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 The asymptotic dynamics of de Sitter gravity in three dimensions

2002 ◽  
Vol 19 (3) ◽  
pp. 579-587 ◽  
Author(s):  
Sergio Cacciatori ◽  
Dietmar Klemm
Keyword(s):  
Three Dimensions ◽  
De Sitter ◽  
Asymptotic Dynamics

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 Hamiltonian formulation for the description of interfacial solitary waves

1998 ◽  
Vol 5 (1) ◽  
pp. 3-12 ◽  
Author(s):  
R. Grimshaw ◽  
S. R. Pudjaprasetya
Keyword(s):  
Solitary Waves ◽  
Variable Coefficient ◽  
Hamiltonian Structure ◽  
Vries Equation ◽  
Hamiltonian Formulation ◽  
Constant Density ◽  
Two Fluids ◽  
De Vries ◽  
Lower Fluid ◽  
New Equation

Abstract. We consider solitary waves propagating on the interface between two fluids, each of constant density, for the case when the upper fluid is bounded above by a rigid horizontal plane, but the lower fluid has a variable depth. It is well-known that in this situation, the solitary waves can be described by a variable-coefficient Korteweg-de Vries equation. Here we reconsider the derivation of this equation and present a formulation which preserves the Hamiltonian structure of the underlying system. The result is a new variable-coefficient Korteweg-de Vries equation, which conserves energy to a higher order than the more conventional well-known equation. The new equation is used to describe the transformation of an interfacial solitary wave which propagates into a region of decreasing depth.

scholarly journals Experimental observation of the marginal glass phase in a colloidal glass

2020 ◽  
Vol 117 (11) ◽  
pp. 5714-5718 ◽  
Author(s):  
Andrew P. Hammond ◽  
Eric I. Corwin
Keyword(s):  
Glass Phase ◽  
Tracer Particle ◽  
Mean Field ◽  
Three Dimensions ◽  
Colloidal System ◽  
Time Behavior ◽  
Mean Field Limit ◽  
Time Dynamics ◽  
Stable Glass ◽  
Colloidal Glass

The replica theory of glasses predicts that in the infinite dimensional mean field limit, there exist two distinct glassy phases of matter: stable glass and marginal glass. We have developed a technique to experimentally probe these phases of matter using a colloidal glass. We avoid the difficulties inherent in measuring the long time behavior of glasses by instead focusing on the very short time dynamics of the ballistic to caged transition. We track a single tracer particle within a slowly densifying glass and measure the resulting mean squared displacement (MSD). By analyzing the MSD, we find that upon densification, our colloidal system moves through several states of matter. At lowest densities, it is a subdiffusive liquid. Next, it behaves as a stable glass, marked by the appearance of a plateau in the MSD whose magnitude shrinks with increasing density. However, this shrinking plateau does not shrink to zero; instead, at higher densities, the system behaves as a marginal glass, marked by logarithmic growth in the MSD toward that previous plateau value. Finally, at the highest experimental densities, the system returns to the stable glass phase. This provides direct experimental evidence for the existence of a marginal glass in three dimensions.

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

THREE-DIMENSIONAL LATTICE BOLTZMANN MODEL RESULTS FOR COMPLEX FLUIDS ORDERING

2005 ◽  
Vol 16 (12) ◽  
pp. 1819-1830
Author(s):  
G. AMATI ◽  
F. MASSAIOLI ◽  
G. GONNELLA ◽  
AIGUO XU ◽  
A. LAMURA
Keyword(s):  
Lattice Boltzmann ◽  
Three Dimensional ◽  
Numerical Approach ◽  
Three Dimensions ◽  
Lattice Boltzmann Model ◽  
Domain Growth ◽  
Late Time ◽  
Extended Defects ◽  
Time Dynamics ◽  
Boltzmann Method

The kinetics of domain growth of fluid mixtures quenched from a disordered to a lamellar phase has been studied in three dimensions. We use a numerical approach based on the lattice Boltzmann method (LBM). A novel implementation for LBM which "fuses" the collision and streaming steps is used in order to reduce memory and bandwidth requirements. We find that extended defects between stacks of lamellae with different orientation dominate the late time dynamics.

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