External Transverse Magnetic Field Research Articles

Analytic solution of heat and mass transfer over a permeable stretching plate affected by chemical reaction, internal heating, Dufour-Soret effect and hall effect

The analytical solution is derived for the steady MHD mixed convection, laminar, heat and mass transfer over an isothermal, inclined permeable stretching sheet, immersed in a uniform porous medium in the presence of chemical reaction, thermal radiation, Dufour and Soret effects, an external transverse magnetic field, and internal heating. The governing equations are transformed into a dimensionless coupled system of non-linear ordinary differential equations and then solved analytically by the homotopy analysis method. A parametric study illustrating the influence of the chemical reaction, magnetic field, porous medium inertia parameter, and the Dufour and Soret numbers on the fluid velocity, temperature, and concentration are investigated through the obtained analytic solution. As well as the local Nusselt and the Sherwood numbers is conducted. The obtained results are presented graphically and the physical aspects of the problem are discussed. The obtained solution has been tested numerically for some values of the system parameters. Comparison with previously reported numerical results is tabulated and agreement is recorded. Analytic form of some characteristic parameters, e. g. the local skin-friction coefficient, the local Nusselt number, and the local Sherwood number, stress at the stretching surface, local mass transfer coefficient, the local wall mass flux, the local heat transfer coefficient and the local heat flux, are given due to the obtained analytic solution.

Perturbative quantum Monte Carlo study ofLiHoF4in a transverse magnetic field

Results from a recent quantum Monte Carlo (QMC) study [P. B. Chakraborty et al., Phys. Rev. B 70, 144411 (2004)] of a model of the ${\text{LiHoF}}_{4}$ Ising magnetic material in an external transverse magnetic field, ${B}_{x}$, show a discrepancy with experimental results, even for small ${B}_{x}$ where quantum fluctuations are small. This discrepancy persists asymptotically close to the classical ferromagnet to paramagnet phase transition. In this paper, we numerically reinvestigate the temperature $T$ versus transverse-field phase diagram of ${\text{LiHoF}}_{4}$ in the regime of weak ${B}_{x}$. In this regime, starting from an effective low-energy spin-1/2 description of ${\text{LiHoF}}_{4}$, we apply a cumulant expansion to derive an effective temperature-dependent classical Hamiltonian that incorporates perturbatively the small quantum fluctuations in the vicinity of the classical phase transition at ${B}_{x}=0$. Via this effective classical Hamiltonian, we study the ${B}_{x}\text{\ensuremath{-}}T$ phase diagram via classical Monte Carlo simulations. In particular, we investigate the influence on the phase diagram of various effects that may be at the source of the discrepancy between the previous QMC results and the experimental ones. In particular, we consider two different ways of handling the long-range dipole-dipole interactions and explore how the ${B}_{x}\text{\ensuremath{-}}T$ phase diagram is modified when using different microscopic crystal-field Hamiltonians. The main conclusion of our work is that we fully reproduce the previous QMC results at small ${B}_{x}$. Unfortunately, none of the modifications to the microscopic Hamiltonian that we explore are able to provide a ${B}_{x}\text{\ensuremath{-}}T$ phase diagram compatible with the experiments in the quasiclassical small ${B}_{x}$ regime.

Entanglement of two blocks of spins in the critical Ising model

We compute the entropy of entanglement of two blocks of $L$ spins at a distance $d$ in the ground state of an Ising chain in an external transverse magnetic field. We numerically study the von Neumann entropy for different values of the transverse field. At the critical point we obtain analytical results for blocks of size $L=1$ and 2. In the general case, the critical entropy is shown to be additive when $d\ensuremath{\rightarrow}\ensuremath{\infty}$. Finally, based on simple arguments, we derive an expression for the entropy at the critical point as a function of both $L$ and $d$. This formula is in excellent agreement with numerical results.

