Tangential Field Components Research Articles

Prandtl boundary layer expansion with strong boundary layers for inhomogeneous incompressible magnetohydrodynamics equations in Sobolev framework

We consider the validity of Prandtl boundary layer expansion of solutions to the initial boundary value problem for inhomogeneous incompressible magnetohydrodynamics equations in the half-plane when both viscosity and resistivity coefficients tend to zero, where the no-slip boundary condition is imposed on velocity while the perfectly conducting condition is given on magnetic field. Since there exist strong boundary layers, the essential difficulty in establishing the uniform L∞ estimates of the error functions comes from the unboundedness of vorticity of strong boundary layers. Under the assumptions that the viscosity and resistivity coefficients take the same order of a small parameter and the initial tangential component of magnetic field has a positive lower bound near the boundary, we prove the validity of Prandtl boundary layer ansatz in L∞ sense in Sobolev framework. Compared with the homogeneous incompressible case considered in [33], there exists a strong boundary layer of density. Consequently, some suitable functionals should be designed and the elaborated co-normal energy estimates will be involved in analysis due to the variation of density and the interaction between the density and velocity.

Rayleigh–Taylor instability in an arbitrary direction electrostatic field

Based on the potential flow theory, we carry out the nonlinear analysis for the inviscid incompressible Rayleigh–Taylor instability (RTI) in an arbitrary direction electrostatic field. The analytical expressions for the bubble amplitude and growth rate are presented. The effects of tangential and vertical electrostatic fields upon the bubble dynamics are opposite and depend on permittivity ratio. Agreements with recent simulations are found in the bubble amplitude. The direction of electrostatic field determines which (tangential or vertical) component plays the main role. The stability of the interface depends on whether the tangential and vertical components of the electrostatic field exceed the cut-off electrostatic field which is dependent of the permittivity ratio and the Atwood number. The results of this work demonstrate the importance of the direction of electrostatic field when considering the impact of electrostatic field on RTI.

Joshi–Malafarina–Narayan singularity in weak magnetic field

The importance and significance of magnetic fields in the astrophysical scenario is well known. Many domains of astrophysical black hole physics such as polarized shadow image, high energy emitting processes and jet formation are dependent on the behavior of the magnetic fields in the vicinity of the compact objects. In light of this, we determine the master equation and master differential equation that determine the spatial behavior of the magnetic field inside a matter distribution or vacuum region, of general spherically symmetric metric, which is immersed in a test magnetic field. We also investigate here the case of JMN-1 singularity immersed in a uniform weak magnetic field and determine the behavior of magnetic fields by defining electromagnetic four potential vector. We find that the tangential component of the magnetic field is discontinuous at the matching surface of the JMN-1 singularity with the external Schwarzschild metric, resulting in surface currents. We define the covariant expression of surface current density in this scenario. We also analyze the behavior of center-of-mass energy of two oppositely charged particles in the geometry of the magnetized JMN-1 singularity. We briefly discuss the possible scenarios which would possess a discontinuous magnetic field and implications of the same and future possibilities in the realm of astrophysics are indicated.

Room-Temperature Strong Coupling of Few-Exciton in a Monolayer WS2 with Plasmon and Dispersion Deviation.

Engineering room-temperature strong coupling of few-exciton in transition-metal dichalcogenides (TMDCs) with plasmons promises to construct compact and high-performance quantum optical devices. But it remains unimplemented due to their in-plane excitons. Here, we demonstrate the strong coupling of few-exciton within 10 in monolayer WS2 with the plasmonic mode with a large tangential component of the electric field tightly trapped around the sharp corners of an Au@Ag nanocuboid, the fewest number of excitons observed in the TMDC family so far. Furthermore, we for the first time report a significant deviation with a relative difference of up to 100.6% between the spectrum and eigenlevel splitting dispersions, which increases with decreasing coupling strength. It is also shown that the coupling strength obtained by the conventional concept of both being equal to the measured spectrum splitting is markedly overestimated. Our work enriches the understanding of strong light-matter interactions at room temperature.

