scholarly journals Magnetic flux periodicity in second order topological superconductors

2020 ◽  
Vol 101 (12) ◽  
Author(s):  
Suman Jyoti De ◽  
Udit Khanna ◽  
Sumathi Rao
Keyword(s):  
Magnetic Flux ◽  
Second Order ◽  
Topological Superconductors

Fast and Globally Convergent Nonlinear System Model for 3D Magnetostrictive Systems

2014 ◽  
Author(s):  
Hafez Tari ◽  
Marcelo J. Dapino
Keyword(s):  
Magnetic Field ◽  
Magnetic Flux ◽  
Flux Density ◽  
Error Function ◽  
Second Order ◽  
System Model ◽  
Magnetic Flux Density ◽  
Magnetostrictive Material ◽  
Globally Convergent ◽  
Direct Model

A globally convergent and fully coupled magnetomechanical model for 3D magnetostrictive systems is presented. In magnetostrictive actuators, magnetic field and stress inputs generate magnetic flux density and strain. We refer to models that follow this scheme as direct models (no relation to the direct magnetomechanical effect). In certain design and control situations, inverse models are necessary in which the magnetic field and stress are found from specified magnetic flux density and strains. This inversion typically involves an iterative procedure, which may be prone to convergence issues. An inverse model approach is proposed for arbitrary magnetostrictive materials. The inversion requirement is a continuous and second order differentiable direct model for any chosen magnetostrictive material. The approach is globally convergent, which makes it ideal for use in finite element frameworks. The premise of the proposed iterative system model is to constitute a recursive correction formula based on second order approximations of a novel scalar error function which allows to achieve a faster convergence rate. A continuation approach is then used to achieve global convergence for arbitrary input parameters. To illustrate, Galfenol is chosen as the magnetostrictive material, and analytical derivations of the Jacobian and Hessian matrices are presented. Finally, the computational efficiency of the proposed approach is shown to compare favorably against existing models.

On vertical spinning Alfvén waves in a magnetic flux tube

1992 ◽  
Vol 48 (3) ◽  
pp. 415-434 ◽  
Author(s):  
L. M. B. C. Campos ◽  
N. L. Isaeva
Keyword(s):  
Magnetic Field ◽  
Exact Solution ◽  
Magnetic Flux ◽  
Hall Effect ◽  
Flux Tube ◽  
Critical Level ◽  
Alfven Waves ◽  
Second Order ◽  
Magnetic Flux Tube ◽  
Alfvén Waves

We derive the Alfvén-wave equation for an atmosphere in the presence of a non-uniform vertical magnetic field and the Hall effect, allowing for Alfvén speed and ion gyrofrequency that may vary with altitude; the pair of coupled second-order differential equations for the horizontal wave variables, namely magnetic field or velocity perturbations, is reduced to a single complex, second-order differential equation. The latter is applied to spinning Alfvén waves in a magnetic flux tube, in magnetohydrostatic equilibrium, in an isothermal atmosphere. The exact solution is found in terms of hypergeometric functions, from which it is shown that at ‘high altitude’the magnetic field perturbation tends to grow to a non-small fraction of the background magnetic field. By ‘high-altitude’ is meant far above the critical level, which acts as a reflecting layer for left-polarized waves incident from below, i.e. from the ‘low-altitude’ range. We also obtain the exact solution near the critical level, where the left-polarized wave has a logarithmic singularity, and the right-polarized wave is finite. The latter is plotted in this region of wave frequency comparable to ion gyrofrequency, and it is shown that the Hall effect can cause oscillations of wave amplitude and non-monotonic phases with slope of alternating sign. The latter corresponds to ‘tunnelling’, i.e. waves propagating in opposite directions or trapped in adjoining atmospheric layers; this could explain the appearance of inward- and outward-propagating waves, with almost random phases, in the solar wind beyond the earth, for which the Hall effect on Alfvén waves should be significant.

scholarly journals Quadrupole spin polarization as signature of second-order topological superconductors

2021 ◽  
Vol 103 (4) ◽  
Author(s):  
Kirill Plekhanov ◽  
Niclas Müller ◽  
Yanick Volpez ◽  
Dante M. Kennes ◽  
Herbert Schoeller ◽  
...  
Keyword(s):  
Spin Polarization ◽  
Second Order ◽  
Quadrupole Spin ◽  
Topological Superconductors

scholarly journals Lattice-Symmetry-Assisted Second-Order Topological Superconductors and Majorana Patterns

2019 ◽  
Vol 123 (15) ◽  
Author(s):  
Xiao-Hong Pan ◽  
Kai-Jie Yang ◽  
Li Chen ◽  
Gang Xu ◽  
Chao-Xing Liu ◽  
...  
Keyword(s):  
Second Order ◽  
Topological Superconductors ◽  
Lattice Symmetry

scholarly journals Majorana corner flat bands in two-dimensional second-order topological superconductors

2020 ◽  
Vol 101 (10) ◽  
Author(s):  
Majid Kheirkhah ◽  
Yuki Nagai ◽  
Chun Chen ◽  
Frank Marsiglio
Keyword(s):  
Second Order ◽  
Two Dimensional ◽  
Flat Bands ◽  
Topological Superconductors
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