Microfluidic step-emulsification in axisymmetric geometry.
Chakraborty, I; Ricouvier, J; Yazhgur, P; Tabeling, P; Leshansky, A M
2017-10-25
Biphasic step-emulsification (Z. Li et al., Lab Chip, 2015, 15, 1023) is a promising microfluidic technique for high-throughput production of μm and sub-μm highly monodisperse droplets. The step-emulsifier consists of a shallow (Hele-Shaw) microchannel operating with two co-flowing immiscible liquids and an abrupt expansion (i.e., step) to a deep and wide reservoir. Under certain conditions the confined stream of the disperse phase, engulfed by the co-flowing continuous phase, breaks into small highly monodisperse droplets at the step. Theoretical investigation of the corresponding hydrodynamics is complicated due to the complex geometry of the planar device, calling for numerical approaches. However, direct numerical simulations of the three dimensional surface-tension-dominated biphasic flows in confined geometries are computationally expensive. In the present paper we study a model problem of axisymmetric step-emulsification. This setup consists of a stable core-annular biphasic flow in a cylindrical capillary tube connected co-axially to a reservoir tube of a larger diameter through a sudden expansion mimicking the edge of the planar step-emulsifier. We demonstrate that the axisymmetric setup exhibits similar regimes of droplet generation to the planar device. A detailed parametric study of the underlying hydrodynamics is feasible via inexpensive (two dimensional) simulations owing to the axial symmetry. The phase diagram quantifying the different regimes of droplet generation in terms of governing dimensionless parameters is presented. We show that in qualitative agreement with experiments in planar devices, the size of the droplets generated in the step-emulsification regime is independent of the capillary number and almost insensitive to the viscosity ratio. These findings confirm that the step-emulsification regime is solely controlled by surface tension. The numerical predictions are in excellent agreement with in-house experiments with the axisymmetric
Compact formulas for bounce/transit averaging in axisymmetric tokamak geometry
Energy Technology Data Exchange (ETDEWEB)
Duthoit, F.-X. [SNU Division of Graduate Education for Sustainabilization of Foundation Energy, Seoul National University, Seoul 151-742 (Korea, Republic of); Brizard, A. J. [Department of Physics, Saint Michael' s College, Colchester, Vermont 05439 (United States); Hahm, T. S. [Department of Nuclear Engineering, Seoul National University, Seoul 151-742 (Korea, Republic of)
2014-12-15
Compact formulas for bounce and transit orbit averaging of the fluctuation-amplitude eikonal factor in axisymmetric tokamak geometry, which is frequently encountered in bounce-gyrokinetic description of microturbulence, are given in terms of the Jacobi elliptic functions and elliptic integrals. These formulas are readily applicable to the calculation of the neoclassical susceptibility in the framework of modern bounce-gyrokinetic theory. In the long-wavelength limit for axisymmetric electrostatic perturbations, we recover the expression for the Rosenbluth-Hinton residual zonal flow [M. N. Rosenbluth and F. L. Hinton, Phys. Rev. Lett. 80, 724 (1998)] accurately.
Reynolds number and geometry effects in laminar axisymmetric isothermal counterflows
Scribano, Gianfranco
2016-12-29
The counterflow configuration is a canonical stagnation flow, featuring two opposed impinging round jets and a mixing layer across the stagnation plane. Although counterflows are used extensively in the study of reactive mixtures and other applications where mixing of two streams is required, quantitative data on the scaling properties of the flow field are lacking. The aim of this work is to characterize the velocity and mixing fields in isothermal counterflows over a wide range of conditions. The study features both experimental data from particle image velocimetry and results from detailed axisymmetric simulations. The scaling laws for the nondimensional velocity and mixture fraction are obtained as a function of an appropriate Reynolds number and the ratio of the separation distance of the nozzles to their diameter. In the range of flow configurations investigated, the nondimensional fields are found to depend primarily on the separation ratio and, to a lesser extent, the Reynolds number. The marked dependence of the velocity field with respect to the separation ratio is linked to a high pressure region at the stagnation point. On the other hand, Reynolds number effects highlight the role played by the wall boundary layer on the interior of the nozzles, which becomes less important as the separation ratio decreases. The normalized strain rate and scalar dissipation rate at the stagnation plane are found to attain limiting values only for high values of the Reynolds number. These asymptotic values depend markedly on the separation ratio and differ significantly from the values produced by analytical models. The scaling of the mixing field does not show a limiting behavior as the separation ratio decreases to the smallest practical value considered.
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...
Auluck, S. K. H.
2017-11-01
This paper continues earlier discussion [S. K. H. Auluck, Phys. Plasmas 21, 102515 (2014)] concerning the formulation of conservation laws of mass, momentum, and energy in a local curvilinear coordinate system in the dense plasma focus. This formulation makes use of the revised Gratton-Vargas snowplow model [S. K. H. Auluck, Phys. Plasmas 20, 112501 (2013)], which provides an analytically defined imaginary surface in three dimensions which resembles the experimentally determined shape of the plasma. Unit vectors along the local tangent to this surface, along the azimuth, and along the local normal define a right-handed orthogonal local curvilinear coordinate system. The simplifying assumption that physical quantities have significant variation only along the normal enables writing laws of conservation of mass, momentum, and energy in the form of effectively one-dimensional hyperbolic conservation law equations using expressions for various differential operators derived for this coordinate system. This formulation demonstrates the highly non-trivial result that the axial magnetic field and toroidally streaming fast ions, experimentally observed by multiple prestigious laboratories, are natural consequences of conservation of mass, momentum, and energy in the curved geometry of the dense plasma focus current sheath. The present paper continues the discussion in the context of a 3-region shock structure similar to the one experimentally observed: an unperturbed region followed by a hydrodynamic shock containing some current followed by a magnetic piston. Rankine-Hugoniot conditions are derived, and expressions are obtained for the specific volumes and pressures using the mass-flux between the hydrodynamic shock and the magnetic piston and current fraction in the hydrodynamic shock as unknown parameters. For the special case of a magnetic piston that remains continuously in contact with the fluid being pushed, the theory gives closed form algebraic results for the
International Nuclear Information System (INIS)
Burger, M. J.
1981-01-01
1 - Description of problem or function: The ZONE program is a finite element mesh generator which produces the nodes and element description of any two-dimensional geometry. The geometry is divided into a mesh of quadrilateral and triangular zones defined by node points taken in a counter-clockwise sequence. The zones are arranged sequentially in an ordered march through the geometry. The order can be chosen so that the minimum bandwidth is obtained. The mesh that is generated can be used as input to any two-dimensional as well as any axisymmetrical structure program. 2 - Method of solution: The basic concept used is the definition of a two-dimensional structure by the intersection of two sets of lines which describe the geometric and material boundaries. A set of lines called meridians define the geometric and material boundaries and generally run in the same direction. Another set of linear line segments called rays which intersect the meridians are also defined at the material and geometric boundaries. The section of the structure between successive rays is called a region. The ray segment between any two consecutive ray-meridian intersections or void area in the structure is called a layer and is described as passing through, or bounding a material. The boundaries can be directly defined as a sequence of straight line segments or can be computed in terms of elliptic segments or circular arcs. A meridian or ray can also be made to follow a previously-defined meridian or ray at a fixed distance by invoking an offset option. 3 - Restrictions on the complexity of the problem: The following are limited only by a DIMENSION statement. The code currently has a maxima of: 100 coordinate points defining a meridian or ray, 40 meridians, 40 layers. There are no limits on the number of zones or nodes for any problems
The computation of multiple MHD equilibria in axisymmetric and straight geometry
International Nuclear Information System (INIS)
Thomas, C.Ll.
1979-01-01
The details of the numerical methods used in codes for computing MHD equilibria in discrete conductor configurations are described with both code users and code writers in mind. Results produced by the codes have been successfully verified against analytic results and independent computations. The axisymmetric code has proved to be a valuable diagnostic aid for the TOSCA experiment. The user images of the codes are described in the appendices. (author)
Nagataki, Shigehiro
1999-01-01
We have tried to reproduce the solar system abundances using the nucleosynthesis products of Type Ia and Type II supernovae. In particular, we examined the effects of axisymmetrically deformed explosions in Type II supernovae. 44Ca and 47,48Ti are enhanced considerably in axisymmetrically deformed explosion models because of the active alpha-rich freezeout. The enhancement of nuclei around A=45 is a welcome result since it solves the problem of the nuclei shortage. Moreover, 59Co, 63,65Cu, and 66Zn are enhanced enough to reproduce the solar system abundances. The enhancement of Cu and Zn means the possibility that these nuclei, which have been said to be produced by the slow process, can be synthesized fairly well during the explosive nucleosynthesis. To discuss their origin quantitatively, the position of the mass cut is a very important parameter that is very difficult to determine numerically at present. We also stress that an axisymmetrically deformed explosion of Type II supernovae of the degree that is considered in this analysis is not excluded by the results of calculations of explosive nucleosynthesis, that is, the nucleosynthesis products are not extremely disturbed and the solar system abundances can be reproduced fairly well by the axisymmetrically deformed explosion models. This conclusion will be good for the theory of core collapse including the rotation of an iron core, magnetic field, and axisymmetrically modified neutrino radiation from a rotating protoneutron star, which possibly can cause an axisymmetrically deformed explosion.
HEATMESH, Geometry Data Generator for Heat Transfer Calculation in Axisymmetric System
International Nuclear Information System (INIS)
Gabrielson, V.K.
1972-01-01
1 - Description of problem or function: HEATMESH is used to generate geometrical data required for studies of heat transfer in axisymmetric structures represented as surfaces of revolution. The program consists of two distinct phases. The first subdivides the given parts into a nodal network and evaluates the geometrical properties of the nodes. The second determines adjacent nodes and edits geometrical data for the thermal model. 2 - Method of solution: The structure to be studied, represented as a body of revolution, is divided into parts having common material properties and represented as bodies of revolution. Each part is then described as four surfaces of revolution subdivided into nodes which form a mesh. Data for each part are collected, i. e. volume, area, and part number of each node, and node surfaces on the part boundary and inside the part boundary. The distance between the center and the midpoint of each surface of the node is tabulated also. 3 - Restrictions on the complexity of the problem: Number of subdivisions between 1 and 50 for sides 1 and 3, Number of subdivisions between 1 and 12 for sides 2 and 4
New method for computing ideal MHD normal modes in axisymmetric toroidal geometry
International Nuclear Information System (INIS)
Wysocki, F.; Grimm, R.C.
1984-11-01
Analytic elimination of the two magnetic surface components of the displacement vector permits the normal mode ideal MHD equations to be reduced to a scalar form. A Galerkin procedure, similar to that used in the PEST codes, is implemented to determine the normal modes computationally. The method retains the efficient stability capabilities of the PEST 2 energy principle code, while allowing computation of the normal mode frequencies and eigenfunctions, if desired. The procedure is illustrated by comparison with earlier various of PEST and by application to tilting modes in spheromaks, and to stable discrete Alfven waves in tokamak geometry
International Nuclear Information System (INIS)
Kelleher, W.P.
