Presence Of Transverse Magnetic Field Research Articles

Magnetic phases of XY model with three-spin terms: interplay of topology and entanglement

Magnetic and topological properties along with quantum correlations in terms of several entanglement measures have been investigated for an antiferromagnetic (AFM) spin-1/2 XY model in the presence of transverse magnetic field and XZX−YZY type of three-spin interactions. Symmetries of the spin Hamiltonian have been identified. Under the Jordan–Wigner transformation, the spin Hamiltonian converted into spinless superconducting model with nearest neighbor (NN) hopping and Cooper pairing terms in addition to next NN Cooper pairing potential. Long range AFM order has been studied in terms of staggered spin–spin correlation functions, while the topological orders have been characterized by winding numbers. Magnetic and topological phase diagrams have been prepared. Faithful coexistence of magnetic and topological superconducting phases is found in the entire parameter regime. Boundaries of various quantum phases have been marked and positions of bicritical points have been identified.

Quantum phases of spin-1/2 extended XY model in transverse magnetic field

In this study, a spin-1/2 extended anisotropic XY chain has been introduced in which both time reversal and SU(2) symmetries are broken but Z 2 symmetry is preserved. Magnetic and topological phase diagrams in the parameter space have been drawn in the presence of transverse magnetic field. Entanglement measures like mutual information and quantum discord are also evaluated and it indicates that these transitions are second order in nature. Quantum phase transition is noted at zero magnetic field, as well as magnetic long range order is found to withstand magnetic field of any strength. Exact analytic results for spin-spin correlation functions have been obtained in terms of Jordan-Wigner fermionization. Existence of long range magnetic order has been investigated numerically by finding correlation functions as well as the Binder cumulant in the ground state. Dispersion relation, ground state energy, and energy gap are obtained analytically. In order to find the topologically nontrivial phase, sign of Pfaffian invariant and value of winding number have been evaluated. Both magnetic and topological phases are robust against the magnetic field and found to move coercively in the parameter space with the variation of its strength. Long range orders along two orthogonal directions and two different topological phases are found and their one-to-one correspondence has been found. Finally casting the spinless fermions onto Majorana fermions, properties of zero energy edge states are studied. Three different kinds of Majorana pairings are noted. In the trivial phase, next-nearest-neighbor Majorana pairing is found, whereas two different types of nearest-neighbor Majorana pairings are identified in the topological superconducting phase.

Magnetohydrodynamics and viscosity variation in couple stress squeeze film lubrication between rough flat and curved circular plates

A simplified mathematical model has been developed for understanding combined effects of surface roughness, viscosity variation and couple stresses on the squeeze film behaviour of a flat and a curved circular plate in the presence of transverse magnetic field. The Stokes (1966) couple stress fluid model is included to account for the couple stresses arising due to the presence of microstructure additives in the lubricant. In the context of Christensen’s (1969) stochastic theory for the lubrication of rough surfaces, two types of one-dimensional roughness patterns (radial and azimuthal) are considered. The governing modified stochastic Reynolds type equations are derived for these roughness patterns. Expressions for the mean squeeze film characteristics are obtained. Numerical computations of the results show that the azimuthal roughness pattern on the curved circular and flat plate results in more pressure buildup whereas performance of the squeeze film suffers due to the radial roughness pattern. Further the Lorentz force characterized by the Hartmann number, couple stress parameter and viscosity variation parameter improve the performance of the squeeze film lubrication as compared to the classical case (Non-magnetic, Newtonian case and non-viscous case).

Magnetohydrodynamic hybrid nanofluid flow through moving thin needle considering variable viscosity and thermal conductivity

