Cellular neural network to the spherical harmonics approximation of neutron transport equation in x–y geometry

International Nuclear Information System (INIS)

Pirouzmand, Ahmad; Hadad, Kamal

2012-01-01

Highlights: ► This paper describes the solution of time-dependent neutron transport equation. ► We use a novel method based on cellular neural networks (CNNs) coupled with the spherical harmonics method. ► We apply the CNN model to simulate step and ramp perturbation transients in a core. ► The accuracy and capabilities of the CNN model are examined for x–y geometry. - Abstract: In an earlier paper we utilized a novel method using cellular neural networks (CNNs) coupled with spherical harmonics method to solve the steady state neutron transport equation in x–y geometry. Here, the previous work is extended to the study of time-dependent neutron transport equation. To achieve this goal, an equivalent electrical circuit based on a second-order form of time-dependent neutron transport equation and one equivalent group of neutron precursor density is obtained by the CNN method. The CNN model is used to simulate step and ramp perturbation transients in a typical 2D core.

Numerical simulation of direct-drive ICF ignition in spherical geometry

International Nuclear Information System (INIS)

Yu Xiaojin

2006-01-01

The basic condition required for achieving central ignition is producing a hot spot with 10 keV temperature and 0.3 g/cm 2 surface density. Growth of hydrodynamic instability during deceleration phase will destroy the symmetric-drive, reduce the volume of central hot spot and make a harmful effect on ignition. Based on the LARED-S code, considering the thermonuclear reaction and α-particle heating, a numerical study of direct-drive ICF in spherical geometry is made. One-dimensional results agree well with the NIF ignition target designs, and show that the α-particle heating plays an important role in marginal ignition. Two-dimensional results show that the growth of hydrodynamic instability during deceleration phase makes a harmful effect on ignition. (authors)

Contribution to study of interfaces instabilities in plane, cylindrical and spherical geometry

Science.gov (United States)

Toque, Nathalie

1996-12-01

This thesis proposes several experiments of hydrodynamical instabilities which are studied, numerically and theoretically. The experiments are in plane and cylindrical geometry. Their X-ray radiographies show the evolution of an interface between two solid media crossed by a detonation wave. These materials are initially solid. They become liquide under shock wave or stay between two phases, solid and liquid. The numerical study aims at simulating with the codes EAD and Ouranos, the interfaces instabilities which appear in the experiments. The experimental radiographies and the numerical pictures are in quite good agreement. The theoretical study suggests to modelise a spatio-temporal part of the experiments to obtain the quantitative development of perturbations at the interfaces and in the flows. The models are linear and in plane, cylindrical and spherical geometry. They preceed the inoming study of transition between linear and non linear development of instabilities in multifluids flows crossed by shock waves.

Nonlocal Electrostatics in Spherical Geometries Using Eigenfunction Expansions of Boundary-Integral Operators.

Science.gov (United States)

Bardhan, Jaydeep P; Knepley, Matthew G; Brune, Peter

2015-01-01

In this paper, we present an exact, infinite-series solution to Lorentz nonlocal continuum electrostatics for an arbitrary charge distribution in a spherical solute. Our approach relies on two key steps: (1) re-formulating the PDE problem using boundary-integral equations, and (2) diagonalizing the boundary-integral operators using the fact that their eigenfunctions are the surface spherical harmonics. To introduce this uncommon approach for calculations in separable geometries, we first re-derive Kirkwood's classic results for a protein surrounded concentrically by a pure-water ion-exclusion (Stern) layer and then a dilute electrolyte, which is modeled with the linearized Poisson-Boltzmann equation. The eigenfunction-expansion approach provides a computationally efficient way to test some implications of nonlocal models, including estimating the reasonable range of the nonlocal length-scale parameter λ. Our results suggest that nonlocal solvent response may help to reduce the need for very high dielectric constants in calculating pH-dependent protein behavior, though more sophisticated nonlocal models are needed to resolve this question in full. An open-source MATLAB implementation of our approach is freely available online.

Time-dependent integral transport equation kernels, leakage rates and collision rates for plane and spherical geometry

International Nuclear Information System (INIS)

Henderson, D.L.

1987-01-01

Time-dependent integral transport equation flux and current kernels for plane and spherical geometry are derived for homogeneous media. Using the multiple collision formalism, isotropic sources that are delta distributions in time are considered for four different problems. The plane geometry flux kernel is applied to a uniformly distributed source within an infinite medium and to a surface source in a semi-infinite medium. The spherical flux kernel is applied to a point source in an infinite medium and to a point source at the origin of a finite sphere. The time-dependent first-flight leakage rates corresponding to the existing steady state first-flight escape probabilities are computed by the Laplace transform technique assuming a delta distribution source in time. The case of a constant source emitting neutrons over a time interval, Δt, for a spatially uniform source is obtained for a slab and a sphere. Time-dependent first-flight leakage rates are also determined for the general two region spherical medium problem for isotropic sources with a delta distribution in time uniformly distributed throughout both the inner and outer regions. The time-dependent collision rates due to the uncollided neutrons are computed for a slab and a sphere using the time-dependent first-flight leakage rates and the time-dependent continuity equation. The case of a constant source emitting neutrons over a time interval, Δt, is also considered

Particle Trapping and Dropouts in Magnetic Turbulence in a Spherical Geometry

Science.gov (United States)

Tooprakai, P.; Ruffolo, D.; Matthaeus, W. H.; Chuychai, P.

2006-12-01

The observed dropouts of solar energetic particles from impulsive solar events (i.e., the inhomogeneity and sharp gradients in particle density) indicate the partial filamentation of magnetic connection from small regions of the corona to Earth orbit. This can be understood in terms of persistent trapping of field lines due to small- scale topological structures in the solar wind. We further explore how this turbulence structure should be manifest in particle observations, by evaluating particle trajectories obtained from the Newton-Lorentz equations. By adapting a two-component model of turbulence to spherical geometry, we include the adiabatic focusing of particles. The 2D magnetic field is generated by either 1) a 2D fast Fourier transform, a valid approximation over a small angular region, or 2) a spherical harmonic series with ℓ up to 2000. Dropout features at 1 AU are clearly indicated for low-energy particles, but these features are washed out for E >~ 100 MeV. Different time-intensity profiles are found at locations at 1 AU that are distinct with regard to the small-scale topology. Partially supported by the Thailand Research Fund, the Rachadapisek Sompoj Fund of Chulalongkorn University, and NASA Grant NNG05GG83G.

The synchrotron-self-Compton process in spherical geometries. I - Theoretical framework

Science.gov (United States)

Band, D. L.; Grindlay, J. E.

1985-01-01

Both spatial and spectral accuracies are stressed in the present method for the calculation of the synchrotron-self-Compton model in spherical geometries, especially in the partially opaque regime of the synchrotron spectrum of inhomogeneous sources that can span a few frequency decades and contribute a significant portion of the scattered flux. A formalism is developed that permits accurate calculation of incident photon density throughout an optically thin sphere. An approximation to the Klein-Nishina cross section is used to model the effects of variable electron and incident photon cutoffs, as well as the decrease in the cross section at high energies. General results are derived for the case of inhomogeneous sources with power law profiles in both electron density and magnetic field.

Nonlocal Electrostatics in Spherical Geometries Using Eigenfunction Expansions of Boundary-Integral Operators

Science.gov (United States)

Bardhan, Jaydeep P.; Knepley, Matthew G.; Brune, Peter

2015-01-01

In this paper, we present an exact, infinite-series solution to Lorentz nonlocal continuum electrostatics for an arbitrary charge distribution in a spherical solute. Our approach relies on two key steps: (1) re-formulating the PDE problem using boundary-integral equations, and (2) diagonalizing the boundary-integral operators using the fact that their eigenfunctions are the surface spherical harmonics. To introduce this uncommon approach for calculations in separable geometries, we first re-derive Kirkwood’s classic results for a protein surrounded concentrically by a pure-water ion-exclusion (Stern) layer and then a dilute electrolyte, which is modeled with the linearized Poisson–Boltzmann equation. The eigenfunction-expansion approach provides a computationally efficient way to test some implications of nonlocal models, including estimating the reasonable range of the nonlocal length-scale parameter λ. Our results suggest that nonlocal solvent response may help to reduce the need for very high dielectric constants in calculating pH-dependent protein behavior, though more sophisticated nonlocal models are needed to resolve this question in full. An open-source MATLAB implementation of our approach is freely available online. PMID:26273581

Diffusion Coefficient Calculations With Low Order Legendre Polynomial and Chebyshev Polynomial Approximation for the Transport Equation in Spherical Geometry

International Nuclear Information System (INIS)

Yasa, F.; Anli, F.; Guengoer, S.

2007-01-01

We present analytical calculations of spherically symmetric radioactive transfer and neutron transport using a hypothesis of P1 and T1 low order polynomial approximation for diffusion coefficient D. Transport equation in spherical geometry is considered as the pseudo slab equation. The validity of polynomial expansionion in transport theory is investigated through a comparison with classic diffusion theory. It is found that for causes when the fluctuation of the scattering cross section dominates, the quantitative difference between the polynomial approximation and diffusion results was physically acceptable in general

Finite element analysis of the neutron transport equation in spherical geometry

International Nuclear Information System (INIS)

Kim, Yong Ill; Kim, Jong Kyung; Suk, Soo Dong

1992-01-01

The Galerkin formulation of the finite element method is applied to the integral law of the first-order form of the one-group neutron transport equation in one-dimensional spherical geometry. Piecewise linear or quadratic Lagrange polynomials are utilized in the integral law for the angular flux to establish a set of linear algebraic equations. Numerical analyses are performed for the scalar flux distribution in a heterogeneous sphere as well as for the criticality problem in a uniform sphere. For the criticality problems in the uniform sphere, the results of the finite element method, with the use of continuous finite elements in space and angle, are compared with the exact solutions. In the heterogeneous problem, the scalar flux distribution obtained by using discontinuous angular and spatical finite elements is in good agreement with that from the ANISN code calculation. (Author)

Spherical solitons in Earth’S mesosphere plasma

International Nuclear Information System (INIS)

Annou, K.; Annou, R.

2016-01-01

Soliton formation in Earth’s mesosphere plasma is described. Nonlinear acoustic waves in plasmas with two-temperature ions and a variable dust charge where transverse perturbation is dealt with are studied in bounded spherical geometry. Using the perturbation method, a spherical Kadomtsev–Petviashvili equation that describes dust acoustic waves is derived. It is found that the parameters taken into account have significant effects on the properties of nonlinear waves in spherical geometry

SASKTRAN: A spherical geometry radiative transfer code for efficient estimation of limb scattered sunlight

International Nuclear Information System (INIS)

Bourassa, A.E.; Degenstein, D.A.; Llewellyn, E.J.

2008-01-01

The inversion of satellite-based observations of limb scattered sunlight for the retrieval of constituent species requires an efficient and accurate modelling of the measurement. We present the development of the SASKTRAN radiative transfer model for the prediction of limb scatter measurements at optical wavelengths by method of successive orders along rays traced in a spherical atmosphere. The component of the signal due to the first two scattering events of the solar beam is accounted for directly along rays traced in the three-dimensional geometry. Simplifying assumptions in successive scattering orders provide computational optimizations without severely compromising the accuracy of the solution. SASKTRAN is designed for the analysis of measurements from the OSIRIS instrument and the implementation of the algorithm is efficient such that the code is suitable for the inversion of OSIRIS profiles on desktop computers. SASKTRAN total limb radiance profiles generally compare better with Monte-Carlo reference models over a large range of solar conditions than the approximate spherical and plane-parallel models typically used for inversions

Cellular neural network to the spherical harmonics approximation of neutron transport equation in x-y geometry. Part I: Modeling and verification for time-independent solution

International Nuclear Information System (INIS)

Pirouzmand, Ahmad; Hadad, Kamal

2011-01-01

Highlights: → This paper describes the solution of time-independent neutron transport equation. → Using a novel method based on cellular neural networks (CNNs) coupled with P N method. → Utilize the CNN model to simulate spatial scalar flux distribution in steady state. → The accuracy, stability, and capabilities of CNN model are examined in x-y geometry. - Abstract: This paper describes a novel method based on using cellular neural networks (CNN) coupled with spherical harmonics method (P N ) to solve the time-independent neutron transport equation in x-y geometry. To achieve this, an equivalent electrical circuit based on second-order form of neutron transport equation and relevant boundary conditions is obtained using CNN method. We use the CNN model to simulate spatial response of scalar flux distribution in the steady state condition for different order of spherical harmonics approximations. The accuracy, stability, and capabilities of CNN model are examined in 2D Cartesian geometry for fixed source and criticality problems.

Solution of multigroup transport equation in x-y-z geometry by the spherical harmonics method using finite Fourier transformation

International Nuclear Information System (INIS)

Kobayashi, Keisuke; Kikuchi, Hirohiko; Tsutsuguchi, Ken

1993-01-01

A neutron multigroup transport equation in x-y-z geometry is solved by the spherical harmonics method using finite Fourier transformation. Using the first term of the Fourier series for the space variables of spherical harmonics moments, three-point finite difference like equations are derived for x-, y- and z-axis directions, which are more consistent and accurate than those derived using the usual finite difference approximation, and these equations are solved by the iteration method in each axis direction alternatively. A method to find an optimum acceleration factor for this inner iteration is described. It is shown in the numerical examples that the present method gives higher accuracy with less mesh points that the usual finite difference method. (author)

January: IBM 7094 programme for the resolution of cell problems in planar, spherical and cylindrical geometry using the double P{sub n} approximation; Janvier: programme de resolution sur IBM 7094 des problemes de cellules en geometrie plane, spherique et cylindrique dans l'approximation double P{sub n}

Energy Technology Data Exchange (ETDEWEB)

Amouyal, A; Tariel, H [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

1966-07-01

Code name: January 1{sup st} SCEA 011S. 2) Computer: IBM 7094; Programme system: Fortran II, 2{sup nd} version. 3) Nature of the problem: resolution of cell problems with one space variable (planar, spherical and cylindrical geometries) and with one energy group, with isotropic sources in the double P{sub n} approximation (DP 1 and DP 3 approximation in planar and spherical geometries, DP 1 and DP 2 in cylindrical geometry). 4) Method used: the differential equations with limiting conditions are transformed into differential system with initial conditions which are integrated by a separate-step method. 5) Restrictions: number of physical media < 100, number of geometrical regions < 100, number of points < 1000. 6) Physical approximations: limiting conditions for reflection, black body or grey body (restrictions for spherical and cylindrical geometries). The diffusion can include an isotropy term in cylindrical geometry, 2 terms in the other geometries. Taking into account of macroscopic data. 7) Duration: calculation time for a network of 100 points: planar and spherical geometry: double P 1 1 second, D P 3 = 4 seconds; cylindrical geometry: double P 1 2 seconds, D P 2 = 4 seconds. To these times should be added the 3 seconds required for the output. 8) State of the programme under production. (authors) [French] 1) Nom du Code: Janvier 1 SCEA 011S. 2) Calculateur: IBM 7094; Systeme de programmation: Fortran II version-2. 3) Nature du probleme: resolution des problemes de cellule a une variable d'espace (geometries plane, spherique et cylindrique) et un groupe d'energie, avec sources isotropes, dans l'approxirnation double P{sub n} (Approximations DP 1 et DP 3 en geometrie plane et spherique, approximations DP 1 et DP 2 en geometrie cylindrique). Methode employee: les equations differentielles avec conditions aux limites sont transformees en systemes differentiels avec conditions initiales que l'on integre par une methode a pas separes. 5) Restrictions: nombre de

Solution of Einstein's Geometrical Gravitational Field Equations Exterior to Astrophysically Real or Hypothetical Time Varying Distributions of Mass within Regions of Spherical Geometry

Directory of Open Access Journals (Sweden)

Chifu E. N.

2009-07-01

Full Text Available Here, we present a profound and complete analytical solution to Einstein’s gravitational field equations exterior to astrophysically real or hypothetical time varying distribu- tions of mass or pressure within regions of spherical geometry. The single arbitrary function f in our proposed exterior metric tensor and constructed field equations makes our method unique, mathematically less combersome and astrophysically satisfactory. The obtained solution of Einstein’s gravitational field equations tends out to be a gen- eralization of Newton’s gravitational scalar potential exterior to the spherical mass or pressure distribution under consideration

Geometry

CERN Document Server

Prasolov, V V

2015-01-01

This book provides a systematic introduction to various geometries, including Euclidean, affine, projective, spherical, and hyperbolic geometries. Also included is a chapter on infinite-dimensional generalizations of Euclidean and affine geometries. A uniform approach to different geometries, based on Klein's Erlangen Program is suggested, and similarities of various phenomena in all geometries are traced. An important notion of duality of geometric objects is highlighted throughout the book. The authors also include a detailed presentation of the theory of conics and quadrics, including the theory of conics for non-Euclidean geometries. The book contains many beautiful geometric facts and has plenty of problems, most of them with solutions, which nicely supplement the main text. With more than 150 figures illustrating the arguments, the book can be recommended as a textbook for undergraduate and graduate-level courses in geometry.

Geometry of the Universe

International Nuclear Information System (INIS)

Gurevich, L.Eh.; Gliner, Eh.B.

1978-01-01

Problems of investigating the Universe space-time geometry are described on a popular level. Immediate space-time geometries, corresponding to three cosmologic models are considered. Space-time geometry of a closed model is the spherical Riemann geonetry, of an open model - is the Lobachevskij geometry; and of a plane model - is the Euclidean geometry. The Universe real geometry in the contemporary epoch of development is based on the data testifying to the fact that the Universe is infinitely expanding

First results of spherical GEMs

CERN Document Server

Pinto, Serge Duarte; Brock, Ian; Croci, Gabriele; David, Eric; de Oliveira, Rui; Ropelewski, Leszek; van Stenis, Miranda; Taureg, Hans; Villa, Marco

2010-01-01

We developed a method to make GEM foils with a spherical geometry. Tests of this procedure and with the resulting spherical GEMs are presented. Together with a spherical drift electrode, a spherical conversion gap can be formed. This eliminates the parallax error for detection of x-rays, neutrons or UV photons when a gaseous converter is used. This parallax error limits the spatial resolution at wide scattering angles. Besides spherical GEMs, we have developed curved spacers to maintain accurate spacing, and a conical field cage to prevent edge distortion of the radial drift field up to the limit of the angular acceptance of the detector. With these components first tests are done in a setup with a spherical entrance window but a planar readout structure; results will be presented and discussed. A flat readout structure poses difficulties, however. Therefore we will show advanced plans to make a prototype of an entirely spherical double-GEM detector, including a spherical 2D readout structure. This detector w...

Self-similar solutions for implosion and reflection of coalesced shocks in a plasma : spherical and cylindrical geometries

International Nuclear Information System (INIS)

Chavda, L.K.

1978-01-01

Approximate analytic solutions to the self-similar equations of gas dynamics for a plasma, treated as an ideal gas with specific heat ratio γ=5/3 are obtained for the implosion and subsequent reflection of various types of shock sequences in spherical and cylindrical geometries. This is based on the lowest-order polynomial approximation in the reduced fluid velocity, for a suitable nonlinear function of the sound velocity and the fluid velocity. However, the method developed here is powerful enough to be extended analytically to higher order polynomial approximations, to obtain successive approximations to the exact self-similar solutions. Also obtained, for the first time, are exact asymptotic solutions, in analytic form, for the reflected shocks. Criteria are given that may enable one to make a choice between the two geometries for maximising compression or temperature of the gas. These solutions should be useful in the study of inertial confinement of a plasma. (author)

ONETRAN, 1-D Transport in Planar, Cylindrical, Spherical Geometry for Homogeneous, Inhomogeneous Problem, Anisotropic Source

International Nuclear Information System (INIS)

1982-01-01

1 - Description of problem or function: ONETRAN solves the one- dimensional multigroup transport equation in plane, cylindrical, spherical, and two-angle plane geometries. Both regular and adjoint, inhomogeneous and homogeneous (K-eff and eigenvalue searches) problems subject to vacuum, reflective, periodic, white, albedo or inhomogeneous boundary flux conditions are solved. General anisotropic scattering is allowed and anisotropic inhomogeneous sources are permitted. 2 - Method of solution: The discrete ordinates approximation for the angular variable is used with the diamond (central) difference approximation for the angular extrapolation in curved geometries. A linear discontinuous finite element representation for the angular flux in each spatial mesh cell is used. Negative fluxes are eliminated by a local set-to-zero and correct algorithm. Standard inner (within-group) iteration cycles are accelerated by system re-balance, coarse mesh re-balance, or Chebyshev acceleration. Outer iteration cycles are accelerated by coarse-mesh re-balance. 3 - Restrictions on the complexity of the problem: Variable dimensioning is used so that any combination of problem parameters leading to a container array less than MAXCOR can be accommodated. On CDC machines MAXCOR can be about 25 000 words and peripheral storage is used for most group-dependent data

MODELING MAGNETIC FIELD STRUCTURE OF A SOLAR ACTIVE REGION CORONA USING NONLINEAR FORCE-FREE FIELDS IN SPHERICAL GEOMETRY

International Nuclear Information System (INIS)

Guo, Y.; Ding, M. D.; Liu, Y.; Sun, X. D.; DeRosa, M. L.; Wiegelmann, T.

2012-01-01

We test a nonlinear force-free field (NLFFF) optimization code in spherical geometry using an analytical solution from Low and Lou. Several tests are run, ranging from idealized cases where exact vector field data are provided on all boundaries, to cases where noisy vector data are provided on only the lower boundary (approximating the solar problem). Analytical tests also show that the NLFFF code in the spherical geometry performs better than that in the Cartesian one when the field of view of the bottom boundary is large, say, 20° × 20°. Additionally, we apply the NLFFF model to an active region observed by the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory (SDO) both before and after an M8.7 flare. For each observation time, we initialize the models using potential field source surface (PFSS) extrapolations based on either a synoptic chart or a flux-dispersal model, and compare the resulting NLFFF models. The results show that NLFFF extrapolations using the flux-dispersal model as the boundary condition have slightly lower, therefore better, force-free, and divergence-free metrics, and contain larger free magnetic energy. By comparing the extrapolated magnetic field lines with the extreme ultraviolet (EUV) observations by the Atmospheric Imaging Assembly on board SDO, we find that the NLFFF performs better than the PFSS not only for the core field of the flare productive region, but also for large EUV loops higher than 50 Mm.

Local Instruction Theory (LIT) on spherical geometry for enhancement students’ strategic competence

Science.gov (United States)

Nuraida, I.; Kusumah, Y. S.; Kartasasmita, B. G.

2018-03-01

This research focused on the analysis of the materials spherical geometry of the wake in an attempt to enhancemet the strategic competence of students and to produce learning trajectory. That is because the materials that are used less catchy concept gives students. Learning materials with Local Instructional Theory (LIT) can enhancemet the strategic competence of the students. This research aims to study the difference of achievement and improving the strategic competence of the students who got the Realistics Mathematics Education (RME) and (LIT) with conventional learning. This research is the Design Research with two cycles. This research has three phases i.e. 1) preparing for the experiment/preliminary; 2) teaching eksperiment; 3) retrospective analysis. The population of the research was the whole IX group junior high school 1 Rajapolah with samples of IXg and IXj group. Results of the analysis of the data shows that students based on Mathematical Prior Knowledge (MPK) acquire learning achievement have RME and LIT and enhancement strategic competence of the mathematical that are higher than those of students who obtain the conventional learning.

Determination of a basic set of Eigen-functions and of the corresponding norm in the case of the one-velocity integral differential Boltzmann equation in spherical geometry

International Nuclear Information System (INIS)

Lafore, P.

1965-01-01

The object of the present work is to draw up a basic set of orthogonal eigenfunctions; resolution of the one-velocity integral-differential Boltzmann equation; this in the case of a spherical geometry system. (author) [fr

Aircraft navigation and surveillance analysis for a spherical earth

Science.gov (United States)

2014-10-01

This memorandum addresses a fundamental function in surveillance and navigation analysis : quantifying the geometry of two or more locations relative to each other and to a spherical earth. Here, geometry refers to: (a) points (idealized lo...

TIMEX, 1-D Time-Dependent Multigroup Transport Theory with Delayed Neutron, Planar Cylindrical and Spherical Geometry

International Nuclear Information System (INIS)

Hill, T. R.; Reed, W. H.

1980-01-01

1 - Description of problem or function: TIMEX solves the time- dependent, one-dimensional multigroup transport equation with delayed neutrons in plane, cylindrical, spherical, and two-angle plane geometries. Both regular and adjoint, inhomogeneous and homogeneous problems subject to vacuum, reflective, periodic, white, albedo or inhomogeneous boundary flux conditions are solved. General anisotropic scattering is allowed and anisotropic inhomogeneous sources are permitted. 2 - Method of solution: The discrete ordinates approximation for the angular variable is used with the diamond (central) difference approximation for the angular extrapolation in curved geometries. A linear discontinuous finite element representation for the angular flux in each spatial mesh cell is used. Negative fluxes are eliminated by a local set-to-zero and correct algorithm. The time variable is differenced by an explicit technique that is unconditionally stable so that arbitrarily large time-steps can be taken. Two acceleration methods, exponential extrapolation and re-balance, are utilized to improve the accuracy of the time differencing scheme. 3 - Restrictions on the complexity of the problem: Variable dimensioning is used so that any combination of problem parameters leading to a container array less than MAXCOR can be accommodated. In addition, the CDC version permits the use of extended core storage less than MAXECS

Rayleigh-Taylor instability in multi-structured spherical targets

International Nuclear Information System (INIS)

Gupta, N.K.; Lawande, S.V.

1986-01-01

An eigenvalue equation for the exponential growth rate of the Rayleigh-Taylor instability is derived in spherical geometry. The free surface and jump boundary conditions are obtained from the eigenvalue equation. The eigenvalue equation is solved in the cases where the initial fluid density profile has a step function or exponential variation in space and analytical formulae for growth rate of the instability are obtained. The solutions for the step function are generalized for any number N of spherical zones forming an arbitrary fluid density profile. The results of the numerical calculations for N spherical zones are compared with the exact analytical results for exponential fluid density profile with N=10 and a good agreement is observed. The formalism is further used to study the effects of density gradients on Rayleigh-Taylor instability in spherical geometry. Also analytical formulae are presented for a particular case of N=3 and shell targets. The formalism developed here can be used to study the growth of the instability in present day multi-structured shell targets. (author)

Axi-symmetric patterns of active polar filaments on spherical and composite surfaces

Science.gov (United States)

Srivastava, Pragya; Rao, Madan

2014-03-01

Experiments performed on Fission Yeast cells of cylindrical and spherical shapes, rod-shaped bacteria and reconstituted cylindrical liposomes suggest the influence of cell geometry on patterning of cortical actin. A theoretical model based on active hydrodynamic description of cortical actin that includes curvature-orientation coupling predicts spontaneous formation of acto-myosin rings, cables and nodes on cylindrical and spherical geometries [P. Srivastava et al, PRL 110, 168104(2013)]. Stability and dynamics of these patterns is also affected by the cellular shape and has been observed in experiments performed on Fission Yeast cells of spherical shape. Motivated by this, we study the stability and dynamics of axi-symmetric patterns of active polar filaments on the surfaces of spherical, saddle shaped and conical geometry and classify the stable steady state patterns on these surfaces. Based on the analysis of the fluorescence images of Myosin-II during ring slippage we propose a simple mechanical model for ring-sliding based on force balance and make quantitative comparison with the experiments performed on Fission Yeast cells. NSF Grant DMR-1004789 and Syracuse Soft Matter Program.

MISR Dark Water aerosol retrievals: operational algorithm sensitivity to particle non-sphericity

Directory of Open Access Journals (Sweden)

O. V. Kalashnikova

2013-08-01

Full Text Available The aim of this study is to theoretically investigate the sensitivity of the Multi-angle Imaging SpectroRadiometer (MISR operational (version 22 Dark Water retrieval algorithm to aerosol non-sphericity over the global oceans under actual observing conditions, accounting for current algorithm assumptions. Non-spherical (dust aerosol models, which were introduced in version 16 of the MISR aerosol product, improved the quality and coverage of retrievals in dusty regions. Due to the sensitivity of the retrieval to the presence of non-spherical aerosols, the MISR aerosol product has been successfully used to track the location and evolution of mineral dust plumes from the Sahara across the Atlantic, for example. However, the MISR global non-spherical aerosol optical depth (AOD fraction product has been found to have several climatological artifacts superimposed on valid detections of mineral dust, including high non-spherical fraction in the Southern Ocean and seasonally variable bands of high non-sphericity. In this paper we introduce a formal approach to examine the ability of the operational MISR Dark Water algorithm to distinguish among various spherical and non-spherical particles as a function of the variable MISR viewing geometry. We demonstrate the following under the criteria currently implemented: (1 Dark Water retrieval sensitivity to particle non-sphericity decreases for AOD below about 0.1 primarily due to an unnecessarily large lower bound imposed on the uncertainty in MISR observations at low light levels, and improves when this lower bound is removed; (2 Dark Water retrievals are able to distinguish between the spherical and non-spherical particles currently used for all MISR viewing geometries when the AOD exceeds 0.1; (3 the sensitivity of the MISR retrievals to aerosol non-sphericity varies in a complex way that depends on the sampling of the scattering phase function and the contribution from multiple scattering; and (4 non-sphericity

Non-euclidean geometry

CERN Document Server

Coxeter, HSM

1965-01-01

This textbook introduces non-Euclidean geometry, and the third edition adds a new chapter, including a description of the two families of 'mid-lines' between two given lines and an elementary derivation of the basic formulae of spherical trigonometry and hyperbolic trigonometry, and other new material.

Geometric Monte Carlo and black Janus geometries

Energy Technology Data Exchange (ETDEWEB)

Bak, Dongsu, E-mail: dsbak@uos.ac.kr [Physics Department, University of Seoul, Seoul 02504 (Korea, Republic of); B.W. Lee Center for Fields, Gravity & Strings, Institute for Basic Sciences, Daejeon 34047 (Korea, Republic of); Kim, Chanju, E-mail: cjkim@ewha.ac.kr [Department of Physics, Ewha Womans University, Seoul 03760 (Korea, Republic of); Kim, Kyung Kiu, E-mail: kimkyungkiu@gmail.com [Department of Physics, Sejong University, Seoul 05006 (Korea, Republic of); Department of Physics, College of Science, Yonsei University, Seoul 03722 (Korea, Republic of); Min, Hyunsoo, E-mail: hsmin@uos.ac.kr [Physics Department, University of Seoul, Seoul 02504 (Korea, Republic of); Song, Jeong-Pil, E-mail: jeong_pil_song@brown.edu [Department of Chemistry, Brown University, Providence, RI 02912 (United States)

2017-04-10

We describe an application of the Monte Carlo method to the Janus deformation of the black brane background. We present numerical results for three and five dimensional black Janus geometries with planar and spherical interfaces. In particular, we argue that the 5D geometry with a spherical interface has an application in understanding the finite temperature bag-like QCD model via the AdS/CFT correspondence. The accuracy and convergence of the algorithm are evaluated with respect to the grid spacing. The systematic errors of the method are determined using an exact solution of 3D black Janus. This numerical approach for solving linear problems is unaffected initial guess of a trial solution and can handle an arbitrary geometry under various boundary conditions in the presence of source fields.

Parallelization of a spherical Sn transport theory algorithm

International Nuclear Information System (INIS)

Haghighat, A.

1989-01-01

The work described in this paper derives a parallel algorithm for an R-dependent spherical S N transport theory algorithm and studies its performance by testing different sample problems. The S N transport method is one of the most accurate techniques used to solve the linear Boltzmann equation. Several studies have been done on the vectorization of the S N algorithms; however, very few studies have been performed on the parallelization of this algorithm. Weinke and Hommoto have looked at the parallel processing of the different energy groups, and Azmy recently studied the parallel processing of the inner iterations of an X-Y S N nodal transport theory method. Both studies have reported very encouraging results, which have prompted us to look at the parallel processing of an R-dependent S N spherical geometry algorithm. This geometry was chosen because, in spite of its simplicity, it contains the complications of the curvilinear geometries (i.e., redistribution of neutrons over the discretized angular bins)

Geometric scalar theory of gravity beyond spherical symmetry

Science.gov (United States)

Moschella, U.; Novello, M.

2017-04-01

We construct several exact solutions for a recently proposed geometric scalar theory of gravity. We focus on a class of axisymmetric geometries and a big-bang-like geometry and discuss their Lorentzian character. The axisymmetric solutions are parametrized by an integer angular momentum l . The l =0 (spherical) case gives rise to the Schwarzschild geometry. The other solutions have naked singular surfaces. While not a priori obvious, all the solutions that we present here are globally Lorentzian. The Lorentzian signature appears to be a robust property of the disformal geometries solving the vacuum geometric scalar theory of gravity equations.

Radiation transport simulation of the Martian GCR surface flux and dose estimation using spherical geometry in PHITS compared to MSL-RAD measurements.

Science.gov (United States)

Flores-McLaughlin, John

2017-08-01

Planetary bodies and spacecraft are predominantly exposed to isotropic radiation environments that are subject to transport and interaction in various material compositions and geometries. Specifically, the Martian surface radiation environment is composed of galactic cosmic radiation, secondary particles produced by their interaction with the Martian atmosphere, albedo particles from the Martian regolith and occasional solar particle events. Despite this complex physical environment with potentially significant locational and geometric dependencies, computational resources often limit radiation environment calculations to a one-dimensional or slab geometry specification. To better account for Martian geometry, spherical volumes with respective Martian material densities are adopted in this model. This physical description is modeled with the PHITS radiation transport code and compared to a portion of measurements from the Radiation Assessment Detector of the Mars Science Laboratory. Particle spectra measured between 15 November 2015 and 15 January 2016 and PHITS model results calculated for this time period are compared. Results indicate good agreement between simulated dose rates, proton, neutron and gamma spectra. This work was originally presented at the 1st Mars Space Radiation Modeling Workshop held in 2016 in Boulder, CO. Copyright © 2017. Published by Elsevier Ltd.

Modeling mantle convection in the spherical annulus

Science.gov (United States)

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.

Optical geometry across the horizon

International Nuclear Information System (INIS)

Jonsson, Rickard

2006-01-01

In a recent paper (Jonsson and Westman 2006 Class. Quantum Grav. 23 61), a generalization of optical geometry, assuming a non-shearing reference congruence, is discussed. Here we illustrate that this formalism can be applied to (a finite four-volume) of any spherically symmetric spacetime. In particular we apply the formalism, using a non-static reference congruence, to do optical geometry across the horizon of a static black hole. While the resulting geometry in principle is time dependent, we can choose the reference congruence in such a manner that an embedding of the geometry always looks the same. Relative to the embedded geometry the reference points are then moving. We discuss the motion of photons, inertial forces and gyroscope precession in this framework

Numerical simulation of high-energy-electron gerated field in dielectrics of various geometries. Final report, June 1, 1979-May 15, 1980

International Nuclear Information System (INIS)

Yee, K.S.

1980-01-01

It has been observed that the exposure of dielectrics to electron beams can produce an electric field of sufficient magnitude to cause dielectric breakdown. The present investigations will be directed to calculate the electric field intensity in dielectrics under spherical and cylindrical geometries. In the spherical geometry the method of multiple images renders the full numerical calculation unnecessary, whereas in a finite length cylindrical geometry the full numerical calculation seems to be inevitable. A description and results of the spherical geometry are presented and a more detailed presentation of the finite cylinder geometry is given

Sub-critical pulsed neutron experiments with uranyl nitrate solutions in spherical geometry

International Nuclear Information System (INIS)

Gurin, Victor N.; Ryazanov, Boris G.; Sviridov, Victor I.; Volnistov, Vladimir V.

2003-01-01

The pulse source method is used to study homogeneous solution assemblies. Three sets of sub-critical pulse experiments with spherical tanks filled with water solution of uranyl nitrate (90% enrichment) were carried out at the RF-GS facility, Obninsk, Russia. Seven spherical tanks with the volume within the range of 1.29 L to 19.8 L were used in the experiments. Three uranium concentrations were studied, i.e. 20.7, 29.6 and 37.5 g/L. The sub-critical experiments were analyzed with the MCNP 4A code based on the Monte-Carlo method, and with ENDF/B-V library. (author)

Theory and applications of spherical microphone array processing

CERN Document Server

Jarrett, Daniel P; Naylor, Patrick A

2017-01-01

This book presents the signal processing algorithms that have been developed to process the signals acquired by a spherical microphone array. Spherical microphone arrays can be used to capture the sound field in three dimensions and have received significant interest from researchers and audio engineers. Algorithms for spherical array processing are different to corresponding algorithms already known in the literature of linear and planar arrays because the spherical geometry can be exploited to great beneficial effect. The authors aim to advance the field of spherical array processing by helping those new to the field to study it efficiently and from a single source, as well as by offering a way for more experienced researchers and engineers to consolidate their understanding, adding either or both of breadth and depth. The level of the presentation corresponds to graduate studies at MSc and PhD level. This book begins with a presentation of some of the essential mathematical and physical theory relevant to ...

An Angular Leakage Correction for Modeling a Hemisphere, Using One-Dimensional Spherical Coordinates

International Nuclear Information System (INIS)

Schwinkendorf, K.N.; Eberle, C.S.

2003-01-01

A radially dependent, angular leakage correction was applied to a one-dimensional, multigroup neutron diffusion theory computer code to accurately model hemispherical geometry. This method allows the analyst to model hemispherical geometry, important in nuclear criticality safety analyses, with one-dimensional computer codes, which execute very quickly. Rapid turnaround times for scoping studies thus may be realized. This method uses an approach analogous to an axial leakage correction in a one-dimensional cylinder calculation. The two-dimensional Laplace operator was preserved in spherical geometry using a leakage correction proportional to 1/r 2 , which was folded into the one-dimensional spherical calculation on a mesh-by-mesh basis. Hemispherical geometry is of interest to criticality safety because of its similarity to piles of spilled fissile material and accumulations of fissile material in process containers. A hemisphere also provides a more realistic calculational model for spilled fissile material than does a sphere

Detection based on rainbow refractometry of droplet sphericity in liquid-liquid systems.

Science.gov (United States)

Lohner, H; Lehmann, P; Bauckhage, K

1999-03-01

The shape of droplets in liquid-liquid systems influences their mass and momentum transfer processes. The deviation from sphericity of rising droplets in liquid-liquid systems was investigated for different droplet sizes. Rainbow refractometry permits one to test, in this case, whether the use of laser-optical particle sizing will be correct or faulty. Since the assumption of spherical particle geometry is a general basis of laser-optical particle-sizing techniques such as rainbow refractometry or phase Doppler anemometry, deviation from the spherical shape results in a measuring error. A sphericity check based on rainbow refractometry is introduced.

Integrals of products of spherical functions

International Nuclear Information System (INIS)

Veverka, O.

1975-01-01

Various branches of mathematical physics use integral formulas of the products of spherical functions. In quantum mechanics and in transport theory the integrals ∫sub((4π))dΩ vectorYsub(s)sup(t)(Ω vector)Ysub(l)sup(k)(Ω vector)Ysub(n)sup(m)(Ω vector), ∫sub(-1)sup(1)dμPsub(s)sup(t)(μ)Psub(l)sup(k)(μ)Psub(n)sup(m)(μ), ∫sub(-1)sup(1)dμPsub(s)(μ)Psub(l)(μ)Psub(n)(μ) are generally applied, where Ysub(α)sup(β)(Ω vector) are spherical harmonics, Psub(α)sup(β)(μ) are associated Legendre functions, and Psub(α)(μ) are Legendre polynomials. In the paper, the general procedure of calculating the integrals of the products of any combination of spherical functions is given. The procedure is referred to in a report on the boundary conditions for the cylindrical geometry in neutron transport theory for both the outer and inner cylindrical boundaries. (author)

Integral Transport Theory in One-dimensional Geometries

Energy Technology Data Exchange (ETDEWEB)

Carlvik, I

1966-06-15

A method called DIT (Discrete Integral Transport) has been developed for the numerical solution of the transport equation in one-dimensional systems. The characteristic features of the method are Gaussian integration over the coordinate as described by Kobayashi and Nishihara, and a particular scheme for the calculation of matrix elements in annular and spherical geometry that has been used for collision probabilities in earlier Flurig programmes. The paper gives a general theory including such things as anisotropic scattering and multi-pole fluxes, and it gives a brief description of the Flurig scheme. Annular geometry is treated in some detail, and corresponding formulae are given for spherical and plane geometry. There are many similarities between DIT and the method of collision probabilities. DIT is in many cases faster, because for a certain accuracy in the fluxes DIT often needs fewer space points than the method of collision probabilities needs regions. Several computer codes using DIT, both one-group and multigroup, have been written. It is anticipated that experience gained in calculations with these codes will be reported in another paper.

Transient neutrons flux behaviour in a spherical reactor core

International Nuclear Information System (INIS)

Souza, A.W.A. de.

1978-11-01

This work studies the transient neutron flux in a fast reactor of spherical geometry. The burning of U 235 nuclei is equated and two kinds of reflector were studied. The numeric solutions are then compared with the results for those reflectors. (author) [pt

Strongly Localized Image States of Spherical Graphitic Particles

Directory of Open Access Journals (Sweden)

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 more realistic estimate of the variances and systematic errors in spherical harmonic geomagnetic field models

DEFF Research Database (Denmark)

Lowes, F.J.; Olsen, Nils

2004-01-01

Most modern spherical harmonic geomagnetic models based on satellite data include estimates of the variances of the spherical harmonic coefficients of the model; these estimates are based on the geometry of the data and the fitting functions, and on the magnitude of the residuals. However...

Using satellite technology (global positioning system) to teach the spherical polar coordinate system

International Nuclear Information System (INIS)

O'Brien, William P Jr

2003-01-01

Students discover the equivalence between plausible geographic variables (co-latitude and longitude) of the Earth and less-familiar geometric variables (polar and azimuthal angles) of spherical polar coordinates by collecting and analysing positional data recorded during field exercises with a handheld global positioning system (GPS) receiver. This pedagogical approach to teaching spherical geometry, based on field experience rather than classroom theory, uses GPS technology to capture the curiosity of contemporary students, technical or otherwise, who might not normally find the topic of the spherical polar coordinate system comprehensible, relevant or interesting

K-FIX, Transient 2 Phase Flow Hydrodynamic in 2-D Planar or Cylindrical Geometry, Eulerian Method

International Nuclear Information System (INIS)

Rivard, W. C.; Torrey, M. D.

1980-01-01

1 - Description of problem or function: The transient dynamics of two- dimensional, two-phase flow with interfacial exchange are calculated at all flow speeds. Each phase is described in terms of its own density, velocity, and temperature. Separate sets of field equations govern the gas and liquid phase dynamics. The six field equations for the two phases couple through mass, momentum, and energy exchange. 2 - Method of solution: The equations are solved using an Eulerian finite difference technique that implicitly couples the rates of phase transitions, momentum, and energy exchange to determination of the pressure, density, and velocity fields. The implicit solution is accomplished iteratively using a point relaxation technique without linearizing the equations, thus eliminating the need for numerous derivative terms. Solutions can be obtained in one and two space dimensions in plane geometry and in cylindrical geometry with axial symmetry and zero azimuthal velocity. Solutions in spherical geometry can also be obtained in one space dimension. The geometric region of interest is divided into many finite-sized, space-fixed zones called cells which form the computing mesh. In plane geometry the cells are rectangular cylinders, in cylindrical geometry they are toroids with rectangular cross section, and in spherical geometry they are spherical shells

Compact magnetic confinement fusion: Spherical torus and compact torus

Directory of Open Access Journals (Sweden)

Zhe Gao

2016-05-01

Full Text Available The spherical torus (ST and compact torus (CT are two kinds of alternative magnetic confinement fusion concepts with compact geometry. The ST is actually a sub-category of tokamak with a low aspect ratio; while the CT is a toroidal magnetic configuration with a simply-connected geometry including spheromak and field reversed pinch. The ST and CT have potential advantages for ultimate fusion reactor; while at present they can also provide unique fusion science and technology contributions for mainstream fusion research. However, some critical scientific and technology issues should be extensively investigated.

Critical experiments on single-unit spherical plutonium geometries reflected and moderated by oil

International Nuclear Information System (INIS)

Rothe, R.E.

1997-05-01

Experimental critical configurations are reported for several dozen spherical and hemispherical single-unit assemblies of plutonium metal. Most were solid but many were hollow-centered, thick, shell-like geometries. All were constructed of nested plutonium (mostly 2139 Pu) metal hemispherical shells. Three kinds of critical configurations are reported. Two required interpolation and/or extrapolation of data to obtain the critical mass because reflector conditions were essentially infinite. The first finds the plutonium essentially fully reflected by a hydrogen-rich oil; the second is essentially unreflected. The third kind reports the critical oil reflector height above a large plutonium metal assembly of accurately known mass (no interpolation required) when that mass was too great to permit full oil reflection. Some configurations had thicknesses of mild steel just outside the plutonium metal, separating it from the oil. These experiments were performed at the Rocky Flats Critical Mass Laboratory in the late 1960s. They have not been published in a form suitable for benchmark-quality comparisons against state-of-the-art computational techniques until this paper. The age of the data and other factors lead to some difficulty in reconstructing aspects of the program and may, in turn, decrease confidence in certain details. Whenever this is true, the point is acknowledged. The plutonium metal was alpha-phase 239 Pu containing 5.9 wt-% 240 Pu. All assemblies were formed by nesting 1.667-mm-thick (nominal) bare plutonium metal hemispherical shells, also called hemishells, until the desired configuration was achieved. Very small tolerance gaps machined into radial dimensions reduced the effective density a small amount in all cases. Steel components were also nested hemispherical shells; but these were nominally 3.333-mm thick. Oil was used as the reflector because of its chemical compatibility with plutonium metal

From the second gradient operator and second class of integral theorems to Gaussian or spherical mapping invariants

Institute of Scientific and Technical Information of China (English)

YIN Ya-jun; WU Ji-ye; HUANG Ke-zhi; FAN Qin-shan

2008-01-01

By combining of the second gradient operator, the second class of integral theorems, the Gaussian-curvature-based integral theorems and the Gaussian (or spherical) mapping, a series of invariants or geometric conservation quantities under Gaussian (or spherical) mapping are revealed. From these mapping invariants important transformations between original curved surface and the spherical surface are derived. The potential applications of these invariants and transformations to geometry are discussed.

Recent Progress on Spherical Torus Research

Energy Technology Data Exchange (ETDEWEB)

Ono, Masayuki [PPPL; Kaita, Robert [PPPL

2014-01-01

The spherical torus or spherical tokamak (ST) is a member of the tokamak family with its aspect ratio (A = R0/a) reduced to A ~ 1.5, well below the normal tokamak operating range of A ≥ 2.5. As the aspect ratio is reduced, the ideal tokamak beta β (radio of plasma to magnetic pressure) stability limit increases rapidly, approximately as β ~ 1/A. The plasma current it can sustain for a given edge safety factor q-95 also increases rapidly. Because of the above, as well as the natural elongation κ, which makes its plasma shape appear spherical, the ST configuration can yield exceptionally high tokamak performance in a compact geometry. Due to its compactness and high performance, the ST configuration has various near term applications, including a compact fusion neutron source with low tritium consumption, in addition to its longer term goal of attractive fusion energy power source. Since the start of the two megaampere class ST facilities in 2000, National Spherical Torus Experiment (NSTX) in the US and Mega Ampere Spherical Tokamak (MAST) in UK, active ST research has been conducted worldwide. More than sixteen ST research facilities operating during this period have achieved remarkable advances in all of fusion science areas, involving fundamental fusion energy science as well as innovation. These results suggest exciting future prospects for ST research both near term and longer term. The present paper reviews the scientific progress made by the worldwide ST research community during this new mega-ampere-ST era.

Phonon impact on optical control schemes of quantum dots: Role of quantum dot geometry and symmetry

Science.gov (United States)

Lüker, S.; Kuhn, T.; Reiter, D. E.

2017-12-01

Phonons strongly influence the optical control of semiconductor quantum dots. When modeling the electron-phonon interaction in several theoretical approaches, the quantum dot geometry is approximated by a spherical structure, though typical self-assembled quantum dots are strongly lens-shaped. By explicitly comparing simulations of a spherical and a lens-shaped dot using a well-established correlation expansion approach, we show that, indeed, lens-shaped dots can be exactly mapped to a spherical geometry when studying the phonon influence on the electronic system. We also give a recipe to reproduce spectral densities from more involved dots by rather simple spherical models. On the other hand, breaking the spherical symmetry has a pronounced impact on the spatiotemporal properties of the phonon dynamics. As an example we show that for a lens-shaped quantum dot, the phonon emission is strongly concentrated along the direction of the smallest axis of the dot, which is important for the use of phonons for the communication between different dots.

CBM RICH geometry optimization

Energy Technology Data Exchange (ETDEWEB)

Mahmoud, Tariq; Hoehne, Claudia [II. Physikalisches Institut, Giessen Univ. (Germany); Collaboration: CBM-Collaboration

2016-07-01

The Compressed Baryonic Matter (CBM) experiment at the future FAIR complex will investigate the phase diagram of strongly interacting matter at high baryon density and moderate temperatures in A+A collisions from 2-11 AGeV (SIS100) beam energy. The main electron identification detector in the CBM experiment will be a RICH detector with a CO{sub 2} gaseous-radiator, focusing spherical glass mirrors, and MAPMT photo-detectors being placed on a PMT-plane. The RICH detector is located directly behind the CBM dipole magnet. As the final magnet geometry is now available, some changes in the RICH geometry become necessary. In order to guarantee a magnetic field of 1 mT at maximum in the PMT plane for effective operation of the MAPMTs, two measures have to be taken: The PMT plane is moved outwards of the stray field by tilting the mirrors by 10 degrees and shielding boxes have been designed. In this contribution the results of the geometry optimization procedure are presented.

A new expression for determination of fluences from a spherical moderator neutron source for the calibration of spherical neutron measuring devices

International Nuclear Information System (INIS)

Khoshnoodi, M.; Sohrabi, M.

1997-01-01

A new expression modifying the inverse square law for determination of neutron fluences from spherical moderator neutron sources is reported. The formalism is based on the neutron fluence at a point outside the moderator as the summation of fluxes of two groups of neutrons: direct neutrons from the central region of the moderator, and moderated neutrons which, to a first approximation, are scattered from the outermost layers of the spherical moderator. The expression has been further developed for spherical neutron measuring devices with an appropriate geometry factor which corrects the reading of the device for non-uniform irradiation of the detector. The combination of the new fluence function and those of the air and room scattered components introduce a calibration model. The fluence relationship obtained for moderated sources may conveniently be used for calculating the more rapid change of neutron dose at close distances than that which is based on the inverse square dependence. (author)

Relativistic Mechanics in Gravitational Fields Exterior to Rotating Homogeneous Mass Distributions within Spherical Geometry

Directory of Open Access Journals (Sweden)

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.

Quantification of intraventricular hemorrhage is consistent using a spherical sensitivity matrix

Science.gov (United States)

Tang, Te; Sadleir, Rosalind

2010-04-01

We have developed a robust current pattern for detection of intraventricular hemorrhage (IVH). In this study, the current pattern was applied on two realistic shaped neonatal head models and one head-shaped phantom. We found that a sensitivity matrix calculated from a spherical model gave us satisfactory reconstructions in terms of both image quality and quantification. Incorporating correct geometry information into the forward model improved image quality. However, it did not improve quantification accuracy. The results indicate that using a spherical matrix may be a more practical choice for monitoring IVH volumes in neonates.

Weyl geometry and the nonlinear mechanics of distributed point defects

KAUST Repository

Yavari, A.; Goriely, A.

2012-01-01

The residual stress field of a nonlinear elastic solid with a spherically symmetric distribution of point defects is obtained explicitly using methods from differential geometry. The material manifold of a solid with distributed point defects

Spherically Symmetric Geometries in f(T) and f(R) Gravitational Theories

International Nuclear Information System (INIS)

Nashed, Gamal G. L.

2015-01-01

Using the well know relation between Ricci scalar, R, and torsion scalar, T, that is, R=-T-2∇_αT"α, we show that, for any spherically symmetric spacetime whose (i) scalar torsion vanishing, that is, T=T_μ_ν"αS_α"μ"ν=0 or (ii) total derivative term, that is, ∇_αT"α with T"α is the contraction of the torsion, vanishing, or (iii) the combination of scalar torsion and total derivative term vanishing, could be solution for f(T) and f(R) gravitational theories.

The spherical harmonics method, 1 (general development of the theory)

International Nuclear Information System (INIS)

Mark, C.

1957-02-01

A method of obtaining approximate solutions of the transport equation is presented in a form applicable in principle to any geometry. The approximation will give good results in cases where the angular distribution is not very anisotropic. The basis of the approximation is to expand the density per unit solid angle Ψ(→/r, →/Ω) in spherical harmonic tensors formed from →/Ω the unit vector in the direction of velocity, and to break off the expansion. A differential equation whose degree increases with the order of the approximation is obtained for the total density Ψ (o) (r). This equation has the form where the numbers ν i depend on the order of the approximation and on the value of the parameter a of the medium, but not at all on the geometry. When the equation for the total density is an ordinary equation, we simulate the physical condition of continuity of Ψ(→/r, →/Ω) at a boundary in a multi-medium problem by requiring that the spherical harmonic moments of Ψ(→/r, →/Ω) which we retain be continuous; and this determines the constants in the solution for Ψ (o) (→/r. The form of the solution for the total density and the necessary moments in an approximation of general order is given explicitly for plane and spherical symmetry; and for cylindrical symmetry the solution is given for two low-order approximations. In a later report (CRT-338, Revised) the application of the method to several problems involving plane and spherical symmetry will be discussed in detail and the results of a number of examples already worked will also be given. (author)

Analysis and implementation of a space resolving spherical crystal spectrometer for x-ray Thomson scattering experiments.

Science.gov (United States)

Harding, E C; Ao, T; Bailey, J E; Loisel, G; Sinars, D B; Geissel, M; Rochau, G A; Smith, I C

2015-04-01

The application of a space-resolving spectrometer to X-ray Thomson Scattering (XRTS) experiments has the potential to advance the study of warm dense matter. This has motivated the design of a spherical crystal spectrometer, which is a doubly focusing geometry with an overall high sensitivity and the capability of providing high-resolution, space-resolved spectra. A detailed analysis of the image fluence and crystal throughput in this geometry is carried out and analytical estimates of these quantities are presented. This analysis informed the design of a new spectrometer intended for future XRTS experiments on the Z-machine. The new spectrometer collects 6 keV x-rays with a spherically bent Ge (422) crystal and focuses the collected x-rays onto the Rowland circle. The spectrometer was built and then tested with a foam target. The resulting high-quality spectra prove that a spherical spectrometer is a viable diagnostic for XRTS experiments.

New diffusion-like solutions of one-speed transport equations in spherical geometry

International Nuclear Information System (INIS)

Sahni, D.C.

1988-01-01

Stationary, one-speed, spherically symmetric transport equations are considered in a conservative medium. Closed-form expressions are obtained for the angular flux ψ(r, μ) that yield a total flux varying as 1/r by using Sonine transforms. Properties of this solution are studied and it is shown that the solution can not be identified as a diffusion mode solution of the transport equation. Limitations of the Sonine transform technique are noted. (author)

Studies of spherical inertial-electrostatic confinement

International Nuclear Information System (INIS)

Miley, G.H.

1992-01-01

Theoretical and experimental results from studies of Spherical Inertial-Electrostatic Confinement (SIEC) are presented. This principle of IEC involves the confinement by multiple potential wells created by ion injection into a spherical device containing biased grids. A semitransparent cathode accelerates ions, generating a spherical ion-beam flow which converges at the center of the spherical volume, creating a space charge (potential well) region. An electron flow is created by the core (virtual anode) region, forming in turn a virtual cathode. Ions trapped inside this well oscillate back and forth until they fuse or degrade in energy. Such multiple wells with virtual anodes and cathodes, have been called ''Poissors'' following the original work by Farnsworth and by Hirsch. Fusion within the core occurs by reactions between non-Maxwellian beam-beam type ions. This has the potential for achieving a high power density and also for burning both D-T and advanced fuels. If successful, such a device would be attractive for a variety of high power density applications, e.g., space power or as a neutron source based on D-D or D-T operation. Simulations of recent SIEC experiments have been carried out using the XL-code, to solve Poisson's equation, self-consistently with the collisionless Vlasov equation in spherical geometry for several current species and grid parameters. The potential profile predictions are reasonably consistent with experimental results. Potential well measurements used a collimated proton detector. Results indicate that an ∼ 15-kV virtual anode, at least one centimeter in radius, was formed in a spherical device with a cathode potential of 30 kV using an ion current of ∼ 30 mA. Analysis indicates D + densities on the order of 10 9 cm -3 , and D 2 + densities on the order of 10 10 cm -3 . Steady-state D-D neutron emission of about 10 6 n/sec is observed

Cartilage microindentation using cylindrical and spherical optical fiber indenters with integrated Bragg gratings as force sensors

Science.gov (United States)

Marchi, G.; Canti, O.; Baier, V.; Micallef, W.; Hartmann, B.; Alberton, P.; Aszodi, A.; Clausen-Schaumann, H.; Roths, J.