1987-01-01
In the assessment of Magnetohydrodynamic (MHD) equilibrium and Poloidal Field Coil (PFC) arrangement for toroidal axisymmetric geometry, the Grad-Shafranov equation must be solved, either analytically or numerically. Existing numerical tools have been developed primarily for mainframe usage and can prove cumbersome for screening assessments and parametric evaluations. The objective of this thesis was to develop a personal computer (PC)-based calculational tool for assessing MHD/PFC problems in a highly interactive mode, well suited for scoping studies. The approach adopted involves a two-step process: first the MHD equilibrium is calculated and then the PFC arrangement, consistent with the equilibrium, is determined in an interactive design environment. The PC-based system developed consists of two programs: (1) PCEQ, which solve the MHD equilibrium problem and (2) PFDE-SIGN, which is employed to arrive at a PFC arrangement. PCEQ provides an output file including, but not limited to, the following: poloidal beta, total beta, safety factors, q, on axis and on edge. PCEQ plots the following contours and/or profiles: flux, pressure and toroidal current density, safety factor, and ratio of plasma toroidal field to vacuum field
Geometry of the TJ-II in Astra 6.0
International Nuclear Information System (INIS)
Lopez-Bruna, D.; Romero, J.A.; Castejon, F.
2006-01-01
One of the most exploited features of the TJ-II Heliac, a facility in the Laboratorio Nacional de Fusion (CIEMAT, Madrid), is its ability to explore plasmas in different magnetic configurations. For this reason, there are available libraries that provide the metrics and associated magnitudes for many among all possible configurations. On the other hand, the transport codes that can normally be used to perform transport calculations cannot dea properly with these geometries, which is especially delicate when there are induced plasma currents. In the present work we adopt ASTRA, a transport analysis shell, to study the approximations performed when calculations that impose axi-symmetry (as ASTRA does) are performed on magnetic configurations that are not really axi-symmetric. After describing how we obtain those TJ-II metric averages that must be set in ASTRA, we perform two comparisons: (i) we obtain the vacuum rotational transform as deduced from the metric coefficients but imposing axisymmetry, and compare the results with the rotational transform yielded by the existing libraries; and (ii) we build a ID transport code with TJ-II metrics so its results can be compared with those of ASTRA. In both cases, the differences found indicate that evaluating the evolution of the rotational transform under ohmic induction and transport evolution is acceptable assuming that the geometry itself does not evolve. (Author) 11 refs
Gas dynamics of H II regions. II. Two-dimensional axisymmetric calculations
International Nuclear Information System (INIS)
Bodenheimer, P.; Tenorio-Tagle, G.; Yorke, H.W.
1979-01-01
The evolution of H II regions is calculated with a two-dimensional hydrodynamic numerical procedure under the assumption that the exciting star is born within a cool molecular cloud whose density is about 10 3 particles cm -3 . As the ionization of the cloud's edge is completed, a large pressure gradient is set up and ionized cloud material expands into the ionized low-density (1 particle cm -3 ) intercloud medium, with velocities larger than 30 km s -1 .The calculations are made under the simplifying assumptions that (i) within the H II region, ionization equilibrium holds at all times, (ii) the ionization front is a discontinuity, thus its detailed structure is not calculated, (iii) the temperature of each region (H II region, neutral cloud, and intercloud medium) is constant in time, (iv) all ionizing photons come radially from the exciting star. Four cases are calculated and compared with observations: (1) the edge of the cloud is overrun by a supersonic ionization front, (2) the initial Stroemgren sphere surrounding the star lies deep inside the cloud, thus the cloud's edge is ionized by a subsonic ionization front, (3) the ionization front breaks through two opposite faces of the same cloud simultaneously, (4) the flow encounters an isolated globule of density 10 3 particles cm -3 shortly after emerging from the molecular cloud.The phenomena here considered show how evolving H II regions are an important input of kinetic energy to the interstellar medium
Axisymmetric instability in a noncircular tokamak
International Nuclear Information System (INIS)
Lipschultz, B.
1979-10-01
The stability of dee, inverse-dee and square cross section plasmas to axisymmetric modes has been investigated experimentally in Tokapole II, a tokamak with a four-null poloidal divertor. Experimental results are closely compared with predictions of two numerical stability codes - the PEST code (ideal MHD, linear stability) adapted to tokapole geometry and a code which follows the nonlinear evolution of shapes similar to tokapole equilibria
Left Ventricular Geometry In Nigerians With Type II Diabetes Mellitus ...
African Journals Online (AJOL)
Background: Left ventricular hypertrophy is independently associated with increased incidence of cardiovascular disease, cardiovascular and all cause mortality. In a relatively healthy hypertensive adult population, type II diabetes is associated with higher left ventricular mass, concentric left ventricular geometry and lower ...
International Nuclear Information System (INIS)
Souza, Altivo Monteiro de
2008-12-01
The world energy consumption has been increasing strongly in recent years. Nuclear energy has been regarded as a suitable option to supply this growing energy demand in industrial scale. In view of the need of improving the understanding and capacity of analysis of nuclear power plants, modern simulation techniques for flow and heat transfer problems are gaining greater importance. A large number of problems found in nuclear reactor engineering can be dealt assuming axial symmetry. Thus, in this work a stabilized finite element formulation for the solution of the Navier-Stokes and energy equations for axisymmetric problems have been developed and tested. The formulation has been implemented in the NS S OLVER M PI 2 D A program developed at the Parallel Computation Laboratory of the Instituto de Engenharia Nuclear (LCP/IEN) and is now available either for safety analysis or design of nuclear systems. (author)
On solution of Maxwell's equations in axisymmetric domains with edges. Part II: Numerical aspects
International Nuclear Information System (INIS)
Nkemzi, Boniface
2003-10-01
In this paper we consider the Fourier-finite-element method for treating the Maxwell's equations in three-dimensional axisymmetric domains with reentrant edges. By means of partial Fourier analysis, the 3D BVP is decomposed into an infinite sequence of 2D variational equations in the plane meridian domain of the axisymmetric domain, a finite number of which is considered and treated using nodal H 1 -conforming finite elements. For domains with reentrant edges, the singular field method is employed to compensate the singular behavior of the solutions. Emphases are given to estimates of the Fourier-finite-element approximation error and convergence analysis in the H 1 -norm under different regularity assumptions. (author)
Heumann, Holger; Rapetti, Francesca
2017-04-01
Existing finite element implementations for the computation of free-boundary axisymmetric plasma equilibria approximate the unknown poloidal flux function by standard lowest order continuous finite elements with discontinuous gradients. As a consequence, the location of critical points of the poloidal flux, that are of paramount importance in tokamak engineering, is constrained to nodes of the mesh leading to undesired jumps in transient problems. Moreover, recent numerical results for the self-consistent coupling of equilibrium with resistive diffusion and transport suggest the necessity of higher regularity when approximating the flux map. In this work we propose a mortar element method that employs two overlapping meshes. One mesh with Cartesian quadrilaterals covers the vacuum chamber domain accessible by the plasma and one mesh with triangles discretizes the region outside. The two meshes overlap in a narrow region. This approach gives the flexibility to achieve easily and at low cost higher order regularity for the approximation of the flux function in the domain covered by the plasma, while preserving accurate meshing of the geometric details outside this region. The continuity of the numerical solution in the region of overlap is weakly enforced by a mortar-like mapping.
Absorption of acoustic waves by sunspots. II - Resonance absorption in axisymmetric fibril models
Rosenthal, C. S.
1992-01-01
Analytical calculations of acoustic waves scattered by sunspots which concentrate on the absorption at the magnetohydrodynamic Alfven resonance are extended to the case of a flux-tube embedded in a uniform atmosphere. The model is based on a flux-tubes of varying radius that are highly structured, translationally invariant, and axisymmetric. The absorbed fractional energy is determined for different flux-densities and subphotospheric locations with attention given to the effects of twist. When the flux is highly concentrated into annuli efficient absorption is possible even when the mean magnetic flux density is low. The model demonstrates low absorption at low azimuthal orders even in the presence of twist which generally increases the range of wave numbers over which efficient absorption can occur. Resonance absorption is concluded to be an efficient mechanism in monolithic sunspots, fibril sunspots, and plage fields.
Geometry of the TJ-II in Astra 6.0; Geometria del TJ-II en Astra 6.0
Energy Technology Data Exchange (ETDEWEB)
Lopez-Bruna, D.; Romero, J.A.; Castejon, F.
2006-07-01
One of the most exploited features of the TJ-II Heliac, a facility in the Laboratorio Nacional de Fusion (CIEMAT, Madrid), is its ability to explore plasmas in different magnetic configurations. For this reason, there are available libraries that provide the metrics and associated magnitudes for many among all possible configurations. On the other hand, the transport codes that can normally be used to perform transport calculations cannot dea properly with these geometries, which is especially delicate when there are induced plasma currents. In the present work we adopt ASTRA, a transport analysis shell, to study the approximations performed when calculations that impose axi-symmetry (as ASTRA does) are performed on magnetic configurations that are not really axi-symmetric. After describing how we obtain those TJ-II metric averages that must be set in ASTRA, we perform two comparisons: (i) we obtain the vacuum rotational transform as deduced from the metric coefficients but imposing axisymmetry, and compare the results with the rotational transform yielded by the existing libraries; and (ii) we build a ID transport code with TJ-II metrics so its results can be compared with those of ASTRA. In both cases, the differences found indicate that evaluating the evolution of the rotational transform under ohmic induction and transport evolution is acceptable assuming that the geometry itself does not evolve. (Author) 11 refs.
Sossinsky, A B
2012-01-01
The book is an innovative modern exposition of geometry, or rather, of geometries; it is the first textbook in which Felix Klein's Erlangen Program (the action of transformation groups) is systematically used as the basis for defining various geometries. The course of study presented is dedicated to the proposition that all geometries are created equal--although some, of course, remain more equal than others. The author concentrates on several of the more distinguished and beautiful ones, which include what he terms "toy geometries", the geometries of Platonic bodies, discrete geometries, and classical continuous geometries. The text is based on first-year semester course lectures delivered at the Independent University of Moscow in 2003 and 2006. It is by no means a formal algebraic or analytic treatment of geometric topics, but rather, a highly visual exposition containing upwards of 200 illustrations. The reader is expected to possess a familiarity with elementary Euclidean geometry, albeit those lacking t...
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 ...
Prasolov, V V
2015-01-01
This book provides a systematic introduction to various geometries, including Euclidean, affine, projective, spherical, and hyperbolic geometries. Also included is a chapter on infinite-dimensional generalizations of Euclidean and affine geometries. A uniform approach to different geometries, based on Klein's Erlangen Program is suggested, and similarities of various phenomena in all geometries are traced. An important notion of duality of geometric objects is highlighted throughout the book. The authors also include a detailed presentation of the theory of conics and quadrics, including the theory of conics for non-Euclidean geometries. The book contains many beautiful geometric facts and has plenty of problems, most of them with solutions, which nicely supplement the main text. With more than 150 figures illustrating the arguments, the book can be recommended as a textbook for undergraduate and graduate-level courses in geometry.
Modified geometry three-layered tablet as a platform for class II ...
African Journals Online (AJOL)
Modified geometry three-layered tablet as a platform for class II drugs zero-order release system. Abdullah Monahi Albogami, Mustafa E. Omer, Abdulkareem M. Al Bekairy, Abdulmalik Alkatheri, Alaa Eldeen B. Yassin ...
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
Axisymmetric instability in a noncircular tokamak: experiment and theory
International Nuclear Information System (INIS)
Lipschultz, B.; Prager, S.C.; Todd, A.M.M.; Delucia, J.
1979-09-01
The stability of dee, inverse-dee and square cross section plasmas to axisymmetric modes has been investigated experimentally in Tokapole II, a tokamak with a four-null poloidal divertor. Experimental results are closely compared with predictions of two numerical stability codes -- the PEST code (ideal MHD, linear stability) adapted to tokapole geometry and a code which follows the nonlinear evolution of shapes similar to tokapole equilibria. Experimentally, the square is vertically stable and both dee's unstable to a vertical nonrigid axisymmetric shift. The central magnetic axis displacement grows exponentially with a growth time approximately 10 3 poloidal Alfven times plasma time. Proper initial positioning of the plasma on the midplane allows passive feedback to nonlinearly restore vertical motion to a small stable oscillation. Experimental poloidal flux plots are produced directly from internal magnetic probe measurements
International Nuclear Information System (INIS)
Cambon, S.; Lacoste, P.
