Finite element analysis of bimodulus composite stiffened thin shells of revolution

This paper is a sequel to the work published by the first and third authors[l] on stiffened laminated shells of revolution made of unimodular materials (materials having identical properties in tension and compression). A finite element analysis of laminated bimodulus composite thin shells of revolution, reinforced by laminated bimodulus composite stiffeners is reported herein. A 48 dot doubly curved quadrilateral laminated anisotropic shell of revolution finite element and it's two compatible 16 dof stiffener finite elements namely: (i) a laminated anisotropic parallel circle stiffener element (PCSE) and (ii) a laminated anisotropic meridional stiffener element (MSE) have been used iteratively. The constitutive relationship of each layer is assumed to depend on whether the fiberdirection strain is tensile or compressive. The true state of strain or stress is realized when the locations of the neutral surfaces in the shell and the stiffeners remain unaltered (to a specified accuracy) between two successive iterations. The solutions for static loading of a stiffened plate, a stiffened cylindrical shell. and a stiffened spherical shell, all made of bimodulus composite materials, have been presented.

On the control of rapidly rotating convection by an axially varying magnetic field

The magnetic field in rapidly rotating dynamos is spatially inhomogeneous. The axial variation of the magnetic field is of particular importance because tall columnar vortices aligned with the rotation axis form at the onset of convection. The classical picture of magnetoconvection with constant or axially varying magnetic fields is that the Rayleigh number and wavenumber at onset decrease appreciably from their non-magnetic values. Nonlinear dynamo simulations show that the axial lengthscale of the self-generated azimuthal magnetic field becomes progressively smaller as we move towards a rapidly rotating regime. With a small-scale field, however, the magnetic control of convection is different from that in previous studies with a uniform or large-scale field. This study looks at the competing viscous and magnetic mode instabilities when the Ekman number E (ratio of viscous to Coriolis forces) is small. As the applied magnetic field strength (measured by the Elsasser number Lambda) increases, the critical Rayleigh number for onset of convection initially increases in a viscous branch, reaches an apex where both viscous and magnetic instabilities co-exist, and then falls in the magnetic branch. The magnetic mode of onset is notable for its dramatic suppression of convection in the bulk of the fluid layer where the field is weak. The viscous-magnetic mode transition occurs at Lambda similar to 1, which implies that small-scale convection can exist at field strengths higher than previously thought. In spherical shell dynamos with basal heating, convection near the tangent cylinder is likely to be in the magnetic mode. The wavenumber of convection is only slightly reduced by the self-generated magnetic field at Lambda similar to 1, in agreement with previous planetary dynamo models. The back reaction of the magnetic field on the flow is, however, visible in the difference in kinetic helicity between cyclonic and anticyclonic vortices.

Two new integral transforms and their applications

This thesis is in two parts. In Part I the independent variable θ in the trigonometric form of Legendre's equation is extended to the range ( -∞, ∞). The associated spectral representation is an infinite integral transform whose kernel is the analytic continuation of the associated Legendre function of the second kind into the complex θ-plane. This new transform is applied to the problems of waves on a spherical shell, heat flow on a spherical shell, and the gravitational potential of a sphere. In each case the resulting alternative representation of the solution is more suited to direct physical interpretation than the standard forms.

In Part II separation of variables is applied to the initial-value problem of the propagation of acoustic waves in an underwater sound channel. The Epstein symmetric profile is taken to describe the variation of sound with depth. The spectral representation associated with the separated depth equation is found to contain an integral and a series. A point source is assumed to be located in the channel. The nature of the disturbance at a point in the vicinity of the channel far removed from the source is investigated.

Some approximate solutions of dynamic problems in the linear theory of thin elastic shells

Some aspects of wave propagation in thin elastic shells are considered. The governing equations are derived by a method which makes their relationship to the exact equations of linear elasticity quite clear. Finite wave propagation speeds are ensured by the inclusion of the appropriate physical effects.

The problem of a constant pressure front moving with constant velocity along a semi-infinite circular cylindrical shell is studied. The behavior of the solution immediately under the leading wave is found, as well as the short time solution behind the characteristic wavefronts. The main long time disturbance is found to travel with the velocity of very long longitudinal waves in a bar and an expression for this part of the solution is given.

When a constant moment is applied to the lip of an open spherical shell, there is an interesting effect due to the focusing of the waves. This phenomenon is studied and an expression is derived for the wavefront behavior for the first passage of the leading wave and its first reflection.

For the two problems mentioned, the method used involves reducing the governing partial differential equations to ordinary differential equations by means of a Laplace transform in time. The information sought is then extracted by doing the appropriate asymptotic expansion with the Laplace variable as parameter.

Three-dimensional models of mantle convection : influence of phase transitions and temperature-dependent viscosity

Two of the most important questions in mantle dynamics are investigated in three separate studies: the influence of phase transitions (studies 1 and 2), and the influence of temperature-dependent viscosity (study 3).

