Magnetic Boundary Conditions Research Articles

Proton radiography inversions with source extraction and comparison to mesh methods.

Proton radiography is a central diagnostic technique for measuring electromagnetic (EM) fields in high-energy-density, laser-produced plasmas. In this technique, protons traverse the plasma where they accumulate small EM deflections which lead to variations in the proton fluence pattern on a detector. Path-integrated EM fields can then be extracted from the fluence image through an inversion process. In this work, experiments of laser-driven foils were conducted on the OMEGA laser and magnetic field reconstructions were performed using both "fluence-based" techniques and high-fidelity "mesh-based" methods. We implement nonzero boundary conditions into the inversion and show their importance by comparing against mesh measurements. Good agreement between the methods is found only when nonzero boundary conditions are used. We also introduce an approach to determine the unperturbed proton source profile, which is a required input in fluence reconstruction algorithms. In this approach, a fluence inversion is embedded inside of a mesh region, which provides overconstrained magnetic boundary conditions. A source profile is then iteratively optimized to satisfy the boundary information. This method substantially enhances the accuracy in recovering EM fields. Lastly, we propose a scheme to quantify uncertainty in the final inversion that is introduced through errors in the source retrieval.

Evaluating the Electromagnetic Field Problem Generated by the Power Transmission Line Using High Order Compact Method

This paper compares a finite difference method-based computational scheme for evaluating electromagnetic field problems in power transmission lines in cases of on surface and in Ground. The scheme uses Maxwell's partial differential equations to represent electric and magnetic field components and approximate boundary conditions. The High Order Compact Method (HOC) is applied to estimate the electric field (Ez )in ground and compares it with the standard central difference scheme. The HOC produces more accurate results than the traditional central approximation at 99.7% for the electric field Ez. It also calculates both of Electric and magnetic intensity to evaluate the effect of Electric and magnetic intensities in ground and on surface respect to distance.

Magnetic field analysis and modeling of gradient coils based on ferromagnetic coupling inside magnetically shielded cylinder

To accurately analyze the magnetic field of gradient coils inside a magnetically shielded cylinder (MSC) and enhance the precision of remanence compensation, analytical models for calculating the magnetic field of the gradient coils are proposed. First, the coupling between the high-permeability MSC and the coils is accurately analyzed based on Green’ s function method, magnetic field boundary conditions and image method. Secondly, the current density of four commonly used gradient coils is analyzed, and analytical models for the magnetic fields of these four types of gradient coils are established. Finally, the validity of the analytical models is proved through finite element simulations and experimental tests. The experimental results indicate that within the range of x,z∈−80,80mm (± 0.5R), the analytical values have good consistency with experimental values, and the maximum relative error between the two is only 0.91%. The analytical models will be beneficial to the research on the coil optimization design inside the MSC.

Inequalities à la Pólya for the Aharonov–Bohm eigenvalues of the disk

We prove an analogue of Pólya’s conjecture for the eigenvalues of the magnetic Schrödinger operator with Aharonov–Bohm potential on the disk for Dirichlet and magnetic Neumann boundary conditions. This answers a question posed by R. L. Frank and A. M. Hansson.

Boundary condition effects on runaway electron mitigation coil modeling for the SPARC and DIII-D tokamaks

Extended-MHD modeling of planned Runaway Electron Mitigation Coils (REMC) for SPARC and DIII-D is performed with the NIMROD code. A coil has been designed for each machine, with the two differing in shape and location, but both having n = 1 symmetry (with n the toroidal mode number). Compared to previous modeling efforts, three improvements are made to the simulations boundary conditions. First a resistive wall model is used in place of an ideal wall. Second, the ThinCurr code is used to compute the time-dependent 3D fields used as magnetic boundary conditions for the simulations. Third, the simulation boundary is moved from the first-wall location to the Vacuum Vessel (VV), which extends the boundary past the location of the internal REMC. To remove the 3D coil from the simulation domain, an equivalent set of 3D fields is calculated at the VV boundary that produce approximately the same field distribution at the last closed flux surface assuming vacuum between the two. Each of these three boundary condition improvements leads to an improvement in the predicted performance of the REMC for both machines. The resistive wall alone primarily effects the resonance of the coil with the plasma after the TQ, affecting the q-profile evolution in the SPARC modeling, and allowing the applied spectrum to be modified in response to the plasma in the DIII-D modeling. The movement of the simulation boundary has the most significant effect on the RE confinement overall, including in the early stages, particularly for a DIII-D inner wall limited equilibrium, where the RE loss fraction increases from 90% to > 99%, with SPARC RE losses also occurring much earlier when the boundary is placed at the VV.