2011-01-01
We propose a finite element method to solve the axisymmetric scattering problem posed on a regular bounded domain. Here we shall show how to reduce the initial 3D problem into a truncated sum of 2D independent problems posed into a meridian plane of the object. Each of these problem results in the coupling of a partial differential equation into the interior domain and an integral equation on the surface simulating the free space. Then variational volume and boundary integral formulations of Maxwell's equation on regular surfaces are derived. We introduce some general finite element adapted to cylindrical coordinates and constructed from nodal and mixed finite element both for the interior (volume) and for the integral equation (surface). (authors)
An excursion through elementary mathematics, volume ii euclidean geometry
Caminha Muniz Neto, Antonio
2018-01-01
This book provides a comprehensive, in-depth overview of elementary mathematics as explored in Mathematical Olympiads around the world. It expands on topics usually encountered in high school and could even be used as preparation for a first-semester undergraduate course. This second volume covers Plane Geometry, Trigonometry, Space Geometry, Vectors in the Plane, Solids and much more. As part of a collection, the book differs from other publications in this field by not being a mere selection of questions or a set of tips and tricks that applies to specific problems. It starts from the most basic theoretical principles, without being either too general or too axiomatic. Examples and problems are discussed only if they are helpful as applications of the theory. Propositions are proved in detail and subsequently applied to Olympic problems or to other problems at the Olympic level. The book also explores some of the hardest problems presented at National and International Mathematics Olympiads, as well as many...
Differential geometry based solvation model II: Lagrangian formulation.
Chen, Zhan; Baker, Nathan A; Wei, G W
2011-12-01
Solvation is an elementary process in nature and is of paramount importance to more sophisticated chemical, biological and biomolecular processes. The understanding of solvation is an essential prerequisite for the quantitative description and analysis of biomolecular systems. This work presents a Lagrangian formulation of our differential geometry based solvation models. The Lagrangian representation of biomolecular surfaces has a few utilities/advantages. First, it provides an essential basis for biomolecular visualization, surface electrostatic potential map and visual perception of biomolecules. Additionally, it is consistent with the conventional setting of implicit solvent theories and thus, many existing theoretical algorithms and computational software packages can be directly employed. Finally, the Lagrangian representation does not need to resort to artificially enlarged van der Waals radii as often required by the Eulerian representation in solvation analysis. The main goal of the present work is to analyze the connection, similarity and difference between the Eulerian and Lagrangian formalisms of the solvation model. Such analysis is important to the understanding of the differential geometry based solvation model. The present model extends the scaled particle theory of nonpolar solvation model with a solvent-solute interaction potential. The nonpolar solvation model is completed with a Poisson-Boltzmann (PB) theory based polar solvation model. The differential geometry theory of surfaces is employed to provide a natural description of solvent-solute interfaces. The optimization of the total free energy functional, which encompasses the polar and nonpolar contributions, leads to coupled potential driven geometric flow and PB equations. Due to the development of singularities and nonsmooth manifolds in the Lagrangian representation, the resulting potential-driven geometric flow equation is embedded into the Eulerian representation for the purpose of
Geometry and Framework Interactions of Zeolite-Encapsulated Copper(II)-Histidine Complexes
Weckhuysen, B.M.; Grommen, R.; Manikandan, P.; Gao, Y.; Shane, T.; Shane, J.J.; Schoonheydt, R.A.; Goldfarb, D.
2000-01-01
The coordination geometry of zeolite-encapsulated copper(II)-histidine (CuHis) complexes, prepared by ion exchange of the complexes from aqueous solutions into zeolite NaY, was determined by a combination of UV-vis-NIR diffuse reflectance spectroscopy (DRS), X-band EPR, electron-spin-echo envelope
Type II InAs/GaAsSb quantum dots: Highly tunable exciton geometry and topology
Energy Technology Data Exchange (ETDEWEB)
Llorens, J. M.; Wewior, L.; Cardozo de Oliveira, E. R.; Alén, B., E-mail: benito.alen@csic.es [IMM-Instituto de Microelectrónica de Madrid (CNM-CSIC), Isaac Newton 8, PTM, E-28760 Tres Cantos, Madrid (Spain); Ulloa, J. M.; Utrilla, A. D.; Guzmán, A.; Hierro, A. [Institute for Systems based on Optoelectronics and Microtechnology (ISOM), Universidad Politécnica de Madrid, Ciudad Universitaria s/n, 28040 Madrid (Spain)
2015-11-02
External control over the electron and hole wavefunctions geometry and topology is investigated in a p-i-n diode embedding a dot-in-a-well InAs/GaAsSb quantum structure with type II band alignment. We find highly tunable exciton dipole moments and largely decoupled exciton recombination and ionization dynamics. We also predicted a bias regime where the hole wavefunction topology changes continuously from quantum dot-like to quantum ring-like as a function of the external bias. All these properties have great potential in advanced electro-optical applications and in the investigation of fundamental spin-orbit phenomena.
LRS Bianchi Type II Massive String Cosmological Models with Magnetic Field in Lyra's Geometry
Directory of Open Access Journals (Sweden)
Raj Bali
2013-01-01
Full Text Available Bianchi type II massive string cosmological models with magnetic field and time dependent gauge function ( in the frame work of Lyra's geometry are investigated. The magnetic field is in -plane. To get the deterministic solution, we have assumed that the shear ( is proportional to the expansion (. This leads to , where and are metric potentials and is a constant. We find that the models start with a big bang at initial singularity and expansion decreases due to lapse of time. The anisotropy is maintained throughout but the model isotropizes when . The physical and geometrical aspects of the model in the presence and absence of magnetic field are also discussed.
Li, Li; Li, YanYan; Yan, Xukai
2018-05-01
We classify all (- 1)-homogeneous axisymmetric no-swirl solutions of incompressible stationary Navier-Stokes equations in three dimension which are smooth on the unit sphere minus the south and north poles, parameterizing them as a four dimensional surface with boundary in appropriate function spaces. Then we establish smoothness properties of the solution surface in the four parameters. The smoothness properties will be used in a subsequent paper where we study the existence of (- 1)-homogeneous axisymmetric solutions with non-zero swirl on S2 ∖ { S , N }, emanating from the four dimensional solution surface.
XAFS study of copper(II) complexes with square planar and square pyramidal coordination geometries
Gaur, A.; Klysubun, W.; Nitin Nair, N.; Shrivastava, B. D.; Prasad, J.; Srivastava, K.
2016-08-01
X-ray absorption fine structure of six Cu(II) complexes, Cu2(Clna)4 2H2O (1), Cu2(ac)4 2H2O (2), Cu2(phac)4 (pyz) (3), Cu2(bpy)2(na)2 H2O (ClO4) (4), Cu2(teen)4(OH)2(ClO4)2 (5) and Cu2(tmen)4(OH)2(ClO4)2 (6) (where ac, phac, pyz, bpy, na, teen, tmen = acetate, phenyl acetate, pyrazole, bipyridine, nicotinic acid, tetraethyethylenediamine, tetramethylethylenediamine, respectively), which were supposed to have square pyramidal and square planar coordination geometries have been investigated. The differences observed in the X-ray absorption near edge structure (XANES) features of the standard compounds having four, five and six coordination geometry points towards presence of square planar and square pyramidal geometry around Cu centre in the studied complexes. The presence of intense pre-edge feature in the spectra of four complexes, 1-4, indicates square pyramidal coordination. Another important XANES feature, present in complexes 5 and 6, is prominent shoulder in the rising part of edge whose intensity decreases in the presence of axial ligands and thus indicates four coordination in these complexes. Ab initio calculations were carried out for square planar and square pyramidal Cu centres to observe the variation of 4p density of states in the presence and absence of axial ligands. To determine the number and distance of scattering atoms around Cu centre in the complexes, EXAFS analysis has been done using the paths obtained from Cu(II) oxide model and an axial Cu-O path from model of a square pyramidal complex. The results obtained from EXAFS analysis have been reported which confirmed the inference drawn from XANES features. Thus, it has been shown that these paths from model of a standard compound can be used to determine the structural parameters for complexes having unknown structure.
Gaur, A.; Klysubun, W.; Soni, Balram; Shrivastava, B. D.; Prasad, J.; Srivastava, K.
2016-10-01
X-ray absorption spectroscopy (XAS) is very useful in revealing the information about geometric and electronic structure of a transition-metal absorber and thus commonly used for determination of metal-ligand coordination. But XAFS analysis becomes difficult if differently coordinated metal centers are present in a system. In the present investigation, existence of distinct coordination geometries around metal centres have been studied by XAFS in a series of trimesic acid Cu(II) complexes. The complexes studied are: Cu3(tma)2(im)6 8H2O (1), Cu3(tma)2(mim)6 17H2O (2), Cu3(tma)2(tmen)3 8.5H2O (3), Cu3(tma) (pmd)3 6H2O (ClO4)3 (4) and Cu3(tma)2 3H2O (5). These complexes have not only Cu metal centres with different coordination but in complexes 1-3, there are multiple coordination geometries present around Cu centres. Using XANES spectra, different coordination geometries present in these complexes have been identified. The variation observed in the pre-edge features and edge features have been correlated with the distortion of the specific coordination environment around Cu centres in the complexes. XANES spectra have been calculated for the distinct metal centres present in the complexes by employing ab-initio calculations. These individual spectra have been used to resolve the spectral contribution of the Cu centres to the particular XANES features exhibited by the experimental spectra of the multinuclear complexes. Also, the variation in the 4p density of states have been calculated for the different Cu centres and then correlated with the features originated from corresponding coordination of Cu. Thus, these spectral features have been successfully utilized to detect the presence of the discrete metal centres in a system. The inferences about the coordination geometry have been supported by EXAFS analysis which has been used to determine the structural parameters for these complexes.
Kramer, S. L.; Ghosh, V. J.; Breitfeller, M.; Wahl, W.
2016-11-01
Third generation high brightness light sources are designed to have low emittance and high current beams, which contribute to higher beam loss rates that will be compensated by Top-Off injection. Shielding for these higher loss rates will be critical to protect the projected higher occupancy factors for the users. Top-Off injection requires a full energy injector, which will demand greater consideration of the potential abnormal beam miss-steering and localized losses that could occur. The high energy electron injection beam produces significantly higher neutron component dose to the experimental floor than a lower energy beam injection and ramped operations. Minimizing this dose will require adequate knowledge of where the miss-steered beam can occur and sufficient EM shielding close to the loss point, in order to attenuate the energy of the particles in the EM shower below the neutron production threshold (weaknesses in the design before a high radiation incident occurs. The effort required to adequately define the accelerator geometry for these codes has been greatly reduced with the implementation of the graphical interface of FLAIR to FLUKA. This made the effective shielding process for NSLS-II quite accurate and reliable. The principles used to provide supplemental shielding to the NSLS-II accelerators and the lessons learned from this process are presented.
