scholarly journals On the porous continuum-scale modeling of gravity-driven fingers in unsaturated materials: Numerical solution of a hypodiffusive governing equation that incorporates a hold-back-pile-up effect

2003 ◽  
Vol 39 (6) ◽  
Author(s):  
Mehdi Eliassi ◽  
Robert J. Glass
Keyword(s):  
Numerical Solution ◽  
Governing Equation ◽  
Scale Modeling ◽  
Pile Up ◽  
Gravity Driven ◽  
Continuum Scale

scholarly journals Solutions of the Force-Free Duffing-van der Pol Oscillator Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
Najeeb Alam Khan ◽  
Muhammad Jamil ◽  
Syed Anwar Ali ◽  
Nadeem Alam Khan
Keyword(s):  
Approximate Solution ◽  
Numerical Solution ◽  
Approximate Method ◽  
Governing Equation ◽  
Laplace Transformation ◽  
Large Time ◽  
Van Der Pol Oscillator ◽  
Van Der Pol ◽  
Alternative Framework ◽  
Runge Kutta

A new approximate method for solving the nonlinear Duffing-van der pol oscillator equation is proposed. The proposed scheme depends only on the two components of homotopy series, the Laplace transformation and, the Padé approximants. The proposed method introduces an alternative framework designed to overcome the difficulty of capturing the behavior of the solution and give a good approximation to the solution for a large time. The Runge-Kutta algorithm was used to solve the governing equation via numerical solution. Finally, to demonstrate the validity of the proposed method, the response of the oscillator, which was obtained from approximate solution, has been shown graphically and compared with that of numerical solution.

From dawn to dusk

2018 ◽  
Vol 102 (554) ◽  
pp. 246-256
Author(s):  
John D. Mahony
Keyword(s):  
Point Source ◽  
Numerical Solution ◽  
Governing Equation ◽  
Winter Solstice ◽  
Tangency Condition ◽  
Problem Corner

It used to be the case in some jurisdictions that a rhythmic knell of the Angelus bell would mark the onset of dawn, noon and the passing of a day at dusk. Between these times there is daylight whose duration varies from place to place and from day to day and which can be predicted either exactly or approximately. An illuminating problem concerning the number of daylight hours at a winter solstice in London was posed recently and answered in the Problem Corner of The Mathematical Gazette [1]. It was shown, for example, that a calculation of daylight hours rested strictly upon the numerical solution to a transcendental trigonometric equation. Related references to earlier works in the Gazette involving a point source Sun were also given.The purpose of this note is multifold. First, it is to point out that the above-cited equation might be viewed also as a “Sun-ray-to-Earth tangency condition”. Such a condition was developed earlier by the author in a publication that is now defunct [2], and so for completeness the steps necessary to establish the condition will be produced again here. Second, it will be evident from the manner of its derivation that the governing equation is valid at all orbit points, not just at a given solstice.

scholarly journals Continuum-Scale Modeling of Liquid Redistribution in a Stack of Thin Hydrophilic Fibrous Layers

2018 ◽  
Vol 122 (1) ◽  
pp. 203-219 ◽  
Author(s):  
Amir Hossein Tavangarrad ◽  
Behzad Mohebbi ◽  
S. Majid Hassanizadeh ◽  
Rodrigo Rosati ◽  
Jan Claussen ◽  
...  
Keyword(s):  
Scale Modeling ◽  
Continuum Scale

scholarly journals Continuum-scale modeling of water infiltration into a stack of two thin fibrous layers and their inter-layer space

2019 ◽  
Vol 207 ◽  
pp. 769-779 ◽  
Author(s):  
Amir Hossein Tavangarrad ◽  
Behzad Mohebbi ◽  
Chaozhong Qin ◽  
S. Majid Hassanizadeh ◽  
Rodrigo Rosati ◽  
...  
Keyword(s):  
Water Infiltration ◽  
Scale Modeling ◽  
Continuum Scale
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