Diffusion-reaction approach to electronic relaxation in solution: Exact solution of Smoluchowski equation for parabolic potential in presence of a rectangular sink

2021 ◽  
pp. 111206
Author(s):  
Proma Mondal ◽  
Aniruddha Chakraborty
Keyword(s):  
Exact Solution ◽  
Smoluchowski Equation ◽  
Diffusion Reaction ◽  
Electronic Relaxation ◽  
Parabolic Potential

3D Unsteady Convection-Diffusion-Reaction via GFEM Solver

2015 ◽  
Vol 751 ◽  
pp. 313-318
Author(s):  
Estaner Claro Romão ◽  
Luiz Felipe Mendes de Moura
Keyword(s):  
Numerical Simulation ◽  
Exact Solution ◽  
Galerkin Method ◽  
Diffusion Reaction ◽  
Convection Diffusion ◽  
Temporal Discretization ◽  
Physical Problems ◽  
Important Study ◽  
Initial Idea ◽  
The Galerkin Method

In this paper, an important study on the application of the α family of temporal discretization is presented. For spatial discretization the Galerkin Method (GFEM) was used. With the variation of the α coefficient in temporal discretization and through one numerical applications with exact solution, it will be possible to have an initial idea on how each one of the two suggested methods behaves. It is expected that this study can be able to advance several other studies within the domain of numerical simulation of physical problems. It is important to note that for all applications we will use a mesh that is considered gross, with the purpose of presenting a method that is robust, precise and mainly computationally economic.

scholarly journals Finite element based hybrid techniques for advection-diffusion-reaction processes

2018 ◽  
Vol 8 (2) ◽  
pp. 127-136
Author(s):  
Murat Sari ◽  
Huseyin Tunc
Keyword(s):  
Exact Solution ◽  
Finite Element ◽  
Numerical Solutions ◽  
Diffusion Reaction ◽  
Optimization Approach ◽  
B Spline ◽  
Hybrid Techniques ◽  
Advection Diffusion ◽  
Pure Diffusion ◽  
Spline Basis

In this paper, numerical solutions of the advection-diffusion-reaction (ADR) equation are investigated using the Galerkin, collocation and Taylor-Galerkin cubic B-spline finite element method in strong form of spatial elements using an ?-family optimization approach for time variation. The main objective of this article is to capture effective results of the finite element techniques with B-spline basis functions under the consideration of the ADR processes. All produced results are compared with the exact solution and the literature for various versions of problems including pure advection, pure diffusion, advection-diffusion, and advection-diffusion-reaction equations. It is proved that the present methods have good agreement with the exact solution and the literature.

Observation by HVEM of the martensite transformation and the superconducting transition in Nb3Sn

1988 ◽  
Vol 46 ◽  
pp. 788-789
Author(s):  
M. A. Kirk ◽  
M. C. Baker ◽  
B. J. Kestel ◽  
H. W. Weber
Keyword(s):  
Thin Films ◽  
Low Temperature ◽  
Superconducting State ◽  
Martensite Transformation ◽  
Sputter Deposition ◽  
Diffusion Reaction ◽  
Solute Diffusion ◽  
Superconducting Transition ◽  
Twin Boundaries ◽  
Martensite Structure

It is well known that a number of compound superconductors with the A15 structure undergo a martensite transformation when cooled to the superconducting state. Nb3Sn is one of those compounds that transforms, at least partially, from a cubic to tetragonal structure near 43 K. To our knowledge this transformation in Nb3Sn has not been studied by TEM. In fact, the only low temperature TEM study of an A15 material, V3Si, was performed by Goringe and Valdre over 20 years ago. They found the martensite structure in some foil areas at temperatures between 11 and 29 K, accompanied by faults that consisted of coherent twin boundaries on {110} planes. In pursuing our studies of irradiation defects in superconductors, we are the first to observe by TEM a similar martensite structure in Nb3Sn.Samples of Nb3Sn suitable for TEM studies have been produced by both a liquid solute diffusion reaction and by sputter deposition of thin films.

Exact solution of a four-site crystal model for an intermediate-valence system

1986 ◽  
Vol 47 (6) ◽  
pp. 1029-1034 ◽  
Author(s):  
J.C. Parlebas ◽  
R.H. Victora ◽  
L.M. Falicov
Keyword(s):  
Exact Solution ◽  
Intermediate Valence ◽  
Crystal Model
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