2018-02-01

Fiber optic microindentation sensors that have the potential to be integrated into arthroscopic instruments and to allow localizing degraded articular cartilage are presented in this paper. The indenters consist of optical fibers with integrated Bragg gratings as force sensors. In a basic configuration, the tip of the fiber optic indenter consists of a cleaved fiber end, forming a cylindrical flat punch indenter geometry. When using this indenter geometry, high stresses at the edges of the cylinder are present, which can disrupt the tissue structure. This is avoided with an improved version of the indenter. A spherical indenter tip that is formed by melting the end of the glass fiber. The spherical fiber tip shows the additional advantage of strongly reducing reflections from the fiber end. This allows a reduction of the length of the fiber optic sensor element from 65 mm of the flat punch type to 27 mm of the spherical punch. In order to compare the performance of both indenter types, in vitro stress-relaxation indentation experiments were performed on bovine articular cartilage with both indenter types, to assess biomechanical properties of bovine articular cartilage. For indentation depths between 60 μm and 300 μm, the measurements with both indenter types agreed very well with each other. This shows that both indenter geometries are suitable for microindentation measuremnts . The spherical indenter however has the additional advantage that it minimizes the risk to damage the surface of the tissue and has less than half dimensions than the flat indenter.

Stress intensity factors for complete internal and external cracks in spherical shells

International Nuclear Information System (INIS)

Chao, Y.J.; Chen, H.

1989-01-01

Cracks or flows found in the nuclear structure must be fully evaluated to assure the safety of the plant. The weight function method has been widely used in the determination of stress intensity factors for cracks under stress gradient e.g. for thermal shock loading. The unique features of the weight function method is that once the weight function for a particular cracked geometry is determined the stress intensity factors at the crack tip for any loading applied to the flawed structure can be calculated by a simple integration. In this paper the stress intensity factors of the complete, part-through internal and external cracks in a spherical shell are determined. The finite element method was used to develop the weight functions for the flawed geometry. The approximate crack surface profile was used to derive the weight functions. The stress intensity factors associated with the cracks in spherical shells under internal pressure are determined by both the weight functions and the direct finite element method

Observations on the CANDLE burn-up in various geometries

International Nuclear Information System (INIS)

Seifritz, W.

2007-01-01

We have looked at all geometrical conditions under which an auto catalytically propagating burnup wave (CANDLE burn-up) is possible. Thereby, the Sine Gordon equation finds a new place in the burn-up theory of nuclear fission reactors. For a practical reactor design the axially burning 'spaghetti' reactor and the azimuthally burning 'pancake' reactor, respectively, seem to be the most promising geometries for a practical reactor design. Radial and spherical burn-waves in cylindrical and spherical geometry, respectively, are principally impossible. Also, the possible applicability of such fission burn-waves on the OKLO-phenomenon and the GEOREACTOR in the center of Earth, postulated by Herndon, is discussed. A fast CANDLE-reactor can work with only depleted uranium. Therefore, uranium mining and uranium-enrichment are not necessary anymore. Furthermore, it is also possible to dispense with reprocessing because the uranium utilization factor is as high as about 40%. Thus, this completely new reactor type can open a new era of reactor technology

The spherical harmonics method, 1 (general development of the theory)

Energy Technology Data Exchange (ETDEWEB)

Mark, C

1957-02-15

A method of obtaining approximate solutions of the transport equation is presented in a form applicable in principle to any geometry. The approximation will give good results in cases where the angular distribution is not very anisotropic. The basis of the approximation is to expand the density per unit solid angle {Psi}({yields}/r, {yields}/{Omega}) in spherical harmonic tensors formed from {yields}/{Omega} the unit vector in the direction of velocity, and to break off the expansion. A differential equation whose degree increases with the order of the approximation is obtained for the total density {Psi}{sup (o)}(r). This equation has the form where the numbers {nu}{sub i} depend on the order of the approximation and on the value of the parameter a of the medium, but not at all on the geometry. When the equation for the total density is an ordinary equation, we simulate the physical condition of continuity of {Psi}({yields}/r, {yields}/{Omega}) at a boundary in a multi-medium problem by requiring that the spherical harmonic moments of {Psi}({yields}/r, {yields}/{Omega}) which we retain be continuous; and this determines the constants in the solution for {Psi}{sup (o)}({yields}/r. The form of the solution for the total density and the necessary moments in an approximation of general order is given explicitly for plane and spherical symmetry; and for cylindrical symmetry the solution is given for two low-order approximations. In a later report (CRT-338, Revised) the application of the method to several problems involving plane and spherical symmetry will be discussed in detail and the results of a number of examples already worked will also be given. (author)

Quantification of intraventricular hemorrhage with electrical impedance tomography using a spherical model

International Nuclear Information System (INIS)

Tang, T; Sadleir, R J

2011-01-01

We have developed a robust EEG-based current pattern which shows promise for the detection of intraventricular hemorrhage (IVH) in neonates. Our reconstructions to date are based on a layered spherical head model. In this study, the current pattern was used to gather data from three realistic-shaped neonatal head models and a physical phantom based on one of these models. We found that a sensitivity matrix calculated from a spherical model gave us satisfactory reconstructions in terms of both image quality and quantification. Incorporating correct geometry information into the forward model improved image quality. However, it did not improve quantification accuracy. The results indicate that using a spherical matrix may be a more practical choice for monitoring IVH volumes in neonates for whom patient-specific models are not available

The geometry of celestial mechanics

CERN Document Server

Geiges, Hansjörg

2016-01-01

Celestial mechanics is the branch of mathematical astronomy devoted to studying the motions of celestial bodies subject to the Newtonian law of gravitation. This mathematical introductory textbook reveals that even the most basic question in celestial mechanics, the Kepler problem, leads to a cornucopia of geometric concepts: conformal and projective transformations, spherical and hyperbolic geometry, notions of curvature, and the topology of geodesic flows. For advanced undergraduate and beginning graduate students, this book explores the geometric concepts underlying celestial mechanics and is an ideal companion for introductory courses. The focus on the history of geometric ideas makes it perfect supplementary reading for students in elementary geometry and topology. Numerous exercises, historical notes and an extensive bibliography provide all the contextual information required to gain a solid grounding in celestial mechanics.

Space-Time Geometry of Quark and Strange Quark Matter

Institute of Scientific and Technical Information of China (English)

无

2007-01-01

We study quark and strange quark matter in the context of general relativity. For this purpose, we solve Einstein's field equations for quark and strange quark matter in spherical symmetric space-times. We analyze strange quark matter for the different equations of state (EOS) in the spherical symmetric space-times, thus we are able to obtain the space-time geometries of quark and strange quark matter. Also, we discuss die features of the obtained solutions. The obtained solutions are consistent with the results of Brookhaven Laboratory, i.e. the quark-gluon plasma has a vanishing shear (i.e. quark-gluon plasma is perfect).

Coherent radiation by a spherical medium of resonant atoms

International Nuclear Information System (INIS)

Prasad, Sudhakar; Glauber, Roy J.

2010-01-01

Radiation by the atoms of a resonant medium is a cooperative process in which the medium participates as a whole. In two previous papers we treated this problem for the case of a medium having slab geometry, which, under plane-wave excitation, supports coherent waves that propagate in one dimension. We extend the treatment here to the three-dimensional problem, focusing principally on the case of spherical geometry. By regarding the radiation field as a superposition of electric and magnetic multipole fields of different orders, we express it in terms of suitably defined scalar fields. The latter fields possess a sequence of exponentially decaying eigenmodes corresponding to each multipole order. We consider several examples of spherically symmetric initial excitations of a sphere. Small uniformly excited spheres, we find, tend to radiate superradiantly, while the radiation from a large sphere with an initially excited inner core exhibits temporal oscillations that result from the participation of a large number of coherently excited amplitudes in different modes. The frequency spectrum of the emitted radiation possesses a rich structure, including a frequency gap for large spheres and sharply defined and closely spaced peaks caused by the small frequency shifts and even smaller decay rates characteristic of the majority of eigenmodes.

Spherical-shell boundaries for two-dimensional compressible convection in a star

Science.gov (United States)

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

Phase behavior of charged hydrophobic colloids on flat and spherical surfaces

Science.gov (United States)

Kelleher, Colm P.

For a broad class of two-dimensional (2D) materials, the transition from isotropic fluid to crystalline solid is described by the theory of melting due to Kosterlitz, Thouless, Halperin, Nelson and Young (KTHNY). According to this theory, long-range order is achieved via elimination of the topological defects which proliferate in the fluid phase. However, many natural and man-made 2D systems posses spatial curvature and/or non-trivial topology, which require the presence of topological defects, even at T=0. In principle, the presence of these defects could profoundly affect the phase behavior of such a system. In this thesis, we develop and characterize an experimental system of charged colloidal particles that bind electrostatically to the interface between an oil and an aqueous phase. Depending on how we prepare the sample, this fluid interface may be flat, spherical, or have a more complicated geometry. Focusing on the cases where the interface is flat or spherical, we measure the interactions between the particles, and probe various aspects of their phase behavior. On flat interfaces, this phase behavior is well-described by KTHNY theory. In spherical geometries, however, we observe spatial structures and inhomogeneous dynamics that cannot be captured by the measures traditionally used to describe flat-space phase behavior. We show that, in the spherical system, ordering is achieved by a novel mechanism: sequestration of topological defects into freely-terminating grain boundaries ("scars"), and simultaneous spatial organization of the scars themselves on the vertices of an icosahedron. The emergence of icosahedral order coincides with the localization of mobility into isolated "lakes" of fluid or glassy particles, situated at the icosahedron vertices. These lakes are embedded in a rigid, connected "continent" of locally crystalline particles.

Worldwide complete spherical Bouguer and isostatic anomaly maps

Science.gov (United States)

Bonvalot, S.; Balmino, G.; Briais, A.; Peyrefitte, A.; Vales, N.; Biancale, R.; Gabalda, G.; Reinquin, F.

2011-12-01

We present here a set of digital maps of the Earth's gravity anomalies (surface "free air", Bouguer and isostatic), computed at Bureau Gravimetric International (BGI) as a contribution to the Global Geodetic Observing Systems (GGOS) and to the global geophysical maps published by the Commission for the Geological Map of the World (CGMW). The free air and Bouguer anomaly concept is extensively used in geophysical interpretation to investigate the density distributions in the Earth's interior. Complete Bouguer anomalies (including terrain effects) are usually computed at regional scales by integrating the gravity attraction of topography elements over and beyond a given area (under planar or spherical approximations). Here, we developed and applied a worldwide spherical approach aimed to provide a set of homogeneous and high resolution gravity anomaly maps and grids computed at the Earth's surface, taking into account a realistic Earth model and reconciling geophysical and geodetic definitions of gravity anomalies. This first version (1.0) has been computed by spherical harmonics analysis / synthesis of the Earth's topography-bathymetry up to degree 10800. The detailed theory of the spherical harmonics approach is given in Balmino et al., (Journal of Geodesy, submitted). The Bouguer and terrain corrections have thus been computed in spherical geometry at 1'x1' resolution using the ETOPO1 topography/bathymetry, ice surface and bedrock models from the NOAA (National Oceanic and Atmospheric Administration) and taking into account precise characteristics (boundaries and densities) of major lakes, inner seas, polar caps and of land areas below sea level. Isostatic corrections have been computed according to the Airy Heiskanen model in spherical geometry for a constant depth of compensation of 30km. The gravity information given here is provided by the Earth Geopotential Model (EGM2008), developed at degree 2160 by the National Geospatial Intelligence Agency (NGA) (Pavlis

Development of Spherical Near Field Model for Geological Radioactive Waste Repository

International Nuclear Information System (INIS)

Kim, S. Y.; Lee, K. J.; Chang, S. H.; Lee, K. J.; Chang, S. H.

2012-01-01

Modeling for geological radioactive waste repository can be divided into 3 parts. They are near field modeling related to engineered barrier, far field modeling related to natural barrier and biosphere modeling. In order to make the general application for safety assessment of geological waste repository, spherical geometry near field model has been developed. This model can be used quite extensively when users calculate equivalent spherical geometry for specific engineered barrier like equivalent waste radius, equivalent barrier radius and etc. Only diffusion was considered for general purpose but advection part can be updated. Goldsim and Goldsim Radionuclide Transport (RT) module were chosen and used as developing tool for the flexible modeling. Developer can freely make their own model with developer friendly graphic interface by using Goldsim. Furthermore, model with user friendly graphic interface can be developed by using Goldsim Dashboard Authoring module. The model has been validated by comparing the result with that of another model, inserting similar inputs and conditions. The model has been proved to be reasonably operating from the comparison result by validation process. Cylindrical model can be developed as a further work based on the knowledge and experience from this research

Development of Spherical Near Field Model for Geological Radioactive Waste Repository

Energy Technology Data Exchange (ETDEWEB)

Kim, S. Y.; Lee, K. J.; Chang, S. H. [Korea Advanced Institute of Science and Technology, Daejeon (Korea, Republic of); Lee, K. J.; Chang, S. H. [Khalifa Univ. of Science/Technology and Research, Abu Dhabi (United Arab Emirates)

2012-03-15

Modeling for geological radioactive waste repository can be divided into 3 parts. They are near field modeling related to engineered barrier, far field modeling related to natural barrier and biosphere modeling. In order to make the general application for safety assessment of geological waste repository, spherical geometry near field model has been developed. This model can be used quite extensively when users calculate equivalent spherical geometry for specific engineered barrier like equivalent waste radius, equivalent barrier radius and etc. Only diffusion was considered for general purpose but advection part can be updated. Goldsim and Goldsim Radionuclide Transport (RT) module were chosen and used as developing tool for the flexible modeling. Developer can freely make their own model with developer friendly graphic interface by using Goldsim. Furthermore, model with user friendly graphic interface can be developed by using Goldsim Dashboard Authoring module. The model has been validated by comparing the result with that of another model, inserting similar inputs and conditions. The model has been proved to be reasonably operating from the comparison result by validation process. Cylindrical model can be developed as a further work based on the knowledge and experience from this research.

One-degree-of-freedom spherical model for the passive motion of the human ankle joint.

Science.gov (United States)

Sancisi, Nicola; Baldisserri, Benedetta; Parenti-Castelli, Vincenzo; Belvedere, Claudio; Leardini, Alberto

2014-04-01

Mathematical modelling of mobility at the human ankle joint is essential for prosthetics and orthotic design. The scope of this study is to show that the ankle joint passive motion can be represented by a one-degree-of-freedom spherical motion. Moreover, this motion is modelled by a one-degree-of-freedom spherical parallel mechanism model, and the optimal pivot-point position is determined. Passive motion and anatomical data were taken from in vitro experiments in nine lower limb specimens. For each of these, a spherical mechanism, including the tibiofibular and talocalcaneal segments connected by a spherical pair and by the calcaneofibular and tibiocalcaneal ligament links, was defined from the corresponding experimental kinematics and geometry. An iterative procedure was used to optimize the geometry of the model, able to predict original experimental motion. The results of the simulations showed a good replication of the original natural motion, despite the numerous model assumptions and simplifications, with mean differences between experiments and predictions smaller than 1.3 mm (average 0.33 mm) for the three joint position components and smaller than 0.7° (average 0.32°) for the two out-of-sagittal plane rotations, once plotted versus the full flexion arc. The relevant pivot-point position after model optimization was found within the tibial mortise, but not exactly in a central location. The present combined experimental and modelling analysis of passive motion at the human ankle joint shows that a one degree-of-freedom spherical mechanism predicts well what is observed in real joints, although its computational complexity is comparable to the standard hinge joint model.

Short wavelength laser-plasma interaction experiments in a spherical geometry

International Nuclear Information System (INIS)

Keck, R.L.

1984-01-01

Short wavelength (250 to 500 nm) lasers should provide reduced fast electron preheat and increased laser-pellet coupling efficiency when used as laser fusion drivers. As part of an ongoing effort to study short wavelength laser plasm interaction, six beams of the 24 beam OMEGA Nd-glass laser system have been converted to operation at the third harmonic. This system is capable of providing in excess of 250 Joules of 351 nm light on spherical targets at intensities up to 2 x 10/sup 15/ W/cm/sup 2/. To date, experiments have been performed to study the uniformity of irradiation, laser absorption, fast electron production and preheat, energy transport within the target and underdense plasma instabilities. Both x-ray continuum measurements and Kα line measurements indicate that the absorption is dominated by inverse bremsstrahlung. Electron energy transport has been studied using x-ray burn-through and charge collector measurements. The results show that with 351 nm irradiation ablation pressures of order 100 Mbars are generated at intensities of 10/sup 15/ W/cm/sup 2/

Generalization of Asaoka method to linearly anisotropic scattering: benchmark data in cylindrical geometry

International Nuclear Information System (INIS)

Sanchez, Richard.

1975-11-01

The Integral Transform Method for the neutron transport equation has been developed in last years by Asaoka and others. The method uses Fourier transform techniques in solving isotropic one-dimensional transport problems in homogeneous media. The method has been extended to linearly anisotropic transport in one-dimensional homogeneous media. Series expansions were also obtained using Hembd techniques for the new anisotropic matrix elements in cylindrical geometry. Carlvik spatial-spherical harmonics method was generalized to solve the same problem. By applying a relation between the isotropic and anisotropic one-dimensional kernels, it was demonstrated that anisotropic matrix elements can be calculated by a linear combination of a few isotropic matrix elements. This means in practice that the anisotropic problem of order N with the N+2 isotropic matrix for the plane and spherical geometries, and N+1 isotropic matrix for cylindrical geometries can be solved. A method of solving linearly anisotropic one-dimensional transport problems in homogeneous media was defined by applying Mika and Stankiewicz observations: isotropic matrix elements were computed by Hembd series and anisotropic matrix elements then calculated from recursive relations. The method has been applied to albedo and critical problems in cylindrical geometries. Finally, a number of results were computed with 12-digit accuracy for use as benchmarks [fr

Cylindrical geometry for proportional and drift chambers

International Nuclear Information System (INIS)

Sadoulet, B.

1975-06-01

For experiments performed around storage rings such as e + e - rings or the ISR pp rings, cylindrical wire chambers are very attractive. They surround the beam pipe completely without any dead region in the azimuth, and fit well with the geometry of events where particles are more or less spherically produced. Unfortunately, cylindrical proportional or drift chambers are difficult to make. Problems are discussed and two approaches to fabricating the cathodes are discussed. (WHK)

Effect of conductor geometry on source localization: Implications for epilepsy studies

International Nuclear Information System (INIS)

Schlitt, H.; Heller, L.; Best, E.; Ranken, D.; Aaron, R.

1994-01-01

We shall discuss the effects of conductor geometry on source localization for applications in epilepsy studies. The most popular conductor model for clinical MEG studies is a homogeneous sphere. However, several studies have indicated that a sphere is a poor model for the head when the sources are deep, as is the case for epileptic foci in the mesial temporal lobe. We believe that replacing the spherical model with a more realistic one in the inverse fitting procedure will improve the accuracy of localizing epileptic sources. In order to include a realistic head model in the inverse problem, we must first solve the forward problem for the realistic conductor geometry. We create a conductor geometry model from MR images, and then solve the forward problem via a boundary integral equation for the electric potential due to a specified primary source. One the electric potential is known, the magnetic field can be calculated directly. The most time-intensive part of the problem is generating the conductor model; fortunately, this needs to be done only once for each patient. It takes little time to change the primary current and calculate a new magnetic field for use in the inverse fitting procedure. We present the results of a series of computer simulations in which we investigate the localization accuracy due to replacing the spherical model with the realistic head model in the inverse fitting procedure. The data to be fit consist of a computer generated magnetic field due to a known current dipole in a realistic head model, with added noise. We compare the localization errors when this field is fit using a spherical model to the fit using a realistic head model. Using a spherical model is comparable to what is usually done when localizing epileptic sources in humans, where the conductor model used in the inverse fitting procedure does not correspond to the actual head

Non-spherical micelles in an oil-in-water cubic phase

DEFF Research Database (Denmark)

Leaver, M.; Rajagopalan, V.; Ulf, O.

2000-01-01

phase, both with and without SDS, was established by NMR self-diffusion. In addition H-2 NMR relaxation experiments have demonstrated that the micelles in the cubic phase are non-spherical, having grown and changed shape upon formation of the cubic phase from the micellar solution. Small angle...... associated with the micellar cubic phase, Pm3n and Fd3m. The micellar volumes calculated for these space groups are similar and are consistent with a change in micellar geometry from spherical to prolate.......The cubic phase formed between the microemulsion and hexagonal phases of the ternary pentaethylene glycol dodecyl ether (C12E5)-decane-water system and that doped with small amounts of sodium dodecylsulfate (SDS) have been investigated. The presence of discrete oil-swollen micelles in the cubic...

SPHERE: a spherical-geometry multimaterial electron/photon Monte Carlo transport code

International Nuclear Information System (INIS)

Halbleib, J.A. Sr.

1977-06-01

SPHERE provides experimenters and theorists with a method for the routine solution of coupled electron/photon transport through multimaterial configurations possessing spherical symmetry. Emphasis is placed upon operational simplicity without sacrificing the rigor of the model. SPHERE combines condensed-history electron Monte Carlo with conventional single-scattering photon Monte Carlo in order to describe the transport of all generations of particles from several MeV down to 1.0 and 10.0 keV for electrons and photons, respectively. The model is more accurate at the higher energies, with a less rigorous description of the particle cascade at energies where the shell structure of the transport media becomes important. Flexibility of construction permits the user to tailor the model to specific applications and to extend the capabilities of the model to more sophisticated applications through relatively simple update procedures. 8 figs., 3 tables

Implementation of a parallel algorithm for spherical SN calculations on the IBM 3090

International Nuclear Information System (INIS)

Haghighat, A.; Lawrence, R.D.

1989-01-01

Parallel S N algorithms based on domain decomposition in angle are straightforward to develop in Cartesian geometry because the computation of the angular fluxes for a specific discrete ordinate can be performed independently of all other angles. This is not the case for curvilinear geometries, where the angular redistribution component of the discretized streaming operator results in coupling between angular fluxes along adjacent discrete ordinates. Previously, the authors developed a parallel algorithm for S N calculations in spherical geometry and examined its iterative convergence for criticality and detector problems with differing scattering/absorption ratios. In this paper, the authors describe the implementation of the algorithm on an IBM 3090 Model 400 (four processors) and present computational results illustrating the efficiency of the algorithm relative to serial execution

Thermal compatibility of dental ceramic systems using cylindrical and spherical geometries

Science.gov (United States)

DeHoff, Paul H.; Barrett, Allyson A.; Lee, Robert B.; Anusavice, Kenneth J.

2009-01-01

Objective To test the hypothesis that bilayer ceramic cylinders and spheres can provide valid confirmation of thermal incompatibility stresses predicted by finite element analyses. Methods A commercial core ceramic and an experimental core ceramic were used to fabricate open-ended cylinders and core ceramic spheres. The core cylinders and spheres were veneered with one of four commercial dental ceramics representing four thermally compatible groups and four thermally incompatible groups. Axisymmetric thermal and viscoelastic elements in the ANSYS finite element program were used to calculate temperatures and stresses for each geometry and ceramic combination. This process required a transient heat transfer analysis for each combination to determine input temperatures for the structural model. Results After fabrication, each specimen was examined visually using fiberoptic transillumination for evidence of cracking. There were 100% failures of the thermally incompatible cylinders while none of the thermally compatible combinations failed. Among the spheres, 100% of the thermally incompatible systems failed, 16% of one of the thermally compatible systems failed, and none of the remaining compatible combinations failed. The calculated stress values were in general agreement with the experimental observations, i.e., low residual stresses for the specimens that did not fail and high residual stresses for the specimens that did fail. Significance Simple screening geometries can be used to identify highly incompatible ceramic combinations, but they do not identify marginally incompatible systems. PMID:17949805

Synthetic Landau Levels and Spinor Vortex Matter on a Haldane Spherical Surface with a Magnetic Monopole.

Science.gov (United States)

Zhou, Xiang-Fa; Wu, Congjun; Guo, Guang-Can; Wang, Ruquan; Pu, Han; Zhou, Zheng-Wei

2018-03-30

We present a flexible scheme to realize exact flat Landau levels on curved spherical geometry in a system of spinful cold atoms. This is achieved by applying the Floquet engineering of a magnetic quadrupole field to create a synthetic monopole field in real space. The system can be exactly mapped to the electron-monopole system on a sphere, thus realizing Haldane's spherical geometry for fractional quantum Hall physics. This method works for either bosons or fermions. We investigate the ground-state vortex pattern for an s-wave interacting atomic condensate by mapping this system to the classical Thompson's problem. The distortion and stability of the vortex pattern are further studied in the presence of dipolar interaction. Our scheme is compatible with the current experimental setup, and may serve as a promising route of investigating quantum Hall physics and exotic spinor vortex matter on curved space.

Three-dimensional ray tracing in spherical and elliptical generalized Luneburg lenses for application in the human eye lens.

Science.gov (United States)

Gómez-Correa, J E; Coello, V; Garza-Rivera, A; Puente, N P; Chávez-Cerda, S

2016-03-10

Ray tracing in spherical Luneburg lenses has always been represented in 2D. All propagation planes in a 3D spherical Luneburg lens generate the same ray tracing, due to its radial symmetry. A geometry without radial symmetry generates a different ray tracing. For this reason, a new ray tracing method in 3D through spherical and elliptical Luneburg lenses using 2D methods is proposed. The physics of the propagation is shown here, which allows us to make a ray tracing associated with a vortex beam. A 3D ray tracing in a composite modified Luneburg lens that represents the human eye lens is also presented.

Morphological and electrochemical studies of spherical boron doped diamond electrodes

Energy Technology Data Exchange (ETDEWEB)

Mendes de Barros, R.C. [IQ/USP, Av. Lineu Prestes, 748, Bloco 2 Superior, Cidade Universitaria, Sao Paulo/SP, 05508-900 (Brazil); Ferreira, N.G. [LAS/INPE, Av. dos Astronautas, 1758, Jardim da Granja, Sao Jose dos Campos/SP, 12245-970 (Brazil); Azevedo, A.F. [LAS/INPE, Av. dos Astronautas, 1758, Jardim da Granja, Sao Jose dos Campos/SP, 12245-970 (Brazil); Corat, E.J. [LAS/INPE, Av. dos Astronautas, 1758, Jardim da Granja, Sao Jose dos Campos/SP, 12245-970 (Brazil); Sumodjo, P.T.A. [IQ/USP, Av. Lineu Prestes, 748, Bloco 2 Superior, Cidade Universitaria, Sao Paulo/SP, 05508-900 (Brazil); Serrano, S.H.P. [IQ/USP, Av. Lineu Prestes, 748, Bloco 2 Superior, Cidade Universitaria, Sao Paulo/SP, 05508-900 (Brazil)]. E-mail: shps@iq.usp.br

2006-08-14

Morphological and electrochemical characteristics of boron doped diamond electrode in new geometric shape are presented. The main purpose of this study is a comparison among voltammetric behavior of planar glassy carbon electrode (GCE), planar boron doped diamond electrode (PDDE) and spherical boron doped diamond electrode (SDDE), obtained from similar experimental parameters. SDDE was obtained by the growth of boron doped film on textured molybdenum tip. This electrode does not present microelectrode characteristics. However, its voltammetric peak current, determined at low scan rates, is largest associated to the smallest {delta}E {sub p} values for ferrocyanide system when compared with PDDE or GCE. In addition, the capacitance is about 200 times smaller than that for GCE. These results show that the analytical performance of boron doped diamond electrodes can be implemented just by the change of sensor geometry, from plane to spherical shape.

Transmission probability method for solving neutron transport equation in three-dimensional triangular-z geometry

Energy Technology Data Exchange (ETDEWEB)

Liu Guoming [Department of Nuclear Engineering, Xi' an Jiaotong University, Xi' an, Shaanxi 710049 (China)], E-mail: gmliusy@gmail.com; Wu Hongchun; Cao Liangzhi [Department of Nuclear Engineering, Xi' an Jiaotong University, Xi' an, Shaanxi 710049 (China)

2008-09-15

This paper presents a transmission probability method (TPM) to solve the neutron transport equation in three-dimensional triangular-z geometry. The source within the mesh is assumed to be spatially uniform and isotropic. At the mesh surface, the constant and the simplified P{sub 1} approximation are invoked for the anisotropic angular flux distribution. Based on this model, a code TPMTDT is encoded. It was verified by three 3D Takeda benchmark problems, in which the first two problems are in XYZ geometry and the last one is in hexagonal-z geometry, and an unstructured geometry problem. The results of the present method agree well with those of Monte-Carlo calculation method and Spherical Harmonics (P{sub N}) method.

Studies of spherical tori, stellarators and anisotropic pressure with M3D

International Nuclear Information System (INIS)

Sugiyama, L.E.; Park, W.; Hudson, S.; Tang, X.-Z.; Strauss, H.R.; Stutman, D.

2001-01-01

The M3D (Multi-level 3D) project simulates plasmas using multiple levels of physics, geometry, and grid models in one code package. The M3D code has been extended to fundamentally nonaxisymmetric and small aspect ratio, R/a>or∼1, configurations. Applications include the nonlinear stability of the NSTX spherical torus and the spherical pinch, and the relaxation of stellarator equilibria. The fluid-level physics model has been extended to evolve the anisotropic pressures p jparallel and p jperpendicular for the ion and electron species. Results show that when the density evolves, other terms in addition to the neoclassical collisional parallel viscous force, such as B· ∇p e in the Ohm's law, can be strongly destabilizing for nonlinear magnetic islands. (author)

Regularised reconstruction of sound fields with a spherical microphone array

DEFF Research Database (Denmark)

Granados Corsellas, Alba; Jacobsen, Finn; Fernandez Grande, Efren

2013-01-01

implementation might lead to disastrous reconstructions. A large number of regularisation tools based on singular value decomposition are available, and it has been found that the acoustic holography problem for certain geometries can be formulated in such a way that similarities to singular value decomposition...... become apparent. Hence, a number of regularisation methods, including truncated singular value decomposition, standard Tikhonov, constrained Tikhonov, iterative Tikhonov, Landweber and Rutishauser, have been adapted for spherical near field acoustic holography. The accuracy of the methods is examined...

Projection methods for line radiative transfer in spherical media.

Science.gov (United States)

Anusha, L. S.; Nagendra, K. N.

An efficient numerical method called the Preconditioned Bi-Conjugate Gradient (Pre-BiCG) method is presented for the solution of radiative transfer equation in spherical geometry. A variant of this method called Stabilized Preconditioned Bi-Conjugate Gradient (Pre-BiCG-STAB) is also presented. These methods are based on projections on the subspaces of the n dimensional Euclidean space mathbb {R}n called Krylov subspaces. The methods are shown to be faster in terms of convergence rate compared to the contemporary iterative methods such as Jacobi, Gauss-Seidel and Successive Over Relaxation (SOR).

Numerical simulation of internal reconnection event in spherical tokamak

International Nuclear Information System (INIS)

Hayashi, Takaya; Mizuguchi, Naoki; Sato, Tetsuya

1999-07-01

Three-dimensional magnetohydrodynamic simulations are executed in a full toroidal geometry to clarify the physical mechanisms of the Internal Reconnection Event (IRE), which is observed in the spherical tokamak experiments. The simulation results reproduce several main properties of IRE. Comparison between the numerical results and experimental observation indicates fairly good agreements regarding nonlinear behavior, such as appearance of localized helical distortion, appearance of characteristic conical shape in the pressure profile during thermal quench, and subsequent appearance of the m=2/n=1 type helical distortion of the torus. (author)

Analog geometry in an expanding fluid from AdS/CFT perspective

Science.gov (United States)

Bilić, Neven; Domazet, Silvije; Tolić, Dijana

2015-04-01

The dynamics of an expanding hadron fluid at temperatures below the chiral transition is studied in the framework of AdS/CFT correspondence. We establish a correspondence between the asymptotic AdS geometry in the 4 + 1 dimensional bulk with the analog spacetime geometry on its 3 + 1 dimensional boundary with the background fluid undergoing a spherical Bjorken type expansion. The analog metric tensor on the boundary depends locally on the soft pion dispersion relation and the four-velocity of the fluid. The AdS/CFT correspondence provides a relation between the pion velocity and the critical temperature of the chiral phase transition.

The ''Dolphin'' power laser installation for spherical thermonuclear target heating

International Nuclear Information System (INIS)

Basov, N.G.; Bykovskij, N.E.; Danilov, A.E.

1978-01-01

12-channel laser installation the ''Dolphin'' for thermonuclear target heating in the radiation spheric geometry has been developed to carry out series of physical investigations of laser-thermonuclear plasma system, optimization of target heating conditions and obtaining a comparatively large value of thermonuclear output in ratio to the energy of absorbed light radiation in the target. The description of installation main elements, consisting of the following components, is given: 1)neodymium laser with the maximum permissible radiation energy of 10kJ, with light pulse duration of 10 -10 /10 -9 c and radiation divergence of approximately 5x10 -4 rad; 2)vacuum chamber, where laser radiation interaction with plasma takes place; 3)diagnostic means of laser and plasma parameters and 4)focus system. The focus system provides a high degree of target spherical radiation symmetry at current maximum density on its surface of approximately 10 15 W/cm 2

A Comparison of Angular Difference Schemes for One-Dimensional Spherical Geometry SN Equations

International Nuclear Information System (INIS)

Lathrop, K.D.

2000-01-01

To investigate errors caused by angular differencing in approximating the streaming terms of the transport equation, five different approximations are evaluated for three test problems in one-dimensional spherical geometry. The following schemes are compared: diamond, special truncation error minimizing weighted diamond, linear continuous (the original S N scheme), linear discontinuous, and new quadratic continuous. To isolate errors caused by angular differencing, the approximations are derived from the transport equation without spatial differencing, and the resulting coupled ordinary differential equations (ODEs) are solved with an ODE solver. Results from the approximations are compared with analytic solutions derived for two-region purely absorbing spheres. Most of the approximations are derived by taking moments of the conservation form of the transport equation. The quadratic continuous approximation is derived taking the zeroth moment of both the transport equation and the first angular derivative of the transport equation. The advantages of this approach are described. In all of the approximations, the desirability is shown of using an initializing computation of the μ = -1 angular flux to correctly compute the central flux and of having a difference approximation that ensures this central flux is the same for all directions. The behavior of the standard discrete ordinates equations in the diffusion limit is reviewed, and the linear and quadratic continuous approximations are shown to have the correct diffusion limit if an equal interval discrete quadrature is used.In all three test problems, the weighted diamond difference approximation has smaller maximum and average relative flux errors than the diamond or the linear continuous difference approximations. The quadratic continuous approximation and the linear discontinuous approximation are both more accurate than the other approximations, and the quadratic continuous approximation has a decided edge

A comparison of angular difference schemes for one-dimensional spherical geometry SN equations

International Nuclear Information System (INIS)

Lathrop, K.D.

2000-01-01

To investigate errors caused by angular differencing in approximating the streaming terms of the transport equation, five different approximations are evaluated for three test problems in one-dimensional spherical geometry. The following schemes are compared: diamond, special truncation error minimizing weighted diamond, linear continuous (the original S N scheme), linear discontinuous, and new quadratic continuous. To isolate errors caused by angular differencing, the approximations are derived from the transport equation without spatial differencing, and the resulting coupled ordinary differential equations (ODEs) are solved with an ODE solver. Results from the approximations are compared with analytic solutions derived for two-region purely absorbing spheres. Most of the approximations are derived by taking moments of the conservation form of the transport equation. The quadratic continuous approximation is derived taking the zeroth moment of both the transport equation and the first angular derivative of the transport equation. The advantages of this approach are described, In all of the approximations, the desirability is shown of using an initializing computation of the μ = -1 angular flux to correctly compute the central flux and of having a difference approximation that ensures this central flux is the same for all directions. The behavior of the standard discrete ordinates equations in the diffusion limit is reviewed, and the linear and quadratic continuous approximations are shown to have the correct diffusion limit if an equal interval discrete quadrature is used. In all three test problems, the weighted diamond difference approximation has smaller maximum and average relative flux errors than the diamond or the linear continuous difference approximations. The quadratic continuous approximation and the linear discontinuous approximation are both more accurate than the other approximations, and the quadratic continuous approximation has a decided edge

Cylindrical and Spherical Active Coated Nanoparticles as Nanoantennas: Active nanoparticles as nanoantennas

DEFF Research Database (Denmark)

Arslanagic, Samel; Ziolkowski, Richard W.

2017-01-01

In this article, we review the fundamental properties of several spherical and cylindrical, passive, and active coated nanoparticles (CNPs) with an emphasis on their potential for nanoantenna and nanoamplifier synthesis. For the spherical geometries, the nanoparticles are excited by an electric...... Hertzian dipole (EHD), which represents, e.g., a stimulated atom or molecule. The cylindrical nanoparticles are excited by a magnetic line source (MLS). In the active cases, gain is added to the core region of the particle. For simplicity, it is represented by a canonical, frequency-independent gain model....... We demonstrate that specific CNPs can be designed to be resonant and well matched to their respective excitation sources. With active cores, these designs can lead to extremely large total radiated powers. For both configurations, insights into the effects of the nanoparticle material composition...

Spherical neutron generator

Science.gov (United States)

Leung, Ka-Ngo

2006-11-21

A spherical neutron generator is formed with a small spherical target and a spherical shell RF-driven plasma ion source surrounding the target. A deuterium (or deuterium and tritium) ion plasma is produced by RF excitation in the plasma ion source using an RF antenna. The plasma generation region is a spherical shell between an outer chamber and an inner extraction electrode. A spherical neutron generating target is at the center of the chamber and is biased negatively with respect to the extraction electrode which contains many holes. Ions passing through the holes in the extraction electrode are focused onto the target which produces neutrons by D-D or D-T reactions.

Geometry of the solar wind transition region during the 11-year solar cycle

International Nuclear Information System (INIS)

Lotova, N.A.; Blums, D.F.

1986-01-01

Geometry of the solar wind transition region and its dynamics during the 11-year solar cycle is investigated. It is shown that the space geometry of the transition region suffers considerable changes. In the years of minimum of solar activity (1975-1977) the transition region has a form close to elliptical, shifts nearer to the Sun, while its width decreases. During the years of maximum of Solar activity (1979-1981) the form of the transition region becomes close to spherically symmetric, is located further from the Sun and its width is increased

Analytical method for analysis of electromagnetic scattering from inhomogeneous spherical structures using duality principles

Science.gov (United States)

Kiani, M.; Abdolali, A.; Safari, M.

2018-03-01

In this article, an analytical approach is presented for the analysis of electromagnetic (EM) scattering from radially inhomogeneous spherical structures (RISSs) based on the duality principle. According to the spherical symmetry, similar angular dependencies in all the regions are considered using spherical harmonics. To extract the radial dependency, the system of differential equations of wave propagation toward the inhomogeneity direction is equated with the dual planar ones. A general duality between electromagnetic fields and parameters and scattering parameters of the two structures is introduced. The validity of the proposed approach is verified through a comprehensive example. The presented approach substitutes a complicated problem in spherical coordinate to an easy, well posed, and previously solved problem in planar geometry. This approach is valid for all continuously varying inhomogeneity profiles. One of the major advantages of the proposed method is the capability of studying two general and applicable types of RISSs. As an interesting application, a class of lens antenna based on the physical concept of the gradient refractive index material is introduced. The approach is used to analyze the EM scattering from the structure and validate strong performance of the lens.

Three-Dimensional Exact Free Vibration Analysis of Spherical, Cylindrical, and Flat One-Layered Panels

Directory of Open Access Journals (Sweden)

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.

Dealing with imperfection: quantifying potential length scale artefacts from nominally spherical indenter probes

International Nuclear Information System (INIS)

Constantinides, G; Silva, E C C M; Blackman, G S; Vliet, K J Van

2007-01-01

Instrumented nanoindenters are commonly employed to extract elastic, plastic or time-dependent mechanical properties of the indented material surface. In several important cases, accurate determination of the indenter probe radii is essential for the proper analytical interpretation of the experimental response, and it cannot be circumvented by an experimentally determined expression for the contact area as a function of depth. Current approaches quantify the indenter probe radii via inference from a series of indents on a material with known elastic modulus (e.g., fused quartz) or through the fitting of two-dimensional projected images acquired via atomic force microscopy (AFM) or scanning electron microscopy (SEM) images. Here, we propose a more robust methodology, based on concepts of differential geometry, for the accurate determination of three-dimensional indenter probe geometry. The methodology is presented and demonstrated for four conospherical indenters with probe radii of the order of 1-10 μm. The deviation of extracted radii with manufacturer specifications is emphasized and the limits of spherical approximations are presented. All four probes deviate from the assumed spherical geometry, such that the effective radii are not independent of distance from the probe apex. Significant errors in interpretation of material behaviour will result if this deviation is unaccounted for during the analysis of indentation load-depth responses obtained from material surfaces of interest, including observation of an artificial length scale that could be misinterpreted as an effect attributable to material length scales less than tens of nanometres in size or extent

DOE FES FY2017 Joint Research Target Fourth Quarter Milestone Report for theNational Spherical Torus Experiment Upgrade.

Energy Technology Data Exchange (ETDEWEB)

Soukhanovskii, V. A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

2017-09-13

A successful high-performance plasma operation with a radiative divertor has been demonstrated on many tokamak devices, however, significant uncertainty remains in accurately modeling detachment thresholds, and in how detachment depends on divertor geometry. Whereas it was originally planned to perform dedicated divertor experiments on the National Spherical Tokamak Upgrade to address critical detachment and divertor geometry questions for this milestone, the experiments were deferred due to technical difficulties. Instead, existing NSTX divertor data was summarized and re-analyzed where applicable, and additional simulations were performed.

Solar Proton Transport within an ICRU Sphere Surrounded by a Complex Shield: Combinatorial Geometry

Science.gov (United States)

Wilson, John W.; Slaba, Tony C.; Badavi, Francis F.; Reddell, Brandon D.; Bahadori, Amir A.

2015-01-01

The 3DHZETRN code, with improved neutron and light ion (Z (is) less than 2) transport procedures, was recently developed and compared to Monte Carlo (MC) simulations using simplified spherical geometries. It was shown that 3DHZETRN agrees with the MC codes to the extent they agree with each other. In the present report, the 3DHZETRN code is extended to enable analysis in general combinatorial geometry. A more complex shielding structure with internal parts surrounding a tissue sphere is considered and compared against MC simulations. It is shown that even in the more complex geometry, 3DHZETRN agrees well with the MC codes and maintains a high degree of computational efficiency.

Spherical sampling

CERN Document Server

Freeden, Willi; Schreiner, Michael

2018-01-01

This book presents, in a consistent and unified overview, results and developments in the field of today´s spherical sampling, particularly arising in mathematical geosciences. Although the book often refers to original contributions, the authors made them accessible to (graduate) students and scientists not only from mathematics but also from geosciences and geoengineering. Building a library of topics in spherical sampling theory it shows how advances in this theory lead to new discoveries in mathematical, geodetic, geophysical as well as other scientific branches like neuro-medicine. A must-to-read for everybody working in the area of spherical sampling.

Spherical harmonics and energy polynomial solution of the Boltzmann equation for neutrons, 1

International Nuclear Information System (INIS)

Toledo, P.S. de

1974-01-01

The approximate solution of the source-free energy-dependent Boltzmann transport equation for neutrons in plane geometry and isotropic scattering case was given by Leonard and Ferziger using a truncated development in a series of energy-polynomials for the energy dependent neutron flux and solving exactly for the angular dependence. The presence in the general solution of eigenfunctions belonging to a continuous spectrum gives rise to difficult analytical problems in the application of their method even to simple problems. To avoid such difficulties, the angular dependence is treated by a spherical harmonics method and a general solution of the energy-dependent transport equation in plane geometry and isotropic scattering is obtained, in spite of the appearance of matrices as argument of the angular polynomials [pt

Emergent geometry of membranes

Energy Technology Data Exchange (ETDEWEB)

Badyn, Mathias Hudoba de; Karczmarek, Joanna L.; Sabella-Garnier, Philippe; Yeh, Ken Huai-Che [Department of Physics and Astronomy, University of British Columbia,6224 Agricultural Road, Vancouver (Canada)

2015-11-13

In work http://dx.doi.org/10.1103/PhysRevD.86.086001, a surface embedded in flat ℝ{sup 3} is associated to any three hermitian matrices. We study this emergent surface when the matrices are large, by constructing coherent states corresponding to points in the emergent geometry. We find the original matrices determine not only shape of the emergent surface, but also a unique Poisson structure. We prove that commutators of matrix operators correspond to Poisson brackets. Through our construction, we can realize arbitrary noncommutative membranes: for example, we examine a round sphere with a non-spherically symmetric Poisson structure. We also give a natural construction for a noncommutative torus embedded in ℝ{sup 3}. Finally, we make remarks about area and find matrix equations for minimal area surfaces.

A link between quantum entanglement, secant varieties and sphericity

International Nuclear Information System (INIS)

Sawicki, A; Tsanov, V V

2013-01-01

In this paper, we shed light on the relations between three concepts studied in representation theory, algebraic geometry and quantum information theory. First—spherical actions of reductive groups on projective spaces. Second—secant varieties of homogeneous projective varieties, and the related notions of rank and border rank. Third—quantum entanglement. Our main result concerns the relation between the problem of the state reconstruction from its reduced one-particle density matrices and the minimal number of separable summands in its decomposition. More precisely, we show that sphericity implies that states of a given rank cannot be approximated by states of a lower rank. We call states for which such an approximation is possible exceptional states. For three, important from a quantum entanglement perspective, cases of distinguishable, fermionic and bosonic particles, we also show that non-sphericity implies the existence of exceptional states. Remarkably, the exceptional states belong to non-bipartite entanglement classes. In particular, we show that the W-type states and their appropriate modifications are exceptional states stemming from the second secant variety for three cases above. We point out that the existence of the exceptional states is a physical obstruction for deciding the local unitary equivalence of states by means of the one-particle-reduced density matrices. Finally, for a number of systems of distinguishable particles with a known orbit structure, we list all exceptional states and discuss their possible importance in entanglement theory. (paper)

PRECONDITIONED BI-CONJUGATE GRADIENT METHOD FOR RADIATIVE TRANSFER IN SPHERICAL MEDIA

International Nuclear Information System (INIS)

Anusha, L. S.; Nagendra, K. N.; Paletou, F.; Leger, L.

2009-01-01

A robust numerical method called the Preconditioned Bi-Conjugate Gradient (Pre-BiCG) method is proposed for the solution of the radiative transfer equation in spherical geometry. A variant of this method called Stabilized Preconditioned Bi-Conjugate Gradient (Pre-BiCG-STAB) is also presented. These are iterative methods based on the construction of a set of bi-orthogonal vectors. The application of the Pre-BiCG method in some benchmark tests shows that the method is quite versatile, and can handle difficult problems that may arise in astrophysical radiative transfer theory.

Solar proton exposure of an ICRU sphere within a complex structure Part I: Combinatorial geometry.

Science.gov (United States)

Wilson, John W; Slaba, Tony C; Badavi, Francis F; Reddell, Brandon D; Bahadori, Amir A

2016-06-01

The 3DHZETRN code, with improved neutron and light ion (Z≤2) transport procedures, was recently developed and compared to Monte Carlo (MC) simulations using simplified spherical geometries. It was shown that 3DHZETRN agrees with the MC codes to the extent they agree with each other. In the present report, the 3DHZETRN code is extended to enable analysis in general combinatorial geometry. A more complex shielding structure with internal parts surrounding a tissue sphere is considered and compared against MC simulations. It is shown that even in the more complex geometry, 3DHZETRN agrees well with the MC codes and maintains a high degree of computational efficiency. Published by Elsevier Ltd.

Spherical Bessel transform via exponential sum approximation of spherical Bessel function

Science.gov (United States)

Ikeno, Hidekazu

2018-02-01

A new algorithm for numerical evaluation of spherical Bessel transform is proposed in this paper. In this method, the spherical Bessel function is approximately represented as an exponential sum with complex parameters. This is obtained by expressing an integral representation of spherical Bessel function in complex plane, and discretizing contour integrals along steepest descent paths and a contour path parallel to real axis using numerical quadrature rule with the double-exponential transformation. The number of terms in the expression is reduced using the modified balanced truncation method. The residual part of integrand is also expanded by exponential functions using Prony-like method. The spherical Bessel transform can be evaluated analytically on arbitrary points in half-open interval.

Uniqueness of flat spherically symmetric spacelike hypersurfaces admitted by spherically symmetric static spacetimes

Science.gov (United States)

Beig, Robert; Siddiqui, Azad A.

2007-11-01

It is known that spherically symmetric static spacetimes admit a foliation by flat hypersurfaces. Such foliations have explicitly been constructed for some spacetimes, using different approaches, but none of them have proved or even discussed the uniqueness of these foliations. The issue of uniqueness becomes more important due to suitability of flat foliations for studying black hole physics. Here, flat spherically symmetric spacelike hypersurfaces are obtained by a direct method. It is found that spherically symmetric static spacetimes admit flat spherically symmetric hypersurfaces, and that these hypersurfaces are unique up to translation under the timelike Killing vector. This result guarantees the uniqueness of flat spherically symmetric foliations for such spacetimes.

Electro-optic spatial decoding on the spherical-wavefront Coulomb fields of plasma electron sources.

Science.gov (United States)

Huang, K; Esirkepov, T; Koga, J K; Kotaki, H; Mori, M; Hayashi, Y; Nakanii, N; Bulanov, S V; Kando, M

2018-02-13

Detections of the pulse durations and arrival timings of relativistic electron beams are important issues in accelerator physics. Electro-optic diagnostics on the Coulomb fields of electron beams have the advantages of single shot and non-destructive characteristics. We present a study of introducing the electro-optic spatial decoding technique to laser wakefield acceleration. By placing an electro-optic crystal very close to a gas target, we discovered that the Coulomb field of the electron beam possessed a spherical wavefront and was inconsistent with the previously widely used model. The field structure was demonstrated by experimental measurement, analytic calculations and simulations. A temporal mapping relationship with generality was derived in a geometry where the signals had spherical wavefronts. This study could be helpful for the applications of electro-optic diagnostics in laser plasma acceleration experiments.

Spinning geometry = Twisted geometry

International Nuclear Information System (INIS)

Freidel, Laurent; Ziprick, Jonathan

2014-01-01

It is well known that the SU(2)-gauge invariant phase space of loop gravity can be represented in terms of twisted geometries. These are piecewise-linear-flat geometries obtained by gluing together polyhedra, but the resulting geometries are not continuous across the faces. Here we show that this phase space can also be represented by continuous, piecewise-flat three-geometries called spinning geometries. These are composed of metric-flat three-cells glued together consistently. The geometry of each cell and the manner in which they are glued is compatible with the choice of fluxes and holonomies. We first remark that the fluxes provide each edge with an angular momentum. By studying the piecewise-flat geometries which minimize edge lengths, we show that these angular momenta can be literally interpreted as the spin of the edges: the geometries of all edges are necessarily helices. We also show that the compatibility of the gluing maps with the holonomy data results in the same conclusion. This shows that a spinning geometry represents a way to glue together the three-cells of a twisted geometry to form a continuous geometry which represents a point in the loop gravity phase space. (paper)

Semi-Numerical Studies of the Three-Meter Spherical Couette Experiment Utilizing Data Assimilation

Science.gov (United States)

Burnett, Sarah; Rojas, Ruben; Perevalov, Artur; Lathrop, Daniel; Ide, Kayo; Schaeffer, Nathanael

2017-11-01

The model of the Earth's magnetic field has been investigated in recent years through experiments and numerical models. At the University of Maryland, experimental studies are implemented in a three-meter spherical Couette device filled with liquid sodium. The inner and outer spheres of this apparatus mimic the planet's inner core and core-mantle boundary, respectively. These experiments incorporate high velocity flows with Reynolds numbers 108 . In spherical Couette geometry, the numerical scheme applied to this work features finite difference methods in the radial direction and pseudospectral spherical harmonic transforms elsewhere. Adding to the numerical model, data assimilation integrates the experimental outer-layer magnetic field measurements. This semi-numerical model can then be compared to the experimental results as well as forecasting magnetic field changes. Data assimilation makes it possible to get estimates of internal motions of the three-meter experiment that would otherwise be intrusive or impossible to obtain in experiments or too computationally expensive with a purely numerical code. If we can provide accurate models of the three-meter device, it is possible to attempt to model the geomagnetic field. We gratefully acknowledge the support of NSF Grant No. EAR1417148 & DGE1322106.

NRN, Removal-Diffusion for Squares and Cylindrical Geometry with Energy Transfer Matrix

International Nuclear Information System (INIS)

Olson, G.

1981-01-01

A - Nature of physical problem solved: A system of programmes using the NRN shield design method. NRN consists of the following programmes: 1) Data preparation programme NECO. 2) Multigroup removal programmes REBOX for box geometry and REMC for spherical and cylindrical geometries. 3) Multigroup diffusion - and slowing down programme NEDI. B - Method of solution: The NRN method presents a new approach in the formulation of removal-diffusion theory. The removal cross section is redefined and the slowing down between the multi-group diffusion equations is treated with a complete energy-transfer matrix rather than in an age theory approximation. CDC 3400 version was offered by Tesperhude (Gesellschaft fuer Kernenergieverwertung in Schiffbau und Schiffahrt MBH., Germany)

Dark matter and localised fermions from spherical orbifolds?

Energy Technology Data Exchange (ETDEWEB)

Cacciapaglia, Giacomo; Deandrea, Aldo [Université de Lyon,Lyon (France); Université Lyon 1, CNRS/IN2P3, UMR5822 IPNL,F-69622 Villeurbanne Cedex (France); Deutschmann, Nicolas [Université de Lyon,Lyon (France); Université Lyon 1, CNRS/IN2P3, UMR5822 IPNL,F-69622 Villeurbanne Cedex (France); Centre for Cosmology, Particle Physics and Phenomenology (CP3),Université catholique de Louvain,Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve (Belgium)

2016-04-14

We study a class of six-dimensional models based on positive curvature surfaces (spherical 2-orbifolds) as extra-spaces. Using the Newman-Penrose formalism, we discuss the particle spectrum in this class of models. The fermion spectrum problem, which has been addressed with flux compactifications in the past, can be avoided using localised fermions. In this framework, we find that there are four types of geometry compatible with the existence of a stable dark matter candidate and we study the simplest case in detail. Using the complementarity between collider resonance searches and relic density constraints, we show that this class of models is under tension, unless the model lies in a funnel region characterised by a resonant Higgs s-channel in the dark matter annihilation.

Spinor Casimir densities for a spherical shell in the global monopole spacetime

International Nuclear Information System (INIS)

Saharian, A A; Mello, E R Bezerra de

2004-01-01

We investigate the vacuum expectation values of the energy-momentum tensor and the fermionic condensate associated with a massive spinor field obeying the MIT bag boundary condition on a spherical shell in the global monopole spacetime. In order to do that, we use the generalized Abel-Plana summation formula. As we shall see, this procedure allows us to extract from the vacuum expectation values the contribution coming from the unbounded spacetime and to explicitly present the boundary induced parts. As regards the boundary induced contribution, two distinct situations are examined: the vacuum average effects inside and outside the spherical shell. The asymptotic behaviour of the vacuum densities is investigated near the sphere centre and near the surface, and at large distances from the sphere. In the limit of strong gravitational field corresponding to small values of the parameter describing the solid angle deficit in the global monopole geometry, the sphere induced expectation values are exponentially suppressed. We discuss, as a special case, the fermionic vacuum densities for the spherical shell on the background of the Minkowski spacetime. Previous approaches to this problem within the framework of the QCD bag models have been global and our calculation is a local extension of these contributions

ASPECT RATIO DEPENDENCE OF THE FREE-FALL TIME FOR NON-SPHERICAL SYMMETRIES

Energy Technology Data Exchange (ETDEWEB)

Pon, Andy; Johnstone, Doug [Department of Physics and Astronomy, University of Victoria, P.O. Box 3055, STN CSC, Victoria, BC V8W 3P6 (Canada); Toala, Jesus A. [Instituto de Astrofisica de Andalucia, CSIC, Glorieta de la Astronomia s/n, E-18008, Granada (Spain); Vazquez-Semadeni, Enrique; Gomez, Gilberto C. [Centro de Radioastronomia y Astrofisica, Universidad Nacional Autonoma de Mexico, Campus Morelia Apartado Postal 3-72, 58090 Morelia, Michoacan (Mexico); Heitsch, Fabian, E-mail: arpon@uvic.ca, E-mail: Douglas.Johnstone@nrc-cnrc.gc.ca, E-mail: toala@iaa.es, E-mail: e.vazquez@crya.unam.mx, E-mail: g.gomez@crya.unam.mx, E-mail: fheitsch@unc.edu [Department of Physics and Astronomy, University of North Carolina Chapel Hill, CB 3255, Phillips Hall, Chapel Hill, NC 27599 (United States)

2012-09-10

We investigate the collapse of non-spherical substructures, such as sheets and filaments, which are ubiquitous in molecular clouds. Such non-spherical substructures collapse homologously in their interiors but are influenced by an edge effect that causes their edges to be preferentially accelerated. We analytically compute the homologous collapse timescales of the interiors of uniform-density, self-gravitating filaments and find that the homologous collapse timescale scales linearly with the aspect ratio. The characteristic timescale for an edge-driven collapse mode in a filament, however, is shown to have a square-root dependence on the aspect ratio. For both filaments and circular sheets, we find that selective edge acceleration becomes more important with increasing aspect ratio. In general, we find that lower dimensional objects and objects with larger aspect ratios have longer collapse timescales. We show that estimates for star formation rates, based upon gas densities, can be overestimated by an order of magnitude if the geometry of a cloud is not taken into account.

