Characterizing Student Mathematics Teachers' Levels of Understanding in Spherical Geometry
Guven, Bulent; Baki, Adnan
2010-01-01
This article presents an exploratory study aimed at the identification of students' levels of understanding in spherical geometry as van Hiele did for Euclidean geometry. To do this, we developed and implemented a spherical geometry course for student mathematics teachers. Six structured, "task-based interviews" were held with eight student…
Students Discovering Spherical Geometry Using Dynamic Geometry Software
Guven, Bulent; Karatas, Ilhan
2009-01-01
Dynamic geometry software (DGS) such as Cabri and Geometers' Sketchpad has been regularly used worldwide for teaching and learning Euclidean geometry for a long time. The DGS with its inductive nature allows students to learn Euclidean geometry via explorations. However, with respect to non-Euclidean geometries, do we need to introduce them to…
Space Radiation Detector with Spherical Geometry
Wrbanek, John D. (Inventor); Fralick, Gustave C. (Inventor); Wrbanek, Susan Y. (Inventor)
2012-01-01
A particle detector is provided, the particle detector including a spherical Cherenkov detector, and at least one pair of detector stacks. In an embodiment of the invention, the Cherenkov detector includes a sphere of ultraviolet transparent material, coated by an ultraviolet reflecting material that has at least one open port. The Cherenkov detector further includes at least one photodetector configured to detect ultraviolet light emitted from a particle within the sphere. In an embodiment of the invention, each detector stack includes one or more detectors configured to detect a particle traversing the sphere.
International Nuclear Information System (INIS)
Sahni, D.C.; Sharma, A.
2000-01-01
The integral form of one-speed, spherically symmetric neutron transport equation with isotropic scattering is considered. Two standard problems are solved using normal mode expansion technique. The expansion coefficients are obtained by solving their singular integral equations. It is shown that these expansion coefficients provide a representation of all spherical harmonics moments of the angular flux as a superposition of Bessel functions. It is seen that large errors occur in the computation of higher moments unless we take certain precautions. The reasons for this phenomenon are explained. They throw some light on the failure of spherical harmonics method in treating spherical geometry problems as observed by Aronsson
Mukta, K. N.; MacLaurin, J. N.; Robinson, P. A.
2017-11-01
Corticothalamic neural field theory is applied to a spherical geometry to better model neural activity in the human brain and is also compared with planar approximations. The frequency power spectrum, correlation, and coherence functions are computed analytically and numerically. The effects of cortical boundary conditions and resulting modal aspects of spherical corticothalamic dynamics are explored, showing that the results of spherical and finite planar geometries converge to those for the infinite planar geometry in the limit of large brain size. Estimates are made of the point at which modal series can be truncated and it is found that for physiologically plausible parameters only the lowest few spatial eigenmodes are needed for an accurate representation of macroscopic brain activity. A difference between the geometries is that there is a low-frequency 1 /f spectrum in the infinite planar geometry, whereas in the spherical geometry it is 1 /f2 . Another difference is that the alpha peak in the spherical geometry is sharper and stronger than in the planar geometry. Cortical modal effects can lead to a double alpha peak structure in the power spectrum, although the main determinant of the alpha peak is corticothalamic feedback. In the spherical geometry, the cross spectrum between two points is found to only depend on their relative distance apart. At small spatial separations the low-frequency cross spectrum is stronger than for an infinite planar geometry and the alpha peak is sharper and stronger due to the partitioning of the energy into discrete modes. In the spherical geometry, the coherence function between points decays monotonically as their separation increases at a fixed frequency, but persists further at resonant frequencies. The correlation between two points is found to be positive, regardless of the time lag and spatial separation, but decays monotonically as the separation increases at fixed time lag. At fixed distance the correlation has peaks
Mukta, K N; MacLaurin, J N; Robinson, P A
2017-11-01
Corticothalamic neural field theory is applied to a spherical geometry to better model neural activity in the human brain and is also compared with planar approximations. The frequency power spectrum, correlation, and coherence functions are computed analytically and numerically. The effects of cortical boundary conditions and resulting modal aspects of spherical corticothalamic dynamics are explored, showing that the results of spherical and finite planar geometries converge to those for the infinite planar geometry in the limit of large brain size. Estimates are made of the point at which modal series can be truncated and it is found that for physiologically plausible parameters only the lowest few spatial eigenmodes are needed for an accurate representation of macroscopic brain activity. A difference between the geometries is that there is a low-frequency 1/f spectrum in the infinite planar geometry, whereas in the spherical geometry it is 1/f^{2}. Another difference is that the alpha peak in the spherical geometry is sharper and stronger than in the planar geometry. Cortical modal effects can lead to a double alpha peak structure in the power spectrum, although the main determinant of the alpha peak is corticothalamic feedback. In the spherical geometry, the cross spectrum between two points is found to only depend on their relative distance apart. At small spatial separations the low-frequency cross spectrum is stronger than for an infinite planar geometry and the alpha peak is sharper and stronger due to the partitioning of the energy into discrete modes. In the spherical geometry, the coherence function between points decays monotonically as their separation increases at a fixed frequency, but persists further at resonant frequencies. The correlation between two points is found to be positive, regardless of the time lag and spatial separation, but decays monotonically as the separation increases at fixed time lag. At fixed distance the correlation has peaks
Shock-driven Turbulent Mixing in Spherically Confined Geometries
Boureima, Ismael; Ramaprabhu, Praveen
2017-11-01
We report results from detailed numerical simulations of turbulent mixing generated by shock passage through a material interface separating two gases in a spherical configuration. The problem definition is similar to the spherical implosion defined by. In this configuration, a spherical shock converges on a perturbed interface between gases with differing properties. During the implosion, perturbations at the interface are subjected to growth due to the RM instability, the RT instability, as well as Bell-Plesset effects. We report on several quantities of interest to the turbulence modeling community, including the turbulent kinetic energy, the anisotropy tensor, density self-correlation, atomic mixing etc. The simulations were performed using the FLASH code, at a resolution of 3072 x 1024 x 1024 in the radial, azimuthal and polar directions. We also report preliminary results from a study in which the convergence ratio of the implosion is varied by modifying the adiabatic index of the inner material.
International Nuclear Information System (INIS)
Kobayashi, K.
2009-01-01
In 2001, an international cooperation on the 3D radiation transport benchmarks for simple geometries with void region was performed under the leadership of E. Sartori of OECD/NEA. There were contributions from eight institutions, where 6 contributions were by the discrete ordinate method and only two were by the spherical harmonics method. The 3D spherical harmonics program FFT3 by the finite Fourier transformation method has been improved for this presentation, and benchmark solutions for the 2D and 3D simple geometries with void region by the FFT2 and FFT3 are given showing fairly good accuracy. (authors)
Gorter-Mellink pulsed-source problem in cylindrical and spherical geometry
International Nuclear Information System (INIS)
Dresner, L.
1991-01-01
An exact solution to the Gorter-Mellink pulsed-source problem is known in plane geometry. According to this solution, the central temperature falls as t -3/2 , where t is the elapsed time after an instantaneous, plane pulse. No such exact solutions are known to the pulsed-source problem in cylindrical and spherical geometry. But in cylindrical geometry, it can be shown that if the initial condition is an instantaneous temperature rise ΔT inside a cylinder of radius R, the central temperature is bounded from above by a decreasing exponential function of time. The relaxation time of this exponential is related to ΔT and R. In spherical geometry, it can be shown that if the initial condition is an instantaneous temperature rise ΔT inside a sphere of radius R, the central temperature is bounded from above by a function proportional to (t 0 -t) 9/2 . The extinction time t 0 is related to ΔT and R. These predictions have not been tested by experiment, and the author recommends such experiments. 2 refs., 3 figs
Negative ion sources equipped with continuous annular and spherical geometry surface ionizers
International Nuclear Information System (INIS)
Alton, G.D.; Mills, G.D.
1985-01-01
Axial geometry negative ion sources have been designed, developed, and evaluated for use in conjunction with tandem accelerator applications. These sources utilize continuous surface solid tungsten ionizers in either annular or spherical geometries to effect ionization of cesium vapor, which in turn is used to sputter a negatively biased probe containing the material of interest. The annular ionizer geometry source has been incorporated as an ''on-line'' source for routine operation of the Holifield Heavy Ion Research Facility (HHIRF) tandem accelerator. Both test stand and tandem accelerator operational experience indicate that such sources are reliable, long lived, stably operating and prolific producers of a wide spectrum of negative ions. To date these sources have been used to produce more than 18 negative ion species including Ag - , Au - , B - , CaH 3 - , Cl - , CrH 2 - , Cu - , Lu - , MgH 3 - , Mo - , Ni - , O - , S - , Si - , Sn - , TiH 3 - , Tm - , and Yb - . Details of the mechanical design features and computational techniques utilized in arriving at the final electrode configuration are presented in the text. Examples of data pertinent to source operation, the dependence of negative ion yields on certain source operational parameters and of intensities typical of a particular negative ion source are also given. 12 refs., 10 figs
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)
The synchrotron-self-Compton process in spherical geometries. I - Theoretical framework
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.
Energy Technology Data Exchange (ETDEWEB)
Williamson, D.L.; Hack, J.J.; Jakob, R.; Swarztrauber, P.N. (National Center for Atmospheric Research, Boulder, CO (United States)); Drake, J.B. (Oak Ridge National Lab., TN (United States))
1991-08-01
A suite of seven test cases is proposed for the evaluation of numerical methods intended for the solution of the shallow water equations in spherical geometry. The shallow water equations exhibit the major difficulties associated with the horizontal dynamical aspects of atmospheric modeling on the spherical earth. These cases are designed for use in the evaluation of numerical methods proposed for climate modeling and to identify the potential trade-offs which must always be made in numerical modeling. Before a proposed scheme is applied to a full baroclinic atmospheric model it must perform well on these problems in comparison with other currently accepted numerical methods. The cases are presented in order of complexity. They consist of advection across the poles, steady state geostrophically balanced flow of both global and local scales, forced nonlinear advection of an isolated low, zonal flow impinging on an isolated mountain, Rossby-Haurwitz waves and observed atmospheric states. One of the cases is also identified as a computer performance/algorithm efficiency benchmark for assessing the performance of algorithms adapted to massively parallel computers. 31 refs.
International Nuclear Information System (INIS)
Matausek, M.V.; Milosevic, M.
1986-01-01
In the present paper a generalization is performed of a procedure to solve multigroup spherical harmonics equations, which has originally been proposed and developed for one-dimensional systems in cylindrical or spherical geometry, and later extended for a special case of a two-dimensional system in r-z geometry. The expressions are derived for the axial and the radial dependence of the group values of the neutron flux moments, in the P-3 approximation of the spherical harmonics method, in a cylindrically symmetrical system with an arbitrary number of material regions in both r- and z-directions. In the special case of an axially homogeneous system, these expressions reduce to the relations derived previously. (author)
Hansen, Ulrich; Maas, Christian
2017-04-01
About 4.5 billion years ago the early Earth experienced several giant impacts that lead to one or more deep terrestrial magma oceans of global extent. The crystallization of these vigorously convecting magma oceans is of key importance for the chemical structure of the Earth, the subsequent mantle evolution as well as for the initial conditions for the onset of plate tectonics. Due to the fast planetary rotation of the early Earth and the small magma viscosity, rotation probably had a profound effect on early differentiation processes and could for example influence the presence and distribution of chemical heterogeneities in the Earth's mantle [e.g. Matyska et al., 1994, Garnero and McNamara, 2008]. Previous work in Cartesian geometry revealed a strong influence of rotation as well as of latitude on the crystal settling in a terrestrial magma ocean [Maas and Hansen, 2015]. Based on the preceding study we developed a spherical shell model that allows to study crystal settling in-between pole and equator as well as the migration of crystals between these regions. Further we included centrifugal forces on the crystals, which significantly affect the lateral and radial distribution of the crystals. Depending on the strength of rotation the particles accumulate at mid-latitude or at the equator. At high rotation rates the dynamics of fluid and particles are dominated by jet-like motions in longitudinal direction that have different directions on northern and southern hemisphere. All in all the first numerical experiments in spherical geometry agree with Maas and Hansen [2015] that the crystal distribution crucially depends on latitude, rotational strength and crystal density. References E. J. Garnero and A. K. McNamara. Structure and dynamics of earth's lower mantle. Science, 320(5876):626-628, 2008. C. Maas and U. Hansen. Eff ects of earth's rotation on the early di erentiation of a terrestrial magma ocean. Journal of Geophysical Research: Solid Earth, 120
International Nuclear Information System (INIS)
Alton, G.D.; McConnell, J.W.; Tajima, S.; Nelson, G.S.
1986-01-01
A digitally controlled emittance measurement, data acquisition and processing system has been designed, implemented and used to determine emittances of negative ion beams extracted from high-intensity negative-ion sources equipped with cylindrical and spherical geometry cesium surface ionizers. Comparative studies indicate that the emittances of ion beams extracted from the source equipped with a spherical geometry ionizer are lower by 13% to 21% than those extracted from the source equipped with a cylindrical geometry ionizer. This difference may be attributable to geometric factors rather than differences in the sizes of the emission areas at the points of negative-ion generation. Studies reveal that the emittances of these sources are independent of ion mass for most of the materials investigated and independent of ion current over the range of ion currents used in these investigations (4μA to 12 μA)
Critical experiments on single-unit spherical plutonium geometries reflected and moderated by oil
Energy Technology Data Exchange (ETDEWEB)
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 {sup 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 {sup 239}Pu containing 5.9 wt-% {sup 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.
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
International Nuclear Information System (INIS)
Bogado Leite, S.Q.
1997-01-01
Escape and transmission probabilities, defined in terms of both the region the neutron originates from and the region it penetrates, are used to develop new interface-current relations for unit-cells with an arbitrary number of annular regions in cylindrical and spherical geometries. Comparisons with currents, obtained in terms of standard transmission and escape probabilities, as well as with accurate results reported in the literature, are presented for selected situations, showing significant discrepancies between the two models. (author)
International Nuclear Information System (INIS)
Novkovic, D.; Tomasevic, M.; Subotic, K.
1998-01-01
A system of reduced differential equations generally valid for plane-parallel, cylindrical and spherical ionization chambers, which is appropriate for numerical solution, has been derived. The system has been solved numerically for plane-parallel and spherical ionization chambers filled with air. The comparison of the calculated results of Armstrong and Tate, for plane-parallel ionization chambers, and Sprinkle and Tate, for spherical ionization chambers, with the present calculations has shown a good agreement. The calculated values for ionization chambers filled with CO 2 were also in good agreement with the experimental data of Moriuchi et al. (author)
Energy Technology Data Exchange (ETDEWEB)
Morice, J. [Bordeaux-1 Univ., Ecole Matmeca, 33 - Talence (France); Jaouen, St. [CEA Bruyeres-le-Chatel, Dept. Sciences de la Simulation et de l' Information, 91 (France)
2003-07-01
We derive the systems of equations satisfied by the linear Lagrangian perturbations of gas dynamics in planar, cylindrical and spherical geometries, using the canonical forms pointed out by B. Despres et al. (B. Despres, 2001 B. Despres and C. Mazeran, 2003). One of the interests of this approach is that it should be applied to more complex models (those which enter the B. Despres' formalism as 2T-hydrodynamics, MHD, reactive gas dynamics, etc.). Another one is that it is rather easy to derive entropic numerical schemes for the basic flow and their linearized versions for the perturbations. (authors)
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
Analysis of non-spherical grid geometry for distortion-free LEED apparatus with micro channel plate
International Nuclear Information System (INIS)
Okano, Tatsuo; Ohsaki, Akihiko; Sakurai, Makoto; Honda, Tohru; Tuzi, Yutaka
1985-01-01
A design of non-spherical grid structure for the distortion-free LEED apparalus with a micro channel plate (MCP) is described. The grid structure is assumed as an interface of two electrostatic potentials. The potential interface refracts the diffracted electrons and the LEED patterns can be projected on the MCP just like those observed on a spherical fluorescent screen. The shape of the potential interface is described by a differential equation and numerically calculated for several conditions. The most appropriate geometry is determined by the easiness of the mechanical construction. The effect of energy distribution of diffracted electrons is numerically estimated and the deviation is proved to be negligibly small for most applications. (author)
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.
Spherically Symmetric Geometries in f(T and f(R Gravitational Theories
Directory of Open Access Journals (Sweden)
Gamal G. L. Nashed
2015-01-01
Full Text Available Using the well know relation between Ricci scalar, R, and torsion scalar, T, that is, R=-T-2∇αTα, we show that, for any spherically symmetric spacetime whose (i scalar torsion vanishing, that is, T=TμναSαμν=0 or (ii total derivative term, that is, ∇αTα with Tα 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.
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
Reuter, K.; Jenko, F.; Forest, C. B.; Bayliss, R. A.
2008-08-01
A parallel implementation of a nonlinear pseudo-spectral MHD code for the simulation of turbulent dynamos in spherical geometry is reported. It employs a dual domain decomposition technique in both real and spectral space. It is shown that this method shows nearly ideal scaling going up to 128 CPUs on Beowulf-type clusters with fast interconnect. Furthermore, the potential of exploiting single precision arithmetic on standard x86 processors is examined. It is pointed out that the MHD code thereby achieves a maximum speedup of 1.7, whereas the validity of the computations is still granted. The combination of both measures will allow for the direct numerical simulation of highly turbulent cases ( 1500
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 ...
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 distributions 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 generalization of Newton's gravitational scalar potential exterior to the spherical mass or pressure distribution under consideration.
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
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
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.
DEFF Research Database (Denmark)
Byg din egen boomerang, kast den, se den flyve, forstå hvorfor og hvordan den vender tilbage, og grib den. Det handler om opdriften på vingerne når du flyver, men det handler også og allermest om den mærkværdige gyroskop-effekt, du bruger til at holde balancen, når du kører på cykel. Vi vil bruge...... matematik, geometri, og fysik til at forstå, hvad det er, der foregår....
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.
International Nuclear Information System (INIS)
Fenstermacher, T.E.
1981-01-01
The solution of the neutron transport equation has long been a subject of intense interest to nuclear engineers. Present computer codes for the solution of this equation, however, are expensive to run for large, multidimensional problems, and also suffer from computational problems such as the ray effect. A method has been developed which eliminates many of these problems. It consists of transforming the transport equation into a set of linear partial differential equations by the use of spherical harmonics. The problem volume is divided into mesh boxes, and the flux components are approximated within each mesh box by spatially orthogonal quadratic polynomials, which need not be continuous at mesh box interfaces. A variational principle is developed, and used to solve for the unknown coefficients of these polynomials. Both one dimensional and two dimensional computer codes using this method have been written. The codes have each been tested on several test cases, and the solutions checked against solutions obtained by other methods. While the codes have some difficulty in modeling sharp transients, they produce excellent results on problems where the characteristic lengths are many mean free paths. On one test case, the two dimensional code, SHOP/2D, required only one-fourth the computer time required by the finite difference, discrete ordinates code TWOTRAN to produce a solution. In addition, SHOP/2D converged much better than TWOTRAN and produced more physical-appearing results
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
Kugland, Nathan; Doeppner, Tilo; Glenzer, Siegfried; Constantin, Carmen; Niemann, Chris; Neumayer, Paul
2015-04-07
A method is provided for characterizing spectrometric properties (e.g., peak reflectivity, reflection curve width, and Bragg angle offset) of the K.alpha. emission line reflected narrowly off angle of the direct reflection of a bent crystal and in particular of a spherically bent quartz 200 crystal by analyzing the off-angle x-ray emission from a stronger emission line reflected at angles far from normal incidence. The bent quartz crystal can therefore accurately image argon K.alpha. x-rays at near-normal incidence (Bragg angle of approximately 81 degrees). The method is useful for in-situ calibration of instruments employing the crystal as a grating by first operating the crystal as a high throughput focusing monochromator on the Rowland circle at angles far from normal incidence (Bragg angle approximately 68 degrees) to make a reflection curve with the He-like x-rays such as the He-.alpha. emission line observed from a laser-excited plasma.
Wenninger, Magnus J
2012-01-01
Well-illustrated, practical approach to creating star-faced spherical forms that can serve as basic structures for geodesic domes. Complete instructions for making models from circular bands of paper with just a ruler and compass. Discusses tessellation, or tiling, and how to make spherical models of the semiregular solids and concludes with a discussion of the relationship of polyhedra to geodesic domes and directions for building models of domes. "". . . very pleasant reading."" - Science. 1979 edition.
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...
Optics of laser plasmas in spherical geometry
International Nuclear Information System (INIS)
Mulser, P.; Kessel, C. van.
1977-05-01
Analytical formulae for classical reflection from pellets and plane targets under normal incidence are presented and the maximum electric field increase in smooth density profiles is determined. Density profile distortions due to light pressure and their influence on pellet compression are discussed in a steady state model. (orig.) [de
Spherical CR geometry and Dehn surgery
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
Aircraft navigation and surveillance analysis for a spherical earth
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...
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)
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.
A least-squares finite-element Sn method for solving first-order neutron transport equation
International Nuclear Information System (INIS)
Ju Haitao; Wu Hongchun; Zhou Yongqiang; Cao Liangzhi; Yao Dong; Xian, Chun-Yu
2007-01-01
A discrete ordinates finite-element method for solving the two-dimensional first-order neutron transport equation is derived using the least-squares variation. It avoids the singularity in void regions of the method derived from the second-order equation which contains the inversion of the cross-section. Different from using the standard Galerkin variation to the first-order equation, the least-squares variation results in a symmetric matrix, which can be solved easily and effectively. To eliminate the discontinuity of the angular flux on the vacuum boundary in the spherical harmonics method, the angle variable is discretized by the discrete ordinates method. A two-dimensional transport simulation code is developed and applied to some benchmark problems with unstructured geometry. The numerical results verified the validity of this method
A proposal for a spherical option in WIMS
International Nuclear Information System (INIS)
Roth, M.J.
1982-05-01
A description is presented of how a spherical option may be put into WIMS-E. There is no proposal to make any change to WIMSD4, but some recommendations are made as to how spherical geometry may be simulated in WIMSD4 or indeed in WIMS-E prior to these proposed changes. (U.K.)
Holme, Audun
1988-01-01
This volume presents selected papers resulting from the meeting at Sundance on enumerative algebraic geometry. The papers are original research articles and concentrate on the underlying geometry of the subject.
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.
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
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
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.
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
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.
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
Faulkner, Thomas Ewan
1952-01-01
This text explores the methods of the projective geometry of the plane. Some knowledge of the elements of metrical and analytical geometry is assumed; a rigorous first chapter serves to prepare readers. Following an introduction to the methods of the symbolic notation, the text advances to a consideration of the theory of one-to-one correspondence. It derives the projective properties of the conic and discusses the representation of these properties by the general equation of the second degree. A study of the relationship between Euclidean and projective geometry concludes the presentation. Nu
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.
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...
Lefschetz, Solomon
2005-01-01
An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this text for advanced undergraduate students is particularly relevant to those more familiar with analysis than algebra. 1953 edition.
Geometric scalar theory of gravity beyond spherical symmetry
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.
Peeples, Steven
2015-01-01
A three degree of freedom (DOF) spherical actuator is proposed that will replace functions requiring three single DOF actuators in robotic manipulators providing space and weight savings while reducing the overall failure rate. Exploration satellites, Space Station payload manipulators, and rovers requiring pan, tilt, and rotate movements need an actuator for each function. Not only does each actuator introduce additional failure modes and require bulky mechanical gimbals, each contains many moving parts, decreasing mean time to failure. A conventional robotic manipulator is shown in figure 1. Spherical motors perform all three actuation functions, i.e., three DOF, with only one moving part. Given a standard three actuator system whose actuators have a given failure rate compared to a spherical motor with an equal failure rate, the three actuator system is three times as likely to fail over the latter. The Jet Propulsion Laboratory reliability studies of NASA robotic spacecraft have shown that mechanical hardware/mechanism failures are more frequent and more likely to significantly affect mission success than are electronic failures. Unfortunately, previously designed spherical motors have been unable to provide the performance needed by space missions. This inadequacy is also why they are unavailable commercially. An improved patentable spherically actuated motor (SAM) is proposed to provide the performance and versatility required by NASA missions.
Theory and applications of spherical microphone array processing
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 ...
Spherical geodesic mesh generation
Energy Technology Data Exchange (ETDEWEB)
Fung, Jimmy [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Kenamond, Mark Andrew [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Burton, Donald E. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Shashkov, Mikhail Jurievich [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-02-27
In ALE simulations with moving meshes, mesh topology has a direct influence on feature representation and code robustness. In three-dimensional simulations, modeling spherical volumes and features is particularly challenging for a hydrodynamics code. Calculations on traditional spherical meshes (such as spin meshes) often lead to errors and symmetry breaking. Although the underlying differencing scheme may be modified to rectify this, the differencing scheme may not be accessible. This work documents the use of spherical geodesic meshes to mitigate solution-mesh coupling. These meshes are generated notionally by connecting geodesic surface meshes to produce triangular-prismatic volume meshes. This mesh topology is fundamentally different from traditional mesh topologies and displays superior qualities such as topological symmetry. This work describes the geodesic mesh topology as well as motivating demonstrations with the FLAG hydrocode.
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,
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
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
Desseyn, H. O.; And Others
1985-01-01
Compares linear-nonlinear and planar-nonplanar geometry through the valence-shell electron pairs repulsion (V.S.E.P.R.), Mulliken-Walsh, and electrostatic force theories. Indicates that although the V.S.E.P.R. theory has more advantages for elementary courses, an explanation of the best features of the different theories offers students a better…
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 1; Issue 8. Geometry VI - Space-the Final Frontier. Kapil H Paranjape. Series Article Volume 1 Issue 8 August 1996 pp 28-33. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/001/08/0028-0033 ...
Geometry -----------~--------------RESONANCE
Indian Academy of Sciences (India)
Mathematicians were at war with one another because Euclid's axioms for geometry were not entirely acceptable to all. Archi- medes, Pasch and others introduced further axioms as they thought that Euclid had missed a few, while other mathematicians were bothered by the non-elementary nature of the parallel axiom.
International Nuclear Information System (INIS)
Strominger, A.
1990-01-01
A special manifold is an allowed target manifold for the vector multiplets of D=4, N=2 supergravity. These manifolds are of interest for string theory because the moduli spaces of Calabi-Yau threefolds and c=9, (2,2) conformal field theories are special. Previous work has given a local, coordinate-dependent characterization of special geometry. A global description of special geometries is given herein, and their properties are studied. A special manifold M of complex dimension n is characterized by the existence of a holomorphic Sp(2n+2,R)xGL(1,C) vector bundle over M with a nowhere-vanishing holomorphic section Ω. The Kaehler potential on M is the logarithm of the Sp(2n+2,R) invariant norm of Ω. (orig.)
Directory of Open Access Journals (Sweden)
Leonardo Paris
2012-06-01
Full Text Available Lo studio degli ingranaggi si basa sulle geometrie coniugate in cui due curve o due superfici si mantengono costantemente in contatto pur se in movimento reciproco. La teoria geometrica degli ingranaggi fino alla fine del XIX secolo era uno dei molteplici rami nelle applicazioni della Geometria Descrittiva. Lo studio si basa sulla conoscenza delle principali proprietà delle curve piane e gobbe e delle loro derivate. La specificità del tema è che queste geometrie nel momento in cui si devono relazionare con le loro coniugate, devono rispettare dei vincoli che altrimenti non avrebbero. Si vuole evidenziare attraverso casi concreti il ruolo della geometria descrittiva nel passaggio dal teorico al pratico riproponendo in chiave informatica, temi e procedure di indagine spesso passati in secondo piano se non addirittura dimenticati.
Petersen, Peter
2016-01-01
Intended for a one year course, this text serves as a single source, introducing readers to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry. This is one of the few Works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory. The book will appeal to a readership that have a basic knowledge of standard manifold theory, including tensors, forms, and Lie groups. Important revisions to the third edition include: a substantial addition of unique and enriching exercises scattered throughout the text; inclusion of an increased number of coordinate calculations of connection and curvature; addition of general formulas for curvature on Lie Groups and submersions; integration of variational calculus into the text allowing for an early treatment of the Sphere theorem using a proof by Berger; incorporation of several recent results about manifolds with posit...
General Geometry and Geometry of Electromagnetism
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...
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
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)
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....
Applications of Differential Geometry to Cartography
Benitez, Julio; Thome, Nestor
2004-01-01
This work introduces an application of differential geometry to cartography. The mathematical aspects of some geographical projections of Earth surface are revealed together with some of its more important properties. An important problem since the discovery of the 'spherical' form of the Earth is how to compose a reliable map of the surface of…
Ciarlet, Philippe G
2007-01-01
This book gives the basic notions of differential geometry, such as the metric tensor, the Riemann curvature tensor, the fundamental forms of a surface, covariant derivatives, and the fundamental theorem of surface theory in a selfcontained and accessible manner. Although the field is often considered a classical one, it has recently been rejuvenated, thanks to the manifold applications where it plays an essential role. The book presents some important applications to shells, such as the theory of linearly and nonlinearly elastic shells, the implementation of numerical methods for shells, and
On d = 4 Yang-Mills instantons in a spherically symmetric background
Brihaye, Y.; Radu, E.
2006-09-01
We present arguments for the existence of self-dual Yang-Mills instantons for several spherically symmetric backgrounds with Euclidean signature. The time-independent Yang-Mills field has finite action and a vanishing energy momentum tensor and does not disturb the geometry. We conjecture the existence of similar solutions for any nonextremal SO(3)-spherically symmetric background.
On $d=4$ Yang-Mills instantons in a spherically symmetric background
Brihaye, Yves; Radu, Eugen
2006-01-01
We present arguments for the existence of self-dual Yang-Mills instantons for several spherically symmetric backgrounds with Euclidean signature. The time-independent Yang-Mills field has finite action and a vanishing energy momentum tensor and does not disturb the geometry. We conjecture the existence of similar solutions for any nonextremal SO(3)-spherically symmetric background.
Fundamentals of spherical array processing
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...
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.
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)
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)
The ETE spherical Tokamak project
International Nuclear Information System (INIS)
Ludwig, Gerson Otto; Andrade, Maria Celia Ramos de; Barbosa, Luis Filipe Wiltgen
1999-01-01
This paper describes the general characteristics of spherical tokamaks, with a brief overview of work in the area of spherical torus already performed or in progress at several institutions. The paper presents also the historical development of the ETE (Spherical Tokamak Experiment) project, its research program, technical characteristics and status of construction in September, 1998 at the Associated plasma Laboratory (LAP) of the National Institute for Space Research (INPE) in Brazil. (author)
The ETE spherical Tokamak project
Energy Technology Data Exchange (ETDEWEB)
Ludwig, Gerson Otto; Andrade, Maria Celia Ramos de; Barbosa, Luis Filipe Wiltgen [Instituto Nacional de Pesquisas Espaciais (INPE), Sao Jose dos Campos, SP (Brazil). Lab. Associado de Plasma] [and others]. E-mail: ludwig@plasma.inpe.br
1999-07-01
This paper describes the general characteristics of spherical tokamaks, with a brief overview of work in the area of spherical torus already performed or in progress at several institutions. The paper presents also the historical development of the ETE (Spherical Tokamak Experiment) project, its research program, technical characteristics and status of construction in September, 1998 at the Associated plasma Laboratory (LAP) of the National Institute for Space Research (INPE) in Brazil. (author)
Spherical grating spectrometers
O'Donoghue, Darragh; Clemens, J. Christopher
2014-07-01
We describe designs for spectrometers employing convex dispersers. The Offner spectrometer was the first such instrument; it has almost exclusively been employed on satellite platforms, and has had little impact on ground-based instruments. We have learned how to fabricate curved Volume Phase Holographic (VPH) gratings and, in contrast to the planar gratings of traditional spectrometers, describe how such devices can be used in optical/infrared spectrometers designed specifically for curved diffraction gratings. Volume Phase Holographic gratings are highly efficient compared to conventional surface relief gratings; they have become the disperser of choice in optical / NIR spectrometers. The advantage of spectrometers with curved VPH dispersers is the very small number of optical elements used (the simplest comprising a grating and a spherical mirror), as well as illumination of mirrors off axis, resulting in greater efficiency and reduction in size. We describe a "Half Offner" spectrometer, an even simpler version of the Offner spectrometer. We present an entirely novel design, the Spherical Transmission Grating Spectrometer (STGS), and discuss exemplary applications, including a design for a double-beam spectrometer without any requirement for a dichroic. This paradigm change in spectrometer design offers an alternative to all-refractive astronomical spectrometer designs, using expensive, fragile lens elements fabricated from CaF2 or even more exotic materials. The unobscured mirror layout avoids a major drawback of the previous generation of catadioptric spectrometer designs. We describe laboratory measurements of the efficiency and image quality of a curved VPH grating in a STGS design, demonstrating, simultaneously, efficiency comparable to planar VPH gratings along with good image quality. The stage is now set for construction of a prototype instrument with impressive performance.