In modern science and technology, industrial applications that deal with the problem of continuously moving thin needle, surrounded with fluid in sectors like hot rolling, crystal growing, heat extrusion, glass fiber drawing, etc., are rapidly increasing. Such processes involve high temperatures which may affect the fluid properties that is, viscosity and thermal conductivity. So, it’s crucial to understand temperature-dependent fluid properties. Focused on these assumptions, the main objective of the current research work is to investigate how temperature-dependent fluid properties might improve the heat transfer efficiency and performance evolution of hybrid nanofluid in the presence of transverse magnetic field over a moving thin needle. Variable Prandtl number is also introduced to observe flow fluctuation, the effect of adding nanoparticles, and enhancement in heat transmission. The results are obtained for different needle thicknesses, temperature-dependent viscosity, temperature-dependent thermal conductivity, and heat generation. Moreover, Fe3O4/Graphene nanoparticles are considered to be dispersed in water. The governing partial differential equations of flow and heat transfer are transformed into a system of coupled nonlinear ordinary differential equations using analysis of similarity conversion. Subsequently, the numerical solution of the problem is attained by employing the MAPLE software. The fourth-fifth-order Runge-Kutta-Fehlberg (RFK45) approach is used by default in this MAPLE program to address the numerical problem of boundary value. The velocity and temperature field are pictured for different values of the parameters as well as physical quantities of interest such as skin friction coefficient and rate of heat transfer are visually depicted in graphs and tables. It is found that fluid motion and energy transport are highly regulated by the variation of magnetic field strength. As the volume fraction of Fe3O4 is increased, the heat generation, and thermal conductivity parameter vehemently enhance the temperature profile which leads to a rise in thermal boundary layer. A strong augmentation in the heat transfer rate has been found with the increment in the variable Prandtl number.

Effect of horizontal aspect ratio on convection rolls in the presence of transverse magnetic field

We perform three-dimensional direct numerical simulations to investigate the effect of transverse magnetic field on the convection rolls of electrically conducting fluids using the classical Rayleigh–Bénard convection model. The control parameters “Q” (the Chandrasekhar number), “r” (the reduced Rayleigh number), and “Γ” (horizontal aspect ratio) are varied in the ranges 0≤Q≤2000, 1≤r≤25, and 1/2≤Γ≤2, respectively, for two different Prandtl numbers (Pr=0.025 and 0.1). In the absence of the magnetic field, the system allows convection in the form of two dimensional rolls near the onset, and it is suppressed by the Lorentz force appearing in the presence of transverse magnetic field. As a result, primary instability is moved toward higher r for Q>0, and the movement increases with Γ. Interestingly, for weak to moderate magnetic fields, there exists two different kinds of onset depending on Γ and Q. Steady oblique rolls (SOR) and transverse rolls (STR) are preferred at the onset accordingly as Γ<1 and Γ>1, respectively, while for Γ = 1, both STR and SOR are found to occur at the onset depending on Q. On the other hand, stronger transverse magnetic field orients the flow toward itself for Γ≥1. In the considered parameter regime, diverse routes to chaos including period-doubling, quasiperiodic, intermittent, and transient are observed close to the onset along with some interesting scaling laws associated with the oscillatory instability of the rolls.

3D Thermo-fluid MHD simulation in a complex flow geometry

In the Magneto-hydrodynamic (MHD) flow, electric current induces inside the fluid domain due to induced e. m. f when an electrically conducting fluid flows in presence of transverse magnetic field. In the present work, the 3D thermo-fluid MHD analysis has been performed for the flow geometry, which is to be tested in the liquid lead lithium MHD (LLMHD) loop. The chosen flow geometry consists of inlet/outlet circular pipes, manifolds and three rectangular channels with parallel flow configurations. Here, three rectangular channels are coupled at the inlet/outlet manifold. Sudden expansion and contraction occur at the inlet and outlet manifold respectively. The 3D thermo-fluid MHD analysis result at magnetic field of 1.4T and flow rate of 3 kg/s have been discussed. The numerical MHD results of induced electric potential, electric current, pressure, temperature and flow distributions are discussed in detail. The inlet/outlet circular pipes and manifolds are found to be the main contributors of the total pressure drop. The qualitative discussion has also been made on the impact of magnetic field on flow distribution among the flow channels with parallel flow configurations.