ASPECT RATIO DEPENDENCE OF THE FREE-FALL TIME FOR NON-SPHERICAL SYMMETRIES

International Nuclear Information System (INIS)

Pon, Andy; Johnstone, Doug; Toalá, Jesús A.; Vázquez-Semadeni, Enrique; Gómez, Gilberto C.; Heitsch, Fabian

2012-01-01

We investigate the collapse of non-spherical substructures, such as sheets and filaments, which are ubiquitous in molecular clouds. Such non-spherical substructures collapse homologously in their interiors but are influenced by an edge effect that causes their edges to be preferentially accelerated. We analytically compute the homologous collapse timescales of the interiors of uniform-density, self-gravitating filaments and find that the homologous collapse timescale scales linearly with the aspect ratio. The characteristic timescale for an edge-driven collapse mode in a filament, however, is shown to have a square-root dependence on the aspect ratio. For both filaments and circular sheets, we find that selective edge acceleration becomes more important with increasing aspect ratio. In general, we find that lower dimensional objects and objects with larger aspect ratios have longer collapse timescales. We show that estimates for star formation rates, based upon gas densities, can be overestimated by an order of magnitude if the geometry of a cloud is not taken into account.

Evolution of the spherical clusters

International Nuclear Information System (INIS)

Surdin, V.G.

1978-01-01

The possible processes of the Galaxy spherical clusters formation and evolution are described on a popular level. The orbits of spherical cluster motion and their spatial velocities are determined. Given are the distrbutions of spherical cluster stars according to their velocities and the observed distribution of spherical clusters in the area of the Galaxy slow evolution. The dissipation and dynamic friction processes destructing clusters with the mass less than 10 4 of solar mass and bringing about the reduction of clusters in the Galaxy are considered. The paradox of forming mainly X-ray sources in spherical clusters is explained. The schematic image of possible ways of forming X-ray sources in spherical clusters is given

Fundamentals of spherical array processing

CERN Document Server

Rafaely, Boaz

2015-01-01

This book provides a comprehensive introduction to the theory and practice of spherical microphone arrays. It is written for graduate students, researchers and engineers who work with spherical microphone arrays in a wide range of applications.   The first two chapters provide the reader with the necessary mathematical and physical background, including an introduction to the spherical Fourier transform and the formulation of plane-wave sound fields in the spherical harmonic domain. The third chapter covers the theory of spatial sampling, employed when selecting the positions of microphones to sample sound pressure functions in space. Subsequent chapters present various spherical array configurations, including the popular rigid-sphere-based configuration. Beamforming (spatial filtering) in the spherical harmonics domain, including axis-symmetric beamforming, and the performance measures of directivity index and white noise gain are introduced, and a range of optimal beamformers for spherical arrays, includi...

Thermal transport measurements of uv laser irradiated spherical targets

International Nuclear Information System (INIS)

Jaanimagi, P.A.; Delettrez, J.; Henke, B.L.; Richardson, M.C.

1985-01-01

New measurements are presented of thermal transport in spherical geometry using time-resolved x-ray spectroscopy. We determine the time dependence of the mass ablation rate m(dot) by following the progress of the ablation surface through thin layers of material embedded at various depths below the surface of the target. These measurements made with 6 and 12 uv (351 nm) beams from OMEGA are compared to previous thermal transport data and are in qualitative agreement with detailed LILAC hydrodynamic code simulations which predict a sharp decrease in m(dot) after the peak of the laser pulse. Non-uniform laser irradiation of the target results in the anomalously high values of m(dot) measured in these experiments

Analytical Solutions of Electromagnetic Fields from Current Dipole Moment on Spherical Conductor in a Low-Frequency Approximation

International Nuclear Information System (INIS)

Okita, Taishi; Takagi, Toshiyuki

2010-01-01

We analytically derive the solutions for electromagnetic fields of electric current dipole moment, which is placed in the exterior of the spherical homogeneous conductor, and is pointed along the radial direction. The dipole moment is driven in the low frequency f = 1 kHz and high frequency f = 1 GHz regimes. The electrical properties of the conductor are appropriately chosen in each frequency. Electromagnetic fields are rigorously formulated at an arbitrary point in a spherical geometry, in which the magnetic vector potential is straightforwardly given by the Biot-Savart formula, and the scalar potential is expanded with the Legendre polynomials, taking into account the appropriate boundary conditions at the spherical surface of the conductor. The induced electric fields are numerically calculated along the several paths in the low and high frequency excitation. The self-consistent solutions obtained in this work will be of much importance in a wide region of electromagnetic induction problems. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

Interior and exterior resonances in acoustic scattering. pt. 1 - spherical targets

International Nuclear Information System (INIS)

Gaunaurd, G.C.; Tanglis, E.; Uberall, H.; Brill, D.

1983-01-01

In acoustic scattering from elastic objects, resonance features appear in the returned echo at frequencies at which the object's eigenfrequencies are located, which are explained by the excitation of 'interior' creeping waves. Corresponding resonance terms may be split off from the total scattering amplitude, leaving behind an apparently nonresonant background amplitude. This is demonstrated here for scatterers of spherical geometry and in a companion paper also for scatterers of arbitrary geometry, by using the T-matrix approach. For the case of near-impenetrable spheres, it is subsequently shown that the background amplitude can be split further into specularly reflected contributions, plus highly attenuated resonance terms which are explained by the excitation of 'exterior' (Franz-type) creeping waves. The singularity structure of the scattering function is shown mathematically, by using the R-matrix approach of the nuclear-scattering theory, as that of a meromorphic function 'without' any additional 'entire function' (as had been postulated by the singularity expansion method)

Parallel/vector algorithms for the spherical SN transport theory method

International Nuclear Information System (INIS)

Haghighat, A.; Mattis, R.E.

1990-01-01

This paper discusses vector and parallel processing of a 1-D curvilinear (i.e. spherical) S N transport theory algorithm on the Cornell National SuperComputer Facility (CNSF) IBM 3090/600E. Two different vector algorithms were developed and parallelized based on angular decomposition. It is shown that significant speedups are attainable. For example, for problems with large granularity, using 4 processors, the parallel/vector algorithm achieves speedups (for wall-clock time) of more than 4.5 relative to the old serial/scalar algorithm. Furthermore, this work has demonstrated the existing potential for the development of faster processing vector and parallel algorithms for multidimensional curvilinear geometries. (author)

Hopf algebras in noncommutative geometry

International Nuclear Information System (INIS)

Varilly, Joseph C.

2001-10-01

We give an introductory survey to the use of Hopf algebras in several problems of non- commutative geometry. The main example, the Hopf algebra of rooted trees, is a graded, connected Hopf algebra arising from a universal construction. We show its relation to the algebra of transverse differential operators introduced by Connes and Moscovici in order to compute a local index formula in cyclic cohomology, and to the several Hopf algebras defined by Connes and Kreimer to simplify the combinatorics of perturbative renormalization. We explain how characteristic classes for a Hopf module algebra can be obtained from the cyclic cohomology of the Hopf algebra which acts on it. Finally, we discuss the theory of non- commutative spherical manifolds and show how they arise as homogeneous spaces of certain compact quantum groups. (author)

Spherical CNNs

OpenAIRE

Cohen, Taco S.; Geiger, Mario; Koehler, Jonas; Welling, Max

2018-01-01

Convolutional Neural Networks (CNNs) have become the method of choice for learning problems involving 2D planar images. However, a number of problems of recent interest have created a demand for models that can analyze spherical images. Examples include omnidirectional vision for drones, robots, and autonomous cars, molecular regression problems, and global weather and climate modelling. A naive application of convolutional networks to a planar projection of the spherical signal is destined t...

Dark energy, antimatter gravity and geometry of the Universe

CERN Document Server

Hajdukovic, Dragan Slavkov

2010-01-01

This article is based on two hypotheses. The first one is the existence of the gravitational repulsion between particles and antiparticles. Consequently, virtual particle-antiparticle pairs in the quantum vacuum might be considered as gravitational dipoles. The second hypothesis is that the Universe has geometry of a four-dimensional hyper-spherical shell with thickness equal to the Compton wavelength of a pion, which is a simple generalization of the usual geometry of a 3-hypersphere. It is striking that these two hypotheses lead to a simple relation for the gravitational mass density of the vacuum, which is in very good agreement with the observed dark energy density. It might be a sign that QCD fields provide the largest contribution to the gravitational mass of the physical vacuum; contrary to the prediction of the Standard Model that QCD contribution is much smaller than some other contributions.

A numerical model of mantle convection with deformable, mobile continental lithosphere within three-dimensional spherical geometry

Science.gov (United States)

Yoshida, M.

2010-12-01

A new numerical simulation model of mantle convection with a compositionally and rheologically heterogeneous, deformable, mobile continental lithosphere is presented for the first time by using three-dimensional regional spherical-shell geometry (Yoshida, 2010, Earth Planet. Sci. Lett.). The numerical results revealed that one of major factor that realizes the supercontinental breakup and subsequent continental drift is a pre-existing, weak (low-viscosity) continental margin (WCM) in the supercontinent. Characteristic tectonic structures such as young orogenic belts and suture zones in a continent are expected to be mechanically weaker than the stable part of the continental lithosphere with the cratonic root (or cratonic lithosphere) and yield lateral viscosity variations in the continental lithosphere. In the present-day Earth's lithosphere, the pre-existing, mechanically weak zones emerge as a diffuse plate boundary. However, the dynamic role of the WCM in the stability of continental lithosphere has not been understood in terms of geophysics. In my numerical model, a compositionally buoyant and highly viscous continental assemblage with pre-existing WCMs, analogous to the past supercontinent, is modeled and imposed on well-developed mantle convection whose vigor of convection, internal heating rate, and rheological parameters are appropriate for the Earth's mantle. The visco-plastic oceanic lithosphere and the associated subduction of oceanic plates are incorporated. The time integration of the advection of continental materials with zero chemical diffusion is performed by a tracer particle method. The time evolution of mantle convection after setting the model supercontinent is followed over 800 Myr. Earth-like continental drift is successfully reproduced, and the characteristic thermal interaction between the mantle and the continent/supercontinent is observed in my new numerical model. Results reveal that the WCM protects the cratonic lithosphere from being

Preparation and Optical Properties of Spherical Inverse Opals by Liquid Phase Deposition Using Spherical Colloidal Crystals

International Nuclear Information System (INIS)

Aoi, Y; Tominaga, T

2013-01-01

Titanium dioxide (TiO 2 ) inverse opals in spherical shape were prepared by liquid phase deposition (LPD) using spherical colloidal crystals as templates. Spherical colloidal crystals were produced by ink-jet drying technique. Aqueous emulsion droplets that contain polystyrene latex particles were ejected into air and dried. Closely packed colloidal crystals with spherical shape were obtained. The obtained spherical colloidal crystals were used as templates for the LPD. The templates were dispersed in the deposition solution of the LPD, i.e. a mixed solution of ammonium hexafluorotitanate and boric acid and reacted for 4 h at 30 °C. After the LPD process, the interstitial spaces of the spherical colloidal crystals were completely filled with titanium oxide. Subsequent heat treatment resulted in removal of templates and spherical titanium dioxide inverse opals. The spherical shape of the template was retained. SEM observations indicated that the periodic ordered voids were surrounded by titanium dioxide. The optical reflectance spectra indicated that the optical properties of the spherical titanium dioxide inverse opals were due to Bragg diffractions from the ordered structure. Filling in the voids of the inverse opals with different solvents caused remarkable changes in the reflectance peak.

Left Ventricular Geometry and Blood Pressure as Predictors of Adverse Progression of Fabry Cardiomyopathy.

Science.gov (United States)

Krämer, Johannes; Bijnens, Bart; Störk, Stefan; Ritter, Christian O; Liu, Dan; Ertl, Georg; Wanner, Christoph; Weidemann, Frank

2015-01-01

In spite of several research studies help to describe the heart in Fabry disease (FD), the cardiomyopathy is not entirely understood. In addition, the impact of blood pressure and alterations in geometry have not been systematically evaluated. In 74 FD patients (mean age 36±12 years; 45 females) the extent of myocardial fibrosis and its progression were quantified using cardiac magnetic-resonance-imaging with late enhancement technique (LE). Results were compared to standard echocardiography complemented by 2D-speckle-tracking, 3D-sphericity-index (SI) and standardized blood pressure measurement. At baseline, no patient received enzyme replacement therapy (ERT). After 51±24 months, a follow-up examination was performed. Systolic blood pressure (SBP) was higher in patients with vs. without LE: 123±17 mmHg vs. 115±13 mmHg; P = 0.04. A positive correlation was found between SI and the amount of LE-positive myocardium (r = 0.51; PAUC = 0.785; P<0.05). LV geometry as assessed by the sphericity index is altered in relation to the stage of the Fabry cardiomyopathy. Although patients with FD are not hypertensive, the SBP has a clear impact on the progression of the cardiomyopathy.

Friction factor for water flow through packed beds of spherical and non-spherical particles

Directory of Open Access Journals (Sweden)

Kaluđerović-Radoičić Tatjana

2017-01-01

Full Text Available The aim of this work was the experimental evaluation of different friction factor correlations for water flow through packed beds of spherical and non-spherical particles at ambient temperature. The experiments were performed by measuring the pressure drop across the bed. Packed beds made of monosized glass spherical particles of seven different diameters were used, as well as beds made of 16 fractions of quartz filtration sand obtained by sieving (polydisperse non-spherical particles. The range of bed voidages was 0.359–0.486, while the range of bed particle Reynolds numbers was from 0.3 to 286 for spherical particles and from 0.1 to 50 for non-spherical particles. The obtained results were compared using a number of available literature correlations. In order to improve the correlation results for spherical particles, a new simple equation was proposed in the form of Ergun’s equation, with modified coefficients. The new correlation had a mean absolute deviation between experimental and calculated values of pressure drop of 9.04%. For non-spherical quartz filtration sand particles the best fit was obtained using Ergun’s equation, with a mean absolute deviation of 10.36%. Surface-volume diameter (dSV necessary for correlating the data for filtration sand particles was calculated based on correlations for dV = f(dm and Ψ = f(dm. [Project of the Serbian Ministry of Education, Science and Technological Development, Grant no. ON172022

Progress in octahedral spherical hohlraum study

Directory of Open Access Journals (Sweden)

Ke Lan

2016-01-01

Full Text Available In this paper, we give a review of our theoretical and experimental progress in octahedral spherical hohlraum study. From our theoretical study, the octahedral spherical hohlraums with 6 Laser Entrance Holes (LEHs of octahedral symmetry have robust high symmetry during the capsule implosion at hohlraum-to-capsule radius ratio larger than 3.7. In addition, the octahedral spherical hohlraums also have potential superiority on low backscattering without supplementary technology. We studied the laser arrangement and constraints of the octahedral spherical hohlraums, and gave a design on the laser arrangement for ignition octahedral hohlraums. As a result, the injection angle of laser beams of 50°–60° was proposed as the optimum candidate range for the octahedral spherical hohlraums. We proposed a novel octahedral spherical hohlraum with cylindrical LEHs and LEH shields, in order to increase the laser coupling efficiency and improve the capsule symmetry and to mitigate the influence of the wall blowoff on laser transport. We studied on the sensitivity of the octahedral spherical hohlraums to random errors and compared the sensitivity among the octahedral spherical hohlraums, the rugby hohlraums and the cylindrical hohlraums, and the results show that the octahedral spherical hohlraums are robust to these random errors while the cylindrical hohlraums are the most sensitive. Up till to now, we have carried out three experiments on the spherical hohlraum with 2 LEHs on Shenguang(SG laser facilities, including demonstration of improving laser transport by using the cylindrical LEHs in the spherical hohlraums, spherical hohlraum energetics on the SGIII prototype laser facility, and comparisons of laser plasma instabilities between the spherical hohlraums and the cylindrical hohlraums on the SGIII laser facility.

Semi-Numerical Studies of the Three-Meter Spherical Couette Experiment Utilizing Data Assimilation

Science.gov (United States)

Burnett, S. C.; Rojas, R.; Perevalov, A.; Lathrop, D. P.

2017-12-01

The model of the Earth's magnetic field has been investigated in recent years through experiments and numerical models. At the University of Maryland, experimental studies are implemented in a three-meter spherical Couette device filled with liquid sodium. The inner and outer spheres of this apparatus mimic the planet's inner core and core-mantle boundary, respectively. These experiments incorporate high velocity flows with Reynolds numbers 108. In spherical Couette geometry, the numerical scheme applied to this work features finite difference methods in the radial direction and pseudospectral spherical harmonic transforms elsewhere [Schaeffer, N. G3 (2013)]. Adding to the numerical model, data assimilation integrates the experimental outer-layer magnetic field measurements. This semi-numerical model can then be compared to the experimental results as well as forecasting magnetic field changes. Data assimilation makes it possible to get estimates of internal motions of the three-meter experiment that would otherwise be intrusive or impossible to obtain in experiments or too computationally expensive with a purely numerical code. If we can provide accurate models of the three-meter device, it is possible to attempt to model the geomagnetic field. We gratefully acknowledge the support of NSF Grant No. EAR1417148 & DGE1322106.

Weyl geometry and the nonlinear mechanics of distributed point defects

KAUST Repository

Yavari, A.

2012-09-05

The residual stress field of a nonlinear elastic solid with a spherically symmetric distribution of point defects is obtained explicitly using methods from differential geometry. The material manifold of a solid with distributed point defects-where the body is stress-free-is a flat Weyl manifold, i.e. a manifold with an affine connection that has non-metricity with vanishing traceless part, but both its torsion and curvature tensors vanish. Given a spherically symmetric point defect distribution, we construct its Weyl material manifold using the method of Cartan\\'s moving frames. Having the material manifold, the anelasticity problem is transformed to a nonlinear elasticity problem and reduces the problem of computing the residual stresses to finding an embedding into the Euclidean ambient space. In the case of incompressible neo-Hookean solids, we calculate explicitly this residual stress field. We consider the example of a finite ball and a point defect distribution uniform in a smaller ball and vanishing elsewhere. We show that the residual stress field inside the smaller ball is uniform and hydrostatic. We also prove a nonlinear analogue of Eshelby\\'s celebrated inclusion problem for a spherical inclusion in an isotropic incompressible nonlinear solid. © 2012 The Royal Society.

General Geometry and Geometry of Electromagnetism

OpenAIRE

Shahverdiyev, Shervgi S.

2002-01-01

It is shown that Electromagnetism creates geometry different from Riemannian geometry. General geometry including Riemannian geometry as a special case is constructed. It is proven that the most simplest special case of General Geometry is geometry underlying Electromagnetism. Action for electromagnetic field and Maxwell equations are derived from curvature function of geometry underlying Electromagnetism. And it is shown that equation of motion for a particle interacting with electromagnetic...

Classical molecular dynamics and quantum abs-initio studies on lithium-intercalation in interconnected hollow spherical nano-spheres of amorphous Silicon

DEFF Research Database (Denmark)

Bhowmik, Arghya; Malik, R.; Prakash, S.

2016-01-01

A high concentration of lithium, corresponding to charge capacity of ~4200 mAh/g, can be intercalated in silicon. Unfortunately, due to high intercalation strain leading to fracture and consequent poor cyclability, silicon cannot be used as anode in lithium ion batteries. But recently interconnec......A high concentration of lithium, corresponding to charge capacity of ~4200 mAh/g, can be intercalated in silicon. Unfortunately, due to high intercalation strain leading to fracture and consequent poor cyclability, silicon cannot be used as anode in lithium ion batteries. But recently...... interconnected hollow nano-spheres of amorphous silicon have been found to exhibit high cyclability. The absence of fracture upon lithiation and the high cyclability has been attributed to reduction in intercalation stress due to hollow spherical geometry of the silicon nano-particles. The present work argues...... that the hollow spherical geometry alone cannot ensure the absence of fracture. Using classical molecular dynamics and density functional theory based simulations; satisfactory explanation to the absence of fracture has been explored at the atomic scale....

Surface critical behavior and scaling functions for the three-dimensional mean spherical model

Energy Technology Data Exchange (ETDEWEB)

Amin, Magdy E. [Mathematics Department, Ar' ar Teacher College, Kingdom of Saudi Arabia (Saudi Arabia) and Mathematics Department, Faculty of Science, Minia University (Egypt)]. E-mail: aminmagdy@yahoo.com

2006-10-09

The d-dimensional mean spherical model on a fully finite L{sup d} simple cubic lattice with Neumann-Dirichlet boundary conditions is considered in the presence of a surface external fields acting at the surfaces bounding the system. Exact calculations are evaluated for the fully finite system and in the case of a film geometry Lx{approx}{sup d-1}. Critical finite-size scaling functions both for the specific heat and the mean-square magnetization are derived and investigated close to and below the bulk critical temperature K{sub c}.

Quantization of the Schwarzschild geometry

International Nuclear Information System (INIS)

Melas, Evangelos

2013-01-01

The conditional symmetries of the reduced Einstein-Hilbert action emerging from a static, spherically symmetric geometry are used as supplementary conditions on the wave function. Based on their integrability conditions, only one of the three existing symmetries can be consistently imposed, while the unique Casimir invariant, being the product of the remaining two symmetries, is calculated as the only possible second condition on the wave function. This quadratic integral of motion is identified with the reparametrization generator, as an implication of the uniqueness of the dynamical evolution, by fixing a suitable parametrization of the r-lapse function. In this parametrization, the determinant of the supermetric plays the role of the mesure. The combined Wheeler – DeWitt and linear conditional symmetry equations are analytically solved. The solutions obtained depend on the product of the two ''scale factors''.

Solutions of transport equation in (X-Y-Z) three-dimensional geometry by finite element method and spherical harmonic expansion

International Nuclear Information System (INIS)

Fernandes, A.; Maiorino, J.R.

1989-01-01

This work presents a method to solve the neutron transport equation in thre space dimensions. The angular flux is aproximated by spherical harmonics and the finite element method is applied to the space component. The program originated by the analytical development is being tested and some results are presented. (author) [pt

Application of Mie theory to assess structure of spheroidal scattering in backscattering geometries.

Science.gov (United States)

Chalut, Kevin J; Giacomelli, Michael G; Wax, Adam

2008-08-01

Inverse light scattering analysis seeks to associate measured scattering properties with the most probable theoretical scattering distribution. Although Mie theory is a spherical scattering model, it has been used successfully for discerning the geometry of spheroidal scatterers. The goal of this study was an in-depth evaluation of the consequences of analyzing the structure of spheroidal geometries, which are relevant to cell and tissue studies in biology, by employing Mie-theory-based inverse light scattering analysis. As a basis for this study, the scattering from spheroidal geometries was modeled using T-matrix theory and used as test data. In a previous study, we used this technique to investigate the case of spheroidal scatterers aligned with the optical axis. In the present study, we look at a broader scope which includes the effects of aspect ratio, orientation, refractive index, and incident light polarization. Over this wide range of parameters, our results indicate that this method provides a good estimate of spheroidal structure.

Eccentricity in Images of Circular and Spherical Targets and its Impact to 3D Object Reconstruction

Directory of Open Access Journals (Sweden)

T. Luhmann

2014-06-01

Full Text Available This paper discusses a feature of projective geometry which causes eccentricity in the image measurement of circular and spherical targets. While it is commonly known that flat circular targets can have a significant displacement of the elliptical image centre with respect to the true imaged circle centre, it can also be shown that the a similar effect exists for spherical targets. Both types of targets are imaged with an elliptical contour. As a result, if measurement methods based on ellipses are used to detect the target (e.g. best-fit ellipses, the calculated ellipse centre does not correspond to the desired target centre in 3D space. This paper firstly discusses the use and measurement of circular and spherical targets. It then describes the geometrical projection model in order to demonstrate the eccentricity in image space. Based on numerical simulations, the eccentricity in the image is further quantified and investigated. Finally, the resulting effect in 3D space is estimated for stereo and multi-image intersections. It can be stated that the eccentricity is larger than usually assumed, and must be compensated for high-accuracy applications. Spherical targets do not show better results than circular targets. The paper is an updated version of Luhmann (2014 new experimental investigations on the effect of length measurement errors.

The influence of polyol type on cell geometry and the thermal stability of polyurethane foams

Directory of Open Access Journals (Sweden)

Prendžov Slobodan J.

2006-01-01

Full Text Available The aim of this study was to examine the influence of substituting defined amounts of polyol Voranol 3322 by polyol Voranol CP 1055 on the cell geometry and thermal stability of the synthesized flexible polyurethane foams. The influence of the amount of antipyrene on the cell geometry and their thermal stability was also investigated. The following components were used in the synthesis of the polyurethanes: a mixture of two polyols (Voranol 3322 with the hydroxyl number 47 mg KOH/g, mean molecular mass 3400 and Voranol CP 1055 with the hydroxyl number 156 mg KOH/g, mean molecular mass 1000, toluene discarnate as the isocyanate component, a combination of an organic-metallic compound and a tertiary amine as catalysts, surfactant and water as the coreactant. The thermal stability was determined by thermogravimetric analysis (in a nitrogen atmosphere. The cell geometry was analyzed by optical microscopy. Examination of the cell geometry revealed different cell shapes. The form factor as an indicator of cell deviation from spherical shape increased (more round forms were observed with increasing amount of Voranol CP 1055. The TG examination showed that specimens with 6 and 8 g of Voranol 3322 substituted by Voranol CP 1055 completely degraded at 350 °C, while foams with 10 and 12 g of Voranol 3322 substituted by Voranol CP 1055 displayed lower mass loss at higher temperatures and had residual masses of 46 % and 43 % at 600°C respectively. The addition of antipyrene in an amount of 1% (based on the amount of polyol contributed to improved thermal stability, no visible color change of the specimen tested at 210°C for 40 minutes, and to rounder cell forms. Considering the obtained results it can be concluded that an increase in the amount of Voranol CP 1055 yielded more spherically shaped cells and better thermal stability of the synthesized flexible polyurethane foams. The addition of antipyrene improves the thermal stability and the cell geometry.

Static spherically symmetric wormholes in f(R, T) gravity

Energy Technology Data Exchange (ETDEWEB)

Zubair, M.; Ahmad, Yasir [Institute Of Information Technology, Department of Mathematics, COMSATS, Lahore (Pakistan); Waheed, Saira [Prince Mohammad Bin Fahd University, Al Khobar (Saudi Arabia)

2016-08-15

In this work, we explore wormhole solutions in f(R, T) theory of gravity, where R is the scalar curvature and T is the trace of stress-energy tensor of matter. To investigate this, we consider a static spherically symmetric geometry with matter contents as anisotropic, isotropic, and barotropic fluids in three separate cases. By taking into account the Starobinsky f(R) model, we analyze the behavior of energy conditions for these different kinds of fluids. It is shown that the wormhole solutions can be constructed without exotic matter in few regions of space-time. We also give the graphical illustration of the results obtained and discuss the equilibrium picture for the anisotropic case only. It is concluded that the wormhole solutions with anisotropic matter are realistic and stable in this theory of gravity. (orig.)

Spherical sila- and germa-homoaromaticity.

Science.gov (United States)

Chen, Zhongfang; Hirsch, Andreas; Nagase, Shigeru; Thiel, Walter; Schleyer, Paul von Ragué

2003-12-17

Guided by the 2(N + 1)2 electron-counting rule for spherical aromatic molecules, we have designed various spherical sila- and germa-homoaromatic systems rich in group 14 elements. Their aromaticity is revealed by density-functional computations of their structures and the nucleus-independent chemical shifts (NICS). Besides the formerly used endohedral inclusion strategy, spherical homoaromaticity is another way to stabilize silicon and germanium clusters.

A multi purpose 4 π counter spherical ionization chamber type

International Nuclear Information System (INIS)

Calin, Marian Romeo; Calin, Adrian Cantemir

2004-01-01

A pressurized ionization chamber detector able to measure radioactive sources in internal 2π or 4π geometry was built in order to characterize alpha and beta radioactive sources, i.e. to calibrate these sources by relative method and to test the behavior of gas mixtures in pressurized-gas radiation detectors. The detector we made is of spherical shape and works by collecting in a uniform electric field the ionization charges resulting from the interaction of ionizing radiation with gas in the sensitive volume of the chamber. An ionizing current proportional to the activity of the radioactive source to be measured is obtained. In this paper a gas counter with a spherical symmetry is described. This detector can work in a very satisfactory manner, either as a flow counter or as a ionization chamber reaching in the latter case a good α pulse height resolution, even with large emitting sources. Calculations are made in order to find the dependence of the pulse shape on the direction of emission of an α-particle by a point source in the chamber (finite track). A good agreement is found between these calculations and the experimental tests performed, which show that this dependence can be employed in high efficiency measurements of angular α-γ correlations. (authors)

Flyby Characterization of Lower-Degree Spherical Harmonics Around Small Bodies

Science.gov (United States)

Takahashi, Yu; Broschart, Stephen; Lantoine, Gregory

2014-01-01

Interest in studying small bodies has grown significantly in the last two decades, and there are a number of past, present, and future missions. These small body missions challenge navigators with significantly different kinds of problems than the planets and moons do. The small bodies' shape is often irregular and their gravitational field significantly weak, which make the designing of a stable orbit a complex dynamical problem. In the initial phase of spacecraft rendezvous with a small body, the determination of the gravitational parameter and lower-degree spherical harmonics are of crucial importance for safe navigation purposes. This motivates studying how well one can determine the total mass and lower-degree spherical harmonics in a relatively short time in the initial phase of the spacecraft rendezvous via flybys. A quick turnaround for the gravity data is of high value since it will facilitate the subsequent mission design of the main scientific observation campaign. We will present how one can approach the problem to determine a desirable flyby geometry for a general small body. We will work in the non-dimensional formulation since it will generalize our results across different size/mass bodies and the rotation rate for a specific combination of gravitational coefficients.

Influence of the Ringwoodite-Perovskite transition on mantle convection in spherical geometry as a function of Clapeyron slope and Rayleigh number

Directory of Open Access Journals (Sweden)

M. Wolstencroft

2011-12-01

Full Text Available We investigate the influence on mantle convection of the negative Clapeyron slope ringwoodite to perovskite and ferro-periclase mantle phase transition, which is correlated with the seismic discontinuity at 660 km depth. In particular, we focus on understanding the influence of the magnitude of the Clapeyron slope (as measured by the Phase Buoyancy parameter, P and the vigour of convection (as measured by the Rayleigh number, Ra on mantle convection. We have undertaken 76 simulations of isoviscous mantle convection in spherical geometry, varying Ra and P. Three domains of behaviour were found: layered convection for high Ra and more negative P, whole mantle convection for low Ra and less negative P, and transitional behaviour in an intervening domain. The boundary between the layered and transitional domain was fit by a curve P = α Ra^β where α = −1.05, and β = −0.1, and the fit for the boundary between the transitional and whole mantle convection domain was α = −4.8, and β = −0.25. These two curves converge at Ra ≈ 2.5 × 10⁴ (well below Earth mantle vigour and P ≈ −0.38. Extrapolating to high Ra, which is likely earlier in Earth history, this work suggests a large transitional domain. It is therefore likely that convection in the Archean would have been influenced by this phase change, with Earth being at least in the transitional domain, if not the layered domain.

Separation of attractors in 1-modulus quantum corrected special geometry

CERN Document Server

Bellucci, S; Marrani, A; Shcherbakov, A

2008-01-01

We study the solutions to the N=2, d=4 Attractor Equations in a dyonic, extremal, static, spherically symmetric and asymptotically flat black hole background, in the simplest case of perturbative quantum corrected cubic Special Kahler geometry consistent with continuous axion-shift symmetry, namely in the 1-modulus Special Kahler geometry described (in a suitable special symplectic coordinate) by the holomorphic Kahler gauge-invariant prepotential F=t^3+i*lambda, with lambda real. By performing computations in the ``magnetic'' charge configuration, we find evidence for interesting phenomena (absent in the classical limit of vanishing lambda). Namely, for a certain range of the quantum parameter lambda we find a ``splitting'' of attractors, i.e. the existence of multiple solutions to the Attractor Equations for fixed supporting charge configuration. This corresponds to the existence of ``area codes'' in the radial evolution of the scalar t, determined by the various disconnected regions of the moduli space, wh...

From Spheric to Aspheric Solid Polymer Lenses: A Review

Directory of Open Access Journals (Sweden)

Kuo-Yung Hung

2011-01-01

Full Text Available This paper presents a new approach in the use of MEMS technology to fabricate micro-optofluidic polymer solid lenses in order to achieve the desired profile, focal length, numerical aperture, and spot size. The resulting polymer solid lenses can be applied in optical data storage systems, imaging systems, and automated optical inspection systems. In order to meet the various needs of different applications, polymer solid lenses may have a spherical or aspherical shape. The method of fabricating polymer solid lenses is different from methods used to fabricate tunable lenses with variable focal length or needing an external control system to change the lens geometry. The current trend in polymer solid lenses is toward the fabrication of microlenses with a high numerical aperture, small clear aperture (<2 mm, and high transmittance. In this paper we focus on the use of thermal energy and electrostatic force in shaping the lens profile, including both spherical and aspherical lenses. In addition, the paper discusses how to fabricate a lens with a high numerical aperture of 0.6 using MEMS and also compares the optical characteristics of polymer lens materials, including SU-8, Norland Optical Adhesive (NOA, and cyclic olefin copolymer (COC. Finally, new concepts and applications related to micro-optofluidic lenses and polymer materials are also discussed.

Temporal dependence of the mass ablation rate in uv irradiated spherical targets

International Nuclear Information System (INIS)

Delettrez, J.; Jaanimagi, P.A.; Henke, B.L.; Richardson, M.C.

1985-01-01

In this talk, measurements of thermal transport in spherical geometry using time-resolved x-ray spectroscopy are presented. The time dependence of the mass ablation rate (m) is determined by following the progress of the ablation surface through thin layers of material embedded at various depths below the surface of the target. These measurements made with 6, 12 and 24 uv (351 nm) beams from OMEGA are compared to previous thermal transport data and are in qualitative agreement with detailed LILAC hydrodynamic code simulations which predict a sharp decrease in m after the peak of the laser pulse. Viewgraphs of the talk comprise the report

Monte Carlo calculation of Dancoff factors in irregular geometries

International Nuclear Information System (INIS)

Feher, S.; Hoogenboom, J.E.; Leege, P.F.A. de; Valko, J.

1994-01-01

A Monte Carlo program is described that calculates Dancoff factors in arbitrary arrangements of cylindrical or spherical fuel elements. The fuel elements can have different diameters and material compositions, and they are allowed to be black or partially transparent. Calculations of the Dancoff factor is based on its collision probability definition. The Monte Carlo approach is recommended because it is equally applicable in simple and in complicated geometries. It is shown that some of the commonly used algorithms are inaccurate even in infinite regular lattices. An example of application includes the Canada deuterium uranium (CANDU) 37-pin fuel bundle, which requires different Dancoff factors for the symmetrically different fuel pin positions

The solution of the multigroup neutron transport equation using spherical harmonics

International Nuclear Information System (INIS)

Fletcher, K.

1981-01-01

A solution of the multi-group neutron transport equation in up to three space dimensions is presented. The flux is expanded in a series of unnormalised spherical harmonics. Using the various recurrence formulae a linked set of first order differential equations is obtained for the moments psisup(g)sub(lm)(r), γsup(g)sub(lm)(r). Terms with odd l are eliminated resulting in a second order system which is solved by two methods. The first is a finite difference formulation using an iterative procedure, secondly, in XYZ and XY geometry a finite element solution is given. Results for a test problem using both methods are exhibited and compared. (orig./RW) [de

Scalar self-energy for a charged particle in global monopole spacetime with a spherical boundary

International Nuclear Information System (INIS)

De Mello, E R Bezerra; Saharian, A A

2012-01-01

We analyze combined effects of the geometry produced by a global monopole and a concentric spherical boundary on the self-energy of a point-like scalar charged test particle at rest. We assume that the boundary is outside the monopole's core with a general spherically symmetric inner structure. An important quantity to this analysis is the three-dimensional Green function associated with this system. For both Dirichlet and Neumann boundary conditions obeyed by the scalar field on the sphere, the Green function presents a structure that contains contributions due to the background geometry of the spacetime and the boundary. Consequently, the corresponding induced scalar self-energy also presents a similar structure. For points near the sphere, the boundary-induced part dominates and the self-force is repulsive/attractive with respect to the boundary for Dirichlet/Neumann boundary condition. In the region outside the sphere at large distances from it, the boundary-free part in the self-energy dominates and the corresponding self-force can be either attractive or repulsive with dependence of the curvature coupling parameter for scalar field. In particular, for the minimal coupling we show the presence of a stable equilibrium point for the Dirichlet boundary condition. In the region inside the sphere, the nature of the self-force depends on the specific model for the monopole's core. As illustrations of the general procedure adopted, we shall consider two distinct models, namely the flower-pot and the ballpoint-pen ones. (paper)

Spherical tokamak development in Brazil

Energy Technology Data Exchange (ETDEWEB)

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 tokamak development in Brazil

International Nuclear Information System (INIS)

Ludwig, Gerson Otto; Bosco, Edson Del; Ferreira, Julio Guimaraes

2003-01-01

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)

Geometries

CERN Document Server

Sossinsky, A B

2012-01-01

The book is an innovative modern exposition of geometry, or rather, of geometries; it is the first textbook in which Felix Klein's Erlangen Program (the action of transformation groups) is systematically used as the basis for defining various geometries. The course of study presented is dedicated to the proposition that all geometries are created equal--although some, of course, remain more equal than others. The author concentrates on several of the more distinguished and beautiful ones, which include what he terms "toy geometries", the geometries of Platonic bodies, discrete geometries, and classical continuous geometries. The text is based on first-year semester course lectures delivered at the Independent University of Moscow in 2003 and 2006. It is by no means a formal algebraic or analytic treatment of geometric topics, but rather, a highly visual exposition containing upwards of 200 illustrations. The reader is expected to possess a familiarity with elementary Euclidean geometry, albeit those lacking t...

Quasi-spherical compression of a spark-channel plasma

International Nuclear Information System (INIS)

Panarella, E.

1980-01-01

An axial spark channel in deuterium has been used as a target for implosive shock waves created with a conventional cylindrical theta-pinch device. The compression of the channel by the implosive waves raised the plasma electron temperature to approximately 120 eV for approximately 6 kJ of condenser bank energy and 1 Torr initial gas pressure. In order to improve the efficiency of compression of the channel plasma and to reduce the end losses inherent in the cylindrical configuration, the theta-pinch geometry was then converted from cylindrical into spherical. Under identical conditions of gas pressure and condenser bank energy, the electron temperature now peaked at approximately 400 eV. When the bank energy was increased to approximately 10 kJ, neutron production was observed. The total neutron output per shot ranged from 10 5 to 10 6 and increased inversely with the pinch discharge volume

Proton recoil spectra in spherical proportional counters calculated with finite element and Monte Carlo methods

Energy Technology Data Exchange (ETDEWEB)

Benmosbah, M. [Laboratoire de Chimie Physique et Rayonnement Alain Chambaudet, UMR CEA E4, Universite de Franche-Comte, 16 route de Gray, 25030 Besancon Cedex (France); Groetz, J.E. [Laboratoire de Chimie Physique et Rayonnement Alain Chambaudet, UMR CEA E4, Universite de Franche-Comte, 16 route de Gray, 25030 Besancon Cedex (France)], E-mail: jegroetz@univ-fcomte.fr; Crovisier, P. [Service de Protection contre les Rayonnements, CEA Valduc, 21120 Is/Tille (France); Asselineau, B. [Laboratoire de Metrologie et de Dosimetrie des Neutrons, IRSN, Cadarache BP3, 13115 St Paul-lez-Durance (France); Truffert, H.; Cadiou, A. [AREVA NC, Etablissement de la Hague, DQSSE/PR/E/D, 50444 Beaumont-Hague Cedex (France)

2008-08-11

Proton recoil spectra were calculated for various spherical proportional counters using Monte Carlo simulation combined with the finite element method. Electric field lines and strength were calculated by defining an appropriate mesh and solving the Laplace equation with the associated boundary conditions, taking into account the geometry of every counter. Thus, different regions were defined in the counter with various coefficients for the energy deposition in the Monte Carlo transport code MCNPX. Results from the calculations are in good agreement with measurements for three different gas pressures at various neutron energies.

Energy levels of GaAs/Al{sub x}Ga{sub 1-x}As/AlAs spherical quantum dot with an impurity

Energy Technology Data Exchange (ETDEWEB)

Boz, Figen Karaca, E-mail: figenb@trakya.edu.tr; Nisanci, Beyza; Aktas, Saban; Okan, S. Erol

2016-11-30

Highlights: • Energy levels and probability distribution of an electron in GaAs/AlxGa1-xAs/AlAs spherical quantum dot were calculated. • The size effects on the electronic binding energy were determined within a core/shell/shell model. • The differences between the impurity energies of the first and the second levels are detected. - Abstract: We have calculated the energy levels and the radial probability distributions of an electron with an impurity in a spherical quantum dot which is layered as GaAs/Al{sub x}Ga{sub 1-x}As/AlAs. The numerical method used is the fourth-order Runge–Kutta method in the framework of the effective mass approximation. The variation of the energy levels have been calculated as functions of the radius of the GaAs sphere and the thickness of Al{sub x}Ga{sub 1-x}As spherical layer considering effective mass and dielectric constant mismatches. The results have presented the importance of the geometry on the electronic properties of the spherical GaAs/Al{sub x}Ga{sub 1-x}As/AlAs quantum dot.

Hybrid simplified spherical harmonics with diffusion equation for light propagation in tissues

International Nuclear Information System (INIS)

Chen, Xueli; Sun, Fangfang; Yang, Defu; Ren, Shenghan; Liang, Jimin; Zhang, Qian

2015-01-01

Aiming at the limitations of the simplified spherical harmonics approximation (SP N ) and diffusion equation (DE) in describing the light propagation in tissues, a hybrid simplified spherical harmonics with diffusion equation (HSDE) based diffuse light transport model is proposed. In the HSDE model, the living body is first segmented into several major organs, and then the organs are divided into high scattering tissues and other tissues. DE and SP N are employed to describe the light propagation in these two kinds of tissues respectively, which are finally coupled using the established boundary coupling condition. The HSDE model makes full use of the advantages of SP N and DE, and abandons their disadvantages, so that it can provide a perfect balance between accuracy and computation time. Using the finite element method, the HSDE is solved for light flux density map on body surface. The accuracy and efficiency of the HSDE are validated with both regular geometries and digital mouse model based simulations. Corresponding results reveal that a comparable accuracy and much less computation time are achieved compared with the SP N model as well as a much better accuracy compared with the DE one. (paper)

Hybrid simplified spherical harmonics with diffusion equation for light propagation in tissues.

Science.gov (United States)

Chen, Xueli; Sun, Fangfang; Yang, Defu; Ren, Shenghan; Zhang, Qian; Liang, Jimin

2015-08-21

Aiming at the limitations of the simplified spherical harmonics approximation (SPN) and diffusion equation (DE) in describing the light propagation in tissues, a hybrid simplified spherical harmonics with diffusion equation (HSDE) based diffuse light transport model is proposed. In the HSDE model, the living body is first segmented into several major organs, and then the organs are divided into high scattering tissues and other tissues. DE and SPN are employed to describe the light propagation in these two kinds of tissues respectively, which are finally coupled using the established boundary coupling condition. The HSDE model makes full use of the advantages of SPN and DE, and abandons their disadvantages, so that it can provide a perfect balance between accuracy and computation time. Using the finite element method, the HSDE is solved for light flux density map on body surface. The accuracy and efficiency of the HSDE are validated with both regular geometries and digital mouse model based simulations. Corresponding results reveal that a comparable accuracy and much less computation time are achieved compared with the SPN model as well as a much better accuracy compared with the DE one.

Geometry of lengths, areas, and volumes two-dimensional spaces, volume 1

CERN Document Server

Cannon, James W

2017-01-01

This is the first of a three volume collection devoted to the geometry, topology, and curvature of 2-dimensional spaces. The collection provides a guided tour through a wide range of topics by one of the twentieth century's masters of geometric topology. The books are accessible to college and graduate students and provide perspective and insight to mathematicians at all levels who are interested in geometry and topology. The first volume begins with length measurement as dominated by the Pythagorean Theorem (three proofs) with application to number theory; areas measured by slicing and scaling, where Archimedes uses the physical weights and balances to calculate spherical volume and is led to the invention of calculus; areas by cut and paste, leading to the Bolyai-Gerwien theorem on squaring polygons; areas by counting, leading to the theory of continued fractions, the efficient rational approximation of real numbers, and Minkowski's theorem on convex bodies; straight-edge and compass constructions, giving c...

Assessing the mechanical properties of nuclear materials using spherical nano-indentation

International Nuclear Information System (INIS)

Hickey, J.; Hardie, C.

2015-01-01

This paper reports on the assessment of a nano-indentation test, using tips of spherical geometry, to calculate the mechanical properties of nuclear materials at the micron-scale. The test method is based on incrementally loading and unloading the tip into a sample of material with unknown mechanical properties. The incremental indentation stress, strain and elastic modulus are calculated by analysing each increment's unload curve. Two samples of iron and tungsten were used with a spherical indenter tip with an apparent radius of 30 μm. The method for calculating the mechanical properties is based on two markers that define the top and bottom of each load increment's unload curve. As such, the bottom marker can be moved down the unload curve to increase the proportion of data included in the results. This simulates increasing the percent unloaded from just one data set. The results showed that increasing the percent unloaded during each increment was beneficial as it reduced the effects of creep at the top of the unload curve and pile-up of material around the indenter tip as the test progressed. However, it is likely that increasing the percentage unloaded results in the inclusion of a higher proportion of reverse plasticity effects in the calculated results. (authors)

The spherical harmonics method, II (application to problems with plane and spherical symmetry)

Energy Technology Data Exchange (ETDEWEB)

Mark, C

1958-12-15

The application of the spherical harmonic method to problems with plane or spherical symmetry is discussed in detail. The numerical results of some applications already made are included to indicate the degree of convergence obtained. Formulae for dealing with distributions of isotropic sources are developed. Tables useful in applying the method are given in Section 11. (author)

Classical molecular dynamics and quantum ab-initio studies on lithium-intercalation in interconnected hollow spherical nano-spheres of amorphous silicon

Energy Technology Data Exchange (ETDEWEB)

Bhowmik, A. [Atomic Scale Modelling and Materials, Department of Energy Conversion and Storage, Technical University of Denmark, Rios Campus, Frederiksborgvej 399, DK-4000 Roskilde (Denmark); Malik, R. [Department of Metallurgical and Materials Engineering, Indian Institute of Technology Kharagpur, 721302 (India); Prakash, S. [Defense Metallurgical Research Laboratory, Hyderabad (India); Sarkar, T.; Bharadwaj, M.D. [Center for Study of Science Technology and Policy, Bangalore 560094 (India); Aich, S. [Department of Metallurgical and Materials Engineering, Indian Institute of Technology Kharagpur, 721302 (India); Ghosh, S., E-mail: sudipto@metal.iitkgp.ernet.in [Department of Metallurgical and Materials Engineering, Indian Institute of Technology Kharagpur, 721302 (India)

2016-04-25

A high concentration of lithium, corresponding to charge capacity of ∼4200 mAh/g, can be intercalated in silicon. Unfortunately, due to high intercalation strain leading to fracture and consequent poor cyclability, silicon cannot be used as anode in lithium ion batteries. But recently interconnected hollow nano-spheres of amorphous silicon have been found to exhibit high cyclability. The absence of fracture upon lithiation and the high cyclability has been attributed to reduction in intercalation stress due to hollow spherical geometry of the silicon nano-particles. The present work argues that the hollow spherical geometry alone cannot ensure the absence of fracture. Using classical molecular dynamics and density functional theory based simulations; satisfactory explanation to the absence of fracture has been explored at the atomic scale. - Highlights: • Interconnected nanoshells of amorphous Si: best available lithium ion cell anode. • High cycle life not understood in the light of poor K{sub IC} of amorphous Si. • MD reveals: atomic density of interconnected structure is ∼16% less than bulk Si. • Leads to drastic reduction (DFT) in lithiation σ & metal like e{sup −} structure (high K{sub IC}). • Lowering of lithiation σ and increase in K{sub IC} result in high cycle life.

Analytical form of current-voltage characteristic of parallel-plane, cylindrical and spherical ionization chambers with homogeneous ionization

Energy Technology Data Exchange (ETDEWEB)

Stoyanov, D G [Faculty of Engineering and Pedagogy in Sliven, Technical University of Sofia, 59, Bourgasko Shaussee Blvd, 8800 Sliven (Bulgaria)

2007-11-15

The elementary processes taking place in the formation of charged particles and their flow in parallel-plane, cylindrical and spherical geometry cases of ionization chamber are considered. On the basis of particles and charges balance a differential equation describing the distribution of current densities in the ionization chamber volume is obtained. As a result of the differential equation solution an analytical form of the current-voltage characteristic of an ionization chamber with homogeneous ionization is obtained. For the parallel-plane case comparision with experimental data is performed.

Analytical form of current-voltage characteristic of parallel-plane, cylindrical and spherical ionization chambers with homogeneous ionization

International Nuclear Information System (INIS)

Stoyanov, D G

2007-01-01

The elementary processes taking place in the formation of charged particles and their flow in parallel-plane, cylindrical and spherical geometry cases of ionization chamber are considered. On the basis of particles and charges balance a differential equation describing the distribution of current densities in the ionization chamber volume is obtained. As a result of the differential equation solution an analytical form of the current-voltage characteristic of an ionization chamber with homogeneous ionization is obtained. For the parallel-plane case comparision with experimental data is performed

Criticality safety validation: Simple geometry, single unit 233U systems

International Nuclear Information System (INIS)

Putman, V.L.

1997-06-01

Typically used LMITCO criticality safety computational methods are evaluated for suitability when applied to INEEL 233 U systems which reasonably can be modeled as simple-geometry, single-unit systems. Sixty-seven critical experiments of uranium highly enriched in 233 U, including 57 aqueous solution, thermal-energy systems and 10 metal, fast-energy systems, were modeled. These experiments include 41 cylindrical and 26 spherical cores, and 41 reflected and 26 unreflected systems. No experiments were found for intermediate-neutron-energy ranges, or with interstitial non-hydrogenous materials typical of waste systems, mixed 233 U and plutonium, or reflectors such as steel, lead, or concrete. No simple geometry experiments were found with cubic or annular cores, or approximating infinite sea systems. Calculations were performed with various tools and methodologies. Nine cross-section libraries, based on ENDF/B-IV, -V, or -VI.2, or on Hansen-Roach source data, were used with cross-section processing methods of MCNP or SCALE. The k eff calculations were performed with neutral-particle transport and Monte Carlo methods of criticality codes DANT, MCNP 4A, and KENO Va

World Gravity Map: a set of global complete spherical Bouguer and isostatic anomaly maps and grids

Science.gov (United States)

Bonvalot, S.; Balmino, G.; Briais, A.; Kuhn, M.; Peyrefitte, A.; Vales, N.; Biancale, R.; Gabalda, G.; Reinquin, F.

2012-04-01

We present here a set of digital maps of the Earth's gravity anomalies (surface free air, Bouguer and isostatic), computed at Bureau Gravimetric International (BGI) as a contribution to the Global Geodetic Observing Systems (GGOS) and to the global geophysical maps published by the Commission for the Geological Map of the World (CGMW) with support of UNESCO and other institutions. The Bouguer anomaly concept is extensively used in geophysical interpretation to investigate the density distributions in the Earth's interior. Complete Bouguer anomalies (including terrain effects) are usually computed at regional scales by integrating the gravity attraction of topography elements over and beyond a given area (under planar or spherical approximations). Here, we developed and applied a worldwide spherical approach aimed to provide a set of homogeneous and high resolution gravity anomaly maps and grids computed at the Earth's surface, taking into account a realistic Earth model and reconciling geophysical and geodetic definitions of gravity anomalies. This first version (1.0) has been computed by spherical harmonics analysis / synthesis of the Earth's topography-bathymetry up to degree 10800. The detailed theory of the spherical harmonics approach is given in Balmino et al., (Journal of Geodesy, 2011). The Bouguer and terrain corrections have thus been computed in spherical geometry at 1'x1' resolution using the ETOPO1 topography/bathymetry, ice surface and bedrock models from the NOAA (National Oceanic and Atmospheric Administration) and taking into account precise characteristics (boundaries and densities) of major lakes, inner seas, polar caps and of land areas below sea level. Isostatic corrections have been computed according to the Airy-Heiskanen model in spherical geometry for a constant depth of compensation of 30km. The gravity information given here is provided by the Earth Geopotential Model (EGM2008), developed at degree 2160 by the National Geospatial

Statistical Mechanics of Thin Spherical Shells

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Andrej Košmrlj

2017-01-01

Full Text Available 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.

Biofilm formation in geometries with different surface curvature and oxygen availability

International Nuclear Information System (INIS)

Chang, Ya-Wen; Fragkopoulos, Alexandros A; Kim, Harold D; Fernández-Nieves, Alberto; Marquez, Samantha M; Angelini, Thomas E

2015-01-01

Bacteria in the natural environment exist as interface-associated colonies known as biofilms . Complex mechanisms are often involved in biofilm formation and development. Despite the understanding of the molecular mechanisms involved in biofilm formation, it remains unclear how physical effects in standing cultures influence biofilm development. The topology of the solid interface has been suggested as one of the physical cues influencing bacteria-surface interactions and biofilm development. Using the model organism Bacillus subtilis, we study the transformation of swimming bacteria in liquid culture into robust biofilms in a range of confinement geometries (planar, spherical and toroidal) and interfaces (air/water, silicone/water, and silicone elastomer/water). We find that B. subtilis form submerged biofilms at both solid and liquid interfaces in addition to air-water pellicles. When confined, bacteria grow on curved surfaces of both positive and negative Gaussian curvature. However, the confinement geometry does affect the resulting biofilm roughness and relative coverage. We also find that the biofilm location is governed by oxygen availability as well as by gravitational effects; these compete with each other in some situations. Overall, our results demonstrate that confinement geometry is an effective way to control oxygen availability and subsequently biofilm growth. (paper)

Influences of target geometry on the microdosimetry of alpha particles in water

International Nuclear Information System (INIS)

Huston, T.E.

