On: “New prospects in shallow depth electrical surveying for archeological and pedological applications” by A. Hesse, A. Jolivet and A. Tabbagh (GEOPHYSICS, 51, 585–594, March 1986).

Geophysics ◽  
1989 ◽  
Vol 54 (10) ◽  
pp. 1355-1355
Author(s):  
Mark Goldman
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Maxwell Equations ◽  
Forward Solution ◽  
Nonzero Component ◽  
Vector Identity ◽  
Governing Differential Equation ◽  
Vector Operator ◽  
Displacement Currents ◽  
The Magnetic Field

The forward solution given by Hesse et al. is incorrect. The error is a result of the erroneous governing differential equation [their equation (2)], which for the only nonzero component of the magnetic field has the following form: [Formula: see text]Unfortunately, the authors did not show how they arrived at this equation, but the mistake is so frequently encountered that its origin can be reconstructed quite easily. Indeed, by neglecting displacement currents in the fourth Maxwell equation and by applying the vector operator ∇× to both parts of the equation, we obtain [Formula: see text]Making use of the well known vector identity [Formula: see text]and of the first and third Maxwell equations, we obtain [Formula: see text]

Existence conditions for collisionless hydromagnetic shock waves along the magnetic field

1971 ◽  
Vol 6 (3) ◽  
pp. 467-493 ◽  
Author(s):  
Yusuke Kato† ◽  
Masayoshi Tajiri ◽  
Tosiya Taniuti
Keyword(s):  
Magnetic Field ◽  
Shock Waves ◽  
Flow Velocity ◽  
Maxwell Equations ◽  
Collisionless Plasma ◽  
Electrostatic Waves ◽  
Pressure Anisotropy ◽  
Existence Conditions ◽  
Upstream Flow ◽  
The Magnetic Field

This paper is concerned with existence conditions for steady hydromagnetic shock waves propagating in a collisionless plasma along an applied magnetic field. The electrostatic waves are excluded. The conditions are based on the requirement that solutions of the Vlasov-Maxwell equations deviate from a uniform state ahead of a wave. They are given as the conditions on the upstream flow velocity in the wave frame (i.e. in the form of inequalities among the upstream flow velocity and some critical velocities). The conditions crucially depend on the pressure anisotropy, and demonstrate possibilities of exacting collisionless shock waves for high β plasmas.

Whistler instability in plasmas with anisotropic and non-Maxwellian velocity distributions

1971 ◽  
Vol 6 (3) ◽  
pp. 449-456 ◽  
Author(s):  
Kai Fong Lee
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Waves ◽  
Maxwell Equations ◽  
Transverse Velocity ◽  
Distribution Functions ◽  
Loss Cone ◽  
Circularly Polarized ◽  
Electron Plasmas ◽  
Thermal Spread ◽  
The Magnetic Field

The instability of right-handed, circularly polarized electromagnetic waves, propagating along an external magnetic field (whistler mode), is studied for electron plasmas with distribution functions peaked at some non-zero value of the transverse velocity. Based on the linearized Vlasov-Maxwell equations, the criteria for instability are given both for non-resonant instabilities arising from distribution functions with no thermal spread parallel to the magnetic field, and for resonant instabilities arising from distribution functions with Maxwellian dependence in the parallel velocities. It is found that, in general, the higher the average perpendicular energy, the more is the plasma susceptible to the whistler instability. These criteria are then applied to a sharply peaked ring distribution, and to loss-cone distributions of the Dory, Guest & Harris (1965) type.

On the boundary operator in electromagnetic scattering

1986 ◽  
Vol 103 (1-2) ◽  
pp. 91-98 ◽  
Author(s):  
Rainer Kress
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Electromagnetic Scattering ◽  
Maxwell Equations ◽  
Boundary Operator ◽  
Hölder Continuous ◽  
Operator Mapping ◽  
Time Harmonic ◽  
Continuous Surface ◽  
The Magnetic Field

SynopsisFor radiating solutions to the time-harmonic Maxwell equations, it is shown that the boundary operator mapping the tangential components of the electric field into the tangential components of the magnetic field is a bounded bijective operator from the space of Holder continuous tangential fields with Hölder continuous surface divergence onto itself.