MHD channel flow control in 2D: Mixing enhancement by boundary feedback

A nonlinear Lyapunov-based boundary feedback control law is proposed for mixing enhancement in a 2D magnetohydrodynamic (MHD) channel flow, also known as Hartmann flow, which is electrically conducting, incompressible, and subject to an external transverse magnetic field. The MHD model is a combination of the Navier–Stokes PDE and the Magnetic Induction PDE, which is derived from the Maxwell equations. Pressure sensors, magnetic field sensors, and micro-jets embedded into the walls of the flow domain are employed for mixing enhancement feedback. The proposed control law, designed using passivity ideas, is optimal in the sense that it maximizes a measure related to mixing (which incorporates stretching and folding of material elements), while at the same time minimizing the control and sensing efforts. A DNS code is developed, based on a hybrid Fourier pseudospectral-finite difference discretization and the fractional step technique, to numerically assess the controller.

INFORMATION GEOMETRY, INFERENCE METHODS AND CHAOTIC ENERGY LEVELS STATISTICS

In this letter, we propose a novel information-geometric characterization of chaotic (integrable) energy level statistics of a quantum antiferromagnetic Ising spin chain in a tilted (transverse) external magnetic field. Finally, we conjecture our results might find some potential physical applications in quantum energy level statistics.

External magnetic field effect on plume images and X-ray emission from a nanosecond laser produced plasma

AbstractThe plume images of the laser produced silver plasma in the absence and presence of 0.45 T transverse magnetic field has been investigated under vacuum ~10−4 torr and in air. An Nd:YAG laser (1.064 µm, 1.1 MW, 9 ns) with intensity ~1012 Wcm−2 was used to generate plasma. A CCD image capture system was used for plasma imaging to explore the plume. A magnetic probe was employed to measure the variation in internal magnetic field of plasma with as well as without 0.45 T external transverse magnetic field. The X-ray emission from plasma in both the cases (with and without B field) was also monitored using two PIN photodiodes filtered with 24 µm Cu and 24 µm Al. The plume images in both the cases were then correlated with the time resolved soft X-ray emission. It was found that the self generated magnetic field of the plasma increases in the presence of magnetic field. Plume images reveal that the confinement of the plume takes place in the presence of magnetic field both in the cases of air and vacuum. Jet and spikes like structures were also observed due to plasma instabilities. Lobe formation in the plume at latter stages of plasma evolution was more prominent in air than under vacuum. X-ray emission signals exhibited an enhancement in the emission under transverse magnetic field. An increased rate of recombination due to high density as a result of plasma confinement across the applied magnetic field was found to be the main reason behind emission enhancement.

Magnetically assisted gas–solid fluidization in a tapered vessel: First report with observations and dimensional analysis

AbstractThe article presents first experimental results on gas–solid fluidization in a tapered bed in presence of an external transverse magnetic field that creates a novel branch in magnetically assisted fluidization. Phase diagrams similar to those used to describe cylindrical beds have been created to distinguish the bed regimes occurring under the action of two principle macroscopic variables such as field intensity and gas flow rate. A detailed analysis and parallelism to the bed behaviour exhibited by non‐magnetic spouted beds of cohesive particles have been performed. Principle process variables such as bed depth, field intensity, particle size, cone angle have been detected. A dimensional analysis utilizing a “pressure transform” of the initial set of variables has been applied to develop scaling relationships. Examples of scaling experimental data pertinent to the minimum spouting point and involving the magnetic granular Bond number have been developed.

Single- and two-particle excitations in a 1D aperiodic sequence of quantum dots

The energy spectrum of single- and two-particle excitations for a one-dimensional aperiodic Fibonacci sequence of quantum dots (QDs) was determined within the pair interaction approximation. The critical behaviour of the energy spectrum and wave functions were obtained. The energy spectrum is a Cantor set of zero Lebesgue measure. The perturbation theory was used to obtain the critical value of the distance between the centres of the neighboring QDs when the first-order corrections to the energy of the excitations were neglected. The contribution of the external transverse magnetic field to particle localization was also considered and the influence of the external field on the first-order corrections to the energy was analyzed. The transmission coefficient was determined using the quasi-classical approximation and the energy level splitting versus the distance between the QDs was obtained. The effect of resonance tunneling of the excitations between QD pairs was studied. Localization occurs at finite values of the perturbations, in contrast to periodic one-dimensional sequences.

