A GENERALIZED VARIATIONAL PRINCIPLE FOR TRANSPORT PHENOMENA

1958 ◽  
Vol 36 (10) ◽  
pp. 1308-1318 ◽  
Author(s):  
G. E. Tauber
Keyword(s):  
Magnetic Field ◽  
Variational Principle ◽  
Ritz Method ◽  
Transport Coefficients ◽  
Distribution Functions ◽  
Generalized Variational Principle ◽  
Lattice Vibrations ◽  
Arbitrary Direction ◽  
Energy Surfaces ◽  
Thermomagnetic Phenomena

A generalized variational principle has been formulated which takes the phonon distribution functions and the external magnetic field into account, is valid for an arbitrary direction of the electric field and polarization of the lattice vibrations, and does not depend on any special form of the energy surfaces. The various transport coefficients, for both thermoelectric and thermomagnetic phenomena, are obtained by the Ritz method in terms of infinite determinants without requiring an explicit solution of the transport equations.

scholarly journals On the semi-inverse method and variational principle

2013 ◽  
Vol 17 (5) ◽  
pp. 1565-1568 ◽  
Author(s):  
Xue-Wei Li ◽  
Ya Li ◽  
Ji-Huan He
Keyword(s):  
Heat Conduction ◽  
Variational Principle ◽  
Inverse Method ◽  
Generalized Variational Principle ◽  
Open Forum ◽  
One Dimensional ◽  
History Of

In this Open Forum, Liu et al. proved the equivalence between He-Lee 2009 variational principle and that by Tao and Chen (Tao, Z. L., Chen, G. H., Thermal Science, 17(2013), pp. 951-952) for one dimensional heat conduction. We confirm the correction of Liu et al.?s proof, and give a short remark on the history of the semi-inverse method for establishment of a generalized variational principle.

scholarly journals Diffusion at the Earth magnetopause: enhancement by Kelvin-Helmholtz instability

2007 ◽  
Vol 25 (1) ◽  
pp. 271-282 ◽  
Author(s):  
R. Smets ◽  
G. Belmont ◽  
D. Delcourt ◽  
L. Rezeau
Keyword(s):  
Magnetic Field ◽  
Distribution Functions ◽  
Larmor Radius ◽  
Simple Analytical Model ◽  
Helmholtz Instability ◽  
Field Reversal ◽  
Finite Larmor Radius ◽  
The Earth ◽  
Specific Distribution ◽  
The Magnetic Field

Abstract. Using hybrid simulations, we examine how particles can diffuse across the Earth's magnetopause because of finite Larmor radius effects. We focus on tangential discontinuities and consider a reversal of the magnetic field that closely models the magnetopause under southward interplanetary magnetic field. When the Larmor radius is on the order of the field reversal thickness, we show that particles can cross the discontinuity. We also show that with a realistic initial shear flow, a Kelvin-Helmholtz instability develops that increases the efficiency of the crossing process. We investigate the distribution functions of the transmitted ions and demonstrate that they are structured according to a D-shape. It accordingly appears that magnetic reconnection at the magnetopause is not the only process that leads to such specific distribution functions. A simple analytical model that describes the built-up of these functions is proposed.

Magnetic quantum oscillations in doped antiferromagnets

2017 ◽  
Vol 31 (25) ◽  
pp. 1745015
Author(s):  
V. V. Kabanov
Keyword(s):  
Magnetic Field ◽  
Polar Angle ◽  
Two Dimensional ◽  
Plane Angle ◽  
Arbitrary Direction ◽  
Magnetization Direction ◽  
Quantum Oscillations ◽  
Out Of Plane ◽  
Plane Direction ◽  
Magnetic Quantum Oscillations

Energy spectrum of electrons (holes) doped into two-dimensional (2D) antiferromagnetic (AF) semiconductors is quantized in an external magnetic field of arbitrary direction. A peculiar dependence of de Haas–van Alphen (dHvA) magneto-oscillation amplitudes on the azimuthal in-plane angle from the magnetization direction and on the polar angle from the out-of-plane direction is found. The angular dependence of the amplitude is different if the measurements are performed in the field above and below of the spin-flop field.

