The dynamo bifurcation in rotating spherical shells
Morin, Vincent; 10.1142/S021797920906378X
2010-01-01
We investigate the nature of the dynamo bifurcation in a configuration applicable to the Earth's liquid outer core, i.e. in a rotating spherical shell with thermally driven motions. We show that the nature of the bifurcation, which can be either supercritical or subcritical or even take the form of isola (or detached lobes) strongly depends on the parameters. This dependence is described in a range of parameters numerically accessible (which unfortunately remains remote from geophysical application), and we show how the magnetic Prandtl number and the Ekman number control these transitions.
Scaling regimes in spherical shell rotating convection
Gastine, T; Aubert, J
2016-01-01
Rayleigh-B\\'enard convection in rotating spherical shells can be considered as a simplified analogue of many astrophysical and geophysical fluid flows. Here, we use three-dimensional direct numerical simulations to study this physical process. We construct a dataset of more than 200 numerical models that cover a broad parameter range with Ekman numbers spanning $3\\times 10^{-7} \\leq E \\leq 10^{-1}$, Rayleigh numbers within the range $10^3 < Ra < 2\\times 10^{10}$ and a Prandtl number unity. We investigate the scaling behaviours of both local (length scales, boundary layers) and global (Nusselt and Reynolds numbers) properties across various physical regimes from onset of rotating convection to weakly-rotating convection. Close to critical, the convective flow is dominated by a triple force balance between viscosity, Coriolis force and buoyancy. For larger supercriticalities, a subset of our numerical data approaches the asymptotic diffusivity-free scaling of rotating convection $Nu\\sim Ra^{3/2}E^{2}$ in ...
Bifurcations of rotating waves in rotating spherical shell convection.
Feudel, F; Tuckerman, L S; Gellert, M; Seehafer, N
2015-11-01
The dynamics and bifurcations of convective waves in rotating and buoyancy-driven spherical Rayleigh-Bénard convection are investigated numerically. The solution branches that arise as rotating waves (RWs) are traced by means of path-following methods, by varying the Rayleigh number as a control parameter for different rotation rates. The dependence of the azimuthal drift frequency of the RWs on the Ekman and Rayleigh numbers is determined and discussed. The influence of the rotation rate on the generation and stability of secondary branches is demonstrated. Multistability is typical in the parameter range considered.
Inertial waves in a differentially rotating spherical shell
Baruteau, C
2012-01-01
We investigate the properties of small-amplitude inertial waves propagating in a differentially rotating incompressible fluid contained in a spherical shell. For cylindrical and shellular rotation profiles and in the inviscid limit, inertial waves obey a second-order partial differential equation of mixed type. Two kinds of inertial modes therefore exist, depending on whether the hyperbolic domain where characteristics propagate covers the whole shell or not. The occurrence of these two kinds of inertial modes is examined, and we show that the range of frequencies at which inertial waves may propagate is broader than with solid-body rotation. Using high-resolution calculations based on a spectral method, we show that, as with solid-body rotation, singular modes with thin shear layers following short-period attractors still exist with differential rotation. They exist even in the case of a full sphere. In the limit of vanishing viscosities, the width of the shear layers seems to weakly depend on the global bac...
Equatorially trapped convection in a rapidly rotating spherical shell
Miquel, Benjamin; Julien, Keith; Knobloch, Edgar
2016-11-01
Convection plays a preponderant role in driving geophysical flows. Unfortunately, these flows are often characterized by rapid rotation (i.e. small Ekman number E) which renders the equations stiff and introduces a scale separation in the system: for example the wavelength of the marginal mode at the onset of convection in a rapidly rotating sphere scales like E 1 / 3 and is modulated by a E 1 / 6 envelope. These scalings keep the fully nonlinear dynamics of the internal convection in Earth's core (E 1015) out of reach from direct numerical simulations, analytical work and experiments on one hand, but advocate for the development of reduced models on the other hand. We present a reduced model derived in a shallow gap spherical shell geometry. As the Rayleigh number is increased, the flow is first destabilized in the equatorial region where the dynamics remains trapped. The linear stability is analyzed and the fully nonlinear dynamics is presented.
Gravito-inertial waves in a differentially rotating spherical shell
Mirouh, Giovanni M; Rieutord, Michel; Ballot, Jérôme
2015-01-01
We study the properties of gravito-inertial waves in a differentially rotating fluid inside a spherical shell. The fluid is modeled with the Boussinesq approximation and has a shellular steady rotation profile that stems from the combined effects of stratification, rotation, and no-slip boundary conditions. The waves properties are examined by computing paths of characteristics in the non-dissipative limit, and by solving the full dissipative eigenvalue problem using a high-resolution spectral method. Gravito-inertial waves are found to obey a mixed-type second-order operator and to be often focused around short-period attractors of characteristics or trapped in a wedge formed by turning surfaces and boundaries. We also find eigenmodes that show a weak dependence with respect to viscosity and heat diffusion just like truly regular modes. Some axisymmetric modes are found unstable and likely destabilized by baroclinic instabilities. Similarly, some non-axisymmetric modes that meet a critical layer (or corotati...
Zonal flow regimes in rotating anelastic spherical shells (Invited)
Gastine, T.; Wicht, J.; Aurnou, J. M.; Heimpel, M. H.
2013-12-01
The surface zonal winds observed in the giant planets form a complex jet pattern with alternating prograde and retrograde direction. While the main equatorial band is prograde on the gas giants, both ice giants have a pronounced retrograde equatorial jet. The depth of these jets is however poorly known and highly debated. Theoretical scenarios range from "shallow models", that assume that these zonal flows are restricted to the outer stably stratified layer; to "deep models" that hypothesise that the surface winds are the signature of deep-seated convection. Most of the numerical models supporting the latter idea employed the Boussinesq approximation where compressibility effects are ignored. While this approximation is suitable for modelling the liquid iron core of terrestrial planets, this becomes questionable in the gas giants interiors, where density increases by several orders of magnitude. To tackle this problem, several numerical models using the "anelastic approximation" have been recently developed to study the compressibility effects while filtering out the fast acoustic waves. Here, we consider such anelastic models of rapidly-rotating spherical shells to explore the properties of the zonal winds in different regimes where either rotation or buoyancy dominates the force balance. We conduct several parameter studies to quantify the dependence of zonal flows on the background density stratification and the driving of convection. We find that the direction of the equatorial wind is controlled by the ratio of buoyancy and Coriolis force. The prograde equatorial band maintained by Reynolds stresses is found in the rotation-dominated regime. At low Ekman numbers, several alternating jets form at high latitude in a similar way to some previous Boussinesq calculations. In cases where buoyancy dominates Coriolis force, the angular momentum per unit mass is homogenised and the equatorial band is retrograde, reminiscent to those observed in the ice giants
The effects of rotation on a double-diffusive layer in a rotating spherical shell
Blies, Patrick; Zaussinger, Florian; Hollerbach, Rainer
2014-01-01
So far, numerical studies of double-diffusive layering in turbulent convective flows have neglected the effects of rotation. We undertake a first step into that direction by investigating how Coriolis forces affect a double-diffusive layer inside a rotating spherical shell. For this purpose we have run simulations in a parameter regime where these layers are expected to form and successively increased the rate of rotation with the result that fast rotation is found to have a similar stabilising effect on the overall convective flux as an increase of the stability ratio $R_{\\rho}$ has in a non-rotating setup. We have also studied to what extent the regimes of rotational constraints suggested by King, Stellmach, and Buffett (2013) for rotation in the case of Rayleigh-B\\'enard convection are influenced by double-diffusive convection: their classification could also be applicable to the case of double-diffusive convection in a spherical shell if it is extended to be also a function of the stability ratio $R_{\\rho...
Takehiro, S.; Sasaki, Y.; Hayashi, Y.-Y.; Yamada, M.
2013-12-01
We investigate generation mechanisms of differential rotation and angular momentum transport caused by Boussinesq thermal convection in a rotating spherical shell based on weakly nonlinear numerical calculations for various values of the Prandtl and Ekman numbers under a setup similar to the solar convection layer. When the Prandtl number is of order unity or less and the rotation rate of the system is small (the Ekman number is larger than O(10-2)), the structure of thermal convection is not governed by the Taylor-Proudman theorem; banana-type convection cells emerge which follow the spherical shell boundaries rather than the rotation axis. Due to the Coriolis effect, the velocity field associated with those types of convection cells accompanies the Reynolds stress which transports angular momentum from high-latitudes to the equatorial region horizontally, and equatorial prograde flows are produced. The surface and internal distributions of differential rotation realized in this regime are quite similar to those observed in the Sun with helioseismology. These results may suggest that we should apply larger values of the eddy diffusivities than those believed so far when we use a low resolution numerical model for thermal convection in the solar interior.
Solar Multi-Scale Convection and Rotation Gradients Studied in Shallow Spherical Shells
De Rosa, M L; Toomre, J
2002-01-01
The differential rotation of the sun, as deduced from helioseismology, exhibits a prominent radial shear layer near the top of the convection zone wherein negative radial gradients of angular velocity are evident in the low- and mid-latitude regions spanning the outer 5% of the solar radius. Supergranulation and related scales of turbulent convection are likely to play a significant role in the maintenance of such radial gradients, and may influence dynamics on a global scale in ways that are not yet understood. To investigate such dynamics, we have constructed a series of three-dimensional numerical simulations of turbulent compressible convection within spherical shells, dealing with shallow domains to make such modeling computationally tractable. These simulations are the first models of solar convection in a spherical geometry that can explicitly resolve both the largest dynamical scales of the system (of order the solar radius) as well as smaller-scale convective overturning motions comparable in size to...
Wang, Junfeng; Miesch, Mark S
2015-01-01
We present a novel and powerful Compressible High-ORder Unstructured Spectral-difference (CHORUS) code for simulating thermal convection and related fluid dynamics in the interiors of stars and planets. The computational geometries are treated as rotating spherical shells filled with stratified gas. The hydrodynamic equations are discretized by a robust and efficient high-order Spectral Difference Method (SDM) on unstructured meshes. The computational stencil of the spectral difference method is compact and advantageous for parallel processing. CHORUS demonstrates excellent parallel performance for all test cases reported in this paper, scaling up to 12,000 cores on the Yellowstone High-Performance Computing cluster at NCAR. The code is verified by defining two benchmark cases for global convection in Jupiter and the Sun. CHORUS results are compared with results from the ASH code and good agreement is found. The CHORUS code creates new opportunities for simulating such varied phenomena as multi-scale solar co...
On the effect of laterally varying boundary heat flux on rapidly rotating spherical shell convection
Sahoo, Swarandeep; Sreenivasan, Binod
2017-08-01
The onset of convection in a rotating spherical shell subject to laterally varying heat flux at the outer boundary is considered in this paper. The focus is on the geophysically relevant regime of rapid rotation (low Ekman number) where the natural length scale of convection is significantly smaller than the length scale imposed by the boundary heat flux pattern. Contrary to earlier studies at a higher Ekman number, we find a substantial reduction in the onset Rayleigh number Rac with increasing lateral variation. The decrease in Rac is shown to be closely correlated to the equatorial heat flux surplus in the steady, basic state solution. The consistency of such a correlation makes the estimation of Rac possible without solving the full stability problem. The steady baroclinic flow has a strong cyclone-anticyclone asymmetry in the kinetic helicity only for equatorially symmetric lateral variations, with possible implications for dynamo action. Equatorially antisymmetric variations, on the other hand, break the symmetry of the mean flow, in turn negating its helicity. Analysis of the perturbation solution reveals strongly localized clusters through which convection rolls drift in and out at a frequency higher than that for the reference case with homogeneous boundary heat flux. Large lateral variations produce a marked decrease in the azimuthal length scale of columns, which indicates that small-scale motions are essential to the transport of heat in rapidly rotating, localized convection. With an equatorially antisymmetric heat flux pattern, convection in individual clusters goes through an asynchronous wax-wane cycle whose frequency is much lower than the drift rate of the columns. These continual variations in convection intensity may in turn result in fluctuations in the magnetic field intensity, an effect that needs to be considered in dynamo models. Finally, there is a notable analogy between the role of a laterally varying boundary heat flux and the role of a
Heimpel, Moritz; Aurnou, Jonathan
2007-04-01
The origin of zonal jets on the jovian planets has long been a topic of scientific debate. In this paper we show that deep convection in a spherical shell can generate zonal flow comparable to that observed on Jupiter and Saturn, including a broad prograde equatorial jet and multiple alternating jets at higher latitudes. We present fully turbulent, 3D spherical numerical simulations of rapidly rotating convection with different spherical shell geometries. The resulting global flow fields tend to be segregated into three regions (north, equatorial, and south), bounded by the tangent cylinder that circumscribes the inner boundary equator. In all of our simulations a strong prograde equatorial jet forms outside the tangent cylinder, whereas multiple jets form in the northern and southern hemispheres, inside the tangent cylinder. The jet scaling of our numerical models and of Jupiter and Saturn is consistent with the theory of geostrophic turbulence, which we extend to include the effect of spherical shell geometry. Zonal flow in a spherical shell is distinguished from that in a full sphere or a shallow layer by the effect of the tangent cylinder, which marks a reversal in the sign of the planetary β-parameter and a jump in the Rhines length. This jump is manifest in the numerical simulations as a sharp equatorward increase in jet widths—a transition that is also observed on Jupiter and Saturn. The location of this transition gives an estimate of the depth of zonal flow, which seems to be consistent with current models of the jovian and saturnian interiors.
The influence of the magnetic field on the heat transfer rate in rotating spherical shells
Cabello, Ares; Avila, Ruben
2016-11-01
Studies of the relationship between natural convection and magnetic field generation in spherical annular geometries with rotation are essential to understand the internal dynamics of the terrestrial planets. In such studies it is important to calculate and analyze the heat transfer rate at the inner and the outer spheres that confine the spherical gap. Previous investigations indicate that the magnetic field has a stabilizing effect on the onset of the natural convection, reduces the intensity of convection and modifies the flow patterns. However so far it is still unclear how the magnetic field change the heat transfer rate behaviour. We investigate the heat transfer rate (Nu) in a rotating spherical gap with a self gravity field varying linearly with radius, and its relation with the intensity of the magnetic field induced by the geodynamo effect. The Boussinesq fluid equations are solved by using a spectral element method (SEM). To avoid the singularity at the poles, the cubed-sphere algorithm is used to generate the spherical mesh. Several cases are simulated in which the Rayleigh number, the magnetic Reynolds number and the Taylor number are the variable parameters. The flow patterns, the temperature distribution and the Nusselt numbers at both spheres are calculated. Special thanks to DGAPA-UNAM Project PAPIIT IN11731, sponsor of this investigation.
Lee, M. C.; Kendall, J. M., Jr.; Bahrami, P. A.; Wang, T. G.
1986-01-01
Fluid-dynamic and capillary forces can be used to form nearly perfect, very small spherical shells when a liquid that can solidify is passed through an annular die to form an annular jet. Gravity and certain properties of even the most ideal materials, however, can cause slight asymmetries. The primary objective of the present work is the control of this shell formation process in earth laboratories rather than space microgravity, through the development of facilities and methods that minimize the deleterious effects of gravity, aerodynamic drag, and uncontrolled cooling. The spherical shells thus produced can be used in insulation, recyclable filter materials, fire retardants, explosives, heat transport slurries, shock-absorbing armor, and solid rocket motors.
Effects of rotation on crystal settling in a terrestrial magma ocean: Spherical shell model
Maas, C.; Hansen, U.
2015-12-01
Like Moon or Mars, Earth experienced one or several deep magma ocean periods of globalextent in a later stage of its accretion. The crystallization of these magma oceans is of keyimportance for the chemical structure of Earth, the mantle evolution and the onset of platetectonics. Due to the fast rotation of early Earth and the small magma viscosity, rotationprobably had a profound effect on differentiation processes. For example, Matyska et al.[1994] propose that the distribution of heterogeneities like the two large low shear velocityprovinces (LLSVP) at the core mantle boundary is influenced by rotational dynamicsof early Earth. Further Garnero and McNamara [2008] suggest that the LLSVPs arevery long-living anomalies, probably reaching back to the time of differentiation andsolidification of Earth. However, nearly all previous studies neglect the effects of rotation.In our previous work using a Cartesian model, a strong influence of rotation as well asof latitude on the differentiation processes in an early magma ocean was revealed. Weshowed that crystal settling in an early stage of magma ocean crystallization cruciallydepends on latitude as well as on rotational strength and crystal density.In order to overcome the restrictions as to the geometry of the Cartesian model, we arecurrently developing a spherical model to simulate crystal settling in a rotating sphericalshell. This model will allow us not only to investigate crystal settling at the poles andthe equator, but also at latitudes in-between these regions, as well as the migration ofcrystals between poles and equator. ReferencesE. J. Garnero and A. K. McNamara. Structure and dynamics of earth's lower mantle.Science, 320(5876):626-628, 2008.C. Matyska, J. Moser, and D. A. Yuen. The potential influence of radiative heat transferon the formation of megaplumes in the lower mantle. Earth and Planetary ScienceLetters, 125(1):255-266, 1994.
Yadav, Rakesh K; Christensen, Ulrich R; Duarte, Lucia; Reiners, Ansgar
2015-01-01
We study rotating thermal convection in spherical shells as prototype for flow in the cores of terrestrial planets, gas planets or in stars. We base our analysis on a set of about 450 direct numerical simulations of the (magneto)hydrodynamic equations under the Boussinesq approximation. The Ekman number ranges from $10^{-3}$ to $10^{-6}$. Four sets of simulations are considered: non-magnetic simulations and dynamo simulations with either free-slip or no-slip flow boundary conditions. The non-magnetic setup with free-slip boundaries generates the strongest zonal flows. Both non-magnetic simulations with no-slip flow boundary conditions and self-consistent dynamos with free-slip boundaries have drastically reduced zonal-flows. Suppression of shear leads to a substantial gain in heat-transfer efficiency, increasing by a factor of 3 in some cases. Such efficiency enhancement occurs as long as the convection is significantly influenced by rotation. At higher convective driving the heat-transfer efficiency trends t...
Solar Multi-Scale Convection and Rotation Gradients Studied in Shallow Spherical Shells
2002-01-01
The differential rotation of the sun, as deduced from helioseismology, exhibits a prominent radial shear layer near the top of the convection zone wherein negative radial gradients of angular velocity are evident in the low- and mid-latitude regions spanning the outer 5% of the solar radius. Supergranulation and related scales of turbulent convection are likely to play a significant role in the maintenance of such radial gradients, and may influence dynamics on a global scale in ways that are...
Ibragimov, Ranis N.
2016-12-01
The nonlinear Euler equations are used to model two-dimensional atmosphere dynamics in a thin rotating spherical shell. The energy balance is deduced on the basis of two classes of functorially independent invariant solutions associated with the model. It it shown that the energy balance is exactly the conservation law for one class of the solutions whereas the second class of invariant solutions provides and asymptotic convergence of the energy balance to the conservation law.
Automated Shell Theory for Rotating Structures (ASTROS)
Foster, B. J.; Thomas, J. M.
1973-01-01
Computer program can be used to analyze any disk or shell of revolution of arbitrary cross section under inertial loads caused by rotation about shell axis and under various static loads, including thermal gradients. Geometric shapes incorporated in program are ellipsoidal, spherical, ogival, toroidal, conical, circular plate, cylindrical, and parabolic.
Statistical mechanics of thin spherical shells
Kosmrlj, Andrej
2016-01-01
We explore how thermal fluctuations affect the mechanics of thin amorphous spherical shells. In flat membranes with a shear modulus, thermal fluctuations increase the bending rigidity and reduce the in-plane elastic moduli in a scale-dependent fashion. This is still true for spherical shells. However, the additional coupling between the shell curvature, the local in-plane stretching modes and the local out-of-plane undulations, leads to novel phenomena. In spherical shells thermal fluctuations produce a radius-dependent negative effective surface tension, equivalent to applying an inward external pressure. By adapting renormalization group calculations to allow for a spherical background curvature, we show that while small spherical shells are stable, sufficiently large shells are crushed by this thermally generated "pressure". Such shells can be stabilized by an outward osmotic pressure, but the effective shell size grows non-linearly with increasing outward pressure, with the same universal power law expone...
Symmetries and deformations in the spherical shell model
Van Isacker, P.; Pittel, S.
2016-02-01
We discuss symmetries of the spherical shell model that make contact with the geometric collective model of Bohr and Mottelson. The most celebrated symmetry of this kind is SU(3), which is the basis of Elliott’s model of rotation. It corresponds to a deformed mean field induced by a quadrupole interaction in a single major oscillator shell N and can be generalized to include several major shells. As such, Elliott’s SU(3) model establishes the link between the spherical shell model and the (quadrupole component of the) geometric collective model. We introduce the analogue symmetry induced by an octupole interaction in two major oscillator shells N-1 and N, leading to an octupole-deformed solution of the spherical shell model. We show that in the limit of large oscillator shells, N\\to ∞ , the algebraic octupole interaction tends to that of the geometric collective model.
Ibragimov, Nail H. [Department of Mathematics and Science, Blekinge Institute of Technology, SE-371 79 Karlskrona (Sweden); Ibragimov, Ranis N., E-mail: Ranis.Ibragimov@utb.edu [Department of Mathematics, College of Science, Mathematics and Technology, University of Texas at Brownsville, TX 78520 (United States)
2011-10-24
We study the nonlinear incompressible non-viscous fluid flows within a thin rotating atmospheric shell that serve as a simple mathematical description of an atmospheric circulation caused by the temperature difference between the equator and the poles. The model is also superimposed by a particular stationary flow which, under the assumption of no friction and a distribution of temperature dependent only upon latitude, models the zonal west-to-east flows in the upper atmosphere between the Ferrel and Polar cells. Owing to the Coriolis effects, the resulting achievable meteorological flows correspond to the asymptotical stable flows that are being translated along the equatorial plane. The exact solutions in terms of elementary functions are found by using Lie group methods. -- Highlights: → This article provides new exact solutions of the Euler and Navier-Stokes equations. → The exact solutions are written in terms of elementary functions. → The exact solutions were obtained by Lie group analysis. → A wider class of exact solutions is contained in the obtained Lie algebra.
Spherical wave rotation in spherical near-field antenna measurements
Wu, Jian; Larsen, Flemming Holm; Lemanczyk, J.
1991-01-01
The rotation of spherical waves in spherical near-field antenna measurement is discussed. Considering the many difficult but interesting features of the rotation coefficients, an efficient rotation scheme is derived. The main feature of the proposed scheme is to ignore the calculation of the very...
Statistical Mechanics of Thin Spherical Shells
Košmrlj, Andrej; Nelson, David R.
2017-01-01
We explore how thermal fluctuations affect the mechanics of thin amorphous spherical shells. In flat membranes with a shear modulus, thermal fluctuations increase the bending rigidity and reduce the in-plane elastic moduli in a scale-dependent fashion. This is still true for spherical shells. However, the additional coupling between the shell curvature, the local in-plane stretching modes, and the local out-of-plane undulations leads to novel phenomena. In spherical shells, thermal fluctuations produce a radius-dependent negative effective surface tension, equivalent to applying an inward external pressure. By adapting renormalization group calculations to allow for a spherical background curvature, we show that while small spherical shells are stable, sufficiently large shells are crushed by this thermally generated "pressure." Such shells can be stabilized by an outward osmotic pressure, but the effective shell size grows nonlinearly with increasing outward pressure, with the same universal power-law exponent that characterizes the response of fluctuating flat membranes to a uniform tension.
Collapsing spherical null shells in general relativity
S Khakshournia
2011-03-01
Full Text Available In this work, the gravitational collapse of a spherically symmetric null shell with the flat interior and a charged Vaidya exterior spacetimes is studied. There is no gravitational impulsive wave present on the null hypersurface which is shear-free and contracting. It follows that there is a critical radius at which the shell bounces and starts expanding.
Flow past a porous approximate spherical shell
Srinivasacharya, D.
2007-07-01
In this paper, the creeping flow of an incompressible viscous liquid past a porous approximate spherical shell is considered. The flow in the free fluid region outside the shell and in the cavity region of the shell is governed by the Navier Stokes equation. The flow within the porous annulus region of the shell is governed by Darcy’s Law. The boundary conditions used at the interface are continuity of the normal velocity, continuity of the pressure and Beavers and Joseph slip condition. An exact solution for the problem is obtained. An expression for the drag on the porous approximate spherical shell is obtained. The drag experienced by the shell is evaluated numerically for several values of the parameters governing the flow.
Azimuthal dynamo wave in spherical shell convection
Cole, Elizabeth; Mantere, Maarit J; Brandenburg, Axel
2013-01-01
We report the finding of an azimuthal dynamo wave of a low-order (m=1) mode in direct numerical simulations (DNS) of turbulent convection in spherical shells. Such waves are predicted by mean field dynamo theory and have been obtained previously in mean-field models. Observational results both from photometry and Doppler imaging have revealed persistent drifts of spots for several rapidly rotating stars, but, although an azimuthal dynamo wave has been proposed as a possible mechanism responsible for this behavior, it has been judged as unlikely, as practical evidence for such waves from DNS has been lacking. The large-scale magnetic field in our DNS, which is due to self-consistent dynamo action, is dominated by a retrograde m=1 mode. Its pattern speed is nearly independent of latitude and does not reflect the speed of the differential rotation at any depth. The extrema of magnetic m=1 structures coincide reasonably with the maxima of m=2 structures of the temperature. These results provide direct support for...
Ovgun, A.
2016-11-01
We construct a rotating thin-shell wormhole using a Myers-Perry black hole in five dimensions, using the Darmois-Israel junction conditions. The stability of the wormhole is analyzed under perturbations. We find that exotic matter is required at the throat of the wormhole to keep it stable. Our analysis shows that stability of the rotating thin-shell wormhole is possible if suitable parameter values are chosen.
Ovgun, A
2016-01-01
In this article, we construct rotating thin shell wormhole using a Myers-Perry black hole in five dimensions. The stability of the wormhole is analyzed under perturbations follows from the Darmois-Israel junction conditions. We find that it required exotic matter at the throat to keep throat of wormhole stable. Our analysis shows that the stability of the rotating thin-shell wormhole is available with choosing suitable values of parameters.
A static spherically symmetric thin shell wormhole colliding with a spherical thin shell
Gao, Sijie
2015-01-01
We consider a static spherically symmetric thin shell wormhole collides with another thin shell consisting of ordinary matter. By employing the geometrical constraint, which leads to the conservation of energy and momentum, we show that the state after the collision can be solved from the initial data. In the low speed approximation, the solutions are rather simple. The shell may either bounce back or pass through the wormhole. In either case, the wormhole shrinks right after the collision. In the ``bouncing'' case, a surprising result is that the radial speeds before and after the collision satisfy an addition law, which is independent of the masses of the wormhole and the shell. Once the shell passes through the wormhole, we find that the shell always expands. However, the expansion rate is the same as its collapsing rate right before the collision. Finally, we find out the solution for the shell moving together with the wormhole.
PENETRATION OF A SOUND FIELD THROUGH A MULTILAYERED SPHERICAL SHELL
G. Ch. Shushkevich
2013-01-01
Full Text Available An analytical solution of the boundary problem describing the process of penetration of thesound field of a spherical emitter located inside a thin unclosed spherical shell through a permeable multilayered spherical shell is considered. The influence of some parameters of the problem on the value of the sound field weakening (screening coefficient is studied via a numerical simulation.
Vibrations of moderately thick shallow spherical shells at large amplitudes
Sathyamoorthy, M.
1994-04-01
A shallow shell theory is presented for the geometrically nonlinear analysis of moderately thick isotropic spherical shells. Effects of transverse shear deformation and rotatory inertia are included in the governing equations of motion by means of tracing constants. When these effects are ignored, the governing equations readily reduce to those applicable for thin shallow spherical shells. Solutions to the system of thick shell equations are obtained by means of Galerkin's method and the numerical Runge-Kutta procedure. Numerical results are presented for certain cases of shallow spherical shells considering different geometric shell parameters. Transverse shear and rotatory inertia effects are found to be important in linear as well as nonlinear responses of shallow spherical shells. The nonlinear frequency-amplitude behavior is of the softening type for shallow spherical shells and of the hardening type for circular plates. Frequency ratios are lower at any given amplitude when the effects of transverse shear and rotatory inertia are included in the analysis.
Parametric resonance in spherical immersed elastic shells
Ko, William
2014-01-01
We perform a stability analysis for a fluid-structure interaction problem in which a spherical elastic shell or membrane is immersed in a 3D viscous, incompressible fluid. The shell is an idealised structure having zero thickness, and has the same fluid lying both inside and outside. The problem is formulated mathematically using the immersed boundary framework in which Dirac delta functions are employed to capture the two-way interaction between fluid and immersed structure. The elastic structure is driven parametrically via a time-periodic modulation of the elastic membrane stiffness. We perform a Floquet stability analysis, considering the case of both a viscous and inviscid fluid, and demonstrate that the forced fluid-membrane system gives rise to parametric resonances in which the solution becomes unbounded even in the presence of viscosity. The analytical results are validated using numerical simulations with a 3D immersed boundary code for a range of wavenumbers and physical parameter values. Finally, ...
Convective dynamo action in a spherical shell: symmetries and modulation
Raynaud, Raphaël
2016-01-01
We consider dynamo action driven by three-dimensional rotating anelastic convection in a spherical shell. Motivated by the behaviour of the solar dynamo, we examine the interaction of hydromagnetic modes with different symmetries and demonstrate how complicated interactions between convection, differential rotation and magnetic fields may lead to modulation of the basic cycle. For some parameters, Type 1 modulation occurs by the transfer of energy between modes of different symmetries with little change in the overall amplitude, for other parameters, the modulation is of Type 2, where the amplitude is significantly affected (leading to grand minima in activity) without significant changes in symmetry. Most importantly, we identify the presence of "supermodulation" in the solutions, where the activity switches chaotically between Type 1 and Type 2 modulation, this is believed to be an important process in solar activity.
PERFORATION OF PLASTIC SPHERICAL SHELLS UNDER IMPACT BY CYLINDRICAL PROJECTILES
NING Jian-guo; SONG Wei-dong
2006-01-01
The objective is to study the perforation of a plastic spherical shell impacted by a cylindrical projectile. First, the deformation modes of the shell were given by introducing an isometric transformation. Then, the perforation mechanism of the shell was analyzed and an analytical model was advanced. Based on Hamilton principle, the governing equation was obtained and solved using Runge-Kuta method. Finally, some important theoretical predictions were given to describe the perforation mechanism of the shell. The results will play an important role in understanding the perforation mechanism of spherical shells impacted by a projectile.
Inertial wave and zonal flow in librating spherical shells
Lin, Yufeng; Calkin, Michael A
2014-01-01
We numerically study the inertial waves and zonal flows in spherical shells driven by longitudinal libration, an oscillatory variation of rotation rate. Internal shear layers are generated due to breakdown of the Ekman boundary layer at critical latitudes. Our numerical results validate the scaling laws of internal shear layers predicted by previous studies. Mean zonal flows are driven by the non-linear interaction in the boundary layers. Non-linear interaction of inertial waves in the interior fluids has no significant contribution to the zonal flow. Multiple geostrophic shear layers are generated due to non-linearities in the boundary layers at critical latitudes and reflection points of internal shear layers. We also investigate the scaling laws of geostrophic shear layers and extrapolate the results to the planetary setting.
Newtonian and General Relativistic Models of Spherical Shells
Vogt, D
2009-01-01
A family of spherical shells with varying thickness is derived by using a simple Newtonian potential-density pair. Then, a particular isotropic form of a metric in spherical coordinates is used to construct a General Relativistic version of the Newtonian family of shells. The matter of these relativistic shells presents equal azimuthal and polar pressures, while the radial pressure is a constant times the tangential pressure. We also make a first study of stability of both the Newtonian and relativistic families of shells.
Simulation on the aggregation process of spherical particle confined in a spherical shell
Wang, J.; Xu, J. J.; Zhang, L.
2016-04-01
The aggregation process of spherical particles confined in a spherical shell was studied by using a diffusion-limited cluster-cluster aggregation (DLCA) model. The influence of geometrical confinement and wetting-like properties of the spherical shell walls on the particle concentration profile, aggregate structure and aggregation kinetics had been explored. The results show that there will be either depletion or absorption particles near the shell walls depending on the wall properties. It is observed that there are four different types of density distribution which can be realized by modifying the property of the inner or outer spherical shell wall. In addition, the aggregate structure will become more compact in the confined spherical shell comparing to bulk system with the same particle volume fraction. The analysis on the aggregation kinetics indicates that geometrical confinement will promote the aggregation process by reducing the invalid movement of the small aggregates and by constraining the movement of those large aggregates. Due to the concave geometrical characteristic of the outer wall of the spherical shell, its effects on the aggregating kinetics and the structure of the formed aggregates are more evident than those of the inner wall. This study will provide some instructive information of controlling the density distribution of low-density porous polymer hollow spherical shells and helps to predict gel structures developed in confined geometries.
Dynamics of a Spherical Null Shell within the Distributional Formalism
Khakshournia, Samad; Mansouri, Reza
2004-01-01
Dynamics of a null thin shell immersed in a generic spherically symmetric spacetime is obtained within the distributional formalism. It has been shown that the distributional formalism leads to the same result as in the conventional formalism.
Macaraeg, M. G.
1986-01-01
For a Spacelab flight, a model experiment of the earth's atmospheric circulation has been proposed. This experiment is known as the Atmospheric General Circulation Experiment (AGCE). In the experiment concentric spheres will rotate as a solid body, while a dielectric fluid is confined in a portion of the gap between the spheres. A zero gravity environment will be required in the context of the simulation of the gravitational body force on the atmosphere. The present study is concerned with the development of pseudospectral/finite difference (PS/FD) model and its subsequent application to physical cases relevant to the AGCE. The model is based on a hybrid scheme involving a pseudospectral latitudinal formulation, and finite difference radial and time discretization. The advantages of the use of the hybrid PS/FD method compared to a pure second-order accurate finite difference (FD) method are discussed, taking into account the higher accuracy and efficiency of the PS/FD method.
Libration-induced mean flow in a spherical shell
Sauret, Alban
2013-01-01
We investigate the flow in a spherical shell subject to a time harmonic oscillation of its rotation rate, also called longitudinal libration, when the oscillation frequency is larger than twice the mean rotation rate. In this frequency regime, no inertial waves are directly excited by harmonic forcing. We show however that it can generate through non-linear interactions in the Ekman layers a strong mean zonal flow in the interior. An analytical theory is developed using a perturbative approach in the limit of small libration amplitude $\\epsilon$ and small Ekman number $E$. The mean flow is found to be at leading order an azimuthal flow which scales as the square of the libration amplitude and only depends on the cylindrical-radius coordinate. The mean flow also exhibits a discontinuity across the cylinder tangent to the inner sphere. We show that this discontinuity can be smoothed through multi-scale Stewartson layers. The mean flow is also found to possess a weak axial flow which scales as $O(\\epsilon^2 E^{5...
Vibration and Acoustic Radiation from Submerged Spherical Double-Shell
陈军明; 黄玉盈; 陈应波
2003-01-01
Based on the motion differential equations of vibration and acoustic coupling system for a thin elastic spherical double-shell with several elastic plates attached to the shells, in which Dirac-δ functions are employed to introduce the forces and moments applied by the attachments, and by means of expanding field quantities as the Legendre series, a semi-analytic solution is derived for the solution to the vibration and acoustic radiation from a submerged spherical double-shell. This solution has a satisfying computational effectiveness and precision for arbitrary frequency range excitation. It is concluded that the internal plates attached to shells can change significantly the mechanical and acoustical characteristics of shells, and make the coupling system have a very rich resonance frequency spectrum. Moreover, the present method can be used to study the acoustic radiation mechanism of the type of structure.
Casimir energy for spherical shell in Schwarzchild black hole background
Setare, M R
2004-01-01
In this paper, we consider the Casimir energy of massless scalar field which satisfy Dirichlet boundary condition on a spherical shell. Outside the shell, the spacetime is assumed to be described by the Schwarzschild metric, while inside the shell it is taken to be the flat Minkowski space. Using zeta function regularization and heat kernel coefficients we isolate the divergent contributions of the Casimir energy inside and outside the shell, then using the renormalization procedure of the bag model the divergent parts are cancelled, finally obtaining a renormalized expression for the total Casimir energy.
The shell model—simplicity from complexity: some of my best nuclei are spherical
Talmi, Igal
2017-08-01
This article presents shell model applications to spherical nuclei with strong emphasis on semi-magic ones. A successful description of their low lying levels is obtained by applying to them the spherical shell model. These spherical nuclei are rather different from nuclei which exhibit collective phenomena, like rotational spectra. In the present article, several applications of the shell model to nuclei are presented. Only simple cases are considered which do not involve complicated calculations. These cases are sufficient to demonstrate the power of the shell model and to find the important ingredients of the mutual interactions of nucleons. The latter are limited to two-body interactions and it seems that they are the important ones in determination of the structure of nuclei. The interaction which should be used in the shell model (effective interaction) is a highly renormalized version of the bare interaction, between free nucleons. In the absence of a reliable many-body theory of the nucleus, matrix elements of the effective interaction are determined from energies of actual nuclei. General features of these are discussed, with particular attention to matrix elements which lead to nuclear deformation and rotational spectra.
Indentation of pressurized viscoplastic polymer spherical shells
Tvergaard, Viggo; Needleman, A.
2016-01-01
with a conical indenter. The response is analyzed for various values of the shell thickness to radius ratio and various values of the internal pressure. Two sets of material parameters are considered: one set having network stiffening at a moderate strain and the other having no network stiffening until very...
Snap-Through Buckling Problem of Spherical Shell Structure
Sumirin Sumirin
2014-12-01
Full Text Available This paper presents results of a numerical study on the nonlinear behavior of shells undergoing snap-through instability. This research investigates the problem of snap-through buckling of spherical shells applying nonlinear finite element analysis utilizing ANSYS Program. The shell structure was modeled by axisymmetric thin shell of finite elements. Shells undergoing snap-through buckling meet with significant geometric change of their physical configuration, i.e. enduring large deflections during their deformation process. Therefore snap-through buckling of shells basically is a nonlinear problem. Nonlinear numerical operations need to be applied in their analysis. The problem was solved by a scheme of incremental iterative procedures applying Newton-Raphson method in combination with the known line search as well as the arc- length methods. The effects of thickness and depth variation of the shell is taken care of by considering their geometrical parameter l. The results of this study reveal that spherical shell structures subjected to pressure loading experience snap-through instability for values of l≥2.15. A form of ‘turn-back’ of the load-displacement curve took place at load levels prior to the achievement of the critical point. This phenomenon was observed for values of l=5.0 to l=7.0.
Reynolds stress and heat flux in spherical shell convection
Käpylä, P J; Guerrero, G; Brandenburg, A; Chatterjee, P
2010-01-01
Context. Turbulent fluxes of angular momentum and heat due to rotationally affected convection play a key role in determining differential rotation of stars. Aims. We compute turbulent angular momentum and heat transport as functions of the rotation rate from stratified convection. We compare results from spherical and Cartesian models in the same parameter regime in order to study whether restricted geometry introduces artefacts into the results. Methods. We employ direct numerical simulations of turbulent convection in spherical and Cartesian geometries. In order to alleviate the computational cost in the spherical runs and to reach as high spatial resolution as possible, we model only parts of the latitude and longitude. The rotational influence, measured by the Coriolis number or inverse Rossby number, is varied from zero to roughly seven, which is the regime that is likely to be realised in the solar convection zone. Cartesian simulations are performed in overlapping parameter regimes. Results. For slow ...
Reynolds stress and heat flux in spherical shell convection
Käpylä, P. J.; Mantere, M. J.; Guerrero, G.; Brandenburg, A.; Chatterjee, P.
2011-07-01
Context. Turbulent fluxes of angular momentum and enthalpy or heat due to rotationally affected convection play a key role in determining differential rotation of stars. Their dependence on latitude and depth has been determined in the past from convection simulations in Cartesian or spherical simulations. Here we perform a systematic comparison between the two geometries as a function of the rotation rate. Aims: Here we want to extend the earlier studies by using spherical wedges to obtain turbulent angular momentum and heat transport as functions of the rotation rate from stratified convection. We compare results from spherical and Cartesian models in the same parameter regime in order to study whether restricted geometry introduces artefacts into the results. In particular, we want to clarify whether the sharp equatorial profile of the horizontal Reynolds stress found in earlier Cartesian models is also reproduced in spherical geometry. Methods: We employ direct numerical simulations of turbulent convection in spherical and Cartesian geometries. In order to alleviate the computational cost in the spherical runs, and to reach as high spatial resolution as possible, we model only parts of the latitude and longitude. The rotational influence, measured by the Coriolis number or inverse Rossby number, is varied from zero to roughly seven, which is the regime that is likely to be realised in the solar convection zone. Cartesian simulations are performed in overlapping parameter regimes. Results: For slow rotation we find that the radial and latitudinal turbulent angular momentum fluxes are directed inward and equatorward, respectively. In the rapid rotation regime the radial flux changes sign in accordance with earlier numerical results, but in contradiction with theory. The latitudinal flux remains mostly equatorward and develops a maximum close to the equator. In Cartesian simulations this peak can be explained by the strong "banana cells". Their effect in the
Axisymmetric bifurcations of thick spherical shells under inflation and compression
deBotton, G.
2013-01-01
Incremental equilibrium equations and corresponding boundary conditions for an isotropic, hyperelastic and incompressible material are summarized and then specialized to a form suitable for the analysis of a spherical shell subject to an internal or an external pressure. A thick-walled spherical shell during inflation is analyzed using four different material models. Specifically, one and two terms in the Ogden energy formulation, the Gent model and an I1 formulation recently proposed by Lopez-Pamies. We investigate the existence of local pressure maxima and minima and the dependence of the corresponding stretches on the material model and on shell thickness. These results are then used to investigate axisymmetric bifurcations of the inflated shell. The analysis is extended to determine the behavior of a thick-walled spherical shell subject to an external pressure. We find that the results of the two terms Ogden formulation, the Gent and the Lopez-Pamies models are very similar, for the one term Ogden material we identify additional critical stretches, which have not been reported in the literature before.© 2012 Published by Elsevier Ltd.
Shell model for warm rotating nuclei
Matsuo, M.; Yoshida, K. [Kyoto Univ. (Japan); Dossing, T. [Univ. of Copenhagen (Denmark)] [and others
1996-12-31
Utilizing a shell model which combines the cranked Nilsson mean-field and the residual surface and volume delta two-body forces, the authors discuss the onset of rotational damping in normal- and super-deformed nuclei. Calculation for a typical normal deformed nucleus {sup 168}Yb indicates that the rotational damping sets in at around 0.8 MeV above the yrast line, and about 30 rotational bands of various length exists at a given rotational frequency, in overall agreement with experimental findings. It is predicted that the onset of rotational damping changes significantly in different superdeformed nuclei due to the variety of the shell gaps and single-particle orbits associated with the superdeformed mean-field.
Photostrictive actuators for photonic control of shallow spherical shells
Shih, Hui-Ru; Tzou, Horn-Sen
2007-10-01
Photostrictive materials, exhibiting light-induced strain, are of interest for the future generation of wireless remote control photo-actuators. Photostrictive actuators are expected to be used as the driving component in optically controlled flexible structures. In this paper, the photonic control of flexible spherical shells using discrete photostrictive actuators is investigated. This paper presents a coupled opto-piezothermoelastic shell theory that incorporates photovoltaic, pyroelectric and piezoelectric effects, and has the capability to predict the response of a spherical shell driven by the photostrictive actuators. In this study, the effects of actuator location as well as membrane and bending components on the control action have been analyzed. The results obtained indicate that the control forces are mode and location dependent. Analysis also shows that the membrane control action is much more significant than the bending control action.
A Reduction Factor for Buckling Load of Spherical Cap Shells
P.N. Khakina
2011-12-01
Full Text Available The classical buckling theory usually overestimates the buckling load of shells. In this study, a reduction factor is determined using geometrical parameters so as to reduce the classical buckling load to a more realistic value based on the post-buckling load. It is observed that the buckling load is directly proportional to the thickness and rise and inversely proportional to the span of the spherical cap. Finite element modeling and simulation using ABAQUS was conducted to determine the buckling behavior of a spherical cap shell subjected to different initial geometrical imperfections. The load-deflection curves drawn from the simulation formed a plateau at the post-buckling load. It is observed that as the initial geometrical imperfection is increased, the value of the initial buckling load is almost the same as the value of the post-buckling load on the plateau. The results obtained from different shells were used to derive a formula for the reduction factor.
Steady rotation of a composite sphere in a concentric spherical cavity
D. Srinivasacharya; M. Krishna Prasad
2012-01-01
The problem of steady rotation of a composite sphere located at the centre of a spherical container has been investigated.A composite particle referred to in this paper is a spherical solid core covered with a permeable spherical shell.The Brinkman's model for the flow inside the composite sphere and the Stokes equation for the flow in the spherical container were used to study the motion.The torque experienced by the porous spherical particle in the presence of cavity is obtained.The wall correction factor is calculated.In the limiting cases,the analytical solution describing the torque for a porous sphere and for a solid sphere in an unbounded medium are obtained from the present analysis.
The covariant electromagnetic Casimir effect for real conducting spherical shells
Razmi, H
2016-01-01
Using the covariant electromagnetic Casimir effect (previously introduced for real conducting cylindrical shells [1]), the Casimir force experienced by a spherical shell, under Dirichlet boundary condition, is calculated. The renormalization procedure is based on the plasma cut-off frequency for real conductors. The real case of a gold (silver) sphere is considered and the corresponding electromagnetic Casimir force is computed. In the covariant approach, there isn't any decomposition of fields to TE and TM modes; thus, we do not need to consider the Neumann boundary condition in parallel to the Dirichlet problem and then add their corresponding results.
Rotating blade vibration analysis using shells
Leissa, A. W.; Lee, J. K.; Wang, A. J.
1981-01-01
Shallow shell theory and the Ritz method are employed to determine the frequencies and mode shapes of turbomachinery blades having both camber and twist, rotating with non-zero angles of attack. Frequencies obtained for different degrees of shallowness and thickness are compared with results available in the literature, obtained from finite element analyses of nonrotating blades. Frequencies are also determined for a rotating blade, showing the effects of changing the (1) angular velocity of rotation, (2) disk radius and (3) angle of attack, as well as the significance of the most important body force terms.
Orthotropic rotation-free thin shell elements
Munglani, Gautam; Wittel, Falk K; Herrmann, Hans J
2015-01-01
A method to simulate orthotropic behaviour in thin shell finite elements is proposed. The approach is based on the transformation of shape function derivatives, resulting in a new orthogonal basis aligned to a specified preferred direction for all elements. This transformation is carried out solely in the undeformed state leaving minimal additional impact on the computational effort expended to simulate orthotropic materials compared to isotropic, resulting in a straightforward and highly efficient implementation. This method is implemented for rotation-free triangular shells using the finite element framework built on the Kirchhoff--Love theory employing subdivision surfaces. The accuracy of this approach is demonstrated using the deformation of a pinched hemispherical shell (with a 18{\\deg} hole) standard benchmark. To showcase the efficiency of this implementation, the wrinkling of orthotropic sheets under shear displacement is analyzed. It is found that orthotropic subdivision shells are able to capture t...
The secondary buckling transition: wrinkling of buckled spherical shells.
Knoche, Sebastian; Kierfeld, Jan
2014-07-01
We theoretically explain the complete sequence of shapes of deflated spherical shells. Decreasing the volume, the shell remains spherical initially, then undergoes the classical buckling instability, where an axisymmetric dimple appears, and, finally, loses its axisymmetry by wrinkles developing in the vicinity of the dimple edge in a secondary buckling transition. We describe the first axisymmetric buckling transition by numerical integration of the complete set of shape equations and an approximate analytic model due to Pogorelov. In the buckled shape, both approaches exhibit a locally compressive hoop stress in a region where experiments and simulations show the development of polygonal wrinkles, along the dimple edge. In a simplified model based on the stability equations of shallow shells, a critical value for the compressive hoop stress is derived, for which the compressed circumferential fibres will buckle out of their circular shape in order to release the compression. By applying this wrinkling criterion to the solutions of the axisymmetric models, we can calculate the critical volume for the secondary buckling transition. Using the Pogorelov approach, we also obtain an analytical expression for the critical volume at the secondary buckling transition: The critical volume difference scales linearly with the bending stiffness, whereas the critical volume reduction at the classical axisymmetric buckling transition scales with the square root of the bending stiffness. These results are confirmed by another stability analysis in the framework of Donnel, Mushtari and Vlasov (DMV) shell theory, and by numerical simulations available in the literature.
Shell Model for Warm Rotating Nuclei
Matsuo, M; Vigezzi, E; Broglia, R A; Yoshida, K
1997-01-01
In order to provide a microscopic description of levels and E2 transitions in rapidly rotating nuclei with internal excitation energy up to a few MeV, use is made of a shell model which combines the cranked Nilsson mean-field and the residual surface delta two-body force. The damping of collective rotational motion is investigated in the case of a typical rare-earth nucleus, namely \\Yb. It is found that rotational damping sets in at around 0.8 MeV above the yrast line, and the levels which form rotational band structures are thus limited. We predict at a given rotational frequency existence of about 30 rotational bands of various lengths, in overall agreement with the experimental findings. The onset of the rotational damping proceeds quite gradually as a function of the internal excitation energy. The transition region extends up to around 2 MeV above yrast and it is characterized by the presence of scars of discrete rotational bands which extend over few spin values and stand out among the damped transition...
Convection-driven spherical shell dynamos at varying Prandtl numbers
Käpylä, P J; Olspert, N; Warnecke, J; Brandenburg, A
2016-01-01
(abidged) Context: Stellar convection zones are characterized by vigorous high-Reynolds number turbulence at low Prandtl numbers. Aims: We study the dynamo and differential rotation regimes at varying levels of viscous, thermal, and magnetic diffusion. Methods: We perform three-dimensional simulations of stratified fully compressible magnetohydrodynamic convection in rotating spherical wedges at various thermal and magnetic Prandtl numbers. Results: We find that the rotation profiles for high thermal diffusivity show a monotonically increasing angular velocity from the bottom of the convection zone to the top and from the poles toward the equator. For sufficiently rapid rotation, a region of negative radial shear develops at mid-latitudes as the thermal diffusivity is decreased. This coincides with a change in the dynamo mode from poleward propagating activity belts to equatorward propagating ones. Furthermore, the cyclic solutions disappear at the highest magnetic Reynolds numbers. The total magnetic energy ...
Static slightly non-spherically symmetric, and slowly rotating linearised vacuum spacetimes
Saw, Vee-Liem
2015-01-01
We apply the general method of constructing manifolds of revolution around a given curve to derive first order perturbations on the Schwarzschild metric. Two different perturbations are carried out separately: 1) Non-rotating 2-spheres are added along a plane curve slightly deviated from the "Schwarzschild line"; 2) Slow-rotating 2-spheres are added along the "Schwarzschild line". For (1), we obtain the first order vacuum solution, representing the exterior region of a static slightly non-spherically symmetric body. No higher order vacuum solution exists. For (2), we find that the first order vacuum solution is equivalent to the slowly rotating Kerr metric. This is hence a much simpler and geometrically insightful derivation as compared to the gravitomagnetic one, where this rotating-shells construction is a direct manifestation of the frame-dragging phenomenon. A (full non-perturbative) generalisation to this method is explored here, by adding rotating 2-ellipsoids. It turns out however, that this cannot pro...
Turbulent dynamos in spherical shell segments of varying geometrical extent
Mitra, Dhrubaditya; Brandenburg, Axel; Moss, David
2008-01-01
We use three-dimensional direct numerical simulations of the helically forced magnetohydrodynamic equations in spherical shell segments in order to study the effects of changes in the geometrical shape and size of the domain on the growth and saturation of large-scale magnetic fields. We inject kinetic energy along with kinetic helicity in spherical domains via helical forcing using Chandrasekhar-Kendall functions. We use perfect conductor boundary conditions for the magnetic field to ensure that no magnetic helicity escapes the domain boundaries. We find dynamo action giving rise to magnetic fields at scales larger than the characteristic scale of the forcing. The magnetic energy exceeds the kinetic energy over dissipative time scales, similar to that seen earlier in Cartesian simulations in periodic boxes. As we increase the size of the domain in the azimuthal direction we find that the nonlinearly saturated magnetic field organizes itself in long-lived cellular structures with aspect ratios close to unity....
MagIC: Fluid dynamics in a spherical shell simulator
Wicht, J.; Gastine, T.; Barik, A.; Putigny, B.; Yadav, R.; Duarte, L.; Dintrans, B.
2017-09-01
MagIC simulates fluid dynamics in a spherical shell. It solves for the Navier-Stokes equation including Coriolis force, optionally coupled with an induction equation for Magneto-Hydro Dynamics (MHD), a temperature (or entropy) equation and an equation for chemical composition under both the anelastic and the Boussinesq approximations. MagIC uses either Chebyshev polynomials or finite differences in the radial direction and spherical harmonic decomposition in the azimuthal and latitudinal directions. The time-stepping scheme relies on a semi-implicit Crank-Nicolson for the linear terms of the MHD equations and a Adams-Bashforth scheme for the non-linear terms and the Coriolis force.
Inertial modes and their transition to turbulence in a differentially rotating spherical gap flow
Hoff, Michael; Harlander, Uwe; Andrés Triana, Santiago; Egbers, Christoph
2016-04-01
We present a study of inertial modes in a spherical shell experiment. Inertial modes are Coriolis-restored linear wave modes, often arise in rapidly-rotating fluids (e.g. in the Earth's liquid outer core [1]). Recent experimental works showed that inertial modes exist in differentially rotating spherical shells. A set of particular inertial modes, characterized by (l,m,ˆω), where l, m is the polar and azimuthal wavenumber and ˆω = ω/Ωout the dimensionless frequency [2], has been found. It is known that they arise due to eruptions in the Ekman boundary layer of the outer shell. But it is an open issue why only a few modes develop and how they get enhanced. Kelley et al. 2010 [3] showed that some modes draw their energy from detached shear layers (e.g. Stewartson layers) via over-reflection. Additionally, Rieutord et al. (2012) [4] found critical layers within the shear layers below which most of the modes cannot exist. In contrast to other spherical shell experiments, we have a full optical access to the flow. Therefore, we present an experimental study of inertial modes, based on Particle-Image-Velocimetry (PIV) data, in a differentially rotating spherical gap flow where the inner sphere is subrotating or counter-rotating at Ωin with respect to the outer spherical shell at Ωout, characterized by the Rossby number Ro = (Ωin - Ωout)/Ωout. The radius ratio of η = 1/3, with rin = 40mm and rout = 120mm, is close to that of the Earth's core. Our apparatus is running at Ekman numbers (E ≈ 10-5, with E = ν/(Ωoutrout2), two orders of magnitude higher than most of the other experiments. Based on a frequency-Rossby number spectrogram, we can partly confirm previous considerations with respect to the onset of inertial modes. In contrast, the behavior of the modes in the counter-rotation regime is different. We found a triad interaction between three dominant inertial modes, where one is a slow axisymmetric Rossby mode [5]. We show that the amplitude of the most
Spherical thin-shell wormholes and modified Chaplygin gas
Sharif, M.; Azam, M., E-mail: msharif.math@pu.edu.pk, E-mail: azammath@gmail.com [Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore-54590 (Pakistan)
2013-05-01
The purpose of this paper is to construct spherical thin-shell wormhole solutions through cut and paste technique and investigate the stability of these solutions in the vicinity of modified Chaplygin gas. The Darmois-Israel formalism is used to formulate the stresses of the surface concentrating the exotic matter. We explore the stability of the wormhole solutions by using the standard potential method. We conclude that there exist more stable as well as unstable solutions than the previous study with generalized Chaplygin gas [19].
Nonlinear analysis of imperfect squarely-reticulated shallow spherical shells
2007-01-01
Nonlinear behavior of single-layer squarely-reticulated shallow spherical shells with geometrical imperfections subjected to a central concentrated (joint) load has been studied in this paper. Using the asymptotic iteration method, an analytical characteristic relationship between the non-dimensional load and central deflection is obtained. The resulting asymptotic solution can be used readily to perform the analysis of parameters and predict the buckling critical load. Meanwhile, numerical examples are presented and effects of imperfection factor and boundary conditions on buckling of the structures are discussed. Comparisons with data based on the finite element method show good exactness of the resulting solution.
