Normal modes of a waveguide as eigenvectors of a self-adjoint operator pencil

A waveguide with a constant, simply connected section S is considered under the condition that the substance filling the waveguide is characterized by permittivity and permeability that vary smoothly over the section S, but are constant along the waveguide axis. Ideal conductivity conditions are assumed on the walls of the waveguide. On the basis of the previously found representation of the electromagnetic field in such a waveguide using 4 scalar functions, namely, two electric and two magnetic potentials, Maxwells equations are rewritten with respect to the potentials and longitudinal components of the field. It appears possible to exclude potentials from this system and arrive at a pair of integro-differential equations for longitudinal components alone that split into two uncoupled wave equations in the optically homogeneous case. In an optically inhomogeneous case, this approach reduces the problem of finding the normal modes of a waveguide to studying the spectrum of a quadratic self-adjoint operator pencil.

Análisis térmico de los elementos de sujeción del núcleo de un reactor trifásico

In this thesis work the temperature distribution in the frame bolts of a 5 MVA, 115 kV, 60 Hz, three-phase five-limbs shunt reactor is obtained utilizing the finite element method (FEM) and the commercial ANSYS Maxwell software. This because the reactor actually failed while it was running, the failure occurred progressively as the screw insulation was damaged and caused an unwanted temperature rise. A time-harmonic analysis is performed to compute the magnetic field distribution in the reactor and the power losses in the frame bolts. A three-dimensional (3-D) shunt reactor model is utilized, and Maxwell’s equations are solved utilizing scalar and vectorial magnetic potentials. The 3-D electromagnetic shunt reactor model is validated by comparing the value of inductance measured in the laboratory with the value of inductance computed in the 3-D FE simulation. In addition, the core losses computed in the FE simulation are compared with the core losses measured in the laboratory. This thesis work is important for transformer manufacturers which requires an adequate shunt reactor model to analyze it under different operation conditions and to optimize the actual design.

Tunable Bandgaps in Phononic Crystal Microbeams Based on Microstructure, Piezo and Temperature Effects

A new model of non-classical phononic crystal (PC) microbeam for the elastic wave bandgap generation is provided, incorporating microstructure, piezomagnetism, piezoelectricity and temperature effects. The wave equation of a general magneto–electro–elastic (MEE) phononic crystal microbeam is derived, which recovers piezoelectric- and piezomagnetic-based counterparts as special cases. The piezomagnetic and piezoelectric materials are periodically combined to construct the PC microbeam and corresponding bandgaps are obtained by using the plane wave expansion (PWE) method. The effects of the piezomagnetism, piezoelectricity, microstructure, geometrical parameters and applied multi-fields (e.g., external electric potential, external magnetic potential, temperature change) on the bandgaps are discussed. The numerical results reveal that the bandgap frequency is raised with the presence of piezo and microstructure effects. In addition, the geometry parameters play an important role on the bandgap. Furthermore, large bandgaps can be realized by adjusting the external electric and magnetic potentials at micron scale, and lower bandgap frequency can be realized through the temperature rise at all length scales.

Polynomial duality-symmetric lagrangians for free p-forms

We explore the properties of polynomial Lagrangians for chiral p-forms previously proposed by the last named author, and in particular, provide a self-contained treatment of the symmetries and equations of motion that shows a great economy and simplicity of this formalism. We further use analogous techniques to construct polynomial democratic Lagrangians for general p-forms where electric and magnetic potentials appear on equal footing as explicit dynamical variables. Due to our reliance on the differential form notation, the construction is compact and universally valid for forms of all ranks, in any number of dimensions.

Inequalities involving Aharonov–Bohm magnetic potentials in dimensions 2 and 3

This paper is devoted to a collection of results on nonlinear interpolation inequalities associated with Schrödinger operators involving Aharonov–Bohm magnetic potentials, and to some consequences. As symmetry plays an important role for establishing optimality results, we shall consider various cases corresponding to a circle, a two-dimensional sphere or a two-dimensional torus, and also the Euclidean spaces of dimensions 2 and 3. Most of the results are new and we put the emphasis on the methods, as very little is known on symmetry, rigidity and optimality in the presence of a magnetic field. The most spectacular applications are new magnetic Hardy inequalities in dimensions [Formula: see text] and [Formula: see text].

