scholarly journals Covering Graphs, Magnetic Spectral Gaps and Applications to Polymers and Nanoribbons

Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1163 ◽  
Author(s):  
John Stewart Fabila-Carrasco ◽  
Fernando Lledó
Keyword(s):  
Magnetic Field ◽  
Control Parameter ◽  
Spectral Band ◽  
Sufficient Conditions ◽  
Magnetic Potential ◽  
Spectral Gaps ◽  
Spectral Bands ◽  
Covering Graph ◽  
Abelian Lattice ◽  
Band Gap Structure

In this article, we analyze the spectrum of discrete magnetic Laplacians (DML) on an infinite covering graph G ˜ → G = G ˜ / Γ with (Abelian) lattice group Γ and periodic magnetic potential β ˜ . We give sufficient conditions for the existence of spectral gaps in the spectrum of the DML and study how these depend on β ˜ . The magnetic potential can be interpreted as a control parameter for the spectral bands and gaps. We apply these results to describe the spectral band/gap structure of polymers (polyacetylene) and nanoribbons in the presence of a constant magnetic field.

Peierls’ substitution via minimal coupling and magnetic pseudo-differential calculus

2019 ◽  
Vol 31 (03) ◽  
pp. 1950008
Author(s):  
Horia D. Cornean ◽  
Viorel Iftimie ◽  
Radu Purice
Keyword(s):  
Magnetic Field ◽  
Differential Calculus ◽  
Spectral Band ◽  
Spatial Decay ◽  
Minimal Coupling ◽  
Field Perturbation ◽  
Wannier Functions ◽  
Weak Magnetic Fields ◽  
The Magnetic Field ◽  
Magnetic Field Perturbation

We revisit the celebrated Peierls–Onsager substitution for weak magnetic fields with no spatial decay conditions. We assume that the non-magnetic [Formula: see text]-periodic Hamiltonian has an isolated spectral band whose Riesz projection has a range which admits a basis generated by [Formula: see text] exponentially localized composite Wannier functions. Then we show that the effective magnetic band Hamiltonian is unitarily equivalent to a Hofstadter-like magnetic matrix living in [Formula: see text]. In addition, if the magnetic field perturbation is slowly variable in space, then the perturbed spectral island is close (in the Hausdorff distance) to the spectrum of a Weyl quantized minimally coupled symbol. This symbol only depends on [Formula: see text] and is [Formula: see text]-periodic; if [Formula: see text], the symbol equals the Bloch eigenvalue itself. In particular, this rigorously formulates a result from 1951 by J. M. Luttinger.

scholarly journals Magneto-rotatory compressible couple-stress fluid heated from below in porous medium

2016 ◽  
Vol 38 (1) ◽  
pp. 55-63
Author(s):  
Chander Bhan Mehta
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Couple Stress ◽  
Normal Modes ◽  
Sufficient Conditions ◽  
Couple Stress Fluid ◽  
Onset Of Convection ◽  
Medium Permeability ◽  
Effects Of Rotation ◽  
The Magnetic Field

Abstract The study is aimed at analysing thermal convection in a compressible couple stress fluid in a porous medium in the presence of rotation and magnetic field. After linearizing the relevant equations, the perturbation equations are analysed in terms of normal modes. A dispersion relation governing the effects of rotation, magnetic field, couple stress parameter and medium permeability have been examined. For a stationary convection, the rotation postpones the onset of convection in a couple stress fluid heated from below in a porous medium in the presence of a magnetic field. Whereas, the magnetic field and couple stress postpones and hastens the onset of convection in the presence of rotation and the medium permeability hastens and postpones the onset of convection with conditions on Taylor number. Further the oscillatory modes are introduced due to the presence of rotation and the magnetic field which were non-existent in their absence, and hence the principle of exchange stands valid. The sufficient conditions for nonexistence of over stability are also obtained.

scholarly journals INCREASING THE EFFICIENCY OF MULTY-VARIANT CALCULATIONS OF ELECTROMAGNETIC FIELD DISTRIBUTION IN MATRIX OF A POLYGRADIENT SEPARATOR

