Keyword(s):  
Exact Solution ◽  
Radiative Transfer ◽  
Laplace Transform ◽  
Transport Equation ◽  
The Laplace Transform

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.

scholarly journals Laplace-SBA Method for Solving Nonlinear Coupled Burger's Equations

2021 ◽  
Vol 14 (3) ◽  
pp. 842-862
Author(s):  
Joseph Bonazebi-Yindoula
Keyword(s):  
Fluid Dynamics ◽  
Exact Solution ◽  
Numerical Methods ◽  
Laplace Transform ◽  
Exact Solutions ◽  
Partial Derivative ◽  
Basic Principles ◽  
The Laplace Transform ◽  
Fluid Dynamics Equations ◽  
Burger's Equations

Burger’s equations, an extension of fluid dynamics equations, are typically solved by several numerical methods. In this article, the laplace-Somé Blaise Abbo method is used to solve nonlinear Burger equations. This method is based on the combination of the laplace transform and the SBA method. After reminders of the laplace transform, the basic principles of the SBA method are described. The process of calculating the Laplace-SBA algorithm for determining the exact solution of a linear or nonlinear partial derivative equation is shown. Thus, three examplesof PDE are solved by this method, which all lead to exact solutions. Our results suggest that this method can be extended to other more complex PDEs.

scholarly journals Exact and unique solution of a transport equation in a semi-infinite medium by Laplace transform and Wiener-Hopf technique

2004 ◽  
Vol 35 (4) ◽  
pp. 347-350
Author(s):  
Z. Islam ◽  
A. Mukherjee ◽  
S. Karanjai
Keyword(s):  
Radiative Transfer ◽  
Laplace Transform ◽  
Transport Equation ◽  
Unique Solution ◽  
Optical Depth ◽  
Axial Symmetry ◽  
Diffuse Reflection ◽  
Infinite Medium ◽  
Plane Parallel ◽  
Emergent Intensity

The equation of radiative transfer in non-conservative case for diffuse reflection in a plane-parallel semi-infinite atmosphere with axial symmetry has been solved by Laplace transform and Wiener-Hopf technique. We have determined the emergent intensity in terms of Chandrasekhar's H-function and the intensity at any optical depth by inversion.

scholarly journals Rigorous time domain responses of polarizable media II

1998 ◽  
Vol 41 (3) ◽  
Author(s):  
M. Caputo ◽  
W. Plastino
Keyword(s):  
Exact Solution ◽  
Laplace Transform ◽  
Time Domain ◽  
Input Data ◽  
Synthetic Data ◽  
Induced Polarization ◽  
Discharge Data ◽  
Time Domain Data ◽  
Previous Note ◽  
The Laplace Transform

We present and test in detail with synthetic data a method which may be used to retrieve the parameters describing the induced polarization properties of media which fit the generally accepted frequency dependent formula of Cole and Cole (1941) (CC model). We use time domain data and rigorous formulae obtained from the exact solution of the problem found in a previous note (Caputo, 1996). The observed data considered here are the theoretical responses of the medium to box inputs of given duration in media defined with different parameters; however, as is usually done, only the discharge data are used (Patella >F2<et al.>F1<, 1987). The curve at the beginning of the discharge is studied in some detail. The method is successful in identifying the parameters when the data fit the CC model; if the medium is not exactly of the CC type the method may also help identify how the medium departs from the CC model. The Laplace Transform of the discharge for a box type input data is also given.

Sign in / Sign up

Export Citation Format

Share Document