A comparative study on the vibration of functionally graded Magneto-Electro-Elastic rectangular plate rested on a Pasternak foundation based on exponential and first-order shear deformation theories

In this paper, the in-plane and out-of-plane free vibrations of the functionally graded magneto-electro-elastic (FG-MEE) rectangular plate on a pasternak foundation were evaluated based on exponential shear deformation theory (ESDT) and first order shear deformation theory (FSDT). The material properties of FG-MEE varied along the thickness according to a power-law distribution model. It was assumed that the FG-MEE plate is subjected to initial external electrical and magnetic potentials; mreover, simply-supported boundary conditions were considered for all the edges of the FG-MEE plate. Firstly, the corresponding partial differential equations (PDEs) were derived using Hamilton’s principle, then, the natural frequencies were determined by solving the obtained equations through Navier’s approach according to the assumed boundary conditions. The results revealed that the natural frequencies of the plate decrease/increase with the increase of the electric/magnetic potentials. Moreover, the results showed a 0.03%, difference between the natural frequencies of the plate with a thickness-to-length ratio of 0.1 based on FSDT and ESDT; when the aspect ratio was increased to 0.2 and 0.3 this difference rose to 0.2% and 0.5%, respectively.

Vibration performance evaluation of smart magneto-electro-elastic nanobeam with consideration of nanomaterial uncertainties

This study is devoted to examining the vibration behaviors of magneto-electro-elastic nanobeams with consideration of nanomaterial uncertainties induced by the atom defect and manufacturing deviation. Based on the nonlocal Timoshenko beam theory, the governing equations of a magneto-electro-elastic nanobeam resting on a Winkler–Pasternak foundation and subjected to electric and magnetic potentials are derived. The material properties of the magneto-electro-elastic nanobeam are treated as uncertain parameters with well-defined bounds to overcome the extensive information required in probabilistic evaluation. The range of natural frequency of the magneto-electro-elastic nanobeam is predicted via a non-probabilistic evaluation methodology, which is validated by comparing with Monte Carlo simulation and probabilistic evaluation methodology. Then, the parametric analyses are performed to reveal the coupling effects of nanomaterial uncertainties, and nonlocal parameter, as well as elastic foundation parameters on the vibration performance of magneto-electro-elastic nanobeams. It is demonstrated that the nanomaterial uncertainties affect the mechanical behaviors of magneto-electro-elastic nanostructures significantly and the present model can be degenerated into the deterministic model as the nanomaterial uncertainty is eliminated.

Analytical Solution for the Creep Problem of a Rotating Functionally Graded Magneto–Electro–Elastic Hollow Cylinder in Thermal Environment

In this paper, an analytical method is presented for the problem of the time-dependent response of a functionally graded magneto–electro–elastic (FGMEE) rotating hollow cylinder in thermal environment. The material properties of FGMEE are supposed to be power-law functions of radius. Applying the equations of equilibrium and electrostatic and magnetostatic equations, a differential equation which includes creep strains is achieved. At first, an exact solution for the primitive stresses, electric and magnetic potentials are achieved by eliminating creep strains in the mentioned differential equation. Then, Prandtl–Reuss equations, as well as Norton’s law, are employed for the FGMEE. Now, creep stress rates can be achieved by considering only creep strains in the mentioned differential equation. As a final step, time-dependent creep stress, electric potential and magnetic potential redistributions at any time can be achieved using an iterative method. Numerical examples are presented to disclose the influence of creep evolution, thermal loading, angular velocity and grading index on the primitive and creep response of the FGMEE hollow cylinder. Results show that the enhancement in tensile hoop stress during the creep evolution must be considered in designing. So, the creep analysis is vital to have more reliable and accurate aerospace smart structures.

Dual models of QCD and their implications

Some of the dual formulations of QCD are reviewed and analyzed for their possible implications especially in non-perturbative sector of QCD at zero temperature. Starting from the Nambu-Mandelstam idea and the ’t Hooft Abelian Projection technique, the effective formulations of QCD like the dual GinzburgLandau formulation and magnetic symmetry based dual QCD formulation have been analyzed in which dual magnetic potentials coupled with monopole field act as fundamental variables. The dual dynamics associated with these models is discussed in the quenched approximation and the analysis of symmetry breaking , flux tube configurations, confinement potential and nature of dual QCD vacuum is presented which establishes magnetic symmetry based dual QCD formulation as a more effective topological viable formulation for analysing the non-perturbative aspects of QCD.