Accretion processes for general spherically symmetric compact objects
International Nuclear Information System (INIS)
Bahamonde, Sebastian; Jamil, Mubasher
2015-01-01
We investigate the accretion process for different spherically symmetric space-time geometries for a static fluid. We analyze this procedure using the most general black hole metric ansatz. After that, we examine the accretion process for specific spherically symmetric metrics obtaining the velocity of the sound during the process and the critical speed of the flow of the fluid around the black hole. In addition, we study the behavior of the rate of change of the mass for each chosen metric for a barotropic fluid. (orig.)
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...
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
Spherical near field acoustic holography with microphones mounted on a rigid spherical surface is used to reconstruct the incident sound field. However, reconstruction outside the sphere is an ill-posed inverse problem, and since this is very sensitive to the measurement noise, straightforward...... 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...
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.
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.
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.
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...
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)
Geometry and groups for cosmic topology
International Nuclear Information System (INIS)
Kramer, Peter
2011-01-01
The Cosmic Microwave Background is measured by satellite observation with great precision. It offers insight into its origin in early states of the universe. Unexpected low multipole amplitudes of the incoming CMB radiation may be due to a multiply connected topology of cosmic 3-space. We present and analyze the geometry and homotopy for the family of Platonic spherical 3-manifolds, provide their harmonic analysis, and formulate topological selection rules.
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)
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 Primary Optical Telescope Testbed
National Aeronautics and Space Administration — This IRAD proposes to continue operation of the Spherical Primary Optical Telescope (SPOT) testbed as an image-based wavefront sensing demonstrator. In addition to...
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)
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)
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
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 H......, source location, and orientation will be given on the basis of studying their near-field and power-flow density distributions, total radiated powers, and directivity properties....
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
Mahé, Louis; Roy, Marie-Françoise
1992-01-01
Ten years after the first Rennes international meeting on real algebraic geometry, the second one looked at the developments in the subject during the intervening decade - see the 6 survey papers listed below. Further contributions from the participants on recent research covered real algebra and geometry, topology of real algebraic varieties and 16thHilbert problem, classical algebraic geometry, techniques in real algebraic geometry, algorithms in real algebraic geometry, semialgebraic geometry, real analytic geometry. CONTENTS: Survey papers: M. Knebusch: Semialgebraic topology in the last ten years.- R. Parimala: Algebraic and topological invariants of real algebraic varieties.- Polotovskii, G.M.: On the classification of decomposing plane algebraic curves.- Scheiderer, C.: Real algebra and its applications to geometry in the last ten years: some major developments and results.- Shustin, E.L.: Topology of real plane algebraic curves.- Silhol, R.: Moduli problems in real algebraic geometry. Further contribu...
International Nuclear Information System (INIS)
Lajoie, M-A.; Marleau, G.
2010-01-01
The analysis of VHTR fuel tends to be difficult when using deterministic methods currently employed in lattice codes notably because of limitations on geometry representation and the stochastic positioning of spherical elements. The method proposed here and implemented in the lattice code DRAGON is to generate the positions of multi-layered spheres using random sequential addition, and to analyze the resulting geometry using a full three-dimensional spherical collision probability method. The preliminary validation runs are consistent with results obtained using a Monte-Carlo method, for both regularly and randomly positioned pins. (author)
Analytical solution of space charge limited current for spherical and cylindrical objects
International Nuclear Information System (INIS)
Oksuz, L.
2006-01-01
Analytical solutions for space charge limited currents in collisionless, electron-free sheaths are given for Cartesian, spherical, and cylindrical geometries. Constant current and current density are assumed. Until now, the problem of space charge limited current has not been solved either directly, in terms of series expansions, or numerically, for spherical and cylindrical objects. Analytical results show that the geometry of the system is important for determining the space charge limited current, sheath thickness, and sheath potential profile. This solution method can be used to solve similar nonlinear differential equations
Spherical Demons: Fast Surface Registration
Yeo, B.T. Thomas; Sabuncu, Mert; Vercauteren, Tom; Ayache, Nicholas; Fischl, Bruce; Golland, Polina
2009-01-01
We present the fast Spherical Demons algorithm for registering two spherical images. By exploiting spherical vector spline interpolation theory, we show that a large class of regularizers for the modified demons objective function can be efficiently implemented on the sphere using convolution. Based on the one parameter subgroups of diffeomorphisms, the resulting registration is diffeomorphic and fast – registration of two cortical mesh models with more than 100k nodes takes less than 5 minutes, comparable to the fastest surface registration algorithms. Moreover, the accuracy of our method compares favorably to the popular FreeSurfer registration algorithm. We validate the technique in two different settings: (1) parcellation in a set of in-vivo cortical surfaces and (2) Brodmann area localization in ex-vivo cortical surfaces. PMID:18979813
Gravitational Field of Spherical Branes
Gogberashvili, Merab
The warped solution of Einstein's equations corresponding to the spherical brane in five-dimensional AdS is considered. This metric represents interiors of black holes on both sides of the brane and can provide gravitational trapping of physical fields on the shell. It is found that the analytic form of the coordinate transformations from the Schwarzschild to co-moving frame that exists only in five dimensions. It is shown that in the static coordinates active gravitational mass of the spherical brane, in agreement with Tolman's formula, is negative, i.e. such objects are gravitationally repulsive.
Spherical agglomeration of acetylsalicylic acid
Directory of Open Access Journals (Sweden)
Polowczyk Izabela
2016-01-01
Full Text Available In this paper spherical agglomeration of acetylsalicylic acid was described. In the first step, the system of good and poor solvents as well as bridging liquid was selected. As a result of a preliminary study, ethyl alcohol, water and carbon tetrachloride were used as the good solvent, poor one, and bridging liquid, respectively. Then, the amount of acetylsalicylic acid and the ratio of the solvents as well as the volume of the bridging liquid were examined. In the last step, the agglomeration conditions, such as mixing intensity and time, were investigated. The spherical agglomerates obtained under optimum conditions could be subjected to a tableting process afterwards.
Magnetic actuation and transition shapes of a bistable spherical cap
Directory of Open Access Journals (Sweden)
E.G. Loukaides
2014-10-01
Full Text Available Multistable shells have been proposed for a variety of applications; however, their actuation is almost exclusively addressed through embedded piezoelectric patches. Additional actuation techniques are needed for applications requiring high strains or where remote actuation is desirable. Part of the reason for the lack of research in this area is the absence of appropriate models describing the detailed deformation and energetics of such shells. This work presents a bistable spherical cap made of iron carbonyl-infused polydimethylsiloxane. The magnetizable structure can be actuated remotely through permanent magnets while the transition is recorded with a high-speed camera. Moreover, the experiment is reproduced in a finite element (FE dynamic model for comparison with the physical observations. High-speed footage of the physical cap inversion together with the FE modeling gives valuable insight on preferable intermediate geometries. Both methods return similar values for the magnetic field strength required for the snap-through. High-strain multistable spherical cap transformation is demonstrated, based on informed material selection. We discover that non-axisymmetric transition shapes are preferred in intermediate geometries by bistable spherical caps. We develop the methods for design and analysis of such actuators, including the feasibility of remote actuation methods for multistable shells.
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 microwave confinement and ball lightning
Robinson, William Richard
This dissertation presents the results of research done on unconventional energy technologies from 1995 to 2009. The present civilization depends on an infrastructure that was constructed and is maintained almost entirely using concentrated fuels and ores, both of which will run out. Diffuse renewable energy sources rely on this same infrastructure, and hence face the same limitations. I first examined sonoluminescence directed toward fusion, but demonstrated theoretically that this is impossible. I next studied Low Energy Nuclear Reactions and developed methods for improving results, although these have not been implemented. In 2000, I began Spherical Microwave Confinement (SMC), which confines and heats plasma with microwaves in a spherical chamber. The reactor was designed and built to provide the data needed to investigate the possibility of achieving fusion conditions with microwave confinement. A second objective was to attempt to create ball lightning (BL). The reactor featured 20 magnetrons, which were driven by a capacitor bank and operated in a 0.2 s pulse mode at 2.45 GHz. These provided 20 kW to an icosahedral array of 20 antennas. Video of plasmas led to a redesign of the antennas to provide better coupling of the microwaves to the plasma. A second improvement was a grid at the base of the antennas, which provided corona electrons and an electric field to aid quick formation of plasmas. Although fusion conditions were never achieved and ball lightning not observed, experience gained from operating this basic, affordable system has been incorporated in a more sophisticated reactor design intended for future research. This would use magnets that were originally planned. The cusp geometry of the magnetic fields is suitable for electron cyclotron resonance in the same type of closed surface that in existing reactors has generated high-temperature plasmas. Should ball lightning be created, it could be a practical power source with nearly ideal
Spherical Pendulum, Actions, and Spin
Richter, Peter H.; Dullin, Holger R.; Waalkens, Holger; Wiersig, Jan
1996-01-01
The classical and quantum mechanics of a spherical pendulum are worked out, including the dynamics of a suspending frame with moment of inertia θ. The presence of two separatrices in the bifurcation diagram of the energy-momentum mapping has its mathematical expression in the hyperelliptic nature of
Testing for Bivariate Spherical Symmetry
Einmahl, J.H.J.; Gantner, M.
2010-01-01
An omnibus test for spherical symmetry in R2 is proposed, employing localized empirical likelihood. The thus obtained test statistic is distri- bution-free under the null hypothesis. The asymptotic null distribution is established and critical values for typical sample sizes, as well as the
A charged spherically symmetric solution
Indian Academy of Sciences (India)
A charged spherically symmetric solution. K MOODLEY, S D MAHARAJ and K S GOVINDER. School of Mathematical and Statistical Sciences, University of Natal, Durban 4041, South Africa. Email: maharaj@nu.ac.za. MS received 8 April 2002; revised 7 April 2003; accepted 23 June 2003. Abstract. We find a solution of the ...
Cooperative effects in spherical spasers
DEFF Research Database (Denmark)
Bordo, Vladimir
2017-01-01
A fully analytical semiclassical theory of cooperative optical processes which occur in an ensemble of molecules embedded in a spherical core-shell nanoparticle is developed from first principles. Both the plasmonic Dicke effect and spaser generation are investigated for the designs in which...
Testing for bivariate spherical symmetry
Einmahl, J.H.J.; Gantner, M.
2012-01-01
An omnibus test for spherical symmetry in R2 is proposed, employing localized empirical likelihood. The thus obtained test statistic is distribution free under the null hypothesis. The asymptotic null distribution is established and critical values for typical sample sizes, as well as the asymptotic
Numerical Simulations of Thermal Convection in Rapidly Rotating Spherical Shell
Energy Technology Data Exchange (ETDEWEB)
Nenkov, Constantine; Peltier, Richard, E-mail: nenkov@atmosp.physics.utoronto.ca, E-mail: peltier@atmosp.physics.utoronto.ca [Department of Physics, University of Toronto Toronto, Ontario, M5S 1A7 (Canada)
2010-11-01
We present a novel numerical model used to simulate convection in the atmospheres of the Gas Giant planets Jupiter and Saturn. Nonlinear, three-dimensional, time-dependant solutions of the anelastic hydrodynamic equations are presented for a stratified, rotating spherical fluid shell heated from below. This new model is specified in terms of a grid-point based methodology which employs a hierarchy of tessellations of the regular icosahedron onto the sphere through the process of recurrent dyadic refinements of the spherical surface. We describe discretizations of the governing equations in which all calculations are performed in Cartesian coordinates in the local neighborhoods of the almost uniform icosahedral grid, a methodology which avoids the potential mathematical and numerical difficulties associated with the pole problem in spherical geometry. Using this methodology we have built our model in primitive equations formulation, whereas the three-dimensional vector velocity field and temperature are directly advanced in time. We show results of thermal convection in rapidly rotating spherical shell which leads to the formation of well pronounced prograde zonal jets at the equator, results which previous experiments with two-dimensional models in the limit of freely evolving turbulence were not able to achieve.
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
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)
Geometry essentials for dummies
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
Introduction to projective geometry
Wylie, C R
2008-01-01
This lucid introductory text offers both an analytic and an axiomatic approach to plane projective geometry. The analytic treatment builds and expands upon students' familiarity with elementary plane analytic geometry and provides a well-motivated approach to projective geometry. Subsequent chapters explore Euclidean and non-Euclidean geometry as specializations of the projective plane, revealing the existence of an infinite number of geometries, each Euclidean in nature but characterized by a different set of distance- and angle-measurement formulas. Outstanding pedagogical features include w
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
Nonlinear MHD simulations of spherical tokamak and helical plasmas
Energy Technology Data Exchange (ETDEWEB)
Hayashi, T.; Mizuguchi, N.; Miura, H.; Kanno, R.; Nakajima, N.; Okamoto, M. [National Inst. for Fusion Science, Toki, Gifu (Japan)
2002-11-01
Nonlinear magnetohydrodynamic (MHD) simulations on relaxation phenomena in a spherical tokamak and a helical plasma, including three-dimensional (3D) equilibrium computations, are executed in full toroidal geometries. For a spherical tokamak, two-step evolution of the medium-n ballooning instabilities and a successive excitation of an internal n=1 crash has been observed. A similar process has been observed in an actual tokamak experiment of TFTR. The process is compared with a previous simulation for another MHD activity that is called the internal reconnection event (IRE). Three dimensional equilibrium code HINT is modified to extend functions, by which an n=1 island structure used for the local island diverter (LID) experiment in the LHD device is analyzed in finite pressure equilibria. Nonlinear simulations are executed for LHD plasma and pressure deformation due to evolution of m=2/n=1 pressure driven mode is observed, which has larger growth rate and saturation level than medium-n ballooning modes. (author)
Spherically symmetric high-velocity plasma expansions into background gases
Tan, T.-H.; Borovsky, J. E.
1986-01-01
Spherically symmetric plasmas with high expansion velocities have been produced by irradiating targets with eight beams from the Helios CO2 laser in the presence of gases at various pressures. Attention was given to the properties of the target-emitted ions in order to obtain information about the ion-acceleration mechanisms in plasma expansions. Photoionization of the ambient gases by the soft X-ray emission from the laser-irradiated targets produced background plasmas, permitting plasma counterstreaming experiments to be performed in spherical geometry. Successful laser-target coupling in the presence of back-ground gases is obtained; modification of the ion acceleration in accordance with isothermal-expansion models is observed; and an absence of collective coupling between collisionless counterstreaming plasmas is found.
Spherically symmetric elasticity in relativity
Energy Technology Data Exchange (ETDEWEB)
Carot, J [Departament de Fisica, Universitat de les Illes Balears, Cra Valldemossa pk 7.5, E-07122 Palma (Spain); Brito, I; Vaz, E G L R, E-mail: jcarot@uib.ca, E-mail: ireneb@mct.uminho.p, E-mail: evaz@mct.uminho.p
2010-05-01
The relativistic theory of elasticity is reviewed within the spherically symmetric context with a view towards the modelling of star interiors possessing elastic properties such as the ones expected in neutron stars. Emphasis is placed on generality in the main sections of the paper, and the results are then applied to specific examples. Along the way, a few general results for spacetimes admitting isometries are deduced, and their consequences are fully exploited in the case of spherical symmetry relating them next to the the case in which the material content of the spacetime is some elastic material. This paper extends and generalizes the pioneering work by Magli and Kijowski [1], Magli [2] and [3], and complements, in a sense, that by Karlovini and Samuelsson in their interesting series of papers [4], [5] and [6].
Small-angle modification of the radiative transfer equation for a pseudo-spherical atmosphere
International Nuclear Information System (INIS)
Efremenko, Dmitry; Doicu, Adrian; Loyola, Diego; Trautmann, Thomas
2013-01-01
The conventional pseudo-spherical technique relies on the separation of the total radiance into the direct solar beam and the diffuse radiance; the direct solar radiance is treated in a spherical geometry, while the diffuse radiance is computed in a plane-parallel geometry. In the small-angle modification of the radiative transfer equation, the total radiance is separated into an anisotropic part and a regular part. In this paper, we pOresent two formulations of the small-angle modification of the radiative transfer equation for a pseudo-spherical atmosphere. In the first formulation, we solve the radiative transfer equation for the diffuse radiance in a pseudo-spherical atmosphere with an additional anisotropic source term computed in a plane-parallel atmosphere, while in the second formulation we solve the radiative transfer equation for the regular solution in a plane-parallel atmosphere with an additional pseudo-spherical correction term. The numerical analysis revealed that the accuracy of the small-angle models is acceptable. -- Highlights: ► The small-angle modification of DOM for a pseudo-spherical atmosphere is formulated. ► The small-angle modification is tested for atmospheric remote sensing. ► The accuracy of small-angle modification is higher than delta-M approximation.
Testing for bivariate spherical symmetry
Einmahl, J.H.J.; Gantner, M.
2012-01-01
An omnibus test for spherical symmetry in R2 is proposed, employing localized empirical likelihood. The thus obtained test statistic is distri- bution-free under the null hypothesis. The asymptotic null distribution is established and critical values for typical sample sizes, as well as the asymptotic ones, are presented. In a simulation study, the good perfor- mance of the test is demonstrated. Furthermore, a real data example is presented.
Solutocapillary convection in spherical shells
Subramanian, Pravin; Zebib, Abdelfattah; McQuillan, Barry
2005-01-01
A linear stability study of solutocapillary driven Marangoni instabilities in small spherical shells is presented. The shells contain a binary fluid with an evaporating solvent. The viscosity is a strong function of the solvent concentration, the inner surface of the shell is assumed impermeable and stress free, while nonlinear boundary conditions are modeled and prescribed at the receding outer boundary. A time-dependent diffusive state is possible and may lose stability through the Marangoni mechanism due to surface tension dependence on solvent concentration (buoyant forces are negligible in this microscale problem). A frozen-time or quasisteady state linear stability analysis is performed to compute the critical Reynolds number and degree of surface harmonics, as well as the maximum growth rate of perturbations at specified parameters. The development of maximum growth rates in time was also computed by solving the initial value problem with random initial conditions. Results from both approaches are in good agreement except at short times where there is dependence on initial conditions. The physical problem models the manufacturing of spherical shells used as targets in inertial confinement fusion experiments where perfect sphericity is demanded for efficient fusion ignition. It is proposed that the Marangoni instability might be the source of observed surface roughness. Comparisons with the available experiments are made with reasonable qualitative and quantitative agreement.
Spherical gearing with intermediate ball elements: parameter ranges with a high contact ratio
Gorbenko, M. V.; Gorbenko, T. I.
2017-02-01
The paper presents analytical research of the geometry and kinematical parameters of spherical gearing with ball intermediate elements. The main attention is paid to the influence of the offset coefficient on the tooth geometry generation, the contact ratio and the motion transmission angle. Intermediate ball element racetracks on the gear are trochoidal curves on a spherical surface. Two areas for the offset coefficient values providing a high value of the contact ratio - basic trochoid (without offset) and prolate trochoid with abutting racetracks of adjacent ball elements ― were revealed. Analysis of the investigated parameters showed that for power transmission, it is preferable to use spherical gearing without an offset, and for kinematic transmission, it is possible to use profiles with a large offset. The present study allows making a rational choice of geometrical parameters depending on the transmission predestination.
Geometry-induced protein pattern formation.
Thalmeier, Dominik; Halatek, Jacob; Frey, Erwin
2016-01-19
Protein patterns are known to adapt to cell shape and serve as spatial templates that choreograph downstream processes like cell polarity or cell division. However, how can pattern-forming proteins sense and respond to the geometry of a cell, and what mechanistic principles underlie pattern formation? Current models invoke mechanisms based on dynamic instabilities arising from nonlinear interactions between proteins but neglect the influence of the spatial geometry itself. Here, we show that patterns can emerge as a direct result of adaptation to cell geometry, in the absence of dynamical instability. We present a generic reaction module that allows protein densities robustly to adapt to the symmetry of the spatial geometry. The key component is an NTPase protein that cycles between nucleotide-dependent membrane-bound and cytosolic states. For elongated cells, we find that the protein dynamics generically leads to a bipolar pattern, which vanishes as the geometry becomes spherically symmetrical. We show that such a reaction module facilitates universal adaptation to cell geometry by sensing the local ratio of membrane area to cytosolic volume. This sensing mechanism is controlled by the membrane affinities of the different states. We apply the theory to explain AtMinD bipolar patterns in [Formula: see text] EcMinDE Escherichia coli. Due to its generic nature, the mechanism could also serve as a hitherto-unrecognized spatial template in many other bacterial systems. Moreover, the robustness of the mechanism enables self-organized optimization of protein patterns by evolutionary processes. Finally, the proposed module can be used to establish geometry-sensitive protein gradients in synthetic biological systems.
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.
Theoretical Study of a Spherical Plasma Focus
Ay, Yasar
A theoretical model is developed for two concentric electrodes spherical plasma focus device in order to investigate the plasma sheath dynamics, radiative emission, and the ion properties. The work focuses on the model development of the plasma sheath dynamics and its validation, followed by studying of the radiation effects and the beam-ion properties in such unique geometry as a pulsed source for neutrons, soft and hard x-rays, and electron and ion beams. Chapter 1 is an introduction on fusion systems including plasma focus. Chapter 2 is an extensive literature survey on plasma focus modeling and experiments including the various radiations and their mechanism. Chapter 3 details modeling and validation of the plasma sheath dynamics model with comparison between hydrogen, deuterium, tritium and deuterium-tritium mixture for the production of pulsed neutrons. Chapter 4 is a study of the radiative phase, in which neutron yield is investigated, as well as the predicted beam-ion properties. Chapter 5 summarizes and discusses the results. Chapter 6 provides concluding remarks and proposed future works. The phases of the developed model are the rundown phase I, rundown phase II, the reflected phase and a radiative phase. The rundown phase I starts immediately after the completion of the gas breakdown and ends when the current sheath reaches the equator point of the spherical shape. Then immediately followed by rundown phase II to start and it ends when the shock front hits the axis, which is the beginning of the reflected shock phase. Reflected shock front moves towards the incoming current sheath and meets it which is both the end of the reflected shock phase and the beginning of the radiative phase. After the reflected shock front and the current sheath meet, the current sheath continues to move radially inward by compressing the produced plasma column until it reaches the axis. Since the discharge current contains important information about the plasma dynamic
Euclidean geometry and transformations
Dodge, Clayton W
1972-01-01
This introduction to Euclidean geometry emphasizes transformations, particularly isometries and similarities. Suitable for undergraduate courses, it includes numerous examples, many with detailed answers. 1972 edition.
International Nuclear Information System (INIS)
Hrivnacova, I; Viren, B
2008-01-01
The Virtual Geometry Model (VGM) was introduced at CHEP in 2004 [1], where its concept, based on the abstract interfaces to geometry objects, has been presented. Since then, it has undergone a design evolution to pure abstract interfaces, it has been consolidated and completed with more advanced features. Currently it is used in Geant4 VMC for the support of TGeo geometry definition with Geant4 native geometry navigation and recently it has been used in the validation of the G4Root tool. The implementation of the VGM for a concrete geometry model represents a small layer between the VGM and the particular native geometry. In addition to the implementations for Geant4 and Root TGeo geometry models, there is now added the third one for AGDD, which together with the existing XML exporter makes the VGM the most advanced tool for exchanging geometry formats providing 9 ways of conversions between Geant4, TGeo, AGDD and GDML models. In this presentation we will give the overview and the present status of the tool, we will review the supported features and point to possible limits in converting geometry models
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
Fundamental concepts of geometry
Meserve, Bruce E
1983-01-01
Demonstrates relationships between different types of geometry. Provides excellent overview of the foundations and historical evolution of geometrical concepts. Exercises (no solutions). Includes 98 illustrations.
Algorithms in Algebraic Geometry
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
Sphere quadtrees - A new data structure to support the visualization of spherically distributed data
Fekete, Gyorgy; Treinish, Lloyd
1990-01-01
The concept of the sphere quadtree (SQT) is introduced to enable the structuring of spherically distributed data to be consistent with its geometry and facilitate mapping of the data onto a flat file system. The SQT is based on the recursive subdivision of the spherical triangles that result from the projection of the faces of an icosahedron onto a sphere. The SQT concept is insensitive to the distortions that occur far from the equator in spherically distributed data sets. Geographic data can be shown at several levels and at any resolution, allowing a system of referencing between data sets of different resolutions as well as data that are not geographically registered. SQTs are found to facilitate the search for particular spherically distributed data sets and improve the efficiency of surface rendering algorithms.
Kaufmann, Matthew L.; Bomer, Megan A.; Powell, Nancy Norem
2009-01-01
Students enter the geometry classroom with a strong concept of fairness and a sense of what it means to "play by the rules," yet many students have difficulty understanding the postulates, or rules, of geometry and their implications. Although they may never have articulated the properties of an axiomatic system, they have gained a practical…
Foundations of algebraic geometry
Weil, A
1946-01-01
This classic is one of the cornerstones of modern algebraic geometry. At the same time, it is entirely self-contained, assuming no knowledge whatsoever of algebraic geometry, and no knowledge of modern algebra beyond the simplest facts about abstract fields and their extensions, and the bare rudiments of the theory of ideals.
Supersymmetric Sigma Model Geometry
Directory of Open Access Journals (Sweden)
Ulf Lindström
2012-08-01
Full Text Available This is a review of how sigma models formulated in Superspace have become important tools for understanding geometry. Topics included are: The (hyperkähler reduction; projective superspace; the generalized Legendre construction; generalized Kähler geometry and constructions of hyperkähler metrics on Hermitian symmetric spaces.
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
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.
A Spherical Aerial Terrestrial Robot
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.
Collisions in spherical stellar systems
Energy Technology Data Exchange (ETDEWEB)
Polyachenko, V.L.; Shukhman, I.G. (AN SSSR, Irkutsk. Sibirskij Inst. Zemnogo Magnetizma Ionosfery i Rasprostraneniya Radiovoln)
From the set of the equations for the stellar distribution function and for the two-particle correlation in the action- angle variables, by averaging over fast finite motions the general expression for the collisional term of a finite stellar system with ''rare'' Coulomb collisions is obtained. In the case of a spherically symmetrical system with the distribution function f/sub 0/=f/sub 0/(E, L) (E, L being the energy and the angular momentum of a star), the kinetic equation is reduced to the standard form of the two-dimensional Fokker-Planck equations.
Spherical Orbifolds for Cosmic Topology
International Nuclear Information System (INIS)
Kramer, Peter
2012-01-01
Harmonic analysis is a tool to infer cosmic topology from the measured astrophysical cosmic microwave background CMB radiation. For overall positive curvature, Platonic spherical manifolds are candidates for this analysis. We combine the specific point symmetry of the Platonic manifolds with their deck transformations. This analysis in topology leads from manifolds to orbifolds. We discuss the deck transformations of the orbifolds and give eigenmodes for the harmonic analysis as linear combinations of Wigner polynomials on the 3-sphere. These provide new tools for detecting cosmic topology from the CMB radiation.
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.
Three-dimensional spherical analyses of cosmological spectroscopic surveys
Nicola, Andrina; Refregier, Alexandre; Amara, Adam; Paranjape, Aseem
2014-09-01
Spectroscopic redshift surveys offer great prospects for constraining the dark sector in cosmology. Future surveys will however be both deep and wide and will thus require an analysis in three-dimensional spherical geometry. We review and compare several methods which have been proposed in the literature for this purpose, focusing in particular on implementations of the spherical harmonic tomography (SHT) power spectrum Clij and the spherical Fourier Bessel (SFB) power spectrum Cl(k ,k'). Using a Fisher analysis, we compare the forecasted constraints on cosmological parameters using these statistics. These constraints typically rely on approximations such as the Limber approximation and make specific choices in the numerical implementation of each statistic. Using a series of toy models, we explore the applicability of these approximations and study the sensitivity of the SHT and SFB statistics to the details of their implementation. In particular, we show that overlapping redshift bins may improve cosmological constraints using the SHT statistic when the number of bins is small, and that the SFB constraints are quite robust to changes in the assumed distance-redshift relation. We also find that the SHT can be tailored to be more sensitive to modes at redshifts close to the survey boundary, while the SFB appears better suited to capture information beyond the smooth shape of the power spectrum. In this context, we discuss the pros and cons of the different techniques and their impact on the design and analysis of future wide field spectroscopic surveys.
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)
d-AO spherical aromaticity in Ce6O8.
Yu, Xiaohu; Oganov, Artem R; Popov, Ivan A; Boldyrev, Alexander I
2016-01-05
After the first introduction of π aromaticity in chemistry to explain the bonding, structure, and reactivity of benzene and its derivatives, this concept was further applied to many other compounds featuring other types of aromaticity (i.e., σ, δ). Thus far, there have been no reports on d-AO-based spherical σ aromaticity. Here, we predict a highly stable bare Ce6O8 cluster of a spherical shape using evolutionary algorithm USPEX and DFT + U calculations. Natural bond orbital analysis, adaptive natural density partitioning algorithm, electron localization function, and partial charge plots demonstrate that bare Ce6O8 cluster exhibits d-AO spherical σ aromaticity, thus explaining its exotic geometry and stability. Ce6O8 complex plays an important role in many reactions and is known to exist in many forms, such as in NH4[Ce6(μ(3)O)5(μ(3)OH)3(μ(2)-C6H5COO)9(NO3)3(DMF)3]*DMF*H2O compound, which is prepared under room temperature, and acts as an oxidizing agent. © 2015 Wiley Periodicals, Inc.
Spherical resonators coated by glass and glass-ceramic films
Ristic, Davor; Chiappini, Andrea; Chiasera, Alessandro; Armellini, Cristina; Carpentiero, Alessandro; Mazzola, Maurizio; Moser, Enrico; Varas, Stefano; Berneschi, Simone; Nunzi Conti, Gualtiero; Pelli, Stefano; Soria, Silvia; Speranza, Giorgio; Lunelli, Lorenzo; Pederzolli, Cecilia; Prudenzano, Francesco; Feron, Patrice; Ivanda, Mile; Cibiel, Gilles; Righini, Giancarlo C.; Ferrari, Maurizio
2012-02-01
Coating of spherical microresonators is a very promising technique for optimizing their optical properties. Optical coatings are constituted by glasses, polymer, and glass ceramics, passive or activated by luminescent species, Glass ceramic activated by rare earth ions are nanocomposite systems that exhibit specific morphologic, structural and spectroscopic properties allowing to develop interesting new physical concepts, for instance the mechanism related to the transparency, as well as novel photonic devices based on the enhancement of the luminescence. At the state of art the fabrication techniques based on bottom-up and top-down approaches appear to be viable although a specific effort is required to achieve the necessary reliability and reproducibility of the preparation protocols. In particular, the dependence of the final product on the specific parent glass and on the employed synthesis still remain an important task of the research in material science. Looking to application, the enhanced spectroscopic properties typical of glass ceramic in respect to those of the amorphous structures constitute an important point for the development of integrated optics devices, including coating of spherical microresonators. Here we present a review regarding spherical microresonators coated by glass and glass-ceramic film activated by Er3+ ions. Er3+ ions appear to be embedded in a crystalline or amorphous environment and the lifetime dynamic is influenced by the geometry and by the morphology of the system. Photoluminescence results and morphologic properties are discussed for both amorphous and glass ceramic films.
