Field Boundary Conditions Research Articles

A reverse Faber-Krahn inequality for the magnetic Laplacian

We consider the first eigenvalue of the magnetic Laplacian in a bounded and simply connected planar domain, with uniform magnetic field and Neumann boundary conditions. We investigate the reverse Faber-Krahn inequality conjectured by S. Fournais and B. Helffer, stating that this eigenvalue is maximized by the disk for a given area. Using the method of level lines, we prove the conjecture for small enough values of the magnetic field (those for which the corresponding eigenfunction in the disk is radial).

Almost classical de Sitter?

The classical-dS scenario in the type II string theories proposes to search for dS vacua of orientifold flux compactifications in a regime where string corrections to the compactified effective field theory are negligible. We study a minimal extension of this scenario in which the leading string corrections to the O-plane/D-brane actions at the 4-derivative order are included but higher orders as well as string corrections in the bulk are self-consistently neglected. Our proposal is motivated by a recent debate about dS solutions with O8-planes which circumvent a classical no-go theorem due to unusual sources leading to so-called permissive boundary conditions for the 10D supergravity fields. We argue that such sources do not arise in classical supergravity but ask whether including the 4-derivative corrections leads to sources that have a similar effect. However, we find that the 4-derivative corrections do not allow meta-stable dS in a class of models with O8-planes and/or D8-branes we consider. We also study related models which in addition contain O6-planes/D6-branes and find that again no meta-stable dS is allowed, both classically and including the 4-derivative corrections. While some of the arguments in this work require the backreaction of the O-plane/D-brane sources to be small, others are valid including the full backreaction.

Implementation of the non-reflection boundary for the seismic response analysis in the framework of non-local general particle dynamics

A thorough understanding of the seismic response of geotechnical structures has always been an aspiration for all engineers. Recently, the non-local general particle dynamics (NLGPD), which considers the variation of material density, has exhibited excellent promise in modelling extremely large deformation and dynamic problems. To extend the capacity of NLGPD to carry out seismic response analysis, four non-reflection boundaries are newly added in the framework of NLGPD in this paper. The viscous boundary allows wave energy to be absorbed by dashpot, in which a stress input method is proposed to input the seismic motion. The viscous-spring boundary can capture the elasticity recovery ability of the far-field medium. The free-field boundary achieves the free-field motion at lateral boundaries in the process of absorbing wave, and the corresponding relation between the points of the main model and the free-field column is determined. The static-dynamic unified boundary is introduced to model the transformation process from fixed boundary conditions in a static state to free field boundary conditions in dynamic analysis. Several representative numerical examples are solved to validate the feasibility of the proposed method. The numerical results show that the NLGPD method provides robustness and broad applicability for the seismic response analysis.

Zero dissipation limit of the anisotropic Boussinesq equations with Navier-slip and Neumann boundary conditions

In this paper, we study the vanishing dissipation limit of the 2D anisotropic Boussinesq equations with the Navier-slip boundary condition for velocity field and the fixed flux boundary condition for temperature in the upper half plane. By constructing boundary layer correctors to compensate for the discrepancies between dissipative equations and non-dissipative equations at the boundary, we prove that the solutions of the anisotropic Boussinesq equations converge to the solutions of the non-dissipative Boussinesq equations in L2-norm. Particularly, we find that the anisotropic dissipation coefficients only affect the rate of convergence, which is different from the phenomenon of the Dirichlet problem of the anisotropic Boussinesq equations in Wang & Xu (2021).

Modeling of fluid‐rigid body interaction in an electrically conducting fluid

AbstractWe derive a mathematical model for the motion of several insulating rigid bodies through an electrically conducting fluid. Starting from a universal model describing this phenomenon in generality, we elaborate (simplifying) physical assumptions under which a mathematical analysis of the model becomes feasible. Our main focus lies on the derivation of the boundary and interface conditions for the electromagnetic fields as well as the derivation of the magnetohydrodynamic approximation carried out via a nondimensionalization of the system.

Molecular dynamics calculations on the Glass temperature and crystallization process of AgAu alloy

In this paper, the molecular dynamics (MD) model is used to study the glass temperature and crystallization process of AgAu alloy under the influence of several factors such as heating rate, atomic number, temperature, annealing time on structural shape, number of structural units, phase transition, and crystallization process. The results show that using the Sutton-Chen (SC) embedded interaction force field and periodic boundary conditions achieved results that are completely consistent with previous results. When increasing the number of atoms and annealing time, the crystallization process increases, and when increasing the heating rate and temperature, the crystallization process decreases. The result of the phase transition is shown when a decrease in temperature leads to increased crystallization and the material changes from a liquid state to a crystalline or amorphous state. The crystallization process is expressed through the number of structural units face-centered cubic (FCC), hexagonal close-packed (HCP), body-centered cubic (BCC), amorphous (Amor), surface shape, radial distribution function (RDF), size (l) and total energy of the system (Etot). When changing the factors that lead to the height of the radial distribution function of the Ag-Au link changing greatly, the length of the Ag-Au link has a very small change in value and is almost constant with rAg-Au = 2.78 Å, when increasing the annealing time, the link length increases to 2.88 Å, and when increasing the heating rate, the link length decreases to 2.68 Å. In addition, successfully determined the glass temperature with AgAu alloy with a 50% Au doping concentration of 535 K. The results obtained with AgAu alloy can be used as a basis for future experimental studies to research and manufacture biosensors for applications in the fields of science, engineering, biology, and medicine.