Effect of ambient environment and magnetic field on laser-induced cobalt plasma

Plasma parameters of magnetically confined Cobalt (Co) plasma have been evaluated by using laser-induced breakdown spectroscopy at various laser irradiances, under different ambient pressures of two environments such as Ar and Ne and at different time delays. The effect of laser irradiance on Co plasma is exposed in the presence and absence of a Transverse Magnetic field (TMF) while keeping environmental gas pressure constant, i.e., 10 Torr. For this purpose, Co pellets were exposed to Nd: YAG laser (1064 nm, 10 ns) at various laser irradiances ranging from 1 to 2.9 GW cm−2. To investigate the impact of background gas pressures, Co pellets were exposed to various pressure varying from 5 to 760 Torr of Ar and Ne. In the case of time delay variation, the Co plasma parameters Texc and ne decrease exponentially. A significantly pronounced effect of the presence of an external TMF of strength 0.9 T on time-integrated Co plasma parameters has been revealed. Plasma parameters Texc and ne are considerably increased in the presence of TMF in both ambient environments because of being constrained to a very small region due to which collisions will be enhanced. Implementation of the 0.9 T TMF on a laser-induced plasma of Co is responsible for the confinement of plasma. The surface morphology of laser-irradiated Co samples was also discussed to confirm the effect of TMF. Fine and uniform structures are observed in samples treated in the presence of TMF by using the SEM technique.

Run‐up flow of MHD fluid between parallel porous plates in the presence of transverse magnetic field

AbstractThis paper investigated the run‐up flow of magnetohydrodynamics (MHD) incompressible, viscous, Newtonian fluid bounded by two parallel horizontal porous plates in the presence of transverse magnetic field. The fluid flow is initially due to constant pressure gradient, placed parallel to the plates. On attaining steady state, the pressure gradient is suddenly withdrawn and the lower porous plate is set into motion in its own plane, this phenomenon is termed as run‐up flow. The transfer of momentum is as a result of the disturbances emanating from the boundary into the fluid. The initial value problem is solved using Laplace transform technique to obtain the closed‐form solution for the velocity in the Laplace domain. Semi‐analytical result is obtained by an inversion technique based on Riemann‐sum approximation to invert the solution for velocity into its corresponding time domain. The mathematical simulation conducted shows that increasing the Hartmann number is observed to decrease the fluid velocity while increasing the pressure gradient is found to enhance the fluid velocity. Furthermore, the opposing effects of suction/injection parameter on the fluid velocity have been established in the research.

Lattice Boltzmann simulation of thermo-magnetic natural convection in an enclosure partially filled with a porous medium

A theoretical analysis of incompressible magnetohydrodynamic (MHD) non-Darcian hydrogravitational convection in a square enclosure partially filled with a highly permeable medium in presence of transverse magnetic field is presented. A non-Darcy model is utilized for the porous region featuring both Darcian linear drag and second order Forchheimer drag components with Brinkman no-slip at the walls. The horizontal (i.e., bottom and Top) wall boundaries are considered adiabatic and impermeable, while the side walls (hot and cold walls) are maintained with different thermal values. The governing momenta and thermal conservation equations with appropriate end conditions are solved by Lattice Boltzmann method (LBM). A parametric examination of the impact of Hartmann number (0 < Ha < 50), Darcy number (0.0001 < Da < 0.1), and Rayleigh number (103 < Ra < 106) on temperature contours and streamline patterns for Helium gas (Prandtl number (Pr) = 0.71) is conducted. The heat flux distributions on the side walls and centre-line velocity are also computed. With greater Darcy number and Rayleigh number, Nusselt number is boosted at the left hot wall and the right cold wall. However, Nusselt number increases as one descends the hot wall toward the lower adiabatic boundary, and subsequently increases asone ascends the cold wall toward the upper adiabatic boundary.

Free convection Hartmann flow of a viscous fluid with damped thermal transport through a cylindrical tube

• Free convection flow of viscous fluid in the presence of transverse magnetic field. • The thermal transport equation with Caputo-Fabrizio fractional integral operator. • The analytical solutions are found by using integral transforms. The free convection flow of a viscous fluid in a cylindrical tube is investigated in this article in the presence of a transverse magnetic field. The Caputo-Fabrizio fractional integral operator is used to generalize the thermal transport equation. Integral transforms, more specifically the Laplace and finite Hankel transforms, are used to find the solutions. The ordinary model is recovered as a particular case by taking the limit, and several more special instances are explored. Graphically, the impacts of the fractional and physical factors are highlighted. For a small and large values of time, the fractional parameter has distinct effects on the temperature and velocity.