Theory of Lubrication With Ferrofluids: Application to Short Bearings

1982 ◽  
Vol 104 (4) ◽  
pp. 510-515 ◽  
Author(s):  
Nicolae Tipei
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Boundary Conditions ◽  
Reynolds Equation ◽  
Viscous Fluids ◽  
Pressure Differential ◽  
Numerical Example ◽  
Bearing Stiffness ◽  
Pyromagnetic Coefficient ◽  
The Magnetic Field

The momentum equations are written for viscous fluids exhibiting magnetic stresses. The velocity profiles are deduced; then from continuity, a pressure differential equation, equivalent to Reynolds equation is obtained. This equation is discussed with emphasis on the case when magnetic stresses derive from a potential, also when the pyromagnetic coefficient vanishes. The boundary conditions for lubrication problems are then formulated. In particular, short bearings with ferromagnetic lubricants are considered. A numerical example yields the pressure diagrams at low and moderate eccentricity ratios and for different speeds. In conclusion, it is shown that ferromagnetic lubricants may improve substantially the performance of bearings operating under low loads and/or at low speeds. However, a correct variation of the magnetic field, toward the center of the lubricated area, is required. Under such conditions, the extent of the active area of the film is increased and bearing stiffness and stability are improved.

scholarly journals On-demand Ferrofluid Droplet Formation With Non-linear Magnetic Permeability in the Presence of a Non-uniform Magnetic Field

2021 ◽  
Author(s):  
Mohamad Ali Bijarchi ◽  
Mohammad Yaghoobi ◽  
Amirhossein Favakeh ◽  
Mohammad Behshad Shafii
Keyword(s):  
Magnetic Field ◽  
Magnetic Susceptibility ◽  
Uniform Magnetic Field ◽  
Maxwell Equations ◽  
Droplet Diameter ◽  
Droplet Formation ◽  
Bond Number ◽  
On Demand ◽  
Drop On Demand ◽  
The Magnetic Field

Abstract The magnetic actuation of ferrofluid droplets offers an inspiring tool in widespread engineering and biological applications. In this study, the dynamics of ferrofluid droplet generation with a Drop-on-Demand feature under a non-uniform magnetic field is investigated by multiscale numerical modeling. Langevin equation is assumed for ferrofluid magnetic susceptibility due to the strong applied magnetic field. Large and small computational domains are considered. In the larger domain, the magnetic field is obtained by solving Maxwell equations. In the smaller domain, a coupling of continuity, Navier Stokes, two-phase flow, and Maxwell equations are solved by utilizing the magnetic field achieved by the larger domain for the boundary condition. The Finite volume method and coupling of level-set and Volume of Fluid methods are used for solving equations. The droplet formation is simulated in a two-dimensional axisymmetric domain. The method of solving fluid and magnetic equations is validated using a benchmark. Then, ferrofluid droplet formation is investigated experimentally and the numerical results are in good agreement with the experimental data. The effect of 12 dimensionless parameters including the ratio of magnetic, gravitational, and surface tension forces, the ratio of the nozzle and magnetic coil dimensions, and ferrofluid to continuous-phase properties ratios are studied. The results showed that by increasing the magnetic Bond number, gravitational Bond number, Ohnesorge number, dimensionless saturation magnetization, initial magnetic susceptibility of ferrofluid, the generated droplet diameter reduces, whereas the formation frequency increases. The same results were observed when decreasing the ferrite core diameter to outer nozzle diameter, density, and viscosity ratios.

On the method of matched asymptotic expansions

1969 ◽  
Vol 65 (1) ◽  
pp. 263-284 ◽  
Author(s):  
L. E. Fraenkel
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Formal Method ◽  
Reynolds Numbers ◽  
Linear Ordinary Differential Equation ◽  
Steady Current ◽  
Formal Procedure ◽  
Small Reynolds Numbers ◽  
The Magnetic Field

AbstractThe formal method of matched expansions is applied to two further examples. The first concerns the magnetic field induced by a steady current in a thin toroidal wire. The second, which involves a non-linear ordinary differential equation of the fourth order, has been chosen to resemble the problem of flow past a circular cylinder at small Reynolds numbers. The results of the formal procedure are proved in each case to be expansions of the exact solution.

scholarly journals ENERGY AND MOMENTUM DISTRIBUTIONS OF THE MAGNETIC SOLUTION TO (2+1) EINSTEIN–MAXWELL GRAVITY

2005 ◽  
Vol 20 (23) ◽  
pp. 1741-1751 ◽  
Author(s):  
TH. GRAMMENOS
Keyword(s):  
Magnetic Field ◽  
Maxwell Equations ◽  
Three Dimensional ◽  
Momentum Density ◽  
Radial Magnetic Field ◽  
Density Distributions ◽  
Static Gravitational Field ◽  
Energy And Momentum ◽  
Momentum Complex ◽  
The Magnetic Field

We use Møller's energy–momentum complex in order to explicitly evaluate the energy and momentum density distributions associated with the three-dimensional magnetic solution to the Einstein–Maxwell equations. The magnetic spacetime under consideration is a one-parametric solution describing the distribution of a radial magnetic field in a three-dimensional AdS background, and representing the superposition of the magnetic field with a 2+1 Einstein static gravitational field.