1992-01-01

Application of microdosimetric concepts to radiation exposure situations requires knowledge of the single-event density function, f 1 (z) , where z denotes specific energy imparted to target matter. Multiple-event density functions are calculated by taking convolutions of f 1 (z) with itself with the overall specific energy density function is then found by employing a compound Poisson process involving single and multiple-event spectra. The f l (z), depends strongly on the geometric details of a the source, target, and all intermediate matter. While most past applications of microdosimetry have been represented targets as spheres, may be better modeled as prolate or oblate spheroids. Using a ray-tracing technique coupled with a continuous-slowing-down approximation, methods are developed and presented for calculating single-event density functions for spheroidal targets irradiated by alpha-emitting point sources. Computational methods are incorporated into a fortran computer code entitled SEROID (single-event density functions for spheroids), which is listed in this paper. This was used to generate several single-event density functions, along with related means and standard deviations in specific energy, for spheroidal targets irradiated by alpha particles. Targets of varying shapes and orientations are examined. Results for non-spherical targets are compared to spherical targets of equal volume in order to assess influences which target geometry has on single-event quantities. From these comparisons it is found that both target shape and orientation are important in adequately characterizing the quantities examined in this study; over-simplifying the target geometry can lead to substantial error

Spherical Tensor Calculus for Local Adaptive Filtering

Science.gov (United States)

Reisert, Marco; Burkhardt, Hans

In 3D image processing tensors play an important role. While rank-1 and rank-2 tensors are well understood and commonly used, higher rank tensors are rare. This is probably due to their cumbersome rotation behavior which prevents a computationally efficient use. In this chapter we want to introduce the notion of a spherical tensor which is based on the irreducible representations of the 3D rotation group. In fact, any ordinary cartesian tensor can be decomposed into a sum of spherical tensors, while each spherical tensor has a quite simple rotation behavior. We introduce so called tensorial harmonics that provide an orthogonal basis for spherical tensor fields of any rank. It is just a generalization of the well known spherical harmonics. Additionally we propose a spherical derivative which connects spherical tensor fields of different degree by differentiation. Based on the proposed theory we present two applications. We propose an efficient algorithm for dense tensor voting in 3D, which makes use of tensorial harmonics decomposition of the tensor-valued voting field. In this way it is possible to perform tensor voting by linear-combinations of convolutions in an efficient way. Secondly, we propose an anisotropic smoothing filter that uses a local shape and orientation adaptive filter kernel which can be computed efficiently by the use spherical derivatives.

Elastic stresses at reinforced nozzles in spherical shells with pressure and moment loading. Phase report 117-9

International Nuclear Information System (INIS)

Rodabaugh, E.C.; Gwaltney, R.C.

1975-01-01

The ASME Boiler and Pressure Vessel Code gives design guidance for nozzles in pressure vessels in the form of ''stress indices.'' These stress indices enable the designer of Class 1 nuclear pressure vessels to quickly determine the magnitude of stresses due to internal pressure loading; a task otherwise requiring an expensive and time-consuming stress analysis. The Code gives stress indices for nozzles in both heads and cylindrical vessels. Results of calculations of stresses in spherical heads or vessels are summarized. The validity of the Code indices for this geometry is examined and, as a result, a few relatively minor changes are recommended. The definitions involved in the use of the Code stress indices are not sufficiently clear and explicit. Accordingly, recommendations for changes in the Code to improve these defintions as well as to correct some obvious errors are presented. These recommendations apply to nozzles in cylindrical vessels and any type of formed head (e.g., spherical, elliptical, torispherical). However, the data presented herein apply only to isolated nozzles in spherical heads or in other heads where the radius of curvature in the vicinity of the nozzle is sphere-like, e.g., as in the center of a torispherical head. (U.S.)

The GeoFlow experiment-spherical Rayleigh-Benard convection under the influence of an artificial central force field

International Nuclear Information System (INIS)

Gellert, M; Beltrame, P; Egbers, C

2005-01-01

Spherical Rayleigh-Benard convection under the influence of an artificial central force field produced by the so-called dielectrophoretic effect is studied as a simplified model of the flow in the outer earth core. The fluid motion there is most probably driving the earth's dynamo and the energy source for the earth's magnetic field. Studying convective flows in earth-like geometry could lead to a deeper understanding of the basics of these processes. This research is a preparatory study for the experiments on the International Space Station (ISS). A bifurcation-theoretical approach shows the existence of heteroclinic cycles between spherical modes (l, l + 1) for the non-rotating system. This behavior depends strong on the radius ratio of the spheres and will be hard to detect in the experiment. For slow rotations interactions of the azimuthal modes (m, m + 1) found in numerical simulations for supercritical states are supposed to be experimentally observable

In planta engineering of gold nanoparticles of desirable geometries by modulating growth conditions: an environment-friendly approach.

Science.gov (United States)

Starnes, Daniel L; Jain, Ajay; Sahi, Shivendra V

2010-09-15

Unique properties of gold nanoparticles (AuNPs) can be achieved by manipulating their geometries. However, it is not known if the shapes and sizes of AuNPs can be modulated in planta. Here, we evaluated the accumulation of gold across taxonomically diverse plant species (alfalfa, cucumber, red clover, ryegrass, sunflower, and oregano). Significant variations were detected in the uptake of gold in the roots ranging from 500 ppm (ryegrass) to 2500 ppm (alfalfa). Alfalfa was selected for subsequent studies due to its ability to accumulate relatively large quantities of gold in its roots. Temporal analysis revealed that most of the AuNPs formed within 6 h of treatment, and the majority of them fall within the size range of 10-30 nm. Spherical AuNPs (1-50 nm) were detected ubiquitously across different treatments. To elucidate the effects of growth variables on the geometries of in planta synthesized AuNPs, alfalfa was subjected to KAuCl(4) (50 ppm) treatment for 3d under different pH, temperature, and light regimes. Interestingly, manipulation of growth conditions triggered a noticeable shift in the relative abundance of spherical, triangular, hexagonal, and rectangular AuNPs providing empirical evidence toward the feasibility of their in planta engineering.

Spiral CT manifestations of spherical pneumonia

International Nuclear Information System (INIS)

Li Xiaohong; Yang Hongwei; Xu Chunmin; Qin Xiu

2008-01-01

Objective: To explore the Spiral CT manifestations and differential diagnosis of spherical pneumonia. Methods: 18 cases of spherical pneumonia and 20 cases of peripheral pulmonary carcinoma were selected, both of them were confirmed by clinic and/or pathology. The SCT findings of both groups were compared retrospectively. Results: Main spiral CT findings of spherical pneumonia were showed as followings: square or triangular lesions adjacent to pleura; with irregular shape, blurry, slightly lobulated margin, sometimes with halo sign. Small inflammatory patches and intensified vascular markings around the lesions were seen. Lesions became smaller or vanished after short-term anti-inflammatory treatment. Conclusion: Spherical pneumonia showed some characteristics on Spiral CT scan, which are helpful in diagnosis and differential diagnosis of this disease. (authors)

Spherical harmonics solutions of multi-dimensional neutron transport equation by finite Fourier transformation

International Nuclear Information System (INIS)

Kobayashi, Keisuke

1977-01-01

A method of solution of a monoenergetic neutron transport equation in P sub(L) approximation is presented for x-y and x-y-z geometries using the finite Fourier transformation. A reactor system is assumed to consist of multiregions in each of which the nuclear cross sections are spatially constant. Since the unknown functions of this method are the spherical harmonics components of the neutron angular flux at the material boundaries alone, the three- and two-dimensional equations are reduced to two- and one-dimensional equations, respectively. The present approach therefore gives fewer unknowns than in the usual series expansion method or in the finite difference method. Some numerical examples are shown for the criticality problem. (auth.)

Non-conformal contact mechanical characteristic analysis on spherical components

Energy Technology Data Exchange (ETDEWEB)

Zhen-zhi, G.; Bin, H.; Zheng-ming, G.; Feng-mei, Y.; Jin, Q [The 2. Artillery Engineering Univ., Xi' an (China)

2017-03-15

Non-conformal spherical-contact mechanical problems is a three-dimensional coordination or similar to the coordination spherical contact. Due to the complexity of the problem of spherical-contact and difficulties of solving higher-order partial differential equations, problems of three-dimensional coordination or similar to the coordination spherical-contact is still no exact analytical method for solving. It is based on three-dimensional taper model is proposed a model based on the contour surface of the spherical contact and concluded of the formula of the contact pressure and constructed of finite element model by contact pressure distribution under the non-conformal spherical. The results shows spherical contact model can reflect non-conformal spherical-contacting mechanical problems more than taper-contacting model, and apply for the actual project.

Limit analysis of spherical pressure vessels with protruding nozzles and associated defects

International Nuclear Information System (INIS)

Goodall, I.W.; Miller, A.G.

1981-04-01

In order to assess the failure of a structure with a defect it is necessary to obtain both a linear elastic fracture solution and a limit analysis of the structure. In combination these solutions enable the analyst to assess structural integrity. This note deals with the second aspect and investigates the effect of a partial penetration defect on the ductile collapse load of a spherical pressure vessel with a protruding nozzle. A lower bound solution is obtained for defects of varying depth around the intersection of the sphere and the cylinder. Results are presented for a typical geometry and it is found that the solution may be simply represented by three different functions depending on the fractional ligament thickness. (author)

Scaling of a fast spherical discharge

Energy Technology Data Exchange (ETDEWEB)

Antsiferov, P. S., E-mail: Ants@isan.troitsk.ru; Dorokhin, L. A. [Russian Academy of Sciences, Institute of Spectroscopy (Russian Federation)

2017-02-15

The influence of the discharge cavity dimensions on the properties of the spherical plasma formed in a fast discharge was studied experimentally. The passage of a current pulse with an amplitude of 30–40 kA and a rise rate of ~10{sup 12} A/s (a fast discharge) through a spherical ceramic (Al{sub 2}O{sub 3}) cavity with an inner diameter of 11 mm filled with argon at a pressure of 80 Pa results in the formation of a 1- to 2-mm-diameter spherical plasma with an electron temperature of several tens of electronvolts and a density of 10{sup 18}–10{sup 19} cm{sup –3}. It is shown that an increase in the inner diameter of the discharge cavity from 11 to 21 mm leads to the fourfold increase in the formation time of the spherical plasma and a decrease in the average ion charge. A decrease in the cavity diameter to 7 mm makes the spherical plasma unstable.

Spherical aberrations of human astigmatic corneas.

Science.gov (United States)

Zhao, Huawei; Dai, Guang-Ming; Chen, Li; Weeber, Henk A; Piers, Patricia A

2011-11-01

To evaluate whether the average spherical aberration of human astigmatic corneas is statistically equivalent to human nonastigmatic corneas. Spherical aberrations of 445 astigmatic corneas prior to laser vision correction were retrospectively investigated to determine Zernike coefficients for central corneal areas 6 mm in diameter using CTView (Sarver and Associates). Data were divided into groups according to cylinder power (0.01 to 0.25 diopters [D], 0.26 to 0.75 D, 0.76 to 1.06 D, 1.07 to 1.53 D, 1.54 to 2.00 D, and >2.00 D) and according to age by decade. Spherical aberrations were correlated with age and astigmatic power among groups and the entire population. Statistical analyses were conducted, and P.05 for all tested groups). Mean spherical aberration of astigmatic corneas was not correlated significantly with cylinder power or age (P>.05). Spherical aberrations are similar to those of nonastigmatic corneas, permitting the use of these additional data in the design of aspheric toric intra-ocular lenses. Copyright 2011, SLACK Incorporated.

Tunable geometry of bacterial inclusion bodies as substrate materials for tissue engineering

Energy Technology Data Exchange (ETDEWEB)

GarcIa-Fruitos, Elena; Seras-Franzoso, JoaquIn; Vazquez, Esther; Villaverde, Antonio [CIBER en BioingenierIa, Biomateriales y Nanomedicina, Bellaterra, 08193 Barcelona (Spain); Institut de Biotecnologia i de Biomedicina and Departament de Genetica i de Microbiologia, Universitat Autonoma de Barcelona, 08193 Bellaterra (Cerdanyola del Valles), Barcelona (Spain)

2010-05-21

A spectrum of materials for biomedical applications is produced in bacteria, and some of them, such as metals or polyhydroxyalkanoates, are straightforwardly obtained as particulate entities. We have explored the biofabrication process of bacterial inclusion bodies, particulate proteinaceous materials (ranging from 50 to 500 nm in diameter) recently recognized as suitable for surface topographical modification and tissue engineering. Inclusion bodies have been widely described as spherical or pseudo-spherical particles with only minor morphological variability, mostly restricted to their size. Here we have identified a cellular gene in Escherichia coli (clpP) that controls the in vivo fabrication process of inclusion bodies. In the absence of the encoded protease, the dynamics of protein deposition is perturbed, resulting in unusual tear-shaped particles with enhanced surface-volume ratios. This fact modifies the ability of inclusion bodies to promote mammalian cell attachment and differentiation upon surface decoration. The implications of the genetic control of inclusion body geometry are discussed in the context of their biological fabrication and regarding the biomedical potential of these protein clusters in regenerative medicine.

Tunable geometry of bacterial inclusion bodies as substrate materials for tissue engineering

International Nuclear Information System (INIS)

GarcIa-Fruitos, Elena; Seras-Franzoso, JoaquIn; Vazquez, Esther; Villaverde, Antonio

2010-01-01

A spectrum of materials for biomedical applications is produced in bacteria, and some of them, such as metals or polyhydroxyalkanoates, are straightforwardly obtained as particulate entities. We have explored the biofabrication process of bacterial inclusion bodies, particulate proteinaceous materials (ranging from 50 to 500 nm in diameter) recently recognized as suitable for surface topographical modification and tissue engineering. Inclusion bodies have been widely described as spherical or pseudo-spherical particles with only minor morphological variability, mostly restricted to their size. Here we have identified a cellular gene in Escherichia coli (clpP) that controls the in vivo fabrication process of inclusion bodies. In the absence of the encoded protease, the dynamics of protein deposition is perturbed, resulting in unusual tear-shaped particles with enhanced surface-volume ratios. This fact modifies the ability of inclusion bodies to promote mammalian cell attachment and differentiation upon surface decoration. The implications of the genetic control of inclusion body geometry are discussed in the context of their biological fabrication and regarding the biomedical potential of these protein clusters in regenerative medicine.

ARGO, 1-D Neutron Diffusion in Slab, Cylindrical, Spherical Geometry from JAERI Fast-Set, ABBN, RCBN

International Nuclear Information System (INIS)

Ikawa, Koji

1971-01-01

1 - Nature of physical problem solved: ARGO is a one-dimensional (slab, cylinder or sphere), multigroup diffusion code for use in fast reactor criticality and kinetic parameter analysis. Three cross section sets, i.e., JAERI-Fast-Set, ABBN-Set and RCBN-Set, of 25 groups are prepared for the code as its library tapes. 2 - Method of solution: Eigenvalues are computed by ordinary source-iteration techniques with ordinary acceleration methods for convergence. 3 - Restrictions on the complexity of the problem: Sphere geometry

Spherical grating based x-ray Talbot interferometry

Energy Technology Data Exchange (ETDEWEB)

Cong, Wenxiang, E-mail: congw@rpi.edu, E-mail: xiy2@rpi.edu, E-mail: wangg6@rpi.edu; Xi, Yan, E-mail: congw@rpi.edu, E-mail: xiy2@rpi.edu, E-mail: wangg6@rpi.edu; Wang, Ge, E-mail: congw@rpi.edu, E-mail: xiy2@rpi.edu, E-mail: wangg6@rpi.edu [Biomedical Imaging Center, Rensselaer Polytechnic Institute, Troy, New York 12180 (United States)

2015-11-15

Purpose: Grating interferometry is a state-of-the-art x-ray imaging approach, which can acquire information on x-ray attenuation, phase shift, and small-angle scattering simultaneously. Phase-contrast imaging and dark-field imaging are very sensitive to microstructural variation and offers superior contrast resolution for biological soft tissues. However, a common x-ray tube is a point-like source. As a result, the popular planar grating imaging configuration seriously restricts the flux of photons and decreases the visibility of signals, yielding a limited field of view. The purpose of this study is to extend the planar x-ray grating imaging theory and methods to a spherical grating scheme for a wider range of preclinical and clinical applications. Methods: A spherical grating matches the wave front of a point x-ray source very well, allowing the perpendicular incidence of x-rays on the grating to achieve a higher visibility over a larger field of view than the planer grating counterpart. A theoretical analysis of the Talbot effect for spherical grating imaging is proposed to establish a basic foundation for x-ray spherical gratings interferometry. An efficient method of spherical grating imaging is also presented to extract attenuation, differential phase, and dark-field images in the x-ray spherical grating interferometer. Results: Talbot self-imaging with spherical gratings is analyzed based on the Rayleigh–Sommerfeld diffraction formula, featuring a periodic angular distribution in a polar coordinate system. The Talbot distance is derived to reveal the Talbot self-imaging pattern. Numerical simulation results show the self-imaging phenomenon of a spherical grating interferometer, which is in agreement with the theoretical prediction. Conclusions: X-ray Talbot interferometry with spherical gratings has a significant practical promise. Relative to planar grating imaging, spherical grating based x-ray Talbot interferometry has a larger field of view and

Spherical grating based x-ray Talbot interferometry

International Nuclear Information System (INIS)

Cong, Wenxiang; Xi, Yan; Wang, Ge

2015-01-01

Purpose: Grating interferometry is a state-of-the-art x-ray imaging approach, which can acquire information on x-ray attenuation, phase shift, and small-angle scattering simultaneously. Phase-contrast imaging and dark-field imaging are very sensitive to microstructural variation and offers superior contrast resolution for biological soft tissues. However, a common x-ray tube is a point-like source. As a result, the popular planar grating imaging configuration seriously restricts the flux of photons and decreases the visibility of signals, yielding a limited field of view. The purpose of this study is to extend the planar x-ray grating imaging theory and methods to a spherical grating scheme for a wider range of preclinical and clinical applications. Methods: A spherical grating matches the wave front of a point x-ray source very well, allowing the perpendicular incidence of x-rays on the grating to achieve a higher visibility over a larger field of view than the planer grating counterpart. A theoretical analysis of the Talbot effect for spherical grating imaging is proposed to establish a basic foundation for x-ray spherical gratings interferometry. An efficient method of spherical grating imaging is also presented to extract attenuation, differential phase, and dark-field images in the x-ray spherical grating interferometer. Results: Talbot self-imaging with spherical gratings is analyzed based on the Rayleigh–Sommerfeld diffraction formula, featuring a periodic angular distribution in a polar coordinate system. The Talbot distance is derived to reveal the Talbot self-imaging pattern. Numerical simulation results show the self-imaging phenomenon of a spherical grating interferometer, which is in agreement with the theoretical prediction. Conclusions: X-ray Talbot interferometry with spherical gratings has a significant practical promise. Relative to planar grating imaging, spherical grating based x-ray Talbot interferometry has a larger field of view and

Effect of electron temperature on small-amplitude electron acoustic solitary waves in non-planar geometry

Science.gov (United States)

Bansal, Sona; Aggarwal, Munish; Gill, Tarsem Singh

2018-04-01

Effects of electron temperature on the propagation of electron acoustic solitary waves in plasma with stationary ions, cold and superthermal hot electrons is investigated in non-planar geometry employing reductive perturbation method. Modified Korteweg-de Vries equation is derived in the small amplitude approximation limit. The analytical and numerical calculations of the KdV equation reveal that the phase velocity of the electron acoustic waves increases as one goes from planar to non planar geometry. It is shown that the electron temperature ratio changes the width and amplitude of the solitary waves and when electron temperature is not taken into account,our results completely agree with the results of Javidan & Pakzad (2012). It is found that at small values of τ , solitary wave structures behave differently in cylindrical ( {m} = 1), spherical ( {m} = 2) and planar geometry ( {m} = 0) but looks similar at large values of τ . These results may be useful to understand the solitary wave characteristics in laboratory and space environments where the plasma have multiple temperature electrons.

Inversion algorithms for the spherical Radon and cosine transform

International Nuclear Information System (INIS)

Louis, A K; Riplinger, M; Spiess, M; Spodarev, E

2011-01-01

We consider two integral transforms which are frequently used in integral geometry and related fields, namely the spherical Radon and cosine transform. Fast algorithms are developed which invert the respective transforms in a numerically stable way. So far, only theoretical inversion formulae or algorithms for atomic measures have been derived, which are not so important for applications. We focus on two- and three-dimensional cases, where we also show that our method leads to a regularization. Numerical results are presented and show the validity of the resulting algorithms. First, we use synthetic data for the inversion of the Radon transform. Then we apply the algorithm for the inversion of the cosine transform to reconstruct the directional distribution of line processes from finitely many intersections of their lines with test lines (2D) or planes (3D), respectively. Finally we apply our method to analyse a series of microscopic two- and three-dimensional images of a fibre system

ELSA- The European Levitated Spherical Actruator

Science.gov (United States)

Ruiz, M.; Serin, J.; Telteu-Nedelcu, D.; De La Vallee Poussin, H.; Onillon, E.; Rossini, L.

2014-08-01

The reaction sphere is a magnetic bearing spherical actuator consisting of a permanent magnet spherical rotor that can be accelerated in any direction. It consists of an 8-pole permanent magnet spherical rotor that is magnetically levitated and can be accelerated about any axis by a 20-pole stator with electromagnets. The spherical actuator is proposed as a potential alternative to traditional momentum exchange devices such as reaction wheels (RWs) or control moment gyroscopes (CMGs). This new actuator provides several benefits such as reduced mass and power supply allocated to the attitude and navigation unit, performance gain, and improved reliability due to the absence of mechanical bearings. The paper presents the work done on the levitated spherical actuator and more precisely the electrical drive including its control unit and power parts. An elegant breadboard is currently being manufactured within the frame of an FP7 project. This project also comprises a feasibility study to show the feasibility of integrating such a system on a flight platform and to identify all the challenges to be solved in terms of technology or components to be developed.

Recent experiences with ultrasonic inservice inspection systems with phased array probes on spherical bottoms of boiling water reactors

International Nuclear Information System (INIS)

Wustenberg, H.; Brekow, G.; Erhard, A.; Hein, E.

1988-01-01

The special geometry of the spherical bottom of boiling water reactors with control rods and measuring nozzles requires a very special surveillance technique during the in-service inspection. Reside visual inspection an ultrasonic inspection has been established due to the requirements of German authorities. A first application of a new phased array system took place August 1987. The 100% inspection of a spherical bottom had been enabled by the application of phased array probes with electronically controlled skewing angles. The data acquisition had been based on the storage of whole A-scans, which had been pixellized into 256 points. This A-scan storage procedure makes possible the application of a simple and fast algorithm to present the data as TD-(time displacement)-scans. Defect reconstruction by echotomographique approaches are under development. This paper presents the ultrasonic technique applied including the phased array probes, the electronic system, as well as the software package used for the control of the inspection parameters depending on the probe position

Spherical Torus Center Stack Design

International Nuclear Information System (INIS)

C. Neumeyer; P. Heitzenroeder; C. Kessel; M. Ono; M. Peng; J. Schmidt; R. Woolley; I. Zatz

2002-01-01

The low aspect ratio spherical torus (ST) configuration requires that the center stack design be optimized within a limited available space, using materials within their established allowables. This paper presents center stack design methods developed by the National Spherical Torus Experiment (NSTX) Project Team during the initial design of NSTX, and more recently for studies of a possible next-step ST (NSST) device

Spherical Demons: Fast Surface Registration

Science.gov (United States)

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

Optical geometry

International Nuclear Information System (INIS)

Robinson, I.; Trautman, A.

1988-01-01

The geometry of classical physics is Lorentzian; but weaker geometries are often more appropriate: null geodesics and electromagnetic fields, for example, are well known to be objects of conformal geometry. To deal with a single null congruence, or with the radiative electromagnetic fields associated with it, even less is needed: flag geometry for the first, optical geometry, with which this paper is chiefly concerned, for the second. The authors establish a natural one-to-one correspondence between optical geometries, considered locally, and three-dimensional Cauchy-Riemann structures. A number of Lorentzian geometries are shown to be equivalent from the optical point of view. For example the Goedel universe, the Taub-NUT metric and Hauser's twisting null solution have an optical geometry isomorphic to the one underlying the Robinson congruence in Minkowski space. The authors present general results on the problem of lifting a CR structure to a Lorentz manifold and, in particular, to Minkowski space; and exhibit the relevance of the deviation form to this problem

Magnetic geometry and physics of advanced divertors: The X-divertor and the snowflake

International Nuclear Information System (INIS)

Kotschenreuther, Mike; Valanju, Prashant; Covele, Brent; Mahajan, Swadesh

2013-01-01

Advanced divertors are magnetic geometries where a second X-point is added in the divertor region to address the serious challenges of burning plasma power exhaust. Invoking physical arguments, numerical work, and detailed model magnetic field analysis, we investigate the magnetic field structure of advanced divertors in the physically relevant region for power exhaust—the scrape-off layer. A primary result of our analysis is the emergence of a physical “metric,” the Divertor Index DI, which quantifies the flux expansion increase as one goes from the main X-point to the strike point. It clearly separates three geometries with distinct consequences for divertor physics—the Standard Divertor (DI = 1), and two advanced geometries—the X-Divertor (XD, DI > 1) and the Snowflake (DI < 1). The XD, therefore, cannot be classified as one variant of the Snowflake. By this measure, recent National Spherical Torus Experiment and DIIID experiments are X-Divertors, not Snowflakes

Magnetic geometry and physics of advanced divertors: The X-divertor and the snowflake

Energy Technology Data Exchange (ETDEWEB)

Kotschenreuther, Mike; Valanju, Prashant; Covele, Brent; Mahajan, Swadesh [Institute for Fusion Studies, The University of Texas at Austin, Austin, Texas 78712 (United States)

2013-10-15

Advanced divertors are magnetic geometries where a second X-point is added in the divertor region to address the serious challenges of burning plasma power exhaust. Invoking physical arguments, numerical work, and detailed model magnetic field analysis, we investigate the magnetic field structure of advanced divertors in the physically relevant region for power exhaust—the scrape-off layer. A primary result of our analysis is the emergence of a physical “metric,” the Divertor Index DI, which quantifies the flux expansion increase as one goes from the main X-point to the strike point. It clearly separates three geometries with distinct consequences for divertor physics—the Standard Divertor (DI = 1), and two advanced geometries—the X-Divertor (XD, DI > 1) and the Snowflake (DI < 1). The XD, therefore, cannot be classified as one variant of the Snowflake. By this measure, recent National Spherical Torus Experiment and DIIID experiments are X-Divertors, not Snowflakes.

Accretion onto a noncommutative geometry inspired black hole

Energy Technology Data Exchange (ETDEWEB)

Kumar, Rahul [Jamia Millia Islamia, Centre for Theoretical Physics, New Delhi (India); Ghosh, Sushant G. [Jamia Millia Islamia, Centre for Theoretical Physics, New Delhi (India); Jamia Millia Islamia, Multidisciplinary Centre for Advanced Research and Studies (MCARS), New Delhi (India); University of KwaZulu-Natal, Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics and Computer Science, Durban (South Africa)

2017-09-15

The spherically symmetric accretion onto a noncommutative (NC) inspired Schwarzschild black hole is treated for a polytropic fluid. The critical accretion rate M, sonic speed a{sub s} and other flow parameters are generalized for the NC inspired static black hole and compared with the results obtained for the standard Schwarzschild black holes. Also explicit expressions for gas compression ratios and temperature profiles below the accretion radius and at the event horizon are derived. This analysis is a generalization of Michel's solution to the NC geometry. Owing to the NC corrected black hole, the accretion flow parameters also have been modified. It turns out that M ∼ M{sup 2} is still achievable but r{sub s} seems to be substantially decreased due to the NC effects. They in turn do affect the accretion process. (orig.)

Introducing geometry concept based on history of Islamic geometry

Science.gov (United States)

Maarif, S.; Wahyudin; Raditya, A.; Perbowo, K. S.

2018-01-01

Geometry is one of the areas of mathematics interesting to discuss. Geometry also has a long history in mathematical developments. Therefore, it is important integrated historical development of geometry in the classroom to increase’ knowledge of how mathematicians earlier finding and constructing a geometric concept. Introduction geometrical concept can be started by introducing the Muslim mathematician who invented these concepts so that students can understand in detail how a concept of geometry can be found. However, the history of mathematics development, especially history of Islamic geometry today is less popular in the world of education in Indonesia. There are several concepts discovered by Muslim mathematicians that should be appreciated by the students in learning geometry. Great ideas of mathematicians Muslim can be used as study materials to supplement religious character values taught by Muslim mathematicians. Additionally, by integrating the history of geometry in teaching geometry are expected to improve motivation and geometrical understanding concept.

Sensitivity Analysis for Iceberg Geometry Shape in Ship-Iceberg Collision in View of Different Material Models

Directory of Open Access Journals (Sweden)

Yan Gao

2014-01-01

Full Text Available The increasing marine activities in Arctic area have brought growing interest in ship-iceberg collision study. The purpose of this paper is to study the iceberg geometry shape effect on the collision process. In order to estimate the sensitivity parameter, five different geometry iceberg models and two iceberg material models are adopted in the analysis. The FEM numerical simulation is used to predict the scenario and the related responses. The simulation results including energy dissipation and impact force are investigated and compared. It is shown that the collision process and energy dissipation are more sensitive to iceberg local shape than other factors when the elastic-plastic iceberg material model is applied. The blunt iceberg models act rigidly while the sharp ones crush easily during the simulation process. With respect to the crushable foam iceberg material model, the iceberg geometry has relatively small influence on the collision process. The spherical iceberg model shows the most rigidity for both iceberg material models and should be paid the most attention for ice-resist design for ships.

The prediction of spherical aberration with schematic eyes.

Science.gov (United States)

Liou, H L; Brennan, N A

1996-07-01

Many model eyes have been proposed; they differ in optical characteristics and therefore have different aberrations and image quality. In predicting the visual performance of the eye, we are most concerned with the central foveal vision. Spherical aberration is the only on-axis monochromatic aberration and can be used as a criterion to assess the degree of resemblance of eye models to the human eye. We reviewed and compiled experimental values of the spherical aberration of the eye, calculated the spherical aberration of several different categories of model eyes and compared the calculated results to the experimental data. Results show an over-estimation of spherical aberration by all models, the finite schematic eyes predicting values of spherical aberration closest to the experimental data. Current model eyes do not predict the average experimental values of the spherical aberration of the eye. A new model eye satisfying this assessment criterion is required for investigations of the visual performance of the eye.

Measurement of Turbulence Modulation by Non-Spherical Particles

DEFF Research Database (Denmark)

Mandø, Matthias; Rosendahl, Lasse

2010-01-01

The change in the turbulence intensity of an air jet resulting from the addition of particles to the flow is measured using Laser Doppler Anemometry. Three distinct shapes are considered: the prolate spheroid, the disk and the sphere. Measurements of the carrier phase and particle phase velocities...... at the centerline of the jet are carried out for mass loadings of 0.5, 1, 1.6 and particle sizes 880μm, 1350μm, 1820μm for spherical particles. For each non-spherical shape only a single size and loading are considered. The turbulence modulation of the carrier phase is found to highly dependent on the turbulence......, the particle mass flow and the integral length scale of the flow. The expression developed on basis of spherical particles only is applied on the data for the non-spherical particles. The results suggest that non-spherical particles attenuate the carrier phase turbulence significantly more than spherical...

Improving neutron multiplicity counting for the spatial dependence of multiplication: Results for spherical plutonium samples

Energy Technology Data Exchange (ETDEWEB)

Göttsche, Malte, E-mail: malte.goettsche@physik.uni-hamburg.de; Kirchner, Gerald

2015-10-21

The fissile mass deduced from a neutron multiplicity counting measurement of high mass dense items is underestimated if the spatial dependence of the multiplication is not taken into account. It is shown that an appropriate physics-based correction successfully removes the bias. It depends on four correction coefficients which can only be exactly determined if the sample geometry and composition are known. In some cases, for example in warhead authentication, available information on the sample will be very limited. MCNPX-PoliMi simulations have been performed to obtain the correction coefficients for a range of spherical plutonium metal geometries, with and without polyethylene reflection placed around the spheres. For hollow spheres, the analysis shows that the correction coefficients can be approximated with high accuracy as a function of the sphere's thickness depending only slightly on the radius. If the thickness remains unknown, less accurate estimates of the correction coefficients can be obtained from the neutron multiplication. The influence of isotopic composition is limited. The correction coefficients become somewhat smaller when reflection is present.

Optimization of Outer Poloidal Field (PF) Coil Configurations for Inductive PF Coil-only Plasma Start-up on Spherical Tori

International Nuclear Information System (INIS)

Wonho Choe; Jayhyun Kim; Masayuki Ono

2004-01-01

The elimination of in-board ohmic heating solenoid is required for the spherical torus (ST) to function as an attractive fusion power plant. An in-board ohmic solenoid, along with the shielding needed for its insulation, increases the size and, hence, the cost of the plant. Here, we investigate using static as well as dynamic codes in ST geometries a solenoid-free start-up concept utilizing a set of out-board poloidal field coils. By using the static code, an optimization of coil positions as well as coil currents was performed to demonstrate that it is indeed possible to create a high quality multi-pole field null region while retaining significant flux (volt-seconds) needed for the subsequent current ramp-up. With the dynamic code that includes the effect of vacuum vessel eddy currents, we then showed that it is possible to maintain a large size field null region for several milliseconds in which sufficient ionization avalanche can develop in the applied toroidal electric field. Under the magnetic geometry typical of a next generation spherical torus experiment, it is shown that the well-known plasma breakdown conditions for conventional ohmic solenoid start-up of E(sub)TB(sub)T/B(sub)P ∼ (0.1-1) kV/m with V(sub)loop ∼ 6 V can be readily met while retaining significant volt-seconds ∼ 4 V-S sufficient to generate multi-MA plasma current in STs

Charge conserving current deposition scheme for PIC simulations in modified spherical coordinates

Science.gov (United States)

Cruz, F.; Grismayer, T.; Fonseca, R. A.; Silva, L. O.

2017-10-01

Global models of pulsar magnetospheres have been actively pursued in recent years. Both macro and microscopic (PIC) descriptions have been used, showing that collective processes of e-e + plasmas dominate the global structure of pulsar magnetospheres. Since these systems are best described in spherical coordinates, the algorithms used in cartesian simulations must be generalized. A problem of particular interest is that of charge conservation in PIC simulations. The complex geometry and irregular grids used to improve the efficiency of these algorithms represent major challenges in the design of a charge conserving scheme. Here we present a new first-order current deposition scheme for a 2D axisymmetric, log-spaced radial grid, that rigorously conserves charge. We benchmark this scheme in different scenarios, by integrating it with a spherical Yee scheme and Boris/Vay pushers. The results show that charge is conserved to machine precision, making it unnecessary to correct the electric field to guarantee charge conservation. This scheme will be particularly important for future studies aiming to bridge the microscopic physical processes of e-e + plasma generation due to QED cascades, its self-consistent acceleration and radiative losses to the global dynamics of pulsar magnetospheres. Work supported by the European Research Council (InPairs ERC-2015-AdG 695088), FCT (Portugal) Grant PD/BD/114307/2016, and the Calouste Gulbenkian Foundation through the 2016 Scientific Research Stimulus Program.

Horizon geometry for Kerr black holes with synchronized hair

Science.gov (United States)

Delgado, Jorge F. M.; Herdeiro, Carlos A. R.; Radu, Eugen

2018-06-01

We study the horizon geometry of Kerr black holes (BHs) with scalar synchronized hair [1], a family of solutions of the Einstein-Klein-Gordon system that continuously connects to vacuum Kerr BHs. We identify the region in parameter space wherein a global isometric embedding in Euclidean 3-space, E3, is possible for the horizon geometry of the hairy BHs. For the Kerr case, such embedding is possible iff the horizon dimensionless spin jH (which equals the total dimensionless spin, j ), the sphericity s and the horizon linear velocity vH are smaller than critical values, j(S ),s(S ),vH(S ), respectively. For the hairy BHs, we find that jH

The ETE spherical Tokamak project. IAEA report

Energy Technology Data Exchange (ETDEWEB)

Ludwig, Gerson Otto; Del Bosco, E.; Berni, L.A.; Ferreira, J.G.; Oliveira, R.M.; Andrade, M.C.R.; Shibata, C.S.; Barroso, J.J.; Castro, P.J.; Patire Junior, H. [Instituto Nacional de Pesquisas Espaciais (INPE), Sao Jose dos Campos, SP (Brazil). Lab. Associado de Plasma]. E-mail: ludwig@plasma.inpe.br

2002-07-01

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 historical development of the ETE (Spherical Tokamak Experiment) project, its research program, technical characteristics and operating conditions as of October, 2002 at the Associated Plasma Laboratory (LAP) of the National Space Research Institute (INPE) in Brazil. (author)

An Analysis of Spherical Particles Distribution Randomly Packed in a Medium for the Monte Carlo Implicit Modeling

Energy Technology Data Exchange (ETDEWEB)

Lee, Jae Yong; Kim, Song Hyun; Shin, Chang Ho; Kim, Jong Kyung [Hanyang Univ., Seoul (Korea, Republic of)

2014-05-15

In this study, as a preliminary study to develop an implicit method having high accuracy, the distribution characteristics of spherical particles were evaluated by using explicit modeling techniques in various volume packing fractions. This study was performed to evaluate implicitly simulated distribution of randomly packed spheres in a medium. At first, an explicit modeling method to simulate random packed spheres in a hexahedron medium was proposed. The distributed characteristics of l{sub p} and r{sub p}, which are used in the particle position sampling, was estimated. It is analyzed that the use of the direct exponential distribution, which is generally used in the implicit modeling, can cause the distribution bias of the spheres. It is expected that the findings in this study can be utilized for improving the accuracy in using the implicit method. Spherical particles, which are randomly distributed in medium, are utilized for the radiation shields, fusion reactor blanket, fuels of VHTR reactors. Due to the difficulty on the simulation of the stochastic distribution, Monte Carlo (MC) method has been mainly considered as the tool for the analysis of the particle transport. For the MC modeling of the spherical particles, three methods are known; repeated structure, explicit modeling, and implicit modeling. Implicit method (called as the track length sampling method) is a modeling method that is the sampling based modeling technique of each spherical geometry (or track length of the sphere) during the MC simulation. Implicit modeling method has advantages in high computational efficiency and user convenience. However, it is noted that the implicit method has lower modeling accuracy in various finite mediums.

Geometry through history Euclidean, hyperbolic, and projective geometries

CERN Document Server

Dillon, Meighan I

2018-01-01

Presented as an engaging discourse, this textbook invites readers to delve into the historical origins and uses of geometry. The narrative traces the influence of Euclid’s system of geometry, as developed in his classic text The Elements, through the Arabic period, the modern era in the West, and up to twentieth century mathematics. Axioms and proof methods used by mathematicians from those periods are explored alongside the problems in Euclidean geometry that lead to their work. Students cultivate skills applicable to much of modern mathematics through sections that integrate concepts like projective and hyperbolic geometry with representative proof-based exercises. For its sophisticated account of ancient to modern geometries, this text assumes only a year of college mathematics as it builds towards its conclusion with algebraic curves and quaternions. Euclid’s work has affected geometry for thousands of years, so this text has something to offer to anyone who wants to broaden their appreciation for the...

Laplacian eigenmodes for spherical spaces

International Nuclear Information System (INIS)

Lachieze-Rey, M; Caillerie, S

2005-01-01

The possibility that our space is multi-rather than singly-connected has gained renewed interest after the discovery of the low power for the first multipoles of the CMB by WMAP. To test the possibility that our space is a multi-connected spherical space, it is necessary to know the eigenmodes of such spaces. Except for lens and prism space, and to some extent for dodecahedral space, this remains an open problem. Here we derive the eigenmodes of all spherical spaces. For dodecahedral space, the demonstration is much shorter, and the calculation method much simpler than before. We also apply our method to tetrahedric, octahedric and icosahedric spaces. This completes the knowledge of eigenmodes for spherical spaces, and opens the door to new observational tests of the cosmic topology. The vector space V k of the eigenfunctions of the Laplacian on the 3-sphere S 3 , corresponding to the same eigenvalue λ k = -k(k + 2), has dimension (k + 1) 2 . We show that the Wigner functions provide a basis for such a space. Using the properties of the latter, we express the behaviour of a general function of V k under an arbitrary rotation G of SO(4). This offers the possibility of selecting those functions of V k which remain invariant under G. Specifying G to be a generator of the holonomy group of a spherical space X, we give the expression of the vector space V x k of the eigenfunctions of X. We provide a method to calculate the eigenmodes up to an arbitrary order. As an illustration, we give the first modes for the spherical spaces mentioned

Glioblastoma: does the pre-treatment geometry matter? A postcontrast T1 MRI-based study

International Nuclear Information System (INIS)

Perez-Beteta, Julian; Martinez-Gonzalez, Alicia; Molina, David; Amo-Salas, Mariano; Luque, Belen; Perez-Garcia, Victor M.; Arregui, Elena; Calvo, Manuel; Borras, Jose M.; Lopez, Carlos; Claramonte, Marta; Barcia, Juan A.; Iglesias, Lidia; Avecillas, Josue; Albillo, David; Navarro, Miguel; Villanueva, Jose M.; Paniagua, Juan C.; Perez-Romasanta, Luis; Martino, Juan; Velasquez, Carlos; Asenjo, Beatriz; Benavides, Manuel; Herruzo, Ismael; Delgado, Maria del Carmen; Valle, Ana del; Falkov, Anthony; Schucht, Philippe; Arana, Estanislao

2017-01-01

The potential of a tumour's volumetric measures obtained from pretreatment MRI sequences of glioblastoma (GBM) patients as predictors of clinical outcome has been controversial. Mathematical models of GBM growth have suggested a relation between a tumour's geometry and its aggressiveness. A multicenter retrospective clinical study was designed to study volumetric and geometrical measures on pretreatment postcontrast T1 MRIs of 117 GBM patients. Clinical variables were collected, tumours segmented, and measures computed including: contrast enhancing (CE), necrotic, and total volumes; maximal tumour diameter; equivalent spherical CE width and several geometric measures of the CE ''rim''. The significance of the measures was studied using proportional hazards analysis and Kaplan-Meier curves. Kaplan-Meier and univariate Cox survival analysis showed that total volume [p = 0.034, Hazard ratio (HR) = 1.574], CE volume (p = 0.017, HR = 1.659), spherical rim width (p = 0.007, HR = 1.749), and geometric heterogeneity (p = 0.015, HR = 1.646) were significant parameters in terms of overall survival (OS). Multivariable Cox analysis for OS provided the later two parameters as age-adjusted predictors of OS (p = 0.043, HR = 1.536 and p = 0.032, HR = 1.570, respectively). Patients with tumours having small geometric heterogeneity and/or spherical rim widths had significantly better prognosis. These novel imaging biomarkers have a strong individual and combined prognostic value for GBM patients. (orig.)

Low-Q Electrically Small Spherical Magnetic Dipole Antennas

DEFF Research Database (Denmark)

Kim, Oleksiy S.

2010-01-01

Three novel electrically small antenna configurations radiating a TE10 spherical mode corresponding to a magnetic dipole are presented and investigated: multiarm spherical helix (MSH) antenna, spherical split ring resonator (S-SRR) antenna, and spherical split ring (SSR) antenna. All three antennas...... are self-resonant, with the input resistance tuned to 50 ohms by an excitation curved dipole/monopole. A prototype of the SSR antenna has been fabricated and measured, yielding results that are consistent with the numerical simulations. Radiation quality factors (Q) of these electrically small antennas (in...

FY 2006 Miniature Spherical Retroreflectors Final Report

Energy Technology Data Exchange (ETDEWEB)

Anheier, Norman C.; Bernacki, Bruce E.; Krishnaswami, Kannan

2006-12-28

Research done by the Infrared Photonics team at Pacific Northwest National Laboratory (PNNL) is focused on developing miniature spherical retroreflectors using the unique optical and material properties of chalcogenide glass to reduce both performance limiting spherical aberrations. The optimized optical performance will provide efficient signal retroreflection that enables a broad range of remote detection scenarios for mid-wave infrared (MWIR) and long-wave infrared (LWIR) sensing applications. Miniature spherical retroreflectors can be developed to aid in the detection of signatures of nuclear proliferation or other chemical vapor or radiation signatures. Miniature spherical retroreflectors are not only well suited to traditional LIDAR methods for chemical plume detection and identification, but could enable remote detection of difficult semi-volatile chemical materials or low level radiation sources.

A spherical Taylor-Couette dynamo

Science.gov (United States)

Marcotte, Florence; Gissinger, Christophe

2016-04-01

We present a new scenario for magnetic field amplification in the planetary interiors where an electrically conducting fluid is confined in a differentially rotating, spherical shell (spherical Couette flow) with thin aspect-ratio. When the angular momentum sufficiently decreases outwards, a primary hydrodynamic instability is widely known to develop in the equatorial region, characterized by pairs of counter-rotating, axisymmetric toroidal vortices (Taylor vortices) similar to those observed in cylindrical Couette flow. We characterize the subcritical dynamo bifurcation due to this spherical Taylor-Couette flow and study its evolution as the flow successively breaks into wavy and turbulent Taylor vortices for increasing Reynolds number. We show that the critical magnetic Reynolds number seems to reach a constant value as the Reynolds number is gradually increased. The role of global rotation on the dynamo threshold and the implications for planetary interiors are finally discussed.

Spherical tokamak development in Brazil

International Nuclear Information System (INIS)

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.; Barbosa, L.F.W.; Patire Junior, H.; The high-power microwave sources group

2003-01-01

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)

Miniaturization of Spherical Magnetodielectric Antennas

DEFF Research Database (Denmark)

Hansen, Troels Vejle

; Arbitrary order of the spherical wave, arbitrary radius of the spherical antenna, as well as arbitrarily large core permeability and/or permittivity, given an inversely proportional frequency variation of the imaginary part(s) and an arbitrary dispersion of the real part(s) - thus describing both lossless...... with a magnetic loss tangent of 1 and relative permeability of 300 yield Q/e equal 65% of the Chu lower bound, with a simultaneous e of 71%....

Spherical tokamak development in Brazil

Energy Technology Data Exchange (ETDEWEB)

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)

L-mode SOL width scaling in the MAST spherical tokamak

International Nuclear Information System (INIS)

Ahn, J-W; Counsell, G F; Kirk, A

2006-01-01

A new data-set of outboard mid-plane scrape-off layer (SOL) heat flux widths, Δ h , has been constructed for L-mode plasmas in the MAST spherical tokamak (ST). The scaling with key plasma parameters such as density, toroidal magnetic field, parallel connection length in the SOL and surface heat flux at the separatrix is investigated. An empirical scaling is developed for the Δ h data-set, which exhibits a strong positive dependence on both the connection length (or edge safety factor) and density and weak or moderate inverse dependences on the surface heat flux and magnetic field, respectively. The empirical scaling is compared with earlier results for a range of tokamaks with conventional geometry, which show weaker dependence on the density and edge safety factor. Importantly, however, the weak negative dependence on the surface heat flux (and thus heating power) is common in both conventional and ST geometries. The experimental data are also used to test a number of dimensionally correct Δ h scalings developed from theoretical models for perpendicular transport in the SOL coupled with classical transport parallel to the magnetic field. A scaling based on perpendicular transport driven by resistive MHD interchange provides the best fit, although several models are close. A subset of the better fitting theoretical scalings are used to extrapolate for Δ h in one design for a future burning ST machine and finally to predict the peak heat loading on the outboard divertor target plate

Architectural geometry

KAUST Repository

Pottmann, Helmut

2014-11-26

Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural geometry, meanwhile contains a great wealth of individual contributions which are relevant in various fields. For mathematicians, the relation to discrete differential geometry is significant, in particular the integrable system viewpoint. Besides, new application contexts have become available for quite some old-established concepts. Regarding graphics and geometry processing, architectural geometry yields interesting new questions but also new objects, e.g. replacing meshes by other combinatorial arrangements. Numerical optimization plays a major role but in itself would be powerless without geometric understanding. Summing up, architectural geometry has become a rewarding field of study. We here survey the main directions which have been pursued, we show real projects where geometric considerations have played a role, and we outline open problems which we think are significant for the future development of both theory and practice of architectural geometry.

Architectural geometry

KAUST Repository

Pottmann, Helmut; Eigensatz, Michael; Vaxman, Amir; Wallner, Johannes

2014-01-01

Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural geometry, meanwhile contains a great wealth of individual contributions which are relevant in various fields. For mathematicians, the relation to discrete differential geometry is significant, in particular the integrable system viewpoint. Besides, new application contexts have become available for quite some old-established concepts. Regarding graphics and geometry processing, architectural geometry yields interesting new questions but also new objects, e.g. replacing meshes by other combinatorial arrangements. Numerical optimization plays a major role but in itself would be powerless without geometric understanding. Summing up, architectural geometry has become a rewarding field of study. We here survey the main directions which have been pursued, we show real projects where geometric considerations have played a role, and we outline open problems which we think are significant for the future development of both theory and practice of architectural geometry.

Two lectures on D-geometry and noncommutative geometry

International Nuclear Information System (INIS)

Douglas, M.R.

1999-01-01

This is a write-up of lectures given at the 1998 Spring School at the Abdus Salam ICTP. We give a conceptual introduction to D-geometry, the study of geometry as seen by D-branes in string theory, and to noncommutative geometry as it has appeared in D-brane and Matrix theory physics. (author)

Turbulence Modulation by Non-Spherical Particles

DEFF Research Database (Denmark)

Mandø, Matthias

This study deals with the interaction between turbulence and non-spherical particles and represents an extension of the modeling framework for particleladen flows. The effect of turbulence on particles is commonly referred to as turbulent dispersion while the effect of particles on the carrier....... This study encompass an outlook on existing work, an experimental study, development of a numerical model and a case study advancing the modeling techniques for pulverized coal combustion to deal with larger non-spherical biomass particles. Firstly, existing knowledge concerning the motion of non......-spherical particles and turbulence modulation are outlined. A complete description of the motion of non-spherical particles is still lacking. However, evidence suggests that the equation of motion for a sphere only represent an asymptotical value for a more general, but yet unformulated, description of the motion...

Transformation of Real Spherical Harmonics under Rotations

Science.gov (United States)

Romanowski, Z.; Krukowski, St.; Jalbout, A. F.

2008-08-01

The algorithm rotating the real spherical harmonics is presented. The convenient and ready to use formulae for l = 0, 1, 2, 3 are listed. The rotation in R3 space is determined by the rotation axis and the rotation angle; the Euler angles are not used. The proposed algorithm consists of three steps. (i) Express the real spherical harmonics as the linear combination of canonical polynomials. (ii) Rotate the canonical polynomials. (iii) Express the rotated canonical polynomials as the linear combination of real spherical harmonics. Since the three step procedure can be treated as a superposition of rotations, the searched rotation matrix for real spherical harmonics is a product of three matrices. The explicit formulae of matrix elements are given for l = 0, 1, 2, 3, what corresponds to s, p, d, f atomic orbitals.

Twistor geometry

NARCIS (Netherlands)

van den Broek, P.M.

1984-01-01

The aim of this paper is to give a detailed exposition of the relation between the geometry of twistor space and the geometry of Minkowski space. The paper has a didactical purpose; no use has been made of differential geometry and cohomology.

Dynamics of a spherical minority game

International Nuclear Information System (INIS)

Galla, T; Coolen, A C C; Sherrington, D

2003-01-01

We present an exact dynamical solution of a spherical version of the batch minority game (MG) with random external information. The control parameters in this model are the ratio of the number of possible values for the public information over the number of agents, and the radius of the spherical constraint on the microscopic degrees of freedom. We find a phase diagram with three phases: two without anomalous response (an oscillating versus a frozen state) and a further frozen phase with divergent integrated response. In contrast to standard MG versions, we can also calculate the volatility exactly. Our study reveals similarities between the spherical and the conventional MG, but also intriguing differences. Numerical simulations confirm our analytical results

Investigation of spherical and concentric mechanism of compound droplets

Directory of Open Access Journals (Sweden)

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.

Geometry

Indian Academy of Sciences (India)

. In the previous article we looked at the origins of synthetic and analytic geometry. More practical minded people, the builders and navigators, were studying two other aspects of geometry- trigonometry and integral calculus. These are actually ...

Criticality safety validation: Simple geometry, single unit {sup 233}U systems

Energy Technology Data Exchange (ETDEWEB)

Putman, V.L.

1997-06-01

Typically used LMITCO criticality safety computational methods are evaluated for suitability when applied to INEEL {sup 233}U systems which reasonably can be modeled as simple-geometry, single-unit systems. Sixty-seven critical experiments of uranium highly enriched in {sup 233}U, including 57 aqueous solution, thermal-energy systems and 10 metal, fast-energy systems, were modeled. These experiments include 41 cylindrical and 26 spherical cores, and 41 reflected and 26 unreflected systems. No experiments were found for intermediate-neutron-energy ranges, or with interstitial non-hydrogenous materials typical of waste systems, mixed {sup 233}U and plutonium, or reflectors such as steel, lead, or concrete. No simple geometry experiments were found with cubic or annular cores, or approximating infinite sea systems. Calculations were performed with various tools and methodologies. Nine cross-section libraries, based on ENDF/B-IV, -V, or -VI.2, or on Hansen-Roach source data, were used with cross-section processing methods of MCNP or SCALE. The k{sub eff} calculations were performed with neutral-particle transport and Monte Carlo methods of criticality codes DANT, MCNP 4A, and KENO Va.

How Spherical Is a Cube (Gravitationally)?

Science.gov (United States)

Sanny, Jeff; Smith, David

2015-01-01

An important concept that is presented in the discussion of Newton's law of universal gravitation is that the gravitational effect external to a spherically symmetric mass distribution is the same as if all of the mass of the distribution were concentrated at the center. By integrating over ring elements of a spherical shell, we show that the…

Spherical cows in dark matter indirect detection

Energy Technology Data Exchange (ETDEWEB)

Bernal, Nicolás [Centro de Investigaciones, Universidad Antonio Nariño, Cra 3 Este # 47A-15, Bogotá (Colombia); Necib, Lina; Slatyer, Tracy R., E-mail: nicolas.bernal@uan.edu.co, E-mail: lnecib@mit.edu, E-mail: tslatyer@mit.edu [Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States)

2016-12-01

Dark matter (DM) halos have long been known to be triaxial, but in studies of possible annihilation and decay signals they are often treated as approximately spherical. In this work, we examine the asymmetry of potential indirect detection signals of DM annihilation and decay, exploiting the large statistics of the hydrodynamic simulation Illustris. We carefully investigate the effects of the baryons on the sphericity of annihilation and decay signals for both the case where the observer is at 8.5 kpc from the center of the halo (exemplified in the case of Milky Way-like halos), and for an observer situated well outside the halo. In the case of Galactic signals, we find that both annihilation and decay signals are expected to be quite symmetric, with axis ratios very different from 1 occurring rarely. In the case of extragalactic signals, while decay signals are still preferentially spherical, the axis ratio for annihilation signals has a much flatter distribution, with elongated profiles appearing frequently. Many of these elongated profiles are due to large subhalos and/or recent mergers. Comparing to gamma-ray emission from the Milky Way and X-ray maps of clusters, we find that the gamma-ray background appears less spherical/more elongated than the expected DM signal from the large majority of halos, and the Galactic gamma ray excess appears very spherical, while the X-ray data would be difficult to distinguish from a DM signal by elongation/sphericity measurements alone.

Mathematical analysis of the boundary-integral based electrostatics estimation approximation for molecular solvation: exact results for spherical inclusions.

Science.gov (United States)

Bardhan, Jaydeep P; Knepley, Matthew G

2011-09-28

We analyze the mathematically rigorous BIBEE (boundary-integral based electrostatics estimation) approximation of the mixed-dielectric continuum model of molecular electrostatics, using the analytically solvable case of a spherical solute containing an arbitrary charge distribution. Our analysis, which builds on Kirkwood's solution using spherical harmonics, clarifies important aspects of the approximation and its relationship to generalized Born models. First, our results suggest a new perspective for analyzing fast electrostatic models: the separation of variables between material properties (the dielectric constants) and geometry (the solute dielectric boundary and charge distribution). Second, we find that the eigenfunctions of the reaction-potential operator are exactly preserved in the BIBEE model for the sphere, which supports the use of this approximation for analyzing charge-charge interactions in molecular binding. Third, a comparison of BIBEE to the recent GBε theory suggests a modified BIBEE model capable of predicting electrostatic solvation free energies to within 4% of a full numerical Poisson calculation. This modified model leads to a projection-framework understanding of BIBEE and suggests opportunities for future improvements. © 2011 American Institute of Physics

Molecular geometry

CERN Document Server

Rodger, Alison

1995-01-01

Molecular Geometry discusses topics relevant to the arrangement of atoms. The book is comprised of seven chapters that tackle several areas of molecular geometry. Chapter 1 reviews the definition and determination of molecular geometry, while Chapter 2 discusses the unified view of stereochemistry and stereochemical changes. Chapter 3 covers the geometry of molecules of second row atoms, and Chapter 4 deals with the main group elements beyond the second row. The book also talks about the complexes of transition metals and f-block elements, and then covers the organometallic compounds and trans

Non-Spherical Gravitational Collapse of Strange Quark Matter

Institute of Scientific and Technical Information of China (English)

Zade S S; Patil K D; Mulkalwar P N

2008-01-01

We study the non-spherical gravitational collapse of the strange quark null fluid.The interesting feature which emerges is that the non-spherical collapse of charged strange quark matter leads to a naked singularity whereas the gravitational collapse of neutral quark matter proceeds to form a black hole.We extend the earlier work of Harko and Cheng[Phys.Lett.A 266 (2000) 249]to the non-spherical case.

