scholarly journals On the Conley conjecture for Reeb flows

2015 ◽  
Vol 26 (07) ◽  
pp. 1550047 ◽  
Author(s):  
Viktor L. Ginzburg ◽  
Başak Z. Gürel ◽  
Leonardo Macarini
Keyword(s):  
Magnetic Field ◽  
Energy Level ◽  
Periodic Orbits ◽  
Geodesic Flow ◽  
Low Energy ◽  
Contact Manifolds ◽  
Reeb Flows ◽  
Circle Bundles ◽  
Conley Conjecture

In this paper, we prove the existence of infinitely many closed Reeb orbits for a certain class of contact manifolds. This result can be viewed as a contact analogue of the Hamiltonian Conley conjecture. The manifolds for which the contact Conley conjecture is established are the pre-quantization circle bundles with aspherical base. As an application, we prove that for a surface of genus at least two with a non-vanishing magnetic field, the twisted geodesic flow has infinitely many periodic orbits on every low energy level.

Transfer optics for high spatial resolution electron spectroscopy

1988 ◽  
Vol 46 ◽  
pp. 666-667
Author(s):  
G. G. Hembree ◽  
Luo Chuan Hong ◽  
P.A. Bennett ◽  
J.A. Venables
Keyword(s):  
Magnetic Field ◽  
Scanning Transmission Electron Microscope ◽  
Low Energy ◽  
Objective Lens ◽  
State University ◽  
Arizona State University ◽  
Initial Field ◽  
Resolution Electron ◽  
Scanning Transmission ◽  
Low Energy Electrons

A new field emission scanning transmission electron microscope has been constructed for the NSF HREM facility at Arizona State University. The microscope is to be used for studies of surfaces, and incorporates several surface-related features, including provision for analysis of secondary and Auger electrons; these electrons are collected through the objective lens from either side of the sample, using the parallelizing action of the magnetic field. This collimates all the low energy electrons, which spiral in the high magnetic field. Given an initial field Bi∼1T, and a final (parallelizing) field Bf∼0.01T, all electrons emerge into a cone of semi-angle θf≤6°. The main practical problem in the way of using this well collimated beam of low energy (0-2keV) electrons is that it is travelling along the path of the (100keV) probing electron beam. To collect and analyze them, they must be deflected off the beam path with minimal effect on the probe position.

STABLE hc/e VORTICES IN SUPERCONDUCTORS WITH SPIN-CHARGE SEPARATION

1992 ◽  
Vol 06 (05n06) ◽  
pp. 509-526
Author(s):  
Subir Sachdev
Keyword(s):  
Magnetic Field ◽  
Magnetic Flux ◽  
Normal State ◽  
Phenomenological Model ◽  
Charge Separation ◽  
Cuprate Superconductors ◽  
Superconducting Phase ◽  
Low Energy ◽  
Large N ◽  
Normal State Properties

A phenomenological model, F, of the superconducting phase of systems with spin-charge separation and antiferromagnetically induced pairing is studied. Above Hc1, magnetic flux can always pierce the superconductor in vortices with flux hc/2e, but regimes are found in which vortices with flux hc/e are preferred. Little-Park and other experiments, which examine periodicities with a varying magnetic field, always observe a period of hc/2e. The low energy properties of a symplectic large-N expansion of a model of the cuprate superconductors are argued to be well described by F. This analysis and some normal state properties of the cuprates suggest that hc/e vortices should be stable at the lowest dopings away from the insulating state at which superconductivity first occurs.

scholarly journals Conformal geodesics on gravitational instantons

2021 ◽  
pp. 1-32
Author(s):  
MACIEJ DUNAJSKI ◽  
PAUL TOD
Keyword(s):  
Magnetic Field ◽  
Geodesic Flow ◽  
Isometry Group ◽  
Three Dimensional ◽  
First Integrals ◽  
Complete Integrability ◽  
Conformal Killing ◽  
Gravitational Instantons ◽  
Geodesic Equations ◽  
Jacobi Equations