Nonlinear analysis of imperfect squarely- reticulated shallow spherical shells
NIE GuoHua; LI ZhiWei
2007-01-01
Nonlinear behavior of single-layer squarely-reticulated shallow spherical shells with geometrical imperfections subjected to a central concentrated (joint) load has been studied in this paper.Using the asymptotic iteration method,an analytical characteristic relationship between the non-dimensional load and central deflection is obtained.The resulting asymptotic solution can be used readily to perform the analysis of parameters and predict the buckling critical load.Meanwhile,numerical examples are presented and effects of imperfection factor and boundary conditions on buckling of the structures are discussed.Comparisons with data based on the finite element method show good exactness of the resulting solution.
On the Curvature Effect of a Relativistic Spherical Shell
Uhm, Z. Lucas; Zhang, Bing
2015-07-01
We consider a relativistic spherical shell and calculate its spectral flux as received by a distant observer. Using two different methods, we derive a simple analytical expression of the observed spectral flux and show that the well-known relation \\hat{α }=2+\\hat{β } (between temporal index \\hat{α } and spectral index \\hat{β }) of the high-latitude emission is naturally achieved in our derivation but holds only when the shell moves with a constant Lorentz factor Γ. Presenting numerical models in which the shell is undergoing acceleration or deceleration, we show that the simple \\hat{α }=2+\\hat{β } relation does indeed deviate as long as Γ is not constant. For the models under acceleration, we find that the light curves produced purely by the high-latitude emission initially exhibit much steeper decay than in the constant Γ case and gradually resume the \\hat{α }=2+\\hat{β } relation in about one and a half orders of magnitude in observer time. For the models under deceleration, the trend is opposite. The light curves made purely by the high-latitude emission initially exhibit a shallower decay than in the constant Γ case and gradually resume the relation \\hat{α }=2+\\hat{β } in a similar order of magnitude in observer time. We also show that how fast the Lorentz factor Γ of the shell increases or decreases is the main ingredient determining the initial steepness or shallowness of the light curves.
On the Curvature Effect of a Relativistic Spherical Shell
Uhm, Z Lucas
2014-01-01
We consider a relativistic spherical shell and calculate its spectral flux as received by a distant observer. Using two different methods, we derive a simple analytical expression of the observed spectral flux and show that the well-known relation $\\hat \\alpha = 2+\\hat \\beta$ (between temporal index $\\hat \\alpha$ and spectral index $\\hat \\beta$) of the high-latitude emission is achieved naturally in our derivation but holds only when the shell moves with a constant Lorentz factor $\\Gamma$. Presenting numerical models where the shell is under acceleration or deceleration, we show that the simple $\\hat \\alpha = 2+\\hat \\beta$ relation is indeed deviated as long as $\\Gamma$ is not constant. For the models under acceleration, we find that the light curves produced purely by the high-latitude emission decay initially much steeper than the constant $\\Gamma$ case and gradually resume the $\\hat \\alpha = 2+\\hat \\beta$ relation in about one and half orders magnitude in observer time. For the models under deceleration, t...
Buckling-driven delamination in layered spherical shells
Sørensen, Kim D.; Jensen, Henrik M.
An analysis of buckling-driven delamination of a layer in a spherical, layered shell has been carried out. The effects of the substrate having a double curvature compared to previous studies of delamination on cylindrical substrates turn out to be non-trivial in the sense that additional to the effect of the shape of the substrate, a new non-dimensional geometrical parameter enters the conditions for steady-state delamination. It is shown that this additional geometrical parameter in most cases of practical relevance has insignificant influence on the fracture mechanical parameters involved for the problem. The consequence is that solutions need to be mapped as a function of one rather than two dimensionless parameters. Furthermore, the shape of the substrate has profound influence especially on initiation of delamination growth.
Convection-driven spherical shell dynamos at varying Prandtl numbers
Käpylä, P. J.; Käpylä, M. J.; Olspert, N.; Warnecke, J.; Brandenburg, A.
2017-02-01
Context. Stellar convection zones are characterized by vigorous high-Reynolds number turbulence at low Prandtl numbers. Aims: We study the dynamo and differential rotation regimes at varying levels of viscous, thermal, and magnetic diffusion. Methods: We perform three-dimensional simulations of stratified fully compressible magnetohydrodynamic convection in rotating spherical wedges at various thermal and magnetic Prandtl numbers (from 0.25 to 2 and from 0.25 to 5, respectively). Differential rotation and large-scale magnetic fields are produced self-consistently. Results: We find that for high thermal diffusivity, the rotation profiles show a monotonically increasing angular velocity from the bottom of the convection zone to the top and from the poles toward the equator. For sufficiently rapid rotation, a region of negative radial shear develops at mid-latitudes as the thermal diffusivity is decreased, corresponding to an increase of the Prandtl number. This coincides with and results in a change of the dynamo mode from poleward propagating activity belts to equatorward propagating ones. Furthermore, the clearly cyclic solutions disappear at the highest magnetic Reynolds numbers and give way to irregular sign changes or quasi-stationary states. The total (mean and fluctuating) magnetic energy increases as a function of the magnetic Reynolds number in the range studied here (5-151), but the energies of the mean magnetic fields level off at high magnetic Reynolds numbers. The differential rotation is strongly affected by the magnetic fields and almost vanishes at the highest magnetic Reynolds numbers. In some of our most turbulent cases, however, we find that two regimes are possible, where either differential rotation is strong and mean magnetic fields are relatively weak, or vice versa. Conclusions: Our simulations indicate a strong nonlinear feedback of magnetic fields on differential rotation, leading to qualitative changes in the behaviors of large
Koch, S; Harlander, U; Egbers, C [Department of Aerodynamics and Fluid Mechanics, Brandenburg University of Technology Cottbus, Siemens-Halske-Ring 14, D-03046 Cottbus (Germany); Hollerbach, R, E-mail: uwe.harlander@tu-cottbus.de [Institute of Geophysics, ETH Zuerich, Sonneggstrasse 5, CH-8092 Zurich (Switzerland)
2013-06-15
We begin with an experimental investigation of the flow induced in a rotating spherical shell. The shell globally rotates with angular velocity {Omega}. A further periodic oscillation with angular velocity 0 Less-Than-Or-Slanted-Equal-To {omega} Less-Than-Or-Slanted-Equal-To 2{Omega}, a so-called longitudinal libration, is added on the inner sphere's rotation. The primary response is inertial waves spawned at the critical latitudes on the inner sphere, and propagating throughout the shell along inclined characteristics. For sufficiently large libration amplitudes, the higher harmonics also become important. Those harmonics whose frequencies are still less than 2{Omega} behave as inertial waves themselves, propagating along their own characteristics. The steady component of the flow consists of a prograde zonal jet on the cylinder tangent to the inner sphere and parallel to the axis of rotation, and increases with decreasing Ekman number. The jet becomes unstable for larger forcing amplitudes as can be deduced from the preliminary particle image velocimetry observations. Finally, a wave attractor is experimentally detected in the spherical shell as the pattern of largest variance. These findings are reproduced in a two-dimensional numerical investigation of the flow, and certain aspects can be studied numerically in greater detail. One aspect is the scaling of the width of the inertial shear layers and the width of the steady jet. Another is the partitioning of the kinetic energy between the forced wave, its harmonics and the mean flow. Finally, the numerical simulations allow for an investigation of instabilities, too local to be found experimentally. For strong libration amplitudes, the boundary layer on the inner sphere becomes unstable, triggering localized Goertler vortices during the prograde phase of the forcing. This instability is important for the transition to turbulence of the spherical shell flow. (paper)
Circumferential-wave phase velocities for empty, fluid-immersed spherical metal shells
Überall, Herbert; Ahyi, A. C.; Raju, P. K.
2002-01-01
-loaded, evacuated spherical metal shells of aluminum, stainless steel, and tungsten carbide. In particular, the characteristic upturn of the dispersion curves of low-order shell-borne circumferential waves (A or A0 waves) which takes place on spherical shells when the frequency tends towards very low values......, is demonstrated here for all cases of the metals under consideration. ©2002 Acoustical Society of America....
Guo, Xiaoxia; Zhao, Kongshuang
2017-07-01
We report here a dielectric study on cationic and anionic spherical polyelectrolyte brush (SPB) (consisting of a polystyrene (PS) core and poly (2-aminoethylmethacrylate hydrochloride (PAEMH) chains or poly (acrylic acid) (PAA) chains grafted onto the core) suspensions over a frequency range of 40 Hz-110 MHz. The relaxation behavior of the suspensions shows significant changes in the brush layer properties when changing the particle mass fraction or pH of the system. After eliminating the electrode polarization effect at a low frequency, two definite relaxations related to interfacial polarization, around 100 kHz and 10 MHz respectively, are observed. Based on a single layer spherical-shell model, we developed a curve-fitting procedure to analyze such dielectric spectra for soft particles, and then calculated the dielectric properties of the components of the SPBs (such as the permittivities and conductivities of the layer and solution phase), especially the layer thickness d s of the polyelectrolyte chain (PE) layer. We also found a larger confinement degree of counterions in the PAEMH brush due to the protonation of the amino group. Moreover, the repulsive force between the SPB particles is evaluated by using the d s combined with the relative theoretical formulas. We conclude that by raising (reducing) the acidity of the system, the stability of the PAEMH-SPB (PAA-SPB) suspension was improved. An increase in particle concentration can also improve the stability of these two dispersions.
Rotationally invariant clustering of diffusion MRI data using spherical harmonics
Liptrot, Matthew George; Lauze, Francois Bernard
classification of DWI data can be performed without the need for a model reconstruction step. This avoids the potential confounds and uncertainty that such models may impose, and has the benefit of being computable directly from the DWI volumes. As such, the method could prove useful in subsequent pre-processing...... simple features that are invariant to the rotation of the highly orientational diffusion data. This provides a way to directly classify voxels whose diffusion characteristics are similar yet whose primary diffusion orientations differ. Subsequent application of machine-learning to the spherical harmonic...... data as a collection of spherical basis functions. We use the derived coefficients as voxelwise feature vectors for classification. Using a simple Gaussian mixture model, we examined the classification performance for a range of sub-classes (3-20). The results were compared against existing...
Faraday Wave Turbulence on a Spherical Liquid Shell
Holt, R. Glynn; Trinh, Eugene H.
1996-01-01
Millimeter-radius liquid shells are acoustically levitated in an ultrasonic field. Capillary waves are observed on the shells. At low energies (minimal acoustic amplitude, thick shell) a resonance is observed between the symmetric and antisymmetric thin film oscillation modes. At high energies (high acoustic pressure, thin shell) the shell becomes fully covered with high-amplitude waves. Temporal spectra of scattered light from the shell in this regime exhibit a power-law decay indicative of turbulence.
PMMA/PMMA core-shell particles with ellipsoidal, fluorescent cores: accessing rotational dynamics.
Klein, Matthias K; Klinkenberg, Nele; Schuetter, Stefan; Saenger, Nicolai; Pfleiderer, Patrick; Zumbusch, Andreas
2015-03-10
For several decades, nonaqueous dispersions of PMMA particles have played an important role in colloid research. They have found application as colloidal model systems, which are used to probe glassy dynamics or to explore crystal nucleation. To date, most research has focused on spherical particles, in which only translational motion can be investigated. Recently, however, there has been a surge of interest in analyzing also rotational dynamics. In this contribution, we introduce a new class of core-shell particles, which can be used as rotational probes. The colloids described herein are composed of shape anisotropic, fluorescent cores covered with nonfluorescent PMMA shells. The core-shell particles are built up in four steps. In a first step, we produce fluorescent and photo-cross-linkable PMMA colloids. In the second step, these particles are thermomechanically elongated and fixed in defined ellipsoidal shapes by photo-cross-linking. Subsequently, we cover the cross-linked, fluorescent core with a nonfluorescent PMMA shell. The shape of the resulting core-shell colloids is tunable between the initial anisotropic and perfect spherical shape. For shaping, we apply a simple solvent swelling procedure. As one option, this method yields perfect PMMA spheres with ellipsoidal, fluorescent centers. We also report morphological particle characterization using various fluorescence microscopy techniques. Finally, we demonstrate that the rotational dynamics of individual colloids can be tracked and analyzed.
Rotationally invariant clustering of diffusion MRI data using spherical harmonics
Liptrot, Matthew George; Lauze, François
2016-01-01
simple features that are invariant to the rotation of the highly orientational diffusion data. This provides a way to directly classify voxels whose diffusion characteristics are similar yet whose primary diffusion orientations differ. Subsequent application of machine-learning to the spherical harmonic...... alternatives for tissue classification e.g. fractional anisotropy (FA) or the standard model used by Camino. The approach was implemented on both two publicly-available datasets: an ex-vivo pig brain and in-vivo human brain from the Human Connectome Project (HCP). We have demonstrated how a robust...
Nonlinear r-modes in a spherical shell issues of principle
Levin, Y; Levin, Yuri; Ushomirsky, Greg
1999-01-01
We use a simple physical model to study the nonlinear behaviour of the r-mode instability. We assume that r-modes (Rossby waves) are excited in a thin spherical shell of rotating incompressible fluid. For this case, exact Rossby wave solutions of arbitrary amplitude are known. We find that: (a) These nonlinear Rossby waves carry ZERO physical angular momentum and positive physical energy, which is contrary to the folklore belief that the r-mode angular momentum and energy are negative. (b) Within our model, we confirm the differential drift reported by Rezzolla, Lamb and Shapiro (1999). Radiation reaction is introduced into the model by assuming that the fluid is electrically charged; r-modes are coupled to electromagnetic radiation through current (magnetic) multipole moments. We find that: (c) To linear order in the mode amplitude, r-modes are subject to the CFS instability, as expected. (d) Radiation reaction decreases the angular velocity of the shell and causes differential rotation (which is distinct fr...
Effects of rotation amplitude on arm movement when rotating a spherical object.
Lardy, Julien; Beurier, Georges; Wang, Xuguang
2012-01-01
Arm movements when rotating a spherical object were experimentally investigated. Twelve volunteers participated in the experiment and were asked to rotate a sphere for a large range of amplitude. Results showed that subjects anticipated their posture at the beginning of object manipulation even for low rotation amplitudes. The way of anticipation strongly depended on rotation direction. The end-state comfort hypothesis, effects of joint limits and principle of minimum work were examined for explaining motion control. The anticipation would ensure a better end-state comfort while avoiding joint limits in case of higher amplitude of object rotation. Meanwhile, it should not deteriorate the comfort at the beginning of manipulation too much. High postural variability for low rotation amplitude tasks suggested that there might exist a range of postures of similar level of comfort. These findings will be useful in developing human behaviour-based motion simulations for digital human. Arm movement was investigated when rotating a spherical object with a large range of amplitude. The end-state comfort hypothesis, effects of joint limits and principle of minimum work were examined for explaining motion control. Results will be helpful for a better design of rotary controls and for developing motion simulation algorithms.
Rotationally invariant clustering of diffusion MRI data using spherical harmonics
Liptrot, Matthew; Lauze, François
2016-03-01
We present a simple approach to the voxelwise classification of brain tissue acquired with diffusion weighted MRI (DWI). The approach leverages the power of spherical harmonics to summarise the diffusion information, sampled at many points over a sphere, using only a handful of coefficients. We use simple features that are invariant to the rotation of the highly orientational diffusion data. This provides a way to directly classify voxels whose diffusion characteristics are similar yet whose primary diffusion orientations differ. Subsequent application of machine-learning to the spherical harmonic coefficients therefore may permit classification of DWI voxels according to their inferred underlying fibre properties, whilst ignoring the specifics of orientation. After smoothing apparent diffusion coefficients volumes, we apply a spherical harmonic transform, which models the multi-directional diffusion data as a collection of spherical basis functions. We use the derived coefficients as voxelwise feature vectors for classification. Using a simple Gaussian mixture model, we examined the classification performance for a range of sub-classes (3-20). The results were compared against existing alternatives for tissue classification e.g. fractional anisotropy (FA) or the standard model used by Camino.1 The approach was implemented on both two publicly-available datasets: an ex-vivo pig brain and in-vivo human brain from the Human Connectome Project (HCP). We have demonstrated how a robust classification of DWI data can be performed without the need for a model reconstruction step. This avoids the potential confounds and uncertainty that such models may impose, and has the benefit of being computable directly from the DWI volumes. As such, the method could prove useful in subsequent pre-processing stages, such as model fitting, where it could inform about individual voxel complexities and improve model parameter choice.
Sound scattering from partially water-filled elastic spherical shell with an internal elastic plate
SUN Yang; XU Haiting
2008-01-01
According to the equation of motion in the elastic medium and integral equation of target scattering, the sound scattering from the partially water-filled elastic spherical shells with and without an inner plate is studied using the finite element and boundary element method,and the scattering normalized form functions of the shell filled with different volume of water are computed and the mechanism of resonance scattering is analyzed. The results show that the resonance of the shell with partially water-filled and without the plate is mainly related to the volume of water, and the resonance is produced by inner water and the spherical shell. The resonance characteristics of partially water-filled elastic shell with the plate are similar to that of empty structured elastic spherical shell, and the sound field in inner water is weaker which indicates the main resonance characteristics are decided by spherical shell and the plate. In addition, the scattering characteristics of spherical shell with plate and one side full water-filled are greatly different from the partially water-filled ones.
DYNAMIC SIMULATION OF ROTATING SHELLS COUPLED WITH LIQUID
Wei Fayuan; Li Shiqi; Zhong Yifang; Huang Yuying
2001-01-01
The dynamic behaviors of rotating shells coupled with liquid are shown. The shell under consideration has arbitrary boundary conditions and a complex shape. A modified boundary element method and finite strip technique are used to improve the computing efficiency and to guarantee the continuity conditions on the liquid-shell interaction plane. The effects of various parameters such as shell's thickness and liquid depth are investigated. Dynamic simulations are applied to several typical shell-liquid systems, and the natural frequencies, mode shapes and response of vibration are calculated numerically.
The form of the free surface of hydrogen isotopes in the spherical shell
Izgorodin, V. M.; Solomatina, E. Y.; Pepelyaev, A. P.; Osetrov, E. I.; Rogozhina, M. A.
2016-09-01
Initial study of hydrogen isotopes distribution on inner surface of a hollow spherical shell under cryogenic conditions is given. Comparison of theoretical and experimental surfaces of ice layers of various hydrogen isotopes is performed.
Cr/alpha-Cr2O3 monodispersed spherical core-shell particles based solar absorbers
Khamlich, S
2011-07-01
Full Text Available Monodispersed spherical core-shell particles of Cr/alpha-Cr2O3 cermet ACG coatings investigated within this contribution could be successfully employed in thermal converters. Their selectivity depends on their chemical, physical and structural...
On Perturbation Solutions for Axisymmetric Bending Boundary Values of a Deep Thin Spherical Shell
Rong Xiao
2014-01-01
Full Text Available On the basis of the general theory of elastic thin shells and the Kirchhoff-Love hypothesis, a fundamental equation for a thin shell under the moment theory is established. In this study, the author derives Reissner’s equation with a transverse shear force Q1 and the displacement component w. These basic unknown quantities are derived considering the axisymmetry of the deep, thin spherical shell and manage to constitute a boundary value question of axisymmetric bending of the deep thin spherical shell under boundary conditions. The asymptotic solution is obtained by the composite expansion method. At the end of this paper, to prove the correctness and accuracy of the derivation, an example is given to compare the numerical solution by ANSYS and the perturbation solution. Meanwhile, the effects of material and geometric parameters on the nonlinear response of axisymmetric deep thin spherical shell under uniform external pressure are also analyzed in this paper.
Trapped flux reduction in a spherical niobium shell at 1 mG
Brumley, Robert W.; Buchman, Saps; Xiao, Yueming
1994-02-01
We have developed a method to reduce flux trapped in a superconducting spherical shell. A normal spot on the shell sweeps flux lines until they close in on themselves. Using this technique the dipole moment corresponding to a trapped field of 1 mG has been reduced to about 6% of its original level.
Stress concentration in a transversely isotropic spherical shell with two circular rigid inclusions
Chekhov, V. N.; Zakora, S. V.
2011-10-01
The refined Timoshenko-type theory that takes into account the transverse shear strains is used to find an analytic solution for the stress state of transversely isotropic shallow spherical shell with two circular rigid inclusions. The case of a shell with closely spaced rigid inclusions of unequal radii under internal pressure is analyzed numerically. The stresses in the shell increase considerably with decrease in the distance between the inclusions and increase in the transverse shear parameter
Kozyreff, Gregory
2016-01-01
We derive formulas for Whispering Gallery Mode resonances and bending losses in infinite cylindrical dielectric shells and sets of concentric cylindrical shells. The formulas also apply to spherical shells and to sections of bent waveguides. The derivation is based on a WKB treatment of Helmholtz equation and can in principle be extended to any number of concentric shells. A distinctive limit analytically arises in the analysis when two shells are brought at very close distance to one another. In that limit, the two shells act as a slot waveguide. If the two shells are sufficiently apart, we identify a structural resonance between the individual shells, which can either lead to a substantial enhancement or suppression of radiation losses.
Kozyreff, Gregory; Acharyya, Nirmalendu
2016-12-12
We derive formulas for whispering gallery mode resonances and bending losses in infinite cylindrical dielectric shells and sets of concentric cylindrical shells. The formulas also apply to spherical shells and to sections of bent waveguides. The derivation is based on a Wentzel-Kramers-Brillouin (WKB) treatment of Helmholtz equation and can in principle be extended to any number of concentric shells. A distinctive limit analytically arises in the analysis when two shells are brought at very close distance to one another. In that limit, the two shells act as a slot waveguide. If the two shells are sufficiently apart, we identify a structural resonance between the individual shells, which can either lead to a substantial enhancement or suppression of radiation losses.
The use of rotating electric are for spherical particle production
Bica, Ion
2000-08-01
Full Text Available This work presents an experimental device designed to obtain spherical partióles by means of a rotating electric are. A rotation frequency of the electric are of 750 s^{-1}, a voltage of 50 V (dc and a current of 100 A was used. The mass flow rate was 3 g.min^{-1}. Under these conditions particles of 15 to 20 μm in diameter were obtained.
Este trabajo presenta la instalación experimental destinada a la obtención de partículas esféricas utilizando un arco eléctrico rotatorio. Para ello se utilizó una frecuencia de rotación del arco eléctrico de 750 s^{-1} a un voltaje del arco de 50 V (cc y una corriente de 100 A. La velocidad de flujo de materia fue de 3 g.min^{-1} obteniéndose partículas de diámetros comprendidos entre 15 y 20 μm.
Nonlinear thermomechanical deformation behaviour of P-FGM shallow spherical shell panel
Vishesh Ranjan Kar; Subrata Kumar Panda
2016-01-01
In the present article, the linear and the nonlinear deformation behaviour of functionally graded (FG) spherical shell panel are examined under thermomechanical load. The temperature-dependent effective material properties of FG shell panel are evaluated using Voigt’s micro-mechanical rule in conjunction with power-law distribution. The nonlinear mathematical model of the FG shell panel is developed based on higher-order shear deformation theory and Green-Lagrange type geometrical nonlinearity. The desired nonlinear governing equation of the FG shell panel is computed using the variational principle. The model is discretised through suitable nonlinear finite element steps and solved using direct iterative method. The convergence and the val-idation behaviour of the present numerical model are performed to show the efficacy of the model. The effect of different parameters on the nonlinear deformation behaviour of FG spherical shell panel is highlighted by solving numerous examples.
Nonlinear thermomechanical deformation behaviour of P-FGM shallow spherical shell panel
Vishesh Ranjan Kar
2016-02-01
Full Text Available In the present article, the linear and the nonlinear deformation behaviour of functionally graded (FG spherical shell panel are examined under thermomechanical load. The temperature-dependent effective material properties of FG shell panel are evaluated using Voigt’s micro-mechanical rule in conjunction with power-law distribution. The nonlinear mathematical model of the FG shell panel is developed based on higher-order shear deformation theory and Green-Lagrange type geometrical nonlinearity. The desired nonlinear governing equation of the FG shell panel is computed using the variational principle. The model is discretised through suitable nonlinear finite element steps and solved using direct iterative method. The convergence and the validation behaviour of the present numerical model are performed to show the efficacy of the model. The effect of different parameters on the nonlinear deformation behaviour of FG spherical shell panel is highlighted by solving numerous examples.
Hansen, Ulrich; Maas, Christian
2017-04-01
About 4.5 billion years ago the early Earth experienced several giant impacts that lead to one or more deep terrestrial magma oceans of global extent. The crystallization of these vigorously convecting magma oceans is of key importance for the chemical structure of the Earth, the subsequent mantle evolution as well as for the initial conditions for the onset of plate tectonics. Due to the fast planetary rotation of the early Earth and the small magma viscosity, rotation probably had a profound effect on early differentiation processes and could for example influence the presence and distribution of chemical heterogeneities in the Earth's mantle [e.g. Matyska et al., 1994, Garnero and McNamara, 2008]. Previous work in Cartesian geometry revealed a strong influence of rotation as well as of latitude on the crystal settling in a terrestrial magma ocean [Maas and Hansen, 2015]. Based on the preceding study we developed a spherical shell model that allows to study crystal settling in-between pole and equator as well as the migration of crystals between these regions. Further we included centrifugal forces on the crystals, which significantly affect the lateral and radial distribution of the crystals. Depending on the strength of rotation the particles accumulate at mid-latitude or at the equator. At high rotation rates the dynamics of fluid and particles are dominated by jet-like motions in longitudinal direction that have different directions on northern and southern hemisphere. All in all the first numerical experiments in spherical geometry agree with Maas and Hansen [2015] that the crystal distribution crucially depends on latitude, rotational strength and crystal density. References E. J. Garnero and A. K. McNamara. Structure and dynamics of earth's lower mantle. Science, 320(5876):626-628, 2008. C. Maas and U. Hansen. Eff ects of earth's rotation on the early di erentiation of a terrestrial magma ocean. Journal of Geophysical Research: Solid Earth, 120
Spherical-shell boundaries for two-dimensional compressible convection in a star
Pratt, J.; Baraffe, I.; Goffrey, T.; Geroux, C.; Viallet, M.; Folini, D.; Constantino, T.; Popov, M.; Walder, R.
2016-10-01
Context. Studies of stellar convection typically use a spherical-shell geometry. The radial extent of the shell and the boundary conditions applied are based on the model of the star investigated. We study the impact of different two-dimensional spherical shells on compressible convection. Realistic profiles for density and temperature from an established one-dimensional stellar evolution code are used to produce a model of a large stellar convection zone representative of a young low-mass star, like our sun at 106 years of age. Aims: We analyze how the radial extent of the spherical shell changes the convective dynamics that result in the deep interior of the young sun model, far from the surface. In the near-surface layers, simple small-scale convection develops from the profiles of temperature and density. A central radiative zone below the convection zone provides a lower boundary on the convection zone. The inclusion of either of these physically distinct layers in the spherical shell can potentially affect the characteristics of deep convection. Methods: We perform hydrodynamic implicit large eddy simulations of compressible convection using the MUltidimensional Stellar Implicit Code (MUSIC). Because MUSIC has been designed to use realistic stellar models produced from one-dimensional stellar evolution calculations, MUSIC simulations are capable of seamlessly modeling a whole star. Simulations in two-dimensional spherical shells that have different radial extents are performed over tens or even hundreds of convective turnover times, permitting the collection of well-converged statistics. Results: To measure the impact of the spherical-shell geometry and our treatment of boundaries, we evaluate basic statistics of the convective turnover time, the convective velocity, and the overshooting layer. These quantities are selected for their relevance to one-dimensional stellar evolution calculations, so that our results are focused toward studies exploiting the so
Topologically stable magnetization states on a spherical shell: Curvature-stabilized skyrmions
Kravchuk, Volodymyr P.; Rößler, Ulrich K.; Volkov, Oleksii M.; Sheka, Denis D.; van den Brink, Jeroen; Makarov, Denys; Fuchs, Hagen; Fangohr, Hans; Gaididei, Yuri
2016-10-01
Topologically stable structures include vortices in a wide variety of matter, skyrmions in ferro- and antiferromagnets, and hedgehog point defects in liquid crystals and ferromagnets. These are characterized by integer-valued topological quantum numbers. In this context, closed surfaces are a prominent subject of study as they form a link between fundamental mathematical theorems and real physical systems. Here we perform an analysis on the topology and stability of equilibrium magnetization states for a thin spherical shell with easy-axis anisotropy in normal directions. Skyrmion solutions are found for a range of parameters. These magnetic skyrmions on a spherical shell have two distinct differences compared to their planar counterpart: (i) they are topologically trivial and (ii) can be stabilized by curvature effects, even when Dzyaloshinskii-Moriya interactions are absent. Due to its specific topological nature a skyrmion on a spherical shell can be simply induced by a uniform external magnetic field.
Buckling-driven Delamination in Layered Spherical Shells
Sørensen, Kim Dalsten; Jensen, Henrik Myhre
2008-01-01
An analysis of buckling-driven delamination of a thin film on a spherical substrate has been carried out. The effects of the substrate having a double curvature compared to previous studies of delamination on cylindrical substrates turn out to be non-trivial: In addition to the effect of the shap...
Preparation of Hollow Spherical and Core/shell Structured Powders by Plasma Processing
ZHANG; Xiaofeng; ZHOU; Kesong; DENG; Changguang; SONG; Jinbing; ZHANG; Jifu; DONG; Shujuan
2015-01-01
Four types of hollow spherical micro- and nano-szied powders of ZrO2-7wt.%Y2O3(7YSZ), ZrO2-7wt.%Y2O3, Al2O3-13 wt.% TiO2(AT) and WC as well as one type of core/shell structured powder of ZrB2-30 wt.%Mo Si2 were prepared via plasma processing. In addition, the formation mechanisms of hollow spherical and core/shell structured powders prepared via plasma processing were also proposed.
Models of spherical shells as sources of Majumdar-Papapetrou type spacetimes
García-Reyes, Gonzalo
2016-01-01
By starting with a seed Newtonian potential-density pair we construct relativistic thick spherical shell models for a Majumdar-Papapetrou type conformastatic spacetime. As simple example, we considerer a family of Plummer type relativistic spherical shells. These objects are then used to model a system composite by a dust disk and a halo of matter. We study the equatorial circular motion of test particles around the structures. Also the stability of the orbits is analyzed for radial perturbation using an extension of the Rayleigh criterion. The models considered satisfying all the energy conditions.
Toyoda, K.; Yasuzawa, Y.; Kagawa, K.; Sugimoto, S. [Kyushu University, Fukuoka (Japan). Faculty of Engineering
1997-10-01
Vibration characteristics of the semi-spherical shell fixed in water with bidirectional curvatures were studied experimentally. Various marine structures have been devised as relay station for life spaces or submarine resource excavation. As compared with land structures, marine structures are constantly under a severe condition subjected to hydrostatic pressure, and requires advanced technologies. The experimental result, numerical computation result by analytical code DASOR (Dynamic Analysis of Shell of Revolution) and theoretical analysis result were compared with each other. FEM and BEM were used in DASOR computation for the axisymmetric thin semi-spherical shell and circumferential liquid, respectively. Due to an added mass effect, the natural frequency decreased with an increase in water level regardless of mode orders. However, the water level over the top of the semi-spherical shell caused the nearly constant natural frequencies of 30-40% of that in the air. The computation result by DASOR well agreed with the experimental result demonstrating its validity. 4 refs., 13 figs., 1 tab.
Remarks on the Rayleigh-Benard Convection on Spherical Shells
Wang, Shouhong
2011-01-01
The main objective of this article is to study the effect of spherical geometry on dynamic transitions and pattern formation for the Rayleigh-Benard convection. The study is mainly motivated by the importance of spherical geometry and convection in geophysical flows. It is shown in particular that the system always undergoes a continuous (Type-I) transition to a $2l_c$-dimensional sphere $S^{2lc}$, where lc is the critical wave length corresponding to the critical Rayleigh number. Furthermore, it has shown in [12] that it is critical to add nonisotropic turbulent friction terms in the momentum equation to capture the large-scale atmospheric and oceanic circulation patterns. We show in particular that the system with turbulent friction terms added undergoes the same type of dynamic transition, and obtain an explicit formula linking the critical wave number (pattern selection), the aspect ratio, and the ratio between the horizontal and vertical turbulent friction coefficients.
Spherical Shell Cosmological Model and Uniformity of Cosmic Microwave Background Radiation
Vlahovic, Branislav
2012-01-01
Considered is spherical shell as a model for visible universe and parameters that such model must have to comply with the observable data. The topology of the model requires that motion of all galaxies and light must be confined inside a spherical shell. Consequently the observable universe cannot be defined as a sphere centered on the observer, rather it is an arc length within the volume of the spherical shell. The radius of the shell is 4.46 $\\pm$ 0.06 Gpc, which is for factor $\\pi$ smaller than radius of a corresponding 3-sphere. However the event horizon, defined as the arc length inside the shell, has the size of 14.0 $\\pm$ 0.2 Gpc, which is in agreement with the observable data. The model predicts, without inflation theory, the isotropy and uniformity of the CMB. It predicts the correct value for the Hubble constant $H_0$ = 67.26 $\\pm$ 0.90 km/s/Mpc, the cosmic expansion rate $H(z)$, and the speed of the event horizon in agreement with observations. The theoretical suport for shell model comes from gen...
Dynamics of a self gravitating light-like matter shell with spherical symmetry
Kijowski, Jerzy
2008-01-01
Complete hamiltonian description of the physical system composed of a null matter shell interacting with the gravitational field is provided. In spherically symmetric case, the phase space of the system is effectively reduced with respect to the Gauss-Codazzi constraints. The Hamiltonian of the system (numerically equal to the value of the ADM mass) is explicitly calculated in terms of the "true degrees of freedom", i.e. as a function on the reduced phase space. Geometric interpretation of the momentum canonically conjugate to the shell's radius is given. Transformation between different time parameterizations of the shell is discussed.
Modal Testing Repeatability of a Population of Spherical Shells
Robertson, A. [HYTEC, Inc., Boulder, CO (United States); Hemez, F. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Salazar, I. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Duffey, T. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2004-05-01
In this study, we investigated the variability in modal frequencies obtained from testing a set of hollow, almost spherical marine floats. We investigated four sources of variability: unit-to-unit variability, operator-to-operator variability, test repetition, and accelerometer placement. Because we measured the excitation and response of the marine floats, we were able to estimate impulse response and frequency response functions. Variability is assessed by measuring the deviation of each frequency response function from the mean curve for its test group.
ZHU Yong-an; WANG Fan; LIU Ren-huai
2008-01-01
The nonlinear thermal buckling of symmetrically laminated cylindrically orthotropic shallow spherical shell under temperature field and uniform pressure including transverse shear is studied.Also the analytic formulas for determining the critical buckling loads under different temperature fields are obtained by using the modified iteration method.The effect of transverse shear deformation and different temperature fields on critical buckling load is discussed.
Şahan, Mehmet Fatih
2017-02-01
In this paper, the viscoelastic damped response of cross-ply laminated shallow spherical shells is investigated numerically in a transformed Laplace space. In the proposed approach, the governing differential equations of cross-ply laminated shallow spherical shell are derived using the dynamic version of the principle of virtual displacements. Following this, the Laplace transform is employed in the transient analysis of viscoelastic laminated shell problem. Also, damping can be incorporated with ease in the transformed domain. The transformed time-independent equations in spatial coordinate are solved numerically by Gauss elimination. Numerical inverse transformation of the results into the real domain are operated by the modified Durbin transform method. Verification of the presented method is carried out by comparing the results with those obtained by the Newmark method and ANSYS finite element software. Furthermore, the developed solution approach is applied to problems with several impulsive loads. The novelty of the present study lies in the fact that a combination of the Navier method and Laplace transform is employed in the analysis of cross-ply laminated shallow spherical viscoelastic shells. The numerical sample results have proved that the presented method constitutes a highly accurate and efficient solution, which can be easily applied to the laminated viscoelastic shell problems.
Shatalov, MY
2011-01-01
Full Text Available Standing waves can exist as stable vibrating patterns in perfect structures such as spherical bodies, and inertial rotation of the body causes precession (Bryan’seffect). However, an imperfection such as light mass anisotropy destroys the standing...
The relativistic spherical δ -shell interaction in R3: Spectrum and approximation
Mas, Albert; Pizzichillo, Fabio
2017-08-01
This note revolves on the free Dirac operator in R3 and its δ -shell interaction with electrostatic potentials supported on a sphere. On one hand, we characterize the eigenstates of those couplings by finding sharp constants and minimizers of some precise inequalities related to an uncertainty principle. On the other hand, we prove that the domains given by Dittrich et al. [J. Math. Phys. 30(12), 2875-2882 (1989)] and by Arrizabalaga et al. [J. Math. Pures Appl. 102(4), 617-639 (2014)] for the realization of an electrostatic spherical shell interaction coincide. Finally, we explore the spectral relation between the shell interaction and its approximation by short range potentials with shrinking support, improving previous results in the spherical case.
Bozic, Anze Losdorfer; Podgornik, Rudolf
2010-01-01
We investigate the electrostatics of a partially formed, charged spherical shell in a salt solution. We solve the problem numerically at the Poisson-Boltzmann level and analytically in the Debye-Huckel regime. From the results on energetics of partially formed shells we examine the stability of tethered (crystalline) and fluid shells towards rupture. We clearly delineate different regimes of stability towards rupture, where, for fluid shells, we also include the effects of bending elasticity of the shells. Our analysis shows how charging of the shell induces its instability towards rupture but also provides insight regarding growth of charged shells.
Experimental evaluation of the Magnus force coefficient of the rotating spherical particle
Lukerchenko, Nikolay
2005-01-01
The Magnus force coefficient was determined from comparison of theoretical and experimental trajectory of rotating spherical particle falling in calm water. Theoretical trajectories of the particle were calculated using 2D numerical model of the rotating spherical particle moving in fluid and the proper value of the Magnus force coefficient was established from condition of the best fitting of the experimental trajectory by the calculated one. The mutual influence of the translational and rot...
The N = 16 spherical shell closure in 24O
Tshoo, K; Bhang, H; Choi, S; Nakamura, T; Kondo, Y; Deguchi, S; Kawada, Y; Kobayashi, N; Nakayama, Y; Tanaka, K N; Tanaka, N; Aoi, N; Ishihara, M; Motobayashi, T; Otsu, H; Sakurai, H; Takeuchi, S; Togano, Y; Yoneda, K; Li, Z H; Delaunay, F; Gibelin, J; Marqués, F M; Orr, N A; Honda, T; Matsushita, M; Kobayashi, T; Miyashita, Y; Sumikama, T; Yoshinaga, K; Shimoura, S; Sohler, D; Zheng, T; Cao, Z X
2012-01-01
The unbound excited states of the neutron drip-line isotope 24O have been investigated via the 24O(p,p')23O+n reaction in inverse kinematics at a beam energy of 62 MeV/nucleon. The decay energy spectrum of 24O* was reconstructed from the momenta of 23O and the neutron. The spin-parity of the first excited state, observed at Ex = 4.65 +/- 0.14 MeV, was determined to be Jpi = 2+ from the angular distribution of the cross section. Higher lying states were also observed. The quadrupole transition parameter beta2 of the 2+ state was deduced, for the first time, to be 0.15 +/- 0.04. The relatively high excitation energy and small beta2 value are indicative of the N = 16 shell closure in 24O.
Three-dimensional natural convection in a narrow spherical shell
Liu, Ming; Egbers, Christoph
The convective motions in a shallow fluid layer between two concentric spheres in the presence of a constant axial force field have been studied numerically. The aspect ratio of the fluid layer to inner radius is beta =0.08, the Prandtl number Pra =37.5. A three-dimensional time-dependent numerical code is used to solve the governing equations in primitive variables. Convection in the sphe rical shell has then a highly three-dimensional nature. Characteristic flow patterns with a large number of banana-type cells, oriented in north-south direction and aligned in the azimuthal direction, are formed on the northern hemisphere, which grow gradually into the equatorial region accompanied by the generation of new cells as the Rayleigh number is increased. Various characteristics of these flows as well as their transient evolution are investigated for Rayleigh numbers up to 20 000.
Yüksel, Yusuf
2017-03-01
By using Monte Carlo simulations for classical Heisenberg spins, we study the critical phenomena and ferrimagnetic properties of spherical nanoparticles with core-shell geometry. The particle core is composed of ferromagnetic spins, and it is coated by a ferromagnetic shell. Total size of the particle is fixed but the thickness of the shell is varied in such a way that the shell layer is grown at the expense of the core. Effects of the shell thickness, as well as dynamic magnetic field parameters such as oscillation period and field amplitude on the magnetization profiles, dynamic hysteresis loops and phase diagrams have been investigated for the present system. It has been found that as the shell thickness varies then the easy axis magnetization of the overall system may exhibit Q-, P-, L- and N- type behaviors based on the Neél terminology. We also found that three distinct anomalies originate in the thermal variation of specific heat with increasing field period. Dynamic hysteresis loops corresponding to off-axial magnetization components exhibit unconventional behavior such as double rings with symmetric shapes around the vertical axis over the h (t) = 0 line which may originate due to the stochastic resonance behavior of these components.
Meridional trapping and zonal propagation of inertial waves in a rotating fluid shell
Rabitti, Anna
2014-01-01
Inertial waves propagate in homogeneous rotating fluids, and constitute a challenging and simplified case study for the broader class of inertio-gravity waves, present in all geophysical and astrophysical media, and responsible for energetically costly processes as diapycnal and angular momentum mixing. However, a complete analytical description and understanding of internal waves in arbitrarily shaped enclosed domains, such as the ocean, or a planet liquid core, is still missing. In this work, the inviscid, linear inertial wave field is investigated by means of three dimensional ray tracing in spherical shell domains, having in mind possible oceanographic applications. Rays are here classically interpreted as representative of energy paths. But in contrast with previous studies, they are now launched with a non-zero initial zonal component allowing for a more realistic, localized forcing, and the development of azimuthal inhomogeneities. We find that meridional planes generally act in the shell geometry as a...
A New Triangular Flat Shell Element With Drilling Rotations
Damkilde, Lars
2008-01-01
A new flat triangular shell element has been developed based on a newly developed triangular plate bending element by the author and a new triangular membrane element with drilling degrees of freedom. The advantage of the drilling degree of freedom is that no special precautions have to be made...... in connecting with assembly of elements. Due to the drilling rotations all nodal degrees of freedom have stiffness, and therefore no artificial suppression of degrees of freedom are needed for flat or almost flat parts of the shell structure....
Gravitational collapse with rotating thin shells and cosmic censorship
Rocha, Jorge V
2015-01-01
Gravitational collapse of matter in the presence of rotation is a mostly unexplored topic but it might have important implications for cosmic censorship. Recently a convenient setup was identified to address this problem, by considering thin matter shells at the interface between two equal angular momenta Myers-Perry spacetimes in five dimensions. This note provides more details about the matching of such cohomogeneity-1 spacetimes and extends the results obtained therein to arbitrary higher odd dimensions. It is also pointed out that oscillatory orbits for shells in asymptotically flat spacetimes can be naturally obtained if the matter has a negative pressure component.
BIPOLAR MAGNETIC SPOTS FROM DYNAMOS IN STRATIFIED SPHERICAL SHELL TURBULENCE
Jabbari, Sarah; Brandenburg, Axel; Kleeorin, Nathan; Mitra, Dhrubaditya; Rogachevskii, Igor, E-mail: sarahjab@kth.se [Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, SE-10691 Stockholm (Sweden)
2015-06-01
Recent work by Mitra et al. (2014) has shown that in strongly stratified forced two-layer turbulence with helicity and corresponding large-scale dynamo action in the lower layer, and nonhelical turbulence in the upper, a magnetic field occurs in the upper layer in the form of sharply bounded bipolar magnetic spots. Here we extend this model to spherical wedge geometry covering the northern hemisphere up to 75° latitude and an azimuthal extent of 180°. The kinetic helicity and therefore also the large-scale magnetic field are strongest at low latitudes. For moderately strong stratification, several bipolar spots form that eventually fill the full longitudinal extent. At early times, the polarity of spots reflects the orientation of the underlying azimuthal field, as expected from Parker’s Ω-shaped flux loops. At late times their tilt changes such that there is a radial field of opposite orientation at different latitudes separated by about 10°. Our model demonstrates the spontaneous formation of spots of sizes much larger than the pressure scale height. Their tendency to produce filling factors close to unity is argued to be reminiscent of highly active stars. We confirm that strong stratification and strong scale separation are essential ingredients behind magnetic spot formation, which appears to be associated with downflows at larger depths.
Time-frequency analysis of the bistatic acoustic scattering from a spherical elastic shell.
Anderson, Shaun D; Sabra, Karim G; Zakharia, Manell E; Sessarego, Jean-Pierre
2012-01-01
The development of low-frequency sonar systems, using, for instance, a network of autonomous systems in unmanned vehicles, provides a practical means for bistatic measurements (i.e., when the source and receiver are widely separated) allowing for multiple viewpoints of the target of interest. Time-frequency analysis, in particular, Wigner-Ville analysis, takes advantage of the evolution time dependent aspect of the echo spectrum to differentiate a man-made target, such as an elastic spherical shell, from a natural object of the similar shape. A key energetic feature of fluid-loaded and thin spherical shell is the coincidence pattern, also referred to as the mid-frequency enhancement (MFE), that results from antisymmetric Lamb-waves propagating around the circumference of the shell. This article investigates numerically the bistatic variations of the MFE with respect to the monostatic configuration using the Wigner-Ville analysis. The observed time-frequency shifts of the MFE are modeled using a previously derived quantitative ray theory by Zhang et al. [J. Acoust. Soc. Am. 91, 1862-1874 (1993)] for spherical shell's scattering. Additionally, the advantage of an optimal array beamformer, based on joint time delays and frequency shifts is illustrated for enhancing the detection of the MFE recorded across a bistatic receiver array when compared to a conventional time-delay beamformer.
Acceleration of near-field scattering from an inhomogeneous spherical shell
M D Sharma
2005-08-01
The three dimensional scattering of near-field, from a point source, is studied for acceleration in the time domain. The perturbation method is applied to define the acceleration for the first order scattering from a weak inhomogeneity in a homogeneous surrounding. A body force, arising from the interaction between the primary waves and the inhomogeneity, acts as the source generating the scattered motion. The acceleration of scattered waves is related to the velocity and density fluctuations of the inhomogeneity. No restrictions are placed on the inhomogeneity size or locations of the source and receiver. Decoupling of scattered motion enables the identification of different phases. Integral expressions are derived for the scattering acceleration due to the incidence of near-field wave (from an impulsive point force) at a radially inhomogeneous volume element. These integrals are solved further for scattering from an inhomogeneous spherical shell. The accelerations for back scattering are obtained as a special case. These accelerations are simple analytically solvable expressions in closed form. Only spherical asymmetry of wave velocity inhomogeneity can affect the scattered acceleration. Scattered acceleration is affected by the gradient of wave velocity inhomogeneity. The back scattering of near-field from a spherical shell, is independent of radial inhomogeneity of wave velocity. Inhomogeneity with smoothly perturbed wave velocity does not back-scatter any acceleration. Accelerations are computed numerically for scattering from a part of inhomogeneous spherical shell. Hypothetical models are considered to study the effects of the distances of spherical shell from source, receiver, its thickness and its position relative to the direction of impulsive force.
Periodic mesoporous organosilica (PMO) materials with uniform spherical core-shell structure.
Haffer, Stefanie; Tiemann, Michael; Fröba, Michael
2010-09-10
We report the synthesis of monodisperse, spherical periodic mesoporous organosilica (PMO) materials. The particles have diameters between about 350 and 550 nm. They exhibit a regular core-shell structure with a solid, non-porous silica core and a mesoporous PMO shell with a thickness of approximately 75 nm and uniform pores of about 1.7 nm. The synthesis of the core and the shell is carried out in a one-pot, two-stage synthesis and can be accomplished at temperatures between 25 and 100 °C. Higher synthesis temperatures lead to substantial shrinking of the solid core, generating an empty void between core and shell. This leads to interesting cavitation phenomena in the nitrogen physisorption analysis at 77.4 K.
On the shape and orientation control of an orbiting shallow spherical shell structure
Bainum, P. M.; Reddy, A. S. S. R.
1982-01-01
The dynamics of orbiting shallow flexible spherical shell structures under the influence of control actuators was studied. Control laws are developed to provide both attitude and shape control of the structure. The elastic modal frequencies for the fundamental and lower modes are closely grouped due to the effect of the shell curvature. The shell is gravity stabilized by a spring loaded dumbbell type damper attached at its apex. Control laws are developed based on the pole clustering techniques. Savings in fuel consumption can be realized by using the hybrid shell dumbbell system together with point actuators. It is indicated that instability may result by not including the orbital and first order gravity gradient effects in the plant prior to control law design.
On the shape and orientation control of orbiting shallow spherical shell structure
Bainum, P. M.; Reddy, A. S. S. R.
1983-01-01
The dynamics of orbiting shallow flexible spherical shell structures under the influence of control actuators was studied. Control laws are developed to provide both attitude and shape control of the structure. The elastic modal frequencies for the fundamental and lower modes are closely grouped due to the effect of the shell curvature. The shell is gravity stabilized by a spring loaded dumbell type damper attached at its apex. Control laws are developed based on the pole clustering techniques. Savings in fuel consumption can be realized by using the hybrid shell dumbbell system together with point actuators. It is indicated that instability may result by not including the orbital and first order gravity gradient effects in the plant prior to control law design. Previously announced in STAR as N82-17243
Kinetic Model for a Spherical Rolling Robot with Soft Shell in a Beeline Motion
Sheng Zhang
2014-02-01
Full Text Available A simplified kinetic model called Spring Pendulum is developed for a spherical rolling robot with soft shell in order to meet the needs of attitude stabilization and controlling for the robot. The elasticity and plasticity of soft shell is represented by some uniform springs connected to the bracket in this model. The expression of the kinetic model is deduced from Newtonian mechanics principles. Testing data of the driving angle acquired from a prototype built by authors indicate that testing data curve accords to the theoretic kinetic characteristic curve, so the kinetic model is validated
Glass shell manufacturing in space. [residual gases in spherical shells made from metal-organic gels
Nolen, R. J.; Ebner, M. A.; Downs, R. L.
1980-01-01
Residual gases always found in glass shells are CO2, O2 and N2. In those cases where high water vapor pressure is maintained in the furnace, water is also found in the shells. Other evidence for the existence of water in shells is the presence of water-induced surface weathering of the interior shell surface. Water and CO2 are the predominant volatiles generated by the pyrolysis of both inorganic and hydrolyzed metal-organic gels. The pyrolysates of unhydrolyzed metal-organic gels also contain, in addition to water and CO2, significant levels of organic volatiles, such as ethanol and some hydrocarbons; on complete oxidation, these produce CO2 and water as well. Water is most likely the initial blowing agent, it is produced copiously during the initial stages of heating. In the later stages, CO2 becomes the dominant gas as H2O is lost at increasing rates. Water in the shell arises mainly from gel dehydration, CO2 by sodium bicarbonate/carbonate decomposition and carbon oxidation, and O2 and N2 by permeation of the ambient furnace air through the molten shell wall.
Spherical-shell boundaries for two-dimensional compressible convection in a star
Pratt, J; Goffrey, T; Geroux, C; Viallet, M; Folini, D; Constantino, T; Popov, M; Walder, R
2016-01-01
Context: We study the impact of two-dimensional spherical shells on compressible convection. Realistic profiles for density and temperature from a one-dimensional stellar evolution code are used to produce a model of a large stellar convection zone representative of a young low-mass star. Methods: We perform hydrodynamic implicit large-eddy simulations of compressible convection using the MUltidimensional Stellar Implicit Code (MUSIC). Because MUSIC has been designed to use realistic stellar models produced from one-dimensional stellar evolution calculations, MUSIC simulations are capable of seamlessly modeling a whole star. Simulations in two-dimensional spherical shells that have different radial extents are performed over hundreds of convective turnover times, permitting the collection of well-converged statistics. Results: We evaluate basic statistics of the convective turnover time, the convective velocity, and the overshooting layer. These quantities are selected for their relevance to one-dimensional s...
Ambiguity of the critical load for spherical shells with shear damageability of the material
Babich, D. V.; Dorodnykh, T. I.
2016-06-01
The structural-probabilistic approach to the modeling of combined crack formation and material deformation processes is used to develop a technique for solving bifurcation stability problems for thin-walled structural members made of damageable materials under single and repeated loadings. The example of a uniformly compressed spherical shell is used to show that, under repeated loading, thin-walled structural members made of shear damageable materials can lose stability under loads smaller than the upper critical loads. The ambiguity of the critical loads for various damage accumulation processes in the material of thin-walled structures depends on the level and character of loading. This phenomenon can be one possible cause of the experimental data spread and the discrepancy between theoretical and experimental results used to determine the critical loads for spherical and cylindrical shells.
Asari, Yusuke; Takeda, Kyozaburo; Tamura, Hiroyuki
2005-04-01
We theoretically studied the electronic structure of the three-dimensional spherical parabolic quantum dot (3D-SPQD) under a magnetic field. We obtained the quantum dot orbitals (QDOs) and determined the ground state by using the extended UHF approach where the expectation values of the z component of the total orbital angular momentum are conserved during the scf-procedure. The single-electron treatment predicts that the applied magnetic field (B) creates k-th new shells at the magnetic field of Bk=k(k+2)/(k+1)ω0 with the shell-energy interval of \\hbarω0/(k+1), where ω0(=\\hbar/m*l02) is the characteristic frequency originating from the spherical parabolic confinement potential. These shells are formed by the level crossing among multiple QDOs. The interelectron interaction breaks the simple level crossing but causes complicated dependences among the total energy, the chemical potential and their differences (magic numbers) with the magnetic field or the number of confinement electrons. The ground state having a higher spin multiplicity is theoretically predicted on the basis of the \\textit{quasi}-degeneracies of the QDOs around these shells.
ChenJnnming; HuangYuying
2003-01-01
Based on the motion differential equations of vibration and acoustic coupling system for thin elastic spherical shell with an elastic plate attached to its internal surface, in which Dirac-δ functions are employed to introduce the moments and forces applied by the attachment on the surface of shell, by means of expanding field quantities as Legendre series, a semi-analytic solution is derived for the vibration and acoustic radiation from a submerged stiffened spherical shell with a deck-type internal plate, which has a satisfactory computational effectiveness and precision for an arbitrary frequency range. It is easy to analyze the effect of the internal plate on the acoustic radiation field by using the formulas obtained by the method proposed. It is concluded that the internal plate can significantly change the mechanical and acoustic characteristics of shell, and give the coupling system a very rich resonance frequency spectrum. Moreover, the method can be used to study the acoustic radiation mechanism in similar structures as the one studied here.
Resonant vibrations and acoustic radiation of rotating spherical structures.
Shatalov, M
2006-07-01
Full Text Available and the second – equality of radial displacements of the sphere and the medium at r a= . mn − component of pressure in the acoustic medium is ( ( ) ( ) ( ) ( )2n n nh kr j kr i y kr= − ⋅ - Hankel spherical function, ( )mc - speed of sound in the acoustical... loaded surface for 2, 2; 3, 2; 3, 3n m n m n m= = = = = = . Parameters of the acoustic medium are: sound speed - ( ) 1500m mc s = and mass density - ( ) 31000m kg m ρ = . Corresponding values of the Bryan’s factors of the spheroidal modes are also...
Spherical convective dynamos in the rapidly rotating asymptotic regime
Aubert, Julien; Fournier, Alexandre
2016-01-01
Self-sustained convective dynamos in planetary systems operate in an asymptotic regime of rapid rotation, where a balance is thought to hold between the Coriolis, pressure, buoyancy and Lorentz forces (the MAC balance). Classical numerical solutions have previously been obtained in a regime of moderate rotation where viscous and inertial forces are still significant. We define a unidimensional path in parameter space between classical models and asymptotic conditions from the requirements to enforce a MAC balance and to preserve the ratio between the magnetic diffusion and convective overturn times (the magnetic Reynolds number). Direct numerical simulations performed along this path show that the spatial structure of the solution at scales larger than the magnetic dissipation length is largely invariant. This enables the definition of large-eddy simulations resting on the assumption that small-scale details of the hydrodynamic turbulence are irrelevant to the determination of the large-scale asymptotic state...
