scholarly journals Analytic solution of the Ornstein-Zernike relation for inhomogeneous liquids

2016 ◽  
Vol 145 (23) ◽  
pp. 234508 ◽  
Author(s):  
Yan He ◽  
Stuart A. Rice ◽  
Xinliang Xu
Keyword(s):  
Analytic Solution ◽  
Inhomogeneous Liquids

An Analytic Solution for the Noncoplanar P4P Problem with An Uncalibrated Camera

2011 ◽  
Vol 34 (4) ◽  
pp. 748-754 ◽  
Author(s):  
Yang GUO ◽  
Xiang-De ZHANG ◽  
Xin-He XU
Keyword(s):  
Analytic Solution ◽  
Uncalibrated Camera

On the convective diffusion under partial slip at wall

1989 ◽  
Vol 54 (4) ◽  
pp. 967-980 ◽  
Author(s):  
Ondřej Wein ◽  
Petr Kučera
Keyword(s):  
Mass Transfer ◽  
Numerical Solution ◽  
Analytic Solution ◽  
Convective Diffusion ◽  
Linear Velocity ◽  
Partial Slip ◽  
Accurate Calculation ◽  
Transfer Coefficients ◽  
Empirical Formulas ◽  
Mass Transfer Coefficients

Extended Leveque problem is studied for linear velocity profiles, vx(z) = u + qz. The existing analytic solution is reconsidered and shown to be inapplicable for the accurate calculation of mean mass-transfer coefficients. A numerical solution is reported and its accuracy is checked in detail. Simple but fairly accurate empirical formulas are suggested for the calculating of local and mean mass-transfer coefficients.

Analytic solution to the problem of the couette flow in a plane channel with infinitely large parallel walls

2011 ◽  
Vol 56 (1) ◽  
pp. 49-54 ◽  
Author(s):  
V. N. Popov ◽  
I. V. Testova ◽  
A. A. Yushkanov
Keyword(s):  
Couette Flow ◽  
Analytic Solution ◽  
Plane Channel

scholarly journals A New Approach for Approximate Solution of ADE: Physical-Based Modeling of Carriers in Doping Region

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 458
Author(s):  
Leobardo Hernandez-Gonzalez ◽  
Jazmin Ramirez-Hernandez ◽  
Oswaldo Ulises Juarez-Sandoval ◽  
Miguel Angel Olivares-Robles ◽  
Ramon Blanco Sanchez ◽  
...  
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Analytic Solution ◽  
Order Differential Equation ◽  
Electric Circuit ◽  
New Approach ◽  
In Doping ◽  
Electric Behavior ◽  
Spatio Temporal ◽  
Physical Phenomena

The electric behavior in semiconductor devices is the result of the electric carriers’ injection and evacuation in the low doping region, N-. The carrier’s dynamic is determined by the ambipolar diffusion equation (ADE), which involves the main physical phenomena in the low doping region. The ADE does not have a direct analytic solution since it is a spatio-temporal second-order differential equation. The numerical solution is the most used, but is inadequate to be integrated into commercial electric circuit simulators. In this paper, an empiric approximation is proposed as the solution of the ADE. The proposed solution was validated using the final equations that were implemented in a simulator; the results were compared with the experimental results in each phase, obtaining a similarity in the current waveforms. Finally, an advantage of the proposed methodology is that the final expressions obtained can be easily implemented in commercial simulators.

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