Magnetohydrodynamics of a viscous spherical layer rotating in a strong potential field

An analytic solution is given for classical magnetohydrodynamic (MHD) problem of almost rigid-body rotation of a viscous, conducting spherical layer of liquid in an axisymmetric potential magnetic field. Large-scale flows bounded by rigid spheres are described for the first time in a new approximation. Two problems are solved: (1) in which both spheres are insulators and (2) in which the outer sphere is an insulator and the inner sphere a conductor. Axially symmetric flows and azimuthal magnetic fields are maintained by a slightly faster rotation of the inner sphere. The primary regeneration takes place in the boundary and shear MHD layers. The shear layers, described here for the first time, smooth out the large gradients at the boundaries of the MHD structures encompassed by them. There is essentially no azimuthal magnetic field inside these original structures, which are bounded by potential contours tangent to the spheres. An applied constant magnetic field creates a rigid MHD structure outside an axial cylinder tangent to the inner sphere. Inside the cylinder the rotation is faster and the meridional flux depends on height. A magnetic dipole forms a structure tangent to the outer equator. Outside the structure, the rotation is also rigid-body when both spheres are insulators. When a conducting sphere is present, the liquid rotates differentially everywhere, while near the axis and inside the MHD structure, it rotates even faster than the inner sphere. The last example of a general solution is a quadrupole magnetic field. In this case, two equatorially symmetric MHD structures are formed which rotate together with the inner sphere. Outside the structures, as in the most general case, the rotation is differential, the azimuthal magnetic field falls off as the first power of the applied field, and the meridional flux falls off as the square of the field in the first problem, and as the cube in the second. Zh. éksp. Teor. Fiz. 112, 2056–2078 (December 1997)     

Verification of a new quantum simulation approach through its application to two-dimensional Ising lattices

A new quantum simulation approach has been applied in the present work to the two-dimensional (2D) ferromagnetic and antiferromagnetic Ising lattices to calculate their magnetic structures, magnetizations, free energies and specific heats in the absence of an external magnetic field. Surprisingly, no size effects could be observed in our simulations performed for the Ising lattices of different sizes. Most importantly, our calculated spontaneous thermally averaged spins for the two kinds of systems are exactly same as those evaluated with quantum mean field theory, and the magnetic structures simulated at all chosen temperatures are perfectly ferromagnetic or antiferromagnetic, verifying the correctness and applicability of our quantum model and computational algorithm. On the other hand, if the classical Monte Carlo (CMC) method is applied to the ferromagnetic 2D Ising lattice with S=1, it is able to generate correct magnetization well consistent with Onsager's theory; but in the case of S=1/2, the computational results of CMC are incomparable to those predicted with the quantum mean field theory, giving rise to very much reduced magnetization and considerably underestimated Curie temperature. The difficulty met by the CMC method is mainly caused by its improperly calculated exchange energy of the randomly selected spin in every simulation step, especially immediately below the transition temperature, where the thermal averages of spins are much less than 1/2, however they are assigned to ±1/2 by CMC to evaluate the exchange energies of the spins, such improper manipulation is obviously impossible to lead the code to converge to the right equilibrium states of the spin systems.     

The onset of rotational motion of dusty plasma structures in strata of a glow discharge in a magnetic field

An interpretation is given to the previously observed action of a magnetic field on the state of a dusty plasma structure in strata of a glow discharge. The conditions of previous experiments are analyzed, in which a nonuniform rotation and a change in the degree of order of a dusty plasma structure (the translational order), as well as a correlation between them, were revealed. Based on this analysis and on data in the literature on dusty plasmas in a magnetic field, a hypothesis is made that the reason for the rotation of the structure is the ion drag force. Additional experiments on the observation of the onset of rotational motion of a structure in “weak” and “strong” magnetic fields are conducted. It is shown that rotation reversal (and rearrangement of the order of the structure) is caused by changes in the direction of ionic flows—from internal regions of the structure to its periphery and vice versa—in the weak and strong magnetic fields. The results obtained agree qualitatively with the hypothesis adopted, as well as with the data of the two-dimensional theory of strata.     