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.

Flux and symmetry effects on quantum tunneling

Motivated by the analysis of the tunneling effect for the magnetic Laplacian, we introduce an abstract framework for the spectral reduction of a self-adjoint operator to a hermitian matrix. We illustrate this framework by three applications, firstly the electro-magnetic Laplacian with constant magnetic field and three equidistant potential wells, secondly a pure constant magnetic field and Neumann boundary condition in a smoothed triangle, and thirdly a magnetic step where the discontinuity line is a smoothed triangle. Flux effects are visible in the three aforementioned settings through the occurrence of eigenvalue crossings. Moreover, in the electro-magnetic Laplacian setting with double well radial potential, we rule out an artificial condition on the distance of the wells and extend the range of validity for the tunneling approximation recently established in Fefferman et al. (SIAM J Math Anal 54: 1105–1130, 2022), Helffer & Kachmar (Pure Appl Anal, 2024), thereby settling the problem of electro-magnetic tunneling under constant magnetic field and a sum of translated radial electric potentials.

Experimental investigation of air step cooling by the combination of spray and chord grid for mine cooling

To address the issues of heat and humidity hazards, as well as insufficient air volume in deep mining operations, a novel cooling method combining spray and chord grid is proposed. To investigate the cooling dynamics, an experimental platform integrating both spray and chord grid components is independently developed. Field boundary conditions are simulated to conduct orthogonal experimental research. Under the experimental parameters of an inlet air temperature of 32 °C, relative humidity of 88 %, and initial spray water temperature of 26 °C, the effects of water-air ratio, nozzle distance, and other parameters on inlet and outlet temperature, as well as moisture content, are quantified. These influencing factors are analyzed through range analysis. Results demonstrate that the water-air ratio has a greater impact on cooling compared to the nozzle distance. Notably, when the water-air ratio and nozzle distance reach critical values of 0.6 and 70 cm respectively, the cooling rate begins to plateau. Furthermore, comparative analysis of the cooling and dehumidification effects of single spray versus spray + chord grid reveals that the cooling capacity of single spray systems can be surpassed by incorporating a chord grid. Specifically, the combination of spray + chord grid achieves superior cooling effects with lower water consumption.

Casimir Energy in (2 + 1)-Dimensional Field Theories

We explore the dependence of vacuum energy on the boundary conditions for massive scalar fields in (2 + 1)-dimensional spacetimes. We consider the simplest geometrical setup given by a two-dimensional space bounded by two homogeneous parallel wires in order to compare it with the non-perturbative behaviour of the Casimir energy for non-Abelian gauge theories in (2 + 1) dimensions. Our results show the existence of two types of boundary conditions which give rise to two different asymptotic exponential decay regimes of the Casimir energy at large distances. The two families are distinguished by the feature that the boundary conditions involve or not interrelations between the behaviour of the fields at the two boundaries. Non-perturbative numerical simulations and analytical arguments show such an exponential decay for Dirichlet boundary conditions of SU(2) gauge theories. The verification that this behaviour is modified for other types of boundary conditions requires further numerical work. Subdominant corrections in the low-temperature regime are very relevant for numerical simulations, and they are also analysed in this paper.

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.

Analytical analysis and heat transfer of CuO and MgO engine oil base nanofluid with the influence of dynamic viscosity, magnetic field, and convective boundary conditions

AbstractThis research work investigates the semi‐numerical analysis and heat transfer of MHD 2D, Copper Oxide, and Magnesium oxide engine oil base nanofluid with the consider effect of dynamic viscosity and convective boundary conditions (BCs). The convective BCs and the effect of dynamic viscosity on an extensible surface are considered by the flow system. We converted a set of PDEs into NODEs by applying the appropriate transformations. Using the HAM, we solve this dimensionless coupled equation one for temperature and other for velocity. The impact of various parameters for both temperature and velocity are demonstrated, such as the slip parameter, magnetic parameter (MP), Eckert number (EN), PN, and dynamic viscosity. In response to changes in developing factors, the flow features, such as temperature profiles (TPs) and velocity profiles (VPs), are analyzed and simulated using a physical description. The results of this study add to our knowledge of how engine oil‐based nanofluids promote heat transmission and offer practical advice for thermal management and engineering applications.

