scholarly journals Revised Formulation of Fick’s, Fourier’s, and Newton’s Laws for Spatially Varying Linear Transport Coefficients

ACS Omega ◽  
2019 ◽  
Vol 4 (6) ◽  
pp. 11215-11222 ◽  
Author(s):  
You-Yeon Won ◽  
Doraiswami Ramkrishna
Keyword(s):  
Transport Coefficients ◽  
Linear Transport ◽  
Newton’S Laws ◽  
Spatially Varying

SOLUTION OF THE QUANTUM BOLTZMANN EQUATION IN LINEAR TRANSPORT

2002 ◽  
Vol 09 (05n06) ◽  
pp. 1761-1763
Author(s):  
B. A. PAEZ ◽  
A. MORENO ◽  
H. MÉNDEZ
Keyword(s):  
Boltzmann Equation ◽  
Green’S Function ◽  
Green's Function ◽  
Function Method ◽  
Transport Coefficients ◽  
Power Coefficient ◽  
Green’S Function Method ◽  
Nonequilibrium Distribution ◽  
Quantum Boltzmann Equation ◽  
Linear Transport

The one-dimensional quantum Boltzmann equation in linear transport approximation was solved using the nonequilibrium Green's function method, and based on the lifetime approximation. As an example, the effect of interactions with electric fields were included, and the thermoelectric power coefficient (α) was evaluated, based on calculations of the statistical density current in a stationary regime over the nonequilibrium distribution function, and by the Green's function method. Results are compared in order to explore the advantages of each one, in evaluating the other kinetic transport coefficients.

Deviations From the Linear Transport Laws and Corrections to the Onsager Reciprocal Relations

1976 ◽  
Vol 43 (3) ◽  
pp. 409-413 ◽  
Author(s):  
W. A. Scheffler ◽  
J. S. Dahler ◽  
W. E. Ibele
Keyword(s):  
Order Approximation ◽  
Transition Probability ◽  
Transport Coefficients ◽  
Functional Integral ◽  
Reciprocal Relations ◽  
First Order ◽  
Linear Transport ◽  
First Order Approximation ◽  
Onsager Reciprocal Relations ◽  
Transport Laws

An extension of the linear transport laws is derived from first principles of statistical mechanics. The resulting transport laws include both relaxation and nonlinear terms. It is found when these terms are included the Onsager reciprocal relations are no longer valid. Therefore, the development gives the limit of validity of the Onsager relations, as well as expressing the transport coefficients as correlation functions of the dynamical variables. In order to show the validity of the procedure used, a functional integral is derived as a first-order approximation for the transition probability. This integral when evaluated verifies the assumption of Onsager and Machlup for the transition probability for the linear transport laws.

A simple demonstration of Newton's laws

1978 ◽  
Vol 124 (4) ◽  
pp. 717-719
Author(s):  
Lev A. Gribov ◽  
A.N. Gornostaev
Keyword(s):  
Simple Demonstration ◽  
Newton’S Laws
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