An implicit Keller box approach for solution of MHD three-dimensional flow through a porous medium

The present study investigates the Soret and Dufour effect on free-convection flow of a viscous incompressible fluid through a porous medium bounded by an infinite vertical porous plate with chemical reaction and viscous dissipation is investigated with aid of Implicit Keller box and regular perturbation methods. The flow is assumed in the presence of transverse magnetic field. Characteristics of Velocity, Temperature and Concentration are obtained and graphical interpretation is made. The observation of these results reflects that velocity and thermal boundary layer thickness decrease with the increase of radiation parameter. Graphical interpretations establish a good agreement in a realistic sense.

Surface Structuring and Thin Film Coating through Additive Concept Using Laser Induced Plasma of Mg Alloy: A Comparison between the Presence and Absence of Transverse Magnetic Field (TMF)

In the present study, the influence of a 1.1 tesla Transverse Magnetic Field (TMF) on Laser-Induced Breakdown Spectroscopy (LIBS) of Mg-alloy plasma has been explored. The Mg plasma was produced using an Nd: YAG laser (1064 nm, 10 ns) at an intensity of 2 GW/cm2. Inert gases of Ar, Ne, and He were filled as environmental gases at pressures ranging from 1 to 100 Torr. Optical emission spectra from laser-produced plasma were detected with the help of a spectrometer, and plasma parameters such as excitation temperature (Texc) and electron number density (ne) were evaluated. Enhancement in the Mg plasma’s Texc and ne in the presence of TMF was noticed under all experimental conditions, including different ambient gases with varying pressures and time delays (0.42 µs–9.58 µs). Plasma confinement by applied TMF was analytically evaluated through thermal beta (βt) values, which were &lt;1 under all circumstances. The highest Texc and ne values (17,259 K and 11.5 × 1017 cm−3) for Mg-alloy plasma were obtained with ambient Ar in TMF, while the lowest values (8793 K and 1.0 × 1017 cm−3) were obtained in presence of He gas in the absence of TMF. SEM analysis was used to determine the surface structure of laser-ablated Mg alloy in the presence and absence of TMF. It revealed that the formation of cones, cavities, and non-uniform melting are characteristic features of ambient Ar, while spikes and cavities are prominent features in Ne gas environments. Conical spikes and dendrites are distinct features when ambient He is present. In comparison with the field-free condition, distinct and well-defined structures were observed in the presence of TMF. By controlling LPP parameters, the surface structuring of Mg alloy can be controlled. The optimization and enhancement of LPP parameters make it a highly useful tool for thin film deposition, coatings of multilayers, and ion implantation/doping.

Tuning the adiabaticity of spin dynamics in diamond nitrogen vacancy centers

We study the spin dynamics of diamond nitrogen vacancy (NV) centers in an oscillating magnetic field along the symmetry axis of the NV in the presence of transverse magnetic fields. It is well-known that the coupling between the otherwise degenerate Zeeman levels |M S = ±1⟩ due to strain and electric fields is responsible for a Landau–Zener process near the pseudo-crossing of the adiabatic energy levels when the axial component of the oscillating magnetic field changes sign. We derive an effective two-level Hamiltonian for the NV system that includes coupling between the two levels via virtual transitions into the third far-detuned level |M S = 0⟩ induced by transverse magnetic fields. This coupling adds to the coupling due to strain and electric fields, with a phase that depends on the direction of the transverse field in the plane perpendicular to the NV axis. Hence, the total coupling of the Zeeman levels can be tuned to control the adiabaticity of spin dynamics by fully or partially compensating the effect of the strain and electric fields, or by enhancing it. Moreover, by varying the strength and direction of the transverse magnetic fields, one can determine the strength and direction of the local strain and electric fields at the position of the NV center, and even the external stress and electric field. The nuclear spin hyperfine interaction is shown to introduce a nuclear spin dependent offset of the axial magnetic field for which the pseudo-crossing occurs, while the adiabaticity remains unaffected by the nuclear spin. If the NV center is coupled to the environment, modeled by a bath with a Gaussian white noise spectrum, as appropriate for NVs near the diamond surface, then the spin dynamics is accompanied by relaxation of the Zeeman level populations and decoherence with a non-monotonic decrease of the purity of the system. The results presented here have important impact for metrology with NV centers, quantum control of spin systems in solids and coupled dynamics of spin and rotations in levitated nano-objects in the presence of magnetic fields.