2021 ◽  
Author(s):  
Jasim Mohmed Jasim Jasim ◽  
Iryna Shvedchykova ◽  
Igor Panasiuk ◽  
Julia Romanchenko ◽  
Inna Melkonova
Keyword(s):  
Magnetic Field ◽  
Field Distribution ◽  
Three Dimensional ◽  
Magnetic Potential ◽  
Geometric Parameters ◽  
Two Dimensional ◽  
Air Gaps ◽  
Vector Magnetic Potential ◽  
Electromagnetic Separator ◽  
The Magnetic Field

An approach is proposed to carry out multivariate calculations of the magnetic field distribution in the working gaps of a plate polygradient matrix of an electromagnetic separator, based on a combination of the advantages of two- and three-dimensional computer modeling. Two-dimensional geometric models of computational domains are developed, which differ in the geometric dimensions of the plate matrix elements and working air gaps. To determine the vector magnetic potential at the boundaries of two-dimensional computational domains, a computational 3D experiment is carried out. For this, three variants of the electromagnetic separator are selected, which differ in the size of the working air gaps of the polygradient matrices. For them, three-dimensional computer models are built, the spatial distribution of the magnetic field in the working intervals of the electromagnetic separator matrix and the obtained numerical values of the vector magnetic potential at the boundaries of the computational domains are investigated. The determination of the values of the vector magnetic potential for all other models is carried out by interpolation. The obtained values of the vector magnetic potential are used to set the boundary conditions in a computational 2D experiment. An approach to the choice of a rational version of a lamellar matrix is substantiated, which provides a solution to the problem according to the criterion of the effective area of the working area. Using the method of simple enumeration, a variant of the structure of a polygradient matrix with rational geometric parameters is selected. The productivity of the electromagnetic separator with rational geometric parameters of the matrix increased by 3–5 % with the same efficiency of extraction of ferromagnetic inclusions in comparison with the basic version of the device

scholarly journals Cellular automata model of magnetospheric-ionospheric coupling

2003 ◽  
Vol 21 (9) ◽  
pp. 1931-1938 ◽  
Author(s):  
B. V. Kozelov ◽  
T. V. Kozelova
Keyword(s):  
Magnetic Field ◽  
Solar Wind ◽  
Cellular Automata ◽  
Interplanetary Magnetic Field ◽  
Control Parameter ◽  
Energy Content ◽  
Nonlinear Phenomena ◽  
Cellular Automata Model ◽  
The Earth ◽  
Magnetospheric Tail

Abstract. We propose a cellular automata model (CAM) to describe the substorm activity of the magnetospheric-ionospheric system. The state of each cell in the model is described by two numbers that correspond to the energy content in a region of the current sheet in the magnetospheric tail and to the conductivity of the ionospheric domain that is magnetically connected with this region. The driving force of the system is supposed to be provided by the solar wind that is convected along the two boundaries of the system. The energy flux inside is ensured by the penetration of the energy from the solar wind into the array of cells (magnetospheric tail) with a finite velocity. The third boundary (near to the Earth) is closed and the fourth boundary is opened, thereby modeling the flux far away from the tail. The energy dissipation in the system is quite similar to other CAM models, when the energy in a particular cell exceeds some pre-defined threshold, and the part of the energy excess is redistributed between the neighbouring cells. The second number attributed to each cell mimics ionospheric conductivity that can allow for a part of the energy to be shed on field-aligned currents. The feedback between "ionosphere" and "magnetospheric tail" is provided by the change in a part of the energy, which is redistributed in the tail when the threshold is surpassed. The control parameter of the model is the z-component of the interplanetary magnetic field (Bz IMF), "frozen" into the solar wind. To study the internal dynamics of the system at the beginning, this control parameter is taken to be constant. The dynamics of the system undergoes several bifurcations, when the constant varies from - 0.6 to - 6.0. The Bz IMF input results in the periodic transients (activation regions) and the inter-transient period decreases with the decrease of Bz. At the same time the onset of activations in the array shifts towards the "Earth". When the modulus of the Bz IMF exceeds some threshold value, the transition takes place from periodic to chaotic dynamics. In the second part of the work we have chosen as the source the real values of the z-component of the interplanetary magnetic field taken from satellite observations. We have shown that in this case the statistical properties of the transients reproduce the characteristic features observed by Lui et al. (2000).Key words. Magnetospheric physics (magnetosphere-ionosphere interactions) – Space plasma physics (nonlinear phenomena)

scholarly journals TOPOGRAPHIC EFFECT ON SPECTRAL VEGETATION INDICES FROM LANDSAT TM DATA: IS TOPOGRAPHIC CORRECTION NECESSARY?

