Schwinger's method for the fermionic Casimir effect at finite temperature

The Casimir energy of a massive Dirac field at finite temperature and confined between two parallel infinite plates is computed using a method proposed by Schwinger. The boundary conditions are those of zero current through the plates, as inspired by quark confinement in the MIT bag model for hadrons. We use Schwinger's original regularization by a cutoff in proper-time. We comment on the analytical continuation method of regularization, which allows the employment of Epstein function techniques, and on the different possible expressions for the final answer.     

Schwinger's method for the massive Casimir effect

We apply a method recently proposed by Schwinger to the massive scalar field to calculate the Casimir effect. The method is applied with two different regularization schemes: Schwinger's original one by means of Poisson formula and another one by means of analytical continuation.     

Harmonic Green's functions for flexural waves in semi-infinite plates with arbitrary boundary conditions and high-frequency approximation for convex polygonal plates

This paper provides a method for obtaining the harmonic Green's function for flexural waves in semi-infinite plates with arbitrary boundary conditions and a high frequency approximation of the Green's function in the case of convex polygonal plates, by using a generalised image source method. The classical image source method consists in describing the response of a point-driven polygonal plate as a superposition of contributions from the original source and virtual sources located outside of the plate, which represent successive reflections on the boundaries. The proposed approach extends the image source method to plates including boundaries that induce coupling between propagating and evanescent components of the field and on which reflection depends on the angle of incidence. This is achieved by writing the original source as a Fourier transform representing a continuous sum of propagating and evanescent plane waves incident on the boundaries. Thus, the image source contributions arise as continuous sums of reflected plane waves. For semi-infinite plates, the exact Green's function is obtained for an arbitrary set of boundary conditions. For polygonal plates, a high-frequency approximation of the Green's function is obtained by neglecting evanescent waves for the second and subsequent reflections on the edges. The method is compared to exact and finite element solutions and evaluated in terms of its frequency range of applicability.     

ABSOLUTELY UNSTABLE WAVES IN INVISCID HYDROELASTIC SYSTEMS

The effect of inviscid plug flow on the stability of several hydroelastic systems is investigated by determining the absolute or convective nature of the instability from the linear dispersion relation. The fluid-structure systems consist of plates and membranes with bounded and unbounded flow. A method is proposed to derive systematically in parameter space the boundary between convective and absolute instability, based on the particular symmetries of the dispersion relation as originally noted by Crighton and Oswell. This method is then applied to the case of plates with superimposed tension, thick plates with rotary inertia and walls made of plates or membranes bounding channel flow, oscillating in a sinuous or varicose mode of deformation. A relation is drawn with solutions by previous authors for plates, for pipes and for the Kelvin-Helmholtz instability with surface tension. To illustrate these results some temporal evolutions are calculated by using an integration in the wavenumber space. Based on the large set of new cases solved in the paper some general trends are discussed as to the influence of flow velocity, confinement and structural stiffness on the existence of absolutely unstable waves in inviscid hydroelastic systems.     

Transient vibration analysis of a completely free plate using modes obtained by Gorman's superposition method

This paper shows that the transient response of a plate undergoing flexural vibration can be calculated accurately and efficiently using the natural frequencies and modes obtained from the superposition method. The response of a completely free plate is used to demonstrate this. The case considered is one where all supports of a simply supported thin rectangular plate under self weight are suddenly removed. The resulting motion consists of a combination of the natural modes of a completely free plate. The modal superposition method is used for determining the transient response, and the natural frequencies and mode shapes of the plates used are obtained by Gorman's superposition method. These are compared with corresponding results based on the modes using the Rayleigh-Ritz method using the ordinary and degenerated free-free beam functions. There is an excellent agreement between the results from both approaches but the superposition method has shown faster convergence and the results may serve as benchmarks for the transient response of completely free plates.     

Transverse vibrations of thin,elastic plates with concentrated masses and internal elastic supports

The fundamental frequency of vibration of a plate carrying concentrated masses and with internal elastic supports is determined. The case of an orthotropic, rectangular plate elastically restrained against rotation along the four edges is tackled first by using simple polynomial approximations and the Galerkin method. Then, vibrations of clamped and simply supported isotropic plates of regular polygonal shape are studied by using the conformal mapping technique coupled with the variational method. Finally the case of a circular plate elastically restrained against translation and rotation is considered.     