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
Casimir effect in spherical shells
International Nuclear Information System (INIS)
Ruggiero, J.R.
1985-01-01
The analytic regularization method is applied to study the Casimir effect for spherical cavities. Although many works have been presented in the past few years, problems related to the elimination of the regulator parameter still remain. A way to calculate the zero point energy of a perfectly conducting spherical shell which is a miscellaneous of those presented early is here proposed, How a cancelation of divergent terms occurs and how a finite parte is obtained after the elimination of the regulator parameter is shown. As a by-product the zero point energy of the interior vibration modes is obtained and this has some relevance to the quarks bag model. This relev ance is also discussed. The calculation of the energy fom the density view is also discussed. Some works in this field are criticized. The logarithmic divergent terms in the zero point energy are studied when the interior and exterior of the sphere are considered as a medium not dispersive and characterized by a dielectric constants ε 1 and ε 2 and peermeability constants μ 1 and μ 2 respectivelly. The logarithmic divergent terms are not present in the case of ε i μ i =K, with K some constant and i=1,2. (author) [pt
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
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.
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
Complex and symplectic geometry
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.
How should spin-weighted spherical functions be defined?
Boyle, Michael
2016-09-01
Spin-weighted spherical functions provide a useful tool for analyzing tensor-valued functions on the sphere. A tensor field can be decomposed into complex-valued functions by taking contractions with tangent vectors on the sphere and the normal to the sphere. These component functions are usually presented as functions on the sphere itself, but this requires an implicit choice of distinguished tangent vectors with which to contract. Thus, we may more accurately say that spin-weighted spherical functions are functions of both a point on the sphere and a choice of frame in the tangent space at that point. The distinction becomes extremely important when transforming the coordinates in which these functions are expressed, because the implicit choice of frame will also transform. Here, it is proposed that spin-weighted spherical functions should be treated as functions on the spin or rotation groups, which simultaneously tracks the point on the sphere and the choice of tangent frame by rotating elements of an orthonormal basis. In practice, the functions simply take a quaternion argument and produce a complex value. This approach more cleanly reflects the geometry involved, and allows for a more elegant description of the behavior of spin-weighted functions. In this form, the spin-weighted spherical harmonics have simple expressions as elements of the Wigner 𝔇 representations, and transformations under rotation are simple. Two variants of the angular-momentum operator are defined directly in terms of the spin group; one is the standard angular-momentum operator L, while the other is shown to be related to the spin-raising operator ð.
Busemann, Herbert
2005-01-01
A comprehensive approach to qualitative problems in intrinsic differential geometry, this text examines Desarguesian spaces, perpendiculars and parallels, covering spaces, the influence of the sign of the curvature on geodesics, more. 1955 edition. Includes 66 figures.
Introduction to tropical geometry
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...
Melzak, Z A
2008-01-01
Intended for students of many different backgrounds with only a modest knowledge of mathematics, this text features self-contained chapters that can be adapted to several types of geometry courses. 1983 edition.
Rudiments of algebraic geometry
Jenner, WE
2017-01-01
Aimed at advanced undergraduate students of mathematics, this concise text covers the basics of algebraic geometry. Topics include affine spaces, projective spaces, rational curves, algebraic sets with group structure, more. 1963 edition.
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.
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...
Lectures on Symplectic Geometry
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...
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)
Relationships between solid spherical and toroidal harmonics
Majic, Matt; Ru, Eric C. Le
2018-01-01
We derive new relationships expressing solid spherical harmonics as series of toroidal harmonics and vice versa. The expansions include regular and irregular spherical harmonics, ring and axial toroidal harmonics of even and odd parity about the plane of the torus. The expansion coefficients are given in terms of a recurrence relation. As an example application we apply one of the expansions to express the potential of a charged conducting torus on a basis of spherical harmonics.
Implosions and hypertoric geometry
DEFF Research Database (Denmark)
Dancer, A.; Kirwan, F.; Swann, A.
2013-01-01
The geometry of the universal hyperkahler implosion for SU (n) is explored. In particular, we show that the universal hyperkahler implosion naturally contains a hypertoric variety described in terms of quivers. Furthermore, we discuss a gauge theoretic approach to hyperkahler implosion.......The geometry of the universal hyperkahler implosion for SU (n) is explored. In particular, we show that the universal hyperkahler implosion naturally contains a hypertoric variety described in terms of quivers. Furthermore, we discuss a gauge theoretic approach to hyperkahler implosion....
Intermediate algebra & analytic geometry
Gondin, William R
1967-01-01
Intermediate Algebra & Analytic Geometry Made Simple focuses on the principles, processes, calculations, and methodologies involved in intermediate algebra and analytic geometry. The publication first offers information on linear equations in two unknowns and variables, functions, and graphs. Discussions focus on graphic interpretations, explicit and implicit functions, first quadrant graphs, variables and functions, determinate and indeterminate systems, independent and dependent equations, and defective and redundant systems. The text then examines quadratic equations in one variable, system
Spherical Collapse in Chameleon Models
Brax, Ph; Steer, D A
2010-01-01
We study the gravitational collapse of an overdensity of nonrelativistic matter under the action of gravity and a chameleon scalar field. We show that the spherical collapse model is modified by the presence of a chameleon field. In particular, we find that even though the chameleon effects can be potentially large at small scales, for a large enough initial size of the inhomogeneity the collapsing region possesses a thin shell that shields the modification of gravity induced by the chameleon field, recovering the standard gravity results. We analyse the behaviour of a collapsing shell in a cosmological setting in the presence of a thin shell and find that, in contrast to the usual case, the critical density for collapse depends on the initial comoving size of the inhomogeneity.
Spherical collapse in chameleon models
International Nuclear Information System (INIS)
Brax, Ph.; Rosenfeld, R.; Steer, D.A.
2010-01-01
We study the gravitational collapse of an overdensity of nonrelativistic matter under the action of gravity and a chameleon scalar field. We show that the spherical collapse model is modified by the presence of a chameleon field. In particular, we find that even though the chameleon effects can be potentially large at small scales, for a large enough initial size of the inhomogeneity the collapsing region possesses a thin shell that shields the modification of gravity induced by the chameleon field, recovering the standard gravity results. We analyse the behaviour of a collapsing shell in a cosmological setting in the presence of a thin shell and find that, in contrast to the usual case, the critical density for collapse in principle depends on the initial comoving size of the inhomogeneity
Osborne, I.; Brownson, E.; Eulisse, G.; Jones, C. D.; Lange, D. J.; Sexton-Kennedy, E.
2014-06-01
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.
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
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.
Quantification of intraventricular hemorrhage is consistent using a spherical sensitivity matrix
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.
DEFF Research Database (Denmark)
Lowes, F.J.; Olsen, Nils
2004-01-01
, led to quite inaccurate variance estimates. We estimate correction factors which range from 1/4 to 20, with the largest increases being for the zonal, m = 0, and sectorial, m = n, terms. With no correction, the OSVM variances give a mean-square vector field error of prediction over the Earth's surface......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...
Sources of hyperbolic geometry
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...
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
Spherically symmetric inhomogeneous dust collapse in higher ...
Indian Academy of Sciences (India)
We consider a collapsing spherically symmetric inhomogeneous dust cloud in higher dimensional space-time. ... The existence of strong curvature naked singularities in gravitational collapse of spherically symmetric space-times ... where an over dot denotes partial derivative with respect to t. The functions F(r) and f(r).
How Spherical Is a Cube (Gravitationally)?
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…
2002-01-01
Discrete geometry investigates combinatorial properties of configurations of geometric objects. To a working mathematician or computer scientist, it offers sophisticated results and techniques of great diversity and it is a foundation for fields such as computational geometry or combinatorial optimization. This book is primarily a textbook introduction to various areas of discrete geometry. In each area, it explains several key results and methods, in an accessible and concrete manner. It also contains more advanced material in separate sections and thus it can serve as a collection of surveys in several narrower subfields. The main topics include: basics on convex sets, convex polytopes, and hyperplane arrangements; combinatorial complexity of geometric configurations; intersection patterns and transversals of convex sets; geometric Ramsey-type results; polyhedral combinatorics and high-dimensional convexity; and lastly, embeddings of finite metric spaces into normed spaces. Jiri Matousek is Professor of Com...
Ochiai, T.; Nacher, J. C.
2011-09-01
Recently, the application of geometry and conformal mappings to artificial materials (metamaterials) has attracted the attention in various research communities. These materials, characterized by a unique man-made structure, have unusual optical properties, which materials found in nature do not exhibit. By applying the geometry and conformal mappings theory to metamaterial science, it may be possible to realize so-called "Harry Potter cloaking device". Although such a device is still in the science fiction realm, several works have shown that by using such metamaterials it may be possible to control the direction of the electromagnetic field at will. We could then make an object hidden inside of a cloaking device. Here, we will explain how to design invisibility device using differential geometry and conformal mappings.
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...
Cecil, Thomas E
2015-01-01
This exposition provides the state-of-the art on the differential geometry of hypersurfaces in real, complex, and quaternionic space forms. Special emphasis is placed on isoparametric and Dupin hypersurfaces in real space forms as well as Hopf hypersurfaces in complex space forms. The book is accessible to a reader who has completed a one-year graduate course in differential geometry. The text, including open problems and an extensive list of references, is an excellent resource for researchers in this area. Geometry of Hypersurfaces begins with the basic theory of submanifolds in real space forms. Topics include shape operators, principal curvatures and foliations, tubes and parallel hypersurfaces, curvature spheres and focal submanifolds. The focus then turns to the theory of isoparametric hypersurfaces in spheres. Important examples and classification results are given, including the construction of isoparametric hypersurfaces based on representations of Clifford algebras. An in-depth treatment of Dupin hy...
Intrinsic cylindrical and spherical waves
International Nuclear Information System (INIS)
Ludlow, I K
2008-01-01
Intrinsic waveforms associated with cylindrical and spherical Bessel functions are obtained by eliminating the factors responsible for the inverse radius and inverse square radius laws of wave power per unit area of wavefront. The resulting expressions are Riccati-Bessel functions for both cases and these can be written in terms of amplitude and phase functions of order v and wave variable z. When z is real, it is shown that a spatial phase angle of the intrinsic wave can be defined and this, together with its amplitude function, is systematically investigated for a range of fixed orders and varying z. The derivatives of Riccati-Bessel functions are also examined. All the component functions exhibit different behaviour in the near field depending on the order being less than, equal to or greater than 1/2. Plots of the phase angle can be used to display the locations of the zeros of the general Riccati-Bessel functions and lead to new relations concerning the ordering of the real zeros of Bessel functions and the occurrence of multiple zeros when the argument of the Bessel function is fixed
Osmotic buckling of spherical capsules.
Knoche, Sebastian; Kierfeld, Jan
2014-11-07
We study the buckling of elastic spherical shells under osmotic pressure with the osmolyte concentration of the exterior solution as a control parameter. We compare our results for the bifurcation behavior with results for buckling under mechanical pressure control, that is, with an empty capsule interior. We find striking differences for the buckling states between osmotic and mechanical buckling. Mechanical pressure control always leads to fully collapsed states with opposite sides in contact, whereas uncollapsed states with a single finite dimple are generic for osmotic pressure control. For sufficiently large interior osmolyte concentrations, osmotic pressure control is qualitatively similar to buckling under volume control with the volume prescribed by the osmolyte concentrations inside and outside the shell. We present a quantitative theory which also captures the influence of shell elasticity on the relationship between osmotic pressure and volume. These findings are relevant for the control of buckled shapes in applications. We show how the osmolyte concentration can be used to control the volume of buckled shells. An accurate analytical formula is derived for the relationship between the osmotic pressure, the elastic moduli and the volume of buckled capsules. This also allows use of elastic capsules as osmotic pressure sensors or deduction of elastic properties and the internal osmolyte concentration from shape changes in response to osmotic pressure changes. We apply our findings to published experimental data on polyelectrolyte capsules.
Yale, Paul B
2012-01-01
This book is an introduction to the geometry of Euclidean, affine, and projective spaces with special emphasis on the important groups of symmetries of these spaces. The two major objectives of the text are to introduce the main ideas of affine and projective spaces and to develop facility in handling transformations and groups of transformations. Since there are many good texts on affine and projective planes, the author has concentrated on the n-dimensional cases.Designed to be used in advanced undergraduate mathematics or physics courses, the book focuses on ""practical geometry,"" emphasi
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
MacKeown, P. K.
1984-01-01
Clarifies two concepts of gravity--those of a fictitious force and those of how space and time may have geometry. Reviews the position of Newton's theory of gravity in the context of special relativity and considers why gravity (as distinct from electromagnetics) lends itself to Einstein's revolutionary interpretation. (JN)
Implosions and hypertoric geometry
DEFF Research Database (Denmark)
Dancer, A.; Kirwan, F.; Swann, A.
2013-01-01
The geometry of the universal hyperkahler implosion for SU (n) is explored. In particular, we show that the universal hyperkahler implosion naturally contains a hypertoric variety described in terms of quivers. Furthermore, we discuss a gauge theoretic approach to hyperkahler implosion....
Boyer, Carl B
2012-01-01
Designed as an integrated survey of the development of analytic geometry, this study presents the concepts and contributions from before the Alexandrian Age through the eras of the great French mathematicians Fermat and Descartes, and on through Newton and Euler to the "Golden Age," from 1789 to 1850.
Hartshorne, Robin
2000-01-01
In recent years, I have been teaching a junior-senior-level course on the classi cal geometries. This book has grown out of that teaching experience. I assume only high-school geometry and some abstract algebra. The course begins in Chapter 1 with a critical examination of Euclid's Elements. Students are expected to read concurrently Books I-IV of Euclid's text, which must be obtained sepa rately. The remainder of the book is an exploration of questions that arise natu rally from this reading, together with their modern answers. To shore up the foundations we use Hilbert's axioms. The Cartesian plane over a field provides an analytic model of the theory, and conversely, we see that one can introduce coordinates into an abstract geometry. The theory of area is analyzed by cutting figures into triangles. The algebra of field extensions provides a method for deciding which geometrical constructions are possible. The investigation of the parallel postulate leads to the various non-Euclidean geometries. And ...
Wares, Arsalan; Elstak, Iwan
2017-01-01
The purpose of this paper is to describe the mathematics that emanates from the construction of an origami box. We first construct a simple origami box from a rectangular sheet and then discuss some of the mathematical questions that arise in the context of geometry and algebra. The activity can be used as a context for illustrating how algebra…
DEFF Research Database (Denmark)
Frisvad, Jeppe Revall
2008-01-01
, whether the shape of the material should be coupled to the appearance model or not, etc. A generalised concept of shape and geometry is presented to provide a framework for handling these many degrees of freedom. Constraints between input and output parameters are modelled as multidimensional shapes...
Diophantine geometry an introduction
Hindry, Marc
2000-01-01
This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and professional mathematicians. In each part of the book, the reader will find numerous exercises.
Metrics for Probabilistic Geometries
DEFF Research Database (Denmark)
Tosi, Alessandra; Hauberg, Søren; Vellido, Alfredo
2014-01-01
We investigate the geometrical structure of probabilistic generative dimensionality reduction models using the tools of Riemannian geometry. We explicitly define a distribution over the natural metric given by the models. We provide the necessary algorithms to compute expected metric tensors where...
Towards relativistic quantum geometry
Energy Technology Data Exchange (ETDEWEB)
Ridao, Luis Santiago [Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina); Bellini, Mauricio, E-mail: mbellini@mdp.edu.ar [Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350, C.P. 7600, Mar del Plata (Argentina); Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina)
2015-12-17
We obtain a gauge-invariant relativistic quantum geometry by using a Weylian-like manifold with a geometric scalar field which provides a gauge-invariant relativistic quantum theory in which the algebra of the Weylian-like field depends on observers. An example for a Reissner–Nordström black-hole is studied.
Hsü, K J; Hsü, A J
1990-01-01
Music critics have compared Bach's music to the precision of mathematics. What "mathematics" and what "precision" are the questions for a curious scientist. The purpose of this short note is to suggest that the mathematics is, at least in part, Mandelbrot's fractal geometry and the precision is the deviation from a log-log linear plot.
Cooper, Brett D.; Barger, Rita
2009-01-01
The many connections between music and mathematics are well known. The length of a plucked string determines its tone, the time signature of a piece of music is a ratio, and note durations are measured in fractions. One connection commonly overlooked is that between music and geometry--specifically, geometric transformations, including…
Atiyah, M.; Dijkgraaf, R.; Hitchin, N.
2010-01-01
We review the remarkably fruitful interactions between mathematics and quantum physics in the past decades, pointing out some general trends and highlighting several examples, such as the counting of curves in algebraic geometry, invariants of knots and four-dimensional topology.
Martin, John
2010-01-01
The cycloid has been called the Helen of Geometry, not only because of its beautiful properties but also because of the quarrels it provoked between famous mathematicians of the 17th century. This article surveys the history of the cycloid and its importance in the development of the calculus.
Sliding vane geometry turbines
Sun, Harold Huimin; Zhang, Jizhong; Hu, Liangjun; Hanna, Dave R
2014-12-30
Various systems and methods are described for a variable geometry turbine. In one example, a turbine nozzle comprises a central axis and a nozzle vane. The nozzle vane includes a stationary vane and a sliding vane. The sliding vane is positioned to slide in a direction substantially tangent to an inner circumference of the turbine nozzle and in contact with the stationary vane.
DEFF Research Database (Denmark)
Booss-Bavnbek, Bernhelm
2011-01-01
This paper applies I.M. Gelfand's distinction between adequate and non-adequate use of mathematical language in different contexts to the newly opened window of model-based measurements of intracellular dynamics. The specifics of geometry and dynamics on the mesoscale of cell physiology are elabo...
Spherical aberration in contact lens wear.
Lindskoog Pettersson, A; Jarkö, C; Alvin, A; Unsbo, P; Brautaset, R
2008-08-01
The aim of the present studies was to investigate the effect on spherical aberration of different non custom-made contact lenses, both with and without aberration control. A wavefront analyser (Zywave, Bausch & Lomb) was used to measure the aberrations in each subject's right eye uncorrected and with the different contact lenses. The first study evaluated residual spherical aberration with a standard lens (Focus Dailies Disposable, Ciba Vision) and with an aberration controlled contact lens (ACCL) (Definition AC, Optical Connection Inc.). The second study evaluated the residual spherical aberrations with a monthly disposable silicone hydrogel lens with aberration reduction (PureVision, Bausch & Lomb). Uncorrected spherical aberration was positive for all pupil sizes in both studies. In the first study, residual spherical aberration was close to zero with the standard lens for all pupil sizes whereas the ACCL over-corrected spherical aberration. The results of the second study showed that the monthly disposable lens also over-corrected the aberration making it negative. The changes in aberration were statistically significant (plenses. Since the amount of aberration varies individually we suggest that aberrations should be measured with lenses on the eye if the aim is to change spherical aberration in a certain direction.
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.)
Static spherical wormhole models in f (R, T) gravity
Yousaf, Z.; Ilyas, M.; Zaeem-ul-Haq Bhatti, M.
2017-06-01
This paper explores the possibility of the existence of wormhole geometries coupled with relativistic matter configurations by taking a particular model of f(R,T) gravity (where T is the trace of energy-momentum tensor). For this purpose, we take the static form of spherically symmetric spacetime and after assuming a specific form of matter and combinations of shape function, the validity of energy conditions is checked. We have discussed our results through graphical representation and studied the equilibrium background of wormhole models by taking an anisotropic fluid. The extra curvature quantities coming from f(R,T) gravity could be interpreted as a gravitational entity supporting these non-standard astrophysical wormhole models. We have shown that in the context of anisotropic fluid and R+α R^2+λ T gravity, wormhole models could possibly exist in few zones in the space of parameters without the need for exotic matter.
Static spherically symmetric wormholes in f( R, T) gravity
Zubair, M.; Waheed, Saira; Ahmad, Yasir
2016-08-01
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.
Novel Electrically Small Spherical Electric Dipole Antenna
DEFF Research Database (Denmark)
Kim, Oleksiy S.
2010-01-01
This paper introduces a novel electrically small spherical meander antenna. Horizontal sections of the meander are composed of wire loops, radii of which are chosen so that the whole structure is conformal to a sphere of radius a. To form the meander the loops are connected by wires at a meridian...... plane. The antenna operates as an electric dipole, i.e. it radiates the TM10 spherical mode. The antenna is self-resonant and can be matched to a wide range of input feed lines without an external matching network. In this paper, a spherical meander antenna of the size ka = 0.27 and the input impedance...
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.
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)
Kinetic Damping in the Spectrum of the Spherical Impedance Probe
Oberrath, Jens; Brinkmann, Ralf Peter
2015-09-01
Active plasma resonance spectroscopy is a widely used diagnostic method and several probes in different designs have been invented. One of them is the Spherical Impedance Probe. Its resonance behavior and the influence of kinetic effects on it can be described by a general kinetic model presented by the authors. It was theoretically shown that kinetic effects are responsible for a broadening of the resonance peak in the spectrum. However, the broadening of the resonance peak in a kinetically determined spectrum in the geometry of an existing probe is not evaluated, yet. We present such a spectrum of the Spherical Impedance Probe. Therefore, the general solution of the model is expanded in an orthonormal system of basis-functions. This expansion is truncated to determine an approximated spectrum. Its resonance peak shows clearly a broadening compared to a peak in a spectrum, which is determined by a fluiddynamical model. The authors acknowledge the support by the Research Service of Leuphana University Lueneburg, the Deutsche Forschungsgemeinschaft via the Ruhr University Research School and the Federal Ministry of Education and Research in frame of the PluTO+ projekt.
Selection of regenerator geometry for magnetic refrigerator applications
Barclay, J. A.; Sarangi, S.
1984-12-01
In an effort to develop magnetic regenerators of high efficiency the following geometries were considered: (1) tube channels in solid block; (2) stack of perforated plates normal to the fluid flow direction; (3) stack of solid plates parallel to fluid flow direction, and packed bed of spherical particles; (4) loose packed; and (5) sintered. The overall efficiency of the regenerator, considering heat transfer, longitudinal conduction, and fluid pressure drop, was computed for all the above arrangements as a function of geometrical variables, such as overall length and particle diameter or plate thickness. The results yield the optimum geometry for a given combination of other controlling parameters, such as frequency, porosity, and fluid properties. The different geometries are compared under the constraint that the mass of magnetic material is the same for all. This condition is peculiar to the magnetic refrigeration process because the net refrigeration and driving forces are proportional to the mass of magnetic material.
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....
Spherically symmetric inhomogeneous dust collapse in higher ...
Indian Academy of Sciences (India)
We consider a collapsing spherically symmetric inhomogeneous dust cloud in higher dimensional space-time. We show that the central singularity of collapse can be a strong curvature or a weak curvature naked singularity depending on the initial density distribution.
Spherical designs and anticoherent spin states
International Nuclear Information System (INIS)
Crann, Jason; Pereira, Rajesh; Kribs, David W
2010-01-01
Anticoherent spin states are quantum states that exhibit maximally nonclassical behaviour in a certain sense. Any spin state whose Majorana representation is a Platonic solid is called a perfect state. By direct calculation, it has been shown that any perfect state is an anticoherent spin state. We show that any spin state whose Majorana representation is both the orbit of a finite subgroup of O(3) and a spherical t-design must be an anticoherent spin state of order t. Since all Platonic solids are spherical designs, this result gives an explanation of the anticoherence of perfect states and explains their observed order. We also show that any spin state whose Majorana representation lies in any single open hemisphere cannot be anticoherent of any order. This result is then used to give further relations between spherical designs and anticoherent spin states. We also pose some questions relating spherical designs and geometric entanglement.
Transformation of Real Spherical Harmonics under Rotations
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.
Spherical stochastic neighbor embedding of hyperspectral data
CSIR Research Space (South Africa)
Lunga, D
2012-07-01
Full Text Available of spherical coordinates. This allows the use of an Exit probability distribution to discover the nonlinear characteristics that are inherent in hyperspectral data. In addition, the method directly learns the probability distribution over neighboring pixel maps...
Feasibility study for the Spherical Torus Experiment
International Nuclear Information System (INIS)
Lazarus, E.A.; Attenberger, S.E.; Baylor, L.R.
1985-10-01
The design of the Spherical Torus Experiment (STX) is discussed. The physics of the plasma are given in a magnetohydrodynamic model. The structural aspects and instrumentation of the device are described. 19 refs., 103 figs
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)
Transformational plane geometry
Umble, Ronald N
2014-01-01
Axioms of Euclidean Plane Geometry The Existence and Incidence Postulates The Distance and Ruler Postulates The Plane Separation Postulate The Protractor Postulate The Side-Angle-Side Postulate and the Euclidean Parallel Postulate Theorems of Euclidean Plane Geometry The Exterior Angle Theorem Triangle Congruence Theorems The Alternate Interior Angles Theorem and the Angle Sum Theorem Similar Triangles Introduction to Transformations, Isometries, and Similarities Transformations Isometries and SimilaritiesAppendix: Proof of Surjectivity Translations, Rotations, and Reflections Translations Rotations Reflections Appendix: Geometer's Sketchpad Commands Required by Exploratory Activities Compositions of Translations, Rotations, and Reflections The Three Points Theorem Rotations as Compositions of Two Reflections Translations as Compositions of Two Halfturns or Two Reflections The Angle Addition Theorem Glide Reflections Classification of Isometries The Fundamental Theorem and Congruence Classification of Isometr...
Multivariate calculus and geometry
Dineen, Seán
2014-01-01
Multivariate calculus can be understood best by combining geometric insight, intuitive arguments, detailed explanations and mathematical reasoning. This textbook has successfully followed this programme. It additionally provides a solid description of the basic concepts, via familiar examples, which are then tested in technically demanding situations. In this new edition the introductory chapter and two of the chapters on the geometry of surfaces have been revised. Some exercises have been replaced and others provided with expanded solutions. Familiarity with partial derivatives and a course in linear algebra are essential prerequisites for readers of this book. Multivariate Calculus and Geometry is aimed primarily at higher level undergraduates in the mathematical sciences. The inclusion of many practical examples involving problems of several variables will appeal to mathematics, science and engineering students.
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....
A Spherical Electro Optic High Voltage Sensor
1989-06-01
the application of an electric field applied to the EO crystal, and a photodetector senses the pattern movement. The sensor can be made small (e.g...spherical symmetry simplifies analysis; a uniform£ exists within a spherical dielectric when immursed in a uniform E; conoscopic light production...of an electric field applied to the EO crystal, and a photodetector senses the pattern movement. The sensor can be made small (e.g. < 3mm diam
Algebra, Arithmetic, and Geometry
Tschinkel, Yuri
2009-01-01
The two volumes of "Algebra, Arithmetic, and Geometry: In Honor of Y.I. Manin" are composed of invited expository articles and extensions detailing Manin's contributions to the subjects, and are in celebration of his 70th birthday. The well-respected and distinguished contributors include: Behrend, Berkovich, Bost, Bressler, Calaque, Carlson, Chambert-Loir, Colombo, Connes, Consani, Dabrowski, Deninger, Dolgachev, Donaldson, Ekedahl, Elsenhans, Enriques, Etingof, Fock, Friedlander, Geemen, Getzler, Goncharov, Harris, Iskovskikh, Jahnel, Kaledin, Kapranov, Katz, Kaufmann, Kollar, Kont
DEFF Research Database (Denmark)
Tamke, Martin; Ramsgaard Thomsen, Mette; Riiber Nielsen, Jacob
2009-01-01
The versatility of wood constructions and traditional wood joints for the production of non standard elements was in focus of a design based research. Herein we established a seamless process from digital design to fabrication. A first research phase centered on the development of a robust...... parametric model and a generic design language a later explored the possibilities to construct complex shaped geometries with self registering joints on modern wood crafting machines. The research was carried out as collaboration with industrial partners....
DEFF Research Database (Denmark)
Tamke, Martin; Ramsgaard Thomsen, Mette; Riiber Nielsen, Jacob
2009-01-01
The versatility of wood constructions and traditional wood joints for the production of non standard elements was in focus of a design based research. Herein we established a seamless process from digital design to fabrication. A first research phase centered on the development of a robust parame...... parametric model and a generic design language a later explored the possibilities to construct complex shaped geometries with self registering joints on modern wood crafting machines. The research was carried out as collaboration with industrial partners....
Introducing geometry concept based on history of Islamic geometry
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.
Integral geometry and valuations
Solanes, Gil
2014-01-01
Valuations are finitely additive functionals on the space of convex bodies. Their study has become a central subject in convexity theory, with fundamental applications to integral geometry. In the last years there has been significant progress in the theory of valuations, which in turn has led to important achievements in integral geometry. This book originated from two courses delivered by the authors at the CRM and provides a self-contained introduction to these topics, covering most of the recent advances. The first part, by Semyon Alesker, is devoted to the theory of convex valuations, with emphasis on the latest developments. A special focus is put on the new fundamental structures of the space of valuations discovered after Alesker's irreducibility theorem. Moreover, the author describes the newly developed theory of valuations on manifolds. In the second part, Joseph H. G. Fu gives a modern introduction to integral geometry in the sense of Blaschke and Santaló, based on the notions and tools presented...
Integral geometry and holography
Energy Technology Data Exchange (ETDEWEB)
Czech, Bartłomiej; Lamprou, Lampros; McCandlish, Samuel [Stanford Institute for Theoretical Physics, Department of Physics, Stanford University,Stanford, CA 94305 (United States); Sully, James [Theory Group, SLAC National Accelerator Laboratory,Menlo Park, CA 94025 (United States)
2015-10-27
We present a mathematical framework which underlies the connection between information theory and the bulk spacetime in the AdS{sub 3}/CFT{sub 2} correspondence. A key concept is kinematic space: an auxiliary Lorentzian geometry whose metric is defined in terms of conditional mutual informations and which organizes the entanglement pattern of a CFT state. When the field theory has a holographic dual obeying the Ryu-Takayanagi proposal, kinematic space has a direct geometric meaning: it is the space of bulk geodesics studied in integral geometry. Lengths of bulk curves are computed by kinematic volumes, giving a precise entropic interpretation of the length of any bulk curve. We explain how basic geometric concepts — points, distances and angles — are reflected in kinematic space, allowing one to reconstruct a large class of spatial bulk geometries from boundary entanglement entropies. In this way, kinematic space translates between information theoretic and geometric descriptions of a CFT state. As an example, we discuss in detail the static slice of AdS{sub 3} whose kinematic space is two-dimensional de Sitter space.
Introductory non-Euclidean geometry
Manning, Henry Parker
1963-01-01
This fine and versatile introduction begins with the theorems common to Euclidean and non-Euclidean geometry, and then it addresses the specific differences that constitute elliptic and hyperbolic geometry. 1901 edition.
Matter in toy dynamical geometries
International Nuclear Information System (INIS)
Konopka, Tomasz
2009-01-01
One of the objectives of theories describing quantum dynamical geometry is to compute expectation values of geometrical observables. The results of such computations can be affected by whether or not matter is taken into account. It is thus important to understand to what extent and to what effect matter can affect dynamical geometries. Using a simple model, it is shown that matter can effectively mold a geometry into an isotropic configuration. Implications for 'atomistic' models of quantum geometry are briefly discussed.
Spherical-shell boundaries for two-dimensional compressible convection in a star
Pratt, J.; Baraffe, I.; Goffrey, T.; Geroux, C.; Viallet, M.; Folini, D.; Constantino, T.; Popov, M.; Walder, R.