Entropy analysis on unsteady MHD biviscosity nanofluid flow with convective heat transfer in a permeable radiative stretchable rotating disk

We examine the entropy analysis in three-dimensional hydromagnetic flow and convective heat transport of a biviscosity nanofluid over a rotating porous disk with a time-dependent stretching rate in the direction of the radius of the circular disk. We also examine the influence of thermal radiation and viscous dissipation due to nanoparticles and applied magnetic field. We invoked suitable self-similar transformations to covert the modeled coupled nonlinear PDEs into a set of nonlinear ODEs. The transformed system of equations is then worked out numerically by a well-known shooting technique and the fourth-order Runge–Kutta–Fehlberge method. The rotating phenomenon yields an additional parameter known as a rotation parameter, which controls the disk’s rotation. The study shows that the fluid motion is accelerated along the radial and cross-radial directions with an increase in the rotation of the disk. The skin-friction and the heat transfer rate at the disk strongly depend on the rotation of the disk, permeability of the porous medium, thermal radiation, and nanoparticle size. The Bejan number quantifies the entropy production of the system. It has a considerable impact on the magnetic field, rotation of the disk, thermal radiation, and Biot number. The efficient performance of the system is possible by a suitable choice of the physical parameters discussed in this article.     

Thermal fluctuation electromagnetic field as a reason for the sensitivity of a condensed diamagnetic medium to weak actions

Interaction between the thermal fluctuation electromagnetic field of a condensed medium and a weak external factor, say, a weak effective magnetic field including an external magnetic field, rigid rotation of the medium, and Coriolis force, imparts a torque to any charged free or bound particles (atoms, molecules, etc.). which indicates that the medium is sensitive to weak actions. The torque is proportional to thermal energy kT and may increase substantially under the cyclotron resonance conditions. The so-called kT problem is solved, so that many observations having to do with the field of physics that can be called the physics of weak actions (?kT) can now be theoretically explained.     

Nonlinear Rayleigh–Taylor instability of two superposed magnetic fluids under parallel rotation and a normal magnetic field

The Rayleigh–Taylor instability (RTI) of a ferrofluid has been the subject of recent research, because of its implications on the stability of stellar and planetary interiors. This paper analyzes the effects of rotation and magnetic field on nonlinear RTI of two superposed ferrofluids. It is considered that the system is subjected to uniform parallel rotation and normal magnetic field. Surface tension acts at the interface. The method of multiple scales is utilized to obtain the solutions and dispersion relations are obtained for the nonlinear problem of RTI of magnetic fluids. Finally the stability of the problem is discussed.     

Phenomenological analysis of thermal hysteresis in Ni-Mn-Ga Heusler alloys

The manipulation of thermal hysteresis in Ni-Mn-Ga Heusler alloys with coupled magnetostructural phase transition is studied theoretically using the Landau theory, including magnetic, elastic and crystal lattice modulation order parameters as well as an external magnetic field. It is shown that for the assigned combination of phenomenological parameters, in the phase diagrams, the Austenite–Martensite first-order phase transition has a finite (critical) point in which the thermal hysteresis is disappeared. Moreover, this point depends on the relation between modulation and elastic constants as well as on the magnetic field. Obtained results have been compared with other theoretical end experimental data.     

Thermal parametric turbulence in a plasma

A theory of thermal parametric instability (TPI) in an inhomogeneous magnetoplasma is developed. The threshold pump wave amplitude and increments of TPI are obtained. The spacial spectra of plasma waves and magnetic field aligned density perturbations are determined at the nonlinear stage of TPI, perturbation intensity dependence on pump energy is also analyzed. The theoretical results are applied to explain the ionospheric modification experiments.     

Symmetric behavior of vortex states of superconducting networks in a magnetic field

We present magnetic field dependence of phase transition temperature and vortex configuration of superconducting networks based on theoretical study. The applied magnetic field is called “filling field” that is defined by applied magnetic flux (in unit of the flux quantum) per unit loop of the superconducting network. If a superconducting network is composed of very thin wires whose thicknesses are less than coherence length, the de Gennes–Alexander (dGA) theory is applicable. We have already shown that field dependences of transition temperature curves have symmetric behavior about the filling field of 1/2 by solving the dGA equation numerically in square lattices, honeycomb lattices, cubic lattices and those with randomly lack of wires networks. Many experimental studies also show the symmetric behavior. In this paper, we make an explicit theoretical explanation of symmetric behaviors of superconducting network respect to the applied field.     

