The modified equations

2005 ◽  
pp. 105-141
Keyword(s):  
Modified Equations

scholarly journals Analysis Infiltration Waters in Various Forms of Irrigation Channels by Using Dual Reciprocity Boundary Element Method

2020 ◽  
Vol 6 (1) ◽  
pp. 52-65
Author(s):  
Ana Nurhasanah ◽  
Muhammad Manaqib ◽  
Irma Fauziah
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Clay Soils ◽  
Flat Channel ◽  
Modified Equations ◽  
Richard's Equation ◽  
Irrigation Channels ◽  
Channel Surface ◽  
Dimensionless Variables ◽  
Element Method

This research discusses the infiltration of furrow irrigation invarious forms of irrigation channels in homogeneous soils. The governing equation of the problems is a Richard’s Equation. This equation is transformed using a set of transformation including Kirchhoff and dimensionless variables into Helmholtz modified equations. Furthermore with Dual Reciprocity Boundary Element Method (DRBEM), numerical solution of modified Helmholtz equation obtained. The proposed method is tested on problem involved infiltration from periodic flat channels, non-flat channels without impermeable and non-flat channels with impermeable. The greatest value of suction potential and water content is located below the channel surface. The most water consecutively is a non-flat channel without impermeable, non-flat channel with impermeable and flat channel on Lakish Clay soils.  

UNUSUAL HYDRODYNAMICS

1987 ◽  
Vol 02 (05) ◽  
pp. 1591-1615 ◽  
Author(s):  
V.A. BEREZIN
Keyword(s):  
Black Hole ◽  
Cosmological Model ◽  
Production Process ◽  
Particle Production ◽  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Momentum Tensor ◽  
Point Of View ◽  
Modified Equations ◽  
Nonsingular Cosmological Model

A method for the phenomenological description of particle production is proposed. Correspondingly modified equations of motion and energy-momentum tensor are obtained. In order to illustrate this method we reconsider from the new point of view of (i) the C-field Hoyle-Narlikar cosmology, (ii) the influence of the particle production process on metric inside the event horizon of a charged black hole and (iii) a nonsingular cosmological model.

scholarly journals Modification of the Electron Entropy Production in a Plasma

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 935
Author(s):  
Juan F. García-Camacho ◽  
Gonzalo Ares de Parga ◽  
Karen Arango-Reyes ◽  
Encarnación Salinas-Hernández ◽  
Samuel Domínguez-Hernández
Keyword(s):  
Entropy Production ◽  
Equations Of State ◽  
Hermite Polynomials ◽  
Ideal Gas ◽  
Modified Equations ◽  
Modified Entropy ◽  
The Ideal

A modified expression of the electron entropy production in a plasma is deduced by means of the Kelly equations of state instead of the ideal gas equations of state. From the Debye–Hückel model which considers the interaction between the charges, such equations of state are derived for a plasma and the entropy is deduced. The technique to obtain the modified entropy production is based on usual developments but including the modified equations of state giving the regular result plus some extra terms. We derive an expression of the modified entropy production in terms of the tensorial Hermitian moments hr1…rm(m) by means of the irreducible tensorial Hermite polynomials.

Modified equations for ODEs

1994 ◽  
pp. 63-74 ◽  
Author(s):  
M. P. Calvo ◽  
A. Murua ◽  
J. M. Sanz-Serna
Keyword(s):  
Modified Equations
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