2016-10-01
Context. Studies of stellar convection typically use a spherical-shell geometry. The radial extent of the shell and the boundary conditions applied are based on the model of the star investigated. We study the impact of different two-dimensional spherical shells on compressible convection. Realistic profiles for density and temperature from an established one-dimensional stellar evolution code are used to produce a model of a large stellar convection zone representative of a young low-mass star, like our sun at 106 years of age. Aims: We analyze how the radial extent of the spherical shell changes the convective dynamics that result in the deep interior of the young sun model, far from the surface. In the near-surface layers, simple small-scale convection develops from the profiles of temperature and density. A central radiative zone below the convection zone provides a lower boundary on the convection zone. The inclusion of either of these physically distinct layers in the spherical shell can potentially affect the characteristics of deep convection. Methods: We perform hydrodynamic implicit large eddy simulations of compressible convection using the MUltidimensional Stellar Implicit Code (MUSIC). Because MUSIC has been designed to use realistic stellar models produced from one-dimensional stellar evolution calculations, MUSIC simulations are capable of seamlessly modeling a whole star. Simulations in two-dimensional spherical shells that have different radial extents are performed over tens or even hundreds of convective turnover times, permitting the collection of well-converged statistics. Results: To measure the impact of the spherical-shell geometry and our treatment of boundaries, we evaluate basic statistics of the convective turnover time, the convective velocity, and the overshooting layer. These quantities are selected for their relevance to one-dimensional stellar evolution calculations, so that our results are focused toward studies exploiting the so
Energy Technology Data Exchange (ETDEWEB)
Hook, D W [Blackett Laboratory, Imperial College of Science Technology and Medicine, University of London, Prince Consort Road, London, SW7 2BW (United Kingdom)
2008-01-11
A geometric framework for quantum mechanics arose during the mid 1970s when authors such as Cantoni explored the notion of generalized transition probabilities, and Kibble promoted the idea that the space of pure quantum states provides a natural quantum mechanical analogue for classical phase space. This central idea can be seen easily since the projection of Schroedinger's equation from a Hilbert space into the space of pure spaces is a set of Hamilton's equations. Over the intervening years considerable work has been carried out by a variety of authors and a mature description of quantum mechanics in geometric terms has emerged with many applications. This current offering would seem ideally placed to review the last thirty years of progress and relate this to the most recent work in quantum entanglement. Bengtsson and Zyczkowski's beautifully illustrated volume, Geometry of Quantum States (referred to as GQS from now on) attempts to cover considerable ground in its 466 pages. Its topics range from colour theory in Chapter 1 to quantum entanglement in Chapter 15-to say that this is a whirlwind tour is, perhaps, no understatement. The use of the work 'introduction' in the subtitle of GQS, might suggest to the reader that this work be viewed as a textbook and I think that this interpretation would be incorrect. The authors have chosen to present a survey of different topics with the specific aim to introduce entanglement in geometric terms-the book is not intended as a pedagogical introduction to the geometric approach to quantum mechanics. Each of the fifteen chapters is a short, and mostly self-contained, essay on a particular aspect or application of geometry in the context of quantum mechanics with entanglement being addressed specifically in the final chapter. The chapters fall into three classifications: those concerned with the mathematical background, those which discuss quantum theory and the foundational aspects of the geometric
Teaching of Geometry in Bulgaria
Bankov, Kiril
2013-01-01
Geometry plays an important role in the school mathematics curriculum all around the world. Teaching of geometry varies a lot (Hoyls, Foxman, & Kuchemann, 2001). Many countries revise the objectives, the content, and the approaches to the geometry in school. Studies of the processes show that there are not common trends of these changes…
Graded geometry and Poisson reduction
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
Functional integration over geometries
International Nuclear Information System (INIS)
Mottola, E.
1995-01-01
The geometric construction of the functional integral over coset spaces M/G is reviewed. The inner product on the cotangent space of infinitesimal deformations of M defines an invariant distance and volume form, or functional integration measure on the full configuration space. Then, by a simple change of coordinates parameterizing the gauge fiber G, the functional measure on the coset space M/G is deduced. This change of integration variables leads to a Jacobian which is entirely equivalent to the Faddeev--Popov determinant of the more traditional gauge fixed approach in non-abelian gauge theory. If the general construction is applied to the case where G is the group of coordinate reparameterizations of spacetime, the continuum functional integral over geometries, i.e. metrics modulo coordinate reparameterizations may be defined. The invariant functional integration measure is used to derive the trace anomaly and effective action for the conformal part of the metric in two and four dimensional spacetime. In two dimensions this approach generates the Polyakov--Liouville action of closed bosonic non-critical string theory. In four dimensions the corresponding effective action leads to novel conclusions on the importance of quantum effects in gravity in the far infrared, and in particular, a dramatic modification of the classical Einstein theory at cosmological distance scales, signaled first by the quantum instability of classical de Sitter spacetime. Finite volume scaling relations for the functional integral of quantum gravity in two and four dimensions are derived, and comparison with the discretized dynamical triangulation approach to the integration over geometries are discussed. Outstanding unsolved problems in both the continuum definition and the simplicial approach to the functional integral over geometries are highlighted
Gillespie, Ronald J; Robinson, Edward A
2005-05-01
Although the structure of almost any molecule can now be obtained by ab initio calculations chemists still look for simple answers to the question "What determines the geometry of a given molecule?" For this purpose they make use of various models such as the VSEPR model and qualitative quantum mechanical models such as those based on the valence bond theory. The present state of such models, and the support for them provided by recently developed methods for analyzing calculated electron densities, are reviewed and discussed in this tutorial review.
2015-01-01
This stimulating volume offers a broad collection of the principles of geometry and trigonometry and contains colorful diagrams to bring mathematical principles to life. Subjects are enriched by references to famous mathematicians and their ideas, and the stories are presented in a very comprehensible way. Readers investigate the relationships of points, lines, surfaces, and solids. They study construction methods for drawing figures, a wealth of facts about these figures, and above all, methods to prove the facts. They learn about triangle measure for circular motion, sine and cosine, tangent
Abhyankar, Shreeram Shankar
1964-01-01
This book provides, for use in a graduate course or for self-study by graduate students, a well-motivated treatment of several topics, especially the following: (1) algebraic treatment of several complex variables; (2) geometric approach to algebraic geometry via analytic sets; (3) survey of local algebra; (4) survey of sheaf theory. The book has been written in the spirit of Weierstrass. Power series play the dominant role. The treatment, being algebraic, is not restricted to complex numbers, but remains valid over any complete-valued field. This makes it applicable to situations arising from
Flegg, H Graham
2001-01-01
This excellent introduction to topology eases first-year math students and general readers into the subject by surveying its concepts in a descriptive and intuitive way, attempting to build a bridge from the familiar concepts of geometry to the formalized study of topology. The first three chapters focus on congruence classes defined by transformations in real Euclidean space. As the number of permitted transformations increases, these classes become larger, and their common topological properties become intuitively clear. Chapters 4-12 give a largely intuitive presentation of selected topics.
Kendig, Keith
2015-01-01
Designed to make learning introductory algebraic geometry as easy as possible, this text is intended for advanced undergraduates and graduate students who have taken a one-year course in algebra and are familiar with complex analysis. This newly updated second edition enhances the original treatment's extensive use of concrete examples and exercises with numerous figures that have been specially redrawn in Adobe Illustrator. An introductory chapter that focuses on examples of curves is followed by a more rigorous and careful look at plane curves. Subsequent chapters explore commutative ring th
Gruber, Peter M
1987-01-01
This volume contains a fairly complete picture of the geometry of numbers, including relations to other branches of mathematics such as analytic number theory, diophantine approximation, coding and numerical analysis. It deals with convex or non-convex bodies and lattices in euclidean space, etc.This second edition was prepared jointly by P.M. Gruber and the author of the first edition. The authors have retained the existing text (with minor corrections) while adding to each chapter supplementary sections on the more recent developments. While this method may have drawbacks, it has the definit
REA, The Editors of
2012-01-01
REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Geometry I includes methods of proof, points, lines, planes, angles, congruent angles and line segments, triangles, parallelism, quadrilaterals, geometric inequalities, and geometric
Dooner, David B
2012-01-01
Building on the first edition published in 1995 this new edition of Kinematic Geometry of Gearing has been extensively revised and updated with new and original material. This includes the methodology for general tooth forms, radius of torsure', cylinder of osculation, and cylindroid of torsure; the author has also completely reworked the '3 laws of gearing', the first law re-written to better parallel the existing 'Law of Gearing" as pioneered by Leonard Euler, expanded from Euler's original law to encompass non-circular gears and hypoid gears, the 2nd law of gearing describing a unique relat
One-degree-of-freedom spherical model for the passive motion of the human ankle joint.
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.
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.
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
Statistical Mechanics of Thin Spherical Shells
Directory of Open Access Journals (Sweden)
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.
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
Solar Proton Transport within an ICRU Sphere Surrounded by a Complex Shield: Combinatorial Geometry
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.
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.
A spherical Taylor-Couette dynamo
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.
Design and implementation of spherical ultrasonic motor.
Mashimo, Tomoaki; Toyama, Shigeki; Ishida, Hiroshi
2009-11-01
We present a mechanical design and implementation of spherical ultrasonic motor (SUSM) that is an actuator with multiple rotational degrees of freedom (multi-DOF). The motor is constructed of 3 annular stators and a spherical rotor and is much smaller and simpler than conventional multi-DOF mechanisms such as gimbals using servomotors. We designed a novel SUSM using experimental data from a single annular stator and a finite element method. The SUSM using a spherical rotor of diameter 20 mm without any reduction gear has demonstrated advantages of high responsiveness, good accuracy, and high torque at low speed. The dynamic implementation of SUSM was consistent with the driving model of SUSM based on a friction drive.
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)
Electromagnetic cloaking in higher order spherical cloaks
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.
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
Background reduction of a spherical gaseous detector
Energy Technology Data Exchange (ETDEWEB)
Fard, Ali Dastgheibi [Laboratoire Souterrain de Modane, France ali.dastgheibi-fard@lsm.in2p3.fr (France); Loaiza, Pia; Piquemal, Fabrice [Laboratoire Souterrain de Modane (France); Giomataris, Ioannis; Gray, David; Gros, Michel; Magnier, Patrick; Navick, Xavier-François [CEA Saclay - IRFU/SEDI - 91191 Gif sur Yvette (France); Savvidis, Ilias [Aristotle University of Thessaloniki (Greece)
2015-08-17
The Spherical gaseous detector (or Spherical Proportional Counter, SPC) is a novel type of detector. It consists of a large spherical volume filled with gas, using a single detection readout channel. The detector allows 100 % detection efficiency. SEDINE is a low background version of SPC installed at the Laboratoire Souterrain de Modane (LSM) underground laboratory (4800 m.w.e) looking for rare events at very low energy threshold, below 100 eV. This work presents the details on the chemical cleaning to reduce internal {sup 210}Pb surface contamination on the copper vessel and the external radon reduction achieved via circulation of pure air inside anti-radon tent. It will be also show the radon measurement of pure gases (Ar, N, Ne, etc) which are used in the underground laboratory for the low background experiments.
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
Spherical shock waves in general relativity
International Nuclear Information System (INIS)
Nutku, Y.
1991-01-01
We present the metric appropriate to a spherical shock wave in the framework of general relativity. This is a Petrov type-N vacuum solution of the Einstein field equations where the metric is continuous across the shock and the Riemann tensor suffers a step-function discontinuity. Spherical gravitational waves are described by type-N Robinson-Trautman metrics. However, for shock waves the Robinson-Trautman solutions are unacceptable because the metric becomes discontinuous in the Robinson-Trautman coordinate system. Other coordinate systems that have so far been introduced for describing Robinson-Trautman solutions also suffer from the same defect. We shall present the C 0 -form of the metric appropriate to spherical shock waves using Penrose's approach of identification with warp. Further extensions of Penrose's method yield accelerating, as well as coupled electromagnetic-gravitational shock-wave solutions
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)
Stability of spherical gravitating collisionless systems
Energy Technology Data Exchange (ETDEWEB)
Polyachenko, V.L.
1988-03-01
A unified method that uses a procedure, established in the paper, for reducing the problem of the stability of a spherical system to the analogous problem of perturbations of the simplest form in a corresponding cylindrical system provides the framework for investigating the stability of collisionless star clusters with different types of anisotropy of the velocity distribution. For spherical systems embedded in a massive halo or possessing a large central mass, equations - in the simplest case integral equations - for the eigenfunctions and eigenfrequencies of the oscillations are derived.
Overview of spherical tokamak research in Japan
Takase, Y.; Ejiri, A.; Fujita, T.; Fukumoto, N.; Fukuyama, A.; Hanada, K.; Idei, H.; Nagata, M.; Ono, Y.; Tanaka, H.; Uchida, M.; Horiuchi, R.; Kamada, Y.; Kasahara, H.; Masuzaki, S.; Nagayama, Y.; Oishi, T.; Saito, K.; Takeiri, Y.; Tsuji-Iio, S.
2017-10-01
Nationally coordinated research on spherical tokamak is being conducted in Japan. Recent achievements include: (i) plasma current start-up and ramp-up without the use of the central solenoid by RF waves (in electron cyclotron and lower hybrid frequency ranges), (ii) plasma current start-up by AC Ohmic operation and by coaxial helicity injection, (iii) development of an advanced fuelling technique by compact toroid injection, (iv) ultra-long-pulse operation and particle control using a high temperature metal wall, (v) access to the ultra-high-β regime by high-power reconnection heating, and (vi) improvement of spherical tokamak plasma stability by externally applied helical field.
Electrode shapes for spherical Pierce flow
International Nuclear Information System (INIS)
Mueller, D.W.
1981-01-01
The problem of obtaining the electrode shapes to produce a conically converging proton beam that has constant current density over each spherical surface of convergence is treated in spherical coordinates. A cone is taken from the Langmuir and Blodgett solution for the region within, and at the edge of, the conically converging beam. A solution for the LaPlace equation, required for the region outside the beam, is in terms of a power series in r and the Legendre polynomials of cos phi
Hydrogen storage in spherical nanoporous carbons
Terrés, E.; Panella, B.; Hayashi, T.; Kim, Y. A.; Endo, M.; Dominguez, J. M.; Hirscher, M.; Terrones, H.; Terrones, M.
2005-02-01
We report H 2 storage capacities up to 2.7 wt% at 77 K in spherical nanoporous carbons exhibiting periodic arrays of pores and surface areas between 946 and 1646 m 2/g. The materials were produced via the pyrolysis of sucrose (C 12H 22O 11) embedded inside a spherical form of MCM-48 at 1000 °C in an inert atmosphere. Our results open up new possibilities for producing carbon nanomaterials with large surface areas, which are able to store hydrogen with attractive yields.
DEFF Research Database (Denmark)
Niordson, Christian F.; Nielsen, S.B.
2006-01-01
of the transverse deflection is modified by in-plane tectonic forces originating e.g. at plate boundaries. However, geoscience applications of the coupling between transverse deflections and boundary conditions have been restricted to the one-dimensional thin-plate model. In this paper we extend the model...... to a spherical thin elastic shell. This configuration is required when geoscience studies move from local scenarios, where the flat-Earth approximation holds, to plate-scale or global scenarios, where the correct application of far-field boundary conditions and the spherical geometry becomes of primary...
Meng, Q E; Liu, F; Fisher, J; Jin, Z M
2011-01-01
Effective lubrication performance of metal-on-metal hip implants only requires optimum conformity within the main loaded area, while it is advantageous to increase the clearance in the equatorial region. Such a varying clearance can be achieved by using non-spherical bearing surfaces for either acetabular or femoral components. An elastohydrodynamic lubrication model of a novel metal-on-metal hip prosthesis using a non-spherical femoral bearing surface against a spherical cup was solved under loading and motion conditions specified by ISO standard. A full numerical methodology of considering the geometric variation in the rotating non-spherical head in elastohydrodynamic lubrication solution was presented, which is applicable to all non-spherical head designs. The lubrication performance of a hip prosthesis using a specific non-spherical femoral head, Alpharabola, was analysed and compared with those of spherical bearing surfaces and a non-spherical Alpharabola cup investigated in previous studies. The sensitivity of the lubrication performance to the anteversion angle of the Alpharabola head was also investigated. Results showed that the non-spherical head introduced a large squeeze-film action and also led to a large variation in clearance within the loaded area. With the same equatorial clearance, the lubrication performance of the metal-on-metal hip prosthesis using an Alpharabola head was better than that of the conventional spherical bearings but worse than that of the metal-on-metal hip prosthesis using an Alpharabola cup. The reduction in the lubrication performance caused by the initial anteversion angle of the non-spherical head was small, compared with the improvement resulted from the non-spherical geometry.
Geometry through history Euclidean, hyperbolic, and projective geometries
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...
Geometry through history euclidean, hyperbolic, and projective geometries
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...
Bochnak, Jacek; Roy, Marie-Françoise
1998-01-01
This book is a systematic treatment of real algebraic geometry, a subject that has strong interrelation with other areas of mathematics: singularity theory, differential topology, quadratic forms, commutative algebra, model theory, complexity theory etc. The careful and clearly written account covers both basic concepts and up-to-date research topics. It may be used as text for a graduate course. The present edition is a substantially revised and expanded English version of the book "Géometrie algébrique réelle" originally published in French, in 1987, as Volume 12 of ERGEBNISSE. Since the publication of the French version the theory has made advances in several directions. Many of these are included in this English version. Thus the English book may be regarded as a completely new treatment of the subject.
Numerical optimization of spherical variable-line-spacing grating X-ray spectrometers
International Nuclear Information System (INIS)
Strocov, V. N.; Schmitt, T.; Flechsig, U.; Patthey, L.; Chiuzbăian, G. S.
2011-01-01
Operation of an X-ray spectrometer based on a spherical variable-line-spacing grating is analyzed using dedicated ray-tracing software allowing fast optimization of the grating parameters and spectrometer geometry. Operation of an X-ray spectrometer based on a spherical variable-line-spacing (VLS) grating is analyzed using dedicated ray-tracing software allowing fast optimization of the grating parameters and spectrometer geometry. The analysis is illustrated with optical design of a model spectrometer to deliver a resolving power above 20400 at a photon energy of 930 eV (Cu L-edge). With this energy taken as reference, the VLS coefficients are optimized to cancel the lineshape asymmetry (mostly from the coma aberrations) as well as minimize the symmetric aberration broadening at large grating illuminations, dramatically increasing the aberration-limited vertical acceptance of the spectrometer. For any energy away from the reference, corrections to the entrance arm and light incidence angle on the grating are evaluated to maintain the exactly symmetric lineshape. Furthermore, operational modes when these corrections are coordinated are evaluated to maintain either energy-independent focal curve inclination or maximal aberration-limited spectrometer acceptance. The results are supported by analytical evaluation of the coma term of the optical path function. This analysis thus gives a recipe for designing a high-resolution spherical VLS grating spectrometer operating with negligible aberrations at large acceptance and over an extended energy range
Molecular dynamics simulation study of friction force and torque on a rough spherical particle.
Kohale, Swapnil C; Khare, Rajesh
2010-06-21
Recent developments in techniques of micro- and nanofluidics have led to an increased interest in nanoscale hydrodynamics in confined geometries. In our previous study [S. C. Kohale and R. Khare, J. Chem. Phys. 129, 164706 (2008)], we analyzed the friction force experienced by a smooth spherical particle that is translating in a fluid confined between parallel plates. The magnitude of three effects--velocity slip at particle surface, the presence of confining surfaces, and the cooperative hydrodynamic interactions between periodic images of the moving particle--that determine the friction force was quantified in that work using molecular dynamics simulations. In this work, we have studied the motion of a rough spherical particle in a confined geometry. Specifically, the friction force experienced by a translating particle and the torque experienced by a rotating particle are studied using molecular dynamics simulations. Our results demonstrate that the surface roughness of the particle significantly reduces the slip at the particle surface, thus leading to higher values of the friction force and hence a better agreement with the continuum predictions. The particle size dependence of the friction force and the torque values is shown to be consistent with the expectations from the continuum theory. As was observed for the smooth sphere, the cooperative hydrodynamic interactions between the images of the sphere have a significant effect on the value of the friction force experienced by the translating sphere. On the other hand, the torque experienced by a spherical particle that is rotating at the channel center is insensitive to this effect.
Numerical optimization of spherical variable-line-spacing grating X-ray spectrometers
Energy Technology Data Exchange (ETDEWEB)
Strocov, V. N., E-mail: vladimir.strocov@psi.ch; Schmitt, T.; Flechsig, U.; Patthey, L. [Swiss Light Source, Paul Scherrer Institut, CH-5232 Villigen-PSI (Switzerland); Chiuzbăian, G. S. [UPMC University Paris 06, CNRS UMR 7614, Laboratoire de Chimie Physique - Matière et Rayonnement, 75321 Paris Cedex 05 (France)
2011-03-01
Operation of an X-ray spectrometer based on a spherical variable-line-spacing grating is analyzed using dedicated ray-tracing software allowing fast optimization of the grating parameters and spectrometer geometry. Operation of an X-ray spectrometer based on a spherical variable-line-spacing (VLS) grating is analyzed using dedicated ray-tracing software allowing fast optimization of the grating parameters and spectrometer geometry. The analysis is illustrated with optical design of a model spectrometer to deliver a resolving power above 20400 at a photon energy of 930 eV (Cu L-edge). With this energy taken as reference, the VLS coefficients are optimized to cancel the lineshape asymmetry (mostly from the coma aberrations) as well as minimize the symmetric aberration broadening at large grating illuminations, dramatically increasing the aberration-limited vertical acceptance of the spectrometer. For any energy away from the reference, corrections to the entrance arm and light incidence angle on the grating are evaluated to maintain the exactly symmetric lineshape. Furthermore, operational modes when these corrections are coordinated are evaluated to maintain either energy-independent focal curve inclination or maximal aberration-limited spectrometer acceptance. The results are supported by analytical evaluation of the coma term of the optical path function. This analysis thus gives a recipe for designing a high-resolution spherical VLS grating spectrometer operating with negligible aberrations at large acceptance and over an extended energy range.
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.
Higher geometry an introduction to advanced methods in analytic geometry
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
Flow and scour around spherical bodies
DEFF Research Database (Denmark)
Truelsen, Christoffer
2003-01-01
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 collapse models with clustered dark energy
Chang, Chia-Chun; Lee, Wolung; Ng, Kin-Wang
2018-03-01
We investigate the clustering effect of dark energy (DE) in the formation of galaxy clusters using the spherical collapse model. Assuming a fully clustered DE component, the spherical overdense region is treated as an isolated system which conserves the energy separately for both matter and DE inside the spherical region. Then, by introducing a parameter r to characterize the degree of DE clustering, which is defined by the nonlinear density contrast ratio of matter to DE at turnaround in the recollapsing process, i.e. r ≡δde,taNL /δm,taNL, we are able to uniquely determine the spherical collapsing process and hence obtain the virialized overdensity Δvir through a proper virialization scheme. Estimation of the virialized overdensities from current observation on galaxy clusters suggests that 0 . 5 clustered DE with w < - 0 . 9. Also, we compare our method to the linear perturbation theory that deals with the growth of DE perturbation at early times. While both results are consistent with each other, our method is practically simple and it shows that the collapse process is rather independent of initial DE perturbation and its evolution at early times.
Preparations of spherical polymeric particles from Tanzanian ...
African Journals Online (AJOL)
Spherical Polymeric Particles (SPP) have been prepared from Tanzanian Cashew Nut Shell Liquid (CNSL) by suspension polymerization technique involving either step-growth or chain- growth polymerization mechanisms. The sizes of the SPP, which ranged from 0.1 to 2.0 mm were strongly influenced by the amounts of ...
Nonlinear evolution of stellar spherical systems
Energy Technology Data Exchange (ETDEWEB)
Polyachenko, V.L. (AN SSSR, Irkutsk. Sibirskij Inst. Zemnogo Magnetizma Ionosfery i Rasprostraneniya Radiovoln)
1981-03-01
A universal method for computer realization of collisionless models according to a given distribution function is suggested. By employing this method it is shown that the development of instabilities in spherically-symmetric systems with nearly radial trajectories of the system constituents leads to a distinct elliptical deformation of the system.
Brachistochrone of a Spherical Uniform Mass Distribution
Mitchell, David R.
2006-01-01
We solve the brachistochrone problem for a particle travelling through a spherical mass distribution of uniform density. We examine the connection between this problem and the popular "gravity elevator" result. The solution is compared to the well known brachistochrone problem of a particle in a uniform gravitational field.
Compressive sensing with a spherical microphone array
DEFF Research Database (Denmark)
Fernandez Grande, Efren; Xenaki, Angeliki
2016-01-01
A wave expansion method is proposed in this work, based on measurements with a spherical microphone array, and formulated in the framework provided by Compressive Sensing. The method promotes sparse solutions via ‘1-norm minimization, so that the measured data are represented by few basis functions...
Sparse acoustic imaging with a spherical array
DEFF Research Database (Denmark)
Fernandez Grande, Efren; Xenaki, Angeliki
2015-01-01
proposes a plane wave expansion method based on measurements with a spherical microphone array, and solved in the framework provided by Compressed Sensing. The proposed methodology results in a sparse solution, i.e. few non-zero coefficients, and it is suitable for both source localization and sound field...
Added Mass of a Spherical Cap Body
Czech Academy of Sciences Publication Activity Database
Šimčík, Miroslav; Punčochář, Miroslav; Růžička, Marek
2014-01-01
Roč. 118, OCT 18 (2014), s. 1-8 ISSN 0009-2509 R&D Projects: GA MŠk(CZ) LD13018 Institutional support: RVO:67985858 Keywords : spherical cap * added mass * single particle Subject RIV: CI - Industrial Chemistry, Chemical Engineering Impact factor: 2.337, year: 2014
Exact solutions of the spherically symmetric multidimensional ...
African Journals Online (AJOL)
The complete orthonormalised energy eigenfunctions and the energy eigenvalues of the spherically symmetric isotropic harmonic oscillator in N dimensions, are obtained through the methods of separation of variables. Also, the degeneracy of the energy levels are examined. KEY WORDS: - Schrödinger Equation, Isotropic ...
Current drive in spherical tokamak plasmas
International Nuclear Information System (INIS)
Storer, R.
1999-01-01
The early experiments on a spherical rotamak showed that a rotating magnetic field could be used to drive substantial currents and create a compact torus magnetic field configuration. The theoretical analysis of the spherical rotamak has been essentially confined to this class. Recent experiments on the Flinders Rotamak-ST have included a toroidal field, produced by a current-carrying central rod, with encouraging results; for it has been shown that an enhanced current can be driven with this configuration which is the equivalent of a spherical tokamak. This paper will be devoted to a theoretical and computational analysis of this situation. We use a model where the rotating magnetic field is applied to a spherical plasma, with the rotating field oriented parallel to the equatorial plane, taken to be the x-y plane. In our model the ions form a uniform background and the frequency of the rotating Held is very much less than the electron cyclotron frequency (with respect to the rotating field strength) and very much greater than the ion cyclotron frequency. This condition is satisfied by the rotamak experiments
Dynamical instabilities in spherical stellar systems
Energy Technology Data Exchange (ETDEWEB)
Barnes, J.; Hut, P.; Goodman, J.
1986-01-01
The first numerical examples of spherical stellar systems in equilibrium, which are unstable on a dynamical time scale, were found by Henon using N-body code with enforced spherical symmetry. Henon's models have been reexamined using a code which includes nonradical forces to quadrupole order; the key results have been checked using a direct-summation Aarseth code. The radial instability reported by Henon is confirmed; in addition, two nonradial instabilities have been found. In the first kind, seen in models with predominantly radial orbits, the system permanently loses spherical symmetry and settles into a strongly triaxial ellipsoid. In the second kind, which appears in models with nearly circular orbits, the mass distribution exhibits quadrupole-mode oscillations. Analytic estimates and physical interpretations are presented for all three instabilities. The nonradial instabilities are found even in cases where the distribution function decreases with energy, suggesting that dynamical instabilities may be more common in spherical systems than had been previously thought. 25 references.
Collapsing spherical null shells in general relativity
Directory of Open Access Journals (Sweden)
S Khakshournia
2011-03-01
Full Text Available In this work, the gravitational collapse of a spherically symmetric null shell with the flat interior and a charged Vaidya exterior spacetimes is studied. There is no gravitational impulsive wave present on the null hypersurface which is shear-free and contracting. It follows that there is a critical radius at which the shell bounces and starts expanding.
Determining a Sonographic Nomogram for Gallbladder Spherical ...
African Journals Online (AJOL)
The Gallbladder spherical index (GBSI) of 380 volunteers (215 males and 165 females) was assessed using ultrasonography and a model formula to establish a nomogram for a Nigerian population of Igbo descent. The length, width and height of their gallbladders were measured after an overnight fast. Using the model ...
Geodesics in supersymmetric microstate geometries
International Nuclear Information System (INIS)
Eperon, Felicity C
2017-01-01
It has been argued that supersymmetric microstate geometries are classically unstable. One argument for instability involves considering the motion of a massive particle near the ergosurface of such a spacetime. It is shown that the instability can be triggered by a particle that starts arbitrarily far from the ergosurface. Another argument for instability is related to the phenomenon of stable trapping of null geodesics in these geometries. Such trapping is studied in detail for the most symmetrical microstate geometries. It is found that there are several distinct types of trapped null geodesic, both prograde and retrograde. Several important differences between geodesics in microstate geometries and black hole geometries are noted. The Penrose process for energy extraction in these geometries is discussed. (paper)
An introduction to incidence geometry
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...
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.
Directory of Open Access Journals (Sweden)
I. V. Makeev
2016-01-01
Full Text Available Stokes flows in cylindrical and spherical geometry are considered. Such flows are rather natural for geophysics. We derive some exact particular solutions of Stokes and continuity equations for particular dependence of viscosity and density on cylindrical coordinates. These solutions correspond to axisymmetric flows for the case when viscosity is a function of radius. We suggest exact particular solutions of Stokes and continuity equations with variable viscosity and density in spherical coordinates for the case of spherically symmetric viscosity and density distributions. We demonstrate how these solutions can be used for creation of test problems suitable for benchmarking numerical algorithms. Examples of such benchmarking are presented. The advantage of this benchmarking approach is the ability to test numerical algorithms for variable viscosity and density gradients. We suggest numerical scheme of multigrid algorithm for solving Stokes and continuity equations with variable viscosity in a spherical coordinate system. Calculations are performed on a sequence of orthogonal staggered grids. The quality of the numerical scheme was verified by comparing the numerical solution with the analytical solution of the test problem.
Application of linear and spherical flow analysis techniques to field problems--case studies
Energy Technology Data Exchange (ETDEWEB)
Kohlhaas, C.A.; delGiuoice, C.; Abbott, W.A.
1982-09-01
Most engineers examine well-test data only with techniques developed for flow in a horizontal cylindrical-radial pattern toward the wellbore. Spherical and linear flow have application in many reservoir situations. Spherical flow has been examined extensively by many authors as an intermediate period between two radial-flow periods for wells which have a short completion interval in thick formations. Linear flow situations develop early in the life of wells which have been fracture-treated: their early linear-flow periods are followed by radial flow. Linear flow may develop late in a well test after a period of early radial flow due to certain configurations of reservoir geometry. Techniques for analyzing spherical and linear flow are summarized here. Data plots which should be prepared and diagnostic features for recognizing and interpreting spherical and linear flow are outlined. These techniques are applied to three example cases to illustrate the methods of analysis and the types of information which can be developed from such analyses and cannot be obtained from the standard Horner-plot analysis.
Self-designing parametric geometries
Sobester, Andras
2015-01-01
The thesis of this paper is that script-based geometry modelling offers the possibility of building `self-designing' intelligence into parametric airframe geometries. We show how sophisticated heuristics (such as optimizers and complex decision structures) can be readily integrated into the parametric geometry model itself using a script-driven modelling architecture. The result is an opportunity for optimization with the scope of conceptual design and the fidelity of preliminary design. Addi...