A numerical study on MHD Maxwell fluid with nanoparticles over a stretching surface: Impacts of thermal radiation, convective boundary condition and induced magnetic field

The current study investigates the influence of induced magnetic field and convective boundary condition on the behavior of a magnetohydrodynamic (MHD) Maxwell fluid including nanoparticles flowing through a stretching sheet. Furthermore, the analysis considers the existence of radiation. Numerical solutions to the basic governing equations are achieved using the Runge–Kutta–Fehlberg technique. The impact of various physical parameters on concentration, velocity, and temperature profiles is deployed through graphs. The primary conclusions of this study are that increasing the Magnetic parameter decreases the Induced Magnetic field while increasing the Deborah parameter improves the velocity profile. Temperature distribution is growing due to increased estimates of the Radiation, Biot number, and Deborah number values. When the Lewis number values are raised, the concentration profiles get smaller but there is an opposite scenario deployed as the Thermophoresis parameter upsurges. The findings of this study are consistent with those that have been previously reported. The phenomenon of flow induced by a stretched surface finds several applications in various industrial and technological domains, including copper wire production, polymer extrusion, article manufacturing, and fiber synthesis. Induced magnetic fields are extremely prominent in many areas of science and technology, including electromagnetism, magnetic materials, and magnetic resonance imaging (MRI).

Numerical solutions for magneto-convective boundary layer slip flow from a nonlinear stretching sheet with wall transpiration and thermal radiation effects

A mathematical model is presented for magnetohydrodynamic viscous incompressible flow of an electrically conducting Newtonian polymeric fluid from a moving permeable horizontal stretching sheet with variable magnetic field, momentum and thermal slip boundary conditions. The emerging nonlinear ordinary differential boundary value problem is solved numerically by the Runge-Kutta-Fehlberg fourth-fifth order numerical method in Maple symbolic software. The effects of the governing parameters on the dimensionless stream function, dimensionless flow velocity and the dimensionless temperature have been investigated, displayed graphically and discussed. It is found that greater momentum slip and magnetic field parameters reduce the dimensionless velocity. It is further observed that higher values of Prandtl number, thermal slip, and conductionradiation parameter (weaker radiation contribution) reduce the dimensionless temperature whilst stronger magnetic field increases the temperature due to the supplementary work expended in dragging the polymer against the action of the magnetic field which is dissipated as heat. Comparisons of numerical results with previous published results show an excellent agreement. The study finds applications in electro-conductive polymer (ECP) processing systems.

A numerical framework of magneto Williamson hybrid nanofluid over porous sheet; a classical keller box analysis

The current study intends to talk about the unsteady Williamson hybrid nanofluid flow with heat transport across a stretching surface comprising the magnetic hydrodynamic, thermal radiative, suction/injection, and convective boundary condition effects respectively. The study focused on the hybrid Williamson nanofluid, comprising of an EG ethylene glycol (C2H6O2) and two types of nano-solid particles, c zinc oxide and molybdenum disulphide ZnO-MOS2. To accomplish this goal, the modelled expressions are transmitted into dimensionless ODE by making use of several highly established transformations. The aim of the numerical result of the current exploration is studied through Keller Box Analysis (KBA). Tabular data and statistical bar plots are used to compare this strategy. The impact of physical variables such as Magnetic field parameter γ, Williamson fluid variable We, Porous media β, Thermal radiation Rd, Biot number Bi and Prandtl number Pr are analyzed through plots and tables. An augmentation in the strength of the magnetic field and Williamson fluid parameter results in a reduction in velocity. However, a temperature rise is observed for higher values of the Williamson fluid parameter and magnetic parameters. The surface friction drag is diminished by the Forchheimer and Weissenberg values. The rate of mass transfer is strongly positively correlated with both the Schmidt number and chemical reaction. The present study has a remarkable agreement with the results that were previously published, which confirms the application and validation of the Keller-Box scheme.