On the phase diagram of non-spherical nanoparticles

CERN Document Server

Wautelet, M; Hecq, M

2003-01-01

The phase diagram of nanoparticles is known to be a function of their size. In the literature, this is generally demonstrated for cases where their shape is spherical. Here, it is shown theoretically that the phase diagram of non-spherical particles may be calculated from the spherical case, at the same surface area/volume ratio, both with and without surface segregation, provided the surface tension is considered to be isotropic.

Spherical proton emitters

International Nuclear Information System (INIS)

Berg, S.; Semmes, P.B.; Nazarewicz, W.

1997-01-01

Various theoretical approaches to proton emission from spherical nuclei are investigated, and it is found that all the methods employed give very similar results. The calculated decay widths are found to be qualitatively insensitive to the parameters of the proton-nucleus potential, i.e., changing the potential parameters over a fairly large range typically changes the decay width by no more than a factor of ∼3. Proton half-lives of observed heavy proton emitters are, in general, well reproduced by spherical calculations with the spectroscopic factors calculated in the independent quasiparticle approximation. The quantitative agreement with experimental data obtained in our study requires that the parameters of the proton-nucleus potential be chosen carefully. It also suggests that deformed proton emitters will provide invaluable spectroscopic information on the angular momentum decomposition of single-proton orbitals in deformed nuclei. copyright 1997 The American Physical Society

Elastic interaction between surface and spherical pore

International Nuclear Information System (INIS)

Ganeev, G.Z.; Kadyrzhanov, K.K.; Kislitsyn, S.B.; Turkebaev, T.Eh.

2000-01-01

The energy of elastic interaction of a gas-filled spherical cavity with a boundary of an elastic isotropic half-space is determined. The elastic field of a system of a spherical cavity - boundary is represented as an expansion in series of potential functions. The factors of expansions are determined by boundary conditions on a free surface of an elastic half-space and on a spherical surface of a cavity with pressure of gas P. Function of a Tresca-Miesesa on a surface of elastic surface is defined additionally with purpose creep condition determination caused by gas pressure in the cavity. (author)

Glioblastoma: does the pre-treatment geometry matter? A postcontrast T1 MRI-based study

Energy Technology Data Exchange (ETDEWEB)

Perez-Beteta, Julian; Martinez-Gonzalez, Alicia; Molina, David; Amo-Salas, Mariano; Luque, Belen; Perez-Garcia, Victor M. [Universidad de Castilla-La Mancha, Laboratory of Mathematical Oncology, Edificio Politecnico, Instituto de Matematica Aplicada a la Ciencia y la Ingenieria, Ciudad Real (Spain); Arregui, Elena; Calvo, Manuel; Borras, Jose M.; Lopez, Carlos; Claramonte, Marta [Hospital General de Ciudad Real, Ciudad Real (Spain); Barcia, Juan A.; Iglesias, Lidia; Avecillas, Josue [Hospital Clinico San Carlos, Madrid (Spain); Albillo, David; Navarro, Miguel; Villanueva, Jose M.; Paniagua, Juan C.; Perez-Romasanta, Luis [Hospital Universitario de Salamanca, Salamanca (Spain); Martino, Juan; Velasquez, Carlos [Hospital Marques de Valdecilla, Santander (Spain); Asenjo, Beatriz; Benavides, Manuel; Herruzo, Ismael [Hospital Carlos Haya, Malaga (Spain); Delgado, Maria del Carmen; Valle, Ana del [Universidad de Sevilla, Facultad de Matematicas, Sevilla (Spain); Falkov, Anthony [Auckland Radiation Oncology, Auckland (New Zealand); Schucht, Philippe [Bern Inselspital, Neurosurgery Department, Bern (Switzerland); Arana, Estanislao [Instituto Valenciano de Oncologia, Valencia (Spain)

2017-03-15

The potential of a tumour's volumetric measures obtained from pretreatment MRI sequences of glioblastoma (GBM) patients as predictors of clinical outcome has been controversial. Mathematical models of GBM growth have suggested a relation between a tumour's geometry and its aggressiveness. A multicenter retrospective clinical study was designed to study volumetric and geometrical measures on pretreatment postcontrast T1 MRIs of 117 GBM patients. Clinical variables were collected, tumours segmented, and measures computed including: contrast enhancing (CE), necrotic, and total volumes; maximal tumour diameter; equivalent spherical CE width and several geometric measures of the CE ''rim''. The significance of the measures was studied using proportional hazards analysis and Kaplan-Meier curves. Kaplan-Meier and univariate Cox survival analysis showed that total volume [p = 0.034, Hazard ratio (HR) = 1.574], CE volume (p = 0.017, HR = 1.659), spherical rim width (p = 0.007, HR = 1.749), and geometric heterogeneity (p = 0.015, HR = 1.646) were significant parameters in terms of overall survival (OS). Multivariable Cox analysis for OS provided the later two parameters as age-adjusted predictors of OS (p = 0.043, HR = 1.536 and p = 0.032, HR = 1.570, respectively). Patients with tumours having small geometric heterogeneity and/or spherical rim widths had significantly better prognosis. These novel imaging biomarkers have a strong individual and combined prognostic value for GBM patients. (orig.)

Systematic Calibration for a Backpacked Spherical Photogrammetry Imaging System

Science.gov (United States)

Rau, J. Y.; Su, B. W.; Hsiao, K. W.; Jhan, J. P.

2016-06-01

A spherical camera can observe the environment for almost 720 degrees' field of view in one shoot, which is useful for augmented reality, environment documentation, or mobile mapping applications. This paper aims to develop a spherical photogrammetry imaging system for the purpose of 3D measurement through a backpacked mobile mapping system (MMS). The used equipment contains a Ladybug-5 spherical camera, a tactical grade positioning and orientation system (POS), i.e. SPAN-CPT, and an odometer, etc. This research aims to directly apply photogrammetric space intersection technique for 3D mapping from a spherical image stereo-pair. For this purpose, several systematic calibration procedures are required, including lens distortion calibration, relative orientation calibration, boresight calibration for direct georeferencing, and spherical image calibration. The lens distortion is serious on the ladybug-5 camera's original 6 images. Meanwhile, for spherical image mosaicking from these original 6 images, we propose the use of their relative orientation and correct their lens distortion at the same time. However, the constructed spherical image still contains systematic error, which will reduce the 3D measurement accuracy. Later for direct georeferencing purpose, we need to establish a ground control field for boresight/lever-arm calibration. Then, we can apply the calibrated parameters to obtain the exterior orientation parameters (EOPs) of all spherical images. In the end, the 3D positioning accuracy after space intersection will be evaluated, including EOPs obtained by structure from motion method.

Symplectic and Poisson Geometry in Interaction with Analysis, Algebra and Topology & Symplectic Geometry, Noncommutative Geometry and Physics

CERN Document Server

Eliashberg, Yakov; Maeda, Yoshiaki; Symplectic, Poisson, and Noncommutative geometry

2014-01-01

Symplectic geometry originated in physics, but it has flourished as an independent subject in mathematics, together with its offspring, symplectic topology. Symplectic methods have even been applied back to mathematical physics. Noncommutative geometry has developed an alternative mathematical quantization scheme based on a geometric approach to operator algebras. Deformation quantization, a blend of symplectic methods and noncommutative geometry, approaches quantum mechanics from a more algebraic viewpoint, as it addresses quantization as a deformation of Poisson structures. This volume contains seven chapters based on lectures given by invited speakers at two May 2010 workshops held at the Mathematical Sciences Research Institute: Symplectic and Poisson Geometry in Interaction with Analysis, Algebra and Topology (honoring Alan Weinstein, one of the key figures in the field) and Symplectic Geometry, Noncommutative Geometry and Physics. The chapters include presentations of previously unpublished results and ...

Evolving shape coexistence in the lead isotopes: The geometry of configuration mixing in nuclei

International Nuclear Information System (INIS)

Frank, Alejandro; Isacker, Piet van; Vargas, Carlos E.

2004-01-01

A matrix coherent-state approach is applied to the interacting boson model (IBM) with configuration mixing to describe the evolving geometry of neutron-deficient Pb isotopes. It is found that for small mixing with parameters determined previously, the potential energy surface of 186 Pb has three minima, which correspond to spherical, oblate, and prolate shapes, in agreement with recent measurements and mean-field calculations. Away from midshell, in the heavier Pb isotopes, no deformed minima occur. Our analysis suggests that the configuration-mixing IBM, used in conjunction with a matrix coherent-state method, may be a reliable tool for the study of geometric aspects of shape coexistence in nuclei

Spherical Dunkl-monogenics and a factorization of the Dunkl-Laplacian

International Nuclear Information System (INIS)

Fei Minggang; Cerejeiras, Paula; Kaehler, Uwe

2010-01-01

In this paper, we consider and study a factorization of the Dunkl-Laplacian in terms of spherical coordinates. This allows for the construction of a direct sum decomposition of spherical Dunkl-harmonics. By explicit representation in spherical coordinates of Dunkl-harmonics, one obtains explicit projection operators from Dunkl-harmonics to inner (resp. outer) Dunkl-monogenics. Concrete examples of spherical Dunkl-monogenics will be given at the end.

Preparation of spherical particles by vibrating orifice technique

Science.gov (United States)

Shibata, Shuichi; Tomizawa, Atsushi; Yoshikawa, Hidemi; Yano, Tetsuji; Yamane, Masayuki

2000-05-01

Preparation of micrometer-sized spherical particles containing Rhodamine 6G (R6G) has been investigated for the spherical cavity micro-laser. Using phenyl triethoxy silane (PTES) as a starting material, R6G-doped monodisperse spherical particles were prepared by the vibrating orifice technique. Processing consists of two major processes: (1) Hydrolysis and polymerization of PTES and (2) Droplet formation from PTES oligomers by vibrating orifice technique. A cylindrical liquid jet passing through the orifice of 10 and 20 micrometers in diameter breaks up into equal- sized droplets by mechanical vibration. Alcohol solvent of these droplets was evaporated during flying with carrier gas and subsequently solidified in ammonium water trap. For making smooth surface and god shaped particles, control of molecular weight of PTES oligomer was essential. R6G-doped hybrid spherical particles of 4 to 10 micrometers size of cavity structure were successfully obtained. The spherical particles were pumped by a second harmonic pulse of Q- switched Nd:YAG laser and laser emission peaks were observed at wavelengths which correspond to the resonance modes.

Spherical rhenium metal powder

International Nuclear Information System (INIS)

Leonhardt, T.; Moore, N.; Hamister, M.

2001-01-01

The development of a high-density, spherical rhenium powder (SReP) possessing excellent flow characteristics has enabled the use of advanced processing techniques for the manufacture of rhenium components. The techniques that were investigated were vacuum plasma spraying (VPS), direct-hot isostatic pressing (D-HIP), and various other traditional powder metallurgy processing methods of forming rhenium powder into near-net shaped components. The principal disadvantages of standard rhenium metal powder (RMP) for advanced consolidation applications include: poor flow characteristics; high oxygen content; and low and varying packing densities. SReP will lower costs, reduce processing times, and improve yields when manufacturing powder metallurgy rhenium components. The results of the powder characterization of spherical rhenium powder and the consolidation of the SReP are further discussed. (author)

Effects of x-ray and neutron irradiation on spherical colonies

International Nuclear Information System (INIS)

Aramaki, Ryoji

1980-01-01

Responses of in vitro cultured mammalian cells in spherical colonies to 200 kVp x-rays and D-T neutrons were studied using reproductive capacity as a criterion for survival. Cell lines used were FM3A, L5 and Chinese hamster V79. The spherical colonies exposed to x-rays exhibited two-component survival curves. All cells used were more radio-resistant in spherical colonies than in single cell suspensions. It was suggested that this difference in response was attributable to the presence of hypoxic cells in spherical colonies. Dose-modifying Factor (DMF), the ratios of D 0 of the second slopes of the curves for spherical colonies to those for single cells, were 1.6 for FM3A, 1.8 for L5, and 1.7 for Chinese hamster V79. The hypoxic cell fractions in spherical colonies for FM3A, L5, and Chinese hamster V79, were 0.1, 0.6 and 0.4, respectively, resulting in variations in cell survival in spherical colonies following x-radiation. No significant difference was observed between responses of spherical colonies and single cell suspensions to D-T neutrons. FM3A and Chinese hamster V79 showed two-component survival curves when irradiated with neutrons at 37 0 C, but not at 25 0 C. The repair of potentially lethal and sub-lethal damage was also investigated using FM3A in spherical colonies. No detectable repair of potentially lethal damage was observed for x-rays and D-T neutrons. The effect of neutron fractionation was considerably smaller for spherical colonies as compared to single cells. (author)

Spherical convolutions and their application in molecular modelling

DEFF Research Database (Denmark)

Boomsma, Wouter; Frellsen, Jes

2017-01-01

Convolutional neural networks are increasingly used outside the domain of image analysis, in particular in various areas of the natural sciences concerned with spatial data. Such networks often work out-of-the box, and in some cases entire model architectures from image analysis can be carried over...... to other problem domains almost unaltered. Unfortunately, this convenience does not trivially extend to data in non-euclidean spaces, such as spherical data. In this paper, we introduce two strategies for conducting convolutions on the sphere, using either a spherical-polar grid or a grid based...... of spherical convolutions in the context of molecular modelling, by considering structural environments within proteins. We show that the models are capable of learning non-trivial functions in these molecular environments, and that our spherical convolutions generally outperform standard 3D convolutions...

Watermarking on 3D mesh based on spherical wavelet transform.

Science.gov (United States)

Jin, Jian-Qiu; Dai, Min-Ya; Bao, Hu-Jun; Peng, Qun-Sheng

2004-03-01

In this paper we propose a robust watermarking algorithm for 3D mesh. The algorithm is based on spherical wavelet transform. Our basic idea is to decompose the original mesh into a series of details at different scales by using spherical wavelet transform; the watermark is then embedded into the different levels of details. The embedding process includes: global sphere parameterization, spherical uniform sampling, spherical wavelet forward transform, embedding watermark, spherical wavelet inverse transform, and at last resampling the mesh watermarked to recover the topological connectivity of the original model. Experiments showed that our algorithm can improve the capacity of the watermark and the robustness of watermarking against attacks.

What to expect from dynamical modelling of galactic haloes - II. The spherical Jeans equation

Science.gov (United States)

Wang, Wenting; Han, Jiaxin; Cole, Shaun; More, Surhud; Frenk, Carlos; Schaller, Matthieu

2018-06-01

The spherical Jeans equation (SJE) is widely used in dynamical modelling of the Milky Way (MW) halo potential. We use haloes and galaxies from the cosmological Millennium-II simulation and hydrodynamical APOSTLE (A Project of Simulations of The Local Environment) simulations to investigate the performance of the SJE in recovering the underlying mass profiles of MW mass haloes. The best-fitting halo mass and concentration parameters scatter by 25 per cent and 40 per cent around their input values, respectively, when dark matter particles are used as tracers. This scatter becomes as large as a factor of 3 when using star particles instead. This is significantly larger than the estimated statistical uncertainty associated with the use of the SJE. The existence of correlated phase-space structures that violate the steady-state assumption of the SJE as well as non-spherical geometries is the principal source of the scatter. Binary haloes show larger scatter because they are more aspherical in shape and have a more perturbed dynamical state. Our results confirm that the number of independent phase-space structures sets an intrinsic limiting precision on dynamical inferences based on the steady-state assumption. Modelling with a radius-independent velocity anisotropy, or using tracers within a limited outer radius, result in significantly larger scatter, but the ensemble-averaged measurement over the whole halo sample is approximately unbiased.

Arithmetic noncommutative geometry

CERN Document Server

Marcolli, Matilde

2005-01-01

Arithmetic noncommutative geometry denotes the use of ideas and tools from the field of noncommutative geometry, to address questions and reinterpret in a new perspective results and constructions from number theory and arithmetic algebraic geometry. This general philosophy is applied to the geometry and arithmetic of modular curves and to the fibers at archimedean places of arithmetic surfaces and varieties. The main reason why noncommutative geometry can be expected to say something about topics of arithmetic interest lies in the fact that it provides the right framework in which the tools of geometry continue to make sense on spaces that are very singular and apparently very far from the world of algebraic varieties. This provides a way of refining the boundary structure of certain classes of spaces that arise in the context of arithmetic geometry, such as moduli spaces (of which modular curves are the simplest case) or arithmetic varieties (completed by suitable "fibers at infinity"), by adding boundaries...

Spherical CR geometry and Dehn surgery

CERN Document Server

Schwarz, Richard Evan

2007-01-01

This book proves an analogue of William Thurston's celebrated hyperbolic Dehn surgery theorem in the context of complex hyperbolic discrete groups, and then derives two main geometric consequences from it. The first is the construction of large numbers of closed real hyperbolic 3-manifolds which bound complex hyperbolic orbifolds--the only known examples of closed manifolds that simultaneously have these two kinds of geometric structures. The second is a complete understanding of the structure of complex hyperbolic reflection triangle groups in cases where the angle is small. In an accessible

Higher geometry an introduction to advanced methods in analytic geometry

CERN Document Server

Woods, Frederick S

2005-01-01

For students of mathematics with a sound background in analytic geometry and some knowledge of determinants, this volume has long been among the best available expositions of advanced work on projective and algebraic geometry. Developed from Professor Woods' lectures at the Massachusetts Institute of Technology, it bridges the gap between intermediate studies in the field and highly specialized works.With exceptional thoroughness, it presents the most important general concepts and methods of advanced algebraic geometry (as distinguished from differential geometry). It offers a thorough study

Electromagnetic cloaking in higher order spherical cloaks

Science.gov (United States)

Sidhwa, H. H.; Aiyar, R. P. R. C.; Kulkarni, S. V.

2017-06-01

The inception of transformation optics has led to the realisation of the invisibility devices for various applications, one of which is spherical cloaking. In this paper, a formulation for a higher-order spherical cloak has been proposed to reduce its physical thickness significantly by introducing a nonlinear relation between the original and transformed coordinate systems and it has been verified using the ray tracing approach. Analysis has been carried out to observe the anomalies in the variation of refractive index for higher order cloaks indicating the presence of poles in the relevant equations. Furthermore, a higher-order spherical cloak with predefined values of the material characteristics on its inner and outer surfaces has been designed for practical application.

Non-Riemannian geometry

CERN Document Server

Eisenhart, Luther Pfahler

2005-01-01

This concise text by a prominent mathematician deals chiefly with manifolds dominated by the geometry of paths. Topics include asymmetric and symmetric connections, the projective geometry of paths, and the geometry of sub-spaces. 1927 edition.

Spherical Nb single crystals containerlessly grown by electrostatic levitation

International Nuclear Information System (INIS)

Sung, Y.S.; Takeya, H.; Hirata, K.; Togano, K.

2003-01-01

Spherical Nb (T m =2750 K) single crystals were grown via containerless electrostatic levitation (ESL). Samples became spherical at melting in levitation and undercooled typically 300-450 K prior to nucleation. As-processed samples were still spherical without any macroscopic shape change by solidification showing a uniform dendritic surface morphology. Crystallographic {111} planes exposed in equilateral triangular shapes on the surface by preferential macroetching and spotty back-reflection Laue patterns confirm the single crystal nature of the ESL-processed Nb samples. No hysteresis in magnetization between zero field and field cooling also implies a clean defect-free condition of the spherical Nb single crystals

Effect of spherical aberration on scintillations of Gaussian beams in atmospheric turbulence

International Nuclear Information System (INIS)

Ji, Xiaoling; Deng, Jinping

2014-01-01

The effect of spherical aberration on scintillations of Gaussian beams in weak, moderate and strong turbulence is studied using numerical simulation method. It is found that the effect of the negative spherical aberration on the on-axis scintillation index is quite different from that of the positive spherical aberration. In weak turbulence, the positive spherical aberration results in a decrease of the on-axis scintillation index on propagation, but the negative spherical aberration results in an increase of the on-axis scintillation index when the propagation distance is not large. In particular, in weak turbulence the negative spherical aberration may cause peaks of the on-axis scintillation index, and the peaks disappear in moderate and strong turbulence, which is explained in physics. The strong turbulence leads to less discrepancy among scintillations of Gaussian beams with and without spherical aberration. - Highlights: • In weak turbulence scintillations can be suppressed using positive spherical aberration. • In weak turbulence scintillations may be very large due to negative spherical aberration. • The effect of spherical aberration on scintillations is less with increasing of turbulence

Effect of spherical aberration on scintillations of Gaussian beams in atmospheric turbulence

Energy Technology Data Exchange (ETDEWEB)

Ji, Xiaoling, E-mail: jiXL100@163.com; Deng, Jinping

2014-07-18

The effect of spherical aberration on scintillations of Gaussian beams in weak, moderate and strong turbulence is studied using numerical simulation method. It is found that the effect of the negative spherical aberration on the on-axis scintillation index is quite different from that of the positive spherical aberration. In weak turbulence, the positive spherical aberration results in a decrease of the on-axis scintillation index on propagation, but the negative spherical aberration results in an increase of the on-axis scintillation index when the propagation distance is not large. In particular, in weak turbulence the negative spherical aberration may cause peaks of the on-axis scintillation index, and the peaks disappear in moderate and strong turbulence, which is explained in physics. The strong turbulence leads to less discrepancy among scintillations of Gaussian beams with and without spherical aberration. - Highlights: • In weak turbulence scintillations can be suppressed using positive spherical aberration. • In weak turbulence scintillations may be very large due to negative spherical aberration. • The effect of spherical aberration on scintillations is less with increasing of turbulence.

Spherical near-field scanning at the Technical University of Denmark

DEFF Research Database (Denmark)

Hansen, J. E.; Jensen, F.

1988-01-01

The early work (1969-79) on spherical near-field antenna measurements at the Technical University of Denmark (TUD) is outlined. A spherical near-field transmission formula is described and the first probe-corrected spherical near-field measurements are discussed. The TUD-ESA (European Space Agency...

Toric focusing for radiation force applications using a toric lens coupled to a spherically focused transducer.

Science.gov (United States)

Arnal, Bastien; Nguyen, Thu-Mai; O'Donnell, Matthew

2014-12-01

Dynamic elastography using radiation force requires that an ultrasound field be focused during hundreds of microseconds at a pressure of several megapascals. Here, we address the importance of the focal geometry. Although there is usually no control of the elevational focal width in generating a tissue mechanical response, we propose a tunable approach to adapt the focus geometry that can significantly improve radiation force efficiency. Several thin, in-house-made polydimethylsiloxane lenses were designed to modify the focal spot of a spherical transducer. They exhibited low absorption and the focal spot widths were extended up to 8-fold in the elevation direction. Radiation force experiments demonstrated an 8-fold increase in tissue displacements using the same pressure level in a tissue-mimicking phantom with a similar shear wave spectrum, meaning it does not affect elastography resolution. Our results demonstrate that larger tissue responses can be obtained for a given pressure level, or that similar response can be reached at a much lower mechanical index (MI). We envision that this work will impact 3-D elastography using 2-D phased arrays, where such shaping can be achieved electronically with the potential for adaptive optimization.

The Geometry Conference

CERN Document Server

Bárány, Imre; Vilcu, Costin

2016-01-01

This volume presents easy-to-understand yet surprising properties obtained using topological, geometric and graph theoretic tools in the areas covered by the Geometry Conference that took place in Mulhouse, France from September 7–11, 2014 in honour of Tudor Zamfirescu on the occasion of his 70th anniversary. The contributions address subjects in convexity and discrete geometry, in distance geometry or with geometrical flavor in combinatorics, graph theory or non-linear analysis. Written by top experts, these papers highlight the close connections between these fields, as well as ties to other domains of geometry and their reciprocal influence. They offer an overview on recent developments in geometry and its border with discrete mathematics, and provide answers to several open questions. The volume addresses a large audience in mathematics, including researchers and graduate students interested in geometry and geometrical problems.

Hyperbolic geometry

CERN Document Server

Iversen, Birger

1992-01-01

Although it arose from purely theoretical considerations of the underlying axioms of geometry, the work of Einstein and Dirac has demonstrated that hyperbolic geometry is a fundamental aspect of modern physics

Interfacial effect on physical properties of composite media: Interfacial volume fraction with non-spherical hard-core-soft-shell-structured particles.

Science.gov (United States)

Xu, Wenxiang; Duan, Qinglin; Ma, Huaifa; Chen, Wen; Chen, Huisu

2015-11-02

Interfaces are known to be crucial in a variety of fields and the interfacial volume fraction dramatically affects physical properties of composite media. However, it is an open problem with great significance how to determine the interfacial property in composite media with inclusions of complex geometry. By the stereological theory and the nearest-surface distribution functions, we first propose a theoretical framework to symmetrically present the interfacial volume fraction. In order to verify the interesting generalization, we simulate three-phase composite media by employing hard-core-soft-shell structures composed of hard mono-/polydisperse non-spherical particles, soft interfaces, and matrix. We numerically derive the interfacial volume fraction by a Monte Carlo integration scheme. With the theoretical and numerical results, we find that the interfacial volume fraction is strongly dependent on the so-called geometric size factor and sphericity characterizing the geometric shape in spite of anisotropic particle types. As a significant interfacial property, the present theoretical contribution can be further drawn into predicting the effective transport properties of composite materials.

Left Ventricular Geometry and Blood Pressure as Predictors of Adverse Progression of Fabry Cardiomyopathy.

Directory of Open Access Journals (Sweden)

Johannes Krämer

Full Text Available In spite of several research studies help to describe the heart in Fabry disease (FD, the cardiomyopathy is not entirely understood. In addition, the impact of blood pressure and alterations in geometry have not been systematically evaluated.In 74 FD patients (mean age 36±12 years; 45 females the extent of myocardial fibrosis and its progression were quantified using cardiac magnetic-resonance-imaging with late enhancement technique (LE. Results were compared to standard echocardiography complemented by 2D-speckle-tracking, 3D-sphericity-index (SI and standardized blood pressure measurement. At baseline, no patient received enzyme replacement therapy (ERT. After 51±24 months, a follow-up examination was performed.Systolic blood pressure (SBP was higher in patients with vs. without LE: 123±17 mmHg vs. 115±13 mmHg; P = 0.04. A positive correlation was found between SI and the amount of LE-positive myocardium (r = 0.51; P<0.001 indicating an association of higher SI in more advanced stages of the cardiomyopathy. SI at baseline was positively associated with the increase of LE-positive myocardium during follow-up. The highest SBP (125±19 mmHg and also the highest SI (0.32±0.05 was found in the subgroup with a rapidly increasing LE (ie, ≥0.2% per year; n = 16; P = 0.04. Multivariate logistic regression analysis including SI, SBP, EF, left ventricular volumes, wall thickness and NT-proBNP adjusted for age and sex showed SI as the most powerful parameter to detect rapid progression of LE (AUC = 0.785; P<0.05.LV geometry as assessed by the sphericity index is altered in relation to the stage of the Fabry cardiomyopathy. Although patients with FD are not hypertensive, the SBP has a clear impact on the progression of the cardiomyopathy.

Spherical subsystem of galactic radiosources

Energy Technology Data Exchange (ETDEWEB)

Gorshkov, A G; Popov, M V [Moskovskij Gosudarstvennyj Univ. (USSR). Gosudarstvennyj Astronomicheskij Inst. ' ' GAISh' '

1975-05-01

The concentration of statistically complete sampling radiosources of the Ohiof scanning with plane spectra towards the Galaxy centre has been discovered. Quantitative calculations have showed that the sources form a spheric subsystem, which is close in parameters to such old formations in the Galaxy as globular clusters and the RRLsub(YR) type stars. The luminosity of the galaxy spheric subsystem object equals 10/sup 33/ erg/sec, the total number of objects being 7000. The existence of such a subsystem explains s the anomalously by low incline of statistics lgN-lgS in HF scanning PKS (..gamma..-2700Mgz) and the Michigan University scanning (..gamma..=8000Mgz) because the sources of galaxy spheric subsystem make up a considerable share in the total number of sources, especially at high frequencies (50% of sources with a flux greater than a unit of flux per 8000Mgz). It is very probable that the given subsystem consists of the representatives of one of the following class of objects: a) heat sources - the H2H regions with T=10/sup 40/K, Nsub(e)=10/sup 3/, l=1 ps b) supermass black holes with mass M/Mo approximately 10/sup 5/.

A hybrid radial basis function-pseudospectral method for thermal convection in a 3-D spherical shell

KAUST Repository

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 × 10³ and 10⁵. Results from a Ra = 10⁶ 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.

Rapid Prototyping of Electrically Small Spherical Wire Antennas

DEFF Research Database (Denmark)

Kim, Oleksiy S.

2014-01-01

It is shown how modern rapid prototyping technologies can be applied for quick and inexpensive, but still accurate, fabrication of electrically small wire antennas. A well known folded spherical helix antenna and a novel spherical zigzag antenna have been fabricated and tested, exhibiting...

Equilibrium spherically curved two-dimensional Lennard-Jones systems

NARCIS (Netherlands)

Voogd, J.M.; Sloot, P.M.A.; van Dantzig, R.

2005-01-01

To learn about basic aspects of nano-scale spherical molecular shells during their formation, spherically curved two-dimensional N-particle Lennard-Jones systems are simulated, studying curvature evolution paths at zero-temperature. For many N-values (N < 800) equilibrium configu- rations are traced

Stability of the spherical form of nuclei

International Nuclear Information System (INIS)

Sabry, A.A.

1976-08-01

An extension of the mass formula for a spherical nucleus in the drop model to include a largely deformed nucleus of different forms is investigated. It is found that although the spherical form is stable under small deformations from equilibrium, there exists for heavier nuclei another more favourable stable form, which can be approximated by two, or three touching prolate ellipsoids of revolution

Elastic properties of spherically anisotropic piezoelectric composites

International Nuclear Information System (INIS)

En-Bo, Wei; Guo-Qing, Gu; Ying-Ming, Poon

2010-01-01

Effective elastic properties of spherically anisotropic piezoelectric composites, whose spherically anisotropic piezoelectric inclusions are embedded in an infinite non-piezoelectric matrix, are theoretically investigated. Analytical solutions for the elastic displacements and the electric potentials under a uniform external strain are derived exactly. Taking into account of the coupling effects of elasticity, permittivity and piezoelectricity, the formula is derived for estimating the effective elastic properties based on the average field theory in the dilute limit. An elastic response mechanism is revealed, in which the effective elastic properties increase as inclusion piezoelectric properties increase and inclusion dielectric properties decrease. Moreover, a piezoelectric response mechanism, of which the effective piezoelectric response vanishes due to the symmetry of spherically anisotropic composite, is also disclosed. (condensed matter: structure, thermal and mechanical properties)

Flow and scour around spherical bodies

DEFF Research Database (Denmark)

Truelsen, Christoffer

2003-01-01

Spherical bodies placed in the marine environment may bury themselves due to the action of the waves and the current on the sediment in their immediate neighborhood. The present study addresses this topic by a numerical and an experimental investigation of the flow and scour around a spherical body...... results except in the critical flow regime. For flow around a near-wall sphere, a weak horseshoe vortex emerges as the gap ratio becomes less than or equal to 0.3. In Chapter 3, a RANS flow solver has been used to compute the bed shear stress for a near-wall sphere. The model results compare well...... 4, an experimental study on the scour around spherical bodies and self-burial in sand for steady current and waves has been carried out. The effect of the contraction of streamlines is found to be the key element in the scour process both for steady current and waves. Furthermore, it is demonstrated...

Spherical tokamak power plant design issues

International Nuclear Information System (INIS)

Hender, T.C.; Bond, A.; Edwards, J.; Karditsas, P.J.; McClements, K.G.; Mustoe, J.; Sherwood, D.V.; Voss, G.M.; Wilson, H.R.

2000-01-01

The very high β potential of the spherical tokamak has been demonstrated in the START experiment. Systems code studies show the cost of electricity from spherical tokamak power plants, operating at high β in second ballooning mode stable regime, is comparable with fossil fuels and fission. Outline engineering designs are presented based on two concepts for the central rod of the toroidal field (TF) circuit - a room temperature water cooled copper rod or a helium cooled cryogenic aluminium rod. For the copper rod case the TF return limbs are supported by the vacuum vessel, while for the aluminium rod the TF coils form an independent structure. In both cases thermohydraulic and stress calculations indicate the viability of the design. Two-dimensional neutronics calculations show the feasibility of tritium self-sufficiency without an inboard blanket. The spherical tokamak has unique maintenance possibilities based on lowering major component structures into a hot cell beneath the device and these are discussed

On organizing principles of discrete differential geometry. Geometry of spheres

International Nuclear Information System (INIS)

Bobenko, Alexander I; Suris, Yury B

2007-01-01

Discrete differential geometry aims to develop discrete equivalents of the geometric notions and methods of classical differential geometry. This survey contains a discussion of the following two fundamental discretization principles: the transformation group principle (smooth geometric objects and their discretizations are invariant with respect to the same transformation group) and the consistency principle (discretizations of smooth parametrized geometries can be extended to multidimensional consistent nets). The main concrete geometric problem treated here is discretization of curvature-line parametrized surfaces in Lie geometry. Systematic use of the discretization principles leads to a discretization of curvature-line parametrization which unifies circular and conical nets.

Synthesis and characterization of spherical 2-diazo-4,6-dinitrophenol (DDNP)

International Nuclear Information System (INIS)

Yang Zongwei; Liu Yucun; Liu Dengcheng; Yan Liwei; Chen Ji

2010-01-01

Spherical 2-diazo-4,6-dinitrophenol (DDNP) with good flowability and controlled bulk density (0.65-0.95 g/cm 3 ) has been prepared at factory scale by the modified method using 4-methylphenol as crystal control ingredient. Results showed that the yield of product was increased by 5-10%, and the waste water was significantly decreased due to circulation use of waste water compared with traditional method. Synthesized spherical DDNP was characterized by IR, laser granularity measurement, SEM, HPLC and XRD. IR spectrum confirmed the structural features of spherical DDNP. The particle analysis revealed that the modified method could offer spherical DDNP with average particle size of 350 μm and high purity (>98.52%). The XRD peaks of spherical DDNP have similar diffraction angles as those of traditional DDNP. The DSC profile of spherical DDNP showed the exothermic decomposition in the temperature range of 161.2-188.5 deg. C. The product can be pressed at over 40 MPa without dead pressed phenomenon, and the minimum detonating charge of spherical DDNP was measured to be about 0.15 g. Furthermore, impact sensitivity test suggested that spherical DDNP is less sensitive than traditional DDNP.

Periphony-Lattice Mixed-Order Ambisonic Scheme for Spherical Microphone Arrays

DEFF Research Database (Denmark)

Chang, Jiho; Marschall, Marton

2018-01-01

to performance that is independent of the incident direction of the sound waves. On the other hand, mixed-order ambisonic (MOA) schemes that select an appropriate subset of spherical harmonics can improve the performance for horizontal directions at the expense of other directions. This paper proposes an MOA......Most methods for sound field reconstruction and spherical beamforming with spherical microphone arrays are mathematically based on the spherical harmonics expansion. In many cases, this expansion is truncated at a certain order as in higher order ambisonics (HOA). This truncation leads...

Geometry and its applications

CERN Document Server

Meyer, Walter J

2006-01-01

Meyer''s Geometry and Its Applications, Second Edition, combines traditional geometry with current ideas to present a modern approach that is grounded in real-world applications. It balances the deductive approach with discovery learning, and introduces axiomatic, Euclidean geometry, non-Euclidean geometry, and transformational geometry. The text integrates applications and examples throughout and includes historical notes in many chapters. The Second Edition of Geometry and Its Applications is a significant text for any college or university that focuses on geometry''s usefulness in other disciplines. It is especially appropriate for engineering and science majors, as well as future mathematics teachers.* Realistic applications integrated throughout the text, including (but not limited to): - Symmetries of artistic patterns- Physics- Robotics- Computer vision- Computer graphics- Stability of architectural structures- Molecular biology- Medicine- Pattern recognition* Historical notes included in many chapters...

Spherical torus, compact fusion at low field

International Nuclear Information System (INIS)

Peng, Y.K.M.

1985-02-01

A spherical torus is obtained by retaining only the indispensable components on the inboard side of a tokamak plasma, such as a cooled, normal conductor that carries current to produce a toroidal magnetic field. The resulting device features an exceptionally small aspect ratio (ranging from below 2 to about 1.3), a naturally elongated D-shaped plasma cross section, and ramp-up of the plasma current primarily by noninductive means. As a result of the favorable dependence of the tokamak plasma behavior to decreasing aspect ratio, a spherical torus is projected to have small size, high beta, and modest field. Assuming Mirnov confinement scaling, an ignition spherical torus at a field of 2 T features a major radius of 1.5 m, a minor radius of 1.0 m, a plasma current of 14 MA, comparable toroidal and poloidal field coil currents, an average beta of 24%, and a fusion power of 50 MW. At 2 T, a Q = 1 spherical torus will have a major radius of 0.8 m, a minor radius of 0.5 m, and a fusion power of a few megawatts

Effect of ablation geometry on the dynamics, composition, and geometrical shape of thin film plasma

Science.gov (United States)

Mondal, Alamgir; Singh, R. K.; Kumar, Ajai

2018-01-01

The characteristics of plasma plume produced by front and back ablation of thin films have been investigated using fast imaging and optical emission spectroscopy. Ablation geometry dependence of the plume dynamics, its geometrical aspect and composition is emphasized. Also, the effect of an ambient environment and the beam diameter of an ablating laser on the front and back ablations is briefly discussed. Analysis of time resolved images and plasma parameters indicates that the energetic and spherical plasma formed by front ablation is strikingly different in comparison to the slow and nearly cylindrical plasma plume observed in the case of back ablation. Further shock formation, plume confinement, thermalization and validity of different expansion models in these two ablation geometries are also presented. The present study demonstrates the manipulation of kinetic energy, shape, ion/neutral compositions and directionality of the expanding plume by adjusting the experimental configuration, which is highly relevant to its utilization in various applications e.g., generation of energetic particles, tokamak edge plasma diagnostics, thin film deposition, etc.

The spherical limit of the n-vector model and correlation inequaljties

International Nuclear Information System (INIS)

Angelescu, N.; Bundaru, M.; Costache, G.

1978-08-01

The asymptotics of the state of the n-vector model with a finite number of spins in the spherical limit is studied. Besides rederiving the limit free energy, corresponding to a generalized spherical model (with ''spherical constraint'' at every site), we obtain also the limit of the correlation functions, which allow a precise definition of the state of the latter model. Correlation inequalities are proved for ferromagnetic interactions in the asymptotic regime. In particular, it is shown that the generalized spherical model fulfills the expected Griffiths' type inequalities, differing in this respect from the spherical model with overall constraint. (author)

A modular spherical harmonics approach to the neutron transport equation

International Nuclear Information System (INIS)

Inanc, F.; Rohach, A.F.

1989-01-01

A modular nodal method was developed for solving the neutron transport equation in 2-D xy coordinates. The spherical harmonic expansion was used for approximating the second-order even-parity form of the neutron transport equation. The boundary conditions of the spherical harmonics approximation were derived in a form to have forms analogous to the partial currents in the neutron diffusion equation. Relations were developed for generating both the second-order spherical harmonic equations and the boundary conditions in an automated computational algorithm. Nodes using different orders of the spherical harmonics approximation to the transport equation were interfaced through mixed-type boundary conditions. The determination of spherical harmonic orders implemented in the nodes were determined by the scheme in an automated manner. Results of the method compared favorably to benchmark problems. (author)

Beautiful geometry

CERN Document Server

Maor, Eli

2014-01-01

If you've ever thought that mathematics and art don't mix, this stunning visual history of geometry will change your mind. As much a work of art as a book about mathematics, Beautiful Geometry presents more than sixty exquisite color plates illustrating a wide range of geometric patterns and theorems, accompanied by brief accounts of the fascinating history and people behind each. With artwork by Swiss artist Eugen Jost and text by acclaimed math historian Eli Maor, this unique celebration of geometry covers numerous subjects, from straightedge-and-compass constructions to intriguing configur

Effective pair potentials for spherical nanoparticles

International Nuclear Information System (INIS)

Van Zon, Ramses

2009-01-01

An effective description for rigid spherical nanoparticles in a fluid of point particles is presented. The points inside the nanoparticles and the point particles are assumed to interact via spherically symmetric additive pair potentials, while the distribution of points inside the nanoparticles is taken to be spherically symmetric and smooth. The resulting effective pair interactions between a nanoparticle and a point particle, as well as between two nanoparticles, are then given by spherically symmetric potentials. If overlap between particles is allowed, as can occur for some forms of the pair potentials, the effective potential generally has non-analytic points. It is shown that for each effective potential the expressions for different overlapping cases can be written in terms of one analytic auxiliary potential. Even when only non-overlapping situations are possible, the auxiliary potentials facilitate the formulation of the effective potentials. Effective potentials for hollow nanoparticles (appropriate e.g. for buckyballs) are also considered and shown to be related to those for solid nanoparticles. For hollow nanoparticles overlap is more physical, since this covers the case of a smaller particle embedded in a larger, hollow nanoparticle. Finally, explicit expressions are given for the effective potentials derived from basic pair potentials of power law and exponential form, as well as from the commonly used London–van der Waals, Morse, Buckingham, and Lennard-Jones potentials. The applicability of the latter is demonstrated by comparison with an atomic description of nanoparticles with an internal face centered cubic structure

Revolutions of Geometry

CERN Document Server

O'Leary, Michael

2010-01-01

Guides readers through the development of geometry and basic proof writing using a historical approach to the topic. In an effort to fully appreciate the logic and structure of geometric proofs, Revolutions of Geometry places proofs into the context of geometry's history, helping readers to understand that proof writing is crucial to the job of a mathematician. Written for students and educators of mathematics alike, the book guides readers through the rich history and influential works, from ancient times to the present, behind the development of geometry. As a result, readers are successfull

Analogy and Dynamic Geometry System Used to Introduce Three-Dimensional Geometry

Science.gov (United States)

Mammana, M. F.; Micale, B.; Pennisi, M.

2012-01-01

We present a sequence of classroom activities on Euclidean geometry, both plane and space geometry, used to make three dimensional geometry more catchy and simple. The activity consists of a guided research activity that leads the students to discover unexpected properties of two apparently distant geometrical entities, quadrilaterals and…

Information geometry

CERN Document Server

Ay, Nihat; Lê, Hông Vân; Schwachhöfer, Lorenz

2017-01-01

The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemannian geometry and Banach space theory. Parametrised measure models are defined as fundamental geometric objects, which can be both finite or infinite dimensional. Based on these models, canonical tensor fields are introduced and further studied, including the Fisher metric and the Amari-Chentsov tensor, and embeddings of statistical manifolds are investigated. This novel foundation then leads to application highlights, such as generalizations and extensions of the classical uniqueness result of Chentsov or the Cramér-Rao inequality. Additionally, several new application fields of information geometry are highlighted, for instance hierarchical and graphical models, complexity theory, population genetics, or Markov Chain Monte Carlo. The book will be of interest to mathematicians who are interested in geometry, inf...

Self Absorbed Fraction for Electrons and Beta Particles in Small Spherical Volumes

International Nuclear Information System (INIS)

Grosev, D.

2003-01-01

Absorbed fraction and target organ mass are important parameters of internal dosimetry calculations that define the geometry of the system. Standard MIRD (Medical Internal Radiation Dosimetry) formalism assumes that the absorbed fraction for non-penetrating radiations (e.g., electrons, beta particles) is 1. This may not be correct in cases where dimensions of organs/tissues are comparable with the ranges of electrons/beta particles. Such is the case for example in radiodine ablation of thyroid remnant tissue. In this work the self-absorbed fraction (source and target volumes are the same) for monoenergetic electrons and beta particles is calculated for small spherical volumes of various sizes and unit density. Absorbed fraction can be expressed as an integral of the product of two quantities: (a) Scaled beta dose point kernel (mean absorbed dose rate per activity of the point source in infinite homogenous medium), F β ; (b) special geometrical reduction factor (GRF). F β is calculated using EGS4 Monte Carlo (MC) code for transport of electrons and photons. MC source code calculates the deposition of energy inside concentric spherical shells around the isotropic point source of electrons/beta particles in infinite medium (water). Shell thickness was δr=0.02·X 90 , where X 90 represents the radius of the sphere inside which 90% of the source energy is absorbed. Number of concentric spherical shells was 100, 10000 electron histories were started in each program run, and 10 runs were repeated for statistical reason. Numerical integration of the product of F β , calculated by MC program, and GRF for sphere was done using Simpson method. Absorbed fractions were calculated for spheres with mass from 0.01-20 g (r = 0.13 - 1.68 cm). Results are given for monoenergetic electrons with kinetic energy T=0.2, 0.4, 1.0 MeV, and for three beta emitters 1 31I , 3 2P , 9 0Y . For quantitative dosimetric protocols in radioiodine ablation therapy, results for 1 31I are of

Method of producing spherical lithium aluminate particles

International Nuclear Information System (INIS)

Yang, L.; Medico, R.R.; Baugh, W.A.

1983-01-01

Spherical particles of lithium aluminate are formed by initially producing aluminium hydroxide spheroids, and immersing the spheroids in a lithium ion-containing solution to infuse lithium ions into the spheroids. The lithium-infused spheroids are rinsed to remove excess lithium ion from the surface, and the rinsed spheroids are soaked for a period of time in a liquid medium, dried and sintered to form lithium aluminate spherical particles. (author)

Collisions of droplets on spherical particles

Science.gov (United States)

Charalampous, Georgios; Hardalupas, Yannis

2017-10-01

Head-on collisions between droplets and spherical particles are examined for water droplets in the diameter range between 170 μm and 280 μm and spherical particles in the diameter range between 500 μm and 2000 μm. The droplet velocities range between 6 m/s and 11 m/s, while the spherical particles are fixed in space. The Weber and Ohnesorge numbers and ratio of droplet to particle diameter were between 92 deposition and splashing regimes, a regime is observed in the intermediate region, where the droplet forms a stable crown, which does not breakup but propagates along the particle surface and passes around the particle. This regime is prevalent when the droplets collide on small particles. The characteristics of the collision at the onset of rim instability are also described in terms of the location of the film on the particle surface and the orientation and length of the ejected crown. Proper orthogonal decomposition identified that the first 2 modes are enough to capture the overall morphology of the crown at the splashing threshold.

Non-Spherical Microcapsules for Increased Core Content Volume Delivery

Science.gov (United States)

Oliva-Buisson, Yvette J.

2014-01-01

The goal of this project was to advance microencapsulation from the standard spherical microcapsule to a non-spherical, high-aspect ratio (HAR), elongated microcapsule. This was to be accomplished by developing reproducible methods of synthesizing or fabricating robust, non-spherical, HAR microcapsules. An additional goal of this project was to develop the techniques to the point where scale-up of these methods could be examined. Additionally, this project investigated ways to apply the microencapsulation techniques developed as part of this project to self-healing formulations.

Emulating Spherical Wave Channel Models in Multi-probe Anechoic Chamber Setups

DEFF Research Database (Denmark)

Fan, Wei; Carreño, Xavier; Nielsen, Jesper Ødum

2015-01-01

to emulate spherical wave channel models in multi-probe anechoic chamber setups. In this paper, a technique based on the field synthesis principle is proposed to approximate spherical waves emitted from arbitrarily located point sources with arbitrary polarizations. Simulation results show that static......Spherical wave channel modeling has attracted huge research attention for massive multiple-input multiple-output (MIMO) and short-distance MIMO systems. Current research work in multi-probe anechoic chamber systems is limited to reproduce radio channels assuming planar wavefronts. There is a need...... spherical waves can be reproduced with a limited number of probes, and the field synthesis accuracy of spherical wave depends on the location of the source point....

Developement of Spherical Polyurethane Beads

Institute of Scientific and Technical Information of China (English)

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).

Spherical null geodesics of rotating Kerr black holes

International Nuclear Information System (INIS)

Hod, Shahar

2013-01-01

The non-equatorial spherical null geodesics of rotating Kerr black holes are studied analytically. Unlike the extensively studied equatorial circular orbits whose radii are known analytically, no closed-form formula exists in the literature for the radii of generic (non-equatorial) spherical geodesics. We provide here an approximate formula for the radii r ph (a/M;cosi) of these spherical null geodesics, where a/M is the dimensionless angular momentum of the black hole and cos i is an effective inclination angle (with respect to the black-hole equatorial plane) of the orbit. It is well-known that the equatorial circular geodesics of the Kerr spacetime (the prograde and the retrograde orbits with cosi=±1) are characterized by a monotonic dependence of their radii r ph (a/M;cosi=±1) on the dimensionless spin-parameter a/M of the black hole. We use here our novel analytical formula to reveal that this well-known property of the equatorial circular geodesics is actually not a generic property of the Kerr spacetime. In particular, we find that counter-rotating spherical null orbits in the range (3√(3)−√(59))/4≲cosi ph (a/M;cosi=const) on the dimensionless rotation-parameter a/M of the black hole. Furthermore, it is shown that spherical photon orbits of rapidly-rotating black holes are characterized by a critical inclination angle, cosi=√(4/7), above which the coordinate radii of the orbits approach the black-hole radius in the extremal limit. We prove that this critical inclination angle signals a transition in the physical properties of the spherical null geodesics: in particular, it separates orbits which are characterized by finite proper distances to the black-hole horizon from orbits which are characterized by infinite proper distances to the horizon.

Sextupole system for the correction of spherical aberration

Science.gov (United States)

Crewe, A.V.; Kopf, D.A.

In an electron beam device in which an electron beam is developed and then focused by a lens to a particular spot, there is provided a means for eliminating spherical aberration. A sextupole electromagnetic lens is positioned between two focusing lenses. The interaction of the sextupole with the beam compensates for spherical aberration. (GHT)

Models for randomly distributed nanoscopic domains on spherical vesicles

Science.gov (United States)

Anghel, Vinicius N. P.; Bolmatov, Dima; Katsaras, John

2018-06-01

The existence of lipid domains in the plasma membrane of biological systems has proven controversial, primarily due to their nanoscopic size—a length scale difficult to interrogate with most commonly used experimental techniques. Scattering techniques have recently proven capable of studying nanoscopic lipid domains populating spherical vesicles. However, the development of analytical methods able of predicting and analyzing domain pair correlations from such experiments has not kept pace. Here, we developed models for the random distribution of monodisperse, circular nanoscopic domains averaged on the surface of a spherical vesicle. Specifically, the models take into account (i) intradomain correlations corresponding to form factors and interdomain correlations corresponding to pair distribution functions, and (ii) the analytical computation of interdomain correlations for cases of two and three domains on a spherical vesicle. In the case of more than three domains, these correlations are treated either by Monte Carlo simulations or by spherical analogs of the Ornstein-Zernike and Percus-Yevick (PY) equations. Importantly, the spherical analog of the PY equation works best in the case of nanoscopic size domains, a length scale that is mostly inaccessible by experimental approaches such as, for example, fluorescent techniques and optical microscopies. The analytical form factors and structure factors of nanoscopic domains populating a spherical vesicle provide a new and important framework for the quantitative analysis of experimental data from commonly studied phase-separated vesicles used in a wide range of biophysical studies.

JUST: Joint Upgraded Spherical Tokamak

International Nuclear Information System (INIS)

Azizov, E.A.; Dvorkin, N.Ya.; Filatov, O.G.

1997-01-01

The main goals, ideas and the programme of JUST, spherical tokamak (ST) for the plasma burn investigation, are presented. The place and prospects of JUST in thermonuclear investigations are discussed. (author)

Spherical loudspeaker array for local active control of sound.

Science.gov (United States)

Rafaely, Boaz

2009-05-01

Active control of sound has been employed to reduce noise levels around listeners' head using destructive interference from noise-canceling sound sources. Recently, spherical loudspeaker arrays have been studied as multiple-channel sound sources, capable of generating sound fields with high complexity. In this paper, the potential use of a spherical loudspeaker array for local active control of sound is investigated. A theoretical analysis of the primary and secondary sound fields around a spherical sound source reveals that the natural quiet zones for the spherical source have a shell-shape. Using numerical optimization, quiet zones with other shapes are designed, showing potential for quiet zones with extents that are significantly larger than the well-known limit of a tenth of a wavelength for monopole sources. The paper presents several simulation examples showing quiet zones in various configurations.

Geometry essentials for dummies

CERN Document Server

Ryan, Mark

2011-01-01

Just the critical concepts you need to score high in geometry This practical, friendly guide focuses on critical concepts taught in a typical geometry course, from the properties of triangles, parallelograms, circles, and cylinders, to the skills and strategies you need to write geometry proofs. Geometry Essentials For Dummies is perfect for cramming or doing homework, or as a reference for parents helping kids study for exams. Get down to the basics - get a handle on the basics of geometry, from lines, segments, and angles, to vertices, altitudes, and diagonals Conque

Electrically small circularly polarized spherical antenna with air core

DEFF Research Database (Denmark)

Kim, O. S.

2013-01-01

An electrically small circularly polarized self-resonant spherical antenna with air core is presented. The antenna is a modified multiarm spherical helix exciting TM10 and TE10 spherical modes with equal radiated power, and thus yielding perfect circular polarization over the entire far......-field sphere (except the polar regions, where the radiation is low). The self-resonance is achieved by exciting higher-order TM modes, which provide the necessary electric stored energy in the near-field, while contributing negligibly to the far-field radiation of the antenna. The antenna has electrical size...

The Spherical Deformation Model

DEFF Research Database (Denmark)

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 s...

3D Printing Electrically Small Spherical Antennas

DEFF Research Database (Denmark)

Kim, Oleksiy S.

2013-01-01

3D printing is applied for rapid prototyping of an electrically small spherical wire antenna. The model is first printed in plastic and subsequently covered with several layers of conductive paint. Measured results are in good agreement with simulations.......3D printing is applied for rapid prototyping of an electrically small spherical wire antenna. The model is first printed in plastic and subsequently covered with several layers of conductive paint. Measured results are in good agreement with simulations....

START: the creation of a spherical tokamak

International Nuclear Information System (INIS)

Sykes, Alan

1992-01-01

The START (Small Tight Aspect Ratio Tokamak) plasma fusion experiment is now operational at AEA Fusion's Culham Laboratory. It is the world's first experiment to explore an extreme limit of the tokamak - the Spherical Tokamak - which theoretical studies predict may have substantial advantages in the search for economic fusion power. The Head of the START project, describes the concept, some of the initial experimental results and the possibility of developing a spherical tokamak power reactor. (author)

Visualization of flow patterns in shaking vessels with various geometry; Shushu no kika keijo wo motsu yodo kakuhan sonai no ryudo jotai no kashika

Energy Technology Data Exchange (ETDEWEB)

Kato, Y; Hiraoka, S; Tada, Y; Ue, T [Nagoya Institute of Technology, Nagoya (Japan); Koh, S [Toyo Engineering Corp., Tokyo (Japan); Lee, Y [Keimyung University, (Korea, Republic of)

1996-03-10

The flow patterns in shaking vessels with various geometries were visualized with a tracer method using aluminum powder. The spherical and conical vessels were effective for the shake mixing in the same manner as the cylindrical vessel, because these vessels have circular cross sections that develop the rotational flow. Neither a rectangular vessel nor a cylindrical vessel with baffles should be used for shake mixing, because rotational flows are not developed in these vessels. 2 refs., 6 figs.

Buckling strength of spherical shells under combined loads

International Nuclear Information System (INIS)

Nagashima, H.; Kokubo, K.; Takayanagi, M.; Hayasaka, Y.; Kume, T.; Nagata, T.

1995-01-01

Many studies on buckling of cylindrical shells have been conducted, and many buckling evaluation equations have been proposed for actual plant designs; however, buckling of spherical shells under combined horizontal and vertical loads cannot be evaluated due to insufficient data. There is a particular lack of buckling data for spherical shells under lateral loads. To establish a method for estimating the buckling strength of spherical shells, we investigate the interactions between horizontal and vertical (compressive tensile) loads by conducting buckling tests. Applying several combinations of these loads in tests and using computer linear analysis, we obtain interaction curves. This study reports on the buckling tests conducted using spherical shell 1120 mm in dia., 0.7 mm thick and 696 mm high, which are shaped individually by press-forming and finally joined together by four meridional welds, using a specially made jig. Initial imperfections before testing and local deformations after each loading increment during testing are measured with special measuring equipment, and the interaction curve of horizontal and vertical loads and effect of imperfection on the buckling strength of spherical shells are obtained. Nonlinear FEM programs are developed using an 8-node isoparametric shell element and a four-node quadrilateral element of C 0 type with reduced integration based upon a Mindlin-Reissner theory which includes transverse shear. Actual initial imperfections are generally in irregular patterns. Thus, there may be several definitions of the equivalent magnitudes of initial imperfections related to buckling loads. Equivalent magnitudes have no practical meaning unless they can be obtained easily not only for small structures such as test shells but also for large actual structures. In the present study, we define the equivalent magnitude of initial imperfections as the maximum local ruggedness measured radially from a circular temperature having a radius equal

Color from hierarchy: Diverse optical properties of micron-sized spherical colloidal assemblies.