Metastability for the degenerate Potts Model with positive external magnetic field under Glauber dynamics

We consider the ferromagnetic q-state Potts model on a finite grid graph with non-zero external field and periodic boundary conditions. The system evolves according to Glauber-type dynamics described by the Metropolis algorithm, and we focus on the low temperature asymptotic regime. We analyze the case of positive external magnetic field associated to one spin value. In this energy landscape there is one stable configuration and q−1 metastable states. We study the asymptotic behavior of the first hitting time from any metastable state to the stable configuration as β→∞ in probability, in expectation, and in distribution. We also identify the exponent of the mixing time and find an upper and a lower bound for the spectral gap. Finally, we identify all the minimal gates and the tube of typical trajectories for the transition from any metastable state to the unique stable configuration by giving a geometric characterization.

The wall effect in a plane counterflow channel

Abstract In this paper, we study the influence of the boundary conditions of the velocity fields in superfluid helium counterflow experiments. To make progress, we perform numerical simulations where we allow a slip velocity of the viscous component at the walls, and observe how this impacts on velocity fields and density profiles of distribution of quantized vortices. We conclude that the presence of a slip velocity at the walls generates a more homogeneous vortex distribution throughout the channel.

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.

Influence of boundary conditions on the behavior of laminated glass curved beam with delamination effect: An experimental and numerical investigation

The delamination phenomena of laminated glass structures are issues that are not perfectly understood and remain problematic to predict due to the nonlinearity of the geometric response. A research study is undertaken to investigate the behavior of laminated glass curved beams with initial delamination exposed to different boundary conditions. A mathematical model which contains nonlinear field equations and boundary conditions is developed. An iterative procedure for the solution of field equations is implemented. In addition, experiments are conducted and finite element model is developed to determine the effectiveness of model. The results are in good agreement. These results contribute to a better understanding of the complex response phenomena exhibited by curved laminated glass beams subjected to initial delaminations. Research findings allow a better insight in the behavior of the delamination in laminated glass, including the deflections and stresses. Based on the developed model it is possible to determine the effects of position and size of delaminations on the behavior of laminated glass curved beams under different boundary conditions.

Phase matching of electromagnetic wave on moving interface

Due to the boundary conditions of electromagnetic fields and phase matching of electro magnetic waves on interface being the basis to drive the Snell’s laws and Fresnel’s laws, they are also crucial for the analysis of electromagnetic wave propagation in a moving medium. There are mainly two methods to derive the boundary conditions of electromagnetic fields on moving interface. One of them is to use the kinematic integral form, yet this method is based on the classical time-space, and the other is based on the relativistic transformation, the boundary conditions are derived from the scaling effect with geometric method, or from the principle of relativity directly. However, the first one has a form the same as the form obtained by using the kinematic integral form, while the second one obtains a different form. At the same time, the phase matching of electromagnetic wave on moving interface is only discussed by Galileo transformation, however this is unreasonable, because of the relativistic effect cannot be ignored here. Therefore, it is necessary to reexamine the boundary conditions of electromagnetic fields and phase matching of electromagnetic wave on moving interface. Herein, firstly, the relativistic transformation formula of the unit normal vector of moving surface is derived from the surface equation and principle of relativity. Secondly, the boundary conditions of electromagnetic fields on moving interface are given based on the relativistic transformation formula and the non-relativistic transformation formula of the unit normal vector and electromagnetic fields, which show that the boundary conditions of electromagnetic fields on moving interface under the relativistic case and the non-relativistic case have the same form. This is not accidental but definite, because the change of flux of electromagnetic fields, like the change of magnetic flux, from the induction of electromagnetic filed is the same as that from the variation of surface element. Thirdly, the phase matching of electromagnetic wave on moving interface is given based on the relativistic transformation formula of the unit normal vector and the phase matching of electromagnetic wave on resting interface. In the problem of light incident on a homogeneous medium moving at a constant velocity in vacuum or air, using the phase matching of electromagnetic wave on moving interface, the same results can be easily obtained through other methods. The discussion in this study belongs to classical electrodynamics with no quantum effects considered, but the results will provide some conveniences for theoretically analyzing electromagnetic communication, remote sensing and telemetering.

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.

3d exceptional gauge theories and boundary confinement

We find boundary confining dualities of 3d N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 supersymmetric gauge theories with exceptional gauge groups. The half-indices which enumerate the boundary BPS local operators in the presence of Neumann and Dirichlet boundary conditions for gauge fields are identified with the Askey-Wilson type q-beta integrals and Macdonald type sums respectively. New conjectural identities of E6 and E7 integrals and sums are derived from the boundary confining dualities. We also consider theories with a vector multiplet and adjoint chiral, which correspond to an N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 vector multiplet, with appropriate boundary conditions. We argue for the boundary confinement of the N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 vector multiplet and comment on such theories also with classical gauge groups.