Energy Technology Data Exchange (ETDEWEB)
Iga, Keita; Watanabe, Shunichi; Niino, Hiroshi; Misawa, Nobuhiko [Atmosphere and Ocean Research Institute, The University of Tokyo, 5-1-5, Kashiwanoha, Kashiwa, Chiba 277-8564 (Japan); Yokota, Sho [Meteorological Research Institute, 1-1 Nagamine, Tsukuba, Ibaraki 305-0052 (Japan); Ikeda, Takashi, E-mail: iga@aori.u-tokyo.ac.jp [Japan Patent Office, 3-4-3 Kasumigaseki, Chiyoda, Tokyo 100-8915 (Japan)
2017-12-15
The theory of axisymmetric flow in a cylindrical container with a rotating bottom, as described in Part I, is validated against the results of previous and our own laboratory experiments. First, deformation of the water surface is derived using the velocity distribution of the axisymmetric flow obtained by the theory. The form of the water surface is classified into three regimes, and the rotation rates of the transitions between these regimes are determined. The parameters predicted from this theory are compared with the results measured in laboratory experiments and also with data from previous experimental studies. The theory predicts the experimental data well, but a slight difference was found in the narrow region close to the side wall. Corrections estimated by considering the fluid behavior around the side wall boundary layer successfully explain most of the discrepancies. This theory appears to predict the results of the laboratory experiments very well, much better than a theory using an assumption of quadratic drag as a model of turbulent boundary layers. (paper)
International Nuclear Information System (INIS)
Patel, M.D.
1978-01-01
The Einstein's field equations for an enveloping radiating zone surrounding rotating axisymmetric collapsing source are studied. The solution has singularity along the axis of rotation. It is proved that on null hyper surface u = 0, the solution of the field equation for the radiating zone match with solution of axially symmetric vacuum field equations obtained by the author. Landau Lifshitz complex is used to obtain conserved total mass. (author)
International Nuclear Information System (INIS)
Will, C.M.
1975-01-01
We present a detailed description of the phenomenon of energy extraction (''Penrose'') from a slowly rotating black hole perturbed by a stationary axisymmetric ring of matter, and show that the gravitational interaction between the ring and the particles used in the Penrose process must be taken into account. For the case of a black-hole-ring configuration of ''minimum enregy'' we show that a Penrose process can extract further energy, but that by measns of their gravitational forces, the particles used in the process cause the radius of the ring to change, releasing precisely sufficient gravitational potential energy to make up for that extracted. By analyzing the properties of circular test-particle orbits in black-hole-ring spacetimes, we show quantitatively how this change in radius is produced. A ''differential mass formula'' relating the total masses of neighboring black-hole-ring configurations is also derived
Energy Technology Data Exchange (ETDEWEB)
Souza, Altivo Monteiro de
2008-12-15
The world energy consumption has been increasing strongly in recent years. Nuclear energy has been regarded as a suitable option to supply this growing energy demand in industrial scale. In view of the need of improving the understanding and capacity of analysis of nuclear power plants, modern simulation techniques for flow and heat transfer problems are gaining greater importance. A large number of problems found in nuclear reactor engineering can be dealt assuming axial symmetry. Thus, in this work a stabilized finite element formulation for the solution of the Navier-Stokes and energy equations for axisymmetric problems have been developed and tested. The formulation has been implemented in the NS{sub S}OLVER{sub M}PI{sub 2}D{sub A} program developed at the Parallel Computation Laboratory of the Instituto de Engenharia Nuclear (LCP/IEN) and is now available either for safety analysis or design of nuclear systems. (author)
Axisymmetric control in tokamaks
International Nuclear Information System (INIS)
Humphreys, D.A.
1991-02-01
Vertically elongated tokamak plasmas are intrinsically susceptible to vertical axisymmetric instabilities as a result of the quadrupole field which must be applied to produce the elongation. The present work analyzes the axisymmetric control necessary to stabilize elongated equilibria, with special application to the Alcator C-MOD tokamak. A rigid current-conserving filamentary plasma model is applied to Alcator C-MOD stability analysis, and limitations of the model are addressed. A more physically accurate nonrigid plasma model is developed using a perturbed equilibrium approach to estimate linearized plasma response to conductor current variations. This model includes novel flux conservation and vacuum vessel stabilization effects. It is found that the nonrigid model predicts significantly higher growth rates than predicted by the rigid model applied to the same equilibria. The nonrigid model is then applied to active control system design. Multivariable pole placement techniques are used to determine performance optimized control laws. Formalisms are developed for implementing and improving nominal feedback laws using the C-MOD digital-analog hybrid control system architecture. A proportional-derivative output observer which does not require solution of the nonlinear Ricatti equation is developed to help accomplish this implementation. The nonrigid flux conserving perturbed equilibrium plasma model indicates that equilibria with separatrix elongation of at least κ sep = 1.85 can be stabilized robustly with the present control architecture and conductor/sensor configuration
A new periodic imperfect quasi axisymmetric shell element
International Nuclear Information System (INIS)
Combescure, A.; Garuti, G.
1983-08-01
The object of this paper is to give the formulation and the validation of a ''quasi axisymmetric'' shell element: the main idea is to develop the theory of an imperfect quasi axisymmetric shell element. The imperfection is a variation of the circumferential radius of curvature rsub(theta). The equations are obtained by transporting the equilibrium equations from the actual geometry onto the theoretical axisymmetric (rsub(theta)=r 0 geometry. It is shown that the main hypothesis convenient to perform simply this transformation is that the membrane strains associated with that variation of geometry are less than 1% (that is always the case if you suppose that the imperfect structure is obtained from the perfect one by an inextensional displacement field). The formulation of the element is given in the general case. The rigidity matrices, are given in the particular case in which the imperfection has a component on a single Fourier harmonic. The comparison of theoretical and computed, 3D and quasi axisymmetric, solution or a very simple case shows the influence of the number of the Fourier harmonics chosen on the response of the structure. The influence of the initial imperfections on the natural frequency are studied with element and compared with 3D calculations. Comparison of 3D, quasi axisymmetric, and analytical buckling loads are given and explained. This element gives a very efficient tool for the calculation of thin shells of revolution (which are always imperfect) and especially unables easy parametric study of the variation of the buckling load and eigen frequencies with the amplitude and shapes of non axisymmetric imperfections
Women in numbers Europe II contributions to number theory and arithmetic geometry
Ozman, Ekin; Johnson-Leung, Jennifer; Newton, Rachel
2018-01-01
Inspired by the September 2016 conference of the same name, this second volume highlights recent research in a wide range of topics in contemporary number theory and arithmetic geometry. Research reports from projects started at the conference, expository papers describing ongoing research, and contributed papers from women number theorists outside the conference make up this diverse volume. Topics cover a broad range of topics such as arithmetic dynamics, failure of local-global principles, geometry in positive characteristics, and heights of algebraic integers. The use of tools from algebra, analysis and geometry, as well as computational methods exemplifies the wealth of techniques available to modern researchers in number theory. Exploring connections between different branches of mathematics and combining different points of view, these papers continue the tradition of supporting and highlighting the contributions of women number theorists at a variety of career stages. Perfect for students and researche...
Axisymmetric tokamak scapeoff transport
International Nuclear Information System (INIS)
Singer, C.E.; Langer, W.D.
1982-08-01
We present the first self-consistent estimate of the magnitude of each term in a fluid treatment of plasma transport for a plasma lying in regions of open field lines in an axisymmetric tokamak. The fluid consists of a pure hydrogen plasma with sources which arise from its interaction with neutral hydrogen atoms. The analysis and results are limited to the high collisionality regime, which is optimal for a gaseous neutralizer divertor, or to a cold plasma mantle in a tokamak reactor. In this regime, both classical and neoclassical transport processes are important, and loss of particles and energy by diamagnetic flow are also significant. The prospect of extending the analysis to the lower collisionality regimes encountered in many existing experiments is discussed
International Nuclear Information System (INIS)
Forkl, A.; Kronmueller, H.
1995-01-01
The distribution of the critical current density j c (r) in hard type-II superconductors depends strongly on their sample geometry. Rules are given for the construction of j c (r). Samples with homogeneous thickness are divided into cakelike regions with a unique current direction. The spatial magnetic flux density distribution and the magnetic polarization of such a cakelike unit cell with homogeneous current density are calculated analytically. The magnetic polarization and magnetic flux density distribution of a superconductor in the mixed state is then given by an adequate superposition of the unit cell solutions. The theoretical results show good agreement with magneto-optically determined magnetic flux density distributions of a quadratic thin superconducting YBa 2 Cu 3 O 7-x film. The current density distribution is discussed for several sample geometries
DEFF Research Database (Denmark)
Krauss, M; Olsen, Lars; Antony, J
2002-01-01
Models of the metal ion binding sites of native ZnZn and of cadmium-substituted ZnCd and CdCd phosphotriesterase, including full amino acid side chains, were geometry optimized with quantum mechanical methods, with effective fragment potentials (EFP) representing the protein environment surroundi...... to the Od1 of the carboxylate of the first-shell aspartate designated M 1, but the energy difference between Cd1Zn2 and the lowest energy Zn1Cd2 structure is only about 2 kcal/mol and decreasing with the addition of water molecules. The Zn1Cd2 arrangement is found experimentally....
Almost-commutative geometries beyond the standard model II: new colours
International Nuclear Information System (INIS)
Stephan, Christoph A
2007-01-01
We will present an extension of the standard model of particle physics in its almost-commutative formulation. This extension is guided by the minimal approach to almost-commutative geometries employed by Iochum et al (2004 J. Math. Phys. 45 5003 (Preprint hep-th/0312276)), Jureit and Stephan (2005 J. Math. Phys. 46 043512 (Preprint hep-th/0501134)), Schuecker (2005 Preprint hep-th/0501181), Jureit et al (2005 J. Math. Phys. 46 072303 (Preprint hep-th/0503190)) and Jureit and Stephan (2006 Preprint hep-th/0610040), although the model presented here is not minimal itself. The corresponding almost-commutative geometry leads to a Yang-Mills-Higgs model which consists of the standard model and two new fermions of opposite electromagnetic charge which may possess a new colour-like gauge group. As a new phenomenon, grand unification is no longer required by the spectral action
On the computation of steady Hopper flows. II: von Mises materials in various geometries
Gremaud, Pierre A.; Matthews, John V.; O'Malley, Meghan
2004-11-01
Similarity solutions are constructed for the flow of granular materials through hoppers. Unlike previous work, the present approach applies to nonaxisymmetric containers. The model involves ten unknowns (stresses, velocity, and plasticity function) determined by nine nonlinear first order partial differential equations together with a quadratic algebraic constraint (yield condition). A pseudospectral discretization is applied; the resulting problem is solved with a trust region method. The important role of the hopper geometry on the flow is illustrated by several numerical experiments of industrial relevance.
On the computation of steady Hopper flows II: von Mises materials in various geometries
International Nuclear Information System (INIS)
Gremaud, Pierre A.; Matthews, John V.; O'Malley, Meghan
2004-01-01
Similarity solutions are constructed for the flow of granular materials through hoppers. Unlike previous work, the present approach applies to nonaxisymmetric containers. The model involves ten unknowns (stresses, velocity, and plasticity function) determined by nine nonlinear first order partial differential equations together with a quadratic algebraic constraint (yield condition). A pseudospectral discretization is applied; the resulting problem is solved with a trust region method. The important role of the hopper geometry on the flow is illustrated by several numerical experiments of industrial relevance
Finley, Adam J.; Matt, Sean P.
2018-02-01
During the lifetime of Sun-like or low-mass stars a significant amount of angular momentum is removed through magnetized stellar winds. This process is often assumed to be governed by the dipolar component of the magnetic field. However, observed magnetic fields can host strong quadrupolar and/or octupolar components, which may influence the resulting spin-down torque on the star. In Paper I, we used the MHD code PLUTO to compute steady-state solutions for stellar winds containing a mixture of dipole and quadrupole geometries. We showed the combined winds to be more complex than a simple sum of winds with these individual components. This work follows the same method as Paper I, including the octupole geometry, which not only increases the field complexity but also, more fundamentally, looks for the first time at combining the same symmetry family of fields, with the field polarity of the dipole and octupole geometries reversing over the equator (unlike the symmetric quadrupole). We show, as in Paper I, that the lowest-order component typically dominates the spin-down torque. Specifically, the dipole component is the most significant in governing the spin-down torque for mixed geometries and under most conditions for real stars. We present a general torque formulation that includes the effects of complex, mixed fields, which predicts the torque for all the simulations to within 20% precision, and the majority to within ≈5%. This can be used as an input for rotational evolution calculations in cases where the individual magnetic components are known.