YUAN Xue-gang; ZHU Zheng-you; CHENG Chang-jun
2005-01-01
The radial symmetric motion problem was examined for a spherical shell composed of a class of imperfect incompressible hyper-elastic materials, in which the materials may be viewed as the homogeneous incompressible isotropic neo-Hookean material with radial perturbations. A second-order nonlinear ordinary differential equation that describes the radial motion of the inner surface of the shell was obtained.And the first integral of the equation was then carried out. Via analyzing the dynamical properties of the solution of the differential equation, the effects of the prescribed imperfection parameter of the material and the ratio of the inner and the outer radii of the underformed shell on the motion of the inner surface of the shell were discussed,and the corresponding numerical examples were carried out simultaneously. In particular, for some given parameters, it was proved that, there exists a positive critical value, and the motion of the inner surface with respect to time will present a nonlinear periodic oscillation as the difference between the inner and the outer presses does not exceed the critical value. However, as the difference exceeds the critical value, the motion of the inner surface with respect to time will increase infinitely. That is to say,the shell will be destroyed ultimately.
General thermo-elastic solution of radially heterogeneous, spherically isotropic rotating sphere
Bayat, Yahya; EkhteraeiToussi, THamid [Ferdowsi University of Mashhad, Mashhad (Iran, Islamic Republic of)
2015-06-15
A thick walled rotating spherical object made of transversely isotropic functionally graded materials (FGMs) with general types of thermo-mechanical boundary conditions is studied. The thermo-mechanical governing equations consisting of decoupled thermal and mechanical equations are represented. The centrifugal body forces of the rotation are considered in the modeling phase. The unsymmetrical thermo-mechanical boundary conditions and rotational body forces are expressed in terms of the Legendre series. The series method is also implemented in the solution of the resulting equations. The solutions are checked with the known literature and FEM based solutions of ABAQUS software. The effects of anisotropy and heterogeneity are studied through the case studies and the results are represented in different figures. The newly developed series form solution is applicable to the rotating FGM spherical transversely isotropic vessels having nonsymmetrical thermo-mechanical boundary condition.
Shen, Fei; An, Ning; Tao, Yifei; Zhou, Hongping; Jiang, Zhaoneng; Guo, Zhongyi
2017-08-01
We have investigated the scattering properties of an individual core-shell nanoparticle using the Mie theory, which can be tuned to support both electric and magnetic modes simultaneously. In general, the suppression of forward scattering can be realized by the second Kerker condition. Here, a novel mechanism has to be adopted to explain zero-forward scattering, which originates from the complex interactions between dipolar and quadrupolar modes. However, for lossy and lossless core-shell spherical nanoparticles, zero-forward scattering can never be achieved because the real parts of Mie expansion coefficients are always positive. By adding proper gain in dielectric shell, zero-forward scattering can be found at certain incident wavelengths, which means that all electric and magnetic responses in Mie scattering can be counteracted totally in the forward direction. In addition, if the absolute values of dipolar and quadrupolar terms are in the same order of magnitude, the local scattering minimum and maximum can be produced away from the forward and backward directions due to the interacting effect between the dipolar and quadrupolar terms. Furthermore, by adding suitable gain in shell, super-forward scattering can also be realized at certain incident wavelengths. We also demonstrated that anomalously weak scattering or superscattering could be obtained for the core-shell nanoparticles with suitable gain in shell. In particular, for such a choice of suitable gain in shell, we can obtain zero-forward scattering and anomalously weak scattering at the same wavelength as well as super-forward scattering at another wavelength. These features may provide new opportunities for cloaking, plasmonic lasers, optical antennas, and so on.
Analysis of stress-strain state of the spherical shallow shell with inclusion
O.B. Kozin
2016-05-01
Full Text Available Development of effective methods of determining the stress-strain state thin-walled structures with inclusions, reinforcements and other stress concentrators is an important task, both from a theoretical and practical point of view, by reason of their great practical application. Aim: The aim of the research is to analyze the elastic-deformed state of a spherical shallow shell. Materials and Methods: In this work, based on the generalized scheme of integral transformations, a constructive method of direct numerical-analytical solutions of boundary value problem of calculating the stress-strain state of a spherical shallow shell with the inclusion in bending is proposed. Results: The results of numerical calculations are presented. Calculations allow predicting the value of deformation of the cylindrical shells structure with reinforcements and determining the optimum parameters for the design or manufacture. The obtained results can be used in determining the strength characteristics of structural elements that consist of composite materials. The article contains comparative analysis of the results and demonstrates the effectiveness of the method for solving this class of problems.
Spherically Symmetric and Rotating Wormholes Produced by Lightlike Branes
Guendelman, Eduardo; Nissimov, Emil; Pacheva, Svetlana
2009-01-01
Lightlike p-branes (LL-branes) with dynamical (variable) tension allow simple and elegant Polyakov-type and dual to it Nambu-Goto-like world-volume action formulations. Here we first briefly describe the dynamics of LL-branes as test objects in various physically interesting gravitational backgrounds of black hole type, including rotating ones. Next we show that LL-branes are the appropriate gravitational sources that provide proper matter energy momentum tensors in the Einstein equations of motion needed to generate traversable wormhole solutions, in particular, self-consistent cylindrical rotating wormholes, with the LL-branes occupying their throats. Here a major role is being played by the dynamical LL-brane tension which turns out to be negative but may be of arbitrary small magnitude. As a particular solution we obtain traversable wormhole with Schwarzschild geometry generated by a LL-brane positioned at the wormhole throat, which represents the correct consistent realization of the original Einstein-Ro...
Lebiedzik, Catherine
1995-01-01
Development of design tools to furnish optimal acoustic environments for lightweight aircraft demands the ability to simulate the acoustic system on a workstation. In order to form an effective mathematical model of the phenomena at hand, we have begun by studying the propagation of acoustic waves inside closed spherical shells. Using a fully-coupled fluid-structure interaction model based upon variational principles, we have written a finite element analysis program and are in the process of examining several test cases. Future investigations are planned to increase model accuracy by incorporating non-linear and viscous effects.
Tan, Bing; Rankin, Stephen E
2005-08-30
Hollow spherical silica particles with hexagonally ordered mesoporous shells are synthesized with the dual use of cetyltrimethylammonium bromide (CTAB) and unmodified polystyrene latex microspheres as templates in concentrated aqueous ammonia. In most of the hollow mesoporous particles, cylindrical pores run parallel to the hollow core due to interactions of CTAB/silica aggregates with the latices. Effects on the product structure of the CTAB:latex ratio, the amount of aqueous ammonia, and the latex size are studied. Hollow particles with hexagonally patterned mesoporous shells are obtained at moderate CTAB:latex ratios. Too little CTAB causes silica shell growth without surfactant templating, and too much induces nucleation of new mesoporous silica particles without latex cores. The concentration of ammonia must be large to induce co-assembly of CTAB, silica, and latex into dispersed particles. The results are consistent with the formation of particles by addition of CTAB/silica aggregates to the surface of latex microspheres. When the size and number density of the latex microspheres are changed, the size of the hollow core and the shell thickness can be controlled. However, if the microspheres are too small (50 nm in this case), agglomerated particles with many hollow voids are obtained, most likely due to colloidal instability.
Ibral, Asmaa [Equipe d' Optique et Electronique du Solide, Département de Physique, Faculté des Sciences, Université Chouaïb Doukkali, B. P. 20 El Jadida principale, El Jadida, Royaume du Maroc (Morocco); Laboratoire d' Instrumentation, Mesure et Contrôle, Département de Physique, Faculté des Sciences, Université Chouaïb Doukkali, B. P. 20 El Jadida principale, El Jadida, Royaume du Maroc (Morocco); Zouitine, Asmaa [Département de Physique, Ecole Nationale Supérieure d' Enseignement Technique, Université Mohammed V Souissi, B. P. 6207 Rabat-Instituts, Rabat, Royaume du Maroc (Morocco); Assaid, El Mahdi, E-mail: eassaid@yahoo.fr [Equipe d' Optique et Electronique du Solide, Département de Physique, Faculté des Sciences, Université Chouaïb Doukkali, B. P. 20 El Jadida principale, El Jadida, Royaume du Maroc (Morocco); Laboratoire d' Instrumentation, Mesure et Contrôle, Département de Physique, Faculté des Sciences, Université Chouaïb Doukkali, B. P. 20 El Jadida principale, El Jadida, Royaume du Maroc (Morocco); and others
2015-02-01
Poisson equation is solved analytically in the case of a point charge placed anywhere in a spherical core/shell nanostructure, immersed in aqueous or organic solution or embedded in semiconducting or insulating matrix. Conduction and valence band-edge alignments between core and shell are described by finite height barriers. Influence of polarization charges induced at the surfaces where two adjacent materials meet is taken into account. Original expressions of electrostatic potential created everywhere in the space by a source point charge are derived. Expressions of self-polarization potential describing the interaction of a point charge with its own image–charge are deduced. Contributions of double dielectric constant mismatch to electron and hole ground state energies as well as nanostructure effective gap are calculated via first order perturbation theory and also by finite difference approach. Dependencies of electron, hole and gap energies against core to shell radii ratio are determined in the case of ZnS/CdSe core/shell nanostructure immersed in water or in toluene. It appears that finite difference approach is more efficient than first order perturbation method and that the effect of polarization charge may in no case be neglected as its contribution can reach a significant proportion of the value of nanostructure gap.
Chifu E. N.
2009-07-01
Full Text Available General Relativistic metric tensors for gravitational fields exterior to homogeneous spherical mass distributions rotating with constant angular velocity about a fixed di- ameter are constructed. The coeffcients of affine connection for the gravitational field are used to derive equations of motion for test particles. The laws of conservation of energy and angular momentum are deduced using the generalized Lagrangian. The law of conservation of angular momentum is found to be equal to that in Schwarzschild’s gravitational field. The planetary equation of motion and the equation of motion for a photon in the vicinity of the rotating spherical mass distribution have rotational terms not found in Schwarzschild’s field.
Stochastic Circumplanetary Dynamics of Rotating Non-Spherical Dust Particles
Makuch, Martin; Brilliantov, N. V.; Sremcevic, M.; Spahn, F.; Krivov, A. V.
2006-12-01
Influence of stochastically fluctuating radiation pressure on the dynamics of dust grains on circumplanetary orbits was studied. Stochasticity stems from the permanent change of the particle cross-section due to rotation of nonspherical grains, exposed to the solar radiation. We found that stochasticity depends on the characteristic angular velocity of particles which, according to our estimates, spins very fast on the time scale of the orbital motion. According to this we modelled the stochastic part of the radiation pressure by a Gaussian white noise. Gauss perturbation equations with the radiation pressure being a sum of the deterministic and stochastic component have been used. We observed monotonous increasing standard deviation of the orbital elements, that is, the diffusive-like behaviour of the ensemble, which results in a spatial spreading of initially confined set of particles. By linear approximation we obtained expression for the effective diffusion coefficients and estimate their dependence on the geometrical characteristics of particles and their spin. Teoretical results were compared with numerical simulations performed for the putative dust tori of Mars. Our theory agrees fairly well with simulations for the initial period of the system evolution. The agreement however deteriorates with increasing time where impact of the non-linear terms of the perturbation equations becomes important. Analysis shows that the theoretical results may estimate the low boundary of the time-dependent standard deviation of the orbital elements. In the case of dust ejected from Martian moon Deimos we observed a change of orbital elements up to 10% of their initial values during the first 1000 years of orbital evolution. Our results indicate that the stochastic modulation of the radiation pressure can play an important role in the circumplanetary dynamics of dust and may, together with further noise sources (shadow, planetary bowshock, charge fluctuations, etc
Tearing of thin spherical shells adhered to equally curved rigid substrates
McMahan, Connor; Lee, Anna; Marthelot, Joel; Reis, Pedro
Lasik (Laser-Assisted in Situ Keratomileusis) eye surgery involves the tearing of the corneal epithelium to remodel the corneal stroma for corrections such as myopia, hyperopia and astigmatism. One issue with this procedure is that during the tearing of the corneal epithelium, if the two propagating cracks coalesce, a flap detaches which could cause significant complications in the recovery of the patient. We seek to gain a predictive physical understanding of this process by performing precision desktop experiments on an analogue model system. First, thin spherical shells of nearly uniform thickness are fabricated by the coating of hemispherical molds with a polymer solution, which upon curing yields an elastic and brittle structure. We then create two notches near the equator of the shell and tear a flap by pulling tangentially to the spherical substrate, towards its pole. The resulting fracture paths are characterized by high-resolution 3D digital scanning. Our primary focus is on establishing how the positive Gaussian curvature of the system affects the path of the crack tip. Our results are directly contrasted against previous studies on systems with zero Gaussian curvature, where films were torn from planar and cylindrical substrates.
Buckling Capacity Curves for Steel Spherical Shells Loaded by the External Pressure
Błażejewski Paweł
2015-03-01
Full Text Available Assessment of buckling resistance of pressurised spherical cap is not an easy task. There exist two different approaches which allow to achieve this goal. The first approach involves performing advanced numerical analyses in which material and geometrical nonlinearities would be taken into account as well as considering the worst imperfections of the defined amplitude. This kind of analysis is customarily called GMNIA and is carried out by means of the computer software based on FEM. The other, comparatively easier approach, relies on the utilisation of earlier prepared procedures which enable determination of the critical resistance pRcr, the plastic resistance pRpl and buckling parameters a, b, h, l 0 needed to the definition of the standard buckling resistance curve. The determination of the buckling capacity curve for the particular class of spherical caps is the principal goal of this work. The method of determination of the critical pressure and the plastic resistance were described by the authors in [1] whereas the worst imperfection mode for the considered class of spherical shells was found in [2]. The determination of buckling parameters defining the buckling capacity curve for the whole class of shells is more complicated task. For this reason the authors focused their attention on spherical steel caps with the radius to thickness ratio of R/t = 500, the semi angle j = 30o and the boundary condition BC2 (the clamped supporting edge. Taking into account all imperfection forms considered in [2] and different amplitudes expressed by the multiple of the shell thickness, sets of buckling parameters defining the capacity curve were determined. These parameters were determined by the methods proposed by Rotter in [3] and [4] where the method of determination of the exponent h by means of additional parameter k was presented. As a result of the performed analyses the standard capacity curves for all considered imperfection modes and
Tidal instability in a rotating and differentially heated ellipsoidal shell
Cébron, David; Bars, Michael Le; 10.1111/j.1365-246X.2010.04712.x
2010-01-01
The stability of a rotating flow in a triaxial ellipsoidal shell with an imposed temperature difference between inner and outer boundaries is studied numerically. We demonstrate that (i) a stable temperature field encourages the tidal instability, (ii) the tidal instability can grow on a convective flow, which confirms its relevance to geo- and astrophysical contexts and (iii) its growth rate decreases when the intensity of convection increases. Simple scaling laws characterizing the evolution of the heat flux based on a competition between viscous and thermal boundary layers are derived analytically and verified numerically. Our results confirm that thermal and tidal effects have to be simultaneously taken into account when studying geophysical and astrophysical flows.
Rodríguez-Magdaleno, K. A.; Pérez-Álvarez, R.; Martínez-Orozco, J. C.; Pernas-Salomón, R.
2017-04-01
In this work the generation of an intermediate band of energy levels from multi-shell spherical GaAs /AlxGa1-x As quantum dot shells-size distribution is reported. Within the effective mass approximation the electronic structure of a GaAs spherical quantum-dot surrounded by one, two and three shells is studied in detail using a numerically stable transfer matrix method. We found that a shells-size distribution characterized by continuously wider GaAs domains is a suitable mechanism to generate the intermediate band whose width is also dependent on the Aluminium concentration x. Our results suggest that this effective mechanism can be used for the design of wider intermediate band than reported in other quantum systems with possible solar cells enhanced performance.
Hanson Huang
1996-01-01
Full Text Available A detailed solution to the transient interaction of plane acoustic waves with a spherical elastic shell was obtained more than a quarter of a century ago based on the classical separation of variables, series expansion, and Laplace transform techniques. An eight-term summation of the time history series was sufficient for the convergence of the shell deflection and strain, and to a lesser degree, the shell velocity. Since then, the results have been used routinely for validation of solution techniques and computer methods for the evaluation of underwater explosion response of submerged structures. By utilizing modern algorithms and exploiting recent advances of computer capacities and floating point mathematics, sufficient terms of the inverse Laplace transform series solution can now be accurately computed. Together with the application of the Cesaro summation using up to 70 terms of the series, two primary deficiencies of the previous solution are now remedied: meaningful time histories of higher time derivative data such as acceleration and pressure are now generated using a sufficient number of terms in the series; and uniform convergence around the discontinuous step wave front is now obtained, completely eradicating spurious oscillations due to the Gibbs' phenomenon. New results of time histories of response items of interest are presented.
Compressional Alfvén eigenmodes in rotating spherical tokamak plasmas
Smith, H. M.; Fredrickson, E. D.
2017-03-01
Spherical tokamaks often have a considerable toroidal plasma rotation of several tens of kHz. Compressional Alfvén eigenmodes in such devices therefore experience a frequency shift, which if the plasma were rotating as a rigid body, would be a simple Doppler shift. However, since the rotation frequency depends on minor radius, the eigenmodes are affected in a more complicated way. The eigenmode solver CAE3B (Smith et al 2009 Plasma Phys. Control. Fusion 51 075001) has been extended to account for toroidal plasma rotation. The results show that the eigenfrequency shift due to rotation can be approximated by a rigid body rotation with a frequency computed from a spatial average of the real rotation profile weighted with the eigenmode amplitude. To investigate the effect of extending the computational domain to the vessel wall, a simplified eigenmode equation, yet retaining plasma rotation, is solved by a modified version of the CAE code used in Fredrickson et al (2013 Phys. Plasmas 20 042112). In summary, both solving the full eigenmode equation, as in the CAE3B code, and placing the boundary at the vessel wall, as in the CAE code, significantly influences the calculated eigenfrequencies.
无
2008-01-01
Plastic limit load of viscoplastic thick-walled cylinder and spherical shell subjected to internal pressure is investigated analytically using a strain gradient plastic-itv theory. As a result, the current solutions can capture the size effect at the micron scale. Numerical results show that the smaller the inner radius of the cylinder or spherical shell, the more significant the scale effects. Results also show that the size effect is more evident with increasing strain or strain-rate sensitivity index. The classical plastic-based solutions of the same problems are shown to be a special case of the present solution.
Grekova, E. F.
2012-09-01
We consider a linear reduced Cosserat medium: a linear elastic continuum, whose point bodies possess kinematically independent translational and rotational degrees of freedom, but the strain energy does not depend on the gradient of rotation of particles. In such a medium the force stress tensor is asymmetric, but the couple stress tensor is zero. This model can be applied for description of soils and granular media. Since for the time being the experimental technique for measurement of rotational deformations is not well developed, we investigate how the presence of rotational degrees of freedom affects the dynamics of translational displacements. We consider the case of the spherical tensor of inertia and isotropy with respect to the rotational degrees of freedom. Integration of the equation of balance of torques lets us in several cases to put in correspondence a linear reduced Cosserat continuum with the spherical tensor of inertia with a classical (non-polar elastic linear) medium with memory with the same equation for the balance of forces, written in terms of translational displacements. This is possible for the isotropic case and also if the anisotropy is present only in the tensor of elastic constants corresponding to the classical strain tensor. If the material is isotropic with respect to rotational deformations but the (anisotropic) coupling between rotational and classical translational strains is present, then the corresponding classical medium does not exist. If we ignore the rotational degrees of freedom when this coupling is present, this will lead us to the conclusion that the principle of material objectivity is violated.
Jensen, Jens Højgaard
2014-01-01
In a recent paper (Robinson G and Robinson I 2013 Phys. Scr. 88 018101) the authors developed the differential equations which govern the motion of a spherical projectile rotating about an arbitrary axis in the presence of an arbitrary wind, assuming that both the drag force and the lift force are independent of the Reynolds number and proportional to the square of the projectile's velocity. In this paper, by dimensional analysis, the latter assumption is shown to be incorrect for forces depe...
The Three-dimensional Structure of the Cassiopeia A Supernova Remnant. I. The Spherical Shell
Reed, Jeri E.; Hester, J. Jeff; Fabian, A. C.; Winkler, P. F.
1995-02-01
The three-dimensional structure of the Cassiopeia A supernova remnant is explored via 73 long-slit optical spectra (spanning 6250-7600 Å) which cross the face and "jet" region of the nebula. We extracted position, radial velocity, and line intensity information from nearly 25,000 cross sections of these original data, resulting in a library of 3663 fast-moving knots (FMKs) and 450 quasi-stationary flocculi (QSFs) detections. We performed an iterative least-squares spherical fit to the data, using this to convert radial velocities to line-of-sight distances. We have built up a picture of the remnant as a spherical circumstellar shell of 104"5±0"7 radius, corresponding to 5.3 × 1018 cm (1.7 pc). The center on the sky is displaced by 8".7 west and 12".6 north of the proper motion center. The velocity center of our fitted sphere has been redshifted by 770±40 km s-1 from the presumed expansion center at zero velocity. This expansion of the ejecta from a displaced center accounts for the observed radial velocity difference at the front and back faces. The average rate of expansion of the FMKs is 5290±90 km s-1, while the asymmetric values are 4520 km s-1 at the blueshifted face, and 6060 km s-1 at the redshifted face. Based on a comparison of our suite of radial velocities with all the available proper-motion and age data, we find the distance to Cas A to be 3.4+0.3-0.1 kpc. Our kinematic analysis shows the optically emitting ejecta of Cas A have been slowed certainly by less than 7%, and probably by less than 4% and that the velocity of the reverse shock driven into the knots is about 200 km s-1. We conclude that the center of expansion of the supernova is displaced by about 0.36 pc (1.1 × 1018 cm) to the northwest and front of the geometric center of the bubble. The geometry suggests that the density of the surrounding medium is greater in the direction of displacement. The asymmetrically distributed radial velocities of the QSFs, of which 76% are blueshifted
Counter-rotational effects on stability of 2 + 1-dimensional thin-shell wormholes
Mazharimousavi, S.H.; Halilsoy, M. [Eastern Mediterranean University, Department of Physics, Gazimagusa (Turkey)
2014-09-15
The role of angular momentum in a 2 + 1-dimensional rotating thin-shell wormhole (TSW) is considered. Particular emphasis is given to stability when the shells (rings) are counter-rotating. We find that counter-rotating halves make the TSW supported by the equation of state of a linear gas more stable. Under a small velocity dependent perturbation, however, it becomes unstable. (orig.)
Voorhies, C. V.
1999-01-01
The idea that geomagnetic westward drift indicates convective leveling of the planetary momentum gradient within Earth's core is pursued in search of a differentially rotating mean state, upon which various oscillations and secular effects might be superimposed. The desired state conforms to roughly spherical boundary conditions, minimizes dissipative interference with convective cooling in the bulk of the core, yet may aide core cooling by depositing heat in the uppermost core and lower mantle. The variational calculus of stationary dissipation applied to a spherical vortex within the core yields an interesting differential rotation profile akin to spherical Couette flow bounded by thin Hartmann layers. Four boundary conditions are required. To concentrate shear induced dissipation near the core-mantle boundary, these are taken to be: (i) no-slip at the core-mantle interface; (ii) geomagnetically estimated bulk westward flow at the base of the core-mantle boundary layer; (iii) no-slip at the inner-outer core interface; and, to describe magnetic locking of the inner core to the deep outer core, (iv) hydrodynamically stress-free at the inner-outer core boundary. By boldly assuming the axial core angular momentum anomaly to be zero, the super-rotation of the inner core is calculated to be at most 1.5 degrees per year.
THERMOELASTICALLY COUPLED AXISYMMETRIC NONLINEAR VIBRATION OF SHALLOW SPHERICAL AND CONICAL SHELLS
王永岗; 戴诗亮
2004-01-01
The problem of axisymmetric nonlinear vibration for shallow thin spherical and conical shells when temperature and strain fields are coupled is studied. Based on the large deflection theories of von Krmn and the theory of thermoelasticity, the whole governing equations and their simplified type are derived. The time-spatial variables are separated by Galerkin's technique, thus reducing the governing equations to a system of time-dependent nonlinear ordinary differential equation. By means of regular perturbation method and multiple-scales method, the first-order approximate analytical solution for characteristic relation of frequency vs amplitude parameters along with the decay rate of amplitude are obtained, and the effects of different geometric parameters and coupling factors as well as boundary conditions on thermoelastically coupled nonlinear vibration behaviors are discussed.
On the Zero-Point Energy of a Conducting Spherical Shell
Esposito, G; Kirsten, K; Esposito, Giampiero; Kamenshchik, Alexander Yu.; Kirsten, Klaus
1999-01-01
The zero-point energy of a conducting spherical shell is evaluated by imposing boundary conditions on the potential A, and on the ghost fields. The scheme requires that temporal and tangential components of perturbations of A should vanish at the boundary, jointly with the gauge-averaging functional, here chosen of the Lorenz type. Gauge invariance of such boundary conditions is then obtained provided that the ghost fields vanish at the boundary. Normal and longitudinal modes of the potential obey an entangled system of eigenvalue equations, whose solution is a linear combination of Bessel functions under the above assumptions, and with the help of the Feynman choice for a dimensionless gauge parameter. Interestingly, ghost modes cancel exactly the contribution to the Casimir energy resulting from transverse and temporal modes of A, jointly with the decoupled normal mode of A. Moreover, normal and longitudinal components of A for the interior and the exterior problem give a result in complete agreement with t...
Geoid and topography for infinite Prandtl number convection in a spherical shell
Bercovici, D.; Schubert, G.; Zebib, A.
1988-01-01
Geoid anomalies and surface and lower-boundary topographies are calculated for numerically generated thermal convection for an infinite Prandtl number, Boussinesq, axisymmetric spherical fluid shell with constant gravity and viscosity, for heating both entirely from below and entirely from within. Convection solutions are obtained for Rayleigh numbers Ra up to 20 times the critical Ra in heating from below and 27 times critical for heating from within. Geoid parallels surface undulations, and boundary deformation generally increases with increasing cell wavelength. Dimensionless geoid and topography in heating from below are about 5 times greater than in heating from within. Values for heating from within correlate more closely with geophysical data than values from heating from below, suggesting a predominance of internal heating in the mantle. The study emphasizes that dynamically induced topography and geoid are sensitive to the mode of heating in the earth's mantle.
Stabilization of the resistive wall mode using a fake rotating shell
Fitzpatrick, R. [Texas Univ., Austin, TX (United States). Inst. for Fusion Studies; Jensen, T.H. [General Atomics, La Jolla, CA (United States)
1995-11-01
Tokamak plasma performance can, in theory, be greatly improved if the so called resistive wall mode is stabilized. This can be achieved by spinning the plasma rapidly, but such a scheme is not reactor relevant. A more promising approach is to apply external feedback in order to make a resistive shell placed around the plasma act like a perfect conductor. A scheme is outlined by which a network of feedback controlled conductors surrounding the plasma can be made to act like a rotating shell. This fake rotating shell combined with a stationary conventional shell (e.g. the vacuum vessel) can completely stabilize the resistive wall mode. The gain, bandwidth, current, and power requirements of the feedback amplifiers are extremely modest. A previously proposed stabilization scheme (the intelligent shell) is also investigated, and is compared with the fake rotating shell concept. The main disadvantage of the former scheme is that it requires a high gain.
Jouve, Laurene
2009-01-01
We present the first 3D MHD study in spherical geometry of the non-linear dynamical evolution of magnetic flux tubes in a turbulent rotating convection zone. We study numerically the rise of magnetic toroidal flux ropes from the base of a modelled convection zone up to the top of our computational domain where bipolar patches are formed. We compare the dynamical behaviour of flux tubes in a fully convective shell possessing self-consistently generated mean flows such as meridional circulation and differential rotation, with reference calculations done in a quiet isentropic zone. We find that two parameters influence the tubes during their rise through the convection zone: the initial field strength and amount of twist, thus confirming previous findings in Cartesian geometry. Further, when the tube is sufficiently strong with respect to the equipartition field, it rises almost radially independently of the initial latitude (either low or high). By contrast, weaker field cases indicate that downflows and upflow...
Pustovalov, V. K.; Astafyeva, L. G.; Zharov, V. P.
2013-12-01
Modeling of nonlinear dependences of optical properties of spherical two-layered gold core and some material shell nanoparticles (NPs) placed in water on parameters of core and shell was carried out on the basis of the extended Mie theory. Efficiency cross-sections of absorption, scattering and extinction of radiation with wavelength 532 nm by core-shell NPs in the ranges of core radii r00=5-40 nm and of relative NP radii r1/r00=1-8 were calculated (r1-radius of two-layered nanoparticle). Shell materials were used with optical indexes in the ranges of refraction n1=0.2-1.5 and absorption k1=0-3.5 for the presentation of optical properties of wide classes of shell materials (including dielectrics, metals, polymers, vapor shell around gold core). Results show nonlinear dependences of optical properties of two-layered NPs on optical indexes of shell material, core r00 and relative NP r1/r00 radii. Regions with sharp decrease and increase of absorption, scattering and extinction efficiency cross-sections with changing of core and shell parameters were investigated. These dependences should be taken into account for applications of two-layered NPs in laser nanomedicine and optical diagnostics of tissues. The results can be used for experimental investigation of shell formation on NP core and optical determination of geometrical parameters of core and shell of two-layered NPs.
The structure of the spherical tensor forces in the USD and GXPF1A shell model Hamiltonians
WANG Han-Kui; GAO Zao-Chun; CHEN Yong-Shou; GUO Jian-You; CHEN Yong-Jing; TU Ya
2011-01-01
The realistic shell model Hamiltonians, USD and GXPF1A, have been transformed from the particle-particle (normal) representation to the particle-hole representation (multipole-multipole)by using the known formulation in Ref. [1].The obtained multipole-multipole terms were compared with the known spherical tensor forces, including the coupled ones. It is the first time the contributions of the coupled tensor forces to the shell model Hamiltonian have been investigated. It has been shown that some coupled-tensor forces, such as [r2Y2σ]1,also give important contributions to the shell model Hamiltonian.
Sauret, Alban; Morize, Cyprien; Bars, Michael Le; 10.1017/S0022112010004052
2011-01-01
We study both experimentally and numerically the steady zonal flow generated by longitudinal librations of a spherical rotating container. This study follows the recent weakly nonlinear analysis of Busse (2010), developed in the limit of small libration frequency - rotation rate ratio, and large libration frequency - spin-up time product. Using PIV measurements as well as results from axisymmetric numerical simulations, we confirm quantitatively the main features of Busse's analytical solution: the zonal flow takes the form of a retrograde solid body rotation in the fluid interior, which does not depend on the libration frequency nor on the Ekman number, and which varies as the square of the amplitude of excitation. We also report the presence of an unpredicted prograde flow at the equator near the outer wall.
Transient Response of a Fluid-Filled, Thick-Walled Spherical Shell Embedded in an Elastic Medium
Bahari Ako
2016-01-01
Full Text Available The paper addresses the problem of transient elastodynamics analysis of a thick-walled, fluid-filled spherical shell embedded in an elastic medium with an analytical approach. This configuration is investigated at first step for a full-space case. Different constitutive relations for the elastic medium, shell material and filling fluid can be considered, as well as different excitation sources (including S/P wave or plane/spherical incident wave at different locations. With mapmaking visualisation, the wave propagation phenomena can be described and better understood. The methodology is going to be applied to analysis of the tunnels or other shell like structures under the effect of nearby underground explosion.
Rectangular rotation of spherical harmonic expansion of arbitrary high degree and order
Fukushima, Toshio
2017-02-01
In order to move the polar singularity of arbitrary spherical harmonic expansion to a point on the equator, we rotate the expansion around the y-axis by 90° such that the x-axis becomes a new pole. The expansion coefficients are transformed by multiplying a special value of Wigner D-matrix and a normalization factor. The transformation matrix is unchanged whether the coefficients are 4 π fully normalized or Schmidt quasi-normalized. The matrix is recursively computed by the so-called X-number formulation (Fukushima in J Geodesy 86: 271-285, 2012a). As an example, we obtained 2190× 2190 coefficients of the rectangular rotated spherical harmonic expansion of EGM2008. A proper combination of the original and the rotated expansions will be useful in (i) integrating the polar orbits of artificial satellites precisely and (ii) synthesizing/analyzing the gravitational/geomagnetic potentials and their derivatives accurately in the high latitude regions including the arctic and antarctic area.
Drag and Lift Force Acting on a Rotational Spherical Particle in a Logarithmic Boundary Flow
XU Wei-jiang; CHE De-fu; XU Tong-mo
2006-01-01
The drag and lift forces acting on a rotational spherical particle in a logarithmic boundary flow are numerically studied. The effects of the drag velocity and rotational speed of the sphere on the drag force are examined for the particle Reynolds number from 50 to 300 and for the dimensionless rotational angular speed of 0≤Ω≤1.0. The influence of dimensionless roughness height z0of the wall is also evaluated for z0≤10. The results show that the drag forces on a sphere both in a logarithmic flow and in a uniform unsheared flow increase with the increase of the drag velocity. For 50≤Rep≤300, the drag coefficient (-C)D increases with decreased roughness height z0. The time-averaged drag coefficient is also significantly affected by rotational speed of the sphere and roughness height z0 . The lift coefficient -CL increases with increased rotational speed and decreases with increased roughness height.
An investigation of the Buchdahl inequality for spherically symmetric static shells
Andreasson, Haakan [Department of Mathematics, Chalmers, S-41296 Goeteborg (Sweden)
2007-05-15
A classical result by Buchdahl [9] shows that a class of static spherically symmetric solutions of the Einstein equations obey the inequality 2M/R {<=} 8/9, where M is the total ADM mass and R the area radius of the body. Buchdahl's proof rests on the hypotheses that the energy density is non-increasing outwards and that the pressure is isotropic. In this work neither of Buchdahl's hypotheses are assumed. We consider non-isotropic spherically symmetric shells, supported in [R{sub 0}, R{sub 1}], R{sub 0} > 0, of matter models for which the energy density {rho} {>=} 0, and the radial- and tangential pressures p {>=} 0 and q, satisfy p + q {<=} {omega}{rho}, {omega} {>=} 1. Note that this inequality holds with {omega} = 3 for any matter model which satisfies the dominant energy condition. We show a Buchdahl type inequality for shells which are thin; given an {epsilon} < 1/4 there is a {kappa} > 0 such that 2M/R{sub 1} {<=} 1 - {kappa} when R{sub 1}/R{sub 0} 1 + {epsilon}. It is also shown that for a sequence of solutions such that R{sub 1}/R{sub 0} {yields} 1, the limit supremum of 2M/R{sub 1} of the sequence is bounded by ((2{omega} + 1){sup 2} - 1)/(2{omega} + 1){sup 2} (which equals 8/9 if {omega} = 1). We emphasize that no field equations for the matter are used for this result. However, in the second part we consider the Einstein-Vlasov system and use the matter field equation to construct a family of static solutions with the property that R{sub 1}/R{sub 0} {yields} 1. We also show that for this sequence the value 8/9 of 2M/R{sub 1} is attained in the limit (note that {omega} = 1 for Vlasov matter). The energy density of this sequence get more and more peaked, which should be contrasted to the solution for which 2M/R = 8/9 in Buchdahl's original work where {rho} is constant and p blows up at r = 0. Clearly, this solution cannot satisfy the inequality p = q {<=} {omega}{rho}, in particular it violates the dominant energy condition.
Niordson, Christian F.; Nielsen, S.B.
2006-01-01
to a spherical thin elastic shell. This configuration is required when geoscience studies move from local scenarios, where the flat-Earth approximation holds, to plate-scale or global scenarios, where the correct application of far-field boundary conditions and the spherical geometry becomes of primary......The thin elastic plate model (the Kirchhoff model) in one and two space dimensions has proved extremely useful in providing a simple model of transverse deflections of the Earths lithosphere as a function of transverse loads. For example, the foreland basin of a mountain range is explained...
Relativistic dynamics of cylindrical shells of counter-rotating particles
Hamity, V H; Barraco, D E
2007-01-01
Although infinite cylinders are not astrophysical entities, it is possible to learn a great deal about the basic qualitative features of generation of gravitational waves and the behavior of the matter conforming such shells in the limits of very small radius. We describe the analytical model using kinetic theory for the matter and the junction conditions through the shell to obtain its equation of motion. The nature of the static solutions are analyzed, both for a single shell as well as for two concentric shells. In this second case, for a time dependent external shell, we integrate numerically the equation of motion for several values of the constants of the system. Also, a brief description in terms of the Komar mass is given to account for the gravitational wave energy emitted by the system.
Scattering of a spherical pulse from a small inhomogeneity: Dilation and rotation
M D Sharma
2001-09-01
Perturbations in elastic constants and density distinguish a volume inhomogeneity from its homogeneous surroundings. The equation of motion for the first order scattering is studied in the perturbed medium. The scattered waves are generated by the interaction between the primary waves and the inhomogeneity. First order scattering theory is modified to include the source term generating the primary waves. The body force equivalent to the scattering source is presented in a convenient form involving the perturbations in wave velocities and gradient of density perturbation. A procedure is presented to study the scattering of a spherical pulse from a small inhomogeneity, in time domain. The size of inhomogeneity is assumed small as compared to its distance from source and receiver. No restrictions are placed on the positions of source, receiver and inhomogeneity. The dilatation and rotations are calculated for a pulse scattered from an arbitrary point in a spherical volume. The aggregate of the scattered phases from all the points of the inhomogeneity, reaching at a fixed receiver, gives the amount of scattering from the inhomogeneity. The interaction of both P and S waves with inhomogeneity are considered. Dilatation and rotations for scattering are obtained as integral expressions over the solid angle of inhomogeneity. These expressions are computed numerically, for hypothetical models. The effects of source (unit force) orientations, velocity and density perturbations, and size of inhomogeneity, on the scattered phases, are discussed.
Demonstration of counter beam fast heating scheme by using a spherical CD shell target
Mori, Y.; Nishimura, Y.; Hanayama, R.; Nakayama, S.; Ishii, K.; Kitagawa, Y.; Sekine, T.; Takeuchi, Y.; Kurita, T.; Kato, Y.; Sato, N.; Kurita, N.; Kawashima, T.; Hioki, T.; Motohiro, T.; Sunahara, A.; Sentoku, Y.; Miura, E.; Iwamoto, A.; Sakagami, H.
2016-10-01
We report fast heating of a shock-imploded core under counter beam configuration that published in recent. Experiments are performed by using a repetitive IFE driver HAMA. Experiments results show that (i) a shock-imploded core with 70 micron diameter, originally deuterated polystyrene (CD) spherical shell of 500 micron diameter, is flashed by counter irradiating 110 fs, 7 TW laser pulses. The coupling efficiency from the laser to the core emission was inferred 13%. A collisional Particle-In-Cell simulation code PICLS2D indicates a possibility that counter hot electron currents generate magnetic filaments in the imploded core. (ii) Fast electrons with energy bellow a few MeV might be trapped by these filaments in the core region supposed to be contributing to the observed X-ray flash and the high coupling efficiency. These results indicate a possibility that counter irradiating fast heating scheme can improve the energy coupling into the core by hot electrons those are limited to less 10% for one-side irradiation fast heating conducted so far.
A spherical shell target scheme for laser-driven neutron sources
He, Min-Qing, E-mail: he-minqing@iapcm.ac.cn; Zhang, Hua; Wu, Si-Zhong; Wu, Jun-Feng; Chen, Mo [Institute of Applied Physics and Computational Mathematics, Beijing 100094 (China); Cai, Hong-Bo, E-mail: cai-hongbo@iapcm.ac.cn; Zhou, Cang-Tao; Cao, Li-Hua; Zheng, Chun-Yang; Zhu, Shao-Ping; He, X. T. [Institute of Applied Physics and Computational Mathematics, Beijing 100094 (China); HEDPS, Center for Applied Physics and Technology, Peking University, Beijing 100871 (China); Dong, Quan-Li [School of Physics and Optoelectronic Engineering, Ludong University, Yantai 260405 (China); Sheng, Zheng-Ming [Department of Physics, Jiaotong University, Shanghai 200240 (China); Pei, Wen-Bing [Shanghai Institute of Laser Plasma, Shanghai 201800 (China)
2015-12-15
A scheme for neutron production is investigated in which an ultra-intense laser is irradiated into a two-layer (deuterium and aurum) spherical shell target through the cone shaped entrance hole. It is found that the energy conversion efficiency from laser to target can reach as high as 71%, and deuterium ions are heated to a maximum energy of several MeV from the inner layer surface. These ions are accelerated towards the center of the cavity and accumulated finally with a high density up to tens of critical density in several picoseconds. Two different mechanisms account for the efficient yield of the neutrons in the cavity: (1) At the early stage, the neutrons are generated by the high energy deuterium ions based on the “beam-target” approach. (2) At the later stage, the neutrons are generated by the thermonuclear fusion when the most of the deuterium ions reach equilibrium in the cavity. It is also found that a large number of deuterium ions accelerated inward can pass through the target center and the outer Au layer and finally stopped in the CD{sub 2} layer. This also causes efficient yield of neutrons inside the CD{sub 2} layer due to “beam-target” approach. A postprocessor has been designed to evaluate the neutron yield and the neutron spectrum is obtained.
Shanqing Li; Hong Yuan
2010-01-01
The idea of Green quasifunction method is clarified in detail by considering a free vibration problem of simply-supported trapezoidal shallow spherical shell on Winkler foundation.A Green quasifunction is established by using the fundamental solution and boundary equation of the problem.This function satisfies the homogeneous boundary condition of the problem.The mode shape differential equation of the free vibration problem of simply-supported trapezoidal shallow spherical shell on Winkler foundation is reduced to two simultaneous Fredholm integral equations of the second kind by Green formula.There are multiple choices for the normalized boundary equation.Based on a chosen normalized boundary equation,the irregularity of the kernel of integral equations is avoided.Finally,natural frequency is obtained by the condition that there exists a nontrivial solution in the numerically discrete algebraic equations derived from the integral equations.Numerical results show high accuracy of the Green quasi function method.
Rochal, S B; Konevtsova, O V; Myasnikova, A E; Lorman, V L
2016-09-29
We propose the principles of structural organization in spherical nanoassemblies with icosahedral symmetry constituted by asymmetric protein molecules. The approach modifies the paradigmatic geometrical Caspar and Klug (CK) model of icosahedral viral capsids and demonstrates the common origin of both the "anomalous" and conventional capsid structures. In contrast to all previous models of "anomalous" viral capsids the proposed modified model conserves the basic structural principles of the CK approach and reveals the common hidden symmetry underlying all small viral shells. We demonstrate the common genesis of the "anomalous" and conventional capsids and explain their structures in the same frame. The organization principles are derived from the group theory analysis of the positional order on the spherical surface. The relationship between the modified CK geometrical model and the theory of two-dimensional spherical crystallization is discussed. We also apply the proposed approach to complex double-shelled capsids and capsids with protruding knob-like proteins. The introduced notion of commensurability for the concentric nanoshells explains the peculiarities of their organization and helps to predict analogous, but yet undiscovered, double-shelled viral capsid nanostructures.
Schubert, G.; Zebib, A.
1980-01-01
A Galerkin technique is used to study the finite-amplitude axisymmetric steady convective motions of an infinite Prandtl number Boussinesq fluid in a spherical shell. Two types of heating are considered: in one case, convection is driven both by internal heat sources in the fluid and by an externally imposed temperature drop across the shell boundaries; in the other case, only internal heat sources drive convection and the lower boundary of the shell is adiabatic. Two distinct classes of axisymmetric steady states are found to be possible: states characterized by temperature and radial velocity fields that are symmetric about an equatorial plane; and a class of solutions that does not possess any symmetry properties about the equatorial plane.
Mohamed BALAH; Hamdan Naser AL-GHAMEDY
2004-01-01
The paper presents an approach for the formulation of general laminated shells based on a third order shear deformation theory. These shells undergo finite (unlimited in size) rotations and large overall motions but with small strains. A singularity-free parametrization of the rotation field is adopted. The constitutive equations, derived with respect to laminate curvilinear coordinates,are applicable to shell elements with an arbitrary number of orthotropic layers and where the material principal axes can vary from layer to layer. A careful consideration of the consistent linearization procedure pertinent to the proposed parametrization of finite rotations leads to symmetric tangent stiffness matrices. The matrix formulation adopted here makes it possible to implement the present formulation within the framework of the finite element method as a straightforward task.
A Nonlinear Theory of Bending and Buckling of Thin Elastic Shallow Spherical Shells
Kaplan, A; Fung, Y C
1954-01-01
The problem of the finite displacement and buckling, of a shallow spherical dome is investigated both theoretically and experimentally. Experimental results seem to indicate that the classical criterion of buckling is applicable to very shallow spherical domes for which the theoretical calculation was made. A transition to energy criterion for higher domes is also indicated.
Triaxial projected shell model study of chiral rotation in odd-odd nuclei
Bhat, G.H. [Department of Physics, University of Kashmir, Srinagar, 190 006 (India); Sheikh, J.A. [Department of Physics, University of Kashmir, Srinagar, 190 006 (India); Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996 (United States); Palit, R., E-mail: palit@tifr.res.in [Department of Nuclear and Atomic Physics, Tata Institute of Fundamental Research, Colaba, Mumbai, 400 005 (India)
2012-01-20
Chiral rotation observed in {sup 128}Cs is studied using the newly developed microscopic triaxial projected shell model (TPSM) approach. The observed energy levels and the electromagnetic transition probabilities of the nearly degenerate chiral dipole bands in this isotope are well reproduced by the present model. This demonstrates the broad applicability of the TPSM approach, based on a schematic interaction and angular-momentum projection technique, to explain a variety of low- and high-spin phenomena in triaxial rotating nuclei.
Inclusion of temperature dependent shell corrections in Landau theory for hot rotating nuclei
G Shanmugam; P Arumugam
2001-07-01
Landau theory used for studying hot rotating nuclei usually uses zero temperature Strutinsky smoothed total energy for the temperature dependent shell corrections. This is replaced in this work by the temperature dependent Strutinsky smoothed free energy. Our results show that this replacement has only marginal effect for temperatures greater than 1 MeV but plays signiﬁcant role at lower temperatures.
INVESTIGATION OF RANDOM RESPONSE OF ROTATIONAL SHELL WHEN CONSIDERING GEOMETRIC NONLINEAR BEHAVIOUR
GAO Shi-qiao(高世桥); JIN Lei(金磊); H.J.Niemann; LIU Hai-peng(刘海鹏)
2001-01-01
An iteration method of statistic linearization (IMSL) is presented. By this method, an equivalent linear term was formed in geometric relation and then an equivalent stiffness matrix for nonlinear term in vibration equation was established. Using the method to solve the statistic linear vibration equations, the effect of geometric nonlinearity on the random response of rotational shell is obtained.
Dynamical instability in a relativistic cylindrical shell composed of counter rotating particles
Kurita, Yasunari
2011-01-01
We give a perturbative analysis for an infinitesimally thin cylindrical shell composed of counter rotating collisionless particles, originally devised by Apostolatos and Thorne. They found a static solution of the shell and concluded by C-energy argument that it is stable. Recently, the present authors and Ida reanalyzed this system by evaluating the C-energy on the future null infinity and found that the system has an instability, though it was not shown how the system is unstable. In this paper, it is shown in the framework of the linear perturbation theory that, if the constituent particles move slowly, the static shell is unstable in the sense that the perturbation of its circumferential radius oscillates with exponentially growing amplitude, whereas if the speed of the constituent particle exceeds a critical value, the shell just expands or contracts exponentially with time.
SymPix: A spherical grid for efficient sampling of rotationally invariant operators
Seljebotn, Dag Sverre
2015-01-01
We present SymPix, a special-purpose spherical grid optimized for efficient sampling of rotationally invariant linear operators. This grid is conceptually similar to the Gauss-Legendre (GL) grid, aligning sample points with iso-latitude rings located on Legendre polynomial zeros. Unlike the GL grid, however, the number of grid points per ring varies as a function of latitude, avoiding expensive over-sampling near the poles and ensuring nearly equal sky area per grid point. The ratio between the number of grid points in two neighbouring rings is required to be a low-order rational number (3, 2, 1, 4/3, 5/4 or 6/5) to maintain a high degree of symmetries. Our main motivation for this grid is to solve linear systems using multi-grid methods, and to construct efficient preconditioners through pixel-space sampling of the linear operator in question. The GL grid is not suitable for these purposes due to its massive over-sampling near the poles, leading to nearly degenerate linear systems, while HEALPix, another com...
Qin, Jianguo; Jiang, Li; Liu, Rong; Zhang, Xinwei; Ye, Bangjiao; Zhu, Tonghua
2015-01-01
The prompt gamma-ray spectrum from depleted uranium (DU) spherical shells induced by 14 MeV D-T neutrons is measured. Monte Carlo (MC) simulation gives the largest prompt gamma flux with the optimal thickness of the DU spherical shells 3-5 cm and the optimal frequency of neutron pulse 1 MHz. The method of time of flight and pulse shape coincidence with energy (DC-TOF) is proposed, and the subtraction of the background gamma-rays discussed in detail. The electron recoil spectrum and time spectrum of the prompt gamma-rays are obtained based on a 2"*2" BC501A liquid scintillator detector. The energy spectrum and time spectrum of prompt gamma-rays are obtained based on an iterative unfolding method that can remove the influence of {\\gamma}-rays response matrix and pulsed neutron shape. The measured time spectrum and the calculated results are roughly consistent with each other. Experimental prompt gamma-ray spectrum in the 0.4-3 MeV energy region agree well with MC simulation based on the ENDF/BVI.5 library, and ...
Qin, Jian-Guo; Lai, Cai-Feng; Jiang, Li; Liu, Rong Zhang, Xin-Wei; Ye, Bang-Jiao; Zhu, Tong-Hua
2016-01-01
The prompt γ-ray spectrum from depleted uranium (DU) spherical shells induced by 14 MeV D-T neutrons is measured. Monte Carlo (MC) simulation gives the largest prompt γ flux with the optimal thickness of the DU spherical shells 3-5 cm and the optimal frequency of neutron pulse 1 MHz. The method of time of flight and pulse shape coincidence with energy (DC-TOF) is proposed, and the subtraction of the background γ-rays discussed in detail. The electron recoil spectrum and time spectrum of the prompt γ-rays are obtained based on a 2″×2″ BC501A liquid scintillator detector. The energy spectrum and time spectrum of prompt γ-rays are obtained based on an iterative unfolding method that can remove the influence of γ-rays response matrix and pulsed neutron shape. The measured time spectrum and the calculated results are roughly consistent with each other. Experimental prompt γ-ray spectrum in the 0.4-3 MeV energy region agrees well with MC simulation based on the ENDF/BVI.5 library, and the discrepancies for the integral quantities of γ-rays of energy 0.4-1 MeV and 1-3 MeV are 9.2% and 1.1%, respectively. Supported by National Special Magnetic Confinement Fusion Energy Research, China (2015GB108001) and National Natural Science Foundation of China (91226104)
Arfaoui, A.; Mahdouani, M.; Bourguiga, R.
2017-08-01
The two-band model effective mass approximation has been adopted to explain the energy spectra in type-I CdSe core-only and type-II CdSe/CdTe core/shell quantum dots (QDs). As optical properties, the emission wavelength, the electron-hole overlap integral and the radiative recombination lifetime have been investigated. The simulated emission spectra are in good agreement with available experimental results for both core-only and core/shell QDs. The radiative recombination lifetime (τrad) has been investigated in different carrier localization regimes and compared to that corresponding to core-only QDs. We have found a sudden increase in τrad at around r1 1.1 nm suggesting the transition of the heterostructure from the quasi-type-II to the type-II regime. A monotonic increase in τrad with the core and shell sizes (geometric parameters) was observed. Also found is the possibility of increasing τrad over two orders of magnitude with a suitable change in the geometric parameters. The long radiative lifetime produced by increasing the geometric parameters is found due to spatial separation of the carriers, which makes the type-II core/shell QDs made from large core and shell sizes promising for photovoltaic applications.
Investigation of spherical and concentric mechanism of compound droplets
Meifang Liu
2016-07-01
Full Text Available Polymer shells with high sphericity and uniform wall thickness are always needed in the inertial confined fusion (ICF experiments. Driven by the need to control the shape of water-in-oil (W1/O compound droplets, the effects of the density matching level, the interfacial tension and the rotation speed of the continuing fluid field on the sphericity and wall thickness uniformity of the resulting polymer shells were investigated and the spherical and concentric mechanisms were also discussed. The centering of W1/O compound droplets, the location and movement of W1/O compound droplets in the external phase (W2 were significantly affected by the density matching level of the key stage and the rotation speed of the continuing fluid field. Therefore, by optimizing the density matching level and rotation speed, the batch yield of polystyrene (PS shells with high sphericity and uniform wall thickness increased. Moreover, the sphericity also increased by raising the oil/water (O/W2 interfacial tension, which drove a droplet to be spherical. The experimental results show that the spherical driving force is from the interfacial tension affected by the two relative phases, while the concentric driving force, as a resultant force, is not only affected by the three phases, but also by the continuing fluid field. The understanding of spherical and concentric mechanism can provide some guidance for preparing polymer shells with high sphericity and uniform wall thickness.
Ibral, Asmaa [Equipe d’Optique et Electronique du Solide, Département de Physique, Faculté des Sciences, Université Chouaïb Doukkali, B.P. 20 El Jadida Principale, El Jadida 24000 (Morocco); Laboratoire d’Instrumentation, Mesure et Contrôle, Département de Physique, Université Chouaïb Doukkali, B.P. 20 El Jadida Principale, El Jadida (Morocco); Zouitine, Asmae [Département de Physique, Ecole Nationale Supérieure d’Enseignement Technique, Université Mohammed V Souissi, B.P. 6207 Rabat-Instituts, Rabat (Morocco); Assaid, El Mahdi, E-mail: eassaid@yahoo.fr [Equipe d’Optique et Electronique du Solide, Département de Physique, Faculté des Sciences, Université Chouaïb Doukkali, B.P. 20 El Jadida Principale, El Jadida 24000 (Morocco); Laboratoire d’Instrumentation, Mesure et Contrôle, Département de Physique, Université Chouaïb Doukkali, B.P. 20 El Jadida Principale, El Jadida (Morocco); Feddi, El Mustapha [Département de Physique, Ecole Nationale Supérieure d’Enseignement Technique, Université Mohammed V Souissi, B.P. 6207 Rabat-Instituts, Rabat (Morocco); and others
2014-09-15
Ground state energy and wave function of a hydrogen-like off-centre donor impurity, confined anywhere in a ZnS/CdSe spherical core/shell nanostructure are determined in the framework of the envelope function approximation. Conduction band-edge alignment between core and shell of nanostructure is described by a finite height barrier. Dielectric constant mismatch at the surface where core and shell materials meet is taken into account. Electron effective mass mismatch at the inner surface between core and shell is considered. A trial wave function where coulomb attraction between electron and off-centre ionized donor is used to calculate ground state energy via the Ritz variational principle. The numerical approach developed enables access to the dependence of binding energy, coulomb correlation parameter, spatial extension and radial probability density with respect to core radius, shell radius and impurity position inside ZnS/CdSe core/shell nanostructure.
Zebib, A.; Schubert, G.; Dein, J. L.; Paliwal, R. C.
1983-01-01
The influence of shell size and mode of heating on the behavior and stability of axisymmetric, infinite Prandtl number convection in a spherical geometry is studied. Heating from within and below features convection onset governed by a self-adjoint system of equations and boundary conditions. For heating only from within or from below, linearized equations and boundary conditions are non-self-adjoint. Identification of the parameter which initiates the departure from self-adjointness, together with the properties of the self-adjoint solution, provide a basis for calculating the heat transfer characteristics of the non-self-adjoint situations. The investigations are an effort to develop a model for heat transfer in planetary interiors. Further development of the technique by modifying the Galerkin method by the introduction of diagonal mode truncation is suggested to permit the consideration of higher values of the Rayleigh numbers, i.e., those more commensurate with terrestrial planet mantles.