Tsallis Distribution Functions in the Solar Wind: Magnetic Field and Velocity Observations

2007 ◽  
Author(s):  
Leonard F. Burlaga ◽  
Adolfo F. Viñas ◽  
Sumiyoshi Abe ◽  
Hans Herrmann ◽  
Piero Quarati ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Solar Wind ◽  
Distribution Functions ◽  
Solar Wind Magnetic Field ◽  
Tsallis Distribution

Edgewise Bending Vibration Analysis of a Rotating Sandwich Beam with Magnetorheological Elastomer Core

2018 ◽  
Vol 18 (11) ◽  
pp. 1850134 ◽  
Author(s):  
S. Bornassi ◽  
H. M. Navazi ◽  
H. Haddadpour
Keyword(s):  
Magnetic Field ◽  
Layer Thickness ◽  
Rectangular Cross Section ◽  
Ritz Method ◽  
Sandwich Beam ◽  
Beam Theory ◽  
Core Layer ◽  
Magnetorheological Elastomer ◽  
Bending Vibration ◽  
Elastic Layers

The vibration of a rotating sandwich beam with magnetorheological elastomer (MRE) as a core between two elastic layers is theoretically analyzed in this paper. This study is focused on the bending vibration along the edgewise direction of a sandwich beam of rectangular cross-section, which, to the best of our knowledge, has not been addressed yet. The classical Euler–Bernoulli beam theory is used to model the dynamic behavior of the elastic layers. In the modeling, the effect of the MRE layer is considered by incorporating its shear strains and the inertia due to shear deformation and bending motion. The governing equations of motion of the rotating sandwich beam are derived by using the Ritz method and the Lagrange’s equations. The effects of the applied magnetic field, core layer thickness, rotational speed, setting angle and hub radius on the natural frequencies and the corresponding loss factors are investigated parametrically. The results show the significant effect of the magnetic field intensity and the MRE layer thickness on the modal characteristics of the MRE sandwich beam.

Formation of non-thermal electron velocity distribution functions in kinetic magnetic reconnection

2021 ◽  
Author(s):  
Xin Yao ◽  
Patricio A. Muñoz ◽  
Jörg Büchner
Keyword(s):  
Magnetic Field ◽  
Free Energy ◽  
Field Strength ◽  
Magnetic Reconnection ◽  
Electron Beams ◽  
Distribution Functions ◽  
Electron Velocity ◽  
Diffusion Region ◽  
Electron Velocity Distribution ◽  
Velocity Distribution Functions

<div> <div>Magnetic reconnection can convert magnetic energy into non-thermal particle energy in the form of electron beams. Those accelerated electrons can, in turn, cause radio emission in environments such as solar flares. The actual properties of those electron velocity distribution functions (EVDFs) generated by reconnection are still not well understood. In particular the properties that are relevant for the micro-instabilities responsible for radio emission. We aim thus at characterizing the electron distributions functions generated by 3D magnetic reconnection by means of fully kinetic particle-in-cell (PIC) code simulations. Our goal is to characterize the possible sources of free energy of the generated EVDFs in dependence on an external (guide) magnetic field strength. We find that: (1) electron beams with positive gradients in their parallel (to the local magnetic field direction) distribution functions are observed in both diffusion region (parallel crescent-shaped EVDFs) and separatrices (bump-on-tail EVDFs). These non-thermal EVDFs cause counterstreaming and bump-on-tail instabilities. These electrons are adiabatic and preferentially accelerated by a parallel electric field in regions where the magnetic moment is conserved. (2) electron beams with positive gradients in their perpendicular distribution functions are observed in regions with weak magnetic field strength near the current sheet midplane. The characteristic crescent-shaped EVDFs (in perpendicular velocity space) are observed in the diffusion region. These non-thermal EVDFs can cause electron cyclotron maser instabilities. These non-thermal electrons in perpendicular velocity space are mainly non-adiabatic. Their EVDFs are attributed to electrons experiencing an E×B drift and meandering motion. (3) As the guide field strength increases, the number of locations in the current sheet with distributions functions featuring a perpendicular source of free energy significantly decreases.</div> </div>

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