Peristaltic transport of nanofluid with temperature dependent thermal conductivity: A numerical study

Peristaltic flow of nanofluid with temperature-dependent thermal conductivity is investigated. Variation of effective thermal conductivity of nanofluids with temperature is addressed. Mathematical modeling of momentum and energy equation is considered in a symmetric channel. Viscous dissipation, Ohmic heating, and mixed convection are accounted. Applied magnetic field and convective boundary conditions are imposed. Dimensionless expressions are simplified under long wavelength approximation. The relevant problems are solved by numerical technique. Velocity, temperature, pressure, and heat transfer characteristics are studied graphically. Heat transfer rate rapidly increases by increasing the concentration of nanomaterial. Therefore, nanomaterial is used for the cooling process in engineering and biomedical devices.

Time-dependent Dynamics of the Corona

We present in this Letter the first global comparison between traditional line-tied steady-state magnetohydrodynamic models and a new, fully time-dependent thermodynamic magnetohydrodynamic simulation of the global corona. To approximate surface magnetic field distributions and magnitudes around solar minimum, we use the Lockheed Evolving Surface-Flux Assimilation Model to obtain input maps that incorporate flux emergence and surface flows over a full solar rotation, including differential rotation and meridional flows. Each time step evolves the previous state of the plasma with a new magnetic field input boundary condition, mimicking photospheric driving on the Sun. We find that this method produces a qualitatively different corona compared to steady-state models. The magnetic energy levels are higher in the time-dependent model, and coronal holes evolve more along the following edge than they do in steady-state models. Coronal changes, as illustrated with forward-modeled emission maps, evolve on longer timescales with time-dependent driving. We discuss implications for active and quiet Sun scenarios, solar wind formation, and widely used steady-state assumptions like potential field source surface calculations.

Dynamic Behavior Modeling of Natural-Rubber/Polybutadiene-Rubber-Based Hybrid Magnetorheological Elastomer Sandwich Composite Structures.

This study investigates the dynamic characteristics of natural rubber (NR)/polybutadiene rubber (PBR)-based hybrid magnetorheological elastomer (MRE) sandwich composite beams through numerical simulations and finite element analysis, employing Reddy's third-order shear deformation theory. Four distinct hybrid MRE sandwich configurations were examined. The validity of finite element simulations was confirmed by comparing them with results from magnetorheological (MR)-fluid-based composites. Further, parametric analysis explored the influence of magnetic field intensity, boundary conditions, ply orientation, and core thickness on beam vibration responses. The results reveal a notable 10.4% enhancement in natural frequencies in SC4-based beams under a 600 mT magnetic field with clamped-free boundary conditions, attributed to the increased PBR content in MR elastomer cores. However, higher magnetic field intensities result in slight frequency decrements due to filler particle agglomeration. Additionally, augmenting magnetic field intensity and magnetorheological content under clamped-free conditions improves the loss factor by from 66% to 136%, presenting promising prospects for advanced applications. This research contributes to a comprehensive understanding of dynamic behavior and performance enhancement in hybrid MRE sandwich composites, with significant implications for engineering applications. Furthermore, this investigation provides valuable insights into the intricate interplay between magnetic field effects, composite architecture, and vibration response.

A comparative assessment of mono and hybrid magneto nanofluid flow over a stretching cylinder in a permeable medium with generalized Fourier’s law

This study investigates the flow and heat transfer of mono and hybrid nanofluids owing to a stretching cylinder in a porous medium under the influence of a magnetic field and convective boundary condition. The hybrid nanofluid is made up of copper (Cu) and silver (Ag) nanoparticles dispersed in a water-ethylene glycol mixture at a mass ratio of 50:50. The binary mixture of water and ethylene glycol is intermixed with spherical-shaped nanoparticles (copper) to create a mono nanofluid. The study considers the effects of generalized Fourier’s law and heat generation/absorption. The novelty of the study lies in considering the comparison of hybrid and mono nanofluid flows heat transfer efficiency with assumed effects and convective condition at the boundary of the cylinder. A system of ordinary differential equations (ODEs) controlling the flow and heat transport are derived using similarity transformations and are solved numerically using the bvp4c program of MATLAB software. The work explores the ways in which different parameters, such as the shape of the nanoparticles and their volume percentage, affect the pertinent profiles and are depicted in the form of graphical illustrations and numerically tabulated values. The results demonstrate that, in comparison to mono nanofluids, hybrid nanofluids including spherical and blade nanoparticles have a higher heat transfer rate and reduced surface drag when the particle volume fraction is increased in a water-ethylene glycol combination. Furthermore, there is a 0.83% increase in the heat transfer rate for hybrid nanofluids in comparison to mono nanofluids. This is because compared to mono nanofluids, hybrid nanofluids have lower viscosity and better heat conductivity. The results obtained in this study are vetted by making a comparison with published works and an excellent agreement between the values is seen. The study may find use in solar thermal systems, electronic cooling, heat exchangers, and other areas.

