Quasinormal modes and late time tails of perturbation fields on a Schwarzschild-like black hole with a global monopole in the Einstein-bumblebee theory

In this paper we complete a systematic study on quasinormal modes(QNMs) and late time tails for scalar,Dirac and Maxwell fields on a spherically symmetric Schwarzschild-like black hole with a global monopole in the Einstein-bumblebee theory.To look for QNMs,we solve the equations of motion for all perturbation fields considered herein numerically,by employing both the matrix and the WKB methods,and find good agreements for numeric data obtained by these two techniques in the regime when both are valid.The impact of the bumblebee parameter c,the monopole parameter η^(2),and the multipole number l on the fundamental quasinormal frequency are analyzed in detail.Our results are shown in terms of the quasinormal frequency measured by √1+c M ,where M is a black hole mass parameter.We observe,by increasing the parameter c(η^(2)) with fixed first few l,that the real part of QNMs increases for all spin fields;while the magnitude of the imaginary part decreases for scalar and Dirac fields but increases for Maxwell fields.By increasing the multipole numberlwith fixed other parameters,we disclose that the real part of QNMs for all spin fields increases while the magnitude of the imaginary part decreases for scalar and Dirac fields but increases for Maxwell fields.In the eikonal limit(l>>n),QNMs for all spin fields coincide with each other and the real part scale linearly with l.In particular,the asymptotic QNMs approach the corresponding results given by the first order WKB formula,and only the real part of QNMs is dependent on the bumblebee and monopole parameters.In addition,it is shown that the late time behavior is determined not only by the multipole number but also by the bumblebee and monopole parameters,and is distinct for bosonic and fermonic fields.Moreover,the presence of the bumblebee(monopole) field makes the spin fields decay faster.Our results indicate,both in the context of QNMs and late time tails,that the bumblebee field and the monopole field play the same role in determining the dynamic evolution of perturbation fields.

Electromagnetoelastic behaviors of functionally graded piezoelectric solid cylinder and sphere

Analytical studies on electromagnetoelastic behaviors are presented for the functionally graded piezoelectric material （FGPM） solid cylinder and sphere placed in a uniform magnetic field and subjected to the external pressure and electric loading. When the mechanical, electric and magnetic properties of the material obey an identical power law in the radial direction, the exact displacements, stresses, electric potentials and perturbations of magnetic field vector in the FGPM solid cylinder and sphere are obtained by using the infinitesimal theory of electromagnetoelasticity. Numerical examples also show the significant influence of material inhomogeneity. It is interesting to note that selecting a specific value of inhomogeneity parameter β can optimize the electromagnetoelastic responses, which will be of particular importance in modern engineering designs.

Perturbed magnetic field of an infinite plate with a centered crack

Deforming a cracked magnetoelastic body in a magnetic field induces a perturbed magnetic field around the crack. The quantitative relationship between this perturbed field and the stress around the crack is crucial in developing a new generation of magnetism-based nondestructive testing technologies. In this paper, an analytical expression of the perturbed magnetic field induced by structural deforma- tion of an infinite ferromagnetic elastic plate containing a centered crack in a weak external magnetic field is obtained by using the linearized magnetoelastic theory and Fourier transform methods. The main finding is that the perturbed magnetic field intensity is proportional to the applied tensile stress, and is dominated by the displacement gradient on the boundary of the magnetoelastic solid. The tangential component of the perturbed magnetic-field intensity near the crack exhibits an antisymmetric distribution along the crack that reverses its direction sharply across its two faces, while the normal component shows a symmetric distribution along the crack with singular points at the crack tips.

Revisiting the elastic solution for an inner-pressured functionally graded thick-walled tube within a uniform magnetic field

In this paper, the mechanical responses of a thick-walled functionally graded hollow cylinder subject to a uniform magnetic field and inner-pressurized loads are studied. Rather than directly assume the material constants as some specific function forms displayed in pre-studies, we firstly give the volume fractions of different constituents of the functionally graded material(FGM) cylinder and then determine the expressions of the material constants. With the use of the Voigt method, the corresponding analytical solutions of displacements in the radial direction, the strain and stress components, and the perturbation magnetic field vector are derived. In the numerical part, the effects of the volume fraction on the displacement, strain and stress components, and the magnetic perturbation field vector are investigated. Moreover, by some appropriate choices of the material constants, we find that the obtained results in this paper can reduce to some special cases given in the previous studies.

Thermomagnetic viscoelastic responses in a functionally graded hollow structure

This paper presents an analytical solution for the interaction of electric potentials, electric displacements, elastic deformations, and thermoelasticity, and describes electromagnetoelastic responses and perturbation of the magnetic field vector in hollow structures （cylinder or sphere）, subjected to mechanical load and electric potential. The material properties, thermal expansion coefficient and magnetic permeability of the structure are assumed to be graded in the radial direction by a power law distribution. In the present model we consider the solution for the case of a hollow structure made of viscoelastic isotropic material, reinforced by elastic isotropic fibers, this material is considered as structurally anisotropic material. The exact solutions for stresses and perturbations of the magnetic field vector in FGM hollow structures are determined using the infinitesimal theory of magnetothermoelasticity, and then the hollow structure model with viscoelastic material is solved using the correspondence principle and Illyushin＇s approximation method. Finally, numerical results are carried out and discussed.

Study of Heat Transport Across a Quasi-Stochastic Magnetic Field in Magnetic Confined Plasma Physics

Heat diffusion across a non-local quasi-stochastic magnetic field in tokamak plasma is numerically studied. The perturbed magnetic field is found to be a key factor in influencing effective radial heat conductivity whether the magnetic field is stochastic or not. Being different from previous work, a non-local perturbed magnetic field is used. Analytical results and numerical simulation results are compared between the conditions with a full and a quasi-perturbed stochastic field. The analytical results are found to be still consistent with numerical simulation results when the perturbed field is quasi-stochastic.

Matrix method for the solution of RF field perturbations due to local frequency shifts

To tune the accelerating field to the design value in a periodical radio frequency accelerating structure, Slater＇s perturbation theorem is commonly used. This theorem solves a second-order differential equation to obtain the electrical field variation due to a local frequency shift. The solution becomes very difficult for a complex distribution of the local frequency shifts. Noticing the similarity between the field perturbation equation and the equation describing the transverse motion of a particle in a quadrupole channel, we propose in this paper a new method in which the transfer matrix method is applied to the field calculation instead of directly solving the differential equation. The advantage of the matrix method is illustrated in examples.

Application of the transfer matrix for tuning the CSNS-DTL

In the construction of a drift tube LINAC （DTL）, many factors caused during the fabrication and assembly of the structure cells cause the electric field distribution not as the same as the design curve. To solve this problem, the traditional way is to solve the equation of Slater＇s perturbation theorem to obtain the electrical field variation due to local frequency shift. However, that is very difficult under complicated conditions. Since the field perturbation equation is similar to the particle＇s transverse motion equation, which can be simply solved by using the transfer matrix method, we thus propose to apply a transfer matrix method in tuning the DTL. We demonstrate the availability and advantages of this method with 3D microwave code simulation and the LabVIEW calculation program. After two iterations, the initial error of the electric field of 19.5% has been improved greatly down to 1.3%- -4.5%. This indicates that the transfer matrix method is very useful and convenient for the simplification of tuning procedures.