VACUUM BIREFRINGENCE CAUSED BY ARBITRARY SPIN PARTICLES

We study the propagation of a linearly polarized laser beam in the external transverse magnetic field taking into consideration the vacuum polarization by arbitrary spin particles. Induced ellipticity of the beam is evaluated using the effective Lagrangian. With the help of the PVLAS experimental data, we obtain bounds on masses of charged higher spin particles contributed to ellipticity.

Magnetic field effects on spin texturing in a quantum wire with Rashba spin-orbit interaction

A quantum wire with strong Rashba spin-orbit interaction is known to exhibit spatial modulation of spin density along its width owing to coupling between subbands caused by the Rashba interaction. This is known as spin texturing. Here, we show that a transverse external magnetic field introduces additional complex features in spin texturing, some of which reflect the intricate details of the underlying energy dispersion relations of the spin-split subbands. One particularly intriguing feature is a 90\ifmmode^\circ\else\textdegree\fi{} phase shift between the spatial modulations of two orthogonal components of the spin density, which is observed at moderate field strengths and when only the lowest spin-split level is occupied by electrons. Its origin lies in the fact that the Rashba interaction acts as an effective magnetic field whose strength is proportional to the electron's velocity.

Direct numerical simulation of a heat removal configuration for fusion blankets

A series of direct numerical simulations (DNS) are performed to study the natural convection heat transfer between concentric cylinders at several Rayleigh and Hartmann numbers. The buoyant flow is driven by the temperature difference between the inner and the outer walls, with the inner wall being at lower temperature, while an external transverse magnetic field is imposed. Both laminar and turbulent flows are observed depending on the magnitude of the Rayleigh and Hartmann numbers. The resulting flow structures of the cases studied were both laminar and turbulent. The results show the 3D nature of turbulence and the tendency of the magnetic field to form narrow Hartmann layers, 3D jets and wakes at specific azimuthal angles. Some particular features of the turbulent regime as well as the heat transfer are also investigated. The magnetic field effect on the convective heat transfer is assessed via the Nusselt number showing that conduction dominates as the Hartmann number increases.

Considerable rise in the stability of combined superconductors doped by intermetallic compounds with an extremely high low-temperature specific heat

The influence of doping intermetallics based on rare-earth elements and ceramics with an extremely high low-temperature specific heat on the stability of combined NbTi superconductors against electromagnetic disturbances is studied experimentally and theoretically. The objects of investigation are standard NbTi conductors (0.85 mm in diameter) in a copper matrix that are soldered to copper wires containing high-specific-heat dopants. CeCu6, HoCu2, CeAl2, and PrB6 intermetallics (at 4.2 K, their specific heat is on average 150 times that of copper) or Cd2O2S ceramics (at 4.2 K, its specific heat is higher than that of copper by 600 times) are introduced into combined superconductor samples in the form of fine powder. The powder is placed into the copper wire either as one thick (0.6 mm in diameter) strand or as 19 thin (0.1 mm in diameter) strands. An undoped reference sample contains a solid conductor. Samples with a transport current placed in an external transverse magnetic field are subjected to longitudinal magnetic disturbances causing pulsed heating of the samples by eddy currents. The disturbance time is varied in a wide range: from 50 μs to 1.2 ms. To compare the critical energy densities of the disturbances in differently shaped samples, a mathematical technique is developed that is based on analytical solution of the equation of electromagnetic diffusion into the sample. It is found that the critical energy density of doped samples is much higher (by several times) than that of the reference sample. Upon direct cooling of the samples by liquid helium in a vertical channel (the most intense heat removal under steady-state conditions), the effect of stability improvement for the doped samples persists. Moreover, it is shown that the high-specific-heat dopants, raising the heat needed to warm the sample, restrict the heat flux into the liquid and thereby increase the energy removed by the coolant during unsteady heat transfer.