Multisource inverse-geometry CT. Part II. X-ray source design and prototype
Energy Technology Data Exchange (ETDEWEB)
Neculaes, V. Bogdan, E-mail: neculaes@ge.com; Caiafa, Antonio; Cao, Yang; De Man, Bruno; Edic, Peter M.; Frutschy, Kristopher; Gunturi, Satish; Inzinna, Lou; Reynolds, Joseph; Vermilyea, Mark; Wagner, David; Zhang, Xi; Zou, Yun [GE Global Research, Niskayuna, New York 12309 (United States); Pelc, Norbert J. [Department of Radiology, Stanford University, Stanford, California 94305 (United States); Lounsberry, Brian [Healthcare Science Technology, GE Healthcare, West Milwaukee, Wisconsin 53219 (United States)
2016-08-15
Purpose: This paper summarizes the development of a high-power distributed x-ray source, or “multisource,” designed for inverse-geometry computed tomography (CT) applications [see B. De Man et al., “Multisource inverse-geometry CT. Part I. System concept and development,” Med. Phys. 43, 4607–4616 (2016)]. The paper presents the evolution of the source architecture, component design (anode, emitter, beam optics, control electronics, high voltage insulator), and experimental validation. Methods: Dispenser cathode emitters were chosen as electron sources. A modular design was adopted, with eight electron emitters (two rows of four emitters) per module, wherein tungsten targets were brazed onto copper anode blocks—one anode block per module. A specialized ceramic connector provided high voltage standoff capability and cooling oil flow to the anode. A matrix topology and low-noise electronic controls provided switching of the emitters. Results: Four modules (32 x-ray sources in two rows of 16) have been successfully integrated into a single vacuum vessel and operated on an inverse-geometry computed tomography system. Dispenser cathodes provided high beam current (>1000 mA) in pulse mode, and the electrostatic lenses focused the current beam to a small optical focal spot size (0.5 × 1.4 mm). Controlled emitter grid voltage allowed the beam current to be varied for each source, providing the ability to modulate beam current across the fan of the x-ray beam, denoted as a virtual bowtie filter. The custom designed controls achieved x-ray source switching in <1 μs. The cathode-grounded source was operated successfully up to 120 kV. Conclusions: A high-power, distributed x-ray source for inverse-geometry CT applications was successfully designed, fabricated, and operated. Future embodiments may increase the number of spots and utilize fast read out detectors to increase the x-ray flux magnitude further, while still staying within the stationary target inherent
Axisymmetric Liquid Hanging Drops
Meister, Erich C.; Latychevskaia, Tatiana Yu
2006-01-01
The geometry of drops hanging on a circular capillary can be determined by numerically solving a dimensionless differential equation that is independent on any material properties, which enables one to follow the change of the height, surface area, and contact angle of drops hanging on a particular capillary. The results show that the application…
CLASSIFICATION OF STELLAR ORBITS IN AXISYMMETRIC GALAXIES
Energy Technology Data Exchange (ETDEWEB)
Li, Baile; Holley-Bockelmann, Kelly [Department of Physics and Astronomy, Vanderbilt University, Nashville, TN 37235 (United States); Khan, Fazeel Mahmood, E-mail: baile.li@vanderbilt.edu, E-mail: k.holley@vanderbilt.edu, E-mail: khanfazeel.ist@gmail.com [Department of Space Science, Institute of Space Technology, P.O. Box 2750 Islamabad (Pakistan)
2015-09-20
It is known that two supermassive black holes (SMBHs) cannot merge in a spherical galaxy within a Hubble time; an emerging picture is that galaxy geometry, rotation, and large potential perturbations may usher the SMBH binary through the critical three-body scattering phase and ultimately drive the SMBH to coalesce. We explore the orbital content within an N-body model of a mildly flattened, non-rotating, SMBH-embedded elliptical galaxy. When used as the foundation for a study on the SMBH binary coalescence, the black holes bypassed the binary stalling often seen within spherical galaxies and merged on gigayear timescales. Using both frequency-mapping and angular momentum criteria, we identify a wealth of resonant orbits in the axisymmetric model, including saucers, that are absent from an otherwise identical spherical system and that can potentially interact with the binary. We quantified the set of orbits that could be scattered by the SMBH binary, and found that the axisymmetric model contained nearly six times the number of these potential loss cone orbits compared to our equivalent spherical model. In this flattened model, the mass of these orbits is more than three times that of the SMBH, which is consistent with what the SMBH binary needs to scatter to transition into the gravitational wave regime.
Axisymmetric annular curtain stability
International Nuclear Information System (INIS)
Ahmed, Zahir U; Khayat, Roger E; Maissa, Philippe; Mathis, Christian
2012-01-01
A temporal stability analysis was carried out to investigate the stability of an axially moving viscous annular liquid jet subject to axisymmetric disturbances in surrounding co-flowing viscous gas media. We investigated in this study the effects of inertia, surface tension, the gas-to-liquid density ratio, the inner-to-outer radius ratio and the gas-to-liquid viscosity ratio on the stability of the jet. With an increase in inertia, the growth rate of the unstable disturbances is found to increase. The dominant (or most unstable) wavenumber decreases with increasing Reynolds number for larger values of the gas-to-liquid viscosity ratio. However, an opposite tendency for the most unstable wavenumber is predicted for small viscosity ratio in the same inertia range. The surrounding gas density, in the presence of viscosity, always reduces the growth rate, hence stabilizing the flow. There exists a critical value of the density ratio above which the flow becomes stable for very small viscosity ratio, whereas for large viscosity ratio, no stable flow appears in the same range of the density ratio. The curvature has a significant destabilizing effect on the thin annular jet, whereas for a relatively thick jet, the maximum growth rate decreases as the inner radius increases, irrespective of the surrounding gas viscosity. The degree of instability increases with Weber number for a relatively large viscosity ratio. In contrast, for small viscosity ratio, the growth rate exhibits a dramatic dependence on the surface tension. There is a small Weber number range, which depends on the viscosity ratio, where the flow is stable. The viscosity ratio always stabilizes the flow. However, the dominant wavenumber increases with increasing viscosity ratio. The range of unstable wavenumbers is affected only by the curvature effect. (paper)
Numerical methods for axisymmetric and 3D nonlinear beams
Pinton, Gianmarco F.; Trahey, Gregg E.
2005-04-01
Time domain algorithms that solve the Khokhlov--Zabolotzskaya--Kuznetsov (KZK) equation are described and implemented. This equation represents the propagation of finite amplitude sound beams in a homogenous thermoviscous fluid for axisymmetric and fully three dimensional geometries. In the numerical solution each of the terms is considered separately and the numerical methods are compared with known solutions. First and second order operator splitting are used to combine the separate terms in the KZK equation and their convergence is examined.
International Nuclear Information System (INIS)
Coffey, M.W.
1996-01-01
Due to their short coherence lengths and relatively large energy gaps, the high-transition temperature superconductors are very likely candidates as ultraclean materials at low temperature. This class of materials features significantly modified vortex dynamics, with very little dissipation at low temperature. The motion is then dominated by wave propagation, being in general nonlinear. Here two-dimensional vortex motion is investigated in the ultraclean regime for a superconductor described in cylindrical geometry. The small-amplitude limit is assumed, and the focus is on the long-wavelength limit. Results for both zero and nonzero Hall force are presented, with the effects of nonlocal vortex interaction and vortex inertia being included within London theory. Linear and nonlinear problems are studied, with a predisposition toward the more analytically tractable situations. For a nonlinear problem in 2+1 dimensions, the cylindrical Kadomtsev-Petviashvili equation is derived. Hall angle measurements on high-T c superconductors indicate the need to investigate the properties of such a completely integrable wave equation. copyright 1996 The American Physical Society
Geometry of deformed black holes. II. Schwarzschild hole surrounded by a Bach-Weyl ring
Basovník, M.; Semerák, O.
2016-08-01
We continue to study the response of black-hole space-times on the presence of additional strong sources of gravity. Restricting ourselves to static and axially symmetric (electro)vacuum exact solutions of Einstein's equations, we first considered the Majumdar-Papapetrou solution for a binary of extreme black holes in a previous paper, while here we deal with a Schwarzschild black hole surrounded by a concentric thin ring described by the Bach-Weyl solution. The geometry is again revealed on the simplest invariants determined by the metric (lapse function) and its gradient (gravitational acceleration), and by curvature (Kretschmann scalar). Extending the metric inside the black hole along null geodesics tangent to the horizon, we mainly focus on the black-hole interior (specifically, on its sections at constant Killing time) where the quantities behave in a way indicating a surprisingly strong influence of the external source. Being already distinct on the level of potential and acceleration, this is still more pronounced on the level of curvature: for a sufficiently massive and/or nearby (small) ring, the Kretschmann scalar even becomes negative in certain toroidal regions mostly touching the horizon from inside. Such regions have been interpreted as those where magnetic-type curvature dominates, but here we deal with space-times which do not involve rotation and the negative value is achieved due to the electric-type components of the Riemann/Weyl tensor. The Kretschmann scalar also shapes rather nontrivial landscapes outside the horizon.
Axisymmetric Lattice Boltzmann Model of Droplet Impact on Solid Surfaces
Dalgamoni, Hussein; Yong, Xin
2017-11-01
Droplet impact is a ubiquitous fluid phenomena encountered in scientific and engineering applications such as ink-jet printing, coating, electronics manufacturing, and many others. It is of great technological importance to understand the detailed dynamics of drop impact on various surfaces. The lattice Boltzmann method (LBM) emerges as an efficient method for modeling complex fluid systems involving rapidly evolving fluid-fluid and fluid-solid interfaces with complex geometries. In this work, we model droplet impact on flat solid substrates with well-defined wetting behavior using a two-phase axisymmetric LBM with high density and viscosity contrasts. We extend the two-dimensional Lee and Liu model to capture axisymmetric effect in the normal impact. First we compare the 2D axisymmetric results with the 2D and 3D results reported by Lee and Liu to probe the effect of axisymmetric terms. Then, we explore the effects of Weber number, Ohnesorge number, and droplet-surface equilibrium contact angle on the impact. The dynamic contact angle and spreading factor of the droplet during impact are investigated to qualitatively characterize the impact dynamics.