An Engineering Evaluation of Spherical Resorcinol Formaldehyde Resin
Energy Technology Data Exchange (ETDEWEB)
Birdwell Jr, Joseph F [ORNL; Lee, Denise L [ORNL; Taylor, Paul Allen [ORNL; Collins, Robert T [ORNL; Hunt, Rodney Dale [ORNL
2010-09-01
A small column ion exchange (SCIX) system has been proposed for removal of cesium from caustic, supernatant, and dissolved salt solutions stored or generated from high-level tank wastes at the US Department of Energy (DOE) Hanford Site and Savannah River Sites. In both instances, deployment of SCIX systems, either in-tank or near-tank, is a means of expediting waste pretreatment and dispositioning with minimal or no new infrastructure requirements. Conceptually, the treatment approach can utilize a range of ion exchange media. Previously, both crystalline silicotitanate (CST), an inorganic, nonelutable sorbent, and resorcinol-formaldehyde (RF), an organic, elutable resin, have been considered for cesium removal from tank waste. More recently, Pacific Northwest National Laboratory (PNNL) evaluated use of SuperLig{reg_sign} 644, an elutable ion exchange medium, for the subject application. Results of testing indicate hydraulic limitations of the SuperLig{reg_sign} resin, specifically a high pressure drop through packed ion exchange columns. This limitation is likely the result of swelling and shrinkage of the irregularly shaped (granular) resin during repeated conversions between sodium and hydrogen forms as the resin is first loaded then eluted. It is anticipated that a similar flow limitation would exist in columns packed with conventional, granular RF resin. However, use of spherical RF resin is a likely means of mitigating processing limitations due to excessive pressure drop. Although size changes occur as the spherical resin is cycled through loading and elution operations, the geometry of the resin is expected to effectively mitigate the close packing that leads to high pressure drops across ion exchange columns. Multiple evaluations have been performed to determine the feasibility of using spherical RF resin and to obtain data necessary for design of an SCIX process. The work performed consisted of examination of radiation effects on resin performance
Quantum roots in geometry : II
International Nuclear Information System (INIS)
Wanas, M.I.
2006-01-01
The present work is a review of a series of papers, published in the last ten. years, comprising an attempt to find a suitable avenue from geometry to quantum. It shows clearly that, any non-symmetric geometry admits some built-in quantum features. These features disappear completely once the geometry becomes symmetric (torsion-less). It is shown that, torsion of space-time plays an important role in both geometry and physics. It interacts with the spin of the moving particle and with its charge. The first interaction, Spin-Torsion Interaction, has been used to overcome the discrepancy in the results of the COW-experiment. The second interaction, Charge-Torsion Interaction, is similar to the Aharonov-Bohm effect. As a byproduct, a new version of Absolute Parallelism (AP) geometry, the Parameterized Absolute Parallelism (PAP) geometry, has been established and developed. This version can be used to construct field theories that admit some quantum features. Riemannian geometry and conventional AP-geometry are special cases of PAP-geometry
Initiation to global Finslerian geometry
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
Planetary Image Geometry Library
Deen, Robert C.; Pariser, Oleg
2010-01-01
The Planetary Image Geometry (PIG) library is a multi-mission library used for projecting images (EDRs, or Experiment Data Records) and managing their geometry for in-situ missions. A collection of models describes cameras and their articulation, allowing application programs such as mosaickers, terrain generators, and pointing correction tools to be written in a multi-mission manner, without any knowledge of parameters specific to the supported missions. Camera model objects allow transformation of image coordinates to and from view vectors in XYZ space. Pointing models, specific to each mission, describe how to orient the camera models based on telemetry or other information. Surface models describe the surface in general terms. Coordinate system objects manage the various coordinate systems involved in most missions. File objects manage access to metadata (labels, including telemetry information) in the input EDRs and RDRs (Reduced Data Records). Label models manage metadata information in output files. Site objects keep track of different locations where the spacecraft might be at a given time. Radiometry models allow correction of radiometry for an image. Mission objects contain basic mission parameters. Pointing adjustment ("nav") files allow pointing to be corrected. The object-oriented structure (C++) makes it easy to subclass just the pieces of the library that are truly mission-specific. Typically, this involves just the pointing model and coordinate systems, and parts of the file model. Once the library was developed (initially for Mars Polar Lander, MPL), adding new missions ranged from two days to a few months, resulting in significant cost savings as compared to rewriting all the application programs for each mission. Currently supported missions include Mars Pathfinder (MPF), MPL, Mars Exploration Rover (MER), Phoenix, and Mars Science Lab (MSL). Applications based on this library create the majority of operational image RDRs for those missions. A
Non-spherical micelles in an oil-in-water cubic phase
DEFF Research Database (Denmark)
Leaver, M.; Rajagopalan, V.; Ulf, O.
2000-01-01
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...... 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....
Spherically symmetric self-dual Yang-Mills instantons on curved backgrounds in all even dimensions
Radu, Eugen; Tchrakian, D. H.; Yang, Yisong
2008-02-01
We present several different classes of self-dual Yang-Mills instantons in all even d-dimensional backgrounds with Euclidean signature. In d=4p+2 the only solutions we found are on constant curvature dS (de Sitter) and AdS (anti de Sitter) backgrounds and are evaluated in closed form. In d=4p an interesting class of instantons are given on black hole backgrounds. One class of solutions are (Euclidean) time-independent and spherically symmetric in d-1 dimensions, and the other class are spherically symmetric in all d dimensions. Some of the solutions in the former class are evaluated numerically, all the rest being given in closed form. Analytic proofs of existence covering all numerically evaluated solutions are given. All instantons studied have finite action and vanishing energy momentum tensor and do not disturb the geometry.
Nonlinear wave modulation of cylindrical and spherical quantum ion-acoustic solitary waves
Sabry, R.; El-Labany, S. K.; Shukla, P. K.
2008-12-01
Cylindrical and spherical amplitude modulation of quantum ion-acoustic (QIA) envelope solitary waves in a dense quantum plasma comprised of electrons and ions is investigated. For this purpose, a one-dimensional quantum hydrodynamic model and the Poisson equation are considered. By using the standard reductive perturbation technique, a modified nonlinear Schrödinger equation with the geometrical and the quantum effects is derived. The effect of quantum corrections and the effect due to the cylindrical and spherical geometries on the propagation of the QIA envelope solitary waves are examined. It is shown that there exists a modulation instability period depending on the quantum parameter, which does not exist for the one-dimensional classical case.
Bhatia, Rajendra
2013-01-01
This book is an outcome of the Indo-French Workshop on Matrix Information Geometries (MIG): Applications in Sensor and Cognitive Systems Engineering, which was held in Ecole Polytechnique and Thales Research and Technology Center, Palaiseau, France, in February 23-25, 2011. The workshop was generously funded by the Indo-French Centre for the Promotion of Advanced Research (IFCPAR). During the event, 22 renowned invited french or indian speakers gave lectures on their areas of expertise within the field of matrix analysis or processing. From these talks, a total of 17 original contribution or state-of-the-art chapters have been assembled in this volume. All articles were thoroughly peer-reviewed and improved, according to the suggestions of the international referees. The 17 contributions presented are organized in three parts: (1) State-of-the-art surveys & original matrix theory work, (2) Advanced matrix theory for radar processing, and (3) Matrix-based signal processing applications.
Guijosa, A
1999-01-01
This thesis explores some aspects of the recently uncovered connection between gauge theories and gravity, known as the AdS/CFT, or bulk-boundary, correspondence. This is a remarkable statement of equivalence between string or M-theory on certain backgrounds and field theories living on the boundaries of the corresponding spacetimes. Under the duality between four-dimensional N = 4 SU(N) superYang-Mills (SYM) and Type IIB string theory on AdS5 × S5, a baryon is mapped onto N fundamental strings terminating on a wrapped D5-brane. We examine the structure and energetics of this system from the vantage point of the fivebrane worldvolume action, making use of the Born-Infeld string approach. We construct supersymmetric fivebrane embeddings which correspond to gauge theory configurations with n external quarks, 0 ≤ n ≤ N. The extension of these solutions to the full asymptotically flat geometry of N D3-branes provides a detailed description of the creation of strings as the fivebrane is...
Phonon impact on optical control schemes of quantum dots: Role of quantum dot geometry and symmetry
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.
Spherical Bessel transform via exponential sum approximation of spherical Bessel function
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.
Positive geometries and canonical forms
Arkani-Hamed, Nima; Bai, Yuntao; Lam, Thomas
2017-11-01
Recent years have seen a surprising connection between the physics of scattering amplitudes and a class of mathematical objects — the positive Grassmannian, positive loop Grassmannians, tree and loop Amplituhedra — which have been loosely referred to as "positive geometries". The connection between the geometry and physics is provided by a unique differential form canonically determined by the property of having logarithmic singularities (only) on all the boundaries of the space, with residues on each boundary given by the canonical form on that boundary. The structures seen in the physical setting of the Amplituhedron are both rigid and rich enough to motivate an investigation of the notions of "positive geometries" and their associated "canonical forms" as objects of study in their own right, in a more general mathematical setting. In this paper we take the first steps in this direction. We begin by giving a precise definition of positive geometries and canonical forms, and introduce two general methods for finding forms for more complicated positive geometries from simpler ones — via "triangulation" on the one hand, and "push-forward" maps between geometries on the other. We present numerous examples of positive geometries in projective spaces, Grassmannians, and toric, cluster and flag varieties, both for the simplest "simplex-like" geometries and the richer "polytope-like" ones. We also illustrate a number of strategies for computing canonical forms for large classes of positive geometries, ranging from a direct determination exploiting knowledge of zeros and poles, to the use of the general triangulation and push-forward methods, to the representation of the form as volume integrals over dual geometries and contour integrals over auxiliary spaces. These methods yield interesting representations for the canonical forms of wide classes of positive geometries, ranging from the simplest Amplituhedra to new expressions for the volume of arbitrary convex
Phase behavior of charged hydrophobic colloids on flat and spherical surfaces
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.
Surrogate Modeling for Geometry Optimization
DEFF Research Database (Denmark)
Rojas Larrazabal, Marielba de la Caridad; Abraham, Yonas; Holzwarth, Natalie
2009-01-01
A new approach for optimizing the nuclear geometry of an atomic system is described. Instead of the original expensive objective function (energy functional), a small number of simpler surrogates is used.......A new approach for optimizing the nuclear geometry of an atomic system is described. Instead of the original expensive objective function (energy functional), a small number of simpler surrogates is used....
Enumerative Geometry of Hyperplane Arrangements
2012-05-11
NUMBER 6. AUTHOR(SI 5d. PROJECT NUMBER Paul, Thomas Joseph 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS! ESl ...Smith and Bernd Sturmfels. Teaching the geometry of schemes. In Computations in algebraic geometry with Macaulay 2, volume 8 of Algorithms Comput
Spatial geometry and special relativity
DEFF Research Database (Denmark)
Kneubil, Fabiana Botelho
2016-01-01
In this work, it is shown the interplay of relative and absolute entities, which are present in both spatial geometry and special relativity. In order to strengthen the understanding of special relativity, we discuss firstly an instance of geometry and the existence of both frame-dependent and fr...
Molecular motion in restricted geometries
Indian Academy of Sciences (India)
Molecular dynamics in restricted geometries is known to exhibit anomalous behaviour. Diffusion, translational or rotational, of molecules is altered significantly on confinement in restricted geometries. Quasielastic neutron scattering (QENS) offers a unique possibility of studying molecular motion in such systems. Both time ...
Conformal Lorentz geometry revisited
Teleman, Kostake
1996-02-01
. We also show that Mach's principle on inertial motions receives an explanation in our theory by considering the particular geodesic paths, for which one of the partners of an interacting pair is fixed and sent to infinity. In fact we study a dynamical system (W,L) which presents some formal and topological similarities with a system of two particles interacting gravitationally. (W,L) is the only conformally invariant relativistic two-point dynamical system. At the end we show that W can be naturally regarded as the base of a principal GL(2,C)-bundle which comes with a natural connection. We study this bundle from differential geometric point of view. Physical interpretations will be discussed in a future paper. This text is an improvement of a previous version, which was submitted under the title ``Hypertwistor Geometry.'' [See, K. Teleman, ``Hypertwistor Geometry (abstract),'' 14th International Conference on General Relativity and Gravitation, Florence, Italy, 1995.] The change of the title and many other improvements are due to the valuable comments of the referee, who also suggested the author to avoid hazardous interpretations.
Magnetism in curved geometries
Streubel, Robert
Deterministically bending and twisting two-dimensional structures in the three-dimensional (3D) space provide means to modify conventional or to launch novel functionalities by tailoring curvature and 3D shape. The recent developments of 3D curved magnetic geometries, ranging from theoretical predictions over fabrication to characterization using integral means as well as advanced magnetic tomography, will be reviewed. Theoretical works predict a curvature-induced effective anisotropy and effective Dzyaloshinskii-Moriya interaction resulting in a vast of novel effects including magnetochiral effects (chirality symmetry breaking) and topologically induced magnetization patterning. The remarkable development of nanotechnology, e.g. preparation of high-quality extended thin films, nanowires and frameworks via chemical and physical deposition as well as 3D nano printing, has granted first insights into the fundamental properties of 3D shaped magnetic objects. Optimizing magnetic and structural properties of these novel 3D architectures demands new investigation methods, particularly those based on vector tomographic imaging. Magnetic neutron tomography and electron-based 3D imaging, such as electron holography and vector field electron tomography, are well-established techniques to investigate macroscopic and nanoscopic samples, respectively. At the mesoscale, the curved objects can be investigated using the novel method of magnetic X-ray tomography. In spite of experimental challenges to address the appealing theoretical predictions of curvature-induced effects, those 3D magnetic architectures have already proven their application potential for life sciences, targeted delivery, realization of 3D spin-wave filters, and magneto-encephalography devices, to name just a few. DOE BES MSED (DE-AC02-05-CH11231).
Hemingway, Douglas J.; Matsuyama, Isamu
2017-08-01
Isostatic equilibrium is commonly defined as the state achieved when there are no lateral gradients in hydrostatic pressure, and thus no lateral flow, at depth within the lower viscosity mantle that underlies a planetary body's outer crust. In a constant-gravity Cartesian framework, this definition is equivalent to the requirement that columns of equal width contain equal masses. Here we show, however, that this equivalence breaks down when the spherical geometry of the problem is taken into account. Imposing the "equal masses" requirement in a spherical geometry, as is commonly done in the literature, leads to significant lateral pressure gradients along internal equipotential surfaces and thus corresponds to a state of disequilibrium. Compared with the "equal pressures" model we present here, the equal masses model always overestimates the compensation depth—by ˜27% in the case of the lunar highlands and by nearly a factor of 2 in the case of Enceladus.
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.
Technical notes. Spherical harmonics approximations of neutron transport
Energy Technology Data Exchange (ETDEWEB)
Demeny, A.; Dede, K.M.; Erdei, K.
1976-12-01
A double-range spherical harmonics approximation obtained by expanding the angular flux separately in the two regions combined with the conventional single-range spherical harmonics is found to give superior description of neutron transport.
Spontaneous spherical symmetry breaking in atomic confinement
Sveshnikov, Konstantin; Tolokonnikov, Andrey
2017-07-01
The effect of spontaneous breaking of initial SO(3) symmetry is shown to be possible for an H-like atom in the ground state, when it is confined in a spherical box under general boundary conditions of "not going out" through the box surface (i.e. third kind or Robin's ones), for a wide range of physically reasonable values of system parameters. The most novel and nontrivial result, which has not been reported previously, is that such an effect takes place not only for attractive, but also for repulsive interactions of atomic electrons with the cavity environment. Moreover, in the limit of a large box size R ≫ aB the regime of an atom, soaring over a plane with boundary condition of "not going out", is reproduced, rather than a spherically symmetric configuration, which would be expected on the basis of the initial SO(3) symmetry of the problem.
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 the quadrup......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...... results obtained in homogeneous environment is demonstrated. Multipole resonance features in the experimental reflection spectra of particles located on a gold substrate, in the wavelength range of 500-1000 nm, are discussed and theoretically analyzed on the basis of finite-difference time...
Quality metric for spherical panoramic video
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.
Imaging with Spherically Bent Crystals or Reflectors
Energy Technology Data Exchange (ETDEWEB)
Bitter, M; Hill, K W; Scott, S; Ince-Cushman, A; Reinke, M; Podpaly, Y; Rice, J E; Beiersdorfer, P
2010-06-01
This paper consists of two parts: Part I describes the working principle of a recently developed x-ray imaging crystal spectrometer, where the astigmatism of spherically bent crystals is being used with advantage to record spatially resolved spectra of highly charged ions for Doppler measurements of the ion-temperature and toroidal plasmarotation- velocity profiles in tokamak plasmas. This type of spectrometer was thoroughly tested on NSTX and Alcator C-Mod, and its concept was recently adopted for the design of the ITER crystal spectrometers. Part II describes imaging schemes, where the astigmatism has been eliminated by the use of matched pairs of spherically bent crystals or reflectors. These imaging schemes are applicable over a wide range of the electromagnetic radiation, which includes microwaves, visible light, EUV radiation, and x-rays. Potential applications with EUV radiation and x-rays are the diagnosis of laserproduced plasmas, imaging of biological samples with synchrotron radiation, and lithography.
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
Gravito-inertial modes in a differentially rotating spherical shell
Directory of Open Access Journals (Sweden)
Mirouh Giovanni M.
2015-01-01
Full Text Available While many intermediate- and high-mass main sequence stars are rapidly and differentially rotating, the effects of rotation on oscillation modes are poorly known. In this communication we present a first study of axisymmetric gravito-inertial modes in the radiative zone of a differentially rotating star. We consider a simplified model where the radiative zone of the star is a linearly stratified rotating fluid within a spherical shell, with differential rotation due to baroclinic effects. We solve the eigenvalue problem with high-resolution spectral computations and determine the propagation domain of the waves through the theory of characteristics. We explore the propagation properties of two kinds of modes: those that can propagate in the entire shell and those that are restricted to a sub-domain. Some of the modes that we find concentrate kinetic energy around short-period shear layers known as attractors. We describe various geometries for the propagation domains, conditioning the surface visibility of the corresponding modes.
Direct Simulation of Extinction in a Slab of Spherical Particles
Mackowski, D.W.; Mishchenko, Michael I.
2013-01-01
The exact multiple sphere superposition method is used to calculate the coherent and incoherent contributions to the ensemble-averaged electric field amplitude and Poynting vector in systems of randomly positioned nonabsorbing spherical particles. The target systems consist of cylindrical volumes, with radius several times larger than length, containing spheres with positional configurations generated by a Monte Carlo sampling method. Spatially dependent values for coherent electric field amplitude, coherent energy flux, and diffuse energy flux, are calculated by averaging of exact local field and flux values over multiple configurations and over spatially independent directions for fixed target geometry, sphere properties, and sphere volume fraction. Our results reveal exponential attenuation of the coherent field and the coherent energy flux inside the particulate layer and thereby further corroborate the general methodology of the microphysical radiative transfer theory. An effective medium model based on plane wave transmission and reflection by a plane layer is used to model the dependence of the coherent electric field on particle packing density. The effective attenuation coefficient of the random medium, computed from the direct simulations, is found to agree closely with effective medium theories and with measurements. In addition, the simulation results reveal the presence of a counter-propagating component to the coherent field, which arises due to the internal reflection of the main coherent field component by the target boundary. The characteristics of the diffuse flux are compared to, and found to be consistent with, a model based on the diffusion approximation of the radiative transfer theory.
Modeling of laminar forced convection in spherical- pebble packed beds
International Nuclear Information System (INIS)
Hadad, Yaser; Jafarpur, Khosrow
2012-01-01
There are many parameters that have significant effects on forced convection heat transfer in packed beds, including Reynolds and Prandtl numbers of flow, porosity, pebble geometry, local flow conditions, wall and end effects. In addition, there have been many experimental investigations on forced convection heat transfer in packed beds and each have studied the effect of some of these parameters. Yet, there is not a reliable correlation that includes the effect of main parameters: at the same time, the prediction of precise correct limits for very low and high Reynolds numbers is off hand. In this article a general well-known model of convection heat transfer from isothermal bodies, next to some previous reliable experimental data has been used as a basis for a more comprehensive and accurate correlation to calculate the laminar constant temperature pebble-fluid forced convection heat transfer in a homogeneous saturated bed with spherical pebbles. Finally, for corroboration, the present results are compared with previous works and show a very good agreement for laminar flows at any Prandtl number and all porosities
Parametric spherical deconvolution: inferring anatomical connectivity using diffusion MR imaging.
Kaden, Enrico; Knösche, Thomas R; Anwander, Alfred
2007-08-15
The human brain forms a complex neural network with a connectional architecture that is still far from being known in full detail, even at the macroscopic level. The advent of diffusion MR imaging has enabled the exploration of the structural properties of white matter in vivo. In this article we propose a new forward model that maps the microscopic geometry of nervous tissue onto the water diffusion process and further onto the measured MR signals. Our spherical deconvolution approach completely parameterizes the fiber orientation density by a finite mixture of Bingham distributions. In addition, we define the term anatomical connectivity, taking the underlying image modality into account. This neurophysiological metric may represent the proportion of the nerve fibers originating in the source area which intersect a given target region. The specified inverse problem is solved by Bayesian statistics. Posterior probability maps denote the probability that the connectivity value exceeds a chosen threshold, conditional upon the noisy observations. These maps allow us to draw inferences about the structural organization of the cerebral cortex. Moreover, we will demonstrate the proposed approach with diffusion-weighted data sets featuring high angular resolution.
Spherical Harmonic Solutions to the 3D Kobayashi Benchmark Suite
International Nuclear Information System (INIS)
Brown, P.N.; Chang, B.; Hanebutte, U.R.
1999-01-01
Spherical harmonic solutions of order 5, 9 and 21 on spatial grids containing up to 3.3 million cells are presented for the Kobayashi benchmark suite. This suite of three problems with simple geometry of pure absorber with large void region was proposed by Professor Kobayashi at an OECD/NEA meeting in 1996. Each of the three problems contains a source, a void and a shield region. Problem 1 can best be described as a box in a box problem, where a source region is surrounded by a square void region which itself is embedded in a square shield region. Problems 2 and 3 represent a shield with a void duct. Problem 2 having a straight and problem 3 a dog leg shaped duct. A pure absorber and a 50% scattering case are considered for each of the three problems. The solutions have been obtained with Ardra, a scalable, parallel neutron transport code developed at Lawrence Livermore National Laboratory (LLNL). The Ardra code takes advantage of a two-level parallelization strategy, which combines message passing between processing nodes and thread based parallelism amongst processors on each node. All calculations were performed on the IBM ASCI Blue-Pacific computer at LLNL
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.
New mathematical framework for spherical gravitational collapse
International Nuclear Information System (INIS)
Giambo, Roberto; Giannoni, Fabio; Magli, Giulio; Piccione, Paolo
2003-01-01
A theorem, giving necessary and sufficient condition for naked singularity formation in spherically symmetric non-static spacetimes under hypotheses of physical acceptability, is formulated and proved. The theorem relates the existence of singular null geodesics to the existence of regular curves which are supersolutions of the radial null geodesic equation, and allows us to treat all the known examples of naked singularities from a unified viewpoint. New examples are also found using this approach, and perspectives are discussed. (letter to the editor)
Characteristics and Manufacture of Spherical Smokeless Powders
Botelho, Fernanda Diniz; Galante, Erick Braga Ferrão; Mendes, Álvaro José Boareto
2015-01-01
ABSTRACT: Smokeless propellants have been studied and manufactured for many decades. They can exist in various physical forms and also can have different properties according to the use of each propellant. One important form of smokeless powders is the ball powder, which has spherical grains. The manufacture process of the ball powder has many advantages over the usual way to manufacture a smokeless powder. For example, unstable and even deteriorated nitrocellulose, after being stabilized aga...
Spherical cancer models in tumor biology.
Weiswald, Louis-Bastien; Bellet, Dominique; Dangles-Marie, Virginie
2015-01-01
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. Copyright © 2014 Neoplasia Press, Inc. Published by Elsevier Inc. All rights reserved.
Particles in spherical electromagnetic radiation fields
International Nuclear Information System (INIS)
Mitter, H.; Thaller, B.
1984-03-01
If the time-dependence of a Hamiltonian can be compensated by an appropriate symmetry transformation, the corresponding quantum mechanical problem can be reduced to an effectively stationary one. With this result we investigate the behavior of nonrelativistic particles in a spherical radiation field produced by a rotating source. Then the symmetry transformation corresponds to a rotation. We calculate the transition probabilities in Born approximation. The extension to problems involving an additional Coulomb potential is briefly discussed. (Author)
Diffusion of spherical particles in microcavities
Imperio, A.; Padding, J. T.; Briels, W. J.
2011-01-01
The diffusive motion of a colloidal particle trapped inside a small cavity filled with fluid is reduced by hydrodynamic interactions with the confining walls. In this work, we study these wall effects on a spherical particle entrapped in a closed cylinder. We calculate the diffusion coefficient along the radial, azimuthal and axial direction for different particle positions. At all locations the diffusion is smaller than in a bulk fluid and it becomes anisotropic near the container's walls. W...
Current drive for spherical tokamak plasmas
International Nuclear Information System (INIS)
Storer, R.
1999-01-01
Very low aspect ratio spherical tokamaks have proved to have some very useful and remarkable properties including very high values of the plasma pressure to magnetic field pressure. Following the construction of the Start tokamak, a number of such configurations have been constructed. One of the difficulties encountered is in providing sufficient inductive current drive due to the competing requirements of the need to keep the aspect ratio low and providing the space for the central current-carrying rod with an internal inductive coil. An alternative current drive technique would be very useful. In a parallel development it has been shown that a rotating magnetic field can drive a significant non-linear Hall current in a spherical plasma. Successful experiments of this concept have been made with a device called the Rotamak. In its original configuration this device was a field reversed configuration without a toroidal magnetic field but with a vertical field to establish the magnetic hydrodynamical equilibrium. However, recent modifications have shown that increased current can be driven if a central current-carrying rod is used to provide an applied toroidal field. The new Rotamak has then a spherical tokamak magnetic field structure. This work will present new calculations which model the above structure and include the effect of the applied toroidal field in addition to the steady vertical field and the rotating (current-drive) magnetic field. The problem is fully three dimensional and non-linear and involves the application of interesting computational techniques. The potential of using the rotating field current drive technique for spherical tokamaks will be evaluated
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
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.
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
Weyl geometry and the nonlinear mechanics of distributed point defects
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.
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
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
PENETRATION OF A SOUND FIELD THROUGH A MULTILAYERED SPHERICAL SHELL
Directory of Open Access Journals (Sweden)
G. Ch. Shushkevich
2013-01-01
Full Text Available An analytical solution of the boundary problem describing the process of penetration of thesound field of a spherical emitter located inside a thin unclosed spherical shell through a permeable multilayered spherical shell is considered. The influence of some parameters of the problem on the value of the sound field weakening (screening coefficient is studied via a numerical simulation.
PENETRATION OF A SOUND FIELD THROUGH A MULTILAYERED SPHERICAL SHELL
G. Ch. Shushkevich; N. N. Kiselyova
2013-01-01
An analytical solution of the boundary problem describing the process of penetration of thesound field of a spherical emitter located inside a thin unclosed spherical shell through a permeable multilayered spherical shell is considered. The influence of some parameters of the problem on the value of the sound field weakening (screening) coefficient is studied via a numerical simulation.
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
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
Differential geometry and symmetric spaces
Helgason, Sigurdur
2001-01-01
Sigurdur Helgason's Differential Geometry and Symmetric Spaces was quickly recognized as a remarkable and important book. For many years, it was the standard text both for Riemannian geometry and for the analysis and geometry of symmetric spaces. Several generations of mathematicians relied on it for its clarity and careful attention to detail. Although much has happened in the field since the publication of this book, as demonstrated by Helgason's own three-volume expansion of the original work, this single volume is still an excellent overview of the subjects. For instance, even though there
Differential geometry curves, surfaces, manifolds
Kühnel, Wolfgang
2015-01-01
This carefully written book is an introduction to the beautiful ideas and results of differential geometry. The first half covers the geometry of curves and surfaces, which provide much of the motivation and intuition for the general theory. The second part studies the geometry of general manifolds, with particular emphasis on connections and curvature. The text is illustrated with many figures and examples. The prerequisites are undergraduate analysis and linear algebra. This new edition provides many advancements, including more figures and exercises, and-as a new feature-a good number of so
Fallow), Stray
2009-01-01
Having trouble with geometry? Do Pi, The Pythagorean Theorem, and angle calculations just make your head spin? Relax. With Head First 2D Geometry, you'll master everything from triangles, quads and polygons to the time-saving secrets of similar and congruent angles -- and it'll be quick, painless, and fun. Through entertaining stories and practical examples from the world around you, this book takes you beyond boring problems. You'll actually use what you learn to make real-life decisions, like using angles and parallel lines to crack a mysterious CSI case. Put geometry to work for you, and
Walsh, Edward T
2014-01-01
This introductory text is designed to help undergraduate students develop a solid foundation in geometry. Early chapters progress slowly, cultivating the necessary understanding and self-confidence for the more rapid development that follows. The extensive treatment can be easily adapted to accommodate shorter courses. Starting with the language of mathematics as expressed in the algebra of logic and sets, the text covers geometric sets of points, separation and angles, triangles, parallel lines, similarity, polygons and area, circles, space geometry, and coordinate geometry. Each chapter incl
Energy Technology Data Exchange (ETDEWEB)
Hogan, Craig
2013-03-24
Standard particle theory is based on quantized matter embedded in a classical geometry. Here, a complementary model is proposed, based on classical matter -- massive bodies, without quantum properties -- embedded in a quantum geometry. It does not describe elementary particles, but may be a better, fully consistent quantum description for position states in laboratory-scale systems. Gravitational theory suggests that the geometrical quantum system has an information density of about one qubit per Planck length squared. If so, the model here predicts that the quantum uncertainty of geometry creates a new form of noise in the position of massive bodies, detectable by interferometers.
Kostogryz, N. M.; Yakobchuk, T. M.; Berdyugina, S. V.; Milic, I.
2017-05-01
Context. To properly interpret photometric and polarimetric observations of exoplanetary transits, accurate calculations of center-to-limb variations of intensity and linear polarization of the host star are needed. These variations, in turn, depend on the choice of geometry of stellar atmosphere. Aims: We want to understand the dependence of the flux and the polarization curves during a transit on the choice of the applied approximation for the stellar atmosphere: spherical and plane-parallel. We examine whether simpler plane-parallel models of stellar atmospheres are good enough to interpret the flux and the polarization light curves during planetary transits, or whether more complicated spherical models should be used. Methods: Linear polarization during a transit appears because a planet eclipses a stellar disk and thus breaks left-right symmetry. We calculate the flux and the polarization variations during a transit with given center-to-limb variations of intensity and polarization. Results: We calculate the flux and the polarization variations during transit for a sample of 405 extrasolar systems. Most of them show higher transit polarization for the spherical stellar atmosphere. Our calculations reveal a group of exoplanetary systems that demonstrates lower maximum polarization during the transits with spherical model atmospheres of host stars with effective temperatures of Teff = 4400-5400 K and surface gravity of log g = 4.45-4.65 than that obtained with plane-parallel atmospheres. Moreover, we have found two trends of the transit polarization. The first trend is a decrease in the polarization calculated with spherical model atmosphere of host stars with effective temperatures Teff = 3500-5100 K, and the second shows an increase in the polarization for host stars with Teff = 5100-7000 K. These trends can be explained by the relative variation of temperature and pressure dependences in the plane-parallel and spherical model atmospheres. Conclusions: For
An introduction to differential geometry
Willmore, T J
2012-01-01
This text employs vector methods to explore the classical theory of curves and surfaces. Topics include basic theory of tensor algebra, tensor calculus, calculus of differential forms, and elements of Riemannian geometry. 1959 edition.
Hyperbolic Metamaterials with Complex Geometry
DEFF Research Database (Denmark)
Lavrinenko, Andrei; Andryieuski, Andrei; Zhukovsky, Sergei
2016-01-01
We investigate new geometries of hyperbolic metamaterialssuch as highly corrugated structures, nanoparticle monolayer assemblies, super-structured or vertically arranged multilayersand nanopillars. All structures retain basic propertiesof hyperbolic metamaterials, but have functionality improved...