VARIATIONS IN MAGNETIC PROPERTIES PROPAGATION IN STEEL SHELL STRUCTURE CAUSED BY WELDING (PART 2)

The first stage of the research involves analyzing primary and secondary acoustic wave propagation behavior. The results of the first stage suggest that the properties of shell structures used at every stage of the experiment are distributed unevenly along the generator lines and across the width of the test pipes. In order to conduct a comparative study of properties, the authors of the research introduce the heterogeneity parameter. During the experiment, the parameter is changing locally within two orders of magnitude, even in case of test pipes in their initial state. Equal sensitivity to heterogeneities across steel products is found in its magnetic properties. As numerous studies prove, analyzing variations in magnetic properties makes it possible to detect flaws and areas of their concentration. This method can also be used to estimate the remaining service life. This is a crucial aspect to consider when assessing properties and using the findings to develop digital twins of shell structures. The authors focus on identifying acoustic and magnetic signals coming from flawed shell structures and weld joint areas in particular. For this purpose, magnetic memory method and X-ray analysis are used. It is found that both normal and tangential magnetic field components are sensitive to structural heterogeneities across a steel product. The combination of magnetic memory method and X-ray analysis make it possible to determine how typical weld joint flaws occurring during welding affect the magnetic properties. Sufficient measurements are required for statistical analysis of the findings. It is also possible to introduce further criteria in order to import metal properties correctly into the modelling program using numerical methods.

All-dielectric metasurface refractive index sensor with high figure of merit based on quasi-bound states in the continuum

All-Dielectric metasurfaces are widely used in the field of sense due to their small size, freedom of design, and low radiation loss. However, the optical sensor still has the problem of wide full width at half maximum (FWHM), which leads to a low figure of merit (FOM). In order to solve this problem, an all-dielectric metasurface based on quasi-bound states in the continuum (q-BIC) was proposed for refractive index sensing. The sensor structure consisted of a prism/metasurface/analyte, where the metasurface was composed of periodically arranged subwavelength asymmetric silicon gratings. The asymmetry of the structure led to the coupling of the tangential and radiative field components in the superficial layer at the resonance position, which formed a q-BIC resonance peak with a narrow FWHM in the reflection spectrum. We explained the causes of the q-BIC resonance peak generation by finite element analysis, and analyzed the factors affecting the FWHM, and also simulated the machining errors. The results showed that by reducing the asymmetry of the sensor, it could have a high FOM, with a FOM of 1.35 × 107 RIU−1. In addition, simulated machining errors within ±5 nm showed that small machining errors did not lead to the disappearance of q-BIC, which proved that the sensor had good robustness. These findings had provided ideas for the accurate detection of trace substances.

Sedimentation equilibrium of globular and galaxy clusters

The equilibrium of globular and galaxy clusters is analyzed using a gravitomagnetic (GM) model for a fluid in stationary, axially-symmetric motion. An oblique change of coordinates leads to a free-fall nonlinear force balance equation relating the GM flux function and the gravitational potential. An approximate internal solution of the force balance is obtained introducing trial functions in the form of a sedimentation equilibrium. The internal solution defines the tangential component of the GM field acting on the surface of the cluster. This GM component constitutes the boundary condition that must be used to obtain a self-consistent solution together with Gauss’ and Ampère’s laws. The complete solution is postponed for future work, but a simple application to the classic Coma Cluster problem indicates that the rotating velocity on the surface of the cluster is within the range of observed values, without introducing dark matter.

Results of Hyperbolic Ricci Solitons

We obtain some properties of a hyperbolic Ricci soliton with certain types of potential vector fields, and we point out some conditions when it reduces to a trivial Ricci soliton. We also study those soliton submanifolds whose vector fields are the tangential components of a concurrent vector field on the ambient manifold, and in particular, we show that a totally umbilical hyperbolic Ricci soliton is an Einstein manifold. We prove that if the hyperbolic Ricci soliton hypersurface of a Riemannian manifold of constant curvature and endowed with a concurrent vector field has a parallel shape operator, then it is a metallic-shaped hypersurface, and we determine some conditions for it to be minimal. Moreover, we show that it is also a pseudosymmetric hypersurface.

