Dynamic equations for a fully anisotropic elastic plate

A hierarchy of dynamic plate equations is derived for a fully anisotropic elastic plate. Using power series expansions in the thickness coordinate for the displacement components, recursion relations are obtained among the expansion functions. Adopting these in the boundary conditions on the plate surfaces and along the edges, a set of dynamic equations with pertinent edge boundary conditions are derived on implicit form. These can be truncated to any order and are believed to be asymptotically correct. For the special case of an orthotropic plate, explicit plate equations are presented and compared analytically and numerically to other approximate theories given in the literature. These results show that the present theory capture the plate behavior accurately concerning dispersion curves, eigenfrequencies as well as stress and displacement distributions.     

Phase constant peculiarities of cylindrical zero-index anisotropic metamaterial waveguide

Here, we present the phase constant dependencies of propagating eigenmodes of an open cylindrical anisotropic metamaterial waveguide when the metamaterial permittivity and permeability tensor components may accept values close or equal to zero. Dispersion characteristics of rod and hollow-core waveguides with the radii 0.5, 2.5, and 5 mm at the left-handed polarization of the microwave are shown here. There are unusual shapes of eigenmode dispersion characteristics and anomalous sectors of the characteristics at certain frequencies. The first eigenmode of the rod waveguide with the lowest cutoff frequency is a particularly important mode because it is a single one in the frequency range 1.0?C1.9 GHz, and some small variations on the frequency produce large changes in the phase constant. We can observe packages of dispersion characteristic branches when their cutoff frequencies closed to the metamaterial electric and magnetic plasma frequencies between 1.9 and 3.5 GHz. There are only three modes in the hollow core anisotropic metamaterial waveguide at the frequency range 1.4?C2.8 GHz.     

Non-destructive evaluation of elastic material properties in anisotropic circular cylindrical structures

In this paper, non-axisymmetric guided wave propagation in circular cylindrical, anisotropic structures is studied in a frequency range up to 1 MHz. The investigations are carried out with carbon fibre reinforced tubes. The aim is the experimental determination of their effective linear elastic material properties in a non-destructive way. Therefore, an analytical model of the dispersion equation is fitted to the experimentally detected dispersion curves by systematically adjusting the desired material properties. A total least square scheme accompanied by an outlier detection criterion is used for this optimization task. Since the raw data of the measured dispersion curves contain a lot of noise, these outliers have to be detected and excluded, to achieve accurate results. Good agreement is found between the measured curves and the analytically calculated curves based on the estimated parameters. This fact indicates a high accuracy of the determined material properties.     

A cylindrical liquid-core waveguide

A novel concept for a liquid-core lightguide in cylindrical symmetry is presented. For a concrete 17 cm long device using water as a core and the transparent fluorinated polymer Teflon as a cladding layer, the coupling efficiency and guiding properties are investigated theoretically and compared with experimental results. The guide is found to exhibit low losses. A possible application of this type of guide is investigated by replacing the optical cell of a standard UV/VIS spectrometer by the cylindrical liquid-core waveguide. An increasing sensitivity for especially low concentrations of a polluting dye by a factor of about 15 is observed. Concentrations as low as a few parts per billion of the pollutant can be detected with a good signal-to-noise ratio.     

Ginzburg-Landau equations for anisotropic superconductors

We use the framework of a general quasiclassical theory of superconductivity which allows for arbitrary gap and Fermi surface anisotropy and for impurity scattering in Born approximation. We derive general Ginzburg-Landau integro-differential equations, which comprise all previous limiting cases considered in the literature. From these equations more specialized Ginzburg-Landau equations may easily be derived.     

Separable solutions of nonlinear wave equations

It is shown how to obtain separable solutions, which include travelling-wave solutions as a special case, of a large class of nonlinear wave equations, including the Korteweg-de Vries-Burgers equation and Fisher's equation.     