Advances in discrete differential geometry
2016-01-01
This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. The authors take a closer look at discrete models in differential geometry and dynamical systems. Their curves are polygonal, surfaces are made from triangles and quadrilaterals, and time is discrete. Nevertheless, the difference between the corresponding smooth curves, surfaces and classical dynamical systems with continuous time can hardly be seen. This is the paradigm of structure-preserving discretizations. Current advances in this field are stimulated to a large extent by its relevance for computer graphics and mathematical physics. This book is written by specialists working together on a common research project. It is about differential geometry and dynamical systems, smooth and discrete theories, ...
Chiral pion dynamics for spherical nucleon bags
International Nuclear Information System (INIS)
Vento, V.; Rho, M.; Nyman, E.M.; Jun, J.H.; Brown, G.E.; CEA Centre d'Etudes Nucleaires de Saclay, 91 - Gif-sur-Yvette
1980-01-01
A chirally symmetric quark-bag model for the nucleon is obtained by introducing an explicit, classical, pion field exterior to the bag. The coupling at the bag surface is determined by the requirement of a conserved axial-vector current. The pion field satisfies equations of motion corresponding to the non-linear sigma-model. We study on this paper the simplified case where the bag and the pion field are spherically symmetric. Corrections due to gluon exchange between the quarks are ignored along with other interactions which split the N- and Δ-masses. The equations of motion for the pion field are solved and we find a substantial pion pressure at the bag surface, along with an attractive contribution to the nucleon self-energy. The total energy of the system, bag plus meson cloud, turns out to be approximately Msub(n)c 2 for a wide range of bag radii, from 1.5 fm down to about 0.5 fm. Introduction of a form factor for the pion would extend the range of possible radii to even smaller values. We propose that the bag with the smallest allowed radius be identified with the 'little bag' discussed before. One surprising result of the paper is that as long as one restricts to spherically symmetric bags, restoring chiral symmetry to the bag model makes the axial-vector current coupling constant gsub(A) to be always too large compared with the experimental value for any bag radius, suggesting a deviation from spherical symmetry for the intrinsic bag wave functions of the 'ground-state' hadrons. (orig.)
Uniform illumination of spherical laser fusion targets
International Nuclear Information System (INIS)
Howard, J.E.
1977-01-01
Uniformity of illumination of spherical laser fusion targets is calculated for eight, twelve, and twenty beams arranged according to the symmetry of the Platonic solids. Uniformity is optimized by varying the f/no. of ideal aberration-free lenses, amount of beam overlap, and the shape of the spatial beam profile. The numerical results show twenty-beam illumination to be slightly better than twelve-beam illumination, with eight beams running a poor third. Refractive energy losses due to nonorthogonal illumination and the implications for the design of a practical laser fusion reactor are discussed
Spherical conformal models for compact stars
Energy Technology Data Exchange (ETDEWEB)
Takisa, P.M.; Maharaj, S.D.; Manjonjo, A.M.; Moopanar, S. [University of KwaZulu-Natal, Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics and Computer Science, Durban (South Africa)
2017-10-15
We consider spherical exact models for compact stars with anisotropic pressures and a conformal symmetry. The conformal symmetry condition generates an integral relationship between the gravitational potentials. We solve this condition to find a new anisotropic solution to the Einstein field equations. We demonstrate that the exact solution produces a relativistic model of a compact star. The model generates stellar radii and masses consistent with PSR J1614-2230, Vela X1, PSR J1903+327 and Cen X-3. A detailed physical examination shows that the model is regular, well behaved and stable. The mass-radius limit and the surface red shift are consistent with observational constraints. (orig.)
The spherical tokamak fusion power plant
International Nuclear Information System (INIS)
Wilson, H.R.; Voss, G.; Ahn, J.W.
2003-01-01
The design of a 1GW(e) steady state fusion power plant, based on the spherical tokamak concept, has been further iterated towards a fully self-consistent solution taking account of plasma physics, engineering and neutronics constraints. In particular a plausible solution to exhaust handling is proposed and the steam cycle refined to further improve efficiency. The physics design takes full account of confinement, MHD stability and steady state current drive. It is proposed that such a design may offer a fusion power plant which is easy to maintain: an attractive feature for the power plants following ITER. (author)
Galileon radiation from a spherical collapsing shell
Energy Technology Data Exchange (ETDEWEB)
Martín-García, Javier [Instituto de Física Teórica UAM/CSIC,C/ Nicolás Cabrera 15, E-28049 Madrid (Spain); Vázquez-Mozo, Miguel Á. [Instituto Universitario de Física Fundamental y Matemáticas (IUFFyM),Universidad de Salamanca, Plaza de la Merced s/n, E-37008 Salamanca (Spain)
2017-01-17
Galileon radiation in the collapse of a thin spherical shell of matter is analyzed. In the framework of a cubic Galileon theory, we compute the field profile produced at large distances by a short collapse, finding that the radiated field has two peaks traveling ahead of light fronts. The total energy radiated during the collapse follows a power law scaling with the shell’s physical width and results from two competing effects: a Vainshtein suppression of the emission and an enhancement due to the thinness of the shell.
Spherical Panoramas for Astrophysical Data Visualization
Kent, Brian R.
2017-05-01
Data immersion has advantages in astrophysical visualization. Complex multi-dimensional data and phase spaces can be explored in a seamless and interactive viewing environment. Putting the user in the data is a first step toward immersive data analysis. We present a technique for creating 360° spherical panoramas with astrophysical data. The three-dimensional software package Blender and the Google Spatial Media module are used together to immerse users in data exploration. Several examples employing these methods exhibit how the technique works using different types of astronomical data.
Effect of inclusion geometry and matrix properties on rolling contact fatigue of steel
International Nuclear Information System (INIS)
Tyfour, R. W.
2000-01-01
The work presented in this paper is aimed at studying the effect of inclusion geometry and matrix property on rolling contact fatigue of steel. Rolling contact has been stimulated in laboratory using a twin-disc machine and an on-line crack detection system. It has been shown that soft inclusions, although normally considered harmless, can be good sites for crack initiation and suitable paths for crack propagation. Enough evidence has been given to show that if inclusions can be maintained spherical, they may not affect rolling contact fatigue life. The mechanical properties of the matrix play an important role in helping or hindering the deformation of soft inclusions. Strong matrix around the inclusion makes it less likely for spherical shaped inclusions to transform to stringers, and as a result, preserves the geometry of inclusion. However, soft matrix enables deforming the inclusion and raises the stress concentration at the inclusion edges. (author). 25 refs., 7 figs. 2 tabs
Semi-Numerical Studies of the Three-Meter Spherical Couette Experiment Utilizing Data Assimilation
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.
Transport of barrel and spherical shaped colloids in unsaturated porous media.
Knappenberger, Thorsten; Aramrak, Surachet; Flury, Markus
2015-09-01
Model colloids are usually spherical, but natural colloids have irregular geometries. Transport experiments of spherical colloids may not reflect the transport characteristics of natural colloids in porous media. We investigated saturated and unsaturated transport of colloids with spherical and angular shapes under steady-state, flow conditions. A pulse of negatively-charged colloids was introduced into a silica sand column at three different effective water saturations (Se = 0.31, 0.45, and 1.0). Colloids were introduced under high ionic strength of [106]mM to cause attachment to the secondary energy minimum and later released by changing the pore water to low ionic strength. After the experiment, sand was sampled from different depths (0, -4, and -11 cm) for scanning electron microscopy (SEM) analysis and colloid extraction. Water saturation affected colloid transport with more retention under low than under high saturation. Colloids were retained and released from a secondary energy minimum with more angular-shaped colloids being retained and released. Colloids extracted from the sand revealed highest colloid deposition in the top layer and decreasing deposition with depth. Pore straining and grain-grain wedging dominated colloid retention. Copyright © 2015 Elsevier B.V. All rights reserved.
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
Status of National Spherical Torus Experiment (NSTX)*
Ono, Masayuki
2001-10-01
The main aim of National Spherical Torus Experiment (NSTX) is to establish the fusion physics principles of the innovative spherical torus (ST) concept. The NSTX experimental facility has been operating reliably and its capabilities steadily improving. Due to relatively efficient ohmic current drive and benign halo current behavior, the plasma current was increased to 1.4 MA, which is well above the design value of 1 MA. The plasmas at 1 MA are now routinely heated by NBI to the average toroidal beta value of 20 percent range at 3 kG with electrons and ions in the 1-2 keV range. Even with the “L-mode” edge, the energy confinement time can well exceed the so-called L-mode (and even H-mode) scaling values. As a part of ST tool development, High Harmonic Fast Wave (HHFW) heating has demonstrated efficient electron heating with the central electron temperatures reaching 3.7 keV. HHFW induced H-modes have been also observed. For CHI (Coaxial Helicity Injection) non-inductive start-up, CHI discharges of up to 300 kA of toroidal current and 300 msec duration have been produced from zero current using = 25 kA of injected current. The poster presentation will also include the near term NSTX facility upgrade plan.
Clusters of polyhedra in spherical confinement
Teich, Erin G.; van Anders, Greg; Klotsa, Daphne; Dshemuchadse, Julia; Glotzer, Sharon C.
2016-01-01
Dense particle packing in a confining volume remains a rich, largely unexplored problem, despite applications in blood clotting, plasmonics, industrial packaging and transport, colloidal molecule design, and information storage. Here, we report densest found clusters of the Platonic solids in spherical confinement, for up to N=60 constituent polyhedral particles. We examine the interplay between anisotropic particle shape and isotropic 3D confinement. Densest clusters exhibit a wide variety of symmetry point groups and form in up to three layers at higher N. For many N values, icosahedra and dodecahedra form clusters that resemble sphere clusters. These common structures are layers of optimal spherical codes in most cases, a surprising fact given the significant faceting of the icosahedron and dodecahedron. We also investigate cluster density as a function of N for each particle shape. We find that, in contrast to what happens in bulk, polyhedra often pack less densely than spheres. We also find especially dense clusters at so-called magic numbers of constituent particles. Our results showcase the structural diversity and experimental utility of families of solutions to the packing in confinement problem. PMID:26811458
Quasi-spherical direct drive fusion.
Energy Technology Data Exchange (ETDEWEB)
VanDevender, J. Pace; Abbott, Lucas M.; Langston, William L.; McDaniel, Dillon Heirman; Nash, Thomas J.; Roderick, Norman Frederick; Silva, M.
2007-01-01
The authors present designs of quasi-spherical direction drive z-pinch loads for machines such as ZR at 28 MA load current with a 150 ns implosion time (QSDDI). A double shell system for ZR has produced a 2D simulated yield of 12 MJ, but the drive for this system on ZR has essentially no margin. A double shell system for a 56 MA driver at 150 ns implosion has produced a simulated yield of 130 MJ with considerable margin in attaining the necessary temperature and density-radius product for ignition. They also represent designs for a magnetically insulated current amplifier, (MICA), that modify the attainable ZR load current to 36 MA with a 28 ns rise time. The faster pulse provided by a MICA makes it possible to drive quasi-spherical single shell implosions (QSDD2). They present results from 1D LASNEX and 2D MACH2 simulations of promising low-adiabat cryogenic QSDD2 capsules and 1D LASNEX results of high-adiabat cryogenic QSDD2 capsules.
Spherical aggregates composed of gold nanoparticles
International Nuclear Information System (INIS)
Chen, C-C; Kuo, P-L; Cheng, Y-C
2009-01-01
Alkylated triethylenetetramine (C12E3) was synthesized and used as both a reductant in the preparation of gold nanoparticles by the reduction of HAuCl 4 and a stabilizer in the subsequent self-assembly of the gold nanoparticles. In acidic aqueous solution, spherical aggregates (with a diameter of about 202 ± 22 nm) of gold nanoparticles (with the mean diameter of ∼18.7 nm) were formed. The anion-induced ammonium adsorption of the alkylated amines on the gold nanoparticles was considered to provide the electrostatic repulsion and steric hindrance between the gold nanoparticles, which constituted the barrier that prevented the individual particles from coagulating. However, as the amino groups became deprotonated with increasing pH, the ammonium adsorption was weakened, and the amino groups were desorbed from the gold surface, resulting in discrete gold particles. The results indicate that the morphology of the reduced gold nanoparticles is controllable through pH-'tunable' aggregation under the mediation of the amino groups of alkylated amine to create spherical microstructures.
Vatta, Federica; Meneghini, Fabio; Esposito, Fabrino; Mininel, Stefano; Di Salle, Francesca
2009-01-01
Neural source localization techniques based on electroencephalography (EEG) use scalp potential data to infer the location of underlying neural activity. This procedure entails modeling the sources of EEG activity and modeling the head volume conduction process to link the modeled sources to the EEG, solving the so called EEG forward problem, and reconstructing the brain electrical activity from recorded EEG data, solving the EEG inverse problem. Many factors affect the accuracy of the forward and hence of the inverse problem solution, one of them is the shape of the head model. Realistic head models can lead to more accurate forward problem solutions, but imply heavier computational burdens in comparison to spherical models. Conversely, inverse solutions require the forward model to be computationally efficient. The aim of this study is to investigate the different general potentialities, in terms of EEG source reconstruction, which can be achieved adopting realistic or spherical geometries in head modeling. Previous studies in the literature analyzed the effect of head model geometry presenting results for particular cases of head models. In this paper, we re-address the effect of realistic geometry in head modeling, seeking for more general results by adopting the Montreal Neurological Institute (MNI) phantom model to represent a whole family of realistic head models. This paper presents results of a computer simulation study in which the potentialities of two different four-shell head models are compared, the realistic MNI-based FDM and the corresponding sensor-fitted spherical-shaped model, by means of the Point Spread Function (PSF) correlation maps, with a quantitative analysis of the accuracy in EEG source reconstruction given by head modeling refinement from the spherical to the more complex realistic FDM head modeling.
A Comment on Molecular Geometry
Gomba, Frank J.
1999-12-01
A method of determining the correct molecular geometry of simple molecules and ions with one central atom is proposed. While the usual method of determining the molecular geometry involves first drawing the Lewis structure, this method can be used without doing so. In fact, the Lewis structure need not be drawn at all. The Lewis structure may be drawn as the final step, with the geometry of the simple molecule or ion already established. In the case of diatomic molecules, any atom may be used as the central atom. When hydrogen is present in a multiatom molecule or ion, this method "naturally" eliminates choosing hydrogen; but, any other atom may be used as the central atom to determine the correct geometry. The Lewis structure can then be used to determine the formal charges on the atoms. In this way there is a check on the selection of the central atom, should the correct Lewis structure be desired. Thus, it assumes that one is familiar with both Lewis structures and the valence shell electron pair repulsion (VSEPR) approach to bonding. The approach suggested in this paper will give rapid and accurate molecular geometries, and it is fun !!!
Electrodynamics and Spacetime Geometry: Foundations
Cabral, Francisco; Lobo, Francisco S. N.
2017-02-01
We explore the intimate connection between spacetime geometry and electrodynamics. This link is already implicit in the constitutive relations between the field strengths and excitations, which are an essential part of the axiomatic structure of electromagnetism, clearly formulated via integration theory and differential forms. We review the foundations of classical electromagnetism based on charge and magnetic flux conservation, the Lorentz force and the constitutive relations. These relations introduce the conformal part of the metric and allow the study of electrodynamics for specific spacetime geometries. At the foundational level, we discuss the possibility of generalizing the vacuum constitutive relations, by relaxing the fixed conditions of homogeneity and isotropy, and by assuming that the symmetry properties of the electro-vacuum follow the spacetime isometries. The implications of this extension are briefly discussed in the context of the intimate connection between electromagnetism and the geometry (and causal structure) of spacetime.
Euclidean geometry and its subgeometries
Specht, Edward John; Calkins, Keith G; Rhoads, Donald H
2015-01-01
In this monograph, the authors present a modern development of Euclidean geometry from independent axioms, using up-to-date language and providing detailed proofs. The axioms for incidence, betweenness, and plane separation are close to those of Hilbert. This is the only axiomatic treatment of Euclidean geometry that uses axioms not involving metric notions and that explores congruence and isometries by means of reflection mappings. The authors present thirteen axioms in sequence, proving as many theorems as possible at each stage and, in the process, building up subgeometries, most notably the Pasch and neutral geometries. Standard topics such as the congruence theorems for triangles, embedding the real numbers in a line, and coordinatization of the plane are included, as well as theorems of Pythagoras, Desargues, Pappas, Menelaus, and Ceva. The final chapter covers consistency and independence of axioms, as well as independence of definition properties. There are over 300 exercises; solutions to many of the...
Flux compactifications and generalized geometries
International Nuclear Information System (INIS)
Grana, Mariana
2006-01-01
Following the lectures given at CERN Winter School 2006, we present a pedagogical overview of flux compactifications and generalized geometries, concentrating on closed string fluxes in type II theories. We start by reviewing the supersymmetric flux configurations with maximally symmetric four-dimensional spaces. We then discuss the no-go theorems (and their evasion) for compactifications with fluxes. We analyse the resulting four-dimensional effective theories for Calabi-Yau and Calabi-Yau orientifold compactifications, concentrating on the flux-induced superpotentials. We discuss the generic mechanism of moduli stabilization and illustrate with two examples: the conifold in IIB and a T 6 /(Z 3 x Z 3 ) torus in IIA. We finish by studying the effective action and flux vacua for generalized geometries in the context of generalized complex geometry
Guide to Computational Geometry Processing
DEFF Research Database (Denmark)
Bærentzen, Jakob Andreas; Gravesen, Jens; Anton, François
Optical scanning is rapidly becoming ubiquitous. From industrial laser scanners to medical CT, MR and 3D ultrasound scanners, numerous organizations now have easy access to optical acquisition devices that provide huge volumes of image data. However, the raw geometry data acquired must first...... be processed before it is useful. This Guide to Computational Geometry Processing reviews the algorithms for processing geometric data, with a practical focus on important techniques not covered by traditional courses on computer vision and computer graphics. This is balanced with an introduction...... Provides additional material at a supplementary website Includes self-study exercises throughout the text Graduate students will find this text a valuable, hands-on guide to developing key skills in geometry processing. The book will also serve as a useful reference for professionals wishing to improve...
The prediction of spherical aberration with schematic eyes.
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.
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
Geometry, topology, and string theory
Energy Technology Data Exchange (ETDEWEB)
Varadarajan, Uday [Univ. of California, Berkeley, CA (United States)
2003-01-01
A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect. In particular, situations in which extra dimensions, non-commutative geometries as well as other non-local structures emerge are explored in detail. Further, a preliminary exploration of such issues in Lorentzian space-times with non-trivial causal structures within string theory is initiated.
Stochastic geometry and its applications
Chiu, Sung Nok; Kendall, Wilfrid S; Mecke, Joseph
2013-01-01
An extensive update to a classic text Stochastic geometry and spatial statistics play a fundamental role in many modern branches of physics, materials sciences, engineering, biology and environmental sciences. They offer successful models for the description of random two- and three-dimensional micro and macro structures and statistical methods for their analysis. The previous edition of this book has served as the key reference in its field for over 18 years and is regarded as the best treatment of the subject of stochastic geometry, both as a subject with vital a
Introduction to topology and geometry
Stahl, Saul
2014-01-01
An easily accessible introduction to over three centuries of innovations in geometry Praise for the First Edition ". . . a welcome alternative to compartmentalized treatments bound to the old thinking. This clearly written, well-illustrated book supplies sufficient background to be self-contained." -CHOICE This fully revised new edition offers the most comprehensive coverage of modern geometry currently available at an introductory level. The book strikes a welcome balance between academic rigor and accessibility, providing a complete and cohesive picture of the science with an unparallele
Graphical debugging of combinational geometry
International Nuclear Information System (INIS)
Burns, T.J.; Smith, M.S.
1992-01-01
A graphical debugger for combinatorial geometry being developed at Oak Ridge National Laboratory is described. The prototype debugger consists of two parts: a FORTRAN-based ''view'' generator and a Microsoft Windows application for displaying the geometry. Options and features of both modules are discussed. Examples illustrating the various options available are presented. The potential for utilizing the images produced using the debugger as a visualization tool for the output of the radiation transport codes is discussed as is the future direction of the development
Combinatorial geometry in the plane
Hadwiger, Hugo; Klee, Victor
2014-01-01
Geared toward advanced undergraduates familiar with analysis and college geometry, this concise book discusses theorems on topics restricted to the plane such as convexity, coverings, and graphs. In addition to helping students cultivate rigorous thought, the text encourages the development of mathematical intuition and clarifies the nature of mathematical research.The two-part treatment begins with specific topics including integral distances, covering problems, point set geometry and convexity, simple paradoxes involving point sets, and pure combinatorics, among other subjects. The second pa
Modern differential geometry for physicists
Isham, C J
1989-01-01
These notes are the content of an introductory course on modern, coordinate-free differential geometry which is taken by the first-year theoretical physics PhD students, or by students attending the one-year MSc course "Fundamental Fields and Forces" at Imperial College. The book is concerned entirely with mathematics proper, although the emphasis and detailed topics have been chosen with an eye to the way in which differential geometry is applied these days to modern theoretical physics. This includes not only the traditional area of general relativity but also the theory of Yang-Mills fields
Algebraic geometry and theta functions
Coble, Arthur B
1929-01-01
This book is the result of extending and deepening all questions from algebraic geometry that are connected to the central problem of this book: the determination of the tritangent planes of a space curve of order six and genus four, which the author treated in his Colloquium Lecture in 1928 at Amherst. The first two chapters recall fundamental ideas of algebraic geometry and theta functions in such fashion as will be most helpful in later applications. In order to clearly present the state of the central problem, the author first presents the better-known cases of genus two (Chapter III) and
Geometry, topology, and string theory
International Nuclear Information System (INIS)
Varadarajan, Uday
2003-01-01
A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect. In particular, situations in which extra dimensions, non-commutative geometries as well as other non-local structures emerge are explored in detail. Further, a preliminary exploration of such issues in Lorentzian space-times with non-trivial causal structures within string theory is initiated
Application of spherical gratings in synchrotron radiation spectroscopy
International Nuclear Information System (INIS)
Hogrefe, H.; Howells, M.R.; Hoyer, E.
1986-05-01
The recent development in gracing incidence grating monochromator design is discussed and the performance limiting for such instruments are examined. Especially the aberrations of toroidal and spherical gratings are investigated using the optical path function concept. It is shown that large radius spherical gratings, which can be produced with better slope tolerances than aspherics, also yield smaller overall line curvature than toroids. Therefore, a new simple spherical grating monochromator design is proposed and its performance is analyzed
Analysis of spherical thermo-acoustic radiation in gas
Hanping Hu; Zedong Wang; Hao Wu; Yandong Wang
2012-01-01
A general solution of the spherical thermo-acoustic (TA) radiation from any solid in gas is derived by using a fully thermally-mechanically coupled TA model. Therefore, the characteristics and regularities of spherical TA emission can be studied more completely. It is shown that flat amplitude-frequency response, the most important feature for planar TA emission from technical standpoint, still exists for spherical TA emission, and changes with the radius of a sphere, thickness of TA sample, ...
Canonical quantization of spherically symmetric dust collapse
Vaz, Cenalo; Witten, Louis
2011-12-01
Quantum gravity effects are likely to play a crucial role in determining the outcome of gravitational collapse during its final stages. In this contribution we will outline a canonical quantization of the LeMaitre-Tolman-Bondi (LTB) models, which describe the collapse of spherical, inhomogeneous, non-rotating dust. Although there are many models of gravitational collapse, this particular class of models stands out for its simplicity and the fact that both black holes and naked singularity end states may be realized on the classical level, depending on the initial conditions. We will obtain the appropriate Wheeler-DeWitt equation and then solve it exactly, after regularization on a spatial lattice. The solutions describe Hawking radiation and provide an elegant microcanonical description of black hole entropy, but they raise other questions, most importantly concerning the nature of gravity's fundamental degrees of freedom.
Effects of coating spherical iron oxide nanoparticles
Energy Technology Data Exchange (ETDEWEB)
Milosevic, Irena; Motte, Laurence; Aoun, Bachir; Li, Tao; Ren, Yang; Sun, Chengjun; Saboungi, Marie-Louise
2017-01-01
We investigate the effect of several coatings applied in biomedical applications to iron oxide nanoparticles on the size, structure and composition of the particles. The four structural techniques employed - TEM, DLS, VSM, SAXS and EXAFS - show no significant effects of the coatings on the spherical shape of the bare nanoparticles, the average sizes or the local order around the Fe atoms. The NPs coated with hydroxylmethylene bisphosphonate or catechol have a lower proportion of magnetite than the bare and citrated ones, raising the question whether the former are responsible for increasing the valence state of the oxide on the NP surfaces and lowering the overall proportion of magnetite in the particles. VSM measurements show that these two coatings lead to a slightly higher saturation magnetization than the citrate. This article is part of a Special Issue entitled "Science for Life" Guest Editor: Dr. Austen Angell, Dr. Salvatore Magazu and Dr. Federica Migliardo.
Spherically-Convergent, Advanced-Fuel Systems
Barnes, D. C.; Nebel, R. A.; Schauer, M. M.; Umstadter, K. R.
1998-11-01
Combining nonneutral electron confinement with spherical ion convergence leads to a cm sized reactor volume with high power density.(R. A. Nebel and D. C. Barnes, Fusion Technol.), to appear (1998); D. C. Barnes and R. A. Nebel, Phys. of Plasmas 5, 2498 (1998). This concept is being investigated experimentally,(D. C. Barnes, T. B. Mitchell, and M. M. Schauer, Phys. Plasmas) 4, 1745 (1997). and results will be reported. We argue that D-D operation of such a system offers all the advantages of aneutronic fusion cycles. In particular, no breeding or large tritium inventory is required, and material problems seem tractable based on previous LWR experience. In addition the extremely small unit size leads to a massively modular system which is easily maintained and repaired, suggesting a very high availability. It may also be possible to operate such a system with low or aneutronic fuels. Preliminary work in this direction will be presented.
Space Propulsion via Spherical Torus Fusion Reactor
International Nuclear Information System (INIS)
Williams, Craig H.; Juhasz, Albert J.; Borowski, Stanley K.; Dudzinski, Leonard A.
2003-01-01
A conceptual vehicle design enabling fast outer solar system travel was produced predicated on a small aspect ratio spherical torus nuclear fusion reactor. Analysis revealed that the vehicle could deliver a 108 mt crew habitat payload to Saturn rendezvous in 204 days, with an initial mass in low Earth orbit of 1630 mt. Engineering conceptual design, analysis, and assessment were performed on all major systems including nuclear fusion reactor, magnetic nozzle, power conversion, fast wave plasma heating, fuel pellet injector, startup/re-start fission reactor and battery, and other systems. Detailed fusion reactor design included analysis of plasma characteristics, power balance and utilization, first wall, toroidal field coils, heat transfer, and neutron/X-ray radiation
Laser Pulse Heating of Spherical Metal Particles
Directory of Open Access Journals (Sweden)
Michael I. Tribelsky
2011-12-01
Full Text Available We consider the general problem of laser pulse heating of spherical metal particles with the sizes ranging from nanometers to millimeters. We employ the exact Mie solution of the diffraction problem and solve the heat-transfer equation to determine the maximum temperature rise at the particle surface as a function of optical and thermometric parameters of the problem. Primary attention is paid to the case when the thermal diffusivity of the particle is much larger than that of the environment, as it is in the case of metal particles in fluids. We show that, in this case, for any given duration of the laser pulse, the maximum temperature rise as a function of the particle size reaches a maximum at a certain finite size of the particle. We suggest simple approximate analytical expressions for this dependence, which cover the entire parameter range of the problem and agree well with direct numerical simulations.
Nuclear structure investigations on spherical nuclei
International Nuclear Information System (INIS)
Heisenberg, J.; Calarco, J.; Dawson, J.; Hersman, F.W.
1989-09-01
This report discusses the following topics: electron scattering studies on spherical nuclei; electron scattering from collective states in deformed nuclei; proton and pion scattering studies; 12 C(e,e'p) and 16 O(e,e'p); 12 C(e,e'α) and 16 O(e,e'α); studies at high q at Bates; measurements with rvec e at Bates; 12 C(γ,p); future directions in giant resonance studies; proton knockout from 16 O; quasielastic studies at Bates; triple coincidence studies of nuclear correlations; contributions to (e,e'2p) at KIKHEF; contributions to instrumentation at CEBAF; instrumentation development at UNH; the Bates large acceptance spectrometer toroid; shell model and core polarization calculations; and the relativistic nuclear model
Convection patterns in a spherical fluid shell
Feudel, F.; Bergemann, K.; Tuckerman, L. S.; Egbers, C.; Futterer, B.; Gellert, M.; Hollerbach, R.
2011-04-01
Symmetry-breaking bifurcations have been studied for convection in a nonrotating spherical shell whose outer radius is twice the inner radius, under the influence of an externally applied central force field with a radial dependence proportional to 1/r5. This work is motivated by the GeoFlow experiment, which is performed under microgravity condition at the International Space Station where this particular central force can be generated. In order to predict the observable patterns, simulations together with path-following techniques and stability computations have been applied. Branches of axisymmetric, octahedral, and seven-cell solutions have been traced. The bifurcations producing them have been identified and their stability ranges determined. At higher Rayleigh numbers, time-periodic states with a complex spatiotemporal symmetry are found, which we call breathing patterns.
Simple spherical ablative-implosion model
Energy Technology Data Exchange (ETDEWEB)
Mayer, F.J.; Steele, J.T.; Larsen, J.T.
1980-06-23
A simple model of the ablative implosion of a high-aspect-ratio (shell radius to shell thickness ratio) spherical shell is described. The model is similar in spirit to Rosenbluth's snowplow model. The scaling of the implosion time was determined in terms of the ablation pressure and the shell parameters such as diameter, wall thickness, and shell density, and compared these to complete hydrodynamic code calculations. The energy transfer efficiency from ablation pressure to shell implosion kinetic energy was examined and found to be very efficient. It may be possible to attach a simple heat-transport calculation to our implosion model to describe the laser-driven ablation-implosion process. The model may be useful for determining other energy driven (e.g., ion beam) implosion scaling.
Confined detonations with cylindrical and spherical symmetry
International Nuclear Information System (INIS)
Linan, A.; Lecuona, A.
1979-01-01
An imploding spherical or cylindrical detonation, starting in the interface of the detonantion with an external inert media, used as a reflector, creates on it a strong shock wave moving outward from the interface. An initially weak shock wave appears in the detonated media that travels toward the center, and it could reach the detonation wave, enforcing it in its process of implosion. To describe the fluid field, the Euler s equations are solved by means of expansions valid for the early stages of the process. Isentropic of the type P/pγ-K for the detonated and compressed inert media are used. For liquid or solid reflectors a more appropriate equation is used. (Author) 8 refs
Saltation movement of large spherical particles
Chara, Z.; Dolansky, J.; Kysela, B.
2017-07-01
The paper presents experimental and numerical investigations of the saltation motion of a large spherical particle in an open channel. The channel bottom was roughed by one layer of glass rods of diameter 6 mm. The plastic spheres of diameter 25.7 mm and density 1160 kgm-3 were fed into the water channel and theirs positions were viewed by a digital camera. Two light sheets were placed above and under the channel, so the flow was simultaneously lighted from the top and the bottom. Only particles centers of which moved through the light sheets were recorded. Using a 2D PIV method the trajectories of the spheres and the velocity maps of the channel flow were analyzed. The Lattice-Boldzmann Method (LBM) was used to simulate the particle motion.
Teaching Activity-Based Taxicab Geometry
Ada, Tuba
2013-01-01
This study aimed on the process of teaching taxicab geometry, a non-Euclidean geometry that is easy to understand and similar to Euclidean geometry with its axiomatic structure. In this regard, several teaching activities were designed such as measuring taxicab distance, defining a taxicab circle, finding a geometric locus in taxicab geometry, and…
A multiball read-out for the spherical proportional counter
Giganon, A.; Giomataris, I.; Gros, M.; Katsioulas, I.; Navick, X. F.; Tsiledakis, G.; Savvidis, I.; Dastgheibi-Fard, A.; Brossard, A.