The analytical solution of the MHD equations via Minkowski 2-D space continuum of liquid metals through a square duct under multiple transport effects

The problem of mass, heat transfer due the steady, laminar for mercury and gallium liquids flow in to a square duct in the presence of transverse magnetic field and ultrasonic fields, is tackled analytically resorting to the wave-position ansatz as the unique independent variable in the 2-D Minkowskiinner product space. The MHD system of partial differential equations is solved by assuming the absence of slip boundary conditions. Each of duct wall is electrically insulated, and have a constant temperature and, the fluid is under a constant pressure gradient. The resulting solutions are visualized graphically for the velocity, temperature distribution, induced magnetic field, entropy generation rate and Bejan numbers, which are illustrated according to different suggested values corresponding to the affected fields. Good agreements are found with previous studies.

Hydromagnetic Second-Order Fluid Flow in a Channel with Fluid -Particle Suspension and Viscous Dissipation

This paper deals with the analysis of unsteady flow and heat transfer of second-order fluid with fluid-particle suspension in a vertical channel in the presence of transverse magnetic field with viscous dissipation. The fluid is driven by a constant pressure gradient. The governing partial differential equations are converted in to ordinary differential equation by similarity transformation and solved analytically. The expressions for velocity, temperature, skin friction and heat transfer are obtained. The numerical results depicting the effects of visco-elasticity in combination with other flow parameters involved in the problem are presented graphically and discussed qualitatively.

Quantum phase transitions in long-range interacting hyperuniform spin chains in a transverse field

Hyperuniform states of matter are characterized by anomalous suppression of long-wavelength density fluctuations. While most of interesting cases of disordered hyperuniformity are provided by complex many-body systems like liquids or amorphous solids, classical spin chains with certain long-range interactions have been shown to demonstrate the same phenomenon. It is well-known that the transverse field Ising model shows a quantum phase transition (QPT) at zero temperature. Under the quantum effects of a transverse magnetic field, classical hyperuniform spin chains are expected to lose their hyperuniformity. High-precision simulations of these cases are complicated because of the presence of highly nontrivial long-range interactions. We perform extensive analysis of these systems using density matrix renormalization group to study the possibilities of phase transitions and the mechanism by which they lose hyperuniformity. We discover first-order QPTs in the hyperuniform spin chains. An interesting feature of the phase transitions in these disordered hyperuniform spin chains is that, depending on the parameter values, the presence of transverse magnetic field may remarkably lead to increase in the order of the ground state as measured by the "$\tau$ order metric," even if hyperuniformity is lost. Therefore, it would be possible to design materials to target specific novel quantum behaviors in the presence of a transverse magnetic field. Our numerical investigations suggest that these spin chains can show no more than two QPTs. We further analyze the long-range interacting spin chains via the Jordan-Wigner mapping, showing that under the pairwise interacting approximation and a mean-field treatment, there can be at most two QPTs. Based on these numerical and theoretical explorations, we conjecture that these spin chains can show a maximum of two QPTs at zero temperature.

Hall Effect on ECF Flow along a Rotating Infinite Porous Plate in the Presence of Transverse Magnetic Field

Unsteady extracellular fluid (ECF) flow along with a rotating infinite vertical porous plate in the presence of a transverse magnetic field has been studied numerically. The dimensional governing equations have been non-dimensionalized by useful dimensionless variables. The explicit finite difference method has been used to solve dimensionless equations. The numerical results have been calculated by studio developer FORTRAN 6.6a and MATLAB 2018a. For perfect conducting case, Magnetic Diffusivity Parameter 5 ≤ Pm ≤ 15 has been taken in induction equation. For good accuracy, stability and convergence analysis have been analyzed. Mesh Sensitivity test, steady-state solution test, and code validation test have been performed. For time step τ = 1, the numerical results have been found for the primary velocity, secondary velocity, angular velocity, primary induced magnetic field, secondary induced magnetic field, temperature as well as shear stresses along x and z direction, couple stress along z direction, current densities along x and z direction and the Nusselt number. Finally, the effects of various parameters have been separately discussed and illustrated graphically.