Edge Plasma Response to Non-Axisymmetric Fields in Tokamaks
Energy Technology Data Exchange (ETDEWEB)
Ferraro, N. M.; Lao, L. L.; Buttery, R. J.; Evans, T. E.; Snyder, P. B.; Wade, M.R., E-mail: ferraro@fusion.gat.com [General Atomics, San Diego (United States); Moyer, R. A.; Orlov, D. M. [University of California San Diego, La Jolla (United States); Lanctot, M. J. [Lawrence Livermore National Laboratory, Livermore (United States)
2012-09-15
Full text: The application of non-axisymmetric fields is found to have significant effects on the transport and stability of H-mode tokamak plasmas. These effects include dramatic changes in rotation and particle transport, and may lead to the partial or complete suppression of edge-localized modes (ELMs) under some circumstances. The physical mechanism underlying these effects is presently not well understood, in large part because the response of the plasma to non- axisymmetric fields is significant and complex. Here, recent advances in modeling the plasma response to non-axisymmetric fields are discussed. Calculations using a resistive two-fluid model in diverted toroidal geometry confirm the special role of the perpendicular electron velocity in suppressing the formation of islands in the plasma. The possibility that islands form near the top of the pedestal, where the zero-crossing of the perpendicular electron velocity may coincide with a mode-rational surface, is explored, and the implications for ELM suppression are discussed. Modeling results are compared with empirical data. It is shown that numerical modeling is successful in reproducing some experimentally observed effects of applied non-axisymmetric fields on the edge temperature and density profiles. The numerical model self-consistently includes the plasma, separatrix, and scrape-off layer. Rotation and diamagnetic effects are also included self-consistently. Solutions are calculated using the M3D-C1 extended-MHD code. (and others)
Axi-symmetric patterns of active polar filaments on spherical and composite surfaces
Srivastava, Pragya; Rao, Madan
2014-03-01
Experiments performed on Fission Yeast cells of cylindrical and spherical shapes, rod-shaped bacteria and reconstituted cylindrical liposomes suggest the influence of cell geometry on patterning of cortical actin. A theoretical model based on active hydrodynamic description of cortical actin that includes curvature-orientation coupling predicts spontaneous formation of acto-myosin rings, cables and nodes on cylindrical and spherical geometries [P. Srivastava et al, PRL 110, 168104(2013)]. Stability and dynamics of these patterns is also affected by the cellular shape and has been observed in experiments performed on Fission Yeast cells of spherical shape. Motivated by this, we study the stability and dynamics of axi-symmetric patterns of active polar filaments on the surfaces of spherical, saddle shaped and conical geometry and classify the stable steady state patterns on these surfaces. Based on the analysis of the fluorescence images of Myosin-II during ring slippage we propose a simple mechanical model for ring-sliding based on force balance and make quantitative comparison with the experiments performed on Fission Yeast cells. NSF Grant DMR-1004789 and Syracuse Soft Matter Program.
Theory for stationary nonlinear wave propagation in complex magnetic geometry
International Nuclear Information System (INIS)
Watanabe, T.; Hojo, H.; Nishikawa, Kyoji.
1977-08-01
We present our recent efforts to derive a systematic calculation scheme for nonlinear wave propagation in the self-consistent plasma profile in complex magnetic-field geometry. Basic assumptions and/or approximations are i) use of the collisionless two-fluid model with an equation of state; ii) restriction to a steady state propagation and iii) existence of modified magnetic surface, modification due to Coriolis' force. We discuss four situations: i) weak-field propagation without static flow, ii) arbitrary field strength with flow in axisymmetric system, iii) weak field limit of case ii) and iv) arbitrary field strength in nonaxisymmetric torus. Except for case iii), we derive a simple variation principle, similar to that of Seligar and Whitham, by introducing appropriate coordinates. In cases i) and iii), we derive explicit results for quasilinear profile modification. (auth.)
Numerical computation of gravitational field for general axisymmetric objects
Fukushima, Toshio
2016-10-01
We developed a numerical method to compute the gravitational field of a general axisymmetric object. The method (I) numerically evaluates a double integral of the ring potential by the split quadrature method using the double exponential rules, and (II) derives the acceleration vector by numerically differentiating the numerically integrated potential by Ridder's algorithm. Numerical comparison with the analytical solutions for a finite uniform spheroid and an infinitely extended object of the Miyamoto-Nagai density distribution confirmed the 13- and 11-digit accuracy of the potential and the acceleration vector computed by the method, respectively. By using the method, we present the gravitational potential contour map and/or the rotation curve of various axisymmetric objects: (I) finite uniform objects covering rhombic spindles and circular toroids, (II) infinitely extended spheroids including Sérsic and Navarro-Frenk-White spheroids, and (III) other axisymmetric objects such as an X/peanut-shaped object like NGC 128, a power-law disc with a central hole like the protoplanetary disc of TW Hya, and a tear-drop-shaped toroid like an axisymmetric equilibrium solution of plasma charge distribution in an International Thermonuclear Experimental Reactor-like tokamak. The method is directly applicable to the electrostatic field and will be easily extended for the magnetostatic field. The FORTRAN 90 programs of the new method and some test results are electronically available.
Magnetic fields, stellar feedback, and the geometry of H II regions
Ferland, Gary J.
2009-04-01
Magnetic pressure has long been known to dominate over gas pressure in atomic and molecular regions of the interstellar medium. Here I review several recent observational studies of the relationships between the H+, H0 and H2 regions in M42 (the Orion complex) and M17. A simple picture results. When stars form they push back surrounding material, mainly through the outward momentum of starlight acting on grains, and field lines are dragged with the gas due to flux freezing. The magnetic field is compressed and the magnetic pressure increases until it is able to resist further expansion and the system comes into approximate magnetostatic equilibrium. Magnetic field lines can be preferentially aligned perpendicular to the long axis of quiescent cloud before stars form. After star formation and pushback occurs ionized gas will be constrained to flow along field lines and escape from the system along directions perpendicular to the long axis. The magnetic field may play other roles in the physics of the H II region and associated PDR. Cosmic rays may be enhanced along with the field and provide additional heating of atomic and molecular material. Wave motions may be associated with the field and contribute a component of turbulence to observed line profiles.
Lyapunov stability analysis of magnetohydrodynamic plasma equilibria with axisymmetric toroidal flow
International Nuclear Information System (INIS)
Almaguer, J.A.; Hameiri, E.; Herrera, J.; Holm, D.D.
1988-01-01
Lyapunov stability conditions for ideal magnetohydrodynamic (MHD) plasmas with mass flow in axisymmetric toroidal geometry are determined in the Eulerian representation. Axisymmetric equilibrium solutions of ideal MHD are associated to critical points of a nonlinearly conserved Lyapunov functional consisting of the sum of the total energy and the following flux-weighted quantities: the circulation along field lines, the angular momentum, the toroidal flux, and the mass content within each flux tube. Conditions sufficient for Lyapunov stability of these equilibria against axisymmetric perturbations are found by taking advantage of the Hamiltonian formalism for ideal MHD. In particular [see Eq. (60)], it is sufficient for Lyapunov stability under linearized dynamics that an axisymmetric equilibrium be subsonic in the appropriate rotating frame, lie in the first elliptic regime of the Bernoulli--Grad--Shafranov (BGS) system of equations, and satisfy one additional, more complicated, condition. Effects of boundary conditions, nonlinearity, and three-dimensionality on MHD stability are also discussed
RAXBOD- INVISCID TRANSONIC FLOW OVER AXISYMMETRIC BODIES
Keller, J. D.
1994-01-01
The problem of axisymmetric transonic flow is of interest not only because of the practical application to missile and launch vehicle aerodynamics, but also because of its relation to fully three-dimensional flow in terms of the area rule. The RAXBOD computer program was developed for the analysis of steady, inviscid, irrotational, transonic flow over axisymmetric bodies in free air. RAXBOD uses a finite-difference relaxation method to numerically solve the exact formulation of the disturbance velocity potential with exact surface boundary conditions. Agreement with available experimental results has been good in cases where viscous effects and wind-tunnel wall interference are not important. The governing second-order partial differential equation describing the flow potential is replaced by a system of finite difference equations, including Jameson's "rotated" difference scheme at supersonic points. A stretching is applied to both the normal and tangential coordinates such that the infinite physical space is mapped onto a finite computational space. The boundary condition at infinity can be applied directly and there is no need for an asymptotic far-field solution. The system of finite difference equations is solved by a column relaxation method. In order to obtain both rapid convergence and any desired resolution, the relaxation is performed iteratively on successively refined grids. Input to RAXBOD consists of a description of the body geometry, the free stream conditions, and the desired resolution control parameters. Output from RAXBOD includes computed geometric parameters in the normal and tangential directions, iteration history information, drag coefficients, flow field data in the computational plane, and coordinates of the sonic line. This program is written in FORTRAN IV for batch execution and has been implemented on a CDC 6600 computer with an overlayed central memory requirement of approximately 40K (octal) of 60 bit words. Optional plotted output
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)
EXTINCTION AND DUST GEOMETRY IN M83 H II REGIONS: AN HUBBLE SPACE TELESCOPE/WFC3 STUDY
Energy Technology Data Exchange (ETDEWEB)
Liu, Guilin; Calzetti, Daniela; Hong, Sungryong [Astronomy Department, University of Massachusetts, Amherst, MA 01003 (United States); Whitmore, Bradley [Space Telescope Science Institute, Baltimore, MD 21218 (United States); Chandar, Rupali [Department of Physics and Astronomy, University of Toledo, Toledo, OH 43606 (United States); O' Connell, Robert W. [Astronomy Department, University of Virginia, P.O. Box 3818, Charlottesville, VA 22903 (United States); Blair, William P. [Center for Astrophysical Sciences, Johns Hopkins University, Baltimore, MD 21218 (United States); Cohen, Seth H.; Kim, Hwihyun [School of Earth and Space Exploration, Arizona State University, Tempe, AZ 85287 (United States); Frogel, Jay A., E-mail: liu@pha.jhu.edu [Galaxies Unlimited, Lutherville, MD 21093 (United States)
2013-12-01
We present Hubble Space Telescope/WFC3 narrow-band imaging of the starburst galaxy M83 targeting the hydrogen recombination lines (Hβ, Hα, and Paβ), which we use to investigate the dust extinction in the H II regions. We derive extinction maps with 6 pc spatial resolution from two combinations of hydrogen lines (Hα/Hβ and Hα/Paβ), and show that the longer wavelengths probe larger optical depths, with A{sub V} values larger by ≳1 mag than those derived from the shorter wavelengths. This difference leads to a factor ≳2 discrepancy in the extinction-corrected Hα luminosity, a significant effect when studying extragalactic H II regions. By comparing these observations to a series of simple models, we conclude that a large diversity of absorber/emitter geometric configurations can account for the data, implying a more complex physical structure than the classical foreground ''dust screen'' assumption. However, most data points are bracketed by the foreground screen and a model where dust and emitters are uniformly mixed. When averaged over large (≳100-200 pc) scales, the extinction becomes consistent with a ''dust screen'', suggesting that other geometries tend to be restricted to more local scales. Moreover, the extinction in any region can be described by a combination of the foreground screen and the uniform mixture model with weights of 1/3 and 2/3 in the center (≲2 kpc), respectively, and 2/3 and 1/3 for the rest of the disk. This simple prescription significantly improves the accuracy of the dust extinction corrections and can be especially useful for pixel-based analyses of galaxies similar to M83.
On the axisymmetric Lewis metric
International Nuclear Information System (INIS)
Gariel, J.; Marcilhacy, G.
2001-03-01
We obtain the general solution of the axisymmetric stationary vacuum spacetime of Lewis. After precising the fundamental hypothesis of Lewis, we demonstrate that the solution is related to an arbitrary harmonic function. Formally, these solutions are the same as for the corresponding cylindrically symmetric case, and can be classified in a similar way. Furthermore, the interpretation, in the cylindrically symmetric system, of the field equations as decribing the motion of a classical particle in a central force field is still valid. (author)
Seismic analysis of axisymmetric shells
International Nuclear Information System (INIS)
Jospin, R.J.; Toledo, E.M.; Feijoo, R.A.