scholarly journals Computation of per-unit-length internal impedance of a multilayer cylindrical conductor with possible dielectric layers

2020 ◽  
Vol 33 (4) ◽  
pp. 605-616
Author(s):  
Dino Lovric ◽  
Slavko Vujevic ◽  
Ivan Krolo
Keyword(s):  
Magnetic Field ◽  
Maxwell Equations ◽  
Bessel Functions ◽  
Unit Length ◽  
Dielectric Layers ◽  
Electric And Magnetic Fields ◽  
Electric And Magnetic Field ◽  
Internal Impedance ◽  
Novel Method ◽  
Displacement Currents

In this manuscript, a novel method for computation of per-unit-length internal impedance of a cylindrical multilayer conductor with conductive and dielectric layers is presented in detail. In addition to this, formulas for computation of electric and magnetic field distribution throughout the entire multilayer conductor (including dielectric layers) have been derived. The presented formulas for electric and magnetic field in conductive layers have been directly derived from Maxwell equations using modified Bessel functions. However, electric and magnetic field in dielectric layers has been computed indirectly from the electric and magnetic fields in contiguous conductive layers which reduces the total number of unknowns in the system of equations. Displacement currents have been disregarded in both conductive and dielectric layers. This is justifiable if the conductive layers are good conductors. The validity of introducing these approximations is tested in the paper versus a model that takes into account displacement currents in all types of layers.

TORSION BOUNDS FROM CP VIOLATION α2-DYNAMO IN AXION–PHOTON COSMIC PLASMA

2011 ◽  
Vol 26 (38) ◽  
pp. 2863-2868 ◽  
Author(s):  
L. C. GARCIA DE ANDRADE
Keyword(s):  
Magnetic Field ◽  
Cp Violation ◽  
Maxwell Equations ◽  
Lorentz Violation ◽  
Classical Level ◽  
K Meson ◽  
Field Amplification ◽  
Frequency Peak ◽  
Galactic Dynamos ◽  
The Magnetic Field

Years ago Mohanty and Sarkar [Phys. Lett. B433, 424 (1998)] have placed bounds on torsion mass from K meson physics. In this paper, associating torsion to axions a la Campanelli et al. [Phys. Rev. D72, 123001 (2005)], it is shown that it is possible to place limits on spacetime torsion by considering an efficient α2-dynamo CP violation term. Therefore instead of Kostelecky et al. [Phys. Rev. Lett.100, 111102 (2008)] torsion bounds from Lorentz violation, here torsion bounds are obtained from CP violation through dynamo magnetic field amplification. It is also shown that oscillating photon–axion frequency peak is reduced to 10-7 Hz due to torsion mass (or Planck mass when torsion does not propagate) contribution to the photon–axion–torsion action. Though torsion does not couple to electromagnetic fields at classical level, it does at the quantum level. Recently, Garcia de Andrade [Phys. Lett. B468, 28 (2011)] has shown that the photon sector of Lorentz violation (LV) Lagrangian leads to linear nonstandard Maxwell equations where the magnetic field decays slower giving rise to a seed for galactic dynamos. Torsion constraints of the order of K0≈10-42 GeV can be obtained which are more stringent than the value obtained by Kostelecky et al. A lower bound for the existence of galactic dynamos is obtained for torsion as K0≈10-37 GeV .

ON A NONLINEAR MAXWELL'S SYSTEM IN QUASI-STATIONARY ELECTROMAGNETIC FIELDS

2004 ◽  
Vol 14 (10) ◽  
pp. 1521-1539 ◽  
Author(s):  
HONG-MING YIN
Keyword(s):  
Magnetic Field ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Condition ◽  
Blow Up ◽  
Growth Conditions ◽  
System Generator ◽  
Conductive Medium ◽  
Maxwell’S System ◽  
Displacement Currents ◽  
The Magnetic Field

In this paper we study the motion of a magnetic field H in a conductive medium Ω⊂R3under the influence of a system generator. By neglecting displacement currents, the magnetic field satisfies a nonlinear Maxwell's system: Ht+∇×[ρ(x,t)∇×H]=f(|H|)H, where f(|H|)H represents the magnetic currents depending upon the strength of H. We prove that under appropriate initial and boundary conditions, the system has a global solution and the solution is also unique. Moreover, we show that the solution H will blow up in finite time if f(s) satisfies certain growth conditions. Finally, we generalize the results to the problem associated with a nonlinear boundary condition.

Sign in / Sign up

Export Citation Format

Share Document