Physical insights in thermo-elastic damping and critical magnetic field of an embedded micro/nanobeam resonator

This article investigates the behavior of thermoelastic damping in a micro/nano beam subjected to an external magnetic field and an elastic matrix via small-scale theory. The material properties of the beam, such as Young’s modulus, thermal conductivity, specific heat capacity, and coefficient of thermal expansion, are considered to analyze the physical aspects of thermoelastic damping. Further, the critical magnetic field strength of the nanobeam, which affects magnetic properties, is studied in relation to temperature, magnetic material properties, modenumber, and boundary conditions, leading to important findings for magnetomechanical systems and materials design.

The harmonic resonance and singularity analysis of bifurcation for the magnetized elastic plate with action of time-varying magnetic potential

This paper deals with the superharmonic resonance of a ferromagnetic thin rectangular plate in the air-gap magnetic field excited by armature magnetic potential. Electromagnetic forces applied on the plate by the air-gap magnetic field cause the plate to transversal vibrate, which affects the air-gap magnetic field in turn, resulting the vibration and magnetic field coupling. According to the basic electromagnetic field theory and considering the magnetoelastic coupling effect, the air-gap magnetic field intensity is obtained by solving the Laplace's equation satisfied the air-gap magnetic boundary conditions. The electromagnetic force model of soft ferromagnetic plates is determined based on theories of electromagnetic and elasticity. According to the large deflection theory of plates, basic energy relationships and variational equations of the elastic plate are given. Eventually, the nonlinear magnetoelastic vibration equation of ferromagnetic thin plates is derived using Hamilton's principle and Galerkin method. The multi-scale method is used to solve the superharmonic resonance to obtain the amplitude-frequency response equation and the stability discriminant of solutions. The topological analysis of amplitude-frequency equation is carried out using singularity theory, and the bifurcation characteristics of systems on physical parameter planes in different regions are obtained according to the transition set. The correctness of analytical solutions is verified by comparison with numerical solutions. Through numerical calculations, curves of the static deflection and equivalent magnetic force of plate with parameters are given, and the amplitude curves, dynamic phase plane trajectories and time history diagrams of system response with changes in electromagnetic and structural parameters are plotted. Results show that both the decrease of armature magnetic potential amplitude and the increases of plate thickness and initial air-gap thickness reduce the static deflection. The increase of armature magnetic potential amplitude increases the equivalent magnetic force. As the decrease of initial air-gap thickness and the increases of armature magnetic potential amplitude and excitation force amplitude, the amplitudes of the upper branch and lower branch curves representing stable solutions decrease and increase, respectively, and the single-value solution region increases.

Manipulation of acoustic wave scattering from cylindrical shells using a coating of FG magneto-electro-elastic composite materials: Active acoustic cloaking

Acoustically cloaking an object from view of a system that uses acoustic waves for detection is an attractive and practical capability. The aim of the current investigation is to hide a steel cylinder containing axial flow acoustically, which is achieved through the application of a coating of FG electro-magnetic material. This coating is employed to minimize the sound pressure that is scattered from the structure, and it comprises piezoelectric (BaTiO3) and magnetostrictive (CoFe2O4) make up the coating. Accordingly, the method presented is based on optimal control and incorporates an improved particle swarming optimization algorithm. The decision variables are the magnetic and electrical potentials on the inner and outer surfaces of the coating, whereas the cost function is the scattered acoustic pressure. In other words, what are the values of electrical and magnetic potentials on the inner and outer surfaces of the coating to minimize the scattered pressure? Subsequently, by defining the electrical and magnetic boundary conditions in a certain way, it is feasible to achieve the complete cancelation of scattered sound pressure. The governing equation of each layer is extracted using an orthotropic laminate composite model that is based on the 3-D theory of elasticity. A state-vector method is then applied to obtain the propagator matrix that links the state variables at each layer's surfaces. The results show that the proposed acoustic cloaking technique has an excellent capability for hiding the shell immersed in the fluid.