2017-12-01
We present a novel concept of proportional gas amplification for the read-out of the spherical proportional counter. The standard single-ball read-out presents limitations for large diameter spherical detectors and high-pressure operations. We have developed a multi-ball read-out system which consists of several balls placed at a fixed distance from the center of the spherical vessel. Such a module can tune the volume electric field at the desired value and can also provide detector segmentation with individual ball read-out. In the latter case, the large volume of the vessel becomes a spherical time projection chamber with 3D capabilities.
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.
Fluid Fuel Fluctuations in the Spherical Tank
Directory of Open Access Journals (Sweden)
H. D. Nguyen
2014-01-01
Full Text Available Many authors tried to solve a task concerning small fluctuations of the incompressible ideal liquid, which partially fills a stationary tank of any shape. There is a long list of references to this subject. The article presents a task solution on own fluctuations of liquid in spherical capacity, with boundary conditions on a free surface and a surface with a resistance – drain surface. Relevance of problem consists in assessment of influence of intra tank devices (measuring, intaking, damping devices, etc. on the liquid fuel fluctuations. The special attention is paid to finding the own values and frequencies of the equations of disturbed flow fluctuations with dissipation available on the boundary surfaces. In contrast to the previous examples, the lowering speed and the free surface area at undisturbed state are variable.The article also considers a variation formulation of the auxiliary boundary tasks. In solution of variation tasks, the attached Legendre's functions were used as coordinate functions. Further, after substitution of the variation tasks solution in the boundary conditions and the subsequent mathematical operations the characteristic equation was obtained. To obtain solutions of the cubic characteristic equation Cardano formulas were used. The article also considers the task on the own motions of liquid filling a capacity between two concentric spheres and flowing out via the intake in case there is a free surface. Reliability of the obtained numerical results is confirmed by comparison with calculation results of frequencies resulting from solutions of a task on the own fluctuations of liquid in the spherical capacity with the constant depth of liquid. All numerical calculations were performed using the Matlab environment.
Axiomatic characterization of physical geometry
International Nuclear Information System (INIS)
Schmidt, H.J.
1979-01-01
This book deals with the foundations of a theory which can be considered as the most ancient part of physics, namely Euclidean geometry. It may be viewed as a partial realization of a program set up by G. Ludwig who suggested to formulate geometry explicity as a theory of possible operations with practically rigid bodies, using as basic concepts 'region', 'inclusion' and 'transport'. After an introduction to the problems, in which we sketch also the historical development, we develop a pre-theory with respect to the geometry with the aim to give an interpretation of the above-mentioned basic geometrical concepts in terms of notions which are closely related to experimental situations. The passage from a pure topological analysis of physical space to the differential geometrical view is made in the next section where we use the prerequisites established in the previous chapter to apply the Tits/Freudenthal solution of the Helmholtz-Lie problem. The main theorem of this book is stated in the last section by a characterization of Euclidean geometry. It turns out that two additional postulates are necessary whose empirical meaning we stress by referring to the axiom of dimension. The book might be of interest to scientist working in the field of axiomatics. Unfamiliar readers will be required to have a sound knowledge of topology and group theory. (HJ) 891 HJ/HJ 892 MB
Algebraic Methods in Plane Geometry
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 13; Issue 10. Algebraic Methods in Plane Geometry - The Use of Conic Sections. Shailesh A Shirali. General Article Volume 13 Issue 10 October 2008 pp 916-928. Fulltext. Click here to view fulltext PDF. Permanent link:
Multivariable calculus and differential geometry
Walschap, Gerard
2015-01-01
This text is a modern in-depth study of the subject that includes all the material needed from linear algebra. It then goes on to investigate topics in differential geometry, such as manifolds in Euclidean space, curvature, and the generalization of the fundamental theorem of calculus known as Stokes' theorem.
Stochastic Modelling of River Geometry
DEFF Research Database (Denmark)
Sørensen, John Dalsgaard; Schaarup-Jensen, K.
1996-01-01
Numerical hydrodynamic river models are used in a large number of applications to estimate critical events for rivers. These estimates are subject to a number of uncertainties. In this paper, the problem to evaluate these estimates using probabilistic methods is considered. Stochastic models for ...... for river geometries are formulated and a coupling between hydraulic computational methods and numerical reliability methods is presented....
GEOMETRY AND COMPLEXITY IN ARCHITECTURE
Directory of Open Access Journals (Sweden)
RUSU Maria Ana
2015-06-01
Full Text Available As Constantin Brancuși (1876-1956 said „Simplicity is complexity itself“, simplicity and regularity through the use of basic geometric forms has always played a central role in architectural design, during the 20th century. A diachronic perspective, shows as the use of geometry and mathematics to describe built form provided a common basis for communication between the processes of design, fabrication and stability. Classic ways of representing geometry, based on descriptive methods, favor precise language of bidimensionality easy to represent in a rectangular coordinate system. In recent years, the importance of geometry has been re-emphasized by significant advances in the digital age, where computers are increasingly used in design, fabrication and construction to explore the art of the possible. Contemporary architecture transcend the limitations of Euclidean geometry and create new forms that are emerging through the convergence of complex systems, computational design and robotic fabrication devices, but which can also achieve higher levels of performance. Freeform architectural shapes and structures play an increasingly important role in 21st century architectural design. Through a series of examples, the paper relates to contemporary architectural explorations of complex, curvilinear surfaces in the digital age and discusses how it has required rethinking the mode in which we traditionally operate as architects. The analysis creates the possibility of comparisons between original and current design.
Signature geometry and quantum engineering
Samociuk, Stefan
2013-09-01
As the operating frequency of electromagnetic based devices increase, physical design geometry is playing an ever more important role. Evidence is considered in support of a relationship between the dimensionality of primitive geometric forms, such as transistors, and corresponding electromagnetic coupling efficiency. The industry of electronics is defined as the construction of devices by the patterning of primitive forms to physical materials. Examples are given to show the evolution of these primitives, down to nano scales, are requiring exacting geometry and three dimensional content. Consideration of microwave monolithic integrated circuits,(MMIC), photonics and metamaterials,(MM), support this trend and also add new requirements of strict geometric periodicity and multiplicity. Signature geometries,(SG), are characterized by distinctive attributes and examples are given. The transcendent form transcode algorithm, (TTA) is introduced as a multi dimensional SG and its use in designing photonic integrated circuits and metamaterials is discussed . A creative commons licensed research database, TRANSFORM, containing TTA geometries in OASIS file formats is described. An experimental methodology for using the database is given. Multidimensional SG and extraction of three dimensional cross sections as primitive forms is discussed as a foundation for quantum engineering and the exploitation of phenomena other than the electromagnetic.
Exploring Bundling Theory with Geometry
Eckalbar, John C.
2006-01-01
The author shows how instructors might successfully introduce students in principles and intermediate microeconomic theory classes to the topic of bundling (i.e., the selling of two or more goods as a package, rather than separately). It is surprising how much students can learn using only the tools of high school geometry. To be specific, one can…
Generative CAI in Analytical Geometry.
Uttal, William R.; And Others
A generative computer-assisted instruction system is being developed to tutor students in analytical geometry. The basis of this development is the thesis that a generative teaching system can be developed by establishing and then stimulating a simplified, explicit model of the human tutor. The goal attempted is that of a computer environment…
Stochastic Modelling of River Geometry
DEFF Research Database (Denmark)
Sørensen, John Dalsgaard; Schaarup-Jensen, K.
1996-01-01
Numerical hydrodynamic river models are used in a large number of applications to estimate critical events for rivers. These estimates are subject to a number of uncertainties. In this paper, the problem to evaluate these estimates using probabilistic methods is considered. Stochastic models...... for river geometries are formulated and a coupling between hydraulic computational methods and numerical reliability methods is presented....
M. Deza; M. Laurent (Monique)
1997-01-01
htmlabstractCuts and metrics are well-known objects that arise - independently, but with many deep and fascinating connections - in diverse fields: in graph theory, combinatorial optimization, geometry of numbers, combinatorial matrix theory, statistical physics, VLSI design etc. This book offers a
Analogical Reasoning in Geometry Education
Magdas, Ioana
2015-01-01
The analogical reasoning isn't used only in mathematics but also in everyday life. In this article we approach the analogical reasoning in Geometry Education. The novelty of this article is a classification of geometrical analogies by reasoning type and their exemplification. Our classification includes: analogies for understanding and setting a…
Matter in toy dynamical geometries
Konopka, T.J.
2009-01-01
One of the objectives of theories describing quantum dynamical geometry is to compute expectation values of geometrical observables. The results of such computations can be affected by whether or not matter is taken into account. It is thus important to understand to what extent and to what effect
Complex Numbers and Plane Geometry
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 13; Issue 1. Complex Numbers and Plane Geometry. Anant R Shastri. General Article Volume 13 Issue 1 January 2008 pp 35-53. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/013/01/0035-0053. Keywords.
Learners engaging with transformation geometry
African Journals Online (AJOL)
Grade 12, learners would have been exposed to both visual and analytical strategies. The visual approach is one ... movement), dynamic imagery, memory images and pattern imagery. She found that concrete .... the visual and analytic modes of thinking when working with transformation geometry? We hope then to set out ...
General Relativity: Geometry Meets Physics
Thomsen, Dietrick E.
1975-01-01
Observing the relationship of general relativity and the geometry of space-time, the author questions whether the rest of physics has geometrical explanations. As a partial answer he discusses current research on subatomic particles employing geometric transformations, and cites the existence of geometrical definitions of physical quantities such…
Indian Academy of Sciences (India)
Limit: (of a sequence) A point such that the points of the sequence eventually approach it to within any previously specified distance. Some of the Greek mathematicians were quite confused! For example, let us take an empty cup and put it under a tap. Assume that it is half full in a minute. It is then 3/4-th full in another half.
Indian Academy of Sciences (India)
Huygens, Leibnitz and Newton. (independently) formulated the notion of curvature of a curve. (This was developed by Serret-Frenet into a multiplicity of invariants for curves in higher dimensions. We will concentrate on the curvature defined by Huygens et al). A line then becomes a curve of curvature zero. It is always ...
Indian Academy of Sciences (India)
As in art, understanding is enhanced by doing. Readers are encour- aged to attempt the exercises scattered in the text. The Origin (s). Origin: the starting point of a .... role to play In modem mathematics. Address {or correspondence. Kapil H Paranjape,. Indian Statistical Institute,. 8th Mile, Mysore Road,. Bangalore 560 059 ...
Indian Academy of Sciences (India)
In the previous article the author examined curves and surfaces. One might hope to continue by analogy in many dimensions. The concept of working in many dimensions is so bewildering (yet today so matter-of-course) that it needed the genius ofBemhard Riemann to show us exactly how it can be done. In just one lecture ...
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.)
Coordinate geometry method for capturing and evaluating crown preparation geometry.
Tiu, Janine; Waddell, J Neil; Al-Amleh, Basil; Jansen van Vuuren, Wendy-Ann; Swain, Michael V
2014-09-01
A validated universal method requiring no human input is needed to capture and evaluate preparation geometries in a manner that can be used to see the correlation of different parameters. The purpose of this study was to present a method of capturing and evaluating crown preparation geometry. One manually machined acrylic resin block and 9 randomly selected preparations for ceramic complete crowns prepared by general dentists were selected and prepared. The specimens were scanned (3D scanner; Nobel Biocare), and buccolingual and mesiodistal cross section images were collected. The images were imported into digitizing software (Engauge Digitizer 4.1) to convert the outlines into x and y coordinates. Six points were chosen by using a set of algorithms, and the resulting parameters were calculated. The acrylic resin block was milled with a 12 degree total occlusal convergence (TOC) instrument producing a 12.83 degree TOC. For the other specimens, average TOC values ranged from 18 degrees to 52 degrees. The mean average margin width was 0.70 mm, and the mean average base dimension was 6.23 mm. The surface area/volume ratio, resistance length, and limiting taper were also calculated. The method described provides a basis for accurately evaluating preparation geometry without human input. Copyright © 2014 Editorial Council for the Journal of Prosthetic Dentistry. Published by Elsevier Inc. All rights reserved.
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
International Nuclear Information System (INIS)
Ding Lei; Lai Yuan; He Bin
2005-01-01
It is of importance to localize neural sources from scalp recorded EEG. Low resolution brain electromagnetic tomography (LORETA) has received considerable attention for localizing brain electrical sources. However, most such efforts have used spherical head models in representing the head volume conductor. Investigation of the performance of LORETA in a realistic geometry head model, as compared with the spherical model, will provide useful information guiding interpretation of data obtained by using the spherical head model. The performance of LORETA was evaluated by means of computer simulations. The boundary element method was used to solve the forward problem. A three-shell realistic geometry (RG) head model was constructed from MRI scans of a human subject. Dipole source configurations of a single dipole located at different regions of the brain with varying depth were used to assess the performance of LORETA in different regions of the brain. A three-sphere head model was also used to approximate the RG head model, and similar simulations performed, and results compared with the RG-LORETA with reference to the locations of the simulated sources. Multi-source localizations were discussed and examples given in the RG head model. Localization errors employing the spherical LORETA, with reference to the source locations within the realistic geometry head, were about 20-30 mm, for four brain regions evaluated: frontal, parietal, temporal and occipital regions. Localization errors employing the RG head model were about 10 mm over the same four brain regions. The present simulation results suggest that the use of the RG head model reduces the localization error of LORETA, and that the RG head model based LORETA is desirable if high localization accuracy is needed
Effect of conductor geometry on source localization: Implications for epilepsy studies
Energy Technology Data Exchange (ETDEWEB)
Schlitt, H.; Heller, L.; Best, E.; Ranken, D.; Aaron, R.
1994-07-01
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.
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...
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
Improved endpoint bounds for the lacunary spherical maximal operator
Cladek, Laura; Krause, Ben
2017-01-01
We prove new endpoint bounds for the lacunary spherical maximal operator and as a consequence obtain almost everywhere pointwise convergence of lacunary spherical means for functions locally in $L\\log\\log\\log L(\\log\\log\\log\\log L)^{1+\\epsilon}$ for any $\\epsilon>0$.
Cylindrical and spherical dust-acoustic wave modulations in dusty ...
Indian Academy of Sciences (India)
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 distributions for ions and electrons is investigated. By employing multiple scales technique, a cylindrically and spherically modified nonlinear ...
Characterization of diffusivity based on spherical array processing
DEFF Research Database (Denmark)
Nolan, Melanie; Fernandez Grande, Efren; Jeong, Cheol-Ho
2015-01-01
The purpose of this study is to assess the diffuse field conditions in a reverberant space using a sound field reconstruction method based on spherical microphone array measurements. Spherical microphone arrays are particularly well suited for applications in non-anechoic enclosures, where the so...
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 ...
Demonstrating close-packing of atoms using spherical bubble gums ...
African Journals Online (AJOL)
In this paper, the use of spherical bubble gums (Gum Balls) to demonstrate the close-packing of atoms and ions is presented. Spherical bubble gums having distinctive colours were used to illustrate the different layers in variety of crystalline packing and the formation of tetrahedral and octahedral holes. Students with ...
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
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.
demonstrating close-packing of atoms using spherical bubble gums
African Journals Online (AJOL)
Admin
ABSTRACT: In this paper, the use of spherical bubble gums (Gum Balls) to demonstrate the close-packing of atoms and ions is presented. Spherical bubble gums having distinctive colours were used to illustrate the different layers in variety of crystalline packing and the formation of tetrahedral and octahedral holes.
Creep stresses in a spherical shell under steady state temperature
Verma, Gaurav; Rana, Puneet
2017-10-01
The paper investigates the problem of creep of a spherical structure under the influence of steady state temperature. The problem of creep in spherical shell is solved by using the concept of generalized strain measures and transition hypothesis given by Seth. The problem has reduced to non-linear differential equation for creep transition. This paper deals with the non-linear behaviour of spherical shell under thermal condition. The spherical shell structures are easily vulnerable to creep, shrinkage and thermal effects; a thorough understanding of their time-dependent behaviour has been fully established. The paper aims to provide thermal creep analysis to enhance the effective design and long life of shells, and a theoretical model is developed for calculating creep stresses and strains in a spherical shell with purpose. Results obtained for the problem are depicted graphically.
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
Fractal geometry and computer graphics
Sakas, Georgios; Peitgen, Heinz-Otto; Englert, Gabriele
1992-01-01
Fractal geometry has become popular in the last 15 years, its applications can be found in technology, science, or even arts. Fractal methods and formalism are seen today as a general, abstract, but nevertheless practical instrument for the description of nature in a wide sense. But it was Computer Graphics which made possible the increasing popularity of fractals several years ago, and long after their mathematical formulation. The two disciplines are tightly linked. The book contains the scientificcontributions presented in an international workshop in the "Computer Graphics Center" in Darmstadt, Germany. The target of the workshop was to present the wide spectrum of interrelationships and interactions between Fractal Geometry and Computer Graphics. The topics vary from fundamentals and new theoretical results to various applications and systems development. All contributions are original, unpublished papers.The presentations have been discussed in two working groups; the discussion results, together with a...
Groups and Geometries : Siena Conference
Kantor, William; Lunardon, Guglielmo; Pasini, Antonio; Tamburini, Maria
1998-01-01
On September 1-7, 1996 a conference on Groups and Geometries took place in lovely Siena, Italy. It brought together experts and interested mathematicians from numerous countries. The scientific program centered around invited exposi tory lectures; there also were shorter research announcements, including talks by younger researchers. The conference concerned a broad range of topics in group theory and geometry, with emphasis on recent results and open problems. Special attention was drawn to the interplay between group-theoretic methods and geometric and combinatorial ones. Expanded versions of many of the talks appear in these Proceedings. This volume is intended to provide a stimulating collection of themes for a broad range of algebraists and geometers. Among those themes, represented within the conference or these Proceedings, are aspects of the following: 1. the classification of finite simple groups, 2. the structure and properties of groups of Lie type over finite and algebraically closed fields of f...
Code subspaces for LLM geometries
Berenstein, David; Miller, Alexandra
2018-03-01
We consider effective field theory around classical background geometries with a gauge theory dual, specifically those in the class of LLM geometries. These are dual to half-BPS states of N= 4 SYM. We find that the language of code subspaces is natural for discussing the set of nearby states, which are built by acting with effective fields on these backgrounds. This work extends our previous work by going beyond the strict infinite N limit. We further discuss how one can extract the topology of the state beyond N→∞ and find that, as before, uncertainty and entanglement entropy calculations provide a useful tool to do so. Finally, we discuss obstructions to writing down a globally defined metric operator. We find that the answer depends on the choice of reference state that one starts with. Therefore, within this setup, there is ambiguity in trying to write an operator that describes the metric globally.
Differential geometry and mathematical physics
Rudolph, Gerd
Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and symplectic geometry, • Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous d...
Grassmannian geometry of scattering amplitudes
Arkani-Hamed, Nima; Cachazo, Freddy; Goncharov, Alexander; Postnikov, Alexander; Trnka, Jaroslav
2016-01-01
Outlining a revolutionary reformulation of the foundations of perturbative quantum field theory, this book is a self-contained and authoritative analysis of the application of this new formulation to the case of planar, maximally supersymmetric Yang–Mills theory. The book begins by deriving connections between scattering amplitudes and Grassmannian geometry from first principles before introducing novel physical and mathematical ideas in a systematic manner accessible to both physicists and mathematicians. The principle players in this process are on-shell functions which are closely related to certain sub-strata of Grassmannian manifolds called positroids - in terms of which the classification of on-shell functions and their relations becomes combinatorially manifest. This is an essential introduction to the geometry and combinatorics of the positroid stratification of the Grassmannian and an ideal text for advanced students and researchers working in the areas of field theory, high energy physics, and the...
Foliation theory in algebraic geometry
McKernan, James; Pereira, Jorge
2016-01-01
Featuring a blend of original research papers and comprehensive surveys from an international team of leading researchers in the thriving fields of foliation theory, holomorphic foliations, and birational geometry, this book presents the proceedings of the conference "Foliation Theory in Algebraic Geometry," hosted by the Simons Foundation in New York City in September 2013. Topics covered include: Fano and del Pezzo foliations; the cone theorem and rank one foliations; the structure of symmetric differentials on a smooth complex surface and a local structure theorem for closed symmetric differentials of rank two; an overview of lifting symmetric differentials from varieties with canonical singularities and the applications to the classification of AT bundles on singular varieties; an overview of the powerful theory of the variety of minimal rational tangents introduced by Hwang and Mok; recent examples of varieties which are hyperbolic and yet the Green-Griffiths locus is the whole of X; and a classificati...
Hyperbolic geometry for colour metrics.
Farup, Ivar
2014-05-19
It is well established from both colour difference and colour order perpectives that the colour space cannot be Euclidean. In spite of this, most colour spaces still in use today are Euclidean, and the best Euclidean colour metrics are performing comparably to state-of-the-art non-Euclidean metrics. In this paper, it is shown that a transformation from Euclidean to hyperbolic geometry (i.e., constant negative curvature) for the chromatic plane can significantly improve the performance of Euclidean colour metrics to the point where they are statistically significantly better than state-of-the-art non-Euclidean metrics on standard data sets. The resulting hyperbolic geometry nicely models both qualitatively and quantitatively the hue super-importance phenomenon observed in colour order systems.
Euclidean distance geometry an introduction
Liberti, Leo
2017-01-01
This textbook, the first of its kind, presents the fundamentals of distance geometry: theory, useful methodologies for obtaining solutions, and real world applications. Concise proofs are given and step-by-step algorithms for solving fundamental problems efficiently and precisely are presented in Mathematica®, enabling the reader to experiment with concepts and methods as they are introduced. Descriptive graphics, examples, and problems, accompany the real gems of the text, namely the applications in visualization of graphs, localization of sensor networks, protein conformation from distance data, clock synchronization protocols, robotics, and control of unmanned underwater vehicles, to name several. Aimed at intermediate undergraduates, beginning graduate students, researchers, and practitioners, the reader with a basic knowledge of linear algebra will gain an understanding of the basic theories of distance geometry and why they work in real life.
Holographic thermalization in noncommutative geometry
Directory of Open Access Journals (Sweden)
Xiao-Xiong Zeng
2015-05-01
Full Text Available Gravitational collapse of a shell of dust in noncommutative geometry is probed by the renormalized geodesic length, which is dual to probe the thermalization by the two-point correlation function in the dual conformal field theory. We find that the larger the noncommutative parameter is, the longer the thermalization time is, which implies that the large noncommutative parameter delays the thermalization process. We also investigate how the noncommutative parameter affects the thermalization velocity and thermalization acceleration.
Needle decompositions in Riemannian geometry
Klartag, Bo'az
2017-01-01
The localization technique from convex geometry is generalized to the setting of Riemannian manifolds whose Ricci curvature is bounded from below. In a nutshell, the author's method is based on the following observation: When the Ricci curvature is non-negative, log-concave measures are obtained when conditioning the Riemannian volume measure with respect to a geodesic foliation that is orthogonal to the level sets of a Lipschitz function. The Monge mass transfer problem plays an important role in the author's analysis.
Systematics of IIB spinorial geometry
Gran, U.; Gutowski, J.; Papadopoulos, G.; Roest, D.
2005-01-01
We reduce the classification of all supersymmetric backgrounds of IIB supergravity to the evaluation of the Killing spinor equations and their integrability conditions, which contain the field equations, on five types of spinors. This extends the work of [hep-th/0503046] to IIB supergravity. We give the expressions of the Killing spinor equations on all five types of spinors. In this way, the Killing spinor equations become a linear system for the fluxes, geometry and spacetime derivatives of...
Needle decompositions in riemannian geometry
Klartag, Bo'az
2017-01-01
The localization technique from convex geometry is generalized to the setting of Riemannian manifolds whose Ricci curvature is bounded from below. In a nutshell, the author's method is based on the following observation: When the Ricci curvature is non-negative, log-concave measures are obtained when conditioning the Riemannian volume measure with respect to a geodesic foliation that is orthogonal to the level sets of a Lipschitz function. The Monge mass transfer problem plays an important role in the author's analysis.
Turtle geometry the Python way
Battle, S.
2014-01-01
An introduction to coding using Python’s on-screen ‘turtle’ that can be commanded with a few simple instructions including forward, backward, left and right. The turtle leaves a trace that can be used to draw geometric figures. This workshop is aimed at beginners of all ages. The aim is to learn a smattering of programming and a little bit of geometry in a fun way.
Topics in modern differential geometry
Verstraelen, Leopold
2017-01-01
A variety of introductory articles is provided on a wide range of topics, including variational problems on curves and surfaces with anisotropic curvature. Experts in the fields of Riemannian, Lorentzian and contact geometry present state-of-the-art reviews of their topics. The contributions are written on a graduate level and contain extended bibliographies. The ten chapters are the result of various doctoral courses which were held in 2009 and 2010 at universities in Leuven, Serbia, Romania and Spain.
Excitation of Alfvenic instabilities in spherical tokamaks
International Nuclear Information System (INIS)
McClements, K.G.; Appel, L.C.; Hole, M.J.; Thyagaraja, A.
2003-01-01
Understanding energetic particle confinement in spherical tokamak (STs) is important for optimising the design of ST power plants, and provides a testbed for theoretical modelling under conditions of strong toroidicity and shaping, and high beta. MHD analysis of some recent beam-heated discharges in the MAST ST indicates that high frequency modes observed in these discharges can be identified as toroidal Alfven Eigenmodes (TAEs) and elliptical Alfven Eigenmodes (EAEs). It is possible that such modes could strongly enhance fusion alpha-particle transport in an ST power plant. Computations of TAE growth rates for one particular MAST discharge, made using the HAGIS guiding centre code and benchmarked against analytical estimates, indicate strong drive by sub-Alfvenic neutral beam ions. HAGIS computations using higher mode amplitudes than those observed indicate that whereas co-passing beam ions provide the bulk of he TAE drive, counter-passing ions provide the dominant component of TAE-induced particle losses. Axisymmetric Alfvenic mode activity has been detected during ohmic discharges in MAST. These observations are shown by computational modelling to be consistent with the excitation of global Alfven Eigenmodes (GAEs) with n=0 and low m, driven impulsively by low frequency MHD. (author)
Effects of coating spherical iron oxide nanoparticles.
Milosevic, Irena; Motte, Laurence; Aoun, Bachir; Li, Tao; Ren, Yang; Sun, Chengjun; Saboungi, Marie-Louise
2017-01-01
We investigate the effect of several coatings applied in biomedical applications to iron oxide nanoparticles on the size, structure and composition of the particles. The four structural techniques employed - TEM, DLS, VSM, SAXS and EXAFS - show no significant effects of the coatings on the spherical shape of the bare nanoparticles, the average sizes or the local order around the Fe atoms. The NPs coated with hydroxylmethylene bisphosphonate or catechol have a lower proportion of magnetite than the bare and citrated ones, raising the question whether the former are responsible for increasing the valence state of the oxide on the NP surfaces and lowering the overall proportion of magnetite in the particles. VSM measurements show that these two coatings lead to a slightly higher saturation magnetization than the citrate. This article is part of a Special Issue entitled "Science for Life" Guest Editor: Dr. Austen Angell, Dr. Salvatore Magazù and Dr. Federica Migliardo. Copyright © 2016 Elsevier B.V. All rights reserved.
Transitions between compound states of spherical nuclei
International Nuclear Information System (INIS)
Kadmenskii, S.G.; Markushev, V.P.; Furman, V.I.
1980-01-01
Wigner's statistical matrices are used to study the average reduced g widths and their dispersion for g transitions from a compound state c to another state f, with a lower excitation energy but of arbitrary complexity, for spherical nuclei. It is found that the Porter--Thomas distribution holds for the g widths for all cases of practical interest. In g transitions between compound states c and c' with E/sub g/< or =2 MeV, the most important transitions are M1 transitions involving the major many-quasiparticle components of state c and E1 transitions involving the minor components of state c. It is shown that the strength functions predicted by the various theories for M1 and E1 transitions between compound states with E/sub g/< or =2 MeV are similar. Preference is assigned to the M1-transition version because of experimental results on (n,ga) reactions with thermal and resonance neutrons
Dynamical evolution of spherical stellar systems
International Nuclear Information System (INIS)
Lee, H.M.
1986-01-01
The dynamical effect of heavy mass stars formed out of successive mergers among tidally captured binaries of evolution of spherical stellar systems is investigated. To maximize such effect assumed all tidally captured systems become mergers. Stellar evolution is simulated by computing mean age of mass group and applying death rate as function of mean age. For stellar systems with N = 10 5-6 , combined effect of three body binary heating among heavy mass stars and stellar evolution provides energy to drive post collapse expansion; long-term evolution is dominated by stellar evolution. Long-term behavior of clusters is similar to tidally captured binaries assuming no merger. Observed chemical inhomogeneities among stars in globular clusters may also be explained by stellar mergers. Three-body heating is important in small-N systems, while stellar evolution dominates evolution of large N systems. The effect of primordial degenerate stars is investigated in the second study. Very hard binaries composed of degenerate-normal pair form via tidal capture process and moderately hard degenerate-degenerate binaries form via three-body process. If initial degenerate population is large, initial core-collapse phase may be approximated as collapse of degenerate star. Three-body binaries among degenerate stars eventually provide enough energy to stop collapse and cause reexpansion
Drop impact on spherical soft surfaces
Chen, Simeng; Bertola, Volfango
2017-08-01
The impact of water drops on spherical soft surfaces is investigated experimentally through high-speed imaging. The effect of a convex compliant surface on the dynamics of impacting drops is relevant to various applications, such as 3D ink-jet printing, where drops of fresh material impact on partially cured soft substrates with arbitrary shape. Several quantities which characterize the morphology of impacting drops are measured through image-processing, including the maximum and minimum spreading angles, length of the wetted curve, and dynamic contact angle. In particular, the dynamic contact angle is measured using a novel digital image-processing scheme based on a goniometric mask, which does not require edge fitting. It is shown that the surface with a higher curvature enhances the retraction of the spreading drop; this effect may be due to the difference of energy dissipation induced by the curvature of the surface. In addition, the impact parameters (elastic modulus, diameter ratio, and Weber number) are observed to significantly affect the dynamic contact angle during impact. A quantitative estimation of the deformation energy shows that it is significantly smaller than viscous dissipation.
A spherical cavity model for quadrupolar dielectrics
Dimitrova, Iglika M.; Slavchov, Radomir I.; Ivanov, Tzanko; Mosbach, Sebastian
2016-03-01
The dielectric properties of a fluid composed of molecules possessing both dipole and quadrupole moments are studied based on a model of the Onsager type (molecule in the centre of a spherical cavity). The dielectric permittivity ɛ and the macroscopic quadrupole polarizability αQ of the fluid are related to the basic molecular characteristics (molecular dipole, polarizability, quadrupole, quadrupolarizability). The effect of αQ is to increase the reaction field, to bring forth reaction field gradient, to decrease the cavity field, and to bring forth cavity field gradient. The effects from the quadrupole terms are significant in the case of small cavity size in a non-polar liquid. The quadrupoles in the medium are shown to have a small but measurable effect on the dielectric permittivity of several liquids (Ar, Kr, Xe, CH4, N2, CO2, CS2, C6H6, H2O, CH3OH). The theory is used to calculate the macroscopic quadrupolarizabilities of these fluids as functions of pressure and temperature. The cavity radii are also determined for these liquids, and it is shown that they are functions of density only. This extension of Onsager's theory will be important for non-polar solutions (fuel, crude oil, liquid CO2), especially at increased pressures.
Spherical images and inextensible curved folding
Seffen, Keith A.
2018-02-01
In their study, Duncan and Duncan [Proc. R. Soc. London A 383, 191 (1982), 10.1098/rspa.1982.0126] calculate the shape of an inextensible surface folded in two about a general curve. They find the analytical relationships between pairs of generators linked across the fold curve, the shape of the original path, and the fold angle variation along it. They present two special cases of generator layouts for which the fold angle is uniform or the folded curve remains planar, for simplifying practical folding in sheet-metal processes. We verify their special cases by a graphical treatment according to a method of Gauss. We replace the fold curve by a piecewise linear path, which connects vertices of intersecting pairs of hinge lines. Inspired by the d-cone analysis by Farmer and Calladine [Int. J. Mech. Sci. 47, 509 (2005), 10.1016/j.ijmecsci.2005.02.013], we construct the spherical images for developable folding of successive vertices: the operating conditions of the special cases in Duncan and Duncan are then revealed straightforwardly by the geometric relationships between the images. Our approach may be used to synthesize folding patterns for novel deployable and shape-changing surfaces without need of complex calculation.