Vanishing dissipation limit of solutions to initial boundary value problem for three dimensional incompressible magneto-hydrodynamic equations with transverse magnetic field

In this paper, we study the vanishing dissipation limit of solutions to the initial boundary value problem of three-dimensional incompressible viscous magnetohydrodynamic equations in the upper half space where the magnetic field is assumed to be transverse to the boundary. When the tangential component of the magnetic field is imposed the zero Neumann boundary condition, we can establish the uniform energy estimates of the solutions to the initial boundary value problem in the conormal Sobolev spaces even if the velocity field satisfies the no-slip boundary condition. Then the vanishing dissipation limit of solutions to the initial boundary value problem can be achieved in L∞ sense based on some compactness arguments. Compared with the previous results, our results show that the strong boundary layer can still be prevented by the transverse magnetic field even with the magnetic diffusion.

Analysis of Control Problems for Stationary Magnetohydrodynamics Equations under the Mixed Boundary Conditions for a Magnetic Field

The optimal control problems for stationary magnetohydrodynamic equations under the inhomogeneous mixed boundary conditions for a magnetic field and the Dirichlet condition for velocity are considered. The role of controls in the control problems under study is played by normal and tangential components of the magnetic field given on different parts of the boundary and by the exterior current density. Quadratic tracking-type functionals for velocity, magnetic field or pressure are taken as cost functionals. The global solvability of the control problems under consideration is proved, an optimality system is derived and, based on its analysis, a mathematical apparatus for studying the local uniqueness and stability of the optimal solutions is developed. On the basis of the developed apparatus, the local uniqueness of solutions of control problems for specific cost functionals is proved, and stability estimates of optimal solutions are established.

Huygens' surface excitation for the finite element method applied to Maxwell's equations – A construction based on Nitsche's method

We present a Huygens' surface for the finite element method applied to Maxwell's equations, where the equivalent electric and magnetic surface currents are incorporated in the weak form by means of Nitsche's method. The proposed method preserves the reciprocity of Maxwell's equations and it allows for the computation of the total field inside the Huygens' surface, whereas on its outside only the scattered field is computed. The equivalent magnetic surface current at the Huygens' surface requires a double representation of the discontinuous tangential component of the electric field and we demonstrate that it can be efficiently combined with a previously presented higher-order brick-tetrahedron hybridization. Also, it is demonstrated that the near-to-far-field transformation can be evaluated in an accurate manner if collocated with the Huygens' surface, which allows for a compact computational domain and a reduction in the required computational resources. The proposed Huygens' surface is tested on two scattering problems with perfect electric conductor scatterers: (i) a sphere that demonstrates second-order convergence towards the analytical result for a piecewise linear approximation of the electric field; and (ii) a double ogive with two sharp tips which gives a computed monostatic radar cross section that compares well with measurements and computations in the open literature for both polarizations.

Computational analysis of conductive fluid flow with tangential components of magnetic flux density and electric field in metallic and non-metallic circular pipe

This paper has focused on the study of flow characteristics of a steady conductive fluid through a circular pipe in the presence of an applied transverse uniform magnetic field. A numerical simulation of the fluid flow was performed using a multi-physics computational tool. The radial velocity distribution due to the effect of the tangential component of induced magnetic flux density and electric fields at various axial positions is examined in metallic and non-metallic surfaces of the circular pipe. This simulation study helps to analyse the effect of drag force on the variation in axial velocity close to the metallic and non-metallic walls. The induced electric potential is directed along the normal to the Laplacian tangential surface of the pipe. In addition to that, sigmoidal-shaped field profiles are observed when the fluid flow crosses from the upstream to downstream of the magnet edge and vice versa along the axial length of the circular pipe. Simultaneously, it is observed that the average velocity of the fluid flow decreases for a laminar and increases for turbulent Reynolds number. Streamline plots pertinent flow variable such as flow velocity are presented for non-conducting and conducting walls.

