A solution for the two-dimensional transport equation for photons and electrons in a rectangular domain by the Laplace transform technique

2010 ◽  
Vol 5 (1) ◽  
pp. 25 ◽  
Author(s):  
Barbara D. do Amaral Rodriguez ◽  
Marco Tullio Vilhena ◽  
Volnei Borges
Keyword(s):  
Laplace Transform ◽  
Transport Equation ◽  
Rectangular Domain ◽  
Two Dimensional ◽  
Laplace Transform Technique ◽  
The Laplace Transform

Analysis of the neutron spin structure function g1n by using the Laplace transform technique

2018 ◽  
Vol 27 (08) ◽  
pp. 1850071
Author(s):  
F. Teimoury Azadbakht ◽  
G. R. Boroun ◽  
B. Rezaei
Keyword(s):  
Laplace Transform ◽  
Structure Function ◽  
Spin Structure ◽  
Neutron Spin ◽  
Spin Structure Function ◽  
Transform Method ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Convolution Approach ◽  
Neutron Spin Structure

In this paper, the polarized neutron structure function [Formula: see text] in the [Formula: see text] nucleus is investigated and an analytical solution based on the Laplace transform method for [Formula: see text] is presented. It is shown that the neutron spin structure function can be extracted directly from the polarized nuclear structure function of [Formula: see text]. The nuclear corrections due to the Fermi motion of the nucleons as well as the binding energy considerations are taken into account within the framework of the convolution approach and the polarized structure function of [Formula: see text] nucleus is expressed in terms of the spin structure functions of nucleons and the light-cone momentum distribution of the constituent nucleons. Then, the numerical results for [Formula: see text] are compared with experimental data of the SMC and HERMES collaborations. We found that there is an overall good agreement between the theory and experiments.

scholarly journals The Generalized Solutions of the nth Order Cauchy–Euler Equation

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 932 ◽  
Author(s):  
Amornrat Sangsuwan ◽  
Kamsing Nonlaopon ◽  
Somsak Orankitjaroen ◽  
Ismail Mirumbe
Keyword(s):  
Laplace Transform ◽  
Euler Equation ◽  
Euler Equations ◽  
Generalized Solutions ◽  
Distributional Solutions ◽  
Laplace Transform Technique ◽  
The Laplace Transform

In this paper, we use the Laplace transform technique to examine the generalized solutions of the nth order Cauchy–Euler equations. By interpreting the equations in a distributional way, we found that whether their solution types are classical, weak or distributional solutions relies on the conditions of their coefficients. To illustrate our findings, some examples are exhibited.

scholarly journals New Numerical Treatment for a Family of Two-Dimensional Fractional Fredholm Integro-Differential Equations

Algorithms ◽  
2020 ◽  
Vol 13 (2) ◽  
pp. 37
Author(s):  
Amer Darweesh ◽  
Marwan Alquran ◽  
Khawla Aghzawi
Keyword(s):  
Differential Equations ◽  
Laplace Transform ◽  
Haar Wavelet ◽  
Two Dimensional ◽  
Numerical Treatment ◽  
Wavelet Method ◽  
New Approach ◽  
Robust Algorithm ◽  
Haar Wavelet Method ◽  
The Laplace Transform

In this paper, we present a robust algorithm to solve numerically a family of two-dimensional fractional integro differential equations. The Haar wavelet method is upgraded to include in its construction the Laplace transform step. This modification has proven to reduce the accumulative errors that will be obtained in case of using the regular Haar wavelet technique. Different examples are discussed to serve two goals, the methodology and the accuracy of our new approach.

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.

Study of Transient Coupled Thermoelastic Problems With Relaxation Times

1995 ◽  
Vol 62 (1) ◽  
pp. 208-215 ◽  
Author(s):  
Han-Taw Chen ◽  
Hou-Jee Lin
Keyword(s):  
Boundary Condition ◽  
Laplace Transform ◽  
Temperature Stress ◽  
Control Volume ◽  
Relaxation Times ◽  
Dimensionless Temperature ◽  
Radiation Boundary Condition ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Thermoelastic Problems

A new hybrid numerical method based on the Laplace transform and control volume methods is proposed to analyze transient coupled thermoelastic problems with relaxation times involving a nonlinear radiation boundary condition. The dynamic thermoelastic model of Green and Lindsay is selected for the present study. The following computational procedure is followed for the solution of the present problem. The nonlinear term in the boundary condition is linearized by using the Taylor’s series approximation. Afterward, the time-dependent terms in the linearized equations are removed by the Laplace transform technique, and then the transformed field equations are discretized using the control volume method with suitable shape functions. The nodal dimensionless temperature and displacement in the transform domain are inverted to obtain the actual physical quantities, using the numerical inversion of the Laplace transform method. It is seen from various illustrative problems that the present method has good accuracy and efficiency in predicting the wave propagations of temperature, stress, and displacement. However, it should be noted that the distributions of temperature, stress, and displacement can experience steep jumps at their wavefronts. In the present study, the effects of the relaxation times on these thermoelastic waves are also investigated.

Thermodiffusion with two time delays and Kernel functions

2016 ◽  
Vol 23 (2) ◽  
pp. 195-208 ◽  
Author(s):  
Ahmed S El-Karamany ◽  
Magdy A Ezzat ◽  
Alaa A El-Bary
Keyword(s):  
Laplace Transform ◽  
Kernel Functions ◽  
Transform Domain ◽  
Thermoelastic Diffusion ◽  
One Dimensional ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Isotropic Elastic Medium ◽  
Time Variations ◽  
With Memory

The present work is concerned with the investigation of disturbances in a homogeneous, isotropic elastic medium with memory-dependent derivatives (MDDs). A one-dimensional problem is considered for a half-space whose surface is traction free and subjected to the effects of thermodiffusion. For treatment of time variations, the Laplace-transform technique is utilized. The theories of coupled and of generalized thermoelastic diffusion with one relaxation time follow as limit cases. A direct approach is introduced to obtain the solutions in the Laplace transform domain for different forms of kernel functions and time delay of MDDs, which can be arbitrarily chosen. Numerical inversion is carried out to obtain the distributions of the considered variables in the physical domain and illustrated graphically. Some comparisons are made and shown in figures to estimate the effects of MDD parameters on all studied fields.

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