Reese, D; Rieutord, M
2004-01-01
We carry out numerical and mathematical investigations of shear Alfven waves inside of a spherical shell filled with an incompressible conducting fluid, and bathed in a strong dipolar magnetic field. We focus on axisymmetric toroidal and non-axisymmetric modes, in continuation of a previous work by Rincon & Rieutord (2003). Analytical expressions are obtained for toroidal eigenmodes and their corresponding frequencies at low diffusivities. These oscillations behave like magnetic shear layers, in which the magnetic poles play a key role, and hence become singular when diffusivities vanish. It is also demonstrated that non-axisymmetric modes are split into two categories, namely poloidal or toroidal types, following similar asymptotic behaviours as their axisymmetric counterparts when the diffusivities become arbitrarily small.
Motion of a thin spherically symmetric Shell of Dust in the Schwarzschild field
Schmidt, H -J
2014-01-01
The equation of motion announced in the title was already deduced for the cases the inner metric being flat and the shell being negligibly small (test matter), using surface layers and geodesic trajectories resp. Here we derive the general equation of motion and solve it in closed form for the case of parabolic motion. Especially the motion near the horizon and near the singularity are examined.
Facile and Scalable Synthesis of Monodispersed Spherical Capsules with a Mesoporous Shell
Qi, Genggeng
2010-05-11
Monodispersed HMSs with tunable particle size and shell thickness were successfully synthesized using relatively concentrated polystyrene latex templates and a silica precursor in a weakly basic ethanol/water mixture. The particle size of the capsules can vary from 100 nm to micrometers. These highly engineered monodispersed capsules synthesized by a facile and scalable process may find applications in drug delivery, catalysis, separationm or as biological and chemical microreactors. © 2010 American Chemical Society.
Podesta, M; Fredrickson, E D; Gorelenkov, N N; LeBlanc, B P; Heidbrink, W W; Crocker, N A; Kubota, S
2010-08-19
The effects of a sheared toroidal rotation on the dynamics of bursting Toroidicity-induced Alfven eigenmodes are investigated in neutral beam heated plasmas on the National Spherical Torus Experiment (NSTX) [M. Ono et al., Nucl. Fusion 40 557 (2000)]. The modes have a global character, extending over most of the minor radius. A toroidal rotation shear layer is measured at the location of maximum drive for the modes. Contrary to results from other devices, no clear evidence of increased damping is found. Instead, experiments with simultaneous neutral beam and radio-frequency auxiliary heating show a strong correlation between the dynamics of the modes and the instability drive. It is argued that kinetic effects involving changes in the mode drive and damping mechanisms other than rotation shear, such as continuum damping, are mostly responsible for the bursting dynamics of the modes.
The motion of an arbitrarily rotating spherical projectile and its application to ball games
Robinson, Garry; Robinson, Ian
2013-07-01
In this paper the differential equations which govern the motion of a spherical projectile rotating about an arbitrary axis in the presence of an arbitrary ‘wind’ are developed. Three forces are assumed to act on the projectile: (i) gravity, (ii) a drag force proportional to the square of the projectile's velocity and in the opposite direction to this velocity and (iii) a lift or ‘Magnus’ force also assumed to be proportional to the square of the projectile's velocity and in a direction perpendicular to both this velocity and the angular velocity vector of the projectile. The problem has been coded in Matlab and some illustrative model trajectories are presented for ‘ball-games’, specifically golf and cricket, although the equations could equally well be applied to other ball-games such as tennis, soccer or baseball. Spin about an arbitrary axis allows for the treatment of situations where, for example, the spin has a component about the direction of travel. In the case of a cricket ball the subtle behaviour of so-called ‘drift’, particularly ‘late drift’, and also ‘dip’, which may be produced by a slow bowler's off or leg-spin, are investigated. It is found that the trajectories obtained are broadly in accord with those observed in practice. We envisage that this paper may be useful in two ways: (i) for its inherent scientific value as, to the best of our knowledge, the fundamental equations derived here have not appeared in the literature and (ii) in cultivating student interest in the numerical solution of differential equations, since so many of them actively participate in ball-games, and they will be able to compare their own practical experience with the overall trends indicated by the numerical results. As the paper presents equations which can be further extended, it may be of interest to research workers. However, since only the most basic principles of fundamental mechanics are employed, it should be well within the grasp of first
A hybrid radial basis function-pseudospectral method for thermal convection in a 3-D spherical shell
Wright, G. B.
2010-07-01
A novel hybrid spectral method that combines radial basis function (RBF) and Chebyshev pseudospectral methods in a "2 + 1" approach is presented for numerically simulating thermal convection in a 3-D spherical shell. This is the first study to apply RBFs to a full 3-D physical model in spherical geometry. In addition to being spectrally accurate, RBFs are not defined in terms of any surface-based coordinate system such as spherical coordinates. As a result, when used in the lateral directions, as in this study, they completely circumvent the pole issue with the further advantage that nodes can be "scattered" over the surface of a sphere. In the radial direction, Chebyshev polynomials are used, which are also spectrally accurate and provide the necessary clustering near the boundaries to resolve boundary layers. Applications of this new hybrid methodology are given to the problem of convection in the Earth\\'s mantle, which is modeled by a Boussinesq fluid at infinite Prandtl number. To see whether this numerical technique warrants further investigation, the study limits itself to an isoviscous mantle. Benchmark comparisons are presented with other currently used mantle convection codes for Rayleigh number (Ra) 7 × 10^{3} and 10^{5}. Results from a Ra = 10^{6} simulation are also given. The algorithmic simplicity of the code (mostly due to RBFs) allows it to be written in less than 400 lines of MATLAB and run on a single workstation. We find that our method is very competitive with those currently used in the literature. Copyright 2010 by the American Geophysical Union.
Yoshida, M; Kageyama, Akira; Yoshida, Masaki
2005-01-01
A series of numerical simulations of thermal convection of Boussinesq fluid with infinite Prandtl number, with Rayleigh number $10^7$, and with the strongly temperature- and depth- dependent viscosity in a three-dimensional spherical shell is carried out to study the mantle convection of single-plate terrestrial planets like Venus or Mars without an Earth-like plate tectonics. The strongly temperature-dependent viscosity (the viscosity contrast across the shell is $\\geq 10^5$) make the convection under stagnant-lid short-wavelength structures. Numerous, cylindrical upwelling plumes are developed because of the secondary downwelling plumes arising from the bottom of lid. This convection pattern is inconsistent with that inferred from the geodesic observation of the Venus or Mars. Additional effect of the stratified viscosity at the upper/lower mantle (the viscosity contrast is varied from 30 to 300) are investigated. It is found that the combination of the strongly temperature- and depth-dependent viscosity ca...
Thermal convection in a spherical shell with melting/freezing at either or both of its boundaries
Deguen, Renaud
2013-01-01
In a number of geophysical or planetological settings (Earth's inner core, a silicate mantle crystallizing from a magma ocean, or an ice shell surrounding a deep water ocean) a convecting crystalline layer is in contact with a layer of its melt. Allowing for melting/freezing at one or both of the boundaries of the solid layer is likely to affect the pattern of convection in the layer. We study here the onset of thermal convection in a viscous spherical shell with dynamically induced melting/freezing at either or both of its boundaries. It is shown that the behavior of each interface depends on the value of a dimensional number P, which is the ratio of a melting/freezing timescale over a viscous relaxation timescale. A small value of P corresponds to permeable boundary conditions, while a large value of P corresponds to impermeable boundary conditions. The linear stability analysis predicts a significant effect of semi-permeable boundaries when the number P characterizing either of the boundary is small enough...
康盛亮
2001-01-01
Using the modified method of multiple scales, the nonlinear stability of a truncated shallow spherical shell of variable thickness with a nondeformable rigid body at the center under compound loads is investigated. When the geometrical parameter k is larger,the uniformly valid asymptotic solutions of this problem are obtained and the remainder terms are estimated.
Srnka, L. J.
1976-01-01
The acquisition of thermoremanent magnetization (TRM) by a cooling spherical shell is studied for internal magnetizing dipole fields, using Runcorn's (1975) theorems on magnetostatics. If the shell cools progressively inward, inner regions acquire TRM in a net field composed of the dipole source term plus a uniform field due to the outer magnetized layers. In this case, the global dipole moment and external remanent field are nonzero when the whole shell has cooled below the Curie point and the source dipole has disappeared. The remanent field outside the shell is found to depend on the thickness, radii, and cooling rate of the shell, as well as the coefficient of TRM and the intensity of the magnetizing field. Some implications for the moon's remanent dipole moment are discussed.
THIN - A Computer Program for Analyzing the Axisymmetric Behavior of Thin Spherical Shells
1975-10-01
l) = |Nyr)- M0(I-1)]/A0+[M0(I)- MÖ(]) + M0(I-1)-MÖ(1-1)] "^ Note that the use of this equation is, strictly speaking , not justified in the context of...30 /cö = X cot 0 (Nw1)Nfl) = (crii) efl ) + Kefl)e(Ä)-T >»^0’ :0’CÖ 0; m 29 -■*■- .iwtm timmwv^’’’ —•"~: "’•- tmm...shell that is not near the edge. It will be assumed that the reader is familiar with the matching process so that little of the motivation needs to be
Atomically thin spherical shell-shaped superscatterers based on a Bohr model.
Li, Rujiang; Lin, Xiao; Lin, Shisheng; Liu, Xu; Chen, Hongsheng
2015-12-18
Graphene monolayers can be used for atomically thin three-dimensional shell-shaped superscatterer designs. Due to the excitation of the first-order resonance of transverse magnetic (TM) graphene plasmons, the scattering cross section of the bare subwavelength dielectric particle is enhanced significantly by five orders of magnitude. The superscattering phenomenon can be intuitively understood and interpreted with a Bohr model. In addition, based on the analysis of the Bohr model, it is shown that contrary to the TM case, superscattering is hard to achieve by exciting the resonance of transverse electric (TE) graphene plasmons due to their poor field confinements.
H. Huang
1995-01-01
Full Text Available The nonlinear interaction problem is analyzed by simultaneously solving the mass, momentum, and energy conservation equations together .with appropriate material constitutive equations governing the fluid dynamics of the explosion gaseous product and the water and the structural dynamics of the compliant shell. A finite difference technique in a coupled Eulerian–Lagrangian scheme is used. The computer program PISCES 2DELK is employed to carry out the numerical computations. The results demonstrate that to rigorously analyze the response of a submerged structure to a nearby explosion, the interactions among the explosion shock wave, the structure, its surrounding media, and the explosion bubble need to be considered.
Højgaard Jensen, Jens
2014-06-01
In a recent paper (Robinson G and Robinson I 2013 Phys. Scr. 88 018101) the authors developed the differential equations which govern the motion of a spherical projectile rotating about an arbitrary axis in the presence of an arbitrary wind, assuming that both the drag force and the lift force are independent of the Reynolds number and proportional to the square of the projectile’s velocity. In this paper, by dimensional analysis, the latter assumption is shown to be incorrect for forces dependent on the angular velocity of the projectile, e.g. the lift force.
Transient Dynamic Response of Delaminated Composite Rotating Shallow Shells Subjected to Impact
Amit Karmakar
2006-01-01
Full Text Available In this paper a transient dynamic finite element analysis is presented to study the response of delaminated composite pretwisted rotating shallow shells subjected to low velocity normal impact. Lagrange's equation of motion is used to derive the dynamic equilibrium equation and moderate rotational speeds are considered wherein the Coriolis effect is negligible. An eight noded isoparametric plate bending element is employed in the finite element formulation incorporating rotary inertia and effects of transverse shear deformation based on Mindlin's theory. To satisfy the compatibility of deformation and equilibrium of resultant forces and moments at the delamination crack front a multipoint constraint algorithm is incorporated which leads to unsymmetric stiffness matrices. The modified Hertzian contact law which accounts for permanent indentation is utilized to compute the contact force, and the time dependent equations are solved by Newmark's time integration algorithm. Parametric studies are performed in respect of location of delamination, angle of twist and rotational speed for centrally impacted graphite-epoxy composite cylindrical shells.
Mode- and plasma rotation in a resistive shell reversed-field pinch
Malmberg, J.-A.; Brzozowski, J.; Brunsell, P. R.; Cecconello, M.; Drake, J. R.
2004-02-01
Mode rotation studies in a resistive shell reversed-field pinch, EXTRAP T2R [P. R. Brunsell et al., Plasma Phys. Control. Fusion 43, 1 (2001)] are presented. The phase relations and nonlinear coupling of the resonant modes are characterized and compared with that expected from modeling based on the hypothesis that mode dynamics can be described by a quasi stationary force balance including electromagnetic and viscous forces. Both m=0 and m=1 resonant modes are studied. The m=1 modes have rotation velocities corresponding to the plasma flow velocity (20-60 km/s) in the core region. The rotation velocity decreases towards the end of the discharge, although the plasma flow velocity does not decrease. A rotating phase locked m=1 structure is observed with a velocity of about 60 km/s. The m=0 modes accelerate throughout the discharges and reach velocities as high as 150-250 km/s. The observed m=0 phase locking is consistent with theory for certain conditions, but there are several conditions when the dynamics are not described. This is not unexpected because the assumption of quasi stationarity for the mode spectra is not fulfilled for many conditions. Localized m=0 perturbations are formed in correlation with highly transient discrete dynamo events. These perturbations form at the location of the m=1 phase locked structure, but rotate with a different velocity as they spread out in the toroidal direction.
Ambrus, Victor E
2016-01-01
We consider rigidly rotating states in thermal equilibrium on static spherically symmetric spacetimes. Using the Maxwell-Juttner equilibrium distribution function, onstructed as a solution of the relativistic Boltzmann equation, the equilibrium particle flow four-vector, stress-energy tensor and the transport coefficients in the Marle model are computed. Their properties are discussed in view of the topology of the speed-of-light surface induced by the rotation for two classes of spacetimes: maximally symmetric (Minkowski, de Sitter and anti-de Sitter) and charged (Reissner-Nordstrom) black-hole spacetimes. To facilitate our analysis, we employ a non-holonomic comoving tetrad field, obtained unambiguously by applying a Lorentz boost on a fixed background tetrad.
Bednarek, W
2015-01-01
We consider a simple scenario for the accretion of matter onto a neutron star in order to understand processes in the inner pulsar magnetosphere during the transition stage between different accretion modes. A simple quasi-spherical accretion process onto rotating, magnetized compact object is analyzed in order to search for the radiative signatures which could appear during transition between ejecting and accreting modes. It is argued that different accretion modes can be present in a single neutron star along different magnetic field lines for specific range of parameters characterising the pulsar (rotational period, surface magnetic field strength) and the density of surrounding medium. The radiation processes characteristic for the ejecting pulsar, i.e. curvature and synchrotron radiation produced by primary electrons in the pulsar outer gap, are expected to be modified by the presence of additional thermal radiation from the neutron star surface. We predict that during the transition from the pure ejecto...
Reflection Asymmetric Shell Model for the Description of Octupole Rotational Bands
GAO Zao-Chun; CHEN Yong-Shou
2001-01-01
The reflection asymmetric shell model has been formulated to describe the high spin states of octupole-deformed nuclei. The long-range separable forces of quadrupole, octupole and hexadecapole, as well as monopole and quadrupole pairing, are included in the Hamiltonian. The bases, on which the Hamiltonian is diagonalized, are the eigenstates of angular momentum and parity obtained by projecting the octupole-deformed multi-quasiparticle states onto good angular momentum and good parity. The general features of rotational octupole bands in eveneven nuclei can be reproduced by the model and the calculated result is in good agreement with experiment.
Spherical Couette flow in a dipolar magnetic field
Hollerbach, R; Fournier, A; Hollerbach, Rainer; Canet, Elisabeth; Fournier, Alexandre
2007-01-01
We consider numerically the flow of an electrically conducting fluid in a differentially rotating spherical shell, in a dipolar magnetic field. For infinitesimal differential rotation the flow consists of a super-rotating region, concentrated on the particular field line C just touching the outer sphere, in agreement with previous results. Finite differential rotation suppresses this super-rotation, and pushes it inward, toward the equator of the inner sphere. For sufficiently strong differential rotation the outer boundary layer becomes unstable, yielding time-dependent solutions. Adding an overall rotation suppresses these instabilities again. The results are in qualitative agreement with the DTS liquid sodium experiment.
Kitayama, Yukiya; Takeuchi, Toshifumi
2017-09-18
In this study, a fabrication route towards functional capsule particles was successfully developed by means of a self-templating shell-selective cross-linking strategy that enables us to prepare shell-cross-linked hollow polymer particles directly from homogeneous spherical polymer particles. To prepare redox-responsive degradable capsule particles, a newly designed monomer bearing a photoinduced post-cross-linking group (cinnamoyl group) and a redox-environment-responsive cleavable group (disulfide group), N-cinnamoyl-N'-methyacryloylcystamine (MCC), was synthesized. Redox-responsive degradable capsule particles were successfully prepared from homogeneous spherical poly(MCC)-based particles by a self-templating shell-selective photoinduced cross-linking approach. Moreover, the cargo loading capability of the shell-cross-linked hollow particles was confirmed through a solvent exchange procedure using dyes, polymer precursors and anticancer reagents. Furthermore, redox-responsive degradability of the capsule polymer particles was also confirmed by adding a reducing agent for cleavage of the disulfide linkage. We hope that the efficient fabrication route of functional capsule particles directly from spherical polymer particles opens efficient routes for the fabrication of a wide range of capsule particles; in particular, this technique is robust, productive, and facile because neither additional sacrificial template particles nor toxic solvents are required. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
Hirooka, Y., E-mail: hirooka.yoshihiko@nifs.ac.j [National Institute for Fusion Science, Oroshi, Toki, Gifu 509-5292 (Japan); Zushi, H. [Kyushu University, Kasuga, Fukuoka 816-8580 (Japan); Bhattacharyay, R. [Interdisciplinary Graduate School of Engineering Science, Kyushu University, Kasuga, Fukuoka 816-8580 (Japan); Sakamoto, M.; Idei, H.; Yoshinaga, T. [Kyushu University, Kasuga, Fukuoka 816-8580 (Japan); Nakashima, Y.; Higashizono, Y. [University of Tsukuba, Tsukuba, Ibaraki 305-8577 (Japan)
2009-06-15
Active particle control capabilities of a lithium-gettered rotating drum poloidal limiter have been demonstrated during 50 kW RF-current drive discharges in a compact spherical tokamak with the major and minor radii of 30 and 20 cm, respectively. The pulse length is typically approx300 ms with a flat-top of approx250 ms. The rotating limiter is in the shape of cylinder with the diameter and axial length of 15 and 12 cm, respectively. It has reproducibly been observed that, as soon as the rotating drum is gettered with lithium, hydrogen recycling measured with H{sub a}lpha spectroscopy decreases by a factor of approx3 not only near the limiter but also in the center stack region. Also, the oxygen impurity level measured with O-II spectroscopy is reduced by a factor of approx3. Meanwhile, the core electron temperature increases from around 7 eV to 20 eV along which the flat-top toroidal plasma current is found to nearly double even at the same vertical magnetic field. Comprehensive surface analysis has been conducted to investigate hydrogen and lithium distributions over the rotating drum after plasma exposure.
Wang, Anna; Fung, Jerome; Razavi, Sepideh; Kretzschmar, Ilona; Chaudhary, Kundan; Lewis, Jennifer A; Manoharan, Vinothan N
2013-01-01
We present a new, high-speed technique to track the three-dimensional translation and rotation of non-spherical colloidal particles. We capture digital holograms of micrometer-scale silica rods and sub-micrometer-scale Janus particles freely diffusing in water, and then fit numerical scattering models based on the discrete dipole approximation to the measured holograms. This inverse-scattering approach allows us to extract the the position and orientation of the particles as a function of time, along with static parameters including the size, shape, and refractive index. The best-fit sizes and refractive indices of both particles agree well with expected values. The technique is able to track the center of mass of the rod to a precision of 35 nm and its orientation to a precision of 1.5$^\\circ$, comparable to or better than the precision of other 3D diffusion measurements on non-spherical particles. Furthermore, the measured translational and rotational diffusion coefficients for the silica rods agree with hy...
Ross, T.J. [University of Richmond; Hughes, R.O. [University of Richmond; Beausang, C.W. [University of Richmond; Allmond, James M [ORNL; Angell, C.T. [Lawrence Berkeley National Laboratory (LBNL); Basunia, M.S. [Lawrence Berkeley National Laboratory (LBNL); Bleuel, D.L. [Lawrence Livermore National Laboratory (LLNL); Burke, J.T. [Lawrence Livermore National Laboratory (LLNL); Casperson, R.J. [Lawrence Livermore National Laboratory (LLNL); Escher, J.E. [Lawrence Livermore National Laboratory (LLNL); Fallon, P. [Lawrence Berkeley National Laboratory (LBNL); Hatarik, R. [Lawrence Berkeley National Laboratory (LBNL); Munson, J. [Lawrence Berkeley National Laboratory (LBNL); Paschalis, S. [Lawrence Berkeley National Laboratory (LBNL); Petri, M. [Lawrence Berkeley National Laboratory (LBNL); Phair, L. [Lawrence Berkeley National Laboratory (LBNL); Ressler, J.J. [Lawrence Livermore National Laboratory (LLNL); Scielzo, N.D. [Lawrence Livermore National Laboratory (LLNL)
2013-01-01
Odd-mass gadolinium isotopes around N = 90 were populated by the (p,d ) reaction, utilizing 25-MeV protons, resulting in population of low-spin quasineutron states at energies near and below the Fermi surface. Systematics of the single quasineutron levels populated are presented. A large excitation energy gap is observed between levels originating from the 2d3/2 , 1h11/2 , and 3s1/2 spherical parents (above the N = 64 gap), and the 2d5/2 (below the gap), indicating that the spherical shell model level spacing is maintained at least to moderate deformations.
Harada, T; Iguchi, H; Harada, Tomohiro; Nakao, Ken-ichi; Iguchi, Hideo
1999-01-01
It was recently shown that the metric functions which describe a spherically symmetric space-time with vanishing radial pressure can be explicitly integrated. We investigate the nakedness and curvature strength of the shell-focusing singularity in that space-time. If the singularity is naked, the relation between the circumferential radius and the Misner-Sharp mass is given by $R\\approx 2y_{0} m^{\\beta}$ with $ 1/3<\\beta\\le 1$ along the first radial null geodesic from the singularity. The $\\beta$ is closely related to the curvature strength of the naked singularity. For example, for the outgoing or ingoing null geodesic, if the strong curvature condition (SCC) by Tipler holds, then $\\beta$ must be equal to 1. We define the ``gravity dominance condition'' (GDC) for a geodesic. If GDC is satisfied for the null geodesic, both SCC and the limiting focusing condition (LFC) by Królak hold for $\\beta=1$ and $y_{0}\
Steven M. Grimes; Thomas N. Massey; Allan D. Carlson; James M. Adams; Alireza Haghighat; Michael T. Wenner; Shane R. Gardner
2003-04-25
OAK B204 We have been pursuing a multi-year project, funded by the U.S. Department of Energy, to study neutron scattering interactions in iron. The principal objective of this work is to investigate the well-known deficiency that exists for reactor pressure vessel neutron fluence determinations. Specifically, we are using the spherical-shell transmission method, employing iron shells with different thicknesses, and neutron time-of-flight (TOF) measurements of the scattered neutrons, in an effort to precisely determine specific energy regions over which deficiencies in the non-elastic scattering cross section for neutron scattering in iron appear to exist.
Lemos, José P S; Minamitsuji, Masato
2015-01-01
A rotating thin shell in a (2+1)-dimensional asymptotically AdS spacetime is studied. The spacetime exterior to the shell is the rotating BTZ spacetime and the interior is the empty spacetime with a cosmological constant. Through the Einstein equation in (2+1)-dimensions and the corresponding junction conditions we calculate the dynamical relevant quantities, namely, the rest energy-density, the pressure, and the angular momentum flux density. We also analyze the matter in a frame where its energy-momentum tensor has a perfect fluid form. In addition, we show that Machian effects, such as the dragging of inertial frames, also occur in rotating (2+1)-dimensional spacetimes. The weak and the dominant energy condition for these shells are discussed.
A spherical wave expansion model of sequentially rotated phased arrays with arbitrary elements
Larsen, Niels Vesterdal; Breinbjerg, Olav
2007-01-01
An analytical model of sequentially rotated phased arrays with arbitrary antenna elements is presented. It is applied to different arrays and the improvements of axial ratio bandwidth and copolar directivity are investigated. It is compared to a numerical method of auxiliary Sources model to asce...
Goldreich, Peter M
2009-01-01
A number of synchronous moons are thought to harbor water oceans beneath their outer ice shells. A subsurface ocean frictionally decouples the shell from the interior. This decoupling has led to proposals that a weak tidal or atmospheric torque might cause the shell to rotate differentially with respect to the synchronously rotating interior. Applications along these lines have been made to Europa and Titan. As a result of centrifugal and tidal forces, the oceans of Europa and Titan have ellipsoidal figures whose long axes point toward the parent planet. Any rotation of the shell away from its equilibrium position induces strains thereby increasing its elastic energy. Thus the shell is coupled to the ocean by an elastic torque. Regarding Europa, it is shown that the tidal torque is far too weak to produce stresses that could fracture the ice shell, thus refuting an idea that has been widely advocated. An alternative formation mechanism for large cracks is proposed. Two years of Cassini RADAR observations of T...
MENG Guo-jie; REN Jin-wei; WU Ji-cang; SHEN Xu-hui
2008-01-01
Based on Taylor series expansion and strain components expressions of elastic mechanics, we derive formulae of strain and rotation tensor for small arrays in spherical coordinates system. By linearization process of the formulae, we also derive expressions of strain components and Euler vector uncertainties respectively for subnets using the law of error propagation. Taking GPS velocity field in Sichuan-Yunnan area as an example, we compute dilation rate and maximum shear strain rate field using the above procedure, and their characteristics are preliminarily carried on. Limits of the strain model for small array are also discussed. We make detailed explanations on small array method and the choice of small arrays. How to set weights of GPS observations are further discussed. Moreover relationship between strain and radius of GPS subnets is also analyzed.
Yidong Li, Liyuan Xiao, Yingliang Liu, Pengfei Ai and Xiaobo Chen
2010-01-01
Full Text Available Nanocrystalline SrAl2Si2 O8 :Eu2+ phosphor layers were coated on nonaggregated, monodisperse and spherical SiO2 particles using a hydrothermal homogeneous precipitation. After annealing at 1100 °C, core-shell SiO2@SrAl2 Si2 O8 :Eu2+ particles were obtained. They were characterized with x-ray diffraction (XRD, scanning electron microscopy, transmission electron microscopy and photoluminescence techniques. XRD analysis confirmed the formation of SiO2 @SrAl2 Si2 O8 :Eu2+ particles; it indicated that the SrAl2 Si2 O8 :Eu2+ shells on SiO2 particles consisted of hexagonal crystallites. The core-shell phosphors obtained are well-dispersed submicron spherical particles with a narrow size distribution. The thickness of the coated layer is approximately 20–40 nm. Under ultraviolet excitation (361 nm, the particles emit blue light at about 440 nm due to the Eu2+ ions in their shells.
Svalbonas, V.
1973-01-01
The User's manual for the shell theory automated for rotational structures (STARS) 2B and 2V (buckling, vibrations) is presented. Several features of the program are: (1) arbitrary branching of the shell meridians, (2) arbitrary boundary conditions, (3) minimum input requirements to describe a complex, practical shell of revolution structure, and (4) accurate analysis capability using a minimum number of degrees of freedom.
Bahari, Ako; Popplewell, Neil
2015-05-01
A closed form solution was derived previously for the response of a submerged spherical shell when the shell was excited by a spatially distributed, transient load at its inner surface [Zakout (2001). J. Acoust. Soc. Am. 109(6), 2789-2796]. Numerical results were presented for the modal and total acoustic pressures outside the empty sphere when the load's temporal history corresponded to the Heaviside step function. However, the result presented for the shell's "breathing" mode was inconsistent with these data as it corresponded to the delta Dirac (impulse) function. Furthermore, numerical results, which were given later for the total acoustic pressure responses, did not involve either of these excitations. Consequently the present objective is to rectify these anomalies.
Non-linear rotation-free shell finite-element models for aortic heart valves.
Gilmanov, Anvar; Stolarski, Henryk; Sotiropoulos, Fotis
2017-01-04
Hyperelastic material models have been incorporated in the rotation-free, large deformation, shell finite element (FE) formulation of (Stolarski et al., 2013) and applied to dynamic simulations of aortic heart valve. Two models used in the past in analysis of such problem i.e. the Saint-Venant and May-Newmann-Yin (MNY) material models have been considered and compared. Uniaxial tests for those constitutive equations were performed to verify the formulation and implementation of the models. The issue of leaflets interactions during the closing of the heart valve at the end of systole is considered. The critical role of using non-linear anisotropic model for proper dynamic response of the heart valve especially during the closing phase is demonstrated quantitatively. This work contributes an efficient FE framework for simulating biological tissues and paves the way for high-fidelity flow structure interaction simulations of native and bioprosthetic aortic heart valves. Copyright © 2016. Published by Elsevier Ltd.
Hummel, W.; Vrancken, M.
2000-07-01
We improve the theory of Horne & Marsh on shear broadening in accretion disks of CVs and adapt it to Be star circumstellar disks. Stellar obscuration and shell absorption are taken into account in detail. It is shown that shell absorption is already present in those emission lines where the central depression does not drop below the stellar continuum. The model profiles are fitted to observed symmetric Hα net emission lines with low equivalent width. The derived disk radii range from Rd = 5.3 R_* to Rd = 18 R_* and the surface emissivity varies as ~ R-m with 1.6 (1)/(2) with the optically thick Hα profile of HR 5440 rules out the range of j>(1)/(2). This can be understood by the lack of velocity shear in the outer disk regions. We conclude that Keplerian rotation (j=(1)/(2)) is a valid approximation. Based on observations collected at the German-Spanish Astronomical Center (DSAZ), Calar Alto, operated by the Max-Plank-Institut für Astronomie Heidelberg jointly with the Spanish National Commission for Astronomy. Based on observations collected at the Observatoire de Haute-Provence (OHP), CNRS, France.
Han, Haoya; Li, Li; Wang, Weihua; Tian, Yuchuan; Wang, Yunwei; Wang, Junyou; von Klitzing, Regine; Guo, Xuhong
2017-09-06
Core-shell-corona silica/polymer hybrid nanoparticles with narrow size distribution were prepared in the template of spherical polyelectrolyte brushes (SPB) which consist of a solid polystyrene (PS) core densely grafted with linear poly(acrylic acid) (PAA) chains. The microstructure of obtained hybrid nanoparticles was studied by small-angle X-ray scattering (SAXS) and in combination with dynamic light scattering (DLS) and transmission electron microscopy (TEM). The generation of silica shell within the brush is confirmed by the significant increase of the electron density in the shell, and the silica shell showed a unique inner-loose-outer-dense structure, whose thickness is pH sensitive but is insensitive to ionic strength as revealed by fitting SAXS data. After dissolving the PS core, hollow silica nanoparticles were obtained and determined by SAXS, which should be ideal carriers for pH-triggered drug delivery. SAXS is confirmed to be a powerful method to characterize the core-shell-corona silica/polymer hybrid and hollow silica nanoparticles.
Hoyle state and rotational features in Carbon-12 within a no-core shell-model framework
Dreyfuss, Alison C., E-mail: adreyf1@lsu.edu [Keene State College, Keene, NH 03435 (United States); Launey, Kristina D.; Dytrych, Tomáš; Draayer, Jerry P. [Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803 (United States); Bahri, Chairul [Department of Physics, University of Notre Dame, Notre Dame, IN 46556-5670 (United States)
2013-12-18
By using only a fraction of the model space extended beyond current no-core shell-model limits and a many-nucleon interaction with a single parameter, we gain additional insight within a symmetry-guided shell-model framework, into the many-body dynamics that gives rise to the ground state rotational band together with phenomena tied to alpha-clustering substructures in the low-lying states in {sup 12}C, and in particular, the challenging Hoyle state and its first 2{sup +} and 4{sup +} excitations. For these states, we offer a novel perspective emerging out of no-core shell-model considerations, including a discussion of associated nuclear deformation and matter radii. This, in turn, provides guidance for ab initio shell models by informing key features of nuclear structure and the interaction.
Kozinszky, Zoltan; Surányi, Andrea; Péics, Hajnalka; Molnár, András; Pál, Attila
2015-08-01
The aim of this study was to determine the utility of a new mathematical model in volumetric assessment of the placenta using 2-D ultrasound. Placental volumetry was performed in a prospective cross-sectional survey by virtual organ computer-aided analysis (VOCAL) with the help of a shell-off method in 346 uncomplicated pregnancies according to STROBE (Strengthening the Reporting of Observational Studies in Epidemiology) guidelines. Furthermore, placental thickness, length and height were measured with the 2-D technique to estimate placental volume based on the mathematical formula for the volume of "the shell of the spherical sector." Fetal size was also assessed by 2-D sonography. The placental volumes measured by 2-D and 3-D techniques had a correlation of 0.86. In the first trimester, the correlation was 0.82, and later during pregnancy, it was 0.86. Placental volumetry using "the circle-shaped shell of the spherical sector" mathematical model with 2-D ultrasound technique may be introduced into everyday practice to screen for placental volume deviations associated with adverse pregnancy outcome.
The rotation and translation of non-spherical particles in homogeneous isotropic turbulence
Byron, Margaret
fields. Using these simultaneous measurements, we examine particles' turbulent slip velocity and compare it to particles' quiescent settling velocity, which we measure directly. We observe that the slip velocity is strongly reduced relative to the quiescent case, and explore various mechanisms of particle loitering in turbulence. We further explore the relationship between the instantaneous particle velocity and the instantaneous fluid velocity, and develop a linear parametrization. By comparing our experimental data to a simple one-dimensional flow in the context of this parametrization, we elucidate aspects of slip velocity that are unique to turbulence. We obtain the particles' angular velocity by applying the solid-body rotation equation to velocity measurements at points inside the particle. We find that the expected value of angular velocity magnitude does not vary significantly with particle aspect ratio, as long as particles are nearly neutrally buoyant. Stronger effects on rotation are found for more negatively-buoyant particles. We also investigate particles' inheritance of vorticity from turbulent velocity fields, and find that particle rotation can be predicted by applying a spatial filter to fluid-phase vorticity. The results of this study will allow us to more accurately predict the motion of aspherical particles, giving new insights into oceanic carbon cycling, industrial processes, and other important topics. This analysis will also shed light onto biological questions of navigation, reproduction, and predator-prey interaction by quantifying the turbulence-driven behavior of meso-scale aquatic organisms, allowing researchers to sift out passive vs. active effects in a behaving organism. Lastly, processes that are directly dependent on particle dynamics (e.g., sediment transport, industrial processes) will be informed by our results.
Gerhardt, S. P.; Brennan, D. P.; Buttery, R.; La Haye, R. J.; Sabbagh, S.; Strait, E.; Bell, M.; Bell, R.; Fredrickson, E.; Gates, D.; LeBlanc, B.; Menard, J.; Stutman, D.; Tritz, K.; Yuh, H.
2009-02-24
The onset conditions for the m/n=2/1 neoclassical tearing mode (NTM) are studied in terms of neoclassical drive, triggering instabilities, and toroidal rotation or rotation shear, in the spherical torus NSTX [M. Ono, et al., Nuclear Fusion 40, 557 (2000)]. There are three typical onset conditions for these modes, given in order of increasing neoclassical drive required for mode onset: triggering by energetic particle modes, triggering by edge localized modes, and cases where the modes appear to grow without a trigger. In all cases, the required drive increases with toroidal rotation shear, implying a stabilizing effect from the shear.
Energy spectrum of an exciton in a CdSe/ZnTe type-II core/shell spherical quantum dot
Chafai, A.; Dujardin, F.; Essaoudi, I.; Ainane, A.
2017-01-01
The binding energy of an exciton inside a CdSe/ZnTe core/shell spherical quantum dot was theoretically examined taking into account the dependence of the dielectric constant and charge carriers effective mass on radius, and using the envelope function approximation. Such a structure presents original optical and electronic properties because of the spatial separation of electrons and holes caused by the type-II alignment of energy states. The mean distance between the electron and hole was calculated variationally using a trial function taking into account the coulomb interaction between charge carriers. Our numerical results provide a description to the size dependence of the binding energy of an exciton inside a core/shell nanoheterostructure type-II. Indeed, by controlling the inner and outer radii, we can precisely control the energy spectrum of the exciton.
Giese, Timothy J; York, Darrin M
2008-07-07
We present a novel alternative to the use of Slater-Koster tables for the efficient rotation and gradient evaluation of two-center integrals used in tight-binding Hamiltonian models. The method recasts the problem into an exact, yet implicit, basis representation through which the properties of the spherical tensor gradient operator are exploited. These properties provide a factor of 3 to 4 speedup in the evaluation of the integral gradients and afford a compact code structure that easily extends to high angular momentum without loss in efficiency. Thus, the present work is important in improving the performance of tight-binding models in molecular dynamics simulations and has particular use for methods that require the evaluation of two-center integrals that involve high angular momentum basis functions. These advances have a potential impact for the design of new tight-binding models that incorporate polarization or transition metal basis functions and methods based on electron density fitting of molecular fragments.
Robinson, Garry; Robinson, Ian
2014-06-01
Jensen (2014 Phys. Scr. 89 067001) presents arguments that the expressions that we have used in our recent paper (Robinson and Robinson 2013 Phys. Scr. 88 018101) for the lift force and possibly the drag force acting on a rotating spherical projectile are dimensionally incorrect and therefore cannot be valid. We acknowledge that the alternative equations suggested by Jensen are dimensionally correct, and may well be borne out by future experimental results. However, we demonstrate that our equations are in fact also dimensionally correct, the key concept being that of having the appropriate dimensions for the multiplying constants, an extensively used practice with experimentally determined laws. After a detailed discussion of the situation, a simple illustrative example of Hooke's law for the restoring force, F, due to a mass attached to a spring displaced by a distance x from its equilibrium position is presented, where the spring constant, k, has such units as to render the equation dimensionally correct. Finally we discuss the implications of some relevant existing experimental results for the lift force.
Lemos, José P. S.; Minamitsuji, Masato; Zaslavskii, Oleg B.
2017-02-01
In a (2 +1 )-dimensional spacetime with a negative cosmological constant, the thermodynamics and the entropy of an extremal rotating thin shell, i.e., an extremal rotating ring, are investigated. The outer and inner regions with respect to the shell are taken to be the Bañados-Teitelbom-Zanelli (BTZ) spacetime and the vacuum ground state anti-de Sitter spacetime, respectively. By applying the first law of thermodynamics to the extremal thin shell, one shows that the entropy of the shell is an arbitrary well-behaved function of the gravitational area A+ alone, S =S (A+). When the thin shell approaches its own gravitational radius r+ and turns into an extremal rotating BTZ black hole, it is found that the entropy of the spacetime remains such a function of A+, both when the local temperature of the shell at the gravitational radius is zero and nonzero. It is thus vindicated by this analysis that extremal black holes, here extremal BTZ black holes, have different properties from the corresponding nonextremal black holes, which have a definite entropy, the Bekenstein-Hawking entropy S (A+)=A/+4G , where G is the gravitational constant. It is argued that for extremal black holes, in particular for extremal BTZ black holes, one should set 0 ≤S (A+)≤A/+4G;i.e., the extremal black hole entropy has values in between zero and the maximum Bekenstein-Hawking entropy A/+4 G . Thus, rather than having just two entropies for extremal black holes, as previous results have debated, namely, 0 and A/+4 G , it is shown here that extremal black holes, in particular extremal BTZ black holes, may have a continuous range of entropies, limited by precisely those two entropies. Surely, the entropy that a particular extremal black hole picks must depend on past processes, notably on how it was formed. A remarkable relation between the third law of thermodynamics and the impossibility for a massive body to reach the velocity of light is also found. In addition, in the procedure, it
Finite rotation shells basic equations and finite elements for Reissner kinematics
Wisniewski, K
2010-01-01
This book covers theoretical and computational aspects of non-linear shells. Several advanced topics of shell equations and finite elements - not included in standard textbooks on finite elements - are addressed, and the book includes an extensive bibliography.
Vibration of thick rotating cylindrical shells%旋转厚圆柱壳振动特性分析
郭丹; 褚福磊; 郑兆昌
2001-01-01
The effect of the rotational speed on the vibrationcharacteristics of a thick cylindrical shell was investigated using a nine node super-parametric finite element with shear and axial deformation to study the dynamic performance of the rotating cylindrical shell. Nonlinear plate-shell theory for large deflections was used to analyze the deformation before the cylindrical shell reaches the equilibrium position. Then linear theory was used to analyze the vibration of the shell. The effects of Coriolis acceleration, centrifugal force, initial tension and geometric nonlinearities due to the large deformation were considered in the model. The results showed that the rotating thick cylindrical shell has complicated three-dimension modes. The effects of the rotational speed on the natural frequency for different modes are different. The results provide a theoretical basis and an analytical method for structure design and fault analysis of rotating machinery.%为研究旋转厚圆柱壳的动力特性，采用九结点退化壳体单元有限元法，对于壳体达到平衡位置以前的状态，采用非线性板壳理论求解，然后采用线性理论研究圆柱壳的动力特性。模型中考虑了科氏加速度，离心力，初应力的影响。分析结果显示旋转厚圆柱壳具有复杂的三维模态，旋转速度对不同模态的固有频率的影响不同。该研究为高速离心机、航空发动机等旋转机械中的圆柱壳结构的设计和故障诊断提供了理论依据和分析方法。
深球壳在横向载荷作用下的静态分析%Static Analysis of a Deep Spherical Shell Under Transverse Loads
吴晓; 甘文艳; 赵永刚
2011-01-01
The static deformation of a deep spherical shell under transverse loads is discussed. Its basic e-quation obtained is based on the small transmutation theory of the shell. Shooting method is used to resolve the solution,combined with the shell's boundary conditions. By means of modulating such parameters as e-volving angle,the ratio of thickness and radius,external loads applied the flexibility deformation of a shell has been got and its relationship with those parameters has been explored through numerical calculations. The linear static mechanical behavior of the shell reflects the static mechanical behavior of elastic components.%研究深球壳在横向均布载荷作用下的静态变形问题.从壳体的小变形理论出发得到深球壳的基本方程,结合其对应的边界条件采用打靶法进行求解,调整所取壳体展开的角度、壳体厚度与半径的比值、壳体外载荷等参数和壳体的变形挠度,通过数值结果分析壳体的变形与各参数之间的关系.对深球壳的线性静态力学行为的研究可以反映这一类弹性构件的静态力学特性.
王韩奎; 高早春; 陈永寿; 郭建友; 陈永静; 图雅
2011-01-01
The realistic shell model Hamiltonians, USD and GXPF1A, have been transformed from the particle-particle （normal） representation to the particle-hole representation （multipole-multipole） by using the known formulation in Ref. [1]. The obtained multipole-m
Simpson, E.M.; Kim, Kyekyoon [Lawrence Livermore National Lab., CA (United States)
1994-05-01
A numerical model has been developed to describe the thermally induced behavior of a liquid layer of hydrogen isotopes inside a spherical Inertial Confinement Fusion (ICF) target and to calculate the far-field temperature gradient which will sustain a uniform liquid layer. This method is much faster than the trial-and-error method previously employed. The governing equations are the equations of continuity, momentum, energy, mass diffusion-convection, and conservation of the individual isotopic species. Ordinary and thermal diffusion equations for the diffusion of fluxes of the species are included. These coupled equations are solved by a finite-difference method using upwind schemes, variable mesh, and rigorous boundary conditions. The solution methodology unique to the present problem is discussed in detail. in particular, the significance of the surface tension gradient driven flows (also called Marangoni flows) in forming uniform liquid layers inside ICF targets is demonstrated. Using the theoretical model, the values of the externally applied thermal gradients that give rise to uniform liquid layers of hydrogen inside a cryogenic spherical-shell ICF target are calculated, and the results compared with the existing experimental data.
Multi-Shell Shell Model for Heavy Nuclei
Sun, Y; Sun, Yang; Wu, Cheng-Li
2003-01-01
Performing a shell model calculation for heavy nuclei has been a long-standing problem in nuclear physics. Here we propose one possible solution. The central idea of this proposal is to take the advantages of two existing models, the Projected Shell Model (PSM) and the Fermion Dynamical Symmetry Model (FDSM), to construct a multi-shell shell model. The PSM is an efficient method of coupling quasi-particle excitations to the high-spin rotational motion, whereas the FDSM contains a successful truncation scheme for the low-spin collective modes from the spherical to the well-deformed region. The new shell model is expected to describe simultaneously the single-particle and the low-lying collective excitations of all known types, yet keeping the model space tractable even for the heaviest nuclear systems.
Caurier, E; Nowacki, F; Poves, A
2007-01-01
Large scale shell model calculations, with dimensions reaching 10**9, are carried out to describe the recently observed deformed (ND) and superdeformed (SD) bands based on the first and second excited 0+ states of 40-Ca at 3.35-MeV and 5.21-MeV respectively. A valence space comprising two major oscillator shells, sd and pf, can accommodate most of the relevant degrees of freedom of this problem. The ND band is dominated by configurations with four particles promoted to the pf-shell (4p-4h in short). The SD band by 8p-8h configurations. The ground state of 40-Ca is strongly correlated, but the closed shell still amounts to 65%. The energies of the bands are very well reproduced by the calculations. The out-band transitions connecting the SD band with other states are very small and depend on the details of the mixing among the different np-nh configurations, in spite of that, the calculation describes them reasonably. For the in-band transition probabilities along the SD band, we predict a fairly constant tran...
Harper, Catherine
2006-01-01
Susie MacMurray's Shell installation manifests in Pallant House Gallery, Chichester, like some pulsing exotica, a heavily-textured wall-paper, darkly decorative, heavily luxurious, broodingly present, with more than a hint of the uncanny or the gothic. A remarkable undertaking by an artist of significance, this work's life-span will be just one year, and then it will disappear, leaving no physical trace, but undoubtedly contributing in a much less tangible way to an already rich layering of n...
Mohammad Zamani Nejad
2014-01-01
Full Text Available Using disk form multilayers, a semi-analytical solution has been derived for determination of displacements and stresses in a rotating cylindrical shell with variable thickness under uniform pressure. The thick cylinder is divided into disk form layers form with their thickness corresponding to the thickness of the cylinder. Due to the existence of shear stress in the thick cylindrical shell with variable thickness, the equations governing disk layers are obtained based on first-order shear deformation theory (FSDT. These equations are in the form of a set of general differential equations. Given that the cylinder is divided into n disks, n sets of differential equations are obtained. The solution of this set of equations, applying the boundary conditions and continuity conditions between the layers, yields displacements and stresses. A numerical solution using finite element method (FEM is also presented and good agreement was found.
F. Spada
2006-02-01
Full Text Available A new multiple-scattering Monte Carlo 3-D radiative transfer model named McSCIA (Monte Carlo for SCIAmachy is presented. The backward technique is used to efficiently simulate narrow field of view instruments. The McSCIA algorithm has been formulated as a function of the Earth's radius, and can thus perform simulations for both plane-parallel and spherical atmospheres. The latter geometry is essential for the interpretation of limb satellite measurements, as performed by SCIAMACHY on board of ESA's Envisat. The model can simulate UV-vis-NIR radiation.
First the ray-tracing algorithm is presented in detail, and then successfully validated against literature references, both in plane-parallel and in spherical geometry. A simple 1-D model is used to explain two different ways of treating absorption. One method uses the single scattering albedo while the other uses the equivalence theorem. The equivalence theorem is based on a separation of absorption and scattering. It is shown that both methods give, in a statistical way, identical results for a wide variety of scenarios. Both absorption methods are included in McSCIA, and it is shown that also for a 3-D case both formulations give identical results. McSCIA limb profiles for atmospheres with and without absorption compare well with the one of the state of the art Monte Carlo radiative transfer model MCC++.
A simplification of the photon statistics may lead to very fast calculations of absorption features in the atmosphere. However, these simplifications potentially introduce biases in the results. McSCIA does not use simplifications and is therefore a relatively slow implementation of the equivalence theorem. For the first time, however, the validity of the equivalence theorem is demonstrated in a spherical 3-D radiative transfer model.
El Haouari, M.; Talbi, A.; Feddi, E.; El Ghazi, H.; Oukerroum, A.; Dujardin, F.
2017-01-01
The hydrostatic pressure influence on the binding energy and on the optical properties (linear and third nonlinear) associated to the 1 s - 1 p intersubband transition of single dopant in a AlAs / GaAs spherical core/shell structure is investigated. The combined effects of the problem variables such as the core and shell sizes, the donor position in the structure and the pressure dependence of the physical parameters of the material have been analyzed. Our calculations are performed in the framework of the effective mass approximation and the energies are obtained by using a variational method. The results show that the linear and nonlinear parts of the absorption coefficient and the refractive index associated to the intersubband 1 s - 1 p transition undergo important changes. There are several interesting results to point out such as the shift of the absorption coefficients and refractive index to high values of photon energy. Another significant result is that the donor position considerably affects the optical properties and their corresponding amplitude.
Shatalov, M
2009-05-01
Full Text Available stream_source_info Shatalov2_2009.pdf.txt stream_content_type text/plain stream_size 22572 Content-Encoding UTF-8 stream_name Shatalov2_2009.pdf.txt Content-Type text/plain; charset=UTF-8 1 DYNAMICS OF ROTATING... AND VIBRATING THIN HEMISPHERICAL SHELL WITH MASS AND DAMPING IMPERFECTIONS AND PARAMETRICALLY DRIVEN BY DISCRETE ELECTRODES Michael Shatalov1,2 and Charlotta Coetzee2 1Sensor Science and Technology (SST) of CSIR Material Science and Manufacturing (MSM...
On micropolar theory of shallow shells
Ambartsumian S. A.; Belubekyan M.V.
2010-01-01
The simplified theory of the shallow shells is suggested on the base of the Kirchhoff-Love hypothesis and pseudo-Cosserat medium. The bending and vibrations problem of the shallow spherical shell is investigated. The value of shell small thickness is determined, when micro-rotational are essential. пологая оболочка, микровращение, изгиб, microrotation, bending, vibration
On micropolar theory of shallow shells
Ambartsumian S.A.
2010-09-01
Full Text Available The simplified theory of the shallow shells is suggested on the base of the Kirchhoff-Love hypothesis and pseudo-Cosserat medium. The bending and vibrations problem of the shallow spherical shell is investigated. The value of shell small thickness is determined, when micro-rotational are essential. пологая оболочка, микровращение, изгиб, microrotation, bending, vibration
邓兆祥; 林祥钦; 童中华
2005-01-01
An exponentially expanded space grid technique has been employed in the network simulation of chronoamperometric and voltammetric problems in spherical, cylindrical and rotating-disk electrode systems, leading to an effective simulation strategy for electrochemical problems: exponentially expanded grid network approach (EEGNA). The success of this method is largely due to the improved ability in processing the boundary singularities existing for non-planar diffusions and the enhanced simulation speed and accuracy in contrast to the uniform or quasi-uniform grid network approach.
F. Spada
2006-01-01
Full Text Available A new multiple-scattering Monte Carlo 3-D radiative transfer model named McSCIA (Monte Carlo for SCIAmachy is presented. The backward technique is used to efficiently simulate narrow field of view instruments. The McSCIA algorithm has been formulated as a function of the Earth's radius, and can thus perform simulations for both plane-parallel and spherical atmospheres. The latter geometry is essential for the interpretation of limb satellite measurements, as performed by SCIAMACHY on board of ESA's Envisat. The model can simulate UV-vis-NIR radiation. First the ray-tracing algorithm is presented in detail, and then successfully validated against literature references, both in plane-parallel and in spherical geometry. A simple 1-D model is used to explain two different ways of treating absorption. One method uses the single scattering albedo while the other uses the equivalence theorem. The equivalence theorem is based on a separation of absorption and scattering. It is shown that both methods give, in a statistical way, identical results for a wide variety of scenarios. Both absorption methods are included in McSCIA, and it is shown that also for a 3-D case both formulations give identical results. McSCIA limb profiles for atmospheres with and without absorption compare well with the one of the state of the art Monte Carlo radiative transfer model MCC++. A simplification of the photon statistics may lead to very fast calculations of absorption features in the atmosphere. However, these simplifications potentially introduce biases in the results. McSCIA does not use simplifications and is therefore a relatively slow implementation of the equivalence theorem.
Spherical colloidal photonic crystals.
Zhao, Yuanjin; Shang, Luoran; Cheng, Yao; Gu, Zhongze
2014-12-16
CONSPECTUS: Colloidal photonic crystals (PhCs), periodically arranged monodisperse nanoparticles, have emerged as one of the most promising materials for light manipulation because of their photonic band gaps (PBGs), which affect photons in a manner similar to the effect of semiconductor energy band gaps on electrons. The PBGs arise due to the periodic modulation of the refractive index between the building nanoparticles and the surrounding medium in space with subwavelength period. This leads to light with certain wavelengths or frequencies located in the PBG being prohibited from propagating. Because of this special property, the fabrication and application of colloidal PhCs have attracted increasing interest from researchers. The most simple and economical method for fabrication of colloidal PhCs is the bottom-up approach of nanoparticle self-assembly. Common colloidal PhCs from this approach in nature are gem opals, which are made from the ordered assembly and deposition of spherical silica nanoparticles after years of siliceous sedimentation and compression. Besides naturally occurring opals, a variety of manmade colloidal PhCs with thin film or bulk morphology have also been developed. In principle, because of the effect of Bragg diffraction, these PhC materials show different structural colors when observed from different angles, resulting in brilliant colors and important applications. However, this angle dependence is disadvantageous for the construction of some optical materials and devices in which wide viewing angles are desired. Recently, a series of colloidal PhC materials with spherical macroscopic morphology have been created. Because of their spherical symmetry, the PBGs of spherical colloidal PhCs are independent of rotation under illumination of the surface at a fixed incident angle of the light, broadening the perspective of their applications. Based on droplet templates containing colloidal nanoparticles, these spherical colloidal PhCs can be
Tackley, Paul J.
2008-12-01
Here it is documented how an existing code for modelling mantle convection in a cartesian domain, Stag3D, has been converted to model a 3D spherical shell by using the recently introduced yin-yang grid. StagYY is thus the latest evolution of a code that has been in continuous use and development for about 15 years so incorporates much physics and several features including compressibility, phase transitions, compositional variations, non-linear rheology, parallelisation, tracers to track composition, partial melting and melt migration, and the ability to also model spherical patches, cartesian boxes, and various 2D geometries by changing one input switch. StagYY uses a multigrid solver to obtain a velocity-pressure solution at each timestep on a staggered grid, a finite-volume scheme for advection of temperature and tracers to track composition. Convergence of multigrid solvers in the presence of realistically large viscosity variations has always been a problem; here a new pressure interpolation scheme is presented that can dramatically improve the robustness of the iterations to large viscosity variations, with up to 19 orders of magnitude variation in presented tests. Benchmark tests show that StagYY produces results that are consistent with those produced by other codes. Performance tests show reasonable scaling on a parallel Beowulf cluster up to 64 CPUs, with up to 1.2 billion unknowns solved for in a few minutes. StagYY is designed to be a stand-alone application with no libraries required and if MPI is installed it can be run in parallel. Technical issues and goals for the future are discussed.
Liu, W. H.; Qu, Y.; Ban, S. L.
2017-02-01
The intersubband optical absorption between multi energy levels of electrons in InxGa1-xN/GaN spherical core-shell quantum dots (CSQDs) and ternary mixed crystal and size effects have been investigated by using the principle of density matrix. Electronic eigenstates under the effect of built-in electric field (BEF) have been calculated by a finite element method. The results show that optical absorption between intersubbands with main quantum numbers n = 1 and n = 2 are as important as that between ones with n = 1 and different angular quantum numbers when the BEF is taken into account. In consideration of BEF, the saturation of total optical absorption coefficients (ACs) and secondary peaks of refractive index changes (RICs) appear when incident light intensity I surpasses a certain value. For a given I, the maximum ACs and zero RICs positions in InxGa1-xN/GaN CSQDs with a fixed shell size have a blue-shift when x increases or the core InxGa1-xN radius R1 decreases from 5 nm. However, when R1 > 5 nm, ACs and RICs tend to be stable. The results indicate that effective adjustment of ACs and RICs in CSQDs with BEFs by size is in a limited scale range. The saturation of ACs or secondary peaks of RICs appear more likely in CSQDs with smaller x or larger R1. These results are expected to be helpful both in the further theoretical and experimental study on optic devices consisting of CSQDs.