Study of magnetic properties of Pd1−x Fe x )0.95Mn0.05 alloy using polarized muons and neutrons

The Pd1−xFex)0.95Mn0.05 alloy with random competing interaction was studied by measuring the muon spin relaxation in an external transverse magnetic field and in a zero magnetic field. Using the measured temperature dependence of the dynamic relaxation rate λ and the characteristics of the distribution of local static fields, the phase states of the sample under study are refined. In particular, it is shown that the ferromagnetic and spin-glass states coexist simultaneously in the sample below 25 K. Combined studies of the sample using the μSR and neutron depolarization methods made it possible to determine the size of magnetic inhomogeneities to be 2–6 μm in the temperature range 5–40 K.

Effective Lagrangian at cubic order in electromagnetic fields and vacuum birefringence

The effective Lagrangian of electromagnetic fields at the cubic order in field strength is considered. This generalized Lagrangian is motivated by electrodynamics on non-commutative spaces. We find the canonical and symmetrical energy–momentum tensors and show that the vacuum in the model behaves like an anisotropic medium. The propagation of a linearly polarized laser beam in the external transverse magnetic field is investigated. We obtain the dispersion relation and refraction indexes for two polarizations. From experimental values of the induced ellipticity, reported by PVLAS Collaboration, the constraint on parameters in the effective Lagrangian is evaluated.

Vacuum birefringence from the effective Lagrangian of the electromagnetic field

The propagation of a linearly polarized laser beam in the external transverse magnetic field is studied. We explore the effective Lagrangian of the electromagnetic field. With the help of the effective Lagrangian, Stokes parameters, induced ellipticity, and the angular rotation of the polarization plane of the beam are evaluated. Ellipticity measured in the PVLAS experiment allows us to obtain the relation between two parameters in the effective Lagrangian.

Numerical Evaluation of AC Loss Property in Bi-2223 Tapes Affected by Multifilament Structure

This paper describes the numerical results of AC losses in various types of non-twisted multifilamentary tapes that actual Bi-2223 Ag-sheathed wires are idealized. The penetration process of magnetic flux into the superconductor filaments subject to Bean's critical state model is simulated for the application of an external transverse magnetic field perpendicular to the broadest face of tape wire by means of energy minimization. The AC losses under cyclic fields are calculated from the distribution of a vector potential in an initial state. The influences of arrangements and shapes of the filaments on the losses are investigated as compared with those for a wire that the entire filamentary region is regarded as a homogeneous superconductor.

Penetration of an external magnetic field into a multistrip superconductor/soft-magnet heterostructure

The magnetization of a planar heterostructure of periodically alternating type-II superconductor and soft-magnet strips exposed to a transverse external magnetic field is studied. An integral equation governing the sheet current distribution in the Meissner state of the superconductor constituents is derived. The field of complete penetration of magnetic flux in the critical state of the superconductor constituents is calculated for different widths of the superconductor and the soft-magnet constituents and a range of values of the relative permeability of the soft-magnet constituents.

Numerical simulation of interaction between arc discharge and transverse magnetic field

An unsteady-state three-dimensional numerical model of radiation magnetogasdynamics is used to calculate the structure of an arc discharge which interacts with an external transverse magnetic field and transverse gas flow. The velocity field and the distribution of gas temperature obtained as a result of calculations agree with experimental data. The difference between the calculated and measured values of temperature in the discharge column is approximately 5%.

Thermodynamic properties of the XX model in a chain with a period two and three coupling

The exact solutions for the energy spectrum of the XX model with a periodic coupling and an external transverse magnetic field $h$ are obtained. The diagonalization procedure is discussed, and analytical and numerical solutions are given. Using the solutions for period-two coupling, the free energy, entropy, and specific heat are calculated as functions of temperature and applied transverse external magnetic field. Their expressions show that below a particular value $v$ and above a value $u$ of the magnetic field $|h|$, the entropy and the specific heat vanish exponentially in the low temperature limit.

Statistical Simulation on the Random and Retrograde Motion of Single Cathode Spot of Vacuum Arc

In this paper, a two-dimensional statistical model for a single cathode spot of vacuum arc with copper cathode has been established to simulate its random walk and retrograde motion under external transverse magnetic field. A parameter, k, was used to denote the different probabilities of cathode spot motion in Amperes direction and retrograde direction. With this model, the distribution of the probability density of cathode spot occurring in different area on cathode surface was simulated at different arcing time.