Science.gov (United States)

Vogel, Nicolas; Utech, Stefanie; England, Grant T; Shirman, Tanya; Phillips, Katherine R; Koay, Natalie; Burgess, Ian B; Kolle, Mathias; Weitz, David A; Aizenberg, Joanna

2015-09-01

Materials in nature are characterized by structural order over multiple length scales have evolved for maximum performance and multifunctionality, and are often produced by self-assembly processes. A striking example of this design principle is structural coloration, where interference, diffraction, and absorption effects result in vivid colors. Mimicking this emergence of complex effects from simple building blocks is a key challenge for man-made materials. Here, we show that a simple confined self-assembly process leads to a complex hierarchical geometry that displays a variety of optical effects. Colloidal crystallization in an emulsion droplet creates micron-sized superstructures, termed photonic balls. The curvature imposed by the emulsion droplet leads to frustrated crystallization. We observe spherical colloidal crystals with ordered, crystalline layers and a disordered core. This geometry produces multiple optical effects. The ordered layers give rise to structural color from Bragg diffraction with limited angular dependence and unusual transmission due to the curved nature of the individual crystals. The disordered core contributes nonresonant scattering that induces a macroscopically whitish appearance, which we mitigate by incorporating absorbing gold nanoparticles that suppress scattering and macroscopically purify the color. With increasing size of the constituent colloidal particles, grating diffraction effects dominate, which result from order along the crystal's curved surface and induce a vivid polychromatic appearance. The control of multiple optical effects induced by the hierarchical morphology in photonic balls paves the way to use them as building blocks for complex optical assemblies--potentially as more efficient mimics of structural color as it occurs in nature.

Color from hierarchy: Diverse optical properties of micron-sized spherical colloidal assemblies

Science.gov (United States)

Vogel, Nicolas; Utech, Stefanie; England, Grant T.; Shirman, Tanya; Phillips, Katherine R.; Koay, Natalie; Burgess, Ian B.; Kolle, Mathias; Weitz, David A.; Aizenberg, Joanna

2015-01-01

Materials in nature are characterized by structural order over multiple length scales have evolved for maximum performance and multifunctionality, and are often produced by self-assembly processes. A striking example of this design principle is structural coloration, where interference, diffraction, and absorption effects result in vivid colors. Mimicking this emergence of complex effects from simple building blocks is a key challenge for man-made materials. Here, we show that a simple confined self-assembly process leads to a complex hierarchical geometry that displays a variety of optical effects. Colloidal crystallization in an emulsion droplet creates micron-sized superstructures, termed photonic balls. The curvature imposed by the emulsion droplet leads to frustrated crystallization. We observe spherical colloidal crystals with ordered, crystalline layers and a disordered core. This geometry produces multiple optical effects. The ordered layers give rise to structural color from Bragg diffraction with limited angular dependence and unusual transmission due to the curved nature of the individual crystals. The disordered core contributes nonresonant scattering that induces a macroscopically whitish appearance, which we mitigate by incorporating absorbing gold nanoparticles that suppress scattering and macroscopically purify the color. With increasing size of the constituent colloidal particles, grating diffraction effects dominate, which result from order along the crystal’s curved surface and induce a vivid polychromatic appearance. The control of multiple optical effects induced by the hierarchical morphology in photonic balls paves the way to use them as building blocks for complex optical assemblies—potentially as more efficient mimics of structural color as it occurs in nature. PMID:26290583

Complex analysis and geometry

CERN Document Server

Silva, Alessandro

1993-01-01

The papers in this wide-ranging collection report on the results of investigations from a number of linked disciplines, including complex algebraic geometry, complex analytic geometry of manifolds and spaces, and complex differential geometry.

Simple and Versatile Dynamic Model of Spherical Roller Bearing

Directory of Open Access Journals (Sweden)

Behnam Ghalamchi

2013-01-01

Full Text Available Rolling element bearings are essential components of rotating machinery. The spherical roller bearing (SRB is one variant witnessing increasing use because it is self-aligning and can support high loads. It is becoming increasingly important to understand how the SRB responds dynamically under a variety of conditions. This study introduces a computationally efficient, three-degree-of-freedom, SRB model that was developed to predict the transient dynamic behaviors of a rotor-SRB system. In the model, bearing forces and deflections were calculated as a function of contact deformation and bearing geometry parameters according to the nonlinear Hertzian contact theory. The results reveal how some of the more important parameters, such as diametral clearance, the number of rollers, and osculation number, influence ultimate bearing performance. One pair of calculations looked at bearing displacement with respect to time for two separate arrangements of the caged side-by-side roller arrays, when they are aligned and when they are staggered. As theory suggests, significantly lower displacement variations were predicted for the staggered arrangement. Following model verification, a numerical simulation was carried out successfully for a full rotor-bearing system to demonstrate the application of this newly developed SRB model in a typical real world analysis.

Invariants of the spherical sector in conformal mechanics

International Nuclear Information System (INIS)

Hakobyan, Tigran; Nersessian, Armen; Saghatelian, Armen; Lechtenfeld, Olaf

2011-01-01

A direct relation is established between the constants of motion for conformal mechanics and those for its spherical part. In this way, we find the complete set of functionally independent constants of motion for the so-called cuboctahedric Higgs oscillator, which is just the spherical part of the rational A 3 Calogero model (describing four Calogero particles after decoupling their center of mass).

Babcock and Wilcox plate fabrication experience with uranium silicide spherical fuel

International Nuclear Information System (INIS)

Todd, Lawrence E.; Pace, Brett W.

1996-01-01

This report is written to present the fuel fabrication experience of Babcock and Wilcox using atomized spherical uranium silicide powder. The intent is to demonstrate the ability to fabricate fuel plates using spherical powder and to provide useful information proceeding into the next phase of work using this type of fuel. The limited quantity of resources- spherical powder and time, did not allow for much process optimizing in this work scope. However, the information contained within provides optimism for the future of spherical uranium silicide fuel plate fabrication at Babcock and Wilcox.The success of assembling fuel elements with spherical powder will enable Babcock and Wilcox to reduce overall costs to its customers while still maintaining our reputation for providing high quality research and test reactor products. (author)

Spherical Cancer Models in Tumor Biology

Directory of Open Access Journals (Sweden)

Louis-Bastien Weiswald

2015-01-01

Full Text Available Three-dimensional (3D in vitro models have been used in cancer research as an intermediate model between in vitro cancer cell line cultures and in vivo tumor. Spherical cancer models represent major 3D in vitro models that have been described over the past 4 decades. These models have gained popularity in cancer stem cell research using tumorospheres. Thus, it is crucial to define and clarify the different spherical cancer models thus far described. Here, we focus on in vitro multicellular spheres used in cancer research. All these spherelike structures are characterized by their well-rounded shape, the presence of cancer cells, and their capacity to be maintained as free-floating cultures. We propose a rational classification of the four most commonly used spherical cancer models in cancer research based on culture methods for obtaining them and on subsequent differences in sphere biology: the multicellular tumor spheroid model, first described in the early 70s and obtained by culture of cancer cell lines under nonadherent conditions; tumorospheres, a model of cancer stem cell expansion established in a serum-free medium supplemented with growth factors; tissue-derived tumor spheres and organotypic multicellular spheroids, obtained by tumor tissue mechanical dissociation and cutting. In addition, we describe their applications to and interest in cancer research; in particular, we describe their contribution to chemoresistance, radioresistance, tumorigenicity, and invasion and migration studies. Although these models share a common 3D conformation, each displays its own intrinsic properties. Therefore, the most relevant spherical cancer model must be carefully selected, as a function of the study aim and cancer type.

Erosion and damage by hard spherical particles on glass

NARCIS (Netherlands)

Slikkerveer, P.J.; Verspui, M.A.; Skerka, G.J.E.

1999-01-01

Solid particle impact of hard spherical particles on glass is of fundamental interest because of the presence of a number of different impact regimes. Understanding the impact of spherical particles is also a step toward modeling the behavior of rounded particles. This paper verifies theoretical

Spherical reconciliation for a continuous-variable quantum key distribution

International Nuclear Information System (INIS)

Lu Zhao; Shi Jian-Hong; Li Feng-Guang

2017-01-01

Information reconciliation is a significant step for a continuous-variable quantum key distribution (CV-QKD) system. We propose a reconciliation method that allows two authorized parties to extract a consistent and secure binary key in a CV-QKD protocol, which is based on Gaussian-modulated coherent states and homodyne detection. This method named spherical reconciliation is based on spherical quantization and non-binary low-density parity-check (LDPC) codes. With the suitable signal-to-noise ratio (SNR) and code rate of non-binary LDPC codes, spherical reconciliation algorithm has a high efficiency and can extend the transmission distance of CV-QKD. (paper)

Electrostatic axisymmetric mirror with removable spherical aberration

International Nuclear Information System (INIS)

Birmuzaev, S.B.; Serikbaeva, G.S.; Hizirova, M.A.

1999-01-01

The electrostatic axisymmetric mirror, assembled from three coaxial cylinders with an equal diameter d and under the potential v1, v2 and v3, was computed. The proportions of geometrical and electric parameters of the mirror, with which the spherical 3-order aberration may be eliminated, were determined. The computation outcomes of the case, when the focal power of the mirror is enough large and the object plane in the focus is out of its field, are presented (Fig. 1 - potentials proportion that makes elimination of the spherical aberration possible; Fig. 2 - the focus coordinates when the spherical aberration is eliminated). The geometrical values are presented by d, and the electric ones are presented by v1. The figures on the curves present a length of the second (middle) electrode. The zero point is located in the middle of the gap between the first and second electrodes The investigated mirror may be used as a lens for the transmission electron microscope

A study on heat transfer characteristics of spherical and fibrous alumina nanofluids

International Nuclear Information System (INIS)

Kim, Chang Kyu; Lee, Gyoung-Ja; Rhee, Chang Kyu

2012-01-01

Highlights: ► Spherical and fibrous alumina nanoparticles were prepared by pulsed wire evaporation and hydrolysis methods. ► Fibrous alumina nanofluid exhibited higher thermal conductivity enhancement than spherical one due to entangled structure of nanofibers with high aspect-ratio. ► Decreasing rate of viscosity with temperature for fibrous alumina nanofluid was much larger than that for spherical one. - Abstract: Ethylene glycol based nanofluids containing spherical/fibrous alumina nanoparticles were synthesized by pulsed wire evaporation and hydrolysis methods. The crystallographic and morphological properties of the prepared nanoparticles were analyzed by X-ray diffraction, nitrogen gas adsorption and transmission electron microscopy. The average diameter of spherical alumina nanoparticles was about 80 nm and the alumina nanofibers exhibited a high aspect ratio (length/width). The viscosity and thermal conductivity of the spherical/fibrous alumina nanofluids were experimentally measured in the temperature range from 25 to 80 °C. For the fibrous alumina nanofluid, the increase of temperature raised thermal conductivity but lowered viscosity. On the other hand, for the spherical alumina nanofluid, both thermal conductivity and viscosity were decreased with increasing temperature. In particular, the fibrous alumina nanofluid exhibited a higher enhancement of thermal conductivity than the spherical one due to the well-connected structure between entangled nanofibers with high aspect ratio.

Cylindrical and spherical dust-acoustic wave modulations in dusty ...

Indian Academy of Sciences (India)

Abstract. The nonlinear wave modulation of planar and non-planar (cylindrical and spherical) dust-acoustic waves (DAW) propagating in dusty plasmas, in the presence of non-extensive distribu- tions for ions and electrons is investigated. By employing multiple scales technique, a cylindrically and spherically modified ...

Determining spherical lens correction for astronaut training underwater.

Science.gov (United States)

Porter, Jason; Gibson, C Robert; Strauss, Samuel

2011-09-01

To develop a model that will accurately predict the distance spherical lens correction needed to be worn by National Aeronautics and Space Administration astronauts while training underwater. The replica space suit's helmet contains curved visors that induce refractive power when submersed in water. Anterior surface powers and thicknesses were measured for the helmet's protective and inside visors. The impact of each visor on the helmet's refractive power in water was analyzed using thick lens calculations and Zemax optical design software. Using geometrical optics approximations, a model was developed to determine the optimal distance spherical power needed to be worn underwater based on the helmet's total induced spherical power underwater and the astronaut's manifest spectacle plane correction in air. The validity of the model was tested using data from both eyes of 10 astronauts who trained underwater. The helmet's visors induced a total power of -2.737 D when placed underwater. The required underwater spherical correction (FW) was linearly related to the spectacle plane spherical correction in air (FAir): FW = FAir + 2.356 D. The mean magnitude of the difference between the actual correction worn underwater and the calculated underwater correction was 0.20 ± 0.11 D. The actual and calculated values were highly correlated (r = 0.971) with 70% of eyes having a difference in magnitude of astronauts. The model accurately predicts the actual values worn underwater and can be applied (more generally) to determine a suitable spectacle lens correction to be worn behind other types of masks when submerged underwater.

Flow above and within granular media composed of spherical and non-spherical particles - using a 3D numerical model

Science.gov (United States)

Bartzke, Gerhard; Kuhlmann, Jannis; Huhn, Katrin

2016-04-01

The entrainment of single grains and, hence, their erosion characteristics are dependent on fluid forcing, grain size and density, but also shape variations. To quantitatively describe and capture the hydrodynamic conditions around individual grains, researchers commonly use empirical approaches such as laboratory flume tanks. Nonetheless, it is difficult with such physical experiments to measure the flow velocities in the direct vicinity or within the pore spaces of sediments, at a sufficient resolution and in a non-invasive way. As a result, the hydrodynamic conditions in the water column, at the fluid-porous interface and within pore spaces of a granular medium of various grain shapes is not yet fully understood. For that reason, there is a strong need for numerical models, since these are capable of quantifying fluid speeds within a granular medium. A 3D-SPH (Smooth Particle Hydrodynamics) numerical wave tank model was set up to provide quantitative evidence on the flow velocities in the direct vicinity and in the interior of granular beds composed of two shapes as a complementary method to the difficult task of in situ measurement. On the basis of previous successful numerical wave tank models with SPH, the model geometry was chosen in dimensions of X=2.68 [m], Y=0.48 [m], and Z=0.8 [m]. Three suites of experiments were designed with a range of particle shape models: (1) ellipsoids with the long axis oriented in the across-stream direction, (2) ellipsoids with the long axis oriented in the along-stream direction, and (3) spheres. Particle diameters ranged from 0.04 [m] to 0.08 [m]. A wave was introduced by a vertical paddle that accelerated to 0.8 [m/s] perpendicular to the granular bed. Flow measurements showed that the flow velocity values into the beds were highest when the grains were oriented across the stream direction and lowest in case when the grains were oriented parallel to the stream, indicating that the model was capable to simulate simultaneously

Spectroscopic diagnostics for liquid lithium divertor studies on National Spherical Torus Experiment

International Nuclear Information System (INIS)

Soukhanovskii, V. A.; Roquemore, A. L.; Bell, R. E.; Kaita, R.; Kugel, H. W.

2010-01-01

The use of lithium-coated plasma facing components for plasma density control is studied in the National Spherical Torus Experiment (NSTX). A recently installed liquid lithium divertor (LLD) module has a porous molybdenum surface, separated by a stainless steel liner from a heated copper substrate. Lithium is deposited on the LLD from two evaporators. Two new spectroscopic diagnostics are installed to study the plasma surface interactions on the LLD: (1) A 20-element absolute extreme ultraviolet (AXUV) diode array with a 6 nm bandpass filter centered at 121.6 nm (the Lyman-α transition) for spatially resolved divertor recycling rate measurements in the highly reflective LLD environment, and (2) an ultraviolet-visible-near infrared R=0.67 m imaging Czerny-Turner spectrometer for spatially resolved divertor D I, Li I-II, C I-IV, Mo I, D 2 , LiD, CD emission and ion temperature on and around the LLD module. The use of photometrically calibrated measurements together with atomic physics factors enables studies of recycling and impurity particle fluxes as functions of LLD temperature, ion flux, and divertor geometry.

Plasma viscosity with mass transport in spherical inertial confinement fusion implosion simulations

Energy Technology Data Exchange (ETDEWEB)

Vold, E. L.; Molvig, K. [Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Joglekar, A. S. [University of Michigan, Ann Arbor, Michigan 48109 (United States); Ortega, M. I. [University of New Mexico, Albuquerque, New Mexico 87131 (United States); Moll, R. [University of California, Santa Cruz, California 95064 (United States); Fenn, D. [Florida State University, Tallahassee, Florida 32306 (United States)

2015-11-15

The effects of viscosity and small-scale atomic-level mixing on plasmas in inertial confinement fusion (ICF) currently represent challenges in ICF research. Many current ICF hydrodynamic codes ignore the effects of viscosity though recent research indicates viscosity and mixing by classical transport processes may have a substantial impact on implosion dynamics. We have implemented a Lagrangian hydrodynamic code in one-dimensional spherical geometry with plasma viscosity and mass transport and including a three temperature model for ions, electrons, and radiation treated in a gray radiation diffusion approximation. The code is used to study ICF implosion differences with and without plasma viscosity and to determine the impacts of viscosity on temperature histories and neutron yield. It was found that plasma viscosity has substantial impacts on ICF shock dynamics characterized by shock burn timing, maximum burn temperatures, convergence ratio, and time history of neutron production rates. Plasma viscosity reduces the need for artificial viscosity to maintain numerical stability in the Lagrangian formulation and also modifies the flux-limiting needed for electron thermal conduction.

Geometry

CERN Document Server

Pedoe, Dan

1988-01-01

""A lucid and masterly survey."" - Mathematics Gazette Professor Pedoe is widely known as a fine teacher and a fine geometer. His abilities in both areas are clearly evident in this self-contained, well-written, and lucid introduction to the scope and methods of elementary geometry. It covers the geometry usually included in undergraduate courses in mathematics, except for the theory of convex sets. Based on a course given by the author for several years at the University of Minnesota, the main purpose of the book is to increase geometrical, and therefore mathematical, understanding and to he

[Depth of focus in spherical and aspheric intraocular lenses].

Science.gov (United States)

Nan, Li; Tang, Xin; Liu, Yong-ji

2012-02-01

To investigate depth of focus (DOF) in spherical and aspheric IOL eye models. Computer numerical simulation experiment was used. IOL eye model based on Liou-Brennan eye model was constructed by using ZEMAX optical design software. Different IOL were implanted in this eye model. Monochromatic through focus modulation transfer function (MTF) curves were computed. Pupil and aspheric designs' effect on DOF were analyzed. DOF of eye model increased with pupil shrinkage in 550 nm monochromatic light (FY60AD 1.20 D at 6 mm pupil, 1.35 D at 5 mm pupil, 1.70 D at 4 mm pupil, 2.46 D at 3 mm pupil; YA60BBR 1.24 D at 6 mm pupil, 1.48 D at 5 mm pupil, 1.80 D at 4 mm pupil, 2.50 D at 3 mm pupil). MTF in spherical IOL eye model was higher with minus defocus, this trend was obvious at larger pupil. MTF of aspheric IOL eyes were higher than spherical IOL eyes when well focused at 5 mm pupil, while the DOF was lower in aspheric IOL with negative spherical aberration (Tecnis Z9000 1.31 D, FY60AD 1.35 D, CeeOn911 1.55 D, YA60BBR 1.48 D). DOF decreased less in aspheric IOL with zero spherical aberration (LI61AO 1.42 D). DOF in IOL eye model was higher at smaller pupil. When the pupil was large, well focused aspheric IOL improved optical quality compared with spherical IOL, while DOF and the tolerance to defocus in aspheric IOL were partially lost; this phenomenon was obvious with minus defocus.

Effect of pore geometry on the compressibility of a confined simple fluid

Science.gov (United States)

Dobrzanski, Christopher D.; Maximov, Max A.; Gor, Gennady Y.

2018-02-01

Fluids confined in nanopores exhibit properties different from the properties of the same fluids in bulk; among these properties is the isothermal compressibility or elastic modulus. The modulus of a fluid in nanopores can be extracted from ultrasonic experiments or calculated from molecular simulations. Using Monte Carlo simulations in the grand canonical ensemble, we calculated the modulus for liquid argon at its normal boiling point (87.3 K) adsorbed in model silica pores of two different morphologies and various sizes. For spherical pores, for all the pore sizes (diameters) exceeding 2 nm, we obtained a logarithmic dependence of fluid modulus on the vapor pressure. Calculation of the modulus at saturation showed that the modulus of the fluid in spherical pores is a linear function of the reciprocal pore size. The calculation of the modulus of the fluid in cylindrical pores appeared too scattered to make quantitative conclusions. We performed additional simulations at higher temperature (119.6 K), at which Monte Carlo insertions and removals become more efficient. The results of the simulations at higher temperature confirmed both regularities for cylindrical pores and showed quantitative difference between the fluid moduli in pores of different geometries. Both of the observed regularities for the modulus stem from the Tait-Murnaghan equation applied to the confined fluid. Our results, along with the development of the effective medium theories for nanoporous media, set the groundwork for analysis of the experimentally measured elastic properties of fluid-saturated nanoporous materials.

Complex algebraic geometry

CERN Document Server

Kollár, János

1997-01-01

This volume contains the lectures presented at the third Regional Geometry Institute at Park City in 1993. The lectures provide an introduction to the subject, complex algebraic geometry, making the book suitable as a text for second- and third-year graduate students. The book deals with topics in algebraic geometry where one can reach the level of current research while starting with the basics. Topics covered include the theory of surfaces from the viewpoint of recent higher-dimensional developments, providing an excellent introduction to more advanced topics such as the minimal model program. Also included is an introduction to Hodge theory and intersection homology based on the simple topological ideas of Lefschetz and an overview of the recent interactions between algebraic geometry and theoretical physics, which involve mirror symmetry and string theory.

CMS geometry through 2020

International Nuclear Information System (INIS)

Osborne, I; Brownson, E; Eulisse, G; Jones, C D; Sexton-Kennedy, E; Lange, D J

2014-01-01

CMS faces real challenges with upgrade of the CMS detector through 2020 and beyond. One of the challenges, from the software point of view, is managing upgrade simulations with the same software release as the 2013 scenario. We present the CMS geometry description software model, its integration with the CMS event setup and core software. The CMS geometry configuration and selection is implemented in Python. The tools collect the Python configuration fragments into a script used in CMS workflow. This flexible and automated geometry configuration allows choosing either transient or persistent version of the same scenario and specific version of the same scenario. We describe how the geometries are integrated and validated, and how we define and handle different geometry scenarios in simulation and reconstruction. We discuss how to transparently manage multiple incompatible geometries in the same software release. Several examples are shown based on current implementation assuring consistent choice of scenario conditions. The consequences and implications for multiple/different code algorithms are discussed.

Investigation of Gas Solid Fluidized Bed Dynamics with Non-Spherical Particles

Energy Technology Data Exchange (ETDEWEB)

Choudhuri, Ahsan [Univ. of Texas, El Paso, TX (United States). Dept. of Mechanical Engineering

2013-06-30

One of the largest challenges for 21st century is to fulfill global energy demand while also reducing detrimental impacts of energy generation and use on the environment. Gasification is a promising technology to meet the requirement of reduced emissions without compromising performance. Coal gasification is not an incinerating process; rather than burning coal completely a partial combustion takes place in the presence of steam and limited amounts of oxygen. In this controlled environment, a chemical reaction takes place to produce a mixture of clean synthetic gas. Gas-solid fluidized bed is one such type of gasification technology. During gasification, the mixing behavior of solid (coal) and gas and their flow patterns can be very complicated to understand. Many attempts have taken place in laboratory scale to understand bed hydrodynamics with spherical particles though in actual applications with coal, the particles are non-spherical. This issue drove the documented attempt presented here to investigate fluidized bed behavior using different ranges of non-spherical particles, as well as spherical. For this investigation, various parameters are controlled that included particle size, bed height, bed diameter and particle shape. Particles ranged from 355 µm to 1180 µm, bed diameter varied from 2 cm to 7 cm, two fluidized beds with diameters of 3.4 cm and 12.4 cm, for the spherical and non-spherical shaped particles that were taken into consideration. Pressure drop was measured with increasing superficial gas velocity. The velocity required in order to start to fluidize the particle is called the minimum fluidization velocity, which is one of the most important parameters to design and optimize within a gas-solid fluidized bed. This minimum fluidization velocity was monitored during investigation while observing variables factors and their effect on this velocity. From our investigation, it has been found that minimum fluidization velocity is independent of bed

Normal modes and quality factors of spherical dielectric resonators: I ...

Indian Academy of Sciences (India)

Eigenmodes; spherical resonators; spherical dielectric resonators; quality factors. PACS No. 42.50. .... Alternatively, introducing the angular momentum operator L defined as, L = (1/j)( r × ∇) ...... referee of the article for some helpful comments.

Numerical relativity in spherical coordinates with the Einstein Toolkit

Science.gov (United States)

Mewes, Vassilios; Zlochower, Yosef; Campanelli, Manuela; Ruchlin, Ian; Etienne, Zachariah B.; Baumgarte, Thomas W.

2018-04-01

Numerical relativity codes that do not make assumptions on spatial symmetries most commonly adopt Cartesian coordinates. While these coordinates have many attractive features, spherical coordinates are much better suited to take advantage of approximate symmetries in a number of astrophysical objects, including single stars, black holes, and accretion disks. While the appearance of coordinate singularities often spoils numerical relativity simulations in spherical coordinates, especially in the absence of any symmetry assumptions, it has recently been demonstrated that these problems can be avoided if the coordinate singularities are handled analytically. This is possible with the help of a reference-metric version of the Baumgarte-Shapiro-Shibata-Nakamura formulation together with a proper rescaling of tensorial quantities. In this paper we report on an implementation of this formalism in the Einstein Toolkit. We adapt the Einstein Toolkit infrastructure, originally designed for Cartesian coordinates, to handle spherical coordinates, by providing appropriate boundary conditions at both inner and outer boundaries. We perform numerical simulations for a disturbed Kerr black hole, extract the gravitational wave signal, and demonstrate that the noise in these signals is orders of magnitude smaller when computed on spherical grids rather than Cartesian grids. With the public release of our new Einstein Toolkit thorns, our methods for numerical relativity in spherical coordinates will become available to the entire numerical relativity community.

Gravitational settling of a highly concentrated system of solid spherical particles

Science.gov (United States)

Arkhipov, V. A.; Usanina, A. S.

2017-09-01

In the present paper, we report on the results of an experimental study of the process of gravity sedimentation of a cloud of monodispersed solid spherical particles with initial volume concentration C > 0.03, which was performed in a wide range of Reynolds numbers. An analytical estimate of the settling regimes of spherical particle clouds is presented. A new method for creating a spherical particle cloud with a high concentration of particles is proposed. A qualitative picture of the settling process of a highly concentrated particle cloud under gravity is revealed. A criterial dependence for the drag coefficient of a sedimenting spherical particle cloud as an entity is obtained.

Noncommutative geometry inspired Einstein–Gauss–Bonnet black holes

Science.gov (United States)

Ghosh, Sushant G.

2018-04-01

Low energy limits of a string theory suggests that the gravity action should include quadratic and higher-order curvature terms, in the form of dimensionally continued Gauss–Bonnet densities. Einstein–Gauss–Bonnet is a natural extension of the general relativity to higher dimensions in which the first and second-order terms correspond, respectively, to general relativity and Einstein–Gauss–Bonnet gravity. We obtain five-dimensional (5D) black hole solutions, inspired by a noncommutative geometry, with a static spherically symmetric, Gaussian mass distribution as a source both in the general relativity and Einstein–Gauss–Bonnet gravity cases, and we also analyzes their thermodynamical properties. Owing the noncommutative corrected black hole, the thermodynamic quantities have also been modified, and phase transition is shown to be achievable. The phase transitions for the thermodynamic stability, in both the theories, are characterized by a discontinuity in the specific heat at r_+=rC , with the stable (unstable) branch for r ) rC . The metric of the noncommutative inspired black holes smoothly goes over to the Boulware–Deser solution at large distance. The paper has been appended with a calculation of black hole mass using holographic renormalization.

Analisis Keterampilan Geometri Siswa Dalam Memecahkan Masalah Geometri Berdasarkan Tingkat Berpikir Van Hiele

OpenAIRE

Muhassanah, Nuraini; Sujadi, Imam; Riyadi, Riyadi

2014-01-01

The objective of this research was to describe the VIII grade students geometry skills atSMP N 16 Surakarta in the level 0 (visualization), level 1 (analysis), and level 2 (informaldeduction) van Hiele level of thinking in solving the geometry problem. This research was aqualitative research in the form of case study analyzing deeply the students geometry skill insolving the geometry problem based on van Hiele level of thingking. The subject of this researchwas nine students of VIII grade at ...

Design innovations of the next-step spherical torus experiment and spherical torus development path

International Nuclear Information System (INIS)

Ono, M.; Kessel, C.; Peng, M.

2003-01-01

The spherical torus (ST) fusion energy development path is complementary to the tokamak burning plasma experiment such as ITER as it focuses toward the compact Component Test Facility (CTF) and higher toroidal beta regimes to improve the design of DEMO and a Power Plant. To support the ST development path, one option of a Next Step Spherical Torus (NSST) device is examined. NSST is a 'performance extension' (PE) stage ST with a plasma current of 5 - 10 MA, R = 1.5, B T ≤ 2.7 T with flexible physics capability to 1) Provide a sufficient physics basis for the design of the CTF, 2) Explore advanced operating scenarios with high bootstrap current fraction/high performance regimes, which can then be utilized by CTF, DEMO, and Power Plants, 3) Contribute to the general plasma/fusion science of high β toroidal plasmas. The NSST facility is designed to utilize the TFTR site to minimize the cost and time required for the construction. (author)

Relativistic fluids in spherically symmetric space

International Nuclear Information System (INIS)

Dipankar, R.

1977-12-01

Some of McVittie and Wiltshire's (1977) solutions of Walker's (1935) isotropy conditions for relativistic perfect fluid spheres are generalized. Solutions are spherically symmetric and conformally flat

Comparison of Large eddy dynamo simulation using dynamic sub-grid scale (SGS) model with a fully resolved direct simulation in a rotating spherical shell

Science.gov (United States)

Matsui, H.; Buffett, B. A.

2017-12-01

The flow in the Earth's outer core is expected to have vast length scale from the geometry of the outer core to the thickness of the boundary layer. Because of the limitation of the spatial resolution in the numerical simulations, sub-grid scale (SGS) modeling is required to model the effects of the unresolved field on the large-scale fields. We model the effects of sub-grid scale flow and magnetic field using a dynamic scale similarity model. Four terms are introduced for the momentum flux, heat flux, Lorentz force and magnetic induction. The model was previously used in the convection-driven dynamo in a rotating plane layer and spherical shell using the Finite Element Methods. In the present study, we perform large eddy simulations (LES) using the dynamic scale similarity model. The scale similarity model is implement in Calypso, which is a numerical dynamo model using spherical harmonics expansion. To obtain the SGS terms, the spatial filtering in the horizontal directions is done by taking the convolution of a Gaussian filter expressed in terms of a spherical harmonic expansion, following Jekeli (1981). A Gaussian field is also applied in the radial direction. To verify the present model, we perform a fully resolved direct numerical simulation (DNS) with the truncation of the spherical harmonics L = 255 as a reference. And, we perform unresolved DNS and LES with SGS model on coarser resolution (L= 127, 84, and 63) using the same control parameter as the resolved DNS. We will discuss the verification results by comparison among these simulations and role of small scale fields to large scale fields through the role of the SGS terms in LES.

Next Step Spherical Torus Design Studies

International Nuclear Information System (INIS)

Neumeyer, C.; Heitzenroeder, P.; Kessel, C.; Ono, M.; Peng, M.; Schmidt, J.; Woolley, R.; Zatz, I.

2002-01-01

Studies are underway to identify and characterize a design point for a Next Step Spherical Torus (NSST) experiment. This would be a ''Proof of Performance'' device which would follow and build upon the successes of the National Spherical Torus Experiment (NSTX) a ''Proof of Principle'' device which has operated at PPPL since 1999. With the Decontamination and Decommissioning (DandD) of the Tokamak Fusion Test Reactor (TFTR) nearly completed, the TFTR test cell and facility will soon be available for a device such as NSST. By utilizing the TFTR test cell, NSST can be constructed for a relatively low cost on a short time scale. In addition, while furthering spherical torus (ST) research, this device could achieve modest fusion power gain for short-pulse lengths, a significant step toward future large burning plasma devices now under discussion in the fusion community. The selected design point is Q=2 at HH=1.4, P subscript ''fusion''=60 MW, 5 second pulse, with R subscript ''0''=1.5 m, A=1.6, I subscript ''p''=10vMA, B subscript ''t''=2.6 T, CS flux=16 weber. Most of the research would be conducted in D-D, with a limited D-T campaign during the last years of the program

Semi-empirical simulation of thermoluminescent response under different filter geometries

International Nuclear Information System (INIS)

Shammas, Gabriel Issa Jabra

2006-01-01

Many thermoluminescent materials has been developed and used for photon personal dosimetry but no one has all desired characteristics alone. These characteristics include robustness, high sensitivity, energy photon independence, large range of photon energy detection, good reproducibility, small fading and simple glow curve with peaks above 150 deg C. Calcium Sulfate Dysprosium doped (CaSO 4 :Dy) phosphor Thermoluminescent Dosimeter (TLD) has been used by many laboratories, mainly in Brazil and India. Another interesting phosphor is Calcium Fluoride (CaF 2 ). These phosphor advantages begin to be more required and its disadvantages have became more apparent, in a global market more and more competitive. These phosphors are used in environmental and area monitoring, once they present more sensibility than other phosphors, like LiF:Mg. Theirs mainly disadvantage is a strong energetic dependence response, which must be corrected for theirs application in the field, where photon radiation is unknown a priori. An interesting way do make this correction in orthogonal incidence of the radiation on the phosphor is to interject a plane leaked filter between the beam and the phosphor. In order to reduce the energetic dependence on any incidence angle, reducing the field dose measurement uncertainty too, this work presents a simulation study on spherical filter geometries. It was simulated photon irradiations with Gamma rays of 60 Co and x-rays of 33; 48 and 118 keV, on many incidence angles from zero to ninety degrees. These semi-empirical computational simulations using finite differences in three dimensions were done in spherical coordinates. The results pointed out the best filter thicknesses and widths, in order to optimize the correction on energetic dependence. (author)

Modeling of Neoclassical Tearing Mode Stability for Generalized Toroidal Geometry

International Nuclear Information System (INIS)

A.L. Rosenberg; D.A. Gates; A. Pletzer; J.E. Menard; S.E. Kruger; C.C. Hegna; F. Paoletti; S. Sabbagh

2002-01-01

Neoclassical tearing modes (NTMs) can lead to disruption and loss of confinement. Previous analysis of these modes used large aspect ratio, low beta (plasma pressure/magnetic pressure) approximations to determine the effect of NTMs on tokamak plasmas. A more accurate tool is needed to predict the onset of these instabilities. As a follow-up to recent theoretical work, a code has been written which computes the tearing mode island growth rate for arbitrary tokamak geometry. It calls PEST-3 [A. Pletzer et al., J. Comput. Phys. 115, 530 (1994)] to compute delta prime, the resistive magnetohydrodynamic (MHD) matching parameter. The code also calls the FLUXGRID routines in NIMROD [A.H. Glasser et al., Plasma Phys. Controlled Fusion 41, A747 (1999)] for Dnc, DI and DR [C.C. Hegna, Phys. Plasmas 6, 3980 (1999); A.H. Glasser et al., Phys. Fluids 18, 875 (1975)], which are the bootstrap current driven term and the ideal and resistive interchange mode criterion, respectively. In addition to these components, the NIMROD routines calculate alphas-H, a new correction to the Pfirsch-Schlter term. Finite parallel transport effects were added and a National Spherical Torus Experiment (NSTX) [M. Ono et al., Nucl. Fusion 40, 557 (2000)] equilibrium was analyzed. Another program takes the output of PEST-3 and allows the user to specify the rational surface, island width, and amount of detail near the perturbed surface to visualize the total helical flux. The results of this work will determine the stability of NTMs in an spherical torus (ST) [Y.-K.M. Peng et al., Nucl. Fusion 26, 769 (1986)] plasma with greater accuracy than previously achieved

Algorithms in Algebraic Geometry

CERN Document Server

Dickenstein, Alicia; Sommese, Andrew J

2008-01-01

In the last decade, there has been a burgeoning of activity in the design and implementation of algorithms for algebraic geometric computation. Some of these algorithms were originally designed for abstract algebraic geometry, but now are of interest for use in applications and some of these algorithms were originally designed for applications, but now are of interest for use in abstract algebraic geometry. The workshop on Algorithms in Algebraic Geometry that was held in the framework of the IMA Annual Program Year in Applications of Algebraic Geometry by the Institute for Mathematics and Its

Surface Treatment of a Lithium Limiter for Spherical Torus Plasma Experiments

Energy Technology Data Exchange (ETDEWEB)

Kaita, R.; Majeski, R.; Doerner, R.; Antar, G.; Timberlake, J.; Spaleta, J.; Hoffman, D.; Jones, B.; Munsat, T.; Kugel, H.; Taylor, G.; Stutman, D.; Soukhanovskii, V.; Maingi, R.; Molesa, S.; Efthimion, P.; Menard, J.; Finkenthal, M.; Luckhardt, S.

2001-03-20

The concept of a flowing lithium first wall for a fusion reactor may lead to a significant advance in reactor design, since it could virtually eliminate the concerns with power density and erosion, tritium retention, and cooling associated with solid walls. As part of investigations to determine the feasibility of this approach, plasma interaction questions in a toroidal plasma geometry are being addressed in the Current Drive eXperiment-Upgrade (CDX-U) spherical torus (ST). The first experiments involved a toroidally local lithium limiter (L3). Measurements of pumpout rates indicated that deuterium pumping was greater for the L3 compared to conventional boron carbide limiters. The difference in the pumpout rates between the two limiter types decreased with plasma exposure, but argon glow discharge cleaning was able to restore the pumping effectiveness of the L3. At no point, however, was the extremely low recycling regime reported in previous lithium experiments achieved. This may be due to the much larger lithium surfaces that were exposed to the plasma in the earlier work. The possibility will be studied in the next set of CDX-U experiments, which are to be conducted with a large area, fully toroidal lithium limiter.

Surface Treatment of a Lithium Limiter for Spherical Torus Plasma Experiments

International Nuclear Information System (INIS)

Kaita, R.; Majeski, R.; Doerner, R.; Antar, G.; Timberlake, J.; Spaleta, J.; Hoffman, D.; Jones, B.; Munsat, T.; Kugel, H.; Taylor, G.; Stutman, D.; Soukhanovskii, V.; Maingi, R.; Molesa, S.; Efthimion, P.; Menard, J.; Finkenthal, M.; Luckhardt, S.

2001-01-01

The concept of a flowing lithium first wall for a fusion reactor may lead to a significant advance in reactor design, since it could virtually eliminate the concerns with power density and erosion, tritium retention, and cooling associated with solid walls. As part of investigations to determine the feasibility of this approach, plasma interaction questions in a toroidal plasma geometry are being addressed in the Current Drive eXperiment-Upgrade (CDX-U) spherical torus (ST). The first experiments involved a toroidally local lithium limiter (L3). Measurements of pumpout rates indicated that deuterium pumping was greater for the L3 compared to conventional boron carbide limiters. The difference in the pumpout rates between the two limiter types decreased with plasma exposure, but argon glow discharge cleaning was able to restore the pumping effectiveness of the L3. At no point, however, was the extremely low recycling regime reported in previous lithium experiments achieved. This may be due to the much larger lithium surfaces that were exposed to the plasma in the earlier work. The possibility will be studied in the next set of CDX-U experiments, which are to be conducted with a large area, fully toroidal lithium limiter

Non-Euclidean geometry

CERN Document Server

Kulczycki, Stefan

2008-01-01

This accessible approach features two varieties of proofs: stereometric and planimetric, as well as elementary proofs that employ only the simplest properties of the plane. A short history of geometry precedes a systematic exposition of the principles of non-Euclidean geometry.Starting with fundamental assumptions, the author examines the theorems of Hjelmslev, mapping a plane into a circle, the angle of parallelism and area of a polygon, regular polygons, straight lines and planes in space, and the horosphere. Further development of the theory covers hyperbolic functions, the geometry of suff

Stability of transparent spherically symmetric thin shells and wormholes

International Nuclear Information System (INIS)

Ishak, Mustapha; Lake, Kayll

2002-01-01

The stability of transparent spherically symmetric thin shells (and wormholes) to linearized spherically symmetric perturbations about static equilibrium is examined. This work generalizes and systematizes previous studies and explores the consequences of including the cosmological constant. The approach shows how the existence (or not) of a domain wall dominates the landscape of possible equilibrium configurations

Geometry on the space of geometries

International Nuclear Information System (INIS)

Christodoulakis, T.; Zanelli, J.

1988-06-01

We discuss the geometric structure of the configuration space of pure gravity. This is an infinite dimensional manifold, M, where each point represents one spatial geometry g ij (x). The metric on M is dictated by geometrodynamics, and from it, the Christoffel symbols and Riemann tensor can be found. A ''free geometry'' tracing a geodesic on the manifold describes the time evolution of space in the strong gravity limit. In a regularization previously introduced by the authors, it is found that M does not have the same dimensionality, D, everywhere, and that D is not a scalar, although it is covariantly constant. In this regularization, it is seen that the path integral measure can be absorbed in a renormalization of the cosmological constant. (author). 19 refs

A Lorentzian quantum geometry

Energy Technology Data Exchange (ETDEWEB)

Grotz, Andreas

2011-10-07

In this thesis, a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems is proposed. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal structure. Restricting attention to systems of spin dimension two, we derive the objects of our quantum geometry: the spin space, the tangent space endowed with a Lorentzian metric, connection and curvature. In order to get the correspondence to classical differential geometry, we construct examples of causal fermion systems by regularizing Dirac sea configurations in Minkowski space and on a globally hyperbolic Lorentzian manifold. When removing the regularization, the objects of our quantum geometry reduce to the common objects of spin geometry on Lorentzian manifolds, up to higher order curvature corrections.

A Lorentzian quantum geometry

International Nuclear Information System (INIS)

Grotz, Andreas

2011-01-01

In this thesis, a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems is proposed. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal structure. Restricting attention to systems of spin dimension two, we derive the objects of our quantum geometry: the spin space, the tangent space endowed with a Lorentzian metric, connection and curvature. In order to get the correspondence to classical differential geometry, we construct examples of causal fermion systems by regularizing Dirac sea configurations in Minkowski space and on a globally hyperbolic Lorentzian manifold. When removing the regularization, the objects of our quantum geometry reduce to the common objects of spin geometry on Lorentzian manifolds, up to higher order curvature corrections.

Modelling of UWB Antenna Perturbed by Human Phantom in Spherical Harmonics Space

DEFF Research Database (Denmark)

Mhedhbi, Meriem; Avrillon, Stephane; Pedersen, Troels

2014-01-01

is attractive for simulation purposes. We propose a simple model for the spherical harmonics coefficients allowing to predict the antenna behavior perturbed by a human phantom. The model is based on knowledge of the spherical harmonic coefficients of antenna in free space and the antenna-phantom distance.......In this paper we study how the antenna radiation pattern is perturbed in the presence of a human phantom in terms of changes in the coefficients of the spherical harmonic antenna representation. The spherical harmonic basis allows for a compact representation of the antenna pattern which...

A Spherical Aerial Terrestrial Robot

Science.gov (United States)

Dudley, Christopher J.

This thesis focuses on the design of a novel, ultra-lightweight spherical aerial terrestrial robot (ATR). The ATR has the ability to fly through the air or roll on the ground, for applications that include search and rescue, mapping, surveillance, environmental sensing, and entertainment. The design centers around a micro-quadcopter encased in a lightweight spherical exoskeleton that can rotate about the quadcopter. The spherical exoskeleton offers agile ground locomotion while maintaining characteristics of a basic aerial robot in flying mode. A model of the system dynamics for both modes of locomotion is presented and utilized in simulations to generate potential trajectories for aerial and terrestrial locomotion. Details of the quadcopter and exoskeleton design and fabrication are discussed, including the robot's turning characteristic over ground and the spring-steel exoskeleton with carbon fiber axle. The capabilities of the ATR are experimentally tested and are in good agreement with model-simulated performance. An energy analysis is presented to validate the overall efficiency of the robot in both modes of locomotion. Experimentally-supported estimates show that the ATR can roll along the ground for over 12 minutes and cover the distance of 1.7 km, or it can fly for 4.82 minutes and travel 469 m, on a single 350 mAh battery. Compared to a traditional flying-only robot, the ATR traveling over the same distance in rolling mode is 2.63-times more efficient, and in flying mode the system is only 39 percent less efficient. Experimental results also demonstrate the ATR's transition from rolling to flying mode.

Initial value formulation for the spherically symmetric dust solution

International Nuclear Information System (INIS)

Liu, H.

1990-01-01

An initial value formulation for the dust solution with spherical symmetry is given explicitly in which the initial distributions of dust and its velocity on an initial surface are chosen to be the initial data. As special cases, the Friedmann universe, the Schwarzschild solution in comoving coordinates, and a spherically symmetric and radially inhomogeneous cosmological model are derived

Effect of the spherical Earth on a simple pendulum

OpenAIRE

Burko, Lior M.

2003-01-01

We consider the period of a simple pendulum in the gravitational field of the spherical Earth. Effectively, gravity is enhanced compared with the often used flat Earth approximation, such that the period of the pendulum is shortened. We discuss the flat Earth approximation, and show when the corrections due to the spherical Earth may be of interest.

Geometry and Combinatorics

DEFF Research Database (Denmark)

Kokkendorff, Simon Lyngby

2002-01-01

The subject of this Ph.D.-thesis is somewhere in between continuous and discrete geometry. Chapter 2 treats the geometry of finite point sets in semi-Riemannian hyperquadrics,using a matrix whose entries are a trigonometric function of relative distances in a given point set. The distance...... to the geometry of a simplex in a semi-Riemannian hyperquadric. In chapter 3 we study which finite metric spaces that are realizable in a hyperbolic space in the limit where curvature goes to -∞. We show that such spaces are the so called leaf spaces, the set of degree 1 vertices of weighted trees. We also...... establish results on the limiting geometry of such an isometrically realized leaf space simplex in hyperbolic space, when curvature goes to -∞. Chapter 4 discusses negative type of metric spaces. We give a measure theoretic treatment of this concept and related invariants. The theory developed...

Geometry and billiards

CERN Document Server

Tabachnikov, Serge

2005-01-01

Mathematical billiards describe the motion of a mass point in a domain with elastic reflections off the boundary or, equivalently, the behavior of rays of light in a domain with ideally reflecting boundary. From the point of view of differential geometry, the billiard flow is the geodesic flow on a manifold with boundary. This book is devoted to billiards in their relation with differential geometry, classical mechanics, and geometrical optics. The topics covered include variational principles of billiard motion, symplectic geometry of rays of light and integral geometry, existence and nonexistence of caustics, optical properties of conics and quadrics and completely integrable billiards, periodic billiard trajectories, polygonal billiards, mechanisms of chaos in billiard dynamics, and the lesser-known subject of dual (or outer) billiards. The book is based on an advanced undergraduate topics course (but contains more material than can be realistically taught in one semester). Although the minimum prerequisit...

Drawing Dynamic Geometry Figures Online with Natural Language for Junior High School Geometry

Science.gov (United States)

Wong, Wing-Kwong; Yin, Sheng-Kai; Yang, Chang-Zhe

2012-01-01

This paper presents a tool for drawing dynamic geometric figures by understanding the texts of geometry problems. With the tool, teachers and students can construct dynamic geometric figures on a web page by inputting a geometry problem in natural language. First we need to build the knowledge base for understanding geometry problems. With the…

Development of a spherical neutron rem monitor

International Nuclear Information System (INIS)

Panchal, C.G.; Madhavi, V.; Bansode, P.Y.; Jakati, R.K.; Ghodgaonkar, M.D.; Desai, S.S.; Shaikh, A.M.; Sathian, V.

2007-01-01

A new neutron rem monitor based on spherical LINUS with the state of art electronic circuits has been designed in Electronics Division. This prototype instrument encompasses a spherical double polythene moderator to improve an isotropic response and a lead layer to extend its energy response compared to the conventional neutron rem monitors. A systematic testing and calibration of the energy and directional response of the prototype monitor have been carried out. Although the monitor is expected to perform satisfactorily upto an energy ∼ 55 MeV, at present its response has been tested upto 5 MeV. (author)

Spherical harmonics and integration in superspace

International Nuclear Information System (INIS)

Bie, H de; Sommen, F

2007-01-01

In this paper, the classical theory of spherical harmonics in R m is extended to superspace using techniques from Clifford analysis. After defining a super-Laplace operator and studying some basic properties of polynomial null-solutions of this operator, a new type of integration over the supersphere is introduced by exploiting the formal equivalence with an old result of Pizzetti. This integral is then used to prove orthogonality of spherical harmonics of different degree, Green-like theorems and also an extension of the important Funk-Hecke theorem to superspace. Finally, this integration over the supersphere is used to define an integral over the whole superspace, and it is proven that this is equivalent with the Berezin integral, thus providing a more sound definition of the Berezin integral

Compression dynamics of quasi-spherical wire arrays with different linear mass profiles

International Nuclear Information System (INIS)

Mitrofanov, K. N.; Aleksandrov, V. V.; Gritsuk, A. N.; Grabovski, E. V.; Frolov, I. N.; Laukhin, Ya. N.; Oleinik, G. M.; Ol’khovskaya, O. G.

2016-01-01

Results of experimental studies of the implosion of quasi-spherical wire (or metalized fiber) arrays are presented. The goal of the experiments was to achieve synchronous three-dimensional compression of the plasma produced in different regions of a quasi-spherical array into its geometrical center. To search for optimal synchronization conditions, quasi-spherical arrays with different initial profiles of the linear mass were used. The following dependences of the linear mass on the poloidal angle were used: m_l(θ) ∝ sin"–"1θ and m_l(θ) ∝ sin"–"2θ. The compression dynamics of such arrays was compared with that of quasi-spherical arrays without linear mass profiling, m_l(θ) = const. To verify the experimental data, the spatiotemporal dynamics of plasma compression in quasi-spherical arrays was studied using various diagnostics. The experiments on three-dimensional implosion of quasi-spherical arrays made it possible to study how the frozen-in magnetic field of the discharge current penetrates into the array. By measuring the magnetic field in the plasma of a quasi-spherical array, information is obtained on the processes of plasma production and formation of plasma flows from the wire/fiber regions with and without an additionally deposited mass. It is found that penetration of the magnetic flux depends on the initial linear mass profile m_l(θ) of the quasi-spherical array. From space-resolved spectral measurements and frame imaging of plasma X-ray emission, information is obtained on the dimensions and shape of the X-ray source formed during the implosion of a quasi-spherical array. The intensity of this source is estimated and compared with that of the Z-pinch formed during the implosion of a cylindrical array.

Mixed-Degree Spherical Simplex-Radial Cubature Kalman Filter

Directory of Open Access Journals (Sweden)

Shiyuan Wang

2017-01-01

Full Text Available Conventional low degree spherical simplex-radial cubature Kalman filters often generate low filtering accuracy or even diverge for handling highly nonlinear systems. The high-degree Kalman filters can improve filtering accuracy at the cost of increasing computational complexity; nevertheless their stability will be influenced by the negative weights existing in the high-dimensional systems. To efficiently improve filtering accuracy and stability, a novel mixed-degree spherical simplex-radial cubature Kalman filter (MSSRCKF is proposed in this paper. The accuracy analysis shows that the true posterior mean and covariance calculated by the proposed MSSRCKF can agree accurately with the third-order moment and the second-order moment, respectively. Simulation results show that, in comparison with the conventional spherical simplex-radial cubature Kalman filters that are based on the same degrees, the proposed MSSRCKF can perform superior results from the aspects of filtering accuracy and computational complexity.

Detecting topology in a nearly flat spherical universe

International Nuclear Information System (INIS)

Weeks, Jeffrey; Lehoucq, Roland; Uzan, Jean-Philippe

2003-01-01

When the density parameter is close to unity, the universe has a large curvature radius independent of its being hyperbolic or spherical, or in the limiting case of an infinite curvature radius, flat. Whatever the curvature, the universe may have either a simply connected or a multiply connected topology. In the flat case, the topology scale is arbitrary, and there is no a priori reason for this scale to be of the same order as the size of the observable universe. In the hyperbolic case, any nontrivial topology would almost surely be on a length scale too large to detect. In the spherical case, in contrast, the topology could easily occur on a detectable scale. The present paper shows how, in the spherical case, the assumption of a nearly flat universe simplifies the algorithms for detecting a multiply connected topology, but also reduces the amount of topology that can be seen. This is of primary importance for the upcoming cosmic microwave background data analysis. This paper shows that for spherical spaces one may restrict the search to diametrically opposite pairs of circles in the circles-in-the-sky method and still detect the cyclic factor in the standard factorization of the holonomy group. This vastly decreases the algorithm's run time. If the search is widened to include pairs of candidate circles whose centres are almost opposite and whose relative twist varies slightly, then the cyclic factor along with a cyclic subgroup of the general factor may also be detected. Unfortunately, the full holonomy group is, in general, unobservable in a nearly flat spherical universe, and so a full six-parameter search is unnecessary. Crystallographic methods could also potentially detect the cyclic factor and a cyclic subgroup of the general factor, but nothing else

Detecting topology in a nearly flat spherical universe

Energy Technology Data Exchange (ETDEWEB)

Weeks, Jeffrey [15 Farmer St, Canton NY 13617-1120 (United States); Lehoucq, Roland [CE-Saclay, DSM/DAPNIA/Service d' Astrophysique, F-91191 Gif sur Yvette Cedex (France); Uzan, Jean-Philippe [Institut d' Astrophysique de Paris, GReCO, CNRS-FRE 2435, 98 bis, Bd Arago, 75014 Paris (France)

2003-04-21

When the density parameter is close to unity, the universe has a large curvature radius independent of its being hyperbolic or spherical, or in the limiting case of an infinite curvature radius, flat. Whatever the curvature, the universe may have either a simply connected or a multiply connected topology. In the flat case, the topology scale is arbitrary, and there is no a priori reason for this scale to be of the same order as the size of the observable universe. In the hyperbolic case, any nontrivial topology would almost surely be on a length scale too large to detect. In the spherical case, in contrast, the topology could easily occur on a detectable scale. The present paper shows how, in the spherical case, the assumption of a nearly flat universe simplifies the algorithms for detecting a multiply connected topology, but also reduces the amount of topology that can be seen. This is of primary importance for the upcoming cosmic microwave background data analysis. This paper shows that for spherical spaces one may restrict the search to diametrically opposite pairs of circles in the circles-in-the-sky method and still detect the cyclic factor in the standard factorization of the holonomy group. This vastly decreases the algorithm's run time. If the search is widened to include pairs of candidate circles whose centres are almost opposite and whose relative twist varies slightly, then the cyclic factor along with a cyclic subgroup of the general factor may also be detected. Unfortunately, the full holonomy group is, in general, unobservable in a nearly flat spherical universe, and so a full six-parameter search is unnecessary. Crystallographic methods could also potentially detect the cyclic factor and a cyclic subgroup of the general factor, but nothing else.

Preparation of spherical and cubic Fe{sub 55}Co{sub 45} microstructures for studying the role of particle morphology in magnetorheological suspensions

Energy Technology Data Exchange (ETDEWEB)

Arief, Injamamul; Mukhopadhyay, P.K., E-mail: pkm@bose.res.in

2014-06-01

Cubic and spherical Fe{sub 55}Co{sub 45} alloyed microstructures were synthesized by borohydride reduction from aqueous solutions of metallic precursors, using stabilizers and polymer. Monosodium citrate, sodium acetate and PEG 6000 were utilized as electrostatic stabilizers and polymeric surface modifier. Suitable reaction conditions were maintained for synthesis of predominantly larger particles (0.7 µm to 1.2 µm), that facilitates use in magnetorheological fluids. Surface morphological studies by scanning electron microscopy revealed well shaped cubic and spherical geometry for the citrate and polymer-stabilized Fe{sub 55}Co{sub 45} alloys, while the alloy compositions remained nearly the same for both. X-ray diffractions of the as-prepared and annealed samples under various temperatures showed high degree of crystallinity with increasing temperatures. Studies of D.C. magnetization of the systems reveal that the particles have a core–shell structure, with inner magnetic core having a diameter around 30 nm with a log-normal distribution. Magnetorheological studies were performed with 8 vol% suspensions of as-synthesized particles dispersed in silicone oil (viscosity 30 mPa s at 25 °C) under different magnetic fields. Detailed studies of the magnetorheological properties were studied on these systems for practical use.