2016 ◽  
Vol 22 (1) ◽  
pp. 95-107 ◽  
Author(s):  
Eder Paulo Moreira* ◽  
Márcio de Morisson Valeriano ◽  
Ieda Del Arco Sanches ◽  
Antonio Roberto Formaggio
Keyword(s):  
Near Infrared ◽  
Incidence Angle ◽  
Spectral Band ◽  
Vegetation Indices ◽  
Topographic Effect ◽  
Topographic Correction ◽  
Spectral Bands ◽  
Spectral Vegetation Indices ◽  
Current Availability ◽  
Elevation Model

The full potentiality of spectral vegetation indices (VIs) can only be evaluated after removing topographic, atmospheric and soil background effects from radiometric data. Concerning the former effect, the topographic effect was barely investigated in the context of VIs, despite the current availability correction methods and Digital elevation Model (DEM). In this study, we performed topographic correction on Landsat 5 TM spectral bands and evaluated the topographic effect on four VIs: NDVI, RVI, EVI and SAVI. The evaluation was based on analyses of mean and standard deviation of VIs and TM band 4 (near-infrared), and on linear regression analyses between these variables and the cosine of the solar incidence angle on terrain surface (cos i). The results indicated that VIs are less sensitive to topographic effect than the uncorrected spectral band. Among VIs, NDVI and RVI were less sensitive to topographic effect than EVI and SAVI. All VIs showed to be fully independent of topographic effect only after correction. It can be concluded that the topographic correction is required for a consistent reduction of the topographic effect on the VIs from rugged terrain.

scholarly journals Radiative Properties and Numerical Modeling of C4F7N-CO2-O2 Thermal Plasma

2019 ◽  
Vol 6 (2) ◽  
pp. 144-147
Author(s):  
M. Gnybida ◽  
Ch. Ruempler ◽  
V. R. T. Narayanan
Keyword(s):  
Thermal Plasma ◽  
Spectral Band ◽  
Optimization Procedure ◽  
Optimal Number ◽  
Radiative Properties ◽  
Absorption Coefficients ◽  
Medium Voltage ◽  
Spectral Bands ◽  
Computational Fluid Dynamics Cfd ◽  
Low Global Warming Potential

C<sub>4</sub>F<sub>7</sub>N and C<sub>4</sub>F<sub>7</sub>N-CO<sub>2</sub> mixtures are considered as alternatives to SF<sub>6</sub> for use in medium voltage gas insulated switchgear applications (GIS), due to the low global warming potential and good dielectric properties of C<sub>4</sub>F<sub>7</sub>N. Current work is focused on the calculation of radiative properties (absorption coefficients) of C<sub>4</sub>F<sub>7</sub>N-CO<sub>2</sub> thermal plasma and computational fluid dynamics (CFD) simulations of free burning C<sub>4</sub>F<sub>7</sub>N-CO<sub>2</sub> arcs that are stabilized by natural convection. Absorption coefficients of C<sub>4</sub>F<sub>7</sub>N-CO<sub>2</sub> plasma used in the CFD model are derived from spectral absorption coefficients by Planck averaging. An optimization procedure has been applied to find the optimal number of spectral bands as well as spectral band interval boundaries. Radiation and flow model results for C<sub>4</sub>F<sub>7</sub>N-CO<sub>2</sub> in comparison to SF<sub>6</sub> and air are provided and discussed.

scholarly journals Study of the applicability of the curlometer technique with the four Cluster spacecraft in regions close to Earth

2012 ◽  
Vol 30 (3) ◽  
pp. 597-611 ◽  
Author(s):  
S. Grimald ◽  
I. Dandouras ◽  
P. Robert ◽  
E. Lucek
Keyword(s):  
Magnetic Field ◽  
Current Density ◽  
Ring Current ◽  
Current System ◽  
Sufficient Conditions ◽  
Magnetic Activity ◽  
Inner Magnetosphere ◽  
Good Proxy ◽  
The Magnetic Field ◽  
Magnetospheric Current System