The effective-field theory studies of critical phenomena in a mixed spin-1 and spin-2 Ising model on honeycomb and square lattices

An effective-field theory with correlations has been used to study critical behaviors of a mixed spin-1 and spin-2 Ising system on a honeycomb and square lattices in the absence and presence of a longitudinal magnetic field. The ground-state phase diagram of the model is obtained in the longitudinal magnetic field (h) and a single-ion potential or crystal-field interaction (Δ) plane. The thermal behavior of the sublattice magnetizations of the system are investigated to characterize the nature of (continuous and discontinuous) of the phase transitions and obtain the phase transition temperature. The phase diagrams are presented in the (Δ/|J|, k_BT/|J|) plane. The susceptibility, internal energy and specific heat of the system are numerically examined and some interesting phenomena in these quantities are found due to the absence and presence of the applied longitudinal magnetic field. Moreover, the system undergoes second- and first-order phase transition; hence, the system gives a tricritical point. The system also exhibits reentrant behavior.     

The role of magnetic damping in the r-mode evolution of accreting neutron stars

The magnetic damping rate was introduced in the evolution equations of r-modes,which shows that r-modes can generate strong toroidal magnetic fields in the core of accreting millisecond pulsars inducing by differential rotation.With consideration of the coupling evolution of r-modes,spin and thermal evolution,we investigated the influence of the magnetic damping on the differential rotation of nonlinear r-modes of accreting neutron stars.We derived the coupling evolution equations of the star involving the magnetic damping rate in the framework of second-order r-mode theory.The numerical results show that the magnetic damping suppressed the nonlinear evolution of r-modes since the saturation amplitude is reduced to a great extent.In particular,because of the presence of the generated toroidal magnetic field,the spin-down of the stars is terminated and the viscous heating effects are also weakened.Moreover,we could obtain a stronger generated toroidal magnetic field in the second-order r-mode theory.The gravitational radiation may be detected by the advanced laser interferometer detector LIGO if the amount of differential rotation is small when the r-mode instability becomes active and the accretion rate is not very high.     

Experimental study and CFD simulation of rotational eccentric cylinder in a magnetorheological fluid

In this study, a magnetorheological (MR) fluid is prepared using carbonyl iron filings and low viscosity lubricating oil. The effects of magnetic field and weight percentage of particles on the viscosity of the MR fluid have been measured using a rotational viscometer. The yield stress under an applied magnetic field was also obtained experimentally. In the absence of an applied magnetic field, the MR fluid behaves as a Newtonian fluid. When the magnetic field is applied, the MR fluid behaves like Bingham plastics with a magnetic field dependent yield stress. Afterward, the results compared with those of CFD simulation of two eccentric cylinders in the MR fluid. Results show that the influences of MR effects, caused by the applied magnetic field, on the model characteristics are significant and not negligible. The viscosity is enhanced by increasing of the magnetic field, eccentricity ratio and weight percentage of suspensions. The MR effects and increasing of weight percentage and eccentricity ratio also provide an enhancement in the yield stresses and required total torque for rotation of inner cylinder. Also the simulation results indicate a good representation of the experiment by the model.     

Effects of finite larmor radius and variable gravitational field on thermal instability of fluid layer under rotation in porous medium

The effect of finite Larmor radius, magnetic field, rotation and variable gravitational field on thermal instability of fluid layer in porous medium is investigated. It is found that the principle of exchange of stability is valid in the absence of magnetic field and rotation. The system is stable/unstable depending upon certain conditions in the presence of rotation, magnetic field and medium permeability. The system is stable in presence of finite Larmor radius. The above work has been carried out under research project financed by University Grants Commission New Delhi (India) and the authors are grateful to University Grants Commission for their financial support.     

Effects of rotation on Landau states of electrons on a spherical shell

Based on a previously observed analogy between electromagnetic and non-inertial effects, we investigate the competition between magnetic field and rotation in the quantum motion of an electron constrained to the surface of a sphere. We solve numerically the Schrödinger equation of the problem for the energy eigenvalues and the eigenfunctions and compare the effects of the magnetic field and rotation. We obtain that, for a weak magnetic field, an electron can not distinguish between magnetic field and rotation, since they lead to equivalent behavior. But this is no longer true for strong magnetic fields. However, surprisingly, even though the rotation and magnetic fields play different roles in the electronic properties of the system, when together, each influence of the magnetic field on the energy levels can be separately balanced by rotation. We also show that no matter the intensity of the magnetic field, it is always possible to destroy the Landau levels in the sphere by rotation.     