KEMAJUAN BELAJAR SISWA PADA GEOMETRI TRANSFORMASI MENGGUNAKAN AKTIVITAS REFLEKSI GEOMETRI

Directory of Open Access Journals (Sweden)

Irkham Ulil Albab

2014-10-01

Full Text Available Abstrak: Penelitian ini bertujuan untuk mendeskripsikan kemajuan belajar siswa pada materi geometri transformasi yang didukung dengan serangkaian aktivitas belajar berdasarkan Pendidikan Matematika Realistik Indonesia. Penelitian didesain melalui tiga tahap, yaitu tahapan perancangan desain awal, pengujian desain melalui pembelajaran awal dan pembelajaran eksperimental, dan tahap analisis retrospektif. Dalam penelitian ini, Hypothetical Learning Trajectory, HLT (HLT berperan penting sebagai desain pembelajaran sekaligus instrumen penelitian. HLT diujikan terhadap 26 siswa kelas VII. Data dikumpulkan dengan teknik wawancara, pengamatan, dan catatan lapangan. Hasil penelitian menunjukkan bahwa desain pembelajaran ini mampu menstimulasi siswa untuk memberikan karakteristik refleksi dan transformasi geometri lainnya secara informal, mengklasifikasikannya dalam transformasi isometri pada level kedua, dan menemukan garis bantuan refleksi pada level yang lebih formal. Selain itu, garis bantuan refleksi digunakan oleh siswa untuk menggambar bayangan refleksi dan pola pencerminan serta memahami bentuk rotasi dan translasi sebagai kombinasi refleksi adalah level tertinggi. Keyword: transformasi geometri, kombinasi refleksi, rotasi, translasi, design research, HLT STUDENTS’ LEARNING PROGRESS ON TRANSFORMATION GEOMETRY USING THE GEOMETRY REFLECTION ACTIVITIES Abstract: This study was aimed at describing the students’ learning progress on transformation geometry supported by a set of learning activities based on Indonesian Realistic Mathematics Education. The study was designed into three stages, that is, the preliminary design stage, the design testing through initial instruction and experiment, and the restrospective analysis stage. In this study, Hypothetical Learning Trajectory (HLT played an important role as an instructional design and a research instrument. HLT was tested to 26 seventh grade students. The data were collected through interviews

Spherical Pendulum, Actions, and Spin

NARCIS (Netherlands)

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

Determination of stamp deformation during imprinting on semi-spherical surfaces

DEFF Research Database (Denmark)

Kafka, Jan; Matschuk, Maria; Pranov, Henrik

of sol-gel was applied onto spherical injection mold inserts and subsequently imprinted using a flexible stamp. A hard curing step transformed the sol-gel into a quartz-like and durable material. As an example, we present theory and results regarding the imprint of pillar nanostructures on semi......-spherical mold surfaces. Imprints were realized on three different radii of circumferenceof the spherical mold: R = 0.5 mm, R = 1.0 mm, and R = 2 mm. After hard-curing of theimprinted sol-gel, the inserts were used for cold-mold as well as vario-therm injection molding.The polymer replicas and the inserts were...

Fabrication and Characterization of Nanoenergetic Hollow Spherical Hexanitrostibene (HNS Derivatives

Directory of Open Access Journals (Sweden)

Xiong Cao

2018-05-01

Full Text Available The spherization of nanoenergetic materials is the best way to improve the sensitivity and increase loading densities and detonation properties for weapons and ammunition, but the preparation of spherical nanoenergetic materials with high regularization, uniform size and monodispersity is still a challenge. In this paper, nanoenergetic hollow spherical hexanitrostibene (HNS derivatives were fabricated via a one-pot copolymerization strategy, which is based on the reaction of HNS and piperazine in acetonitrile solution. Characterization results indicated the as-prepared reaction nanoenergetic products were HNS-derived oligomers, where a free radical copolymerization reaction process was inferred. The hollow sphere structure of the HNS derivatives was characterized by scanning electron microscopy (SEM, transmission electron microscope (TEM, and synchrotron radiation X-ray imaging technology. The properties of the nanoenergetic hollow spherical derivatives, including thermal decomposition and sensitivity are discussed in detail. Sensitivity studies showed that the nanoenergetic derivatives exhibited lower impact, friction and spark sensitivity than raw HNS. Thermogravimetric-differential scanning calorimeter (TG-DSC results showed that continuous exothermic decomposition occurred in the whole temperature range, which indicated that nanoenergetic derivatives have a unique role in thermal applications. Therefore, nanoenergetic hollow spherical HNS derivatives could provide a new way to modify the properties of certain energetic compounds and fabricate spherical nanomaterials to improve the charge configuration.

Software Geometry in Simulations

Science.gov (United States)

Alion, Tyler; Viren, Brett; Junk, Tom

2015-04-01

The Long Baseline Neutrino Experiment (LBNE) involves many detectors. The experiment's near detector (ND) facility, may ultimately involve several detectors. The far detector (FD) will be significantly larger than any other Liquid Argon (LAr) detector yet constructed; many prototype detectors are being constructed and studied to motivate a plethora of proposed FD designs. Whether it be a constructed prototype or a proposed ND/FD design, every design must be simulated and analyzed. This presents a considerable challenge to LBNE software experts; each detector geometry must be described to the simulation software in an efficient way which allows for multiple authors to easily collaborate. Furthermore, different geometry versions must be tracked throughout their use. We present a framework called General Geometry Description (GGD), written and developed by LBNE software collaborators for managing software to generate geometries. Though GGD is flexible enough to be used by any experiment working with detectors, we present it's first use in generating Geometry Description Markup Language (GDML) files to interface with LArSoft, a framework of detector simulations, event reconstruction, and data analyses written for all LAr technology users at Fermilab. Brett is the other of the framework discussed here, the General Geometry Description (GGD).

Methods of information geometry

CERN Document Server

Amari, Shun-Ichi

2000-01-01

Information geometry provides the mathematical sciences with a new framework of analysis. It has emerged from the investigation of the natural differential geometric structure on manifolds of probability distributions, which consists of a Riemannian metric defined by the Fisher information and a one-parameter family of affine connections called the \\alpha-connections. The duality between the \\alpha-connection and the (-\\alpha)-connection together with the metric play an essential role in this geometry. This kind of duality, having emerged from manifolds of probability distributions, is ubiquitous, appearing in a variety of problems which might have no explicit relation to probability theory. Through the duality, it is possible to analyze various fundamental problems in a unified perspective. The first half of this book is devoted to a comprehensive introduction to the mathematical foundation of information geometry, including preliminaries from differential geometry, the geometry of manifolds or probability d...

Cylindrical and spherical space equivalents to the plane wave expansion technique of Maxwell's wave equations

Science.gov (United States)

Gauthier, Robert C.; Alzahrani, Mohammed A.; Jafari, Seyed Hamed

2015-02-01

The plane wave expansion (PWM) technique applied to Maxwell's wave equations provides researchers with a supply of information regarding the optical properties of dielectric structures. The technique is well suited for structures that display a linear periodicity. When the focus is directed towards optical resonators and structures that lack linear periodicity the eigen-process can easily exceed computational resources and time constraints. In the case of dielectric structures which display cylindrical or spherical symmetry, a coordinate system specific set of basis functions have been employed to cast Maxwell's wave equations into an eigen-matrix formulation from which the resonator states associated with the dielectric profile can be obtained. As for PWM, the inverse of the dielectric and field components are expanded in the basis functions (Fourier-Fourier-Bessel, FFB, in cylindrical and Fourier- Bessel-Legendre, BLF, in spherical) and orthogonality is employed to form the matrix expressions. The theoretical development details will be presented indicating how certain mathematical complications in the process have been overcome and how the eigen-matrix can be tuned to a specific mode type. The similarities and differences in PWM, FFB and BLF are presented. In the case of structures possessing axial cylindrical symmetry, the inclusion of the z axis component of propagation constant makes the technique applicable to photonic crystal fibers and other waveguide structures. Computational results will be presented for a number of different dielectric geometries including Bragg ring resonators, cylindrical space slot channel waveguides and bottle resonators. Steps to further enhance the computation process will be reported.

Developments in special geometry

International Nuclear Information System (INIS)

Mohaupt, Thomas; Vaughan, Owen

2012-01-01

We review the special geometry of N = 2 supersymmetric vector and hypermultiplets with emphasis on recent developments and applications. A new formulation of the local c-map based on the Hesse potential and special real coordinates is presented. Other recent developments include the Euclidean version of special geometry, and generalizations of special geometry to non-supersymmetric theories. As applications we discuss the proof that the local r-map and c-map preserve geodesic completeness, and the construction of four- and five-dimensional static solutions through dimensional reduction over time. The shared features of the real, complex and quaternionic version of special geometry are stressed throughout.

Segmented gamma scanning method for measuring holdup in the spherical container

International Nuclear Information System (INIS)

Deng Jingshan; Li Ze; Gan Lin; Lu Wenguang; Dong Mingli

2007-01-01

Some special nuclear material (SNM) is inevitably deposited in the facilities (mixer, reactor) of nuclear material process line. Exactly knowing the quantity of nuclear material holdup is very important for nuclear material accountability and critical safety. This paper presents segmented gamma scanning method for SNM holdup measurement of spherical container, at the left, right and back of which other equipments exist so that the detectors can be put at the only front of container for measurement. The nuclear material deposited in the spherical container can be looked as spherical shell source, which is divided into many layers. The detectors scanning spherical shell source are moved layer by layer from the top to the bottom to obtain projection data, with which deposited material distribution can be reconstructed by using Least Square (LS) method or Maximum Likelihood (ML) method. With these methods accurate total holdup can be obtained by summing up all the segmental values reconstructed. In this paper this measurement method for holdup in the spherical container was verified with Monte-Carlo simulation calculation and experiment. (authors)

Thermo-mechanical screening tests to qualify beryllium pebble beds with non-spherical pebbles

Energy Technology Data Exchange (ETDEWEB)

Reimann, Joerg, E-mail: joerg.reimann@partner.kit.edu [IKET, Karlsruhe Institute of Technology, Karlsruhe (Germany); Fretz, Benjamin [KBHF GmbH, Eggenstein-Leopoldshafen (Germany); Pupeschi, Simone [IAM, Karlsruhe Institute of Technology, Karlsruhe (Germany)

2015-10-15

Highlights: • In present ceramic breeder blankets, pebble-shaped beryllium is used as a neutron multiplier. • Spherical pebbles are considered as the candidate material, however, non-spherical particles are of economic interest. • Thermo-mechanical pebble bed data do merely exist for non-spherical beryllium grades. • Uniaxial compression tests (UCTs), combined with the Hot Wire Technique (HWT) were used to measure the stress–strain relations and the thermal conductivity. • A small experimental set-up had to be used and a detailed 3D modelling was of prime importance. • Compared to spherical pebble beds, non-spherical pebble beds are generally softer and mainly the thermal conductivity is lower. - Abstract: In present ceramic breeder blankets, pebble-shaped beryllium is used as a neutron multiplier. Fairly spherical pebbles are considered as a candidate material, however, non-spherical particles are of economic interest because production costs are much lower. Yet, thermo-mechanical pebble bed data do merely exist for these beryllium grades, and the blanket relevant potential of these grades cannot be judged. Screening experiments were performed with three different grades of non-spherical beryllium pebbles, produced by different companies, accompanied by experiments with the reference beryllium pebble beds. Uniaxial compression tests (UCTs), combined with the Hot Wire Technique (HWT), were performed to measure both the stress–strain relation and the thermal conductivity, k, at different stress levels. Because of the limited amounts of the non-spherical materials, the experimental set-ups were small and a detailed 3D modelling was of prime importance in order to prove that the used design was appropriate. Compared to the pebble beds consisting of spherical pebbles, non-spherical pebble beds are generally softer (smaller stress for a given strain), and, mainly as a consequence of this, for a given strain value, the thermal conductivity is lower. This

Vertical Distribution of Dust and Water Ice Aerosols from CRISM Limb-geometry Observations

Science.gov (United States)

Smith, Michael Doyle; Wolff, Michael J.; Clancy, Todd; Kleinbohl, Armin; Murchie, Scott L.

2013-01-01

[1] Near-infrared spectra taken in a limb-viewing geometry by the Compact Reconnaissance Imaging Spectrometer for Mars (CRISM) on board the Mars Reconnaissance Orbiter provide a useful tool for probing atmospheric structure. Specifically, the observed radiance as a function of wavelength and height above the limb enables the vertical distribution of both dust and water ice aerosols to be retrieved. More than a dozen sets of CRISM limb observations have been taken so far providing pole-to-pole cross sections, spanning more than a full Martian year. Radiative transfer modeling is used to model the observations taking into account multiple scattering from aerosols and the spherical geometry of the limb observations. Both dust and water ice vertical profiles often show a significant vertical structure for nearly all seasons and latitudes that is not consistent with the well-mixed or Conrath-v assumptions that have often been used in the past for describing aerosol vertical profiles for retrieval and modeling purposes. Significant variations are seen in the retrieved vertical profiles of dust and water ice aerosol as a function of season. Dust typically extends to higher altitudes (approx. 40-50km) during the perihelion season than during the aphelion season (water ice clouds are common, and water ice aerosols are observed to cap the dust layer in all seasons.

Photodetachment of H− near a Hard Spherical Surface

International Nuclear Information System (INIS)

Haneef, M.; Rahman, A.; Ahmad, Iftikhar; Afaq, A.

2012-01-01

The photodetachment of a hydrogen negative ion (H − ) near a hard spherical surface is investigated by using the theoretical imaging method. The surface is oriented in such a fashion that the laser polarization direction is perpendicular to the principal axis of the spherical surface. Analytical expressions are derived for the detached-electron flux and photodetachment cross section. Strong interference patterns are observed in the detached-electron flux, while no visible oscillations are found in the photodetachment cross section. (atomic and molecular physics)

The design of geometry teaching: learning from the geometry textbooks of Godfrey and Siddons

OpenAIRE

Fujita, Taro; Jones, Keith

2002-01-01

Deciding how to teach geometry remains a demanding task with one of major arguments being about how to combine the intuitive and deductive aspects of geometry into an effective teaching design. In order to try to obtain an insight into tackling this issue, this paper reports an analysis of innovative geometry textbooks which were published in the early part of the 20th Century, a time when significant efforts were being made to improve the teaching and learning of geometry. The analysis sugge...

WAVEMOTH-FAST SPHERICAL HARMONIC TRANSFORMS BY BUTTERFLY MATRIX COMPRESSION

International Nuclear Information System (INIS)

Seljebotn, D. S.

2012-01-01

We present Wavemoth, an experimental open source code for computing scalar spherical harmonic transforms (SHTs). Such transforms are ubiquitous in astronomical data analysis. Our code performs substantially better than existing publicly available codes owing to improvements on two fronts. First, the computational core is made more efficient by using small amounts of pre-computed data, as well as paying attention to CPU instruction pipelining and cache usage. Second, Wavemoth makes use of a fast and numerically stable algorithm based on compressing a set of linear operators in a pre-computation step. The resulting SHT scales as O(L 2 log 2 L) for the resolution range of practical interest, where L denotes the spherical harmonic truncation degree. For low- and medium-range resolutions, Wavemoth tends to be twice as fast as libpsht, which is the current state-of-the-art implementation for the HEALPix grid. At the resolution of the Planck experiment, L ∼ 4000, Wavemoth is between three and six times faster than libpsht, depending on the computer architecture and the required precision. Because of the experimental nature of the project, only spherical harmonic synthesis is currently supported, although adding support for spherical harmonic analysis should be trivial.

Automatic X-ray inspection for the HTR-PM spherical fuel elements

Energy Technology Data Exchange (ETDEWEB)

Yi, DU, E-mail: duyi11@mails.tsinghua.edu.cn [Institute of Nuclear and New Energy Technology (INET), Tsinghua University, Energy Science Building A309, Haidian District, Beijing 100084 (China); Xiangang, WANG, E-mail: wangxiangang@tsinghua.edu.cn [Institute of Nuclear and New Energy Technology (INET), Tsinghua University, Energy Science Building A309, Haidian District, Beijing 100084 (China); Xincheng, XIANG, E-mail: inetxxc@tsinghua.edu.cn [Institute of Nuclear and New Energy Technology (INET), Tsinghua University, Energy Science Building, Haidian District, Beijing 100084 (China); Bing, LIU, E-mail: bingliu@tsinghua.edu.cn [Institute of Nuclear and New Energy Technology (INET), Tsinghua University, Energy Science Building, Haidian District, Beijing 100084 (China)

2014-12-15

Highlights: • An automatic X-ray inspection method is established to characterize HTR pebbles. • The method provides physical characterization and the inner structure of pebbles. • The method can be conducted non-destructively, quickly and automatically. • Sample pebbles were measured with this AXI method for validation. • The method shows the potential to be applied in situ. - Abstract: Inefficient quality assessment and control (QA and C) of spherical fuel elements for high temperature reactor-pebblebed modules (HTR-PM) has been a long-term problem, since conventional methods are labor intensive and cannot reveal the inside information nondestructively. Herein, we proposed a nondestructive, automated X-ray inspection (AXI) method to characterize spherical fuel elements including their inner structures based on X-ray digital radiography (DR). Briefly, DR images at different angles are first obtained and then the chosen important parameters such as spherical diameters, geometric and mass centers, can be automatically extracted and calculated via image processing techniques. Via evaluating sample spherical fuel elements, we proved that this AXI method can be conducted non-destructively, quickly and automatically. This method not only provides accurate physical characterization of spherical fuel elements but also reveals their inner structure with good resolution, showing great potentials to facilitate fast QA and C in HTM-PM spherical fuel element development and production.

Automatic X-ray inspection for the HTR-PM spherical fuel elements

International Nuclear Information System (INIS)

Yi, DU; Xiangang, WANG; Xincheng, XIANG; Bing, LIU

2014-01-01

Highlights: • An automatic X-ray inspection method is established to characterize HTR pebbles. • The method provides physical characterization and the inner structure of pebbles. • The method can be conducted non-destructively, quickly and automatically. • Sample pebbles were measured with this AXI method for validation. • The method shows the potential to be applied in situ. - Abstract: Inefficient quality assessment and control (QA and C) of spherical fuel elements for high temperature reactor-pebblebed modules (HTR-PM) has been a long-term problem, since conventional methods are labor intensive and cannot reveal the inside information nondestructively. Herein, we proposed a nondestructive, automated X-ray inspection (AXI) method to characterize spherical fuel elements including their inner structures based on X-ray digital radiography (DR). Briefly, DR images at different angles are first obtained and then the chosen important parameters such as spherical diameters, geometric and mass centers, can be automatically extracted and calculated via image processing techniques. Via evaluating sample spherical fuel elements, we proved that this AXI method can be conducted non-destructively, quickly and automatically. This method not only provides accurate physical characterization of spherical fuel elements but also reveals their inner structure with good resolution, showing great potentials to facilitate fast QA and C in HTM-PM spherical fuel element development and production

Modeling the Interaction of Mineral Dust with Solar Radiation: Spherical versus Non-spherical Particles

Science.gov (United States)

Hoshyaripour, A.; Vogel, B.; Vogel, H.

2017-12-01

Mineral dust, emitted from arid and semi-arid regions, is the most dominant atmospheric aerosol by mass. Beside detrimental effect on air quality, airborne dust also influences the atmospheric radiation by absorbing and scattering solar and terrestrial radiation. As a result, while the long-term radiative impacts of dust are important for climate, the short-term effects are significant for the photovoltaic energy production. Therefore, it is a vital requirement to accurately forecast the effects of dust on energy budget of the atmosphere and surface. To this end, a major issue is the fact that dust particles are non-spherical. Thus, the optical properties of such particles cannot be calculated precisely using the conventional methods like Mie theory that are often used in climate and numerical weather forecast models. In this study, T-Matrix method is employed, which is able to treat the non-sphericity of particles. Dust particles are assumed to be prolate spheroids with aspect ratio of 1.5 distributed in three lognormal modes. The wavelength-dependent refractive indices of dust are used in T-Matrix algorithm to calculate the extinction coefficient, single scattering albedo, asymmetry parameter and backscattering ratio at different wavelengths. These parameters are then implemented in ICON-ART model (ICOsahedral Nonhydrostatic model with Aerosols and Reactive Trace gases) to conduct a global simulation with 80 km horizontal resolution and 90 vertical levels. April 2014 is selected as the simulation period during which North African dust plumes reached central Europe and Germany. Results show that treatment of non-sphericity reduces the dust AOD in the range of 10 to 30%/. The impacts on diffuse and direct radiation at global, regional and local scales show strong dependency on the size distribution of the airborne dust. The implications for modeling and remote sensing the dust impacts on solar energy are also discussed.

An electromagnetic spherical phased array thermonuclear fusion reactor

International Nuclear Information System (INIS)

Okress, E.C.

1983-01-01

Discussed are salient physics aspects of a microwave singly reentrant spherical periodic phased array of uniformally distributed identical coaxial radiation elements in an essentially simulated infinite array environment. The array is capable of maintaining coherence or phase control (to the limit of the order of 300 GHz) of its spherically converging electromagnetic transverse magnetic mode radiation field, for confinement (and heating) of thermonuclear plasma in steady-state or inertial thermonuclear fusion. The array also incorporates capability for coaxial directional coupler extraction of fusionpower. The radiation elements of the array are shielded against DT Thermonuclear plasma emissions (i.e., neutrons and bremsstrahlung) by either sufficiently (available) low less tangent and cooled, spherically concentric shield (e.g., Titanium oxide); or alternately by identical material dome windows mounted on each radiation element's aperture of the array. The pump microwave power required for thermonuclear fusion feasibility comprises an array of phase-locked available klystron amplifiers (comparable gyratron amplifiers remain to be developed)

Plane-wave decomposition by spherical-convolution microphone array

Science.gov (United States)

Rafaely, Boaz; Park, Munhum

2004-05-01

Reverberant sound fields are widely studied, as they have a significant influence on the acoustic performance of enclosures in a variety of applications. For example, the intelligibility of speech in lecture rooms, the quality of music in auditoria, the noise level in offices, and the production of 3D sound in living rooms are all affected by the enclosed sound field. These sound fields are typically studied through frequency response measurements or statistical measures such as reverberation time, which do not provide detailed spatial information. The aim of the work presented in this seminar is the detailed analysis of reverberant sound fields. A measurement and analysis system based on acoustic theory and signal processing, designed around a spherical microphone array, is presented. Detailed analysis is achieved by decomposition of the sound field into waves, using spherical Fourier transform and spherical convolution. The presentation will include theoretical review, simulation studies, and initial experimental results.

Indicators of Mass in Spherical Stellar Atmospheres

Science.gov (United States)

Lester, John B.; Dinshaw, Rayomond; Neilson, Hilding R.

2013-04-01

Mass is the most important stellar parameter, but it is not directly observable for a single star. Spherical model stellar atmospheres are explicitly characterized by their luminosity ( L⋆), mass ( M⋆), and radius ( R⋆), and observations can now determine directly L⋆ and R⋆. We computed spherical model atmospheres for red giants and for red supergiants holding L⋆ and R⋆ constant at characteristic values for each type of star but varying M⋆, and we searched the predicted flux spectra and surface-brightness distributions for features that changed with mass. For both stellar classes we found similar signatures of the stars’ mass in both the surface-brightness distribution and the flux spectrum. The spectral features have been use previously to determine log 10(g), and now that the luminosity and radius of a non-binary red giant or red supergiant can be observed, spherical model stellar atmospheres can be used to determine a star’s mass from currently achievable spectroscopy. The surface-brightness variations of mass are slightly smaller than can be resolved by current stellar imaging, but they offer the advantage of being less sensitive to the detailed chemical composition of the atmosphere.

Sources of hyperbolic geometry

CERN Document Server

Stillwell, John

1996-01-01

This book presents, for the first time in English, the papers of Beltrami, Klein, and Poincaré that brought hyperbolic geometry into the mainstream of mathematics. A recognition of Beltrami comparable to that given the pioneering works of Bolyai and Lobachevsky seems long overdue-not only because Beltrami rescued hyperbolic geometry from oblivion by proving it to be logically consistent, but because he gave it a concrete meaning (a model) that made hyperbolic geometry part of ordinary mathematics. The models subsequently discovered by Klein and Poincaré brought hyperbolic geometry even further down to earth and paved the way for the current explosion of activity in low-dimensional geometry and topology. By placing the works of these three mathematicians side by side and providing commentaries, this book gives the student, historian, or professional geometer a bird's-eye view of one of the great episodes in mathematics. The unified setting and historical context reveal the insights of Beltrami, Klein, and Po...

Features of spherical uranium-graphite HTGR fuel elements control

International Nuclear Information System (INIS)

Kreindlin, I.I.; Oleynikov, P.P.; Shtan, A.S.

1985-01-01

Control features of spherical HTGR uranium-graphite fuel elements with spherical coated fuel particles are mainly determined by their specific construction and fabrication technology. The technology is chiefly based on methods of ceramic fuel (fuel microspheres fabrication) and graphite production practice it is necessary to deal with a lot of problems from determination of raw materials properties to final fuel elements testing. These procedures are described

Features of spherical uranium-graphite HTGR fuel elements control

Energy Technology Data Exchange (ETDEWEB)

Kreindlin, I I; Oleynikov, P P; Shtan, A S

1985-07-01

Control features of spherical HTGR uranium-graphite fuel elements with spherical coated fuel particles are mainly determined by their specific construction and fabrication technology. The technology is chiefly based on methods of ceramic fuel (fuel microspheres fabrication) and graphite production practice it is necessary to deal with a lot of problems from determination of raw materials properties to final fuel elements testing. These procedures are described.

E-Beam-Cured Layered-Silicate and Spherical Silica Epoxy Nanocomposites (Preprint)

National Research Council Canada - National Science Library

Chen, Chenggang; Anderson, David P

2007-01-01

.... The nanofillers can be two dimensional (layered-silicate) and zero dimensional (spherical silica). Both the spherical silica epoxy nanocomposite and the layered-silicate epoxy nanocomposite can be cured to a high degree of curing...

Quality metric for spherical panoramic video

Science.gov (United States)

Zakharchenko, Vladyslav; Choi, Kwang Pyo; Park, Jeong Hoon

2016-09-01

Virtual reality (VR)/ augmented reality (AR) applications allow users to view artificial content of a surrounding space simulating presence effect with a help of special applications or devices. Synthetic contents production is well known process form computer graphics domain and pipeline has been already fixed in the industry. However emerging multimedia formats for immersive entertainment applications such as free-viewpoint television (FTV) or spherical panoramic video require different approaches in content management and quality assessment. The international standardization on FTV has been promoted by MPEG. This paper is dedicated to discussion of immersive media distribution format and quality estimation process. Accuracy and reliability of the proposed objective quality estimation method had been verified with spherical panoramic images demonstrating good correlation results with subjective quality estimation held by a group of experts.

Analysis of a spherical permanent magnet actuator

International Nuclear Information System (INIS)

Wang, J.; Jewell, G.W.; Howe, D.

1997-01-01

This paper describes a new form of actuator with a spherical permanent magnet rotor and a simple winding arrangement, which is capable of a high specific torque by utilizing a rare-earth permanent magnet. The magnetic-field distribution is established using an analytical technique formulated in spherical coordinates, and the results are validated by finite element analysis. The analytical field solution allows the prediction of the actuator torque and back emf in closed forms. In turn, these facilitate the characterization of the actuator and provide a firm basis for design optimization, system dynamic modeling, and closed-loop control law development. copyright 1997 American Institute of Physics

Flat synchronizations in spherically symmetric space-times

International Nuclear Information System (INIS)

Herrero, Alicia; Morales-Lladosa, Juan Antonio

2010-01-01

It is well known that the Schwarzschild space-time admits a spacelike slicing by flat instants and that the metric is regular at the horizon in the associated adapted coordinates (Painleve-Gullstrand metric form). We consider this type of flat slicings in an arbitrary spherically symmetric space-time. The condition ensuring its existence is analyzed, and then, we prove that, for any spherically symmetric flat slicing, the densities of the Weinberg momenta vanish. Finally, we deduce the Schwarzschild solution in the extended Painleve-Gullstrand-LemaItre metric form by considering the coordinate decomposition of the vacuum Einstein equations with respect to a flat spacelike slicing.

Monodromy in the quantum spherical pendulum

International Nuclear Information System (INIS)

Guillemin, V.; Uribe, A.

1989-01-01

In this article we show that monodromy in the quantum spherical pendulum can be interpreted as a Maslov effect: i.e. as multi-valuedness of a certain generating function of the quantum energy levels. (orig.)

The geometry description markup language

International Nuclear Information System (INIS)

Chytracek, R.

2001-01-01

Currently, a lot of effort is being put on designing complex detectors. A number of simulation and reconstruction frameworks and applications have been developed with the aim to make this job easier. A very important role in this activity is played by the geometry description of the detector apparatus layout and its working environment. However, no real common approach to represent geometry data is available and such data can be found in various forms starting from custom semi-structured text files, source code (C/C++/FORTRAN), to XML and database solutions. The XML (Extensible Markup Language) has proven to provide an interesting approach for describing detector geometries, with several different but incompatible XML-based solutions existing. Therefore, interoperability and geometry data exchange among different frameworks is not possible at present. The author introduces a markup language for geometry descriptions. Its aim is to define a common approach for sharing and exchanging of geometry description data. Its requirements and design have been driven by experience and user feedback from existing projects which have their geometry description in XML

Complex analysis and CR geometry

CERN Document Server

Zampieri, Giuseppe

2008-01-01

Cauchy-Riemann (CR) geometry is the study of manifolds equipped with a system of CR-type equations. Compared to the early days when the purpose of CR geometry was to supply tools for the analysis of the existence and regularity of solutions to the \\bar\\partial-Neumann problem, it has rapidly acquired a life of its own and has became an important topic in differential geometry and the study of non-linear partial differential equations. A full understanding of modern CR geometry requires knowledge of various topics such as real/complex differential and symplectic geometry, foliation theory, the geometric theory of PDE's, and microlocal analysis. Nowadays, the subject of CR geometry is very rich in results, and the amount of material required to reach competence is daunting to graduate students who wish to learn it. However, the present book does not aim at introducing all the topics of current interest in CR geometry. Instead, an attempt is made to be friendly to the novice by moving, in a fairly relaxed way, f...

A Robust Solution of the Spherical Burmester Problem

DEFF Research Database (Denmark)

Angeles, Jorge; Bai, Shaoping

2010-01-01

The problem of spherical four-bar linkage synthesis is revisited in this paper. The work is aimed at developing a robust synthesis method by taking into account both the formulation and the solution method. In addition, the synthesis of linkages with spherical prismatic joints is considered...... by treating them as a special case of the linkages under study. A two-step synthesis method is developed, which sequentially deals with equation-solving by a semigraphical approach and branching-detection. Examples are included to demonstrate the proposed method....

VARIANT: VARIational anisotropic nodal transport for multidimensional Cartesian and hexadgonal geometry calculation

International Nuclear Information System (INIS)

Palmiotti, G.; Carrico, C.B.; Lewis, E.E.

1995-10-01

The theoretical basis, implementation information and numerical results are presented for VARIANT (VARIational Anisotropic Neutron Transport), a FORTRAN module of the DIF3D code system at Argonne National Laboratory. VARIANT employs the variational nodal method to solve multigroup steady-state neutron diffusion and transport problems. The variational nodal method is a hybrid finite element method that guarantees nodal balance and permits spatial refinement through the use of hierarchical complete polynomial trial functions. Angular variables are expanded with complete or simplified P 1 , P 3 or P 5 5 spherical harmonics approximations with full anisotropic scattering capability. Nodal response matrices are obtained, and the within-group equations are solved by red-black or four-color iteration, accelerated by a partitioned matrix algorithm. Fission source and upscatter iterations strategies follow those of DIF3D. Two- and three-dimensional Cartesian and hexagonal geometries are implemented. Forward and adjoint eigenvalue, fixed source, gamma heating, and criticality (concentration) search problems may be performed

Global aspects of complex geometry

CERN Document Server

Catanese, Fabrizio; Huckleberry, Alan T

2006-01-01

Present an overview of developments in Complex Geometry. This book covers topics that range from curve and surface theory through special varieties in higher dimensions, moduli theory, Kahler geometry, and group actions to Hodge theory and characteristic p-geometry.

Population spherical aberration: associations with ametropia, age, corneal curvature, and image quality

Directory of Open Access Journals (Sweden)

Kingston AC

2013-05-01

Full Text Available Amanda C Kingston,1,2 Ian G Cox11Bausch + Lomb, Rochester, NY, USA; 2Department of Biomedical Engineering, University of Rochester, Rochester, NY, USAPurpose: The aim of this analysis was to determine the total ocular wavefront aberration values of a large phakic population of physiologically normal, ametropic eyes, gathered under the same clinical protocol using the same diagnostic wavefront sensor.Materials and methods: Studies were conducted at multiple sites in Asia, North America, Europe, and Australia. A Bausch + Lomb Zywave II Wavefront Aberrometer (Rochester, NY, USA was used to measure the lower and higher order aberrations of each eye. Data analysis was conducted using linear regression analysis to determine the relationship between total spherical aberration, ametropia, age, corneal curvature, and image quality.Results: Linear regression analysis showed no correlation (r = 0.0207, P = 0.4874 between degree of ametropia and the amount of spherical aberration. There was also no correlation when the population was stratified into myopic and hyperopic refractive groups (rm = 0.0529, Pm = 0.0804 and rh = 0.1572, Ph = 0.2754. There was a statistically significant and weak positive correlation (r = 0.1962, P < 0.001 between age and the amount of spherical aberration measured in the eye; spherical aberration became more positive with increasing age. Also, there was a statistically significant and moderately positive correlation (r = 0.3611, P < 0.001 with steepness of corneal curvature; spherical aberration became more positive with increasing power of the anterior corneal surface. Assessment of image quality using optical design software (Zemax™, Bellevue, WA, USA showed that there was an overall benefit in correcting the average spherical aberration of this population.Conclusion: Analysis of this dataset provides insights into the inherent spherical aberration of a typical phakic, pre-presbyopic, population and provides the ability to

Analytic geometry

CERN Document Server

Burdette, A C

1971-01-01

Analytic Geometry covers several fundamental aspects of analytic geometry needed for advanced subjects, including calculus.This book is composed of 12 chapters that review the principles, concepts, and analytic proofs of geometric theorems, families of lines, the normal equation of the line, and related matters. Other chapters highlight the application of graphing, foci, directrices, eccentricity, and conic-related topics. The remaining chapters deal with the concept polar and rectangular coordinates, surfaces and curves, and planes.This book will prove useful to undergraduate trigonometric st

Vector geometry

CERN Document Server

Robinson, Gilbert de B

2011-01-01

This brief undergraduate-level text by a prominent Cambridge-educated mathematician explores the relationship between algebra and geometry. An elementary course in plane geometry is the sole requirement for Gilbert de B. Robinson's text, which is the result of several years of teaching and learning the most effective methods from discussions with students. Topics include lines and planes, determinants and linear equations, matrices, groups and linear transformations, and vectors and vector spaces. Additional subjects range from conics and quadrics to homogeneous coordinates and projective geom

Physics- and engineering knowledge-based geometry repair system for robust parametric CAD geometries

OpenAIRE

Li, Dong

2012-01-01

In modern multi-objective design optimisation, an effective geometry engine is becoming an essential tool and its performance has a significant impact on the entire process. Building a parametric geometry requires difficult compromises between the conflicting goals of robustness and flexibility. The work presents a solution for improving the robustness of parametric geometry models by capturing and modelling relative engineering knowledge into a surrogate model, and deploying it automatically...

Hawking radiation from a spherical loop quantum gravity black hole

International Nuclear Information System (INIS)

Gambini, Rodolfo; Pullin, Jorge

2014-01-01

We introduce quantum field theory on quantum space-times techniques to characterize the quantum vacua as a first step toward studying black hole evaporation in spherical symmetry in loop quantum gravity and compute the Hawking radiation. We use as quantum space-time the recently introduced exact solution of the quantum Einstein equations in vacuum with spherical symmetry and consider a spherically symmetric test scalar field propagating on it. The use of loop quantum gravity techniques in the background space-time naturally regularizes the matter content, solving one of the main obstacles to back-reaction calculations in more traditional treatments. The discreteness of area leads to modifications of the quantum vacua, eliminating the trans-Planckian modes close to the horizon, which in turn eliminates all singularities from physical quantities, like the expectation value of the stress–energy tensor. Apart from this, the Boulware, Hartle–Hawking and Unruh vacua differ little from the treatment on a classical space-time. The asymptotic modes near scri are reproduced very well. We show that the Hawking radiation can be computed, leading to an expression similar to the conventional one but with a high frequency cutoff. Since many of the conclusions concern asymptotic behavior, where the spherical mode of the field behaves in a similar way as higher multipole modes do, the results can be readily generalized to non spherically symmetric fields. (paper)

Lateral phase separation of mixed polymer brushes on planar and spherical surfaces

Science.gov (United States)

van Lehn, Reid; Alexander-Katz, Alfredo

2012-02-01

A mixed polymer brush consists of two (or more) polymer species grafted to a surface at a high density, inducing the polymers to highly stretch to maximize favorable solvent interactions while minimizing polymer overlap. The enthalpic and entropic interactions between the different polymers give rise to lateral phase behavior on the surface. Understanding this phase separation behavior is interesting for applications in nanotemplating and controlled protein adsorption. In this work, we present a novel theoretical model to quickly predict lateral phase separated morphologies of mixed polymer brushes on planar, cylindrical and spherical surfaces. The model combines a Flory-Huggins model for enthalpic interactions between the polymer components with an Alexander-de Gennes model for the entropy of the brush layers. When there is a length difference between the polymer components, these two interactions along with the conformational entropy of the system lead to a range of morphologies including stripes, dimples, mixing, and complete phase separation. The computational efficiency of this model allows for phase diagrams to be generated with great accuracy. The results of our model thus allow for the fast prediction of lateral morphologies on different geometries.

New Constraints on the Geometry and Kinematics of Matter Surrounding the Accretion Flow in X-Ray Binaries from Chandra High-energy Transmission Grating X-Ray Spectroscopy

Science.gov (United States)

Tzanavaris, P.; Yaqoob, T.

2018-03-01

The narrow, neutral Fe Kα fluorescence emission line in X-ray binaries (XRBs) is a powerful probe of the geometry, kinematics, and Fe abundance of matter around the accretion flow. In a recent study it has been claimed, using Chandra High-Energy Transmission Grating (HETG) spectra for a sample of XRBs, that the circumnuclear material is consistent with a solar-abundance, uniform, spherical distribution. It was also claimed that the Fe Kα line was unresolved in all cases by the HETG. However, these conclusions were based on ad hoc models that did not attempt to relate the global column density to the Fe Kα line emission. We revisit the sample and test a self-consistent model of a uniform, spherical X-ray reprocessor against HETG spectra from 56 observations of 14 Galactic XRBs. We find that the model is ruled out in 13/14 sources because a variable Fe abundance is required. In two sources a spherical distribution is viable, but with nonsolar Fe abundance. We also applied a solar-abundance Compton-thick reflection model, which can account for the spectra that are inconsistent with a spherical model, but spectra with a broader bandpass are required to better constrain model parameters. We also robustly measured the velocity width of the Fe Kα line and found FWHM values of up to ∼5000 km s‑1. Only in some spectra was the Fe Kα line unresolved by the HETG.

New Constraints on the Geometry and Kinematics of Matter Surrounding the Accretion Flow in X-Ray Binaries from Chandra High-Energy Transmission Grating X-Ray Spectroscopy

Science.gov (United States)

Tzanavaris, P.; Yaqoob, T.

2018-01-01

The narrow, neutral Fe Ka fluorescence emission line in X-ray binaries (XRBs) is a powerful probe of the geometry, kinematics, and Fe abundance of matter around the accretion flow. In a recent study it has been claimed, using Chandra High-Energy Transmission Grating (HETG) spectra for a sample of XRBs, that the circumnuclear material is consistent with a solar-abundance, uniform, spherical distribution. It was also claimed that the Fe Ka line was unresolved in all cases by the HETG. However, these conclusions were based on ad hoc models that did not attempt to relate the global column density to the Fe Ka line emission. We revisit the sample and test a self-consistent model of a uniform, spherical X-ray reprocessor against HETG spectra from 56 observations of 14 Galactic XRBs. We find that the model is ruled out in 13/14 sources because a variable Fe abundance is required. In two sources a spherical distribution is viable, but with nonsolar Fe abundance. We also applied a solar-abundance Compton-thick reflection model, which can account for the spectra that are inconsistent with a spherical model, but spectra with a broader bandpass are required to better constrain model parameters. We also robustly measured the velocity width of the Fe Ka line and found FWHM values of up to approx. 5000 km/s. Only in some spectra was the Fe Ka line unresolved by the HETG.

Trapped surfaces in spherical stars

International Nuclear Information System (INIS)

Bizon, P.; Malec, E.; O'Murchadha, N.

1988-01-01

We give necessary and sufficient conditions for the existence of trapped surfaces in spherically symmetric spacetimes. These conditions show that the formation of trapped surfaces depends on both the degree of concentration and the average flow of the matter. The result can be considered as a partial validation of the cosmic-censorship hypothesis

Boundary causality versus hyperbolicity for spherical black holes in Gauss–Bonnet gravity

International Nuclear Information System (INIS)

Andrade, Tomás; Cáceres, Elena; Keeler, Cynthia

2017-01-01

We explore the constraints boundary causality places on the allowable Gauss–Bonnet gravitational couplings in asymptotically AdS spaces, specifically considering spherical black hole solutions. We additionally consider the hyperbolicity properties of these solutions, positing that hyperbolicity-violating solutions are sick solutions whose causality properties provide no information about the theory they reside in. For both signs of the Gauss–Bonnet coupling, spherical black holes violate boundary causality at smaller absolute values of the coupling than planar black holes do. For negative coupling, as we tune the Gauss–Bonnet coupling away from zero, both spherical and planar black holes violate hyperbolicity before they violate boundary causality. For positive coupling, the only hyperbolicity-respecting spherical black holes which violate boundary causality do not do so appreciably far from the planar bound. Consequently, eliminating hyperbolicity-violating solutions means the bound on Gauss–Bonnet couplings from the boundary causality of spherical black holes is no tighter than that from planar black holes. (paper)

The Fatigue Life Prediction of Train Wheel Rims Containing Spherical Inclusions

Science.gov (United States)

Li, Yajie; Chen, Huanguo; Cai, Li; Chen, Pei; Qian, Jiacheng; Wu, Jianwei

2018-03-01

It is a common phenomenon that fatigue crack initiation occurs frequently in the inclusions of wheel rims. Research on the fatigue life of wheel rims with spherical inclusions is of great significance on the reliability of wheels. To find the danger point and working condition of a wheel, the stress state of the wheel rim with spherical inclusions was analyzed using the finite element method. Results revealed that curve conditions are dangerous. The critical plane method, based on the cumulative fatigue damage theory, was used to predict the fatigue life of the wheel rim and whether it contained spherical inclusions or not under curve conditions. It was found that the fatigue life of the wheel rim is significantly shorter when the wheel rim contains spherical inclusions. Analysis of the results can provide a theoretical basis and technical support for train operations and maintenance.

Normal range of facial asymmetry in spherical coordinates: a CBCT study

Energy Technology Data Exchange (ETDEWEB)

Yoon, Suk Ja [Dept. of Oral and Maxillofacial Radiology, School of Dentistry, Dental Science Research Institute, Chonnam National University, Gwangju (Korea, Republic of); Wang, Rui Feng [Research Laboratory Specialist Intermediate, Department of Biologic and Material Sciences, School of Dentistry, University of Michigan, Ann Arbor, MI (United States); Na, Hee Ja [Dept. ofDental Hygiene, Honam University, Gwangju (Korea, Republic of); Palomo, Juan Matin [Dept. of Orthodontics, School of Dental Medicine, Case Western Reserve University, Cleveland (United States)

2013-03-15

This study aimed to measure the bilateral differences of facial lines in spherical coordinates from faces within a normal range of asymmetry utilizing cone-beam computed tomography (CBCT). CBCT scans from 22 females with normal symmetric-looking faces (mean age 24 years and 8 months) were selected for the study. The average menton deviation was 1.01{+-}0.66 mm. The spherical coordinates, length, and midsagittal and coronal inclination angles of the ramal and mandibular lines were calculated from CBCT. The bilateral differences in the facial lines were determined. All of the study subjects had minimal bilateral differences of facial lines. The normal range of facial asymmetry of the ramal and mandibular lines was obtained in spherical coordinates. The normal range of facial asymmetry in the spherical coordinate system in this study should be useful as a reference for diagnosing facial asymmetry.

Noncommutative geometry

CERN Document Server

Connes, Alain

1994-01-01

This English version of the path-breaking French book on this subject gives the definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics developed by Alain Connes. Profusely illustrated and invitingly written, this book is ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics, quantization, and elementary particles and fields.Key Features* First full treatment of the subject and its applications* Written by the pioneer of this field* Broad applications in mathemat

Geometry Revealed

CERN Document Server

Berger, Marcel

2010-01-01

Both classical geometry and modern differential geometry have been active subjects of research throughout the 20th century and lie at the heart of many recent advances in mathematics and physics. The underlying motivating concept for the present book is that it offers readers the elements of a modern geometric culture by means of a whole series of visually appealing unsolved (or recently solved) problems that require the creation of concepts and tools of varying abstraction. Starting with such natural, classical objects as lines, planes, circles, spheres, polygons, polyhedra, curves, surfaces,

Discrete differential geometry. Consistency as integrability

OpenAIRE

Bobenko, Alexander I.; Suris, Yuri B.

2005-01-01

A new field of discrete differential geometry is presently emerging on the border between differential and discrete geometry. Whereas classical differential geometry investigates smooth geometric shapes (such as surfaces), and discrete geometry studies geometric shapes with finite number of elements (such as polyhedra), the discrete differential geometry aims at the development of discrete equivalents of notions and methods of smooth surface theory. Current interest in this field derives not ...

On the spherical harmonic expansion of the neutron angular distribution function

Energy Technology Data Exchange (ETDEWEB)

Depken, Sven

1959-03-15

The neutron (one-velocity) angular distribution function is expanded in terms of spherical harmonic tensors. The solution to the equations of the moments is given explicitly and the result is applied to the plane, spherical and cylinder symmetrical cases.

On the spherical harmonic expansion of the neutron angular distribution function

International Nuclear Information System (INIS)

Depken, Sven

1959-03-01

The neutron (one-velocity) angular distribution function is expanded in terms of spherical harmonic tensors. The solution to the equations of the moments is given explicitly and the result is applied to the plane, spherical and cylinder symmetrical cases

Optical properties of spherical gold mesoparticles

DEFF Research Database (Denmark)

Evlyukhin, A. B.; Kuznetsov, A. I.; Novikov, S. M.

2012-01-01

Optical properties of spherical gold particles with diameters of 150-650 nm (mesoparticles) are studied by reflectance spectroscopy. Particles are fabricated by laser-induced transfer of metallic droplets onto metal and dielectric substrates. Contributions of higher multipoles (beyond...

Spinorial Geometry and Branes

International Nuclear Information System (INIS)

Sloane, Peter

2007-01-01

We adapt the spinorial geometry method introduced in [J. Gillard, U. Gran and G. Papadopoulos, 'The spinorial geometry of supersymmetric backgrounds,' Class. Quant. Grav. 22 (2005) 1033 [ (arXiv:hep-th/0410155)

An introduction to incidence geometry

CERN Document Server

De Bruyn, Bart

2016-01-01

This book gives an introduction to the field of Incidence Geometry by discussing the basic families of point-line geometries and introducing some of the mathematical techniques that are essential for their study. The families of geometries covered in this book include among others the generalized polygons, near polygons, polar spaces, dual polar spaces and designs. Also the various relationships between these geometries are investigated. Ovals and ovoids of projective spaces are studied and some applications to particular geometries will be given. A separate chapter introduces the necessary mathematical tools and techniques from graph theory. This chapter itself can be regarded as a self-contained introduction to strongly regular and distance-regular graphs. This book is essentially self-contained, only assuming the knowledge of basic notions from (linear) algebra and projective and affine geometry. Almost all theorems are accompanied with proofs and a list of exercises with full solutions is given at the end...

Importance of aerosol non-sphericity in estimating aerosol radiative forcing in Indo-Gangetic Basin.

Science.gov (United States)

Srivastava, Parul; Dey, Sagnik; Srivastava, Atul Kumar; Singh, Sachchidanand; Mishra, S K; Tiwari, Suresh

2017-12-01

Aerosols are usually presumed spherical in shape while estimating the direct radiative forcing (DRF) using observations or in the models. In the Indo-Gangetic Basin (IGB), a regional aerosol hotspot where dust is a major aerosol species and has been observed to be non-spherical in shape, it is important to test the validity of this assumption. We address this issue using measured chemical composition at megacity Delhi, a representative site of the western IGB. Based on the observation, we choose three non-spherical shapes - spheroid, cylinder and chebyshev, and compute their optical properties. Non-spherical dust enhances aerosol extinction coefficient (β ext ) and single scattering albedo (SSA) at visible wavelengths by >0.05km -1 and >0.04 respectively, while it decreases asymmetry parameter (g) by ~0.1. Accounting non-sphericity leads top-of-the-atmosphere (TOA) dust DRF to more cooling due to enhanced backscattering and increases surface dimming due to enhanced β ext . Outgoing shortwave flux at TOA increases by up to 3.3% for composite aerosols with non-spherical dust externally mixed with other spherical species. Our results show that while non-sphericity needs to be accounted for, choice of shape may not be important in estimating aerosol DRF in the IGB. Copyright © 2017 Elsevier B.V. All rights reserved.

Scattering resonances of ultracold atoms in confined geometries

International Nuclear Information System (INIS)

Saeidian, Shahpoor

2008-01-01

Subject of this thesis is the investigation of the quantum dynamics of ultracold atoms in confined geometries. We discuss the behavior of ground state atoms inside a 3D magnetic quadrupole field. Such atoms in enough weak magnetic fields can be approximately treated as neutral point-like particles. Complementary to the well-known positive energy resonances, we point out the existence of short-lived negative energy resonances. The latter originate from a fundamental symmetry of the underlying Hamiltonian. We drive a mapping of the two branches of the spectrum. Moreover, we analyze atomic hyperfine resonances in a magnetic quadrupole field. This corresponds to the case for which both the hyperfine and Zeeman interaction, are comparable, and should be taken into account. Finally, we develop a general grid method for multichannel scattering of two atoms in a two-dimensional harmonic confinement. With our approach we analyze transverse excitations/deexcitations in the course of the collisional process (distinguishable or identical atoms) including all important partial waves and their couplings due to the broken spherical symmetry. Special attention is paid to suggest a non-trivial extension of the CIRs theory developed so far only for the single-mode regime and zero-energy limit. (orig.)

Scattering resonances of ultracold atoms in confined geometries

Energy Technology Data Exchange (ETDEWEB)

Saeidian, Shahpoor

2008-06-18

Subject of this thesis is the investigation of the quantum dynamics of ultracold atoms in confined geometries. We discuss the behavior of ground state atoms inside a 3D magnetic quadrupole field. Such atoms in enough weak magnetic fields can be approximately treated as neutral point-like particles. Complementary to the well-known positive energy resonances, we point out the existence of short-lived negative energy resonances. The latter originate from a fundamental symmetry of the underlying Hamiltonian. We drive a mapping of the two branches of the spectrum. Moreover, we analyze atomic hyperfine resonances in a magnetic quadrupole field. This corresponds to the case for which both the hyperfine and Zeeman interaction, are comparable, and should be taken into account. Finally, we develop a general grid method for multichannel scattering of two atoms in a two-dimensional harmonic confinement. With our approach we analyze transverse excitations/deexcitations in the course of the collisional process (distinguishable or identical atoms) including all important partial waves and their couplings due to the broken spherical symmetry. Special attention is paid to suggest a non-trivial extension of the CIRs theory developed so far only for the single-mode regime and zero-energy limit. (orig.)

The Spherical Deformation Model

DEFF Research Database (Denmark)

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 s...... a single central section of the object. We use maximum-likelihood-based inference for this purpose and demonstrate the suggested methods on real data....

Classical properties and semiclassical quantization of a spherical nuclear potential

International Nuclear Information System (INIS)

Carbonell, J.; Brut, F.; Arvieu, R.; Touchard, J.

1984-03-01

The geometrical properties of the classical energy-action surface are studied for a nuclear Woods-Saxon-like spherical potential, in connection with the E.B.K. semiclassical method of quantization. Comparisons are made with other well known cases: the spherical harmonic oscillator and the spherical billiard. The shift of single particle energies from A = 208 to A = 16 is calculated by a simple method inspired by the Erhenfest adiabatic invariants. Semiclassical results are then compared with exact Schroedinger energies. It is seen that the most significant features of the single particle spectrum are explained by local properties of the energy action surface (curvature, slope) and by their evolution with the particle number

National Spherical Torus Experiment (NSTX)

International Nuclear Information System (INIS)

Masayuki Ono

2000-01-01

The main aim of National Spherical Torus Experiment (NSTX) is to establish the fusion physics principles of the innovative spherical torus (ST) concept. Physics outcome of the NSTX research program is relevant to near-term applications such as the Volume Neutron Source (VNS) and burning plasmas, and future applications such as the pilot and power plants. The NSTX device began plasma operations in February 1999 and the plasma current was successfully ramped up to the design value of 1 million amperes (MA) on December 14, 1999. The CHI (Coaxial Helicity Injection) and HHFW (High Harmonic Fast Wave) experiments have also started. Stable CHI discharges of up to 133 kA and 130-msec duration have been produced using 20 kA of injected current. Using eight antennas connected to two transmitters, up to 2 MW of HHFW power was successfully coupled to the plasma. The Neutral-beam Injection (NBI) heating system and associated NBI-based diagnostics such as the Charge-exchange Recombination Spectrometer (CHERS) will be operational in October 2000

Spinorial Geometry and Branes

Energy Technology Data Exchange (ETDEWEB)

Sloane, Peter [Department of Mathematics, King' s College, University of London, Strand, London WC2R 2LS (United Kingdom)

2007-09-15

We adapt the spinorial geometry method introduced in [J. Gillard, U. Gran and G. Papadopoulos, 'The spinorial geometry of supersymmetric backgrounds,' Class. Quant. Grav. 22 (2005) 1033 [ (arXiv:hep-th/0410155)

Introduction to non-Euclidean geometry

CERN Document Server

Wolfe, Harold E

2012-01-01

One of the first college-level texts for elementary courses in non-Euclidean geometry, this concise, readable volume is geared toward students familiar with calculus. A full treatment of the historical background explores the centuries-long efforts to prove Euclid's parallel postulate and their triumphant conclusion. Numerous original exercises form an integral part of the book.Topics include hyperbolic plane geometry and hyperbolic plane trigonometry, applications of calculus to the solutions of some problems in hyperbolic geometry, elliptic plane geometry and trigonometry, and the consistenc

Analysis of Random-Loading HTR-PROTEUS Cores with Continuous Energy Monte Carlo Code Based on A Statistical Geometry Model

International Nuclear Information System (INIS)

Murata, Isao; Miyamaru, Hiroyuki

2008-01-01

Spherical elements have remarkable features in various applications in the nuclear engineering field. In 1990's, by the project of HTR-PROTEUS at PSI various pebble bed reactor experiments were conducted including cores with a lot of spherical fuel elements loaded randomly. In this study, criticality experiments of the random-loading HTR-PROTEUS cores were analyzed by MCNP-BALL, which could deal with a random arrangement of spherical fuel elements exactly with a statistical geometry model. As a result of analysis, the calculated effective multiplication factors were in fairly good agreement with the measurements within about 0.5%Δk/k. In comparison with other numerical analysis, our effective multiplication factors were between the experimental values and the VSOP calculations. To investigate the discrepancy of the effective multiplication factors between the experiments and calculations, sensitivity analyses were performed. As the result, the sensitivity of impurity boron concentration was fairly large. The reason of the present slight overestimation was not made clear at present. However, the presently existing difference was thought to be related to the impurity boron concentration, not to the modelling of the reactor and the used nuclear data. From the present study, it was confirmed that MCNP-BALL would have an advantage to conventional transport codes by comparing with their numerical results and the experimental values. As for the criticality experiment of PROTEUS, we would conclude that the two cores of Core 4.2 and 4.3 could be regarded as an equivalent experiment of a reference critical core, which was packed in the packing fraction of RLP. (authors)

Analysis of Random-Loading HTR-PROTEUS Cores with Continuous Energy Monte Carlo Code Based on A Statistical Geometry Model

Energy Technology Data Exchange (ETDEWEB)

Murata, Isao; Miyamaru, Hiroyuki [Division of Electrical, Electronic and Information Engineering, Osaka University, Yamada-oka 2-1, Suita, Osaka, 565-0871 (Japan)

2008-07-01

Spherical elements have remarkable features in various applications in the nuclear engineering field. In 1990's, by the project of HTR-PROTEUS at PSI various pebble bed reactor experiments were conducted including cores with a lot of spherical fuel elements loaded randomly. In this study, criticality experiments of the random-loading HTR-PROTEUS cores were analyzed by MCNP-BALL, which could deal with a random arrangement of spherical fuel elements exactly with a statistical geometry model. As a result of analysis, the calculated effective multiplication factors were in fairly good agreement with the measurements within about 0.5%DELTAk/k. In comparison with other numerical analysis, our effective multiplication factors were between the experimental values and the VSOP calculations. To investigate the discrepancy of the effective multiplication factors between the experiments and calculations, sensitivity analyses were performed. As the result, the sensitivity of impurity boron concentration was fairly large. The reason of the present slight overestimation was not made clear at present. However, the presently existing difference was thought to be related to the impurity boron concentration, not to the modelling of the reactor and the used nuclear data. From the present study, it was confirmed that MCNP-BALL would have an advantage to conventional transport codes by comparing with their numerical results and the experimental values. As for the criticality experiment of PROTEUS, we would conclude that the two cores of Core 4.2 and 4.3 could be regarded as an equivalent experiment of a reference critical core, which was packed in the packing fraction of RLP. (authors)

Effect of the geometry of confining media on the stability and folding rate of α -helix proteins

Science.gov (United States)

Wang, Congyue; Piroozan, Nariman; Javidpour, Leili; Sahimi, Muhammad

2018-05-01

Protein folding in confined media has attracted wide attention over the past 15 years due to its importance to both in vivo and in vitro applications. It is generally believed that protein stability increases by decreasing the size of the confining medium, if the medium's walls are repulsive, and that the maximum folding temperature in confinement is in a pore whose size D0 is only slightly larger than the smallest dimension of a protein's folded state. Until recently, the stability of proteins in pores with a size very close to that of the folded state has not received the attention it deserves. In a previous paper [L. Javidpour and M. Sahimi, J. Chem. Phys. 135, 125101 (2011)], we showed that, contrary to the current theoretical predictions, the maximum folding temperature occurs in larger pores for smaller α-helices. Moreover, in very tight pores, the free energy surface becomes rough, giving rise to a new barrier for protein folding close to the unfolded state. In contrast to unbounded domains, in small nanopores proteins with an α-helical native state that contain the β structures are entropically stabilized implying that folding rates decrease notably and that the free energy surface becomes rougher. In view of the potential significance of such results to interpretation of many sets of experimental data that could not be explained by the current theories, particularly the reported anomalously low rates of folding and the importance of entropic effects on proteins' misfolded states in highly confined environments, we address the following question in the present paper: To what extent the geometry of a confined medium affects the stability and folding rates of proteins? Using millisecond-long molecular dynamics simulations, we study the problem in three types of confining media, namely, cylindrical and slit pores and spherical cavities. Most importantly, we find that the prediction of the previous theories that the dependence of the maximum folding

Characterization of the plasma current quench during disruptions in the National Spherical Torus Experiment

International Nuclear Information System (INIS)

Gerhardt, S.P.; Menard, J.E.

