On Singular Solutions of the Vlasov-Poisson Equations

1993 ◽  
pp. 67-75
Author(s):  
George Majda
Keyword(s):  
Singular Solutions ◽  
Poisson Equations

New singular solutions for the (3+1)-D Protter problem

2018 ◽  
Vol 91 (3) ◽  
pp. 61-68 ◽  
Author(s):  
T.P. Popov ◽  
Keyword(s):  
Singular Solutions

Finite Element Method for Solving Problems with Singular Solutions.

1995 ◽  
Author(s):  
I. Babuska ◽  
B. Andersson ◽  
B. Guo ◽  
H. S. Oh ◽  
J. M. Melenk
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Singular Solutions ◽  
Element Method

scholarly journals Electrodiffusion Phenomena in Neuroscience and the Nernst–Planck–Poisson Equations

Electrochem ◽  
2021 ◽  
Vol 2 (2) ◽  
pp. 197-215
Author(s):  
Jerzy J. Jasielec
Keyword(s):  
Electrical Potential ◽  
Signal Propagation ◽  
Liquid Junction Potential ◽  
Liquid Junction ◽  
Patch Clamp Technique ◽  
Poisson Equations ◽  
Cellular Environment ◽  
Electrochemical Transport ◽  
Insight Into ◽  
Junction Potential

This work is aimed to give an electrochemical insight into the ionic transport phenomena in the cellular environment of organized brain tissue. The Nernst–Planck–Poisson (NPP) model is presented, and its applications in the description of electrodiffusion phenomena relevant in nanoscale neurophysiology are reviewed. These phenomena include: the signal propagation in neurons, the liquid junction potential in extracellular space, electrochemical transport in ion channels, the electrical potential distortions invisible to patch-clamp technique, and calcium transport through mitochondrial membrane. The limitations, as well as the extensions of the NPP model that allow us to overcome these limitations, are also discussed.

scholarly journals Singular solutions in soft limits

2020 ◽  
Vol 2020 (5) ◽  
Author(s):  
Freddy Cachazo ◽  
Bruno Umbert ◽  
Yong Zhang
Keyword(s):  
Singular Solutions

scholarly journals Driving forces on dislocations: finite element analysis in the context of the non-singular dislocation theory

2021 ◽  
Author(s):  
Xiandong Zhou ◽  
Christoph Reimuth ◽  
Peter Stein ◽  
Bai-Xiang Xu
Keyword(s):  
Finite Element ◽  
Dislocation Loop ◽  
Driving Force ◽  
Complex Geometry ◽  
Driving Forces ◽  
Singular Solutions ◽  
Dislocation Model ◽  
Configurational Force ◽  
Element Analysis ◽  
Dislocation Configuration

AbstractThis work presents a regularized eigenstrain formulation around the slip plane of dislocations and the resultant non-singular solutions for various dislocation configurations. Moreover, we derive the generalized Eshelby stress tensor of the configurational force theory in the context of the proposed dislocation model. Based on the non-singular finite element solutions and the generalized configurational force formulation, we calculate the driving force on dislocations of various configurations, including single edge/screw dislocation, dislocation loop, interaction between a vacancy dislocation loop and an edge dislocation, as well as a dislocation cluster. The non-singular solutions and the driving force results are well benchmarked for different cases. The proposed formulation and the numerical scheme can be applied to any general dislocation configuration with complex geometry and loading conditions.

scholarly journals Symmetry and monotonicity of singular solutions of double phase problems

2021 ◽  
Vol 280 ◽  
pp. 435-463
Author(s):  
Stefano Biagi ◽  
Francesco Esposito ◽  
Eugenio Vecchi
Keyword(s):  
Singular Solutions ◽  
Double Phase

Blow-up for the compressible isentropic Navier-Stokes-Poisson equations

2019 ◽  
Vol 70 (1) ◽  
pp. 9-19
Author(s):  
Jianwei Dong ◽  
Junhui Zhu ◽  
Yanping Wang
Keyword(s):  
Blow Up ◽  
Navier Stokes ◽  
Poisson Equations
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