Geometric bounds for the magnetic Neumann eigenvalues in the plane

We consider the eigenvalues of the magnetic Laplacian on a bounded domain Ω of R2 with uniform magnetic field β>0 and magnetic Neumann boundary conditions. We find upper and lower bounds for the ground state energy λ1 and we provide semiclassical estimates in the spirit of Kröger for the first Riesz mean of the eigenvalues. We also discuss upper bounds for the first eigenvalue for non-constant magnetic fields β=β(x) on a simply connected domain in a Riemannian surface.In particular: we prove the upper bound λ1<β for a general plane domain for a constant magnetic field, and the upper bound λ1<maxx∈Ω‾⁡|β(x)| for a variable magnetic field when Ω is simply connected.For smooth domains, we prove a lower bound of λ1 depending only on the intensity of the magnetic field β and the rolling radius of the domain.The estimates on the Riesz mean imply an upper bound for the averages of the first k eigenvalues which is sharp when k→∞ and consists of the semiclassical limit 2πk|Ω| plus an oscillating term.We also construct several examples, showing the importance of the topology: in particular we show that an arbitrarily small tubular neighborhood of a generic simple closed curve has lowest eigenvalue bounded away from zero, contrary to the case of a simply connected domain of small area, for which λ1 is always small.

Quantum controllability on graph-like manifolds through magnetic potentials and boundary conditions

We investigate the controllability of an infinite-dimensional quantum system: a quantum particle confined on a Thick Quantum Graph, a generalisation of Quantum Graphs whose edges are allowed to be manifolds of arbitrary dimension with quasi-δ boundary conditions. This is a particular class of self-adjoint boundary conditions compatible with the graph structure. We prove that global approximate controllability can be achieved using two physically distinct protocols: either using the boundary conditions as controls, or using time-dependent magnetic fields. Both cases have time-dependent domains for the Hamiltonians.

Phase field model for brittle fracture in multiferroic materials

Multiferroic materials, which simultaneously possess piezomagnetic, piezoelectric, and electromagnetic coupling effects, have a wide range of applications in various fields. Multiferroic materials are generally brittle with low fracture toughness, and accurate prediction of the fracture behaviors of multiferroics is challenging. In this work, a phase field model for brittle fracture in multiferroic materials is developed with the help of the Hamilton principle. In light of the second law of thermodynamics, the constitutive equations are derived in the context of the phase field method. The present theoretical framework unifies two classical phase field models and four combinations of the electric and magnetic boundary conditions. The residual controlled staggered algorithm, which enjoys a higher accuracy and lower computational cost, is extended to the fracture problems in the context of magneto-electro-elasticity. Systematic numerical simulations are performed in both 2D and 3D cases. The influences of the external magnetic field, electric field, and electric and magnetic boundary conditions on fracture behaviors of multiferroic materials are studied in detail. The applied magnetic field may not only accelerate or delay the fracture, but also influence the crack path. The present work is beneficial to assess the safety of multiferroic-based devices in engineering applications.

Influence of magnetic boundary conditions on the quantitative modelling of magnetorheological elastomers

The complex magneto-mechanical coupling that governs the material response of magnetorheological elastomers (MREs) requires computational tools to assist the design process. Computational models are usually based on finite element frameworks that often simplify and idealise the magnetic source and the associated magnetic boundary conditions (BCs). However, these simplifications may lead to important disagreement between the actual material behaviour and the modelled one, even at the qualitative level. In this work, we provide a comprehensive study on the influence of magnetic BCs and demonstrate the importance of considering them in the overall material-structure modelling strategy. To this end, we implement a magneto-mechanical framework to model the response of soft- and hard-magnetic MREs under magnetic fields generated by an idealised far-field uniform magnetic source, a permanent magnet, a coil system, and an electromagnet with two iron poles. The results unveil remarkable heterogeneities in computed local magnetostriction and magnetic fields depending on the magnetic setup used. A detailed discussion based on material and structural contributions provides a robust, rigorous, and necessary modelling route for future works.

Algebra of hyperbolic band theory under magnetic field

We explore algebras associated with the hyperbolic band theory under a magnetic field for the first time. We define the magnetic Fuchsian group associated with a higher genus Riemann surface. By imposing the magnetic boundary conditions for the hyperbolic Bloch states, we construct the hyperbolic magnetic Bloch states and investigate their energy spectrum. We give a connection between such magnetic Bloch states and automorphic forms. Our theory is a general extension of the conventional algebra associated with the band theory defined on a Euclidean lattice/space into that of the band theory on a general hyperbolic lattice/Riemann surface.