Bifurcation Problem of Shallow Reticulated Spherical Shells with Rectangular Bottom%矩形底面扁球面网壳的分岔问题
顾小妹
2015-01-01
The nonlinear dynamic equations for reticulated shallow spherical single-layer shells with equi-lateral triangular lattices and rectangular bottom were established by using the method of quasi-shells, and the dynamic solution fulfilling the boundary conditions was given under the clamped conditions.The nonlinear dynamic equations for this problem were obtained by using Galerkin method.The problem of statistic at the equilibrium point of the system was discussed by exponent Floquet.Lastly the bifurcation map of the equilibrium point was plotted by numerical emulation under the differentstate.The movement of the equilibrium point of the sysem under the load of both dynamic and static was indicated.%对曲面为正三角形网格矩形底面扁球面单层网壳，用拟壳法建立非线性动力学方程，在固定夹紧的边界条件下，给出满足边界条件的动态解。通过 Galerkin 法得到该问题的非线性动力学方程，用 Floquent 指数方法研究系统的分岔问题，讨论了平衡点（奇点）领域的稳定性问题。并且通过数字仿真绘出了不同平衡点处系统的分岔图，指出系统在动静载荷作用下平衡位置的变化情况。
Nandini, Patra; Akash, K.; Rohit, Gagrani; Vipul, Singh; Palani, I. A.
2017-09-01
In this work, the liquid-assisted laser ablation of NiTi rotating target has been used as a promising technique for generating spherical NiTi alloy nanoparticles with higher formation efficiency. Nd: YAG nanosecond laser with three different laser wavelengths (355, 532 and 1064 nm), three different laser fluences (30, 40 and 50 J/cm2) and three different rotational speeds (10 RPM, 20 RPM and 30 RPM) of target has been used to ablate the nitinol (Ni-55%, Ti-45%) target. The influences of different laser parameters (wavelengths and fluences) and different RPMs have been studied on the size, morphology and formation of alloy nanoparticles. It has been observed that the formation efficiency is maximum (39.9 mg/h) for smaller size nanoparticle ( 40 nm) at 355 nm wavelength, 50 J/cm2 fluence and 10 RPM rotational speed. On the other hand, we find that the formation efficiency (10.5 mg/h) is lowest with a bigger size of nanoparticle ( 110 nm) at 1064 nm wavelength, 50 J/cm2 fluence and 30 RPM speed. Therefore, this is a promising technique to synthesize spherical alloy nanoparticles with higher ablation efficiency. Thus, the higher ablation of particles helps to improve the optical absorption of the colloidal solution as optical absorption has a direct relation with the particle concentration. The shape and size of particles were characterized through SEM and DLS analysis whereas the crystallinity was confirmed through TEM and XRD analysis, respectively. Moreover, the elemental analysis was done with the help of XPS and EDS and optical absorption through UV-Vis spectrum analysis.
Svalbonas, V.
1973-01-01
A procedure for the structural analysis of stiffened shells of revolution is presented. A digital computer program based on the Love-Reissner first order shell theory was developed. The computer program can analyze orthotropic thin shells of revolution, subjected to unsymmetric distributed loading or concentrated line loads, as well as thermal strains. The geometrical shapes of the shells which may be analyzed are described. The shell wall cross section can be a sheet, sandwich, or reinforced sheet or sandwich. General stiffness input options are also available.
Wu, Xin-Yi; Ghorui, S. K.; Wang, Long-Jun; Kaneko, K.; Sun, Yang
2017-01-01
We analyze the high-spin structure of the even-even 72-80Kr isotopes using the Projected Shell Model (PSM). With the help of the Pfaffian formulas, we have vigorously extended the quasi-particle (qp) basis of the PSM code and applied in this mass region for the first time. We consider a sufficiently large multi-qp configuration space in order to describe high-spin rotational behavior. The results show that the calculation can reproduce most of the known rotational bands with positive- or negative-parity. Moreover, some side bands appearing in the near-yrast region are predicted. The main structure for each band is discussed in terms of multi-qp configurations. The variations in moment of inertia with spin are explained in terms of successive band crossings among the 2-qp, 4-qp, 6-qp, and 8-qp states. The B (E 2) transition probabilities in these bands are also calculated. To further understand the high-spin behavior of these neutron-deficient nuclei and to confirm predictions of the present work, good high-spin data, especially for B (E 2) transitions, are called for.
Kremer, Christoph
2016-01-27
The first part of this thesis revolves around symmetries in the sd-IBA-1. A region of approximate O(6) symmetry for the ground-state band, a partial dynamical symmetry (PDS) of type III, in the parameter space of the extended consistent-Q formalism is identified through quantum number fluctuations. The simultaneous occurrence of a SU(3) quasi dynamical symmetry for nuclei in the region of O(6) PDS is explained via the β=1, γ=0 intrinsic state underlying the ground-state band. The previously unrelated concepts of PDS and QDS are connected for the first time and many nuclei in the rare earth region that approximately satisfy both symmetry requirements are identified. Ground-state to ground-state (p, t) transfer reactions are presented as an experimental signature to identify pairs of nuclei that both exhibit O(6) PDS. In the second part of this thesis inelastic electron scattering off {sup 96}Zr is studied. The experiment was performed at the high resolution Lintott spectrometer at the S-DALINAC and covered a momentum-transfer range of 0.28 - 0.59 fm{sup -1}. Through a relative analysis using Plane Wave Born Approximation (PWBA) the B(E2;2{sup +}{sub 2}→0{sup +}{sub 1}) value is extracted without incurring the additional model dependence of a Distorted Wave Born Approximation (DWBA). By combining this result with known multipole mixing ratios and branching ratios all decay strengths of the 2{sup +}{sub 2} state are determined. A mixing calculation establishes very weak mixing (V{sub mix}=76 keV) between states of the ground-state band and those of the band build on top of the 0{sup +}{sub 2} state which includes the 2{sup +}{sub 2} state. The occurrence of these two isolated bands is interpreted within the shell model in terms of type II shell evolution.
Tang Jiaye; Zhan Cheng; Yang Lixun; Hao Luyuan [Chinese Academy of Sciences Key Laboratory of Materials for Energy Conversion, Department of Materials Science and Engineering, University of Science and Technology of China, Hefei, Anhui 230026 (China); Xu Xin, E-mail: xuxin@ustc.edu.cn [Chinese Academy of Sciences Key Laboratory of Materials for Energy Conversion, Department of Materials Science and Engineering, University of Science and Technology of China, Hefei, Anhui 230026 (China); Simeon, Agathopoulos [Materials Science and Engineering Department, University of Ioannina, GR-451 10 Ioannina (Greece)
2012-02-15
Highlights: Black-Right-Pointing-Pointer A facile method to synthesized high stable spherical Sr{sub 2}Si{sub 5}N{sub 8}:Eu{sup 2+} red phosphors. Black-Right-Pointing-Pointer The synthesis temperature is about 200 Degree-Sign C lower than the traditional method. Black-Right-Pointing-Pointer The h-BN protective film prevents the agglomeration between different spherical particles. Black-Right-Pointing-Pointer This spherical phosphor could be used in white LED and other display techniques. - Abstract: A facile method was designed for the successful synthesis of highly stable spherical (oxo)nitridosilicate phosphors with excellent monodispersity, high coating density and improved luminescent properties. The novel h-BN-encapsulated spherical core-shell SiO{sub 2}-Sr{sub 2}Si{sub 5}N{sub 8}:Eu{sup 2+} red-emitting phosphors were successfully synthesized by an interfacial reaction mechanism followed by a subsequent gas reduction and nitridation process. A thin film of hexagonal boron nitride (h-BN) was formed in situ during the synthesis process, leading to core-shell SiO{sub 2}-Sr{sub 2}Si{sub 5}N{sub 8}:Eu{sup 2+} phosphors with a perfectly spherical shape, narrow size distribution, non-agglomeration and a smooth surface. The particles consist of three layers: the outer h-BN film; the middle Sr{sub 2}Si{sub 5}N{sub 8}:Eu{sup 2+} phosphor shell and the amorphous SiO{sub 2} core. Under UV and blue light excitation, the SiO{sub 2}-Sr{sub 2}Si{sub 5}N{sub 8}:Eu{sup 2+} phosphors show intense red emission due to the 4f{sup 6}5d-4f{sup 7} transition of the Eu{sup 2+} ions. Furthermore, this method is superior to the traditional gas reduction and nitridation method because of the lower temperature at which synthesis occurs.
高轩能; 李超; 江媛
2015-01-01
采用LS-DYNA程序建立了单层球面钢网壳的内爆炸数值模拟计算模型。应用所建模型，对单层球面钢网壳在内爆炸作用下的动力响应进行了数值模拟计算，分析讨论了炸药 TNT 量、矢跨比和爆炸点位置等参数变化对结构动力响应的影响。结果表明，在内爆炸作用下，单层球壳结构的最大位移和最大应力响应随 TNT 量的增加而增大，最大应力响应的增幅小于最大位移；最大位移和最大应力响应随矢跨比的增大呈非线性减小，矢跨比大、跨度小的结构防(抗)爆炸波的能力较强。数值结果还揭示，邻近结构支座1/4跨度范围内的偏心爆炸对结构最为不利，进行防爆和抗爆设计时，应按偏心爆炸效应选取设计控制参数。%A numerical calculation model for simulating the internal explosions in the single-layer spherical steel re-ticulated shell was established by using LS-DYNA. Based on the model,the numerical simulation and calculation of dynamic responses of the single-layer spherical steel reticulated shell were carried out under internal explosions,and the influences of the TNT equivalence of dynamite,the rise-to-span ratio and the position of explosions on the dy-namic responses of the spherical steel reticulated shell wereanalyzed and discussed. The results showed that the maximum displacement and stress responses of the single-layer spherical steel reticulated shell under the internal ex-plosions increase with increasing TNT equivalence of dynamite,but the increasing rate of the maximum stress re-sponse is less than that of the maximum displacement response. The maximum displacement and stress responses of the shell decrease nonlinearly with the increase of the rise-to-span ratio,and the bigger the rise-to-span ratio and the smaller the span of the shell,the stronger the capacity of resistance to(anti-)explosive shock waves. The numerical results also revealed that the eccentric
栗蕾; 郝际平; 李广慧; 黄义
2011-01-01
Based on the theory of Lematire's equivalent strain of damage and in consideration of the damage of bars in a shallow reticulated spherical shell, nonlinear dynamical equations of the deteriorated shallow reticulated spherical shell were put forward by using the quasi-shell method. The method of perturbation-variation was presented, in which the maximal amplitude at the center of the shell was taken as the perturbation parameter. Then the nonlinear vibration equation of the system under fixed and clamped boundary conditions was solved by perturbation-variation method and the corresponding eigen-relation was obtained. Further, Galerkin method was utilized to derive a differential vibration equation, including the 2nd and 3rd order nonlinear terms and an accurate free vibration solution of the deteriorated shell was achieved. Then, the theoretical critical condition of chaos motion was given by using Melnikov function method and the chaos motions of the shell under nonlinear forced vibration were simulated numerically. It is found that the damage bars make the system occur more easily chaos motion.%基于Lematire等效应变损伤理论,计及扁球面网壳各个杆件的损伤影响,应用拟壳法导出了具有损伤的扁球面网壳的动力学非线性控制方程.提出了以中心最大振幅为摄动参数的摄动-变分法的求解方法,对动力非线性控制方程进行了求解,得出了相应的物理量的解析式.据此进行数值分析,得出了相应的特征关系.并用Galerkin方法导出了一个含二次和三次非线性振动微分方程并求解了具有损伤扁球面网壳的的非线性动力学的自由振动方程,给出了准确解.而后利用Melnikov函数法,从理论上给出了考虑损伤的系统发生混沌运动的临界条件,并通过计算机数字仿真证实了考虑损伤的扁球面网壳在非线性强迫振动时存在混沌运动,同时发现损伤使得系统更易发生混沌运动.
From solar-like to anti-solar differential rotation in cool stars
Gastine, T; Morin, J; Reiners, A; Wicht, J
2013-01-01
Stellar differential rotation can be separated into two main regimes: solar-like when the equator rotates faster than the poles and anti-solar when the polar regions rotate faster than the equator. We investigate the transition between these two regimes with 3-D numerical simulations of rotating spherical shells. We conduct a systematic parameter study which also includes models from different research groups. We find that the direction of the differential rotation is governed by the contribution of the Coriolis force in the force balance, independently of the model setup (presence of a magnetic field, thickness of the convective layer, density stratification). Rapidly-rotating cases with a small Rossby number yield solar-like differential rotation, while weakly-rotating models sustain anti-solar differential rotation. Close to the transition, the two kinds of differential rotation are two possible bistable states. This study provides theoretical support for the existence of anti-solar differential rotation i...
Zulhijah, Rizka [Department of Chemical Engineering, Graduate School of Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashi-Hiroshima 739-8527 (Japan); Nandiyanto, Asep Bayu Dani [Departemen Kimia, Fakultas Pendidikan Matematika dan Ilmu Pengetahuan Alam, Universitas Pendidikan Indonesia, Jl. Dr. Setiabudi No. 229, Bandung 40154 (Indonesia); Ogi, Takashi, E-mail: ogit@hiroshima-u.ac.jp [Department of Chemical Engineering, Graduate School of Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashi-Hiroshima 739-8527 (Japan); Iwaki, Toru [Department of Chemical Engineering, Graduate School of Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashi-Hiroshima 739-8527 (Japan); Nakamura, Keitaro [Research Center for Production and Technology, Nisshin Seifun Group, Inc., 5-3-1, Tsurugaoka, Fujimino, Saitama 356-8511 (Japan); Okuyama, Kikuo [Department of Chemical Engineering, Graduate School of Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashi-Hiroshima 739-8527 (Japan)
2015-05-01
The introduction of an oxidation treatment to the synthesis of spherical and core–shell α″-Fe{sub 16}N{sub 2}/Al{sub 2}O{sub 3} nanoparticles (~62 nm) from plasma-synthesized core–shell α-Fe/Al{sub 2}O{sub 3} nanoparticles has been found to result in a high yield of α″-Fe{sub 16}N{sub 2} phase of up to 98%. The oxidation treatment leads the formation of a maghemite phase with open channeled structures along the c-axis, facilitating penetration of H{sub 2} and NH{sub 3} gases during the hydrogen reduction and nitridation steps. The saturation magnetization and magnetic coercivity of the core–shell α″-Fe{sub 16}N{sub 2}/Al{sub 2}O{sub 3} magnetic nanoparticles were found to be 156 emu/g and 1450 Oe, respectively. The detailed effects of the oxidation on the formation of α″-Fe{sub 16}N{sub 2} phase were investigated by characterizing the morphology (SEM, TEM and BET), elemental composition (EDX, EELS, and XAFS) and magnetic properties (Mössbauer and MSPS) of the prepared particles. The good magnetic properties obtained have the potential for future applications such as rare-earth-free magnetic materials. - Highlights: • High yield of α″-Fe{sub 16}N{sub 2} up to 98% was prepared from core–shell α-Fe/Al{sub 2}O{sub 3} NPs. • Introduction of oxidation improved yield of α″-Fe{sub 16}N{sub 2} for large size of NPs. • Oxidation forming microporous structured maghemite facilitated nitridation process. • Particle morphology changed during the nitrogen process due to atomic dislocation. • Core–shell α″-Fe{sub 16}N{sub 2}/Al{sub 2}O{sub 3} nanoparticles showed good magnetic performances.
Kapania, R. K.; Mohan, P.
1996-09-01
Finite element static, free vibration and thermal analysis of thin laminated plates and shells using a three noded triangular flat shell element is presented. The flat shell element is a combination of the Discrete Kirchhoff Theory (DKT) plate bending element and a membrane element derived from the Linear Strain Triangular (LST) element with a total of 18 degrees of freedom (3 translations and 3 rotations per node). Explicit formulations are used for the membrane, bending and membrane-bending coupling stiffness matrices and the thermal load vector. Due to a strong analogy between the induced strain caused by the thermal field and the strain induced in a structure due to an electric field the present formulation is readily applicable for the analysis of structures excited by surface bonded or embedded piezoelectric actuators. The results are presented for (i) static analysis of (a) simply supported square plates under doubly sinusoidal load and uniformly distributed load (b) simply supported spherical shells under a uniformly distributed load, (ii) free vibration analysis of (a) square cantilever plates, (b) skew cantilever plates and (c) simply supported spherical shells; (iii) Thermal deformation analysis of (a) simply supported square plates, (b) simply supported-clamped square plate and (c) simply supported spherical shells. A numerical example is also presented demonstrating the application of the present formulation to analyse a symmetrically laminated graphite/epoxy laminate excited by a layer of piezoelectric polyvinylidene flouride (PVDF). The results presented are in good agreement with those available in the literature.
李正良; 胡浩; 于伟
2015-01-01
Thefreevibrationofajoined,smoothandorthogonallystiffenedcylindrical-sphericalshellundervarious boundary conditions was studied.Based on the simplification of the joined part,the spherical shell is of free boundary condition and the cylindrical shell is of simply supported boundary condition.The Rayleigh-Ritz method was applied to solve the natural frequencies of the structure according to the Flügge's thin shell theory.The natural frequencies were calculated and compared with those by the finite element software ANSYS to confirm the applicability and validity of the simplification.The effects of the shallowness of the spherical shell and the length-to-radius ratio of the joined shell on the free vibrational behavior of the joined structure were investigated.The results indicate that as the semi-angle Φof the sphere increases,the natural frequencies decrease.As the length-to-radius ratio L/Rc increases,the influence of the semi-angle Φof the sphere on the natural frequencies decreases,the natural frequencies decrease gradually and their reducing magnitude descends.%研究不同边界条件下光滑、正交加筋圆柱壳－球壳组合结构的自由振动。通过对圆柱壳与球壳连接处简化处理，视球壳为自由约束，圆柱壳为简支约束，据Flügge 薄壳理论利用Rayleigh-Ritz 法求得结构频率，与有限元软件ANSYS结果比较，验证该方法的适用性及有效性；分析球壳扁率及组合壳体长径比对频率影响。结果表明，球心半角Φ增大结构自振频率降低；长径比L／Rc增大球心半角Φ对组合结构频率影响逐渐减弱，结构自振频率逐渐降低，且降幅减小。
Svalbonas, V.; Ogilvie, P.
1973-01-01
The engineering programming information for the digital computer program for analyzing shell structures is presented. The program is designed to permit small changes such as altering the geometry or a table size to fit the specific requirements. Each major subroutine is discussed and the following subjects are included: (1) subroutine description, (2) pertinent engineering symbols and the FORTRAN coded counterparts, (3) subroutine flow chart, and (4) subroutine FORTRAN listing.
Cooperative effects in spherical spasers
Bordo, Vladimir
2017-01-01
a shell/core contains an arbitrarily large number of active molecules in the vicinity of a metallic core/shell. An essential aspect of the theory is an ab initio account of the feedback from the core/shell boundaries which significantly modifies the molecular dynamics. The theory provides rigorous, albeit......A fully analytical semiclassical theory of cooperative optical processes which occur in an ensemble of molecules embedded in a spherical core-shell nanoparticle is developed from first principles. Both the plasmonic Dicke effect and spaser generation are investigated for the designs in which...
Söderström, P.-A., E-mail: pasoder@ribf.riken.jp; Doornenbal, P.; Nishimura, S.; Baba, H.; Fukuda, N.; Inabe, N.; Isobe, T.; Kubo, T.; Kubono, S.; Suzuki, H.; Takeda, H. [RIKEN Nishina Center, 2-1 Hirosawa, Wako-shi, Saitama 351-0198 (Japan); Regan, P. H. [Department of Physics, University of Surrey, Guildford, GU2 7XH (United Kingdom); National Physical Laboratory, Teddington, Middlesex, TW11 0LW (United Kingdom); Walker, P. M.; Carroll, R.; Lalkovski, S.; Lotay, G.; Patel, Z.; Podolyák, Zs.; Shand, C. M. [Department of Physics, University of Surrey, Guildford, GU2 7XH (United Kingdom); Watanabe, H. [IRCNPC, Beihang University, Beijing 100191 (China); School of Physics and Nuclear Energy Engineering, Beihang University, Beijing 100191 (China); and others
2015-10-15
In this contribution the low-excitation structural properties of the doubly mid-shell nucleus {sup 170}Dy are discussed, with a special empasis on the evolution of the ground state rotational band within the dysprosium isotopic chain. Recent results from an experiment with the EURICA setup at RIKEN are shown in the context of previous measurements at the PRISMA+CLARA as well as the PRISMA+AGATA setups at Laboratori Nazionali di Legnaro. A brief outlook on future planned measurements is also given.
Instabilities of Shercliff and Stewartson layers in spherical Couette flow
Wei, Xing
2010-01-01
We explore numerically the flow induced in a spherical shell by differentially rotating the inner and outer spheres. The fluid is also taken to be electrically conducting (in the low magnetic Reynolds number limit), and a magnetic field is imposed parallel to the axis of rotation. If the outer sphere is stationary, the magnetic field induces a Shercliffe layer on the tangent cylinder, the cylinder just touching the inner sphere and parallel to the field. If the magnetic field is absent, but a strong overall rotation is present, Coriolis effects induce a Stewartson layer on the tangent cylinder. The non-axisymmetric instabilities of both types of layer separately have been studied before; here we consider the two cases side by side, as well as the mixed case, and investigate how magnetic and rotational effects interact. We find that if the differential rotation and the overall rotation are in the same direction, the overall rotation may have a destabilizing influence, whereas if the differential rotation and t...
Christina lily Jasmine, P. [Dept. of Physics, N.M.S. Sermathai Vasan College for Women, Madurai 625 012 (India); John Peter, A., E-mail: a.john.peter@gmail.com [P.G. and Research Dept. of Physics, Government Arts College, Melur, 625 106 Madurai (India); Lee, Chang Woo [Department of Chemical Engineering, College of Engineering, Kyung Hee University, 1732 Deogyeong-daero, Gihung, Yongin, Gyeonggi 446-701 (Korea, Republic of)
2015-05-01
Highlights: • Optical properties of a hydrogenic donor impurity in CdTe/Zn{sub 0.2}Cd{sub 0.8}Te/ZnTe core/shell/shell dot are discussed. • Two parametrical potential of Smorodinsky–Winternitz are considered in this problem. • The dielectric mismatch is included in the Hamiltonian. • The position dependent effective mass is applied. • The intersubband optical absorption, oscillator strength and radiative life time are studied. - Abstract: Electronic and optical properties of a hydrogenic donor impurity in a CdTe/Zn{sub 0.2}Cd{sub 0.8}Te/ZnTe core/shell/shell quantum dot are discussed taking into consideration of geometrical confinement effect. The confining potentials on both the sides of the barrier are different and a two parametrical potential of Smorodinsky–Winternitz is considered in this problem. The dielectric mismatch is included in the Hamiltonian. The position dependent effective mass is applied. The electronic properties are studied using variational method and the optical properties are investigated using the density matrix approach. The intersubband optical absorption, the oscillator strength and the radiative life time between ground and the excited states are studied based on the wave functions and the confined energies with and without the impurity with various dot radii. The results show that the absorption wavelength in type-II core and shell semiconducting nanomaterials can be tuned over a wider range of wavelengths by altering their size and the composition.
Li, Yu-Chun
2016-01-01
Experimentally observed ground state band based on the $1/2^{-}[521]$ Nilsson state and the first exited band based on the $7/2^{-}[514]$ Nilsson state in the odd-$Z$ nucleus $^{255}$Lr are studied by the cranked shell model (CSM) with the paring correlations treated by the particle-number-conserving (PNC) method. This is the first time the detailed theoretical investigations being performed on these rotational bands. Both the experimental kinematic and dynamic moment of inertia ($\\mathcal{J}^{(1)}$ and $\\mathcal{J}^{(2)}$) versus rotational frequency are reproduced quite well by the PNC-CSM calculations. By comparing the theoretical kinematic moment of inertia $\\mathcal{J}^{(1)}$ with the experimental ones extracted from different spin assignments, the spin $17/2^{-}\\rightarrow13/2^{-}$ is assigned to the lowest-lying $196.6(5)$ keV transition of the $1/2^{-}[521]$ band, and $15/2^{-}\\rightarrow11/2^{-}$ to the $189(1)$ keV transition of the $7/2^{-}[514]$ band, respectively. The proton $N=7$ major shell is ...
Bainum, P. M.; Reddy, A. S. S. R.
1981-01-01
A proposed method for controlling the shape and orientation of very large shallow dish type receiver/reflectors to be used in communication, radiometry and in electronic orbital based mail systems involves connecting a rigid light weight dumbell with heavy tip masses to the shell at its apex by a spring loaded double gimballed joint with dampling. To completely damp the system transient motion in all of the important lower frequency modes, an active control system is required. A mathematical model is extended to include the effects of point actuators located at preselected positions on the shell surface. The formulation of the uncontrolled dynamics assumes an a priori knowledge of the frequencies of all the elastic modes to be incorporated within the system model. As an example, three rigid body modes and six elastic modes are included in the model and six actuators are assumed, none of which lies on a nodal line or circle.
Bubble migration in a rotating, liquid-filled sphere
Annamalai, P.; Subramanian, R. S.; Cole, R.
1982-01-01
Results and analysis of ground-based experiments performed to aid in designing experiments on the behavior of bubbles in a rotating liquid body on board the Shuttle in free fall are presented. Spherical shells filled with silicone oil containing a small gas bubble were spun and filmed by high speed motion picture photography. The rotation of the shell and the trajectory of the bubble motion were recorded and the film was exposed to a motion analyzer connected to a keypunch. The analyzer measured Cartesian coordinates as well as angle, frame number, and rotation rate. Optical correction equations were employed to determine the apparent bubble trajectory relative to an inertial frame of reference. An analytical model for the bubble motion was defined, yielding predictions of velocity and position at different times. Rotation of the fluid container is concluded to aid in centering the bubbles.
Gundlach, Carsten
2016-12-01
We express the Einstein-Vlasov system in spherical symmetry in terms of a dimensionless momentum variable z (radial over angular momentum). This regularizes the limit of massless particles, and in that limit allows us to obtain a reduced system in independent variables (t ,r ,z ) only. Similarly, in this limit the Vlasov density function f for static solutions depends on a single variable Q (energy over angular momentum). This reduction allows us to show that any given static metric that has vanishing Ricci scalar, is vacuum at the center and for r >3 M and obeys certain energy conditions uniquely determines a consistent f =k ¯(Q ) (in closed form). Vice versa, any k ¯(Q ) within a certain class uniquely determines a static metric (as the solution of a system of two first-order quasilinear ordinary differential equations). Hence the space of static spherically symmetric solutions of the Einstein-Vlasov system is locally a space of functions of one variable. For a simple two-parameter family of functions k ¯(Q ), we construct the corresponding static spherically symmetric solutions, finding that their compactness is in the interval 0.7 ≲maxr(2 M /r )≤8 /9 . This class of static solutions includes one that agrees with the approximately universal type-I critical solution recently found by Akbarian and Choptuik (AC) in numerical time evolutions. We speculate on what singles it out as the critical solution found by fine-tuning generic data to the collapse threshold, given that AC also found that all static solutions are one-parameter unstable and sit on the threshold of collapse.
Iofa, Mikhail Z
2016-01-01
Geometry of the spacetime with a spherical shell embedded in it is studied in two coordinate systems - in Kodama-Schwarzschild coordinates and in Gaussian normal coordinates. We consider transformations between the coordinate systems as in the 4D spacetime so as at the surface $\\S$ swept in the spacetime by the spherical shell. Extrinsic curvatures of the surface swept by the shell are calculated in both coordinate systems. Applications to the Israel junction conditions are discussed.
Axisymmetric buckling of laminated thick annular spherical cap
Dumir, P. C.; Dube, G. P.; Mallick, A.
2005-03-01
Axisymmetric buckling analysis is presented for moderately thick laminated shallow annular spherical cap under transverse load. Buckling under central ring load and uniformly distributed transverse load, applied statically or as a step function load is considered. The central circular opening is either free or plugged by a rigid central mass or reinforced by a rigid ring. Annular spherical caps have been analysed for clamped and simple supports with movable and immovable inplane edge conditions. The governing equations of the Marguerre-type, first order shear deformation shallow shell theory (FSDT), formulated in terms of transverse deflection w, the rotation ψ of the normal to the midsurface and the stress function Φ, are solved by the orthogonal point collocation method. Typical numerical results for static and dynamic buckling loads for FSDT are compared with the classical lamination theory and the dependence of the effect of the shear deformation on the thickness parameter for various boundary conditions is investigated.
Gundlach, Carsten
2016-01-01
We express the Einstein-Vlasov system in spherical symmetry in terms of a dimensionless momentum variable $z$ (radial over angular momentum). This regularises the limit of massless particles, and in that limit allows us to obtain a reduced system in independent variables $(t,r,z)$ only. Similarly, in this limit the Vlasov density function $f$ for static solutions depends on a single variable $Q$ (energy over angular momentum). This reduction allows us to show that any given static metric which has vanishing Ricci scalar, is vacuum at the centre and for $r>3M$ and obeys certain energy conditions uniquely determines a consistent $f=\\bar k(Q)$ (in closed form). Vice versa, any $\\bar k(Q)$ within a certain class uniquely determines a static metric (as the solution of a system of two first-order quasilinear ODEs). Hence the space of static spherically symmetric solutions of Einstein-Vlasov is locally a space of functions of one variable. For a simple 2-parameter family of functions $\\bar k(Q)$, we construct the co...
Christina lily Jasmine, P.; John Peter, A.; Lee, Chang Woo
2015-05-01
Electronic and optical properties of a hydrogenic donor impurity in a CdTe/Zn0.2Cd0.8Te/ZnTe core/shell/shell quantum dot are discussed taking into consideration of geometrical confinement effect. The confining potentials on both the sides of the barrier are different and a two parametrical potential of Smorodinsky-Winternitz is considered in this problem. The dielectric mismatch is included in the Hamiltonian. The position dependent effective mass is applied. The electronic properties are studied using variational method and the optical properties are investigated using the density matrix approach. The intersubband optical absorption, the oscillator strength and the radiative life time between ground and the excited states are studied based on the wave functions and the confined energies with and without the impurity with various dot radii. The results show that the absorption wavelength in type-II core and shell semiconducting nanomaterials can be tuned over a wider range of wavelengths by altering their size and the composition.
A fast stroboscopic spectral method for rotating systems in numerical relativity
Bonazzola, S; Novák, J; Bonazzola, Silvano; Jaramillo, Jos{\\'e}-Luis; Novak, Jerome
2007-01-01
We present a numerical technique for solving evolution equations, as the wave equation, in the description of rotating astrophysical compact objects in comoving coordinates, which avoids the problems associated with the light cylinder. The technique implements a fast spectral matching between two domains in relative rotation: an inner spherical domain, comoving with the sources and lying strictly inside the light cylinder, and an outer inertial spherical shell. Even though the emphasis is placed on spectral techniques, the matching is independent of the specific manner in which equations are solved inside each domain, and can be adapted to different schemes. We illustrate the strategy with some simple but representative examples.
Gao, Lin; Han, Wenjuan; Li, Xiuying; Wang, Jixiang; Yan, Yongsheng; Li, Chunxiang; Dai, Jiangdong
2015-12-01
A fluorescent core-shell molecularly imprinted polymer based on the surface of SiO2 beads was synthesized and its application in the fluorescence detection of ultra-trace λ-cyhalothrin (LC) was investigated. The shell was prepared by copolymerization of acrylamide with allyl fluorescein in the presence of LC to form recognition sites. The experimental results showed that the thin fluorescent molecularly imprinted polymer (FMIP) film exhibited better selective recognition ability than fluorescent molecularly non-imprinted polymer (FNIP). A new nonlinear relationship between quenching rate and concentration was found in this work. In addition, the nonlinear relationship allowed a lower concentration range of 0-5.0 nM to be described by the Stern-Volmer equation with a correlation coefficient of 0.9929. The experiment results revealed that the SiO2@FMIP was satisfactory as a recognition element for determination of LC in soda water samples. Therefore this study demonstrated the potential of MIP for the recognition and detection of LC in food.
Differential Rotation and Magnetism in Simulations of Fully Convective Stars
Browning, Matthew
2010-01-01
Stars of sufficiently low mass are convective throughout their interiors, and so do not possess an internal boundary layer akin to the solar tachocline. Because that interface figures so prominently in many theories of the solar magnetic dynamo, a widespread expectation had been that fully convective stars would exhibit surface magnetic behavior very different from that realized in more massive stars. Here I describe how recent observations and theoretical models of dynamo action in low-mass stars are partly confirming, and partly confounding, this basic expectation. In particular, I present the results of 3--D MHD simulations of dynamo action by convection in rotating spherical shells that approximate the interiors of 0.3 solar-mass stars at a range of rotation rates. The simulated stars can establish latitudinal differential rotation at their surfaces which is solar-like at ``rapid'' rotation rates (defined within) and anti-solar at slower rotation rates; the differential rotation is greatly reduced by feed...
Romano, Marcello
2012-01-01
The exact analytic solution is introduced for the rotational motion of a rigid body having three equal principal moments of inertia and subjected to an external torque vector which is constant for an observer fixed with the body, and to arbitrary initial angular velocity. In the paper a parametrization of the rotation by three complex numbers is used. In particular, the rows of the rotation matrix are seen as elements of the unit sphere and projected, by stereographic projection, onto points on the complex plane. In this representation, the kinematic differential equation reduces to an equation of Riccati type, which is solved through appropriate choices of substitutions, thereby yielding an analytic solution in terms of confluent hypergeometric functions. The rotation matrix is recovered from the three complex rotation variables by inverse stereographic map. The results of a numerical experiment confirming the exactness of the analytic solution are reported. The newly found analytic solution is valid for any...
Yong, Ee Hou; Nelson, David R; Mahadevan, L
2013-10-25
On microscopic scales, the crystallinity of flexible tethered or cross-linked membranes determines their mechanical response. We show that by controlling the type, number, and distribution of defects on a spherical elastic shell, it is possible to direct the morphology of these structures. Our numerical simulations show that by deflating a crystalline shell with defects, we can create elastic shell analogs of the classical platonic solids. These morphologies arise via a sharp buckling transition from the sphere which is strongly hysteretic in loading or unloading. We construct a minimal Landau theory for the transition using quadratic and cubic invariants of the spherical harmonic modes. Our approach suggests methods to engineer shape into soft spherical shells using a frozen defect topology.
Wenninger, Magnus J
2012-01-01
Well-illustrated, practical approach to creating star-faced spherical forms that can serve as basic structures for geodesic domes. Complete instructions for making models from circular bands of paper with just a ruler and compass. Discusses tessellation, or tiling, and how to make spherical models of the semiregular solids and concludes with a discussion of the relationship of polyhedra to geodesic domes and directions for building models of domes. "". . . very pleasant reading."" - Science. 1979 edition.
Guo, Enyan; Yin, Longwei
2015-01-07
We report on high-performance dye-sensitized solar cells (DSSCs) based on nitrogen doped anatase TiO2-CuxO core-shell mesoporous hybrids synthesized through a facile and controlled combined sol-gel and hydrothermal process in the presence of hexadecylamine as the structure-directing agent. The matching of band edges between CuxO and TiO2 to form a semiconductor heterojunction plays an important role in effective separation of light induced electrons and holes, providing a promising photoanode for DSSCs because of its wide absorption spectrum, high electron injection efficiency, and fast electron transference. DSSCs based on the mesoporous TiO2-CuxO core-shell hybrids show a high short-circuit current density of 9.60 mA cm(-2) and a conversion efficiency of 3.86% under one sun illumination. While DSSCs based on the N-doped mesoporous TiO2-CuxO hybrids exhibit the higher short-circuit current density of 13.24 mA cm(-2) and a conversion efficiency of 4.57% under one sun illumination. In comparison with un-doped TiO2-CuxO hybrids, the doping of nitrogen into the lattice of TiO2 can extend the light absorption in the ultraviolet range to the visible light region and effectively decrease the recombination rate of photo-generated electrons and holes. The presented N-doped mesoporous TiO2-CuxO hybrids as photoanodes could find potential applications for high performance DSSCs.
傅贤超; 唐英; 曹文
2016-01-01
Bridge rotation construction is commonly used to date. Hinge is the key structure. Currently,plane hinge and spherical hinge are both used. The latter is more widely applied while the former is mainly used in light bridge. In this paper,these two hinges were compared in terms of hinge structure design,fabrication,installation,and rotation construction. In this case,plane hinge outweighs spherical hinge in terms of mechanic characteristics and operation properties.%我国采用转体施工工艺的桥梁日益增多,转铰是实现其转体功能的关键结构.目前桥梁平转法施工中转铰一般采用球铰和平面铰,球铰运用比较广泛,而平面铰主要运用于轻型桥梁.本文从转铰结构设计、制作安装、转体施工等方面对两种转铰进行对比分析,论证了平面铰的受力特性和使用性能更加合理.
Li, Yu-Chun; He, Xiao-Tao
2016-07-01
Experimentally observed ground state band based on the 1/2-[521] Nilsson state and the first exited band based on the 7/2-[514] Nilsson state of the odd- Z nucleus 255Lr are studied by the cranked shell model (CSM) with the paring correlations treated by the particle-number-conserving (PNC) method. This is the first time the detailed theoretical investigations are performed on these rotational bands. Both experimental kinematic and dynamic moments of inertia ( J (1) and J (2)) versus rotational frequency are reproduced quite well by the PNC-CSM calculations. By comparing the theoretical kinematic moment of inertia J (1) with the experimental ones extracted from different spin assignments, the spin 17/2- → 13/2- is assigned to the lowest-lying 196.6(5) keV transition of the 1/2-[521] band, and 15/2- → 11/2- to the 189(1) keV transition of the 7/2-[514] band, respectively. The proton N = 7 major shell is included in the calculations. The intruder of the high- j low-Ω 1 j 15/2 (1/2-[770]) orbital at the high spin leads to band-crossings at ħω ≈ 0.20 ( ħω ≈ 0.25) MeV for the 7/2-[514] α = -1/2 ( α = +1/2) band, and at ħω ≈ 0.175 MeV for the 1/2-[521] α = -1/2 band, respectively. Further investigations show that the band-crossing frequencies are quadrupole deformation dependent.
丁卫君; 聂国华; 王榕
2012-01-01
This paper deals with non-linear free vibration of a single-layer reticulated imperfect shallow spherical shell formed by beam members placed in two orthogonal directions based on an equivalent continuum model. Using both the dynamic equilibrium equation and the compatibility equation in terms of deflection and force function, a characteristic relation between the amplitude and frequency of a clamped or hinged shell was derived by asymptotic iteration method. Numerical examples were given to illustrate the effects of boundary constraints and impaction factor on the characteristic relation. Meanwhile, the present results for the fundamental frequency were compared with data by finite element method using ANSYS code. The results show that the present continuum model has enough precision in computation.%基于梁元正交布置的单层网壳的等效连续化模型,研究了含几何初始缺陷的网格扁球壳非线性自由振动问题.基于用挠度和力函数表示的非线性动力平衡方程和变形协调方程,针对简支和固支两种约束条件,采用渐近迭代法得到了网格扁球壳自由振动的非线性幅-频特征关系.通过数值计算分析了边界约束和缺陷因子等对网壳幅-频关系的影响.同时,对于结构基频,理论结果与基于ANSYS的有限元数值结果的比较,验证了网壳等效连续化模型的精度.
Spontaneous spherical symmetry breaking in atomic confinement
Sveshnikov, K
2016-01-01
The effect of spontaneous breaking of initial SO(3) symmetry is shown to be possible for an H-like atom in the ground state, when it is confined in a spherical box under general boundary conditions of "not going out" through the box surface (i.e. third kind or Robin's ones), for a wide range of physically reasonable values of system parameters. The reason is that such boundary conditions could yield a large magnitude of electronic wavefunction in some sector of the box boundary, what in turn promotes atomic displacement from the box center towards this part of the boundary, and so the underlying SO(3) symmetry spontaneously breaks. The emerging Goldstone modes, coinciding with rotations around the box center, restore the symmetry by spreading the atom over a spherical shell localized at some distances from the box center. Atomic confinement inside the cavity proceeds dynamically -- due to the boundary condition the deformation of electronic wavefunction near the boundary works as a spring, that returns the at...
Mapping the omega-effect in the DTS magnetized spherical Couette flow experiment
Nataf, Henri-Claude
2012-01-01
The DTS experiment is a spherical Couette flow experiment with an imposed dipolar magnetic field. Liquid sodium is used as a working fluid. In a series of measurement campaigns, we have obtained data on the mean axisymmetric velocity, the mean induced magnetic field and electric potentials. All these quantities are coupled through the induction equation. In particular, a strong omega-effect is produced by differential rotation within the fluid shell, inducing a significant azimuthal magnetic field. Taking advantage of the simple spherical geometry of the experiment, I expand the azimuthal and meridional fields into Legendre polynomials and derive the expressions that permit to relate all measurements to the radial functions of the velocity field for each harmonic degree. For small magnetic Reynolds numbers Rm the relations are linear, and the toroidal and poloidal equations decouple. Selecting a set of measurements for a given rotation frequency of the inner sphere (Rm = 9.4), I invert simultaneously the velo...
Hydromagnetic quasi-geostrophic modes in rapidly rotating planetary cores
Canet, E.; Finlay, Chris; Fournier, A.
2014-01-01
The core of a terrestrial-type planet consists of a spherical shell of rapidly rotating, electrically conducting, fluid. Such a body supports two distinct classes of quasi-geostrophic (QG) eigenmodes: fast, primarily hydrodynamic, inertial modes with period related to the rotation time scale......, or shorter than, their oscillation time scale.Based on our analysis, we expect Mercury to be in a regime where the slow magnetic modes are of quasi-free decay type. Earth and possibly Ganymede, with their larger Elsasser numbers, may possess slow modes that are in the transition regime of weak diffusion...
The pure rotational spectra of the open-shell diatomic molecules PbI and SnI
Evans, Corey J., E-mail: cje8@le.ac.uk, E-mail: nick.walker@newcastle.ac.uk; Needham, Lisa-Maria E. [Department of Chemistry, University of Leicester, Leicester LE1 7RH (United Kingdom); Walker, Nicholas R., E-mail: cje8@le.ac.uk, E-mail: nick.walker@newcastle.ac.uk; Köckert, Hansjochen; Zaleski, Daniel P.; Stephens, Susanna L. [School of Chemistry, Newcastle University, Newcastle upon Tyne NE1 7RU (United Kingdom)
2015-12-28
Pure rotational spectra of the ground electronic states of lead monoiodide and tin monoiodide have been measured using a chirped pulsed Fourier transform microwave spectrometer over the 7-18.5 GHz region for the first time. Each of PbI and SnI has a X {sup 2}Π{sub 1/2} ground electronic state and may have a hyperfine structure that aids the determination of the electron electric dipole moment. For each species, pure rotational transitions of a number of different isotopologues and their excited vibrational states have been assigned and fitted. A multi-isotopologue Dunham-type analysis was carried out on both species producing values for Y{sub 01}, Y{sub 02}, Y{sub 11}, and Y{sub 21}, along with Λ-doubling constants, magnetic hyperfine constants and nuclear quadrupole coupling constants. The Born-Oppenheimer breakdown parameters for Pb have been evaluated and the parameter rationalized in terms of finite nuclear field effects. Analysis of the bond lengths and hyperfine interaction indicates that the bonding in both PbI and SnI is ionic in nature. Equilibrium bond lengths have been evaluated for both species.
Axisymmetric acoustic scattering from submerged prolate spheroidal shells
Boisvert, Jeffrey E.; Hayek, Sabih I.
2005-09-01
The equations of motion for nonaxisymmetric vibration of prolate spheroidal shells of constant thickness were derived using Hamilton's principle [S. I. Hayek and J. E. Boisvert, J. Acoust. Soc. Am. 114, 2799-2811 (2003)]. The shell theory used in this derivation includes shear deformations and rotatory inertias. The shell displacements and rotations were expanded in infinite series of comparison functions. These include associated Legendre functions in terms of the prolate spheroidal angular coordinate and circular functions in the azimuthal angle coordinate. The shell is insonified by a plane wave incident along the major axis. The external (heavy) fluid loading impedance was computed using an eigenfunction expansion of prolate spheroidal wavefunctions. Far-field scattered acoustic pressure spectra are presented for several shell thickness-to-half-length ratios ranging from 0.005 to 0.1, and for various shape parameters, a, ranging from an elongated spheroidal shell (a=1.01) to a spherical shell (a~100). The far-field directivity of acoustic scattering is presented at selected frequencies. [Work supported by the ONR/ASEE Summer Faculty Research Program.
Development of a spherical aerial vehicle for urban search
Hou, Kang; Sun, Hanxu; Jia, Qingxuan; Zhang, Yanheng
2014-06-01
With the ability to provide close surveillance in narrow space or urban areas, spherical aerial vehicles have been of great interest to many scholars and researchers. The spherical aerial vehicle offers substantial design advantages over the conventional small aerial vehicles. As a kind of small aerial vehicles, spherical aerial vehicle is presented in this paper. Firstly, the unique structure of spherical aerial vehicle is presented in detail. And then as the key component of the spherical aerial vehicle, the meshed spherical shell is analyzed. The shell is made of carbon fiber and is used to protect the inner devices, so the deformation of the shell is analyzed and simulated. Then the experimental results verify the above analysis and the composite carbon fiber material makes the mesh spherical shell small deformation. Considering the whole vehicle has a shell outside, the lift affect of the meshed spherical shell is analyzed. The simulation and experiment results are basically consistent with theoretical analysis, and the impact of the meshed shell has small resistance for the airflow through the sphere.
Magnetic Effects and Differential Rotation Near Transition from Solar to Anti-Solar Profiles
Simitev, Radostin D; Busse, Friedrich H
2015-01-01
We present a set of convective dynamo simulations in rotating spherical fluid shells based on an anelastic approximation of compressible fluids. The simulations extend into a "buoyancy-dominated" regime where the buoyancy forcing is dominant while the Coriolis force is no longer balanced by pressure gradients and strong anti-solar differential rotation develops as a result. Dynamos in this regime are strongly dominated by dipole components but at the same time their magnetic energies are relatively small compared to the corresponding kinetic energies of the flow. Despite being relatively weak the self-sustained magnetic fields are able to reverse the direction of differential rotation to solar-like. We find that the convection in the buoyancy-dominated regime is significantly stronger near the pole than in the equatorial region, leading to non-oscillatory dipolar dynamo solutions. The results are obtained with a new simulation code for modelling of convection and MHD dynamo generation in rotating spherical sh...
Modeling mantle convection in the spherical annulus
Hernlund, John W.; Tackley, Paul J.
2008-12-01
Most methods for modeling mantle convection in a two-dimensional (2D) circular annular domain suffer from innate shortcomings in their ability to capture several characteristics of the spherical shell geometry of planetary mantles. While methods such as rescaling the inner and outer radius to reduce anomalous effects in a 2D polar cylindrical coordinate system have been introduced and widely implemented, such fixes may have other drawbacks that adversely affect the outcome of some kinds of mantle convection studies. Here we propose a new approach that we term the "spherical annulus," which is a 2D slice that bisects the spherical shell and is quantitatively formulated at the equator of a spherical polar coordinate system after neglecting terms in the governing equations related to variations in latitude. Spherical scaling is retained in this approximation since the Jacobian function remains proportional to the square of the radius. We present example calculations to show that the behavior of convection in the spherical annulus compares favorably against calculations performed in other 2D annular domains when measured relative to those in a fully three-dimensional (3D) spherical shell.
Critical Buckling Load on Large Spherical Shells
Wedellsborg, B. W.
1962-01-01
Approximate evaluation for watertanks, hortonspheres, vapor containers, containment vessels for nuclear reactors, and so forth, has been computed, taking into account out-of-roundness and local flattened areas; graphs have been plotted giving critical buckling load as function of maximum radial...
Suddick, Emma C; Six, Johan
2013-11-01
Agricultural soils are responsible for emitting large quantities of nitrous oxide (N2O). The controlled incomplete thermal decomposition of agricultural wastes to produce biochar, once amended to soils, have been hypothesized to increase crop yield, improve soil quality and reduce N2O emissions. To estimate crop yields, soil quality parameters and N2O emissions following the incorporation of a high temperature (900 °C) walnut shell (HTWS) biochar into soil, a one year field campaign with four treatments (control (CONT), biochar (B), compost (COM), and biochar+compost (B+C)) was conducted in a small scale vegetable rotation system in Northern California. Crop yields from five crops (lettuce, winter cover crop, lettuce, bell pepper and Swiss chard) were determined; there were no significant differences in yield between treatments. Biochar amended soils had significant increases in % total carbon (C) and the retention of potassium (K) and calcium (Ca). Annual cumulative N2O fluxes were not significantly different between the four treatments with emissions ranging from 0.91 to 1.12 kg N2O-N ha(-1) yr(-1). Distinct peaks of N2O occurred upon the application of N fertilizers and the greatest mean emissions, ranging from 67.04 to 151.41 g N2O-N ha(-1) day(-1), were observed following the incorporation of the winter cover crop. In conclusion, HTWS biochar application to soils had a pronounced effect on the retention of exchangeable cations such as K and Ca compared to un-amended soils and composted soils, which in turn could reduce leaching of these plant available cations and could thus improve soils with poor nutrient retention. However, HTWS biochar additions to soil had neither a positive or negative effect on crop yield nor cumulative annual emissions of N2O.
赵琛; 刘志朋; 殷涛
2011-01-01
This project is purposed to study the induced electric field energy distribution in human head, which is excited by figure-eight coil used in transcranial magnetic stimulation (TMS). Spiral figure-eight coils (SFOE) and a five-shell spherical model, including scalp, skull, cerebrospinal fluid (CSF) , grey matter and white matter, were established using ANSYS, and transient analysis on induced electric field energy was conducted. Simulation results showed that,under the exciting current of 8 000 A,63.37％ of induced electric field energy was distributed in scalp,30.82％ in CSF, and 2.6％ in grey matter,while the concentration ratio of induced electric field energy in grey matter was up to 15.72％. The proposed method is expected to improve the accuracy of the stimulation study.%研究经颅磁刺激(TMS)下人体头部组织内感应电场能量的分布状况,即组织内焦耳热能损耗情况.提出通过感应电能分配率及感应电能集中性两方面因素,研究蚊香型八字线圈激励下头部模型感应电场能量分布情况.利用ANSYS有限元方法建立蚊香型八字线圈,及包含了头皮、头骨、脑脊液、脑灰质和脑白质的五层球头模型,用瞬态分析方法研究感应电场能量分布.仿真结果表明,对线圈施以8 000 A交流电流时,感应电场能量的63.37%消耗于头皮层,其次是脑脊液层上的30.82%,而脑灰质层仅分配了2.6%,而该层能量集中度为15.72%运用所建立的方法,可为建立逼近于真实条件的头部模型,提高脑神经磁刺激技术聚焦性能和定位性能,提供更加精确的仿真研究结果.
Design aids for stiffened composite shells with cutouts
Sahoo, Sarmila
2017-01-01
This book focuses on the free vibrations of graphite-epoxy laminated composite stiffened shells with cutout both in terms of the natural frequencies and mode shapes. The dynamic analysis of shell structures, which may have complex geometry and arbitrary loading and boundary conditions, is solved efficiently by the finite element method, even including cutouts in shells. The results may be readily used by practicing engineers dealing with stiffened composite shells with cutouts. Several shell forms viz. cylindrical shell, hypar shell, conoidal shell, spherical shell, saddle shell, hyperbolic paraboloidal shell and elliptic paraboloidal shell are considered in the book. The dynamic characteristics of stiffened composite shells with cutout are described in terms of the natural frequency and mode shapes. The size of the cutouts and their positions with respect to the shell centre are varied for different edge constraints of cross-ply and angle-ply laminated composite shells. The effects of these parametric variat...
Euclidean Approach for Entropy of Black Shells
S., J Robel Arenas
2016-01-01
We introduce the concept of black shell, consisting on a massive thin spherical shell contracting toward its gravitational radius from the point of view of an external observer far from the shell, in order to effectively model the gravitational collapse. Considering complementary description of entanglement entropy of a black shell and according to Gibbons-Hawking Euclidean approach, we calculate the Bekenstein-Hawking entropy retrieving horizon integral and discarding boundary at infinity.
Optofluidic encapsulation of crystalline colloidal arrays into spherical membrane.
Kim, Shin-Hyun; Jeon, Seog-Jin; Yang, Seung-Man
2008-05-07
Double emulsion droplets encapsulating crystalline colloidal arrays (CCAs) with a narrow size distribution were produced using an optofluidic device. The shell phase of the double emulsion was a photocurable resin that was photopolymerized downstream of the fluidic channel within 1 s after drop generation. The present optofluidic synthesis scheme was very effective for fabricating highly monodisperse spherical CCAs that were made structurally stable by in situ photopolymerization of the encapsulating shells. The shell thickness and the number of core emulsion drops could be controlled by varying the flow rates of the three coflowing streams in the dripping regime. The spherical CCAs confined in the shell exhibited distinct diffraction patterns in the visible range, in contrast to conventional film-type CCAs. As a result of their structure, the spherical CCAs exhibited photonic band gaps for normal incident light independent of the position on the spherical surface. This property was induced by heterogeneous nucleation at the smooth wall of the spherical emulsion drop during crystallization into a face-centered cubic (fcc) structure. On the other hand, the solidified shells did not permit the penetration of ionic species, enabling the CCAs to maintain their structure in a continuous aqueous phase of high ionic strength for at least 1 month. In addition, the evaporation of water molecules inside the shell was slowed considerably when the core-shell microparticles were exposed to air: It took approximately 6 h for a suspension encapsulated in a thick shell to evaporate completely, which is approximately 1000 times longer than the evaporation time for water droplets with the same volume. Finally, the spherical CCAs additionally exhibited enhanced stability against external electric fields. The spherical geometry and high dielectric constant of the suspension contributed to reducing the electric field inside the shell, thereby inhibiting the electrophoretic movement of
Spherical harmonics in texture analysis
Schaeben, Helmut; van den Boogaart, K. Gerald
2003-07-01
The objective of this contribution is to emphasize the fundamental role of spherical harmonics in constructive approximation on the sphere in general and in texture analysis in particular. The specific purpose is to present some methods of texture analysis and pole-to-orientation probability density inversion in a unifying approach, i.e. to show that the classic harmonic method, the pole density component fit method initially introduced as a distinct alternative, and the spherical wavelet method for high-resolution texture analysis share a common mathematical basis provided by spherical harmonics. Since pole probability density functions and orientation probability density functions are probability density functions defined on the sphere Ω3⊂ R3 or hypersphere Ω4⊂ R4, respectively, they belong at least to the space of measurable and integrable functions L1( Ωd), d=3, 4, respectively. Therefore, first a basic and simplified method to derive real symmetrized spherical harmonics with the mathematical property of providing a representation of rotations or orientations, respectively, is presented. Then, standard orientation or pole probability density functions, respectively, are introduced by summation processes of harmonic series expansions of L1( Ωd) functions, thus avoiding resorting to intuition and heuristics. Eventually, it is shown how a rearrangement of the harmonics leads quite canonically to spherical wavelets, which provide a method for high-resolution texture analysis. This unified point of view clarifies how these methods, e.g. standard functions, apply to texture analysis of EBSD orientation measurements.
A rotating universe outside a Schwarzschild black hole where spacetime itself non-uniformly rotates
Saw, Vee-Liem
2014-01-01
We study a non-uniformly rotating universe outside a Schwarzschild black hole by generating a time-dependent manifold of revolution around a straight line. In this simple model where layers of spherical shells of the universe non-uniformly rotate, the Einstein field equations require this phenomenon to be caused by a static mass-energy distribution with time-dependent $T^{\\phi\\phi}$ (quadratic with time) and $T^{r\\phi}=T^{\\phi r}$ (linear with time). This indicates that a time-dependent stress along a certain direction results in a spacetime shift in that direction. For this model however, such material violates the null energy condition. Incidentally, the various coordinate systems describing the Schwarzschild solution can be viewed as arising from the freedom in parametrising the straight line and the radial function in the general method of constructing spacetime by generating manifolds of revolution around a given curve.
