Two electrons in one-dimensional nanorings:  Exact solutions and interaction energies

2003 ◽  
Vol 68 (4) ◽  
Author(s):  
Jia-Lin Zhu ◽  
Zhensheng Dai ◽  
Xiao Hu
Keyword(s):  
Exact Solutions ◽  
Interaction Energies ◽  
One Dimensional

Transport processes between fluids and clouds of suspended particles: some exact solutions

1957 ◽  
Vol 242 (1231) ◽  
pp. 430-443 ◽  
Keyword(s):  
Exact Solutions ◽  
Turbulent Mixing ◽  
Liquid Fuel ◽  
Transport Processes ◽  
Dimensional System ◽  
Unsteady Heat Transfer ◽  
One Dimensional ◽  
Homogeneous Reactor ◽  
Fourier Equation ◽  
Gas Component

The paper relates to processes such as the burning of pulverized solid fuel and of liquid fuel sprays, absorption of a gas component by a solvent spray, etc., and takes account of convection and turbulent mixing of the cloud. The Eulerian equation of conservation for the steady process is shown to be transformable into the Fourier equation for unsteady heat transfer in a flowing medium. Exact solutions are given for a one-dimensional system, an axially symmetrical system, and the steady-flow homogeneous reactor. Numerical methods are indicated for more complex systems, and the possibility of solution by means of an analogue is pointed out.

Exact Solutions for One-Dimensional Gray Media

2022 ◽  
pp. 467-495
Author(s):  
Michael F. Modest ◽  
Sandip Mazumder
Keyword(s):  
Exact Solutions ◽  
One Dimensional

scholarly journals Exact solutions of a one-dimensional mixture of spinor bosons and spinor fermions

2009 ◽  
Vol 820 (3) ◽  
pp. 753-779
Author(s):  
Shi-Jian Gu ◽  
Junpeng Cao ◽  
Shu Chen ◽  
Hai-Qing Lin
Keyword(s):  
Exact Solutions ◽  
One Dimensional
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