(1) Numerical modeling of mantle convection in a three-dimensional spherical shell incorporating the two major mantle phase transitions reveals an inherently three-dimensional flow pattern characterized by accumulation of cold downwellings above the 670 km discontinuity, and cylindrical 'avalanches' of upper mantle material into the lower mantle. The exothermic phase transition at 400 km depth reduces the degree of layering. A region of strongly-depressed temperature occurs at the base of the mantle. The temperature field is strongly modulated by this partial layering, both locally and in globally-averaged diagnostics. Flow penetration is strongly wavelength-dependent, with easy penetration at long wavelengths but strong inhibition at short wavelengths. The amplitude of the geoid is not significantly affected.

(2) Using a simple criterion for the deflection of an upwelling or downwelling by an endothermic phase transition, the scaling of the critical phase buoyancy parameter with the important lengthscales is obtained. The derived trends match those observed in numerical simulations, i.e., deflection is enhanced by (a) shorter wavelengths, (b) narrower up/downwellings (c) internal heating and (d) narrower phase loops.

(3) A systematic investigation into the effects of temperature-dependent viscosity on mantle convection has been performed in three-dimensional Cartesian geometry, with a factor of 1000-2500 viscosity variation, and Rayleigh numbers of 10^5-10^7. Enormous differences in model behavior are found, depending on the details of rheology, heating mode, compressibility and boundary conditions. Stress-free boundaries, compressibility, and temperature-dependent viscosity all favor long-wavelength flows, even in internally heated cases. However, small cells are obtained with some parameter combinations. Downwelling plumes and upwelling sheets are possible when viscosity is dependent solely on temperature. Viscous dissipation becomes important with temperature-dependent viscosity.

The sensitivity of mantle flow and structure to these various complexities illustrates the importance of performing mantle convection calculations with rheological and thermodynamic properties matching as closely as possible those of the Earth.

Focusing properties of concentric piecewise cylindrical vector beam

The focusing properties of a concentric piecewise cylindrical vector beam is investigated theoretically in this paper. The beam consists of three portions with different and changeable phase retardation and polarization. Numerical simulations show that the evolution of the focal shape is very considerable by changing the radius and polarization rotation angle of each portion of the vector beam. And some interesting focal spots may occur, such as two- or three-peak focus, dark hollow focus, ring focus, and two-ring-peak focus. Corresponding gradient force patterns are also computed, and novel trap patterns, including cup shell shape trap with one trap at its each side along axis, rectangle shell shape trap with one trap at its each side, dumbbell optical trap, spherical shell optical trap, may occur, which shows that the concentric piecewise cylindrical vector beam can be used to construct controllable optical tweezers. (c) 2006 Elsevier GmbH. All rights reserved.

Sound radiation from point-excited structures: Comparison of plate and sphere

Acoustic radiation from a structure can be expressed in terms of modal radiation and modal coefficients. This paper investigates the contributions of these two modal properties to radiation excited by a point force. Sound radiation from two basic structures is considered: a baffled rectangular plate and a closed spherical shell. The plate behaviour is familiar, and governed by the relation between the natural frequency of a mode and its coincidence frequency. For a closed spherical shell, there are either zero or two critical frequencies, depending on the radius and thickness. When there are two the shell radiates well both above and below the two frequencies, and poorly in the frequency range between them. © 2012 Elsevier Ltd. All rights reserved.

Redescription of Difflugia tuberspinifera Hu, Shen, Gu et Gong, 1997 (Protozoa : Rhizopoda : Arcellinida : Difflugiidae) from China

The freshwater testate amoeba Difflugia tuberspinifera Hu et al. 1997 collected from pond and lake in China, is investigated by light and scanning electron microscopy. This little known taxon is redescribed and its morphology, biometry and ecology are supplied. After carefully comparison with other six similar species including Difflugia bartosi Stepanek, D. corona Wallich, D. corona cashi Deflandre, D. corona tuberculata Vucetich, D. muriformis Gauthier-Lievre et Thomas and Netzelia tuberculata (Wallich) Netzal we believe that the sub-spherical to spherical shell, the mulberry-shaped appearance, the 7-10 apertural tooth-like structures, the short collar and the conical spines numbering from 4 to 8 at the upper equatorial region in D. tuberspinifera set it apart from other species. Besides, statistical analysis indicates that D. tuberspinifera is a size-monomorphic species characterized by a main-size class and a small size range and the shell height is significant correlated with other morphometric characters at p < 0.05 excepting the number of aperture tooth-like structures and the number of spines. Moreover, D. tuberspinifera inhabits not only lotic but also lentic environment.

Ultrahigh compression of water using intense heavy ion beams: laboratory planetary physics

Intense heavy ion beams offer a unique tool for generating samples of high energy density matter with extreme conditions of density and pressure that are believed to exist in the interiors of giant planets. An international accelerator facility named FAIR (Facility for Antiprotons and Ion Research) is being constructed at Darmstadt, which will be completed around the year 2015. It is expected that this accelerator facility will deliver a bunched uranium beam with an intensity of 5x10(11) ions per spill with a bunch length of 50-100 ns. An experiment named LAPLAS (Laboratory Planetary Sciences) has been proposed to achieve a low-entropy compression of a sample material like hydrogen or water (which are believed to be abundant in giant planets) that is imploded in a multi-layered target by the ion beam. Detailed numerical simulations have shown that using parameters of the heavy ion beam that will be available at FAIR, one can generate physical conditions that have been predicted to exist in the interior of giant planets. In the present paper, we report simulations of compression of water that show that one can generate a plasma phase as well as a superionic phase of water in the LAPLAS experiments.