Magnetic potential based formulation for linear and non-linear 3D RF sheath simulation

This paper reports a new numerical scheme to simulate the radio-frequency (RF) induced RF sheath, which is suitable for a large 3D simulation. In the RF sheath boundary model, the tangential component of the electric field () is given by the gradient of a scalar electric field potential. We introduce two additional scalar potentials for the tangential components of the magnetic field, which effectively impose the normal electric displacement (D n ) on the plasma sheath boundary condition via in-homogeneous Neumann boundary condition and constrain the tangential electric field on the surface as curl-free (). In our approach, the non-linear sheath impedance is formulated as a natural extension of the large thickness (or asymptotic) sheath limit (), allowing for handling both asymptotic and non-linear regimes seamlessly. The new scheme is implemented using the Petra-M finite element method analysis framework and is verified with simulations in the literature. The significance of non-linearity is discussed in various plasma conditions. An application of this scheme to asymptotic RF sheath simulation on the WEST ICRF antenna side limiters is also discussed.

Impact of anomalous surface boundary conditions on the planar negative‐refractive index lens

It is shown that anomalous boundary conditions at the surface of a negative-refractive-index metamaterial planar lens severely diminishes the resolution of the lens when its relative permittivity and permeability are both −1. Anomalous boundary conditions arise in practical microwave metamaterials that are typically a periodic array of identical unit cells comprising dielectric and conducting elements. For a unit-cell size much smaller than the wavelength, homogenised permittivity and permeability are the constituent parameters of the average fields. Average fields vary on a scale larger than the unit cell size compared to localised fields associated with the constituent elements. Unlike the tangential components of the localised field, tangential components of the average fields are discontinuous across the surface of such materials. This anomalous boundary condition at the lens surface must be described by generalised sheet transition conditions. This study develops expressions for the negative-refractive-index lens optical transfer functions, as a function of spatial frequency, for transverse-electric waves, that account for anomalous surface boundary conditions. Both the simulations and experimental data are used to verify the expressions at a frequency of 3 GHz.

Improved Metallic Enclosure Electromagnetic Imaging Using Ferrite Loaded Antennas

Three-dimensional electromagnetic imaging can be used to monitor grain within metallic grain bins. Data acquisition requires multiple antennas surrounding the imaging space, which are used to transmit and receive the electromagnetic energy inside the bin. Due to their presence inside a metallic enclosure and due to very large mechanical forces these antennas are required to be low profile. In addition, since they are part of the imaging domain, they should be simple to model in the imaging software (i.e., using a point source). Existing half-loop magnetic field antennas meet these design criteria, but can be improved, particularly with better radiation efficiency. Herein, we present an enhanced antenna design: a ferrite-loaded shielded half-loop antenna designed to measure only the tangential component of the magnetic field against the metal enclosure wall, while rejecting the normal component of the electric field. Experimental results in two bins show that the enhanced design improves the signal level over existing probes by 6–18 dB inside a small-scale enclosure and around 20 dB inside a larger 28 m3 (800 bushel) bin. Full 3D imaging results of a high-moisture target within a low-moisture grain background inside the test enclosure show that the enhanced antennas improve the quality of the reconstructed results in the smaller bin, particularly where the antenna performance improvements are prominent.

Hydrodynamic analysis of the magnetic field dependent viscous fluid flow and thermosolutal convection between rotating channels