Sound absorption by resonators in a cylindrical waveguide

The problem on the scattering of a zero-order axisymmetric mode by a ring of equally spaced identical monopole-dipole resonators positioned in the cross section of a wide circular pipe is considered. The solution to the problem is used to formulate the requirements for a set of resonators that provide a complete absorption of the zero-order mode in the pipe.     

Eigenwave asymptotics for smoothly irregular plane anisotropic waveguide

An extension of method of horizontal rays and vertical modes developed for underwater acoustics to the spatially inhomogeneous anisotropic electrodynamic problem is proposed.Leningrad State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 34, No. 7, 790–797, July, 1991.     

New waveguide modes in anisotropic structures

The existence of new hybrid waveguide modes of properly tailored integrated optical waveguides consisting of ultrathin films clad by positive birefringent media is pointed out.     

Study of a slab waveguide loaded with dispersive anisotropic metamaterials

We have numerically studied the characteristics of a slab waveguide loaded with dispersive anisotropic metamaterials. For two typical-structured metamaterials, we have analyzed the tensor expressions of frequency-dependent permittivity and permeability and discussed influences of the resonant cell structures on waveguiding characteristics. Numerical results show that the slab waveguide loaded with anisotropic metamaterials may, to some extent, behave as the slab waveguides of isotropic left-handed metamaterials (LHMs) core and conventional right-handed materials core. To one’s interest, some unusual properties are revealed in this paper, such as the coexistence of the fundamental guided mode and negative group velocity, and extraordinarily large normal or anomalous group velocity dispersion. Our results may find some potential applications in both linear and nonlinear optical technology.     

Asymptotics of eigenwaves of a smooth irregular spherical anisotropic waveguide

Based on the Debye series modified with respect to the method of horizontal beams and vertical modes, the asymptotics of eigenwaves of a smooth irregular anisotropic spherical anisotropic waveguide channel is constructed.State University, St. Petersburg. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, No. 5, pp. 457–466, May, 1995.     

Transient radiation in an anisotropic magnetodielectric plate in a waveguide

We have considered transient radiation of a charged particle in an anisotropic magnetodielectric plate placed into a regular waveguide. It is assumed that the charged particle passes through the plate moving at a constant velocity perpendicularly to the waveguide axis. Wave equations and analytical expressions for transverse electric (TE) and transverse magnetic (TM) fields in different regions of the waveguide have been obtained. Energies of transient radiation of the moving particle have been calculated. The properties of transient radiation and Vavilov–Cherenkov radiation have been analyzed for the case of a rectangular waveguide. Energies of transient radiation have been calculated for the case of a “thin” plate in the waveguide, when the wavelength in the plate is much greater than the length of the plate.     

Optical modes in a plasmonic waveguide with electrically anisotropic metamaterial

We study the optical modes in a plasmonic waveguide with electrically anisotropic metamaterial and dielectric, including symmetric (anti-symmetric) photonic mode and symmetric (anti-symmetric) plasmonic mode. The dispersion curves for these modes are derived, and a graphical method is used to calculate the solution of symmetric photonic mode and anti-symmetric plasmonic mode. By simulation results the conditions of the existence for these modes are deduced in each case.     

Helical waves in a fluid-filled cylindrical elastic shell

Helical normal waves of a waveguide that has the form of a fluid-filled thin elastic shell are considered. A dispersion equation for this kind of wave is derived, and its solutions are presented for certain values of parameters characterizing the problem.     

Charged cylindrical collapse of anisotropic fluid

Following the scheme developed by Misner and Sharp, we discuss the dynamics of gravitational collapse. For this purpose, an interior cylindrically symmetric spacetime is matched to an exterior charged static cylindrically symmetric spacetime using the Darmois matching conditions. Dynamical equations are obtained with matter dissipating in the form of shear viscosity. The effect of charge and dissipative quantities over the cylindrical collapse are studied. Finally, we show that homogeneity in energy density and conformal flatness of spacetime are necessary and sufficient for each other.