1984-01-01
Axisymmetric shells subjected to multiple support excitation are studied. The shells are spatialy discretized by the finite element method and in order to obtain estimates for the maximum values of displacements and stresses the response spectrum tecnique is used. Finally, some numerical results are presented and discussed in the case of a shell of revolution with vertical symmetry axis, subjected to seismic ground motions in the horizontal, vertical and rocking directions. (Author) [pt
Reynolds number and geometry effects in laminar axisymmetric isothermal counterflows
Scribano, Gianfranco; Bisetti, Fabrizio
2016-01-01
dependence of the velocity field with respect to the separation ratio is linked to a high pressure region at the stagnation point. On the other hand, Reynolds number effects highlight the role played by the wall boundary layer on the interior of the nozzles
Ziegler, Ronny; Brendel, Bernhard; Rinneberg, Herbert; Nielsen, Tim
2009-01-21
Using a statistical (chi-square) test on simulated data and a realistic noise model derived from the system's hardware we study the performance of diffuse optical tomography systems for fluorescence imaging. We compare the predicted smallest size of detectable lesions at various positions in slab and cup geometry and model how detection sensitivity depends on breast compression and lesion fluorescence contrast. Our investigation shows that lesion detection is limited by relative noise in slab geometry and by absolute noise in cup geometry.
Stationary axisymmetric Einstein--Maxwell field equations
International Nuclear Information System (INIS)
Catenacci, R.; Diaz Alonso, J.
1976-01-01
We show the existence of a formal identity between Einstein's and Ernst's stationary axisymmetric gravitational field equations and the Einstein--Maxwell and the Ernst equations for the electrostatic and magnetostatic axisymmetric cases. Our equations are invariant under very simple internal symmetry groups, and one of them appears to be new. We also obtain a method for associating two stationary axisymmetric vacuum solutions with every electrostatic known
International Nuclear Information System (INIS)
Katanuma, I.; Kiwamoto, Y.; Adachi, S.; Inutake, M.; Ishii, K.; Yatsu, K.; Sawada, K.; Miyoshi, S.
1987-05-01
Calculations are made for neoclassical resonant-plateau transports in the geometry of the effectively axisymmetrized tandem mirror GAMMA 10 magnetic field, which has minimum B inbord anchors inside the axisymmetric plug/barrier mirror cells. Azimuthal drifts at the local non-axisymmetric regions are included. The radial potential profile is determined by solving selfconsistently the charge neutrality equation. A finite resistance connecting end plate to machine ground provides appropriate boundary conditions on the radial electrostatic potential distribution so that it can be determined uniquely. The calculation is consistent with experimental results of GAMMA 10. (author)
Solar proton exposure of an ICRU sphere within a complex structure part II: Ray-trace geometry.
Slaba, Tony C; Wilson, John W; Badavi, Francis F; Reddell, Brandon D; Bahadori, Amir A
2016-06-01
A computationally efficient 3DHZETRN code with enhanced neutron and light ion (Z ≤ 2) propagation was recently developed for complex, inhomogeneous shield geometry described by combinatorial objects. Comparisons were made between 3DHZETRN results and Monte Carlo (MC) simulations at locations within the combinatorial geometry, and 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 ray-trace geometry. This latest extension enables the code to be used within current engineering design practices utilizing fully detailed vehicle and habitat geometries. Through convergence testing, it is shown that fidelity in an actual shield geometry can be maintained in the discrete ray-trace description by systematically increasing the number of discrete rays used. It is also shown that this fidelity is carried into transport procedures and resulting exposure quantities without sacrificing computational efficiency. Published by Elsevier Ltd.
Axisymmetric plasma equilibria in a Kerr metric
Elsässer, Klaus
2001-10-01
Plasma equilibria near a rotating black hole are considered within the multifluid description. An isothermal two-component plasma with electrons and positrons or ions is determined by four structure functions and the boundary conditions. These structure functions are the Bernoulli function and the toroidal canonical momentum per mass for each species. The quasi-neutrality assumption (no charge density, no toroidal current) allows to solve Maxwell's equations analytically for any axisymmetric stationary metric, and to reduce the fluid equations to one single scalar equation for the stream function \\chi of the positrons or ions, respectively. The basic smallness parameter is the ratio of the skin depth of electrons to the scale length of the metric and fluid quantities, and, in the case of an electron-ion plasma, the mass ratio m_e/m_i. The \\chi-equation can be solved by standard methods, and simple solutions for a Kerr geometry are available; they show characteristic flow patterns, depending on the structure functions and the boundary conditions.
Axisymmetric Plasma Equilibria in General Relativity
Elsässer, Klaus
Axisymmetric plasma equilibria near a rotating black hole are considered within the multifluid description. An isothermal two-component plasma with electrons and positrons or ions is determined by four structure functions and the boundary conditions. These structure functions are the Bernoulli function and the toroidal canonical momentum per mass for each species; they remain arbitrary if no gain and loss processes are considered, in close analogy to the free flux functions in ideal magnetohydrodynamics. Several simplifying assumptions allow the reduction of the basic equations to one single scalar equation for the stream function χ of positrons or ions, respectively, playing the rôle of the Grad/Shafranov equation in magnetohydrodynamics; in particular, Maxwell's equations can be solved analytically for a quasineutral plasma when both the charge density and the toroidal electric current density are negligible (in contrast to the Tokamak situation). The basic smallness parameter is the ratio of the skin depth of electrons to the scale length of the metric and fluid quantities, and, in the case of an electron-ion plasma, the mass ratio me/mi. The χ-equation can be solved by standard methods, and simple solutions for a Kerr geometry are available; they show characteristic flow patterns, depending on the structure functions and the boundary conditions.
DEFF Research Database (Denmark)
Rasmussen, N. G.; Simeoni, G. G.; Lefmann, K.
2016-01-01
A dedicated beam-focusing device has been designed for the direct geometry thermal-cold neutron time-of-flight spectrometer TOFTOF at the neutron facility FRM II (Garching, Germany). The prototype, based on the compressed Archimedes' mirror concept, benefits from the adaptive-optics technology (a...... than 3.5 would have only marginal influence on the optimal behaviour, whereas comparable spectrometers could take advantage of longer focusing segments, with particular impact for the thermal region of the neutron spectrum....
Axisymmetric Magnetic Mirror Fusion-Fission Hybrid
Energy Technology Data Exchange (ETDEWEB)
Moir, R. W. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Martovetsky, N. N. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Molvik, A. W. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Ryutov, D. D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Simonen, T. C. [Univ. of California, Berkeley, CA (United States)
2011-05-13
The achieved performance of the gas dynamic trap version of magnetic mirrors and today’s technology we believe are sufficient with modest further efforts for a neutron source for material testing (Q=P_{fusion}/P_{input}~0.1). The performance needed for commercial power production requires considerable further advances to achieve the necessary high Q>>10. An early application of the mirror, requiring intermediate performance and intermediate values of Q~1 are the hybrid applications. The Axisymmetric Mirror has a number of attractive features as a driver for a fusion-fission hybrid system: geometrical simplicity, inherently steady-state operation, and the presence of the natural divertors in the form of end tanks. This level of physics performance has the virtue of low risk and only modest R&D needed and its simplicity promises economy advantages. Operation at Q~1 allows for relatively low electron temperatures, in the range of 4 keV, for the DT injection energy ~ 80 keV. A simple mirror with the plasma diameter of 1 m and mirror-to-mirror length of 35 m is discussed. Simple circular superconducting coils are based on today’s technology. The positive ion neutral beams are similar to existing units but designed for steady state. A brief qualitative discussion of three groups of physics issues is presented: axial heat loss, MHD stability in the axisymmetric geometry, microstability of sloshing ions. Burning fission reactor wastes by fissioning actinides (transuranics: Pu, Np, Am, Cm, .. or just minor actinides: Np, Am, Cm, …) in the hybrid will multiply fusion’s energy by a factor of ~10 or more and diminish the Q needed to less than 1 to overcome the cost of recirculating power for good economics. The economic value of destroying actinides by fissioning is rather low based on either the cost of long-term storage or even deep geologic disposal so most of the revenues of hybrids will come from electrical power. Hybrids that obtain revenues from
International Nuclear Information System (INIS)
Kramer, S. L.; Ghosh, V. J.; Breitfeller, M.; Wahl, W.
2016-01-01
Third generation high brightness light sources are designed to have low emittance and high current beams, which contribute to higher beam loss rates that will be compensated by Top-Off injection. Shielding for these higher loss rates will be critical to protect the projected higher occupancy factors for the users. Top-Off injection requires a full energy injector, which will demand greater consideration of the potential abnormal beam miss-steering and localized losses that could occur. The high energy electron injection beam produces significantly higher neutron component dose to the experimental floor than a lower energy beam injection and ramped operations. Minimizing this dose will require adequate knowledge of where the miss-steered beam can occur and sufficient EM shielding close to the loss point, in order to attenuate the energy of the particles in the EM shower below the neutron production threshold (<10 MeV), which will spread the incident energy on the bulk shield walls and thereby the dose penetrating the shield walls. Designing supplemental shielding near the loss point using the analytic shielding model is shown to be inadequate because of its lack of geometry specification for the EM shower process. To predict the dose rates outside the tunnel requires detailed description of the geometry and materials that the beam losses will encounter inside the tunnel. Modern radiation shielding Monte-Carlo codes, like FLUKA, can handle this geometric description of the radiation transport process in sufficient detail, allowing accurate predictions of the dose rates expected and the ability to show weaknesses in the design before a high radiation incident occurs. The effort required to adequately define the accelerator geometry for these codes has been greatly reduced with the implementation of the graphical interface of FLAIR to FLUKA. This made the effective shielding process for NSLS-II quite accurate and reliable. Lastly, the principles used to provide
Axisymmetric magnetic mirrors for plasma confinement. Recent development and perspectives
International Nuclear Information System (INIS)
Kruglyakov, E.P.; Dimov, G.I.; Ivanov, A.A.; Koidan, V.S.
2003-01-01
Mirrors are the only one class of fusion systems which completely differs topologically from the systems with closed magnetic configurations. At present, three modern types of different mirror machines for plasma confinement and heating exist in Novosibirsk (Gas Dynamic Trap,- GDT, Multi-mirror,- GOL-3, and Tandem Mirror,- AMBAL-M). All these systems are attractive from the engineering point of view because of very simple axisymmetric geometry of magnetic configurations. In the present paper, the status of different confinement systems is presented. The experiments most crucial for the mirror concept are described such as a demonstration of different principles of suppression of electron heat conductivity (GDT, GOL-3), finding of MHD stable regimes of plasma confinement in axisymmetric geometry of magnetic field (GDT, AMBAL-M), an effective heating of a dense plasma by relativistic electron beam (GOL-3), observation of radial diffusion of quiescent plasma with practically classical diffusion coefficient (AMBAL-M), etc. It should be mentioned that on the basis of the GDT it is possible to make a very important intermediate step. Using 'warm' plasma and oblique injection of fast atoms of D and T one can create a powerful 14 MeV neutron source with a moderate irradiation area (about 1 square meter) and, accordingly, with low tritium consumption. The main plasma parameters achieved are presented and the future perspectives of different mirror machines are outlined. (author)
Modeling and simulation of axisymmetric coating growth on nanofibers
International Nuclear Information System (INIS)
Moore, K.; Clemons, C. B.; Kreider, K. L.; Young, G. W.