The Casimir interaction of a massive vector field between concentric spherical bodies

The Casimir interaction energy due to the vacuum fluctuations of a massive vector field between two perfectly conducting concentric spherical bodies is computed. The TE contribution to the Casimir interaction energy is a direct generalization of the massless case but the TM contribution is much more complicated. Each TM mode is a linear combination of a transverse mode which is the generalization of a TM mode in the massless case and a longitudinal mode that does not appear in the massless case. In contrast to the case of two parallel perfectly conducting plates, there are no TM discrete modes that vanish identically in the perfectly conducting spherical bodies. Numerical simulations show that the Casimir interaction force between the two bodies is always attractive.     

Antisymmetric vibrations of circular plates with thickness varying in a bilinear fashion

The title problem is tackled using simple polynomial co-ordinate functions and the Ritz method. The algorithmic procedure is quite straightforward and yields very accurate results in the case of circular plates of uniform thickness. It can also be easily implemented by a desk computer.     

Realization of Arbitrary Inverse Unitary Transformation of Single Mode Fibre by Using Three Wave Plates

We report a method to realize the arbitrary inverse unitary transformation imposed by a single-mode fibre on photon＇s polarization by the succession of two quarter-wave plates and a half-wave plate. The process of realization is analysed on a Poincar6 sphere due to the fact that unitary transformation does not change the angle formed by polarization state vector. The method is meaningful in quantum communication experiment such as quantum teleportation, in which an unknown arbitrary quantum state should be kept to be unchanged in the case of using a single-mode fibre for time delay.[第一段]     

Prediction method for sound from passing vehicle transmitted through building façade

This study proposes a prediction method for assessing the sound of a passing vehicle that is transmitted through a glass plate, which employs the vibro-acoustic finite-difference time-domain (FDTD) method. The noise that is transmitted through the glass in a building façade, which is affected by the sound-insulation characteristics of its glass plates, can have a psychological influence such as a sleep disorder on the residents. In this study, a prediction method for the spectral characteristics of the transmitting sound through glass plates is proposed. The sound-insulation characteristics of glass plates are obtained using a vibro-acoustic FDTD method, and are then synthesized with the sound of passing vehicles obtained by in situ measurement. Firstly, the sound transmitted through several kinds of glass plates is simulated using the proposed method. Then, in order to confirm the validity of this method, the simulated results are compared to measured sounds transmitted by passing vehicles into a room near the street.     

On the effect of free,rectangular cut-outs along the edge on the transverse vibrations of rectangular plates

The title problem is tackled using two alternative approaches: a simple Rayleigh-Ritz methodology and a finite element algorithmic procedure.Numerical results are obtained in the case of simply supported and clamped plates with free, square holes located at the middle of a plate edge. Experimental values are obtained in the case of clamped plates.It is concluded that the agreement is very good from an engineering viewpoint as long as the hole size is moderate. Since this constitutes a valid restriction in practice when ducts, pipes, etc., traverse plates or slabs, one can say that the Rayleigh-Ritz procedure yields fundamental frequency coefficients which possess sufficient accuracy from a designer's viewpoint.     

Pitch change during reverberant decay

The natural frequencies and mode shapes of a number of box beams are calculated by using the finite element displacement method. The structures are considered as assemblages of plates, and in general it is necessary to consider both the in-plane and transverse motion of the plates. A method of representing these two types of motion in the analysis of the vibrations of box beams is presented. A number of box beams of varying sectional parameters are analysed as systems of plates and the results compared with the predictions of Euler and Timoshenko beam theories. The comparisons show that for short beams constructed of thin plates, the new method can successfully represent the localized plate deformations, which cannot be described by beam theory.     

Transverse vibrations of circular plates of varying thickness with non-uniform edge constraints

Free vibrations of circular plates varying in thickness and with flexible edge supports have been studied by several investigators for the restricted case when the supports are represented by uniformly distributed springs of constant stiffness.In the present study an approximate method is presented for dealing with supports possessing rotational flexibility which varies arbitrarily around the boundary.The method consists in representing the varying stiffness in terms of a Fourier expansion in the polar angle and approximately expressing the displacement function using a summation of polynomial co-ordinate functions which exactly satisfies only the essential boundary condition. The Ritz method is then applied in order to obtain the frequency determinant. The method can be easily extended to the forced vibrations case.     