Orientational Instability and Hysteresis Phenomena in a Ferronematic Liquid Crystal in a Magnetic Field

A magnetic-field-induced orientational structure in a ferronematic (FN) liquid crystal (LC) layer is studied within the continuum theory. The rotation angles of the director and the magnetization and the concentration of magnetic impurity corresponding to a supertwisted orientational structure of the suspension are calculated. It is shown that the deviation angle of the director from the direction of the external field has the hysteresis region in which the orientational structure of the FN changes stepwise from a state with a positive twist of the director to a state with a negative twist. A value of the magnetic field strength is found above which orientational bistability regions arise. It is shown that orientational instability under the rotation of the field most clearly manifests itself in FNs with strong anchoring of particles to the LC matrix. It is established that the effect of magnetic segregation responsible for the redistribution of magnetic particles in the layer leads to the expansion of the hysteresis region and to a decrease in the field at which orientational instability arises. It is shown that, in FNs with soft anchoring between magnetic and LC subsystems, there exist several response modes to a quasistatic rotation of the magnetic field.     

The effect of fractional thermoelasticity on a two-dimensional problem of a mode I crack in a rotating fiber-reinforced thermoelastic medium

This article is concerned with the effect of rotation on the general model of the equations of the generalized thermoe- lasticity for a homogeneous isotropic elastic half-space solid, whose surface is subjected to a Mode-I crack problem. The fractional order theory of thermoelasticity is used to obtain the analytical solutions for displacement components, force stresses, and temperature. The boundary of the crack is subjected to a prescribed stress distribution and temperature. The normal mode analysis technique is used to solve the resulting non-dimensional coupled governing equations of the problem. The variations of the considered variables with the horizontal distance are illustrated graphically. Some particular cases are also discussed in the context of the problem. Effects of the fractional parameter, reinforcement, and rotation on the varia- tions of different field quantities inside the elastic medium are analyzed graphically. Comparisons are made between the results in the presence and those in the absence of fiber-reinforcing, rotating and fractional parameters.     

Spin rotation as an element of polarization experiments on elastic electron-proton scattering

The validity of some rules in the classical theory of spin, which are followed by the Bargmann-Michel-Telegdi formula for a relativistic particle spin rotation in a constant homogeneous magnetic field, is analyzed. In the framework of the quantum theory, we give examples where these rules are violated. Consequences for polarization experiments are discussed.     

The effect of rotation on plane waves in generalized thermo-microstretch elastic solid with one relaxation time for a mode-I crack problem

The present paper is aimed at studying the effect of rotation on the general model of the equations of the generalized thermo-microstretch for a homogeneous isotropic elastic half-space solid,whose surface is subjected to a Mode-I crack problem.The problem is studied in the context of the generalized thermoelasticity Lord-S hulman’s (L-S) theory with one relaxation time,as well as with the classical dynamical coupled theory (CD).The normal mode analysis is used to obtain the exact expressions for the displacement components,the force stresses,the temperature,the couple stresses and the microstress distribution.The variations of the considered variables through the horizontal distance are illustrated graphically.Comparisons of the results are made between the two theories with and without the rotation and the microstretch constants.     

Mode splitting of a cavity with a high-density birefringence rubidium vapor in the superstrong coupling regime

The mode splitting in a system with Doppler-broadened high-density two-level atoms in the presence of magnetic field inside a relatively long optical cavity is studied in the superstrong coupling regime(atoms-cavity coupling strength g√N is near or larger than the cavity free-spectral range?FSR).The effect of a magnetic field applied along the quantization axis is used to break the polarization degeneracy of the cavity and thereby introduce birefringence(or Faraday rotation)into the medium.The cavity modes are further split in the presence of the magnetic field compared with the normal case of the multi-normal-mode splitting of the two-level system near the D2 line of87Rb.The dependence of the mode splitting on the magnetic field and the temperature is studied.The theoretical analysis according to the linear dispersion theory can provide a good explanation.