Abstract. Knowledge of the inner magnetospheric current system (intensity, boundaries, evolution) is one of the key elements for the understanding of the whole magnetospheric current system. In particular, the calculation of the current density and the study of the changes in the ring current is an active field of research as it is a good proxy for the magnetic activity. The curlometer technique allows the current density to be calculated from the magnetic field measured at four different positions inside a given current sheet using the Maxwell-Ampere's law. In 2009, the CLUSTER perigee pass was located at about 2 RE allowing a study of the ring current deep inside the inner magnetosphere, where the pressure gradient is expected to invert direction. In this paper, we use the curlometer in such an orbit. As the method has never been used so deep inside the inner magnetosphere, this study is a test of the curlometer in a part of the magnetosphere where the magnetic field is very high (about 4000 nT) and changes over small distances (ΔB = 1nT in 1000 km). To do so, the curlometer has been applied to calculate the current density from measured and modelled magnetic fields and for different sizes of the tetrahedron. The results show that the current density cannot be calculated using the curlometer technique at low altitude perigee passes, but that the method may be accurate in a [3 RE; 5 RE] or a [6 RE; 8.3 RE] L-shell range. It also demonstrates that the parameters used to estimate the accuracy of the method are necessary, but not sufficient conditions.

scholarly journals Are the photospheric sunspots magnetically force-free in nature?

2010 ◽  
Vol 6 (S273) ◽  
pp. 333-337 ◽  
Author(s):  
Sanjiv Kumar Tiwari
Keyword(s):  
Magnetic Field ◽  
High Resolution ◽  
Magnetic Fields ◽  
Magnetic Energy ◽  
Sufficient Conditions ◽  
Field Measurements ◽  
Magnetic Behaviour ◽  
Optical Telescope ◽  
Energy Gradient ◽  
Necessary And Sufficient

AbstractIn a force-free magnetic field, there is no interaction of field and the plasma in the surrounding atmosphere i.e., electric currents are aligned with the magnetic field, giving rise to zero Lorentz force. The computation of many magnetic parameters like magnetic energy, gradient of twist of sunspot magnetic fields (computed from the force-free parameter α), including any kind of extrapolations heavily hinge on the force-free approximation of the photospheric magnetic fields. The force-free magnetic behaviour of the photospheric sunspot fields has been examined by Metcalf et al. (1995) and Moon et al. (2002) ending with inconsistent results. Metcalf et al. (1995) concluded that the photospheric magnetic fields are far from the force-free nature whereas Moon et al. (2002) found the that the photospheric magnetic fields are not so far from the force-free nature as conventionally regarded. The accurate photospheric vector field measurements with high resolution are needed to examine the force-free nature of sunspots. We use high resolution vector magnetograms obtained from the Solar Optical Telescope/Spectro-Polarimeter (SOT/SP) aboard Hinode to inspect the force-free behaviour of the photospheric sunspot magnetic fields. Both the necessary and sufficient conditions for force-freeness are examined by checking global as well as as local nature of sunspot magnetic fields. We find that the sunspot magnetic fields are very close to the force-free approximation, although they are not completely force-free on the photosphere.

scholarly journals Transient fields produced by a cylindrical electron beam flowing through a plasma

2012 ◽  
Vol 30 (3) ◽  
pp. 497-507
Author(s):  
Marie-Christine Firpo
Keyword(s):  
Magnetic Field ◽  
Electron Beam ◽  
Laplace Transform ◽  
Control Parameter ◽  
Bessel Functions ◽  
Skin Depth ◽  
The Other ◽  
Beam Radius ◽  
Equilibrium Situation ◽  
Detailed Computation

AbstractThe out-of-equilibrium situation in which an initially sharp-edged cylindrical electron beam, that could, e.g., model electrons flowing within a wire, is injected into a plasma is considered. A detailed computation of the subsequently produced magnetic field is presented. The control parameter of the problem is shown to be the ratio of the beam radius to the electron skin depth. Two alternative ways to address analytically the problem are considered: one uses the usual Laplace transform approach, the other one involves Riemann's method in which causality conditions manifest through some integrals of triple products of Bessel functions.

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