Free vibration of polar-orthotropic sector plates

The free vibration of ring-shaped polar-orthotropic sector plates is analyzed by the Ritz method using a spline function as an admissible function for the deflection of the plates. For this purpose, the transverse deflection of a sector plate is written in a series of the products of the deflection function of a sectorial beam and that of a circular beam satisfying the boundary conditions. The deflection function of the sectorial beam is approximately expressed by a quintic spline function, which satisfies the equation of flexural vibration of the beam at each point dividing the beam into small elements. The frequency equation of the plate is derived by the conditions for a stationary value of the Lagrangian. The present method is applied to ring-shaped polar-orthotropic sector plates with some combination of boundary conditions, and the natural frequencies and the mode shapes are calculated numerically up to higher modes. This method is very effective for the study of vibration problems of variously shaped anisotropic plates including these sector plates.     

The dynamic analysis of circular plates and shallow spherical shells

In the investigation reported here an attempt has been made to study the influence of Berger's approximation on the non-linear transient response of circular plates and shallow spherical shells. The governing equations of motion obtained from Berger's approximation are solved by using the rapidly converging Chebyshev series spacewise and the Houbolt scheme for integration in the time domain. Results calculated when using Berger's approximation are compared with exact results. It is shown that Berger's method yields very accurate values for plates and shells under transient loading, in the case of immovable edge conditions.     

Casimir Effect for Dielectric Plates

We generalize Kupisewska method to the three-dimensional system and another derivation of the Casimir effect between two dielectric plates is presented based on the explicit quantization of the electromagnetic field in the presence of dielectrics, where the physical meaning of “evanescent mode” is discussed. The Lifshitz's formula is rederived using all the vacuum mode functions, which include the contribution of the ‘evanescent modes’. Only in the case of the perfect metallic plates will the evanescent modes become unimportant.     

Moment method analysis of charge distribution & capacitance for the dielectric coated tilted plates isolated in free space

This paper presents a method for the evaluation of the capacitance of the dielectric coated metallic plates forming a corner using the method of moments based on the pulse basis function and the point matching. Two integral equations are formed based on the boundary conditions for the potential on the conductor surface and continuity of the normal component of the displacement flux density at the dielectric-free space interface. A set of simultaneous equations are formed from the two integral equations using the method of moments. The total free charge on the conductor surface is found from the solution of the set of simultaneous equations. Numerical data on the capacitance and the charge distribution are presented. The validity of the analysis has been justified by comparing the data on the capacitance that is available in the literature for a metallic structure with the data on the capacitance computed with the present method for a similar structure considering a very low dielectric constant as well as a very thin dielectric coating. Further validation has been carried out by comparing the capacitance data of the specific case when the angle between two metallic plates is 180° forming a dielectric coated metallic rectangular plate for which the capacitance data are available in the literature.     

Scattering phase functions of horizontally oriented hexagonal ice crystals

Finite-difference time domain (FDTD) solutions are first compared with the corresponding T-matrix results for light scattering by circular cylinders with specific orientations. The FDTD method is then utilized to study the scattering properties of horizontally oriented hexagonal ice plates at two wavelengths, 0.55 and 12 μm. The phase functions of horizontally oriented ice plates deviate substantially from their counterparts obtained for randomly oriented particles. Furthermore, we compute the phase functions of horizontally oriented ice crystal columns by using the FDTD method along with two schemes for averaging over the particle orientations. It is shown that the phase functions of hexagonal ice columns with horizontal orientations are not sensitive to the rotation about the principal axes of the particles. Moreover, hexagonal ice crystals and circular cylindrical ice particles have similar optical properties, particularly, at a strongly absorbing wavelength, if the two particle geometries have the same length and aspect ratio defined as the ratio of the radius or semi-width of the cross section of a particle to its length. The phase functions for the two particle geometries are slightly different in the case of weakly absorbing plates with large aspect ratios. However, the solutions for circular cylinders agree well with their counterparts for hexagonal columns.     

Free vibration of plated structures by grillage method

Free vibration of plated structures such as plates, stiffened plates and cellular structures are analysed by the grillage method. The accuracy of the method is assessed by comparing with published results and those of the finite element method. Reasonably good results are obtained by the grillage method, which is less demanding on computer time and thus reduces the cost of analysis substantially. By using the grillage method the influence of the number of stiffeners in a stiffened plate and the number of webs in a cellular structure on the vibration characteristics of plated structures is investigated.     

Using infrared thermography in order to compare laser and hybrid (laser+MIG) welding processes

In order to deepen the understanding of the differences between laser and laser-arc hybrid welding, comparisons were undertaken using thermography. The experiments were carried out for a T assembly of aluminium alloy plates. Modelling, based on the finite element method approach, was realized using IR temperature measurements and seam geometry. For a value of the power supply, depicted as a surface source in the hybrid case, agreement was found between simulated and measured temperatures. The arc power supply efficiency value is similar to the usually used value.