Spherically symmetric scalar field collapse
Koyel Ganguly; Narayan Banerjee
2013-03-01
It is shown that a scalar field, minimally coupled to gravity, may have collapsing modes even when the energy condition is violated, that is, for ( + 3) < 0. This result may be useful in the investigation of the possible clustering of dark energy. All the examples dealt with have apparent horizons formed before the formation of singularity. The singularities formed are shell focussing in nature. The density of the scalar field distribution is seen to diverge at singularity. The Ricci scalar also diverges at the singularity. The interior spherically symmetric metric is matched with exterior Vaidya metric at the hypersurface and the appropriate junction conditions are obtained.
Rotating cylindrical and spherical triboelectric generators
Wang, Zhong Lin; Zhu, Guang; Yang, Ya; Zhang, Hulin; Hu, Youfan; Yang, Jin; Jing, Qingshen
2017-02-14
A generator includes a first member, a second member and a sliding mechanism. The first member includes a first electrode and a first dielectric layer affixed to the first electrode. The first dielectric layer includes a first material that has a first rating on a triboelectric series. The second member includes a second material that has a second rating on the triboelectric series that is different from the first rating. The second member includes a second electrode. The second member is disposed adjacent to the first dielectric layer so that the first dielectric layer is disposed between the first electrode and the second electrode. The sliding mechanism is configured to cause relative movement between the first member and the second member, thereby generating an electric potential imbalance between the first electrode and the second electrode.
Predictive Scaling Laws for Spherical Rotating Dynamos
Oruba, Ludivine
2013-01-01
State of the art numerical models of the Geodynamo are still performed in a parameter regime extremely remote from the values relevant to the physics of the Earth's core. In order to establish a connection between dynamo modeling and the geophysical motivation, scaling laws have been proposed. Such scaling laws establish the dependence of essential quantities (such as the magnetic field strength) on measured or controlled quantities. They allow for a direct confrontation of advanced models with geophysical observations.(...)
于利刚; 李朝晖†; 王仁乾; 马黎黎
2013-01-01
Underwater sound absorption coating is significant to the stealth of a submarine, so it attracts a lot of attention. Underwater sound absorption of visco-elastic composites coating containing micro-spherical glass shell was investigated theoretically. The mechanical and acoustic properties of the composites in response to the volume of the micro-spherical glass shell were analyzed by the effective parameters method. Sound absorption of a single layer composites coating containing different volume of micro-spherical glass shell was calculated by the one-dimensional model, in which sound propagates in multi-layer media. The calculated results show that the sound absorption at low frequencies can be promoted by increasing the volume of micro-spherical glass shell, but the sound absorption at high frequencies is depressed. The volume distribution of the micro-spherical glass shells across the thickness of the coating was optimized by the genetic algorithm. The optimal multi-layer structure can promote the sound absorption at low frequencies, and keep the sound absorption coefficients above a limited value (0.7) at high frequencies. The optimal multi-layer composite coating can work at high pressure since it does not contain hollow macro-structure. Its structure is simple, so the technique of its fabrication should not be complicated. The theoretical method achieved in this paper can be applied in the design of underwater sound absorption coating.% 水下吸声覆盖层对潜艇的隐身具有重要的意义，因此得到了广泛的关注.本文对含有玻璃微球的黏弹性复合材料覆盖层的水下吸声性能进行了理论分析.采用等效参数法计算了玻璃微球的体积含量对复合材料的力学和声学性能的影响.应用声波在多层介质中传播的一维模型，计算了不同玻璃微球体积含量的单层复合材料覆盖层的吸声性能.结果表明，增加玻璃微球的体积含量可以提高覆盖层的低频吸
Chong, Shaokun; Wu, Yifang; Chen, Yuanzhen; Shu, Chengyong; Liu, Yongning
2017-07-01
Serious decay of capacity and voltage for Li-rich layered cathode materials restrict their commercial application for Li-ion batteries. In this paper, a spherical core-shell structure, Li1.2Ni0.2Mn0.6O2@Li1.2Ni0.4Mn0.4O2 was in-situ prepared using hydrothermal method. SEM images as well as the analysis with XPS and EDS verified that the core-shell structure grows well. Electrochemical properties showed that the merits of the both materials have been preserved for high capacity of core material and high voltage as well as superior cycling stability of shell material. C/S-1/1 sample, whose mass proportion of core to shell is 1:1, exhibits the initial discharge capacity of 218 mAh·g-1 with the highest operating voltage of 3.763 V at 0.1C between 2.0 and 4.8 V, splendid cycling stability with the capacity retention of 93.1% and high voltage retention value of 3.335 V after 100 cycles. The improvement of electrochemical performances are attributed to the stable Li1.2Ni0.4Mn0.4O2 protective shell, which is beneficial to improve the electrochemical kinetics, mitigate the morphology evolution and retard the layered-spinel phase transition by restraining the release of O2 and weakening the electrode-electrolyte interfacial reaction.
A Non-axisymmetric Spherical α2-Dynamo
无
2006-01-01
Using the Chebyshev-tau method, the generation of oscillatory nonaxisymmetric stellar magnetic fields by the α2-dynamo is studied in spherical geometry. Following the boundary conditions given by Schubert & Zhang, the spherical α2-dynamo consists of a fully convective spherical shell with inner radius ri and outer radius ro. A comparison of the critical dynamo numbers of axisymmetric and φ-dependent modes for different thicknesses of the convective shell and different α-profiles leads to the following qualitative results: (I) when the angular factor of α-profile is sinnθ cosθ (n = 1, 2, 4) the solutions of the α2-dynamo are oscillatory and non-axisymmetric, (ii) the thinner the convective shell, the more easily is the nonaxisymmetric mode excited and the higher is the latitudinal wave number, (iii) the thickness of the outer convective shell has an effect on the symmetries of the magnetic fields.
Convective Properties of Rotating Two-Dimensional Core-Collapse Supernova Progenitors
Chatzopoulos, Emmanouil; Arnett, W David; Timmes, F X
2016-01-01
We explore the effects of rotation on convective carbon, oxygen, and silicon shell burning during the late stages of evolution in a 20Msun star. Using the Modules for Experiments in Stellar Astrophysics (MESA) we construct 1D stellar models both with no rotation and with an initial rigid rotation of 50% of critical. At different points during the evolution, we map the 1D models into 2D and follow the multidimensional evolution using the FLASH compressible hydrodynamics code for many convective turnover times until a quasi-steady state is reached. We characterize the strength and scale of convective motions via decomposition of the momentum density into vector spherical harmonics. We find that rotation influences the total power in solenoidal modes, with a slightly larger impact for carbon and oxygen shell burning than for silicon shell burning. Including rotation in one-dimensional (1D) stellar evolution models alters the structure of the star in a manner that has a significant impact on the character of mult...
Hamza, Alex V.; Biener, Juergen; Wild, Christoph; Woerner, Eckhard
2016-11-01
A novel method for fabricating diamond shells is introduced. The fabrication of such shells is a multi-step process, which involves diamond chemical vapor deposition on predetermined mandrels followed by polishing, microfabrication of holes, and removal of the mandrel by an etch process. The resultant shells of the present invention can be configured with a surface roughness at the nanometer level (e.g., on the order of down to about 10 nm RMS) on a mm length scale, and exhibit excellent hardness/strength, and good transparency in the both the infra-red and visible. Specifically, a novel process is disclosed herein, which allows coating of spherical substrates with optical-quality diamond films or nanocrystalline diamond films.
Relativistic spherical plasma waves
Bulanov, S. S.; Maksimchuk, A.; Schroeder, C. B.; Zhidkov, A. G.; Esarey, E.; Leemans, W. P.
2012-02-01
Tightly focused laser pulses that diverge or converge in underdense plasma can generate wake waves, having local structures that are spherical waves. Here we study theoretically and numerically relativistic spherical wake waves and their properties, including wave breaking.
Multi-Shell Shell Model for Heavy Nuclei
Sun, Yang; Wu, Cheng-Li
2003-01-01
Performing a shell model calculation for heavy nuclei has been a long-standing problem in nuclear physics. Here we propose one possible solution. The central idea of this proposal is to take the advantages of two existing models, the Projected Shell Model (PSM) and the Fermion Dynamical Symmetry Model (FDSM), to construct a multi-shell shell model. The PSM is an efficient method of coupling quasi-particle excitations to the high-spin rotational motion, whereas the FDSM contains a successful t...
Differential Rotation in Magnetized and Non-magnetized Stars
Mabuchi, Jun; Kageyama, Akira
2015-01-01
Effects of magnetic field on stellar differential rotation are studied by comparing magnetohydrodynamic (MHD) models and their hydrodynamic (HD) counterparts in the broad range of rotation rate and in varying initial rotation profile. Fully-compressible MHD simulations of rotating penetrative convection are performed in a full-spherical shell geometry. Critical conditions for the transition of the differential rotation between faster equator (solar-type) and slower equator (anti-solar type) are explored with focusing on the "Rossby number (${\\rm Ro}$)" and the "convective Rossby number (${\\rm Ro}_{\\rm conv}$)". It is confirmed that the transition is more gradual and the critical value for it is higher in the MHD model than the HD model in the view of the ${\\rm Ro}_{\\rm conv}$-dependence. The rotation profile shows, as observed in earlier studies, the bistability near the transition in the HD model, while it disappears when allowing the growth of magnetic fields except for the model with taking anti-solar type...
Hydrodynamic and magnetohydrodynamic computations inside a rotating sphere
Mininni, P D; Turner, L; 10.1088/1367-2630/9/8/303
2009-01-01
Numerical solutions of the incompressible magnetohydrodynamic (MHD) equations are reported for the interior of a rotating, perfectly-conducting, rigid spherical shell that is insulator-coated on the inside. A previously-reported spectral method is used which relies on a Galerkin expansion in Chandrasekhar-Kendall vector eigenfunctions of the curl. The new ingredient in this set of computations is the rigid rotation of the sphere. After a few purely hydrodynamic examples are sampled (spin down, Ekman pumping, inertial waves), attention is focused on selective decay and the MHD dynamo problem. In dynamo runs, prescribed mechanical forcing excites a persistent velocity field, usually turbulent at modest Reynolds numbers, which in turn amplifies a small seed magnetic field that is introduced. A wide variety of dynamo activity is observed, all at unit magnetic Prandtl number. The code lacks the resolution to probe high Reynolds numbers, but nevertheless interesting dynamo regimes turn out to be plentiful in those ...
Transport coefficients for rigid spherically symmetric polymers or aggregates
Strating, P.; Wiegel, F.W.
1994-01-01
In this paper we investigate the transport properties for rigid spherically symmetric macromolecules, having a segment density distribution falling off as r- lambda . We calculate the rotational and translational diffusion coefficient for a spherically symmetric polymer and the shear viscosity for a
Precursory singularities in spherical gravitational collapse
Lake, Kayll
1992-05-01
General conditions are developed for the formation of naked precursory ('shell-focusing') singularities in spherical gravitational collapse. These singularities owe their nakedness to the fact that the gravitational potential fails to be single valued prior to the onset of a true gravitational singularity. It is argued that they do not violate the spirit of cosmic censorship. Rather, they may well be an essentially generic feature of relativistic gravitational collapse.
A Parametric Study of Mixing in a Granular Flow a Bi-Axial Spherical Tumbler
Christov, Ivan C; Ottino, Julio M; Sturman, Rob
2015-01-01
We report on a computational parameter space study of mixing protocols for a half-full bi-axial spherical granular tumbler. The quality of mixing is quantified via the intensity of segregation (concentration variance) and computed as a function of three system parameters: angles of rotation about each tumbler axis and the flowing layer depth. Only the symmetric case is considered in which the flowing layer depth is the same for each rotation. We also consider the dependence on $\\bar{R}$, which parametrizes the concentric spheroids ("shells") that comprise the volume of the tumbler. The intensity of segregation is computed over 100 periods of the mixing protocol for each choice of parameters. Each curve is classified via a time constant, $\\tau$, and an asymptotic mixing value, $bias$. We find that most choices of angles and most shells throughout the tumbler volume mix well, with mixing near the center of the tumbler being consistently faster (small $\\tau$) and more complete (small $bias$). We conclude with ex...
Shape-tunable core-shell microparticles.
Klein, Matthias K; Saenger, Nicolai R; Schuetter, Stefan; Pfleiderer, Patrick; Zumbusch, Andreas
2014-10-28
Colloidal polymer particles are an important class of materials finding use in both everyday and basic research applications. Tailoring their composition, shape, and functionality is of key importance. In this article, we describe a new class of shape-tunable core-shell microparticles. They are composed of a cross-linked polystyrene (PS) core and a poly(methyl methacrylate) (PMMA) shell of varying thickness. In the first step, we prepared highly cross-linked PS cores, which are subsequently transferred into a nonpolar dispersant. They serve as the seed dispersion for a nonaqueous dispersion polymerization to generate the PMMA shell. The shape of the particles can subsequently be manipulated. After the shell growth stage, the spherical PS/PMMA core-shell colloids exhibit an uneven and wrinkled surface. An additional tempering procedure allows for smoothing the surface of the core-shell colloids. This results in polymer core-shell particles with a perfectly spherical shape. In addition to this thermal smoothing of the PMMA shell, we generated a selection of shape-anisotropic core-shell particles using a thermomechanical stretching procedure. Because of the unique constitution, we can selectively interrogate molecular vibrations in the PS core or the PMMA shell of the colloids using nonlinear optical microscopy techniques. This is of great interest because no photobleaching occurs, such that the particles can be tracked in real space over long times.
Collimation of a spherical collisionless particles stream in Kerr space-time
Takami, Kentaro
2009-01-01
We examine the propagation of collisionless particles emitted from a spherical shell to infinity. The number distribution at infinity, calculated as a function of the polar angle, exhibits a small deviation from uniformity. The number of particles moving from the polar region toward the equatorial plane is slightly larger than that of particles in the opposite direction, for an emission radius $ > 4.5M$ in extreme Kerr space-time. This means that the black hole spin exerts an anti-collimation effect on the particles stream propagating along the rotation axis. We also confirm this property in the weak field limit. The quadrupole moment of the central object produces a force toward the equatorial plane. For a smaller emission radius $r<4.5M$, the absorption of particles into the black hole, the non-uniformity and/or the anisotropy of the emission distribution become much more important.
Magnetic field variation caused by rotational speed change in a magnetohydrodynamic dynamo.
Miyagoshi, Takehiro; Hamano, Yozo
2013-09-20
We have performed numerical magnetohydrodynamic dynamo simulations in a spherical shell with rotational speed or length-of-day (LOD) variation, which is motivated by correlations between geomagnetic field and climatic variations with ice and non-ice ages. The results show that LOD variation leads to magnetic field variation whose amplitude is considerably larger than that of LOD variation. The heat flux at the outer sphere and the zonal flow also change. The mechanism of the magnetic field variation due to LOD variation is also found. The keys are changes of dynamo activity and Joule heating.
A Quantum Mechanical Approach to Nuclear Rotations
Zettili, Nouredine
2014-09-01
We deal with the study of collective motion within the context of a quantum mechanical method - the nuclear Born-Oppenheirmer (NBO) method. We focus in particular on a quantum mechanical approach to nuclear rotations. As an illustration, we utilize the NBO method to study non-spherical, permanently deformed nuclei; in particular, we study nuclei that are axially-symmetric and even, but with non-closed shells. We also focus on a quantum mechanical derivation of formal expressions for the energy and for the moment of inertia. Using trial functions in which the intrinsic structure is described by a mean-field approximation, we then show that the NBO formalism yields the Thouless-Valantin formula for the moment of inertia and that this moment of inertia increases with angular momentum, in agreement with experimental data. We show that the NBO formalism is well equipped to describe low-lying as well as high lying rotational states. Additionally, we establish a connection between the NBO method and the self-consistent Cranking (SCC) model. We deal with the study of collective motion within the context of a quantum mechanical method - the nuclear Born-Oppenheirmer (NBO) method. We focus in particular on a quantum mechanical approach to nuclear rotations. As an illustration, we utilize the NBO method to study non-spherical, permanently deformed nuclei; in particular, we study nuclei that are axially-symmetric and even, but with non-closed shells. We also focus on a quantum mechanical derivation of formal expressions for the energy and for the moment of inertia. Using trial functions in which the intrinsic structure is described by a mean-field approximation, we then show that the NBO formalism yields the Thouless-Valantin formula for the moment of inertia and that this moment of inertia increases with angular momentum, in agreement with experimental data. We show that the NBO formalism is well equipped to describe low-lying as well as high lying rotational states
Plastic instabilities in statically and dynamically loaded spherical vessels
Duffey, Thomas A [Los Alamos National Laboratory; Rodriguez, Edward A [Los Alamos National Laboratory
2010-01-01
Significant changes were made in design limits for pressurized vessels in the 2007 version of the ASME Code (Section VIII, Div. 3) and 2008 and 2009 Addenda. There is now a local damage-mechanics based strain-exhaustion limit as well as the well-known global plastic collapse limit. Moreover, Code Case 2564 (Section VIII, Div. 3) has recently been approved to address impulsively loaded vessels. It is the purpose of this paper to investigate the plastic collapse limit as it applies to dynamically loaded spherical vessels. Plastic instabilities that could potentially develop in spherical shells under symmetric loading conditions are examined for a variety of plastic constitutive relations. First, a literature survey of both static and dynamic instabilities associated with spherical shells is presented. Then, a general plastic instability condition for spherical shells subjected to displacement controlled and impulsive loading is given. This instability condition is evaluated for six plastic and visco-plastic constitutive relations. The role of strain-rate sensitivity on the instability point is investigated. Calculations for statically and dynamically loaded spherical shells are presented, illustrating the formation of instabilities as well as the role of imperfections. Conclusions of this work are that there are two fundamental types of instabilities associated with failure of spherical shells. In the case of impulsively loaded vessels, where the pulse duration is short compared to the fundamental period of the structure, one instability type is found not to occur in the absence of static internal pressure. Moreover, it is found that the specific role of strain-rate sensitivity on the instability strain depends on the form of the constitutive relation assumed.
Quantum Radiation of Uniformly Accelerated Spherical Mirrors
Frolov, V
2001-01-01
We study quantum radiation generated by a uniformly accelerated motion of small spherical mirrors. To obtain Green's function for a scalar massless field we use Wick's rotation. In the Euclidean domain the problem is reduced to finding an electric potential in 4D flat space in the presence of a metallic toroidal boundary. The latter problem is solved by a separation of variables. After performing an inverse Wick's rotation we obtain the Hadamard function in the wave-zone regime and use it to calculate the vacuum fluctuations and the vacuum expectation for the energy density flux in the wave zone.
邱昌贤; 万正权; 黄进浩
2013-01-01
文章将Monte Carlo抽样法和有限元非线性屈曲计算相结合，利用参数化方法模拟了满足Gumble分布和Gauss分布的钢板腐蚀减薄量在超大潜深球壳开孔结构上的分布，对各状况进行了100个样本的计算，并分析了腐蚀量均值和方差对结构在静水外压下极限承载能力的影响，结果表明，腐蚀样本数据分散度的大小几乎不产生影响，产生主要影响的是样本均值，失稳压力随腐蚀减薄量均值的增大而显著地线性降低。%Based on the Monte Carlo sampling theory and FEM nonlinear buckling analysis, APDL program was developed to simulate Gumble & Gauss distributions of corrosion-thinned status of super-diving spheri-cal hull with round hole structure. The calculation of 100 samples was accomplished for each different con-ditions. The influence of sample mean and variance on the collapse pressure of model under external hy-drostatic pressure was also analyzed. Results show that sample variance has little effect on the critical pres-sure, which is mainly determined by corrosion sample mean, and collapse pressure declines evidently and linearly with increment of the mean value of corrosion thinned data.
Thin-shell wormholes in Einstein-Born-Infeld theory
Eiroa, Ernesto F
2015-01-01
We construct spherically symmetric thin-shell wormholes with a generalized Chaplygin gas at the throat, in Born-Infeld electrodynamics coupled to Einstein gravity. We analyze their stability under radial perturbations.
Models for Self-Gravitating Photon Shells and Geons
Andréasson, Håkan; Thaller, Maximilian
2015-01-01
We prove existence of spherically symmetric, static, self-gravitating photon shells as solutions to the massless Einstein-Vlasov system. The solutions are highly relativistic in the sense that the ratio $2m(r)/r$ is close to $8/9$, where $m(r)$ is the Hawking mass and $r$ is the area radius. In 1955 Wheeler constructed, by numerical means, so called idealized spherically symmetric geons, i.e. solutions of the Einstein-Maxwell equations for which the energy momentum tensor is spherically symmetric on a time average. The structure of these solutions is such that the electromagnetic field is confined to a thin shell for which the ratio $2m/r$ is close to $8/9$, i.e., the solutions are highly relativistic photon shells. The solutions presented in this work provide an alternative model for photon shells or idealized spherically symmetric geons.
Ghosh, R.; Chandra, N.; Parida, S.
2009-03-01
This paper reports results of a theoretical study of angle- and spin-resolved photo-Auger electron coincident spectroscopy in the form of entanglement between these two particles emitted from a linear molecule. First, we develop an expression for a density matrix needed for studying spin-entanglement between a photoelectron and an Auger electron. In order to properly represent the molecular symmetries, nuclear rotation, and the spin-dependent interactions (SDIs), we have used symmetry adapted wavefunctions in Hund’s coupling scheme (a) for all the species participating in this two-step process. This expression shows that spin-entanglement in a photo-Auger electron pair in the presence of SDIs very strongly depends upon, among other things, polarization of the ionizing radia- tion, directions of motion and of spin polarization of two ejected electrons, and the dynamics of photoionization and of Auger decay. We have applied this expression, as an example, to a generic linear molecule in its J0, M0 = 0 state. This model calculation clearly brings out the salient features of the spin-entanglement of a photo-Auger electron pair in the presence of the SDIs.
Ghosh, R.; Chandra, N.; Parida, S. [Indian Institute of Technology, Dept. of Physics and Meteorology, Kharagpur (India)
2009-03-15
This paper reports results of a theoretical study of angle- and spin-resolved photo-Auger electron coincident spectroscopy in the form of entanglement between these two particles emitted from a linear molecule. First, we develop an expression for a density matrix needed for studying spin-entanglement between a photoelectron and an Auger electron. In order to properly represent the molecular symmetries, nuclear rotation, and the spin-dependent interactions (SDIs), we have used symmetry adapted wavefunctions in Hund's coupling scheme (a) for all the species participating in this two-step process. This expression shows that spin-entanglement in a photo-Auger electron pair in the presence of SDIs very strongly depends upon, among other things, polarization of the ionizing radiation, directions of motion and of spin polarization of two ejected electrons, and the dynamics of photoionization and of Auger decay. We have applied this expression, as an example, to a generic linear molecule in its J{sub 0}, M{sub 0} = 0 state. This model calculation clearly brings out the salient features of the spin-entanglement of a photo-Auger electron pair in the presence of the SDIs. (authors)
Research on stability design of a bar-reinforced spherical bulkhead
YAO Xiong-liang; LIU Xiang-dong
2007-01-01
In this paper, the stability of a concave spherical stem bulkhead under the pumping load when still lying at the slipway is analyzed. The stability of the spherical stem bulkhead with different shell thickness and reinforcing forms is discussed. According to the results of stability analysis, the optimization design of the spherical stem bulkhead stability is performed. On the basis of considering the machining technical requirements of the bulkhead, a rational design of the spherical stem bulkhead structure is obtained. This paper has a certain value to the design of submarine's spherical stem bulkhead.
Relativistic spherical plasma waves
Bulanov, S S; Schroeder, C B; Zhidkov, A G; Esarey, E; Leemans, W P
2011-01-01
Tightly focused laser pulses as they diverge or converge in underdense plasma can generate wake waves, having local structures that are spherical waves. Here we report on theoretical study of relativistic spherical wake waves and their properties, including wave breaking. These waves may be suitable as particle injectors or as flying mirrors that both reflect and focus radiation, enabling unique X-ray sources and nonlinear QED phenomena.
Thin-shell wormholes linearization stability
Poisson, E; Poisson, Eric; Visser, Matt
1995-01-01
The class of spherically-symmetric thin-shell wormholes provides a particularly elegant collection of exemplars for the study of traversable Lorentzian wormholes. In the present paper we consider linearized (spherically symmetric) perturbations around some assumed static solution of the Einstein field equations. This permits us to relate stability issues to the (linearized) equation of state of the exotic matter which is located at the wormhole throat.
Composite spherically symmetric configurations in Jordan-Brans-Dicke theory
Kozyrev, S
2010-01-01
In this article, a study of the scalar field shells in relativistic spherically symmetric configurations has been performed. We construct the composite solution of Jordan-Brans-Dicke field equation by matching the conformal Brans solutions at each junction surfaces. This approach allows us to associate rigorously with all solutions as a single glued "space", which is a unique differentiable manifold M^4.
Calculation of Eddy currents in the ETE spherical torus
Ludwig, Gerson Otto
2002-07-01
A circuit model based on a Green's function method was developed to evaluate the currents induced during startup in the vessel of ETE (Spherical Tokamak Experiment). The eddy currents distribution is calculated using a thin shell approximation for the vacuum vessel and local curvilinear coordinates. The results are compared with values of the eddy currents measured in ETE. (author)
Dynamics and statics of flexible axially symmetric shallow shells
2006-01-01
In this work, we propose the method for the investigation of stochastic vibrations of deterministic mechanical systems represented by axially symmetric spherical shells. These structure members are widely used as sensitive elements of pressure measuring devices in various branches of measuring and control industry, machine design, and so forth. The proposed method can be easily extended for the investigation of shallow spherical shells, goffer-type membranes, and so on. T...
Analysis of a spherical tank under a local action
Vinogradov, Yu. N.; Konstantinov, M. V.
2016-03-01
A spherical tank, being perfect as far as weight is concerned, is used in spacecraft, where the thin-walled elements (shells) are united by frames. Obviously, local actions on the shell and hence the stress concentration in the shell cannot be avoided. Attempts to make weight structure of the spacecraft perfect inevitably decrease the safetymargin of the components, which is possible only if the stress-strain state of the components is determined with a controlled error. A mathematical model of shell deformation mechanics is proposed for this purpose, and its linear differential equations are obtained with an error that does not exceed the error of Kirchhoff assumptions in the theory of shells. The algorithm for solving these equations contains procedures for estimating the convergence of the Fourier series and the series of the hypergeometric function with a prescribed error, and the problem can be solved analytically.
Spherically Collapsing Matter in AdS, Holography and Shellons
Danielsson, U H; Kruczenski, M; Danielsson, Ulf H.; Keski-Vakkuri, Esko; Kruczenski, Martin
1999-01-01
We investigate the collapse of a spherical shell of matter in an anti-de Sitter space. We search for a holographic description of the collapsing shell in the boundary theory. It turns out that in the boundary theory it is possible to find information about the radial size of the shell. The shell deforms the background spacetime, and the deformed background metric enters into the action of a generic bulk field. As a consequence, the correlators of operators coupling to the bulk field are modified. By studying the analytic structure of the correlators, we find that in the boundary theory there are unstable excitations ("shellons") whose masses are multiples of a scale set by the radius of the shell. We also comment on the relation between black hole formation in the bulk and thermalization in the boundary.
Triaxial rotation in atomic nuclei
CHEN Yong-Shou; GAO Zao-Chun
2009-01-01
The Projected Shell Model has been developed to include the spontaneously broken axial symmetry so that the rapidly rotating triaxial nuclei can be described microscopically. The theory provides an useful tool to gain an insight into how a triaxial nucleus rotates, a fundamental question in nuclear structure. We shall address some current interests that are strongly associated with the triaxial rotation. A feasible method to explore the problem has been suggested.
Colloidal cholesteric liquid crystal in spherical confinement
Li, Yunfeng; Jun-Yan Suen, Jeffrey; Prince, Elisabeth; Larin, Egor M.; Klinkova, Anna; Thérien-Aubin, Héloïse; Zhu, Shoujun; Yang, Bai; Helmy, Amr S.; Lavrentovich, Oleg D.; Kumacheva, Eugenia
2016-08-01
The organization of nanoparticles in constrained geometries is an area of fundamental and practical importance. Spherical confinement of nanocolloids leads to new modes of packing, self-assembly, phase separation and relaxation of colloidal liquids; however, it remains an unexplored area of research for colloidal liquid crystals. Here we report the organization of cholesteric liquid crystal formed by nanorods in spherical droplets. For cholesteric suspensions of cellulose nanocrystals, with progressive confinement, we observe phase separation into a micrometer-size isotropic droplet core and a cholesteric shell formed by concentric nanocrystal layers. Further confinement results in a transition to a bipolar planar cholesteric morphology. The distribution of polymer, metal, carbon or metal oxide nanoparticles in the droplets is governed by the nanoparticle size and yields cholesteric droplets exhibiting fluorescence, plasmonic properties and magnetic actuation. This work advances our understanding of how the interplay of order, confinement and topological defects affects the morphology of soft matter.
Rotating, hydromagnetic laboratory experiment modelling planetary cores
Kelley, Douglas H.
2009-10-01
This dissertation describes a series of laboratory experiments motivated by planetary cores and the dynamo effect, the mechanism by which the flow of an electrically conductive fluid can give rise to a spontaneous magnetic field. Our experimental apparatus, meant to be a laboratory model of Earth's core, contains liquid sodium between an inner, solid sphere and an outer, spherical shell. The fluid is driven by the differential rotation of these two boundaries, each of which is connected to a motor. Applying an axial, DC magnetic field, we use a collection of Hall probes to measure the magnetic induction that results from interactions between the applied field and the flowing, conductive fluid. We have observed and identified inertial modes, which are bulk oscillations of the fluid restored by the Coriolis force. Over-reflection at a shear layer is one mechanism capable of exciting such modes, and we have developed predictions of both onset boundaries and mode selection from over-reflection theory which are consistent with our observations. Also, motivated by previous experimental devices that used ferromagnetic boundaries to achieve dynamo action, we have studied the effects of a soft iron (ferromagnetic) inner sphere on our apparatus, again finding inertial waves. We also find that all behaviors are more broadband and generally more nonlinear in the presence of a ferromagnetic boundary. Our results with a soft iron inner sphere have implications for other hydromagnetic experiments with ferromagnetic boundaries, and are appropriate for comparison to numerical simulations as well. From our observations we conclude that inertial modes almost certainly occur in planetary cores and will occur in future rotating experiments. In fact, the predominance of inertial modes in our experiments and in other recent work leads to a new paradigm for rotating turbulence, starkly different from turbulence theories based on assumptions of isotropy and homogeneity, starting instead
Kumar, Naveen; Kumar, S.; Mandal, S.K. [University of Delhi, Department of Physics and Astrophysics, Delhi (India); Saha, S.; Sethi, J.; Palit, R. [Tata Institute of Fundamental Research, Department of Nuclear and Atomic Physics, Mumbai (India)
2017-02-15
The lifetime measurements were done for the transitions of the dipole (ΔI = 1) bands in {sup 85,86}Sr nuclei using the Doppler Shift Attenuation Method (DSAM). The high-spin states in these nuclei were populated in the {sup 76}Ge({sup 13}C, 4n){sup 85}Sr and {sup 76}Ge({sup 13}C, 3n){sup 86}Sr reactions. The B(M1) transition rates have been obtained for the states of two positive-parity dipole (Δ I = 1) bands in the {sup 85}Sr nucleus and one positive-parity dipole (ΔI = 1) band in the {sup 86} Sr nucleus. The present results on the transition rates are important to know whether these dipole (ΔI = 1) bands have the signatures of Magnetic Rotation (MR). In order to investigate their magnetic character, the experimental results have been compared with the calculations within the framework of hybrid Tilted-Axis-Cranking (TAC) model. On the basis of the TAC calculations, band 2 of the {sup 85}Sr nucleus is assigned the π(g{sub 9/2}){sup 2} x ν(g{sub 9/2}){sup -1} configuration and shows the MR character, while for band 3, the π[(g{sub 9/2}){sup 2}(f{sub 5/2}){sup 2}] x ν(g{sub 9/2}){sup -1} configuration is suggested. In the case of {sup 86}Sr nucleus, band 3 has the π(g{sub 9/2}){sup 2} x ν(g{sub 9/2}){sup -2} configuration below the spin I{sup π} = 16{sup +} and above this spin the π[(g{sub 9/2}){sup 2}(f{sub 5/2}){sup 1}(p{sub 1/2}/p{sub 3/2}){sup 1}] x ν(g{sub 9/2}){sup -2} configuration plays an important role. The experimental B(M1) transition rates show a decreasing trend with the increase in spin and are comparable with the TAC calculations before the I{sup π} = 16{sup +}. (orig.)
Fine Structure of Solar Acoustic Oscillations Due to Rotation
Goode, P. R.; Dziembowski, W.
1984-01-01
The nature of the fine structure of high order, low degree five minute period solar oscillations following from various postulated forms of spherical rotation is predicted. The first and second order effects of rotation are included.
Faraday Rotation Distributions from Stellar Magnetism in Wind-blown Bubbles
Ignace, R.; Pingel, N. M.
2013-03-01
Faraday rotation is a valuable tool for detecting magnetic fields. Here, the technique is considered in relation to wind-blown bubbles. In the context of spherical winds with azimuthal or split monopole stellar magnetic field geometries, we derive maps of the distribution of position angle (P.A.) rotation of linearly polarized radiation across projected bubbles. We show that the morphology of maps for split monopole fields are distinct from those produced by the toroidal field topology; however, the toroidal case is the one most likely to be detectable because of its slower decline in field strength with distance from the star. We also consider the important case of a bubble with a spherical sub-volume that is field-free to approximate crudely a "swept-up" wind interaction between a fast wind (or possibly a supernova ejecta shell) overtaking a slower magnetized wind from a prior state of stellar evolution. With an azimuthal field, the resultant P.A. map displays two arc-like features of opposite rotation measure, similar to observations of the supernova remnant G296.5+10.0. We illustrate how P.A. maps can be used to disentangle Faraday rotation contributions made by the interstellar medium versus the bubble. Although our models involve simplifying assumptions, their consideration leads to a number of general robust conclusions for use in the analysis of radio mapping data sets.
Nejad-Asghar, Mohsen
2010-12-01
Theoretically, stars formed from the collapse of cores in molecular clouds. Historically, the core had been assumed to be a singular isothermal sphere (SIS), and the collapse had been investigated in a self-similar manner. When the rotation and magnetic fields lead to non-symmetric collapse, a spheroidal shape may occur. Here, the result of the centrifugal force and magnetic field gradient is assumed to be in the normal direction to the rotational axis, and its components are supposed to be a fraction β of the local gravitational force. In this research, a collapsing SIS core is considered to find the importance that the parameter β plays in the oblateness of the mass shells, which are the crests of the expansion waves. We apply the Adomian decomposition method to solve the system of nonlinear partial differential equations because the collapse does not occur in a spherically symmetric and self-similar manner. In this way, we obtain a semi-analytical relation for the mass infall rate Ṁ of the shells in the envelope. Near the rotational axis, Ṁ decreases with the increase of the non-dimensional radius ξ, while a direct relation is observed between Ṁ and ξ in the equatorial regions. Also, the values of Ṁ in the polar regions are greater than their equatorial values, and this difference occurs more often at smaller values of ξ. Overall, the results show that before reaching the crest of the expansion wave, the visible shape of the molecular cloud cores can evolve into oblate spheroids. The ratio of major to minor axes of oblate cores increases when increasing the parameter β, and its value can approach the observed elongated shapes of cores in the maps of molecular clouds, such as those in Taurus and Perseus.
李成刚; 尤晶晶; 吴洪涛
2011-01-01
基于卡氏第二定理,推导出椭圆型弹性球铰链柔度、精度的解析表达式.提出弹性球铰链柔度精度比的概念,并以此为性能指标对铰链的设计进行了优化.结果表明:铰链应选用弹性模量大、切变模量小的材料;在保证强度的前提下,应尽量减小椭圆广角、椭圆长短半轴之比以及铰链最小厚度与椭圆短半轴之比.指出在设计弹性铰链时不能仅追求转动性能,还需要考虑其疲劳强度,进而推导出弹性球铰链疲劳强度的校验公式.%Based on the Castigliano's second theorem, the equations were formulated for the compliance and precision of an elliptical flexure spherical hinge. A new concept of compliance accuracy ratio of flexure spherical hinge was proposed, which was used as the performance index of hinges. Optimization was done, and the results show that materials of hinges should be with high elastic modulus and low shear modulus; all of the wide-angle, the ratio of long half axis to short half axis and the ratio of the minimum thickness to short half axis of ellipse should be as little as possible on the premise of ensuring strength. A view point was proposed,that fatigue strength must also be considered except for improving performance while designing the flexure hinges, and the check formula of fatigue strength was derived.
Christov, Ivan C; Ottino, Julio M; Sturman, Rob
2014-01-01
We study 3D chaotic dynamics through an analysis of transport in a granular flow in a half-full spherical tumbler rotated sequentially about two orthogonal axes (a bi-axial "blinking" tumbler). The flow is essentially quasi-2D in any vertical slice of the sphere during rotation about a single axis, and we provide an explicit exact solution to the model in this case. Hence, the cross-sectional flow can be represented by a twist map, allowing us to express the 3D flow as a linked twist map (LTM). We prove that if the rates of rotation about each axis are equal, then (in the absence of stochasticity) particle trajectories are restricted to 2D surfaces consisting of a portion of a hemispherical shell closed by a "cap"; if the rotation rates are unequal, then particles can leave the surface they start on and traverse a volume of the tumbler. The period-one structures of the governing LTM are examined in detail: analytical expressions are provided for the location of period-one curves, their extent into the bulk of...
Konevtsova, O V; Lorman, V L; Rochal, S B
2016-05-01
We consider the symmetry and physical origin of collective displacement modes playing a crucial role in the morphological transformation during the maturation of the HK97 bacteriophage and similar viruses. It is shown that the experimentally observed hexamer deformation and pentamer twist in the HK97 procapsid correspond to the simplest irreducible shear strain mode of a spherical shell. We also show that the icosahedral faceting of the bacteriophage capsid shell is driven by the simplest irreducible radial displacement field. The shear field has the rotational icosahedral symmetry group I while the radial field has the full icosahedral symmetry I_{h}. This difference makes their actions independent. The radial field sign discriminates between the icosahedral and the dodecahedral shapes of the faceted capsid shell, thus making the approach relevant not only for the HK97-like viruses but also for the parvovirus family. In the frame of the Landau-Ginzburg formalism we propose a simple phenomenological model valid for the first reversible step of the HK97 maturation process. The calculated phase diagram illustrates the discontinuous character of the virus shape transformation. The characteristics of the virus shell faceting and expansion obtained in the in vitro and in vivo experiments are related to the decrease in the capsid shell thickness and to the increase of the internal capsid pressure.
Konevtsova, O. V.; Lorman, V. L.; Rochal, S. B.
2016-05-01
We consider the symmetry and physical origin of collective displacement modes playing a crucial role in the morphological transformation during the maturation of the HK97 bacteriophage and similar viruses. It is shown that the experimentally observed hexamer deformation and pentamer twist in the HK97 procapsid correspond to the simplest irreducible shear strain mode of a spherical shell. We also show that the icosahedral faceting of the bacteriophage capsid shell is driven by the simplest irreducible radial displacement field. The shear field has the rotational icosahedral symmetry group I while the radial field has the full icosahedral symmetry Ih. This difference makes their actions independent. The radial field sign discriminates between the icosahedral and the dodecahedral shapes of the faceted capsid shell, thus making the approach relevant not only for the HK97-like viruses but also for the parvovirus family. In the frame of the Landau-Ginzburg formalism we propose a simple phenomenological model valid for the first reversible step of the HK97 maturation process. The calculated phase diagram illustrates the discontinuous character of the virus shape transformation. The characteristics of the virus shell faceting and expansion obtained in the in vitro and in vivo experiments are related to the decrease in the capsid shell thickness and to the increase of the internal capsid pressure.
Spacelike gravitational radiation extraction from rotating binary black holes
Imbiriba, Breno C. O.
2016-07-01
We introduce an alternate method for gravitational radiation extraction for binary black hole mergers where we do not use a single extraction radius at the intermediate field region but instead use a whole spherical shell of three-dimensional (3D) data and continue its evolution using the linearized (Teukolsky) evolution to a final distant radiation extraction radius. We implement this using the Hahndol code for the 3D evolution, and use the “Lazarus” procedure to convert the numerical data into the linearized data. The final waveform is compatible with the ones obtained from the full 3D evolutions with some minor variations that require further study. In the process, we tested the “Lazarus” method with our numerical 3D implementation and gauges showing that even with the advanced gauges suitable for 3D rotating binary evolutions, we recover the same type of limited results obtained in the original work.
Spherical coverage verification
Petkovic, Marko D; Latecki, Longin Jan
2011-01-01
We consider the problem of covering hypersphere by a set of spherical hypercaps. This sort of problem has numerous practical applications such as error correcting codes and reverse k-nearest neighbor problem. Using the reduction of non degenerated concave quadratic programming (QP) problem, we demonstrate that spherical coverage verification is NP hard. We propose a recursive algorithm based on reducing the problem to several lower dimension subproblems. We test the performance of the proposed algorithm on a number of generated constellations. We demonstrate that the proposed algorithm, in spite of its exponential worst-case complexity, is applicable in practice. In contrast, our results indicate that spherical coverage verification using QP solvers that utilize heuristics, due to numerical instability, may produce false positives.
Spherical geodesic mesh generation
Fung, Jimmy [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Kenamond, Mark Andrew [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Burton, Donald E. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Shashkov, Mikhail Jurievich [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-02-27
In ALE simulations with moving meshes, mesh topology has a direct influence on feature representation and code robustness. In three-dimensional simulations, modeling spherical volumes and features is particularly challenging for a hydrodynamics code. Calculations on traditional spherical meshes (such as spin meshes) often lead to errors and symmetry breaking. Although the underlying differencing scheme may be modified to rectify this, the differencing scheme may not be accessible. This work documents the use of spherical geodesic meshes to mitigate solution-mesh coupling. These meshes are generated notionally by connecting geodesic surface meshes to produce triangular-prismatic volume meshes. This mesh topology is fundamentally different from traditional mesh topologies and displays superior qualities such as topological symmetry. This work describes the geodesic mesh topology as well as motivating demonstrations with the FLAG hydrocode.
Erler, Bastian
2012-07-18
Realistic nucleon-nucleon interactions transformed via the Unitary Correlation Operator Method (UCOM) or the Similarity Renormalization Group (SRG) have proven to be a suitable starting point for the description of closed-shell nuclei via mean-field methods like Hartree-Fock (HF). This allows the treatment of a number of heavy nuclei with realistic nucleon-nucleon interactions, which would otherwise only be possible with phenomenological interactions. To include three-nucleon forces in an approximate way, the UCOM or SRG transformed interactions can be augmented by a three-body contact interaction, which is necessary to reproduce measured charge radii. However, many interesting nuclei, including those near the neutron drip line, are far away from closed shells. These nuclei are of great importance for modeling nucleosynthesis processes in the universe, but experiments can only be performed at a few research facilities. In this work, the Hartree Fock (HF) approach with realistic interactions is extended to light deformed nuclei. Pairing correlations are not taken into account. A crucial step in this process is to allow deformed ground states on the mean-field level, as only nuclei with at least one closed shell can be described with spherical HF ground states. To restore the rotational symmetry in the lab frame, exact angular-momentum projection (AMP) is implemented. Constrained HF calculations are used for an approximate variation after projection approach. The AMP-HF description of open-shell nuclei is on par with the pure HF description of closed-shell nuclei. Charge-radii and systematics of binding energies agree well with experiment. However, missing correlations, lead to an underestimated absolute value of the binding energy. Projection on higher angular momenta approximately reproduces the energy systematics of rotational bands. To describe collective excitations, the Random Phase Approximation (RPA) constitutes a well tested approach, which can also be
The Spherical Deformation Model
Hobolth, Asgar
2003-01-01
Miller et al. (1994) describe a model for representing spatial objects with no obvious landmarks. Each object is represented by a global translation and a normal deformation of a sphere. The normal deformation is defined via the orthonormal spherical-harmonic basis. In this paper we analyse...... the spherical deformation model in detail and describe how it may be used to summarize the shape of star-shaped three-dimensional objects with few parameters. It is of interest to make statistical inference about the three-dimensional shape parameters from continuous observations of the surface and from...
Almegaard, Henrik
2004-01-01
A new statical and conceptual model for membrane shell structures - the stringer system - has been found. The principle was first published at the IASS conference in Copenhagen (OHL91), and later the theory has been further developed (ALMO3)(ALMO4). From the analysis of the stringer model it can...... be concluded that all membrane shells can be described by a limited number of basic configurations of which quite a few have free edges....
Stability of generic cylindrical thin shell wormholes
Mazharimousavi, S Habib; Amirabi, Z
2014-01-01
We revisit the stability analysis of cylindrical thin shell wormholes which have been studied in literature so far. Our approach is more systematic and in parallel to the method which is used in spherically symmetric thin shell wormholes. The stability condition is summarized as the positivity of the second derivative of an effective potential at the equilibrium radius, i.e. $V^{\\prime \\prime}\\left(a_{0}\\right) >0$. This may serve as the master equation in all stability problems for the cylindrical thin-shell wormholes.
Bazhenov, V.; Demareva, A.; Baranova, M.; Kibets, A.
2016-11-01
An axisymmetric problem of high strains in a spherical lead shell enclosed into an aluminum “spacesuit” under the influence of pulse overload is considered. The shell straining is described with the use of equations of mechanics of elastoviscoplastic media in Lagrangian variables. Kinematic relations are determined in the current state metrics. Equations of state are taken in the form of equations of the flow theory with isotropic hardening. Contact interaction of a shell and a “spacesuit” is modeled by conditions of non-penetration with friction. Numerical solution under the given boundary and initial conditions is based on the moment schema of the finite element method and the explicit time integration scheme of the "cross". For sampling the space variables 4-node isoparametric finite elements with multilinear forms features are used. As it was shown by the results of calculations, spherical shell suffers significant local forming, characterized by large displacements and rotation angles of finite elements as a rigid body in the process of loading. The calculation results of the residual form are in good agreement with the experimental data.
Spherical distributions : Schoenberg revisited
Steerneman, AGM; van Perlo-ten Kleij, F
2005-01-01
An in-dimensional random vector X is said to have a spherical distribution if and only if its characteristic function is of the form phi(parallel to t parallel to), where t is an element of R-m, parallel to.parallel to denotes the usual Euclidean norm, and phi is a characteristic function on R. A mo
A peridynamic theory for linear elastic shells
Chowdhury, Shubhankar Roy; Roy, Debasish; Reddy, J N
2015-01-01
A state-based peridynamic formulation for linear elastic shells is presented. The emphasis is on introducing, possibly for the first time, a general surface based peridynamic model to represent the deformation characteristics of structures that have one physical dimension much smaller than the other two. A new notion of curved bonds is exploited to cater for force transfer between the peridynamic particles describing the shell. Starting with the three dimensional force and deformation states, appropriate surface based force, moment and several deformation states are arrived at. Upon application on the curved bonds, such states beget the necessary force and deformation vectors governing the motion of the shell. Correctness of our proposal on the peridynamic shell theory is numerically assessed against static deformation of spherical and cylindrical shells and flat plates.
Structural shell analysis understanding and application
Blaauwendraad, Johan
2014-01-01
The mathematical description of the properties of a shell is much more elaborate than those of beam and plate structures. Therefore many engineers and architects are unacquainted with aspects of shell behaviour and design, and are not familiar with sufficiently reliable shell theories for the different shell types as derived in the middle of the 20th century. Rather than contributing to theory development, this university textbook focuses on architectural and civil engineering schools. Of course, practising professionals will profit from it as well. The book deals with thin elastic shells, in particular with cylindrical, conical and spherical types, and with elliptic and hyperbolic paraboloids. The focus is on roofs, chimneys, pressure vessels and storage tanks. Special attention is paid to edge bending disturbance zones, which is indispensable knowledge in FE meshing. A substantial part of the book results from research efforts in the mid 20th century at Delft University of Technology. As such, it is a valua...
A novel approach to thin-shell wormholes and applications
Lobo, Francisco S N; Martín-Moruno, Prado; Montelongo-García, Nadiezhda; Visser, Matt
2015-01-01
A novel framework is presented that can be adapted to a wide class of generic spherically symmetric thin-shell wormholes. By using the Darmois--Israel formalism, we analyze the stability of arbitrary spherically symmetric thin-shell wormholes to linearized perturbations around static solutions. We demonstrate in full generality that the stability of the wormhole is equivalent to choosing suitable properties for the exotic material residing on the wormhole throat. As an application, we consider the thin-shell variant of the Ellis wormhole for the cases of a vanishing momentum flux and non-zero external fluxes.
姚祖福; 黄可龙; 于金刚; 郭军; 李艳华; 方东
2009-01-01
Using 3-mercaptopropyhrimethoxysilane as linker,single gold nanoparticle was successfully encapsulated by silicon oxide shell,and Au@SiO_2 core-sheU nanoparticles were prepared.The nanocomposites were spherical and monodispersal.The gold nanoparticle located at the center of silica nano-sphere.No congregating gold nanoparticles were embedded in one silica sphere.The morphologies of the samples were characterized by transmission electron microscopy(TEM).The chemical contents of the samples were analyzed using energy diffraction X-ray(EDX)spectroscopy.And their optical properties were studied.%采用3-巯基丙基三甲氧基硅烷作为联结剂,成功将单个金纳米粒子包在氧化硅壳中,制得Au@SiO_2核壳纳米粒子;该复合纳米粒子形貌呈球形、单分散性较好,金纳米粒子位于氧化硅球的中心.无团聚的金纳米粒子包覆在氧化硅壳中.采用透射电镜(TEM)对样品的形貌进行了表征,通过能量散射X-射线能谱(EDX)分析了目标物的化学成分,并对所得核壳纳米粒子的光谱性质进行了研究.
徐加初; 张勇
2011-01-01
该文对爆炸冲击作用下夹层开顶扁球壳的非线性轴对称动力稳定性问题进行研究.基于Reissner假设和Hamilton原理,得到了夹层开顶扁球壳在冲击载荷作用下的非线性动力控制方程;采用Galerkin方法对非线性动力控制方程进行求解,得到以刚性中心位移表达的非线性动力响应方程,并应用Runge-Kutta方法进行数值求解,采用以刚性中心位移表达的B-R准则确定冲击临界失稳载荷.最后讨论了壳体几何参数、物理参数对夹层开顶扁球壳冲击临界失稳载荷的影响.%This paper performs a nonlinear dynamic stability analysis of truncated sandwich shallow spherical shells under the action of explosive impacts. Based on Reissner's hypothesis and Hamilton's principle, the nonlinear dynamic governing equation is obtained and solved by Galerkin method and Runge-Kutta method.Budiansky-Roth criterion expressed in terms of rigid center displacements is employed to determine the critical instability load. The effects of geometric parameters and mechanical parameters on impact critical instability load are discussed.
Self-similar spherical metrics with tangential pressure
Gair, J R
2002-01-01
A family of spherically symmetric spacetimes is discussed, which have anisotropic pressure and possess a homothetic Killing vector. The spacetimes are composed of dust with a tangential pressure provided by angular momentum of the dust particles. The solution is given implicitly by an elliptic integral and depends on four arbitrary functions. These represent the initial configurations of angular momentum, mass, energy and position of the shells. The solution is derived by imposing self-similarity in the coordinates R, the shell label, and tau, the proper time experienced by the dust. Conditions for evolution without shell crossing and a description of singularity formation are given and types of solution discussed. General properties of the solutions are illustrated by reference to a particular case, which represents a universe that exists for an infinite time, but in which every shell expands and recollapses in a finite time.
Improvements in the spherical collapse model and dark energy cosmologies
Del Popolo, A.
In the present paper, we study how the effects of deviations from spherical symmetry of a system, produced by angular momentum, and shear stress, influence typical parameters of the spherical collapse model, like the linear density threshold for collapse of the non-relativistic component (δ c) and its virial overdensity (Δ V). The study is performed in the framework of the Einstein-de Sitter and Λ CDM models, and assuming that the vacuum component is not clustering within the homogeneous non-spherical overdensities. We start from the standard spherical top hat model (SCM) which does not take account the non-spherical effects, and we add to this model the shear term and angular momentum term, which are finally expressed in terms of the density contrast, δ . We find that the non-spherical terms change the non-linear evolution of the system and that the collapse stops ``naturally" at the virial radius, differently from the standard spherical collapse model. Moreover, shear and rotation gives rise to higher values of the linear overdensity parameter and different values of Δ V with respect to the standard spherical collapse model.
Spherical coordinate descriptions of cylindrical and spherical Bessel beams.
Poletti, M A
2017-03-01
This paper derives a generalized spherical harmonic description of Bessel beams. The spherical harmonic description of the well-known cylindrical Bessel beams is reviewed and a family of spherical Bessel beams are introduced which can provide a number of azimuthal phase variations for a single beam radial amplitude. The results are verified by numerical simulations.
Axisymmetric pulse train solutions in narrow-gap spherical Couette flow
Child, Adam; Kersalé, Evy
2016-01-01
We numerically compute the flow induced in a spherical shell by fixing the outer sphere and rotating the inner one. The aspect ratio $\\epsilon=(r_o-r_i)/r_i$ is set at 0.04 and 0.02, and in each case the Reynolds number measuring the inner sphere's rotation rate is increased to $\\sim10\\%$ beyond the first bifurcation from the basic state flow. For $\\epsilon =0.04$ the initial bifurcations are the same as in previous numerical work at $\\epsilon=0.154$, and result in steady one- and two-vortex states. Further bifurcations yield travelling wave solutions similar to previous analytic results valid in the $\\epsilon\\to0$ limit. For $\\epsilon=0.02$ the steady one-vortex state no longer exists, and the first bifurcation is directly to these travelling wave solutions, consisting of pulse trains of Taylor vortices travelling toward the equator from both hemispheres, and annihilating there in distinct phase-slip events. We explore these time-dependent solutions in detail, and find that they can be both equatorially symm...
Shell theory automated for rotational structures
Key, J.; Gonas, V. S.; Levine, S.; Ogilvie, P.
1980-01-01
Package of numerical integration programs static, buckling, vibration, and plastic analysis on thin sheels of revolution. Sheels may be subjected to distributed loads, concentrated line loads, and thermal strain. Outputs include stresses, displacement, plastic strains, and vibration and buckling results. Program aids design of aircraft bodies, spacecraft, submarines, and storage tanks. Written in FORTRAN IV for batch execution, program has been implemented on UNIVAC 1108.
Nuclear Rotations and the Born--Oppenheimer Method
Zettili, Nouredine
2009-10-01
We want to discuss the study of nuclear rotations and collective motion within the context of the nuclear Born--Oppenheirmer (NBO) method--a truly quantum mechanical method. As an illustration, we apply the NBO method to study permanently deformed (non-spherical) nuclei; in particular, we study nuclei that are axially-symmetric and even, but with non-closed shells. In the presentation, we focus on the derivation of formal expressions for the energy and for the moment of inertia. Using trial functions in which the intrinsic structure is described in a mean-field approximation, we then show that the NBO formalism yields the Thouless-Valantin formula for the moment of inertia and that this moment of inertia increases with angular momentum, in agreement with experimental data. We show that the NBO formalism is well equipped to describe low-lying as well as high lying rotational states. Additionally, we establish a connection between the NBO method and the self-consistent Cranking (SCC) model, which is known to be successful in reproducing vast amounts of experimental data ranging from low-lying rotational states to high angular momentum states.
Strongly Localized Image States of Spherical Graphitic Particles
Godfrey Gumbs
2014-01-01
Full Text Available We investigate the localization of charged particles by the image potential of spherical shells, such as fullerene buckyballs. These spherical image states exist within surface potentials formed by the competition between the attractive image potential and the repulsive centripetal force arising from the angular motion. The image potential has a power law rather than a logarithmic behavior. This leads to fundamental differences in the nature of the effective potential for the two geometries. Our calculations have shown that the captured charge is more strongly localized closest to the surface for fullerenes than for cylindrical nanotube.