According to research, exposing a person to a magnetic field enhances blood flow and minimizes their risk of suffering a heart attack. Ferrohydrodynamics is the study of fluid motion mechanics that is affected by strong magnetic polarisation forces (FHD). Ferrofluids may transmit heat in a variety of ways by using magnetic fluids. This behaviour is demonstrated by liquid-cooled speakers, which utilise less ferrofluid to prevent heat from reaching the speaker coil. This modification boosts the coil’s ability to expand, which enables the loudspeaker to create high-fidelity sound. It is investigated how the fluid dynamics of spinning, squeezing plates are affected by thermosolutal convection and a magnetic field dependent (MFD) viscosity. Standard differential equations are used to represent the equations of the modified form of Navier Stokes, Maxwell’s, and thermosolutal convection. The magnetic field, modified velocity field equations, and thermosolutal convection equations all yield suitable answers. Additionally computed and thoroughly detailed are the MHD torque and fluid pressure that are imparted to the top plate. To create a technique with quick and certain convergence, the resulting equations for uniform plates are solved using the Homotopy Analysis Method (HAM) with appropriate starting estimates and auxiliary parameters. The validity and reliability of the HAM outcomes are shown by comparing the HAM solutions with the BVP4c numerical solver programme. It has been found that a magnetic Reynolds number lowers the temperature of the fluid as well as the tangential and axial components of the velocity field. Additionally, when the fluid’s MFD viscosity rises, the axial and azimuthal components of the magnetic field behave in opposition to one another. This study has applications in the development of new aircraft take-off gear, magnetorheological airbags for automobiles, heating and cooling systems, bio-prosthetics, and biosensor systems.

An Electrohydrodynamic analysis for the characterisation of fluid flow within conducting and non-conducting channels

This paper presents a generalized non-dimensional theoretical formulation with boundary conditions to analyze the EHD flow within the conducting and non-conducting channels. The substantial effect of normal and tangential components of electric field on fluid flow within the channel is presented through simulation results based on the non-dimensional parameters of strength, penetration, and repulsion of electric forces. The simulation results reveal that the normal component of induced electric field transits the flow regime within surfaces of a channel. The tangential component of applied electric field increases the thickness of viscous boundary layer, leading to skewed velocity profiles.

REMARKS ON SUBMANIFOLDS AS ALMOST eta-RICCI-BOURGUIGNON SOLITONS

We give some characterizations for submanifolds admitting almost $\eta$-Ricci-Bourguignon solitons whose potential vector field is the tangential component of a concurrent vector field on the ambient manifold. We describe the particular cases of umbilical submanifolds and of hypersurfaces in a space with constant curvature.

Computationally Efficient Analytical Model of Interior Permanent Magnet Machines Considering Stator Slotting Effects

Subdomain modeling is among the most reliable and accurate analytical tools for designing and analyzing permanent magnet machines. However, the application of the two-dimensional (2-D) subdomain model is mainly limited to permanent magnet machines with homogeneous rotor structures (with uniform permeability), such as surface-mounted or surface-inset permanent magnet machines. Solving Maxwell's equations and applying 2-D boundary conditions on structures with permanent magnets embedded in the rotor core, such as interior permanent magnet machines, are quite complex. Given the importance of enabling the tangential field component to capture accurate results, a 2-D hybrid analytical solution is proposed and applied to a multilayer interior permanent magnet machine. For this purpose, the radial components of the permanent magnet flux and the armature flux are first calculated using the magnetic circuit and the magnetic islands methods, respectively. Next, their respective tangential flux components are computed by solving Poisson's equation and applying a 1-D boundary condition along the tangential direction. Meanwhile, the stator slotting effect is included via the theory of virtual surface current. Finally, the steady-state performance metrics of the motor are calculated and verified via finite-element and experimental measurement.

Nanoscale Optical Trapping by Means of Dielectric Bowtie

Plasmonic and dielectric tweezers represent a common paradigm for an innovative and efficient optical trapping at the micro/nanoscale. Plasmonic configurations provide subwavelength mode confinement, resulting in very high optical forces, at the expense of a higher thermal effect, that could undermine the biological sample under test. On the contrary, dielectric configurations show limited optical forces values but overcome the thermal challenge. Achieving efficient optical trapping without affecting the sample temperature is still demanding. Here, we propose the design of a silicon (Si)-based dielectric nanobowtie dimer, made by two tip-to-tip triangle semiconductor elements. The combination of the conservation of the normal component of the electric displacement and the tangential component of the electric field, with a consequent large energy field confinement in the trapping site, ensures optical forces of about 27 fN with a power of 6 mW/µm2. The trapping of a virus with a diameter of 100 nm is demonstrated with numerical simulations, calculating a stability S = 1, and a stiffness k = 0.33 fN/nm, within a footprint of 0.96 µm2, preserving the temperature of the sample (temperature variation of 0.3 K).