Abstract We study the integrability of the conformal geodesic flow (also known as the conformal circle flow) on the SO(3)–invariant gravitational instantons. On a hyper–Kähler four–manifold the conformal geodesic equations reduce to geodesic equations of a charged particle moving in a constant self–dual magnetic field. In the case of the anti–self–dual Taub NUT instanton we integrate these equations completely by separating the Hamilton–Jacobi equations, and finding a commuting set of first integrals. This gives the first example of an integrable conformal geodesic flow on a four–manifold which is not a symmetric space. In the case of the Eguchi–Hanson we find all conformal geodesics which lie on the three–dimensional orbits of the isometry group. In the non–hyper–Kähler case of the Fubini–Study metric on $\mathbb{CP}^2$ we use the first integrals arising from the conformal Killing–Yano tensors to recover the known complete integrability of conformal geodesics.

scholarly journals Legendrian contact homology and topological entropy

2019 ◽  
Vol 11 (01) ◽  
pp. 53-108 ◽  
Author(s):  
Marcelo R. R. Alves
Keyword(s):  
Growth Rate ◽  
Topological Entropy ◽  
Infinite Family ◽  
Contact Structures ◽  
Legendrian Knots ◽  
Contact Homology ◽  
Contact Manifolds ◽  
3 Dimensional ◽  
Reeb Flows ◽  
Legendrian Contact Homology

In this paper we study the growth rate of a version of Legendrian contact homology, which we call strip Legendrian contact homology, in 3-dimensional contact manifolds and its relation to the topological entropy of Reeb flows. We show that: if for a pair of Legendrian knots in a contact 3-manifold [Formula: see text] the strip Legendrian contact homology is defined and has exponential homotopical growth with respect to the action, then every Reeb flow on [Formula: see text] has positive topological entropy. This has the following dynamical consequence: for all Reeb flows (even degenerate ones) on [Formula: see text] the number of hyperbolic periodic orbits grows exponentially with respect to the period. We show that for an infinite family of 3-manifolds, infinitely many different contact structures exist that possess a pair of Legendrian knots for which the strip Legendrian contact homology has exponential growth rate.

A 0.19-V minimum input low energy level shifter for extremely low-voltage VLSIs

2015 ◽  
Author(s):  
Ryo Matsuzuka ◽  
Tetsuya Hirose ◽  
Yuzuru Shizuku ◽  
Nobutaka Kuroki ◽  
Masahiro Numa
Keyword(s):  
Energy Level ◽  
Low Voltage ◽  
Low Energy ◽  
Level Shifter

Influence of time-variable solar wind on the response of Mercury’s magnetosphere

2021 ◽  
Author(s):  
Sae Aizawa ◽  
Nicolas André ◽  
Ronan Modolo ◽  
Elisabeth Werner ◽  
Jim Slavin ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Solar Wind ◽  
Charged Particles ◽  
Time Variable ◽  
Low Energy ◽  
Field Of View ◽  
Plasma Measurement ◽  
Electrons And Ions ◽  
Low Energy Electrons ◽  
The Magnetic Field

<p><span lang="EN-GB">BepiColombo is going to conduct its first Mercury flyby in October 2021. During this flyby,  plasma measurement will be obtained and bring new insights on the Hermean magnetosphere and its interaction with the Sun despite the limited field of view of the instruments during the cruise phase. Unlike Mariner-10 ion measurements will be obtained, and unlike MESSENGER, low energy electrons and ions will be measured simultaneously. In this study, we have revisited Mariner 10 and MESSENGER observations with the help of the global hybrid model LatHyS in order to understand the influence of time-variable solar wind and to constraint the plasma environment. We are able to reproduce the magnetic field observations of Mariner 10 along its trajectory with in particular two distinct signatures consisting of a quiet and disturbed state of the magnetosphere. In addition, the plasma spectrogram is also collected in the model and this enables us to detail the properties of the charged particles observed during the flyby. We will discuss all these signatures both in term of an interaction with a time-variable solar wind and localized processes occurring in the magnetosphere. We will then present the virtual sampling of both the magnetic field and plasma spectrogram along BepiColombo’s first Mercury flyby trajectory and discuss the possible signatures to be observed at that time.</span></p>

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