A parametric study on ice formation inside a spherical capsule
Ismail, K.A.R.; Silva, T.M. da [Depto. de Engenharia Termica e de Fluidos - FEM-UNICAMP CP: 6122, CEP 13083-970, SP, Campinas (Brazil); Henriquez, J.R. [Depto. de Engenharia Mecanica - DEMEC, UFPE, CEP 50740-530, PE, Recife (Brazil)
2003-09-01
This paper reports the results of a numerical study on the heat transfer during the process of solidification of water inside a spherical capsule. The governing equations of the problem and associated boundary conditions were formulated and solved using a finite difference approach and a moving grid scheme. The model was optimized and the numerical predictions were validated by comparison with experimental results realized by the authors. The model was also used to investigate the effects of the size and material of the shell, initial temperature of the phase change material and the external temperature of the spherical capsule on the solidified mass fraction and the time for the complete solidification. (authors)
Transitions in a magnetized quasi-laminar spherical Couette Flow
Kaprzyk, C; Seilmayer, M; Stefani, F
2016-01-01
First results of a new spherical Couette experiment are presented. The liquid metal flow in a spherical shell is exposed to a homogeneous axial magnetic field. For a Reynolds number Re=1000, we study the effect of increasing Hartmann number Ha. The resulting flow structures are inspected by ultrasound Doppler velocimetry. With a weak applied magnetic field, we observe an equatorially anti-symmetric jet instability with azimuthal wave number m=3. As the magnetic field strength increases, this instability vanishes. When the field is increased further, an equatorially symmetric return flow instability arises. Our observations are shown to be in good agreement with linear stability analysis and non-linear flow simulations.
A radio-polarisation and rotation measure study of the Gum Nebula and its environment
Purcell, C R; Sun, X H; Carretti, E; Bernardi, G; Haverkorn, M; Kesteven, M J; Poppi, S; Schnitzeler, D H F M; Staveley-Smith, L
2015-01-01
The Gum Nebula is 36 degree wide shell-like emission nebula at a distance of only 450 pc. It has been hypothesised to be an old supernova remnant, fossil HII region, wind-blown bubble, or combination of multiple objects. Here we investigate the magneto-ionic properties of the nebula using data from recent surveys: radio-continuum data from the NRAO VLA and S-band Parkes All Sky Surveys, and H-alpha data from the Southern H-Alpha Sky Survey Atlas. We model the upper part of the nebula as a spherical shell of ionised gas expanding into the ambient medium. We perform a maximum-likelihood Markov chain Monte-Carlo fit to the NVSS rotation measure data, using the H-halpha data to constrain average electron density in the shell $n_e$. Assuming a latitudinal background gradient in RM we find $n_e=1.3^{+0.4}_{-0.4} {\\rm cm}^{-3}$, angular radius $\\phi_{\\rm outer}=22.7^{+0.1}_{-0.1} {\\rm deg}$, shell thickness $dr=18.5^{+1.5}_{-1.4} {\\rm pc}$, ambient magnetic field strength $B_0=3.9^{+4.9}_{-2.2} \\mu{\\rm G}$ and warm ...
Inversion of band patterns in spherical tumblers.
Chen, Pengfei; Lochman, Bryan J; Ottino, Julio M; Lueptow, Richard M
2009-04-10
Bidisperse granular mixtures in spherical tumblers segregate into three bands: one at each pole and one at the equator. For low fill levels, large particles are at the equator; for high fill levels, the opposite occurs. Segregation is robust, though the transition depends on fill level, particle size, and rotational speed. Discrete element method simulations reproduce surface patterns and reveal internal structures. Particle trajectories show that small particles flow farther toward the poles than large particles in the upstream portion of the flowing layer for low fill levels leading to a band of small particles at each pole. The opposite occurs for high fill levels, though more slowly.
G7 BiSpherical Acetabular Shell PMCF Study
2017-08-29
Rheumatoid Arthritis; Osteoarthritis; Noninflammatory Degenerative Joint Disease; Avascular Necrosis; Correction of Functional Deformity; Non-Union Fracture; Femoral Neck Fractures; Trochanteric Fractures
Analytical calculation of the wake potential of a spherical resonator
Sebastian Ratschow
2002-05-01
Full Text Available An analytical formula for the wake potential of a closed spherical resonator with perfectly conducting walls is presented. Mode analysis is used for the calculation. For every rotationally symmetric TM mode the loss parameter is calculated and the formula for the determination of the corresponding frequency is given. The final wake potential is an infinite sum over all modes mentioned above.
The volume of fluid method in spherical coordinates
Janse, A.M.C.; Dijk, P.E.; Kuipers, J.A.M.
2000-01-01
The volume of fluid (VOF) method is a numerical technique to track the developing free surfaces of liquids in motion. This method can, for example, be applied to compute the liquid flow patterns in a rotating cone reactor. For this application a spherical coordinate system is most suited. The novel
Femtosecond dynamics of a spaser and unidirectional emission from a perfectly spherical nanoparticle
Gongora, J. S. Totero
2015-01-01
We investigate the femtosecond dynamics of the spaser emission by combining ab-initio simulations and thermodynamic analysis. Interestingly, the emission is characterized by rotational evolution, opening to the generation of unidirectional emission from perfectly spherical nanoparticles. © OSA 2015.
Variation of space radiation exposure inside spherical and hemispherical geometries
Lin, Z.W. [Department of Physics, East Carolina University, C-209 Howell Science Complex, Greenville, NC 27858-4353 (United States); National Space Science and Technology Center, University of Alabama in Huntsville, Huntsville, AL 35805 (United States)], E-mail: linz@ecu.edu; Baalla, Y. [University of Tennessee Space Institute, Tullahoma, TN 37388 (United States); Townsend, L.W. [Department of Nuclear Engineering, University of Tennessee at Knoxville, Knoxville, TN 37996 (United States)
2009-04-15
We calculate the space radiation exposure to blood-forming organs everywhere inside a hemispherical dome that represents a lunar habitat. We derive the analytical pathlength distribution from any point inside a hemispherical or a spherical shell. Because the average pathlength increases with the distance from the center, the center of the hemispherical dome on the lunar surface has the largest radiation exposure while locations on the inner surface of the dome have the lowest exposure. This conclusion differs from an earlier study on a hemispherical dome but agrees with another earlier study on a spherical-shell shield. We also find that the reduction in the radiation exposure from the center to the inner edge of the dome can be as large as a factor of 3 or more for the radiation from solar particle events while being smaller for the radiation from galactic cosmic rays.
Some shell formulations, in view of their applicability to finite elements
Debongnie, Jean-François
1986-01-01
Surface geometry and shell geometry, in the frame of general tensor calculus. Fundamentals of the theory of thin shells. Expressing strains from curvilinear components of the displacements. Applicability of the preceeding theory to finite elements. Expressing strains from the cartesian components of the displacements. Moderate rotation theory (curvilinear components). Moderate rotation theory (cartesian components). Quasi-plane and almost-plane shells. Shells with shearing strains (cartesian ...
Nonlinear axisymmetric liquid currents in spherical annuli
Astafyeva, N. M.; Vvedenskaya, N. D.; Yavorskaya, I. M.
1978-01-01
A numerical analysis of non-linear axisymmetric viscous flows in spherical annuli of different gap sizes is presented. Only inner sphere was supposed to rotate at a constant angular velocity. The streamlines, lines of constant angular velocity, kinetic energy spectra, and spectra of velocity components are obtained. A total kinetic energy and torque needed to rotate the inner sphere are calculated as functions of Re for different gap sizes. In small-gap annulus nonuniqueness of steady solutions of Navier-Stokes equations is established and regions of different flow regime existences are found. Numerical solutions in a wide-gap annulus and experimental results are used in conclusions about flow stability in the considered range of Re. The comparison of experimental and numerical results shows close qualitative and quantitative agreement.
Georgiev, G. H.; Dinkova, C. L.
2013-10-01
Long spirals in the Euclidean plane have been introduced by A. Kurnosenko five years ago. Using a natural map of the shape sphere into the extended Gaussian plane we study spherical curves that are pre-images of plane long spirals. Loxodromes and spherical spiral antennas are typical examples of such spherical long spirals. The set of all planar spirals leaves invariant under an arbitrary similarity transformation. This set is divided in two disjoint classes by A. Kirnosenko. The first class is consist of the so-called short spirals which are widely used in geometric modeling. The second class of planar long spirals contains well-known logarithmic spiral and Archimedean spirals which have many applications in mathematics, astrophysics and industry. The notion of simplicial shape space is due to D. Kendall. The most popular simplicial shape space of order (2,3) is the set of equivalence classes of similar triangles in the plane. The sphere of radius 1/2 centered at the origin can be considered as a model of this quotient space, so-called the shape sphere. F. Bookstein and J. Lester showed that the one-point extension of the Euclidean plane, so-called the extended Gaussian plane, is another model of the same simplicial shape space. The present paper gives a description of long spirals on the shape sphere by the use a natural conformal mapping between two models. First, we examine long spirals in the extended Gaussian plane. After that, we describe some differential geometric properties of the shape sphere. Finally, we discuss parameterizations of long spirals on the shape sphere.
M. A. Navascués
2013-01-01
Full Text Available This paper tackles the construction of fractal maps on the unit sphere. The functions defined are a generalization of the classical spherical harmonics. The methodology used involves an iterated function system and a linear and bounded operator of functions on the sphere. For a suitable choice of the coefficients of the system, one obtains classical maps on the sphere. The different values of the system parameters provide Bessel sequences, frames, and Riesz fractal bases for the Lebesgue space of the square integrable functions on the sphere. The Laplace series expansion is generalized to a sum in terms of the new fractal mappings.
Arita, Ken-ichiro
2014-01-01
Shell structures in single-particle energy spectra are investigated against regular tetrahedral type deformation using radial power-law potential model. Employing a natural way of shape parametrization which interpolate sphere and regular tetrahedron, we find prominent shell effects at rather large tetrahedral deformations, which bring about shell energies much larger than the cases of spherical and quadrupole type shapes. We discuss the semiclassical origin of these anomalous shell structures using periodic orbit theory.
Centrifugal force induced by relativistically rotating spheroids and cylinders
Katz, Joseph; Bicak, Jiri; 10.1088/0264-9381/28/6/065004
2011-01-01
Starting from the gravitational potential of a Newtonian spheroidal shell we discuss electrically charged rotating prolate spheroidal shells in the Maxwell theory. In particular we consider two confocal charged shells which rotate oppositely in such a way that there is no magnetic field outside the outer shell. In the Einstein theory we solve the Ernst equations in the region where the long prolate spheroids are almost cylindrical; in equatorial regions the exact Lewis "rotating cylindrical" solution is so derived by a limiting procedure from a spatially bound system. In the second part we analyze two cylindrical shells rotating in opposite directions in such a way that the static Levi-Civita metric is produced outside and no angular momentum flux escapes to infinity. The rotation of the local inertial frames in flat space inside the inner cylinder is thus exhibited without any approximation or interpretational difficulties within this model. A test particle within the inner cylinder kept at rest with respect...
Cross, Rod
2013-01-01
A tippe top (see Fig. 1) is usually constructed as a truncated sphere with a cylindrical peg on top, as indicated in Fig. 2(a). When spun rapidly on a horizontal surface, a tippe top spins about a vertical axis while rotating slowly about a horizontal axis until the peg touches the surface. At that point, weight is transferred to the peg, the…
Spherical magnetic nanoparticles fabricated by laser target evaporation
A. P. Safronov
2013-05-01
Full Text Available Magnetic nanoparticles of iron oxide (MNPs were prepared by the laser target evaporation technique (LTE. The main focus was on the fabrication of de-aggregated spherical maghemite MNPs with a narrow size distribution and enhanced effective magnetization. X-ray diffraction, transmission electron microscopy, magnetization and microwave absorption measurements were comparatively analyzed. The shape of the MNPs (mean diameter of 9 nm was very close to being spherical. The lattice constant of the crystalline phase was substantially smaller than that of stoichiometric magnetite but larger than the lattice constant of maghemite. High value of Ms up to 300 K was established. The 300 K ferromagnetic resonance signal is a single line located at a field expected from spherical magnetic particles with negligible magnetic anisotropy. The maximum obtained concentration of water based ferrofluid was as high as 10g/l of magnetic material. In order to understand the temperature and field dependence of MNPs magnetization, we invoke the core-shell model. The nanoparticles is said to have a ferrimagnetic core (roughly 70 percent of the caliper size while the shell consists of surface layers in which the spins are frozen having no long range magnetic order. The core-shell interactions were estimated in frame of random anisotropy model. The obtained assembly of de-aggregated nanoparticles is an example of magnetic nanofluid stable under ambient conditions even without an electrostatic stabilizer.
Magnetic actuation and transition shapes of a bistable spherical cap
E.G. Loukaides
2014-10-01
Full Text Available Multistable shells have been proposed for a variety of applications; however, their actuation is almost exclusively addressed through embedded piezoelectric patches. Additional actuation techniques are needed for applications requiring high strains or where remote actuation is desirable. Part of the reason for the lack of research in this area is the absence of appropriate models describing the detailed deformation and energetics of such shells. This work presents a bistable spherical cap made of iron carbonyl-infused polydimethylsiloxane. The magnetizable structure can be actuated remotely through permanent magnets while the transition is recorded with a high-speed camera. Moreover, the experiment is reproduced in a finite element (FE dynamic model for comparison with the physical observations. High-speed footage of the physical cap inversion together with the FE modeling gives valuable insight on preferable intermediate geometries. Both methods return similar values for the magnetic field strength required for the snap-through. High-strain multistable spherical cap transformation is demonstrated, based on informed material selection. We discover that non-axisymmetric transition shapes are preferred in intermediate geometries by bistable spherical caps. We develop the methods for design and analysis of such actuators, including the feasibility of remote actuation methods for multistable shells.
Holographic Spherically Symmetric Metrics
Petri, Michael
The holographic principle (HP) conjectures, that the maximum number of degrees of freedom of any realistic physical system is proportional to the system's boundary area. The HP has its roots in the study of black holes. It has recently been applied to cosmological solutions. In this article we apply the HP to spherically symmetric static space-times. We find that any regular spherically symmetric object saturating the HP is subject to tight constraints on the (interior) metric, energy-density, temperature and entropy-density. Whenever gravity can be described by a metric theory, gravity is macroscopically scale invariant and the laws of thermodynamics hold locally and globally, the (interior) metric of a regular holographic object is uniquely determined up to a constant factor and the interior matter-state must follow well defined scaling relations. When the metric theory of gravity is general relativity, the interior matter has an overall string equation of state (EOS) and a unique total energy-density. Thus the holographic metric derived in this article can serve as simple interior 4D realization of Mathur's string fuzzball proposal. Some properties of the holographic metric and its possible experimental verification are discussed. The geodesics of the holographic metric describe an isotropically expanding (or contracting) universe with a nearly homogeneous matter-distribution within the local Hubble volume. Due to the overall string EOS the active gravitational mass-density is zero, resulting in a coasting expansion with Ht = 1, which is compatible with the recent GRB-data.
Guenel, M; Mathis, S; Rieutord, M
2016-01-01
Star-planet tidal interactions may result in the excitation of inertial waves in the convective region of stars. In low-mass stars, their dissipation plays a prominent role in the long-term orbital evolution of short-period planets. Turbulent convection can sustain differential rotation in their envelope, with an equatorial acceleration (as in the Sun) or deceleration, which can modify the waves' propagation properties. We explore in this first paper the general propagation properties of free linear inertial waves in a differentially rotating homogeneous fluid inside a spherical shell. We assume that the angular velocity background flow depends on the latitudinal coordinate only, close to what is expected in the external convective envelope of low-mass stars. We use i) an analytical approach in the inviscid case to get the dispersion relation, from which we compute the characteristic trajectories along which energy propagates. This allows us to study the existence of attractor cycles and infer the different f...
Shell deformation studies using holographic interferometry
Parmerter, R. R.
1974-01-01
The buckling of shallow spherical shells under pressure has been the subject of many theoretical and experimental papers. Experimental data above the theoretical buckling load of Huang have given rise to speculation that shallow shell theory may not adequately predict the stability of nonsymmetric modes in higher-rise shells which are normally classified as shallow by the Reissner criterion. This article considers holographic interferometry as a noncontact, high-resolution method of measuring prebuckling deformations. Prebuckling deformations of a lambda = 9, h/b = 0.038 shell are Fourier-analyzed. Buckling is found to occur in an N = 5 mode as predicted by Huang's theory. The N = 4 mode was unusually stable, suggesting that even at this low value of h/b, stabilizing effects may be at work.
MHD Modeling of Differential Rotation in Coronal Holes
Lionello, Roberto; Linker, Jon A.; Mikic, Zoran; Riley, Pete
2004-01-01
The photosphere and the magnetic flux therein undergo differential rotation. Coronal holes appear to rotate almost rigidly. Magnetic reconnection has been invoked to reconcile these phenomena. Mechanism relevant to the formation of the slow solar wind. We have used our MHD model in spherical coordinates to study the effect of differential rotation on coronal holes. We have imposed a magnetic flux distribution similar to and applied differential rotation for the equivalent of 5 solar rotations.
The ETE spherical Tokamak project
Ludwig, Gerson Otto; Andrade, Maria Celia Ramos de; Barbosa, Luis Filipe Wiltgen [Instituto Nacional de Pesquisas Espaciais (INPE), Sao Jose dos Campos, SP (Brazil). Lab. Associado de Plasma] [and others]. E-mail: ludwig@plasma.inpe.br
1999-07-01
This paper describes the general characteristics of spherical tokamaks, with a brief overview of work in the area of spherical torus already performed or in progress at several institutions. The paper presents also the historical development of the ETE (Spherical Tokamak Experiment) project, its research program, technical characteristics and status of construction in September, 1998 at the Associated plasma Laboratory (LAP) of the National Institute for Space Research (INPE) in Brazil. (author)
Spherical tokamak development in Brazil
Ludwig, Gerson Otto; Bosco, Edson Del; Ferreira, Julio Guimaraes [Instituto Nacional de Pesquisas Espaciais (INPE), Sao Jose dos Campos, SP (Brazil). Lab. Associado de Plasma] (and others)
2003-07-01
The general characteristics of spherical tokamaks, or spherical tori, with a brief view of work in this area already performed or in progress at several institutions worldwide are described. The paper presents also the steps in the development of the ETE (Experiment Tokamak spheric) project, its research program, technical characteristics and operating conditions as of December, 2002 a the Associated Plasma Laboratory (LAP) of the National Space Research Institute (INPE) in Brazil. (author)
Spherical artifacts on ferrograms
Jones, W. R., Jr.
1976-01-01
In the past, hollow spheres detected on ferrograms have been interpreted as being due to fretting, abrasion, cavitation erosion, and fatigue-related processes. Here it is reported that such spheres were found to result from the fact that a routine grinding operation on a steel plate was carried out about 20 feet away from the ferrograph. A similar grinding operation was performed on a piece of low carbon steel a few feet from the ferrograph, and after a few minutes of grinding, the resulting ferrogram contained thousands of particles of which more than 90% were spherical. Because of the widespread occurrence of ordinary grinding operations, it seems prudent that those utilizing the ferrograph be cognizant of this type of artifact.
Spherical grating spectrometers
O'Donoghue, Darragh; Clemens, J. Christopher
2014-07-01
We describe designs for spectrometers employing convex dispersers. The Offner spectrometer was the first such instrument; it has almost exclusively been employed on satellite platforms, and has had little impact on ground-based instruments. We have learned how to fabricate curved Volume Phase Holographic (VPH) gratings and, in contrast to the planar gratings of traditional spectrometers, describe how such devices can be used in optical/infrared spectrometers designed specifically for curved diffraction gratings. Volume Phase Holographic gratings are highly efficient compared to conventional surface relief gratings; they have become the disperser of choice in optical / NIR spectrometers. The advantage of spectrometers with curved VPH dispersers is the very small number of optical elements used (the simplest comprising a grating and a spherical mirror), as well as illumination of mirrors off axis, resulting in greater efficiency and reduction in size. We describe a "Half Offner" spectrometer, an even simpler version of the Offner spectrometer. We present an entirely novel design, the Spherical Transmission Grating Spectrometer (STGS), and discuss exemplary applications, including a design for a double-beam spectrometer without any requirement for a dichroic. This paradigm change in spectrometer design offers an alternative to all-refractive astronomical spectrometer designs, using expensive, fragile lens elements fabricated from CaF2 or even more exotic materials. The unobscured mirror layout avoids a major drawback of the previous generation of catadioptric spectrometer designs. We describe laboratory measurements of the efficiency and image quality of a curved VPH grating in a STGS design, demonstrating, simultaneously, efficiency comparable to planar VPH gratings along with good image quality. The stage is now set for construction of a prototype instrument with impressive performance.
Decin, L.; Royer, P.; Cox, N.L.J.; Vandenbussche, B.; Ottensamer, R.; Blommaert, J.A.D.L.; Groenewegen, M.A.T.; Barlow, M.J.; Lim, T.; Kerschbaum, F.; Posch, T.; Waelkens, C.
2011-01-01
We present new Herschel/PACS images at 70, 100, and 160 μm of the well-known, nearby, carbon-rich asymptotic giant branch star IRC+10216 revealing multiple dust shells in its circumstellar envelope. For the first time, dust shells (or arcs) are detected until 320''. The almost spherical shells are n
Uniform approximation from symbol calculus on a spherical phase space
Yu Liang, E-mail: liangyu@wigner.berkeley.edu [Department of Physics, University of California, Berkeley, CA 94720 (United States)
2011-12-16
We use symbol correspondence and quantum normal form theory to develop a more general method for finding uniform asymptotic approximations. We then apply this method to derive a result we announced in an earlier paper, namely the uniform approximation of the 6j-symbol in terms of the rotation matrices. The derivation is based on the Stratonovich-Weyl symbol correspondence between matrix operators and functions on a spherical phase space. The resulting approximation depends on a canonical, or area-preserving, map between two pairs of intersecting level sets on the spherical phase space. (paper)
Construction of Aesthetic Spherical Patterns from Planar IFSs
Chen, Ning; Zhang, Yuting; Chung, K. W.
2016-07-01
To construct symmetrical patterns on the unit sphere from the planar iterative function systems (IFSs), we present a method of constructing IFSs with D3 symmetry which is composed of three-fold rotational symmetries together with reflections. An algorithm is developed to generate strange attractors with D3 symmetry on a triangular face and then project it onto the surface of the unit sphere to form aesthetics patterns with spherical symmetry. As an illustrative example, we consider the regular inscribed icosahedron in the unit sphere which contains 20 triangular faces. This method is valid to randomly generate aesthetic spherical patterns using planar IFSs.
Adiabatic Quasi-Spherical Compressions Driven by Magnetic Pressure for Inertial Confinement Fusion
NASH,THOMAS J.
2000-11-01
The magnetic implosion of a high-Z quasi-spherical shell filled with DT fuel by the 20-MA Z accelerator can heat the fuel to near-ignition temperature. The attainable implosion velocity on Z, 13-cm/{micro}s, is fast enough that thermal losses from the fuel to the shell are small. The high-Z shell traps radiation losses from the fuel, and the fuel reaches a high enough density to reabsorb the trapped radiation. The implosion is then nearly adiabatic. In this case the temperature of the fuel increases as the square of the convergence. The initial temperature of the fuel is set by the heating of an ion acoustic wave to be about 200-eV after a convergence of 4. To reach the ignition temperature of 5-keV an additional convergence of 5 is required. The implosion dynamics of the quasi-spherical implosion is modeled with the 2-D radiation hydrodynamic code LASNEX. LASNEX shows an 8-mm diameter quasi-spherical tungsten shell on Z driving 6-atmospheres of DT fuel nearly to ignition at 3.5-keV with a convergence of 20. The convergence is limited by mass flow along the surface of the quasi-spherical shell. With a convergence of 20 the final spot size is 400-{micro}m in diameter.
Adiabatic Quasi-Spherical Compressions Driven by Magnetic Pressure for Inertial Confinement Fusion
NASH,THOMAS J.
2000-11-01
The magnetic implosion of a high-Z quasi-spherical shell filled with DT fuel by the 20-MA Z accelerator can heat the fuel to near-ignition temperature. The attainable implosion velocity on Z, 13-cm/{micro}s, is fast enough that thermal losses from the fuel to the shell are small. The high-Z shell traps radiation losses from the fuel, and the fuel reaches a high enough density to reabsorb the trapped radiation. The implosion is then nearly adiabatic. In this case the temperature of the fuel increases as the square of the convergence. The initial temperature of the fuel is set by the heating of an ion acoustic wave to be about 200-eV after a convergence of 4. To reach the ignition temperature of 5-keV an additional convergence of 5 is required. The implosion dynamics of the quasi-spherical implosion is modeled with the 2-D radiation hydrodynamic code LASNEX. LASNEX shows an 8-mm diameter quasi-spherical tungsten shell on Z driving 6-atmospheres of DT fuel nearly to ignition at 3.5-keV with a convergence of 20. The convergence is limited by mass flow along the surface of the quasi-spherical shell. With a convergence of 20 the final spot size is 400-{micro}m in diameter.
Dynamics of non-spherical colloidal particles near and at oil-water interfaces
Wang, Anna; Dimiduk, Thomas G.; Fung, Jerome; Chaudhary, Kundan; Lewis, Jennifer A.; Razavi, Sepideh; Kretzschmar, Ilona; Manoharan, Vinothan N.
2014-03-01
Whereas much is known about how spherical colloidal particles interact with and at oil-water interfaces, not much is known about their non-spherical counterparts. The rotation of non-spherically symmetric particles adds extra degrees of freedom to how such particles interact with each other and the interface, so to study their three-dimensional dynamics we must first be able to image the rotation which has so far only been possible in viscous fluids or for particles with large aspect ratios. Here we track both the three-dimensional translation and the rotation of non-spherical colloidal particles at high speeds using the discrete dipole approximation in conjunction with digital holographic microscopy. We study the dynamics of such particles at an oil-water interface to determine interactions and dynamics prior to or after attachment. We aim to connect these measurements to the formation and stability of Pickering emulsions.
Shape coexistence: the shell model view
Poves, A.
2016-02-01
We shall discuss the meaning of the ‘nuclear shape’ in the laboratory frame proper to the spherical shell model. A brief historical promenade will bring us from Elliott’s SU3 breakthrough to today’s large scale shell model calculations. A section is devoted to the algebraic model which extends drastically the field of applicability of Elliot’s SU3, providing a precious heuristic guidance for the exploration of collectivity in the nuclear chart. Shape coexistence and shape mixing will be shown to occur as the result of the competition between the main actors in the nuclear dynamics; the spherical mean field, and the pairing and quadrupole-quadrupole interactions. These ideas will be illustrated with examples in magic nuclei (40Ca and 68Ni); neutron rich semi-magic (32Mg, and 64Cr); and in proton rich N = Z (72Kr).
Resonance scattering of canonical elastic shells in absorbing fluid medium
ZHUO Linkai; FAN Jun; TANG Weilin
2008-01-01
Resonance scattering of elastic spherical shell and cylindrical shell while the sur-rounding fluid medium has absorption is studied. The normal mode solution derived using exact elastic theory and the separation of variables is still applicable. However, the scattering form function has to be modified for the absorbing medium, otherwise the unreasonable resul twould be obtained. The backscattering form function in the absorbing medium is redefined, and the form function of elastic spherical and cylindrical shell with vacuum or solid matter filled is calculated in various absorption conditions. The results show that the absorption of surround-ing fluid leads to notable attenuation of the coincidence resonances in the mid-frequency, but it has a little in fluence on the low-frequency resonance scattering induced by the filler inside the shell.
NIF Double Shell outer-shell experiments
Merritt, E. C.; Montgomery, D. S.; Kline, J. L.; Daughton, W. S.; Wilson, D. C.; Dodd, E. S.; Renner, D. B.; Cardenas, T.; Batha, S. H.
2016-10-01
At the core of the Double Shell concept is the kinetic energy transfer from the outer shell to the inner shell via collision. This collision sets both the implosion shape of the inner shell, from imprinting of the shape of the outer shell, as well as the maximum energy available to compress the DT fuel. Therefore, it is crucial to be able to control the time-dependent shape of the outer shell, such that the outer shell is nominally round at the collision time. We present the experiment results from our sub-scale ( 1 MJ) NIF outer-shell only shape tuning campaign, where we vary shape by changing a turn-on time delay between the same pulse shape on the inner and outer cone beams. This type of shape tuning is unique to this platform and only possible since the Double Shell design uses a single-shock drive (4.5 ns reverse ramp pulse). The outer-shell only targets used a 5.75 mm diameter standard near-vacuum NIF hohlraum with 0.032 mg/cc He gas fill, and a Be capsule with 0.4% uniform Cu dopant, with 242 um thick ablator. We also present results from a third outer-shell only shot used to measure shell trajectory, which is critical in determining the shell impact time. This work conducted under the auspices of the U.S. DOE by LANL under contract DE-AC52-06NA25396.
Härmark, Johan; Hebert, Hans; Koeck, Philip J B
2016-06-01
Intravenously injected microbubbles (MBs) can be utilized as ultrasound contrast agent (CA) resulting in enhanced image quality. A novel CA, consisting of air filled MBs stabilized with a shell of polyvinyl alcohol (PVA) has been developed. These spherical MBs have been decorated with superparamagnetic iron oxide nanoparticles (SPIONs) in order to serve as both ultrasound and magnetic resonance imaging (MRI) CA. In this study, a mathematical model was introduced that determined the shell thickness of two types of SPIONs decorated MBs (Type A and Type B). The shell thickness of MBs is important to determine, as it affects the acoustical properties. In order to investigate the shell thickness, thin sections of plastic embedded MBs were prepared and imaged using transmission electron microscopy (TEM). However, the sections were cut at random distances from the MB center, which affected the observed shell thickness. Hence, the model determined the average shell thickness of the MBs from corrected mean values of the outer and inner radii observed in the TEM sections. The model was validated using simulated slices of MBs with known shell thickness and radius. The average shell thickness of Type A and Type B MBs were 651nm and 637nm, respectively.
Bi-stability in turbulent, rotating spherical Couette flow
Zimmerman, Daniel S; Lathrop, Daniel P; 10.1063/1.3593465
2011-01-01
Flow between concentric spheres of radius ratio $\\eta = r_\\mathrm{i}/r_\\mathrm{o} = 0.35$ is studied in a 3 m outer diameter experiment. We have measured the torques required to maintain constant boundary speeds as well as localized wall shear stress, velocity, and pressure. At low Ekman number $E = 2.1\\times10^{-7}$ and modest Rossby number $0.07 < Ro < 3.4$, the resulting flow is highly turbulent, with a Reynolds number ($Re=Ro/E$) exceeding fifteen million. Several turbulent flow regimes are evident as $Ro$ is varied for fixed $E$. We focus our attention on one flow transition in particular, between $Ro = 1.8$ and $Ro = 2.6$, where the flow shows bistable behavior. For $Ro$ within this range, the flow undergoes intermittent transitions between the states observed alone at adjacent $Ro$ outside the switching range. The two states are clearly distinguished in all measured flow quantities, including a striking reduction in torque demanded from the inner sphere by the state lying at higher $Ro$. The redu...
Thin elastic shells with variable thickness for lithospheric flexure of one-plate planets
Beuthe, Mikael
2007-01-01
Planetary topography can either be modeled as a load supported by the lithosphere, or as a dynamical effect due to lithospheric flexure caused by mantle convection. In both cases the response of the lithosphere to external forces can be calculated with the theory of thin elastic plates or shells. On one-plate planets the spherical geometry of the lithospheric shell plays an important role in the flexure mechanism. So far the equations governing the deformations and stresses of a spherical shell have only been derived under the assumption of a shell of constant thickness. However local studies of gravity and topography data suggest large variations in the thickness of the lithosphere. In this article we obtain the scalar flexure equations governing the deformations of a thin spherical shell with variable thickness or variable Young's modulus. The resulting equations can be solved in succession, except for a system of two simultaneous equations, the solutions of which are the transverse deflection and an associ...
SD-Pair Shell Model for Identical Nuclear Systems
LUO Yan-An; PAN Feng; NING Ping-Zhi; Jerry P. Draayer
2005-01-01
@@ Typical spectra corresponding to vibrational, rotational and γ-soft cases were studied within the framework of nucleon-pair shell model truncated to SD-subspace. It is found that the three limiting cases all can be reproduced approximately. The analysis not only shows that the IBM indeed has a sound shell model foundation, but also confirms that the truncation scheme adopted in the SD-pair shell model seems to be reasonable.
Akbar, M. M.
2017-06-01
It is well known that static spherically symmetric spacetimes can admit foliations by flat spacelike hypersurfaces, which are best described in terms of the Painlevè-Gullstrand coordinates. The uniqueness and existence of such foliations were addressed earlier. In this paper, we prove, purely geometrically, that any possible foliation of a static spherically symmetric spacetime by an arbitrary codimension-one spherical spacelike geometry, up to time translation and rotation, is unique, and we find the algebraic condition under which it exists. This leads us to what can be considered as the most natural generalization of the Painlevè-Gullstrand coordinate system for static spherically symmetric metrics, which, in turn, makes it easy to derive generic conclusions on foliation and to study specific cases as well as to easily reproduce previously obtained generalizations as special cases. In particular, we note that the existence of foliation by flat hypersurfaces guarantees the existence of foliation by hypersurfaces whose Ricci curvature tensor is everywhere non-positive (constant negative curvature is a special case). The study of uniqueness and the existence concurrently solves the question of embeddability of a spherical spacelike geometry in one-dimensional higher static spherically symmetric spacetimes, and this produces known and new results geometrically, without having to go through the momentum and Hamiltonian constraints.
Oscillating Shells in Anti-de Sitter Space
Mas, Javier
2015-01-01
We study the dynamics of a spherically symmetric thin shell of perfect fluid embedded in d-dimensional Anti-de Sitter space-time. In global coordinates, besides collapsing solutions, oscillating solutions are found where the shell bounces back and forth between two radii. The parameter space where these oscillating solutions exist is scanned in arbitrary number of dimensions. As expected AdS3 appears to be singled out.
Static dipole polarizability of shell-confined hydrogen atom
Sen, K. D.; Garza, Jorge; Vargas, Rubicelia; Aquino, Norberto
2002-04-01
Using the Sternheimer perturbation-numerical procedure, calculations of static dipole polarizability are reported for the shell-confined hydrogen atom as defined by two impenetrable concentric spherical walls. Unusually high polarizability states are predicted for the hydrogen atom as the inner sphere radius is increased to larger values inside the outer sphere of a constant radius. Implications of this model in mimicking internal compression leading to the metallic behaviour of the shell-confined hydrogen atoms are discussed.
Analysis and experiment of a vessels shell cover in submarine structure
ZHANG Yu-li; ZENG Guang-wu
2004-01-01
This paper aims to achieve analysis and experiment results that relate to mechanics capability and structural parameter of a special saddle shell of revolution. Theoretically speaking, the saddle shell of revolution consists of a toroidal shell and a spherical shell. The shells simultaneous equations can be solved with harmonious terms. Where, the fundamental equations can be solved by asymptotic exponential perturbation method. The equations of special solution can be solved by Hovozhilovs special solution. This new idea is from a study of some existing solutions of the toroidal shell. The results have been proved by compared with some experimental results. The experiments aims to study the effect caused by change of material parameter, or by change of different geometric dimensions of the saddle shell, which include the change of thickness, the change of radius of shell, and the change of ribs. Finally, the accepted product of the saddle shell were reinforced by a toroidal rib has been submitted.
Turbulent transport coefficients in spherical wedge dynamo simulations of solar-like stars
Warnecke, Jörn; Käpylä, Petri J; Käpylä, Maarit J; Brandenburg, Axel
2016-01-01
We investigate the magnetic field generation in global solar-like convective dynamos in the framework of mean-field theory. We simulate a solar-type star in a wedge-shaped spherical shell, where the interplay between convection and rotation self-consistently drives large-scale dynamo. To analyze the dynamo mechanism we apply the test-field method for azimuthally ($\\phi$) averaged fields to determine the 27 turbulent transport coefficients of the electromotive force, of which 9 are related to the $\\alpha$ effect tensor. This method has previously been used either in simulations in Cartesian coordinates or in the geodynamo context and it is applied here for the first time in simulations of solar-like dynamo action. We find that the $\\phi\\phi$-component of the $\\alpha$ tensor does not follow the profile expected from that of kinetic helicity. Beside the dominant $\\alpha$-$\\Omega$ dynamo, also an $\\alpha^2$ dynamo is locally enhanced. The turbulent pumping velocities significantly alter the effective mean flows a...
Spherical 3D isotropic wavelets
Lanusse, F.; Rassat, A.; Starck, J.-L.
2012-04-01
Context. Future cosmological surveys will provide 3D large scale structure maps with large sky coverage, for which a 3D spherical Fourier-Bessel (SFB) analysis in spherical coordinates is natural. Wavelets are particularly well-suited to the analysis and denoising of cosmological data, but a spherical 3D isotropic wavelet transform does not currently exist to analyse spherical 3D data. Aims: The aim of this paper is to present a new formalism for a spherical 3D isotropic wavelet, i.e. one based on the SFB decomposition of a 3D field and accompany the formalism with a public code to perform wavelet transforms. Methods: We describe a new 3D isotropic spherical wavelet decomposition based on the undecimated wavelet transform (UWT) described in Starck et al. (2006). We also present a new fast discrete spherical Fourier-Bessel transform (DSFBT) based on both a discrete Bessel transform and the HEALPIX angular pixelisation scheme. We test the 3D wavelet transform and as a toy-application, apply a denoising algorithm in wavelet space to the Virgo large box cosmological simulations and find we can successfully remove noise without much loss to the large scale structure. Results: We have described a new spherical 3D isotropic wavelet transform, ideally suited to analyse and denoise future 3D spherical cosmological surveys, which uses a novel DSFBT. We illustrate its potential use for denoising using a toy model. All the algorithms presented in this paper are available for download as a public code called MRS3D at http://jstarck.free.fr/mrs3d.html
Topological Lensing in Spherical Spaces
Gausmann, E; Luminet, Jean Pierre; Uzan, J P; Weeks, J; Gausmann, Evelise; Lehoucq, Roland; Luminet, Jean-Pierre; Uzan, Jean-Philippe; Weeks, Jeffrey
2001-01-01
This article gives the construction and complete classification of all three-dimensional spherical manifolds, and orders them by decreasing volume, in the context of multiconnected universe models with positive spatial curvature. It discusses which spherical topologies are likely to be detectable by crystallographic methods using three-dimensional catalogs of cosmic objects. The expected form of the pair separation histogram is predicted (including the location and height of the spikes) and is compared to computer simulations, showing that this method is stable with respect to observational uncertainties and is well suited for detecting spherical topologies.
Anticavitation and Differential Growth in Elastic Shells
Moulton, Derek E.
2010-07-22
Elastic anticavitation is the phenomenon of a void in an elastic solid collapsing on itself. Under the action of mechanical loading alone typical materials do not admit anticavitation. We study the possibility of anticavitation as a consequence of an imposed differential growth. Working in the geometry of a spherical shell, we seek radial growth functions which cause the shell to deform to a solid sphere. It is shown, surprisingly, that most material models do not admit full anticavitation, even when infinite growth or resorption is imposed at the inner surface of the shell. However, void collapse can occur in a limiting sense when radial and circumferential growth are properly balanced. Growth functions which diverge or vanish at a point arise naturally in a cumulative growth process. © 2010 Springer Science+Business Media B.V.
Stellar rotation effects in polarimetric microlensing
Sajadian, Sedighe
2016-01-01
It is well known that the polarization signal in microlensing events of hot stars is larger than that of main-sequence stars. Most hot stars rapidly rotate around their stellar axes. The stellar rotation makes ellipticity and gravity-darkening effects which break the spherical symmetry of the source shape and the circular symmetry of the source surface brightness respectively. Hence, it causes a net polarization signal for the source star. This polarization signal should be considered in polarimetry microlensing of fast rotating stars. For moderate rotating stars, lensing can magnify or even characterize small polarization signals due to the stellar rotation through polarimetry observations. The gravity-darkening effect due to a rotating source star makes asymmetric perturbations in polarimetry and photometry microlensing curves whose maximum happens when the lens trajectory crosses the projected position of the rotation pole on the sky plane. The stellar ellipticity makes a time shift (i) in the position of ...
Non-Spherical Models of Neutron Stars
Zubairi, O; Romero, A; Mellinger, R; Weber, F; Orsaria, M; Contrera, G
2015-01-01
Non-rotating neutron stars are generally treated in theoretical studies as perfect spheres. Such a treatment, however, may not be correct if strong magnetic fields are present (such as for magnetars) and/or the pressure of the matter in the cores of neutron stars is non-isotropic (e.g., color superconducting). In this paper, we investigate the structure of non-spherical neutron stars in the framework of general relativity. Using a parameterized metric to model non-spherical mass distributions, we first derive a stellar structure equation for deformed neutron stars. Numerical investigations of this model equation show that the gravitational masses of deformed neutron stars depend rather strongly on the degree and type (oblate or prolate) of stellar deformation. In particular, we find that the mass of a neutron star increases with increasing oblateness but decreases with increasing prolateness. If this feature carries over to a full two-dimensional treatment of deformed neutron stars, this opens up the possibil...
Shear-free Null Quasi-Spherical Spacetimes
Bartnik, R A
1997-01-01
The residual gauge freedom within the null quasi-spherical coordinate condition is studied, for spacetimes admitting an {\\em expanding, shear-free} null foliation. The freedom consists of a boost and rotation at each coordinate sphere, corresponding to a specification of inertial frame at each sphere. Explicit formulae involving arbitrary functions of two variables are obtained for the accelerated Minkowski, Schwarzschild, and Robinson-Trautman spacetimes. These examples will be useful as test metrics in numerical relativity.
Greenhouse Effect: Temperature of a Metal Sphere Surrounded by a Glass Shell and Heated by Sunlight
Nguyen, Phuc H.; Matzner, Richard A.
2012-01-01
We study the greenhouse effect on a model satellite consisting of a tungsten sphere surrounded by a thin spherical, concentric glass shell, with a small gap between the sphere and the shell. The system sits in vacuum and is heated by sunlight incident along the "z"-axis. This development is a generalization of the simple treatment of the…
Once again on thin-shell wormholes in scalar-tensor gravity
Bronnikov, Kirill A
2009-01-01
It is proved that all thin-shell wormholes built from two identical regions of vacuum static, spherically symmetric space-times have a negative shell surface energy density in any scalar-tensor theory of gravity with a non-ghost massless scalar field and a non-ghost graviton.
Once again on Thin-Shell Wormholes in Scalar-Tensor Gravity
Bronnikov, Kirill A.; Starobinsky, Alexei A.
It is proved that all thin-shell wormholes built from two identical regions of vacuum static, spherically symmetric spacetimes have a negative shell surface energy density in any scalar-tensor theory of gravity with a non-ghost massless scalar field and a non-ghost graviton.
1968-04-01
loading (e. g. shallow shell theory , Geckeler’s approximation for symmetrically loaded shells, etc.) Although the Shear Deformation and Specialized...interest. Included are the Reissner-Meissner equations, Geckeler’s approximations, shallow - shell theory , Donnell’s theory, and others. A. General Shells of
Woo-Young Jung
2015-04-01
Full Text Available For the solution of geometrically nonlinear analysis of plates and shells, the formulation of a nonlinear nine-node refined first-order shear deformable element-based Lagrangian shell element is presented. Natural co-ordinate-based higher order transverse shear strains are used in present shell element. Using the assumed natural strain method with proper interpolation functions, the present shell element generates neither membrane nor shear locking behavior even when full integration is used in the formulation. Furthermore, a refined first-order shear deformation theory for thin and thick shells, which results in parabolic through-thickness distribution of the transverse shear strains from the formulation based on the third-order shear deformation theory, is proposed. This formulation eliminates the need for shear correction factors in the first-order theory. To avoid difficulties resulting from large increments of the rotations, a scheme of attached reference system is used for the expression of rotations of shell normal. Numerical examples demonstrate that the present element behaves reasonably satisfactorily either for the linear or for geometrically nonlinear analysis of thin and thick plates and shells with large displacement but small strain. Especially, the nonlinear results of slit annular plates with various loads provided the benchmark to test the accuracy of related numerical solutions.
Spherical tokamak development in Brazil
Ludwig, G.O.; Del Bosco, E.; Ferreira, J.G.; Berni, L.A.; Oliveira, R.M.; Andrade, M.C.R.; Shibata, C.S.; Ueda, M.; Barroso, J.J.; Castro, P.J. [Instituto Nacional de Pesquisas Espaciais (INPE), Sao Jose dos Campos, SP (Brazil). Lab. Associado de Plasma; Barbosa, L.F.W. [Universidade do Vale do Paraiba (UNIVAP), Sao Jose dos Campos, SP (Brazil). Faculdade de Engenharia, Arquitetura e Urbanismo; Patire Junior, H. [Instituto Nacional de Pesquisas Espaciais (INPE), Sao Jose dos Campos, SP (Brazil). Div. de Mecanica Espacial e Controle; The high-power microwave sources group
2003-12-01
This paper describes the general characteristics of spherical tokamaks, or spherical tori, with a brief overview of work in this area already performed or in progress at several institutions worldwide. The paper presents also the steps in the development of the ETE (Experimento Tokamak Esferico) project, its research program, technical characteristics and operating conditions as of December, 2002 at the Associated Plasma Laboratory (LAP) of the National Space Research Institute (INPE) in Brazil. (author)
SPHERICAL SHOCK WAVES IN SOLIDS
Differential Equation of Self-Similar Motion; Application of the Theory of Self-Similar Motion to the Problem of Expansion of a Spherical...Self-Similar Solutions of the Problem of Cratering Due to Hypervelocity Impact, and Numerical Integration of the Differential Equation of Spherical...Aluminum, Blast Waves in Other Metals; and Consideration of the Non-Similar Aspects of the Blast Wave Problem ; Experimental Procedure and Results; Singular Point of Ordinary Differential Equations; Numerical Program-Fortran
Polar-direct-drive experiments with contoured-shell targets on OMEGA
Marshall, F. J.; Radha, P. B.; Bonino, M. J.; Delettrez, J. A.; Epstein, R.; Glebov, V. Yu.; Harding, D. R.; Stoeckl, C.; Frenje, J. A.; Gatu Johnson, M.; Séguin, F. H.; Sio, H.; Zylstra, A.; Giraldez, E.
2016-01-01
Polar-driven direct-drive experiments recently performed on the OMEGA Laser System have demonstrated the efficacy of using a target with a contoured shell with varying thickness to improve the symmetry and fusion performance of the implosion. The polar-driven contoured-shell implosions have substantially reduced low mode perturbations compared to polar-driven spherical-shell implosions as diagnosed by x-ray radiographs up to shell stagnation. Fusion yields were increased by more than a factor of ˜2 without increasing the energy of the laser by the use of contoured shells.
Polar-direct-drive experiments with contoured-shell targets on OMEGA
Marshall, F. J.; Radha, P. B.; Bonino, M. J.; Delettrez, J. A.; Epstein, R.; Glebov, V. Yu.; Harding, D. R.; Stoeckl, C. [Laboratory for Laser Energetics, University of Rochester, 250 East River Road, Rochester, New York 14623-1299 (United States); Frenje, J. A.; Gatu Johnson, M.; Séguin, F. H.; Sio, H.; Zylstra, A. [Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States); Giraldez, E. [General Atomics, San Diego, California 92121 (United States)
2016-01-15
Polar-driven direct-drive experiments recently performed on the OMEGA Laser System have demonstrated the efficacy of using a target with a contoured shell with varying thickness to improve the symmetry and fusion performance of the implosion. The polar-driven contoured-shell implosions have substantially reduced low mode perturbations compared to polar-driven spherical-shell implosions as diagnosed by x-ray radiographs up to shell stagnation. Fusion yields were increased by more than a factor of ∼2 without increasing the energy of the laser by the use of contoured shells.
Tuning light concentration inside plasmonic core-shell nanoparticles during laser irradiation
Astafyeva, L. G.; Pustovalov, V. K.; Fritzsche, W.
2017-09-01
Computer modeling was carried out of the intensity distributions of optical (laser) radiation with wavelengths in the range of 180-540 nm concentrated inside spherical two-layered core-shell nanoparticles with the core radii in the range 10-30 nm and shell thicknesses range 5-40 nm during irradiation. Different metals and oxides are used for core and shell materials of nanoparticles. Novel effect of light localizing at the nanoscale inside spherical two-layered core-shell NPs has been established on the base of computer calculations in the frame of the theory of diffraction of electromagnetic radiation on multilayer sphere. Light intensity concentrates in shadow hemisphere of core-shell NPs for the selected values of nanoparticle sizes and radiation wavelengths. These results can be applied in nanophotonics for construction of novel plasmonic devices and photonic components, and for different applications of the core-shell nanoparticles.
Mixing with piecewise isometries on a hemispherical shell
Park, Paul P.; Umbanhowar, Paul B.; Ottino, Julio M.; Lueptow, Richard M.
2016-07-01
We introduce mixing with piecewise isometries (PWIs) on a hemispherical shell, which mimics features of mixing by cutting and shuffling in spherical shells half-filled with granular media. For each PWI, there is an inherent structure on the hemispherical shell known as the exceptional set E, and a particular subset of E, E+, provides insight into how the structure affects mixing. Computer simulations of PWIs are used to visualize mixing and approximations of E+ to demonstrate their connection. While initial conditions of unmixed materials add a layer of complexity, the inherent structure of E+ defines fundamental aspects of mixing by cutting and shuffling.
Interacting shells in AdS spacetime and chaos
Brito, Richard; Cardoso, Vitor; Rocha, Jorge V.
2016-07-01
We study the simplest two-body problem in asymptotically anti-de Sitter spacetime: two, infinitely thin, concentric spherical shells of matter. We include only gravitational interaction between the two shells, but we show that the dynamics of this system is highly nontrivial. We observe prompt collapse to a black hole, delayed collapse and even perpetual oscillatory motion, depending on the initial location of the shells (or their energy content). The system exhibits critical behavior, and we show strong hints that it is also chaotic.
The linear-viscoelastic behaviour of a dispersion of transversely rigid spherical capsules
de Bruin, G.J.; de Bruijn, R.A.; Mellema, J.
1985-01-01
A rheological model has been derived for the linear-viscoelastic behaviour of a dispersion of transversely rigid spherical capsules. The model incorporates finite thickness of the elastic shell of the capsules, anisotropy of the mechanical properties of the interface and finite volume fraction. The
Spherical active coated nano-particles – impact of the electric Hertzian dipole orientation
Arslanagic, Samel; Mostafavi, M.; Malureanu, Radu
2011-01-01
Spherical active coated nano-particles comprised of a silica nano-cylinder core covered with a plasmonic nano-shell are investigated with regard to their near- and far-field properties. The source of excitation is taken to be that of a tangential or a radial electric Hertizan dipole while three...
Shooting for the Stars: The Spherically Confined H-atom Redux.
Glasser, M. L.; Bousquet, Danielle
2003-01-01
Examines an isolated hydrogen atom in its ground state contained within a spherical shell. Demonstrates that by using a mathematical package and a simple shooting process, accurate values of a variety of the properties of compressed hydrogen can be obtained simply and quickly with a few lines of code. (Author/KHR)
Spherical 3D Isotropic Wavelets
Lanusse, F; Starck, J -L
2011-01-01
Future cosmological surveys will provide 3D large scale structure maps with large sky coverage, for which a 3D Spherical Fourier-Bessel (SFB) analysis in is natural. Wavelets are particularly well-suited to the analysis and denoising of cosmological data, but a spherical 3D isotropic wavelet transform does not currently exist to analyse spherical 3D data. The aim of this paper is to present a new formalism for a spherical 3D isotropic wavelet, i.e. one based on the Fourier-Bessel decomposition of a 3D field and accompany the formalism with a public code to perform wavelet transforms. We describe a new 3D isotropic spherical wavelet decomposition based on the undecimated wavelet transform (UWT) described in Starck et al. 2006. We also present a new fast Discrete Spherical Fourier-Bessel Transform (DSFBT) based on both a discrete Bessel Transform and the HEALPIX angular pixelisation scheme. We test the 3D wavelet transform and as a toy-application, apply a denoising algorithm in wavelet space to the Virgo large...
Childs, Peter R N
2010-01-01
Rotating flow is critically important across a wide range of scientific, engineering and product applications, providing design and modeling capability for diverse products such as jet engines, pumps and vacuum cleaners, as well as geophysical flows. Developed over the course of 20 years' research into rotating fluids and associated heat transfer at the University of Sussex Thermo-Fluid Mechanics Research Centre (TFMRC), Rotating Flow is an indispensable reference and resource for all those working within the gas turbine and rotating machinery industries. Traditional fluid and flow dynamics
Salvatore Brischetto
2014-01-01
equilibrium written in orthogonal curvilinear coordinates for the free vibrations of simply supported structures. These equations consider an exact geometry for shells without simplifications. The main novelty is the possibility of a general formulation for different geometries. The equations written in general orthogonal curvilinear coordinates allow the analysis of spherical shell panels and they automatically degenerate into cylindrical shell panel, cylindrical closed shell, and plate cases. Results are proposed for isotropic and orthotropic structures. An exhaustive overview is given of the vibration modes for a number of thickness ratios, imposed wave numbers, geometries, embedded materials, and angles of orthotropy. These results can also be used as reference solutions to validate two-dimensional models for plates and shells in both analytical and numerical form (e.g., closed solutions, finite element method, differential quadrature method, and global collocation method.
Spherical and nonspherical models of primordial black hole formation: exact solutions
Harada, Tomohiro
2015-01-01
We construct spacetimes which provide spherical and nonspherical models of black hole formation in the flat Friedmann-Lemaitre-Robertson-Walker (FLRW) universe with the Lemaitre-Tolman-Bondi solution and the Szekeres quasispherical solution, respectively. These dust solutions may contain both shell-crossing and shell-focusing naked singularities. These singularities can be physically regarded as the breakdown of dust description, where strong pressure gradient force plays a role. We adopt the simultaneous big bang condition to extract a growing mode of adiabatic perturbation in the flat FLRW universe. If the density perturbation has a sufficiently homogeneous central region and a sufficiently sharp transition to the background FLRW universe, its central shell-focusing singularity is globally covered. If the density concentration is {\\it sufficiently large}, there appears no shell-crossing singularity and a black hole is formed. If the density concentration is {\\it not sufficiently large}, there appears shell-...
Differentially-rotating neutron star models with a parametrized rotation profile
Galeazzi, Filippo; Eriguchi, Yoshiharu
2011-01-01
We analyze the impact of the choice rotation law on equilibrium sequences of relativistic differentially-rotating neutron stars in axisymmetry. The maximum allowed mass for each model is strongly affected by the distribution of angular velocity along the radial direction and by the consequent degree of differential rotation. In order to study the wide parameter space implied by the choice of rotation law, we introduce a functional form that generalizes the so called "j-const. law" adopted in all previous work. Using this new rotation law we reproduce the angular velocity profile of differentially-rotating remnants from the coalescence of binary neutron stars in various 3-dimensional dynamical simulations. We compute equilibrium sequences of differentially rotating stars with a polytropic equation of state starting from the spherically symmetric static case. By analyzing the sequences at constant ratio, T/|W|, of rotational kinetic energy to gravitational binding energy, we find that the parameters that best d...
Shell model description of low-lying states in Po and Rn isotopes
Higashiyama, Koji; Yoshinaga, Naotaka
2014-03-01
Nuclear structure of the Po and Rn isotopes is theoretically studied in terms of the spherical shell model with the monopole- and quadrupole-pairing plus quadrupole-quadrupole effective interaction. The experimental energy levels of low-lying states are well reproduced. The shell model results are examined in detail in a pair-truncated shell model. The analysis reveals the alignment of two protons in the 0h9/2 orbital at spin 8.
Shell model description of low-lying states in Po and Rn isotopes
Higashiyama Koji
2014-03-01
Full Text Available Nuclear structure of the Po and Rn isotopes is theoretically studied in terms of the spherical shell model with the monopole- and quadrupole-pairing plus quadrupole-quadrupole effective interaction. The experimental energy levels of low-lying states are well reproduced. The shell model results are examined in detail in a pair-truncated shell model. The analysis reveals the alignment of two protons in the 0h9/2 orbital at spin 8.
