A Digital Diffusion-Reaction Type Filter for Nonlinear Denoising

2009 ◽  
Vol 53 (3-4) ◽  
pp. 371-381 ◽  
Author(s):  
Gerlind Plonka
Mathematics ◽  
2022 ◽  
Vol 10 (1) ◽  
pp. 131
Author(s):  
Mikhail K. Kolev ◽  
Miglena N. Koleva ◽  
Lubin G. Vulkov

In this paper, we consider models of cancer migration and invasion, which consist of two nonlinear parabolic equations (one of the convection–diffusion reaction type and the other of the diffusion–reaction type) and an additional nonlinear ordinary differential equation. The unknowns represent concentrations or densities that cannot be negative. Widely used approximations, such as difference schemes, can produce negative solutions because of truncation errors and can become unstable. We propose a new difference scheme that guarantees the positivity of the numerical solution for arbitrary mesh step sizes. It has explicit and fast performance even for nonlinear reaction terms that consist of sums of positive and negative functions. The numerical examples illustrate the simplicity and efficiency of the method. A numerical simulation of a model of cancer migration is also discussed.


Author(s):  
M. A. Kirk ◽  
M. C. Baker ◽  
B. J. Kestel ◽  
H. W. Weber

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.


2020 ◽  
Author(s):  
Miftachul Hadi

We review the work of Ranjit Kumar, R S Kaushal, Awadhesh Prasad. The work is still in progress.


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