The spheric tokamak programme at Culham
International Nuclear Information System (INIS)
Sykes, A.
1999-01-01
The Spherical Tokamak (ST) is the low aspect ratio limit of the conventional tokamak, and appears to offer attractive physics properties in a simpler device. The START (Small Tight Aspect Ratio Tokamak) experiment provided the world's first demonstration of the properties of hot plasmas in an ST configuration, and was operational at Culham from January 1991 to March 1998, obtaining plasma current of up to 300 kA and pulse durations of ∼ 50 ms. Its successor, MAST is scheduled to obtain first plasma in Autumn 1998 and is a purpose built, high vacuum machine designed to have a tenfold increase in plasma volume with plasma currents up to 2 MA. Current drive and heating will be by a combination of induction-compression as on START, a high-performance central solenoid, 1.5 MW ECRH and 5 MW of Neutral Beam Injection. The promising results from START are reviewed, and the many challenges posed for the next generation of purpose-built STs (such as MAST) are described. (author)
Synchrotron radiation from spherically accreting black holes
International Nuclear Information System (INIS)
Ipser, J.R.; Price, R.H.
1982-01-01
Spherical accretion onto a Schwartzchild black hole, of gas with frozen-in magnetic field, is studied numerically and analytically for a range of hole masses and accretion rates in which synchrotron emission is the dominant radiative mechanism. At small radii the equipartition of magnetic, kinetic, and gravitational energy is assumed to apply, and the gas is heated by dissipation of infalling magnetic energy, turbulent energy, etc. The models can be classified into three types: (a) synchrotron cooling negligible, (b) synchrotron cooling important but synchrotron self-absorption negligible, (c) synchrotron cooling and self-absorption important. In the first case gas temperatures become very high near the horizon but luminosity efficiencies (luminosity/mass-energy accretion rate) are low. In cases (b) and (c) the gas flow near the horizon is essentially isothermal and luminosity efficiencies are fairly high. The analysis and results for the isothermal cases (b) and (c) are valid only for moderate dissipative heating and synchrotron self-absorption. If self-absorption is very strong or if dissipated energy is comparable to infall energy, Comptonization effects, not included in the analysis, become important
Plasmonic and silicon spherical nanoparticle antireflective coatings.
Baryshnikova, K V; Petrov, M I; Babicheva, V E; Belov, P A
2016-03-01
Over the last decade, plasmonic antireflecting nanostructures have been extensively studied to be utilized in various optical and optoelectronic systems such as lenses, solar cells, photodetectors, and others. The growing interest to all-dielectric photonics as an alternative optical technology along with plasmonics motivates us to compare antireflective properties of plasmonic and all-dielectric nanoparticle coatings based on silver and crystalline silicon respectively. Our simulation results for spherical nanoparticles array on top of amorphous silicon show that both silicon and silver coatings demonstrate strong antireflective properties in the visible spectral range. For the first time, we show that zero reflectance from the structure with silicon coatings originates from the destructive interference of electric- and magnetic-dipole responses of nanoparticle array with the wave reflected from the substrate, and we refer to this reflection suppression as substrate-mediated Kerker effect. We theoretically compare the silicon and silver coating effectiveness for the thin-film photovoltaic applications. Silver nanoparticles can be more efficient, enabling up to 30% increase of the overall absorbance in semiconductor layer. Nevertheless, silicon coatings allow up to 64% absorbance increase in the narrow band spectral range because of the substrate-mediated Kerker effect, and band position can be effectively tuned by varying the nanoparticles sizes.
Spherical Process Models for Global Spatial Statistics
Jeong, Jaehong
2017-11-28
Statistical models used in geophysical, environmental, and climate science applications must reflect the curvature of the spatial domain in global data. Over the past few decades, statisticians have developed covariance models that capture the spatial and temporal behavior of these global data sets. Though the geodesic distance is the most natural metric for measuring distance on the surface of a sphere, mathematical limitations have compelled statisticians to use the chordal distance to compute the covariance matrix in many applications instead, which may cause physically unrealistic distortions. Therefore, covariance functions directly defined on a sphere using the geodesic distance are needed. We discuss the issues that arise when dealing with spherical data sets on a global scale and provide references to recent literature. We review the current approaches to building process models on spheres, including the differential operator, the stochastic partial differential equation, the kernel convolution, and the deformation approaches. We illustrate realizations obtained from Gaussian processes with different covariance structures and the use of isotropic and nonstationary covariance models through deformations and geographical indicators for global surface temperature data. To assess the suitability of each method, we compare their log-likelihood values and prediction scores, and we end with a discussion of related research problems.
Geometry success in 20 minutes a day
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
Algebraic Geometry and Number Theory Summer School
Sarıoğlu, Celal; Soulé, Christophe; Zeytin, Ayberk
2017-01-01
This lecture notes volume presents significant contributions from the “Algebraic Geometry and Number Theory” Summer School, held at Galatasaray University, Istanbul, June 2-13, 2014. It addresses subjects ranging from Arakelov geometry and Iwasawa theory to classical projective geometry, birational geometry and equivariant cohomology. Its main aim is to introduce these contemporary research topics to graduate students who plan to specialize in the area of algebraic geometry and/or number theory. All contributions combine main concepts and techniques with motivating examples and illustrative problems for the covered subjects. Naturally, the book will also be of interest to researchers working in algebraic geometry, number theory and related fields.
Number theory III Diophantine geometry
1991-01-01
From the reviews of the first printing of this book, published as Volume 60 of the Encyclopaedia of Mathematical Sciences: "Between number theory and geometry there have been several stimulating influences, and this book records of these enterprises. This author, who has been at the centre of such research for many years, is one of the best guides a reader can hope for. The book is full of beautiful results, open questions, stimulating conjectures and suggestions where to look for future developments. This volume bears witness of the broad scope of knowledge of the author, and the influence of several people who have commented on the manuscript before publication ... Although in the series of number theory, this volume is on diophantine geometry, and the reader will notice that algebraic geometry is present in every chapter. ... The style of the book is clear. Ideas are well explained, and the author helps the reader to pass by several technicalities. Reading and rereading this book I noticed that the topics ...
Introduction to geometry and relativity
2013-01-01
This book provides a lucid introduction to both modern differential geometry and relativity for advanced undergraduates and first-year graduate students of applied mathematics and physical sciences. This book meets an overwhelming need for a book on modern differential geometry and relativity that is student-friendly, and which is also suitable for self-study. The book presumes a minimal level of mathematical maturity so that any student who has completed the standard Calculus sequence should be able to read and understand the book. The key features of the book are: Detailed solutions are provided to the Exercises in each chapter; Many of the missing steps that are often omitted from standard mathematical derivations have been provided to make the book easier to read and understand; A detailed introduction to Electrodynamics is provided so that the book is accessible to students who have not had a formal course in this area; In its treatment of modern differential geometry, the book employs both a modern, c...
Aspects of differential geometry II
Gilkey, Peter
2015-01-01
Differential Geometry is a wide field. We have chosen to concentrate upon certain aspects that are appropriate for an introduction to the subject; we have not attempted an encyclopedic treatment. Book II deals with more advanced material than Book I and is aimed at the graduate level. Chapter 4 deals with additional topics in Riemannian geometry. Properties of real analytic curves given by a single ODE and of surfaces given by a pair of ODEs are studied, and the volume of geodesic balls is treated. An introduction to both holomorphic and Kähler geometry is given. In Chapter 5, the basic properties of de Rham cohomology are discussed, the Hodge Decomposition Theorem, Poincaré duality, and the Künneth formula are proved, and a brief introduction to the theory of characteristic classes is given. In Chapter 6, Lie groups and Lie algebras are dealt with. The exponential map, the classical groups, and geodesics in the context of a bi-invariant metric are discussed. The de Rham cohomology of compact Lie groups an...
Riemannian geometry and geometric analysis
Jost, Jürgen
2017-01-01
This established reference work continues to provide its readers with a gateway to some of the most interesting developments in contemporary geometry. It offers insight into a wide range of topics, including fundamental concepts of Riemannian geometry, such as geodesics, connections and curvature; the basic models and tools of geometric analysis, such as harmonic functions, forms, mappings, eigenvalues, the Dirac operator and the heat flow method; as well as the most important variational principles of theoretical physics, such as Yang-Mills, Ginzburg-Landau or the nonlinear sigma model of quantum field theory. The present volume connects all these topics in a systematic geometric framework. At the same time, it equips the reader with the working tools of the field and enables her or him to delve into geometric research. The 7th edition has been systematically reorganized and updated. Almost no page has been left unchanged. It also includes new material, for instance on symplectic geometry, as well as the B...
Computational geometry for reactor applications
International Nuclear Information System (INIS)
Brown, F.B.; Bischoff, F.G.
1988-01-01
Monte Carlo codes for simulating particle transport involve three basic computational sections: a geometry package for locating particles and computing distances to regional boundaries, a physics package for analyzing interactions between particles and problem materials, and an editing package for determining event statistics and overall results. This paper describes the computational geometry methods in RACER, a vectorized Monte Carlo code used for reactor physics analysis, so that comparisons may be made with techniques used in other codes. The principal applications for RACER are eigenvalue calculations and power distributions associated with reactor core physics analysis. Successive batches of neutrons are run until convergence and acceptable confidence intervals are obtained, with typical problems involving >10 6 histories. As such, the development of computational geometry methods has emphasized two basic needs: a flexible but compact geometric representation that permits accurate modeling of reactor core details and efficient geometric computation to permit very large numbers of histories to be run. The current geometric capabilities meet these needs effectively, supporting a variety of very large and demanding applications
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.
Spherical warm shield design for infrared imaging systems
Tian, Qijie; Chang, Songtao; He, Fengyun; Li, Zhou; Qiao, Yanfeng
2017-09-01
The F-number matching is the primary means to suppress stray radiation for infrared imaging systems. However, it is difficult to achieve exact F-number matching, owing to the restriction from detectors, or multiple F-number design. Hence, an additional shield is required to block the certain thermal radiation. Typical shield is called flat warm shield, which is flat and operates at room temperature. For flat warm shield, it cannot suppress stray radiation while achieving F-number matching. To overcome the restriction, a spherical reflective warm shield is required. First of all, the detailed theory of spherical warm shield design is developed on basis of the principle that stray radiation cannot directly reach the infrared focal plane array. According to the theory developed above, a polished spherical warm shield, whose radius is 18 mm, is designed to match an F/2 infrared detector with an F/4 infrared imaging system. Then, the performance and alignment errors of the designed spherical warm shield are analyzed by simulation. Finally, a contrast experiment between the designed spherical warm shield and two differently processed flat warm shields is performed in a chamber with controllable inside temperatures. The experimental results indicate that the designed spherical warm shield cannot only achieve F-number matching but suppress stray radiation sufficiently. Besides, it is demonstrated that the theory of spherical warm shield design developed in this paper is valid and can be employed by arbitrary infrared imaging systems.
Spherical Accretion in a Uniformly Expanding Universe
Colpi, Monica; Shapiro, Stuart L.; Wasserman, Ira
1996-10-01
We consider spherically symmetric accretion of material from an initially homogeneous, uniformly expanding medium onto a Newtonian point mass M. The gas is assumed to evolve adiabatically with a constant adiabatic index F, which we vary over the range Γ ɛ [1, 5/3]. We use a one-dimensional Lagrangian code to follow the spherical infall of material as a function of time. Outflowing shells gravitationally bound to the point mass fall back, giving rise to a inflow rate that, after a rapid rise, declines as a power law in time. If there were no outflow initially, Bondi accretion would result, with a characteristic accretion time-scale ta,0. For gas initially expanding at a uniform rate, with a radial velocity U = R/t0 at radius R, the behavior of the flow at all subsequent times is determined by ta,0/t0. If ta,0/t0 ≫ 1, the gas has no time to respond to pressure forces, so the fluid motion is nearly collisionless. In this case, only loosely bound shells are influenced by pressure gradients and are pushed outward. The late-time evolution of the mass accretion rate Mdot is close to the result for pure dust, and we develop a semianalytic model that accurately accounts for the small effect of pressure gradients in this limit. In the opposite regime, ta,0/t0 ≪ 1, pressure forces significantly affect the motion of the gas. At sufficiently early times, t ≤ ttr, the flow evolved along a sequence of quasi-stationary, Bondi-like states, with a time-dependent Mdot determined by the slowly varying gas density at large distances. However, at later times, t ≥ ttr, the fluid flow enters a dustllke regime; ttr is the time when the instantaneous Bondi accretion radius reaches the marginally bound radius. The transition time ttr depends sensitively on ta,0/t0 for a given Γ and can greatly exceed t0. We show that there exists a critical value Γ = 11/9, below which the transition from fluid to ballistic motion disappears. As one application of our calculations, we consider the
Nuclear moments of nuclei near sphericity
International Nuclear Information System (INIS)
El Hajjaji, O.
1987-05-01
Magnetic and electric hyperfine interactions are studied by means of low temperature nuclear orientation. The magnetic moment of the 149 Gd isotope and that of 151 Gd are determined. The values follow the same trend as literature values of neighbouring nuclei. The calculated moments of the 7/2 - states using the Mottelson-Nilsson model without configuration mixing are nearly independent of deformation. Thus we assign the decrease of the magnetic moment versus neutron number to many particle coupling in the f shell. The Moessbauer effect detection of nuclear orientation is discussed. Two series of experiences are performed with different finalities. In the first one we determined the electric quadrupole moments of 125m Te and 129 Te. The quadrupole moments confirm the nearly spherical shape of these nuclei. In the second series we describe the Moessbauer effect of the radiation emitted by the daigleter nucleus of 125 I, implanted in two semiconductor matrices, locally oriented at low temperature by the electric field gradient of impurity-vacancy coupling. Despite the difficulty of the cooling down of Te nuclei to lattice temperature, we have shown the existence of the electric field gradient of implanted I into Si and α-Sn and determined their signs. The level mixing resonance is applied on oriented nuclei technique to determine the weak prolate deformation of silver nuclei. Studying the Δm = 3 resonance of 107 Ag m , we etablished the quadrupole moment of this state, which is in good agreement with the theoretical estimations of Moeller and Nix [fr
HFE and Spherical Cryostats MC Study
Energy Technology Data Exchange (ETDEWEB)
Brodsky, Jason P. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2016-09-26
The copper vessel containing the nEXO TPC is surrounded by a buffer of HFE, a liquid refrigerant with very low levels of radioactive element contamination. The HFE is contained within the cryostat’s inner vessel, which is in turn inside the outer vessel. While some HFE may be necessary for stable cooling of nEXO, it is possible that using substantially more than necessary for thermal reasons will help reduce backgrounds originating in the cryostats. Using a larger amount of HFE is accomplished by making the cryostat vessels larger. By itself, increasing the cryostat size somewhat increases the background rate, as the thickness of the cryostat wall must increase at larger sizes. However, the additional space inside the cryostat will be filled with HFE which can absorb gamma rays headed for the TPC. As a result, increasing the HFE reduces the number of backgrounds reaching the TPC. The aim of this study was to determine the relationship between HFE thickness and background rate. Ultimately, this work should support choosing a cryostat and HFE size that satisfies nEXO’s background budget. I have attempted to account for every consequence of changing the cryostat size, although naturally this remains a work in progress until a final design is achieved. At the moment, the scope of the study includes only the spherical cryostat design. This study concludes that increasing cryostat size reduces backgrounds, reaching neglible backgrounds originating from the cryostat at the largest sizes. It also shows that backgrounds originating from the inherent radioactivity of the HFE plateau quickly, so may be considered essentially fixed at any quantity of HFE.
Spherically symmetric ADM gravity with variable G and Λc
International Nuclear Information System (INIS)
Esposito, Giampiero; Rubano, Claudio; Scudellaro, Paolo
2007-01-01
This paper investigates the Arnowitt-Deser-Misner (hereafter ADM) form of spherically symmetric gravity with variable Newton parameter G and cosmological term Λ c . The Newton parameter is here treated as a dynamical variable, rather than being merely an external parameter as in previous work on closely related topics. The resulting Hamilton equations are obtained; interestingly, a static solution exists, which reduces to Schwarzschild geometry in the limit of constant G, describing a Newton parameter ruled by a nonlinear differential equation in the radial variable r. A remarkable limiting case is the one for which the Newton parameter obeys an almost linear growth law at large r. An exact solution for G as a function of r is also obtained in the case of vanishing cosmological constant. Some observational implications of these solutions are obtained and briefly discussed
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)
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)
Entropy function and the attractor mechanism for spherically symmetric extremal black holes
International Nuclear Information System (INIS)
Cai Ronggen; Cao Liming
2007-01-01
In this paper we elaborate on the relation between the entropy formula of Wald and the 'entropy function' method proposed by Sen. For spherically symmetric extremal black holes, it is shown that the expression of extremal black hole entropy given by Sen can be derived from the general entropy definition of Wald, without the help of the treatment of rescaling the AdS 2 part of the near horizon geometry of extremal black holes. In our procedure, we only require that the surface gravity approaches to zero, and it is easy to understand the Legendre transformation of f, the integration of Lagrangian density on the horizon, with respect to the electric charges. Since the Noether charge form can be defined in an 'off-shell' form, we define a corresponding entropy function, with which one can discuss the attractor mechanism for extremal black holes with scalar fields
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
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
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.
On the unique reconstruction of induced spherical magnetizations
International Nuclear Information System (INIS)
Gerhards, Christian
2016-01-01
Recovering spherical magnetizations m from magnetic field data in the exterior is a highly non-unique problem. A spherical Hardy–Hodge decomposition supplies information on what contributions of the magnetization m are recoverable but it does not supply geophysically suitable constraints on m that would guarantee uniqueness for the entire magnetization. In this paper, we focus on the case of induced spherical magnetizations and show that uniqueness is guaranteed if one assumes that the magnetization is compactly supported on the sphere. The results are based on ideas presented in (Baratchart et al 2013 Inverse Problems 29 015004) for the planar setting. (paper)
Non-Spherical Microcapsules for Increased Core Content Volume Delivery
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.
Thornton, Douglas E.; Spencer, Mark F.; Perram, Glen P.
2017-09-01
The effects of deep turbulence in long-range imaging applications presents unique challenges to properly measure and correct for aberrations incurred along the atmospheric path. In practice, digital holography can detect the path-integrated wavefront distortions caused by deep turbulence, and di erent recording geometries offer different benefits depending on the application of interest. Previous studies have evaluated the performance of the off-axis image and pupil plane recording geometries for deep-turbulence sensing. This study models digital holography in the on-axis phase shifting recording geometry using wave optics simulations. In particular, the analysis models spherical-wave propagation through varying deep-turbulence conditions to estimate the complex optical field, and performance is evaluated by calculating the field-estimated Strehl ratio and RMS wavefront error. Altogether, the results show that digital holography in the on-axis phase shifting recording geometry is an effective wavefront-sensing method in the presence of deep turbulence.
Geometry in the Early Years: A Commentary
Dindyal, Jaguthsing
2015-01-01
The primary goal of this paper is to provide a commentary on the teaching and learning of geometry in the early years of schooling with the set of papers in this issue as a guiding factor. It is structured around issues about geometry education of young learners, such as: what should we teach in geometry and why; representation of geometrical…
Blow-Ups in Generalized Complex Geometry
van der Leer Duran, J.L.
2016-01-01
Generalized complex geometry is a theory that unifies complex geometry and symplectic geometry into one single framework. It was introduced by Hitchin and Gualtieri around 2002. In this thesis we address the following question: given a generalized complex manifold together with a submanifold, does
Global affine differential geometry of hypersurfaces
Li, An-Min; Zhao, Guosong; Hu, Zejun
2015-01-01
This book draws a colorful and widespread picture of global affine hypersurface theory up to the most recent state. Moreover, the recent development revealed that affine differential geometry- as differential geometry in general- has an exciting intersection area with other fields of interest, like partial differential equations, global analysis, convex geometry and Riemann surfaces.
Students' Misconceptions and Errors in Transformation Geometry
Ada, Tuba; Kurtulus, Aytac
2010-01-01
This study analyses the students' performances in two-dimensional transformation geometry and explores the mistakes made by the students taking the analytic geometry course given by researchers. An examination was given to students of Education Faculties who have taken the analytic geometry course at Eskisehir Osmangazi University in Turkey. The…
"WGL," a Web Laboratory for Geometry
Quaresma, Pedro; Santos, Vanda; Maric, Milena
2018-01-01
The role of information and communication technologies (ICT) in education is nowadays well recognised. The "Web Geometry Laboratory," is an e-learning, collaborative and adaptive, Web environment for geometry, integrating a well known dynamic geometry system. In a collaborative session, teachers and students, engaged in solving…
Kong, Qingzhao; Fan, Shuli; Bai, Xiaolong; Mo, Y. L.; Song, Gangbing
2017-09-01
Recently developed piezoceramic-based transducers, known as smart aggregates (SAs), have shown their applicability and versatility in various applications of structural health monitoring (SHM). The lead zirconate titanate (PZT) patches embedded inside SAs have different modes that are more suitable for generating or receiving different types of stress waves (e.g. P and S waves, each of which has a unique role in SHM). However, due to the geometry of the 2D PZT patch, the embedded SA can only generate or receive the stress wave in a single direction and thus greatly limits its applications. This paper is the first of a series of two companion papers that introduces the authors’ latest work in developing a novel, embeddable spherical smart aggregate (SSA) for the health monitoring of concrete structures. In addition to the 1D guided wave produced by SA, the SSA embedded in concrete structures can generate or receive omni-directional stress waves that can significantly improve the detection aperture and provide additional functionalities in SHM. In the first paper (Part I), the detailed fabrication procedures with the help of 3D printing technology and electrical characterization of the proposed SSA is presented. The natural frequencies of the SSA were experimentally obtained and further compared with the numerical results. In addition, the influence of the components’ thickness (spherical piezoceramic shell and epoxy) and outer radius (spherical piezoceramic shell and protection concrete) on the natural frequencies of the SSA were analytically studied. The results will help elucidate the key parameters that determine the natural frequencies of the SSA. The natural frequencies of the SSA can thus be designed for suitability in the damage detection of concrete structures. In the second paper (Part II), further numerical and experimental verifications on the performance of the proposed SSA in concrete structures will be discussed.
Losa, Gabriele A
2009-01-01
The extension of the concepts of Fractal Geometry (Mandelbrot [1983]) toward the life sciences has led to significant progress in understanding complex functional properties and architectural / morphological / structural features characterising cells and tissues during ontogenesis and both normal and pathological development processes. It has even been argued that fractal geometry could provide a coherent description of the design principles underlying living organisms (Weibel [1991]). Fractals fulfil a certain number of theoretical and methodological criteria including a high level of organization, shape irregularity, functional and morphological self-similarity, scale invariance, iterative pathways and a peculiar non-integer fractal dimension [FD]. Whereas mathematical objects are deterministic invariant or self-similar over an unlimited range of scales, biological components are statistically self-similar only within a fractal domain defined by upper and lower limits, called scaling window, in which the relationship between the scale of observation and the measured size or length of the object can be established (Losa and Nonnenmacher [1996]). Selected examples will contribute to depict complex biological shapes and structures as fractal entities, and also to show why the application of the fractal principle is valuable for measuring dimensional, geometrical and functional parameters of cells, tissues and organs occurring within the vegetal and animal realms. If the criteria for a strict description of natural fractals are met, then it follows that a Fractal Geometry of Life may be envisaged and all natural objects and biological systems exhibiting self-similar patterns and scaling properties may be considered as belonging to the new subdiscipline of "fractalomics".
International Nuclear Information System (INIS)
Gervais, J.L.
1993-01-01
By analyzing the extrinsic geometry of two dimensional surfaces chirally embedded in C P n (the C P n W-surface), we give exact treatments in various aspects of the classical W-geometry in the conformal gauge: First, the basis of tangent and normal vectors are defined at regular points of the surface, such that their infinitesimal displacements are given by connections which coincide with the vector potentials of the (conformal) A n -Toda Lax pair. Since the latter is known to be intrinsically related with the W symmetries, this gives the geometrical meaning of the A n W-Algebra. Second, W-surfaces are put in one-to-one correspondence with solutions of the conformally-reduced WZNW model, which is such that the Toda fields give the Cartan part in the Gauss decomposition of its solutions. Third, the additional variables of the Toda hierarchy are used as coordinates of C P n . This allows us to show that W-transformations may be extended as particular diffeomorphisms of this target-space. Higher-dimensional generalizations of the WZNW equations are derived and related with the Zakharov-Shabat equations of the Toda hierarchy. Fourth, singular points are studied from a global viewpoint, using our earlier observation that W-surfaces may be regarded as instantons. The global indices of the W-geometry, which are written in terms of the Toda fields, are shown to be the instanton numbers for associated mappings of W-surfaces into the Grassmannians. The relation with the singularities of W-surface is derived by combining the Toda equations with the Gauss-Bonnet theorem. (orig.)
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)
DEM simulations of shear flow of spherical particles mixed with long granular rods
Baran, Oleh
2015-11-01
Using Discrete Element Method (DEM) I investigate the effect of adding rigid rod-shape particles to the granular flow of spherical particles inside ring shear tester. The simulated geometry includes an annulus, bounded by two concentric cylindrical walls rested on a stationary bottom disk and covered with a top lid. Both the top lid and the bottom have protruding vanes oriented radially and uniformly spaced around the annulus, to prevent slipping of the bulk solid, see image at this link. The top lid rotates with a controlled angular speed and applies a constant normal load to the tested material. I analyze the results for shear stress on the top lid as a function of time for the mixture of spheres and rods and compare these results with ones obtained for the same amount of spherical particles without rods. I also present the analysis of the orientation of granular rods in a shear flow and discuss the results in terms of new time-scale related to the mobility of rods.
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.
Articular cartilage response to a sliding load using two different-sized spherical indenters1.
Schätti, Oliver R; Colombo, Vera; Torzilli, Peter A; Gallo, Luigi M
2018-01-01
Cartilage surface contact geometry influences the deformational behavior and stress distribution throughout the extracellular matrix (ECM) under load. To test the correlation between the mechanical and cellular response of articular cartilage when loaded with two different-sized spherical indenters under dynamic reciprocating sliding motion. Articular cartilage explants were subjected to a reciprocating sliding load using a 17.6 mm or 30.2 mm spherical ball for 2000 cycles at 10 mm/s and 4 kg axial load. Deformation of the cartilage was recorded and contact parameters were calculated according to Hertzian theory. After mechanical loading cartilage samples were collected and analyzed for ECM collagen damage, gene regulation and proteoglycan (PG) loss. Significantly higher ECM deformation and strain and lower dynamic effective modulus were found for explants loaded with the smaller diameter indenter whereas contact radius and stress remained unaffected. Also, the 17.6 mm indenter increased PG loss and significantly upregulated genes for ECM proteins and enzymes as compared to the 30.2 mm indenter. Sliding loads that increase ECM deformation/strain were found to induce enzyme-mediated catabolic processes in articular cartilage explants. These observations provide further understanding of how changes in cartilage contact mechanics under dynamic conditions can affect the cellular response.
Mathaes, Roman; Winter, Gerhard; Besheer, Ahmed; Engert, Julia
2015-03-01
Micro- and nanoparticles in drug and vaccine delivery have opened up new possibilities in pharmaceutics. In the past, researchers focused mainly on particle size, surface chemistry and the use of various materials to control particle characteristics and functions. Lately, shape has been acknowledged as an important design parameter having an impact on the interaction with biological systems. In this review, we report on the latest developments in fabrication methods to tailor particle geometry, summarize analytical techniques for non-spherical particles and highlight the most important findings regarding their interaction with biological systems and their potential applications in drug delivery. The impact of shape on particle internalization into different cell types and particle biodistribution has been extensively studied in the past. Current research focuses on shape-dependent uptake mechanisms and applications for tumour therapy and vaccination. Different fabrication methods can be used to produce a variety of different particle types and shapes. Key challenges will be the transfer of new non-spherical particle fabrication methods from lab-scale to industrial large-scale production. Not all techniques may be scalable for the production of high quantities of particles. It will also be challenging to transfer the promising in vitro findings to suitable in vivo models.
Hybrid simplified spherical harmonics with diffusion equation for light propagation in tissues.
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.
Flyby Characterization of Lower-Degree Spherical Harmonics Around Small Bodies
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.
Sabry, R.; Omran, M. A.
2013-04-01
Investigation of nonlinear wave modulation of electron-acoustic solitary wave packets in planar as well as nonplanar geometry is carried out for an unmagnetized two temperature plasma composed of cold and hot (featuring q-nonextensive distribution) electrons with stationary ions. It is shown that in such plasma, propagation of EA wave packets is governed by a modified NLSE which accounts for the geometrical effect and the nonextensivity of the hot electron species. It is found that the nature of the modulational instabilities would be significantly modified due to the geometrical effects, density ratio α of the hot-to-cold electrons species as well as their temperature ratio θ. Also, there exists a modulation instability period for the cylindrical and spherical envelope excitations, which does not exist in the one-dimensional case. Furthermore, spherical EA solitary wave packets are more structurally stable to perturbations than the cylindrical ones. The relevance of the current study to EA wave modulation in auroral zone plasma is highlighted.
High Rayleigh Number 3-D Spherical Mantle Convection with Radial Basis Functions
Flyer, N.; Yuen (3), G. Wright, D.
2009-04-01
In the last quarter of a century many numerical methods, such as finite-differences, finite-volume, their yin-yang variants, finite-elements and pseudo-spectral methods have been used to study the problem of 3-D spherical convection. All have their respective strengths but also serious weaknesses, such as low-order and can involve high algorithmic complexity, as in triangular elements. Spectrally accurate methods do not practically allow for local mesh refinement and often involve cumbersome algebra. We have recently introduced a new grid/mesh-free approach, using radial basis functions ( RBFs) . It has the advantage of being spectrally accurate for arbitrary node layouts in multi-dimensions with extreme algorithmic simplicity, and allows naturally node-refinement. One virtue of the RBF scheme is the ability to use a simple Cartesian geometry while implementing the required boundary conditions for the temperature, velocity and stresses on a spherical surface of both the outer( planetary surface ) and inner shell ( core-mantle boundary ). The velocity and stress components are expressed in terms of the scalar potential approach and the other remaining variable is the perturbed temperature field. We have studied the problem from the weakly nonlinear to a moderately nonlinear regime involving a Rayleigh number, about 1000 times super-critical. Both purely basal and partially internal -heating cases have been considered
Stochastic geometry for image analysis
Descombes, Xavier
2013-01-01
This book develops the stochastic geometry framework for image analysis purpose. Two main frameworks are described: marked point process and random closed sets models. We derive the main issues for defining an appropriate model. The algorithms for sampling and optimizing the models as well as for estimating parameters are reviewed. Numerous applications, covering remote sensing images, biological and medical imaging, are detailed. This book provides all the necessary tools for developing an image analysis application based on modern stochastic modeling.
Geometry of physical dispersion relations
International Nuclear Information System (INIS)
Raetzel, Dennis; Rivera, Sergio; Schuller, Frederic P.
2011-01-01
To serve as a dispersion relation, a cotangent bundle function must satisfy three simple algebraic properties. These conditions are derived from the inescapable physical requirements that local matter field dynamics must be predictive and allow for an observer-independent notion of positive energy. Possible modifications of the standard relativistic dispersion relation are thereby severely restricted. For instance, the dispersion relations associated with popular deformations of Maxwell theory by Gambini-Pullin or Myers-Pospelov are not admissible. Dispersion relations passing the simple algebraic checks derived here correspond to physically admissible Finslerian refinements of Lorentzian geometry.