Prediction of Physical Properties of Yeast Cell Suspensions using Dielectric Spectroscopy

D.J. Currie, M.H. Lee and R.W. Todd, 'Prediction of Physical Properties of Yeast Cell Suspensions using Dielectric Spectroscopy', Conference on Electrical Insulation and Dielectric Phenomena, (CEIDP 2006), Annual Report, pp 672 ? 675, October 15th -18th 2006, Kansas City, Missouri, USA. Organised by IEEE Dielectrics and Electrical Insulation Society.

Electromagnetic energy within coated spheres containing dispersive metamaterials

An exact expression is derived for the time-averaged electromagnetic energy within a magneto-dielectric coated sphere, which is irradiated by a plane and time-harmonic electromagnetic wave. Both the spherical shell and core are considered to be dispersive and lossy, with a realistic dispersion relation of an isotropic split-ring resonator metamaterial. We obtain analytical expressions for the stored electromagnetic energies inside the core and the shell separately and calculate their contributions to the total average energy density. The stored electromagnetic energy is calculated for two situations involving a metamaterial coated sphere: a dielectric shell and dispersive metamaterial core, and vice versa. An explicit relation between the stored energy and the optical absorption efficiency is also obtained. We show that the stored electromagnetic energy is an observable sensitive to field interferences responsible for the Fano effect. This result, together with the fact that the Fano effect is more likely to occur in metamaterials with negative refraction, suggest that our findings may be explored in applications.

Fabrication and luminescent properties of the core-shell structured YNbO4 : Eu3+/Tb3+@SiO2 spherical particles

The core-shell structured YNbO4:Eu3+/Tb3+@SiO2 particles were realized by coating the YNbO4:Etr(3+)/Tb3+ phosphors onto the surface of spherical silica via a sol-gel process. The obtained materials were characterized by means of X-ray diffraction (XRD), field emission scanning electron microscopy (FE-SEM), transmission electron microscopy (TEM), Fourier transform IR spectroscopy (FT-IR), photoluminescence (PL) spectra, and cathodoluminescence (CL) spectra.

Synthesis and characterization of monodisperse spherical SiO2@RE2O3 (RE = rare earth elements) and SiO2@Gd2O3:Ln(3+) (Ln = Eu, Tb, Dy, Sm, Er, Ho) particles with core-shell structure

Spherical SiO2 particles have been coated with rare earth oxide layers by a Pechini sol-gel process, leading to the formation of core-shell structured SiO2@RE2O3 (RE = rare earth elements) and SiO2@Gd2O3:Ln(3+) (Ln = Eu, Tb, Dy, Sm, Er, Ho) particles. X-ray diffraction (XRD), field emission scanning electron microscopy (FE-SEM), transmission electron microscopy (TEM), photoluminescence (PL), and cathodoluminescence spectra as well as lifetimes were used to characterize the resulting SiO2@RE2O3 (RE = rare earth elements) and SiO2@Gd2O3:Ln(3+) (Eu3+, Tb3+, Dy3+, Sm3+, Er3+, Ho3+) samples. The obtained core-shell phosphors have perfect spherical shape with narrow size distribution (average size ca. 380 nm), smooth surface and non-agglomeration. The thickness of shells could be easily controlled by changing the number of deposition cycles (40 nm for two deposition cycles).

Synthesis and luminescence properties of monodisperse spherical Y2O3 : Eu3+@SiO2 particles with core-shell structure

Y2O3: Eu3+ phosphor layers were deposited on monodisperse SiO2 particles with different sizes ( 300, 500, 900, and 1200 nm) via a sol-gel process, resulting in the formation of Y2O3: Eu3+@SiO2 core-shell particles. X-ray diffraction ( XRD), Fourier transform infrared spectroscopy (FT-IR), field emission scanning electron microscopy (FE-SEM), transmission electron microscopy ( TEM), time-resolved photoluminescence ( PL) spectra, and lifetimes were employed to characterize the Y2O3: Eu3+@SiO2 core-shell samples. The results of XRD indicated that the Y2O3: Eu3+ layers began to crystallize on the silica surfaces at 600 degrees C and the crystallinity increased with the elevation of annealing temperature until 900 degrees C. The obtained core-shell particles have perfect spherical shape with narrow size distribution and non-agglomeration. The thickness of the shells could be easily controlled by changing the number of deposition cycles ( 60 nm for three deposition cycles). Under the excitation of ultraviolet ( 250 nm), the Eu3+ ion mainly shows its characteristic red ( 611 nm, D-5(0)-F-7(2)) emissions in the core-shell particles from Y2O3: Eu3+ shells.