A rigorous stability result for the Vlasov-Poisson system in three dimensions

1993 ◽  
Vol 164 (1) ◽  
pp. 133-154 ◽  
Author(s):  
Jürgen Batt ◽  
Gerhard Rein
Keyword(s):  
Stability Result ◽  
Three Dimensions ◽  
Poisson System

Stability of planar rarefaction wave to the 3D bipolar Vlasov–Poisson–Boltzmann system

2019 ◽  
Vol 30 (01) ◽  
pp. 23-104 ◽  
Author(s):  
Shu Wang ◽  
Teng Wang
Keyword(s):  
Wave Propagation ◽  
Boltzmann Equation ◽  
Asymptotic Stability ◽  
Rarefaction Wave ◽  
Stability Result ◽  
Three Dimensions ◽  
Wave Patterns ◽  
Shock Profiles ◽  
Poisson Boltzmann ◽  
Math Phys

We investigate the time-asymptotic stability of planar rarefaction wave for the 3D bipolar Vlasov–Poisson Boltzmann (VPB) system, based on the micro–macro decompositions introduced in [T. P. Liu and S. H. Yu, Boltzmann equation: Micro–macro decompositions and positivity of shock profiles, Comm. Math. Phys. 246 (2004) 133–179; Energy method for the Boltzmann equation, Physica D 188 (2004) 178–192] and our new observations on the underlying wave structures of the equation to overcome the difficulties due to the wave propagation along the transverse directions and its interactions with the planar rarefaction wave. Note that this is the first stability result of basic wave patterns for bipolar VPB system in three dimensions.

Nonneutral Global Solutions for the Electron Euler--Poisson System in Three Dimensions

2013 ◽  
Vol 45 (1) ◽  
pp. 267-278 ◽  
Author(s):  
Pierre Germain ◽  
Nader Masmoudi ◽  
Benoit Pausader
Keyword(s):  
Global Solutions ◽  
Three Dimensions ◽  
Poisson System

scholarly journals Scattering Map for the Vlasov–Poisson System

2021 ◽  
Author(s):  
Patrick Flynn ◽  
Zhimeng Ouyang ◽  
Benoit Pausader ◽  
Klaus Widmayer
Keyword(s):  
Hamiltonian Structure ◽  
Three Dimensions ◽  
Poisson System ◽  
Time Dynamics ◽  
Wave Operators ◽  
Singular Coefficients ◽  
Asymptotic Dynamics ◽  
Scattering Operators ◽  
New Equation ◽  
Conformal Inversion

AbstractWe construct (modified) scattering operators for the Vlasov–Poisson system in three dimensions, mapping small asymptotic dynamics as $$t\rightarrow -\infty$$ t → - ∞ to asymptotic dynamics as $$t\rightarrow +\infty$$ t → + ∞ . The main novelty is the construction of modified wave operators, but we also obtain a new simple proof of modified scattering. Our analysis is guided by the Hamiltonian structure of the Vlasov–Poisson system. Via a pseudo-conformal inversion, we recast the question of asymptotic behavior in terms of local in time dynamics of a new equation with singular coefficients which is approximately integrated using a generating function.

scholarly journals Linear stability of stationary solutions of the Vlasov-Poisson system in three dimensions

1995 ◽  
Vol 130 (2) ◽  
pp. 163-182 ◽  
Author(s):  
J�rgen Batt ◽  
Philip J. Morrison ◽  
Gerhard Rein
Keyword(s):  
Linear Stability ◽  
Stationary Solutions ◽  
Three Dimensions ◽  
Poisson System

High-resolution scanning electron microscopy (HRSEM) of mitochondria from various rat tissues

1988 ◽  
Vol 46 ◽  
pp. 14-15
Author(s):  
P.J. Lea ◽  
M.J. Hollenberg
Keyword(s):  
Electron Microscopy ◽  
Pigment Epithelium ◽  
Retinal Pigment ◽  
Rat Hepatocytes ◽  
Three Dimensions ◽  
Objective Lens ◽  
Rat Tissues ◽  
Thin Sections ◽  
Reconstruction Methods ◽  
Scanning Electron

Our current understanding of mitochondrial ultrastructure has been derived primarily from thin sections using transmission electron microscopy (TEM). This information has been extrapolated into three dimensions by artist's impressions (1) or serial sectioning techniques in combination with computer processing (2). The resolution of serial reconstruction methods is limited by section thickness whereas artist's impressions have obvious disadvantages.In contrast, the new techniques of HRSEM used in this study (3) offer the opportunity to view simultaneously both the internal and external structure of mitochondria directly in three dimensions and in detail.The tridimensional ultrastructure of mitochondria from rat hepatocytes, retinal (retinal pigment epithelium), renal (proximal convoluted tubule) and adrenal cortex cells were studied by HRSEM. The specimens were prepared by aldehyde-osmium fixation in combination with freeze cleavage followed by partial extraction of cytosol with a weak solution of osmium tetroxide (4). The specimens were examined with a Hitachi S-570 scanning electron microscope, resolution better than 30 nm, where the secondary electron detector is located in the column directly above the specimen inserted within the objective lens.

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