scholarly journals Precised approximations in elliptic homogenization beyond the periodic setting

2020 ◽  
Vol 116 (2) ◽  
pp. 93-137
Author(s):  
X. Blanc ◽  
M. Josien ◽  
C. Le Bris
Keyword(s):  
Periodic Setting

Particle energization inside plasmoids: numerical and analytical investigations

2021 ◽  
Author(s):  
Xiaozhou Zhao ◽  
Rony Keppens ◽  
Fabio Bacchini
Keyword(s):  
Test Particle ◽  
Large Scale ◽  
Mass Density ◽  
Magnetic Islands ◽  
Chaotic Flow ◽  
Reynolds Decomposition ◽  
Particle Simulations ◽  
Particle Energization ◽  
Periodic Setting ◽  
A Current

<div> <div> <div> <p>In an idealized system where four magnetic islands interact in a two-dimensional periodic setting, we follow the detailed evolution of current sheets forming in between the islands, as a result of an enforced large-scale merging by magnetohydrodynamic (MHD) simulation. The large-scale island merging is triggered by a perturbation to the velocity field, which drives one pair of islands move towards each other while the other pair of islands are pushed away from one another. The "X"-point located in the midst of the four islands is locally unstable to the perturbation and collapses, producing a current sheet in between with enhanced current and mass density. Using grid-adaptive resistive magnetohydrodynamic (MHD) simulations, we establish that slow near-steady Sweet-Parker reconnection transits to a chaotic, multi-plasmoid fragmented state, when the Lundquist number exceeds about 3×10<sup>4</sup>, well in the range of previous studies on plasmoid instability. The extreme resolution employed in the MHD study shows significant magnetic island substructures. Turbulent and chaotic flow patters are also observed inside the islands. We set forth to explore how charged particles can be accelerated in embedded mini-islands within larger (monster)-islands on the sheet. We study the motion of the particles in a MHD snapshot at a fixed instant of time by the Test-Particle Module incorporated in AMRVAC (). The planar MHD setting artificially causes the largest acceleration in the ignored third direction, but does allow for full analytic study of all aspects leading to the acceleration and the in-plane, projected trapping of particles within embedded mini-islands. The analytic result uses a decomposition of the test particle velocity in slow and fast changing components, akin to the Reynolds decomposition in turbulence studies. The analytic results allow a complete fit to representative proton test particle simulations, which after initial non-relativistic motion throughout the monster island, show the potential of acceleration within a mini-island beyond (√2/2)c≈0.7c, at which speed the acceleration is at its highest efficiency. Acceleration to several hundreds of GeVs can happen within several tens of seconds, for upward traveling protons in counterclockwise mini-islands of sizes smaller than the proton gyroradius.</p> </div> </div> </div><div></div><div></div>

scholarly journals Blow-Up Analysis for the Periodic Two-Component μ-Hunter-Saxton System

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Yunxi Guo ◽  
Tingjian Xiong
Keyword(s):  
Transport Equation ◽  
Wave Breaking ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Blow Up Analysis ◽  
Classic Method ◽  
Two Component ◽  
Localization Analysis ◽  
Spatially Periodic ◽  
Periodic Setting

The two-component μ-Hunter-Saxton system is considered in the spatially periodic setting. Firstly, a wave-breaking criterion is derived by employing the localization analysis of the transport equation theory. Secondly, several sufficient conditions of the blow-up solutions are established by using the classic method. The results obtained in this paper are new and different from those in previous works.

scholarly journals Wavelet deconvolution in a periodic setting

2004 ◽  
Vol 66 (3) ◽  
pp. 547-573 ◽  
Author(s):  
Iain M. Johnstone ◽  
Gerard Kerkyacharian ◽  
Dominique Picard ◽  
Marc Raimondo
Keyword(s):  
Periodic Setting

scholarly journals Projector augmented-wave method: an analysis in a one-dimensional setting

2020 ◽  
Vol 54 (1) ◽  
pp. 25-58
Author(s):  
Mi-Song Dupuy
Keyword(s):  
Numerical Analysis ◽  
Eigenvalue Problem ◽  
Ab Initio Calculations ◽  
Wave Method ◽  
One Dimensional ◽  
The One ◽  
Dimension One ◽  
Projector Augmented Wave ◽  
Periodic Setting ◽  
Periodic Schrödinger Operator

In this article, a numerical analysis of the projector augmented-wave (PAW) method is presented, restricted to the case of dimension one with Dirac potentials modeling the nuclei in a periodic setting. The PAW method is widely used in electronic ab initio calculations, in conjunction with pseudopotentials. It consists in replacing the original electronic Hamiltonian H by a pseudo-Hamiltonian HPAW via the PAW transformation acting in balls around each nuclei. Formally, the new eigenvalue problem has the same eigenvalues as H and smoother eigenfunctions. In practice, the pseudo-Hamiltonian HPAW has to be truncated, introducing an error that is rarely analyzed. In this paper, error estimates on the lowest PAW eigenvalue are proved for the one-dimensional periodic Schrödinger operator with double Dirac potentials.

scholarly journals A weak KAM approach to the periodic stationary Hartree equation

2021 ◽  
Vol 28 (6) ◽  
Author(s):  
L. Zanelli ◽  
F. Mandreoli ◽  
F. Cardin
Keyword(s):  
Ground State ◽  
Kam Theory ◽  
Mean Field ◽  
Hartree Equation ◽  
Many Body ◽  
Semiclassical Asymptotics ◽  
The Mean ◽  
Mean Field Asymptotics ◽  
Periodic Setting ◽  
Integral Identities

AbstractWe present, through weak KAM theory, an investigation of the stationary Hartree equation in the periodic setting. More in details, we study the Mean Field asymptotics of quantum many body operators thanks to various integral identities providing the energy of the ground state and the minimum value of the Hartree functional. Finally, the ground state of the multiple-well case is studied in the semiclassical asymptotics thanks to the Agmon metric.

scholarly journals Wave-Breaking Criterion for the Generalized Weakly Dissipative Periodic Two-Component Hunter-Saxton System

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Jianmei Zhang ◽  
Lixin Tian
Keyword(s):  
Wave Breaking ◽  
Well Posedness ◽  
Two Component ◽  
Periodic Setting

This paper studies the wave-breaking criterion for the generalized weakly dissipative two-component Hunter-Saxton system in the periodic setting. We get local well-posedness for the generalized weakly dissipative two-component Hunter-Saxton system. We study a wave-breaking criterion for solutions and results of wave-breaking solutions with certain initial profiles.

Sign in / Sign up

Export Citation Format

Share Document