Li Ying-Le; Huang Ji-Ying
2006-01-01
The relation between corresponding trigonometric functions in two rotating coordinate systems is presented. The transformation formula for a vector in the two rotating spherical coordinate systems is obtained. The scattering fields for a spherical target irradiated by a plane electromagnetic wave in an arbitrary direction are derived. These fields in a particular case retrogress to those available in the literature. The obtained results have great potential in practical applications.
Stabilization of the resistive shell mode in tokamaks
Fitzpatrick, R.; Aydemir, A.
1995-02-01
The stability of current-driven external-kink modes is investigated in a tokamak plasma surrounded by an external shell of finite electrical conductivity. According to conventional theory, the ideal mode can be stabilized by placing the shell sufficiently close to the plasma, but the non-rotating ``resistive shell mode,`` which grows on the characteristic L/R time of the shell, always persists. It is demonstrated, using both analytic and numerical techniques, that a combination of strong edge plasma rotation and dissipation somewhere inside the plasma is capable of stabilizing the resistive shell mode. This stabilization mechanism does not necessarily depend on toroidicity or presence of resonant surfaces inside the plasma.
Spherical nuclei near the stability line and far from it
Isakov, V. I., E-mail: visakov@thd.pnpi.spb.ru [National Research Centre Kurchatov Institute, Petersburg Nuclear Physics Institute (Russian Federation)
2016-11-15
Results of microscopic and semiphenomenological calculations of features of spherical nuclei lying near the stability line and far from it are presented. The reason why the nuclei being considered are spherical is that they are magic at least in one nucleon sort. The present analysis is performed for Z = 50 and Z = 28 isotopes and for N = 50 isotones, the region extending from neutron-rich to neutron-deficient nuclei being covered. The isotopic dependence of the mean-field spin–orbit nuclear potential is revealed; systematics of energies of levels and probabilities for electromagnetic transitions is examined; and root-mean-square radii of nuclei are calculated, along with the proton- and neutron-density distributions in them. Nuclei in the vicinity of closed shells are considered in detail, and the axial-vector weak coupling constant in nuclei is evaluated. A systematic comparison of the results of calculations with experimental data is performed.
Spherical Coordinate Systems for Streamlining Suited Mobility Analysis
Benson, Elizabeth; Cowley, Matthew S.; Harvill. Lauren; Rajulu, Sudhakar
2014-01-01
When describing human motion, biomechanists generally report joint angles in terms of Euler angle rotation sequences. However, there are known limitations in using this method to describe complex motions such as the shoulder joint during a baseball pitch. Euler angle notation uses a series of three rotations about an axis where each rotation is dependent upon the preceding rotation. As such, the Euler angles need to be regarded as a set to get accurate angle information. Unfortunately, it is often difficult to visualize and understand these complex motion representations. One of our key functions is to help design engineers understand how a human will perform with new designs and all too often traditional use of Euler rotations becomes as much of a hindrance as a help. It is believed that using a spherical coordinate system will allow ABF personnel to more quickly and easily transmit important mobility data to engineers, in a format that is readily understandable and directly translatable to their design efforts. Objectives: The goal of this project is to establish new analysis and visualization techniques to aid in the examination and comprehension of complex motions. Methods: This project consisted of a series of small sub-projects, meant to validate and verify the method before it was implemented in the ABF's data analysis practices. The first stage was a proof of concept, where a mechanical test rig was built and instrumented with an inclinometer, so that its angle from horizontal was known. The test rig was tracked in 3D using an optical motion capture system, and its position and orientation were reported in both Euler and spherical reference systems. The rig was meant to simulate flexion/extension, transverse rotation and abduction/adduction of the human shoulder, but without the variability inherent in human motion. In the second phase of the project, the ABF estimated the error inherent in a spherical coordinate system, and evaluated how this error would
Explosive fragmentation of liquids in spherical geometry
Milne, A.; Longbottom, A.; Frost, D. L.; Loiseau, J.; Goroshin, S.; Petel, O.
2016-07-01
Rapid acceleration of a spherical shell of liquid following central detonation of a high explosive causes the liquid to form fine jets that are similar in appearance to the particle jets that are formed during explosive dispersal of a packed layer of solid particles. Of particular interest is determining the dependence of the scale of the jet-like structures on the physical parameters of the system, including the fluid properties (e.g., density, viscosity, and surface tension) and the ratio of the mass of the liquid to that of the explosive. The present paper presents computational results from a multi-material hydrocode describing the dynamics of the explosive dispersal process. The computations are used to track the overall features of the early stages of dispersal of the liquid layer, including the wave dynamics, and motion of the spall and accretion layers. The results are compared with new experimental results of spherical charges surrounded by a variety of different fluids, including water, glycerol, ethanol, and vegetable oil, which together encompass a significant range of fluid properties. The results show that the number of jet structures is not sensitive to the fluid properties, but primarily dependent on the mass ratio. Above a certain mass ratio of liquid fill-to-explosive burster (F / B), the number of jets is approximately constant and consistent with an empirical model based on the maximum thickness of the accretion layer. For small values of F / B, the number of liquid jets is reduced, in contrast with explosive powder dispersal, where small F / B yields a larger number of particle jets. A hypothetical explanation of these features based on the nucleation of cavitation is explored numerically.
Nonlinear vibration of corrugated shallow shells under Uniform load
YUAN Hong; LIU Ren-huai
2007-01-01
Based on the large deflection dynamic equations of axisymmetric shallow shells of revolution,the nonlinear forced vibration of a corrugated shallow shell under uniform load is investigated.The nonlinear partial differential equations of shallow shell are reduced to the nonlinear integral-differential equations by the method of Green's function. To solve the integral-differential equations,expansion method is used to obtain Green's function.Then the integral-differential equations are reduced to the form with degenerate core by expanding Green's function as series of characteristic function.Therefore,the integral-differential equations become nonlinear ordinary differential equations with regard to time. The amplitude-frequency response under harmonic for is obtained by considering single mode vibration.As a numerical example,forced vibration phenomena of shallow spherical shells with sinusoidal corrugation are studied.The obtained solutions are available for reference to design of corrugated shells
Thin-shell wormholes with a double layer in quadratic F(R) gravity
Eiroa, Ernesto F
2016-01-01
We present a family of spherically symmetric Lorentzian wormholes in quadratic F(R) gravity, with a thin shell of matter corresponding to the throat. At each side of the shell the geometry has a different constant value of the curvature scalar R. The junction conditions determine the equation of state between the pressure and energy density at the throat, where a double layer is also located. We analyze the stability of the configurations under perturbations preserving the spherical symmetry. In particular, we study thin-shell wormholes with mass and charge. We find that there exist values of the parameters for which stable static solutions are possible.
Lekner, John
2008-01-01
Any free-particle wavepacket solution of Schrodinger's equation can be converted by differentiations to wavepackets rotating about the original direction of motion. The angular momentum component along the motion associated with this rotation is an integral multiple of [h-bar]. It is an "intrinsic" angular momentum: independent of origin and…
Research on transmission principle and kinematics analysis for involute spherical gear
PAN Cun-yun; WEN Xi-sen; YANG Kun-yu; XU Xiao-jun; LIU Min; YAO Qi-shui
2006-01-01
A new kind of transmission-type spherical gear called 'ring involute spherical gear mechanism' is introduced.Compared to the famous TRALLFA spherical gear,this new spherical gear has an involute tooth profile,and a ring tooth that is distributed continuously on the surface of the sphere.This allows the gear to overcome two disadvantages of the TRALLFA spherical gear:the drive principle error and the manufacturing difficulty.The new transmission and the formation principle of the tooth's surface of the new spherical gear mechanism are first introduced,then another mechanism,called disk rack,is introduced,which is derived from the spherical gear mechanism when one of the spherical gear's tooth number reaches infinity.To make the research more convenient,every part of the new spherical gear mechanism is named.In the following sections,some problems are discussed,such as the assembly form,the construction characteristics,the correct meshing condition,the continuum transmission condition and so on.Furthermore,the paper deduces the surface formula of the conjugate teeth profiles,which proves that the conjugate teeth profiles is also one of the ringed involute spherical gear.In order to analyze the relationship between two coordinate systems,which is attached respectively to the diving spherical gear and the driven spherical gear,the orientation cosine matrix method is utilized.By series rotational transformation, the kinematics model and inverse kinematics model are deduced.Using the method for calculating the transmission ratio of planet gear train,the relationship of the two oscillating angle between output axis and the bracket is established.Based on the research,the kinematics graphic simulation of spherical gear mechanism and disk rack are made respectively.The results prove correctness of the kinematics model.
Multivalent ion effects on electrostatic stability of virus-like nano-shells
Javidpour, Leili; Lošdorfer Božič, Anže; Naji, Ali; Podgornik, Rudolf
2013-10-01
Electrostatic properties and stability of charged virus-like nano-shells are examined in ionic solutions with monovalent and multivalent ions. A theoretical model based on a thin charged spherical shell and multivalent ions within the "dressed multivalent ion" approximation, yielding their distribution across the shell and the corresponding electrostatic (osmotic) pressure acting on the shell, is compared with extensive implicit Monte-Carlo simulations. It is found to be accurate for positive or low negative surface charge densities of the shell and for sufficiently high (low) monovalent (multivalent) salt concentrations. Phase diagrams involving electrostatic pressure exhibit positive and negative values, corresponding to an outward and an inward facing force on the shell, respectively. This provides an explanation for the high sensitivity of viral shell stability and self-assembly of viral capsid shells on the ionic environment.
Entropy of a self-gravitating electrically charged thin shell and the black hole limit
Lemos, José P S; Zaslavski, Oleg B
2015-01-01
A static self-gravitating electrically charged spherical thin shell embedded in a (3+1)-dimensional spacetime is used to study the thermodynamic and entropic properties of the corresponding spacetime. Inside the shell, the spacetime is flat, outside it is Reissner-Nordstr\\"om, and this establishes the energy density, the pressure, and the electric charge in the shell. Imposing that the shell is at a given local temperature and that the first law of thermodynamics holds on the shell one can find the integrability conditions for the temperature and for the thermodynamic electric potential, the thermodynamic equilibrium states, and the thermodynamic stability conditions. Through the integrability conditions and the first law of thermodynamics an expression for the shell's entropy can be calculated. It is found that the shell's entropy is a function of the shell's gravitational and Cauchy radii alone. A plethora of sets of temperature and electric potential equations of state can be given. One set of equations of...
An effective theory on the light shell
Sajjad, Aqil
We describe work on the construction of an effective field theory on a spherical light shell. The motivation arises from classical electromagnetism: If a collision produces charged particles with zero net charge emerging simultaneously from a point and instantaneously accelerating to the speed of light, then the electromagnetic fields due to these charges lie entirely on a spherical shell expanding at the speed of light. We show that this also applies to classical color radiation from high-energy collisions that produce colored particles. Specifically, the color fields produced in such a process are associated with a non-linear sigma-model on the 2D light shell with specific symmetry-breaking terms. The quantum version of such a picture exhibits asymptotic freedom and should therefore be a useful starting point for a light-shell effective theory for QCD. We start in the simplified context of zero-flavor scalar quantum electrodynamics. Our effective theory has 3 major ingredients: breaking down the fields into soft and hard sectors with the large energy of the hard fields in the radial direction scaled out, a special gauge called light-shell gauge in which the picture simplifies, and a gauge-invariant source defined on a spherical light shell having infinitesimal radius. We match the fields between the effective theory and the full theory, meaning zero-flavor scalar QED. This allows us to compute the amplitude for the production of any number of scalars from the gauge-invariant source. We then find the tree-level amplitude for the emission of a photon using our effective theory and show that our result agrees with the full theory. To calculate loop effects in our effective theory, we need the photon propagator in light-shell gauge. We derive this propagator and use it to calculate the 1-loop correction to the amplitude for the production of a scalar and anti-scalar pair arising from virtual photon effects. This reduces to a pair of purely angular integrals in the
Milking the spherical cow: on aspherical dynamics in spherical coordinates
Pontzen, Andrew; Teyssier, Romain; Governato, Fabio; Gualandris, Alessia; Roth, Nina; Devriendt, Julien
2015-01-01
Galaxies and the dark matter halos that host them are not spherically symmetric, yet spherical symmetry is a helpful simplifying approximation for idealised calculations and analysis of observational data. The assumption leads to an exact conservation of angular momentum for every particle, making the dynamics unrealistic. But how much does that inaccuracy matter in practice for analyses of stellar distribution functions, collisionless relaxation, or dark matter core-creation? We provide a general answer to this question for a wide class of aspherical systems; specifically, we consider distribution functions that are "maximally stable", i.e. that do not evolve at first order when external potentials (which arise from baryons, large scale tidal fields or infalling substructure) are applied. We show that a spherically-symmetric analysis of such systems gives rise to the false conclusion that the density of particles in phase space is ergodic (a function of energy alone). Using this idea we are able to demonstra...
Full light absorption in single arrays of spherical nanoparticles
Ra'di, Y; Kosulnikov, S U; Omelyanovich, M M; Morits, D; Osipov, A V; Simovski, C R; Tretyakov, S A
2015-01-01
In this paper we show that arrays of core-shell nanoparticles function as effective thin absorbers of light. In contrast to known metamaterial absorbers, the introduced absorbers are formed by single planar arrays of spherical inclusions and enable full absorption of light incident on either or both sides of the array. We demonstrate possibilities for realizing different kinds of symmetric absorbers, including resonant, ultra-broadband, angularly selective, and all-angle absorbers. The physical principle behind these designs is explained considering balanced electric and magnetic responses of unit cells. Photovoltaic devices and thermal emitters are the two most important potential applications of the proposed designs.
Casimir Effect in Problems with Spherical Symmetry New Perspectives
Esposito, G; Kirsten, K; Esposito, Giampiero; Kamenshchik, Alexander Yu.; Kirsten, Klaus
1998-01-01
Since Maxwell's theory is a gauge theory, it is quite important to evaluate the corresponding zero-point energy by a careful assignment of boundary conditions on the potential and on the ghost fields. Recent work by the authors has shown that, for a perfectly conducting spherical shell, it is precisely the contribution of longitudinal and normal modes of the potential which enables one to reproduce the result first due to Boyer. For arbitrary values of a gauge parameter, however, the difficult problem remains of having to solve an entangled system of three eigenvalue equations. Such a problem is crucial both for the foundations and for the applications of quantum field theory.
Spherically symmetric steady states of elastic bodies in general relativity
Andréasson, Håkan
2014-01-01
We study the properties of static spherically symmetric elastic bodies in general relativity using both analytical and numerical tools. The materials considered belong to the class of John elastic materials and reduce to perfect fluids when the rigidity parameter is set to zero. We find numerical support that such elastic bodies exist with different possible shapes (balls, single shells and multiple shells) and that their gravitational redshift can be very large ($z\\approx 2.8$) without violating the dominant energy condition. Moreover we show that the elastic body has finite radius even in the case when the constitutive equation of the elastic material is a perturbation of a polytropic fluid without finite radius, thereby concluding that such fluids are structurally unstable within the larger class of elastic matter models under study.
Vassiliev, Dmitri
2017-04-01
We consider an infinite three-dimensional elastic continuum whose material points experience no displacements, only rotations. This framework is a special case of the Cosserat theory of elasticity. Rotations of material points are described mathematically by attaching to each geometric point an orthonormal basis that gives a field of orthonormal bases called the coframe. As the dynamical variables (unknowns) of our theory, we choose the coframe and a density. We write down the general dynamic variational functional for our rotational theory of elasticity, assuming our material to be physically linear but the kinematic model geometrically nonlinear. Allowing geometric nonlinearity is natural when dealing with rotations because rotations in dimension three are inherently nonlinear (rotations about different axes do not commute) and because there is no reason to exclude from our study large rotations such as full turns. The main result of the talk is an explicit construction of a class of time-dependent solutions that we call plane wave solutions; these are travelling waves of rotations. The existence of such explicit closed-form solutions is a non-trivial fact given that our system of Euler-Lagrange equations is highly nonlinear. We also consider a special case of our rotational theory of elasticity which in the stationary setting (harmonic time dependence and arbitrary dependence on spatial coordinates) turns out to be equivalent to a pair of massless Dirac equations. The talk is based on the paper [1]. [1] C.G.Boehmer, R.J.Downes and D.Vassiliev, Rotational elasticity, Quarterly Journal of Mechanics and Applied Mathematics, 2011, vol. 64, p. 415-439. The paper is a heavily revised version of preprint https://arxiv.org/abs/1008.3833
Dobrovolskis, Anthony R.; Cuzzi, Jeffrey N. (Technical Monitor)
1995-01-01
The shape and spin of Neptune's outermost satellite Nereid are still unknown. Ground-based photometry indicates large brightness variations, but different observers report very different lightcurve amplitudes and periods. On the contrary, Voyager 2 images spanning 12 days show no evidence of variations greater than 0.1 mag. The latter suggest either that Nereid is nearly spherical, or that it is rotating slowly. We propose that tides have already despun Nereid's rotation to a period of a few weeks, during the time before the capture of Triton when Nereid was closer to Neptune. Since Nereid reached its present orbit, tides have further despun Nereid to a period on the order of a month. For Nereid's orbital eccentricity of 0.75, tidal evolution ceases when the spin period is still approximately 1/8 of the orbital period. Furthermore, the synchronous resonance becomes quite weak for such high eccentricities, along with other low-order spin orbit commensurabilities. In contrast, high-order resonances become very strong particularly the 6:1, 6.5:1, 7:1, 7.5:1, and 8:1 spin states. If Nereid departs by more than approximately 1% from a sphere, however, these resonances overlap, generating chaos. Our simulations show that Nereid is likely to be in chaotic rotation for any spin period longer than about 2 weeks.
Biomineralisation in Mollusc shells
Dauphin, Y.; Cuif, J. P.; Salomé, M.; Williams, C. T.
2009-04-01
and polysaccharides, with a large range of molecular weights. Proteins are rich in acidic aminoacids (aspartic and glutamic acids). Sugars are usually sulphated, and very acidic. Several hundreds of proteins and sugars are present in the SOM. The compositions of IOM and SOM are characteristic for each layer present in a shell. Topographical relationships of mineral and organic components are visible at different scales of observation. SEM images of etched surfaces display the growth line rhythmicity and concordance between adjacent microstructural units. EPMA maps show similar chemical growth lines in various structures. Whatever the taxa, the average thickness of growth lines is about 2-3 µm, indicating an inner biological rhythm, not dependant on the environmental conditions. Such growth lines are observed in deep sea molluscs at depth where diurnal changes in light and temperature are absent. However, the role of the environment is shown by larger periodicities. Sulphur deserves a special interest, because it is associated with the organic matrices. Electrophoretic data have shown that acidic sulphated sugars are abundant in some layers. XANES analyses confirm these results. New microscopic techniques allow us to obtain images at a submicrometer scale. AFM images show that all the microstructural units (i.e. tablets, prisms etc.), calcite or aragonite, are composed of small sub-spherical granules with a diameter typically of about 50 nm. These granules are surrounded by a thin cortex (about 8 nm) of organic and/or amorphous material, and are organo-composite material as shown by phase images. They do not have crystalline shapes, despite the fact that the units they build are often monocrystalline. Molecular biology and genetic studies confirm that the control of the biomineralisation process is exerted at the scale of the whole organism: the expression of genes encoding major shell matrix proteins clearly indicates a regular separation of calcite and aragonite
Multiple shells in IRC+10216: shell properties
Mauron, N.; Huggins, P. J.
2000-07-01
We report on the properties of the multiple shells in the circumstellar envelope of IRC+10216, using deep optical imaging, including data from the Hubble Space Telescope. The intensity profiles confirm the presence of thin ( ~ 0farcs5 -3'' ec), limb-brightened shells in the envelope, seen in stellar and ambient Galactic light scattered by dust. The shells are spaced at irregular intervals of ~ 5'' ec-20'' ec, corresponding to time scales of 200-800 yr, although intervals as short as ~ 1'' ec (40 yr) are seen close to the star. The location of the main shells shows a good correlation with high-resolution, molecular line maps of the inner envelope, indicating that the dust and gas are well coupled. The shell/intershell density contrast is typically ~ 3, and we find that the shells form the dominant mass component of the circumstellar envelope. The shells exhibit important evolutionary effects: the thickness increases with increasing radius, with an effective dispersion velocity of 0.7 km s-1 and there is evidence for shell interactions. Despite the presence of bipolar structure close to the star, the global shell pattern favors a roughly isotropic, episodic mass loss mechanism, with a range of time scales. Based on observations made with the Canada-France-Hawaii telescope, operated by CNRS, NRCC and UH, and on dearchived observations made with the NASA/ESA Hubble Space Telescope, operated by AURA Inc., under NASA contract NAS5-26555
Pattern formation in rotating fluids
Bühler, Karl
2009-06-01
Flows in nature and technology are often associated with specific structures and pattern. This paper deals with the development and behaviour of such flow pattern. Flow structures are important for the mass, momentum and energy transport. The behaviour of different flow pattern is used by engineers to obtain an efficient mass and energy consumption. Mechanical power is transmitted via the momentum of rotating machine parts. Therefore the physical and mathematical knowledge of these basic concepts is important. Theoretical and experimental investigations of principle experiments are described in the following. We start with the classical problem of the flow between two concentric cylinders where the inner cylinder rotates. Periodic instabilities occur which are called Taylor vortices. The analogy between the cylindrical gap flow, the heat transfer in a horizontal fluid layer exposed to the gravity field and the boundary layer flow along concave boundaries concerning their stability behaviour is addressed. The vortex breakdown phenomenon in a cylinder with rotating cover is also described. A generalization to spherical sectors leads then to investigations with different boundary conditions. The spherical gap flow exhibits interesting phenomena concerning the nonlinear character of the Navier-Stokes equations. Multiple solutions in the nonlinear regime give rise to different routes during the laminar-turbulent transition. The interaction of two rotating spheres results in flow structures with separation and stagnation lines. Experimental results are confirmed by numerical simulations.
Time-dependent correlation buildup in spherical Yukawa balls
Kaehlert, Hanno; Bonitz, Michael
2009-11-01
In recent years it has become possible to create 3D dust crystals in experiments [1], where the particles arrange on concentric spherical shells. Compared to confined ions the interaction between the dust particles is screened, which has been shown to affect the shell occupation of the ground state [2], and the probability of metastable states [3,4]. Here we study dynamical processes in a trapped Yukawa plasma by means of Langevin dynamics simulations, which fully include the Coulomb correlations, the confinement and friction with the neutral gas. By cooling a weakly correlated initial state towards the strong coupling regime, the formation of concentric shells is observed. While in systems with Coulomb interaction the shells clearly emerge at the cluster boundary, they appear almost simultaneously for sufficiently large screening. Monte Carlo simulations are used to show that the sequence, in which radial order is established, is determined by the confinement potential.[4pt] [1] O. Arp, D. Block, A. Piel, and A. Melzer, PRL 93, 165004 (2004)[0pt] [2] H. Baumgartner et al., New J. Phys. 10, 093019 (2008)[0pt] [3] D. Block et al., Phys. Plasmas 15, 040701 (2008)[0pt] [4] H. K"ahlert et al., Phys. Rev. E 78, 036408 (2008)
Jule, L
2015-07-01
Full Text Available We investigate light scattering by core–shell consisting of metal/dielectric composites considering spherical and cylindrical nanoinclusions, within the framework of the conventional Rayleigh approximation. By writing the electric potential...
Zhang, Shuling; Liu, Lingzhi; Guo, Yunliang; Jiang, Zhenhua; Wang, Guibin, E-mail: wgb@jlu.edu.cn
2013-07-15
A new bisphenol monomer, 3-(3,4-dihydroxyphenylimine) pyridine (PYPH), was synthesized via a deoxidization reaction of an amine. A series of novel polyaryletherketone copolymers containing lateral pyridyl groups (PY-PAEKs) based on PYPH, 2,2-di(4-hydroxyphenyl)propane and 4,4′-difluorobenzophenone were prepared by nucleophilic aromatic substitution polycondensation reactions. Furthermore, spherical micelles with rigid PY-PAEKs as the inner cores and flexible polyacrylic acid (PAA) as the outer shells were obtained in a selective solvent (H{sub 2}O) successfully. The formation of the spherical micelles was confirmed by scanning electron and transmission electron microscopy as well as by surface tension measurements. The formation and size of the spherical micelles depended on the weight ratio of PAA/PY-PAEK, the concentration and pH value of the mixed solution containing the PY-PAEK and PAA, and the number of pyridyl groups in the PY-PAEK. The structure of the spherical micelles could be stabilized by a cross-linking reaction between the pyridyl groups of the PY-PAEKs and 1,4-dibromobutane. The diameter of the spherical micelles decreased because of the removal of the PAA shell from the PY-PAEK core after the cross-linking reaction. The resulting stable spherical micelles with rigid backbones did not dissolve in a number of polar solvents and remained unaffected by changes in the pH values. - Graphical abstract: Display Omitted - Highlights: • Polyaryletherketone copolymers containing lateral pyridyl groups were synthesized. • Spherical micelles were prepared using these copolymers and polyacrylic acid. • The copolymers and polyacrylic acid formed the core and the shell of the micelles, respectively. • The obtained micelles were stabilized by a cross-linking reaction. • The cross-linked micelles had rigid backbones, independent of solvents and pH values.
How should spin-weighted spherical functions be defined?
Boyle, Michael
2016-09-01
Spin-weighted spherical functions provide a useful tool for analyzing tensor-valued functions on the sphere. A tensor field can be decomposed into complex-valued functions by taking contractions with tangent vectors on the sphere and the normal to the sphere. These component functions are usually presented as functions on the sphere itself, but this requires an implicit choice of distinguished tangent vectors with which to contract. Thus, we may more accurately say that spin-weighted spherical functions are functions of both a point on the sphere and a choice of frame in the tangent space at that point. The distinction becomes extremely important when transforming the coordinates in which these functions are expressed, because the implicit choice of frame will also transform. Here, it is proposed that spin-weighted spherical functions should be treated as functions on the spin or rotation groups, which simultaneously tracks the point on the sphere and the choice of tangent frame by rotating elements of an orthonormal basis. In practice, the functions simply take a quaternion argument and produce a complex value. This approach more cleanly reflects the geometry involved, and allows for a more elegant description of the behavior of spin-weighted functions. In this form, the spin-weighted spherical harmonics have simple expressions as elements of the Wigner 𝔇 representations, and transformations under rotation are simple. Two variants of the angular-momentum operator are defined directly in terms of the spin group; one is the standard angular-momentum operator L, while the other is shown to be related to the spin-raising operator ð.
Spherical membranes in Matrix theory
Kabat, D; Kabat, Daniel; Taylor, Washington
1998-01-01
We consider membranes of spherical topology in uncompactified Matrix theory. In general for large membranes Matrix theory reproduces the classical membrane dynamics up to 1/N corrections; for certain simple membrane configurations, the equations of motion agree exactly at finite N. We derive a general formula for the one-loop Matrix potential between two finite-sized objects at large separations. Applied to a graviton interacting with a round spherical membrane, we show that the Matrix potential agrees with the naive supergravity potential for large N, but differs at subleading orders in N. The result is quite general: we prove a pair of theorems showing that for large N, after removing the effects of gravitational radiation, the one-loop potential between classical Matrix configurations agrees with the long-distance potential expected from supergravity. As a spherical membrane shrinks, it eventually becomes a black hole. This provides a natural framework to study Schwarzschild black holes in Matrix theory.
Spherical Demons: Fast Surface Registration
Yeo, B.T. Thomas; Sabuncu, Mert; Vercauteren, Tom; Ayache, Nicholas; Fischl, Bruce; Golland, Polina
2009-01-01
We present the fast Spherical Demons algorithm for registering two spherical images. By exploiting spherical vector spline interpolation theory, we show that a large class of regularizers for the modified demons objective function can be efficiently implemented on the sphere using convolution. Based on the one parameter subgroups of diffeomorphisms, the resulting registration is diffeomorphic and fast – registration of two cortical mesh models with more than 100k nodes takes less than 5 minutes, comparable to the fastest surface registration algorithms. Moreover, the accuracy of our method compares favorably to the popular FreeSurfer registration algorithm. We validate the technique in two different settings: (1) parcellation in a set of in-vivo cortical surfaces and (2) Brodmann area localization in ex-vivo cortical surfaces. PMID:18979813
Kurt Hornik
2012-09-01
Full Text Available Clustering text documents is a fundamental task in modern data analysis, requiring approaches which perform well both in terms of solution quality and computational efficiency. Spherical k-means clustering is one approach to address both issues, employing cosine dissimilarities to perform prototype-based partitioning of term weight representations of the documents.This paper presents the theory underlying the standard spherical k-means problem and suitable extensions, and introduces the R extension package skmeans which provides a computational environment for spherical k-means clustering featuring several solvers: a fixed-point and genetic algorithm, and interfaces to two external solvers (CLUTO and Gmeans. Performance of these solvers is investigated by means of a large scale benchmark experiment.
Confirmation of bistable stellar differential rotation profiles
Käpylä, P J; Brandenburg, A
2014-01-01
(abridged) Context: Solar-like differential rotation is characterized by a rapidly rotating equator and slower poles. However, theoretical models and numerical simulations can also result in a slower equator and faster poles when the overall rotation is slow. Aims: We study the critical rotational influence under which differential rotation flips from solar-like (fast equator, slow poles) to an anti-solar one (slow equator, fast poles). We also estimate the non-diffusive ($\\Lambda$-effect) and diffusive (turbulent viscosity) contributions to the Reynolds stress. Methods: We perform three-dimensional numerical simulations of mildly turbulent convection in spherical wedge geometry. We regulate the convective velocities by varying the amount of heat transported by thermal conduction, turbulent diffusion, and resolved convection. Results: Increasing the efficiency of resolved convection leads to a reduction of the rotational influence on the flow and a sharp transition from solar-like to anti-solar differential r...
Wall effects on a rotating sphere
Liu, Qianlong; Prosperetti, Andrea
2010-01-01
The flow induced by a spherical particle spinning in the presence of no-slip planar boundaries is studied by numerical means. In addition to the reference case of an infinite fluid, the situations considered include a sphere rotating near one or two infinite plane walls parallel or perpendicular to
Robustness of oscillatory α2 dynamos in spherical wedges
Cole, E.; Brandenburg, A.; Käpylä, P. J.; Käpylä, M. J.
2016-10-01
Context. Large-scale dynamo simulations are sometimes confined to spherical wedge geometries by imposing artificial boundary conditions at high latitudes. This may lead to spatio-temporal behaviours that are not representative of those in full spherical shells. Aims: We study the connection between spherical wedge and full spherical shell geometries using simple mean-field dynamos. Methods: We solve the equations for one-dimensional time-dependent α2 and α2Ω mean-field dynamos with only latitudinal extent to examine the effects of varying the polar angle θ0 between the latitudinal boundaries and the poles in spherical coordinates. Results: In the case of constant α and ηt profiles, we find oscillatory solutions only with the commonly used perfect conductor boundary condition in a wedge geometry, while for full spheres all boundary conditions produce stationary solutions, indicating that perfect conductor conditions lead to unphysical solutions in such a wedge setup. To search for configurations in which this problem can be alleviated we choose a profile of the turbulent magnetic diffusivity that decreases toward the poles, corresponding to high conductivity there. Oscillatory solutions are now achieved with models extending to the poles, but the magnetic field is strongly concentrated near the poles and the oscillation period is very long. By changing both the turbulent magnetic diffusivity and α profiles so that both effects are more concentrated toward the equator, we see oscillatory dynamos with equatorward drift, shorter cycles, and magnetic fields distributed over a wider range of latitudes. Those profiles thus remove the sensitive and unphysical dependence on θ0. When introducing radial shear, we again see oscillatory dynamos, and the direction of drift follows the Parker-Yoshimura rule. Conclusions: A reduced α effect near the poles with a turbulent diffusivity concentrated toward the equator yields oscillatory dynamos with equatorward migration and
[Spherical crystallization in pharmaceutical technology].
Szabóné, R P; Pintyéné, H K; Kása, P; Erös, I; Hasznosné, N M; Farkas, B
1998-03-01
Physical properties of crystals, such as size, crystal size distribution and morphology, may predetermine the usefulness of crystalline materials in many pharmaceutical application. The above properties can be regulated with the crystallization process. The spherical crystals are suitable for direct tablet-making because of their better flowability and compressibility properties. These crystals can be used in the filling of the capsule. In this work, the spherical crystals such as "single crystal", "poly-crystals" and agglomerates with other excipients are collected from the literature and the experimental results of the authors. A close cooperation between chemists and the pharmaceutical technologists can help for doing steps in this field.
Spherical agglomeration of acetylsalicylic acid
Polowczyk Izabela
2016-01-01
Full Text Available In this paper spherical agglomeration of acetylsalicylic acid was described. In the first step, the system of good and poor solvents as well as bridging liquid was selected. As a result of a preliminary study, ethyl alcohol, water and carbon tetrachloride were used as the good solvent, poor one, and bridging liquid, respectively. Then, the amount of acetylsalicylic acid and the ratio of the solvents as well as the volume of the bridging liquid were examined. In the last step, the agglomeration conditions, such as mixing intensity and time, were investigated. The spherical agglomerates obtained under optimum conditions could be subjected to a tableting process afterwards.
Basketballs as spherical acoustic cavities
Russell, Daniel A.
2010-06-01
The sound field resulting from striking a basketball is found to be rich in frequency content, with over 50 partials in the frequency range of 0-12 kHz. The frequencies are found to closely match theoretical expectations for standing wave patterns inside a spherical cavity. Because of the degenerate nature of the mode shapes, explicit identification of the modes is not possible without internal investigation with a microphone probe. A basketball proves to be an interesting application of a boundary value problem involving spherical coordinates.
Laser-Induced Rotation of Iodine Molecules in Helium Nanodroplets
Shepperson, Benjamin; Sondergaard, Anders A.; Christiansen, Lars
2017-01-01
Rotation of molecules embedded in helium nanodroplets is explored by a combination of fs laser-induced alignment experiments and angulon quasiparticle theory. We demonstrate that at low fluence of the fs alignment pulse, the molecule and its solvation shell can be set into coherent collective...... its helium shell. Our results open novel opportunities for studying nonequilibrium solute-solvent dynamics and quantum thermalization....
Spherical Pendulum Small Oscillations for Slewing Crane Motion
Perig, Alexander V.; Stadnik, Alexander N.; Deriglazov, Alexander I.
2014-01-01
The present paper focuses on the Lagrange mechanics-based description of small oscillations of a spherical pendulum with a uniformly rotating suspension center. The analytical solution of the natural frequencies' problem has been derived for the case of uniform rotation of a crane boom. The payload paths have been found in the inertial reference frame fixed on earth and in the noninertial reference frame, which is connected with the rotating crane boom. The numerical amplitude-frequency characteristics of the relative payload motion have been found. The mechanical interpretation of the terms in Lagrange equations has been outlined. The analytical expression and numerical estimation for cable tension force have been proposed. The numerical computational results, which correlate very accurately with the experimental observations, have been shown. PMID:24526891
The seismicity latitudinal structure, tidal forces, and the Earth rotation.
Levin, Dr; Domanski, Dr; Sasorova, Dr
2012-04-01
The concept about seismicity distribution dependence on the Earth's latitudinal disposition was formed in the last decade. It was stated that seismic activity of the planet is almost absent in the poles and in polar caps of the Earth, clearly expressed maximums in latitudes near 30-45° for both Hemispheres, and the stable minimum near equator reveal. These bimodal distributions are characteristic for a number of seismic events and for released energy as well. Analysis of lunar seismicity demonstrated similar form for the latitudinal distribution of moonquakes. The bimodal form of latitudinal distributions is typical not only for seismicity but also for distribution of hot spots at the Earth and for sunspots initiation regions. The noticeable effects upon earthquake occurrence besides tectonic forces is excited by the tidal forces and by the changes of the Earth figure induced by planet rotation velocity variation. We carried out the assessment of kinetic energy variation caused by deformation of its rotating solid shell. It was demonstrated that the polar radius and average radius of the Earth (under the condition of the equality of the sphere volume and of the geoid volume) are connected by linear relationship where Earth ellipticity plays a dominant role. An equation of ellipsoid of rotation in polar coordinates and equation of free surface of elastic compressible rotating sphere are described by general expression which contains zonal spherical function of latitude of the second-order. This expression has a following unique feature: at the latitude 35°15'52″ the length of radius-vector of geoid coincides with average radius of the Earth, doesn't depend on ellipticity and accordingly on angular velocity of the Earth rotation. At this latitude which received the name "critical latitude", the displacement of radius-vector of geoid is not occurring. Outside of this latitude a variation of angular velocity of the Earth rotation leads to a variation of
Hanasoge, Shravan M.; Duvall, Thomas L., Jr.; Sreenivasan, Katepalli R.
2012-01-01
Convection in the solar interior is thought to comprise structures at a continuum of scales, from large to small. This conclusion emerges from phenomenological studies and numerical simulations though neither covers the proper range of dynamical parameters of solar convection. In the present work, imaging techniques of time-distance helioseismology applied to observational data reveal no long-range order in the convective motion. We conservatively bound the associated velocity magnitudes, as a function of depth and the spherical-harmonic degree l to be 20-100 times weaker than prevailing estimates within the wavenumber band l ux of a solar luminosity outwards? The Sun is seemingly a much faster rotator than previously thought, with advection dominated by Coriolis forces at scales l < 60.
Radio emission from weak spherical shocks in the outskirts of galaxy clusters
Kang, Hyesung
2015-01-01
In Kang (2015) we calculated the acceleration of cosmic-ray electrons and the ensuing radio synchrotron emission at weak spherical shocks that are expected to form in the outskirts of galaxy clusters.There we demonstrated that, at decelerating spherical shocks, the volume integrated spectra of both electrons and radiation deviate significantly from the test-particle power-laws predicted for constant planar shocks, because the shock compression ratio and the flux of injected electrons decrease in time. In this study, we consider spherical blast waves propagating into a constant density core surrounded by an isothermal halo with a decreasing density profile in order to explore how the deceleration rate of the shock speed affects the radio emission from accelerated electrons. The surface brightness profile and the volume-integrated radio spectrum of the model shocks are calculated by assuming a ribbon-like shock surface on a spherical shell and the associated downstream region of relativistic electrons. If the p...
Sheet-like assemblies of spherical particles with point-symmetrical patches.
Mani, Ethayaraja; Sanz, Eduardo; Roy, Soumyajit; Dijkstra, Marjolein; Groenewold, Jan; Kegel, Willem K
2012-04-14
We report a computational study on the spontaneous self-assembly of spherical particles into two-dimensional crystals. The experimental observation of such structures stabilized by spherical objects appeared paradoxical so far. We implement patchy interactions with the patches point-symmetrically (icosahedral and cubic) arranged on the surface of the particle. In these conditions, preference for self-assembly into sheet-like structures is observed. We explain our findings in terms of the inherent symmetry of the patches and the competition between binding energy and vibrational entropy. The simulation results explain why hollow spherical shells observed in some Keplerate-type polyoxometalates (POM) appear. Our results also provide an explanation for the experimentally observed layer-by-layer growth of apoferritin--a quasi-spherical protein.
Finite element analysis of flexible, rotating blades
Mcgee, Oliver G.
1987-01-01
A reference guide that can be used when using the finite element method to approximate the static and dynamic behavior of flexible, rotating blades is given. Important parameters such as twist, sweep, camber, co-planar shell elements, centrifugal loads, and inertia properties are studied. Comparisons are made between NASTRAN elements through published benchmark tests. The main purpose is to summarize blade modeling strategies and to document capabilities and limitations (for flexible, rotating blades) of various NASTRAN elements.
Al Ansari, Mohammed S.
1999-01-01
A simplified method for the design of paraboloid shell footing base on the displacement of the shell's crown where the column axial load is transferred to the footing has been developed. A case study was presented to demonstrate the use of the proposed method and to illustrate its capabilities. The results of the proposed method confirm the ability of the shell model in determining accurate and practical results for the design of paraboloid shell footing. Base on the analytical results of thi...
Shearfree Spherically Symmetric Fluid Models
Sharif, M
2013-01-01
We try to find some exact analytical models of spherically symmetric spacetime of collapsing fluid under shearfree condition. We consider two types of solutions: one is to impose a condition on the mass function while the other is to restrict the pressure. We obtain totally of five exact models, and some of them satisfy the Darmois conditions.
Spherical Pendulum, Actions, and Spin
Richter, Peter H.; Dullin, Holger R.; Waalkens, Holger; Wiersig, Jan
1996-01-01
The classical and quantum mechanics of a spherical pendulum are worked out, including the dynamics of a suspending frame with moment of inertia θ. The presence of two separatrices in the bifurcation diagram of the energy-momentum mapping has its mathematical expression in the hyperelliptic nature of
Kinematic modeling, analysis and test on a quiet spherical pump
Guan, Dong; Wu, Jiu Hui; Jing, Li; Hilton, Harry H.; Lu, Kuan
2016-11-01
In this paper, design and modeling of a novel spherical pump are undertaken. Both sound and vibration properties of the pump are studied experimentally. The working mechanism of the pump is analyzed firstly, and then structural design and kinematic theory are modeled by using two different coordinate systems. Nonlinear kinematic constraint equations are developed using a generalized computational method for spatial kinematic analysis. These equations are solved to yield the displacement, angular velocity and acceleration properties of motion parts with different structural parameters. Sound and vibration characteristics of the spherical pump and traditional solenoid pumps are studied experimentally at different rotating speeds of 1000, 1500, 2000, 2500 and 3000 rev/min. Results indicate that sound pressure levels of the proposed spherical are reduced to 40.7 dB(A), which are 11.1 dB(A) lower than the traditional solenoid pump's 51.8 dB(A) at the rated operating conditions. The sound spectra are analyzed in detail in order to investigate the causes, which are structural pattern and working mechanisms. The proposed spherical pump has many advantages and can be utilized as a substitute for other pumps in some special fields, such as hospital facilities and household appliances.
Acoustic source localization in mixed field using spherical microphone arrays
Huang, Qinghua; Wang, Tong
2014-12-01
Spherical microphone arrays have been used for source localization in three-dimensional space recently. In this paper, a two-stage algorithm is developed to localize mixed far-field and near-field acoustic sources in free-field environment. In the first stage, an array signal model is constructed in the spherical harmonics domain. The recurrent relation of spherical harmonics is independent of far-field and near-field mode strengths. Therefore, it is used to develop spherical estimating signal parameter via rotational invariance technique (ESPRIT)-like approach to estimate directions of arrival (DOAs) for both far-field and near-field sources. In the second stage, based on the estimated DOAs, simple one-dimensional MUSIC spectrum is exploited to distinguish far-field and near-field sources and estimate the ranges of near-field sources. The proposed algorithm can avoid multidimensional search and parameter pairing. Simulation results demonstrate the good performance for localizing far-field sources, or near-field ones, or mixed field sources.
Mendes, Raissa F.P.; Matsas, George E.A.; Lima, William C.C. [Universidade Estadual Paulista Julio de Mesquita Filho (IFT/UNESP), Sao Paulo, SP (Brazil); Vanzella, Daniel A.T. [Universidade de Sao Paulo (IFSC/USP), Sao Carlos, SP (Brazil). Instituto de Fisica
2013-07-01
Full text: Recently, it has been shown that certain space-time evolutions can induce an exponential growth of the vacuum fluctuations of some non-minimally coupled free scalar fields (PRL 104, 161102). This 'vacuum awakening mechanism' may have consequences, in particular, to astrophysics, since the vacuum energy density of the scalar field can grow as large as the nuclear density of neutron stars in few milliseconds once the effect is triggered (PRL 105, 151102). Conversely, the existence of classes of non-minimally coupled scalar fields can be unfavored by the determination of the mass-radius ratio of relativistic stars with known equations of state. For this latter purpose, it is relevant to know if the main features described in the original works are preserved when assumptions such as spherical symmetry or staticity are relaxed. In this presentation, we discuss this mechanism in the context of spheroidal and rotating thin shells, in order to investigate the consequences of deviations from spherical symmetry and staticity on the triggering of the effect. We also make explicit the relation between this vacuum awakening effect and the related classical instability, approached for instance by a quasi-normal mode analysis, and show how quantum fluctuations can be simulated by classical perturbations of a corresponding amplitude. (author)
Schmutzer, E
2005-01-01
In a previous paper we treated within the framework of our Projective Unified Field Theory (Schmutzer 2004, Schmutzer 2005a) the 2-body system (e.g. earth-moon system) with a rotating central body in a rather abstract manner. Here a concrete model of the transfer of angular momentum from the rotating central body to the orbital motion of the whole 2-body system is presented, where particularly the transfer is caused by the inhomogeneous gravitational force of the moon acting on the oceanic waters of the earth, being modeled by a spherical shell around the solid earth. The theory is numerically tested. Key words: transfer of angular momentum from earth to moon, action of the gravitational force of the moon on the waters of the earth.
The similitude research on underwater complex shell-structure based on SEA
WANG San-de; YANG De-sen; SHI Sheng-guo; FANG Er-zheng
2005-01-01
In this paper, the vibration and sound radiation of the underwater complex shell-structure which is the cylindrical shell with hemi-spherical shell on the ends are studied by statistical energy analysis (SEA). The whole shell-structure is divided into the four subsystems, and the SEA physical model and power flow balance equations among these subsystems are established. The similitude relations of input power, coupling loss factor and modal density of the subsystems between the complex shell-structure and its scaled-down model are analyzed. According to the similitude theory and power flow balance equations, when the immerged shell-structures are excited, the similar relations of spatially averaged vibration response and underwater radiating sound power are established for the complex shell-structure and its scaled-down model.
Yolk/shell nanoparticles: classifications, synthesis, properties, and applications.
Purbia, Rahul; Paria, Santanu
2015-12-21
Core/shell nanoparticles were first reported in the early 1990s with a simple spherical core and shell structure, but the area is gradually diversifying in multiple directions such as different shapes, multishells, yolk/shell etc., because of the development of different new properties of the materials, which are useful for several advanced applications. Among different sub-areas of core/shell nanoparticles, yolk/shell nanoparticles (YS NPs) have drawn significant attention in recent years because of their unique properties such as low density, large surface area, ease of interior core functionalization, a good molecular loading capacity in the void space, tunable interstitial void space, and a hollow outer shell. The YS NPs have better properties over simple core/shell or hollow NPs in various fields including biomedical, catalysis, sensors, lithium batteries, adsorbents, DSSCs, microwave absorbers etc., mainly because of the presence of free void space, porous hollow shell, and free core surface. This review presents an extensive classification of YS NPs based on their structures and types of materials, along with synthesis strategies, properties, and applications with which one would be able to draw a complete picture of this area.
Optical properties of hydrogenic impurity in an inhomogeneous infinite spherical quantum dot
Jafari, A.R., E-mail: abed.physic@yahoo.com
2015-01-01
In the present work, using the effective mass approximation, the Schrödinger equation of system is solved in terms of Whittaker functions. The linear and third-order nonlinear optical absorption coefficient (AC) as well as refractive index (RI) changes associated with two intersubbund transitions (1s–2p and 2p–3d) in the case of a GaAs inhomogeneous infinite spherical quantum dot are investigated at different inner radii of shell and shell thicknesses. Regarding this, the optical properties of hydrogenic system are studied by means of compact density approach and dipole approximation. The results show that the system under study is strongly affected by inner radius of shell and shell thickness changes. Also it was found that the transition between orbital with bigger l value shift to higher photon energy region.
Surface corrections to the shell-structure of the moment of inertia
Gorpinchenko, D V; Bartel, J; Blocki, J P
2015-01-01
The moment of inertia for nuclear collective rotations is derived within a semiclassical approach based on the Inglis cranking and the Strutinsky shell-correction methods, improved by surface corrections within the non-perturbative periodic-orbit theory. For adiabatic (statistical-equilibrium) rotations it was approximated by the generalized rigid-body moment of inertia accounting for the shell corrections of the particle density. An improved phase-space trace formula allows to express the shell components of the moment of inertia more accurately in terms of the free-energy shell correction with their ratio evaluated within the extended Thomas-Fermi effective-surface approximation.
Transformation media that rotate electromagnetic fields
Chen, H; Chen, Huanyang
2007-01-01
We suggest a way to manipulate electromagnetic wave by introducing a rotation mapping of coordinates that can be realized by a specific transformation of permittivity and permeability of a shell surrounding an enclosed domain. Inside the enclosed domain, the information from outside will appear as if it comes from a different angle. Numerical simulations were performed to illustrate these properties.
Supersymmetry and eigensurface topology of the spherical quantum pendulum
Schmidt, Burkhard
2014-01-01
We undertook a mutually complementary analytic and computational study of the full-fledged spherical (3D) quantum rotor subject to combined orienting and aligning interactions characterized, respectively, by dimensionless parameters $\\eta$ and $\\zeta$. By making use of supersymmetric quantum mechanics (SUSY QM), we found two sets of conditions under which the problem of a spherical quantum pendulum becomes analytically solvable. These conditions coincide with the loci $\\zeta=\\frac{\\eta^2}{4k^2}$ of the intersections of the eigenenergy surfaces spanned by the $\\eta$ and $\\zeta$ parameters. The integer topological index $k$ is independent of the eigenstate and thus of the projection quantum number $m$. These findings have repercussions for rotational spectra and dynamics of molecules subject to combined permanent and induced dipole interactions.
Thermodynamic Volume Product in Spherically Symmetric and Axisymmetric Spacetime
Pradhan, Parthapratim
2016-01-01
In this Letter, we compute particularly thermodynamic \\emph{volume product, volume sum, volume minus and volume division} for wide variety of spherically symmetric spacetime and axisymmetric spacetime in the frame work of \\emph{extended phase space}. We consider Einstein gravity as well as other than Einstein gravity i.e. \\emph{Ho\\v{r}ava Lifshitz} gravity. We speculate that for spherically symmetric black holes the volume product is mass-independent both in Einstein gravity as well as Ho\\v{r}ava Lifshitz gravity while the other combination is mass-dependent. For axisymmetric black hole spacetime in Einstein gravity all the combination is \\emph{mass-dependent}. There has been no chance to generate any combination of volume product is mass-independent. Interestingly, \\emph{only rotating BTZ black hole} in 3D provides the volume product formula is mass-independent i.e. \\emph{universal} and hence it is quantized.
Surface Plasmon Coupling and Control Using Spherical Cap Structures
Gong, Yu; Joly, Alan G.; Zhang, Xin; El-Khoury, Patrick Z.; Hess, Wayne P.
2017-06-05
Propagating surface plasmons (PSPs) launched from a protruded silver spherical cap structure are investigated using photoemission electron microscopy (PEEM) and finite difference time domain (FDTD) calculations. Our combined experimental and theoretical findings reveal that PSP coupling efficiency is comparable to conventional etched-in plasmonic coupling structures. Additionally, plasmon propagation direction can be varied by a linear rotation of the driving laser polarization. A simple geometric model is proposed in which the plasmon direction selectivity is proportional to the projection of the linear laser polarization on the surface normal. An application for the spherical cap coupler as a gate device is proposed. Overall, our results indicate that protruded cap structures hold great promise as elements in emerging surface plasmon applications.
Enhancement of octupole strength in near spherical nuclei
Robledo, L.M. [Universidad Autonoma de Madrid, Dep. Fisica Teorica, Facultad de Ciencias, Madrid (Spain)
2016-09-15
The validity of the rotational formula used to compute E1 and E3 transition strengths in even-even nuclei is analyzed within the Generator Coordinate Method framework based on mean field wave functions. It turns out that those nuclei with spherical or near spherical shapes the E1 and E3 strengths computed with this formula are strongly underestimated and a sound evaluation of them requires angular-momentum projected wave functions. Results for several isotopic chains with proton number equal to or near magic numbers are analyzed and compared with experimental data. The use of angular-momentum projected wave functions greatly improves the agreement with the scarce experimental data. (orig.)
Method to calculate interior sound field of arbitrary-shaped closed thin shell
WU Jiuhui; CHEN Hualing; HU Xuanli
2001-01-01
The concept of covering-domain means that an arbitrary-shaped closed shell can be approached by a series of closed spherical shells. Based on it, the interior scattering sound field of the arbitrary-shaped closed shell is given. According to the reciprocity theory, the radiating sound field of the elastic surface due to the action of external force is presented. The method presented can also be used to calculate the interior sound fields of arbitraryshaped closed thin shells of which the thickness are either equal or unequal. It is verified to be correct by corresponding test.
Temperature and angular momentum dependence of the quadrupole deformation in sd-shell
P A Ganai; J A Sheikh; I Maqbool; R P Singh
2009-11-01
Temperature and angular momentum dependence of the quadrupole deformation is studied in the middle of the sd-shell for 28Si and 27Si isotopes using the spherical shell model approach. The shell model calculations have been performed using the standard universal sd-shell (USD) interaction and the canonical partition function constructed from the calculated eigensolutions. It is shown that the extracted average quadrupole moments show a transitional behaviour as a function of temperature and the infered transitional temperature is shown to vary with angular momentum. The quadrupole deformation of the individual eigenstate is also analysed.
Dynamics and statics of flexible axially symmetric shallow shells
2006-01-01
Full Text Available In this work, we propose the method for the investigation of stochastic vibrations of deterministic mechanical systems represented by axially symmetric spherical shells. These structure members are widely used as sensitive elements of pressure measuring devices in various branches of measuring and control industry, machine design, and so forth. The proposed method can be easily extended for the investigation of shallow spherical shells, goffer-type membranes, and so on. The so-called charts of control parameters for a shell subjected to a transversal uniformly distributed and local harmonic loading force and resistance moment are constructed. The scenarios of the transition of vibration of shallow-type system into chaotic state are investigated with the use of the theory of differential equations and the theory of nonlinear dynamics. The method of the control of chaotic vibrations of flexible spherical shells subjected to a transversal harmonic load through a synchronized action of either harmonic resistance moment or force is proposed, illustrated, and discussed.
A spectral solution of the magneto-convection equations in spherical geometry
Hollerbach, Rainer
2000-04-01
A fully three-dimensional solution of the magneto-convection equations - the nonlinearly coupled momentum, induction and temperature equations - is presented in spherical geometry. Two very different methods for solving the momentum equation are presented, corresponding to the limits of slow and rapid rotation, and their relative advantages and disadvantages are discussed. The possibility of including a freely rotating, finitely conducting inner core in the solution of the momentum and induction equations is also discussed. Copyright
Wreathes of Magnetism in Rapidly Rotating Suns
Brown, Benjamin P; Brun, Allan Sacha; Toomre, Juri
2009-01-01
When our Sun was young it rotated much more rapidly than now. Observations of young, rapidly rotating stars indicate that many possess substantial magnetic activity and strong axisymmetric magnetic fields. We conduct simulations of dynamo action in rapidly rotating suns with the 3-D MHD anelastic spherical harmonic (ASH) code to explore the complex coupling between rotation, convection and magnetism. Here we study dynamo action realized in the bulk of the convection zone for two systems, rotating at three and five times the current solar rate. We find that substantial organized global-scale magnetic fields are achieved by dynamo action in these systems. Striking wreathes of magnetism are built in the midst of the convection zone, coexisting with the turbulent convection. This is a great surprise, for many solar dynamo theories have suggested that a tachocline of penetration and shear at the base of the convection zone is a crucial ingredient for organized dynamo action, whereas these simulations do not includ...
Developement of Spherical Polyurethane Beads
K. Maeda; H. Ohmori; H. Gyotoku
2005-01-01
@@ 1Results and Discussion We established a new method to produce the spherical polyurethane beads which have narrower distribution of particle size. This narrower distribution was achieved by the polyurethane prepolymer which contains ketimine as a blocked chain-extending agent. Firstly, the prepolymer is dispersed into the aqueous solution containing surfactant. Secondaly, water comes into the inside of prepolymer as oil phase. Thirdly, ketimine is hydrolyzed to amine, and amine reacts with prepolymer immediately to be polyurethane.Our spherical polyurethane beads are very suitable for automotive interior parts especially for instrument panel cover sheet producing under the slush molding method, because of good process ability, excellent durability to the sunlight and mechanical properties at low temperature. See Fig. 1 ,Fig. 2 and Fig. 3 (Page 820).