2008-01-01

A detailed analysis of the plasma current quench in the National Spherical Torus Experiment (M.Ono, et al Nuclear Fusion 40, 557 (2000)) is presented. The fastest current quenches are fit better by a linear waveform than an exponential one. Area-normalized current quench times down to .4 msec/m2 have been observed, compared to the minimum of 1.7 msec/m2 recommendation based on conventional aspect ratio tokamaks; as noted in previous ITPA studies, the difference can be explained by the reduced self-inductance at low aspect ratio and high-elongation. The maximum instantaneous dIp/dt is often many times larger than the mean quench rate, and the plasma current before the disruption is often substantially less than the flat-top value. The poloidal field time-derivative during the disruption, which is directly responsible for driving eddy currents, has been recorded at various locations around the vessel. The Ip quench rate, plasma motion, and magnetic geometry all play important roles in determining the rate of poloidal field change

High-order perturbations of a spherical collapsing star

International Nuclear Information System (INIS)

Brizuela, David; Martin-Garcia, Jose M.; Sperhake, Ulrich; Kokkotas, Kostas D.

2010-01-01

A formalism to deal with high-order perturbations of a general spherical background was developed in earlier work [D. Brizuela, J. M. Martin-Garcia, and G. A. Mena Marugan, Phys. Rev. D 74, 044039 (2006); D. Brizuela, J. M. Martin-Garcia, and G. A. Mena Marugan, Phys. Rev. D 76, 024004 (2007)]. In this paper, we apply it to the particular case of a perfect fluid background. We have expressed the perturbations of the energy-momentum tensor at any order in terms of the perturbed fluid's pressure, density, and velocity. In general, these expressions are not linear and have sources depending on lower-order perturbations. For the second-order case we make the explicit decomposition of these sources in tensor spherical harmonics. Then, a general procedure is given to evolve the perturbative equations of motions of the perfect fluid for any value of the harmonic label. Finally, with the problem of a spherical collapsing star in mind, we discuss the high-order perturbative matching conditions across a timelike surface, in particular, the surface separating the perfect fluid interior from the exterior vacuum.

Synthesis of spherical LiMnPO4/C composite microparticles

International Nuclear Information System (INIS)

Bakenov, Zhumabay; Taniguchi, Izumi

2011-01-01

Highlights: → We could prepare LiMnPO 4 /C composites by a novel preparation method. → The LiMnPO 4 /C composites were spherical particles with a mean diameter of 3.65 μm. → The LiMnPO 4 /C composite cathode exhibited 112 mAh g -1 at 0.05 C. → It also showed a good rate capability up to 5 C at room temperature and 55 o C. -- Abstract: Spherical LiMnPO 4 /C composite microparticles were prepared by a combination of spray pyrolysis and spray drying followed by heat treatment and examined as a cathode material for lithium batteries. The structure, morphology and electrochemical performance of the resulting spherical LiMnPO 4 /C microparticles were characterized by X-ray diffraction, field-emission scanning electron microscopy, transmission electronic microscopy and standard electrochemical techniques. The final sample was identified as a single phase orthorhombic structure of LiMnPO 4 and spherical powders with a geometric mean diameter of 3.65 μm and a geometric standard deviation of 1.34. The electrochemical cells contained the spherical LiMnPO 4 /C microparticles exhibited first discharge capacities of 112 and 130 mAh g -1 at 0.05 C at room temperature and 55 o C, respectively. These also showed a good rate capability up to 5 C at room temperature and 55 o C.

Convection in Slab and Spheroidal Geometries

Science.gov (United States)

Porter, David H.; Woodward, Paul R.; Jacobs, Michael L.

2000-01-01

Three-dimensional numerical simulations of compressible turbulent thermally driven convection, in both slab and spheroidal geometries, are reviewed and analyzed in terms of velocity spectra and mixing-length theory. The same ideal gas model is used in both geometries, and resulting flows are compared. The piecewise-parabolic method (PPM), with either thermal conductivity or photospheric boundary conditions, is used to solve the fluid equations of motion. Fluid motions in both geometries exhibit a Kolmogorov-like k(sup -5/3) range in their velocity spectra. The longest wavelength modes are energetically dominant in both geometries, typically leading to one convection cell dominating the flow. In spheroidal geometry, a dipolar flow dominates the largest scale convective motions. Downflows are intensely turbulent and up drafts are relatively laminar in both geometries. In slab geometry, correlations between temperature and velocity fluctuations, which lead to the enthalpy flux, are fairly independent of depth. In spheroidal geometry this same correlation increases linearly with radius over the inner 70 percent by radius, in which the local pressure scale heights are a sizable fraction of the radius. The effects from the impenetrable boundary conditions in the slab geometry models are confused with the effects from non-local convection. In spheroidal geometry nonlocal effects, due to coherent plumes, are seen as far as several pressure scale heights from the lower boundary and are clearly distinguishable from boundary effects.

Complex and symplectic geometry

CERN Document Server

Medori, Costantino; Tomassini, Adriano

2017-01-01

This book arises from the INdAM Meeting "Complex and Symplectic Geometry", which was held in Cortona in June 2016. Several leading specialists, including young researchers, in the field of complex and symplectic geometry, present the state of the art of their research on topics such as the cohomology of complex manifolds; analytic techniques in Kähler and non-Kähler geometry; almost-complex and symplectic structures; special structures on complex manifolds; and deformations of complex objects. The work is intended for researchers in these areas.

Initiation to global Finslerian geometry

CERN Document Server

Akbar-Zadeh, Hassan

2006-01-01

After a brief description of the evolution of thinking on Finslerian geometry starting from Riemann, Finsler, Berwald and Elie Cartan, the book gives a clear and precise treatment of this geometry. The first three chapters develop the basic notions and methods, introduced by the author, to reach the global problems in Finslerian Geometry. The next five chapters are independent of each other, and deal with among others the geometry of generalized Einstein manifolds, the classification of Finslerian manifolds of constant sectional curvatures. They also give a treatment of isometric, affine, p

Algebraic geometry in India

Indian Academy of Sciences (India)

algebraic geometry but also in related fields like number theory. ... every vector bundle on the affine space is trivial. (equivalently ... les on a compact Riemann surface to unitary rep- ... tial geometry and topology and was generalised in.

Generalizing optical geometry

International Nuclear Information System (INIS)

Jonsson, Rickard; Westman, Hans

2006-01-01

We show that by employing the standard projected curvature as a measure of spatial curvature, we can make a certain generalization of optical geometry (Abramowicz M A and Lasota J-P 1997 Class. Quantum Grav. A 14 23-30). This generalization applies to any spacetime that admits a hypersurface orthogonal shearfree congruence of worldlines. This is a somewhat larger class of spacetimes than the conformally static spacetimes assumed in standard optical geometry. In the generalized optical geometry, which in the generic case is time dependent, photons move with unit speed along spatial geodesics and the sideways force experienced by a particle following a spatially straight line is independent of the velocity. Also gyroscopes moving along spatial geodesics do not precess (relative to the forward direction). Gyroscopes that follow a curved spatial trajectory precess according to a very simple law of three-rotation. We also present an inertial force formalism in coordinate representation for this generalization. Furthermore, we show that by employing a new sense of spatial curvature (Jonsson R 2006 Class. Quantum Grav. 23 1)) closely connected to Fermat's principle, we can make a more extensive generalization of optical geometry that applies to arbitrary spacetimes. In general this optical geometry will be time dependent, but still geodesic photons move with unit speed and follow lines that are spatially straight in the new sense. Also, the sideways experienced (comoving) force on a test particle following a line that is straight in the new sense will be independent of the velocity

First Octahedral Spherical Hohlraum Energetics Experiment at the SGIII Laser Facility

Science.gov (United States)

Huo, Wen Yi; Li, Zhichao; Chen, Yao-Hua; Xie, Xufei; Ren, Guoli; Cao, Hui; Li, Shu; Lan, Ke; Liu, Jie; Li, Yongsheng; Li, Sanwei; Guo, Liang; Liu, Yonggang; Yang, Dong; Jiang, Xiaohua; Hou, Lifei; Du, Huabing; Peng, Xiaoshi; Xu, Tao; Li, Chaoguang; Zhan, Xiayu; Wang, Zhebin; Deng, Keli; Wang, Qiangqiang; Deng, Bo; Wang, Feng; Yang, Jiamin; Liu, Shenye; Jiang, Shaoen; Yuan, Guanghui; Zhang, Haijun; Jiang, Baibin; Zhang, Wei; Gu, Qianqian; He, Zhibing; Du, Kai; Deng, Xuewei; Zhou, Wei; Wang, Liquan; Huang, Xiaoxia; Wang, Yuancheng; Hu, Dongxia; Zheng, Kuixing; Zhu, Qihua; Ding, Yongkun

2018-04-01

The first octahedral spherical hohlraum energetics experiment is accomplished at the SGIII laser facility. For the first time, the 32 laser beams are injected into the octahedral spherical hohlraum through six laser entrance holes. Two techniques are used to diagnose the radiation field of the octahedral spherical hohlraum in order to obtain comprehensive experimental data. The radiation flux streaming out of laser entrance holes is measured by six flat-response x-ray detectors (FXRDs) and four M -band x-ray detectors, which are placed at different locations of the SGIII target chamber. The radiation temperature is derived from the measured flux of FXRD by using the blackbody assumption. The peak radiation temperature inside hohlraum is determined by the shock wave technique. The experimental results show that the octahedral spherical hohlraum radiation temperature is in the range of 170-182 eV with drive laser energies of 71 kJ to 84 kJ. The radiation temperature inside the hohlraum determined by the shock wave technique is about 175 eV at 71 kJ. For the flat-top laser pulse of 3 ns, the conversion efficiency of gas-filled octahedral spherical hohlraum from laser into soft x rays is about 80% according to the two-dimensional numerical simulation.

Hyper-spherical harmonics and anharmonics in m-dimensional space

International Nuclear Information System (INIS)

Shojaei, M.R.; Rajabi, A.A.; Hasanabadi, H.

2008-01-01

In quantum mechanics the hyper-spherical method is one of the most well-established and successful computational tools. The general theory of harmonic polynomials and hyper-spherical harmonics is of central importance in this paper. The interaction potential V is assumed to depend on the hyper-radius ρ only where ρ is the function of the Jacobi relative coordinate x 1 , x 2 ,…, x n which are functions of the particles' relative positions. (author)

Introduction to combinatorial geometry

International Nuclear Information System (INIS)

Gabriel, T.A.; Emmett, M.B.

1985-01-01

The combinatorial geometry package as used in many three-dimensional multimedia Monte Carlo radiation transport codes, such as HETC, MORSE, and EGS, is becoming the preferred way to describe simple and complicated systems. Just about any system can be modeled using the package with relatively few input statements. This can be contrasted against the older style geometry packages in which the required input statements could be large even for relatively simple systems. However, with advancements come some difficulties. The users of combinatorial geometry must be able to visualize more, and, in some instances, all of the system at a time. Errors can be introduced into the modeling which, though slight, and at times hard to detect, can have devastating effects on the calculated results. As with all modeling packages, the best way to learn the combinatorial geometry is to use it, first on a simple system then on more complicated systems. The basic technique for the description of the geometry consists of defining the location and shape of the various zones in terms of the intersections and unions of geometric bodies. The geometric bodies which are generally included in most combinatorial geometry packages are: (1) box, (2) right parallelepiped, (3) sphere, (4) right circular cylinder, (5) right elliptic cylinder, (6) ellipsoid, (7) truncated right cone, (8) right angle wedge, and (9) arbitrary polyhedron. The data necessary to describe each of these bodies are given. As can be easily noted, there are some subsets included for simplicity

Application of identifying transmission spheres for spherical surface testing

Science.gov (United States)

Han, Christopher B.; Ye, Xin; Li, Xueyuan; Wang, Quanzhao; Tang, Shouhong; Han, Sen

2017-06-01

We developed a new application on Microsoft Foundation Classes (MFC) to identify correct transmission spheres (TS) for Spherical Surface Testing (SST). Spherical surfaces are important optical surfaces, and the wide application and high production rate of spherical surfaces necessitates an accurate and highly reliable measuring device. A Fizeau Interferometer is an appropriate tool for SST due to its subnanometer accuracy. It measures the contour of a spherical surface using a common path, which is insensitive to the surrounding circumstances. The Fizeau Interferometer transmits a wide laser beam, creating interference fringes from re-converging light from the transmission sphere and the test surface. To make a successful measurement, the application calculates and determines the appropriate transmission sphere for the test surface. There are 3 main inputs from the test surfaces that are utilized to determine the optimal sizes and F-numbers of the transmission spheres: (1) the curvatures (concave or convex), (2) the Radii of Curvature (ROC), and (3) the aperture sizes. The application will firstly calculate the F-numbers (i.e. ROC divided by aperture) of the test surface, secondly determine the correct aperture size of a convex surface, thirdly verify that the ROC of the test surface must be shorter than the reference surface's ROC of the transmission sphere, and lastly calculate the percentage of area that the test surface will be measured. However, the amount of interferometers and transmission spheres should be optimized when measuring large spherical surfaces to avoid requiring a large amount of interferometers and transmission spheres for each test surface. Current measuring practices involve tedious and potentially inaccurate calculations. This smart application eliminates human calculation errors, optimizes the selection of transmission spheres (including the least number required) and interferometer sizes, and increases efficiency.

Neutron production in a spherical phantom aboard ISS

International Nuclear Information System (INIS)

Tasbaz, A.; Machrafi, R.

2012-01-01

As part of an ongoing research program on radiation monitoring on International Space Station (ISS) that was established to analyze the radiation exposure levels onboard the ISS using different radiation instruments and a spherical phantom to simulate human body. Monte Carlo transport code was used to simulate the interaction of high energy protons and neutrons with the spherical phantom currently onboard ISS. The phantom has been exposed to individual proton energies and to a spectrum of neutrons. The internal to external neutron flux ratio was calculated and compared to the experimental data, recently, measured on the ISS. (author)

Calculations of the possible consequences of molten fuel sodium interactions in subassembly and whole core geometries

International Nuclear Information System (INIS)

Coddington, P.; Fishlock, T.P.; Jakeman, D.

1976-01-01

The possible consequences of molten fuel sodium interactions are calculated using various modelling assumptions and key parameters. And the significance of the choice of assumptions and parameters are discussed. As for subassembly geometry, the results of one-dimensional code EXPEL are compared with the solutions of the one-dimensional Lagrangian equations of a compressible fluid (TOPAL was used). The adequacy of acoustic approximation used in EXPEL is discussed here. The effects of heat transfer time constant on the behaviour of peak pressure are also analyzed by parametric surveys. Other items investigated are the length and position of the interacting zone, the existence of a non-condensable gas volume, and the vapour condensation on cold clad. As for whole core geometry, a simple dynamical model of arc expanding spherical interacting zone immersed in a semi-infinite sea of cold liquid was used (SHORE code). Within the interacting zone a simple heat transfer model (including a heat transfer time and a fragmentation time) was adopted. Vapour blanketing was considered in a number of ways. Representative results of the calculations are given in a table. Containment studies were also performed for ''ducted'' design and ''open pool'' design. The development of new codes in the U.K. for these analysis are also briefly described. (Aoki, K.)

Mechanisms of Stochastic Diffusion of Energetic Ions in Spherical Tori

Energy Technology Data Exchange (ETDEWEB)

Ya.I. Kolesnichenko; R.B. White; Yu.V. Yakovenko

2001-01-18

Stochastic diffusion of the energetic ions in spherical tori is considered. The following issues are addressed: (I) Goldston-White-Boozer diffusion in a rippled field; (ii) cyclotron-resonance-induced diffusion caused by the ripple; (iii) effects of non-conservation of the magnetic moment in an axisymmetric field. It is found that the stochastic diffusion in spherical tori with a weak magnetic field has a number of peculiarities in comparison with conventional tokamaks; in particular, it is characterized by an increased role of mechanisms associated with non-conservation of the particle magnetic moment. It is concluded that in current experiments on National Spherical Torus eXperiment (NSTX) the stochastic diffusion does not have a considerable influence on the confinement of energetic ions.

Spherical Projection Based Straight Line Segment Extraction for Single Station Terrestrial Laser Point Cloud

Directory of Open Access Journals (Sweden)

ZHANG Fan

2015-06-01

Full Text Available Due to the discrete distribution computing errors and lack of adaptability are ubiquitous in the current straight line extraction for TLS data methods. A 3D straight line segment extraction method is proposed based on spherical projection for single station terrestrial laser point clouds. Firstly, horizontal and vertical angles of each laser point are calculated by means of spherical coordinates, intensity panoramic image according to the two angles is generated. Secondly, edges which include straight line features are detected from intensity panoramic image by using of edge detection algorithm. Thirdly, great circles are detected from edges of panoramic image using spherical Hough transform. According to the axiom that a straight line segment in 3D space is a spherical great circle after spherical projection, detecting great circles from spherical projected data sets is essentially detecting straight line segments from 3D data sets without spherical projection. Finally, a robust 3D straight line fitting method is employed to fitting the straight lines and calculating parameters of the straight line segments. Experiments using different data sets and comparison with other methods show the accuracy and applicability of the proposed method.

Influence of atmospheric turbulence on the energy focusability of Gaussian beams with spherical aberration

International Nuclear Information System (INIS)

Deng, Jinping; Ji, Xiaoling

2014-01-01

By using the four-dimensional (4D) computer code of the time-dependent propagation of laser beams through atmospheric turbulence, the influence of atmospheric turbulence on the energy focusability of Gaussian beams with spherical aberration is studied in detail, where the mean-squared beam width, the power in the bucket (PIB), the β parameter and the energy Strehl ratio are taken as the characteristic parameters. It is shown that turbulence results in beam spreading, and the effect of spherical aberration on the beam spreading decreases due to turbulence. Gaussian beams with negative spherical aberration are more affected by turbulence than those with positive spherical aberration. For the negative spherical aberration case, the focus position moves to the source plane due to turbulence. It is mentioned that the influence of turbulence on the energy focusability defined by a certain energy (i.e. PIB = 63%) is very heavy when the negative spherical aberration is very heavy. On the other hand, the influence of turbulence on the energy focusability defined by the energy within a given bucket radius (i.e. mean-squared beam width) is heaviest when a certain negative spherical aberration coefficient is adopted. (papers)

Graded geometry and Poisson reduction

OpenAIRE

Cattaneo, A S; Zambon, M

2009-01-01

The main result of [2] extends the Marsden-Ratiu reduction theorem [4] in Poisson geometry, and is proven by means of graded geometry. In this note we provide the background material about graded geometry necessary for the proof in [2]. Further, we provide an alternative algebraic proof for the main result. ©2009 American Institute of Physics

Comparative dynamics analysis on xonotlite spherical particles synthesized via hydrothermal synthesis

Science.gov (United States)

Liu, F.; Chen, S.; Lin, Q.; Wang, X. D.; Cao, J. X.

2018-01-01

The xonotlite crystals were synthesized via the hydrothermal synthesis manner from CaO and SiO2 as the raw materials with their Si/Ca molar ratio of 1.0. Comparative dynamics analysis on xonotlite spherical particles synthesized via hydrothermal synthesis process was explored in this paper. The accuracy of the dynamic equation of xonotlite spherical particles was verified by two methods, one was comparing the production rate of the xonotlite products calculated by the dynamic equation with the experimental values, and the other was comparing the apparent activation energies calculated by the dynamic equation with that calculated by the Kondo model. The results indicated that the production rates of the xonotlite spherical particles calculated by the dynamic equation were in good agreement with the experimental values and the apparent activation energy of the xonotlite spherical particles calculated by dynamic equation (84 kJ·mol-1) was close to that calculated by Kondo model (77 kJ·mol-1), verifying the high accuracy of the dynamic equation.

Simulation Analysis of Spherical Mechanical Seal Property of Marine Stern Shaft

Directory of Open Access Journals (Sweden)

Zhou Xu Hui

2016-01-01

Full Text Available The finite element model of spherical mechanical seal wasestablished with ANSYS, and the influence of seawater pressure, shaft speed and other factors on the sealing performance was discussed. The study results show that local contact situation of the spherical mechanical seal is in the outside of the seal rings, and both maximum contact pressure and temperature appearat the same position. As sea water pressure and stern shaft rotary speed are increased, the contact pressure and temperature of the spherical seal surface are raised, and when the contact pressure of seal surface is 0, the spherical seal surface forms two zones including contact one and clearance zone. The former is near the outside of the seal ring, the lateris close to the inside of one. These research results are of important theoretical significance and engineering application value for the development of new kinds of mechanical seals, and improvement of both safety and survivability of underwater vehicles.

Geometry of multihadron production

Energy Technology Data Exchange (ETDEWEB)

Bjorken, J.D.

1994-10-01

This summary talk only reviews a small sample of topics featured at this symposium: Introduction; The Geometry and Geography of Phase space; Space-Time Geometry and HBT; Multiplicities, Intermittency, Correlations; Disoriented Chiral Condensate; Deep Inelastic Scattering at HERA; and Other Contributions.

Geometry of multihadron production

International Nuclear Information System (INIS)

Bjorken, J.D.

1994-10-01

This summary talk only reviews a small sample of topics featured at this symposium: Introduction; The Geometry and Geography of Phase space; Space-Time Geometry and HBT; Multiplicities, Intermittency, Correlations; Disoriented Chiral Condensate; Deep Inelastic Scattering at HERA; and Other Contributions

Geometry of higher-dimensional black hole thermodynamics

International Nuclear Information System (INIS)

Aaman, Jan E.; Pidokrajt, Narit

2006-01-01

We investigate thermodynamic curvatures of the Kerr and Reissner-Nordstroem (RN) black holes in spacetime dimensions higher than four. These black holes possess thermodynamic geometries similar to those in four-dimensional spacetime. The thermodynamic geometries are the Ruppeiner geometry and the conformally related Weinhold geometry. The Ruppeiner geometry for a d=5 Kerr black hole is curved and divergent in the extremal limit. For a d≥6 Kerr black hole there is no extremality but the Ruppeiner curvature diverges where one suspects that the black hole becomes unstable. The Weinhold geometry of the Kerr black hole in arbitrary dimension is a flat geometry. For the RN black hole the Ruppeiner geometry is flat in all spacetime dimensions, whereas its Weinhold geometry is curved. In d≥5 the Kerr black hole can possess more than one angular momentum. Finally we discuss the Ruppeiner geometry for the Kerr black hole in d=5 with double angular momenta

Novel spherical hohlraum with cylindrical laser entrance holes and shields

Energy Technology Data Exchange (ETDEWEB)

Lan, Ke [Institute of Applied Physics and Computational Mathematics, Beijing 100088 (China); Center for Applied Physics and Technology, Peking University, Beijing 100871 (China); Zheng, Wudi [Institute of Applied Physics and Computational Mathematics, Beijing 100088 (China)

2014-09-15

Our recent works [K. Lan et al., Phys. Plasmas 21, 010704 (2014); K. Lan et al., Phys. Plasmas 21, 052704 (2014)] have shown that the octahedral spherical hohlraums are superior to the cylindrical hohlraums in both higher symmetry during the capsule implosion and lower backscatter without supplementary technology. However, both the coupling efficiency from the drive laser energy to the capsule and the capsule symmetry decrease remarkably when larger laser entrance holes (LEHs) are used. In addition, the laser beams injected at angles > 45° transport close to the hohlraum wall, thus the wall blowoff causes the LEH to close faster and results in strong laser plasma interactions inside the spherical hohlraums. In this letter, we propose a novel octahedral hohlraum with LEH shields and cylindrical LEHs to alleviate these problems. From our theoretical study, with the LEH shields, the laser coupling efficiency is significantly increased and the capsule symmetry is remarkably improved in the spherical hohlraums. The cylindrical LEHs take advantage of the cylindrical hohlraum near the LEH and mitigate the influence of the blowoff on laser transport inside a spherical hohlraum. The cylindrical LEHs can also be applied to the rugby and elliptical hohlraums.

Novel spherical hohlraum with cylindrical laser entrance holes and shields

International Nuclear Information System (INIS)

Lan, Ke; Zheng, Wudi

2014-01-01

Our recent works [K. Lan et al., Phys. Plasmas 21, 010704 (2014); K. Lan et al., Phys. Plasmas 21, 052704 (2014)] have shown that the octahedral spherical hohlraums are superior to the cylindrical hohlraums in both higher symmetry during the capsule implosion and lower backscatter without supplementary technology. However, both the coupling efficiency from the drive laser energy to the capsule and the capsule symmetry decrease remarkably when larger laser entrance holes (LEHs) are used. In addition, the laser beams injected at angles > 45° transport close to the hohlraum wall, thus the wall blowoff causes the LEH to close faster and results in strong laser plasma interactions inside the spherical hohlraums. In this letter, we propose a novel octahedral hohlraum with LEH shields and cylindrical LEHs to alleviate these problems. From our theoretical study, with the LEH shields, the laser coupling efficiency is significantly increased and the capsule symmetry is remarkably improved in the spherical hohlraums. The cylindrical LEHs take advantage of the cylindrical hohlraum near the LEH and mitigate the influence of the blowoff on laser transport inside a spherical hohlraum. The cylindrical LEHs can also be applied to the rugby and elliptical hohlraums

The impact of the form of the Euler equations for radial flow in cylindrical and spherical coordinates on numerical conservation and accuracy

Science.gov (United States)

Crittenden, P. E.; Balachandar, S.

2018-03-01

The radial one-dimensional Euler equations are often rewritten in what is known as the geometric source form. The differential operator is identical to the Cartesian case, but source terms result. Since the theory and numerical methods for the Cartesian case are well-developed, they are often applied without modification to cylindrical and spherical geometries. However, numerical conservation is lost. In this article, AUSM^+ -up is applied to a numerically conservative (discrete) form of the Euler equations labeled the geometric form, a nearly conservative variation termed the geometric flux form, and the geometric source form. The resulting numerical methods are compared analytically and numerically through three types of test problems: subsonic, smooth, steady-state solutions, Sedov's similarity solution for point or line-source explosions, and shock tube problems. Numerical conservation is analyzed for all three forms in both spherical and cylindrical coordinates. All three forms result in constant enthalpy for steady flows. The spatial truncation errors have essentially the same order of convergence, but the rate constants are superior for the geometric and geometric flux forms for the steady-state solutions. Only the geometric form produces the correct shock location for Sedov's solution, and a direct connection between the errors in the shock locations and energy conservation is found. The shock tube problems are evaluated with respect to feature location using an approximation with a very fine discretization as the benchmark. Extensions to second order appropriate for cylindrical and spherical coordinates are also presented and analyzed numerically. Conclusions are drawn, and recommendations are made. A derivation of the steady-state solution is given in the Appendix.

Current drive experiments on the HIT-II spherical torus

International Nuclear Information System (INIS)

Jarboe, T.R.; Raman, R.; Nelson, B.A.; Holcomb, C.T.; McCollam, K.J.; Sieck, P.E.

1999-01-01

This paper describes the following new achievements from the Helicity Injected Torus (HIT) program: a) formation and sustainment of a toroidal magnetic equilibrium using coaxial helicity injection (CHI) in a conducting shell that has an L/R time much shorter than the pulse length; b) static formation of a spherical torus with plasma current over 180 kA using a transformer and feedback controlled equilibrium coils; and c) production of a current increase in a transformer produced spherical torus using CHI. (author)

Current drive experiments on the HIT-II spherical torus

International Nuclear Information System (INIS)

Jarboe, T.; Raman, R.; Nelson, B.; Holcomb, C.T.; McCollam, K.J.; Sieck, P.E.

2001-01-01

This paper describes the following new achievements from the Helicity Injected Torus (HIT) program: a) formation and sustainment of a toroidal magnetic equilibrium using coaxial helicity injection (CHI) in a conducting shell that has an L/R time much shorter than the pulse length; b) static formation of a spherical torus with plasma current over 180 kA using a transformer and feedback controlled equilibrium coils; and c) production of a current increase in a transformer produced spherical torus using CHI. (author)

Positivity of the spherically averaged atomic one-electron density

DEFF Research Database (Denmark)

Fournais, Søren; Hoffmann-Ostenhof, Maria; Hoffmann-Ostenhof, Thomas

2008-01-01

We investigate the positivity of the spherically averaged atomic one-electron density . For a which stems from a physical ground state we prove that for r ≥  0. This article may be reproduced in its entirety for non-commercial purposes.......We investigate the positivity of the spherically averaged atomic one-electron density . For a which stems from a physical ground state we prove that for r ≥  0. This article may be reproduced in its entirety for non-commercial purposes....

Minimum Q Electrically Small Spherical Magnetic Dipole Antenna - Theory

DEFF Research Database (Denmark)

Breinbjerg, Olav; Kim, Oleksiy S.

2009-01-01

The stored energies, radiated power, and quality factor of a magnetic-dipole antenna, consisting of a spherical electrical surface current density enclosing a magnetic core, is obtained through direct spatial integration of the internally and externally radiated field expressed in terms...... of spherical vector waves. The obtained quality factor agrees with that of Wheeler and Thal for vanishing free-space electric radius but holds also for larger radii and facilitates the optimal choice of permeability in the presence of the resonances....

Lectures on Symplectic Geometry

CERN Document Server

Silva, Ana Cannas

2001-01-01

The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and cl...

Spherical grating spectrometers

Science.gov (United States)

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.

Relative Pose Estimation and Accuracy Verification of Spherical Panoramic Image

Directory of Open Access Journals (Sweden)

XIE Donghai

2017-11-01

Full Text Available This paper improves the method of the traditional 5-point relative pose estimation algorithm, and proposes a relative pose estimation algorithm which is suitable for spherical panoramic images. The algorithm firstly computes the essential matrix, then decomposes the essential matrix to obtain the rotation matrix and the translation vector using SVD, and finally the reconstructed three-dimensional points are used to eliminate the error solution. The innovation of the algorithm lies the derivation of panorama epipolar formula and the use of the spherical distance from the point to the epipolar plane as the error term for the spherical panorama co-planarity function. The simulation experiment shows that when the random noise of the image feature points is within the range of pixel, the error of the three Euler angles is about 0.1°, and the error between the relative translational displacement and the simulated value is about 1.5°. The result of the experiment using the data obtained by the vehicle panorama camera and the POS shows that:the error of the roll angle and pitch angle can be within 0.2°, the error of the heading angle can be within 0.4°, and the error between the relative translational displacement and the POS can be within 2°. The result of our relative pose estimation algorithm is used to generate the spherical panoramic epipolar images, then we extract the key points between the spherical panoramic images and calculate the errors in the column direction. The result shows that the errors is less than 1 pixel.

Water hammer caused by closure of turbine safety spherical valves

Science.gov (United States)

Karadžić, U.; Bergant, A.; Vukoslavčević, P.

2010-08-01

This paper investigates water hammer effects caused by closure of spherical valves against the discharge. During the first phase of modernisation of Perućica high-head hydropower plant (HPP), Montenegro, safety spherical valves (inlet turbine valves) have been refurbished on the first two Pelton turbine units. The valve closure is controlled by the valve actuator (hydraulic servomotor). Because the torque acting on the valve body is dependent on flow conditions the valve closing time may vary significantly for different flow velocities (passive valve). For the passive valve the torques acting on the valve body should be considered in the valve model. The valve closing time results from numerical simulation. On the contrary, for the active valve the valve closing time is assumed prior to simulation. The spherical valve boundary condition is incorporated into the method of characteristics (MOC) algorithm. The staggered (diamond) grid in applying the MOC is used in this paper. The passive valve boundary condition is described by the water hammer equations, the valve equation that relates discharge to pressure head drop and the dynamic equation of the valve body motion (torque equation). The active valve boundary condition is described by the first two equations, respectively. Standard quasi-steady friction model is used for estimating friction losses in plant's tunnel and penstocks. Numerical results using both the active and the passive spherical valve models are compared with results of measurements. It has been found that the influence of flow conditions on the spherical valve closing time is minor for the cases considered. Computed and measured results agree reasonably well.

Water hammer caused by closure of turbine safety spherical valves

International Nuclear Information System (INIS)

Karadzic, U; Vukoslavcevic, P; Bergant, A

2010-01-01

This paper investigates water hammer effects caused by closure of spherical valves against the discharge. During the first phase of modernisation of Perucica high-head hydropower plant (HPP), Montenegro, safety spherical valves (inlet turbine valves) have been refurbished on the first two Pelton turbine units. The valve closure is controlled by the valve actuator (hydraulic servomotor). Because the torque acting on the valve body is dependent on flow conditions the valve closing time may vary significantly for different flow velocities (passive valve). For the passive valve the torques acting on the valve body should be considered in the valve model. The valve closing time results from numerical simulation. On the contrary, for the active valve the valve closing time is assumed prior to simulation. The spherical valve boundary condition is incorporated into the method of characteristics (MOC) algorithm. The staggered (diamond) grid in applying the MOC is used in this paper. The passive valve boundary condition is described by the water hammer equations, the valve equation that relates discharge to pressure head drop and the dynamic equation of the valve body motion (torque equation). The active valve boundary condition is described by the first two equations, respectively. Standard quasi-steady friction model is used for estimating friction losses in plant's tunnel and penstocks. Numerical results using both the active and the passive spherical valve models are compared with results of measurements. It has been found that the influence of flow conditions on the spherical valve closing time is minor for the cases considered. Computed and measured results agree reasonably well.

Water hammer caused by closure of turbine safety spherical valves

Energy Technology Data Exchange (ETDEWEB)

Karadzic, U; Vukoslavcevic, P [Faculty of Mechanical Engineering, University of Montenegro Dzordza Vasingtona nn, Podgorica, 81000 (Montenegro); Bergant, A, E-mail: uros.karadzic@ac.m [LitostrojPower d.o.o., Litostrojska 50, Ljubljana, 1000 (Slovenia)

2010-08-15

This paper investigates water hammer effects caused by closure of spherical valves against the discharge. During the first phase of modernisation of Perucica high-head hydropower plant (HPP), Montenegro, safety spherical valves (inlet turbine valves) have been refurbished on the first two Pelton turbine units. The valve closure is controlled by the valve actuator (hydraulic servomotor). Because the torque acting on the valve body is dependent on flow conditions the valve closing time may vary significantly for different flow velocities (passive valve). For the passive valve the torques acting on the valve body should be considered in the valve model. The valve closing time results from numerical simulation. On the contrary, for the active valve the valve closing time is assumed prior to simulation. The spherical valve boundary condition is incorporated into the method of characteristics (MOC) algorithm. The staggered (diamond) grid in applying the MOC is used in this paper. The passive valve boundary condition is described by the water hammer equations, the valve equation that relates discharge to pressure head drop and the dynamic equation of the valve body motion (torque equation). The active valve boundary condition is described by the first two equations, respectively. Standard quasi-steady friction model is used for estimating friction losses in plant's tunnel and penstocks. Numerical results using both the active and the passive spherical valve models are compared with results of measurements. It has been found that the influence of flow conditions on the spherical valve closing time is minor for the cases considered. Computed and measured results agree reasonably well.

Fabrication and electromechanical examination of a spherical dielectric elastomer actuator

International Nuclear Information System (INIS)

Ahmadi, S; Gooyers, M; Soleimani, M; Menon, C

2013-01-01

In this paper, a procedure for fabricating and testing a seamless spherical dielectric elastomer actuator (DEA) is presented. In previously developed spherical prototypes, the DEA material is pre-strained by a rigid frame to improve the actuator’s output force; however, it is possible to pre-strain a spherical DEA by inflating the sample with a liquid or gas as long as the sample contains the pressure. In this work, a very compliant silicone-based material was used to fabricate a nearly spherical balloon-shaped prototype. The DEA sample was inflated by air and various electrical-actuation regimes were considered. The performance of the DEA sample was studied using an analytical and a finite element-based model. An Ogden hyperelastic model was used in formulation of the analytical model to include nonlinear behavior of the silicone material. Full statistical analysis of the experimental and numerical results was carried out using the root-mean-square (RMS) error and the normalized RMS error. The analytical and FEM results were in good agreement with the experimental data. According to modeling results, it was found that the DEA’s actuation force can be mainly improved by increasing the voltage, reducing the thickness, lowering the stiffness, and/or increasing the initial pressure. As an example, a three-fold increase of the actuation force was found when the thickness was reduced to half of its initial value. This improvement of the efficiency suggests that the spherical DEA is suitable for use in several applications if an appropriate design with optimal governing parameters is developed. (paper)

Double phi-Step theta-Scanning Technique for Spherical Near-Field Antenna Measurements

DEFF Research Database (Denmark)

Laitinen, Tommi

2008-01-01

Probe-corrected spherical near-field antenna measurements with an arbitrary probe set certain requirements on an applicable scanning technique. The computational complexity of the general high-order probe correction technique for an arbitrary probe, that is based on the Phi scanning, is O(N4...... a specific double Phi-step thetas scanning technique for spherical near-field antenna measurements. This technique not only constitutes an alternative spherical scanning technique, but it also enables formulating an associated probe correction technique for arbitrary probes with the computational complexity...

Market response to external events and interventions in spherical minority games

International Nuclear Information System (INIS)

Papadopoulos, P; Coolen, A C C

2008-01-01

We solve the dynamics of large spherical minority games (MG) in the presence of non-negligible time-dependent external contributions to the overall market bid. The latter represent the actions of market regulators or other major natural or political events that impact on the market. In contrast to non-spherical MGs, the spherical formulation allows one to derive closed dynamical order parameter equations in an explicit form and work out the market's response to such events fully analytically. We focus on a comparison between the response to stationary versus oscillating market interventions, and reveal profound and partially unexpected differences in terms of transition lines and the volatility

Complex differential geometry

CERN Document Server

Zheng, Fangyang

2002-01-01

The theory of complex manifolds overlaps with several branches of mathematics, including differential geometry, algebraic geometry, several complex variables, global analysis, topology, algebraic number theory, and mathematical physics. Complex manifolds provide a rich class of geometric objects, for example the (common) zero locus of any generic set of complex polynomials is always a complex manifold. Yet complex manifolds behave differently than generic smooth manifolds; they are more coherent and fragile. The rich yet restrictive character of complex manifolds makes them a special and interesting object of study. This book is a self-contained graduate textbook that discusses the differential geometric aspects of complex manifolds. The first part contains standard materials from general topology, differentiable manifolds, and basic Riemannian geometry. The second part discusses complex manifolds and analytic varieties, sheaves and holomorphic vector bundles, and gives a brief account of the surface classifi...

Computational synthetic geometry

CERN Document Server

Bokowski, Jürgen

1989-01-01

Computational synthetic geometry deals with methods for realizing abstract geometric objects in concrete vector spaces. This research monograph considers a large class of problems from convexity and discrete geometry including constructing convex polytopes from simplicial complexes, vector geometries from incidence structures and hyperplane arrangements from oriented matroids. It turns out that algorithms for these constructions exist if and only if arbitrary polynomial equations are decidable with respect to the underlying field. Besides such complexity theorems a variety of symbolic algorithms are discussed, and the methods are applied to obtain new mathematical results on convex polytopes, projective configurations and the combinatorics of Grassmann varieties. Finally algebraic varieties characterizing matroids and oriented matroids are introduced providing a new basis for applying computer algebra methods in this field. The necessary background knowledge is reviewed briefly. The text is accessible to stud...

Fusion potential for spherical and compact tokamaks

International Nuclear Information System (INIS)

Sandzelius, Mikael

2003-02-01

The tokamak is the most successful fusion experiment today. Despite this, the conventional tokamak has a long way to go before being realized into an economically viable power plant. In this master thesis work, two alternative tokamak configurations to the conventional tokamak has been studied, both of which could be realized to a lower cost. The fusion potential of the spherical and the compact tokamak have been examined with a comparison of the conventional tokamak in mind. The difficulties arising in the two configurations have been treated from a physical point of view concerning the fusion plasma and from a technological standpoint evolving around design, materials and engineering. Both advantages and drawbacks of either configuration have been treated relative to the conventional tokamak. The spherical tokamak shows promising plasma characteristics, notably a high β-value but have troubles with high heat loads and marginal tritium breeding. The compact tokamak operates at a high plasma density and a high magnetic field enabling it to be built considerably smaller than any other tokamak. The most notable down-side being high heat loads and neutron transport problems. With the help of theoretical reactor studies, extrapolating from where we stand today, it is conceivable that the spherical tokamak is closer of being realized of the two. But, as this study shows, the compact tokamak power plant concept offers the most appealing prospect

Fusion potential for spherical and compact tokamaks

Energy Technology Data Exchange (ETDEWEB)

Sandzelius, Mikael

2003-02-01

The tokamak is the most successful fusion experiment today. Despite this, the conventional tokamak has a long way to go before being realized into an economically viable power plant. In this master thesis work, two alternative tokamak configurations to the conventional tokamak has been studied, both of which could be realized to a lower cost. The fusion potential of the spherical and the compact tokamak have been examined with a comparison of the conventional tokamak in mind. The difficulties arising in the two configurations have been treated from a physical point of view concerning the fusion plasma and from a technological standpoint evolving around design, materials and engineering. Both advantages and drawbacks of either configuration have been treated relative to the conventional tokamak. The spherical tokamak shows promising plasma characteristics, notably a high {beta}-value but have troubles with high heat loads and marginal tritium breeding. The compact tokamak operates at a high plasma density and a high magnetic field enabling it to be built considerably smaller than any other tokamak. The most notable down-side being high heat loads and neutron transport problems. With the help of theoretical reactor studies, extrapolating from where we stand today, it is conceivable that the spherical tokamak is closer of being realized of the two. But, as this study shows, the compact tokamak power plant concept offers the most appealing prospect.

Designs and finite geometries

CERN Document Server

1996-01-01

Designs and Finite Geometries brings together in one place important contributions and up-to-date research results in this important area of mathematics. Designs and Finite Geometries serves as an excellent reference, providing insight into some of the most important research issues in the field.

Sphericity in the interacting boson model

International Nuclear Information System (INIS)

Ogata, H.

1977-01-01

The interacting boson model (IBM) of Arima and Iachello is examined. The transition between the rotational and vibrational modes of even-even nuclei is presented as a function of a sphericity parameter, which is determined primarily from yrast band spectra. The backbending feature is reasonably reproduced. (author)

Design and Transmission Analysis of an Asymmetrical Spherical Parallel Manipulator

DEFF Research Database (Denmark)

Wu, Guanglei; Caro, Stéphane; Wang, Jiawei

2015-01-01

analysis and optimal design of the proposed manipulator based on its kinematic analysis. The input and output transmission indices of the manipulator are defined for its optimum design based on the virtual coefficient between the transmission wrenches and twist screws. The sets of optimal parameters......This paper presents an asymmetrical spherical parallel manipulator and its transmissibility analysis. This manipulator contains a center shaft to both generate a decoupled unlimited-torsion motion and support the mobile platform for high positioning accuracy. This work addresses the transmission...... are identified and the distribution of the transmission index is visualized. Moreover, a comparative study regarding to the performances with the symmetrical spherical parallel manipulators is conducted and the comparison shows the advantages of the proposed manipulator with respect to its spherical parallel...

High-Accuracy Spherical Near-Field Measurements for Satellite Antenna Testing

DEFF Research Database (Denmark)

Breinbjerg, Olav

2017-01-01

The spherical near-field antenna measurement technique is unique in combining several distinct advantages and it generally constitutes the most accurate technique for experimental characterization of radiation from antennas. From the outset in 1970, spherical near-field antenna measurements have...... matured into a well-established technique that is widely used for testing antennas for many wireless applications. In particular, for high-accuracy applications, such as remote sensing satellite missions in ESA's Earth Observation Programme with uncertainty requirements at the level of 0.05dB - 0.10d......B, the spherical near-field antenna measurement technique is generally superior. This paper addresses the means to achieving high measurement accuracy; these include the measurement technique per se, its implementation in terms of proper measurement procedures, the use of uncertainty estimates, as well as facility...

Porous spherical shells and microspheres by electrodispersion precipitation

International Nuclear Information System (INIS)

Harris, M.T.; Sisson, W.G.; Basaran, O.A.; Hayes, S.M.; Bobrowski, S.J.

1994-01-01

The ability to reproduce the synthesis of dense- and porous-microspheres and micron-sized spherical shells is very important in (a) the development of ceramics for structural, electronic, catalyst and thermal applications; and (b) the encapsulation of products for controlled-release of drugs, flavors and perfumes, and inks and dyes, and the protection of light-sensitive components and mechanical support of fragile materials. Larger metallic- and ceramic-spherical shells have been used in inertial confinement fusion (ICF) experiments and as catalyst supports. The current paper will focus on a recent technique that has been developed for synthesizing ceramic microspheres and micro-shells. Pulsed electric fields have been used to enhance the dispersion of aqueous metal (Zr and Al) salt solutions from a nozzle and into a nonconducting liquid continuous phase that is immiscible with the aqueous phase. The diameter of the resulting microdroplets ranged in size from approximately 0.1 to 10 μm. Precipitation of hydrous metal oxides occurred as ammonia, which was dissolved in varying amounts in the continuous phase, diffused into the aqueous microdroplets. Spherical shells were formed at higher ammonia concentrations and microspheres were produced at lower ammonia concentrations. Upon drying, dimples appeared in the particles that were synthesized at higher ammonia concentrations. The latter result accords with the well known fact that under certain conditions spherical shells collapse when a fluid is extracted from the core of the particle. No dimples were observed in the microspheres that were produced at lower ammonia concentrations. Analog X-ray dot maps for aluminum and zirconium were done to determine the spatial distribution of each metal in the particles

Fabrication of Spherical AlSi10Mg Powders by Radio Frequency Plasma Spheroidization

Science.gov (United States)

Wang, Linzhi; Liu, Ying; Chang, Sen

2016-05-01

Spherical AlSi10Mg powders were prepared by radio frequency plasma spheroidization from commercial AlSi10Mg powders. The fabrication process parameters and powder characteristics were investigated. Field emission scanning electron microscope, X-ray diffraction, laser particle size analyzer, powder rheometer, and UV/visible/infrared spectrophotometer were used for analyses and measurements of micrographs, phases, granulometric parameters, flowability, and laser absorption properties of the powders, respectively. The results show that the obtained spherical powders exhibit good sphericity, smooth surfaces, favorable dispersity, and excellent fluidity under appropriate feeding rate and flow rate of carrier gas. Further, acicular microstructures of the spherical AlSi10Mg powders are composed of α-Al, Si, and a small amount of Mg2Si phase. In addition, laser absorption values of the spherical AlSi10Mg powders increase obviously compared with raw material, and different spectra have obvious absorption peaks at a wavelength of about 826 nm.

d-geometries revisited

CERN Document Server

Ceresole, Anna; Gnecchi, Alessandra; Marrani, Alessio

2013-01-01

We analyze some properties of the four dimensional supergravity theories which originate from five dimensions upon reduction. They generalize to N>2 extended supersymmetries the d-geometries with cubic prepotentials, familiar from N=2 special K\\"ahler geometry. We emphasize the role of a suitable parametrization of the scalar fields and the corresponding triangular symplectic basis. We also consider applications to the first order flow equations for non-BPS extremal black holes.

METHOD FOR CREATION OF SPHERICAL PANORAMAS FROM IMAGES OBTAINED BY OMNIDIRECTIONAL OPTOELECTRONIC SYSTEMS

Directory of Open Access Journals (Sweden)

V. P. Lazarenko

2016-01-01

Full Text Available Subject of Study. The key feature of spherical panoramas is the maximum possible angle of view (360 × 180 degrees. Omnidirectional optical-electronic systems are able to produce images that show most of this space, but these images are different from the canonical spherical panoramas. This paper proposes a method of converting the circular images obtained by omnidirectional optical systems, to canonical spherical panoramic images with the use ofcalibration procedure of omnidirectional optical-electronic system. Method. The process of spherical panoramas creation consists of three steps.The first step includesthe forming of virtual surface in the object space corresponding to a field of view of the spherical panorama. The surface is defined by the three-dimensional array of pixels.At the second step the coordinates of images of these points in the plane of the detectorare specified. At the third step pixel-by-pixel forming of the output imageisperformed from the original omnidirectional image with the use of coordinates obtained at the second step. Main Results. We have considered the geometric projectionmodel of spherical panoramas. The algorithm has been proposed calculating the three-dimensional array of pixels, characterizing the field of view of a spherical panorama and convenient for practical usage. The developed method is designed to work with omnidirectional optical-electronic systems both with catadioptric optical systems and with fisheye lens. Experimental results confirming the validity of this method are presented. The reprojection mean-square error was equal to 0.794 px. Practical Relevance. The proposed method can be applied in technologies of creating of virtual tours or panoramas of streets where spherical panoramic images are the standard for storing visual information. The method may also find its application in various fields of robotics, orientation and navigation of space vehicles and UAVs.

Interactions between charged spherical macroions

International Nuclear Information System (INIS)

Stevens, M.J.; Falk, M.L.; Robbins, M.O.

1996-01-01

Monte Carlo (MC) simulations were used to study the screened interactions between charged spherical macroions surrounded by discrete counterions, and to test previous theories of screening. The simulations were performed in the primitive cell of the bcc lattice, and in the spherical Wigner endash Seitz cell that is commonly used in approximate calculations. We found that the Wigner endash Seitz approximation is valid even at high volume fractions φ and large macroion charges Z, because the macroion charge becomes strongly screened. Pressures calculated from Poisson endash Boltzmann theory and local density functional theory deviate from MC values as φ and Z increase, but continue to provide upper and lower bounds for the MC results. While Debye endash Hueckel (DH) theory fails badly when the bare charge is used, MC pressures can be fit with an effective DH charge, Z DH , that is nearly independent of volume fraction. As Z diverges, Z DH saturates at zψ max R m /λ, where z is the counterion charge, R m is the macroion radius, λ is the Bjerrum length, and ψ max is a constant of order 10. copyright 1996 American Institute of Physics

Geometry success in 20 minutes a day

CERN Document Server

LLC, LearningExpress

2014-01-01

Whether you're new to geometry or just looking for a refresher, Geometry Success in 20 Minutes a Day offers a 20-step lesson plan that provides quick and thorough instruction in practical, critical skills. Stripped of unnecessary math jargon but bursting with geometry essentials, Geometry Success in 20 Minutes a Day: Covers all vital geometry skills, from the basic building blocks of geometry to ratio, proportion, and similarity to trigonometry and beyond Provides hundreds of practice exercises in test format Applies geometr

Preserving spherical symmetry in axisymmetric coordinates for diffusion problems

International Nuclear Information System (INIS)

Brunner, T. A.; Kolev, T. V.; Bailey, T. S.; Till, A. T.

2013-01-01

Persevering symmetric solutions, even in the under-converged limit, is important to the robustness of production simulation codes. We explore the symmetry preservation in both a continuous nodal and a mixed finite element method. In their standard formulation, neither method preserves spherical solution symmetry in axisymmetric (RZ) coordinates. We propose two methods, one for each family of finite elements, that recover spherical symmetry for low-order finite elements on linear or curvilinear meshes. This is a first step toward understanding achieving symmetry for higher-order elements. (authors)

Enhancement of octupole strength in near spherical nuclei

Energy Technology Data Exchange (ETDEWEB)

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.)

Spherical powder for retaining thermosetting acrylic resin veneers.

Science.gov (United States)

Tanaka, T; Atsuta, M; Uchiyama, Y; Nakabayashi, N; Masuhara, E

1978-03-01

1. Nine different sizes of spherical powder were prepared, and their effectiveness as retentive devices was evaluated against those available commercially. 2. Smaller-diameter spherical powder (No. 5) gave the best results of all retaining devices tested. 3. The physical properties of the resins play an important role in the retentive strength with No. 5 retention beads. The retentive strength was reduced when brittle resin was used. 4. The retentive strength of the resin veneer was greatly affected by the angle of stress at the incisal resin. The retentive strength increased as the angle between the longitudinal axis of the specimen and the direction of stress decreased.

Lectures on coarse geometry

CERN Document Server

Roe, John

2003-01-01

Coarse geometry is the study of spaces (particularly metric spaces) from a 'large scale' point of view, so that two spaces that look the same from a great distance are actually equivalent. This point of view is effective because it is often true that the relevant geometric properties of metric spaces are determined by their coarse geometry. Two examples of important uses of coarse geometry are Gromov's beautiful notion of a hyperbolic group and Mostow's proof of his famous rigidity theorem. The first few chapters of the book provide a general perspective on coarse structures. Even when only metric coarse structures are in view, the abstract framework brings the same simplification as does the passage from epsilons and deltas to open sets when speaking of continuity. The middle section reviews notions of negative curvature and rigidity. Modern interest in large scale geometry derives in large part from Mostow's rigidity theorem and from Gromov's subsequent 'large scale' rendition of the crucial properties of n...

Introduction to tropical geometry

CERN Document Server

Maclagan, Diane

2015-01-01

Tropical geometry is a combinatorial shadow of algebraic geometry, offering new polyhedral tools to compute invariants of algebraic varieties. It is based on tropical algebra, where the sum of two numbers is their minimum and the product is their sum. This turns polynomials into piecewise-linear functions, and their zero sets into polyhedral complexes. These tropical varieties retain a surprising amount of information about their classical counterparts. Tropical geometry is a young subject that has undergone a rapid development since the beginning of the 21st century. While establishing itself as an area in its own right, deep connections have been made to many branches of pure and applied mathematics. This book offers a self-contained introduction to tropical geometry, suitable as a course text for beginning graduate students. Proofs are provided for the main results, such as the Fundamental Theorem and the Structure Theorem. Numerous examples and explicit computations illustrate the main concepts. Each of t...

Geometry Euclid and beyond

CERN Document Server