The flow behaviour of blood in two-phase time-dependent tapered stenosed artery in the presence of transverse magnetic field

In this study, a tapered stenosed artery is considered to notice the effect of transverse magnetic field applied on blood flow to analyze the behavior of the flow with the help of significant flow attributes. The laminar, incompressible and fully developed flow of blood is studied taking into account the variable viscosity. To resemble the problem to real life situation, flow in core region is assumed to be non-Newtonian and flow in peripheral region is assumed to be Newtonian. The constitutive equation of blood is represented by Bingham plastic model in peripheral region and Herschel–Bulkley model in core region. The simulations are carried out for important flow characteristics such as wall shear stress, volumetric flow rate and axial velocity and the behavior is analyzed. We have reported numerical results for different values of physical parameters of interest. Biological implications of the present model are discussed. It has been observed that the important flow attributes are affected in tapered artery with stenosis and it is possible to stabilize the flow with the help of magnetic field applied externally. It is also noticed that the behaviour of flow attributes found by considering variable viscosity is in good agreement with the literature as compared to constant viscosity.

Investigation of the Capabilities of Transverse Magnetic Field Controlled Laser-Induced Plasma Micro-Machining

Abstract Laser-induced plasma micro-machining (LIPMM) has proven a number of advantages in micro-machining due to reduced thermal defects, smaller heat-affected zones, and larger aspect ratios when compared with conventional laser ablation. The present work explores the use of external magnetic fields to further enhance process outcomes in LIPMM. Specifically, machining characteristics and outcomes including plasma intensity, attainable aspect ratios, and surface quality will be explored through a theoretical and experimental study in different classes of materials in a transverse magnetic field controlled LIPMM. First, process improvement mechanisms are illustrated in terms of plasma confinement and laser absorption in transverse magnetic fields. A magnetic field redistribution analysis is performed to reveal the differences in the achievable enhancements in machining characteristics in terms of material characteristics. Second, a set of single-factor experiments is conducted to investigate the effects of the strength and direction of the magnetic field on machining capabilities in magnetic and nonmagnetic materials (410, 304 stainless steels and silicon). The experimental results show that plasma intensity and aspect ratios can be significantly increased in the presence of transverse magnetic fields. The greatest influence on machining capability is achieved in a magnetic material. In this case, plasma intensity and aspect ratios were increased by about 176% and 160%, respectively, when compared with other materials with a magnetic field strength of 0.1 T and a magnetic field direction parallel to the processing direction. Finally, the morphology and cross-section profiles of micro-channels have been measured for verifying the impact on the surface quality of transverse magnetically controlled LIPMM.

Consistency of splitting frequency difference with longtudinal modes spacing variation in Zeeman dual-frequency laser

Phase anisotropy in laser resonant cavity will bring about an influence on laser frequency and polarization, such as laser frequency splitting, of which the frequency difference is determined by their introduced phase retardation. For a helium-neon laser with a small phase retardation in the cavity, the two split modes are very close to each other whose burned holes are overlapped. Then only one mode oscillates while the other is always in lock-in state due to strong mode competition, which forms hidden frequency split. Meanwhile the spacing between adjacent longitudinal modes deviates from original value and produces a certain variation equal to twice the hidden splitting frequency difference. As a result the longitudinal modes spacing variation is dominated by the phase retardation. On the other hand, by applying transverse magnetic field to a laser tube along the polarization direction, the neon atoms will undergo transverse Zeeman effect and be divided into two groups to provide the gain for polarized light beams parallel to the magnetic field and perpendicular to the magnetic field respectively. Then the laser mode competition is greatly weakened so that the two split modes can oscillate simultaneously to obtain the frequency difference. In order to make profound study of the consistency between longitudinal mode spacing variation and splitting mode frequency difference in the presence of transverse magnetic field, the samples of tilted quartz plate or half wave plate is placed into laser cavity to produce phase retardation. By the two mentioned methods, the splitting frequency difference varying with phase retardation of samples is deduced to make a comparison. Two measurements show that the average relative deviation is less than 1%, while the experimental results accord with theoretical analyses quite well. In this way splitting frequency difference of Zeeman dual-frequency laser can be determined accurately, and a new method to measure the phase retardation of half wave plate is provided.