2007-01-01
This work is a modeling and simulation extension of an integrated experimental/modeling investigation of a procedure to coat nanofibers and core-clad nanostructures with thin film materials using plasma enhanced physical vapor deposition. In the experimental effort, electrospun polymer nanofibers are coated with metallic materials under different operating conditions to observe changes in the coating morphology. The modeling effort focuses on linking simple models at the reactor level, nanofiber level, and atomic level to form a comprehensive model. The comprehensive model leads to the definition of an evolution equation for the coating free surface. This equation was previously derived and solved under a single-valued assumption in a polar geometry to determine the coating morphology as a function of operating conditions. The present work considers the axisymmetric geometry and solves the evolution equation without the single-valued assumption and under less restrictive assumptions on the concentration field than the previous work
Experimental studies on an axisymmetric divertor in DIVA(JFT-2a)
International Nuclear Information System (INIS)
Yamamoto, Shin
1979-03-01
DIVA(JFT-2a) is the first tokamak with an axisymmetric divertor in the world. Objectives of the experiments were i) Plasma production and confinement in a tokamak with a separatrix magnetic surface, and ii) divertor effects on radiation loss and plasma confinement. The results so far are as follows: i) The equilibrium with a separatrix magnetic surface is stable during the discharge. ii) There is an ergodic region near the separatrix magnetic surface due to non-axisymmetric magnetic perturbations. iii) The divertor reduces radiation loss and increases energy confinement time. iv) The divertor does not affect the transport process in the main plasma. (author)
Streamline topology of axisymmetric flows
DEFF Research Database (Denmark)
Brøns, Morten
Topological fluid mechanics in the sense of the present paper is the study and classification of flow patterns close to a critical point. Here we discuss the topology of steady viscous incompressible axisymmetric flows in the vicinity of the axis. Following previous studies the velocity field $v...... to the authors knowledge has not been used systematically to high orders in topological fluid mechanics. We compare the general results with experimental and computational results on the Vogel-Ronneberg flow. We show that the topology changes observed when recirculating bubbles on the vortex axis are created...... and interact follow the topological classification and that the complete set of patterns found is contained in a codimension-4 unfolding of the most simple singular configuration....
CRUCIB: an axisymmetric convection code
International Nuclear Information System (INIS)
Bertram, L.A.
1975-03-01
The CRUCIB code was written in support of an experimental program aimed at measurement of thermal diffusivities of refractory liquids. Precise values of diffusivity are necessary to realistic analysis of reactor safety problems, nuclear waste disposal procedures, and fundamental metal forming processes. The code calculates the axisymmetric transient convective motions produced in a right circular cylindrical crucible, which is surface heated by an annular heat pulse. Emphasis of this report is placed on the input-output options of the CRUCIB code, which are tailored to assess the importance of the convective heat transfer in determining the surface temperature distribution. Use is limited to Prandtl numbers less than unity; larger values can be accommodated by replacement of a single block of the code, if desired. (U.S.)
An axisymmetric gravitational collapse code
Energy Technology Data Exchange (ETDEWEB)
Choptuik, Matthew W [CIAR Cosmology and Gravity Program, Department of Physics and Astronomy, University of British Columbia, Vancouver BC, V6T 1Z1 (Canada); Hirschmann, Eric W [Department of Physics and Astronomy, Brigham Young University, Provo, UT 84604 (United States); Liebling, Steven L [Southampton College, Long Island University, Southampton, NY 11968 (United States); Pretorius, Frans [Theoretical Astrophysics, California Institute of Technology, Pasadena, CA 91125 (United States)
2003-05-07
We present a new numerical code designed to solve the Einstein field equations for axisymmetric spacetimes. The long-term goal of this project is to construct a code that will be capable of studying many problems of interest in axisymmetry, including gravitational collapse, critical phenomena, investigations of cosmic censorship and head-on black-hole collisions. Our objective here is to detail the (2+1)+1 formalism we use to arrive at the corresponding system of equations and the numerical methods we use to solve them. We are able to obtain stable evolution, despite the singular nature of the coordinate system on the axis, by enforcing appropriate regularity conditions on all variables and by adding numerical dissipation to hyperbolic equations.
An axisymmetric gravitational collapse code
International Nuclear Information System (INIS)
Choptuik, Matthew W; Hirschmann, Eric W; Liebling, Steven L; Pretorius, Frans
2003-01-01
We present a new numerical code designed to solve the Einstein field equations for axisymmetric spacetimes. The long-term goal of this project is to construct a code that will be capable of studying many problems of interest in axisymmetry, including gravitational collapse, critical phenomena, investigations of cosmic censorship and head-on black-hole collisions. Our objective here is to detail the (2+1)+1 formalism we use to arrive at the corresponding system of equations and the numerical methods we use to solve them. We are able to obtain stable evolution, despite the singular nature of the coordinate system on the axis, by enforcing appropriate regularity conditions on all variables and by adding numerical dissipation to hyperbolic equations
International Nuclear Information System (INIS)
Sitaramayya, M.
1993-11-01
After a brief review of the geometry of Moishezon spaces, their relation with l-convex spaces and a reasonable and up to date understanding of the obstructions for projectivity of Moishezon objects both in singular and non-singular case is given. The geometry of l-convex manifolds and with l-dimensional exceptional set is studied and some problems and conjectures are stated. The tools of cohomology vanishing theorems important for the subject are briefly sketched. Compactifications of C 3 and Stein spaces are finally outlined. given. 111 refs, 2 figs
Variable geometry for supersonic mixed-compression inlets
Sorensen, N. E.; Latham, E. A.; Smeltzer, D. B.
1974-01-01
Study of two-dimensional and axisymmetric supersonic mixed-compression inlet systems has shown that the geometry of both systems can be varied to provide adequate transonic airflow to satisfy the airflow demand of most jet engines. Collapsing geometry systems for both types of inlet systems provide a generous amount of transonic airflow for any design Mach number inlet system. However, the mechanical practicality of collapsing centerbodies for axisymmetric inlet systems is doubtful. Therefore, translating centerbody axisymmetric inlets with auxiliary airflow systems to augment the transonic airflow capability are an attractive alternative. Estimates show that the capture mass-flow ratio at Mach number 1.0 can be increased approximately 0.20 for a very short axisymmetric inlet system designed for Mach number 2.37. With this increase in mass-flow ratio, even variable-cycle engine transonic airflow demand can be matched without oversizing the inlet at the design Mach number.
Axisymmetric magnetohydrodynamic equilibria in local polar coordinates
International Nuclear Information System (INIS)
Clemente, R.A.
1982-01-01
The Grad--Shafranov equation for an ideal magnetohydrodynamic axisymmetric toroidal configuration is solved analytically in a local polar coordinate system using a novel method which produces solutions valid up to the second order in the inverse aspect ratio expansion
Adaptative mixed methods to axisymmetric shells
International Nuclear Information System (INIS)
Malta, S.M.C.; Loula, A.F.D.; Garcia, E.L.M.
1989-09-01
The mixed Petrov-Galerkin method is applied to axisymmetric shells with uniform and non uniform meshes. Numerical experiments with a cylindrical shell showed a significant improvement in convergence and accuracy with adaptive meshes. (A.C.A.S.) [pt
SEAWAT-based simulation of axisymmetric heat transport.
Vandenbohede, Alexander; Louwyck, Andy; Vlamynck, Nele
2014-01-01
Simulation of heat transport has its applications in geothermal exploitation of aquifers and the analysis of temperature dependent chemical reactions. Under homogeneous conditions and in the absence of a regional hydraulic gradient, groundwater flow and heat transport from or to a well exhibit radial symmetry, and governing equations are reduced by one dimension (1D) which increases computational efficiency importantly. Solute transport codes can simulate heat transport and input parameters may be modified such that the Cartesian geometry can handle radial flow. In this article, SEAWAT is evaluated as simulator for heat transport under radial flow conditions. The 1971, 1D analytical solution of Gelhar and Collins is used to compare axisymmetric transport with retardation (i.e., as a result of thermal equilibrium between fluid and solid) and a large diffusion (conduction). It is shown that an axisymmetric simulation compares well with a fully three dimensional (3D) simulation of an aquifer thermal energy storage systems. The influence of grid discretization, solver parameters, and advection solution is illustrated. Because of the high diffusion to simulate conduction, convergence criterion for heat transport must be set much smaller (10(-10) ) than for solute transport (10(-6) ). Grid discretization should be considered carefully, in particular the subdivision of the screen interval. On the other hand, different methods to calculate the pumping or injection rate distribution over different nodes of a multilayer well lead to small differences only. © 2013, National Ground Water Association.
Analytic modeling of axisymmetric disruption halo currents
International Nuclear Information System (INIS)
Humphreys, D.A.; Kellman, A.G.
1999-01-01
Currents which can flow in plasma facing components during disruptions pose a challenge to the design of next generation tokamaks. Induced toroidal eddy currents and both induced and conducted poloidal ''halo'' currents can produce design-limiting electromagnetic loads. While induction of toroidal and poloidal currents in passive structures is a well-understood phenomenon, the driving terms and scalings for poloidal currents flowing on open field lines during disruptions are less well established. A model of halo current evolution is presented in which the current is induced in the halo by decay of the plasma current and change in enclosed toroidal flux while being convected into the halo from the core by plasma motion. Fundamental physical processes and scalings are described in a simplified analytic version of the model. The peak axisymmetric halo current is found to depend on halo and core plasma characteristics during the current quench, including machine and plasma dimensions, resistivities, safety factor, and vertical stability growth rate. Two extreme regimes in poloidal halo current amplitude are identified depending on the minimum halo safety factor reached during the disruption. A 'type I' disruption is characterized by a minimum safety factor that remains relatively high (typically 2 - 3, comparable to the predisruption safety factor), and a relatively low poloidal halo current. A 'type II' disruption is characterized by a minimum safety factor comparable to unity and a relatively high poloidal halo current. Model predictions for these two regimes are found to agree well with halo current measurements from vertical displacement event disruptions in DIII-D [T. S. Taylor, K. H. Burrell, D. R. Baker, G. L. Jackson, R. J. La Haye, M. A. Mahdavi, R. Prater, T. C. Simonen, and A. D. Turnbull, open-quotes Results from the DIII-D Scientific Research Program,close quotes in Proceedings of the 17th IAEA Fusion Energy Conference, Yokohama, 1998, to be published in
Computational method for an axisymmetric laser beam scattered by a body of revolution
International Nuclear Information System (INIS)
Combis, P.; Robiche, J.
2005-01-01
An original hybrid computational method to solve the 2-D problem of the scattering of an axisymmetric laser beam by an arbitrary-shaped inhomogeneous body of revolution is presented. This method relies on a domain decomposition of the scattering zone into concentric spherical radially homogeneous sub-domains and on an expansion of the angular dependence of the fields on the Legendre polynomials. Numerical results for the fields obtained for various scatterers geometries are presented and analyzed. (authors)
Li, Xiaofan; Nie, Qing
2009-01-01
Many applications in materials involve surface diffusion of elastically stressed solids. Study of singularity formation and long-time behavior of such solid surfaces requires accurate simulations in both space and time. Here we present a high-order boundary integral method for an elastically stressed solid with axi-symmetry due to surface diffusions. In this method, the boundary integrals for isotropic elasticity in axi-symmetric geometry are approximated through modified alternating quadratu...
Numerical solutions of ICRF fields in axisymmetric mirrors
International Nuclear Information System (INIS)
Phillips, M.W.
1985-01-01
The results of a new numerical code called GARFIELD (Grumman Aerospace Rf Field code) that calculates ICRF Fields in axisymmetric mirror geometry (such as the central cell of a tandem mirror or an RF test stand) are presented. The code solves the electromagnetic wave equation using a cold plasma dispersion relation with a small collision frequency to simulate absorption. The purpose of the calculation is to examine how ICRF wave structure and propagation is effected by the axial variation of the magnetic field in a mirror for various antenna designs. In the code the wave equation is solved in flux coordinates using a finite element method. This should allow more complex dielectric tensors to be modeled in the future. The resulting matrix is solved iteratively, to maximize the allowable size of the spatial grid. Results for a typical antenna array in a simple mirror will be shown
Supersonic quasi-axisymmetric vortex breakdown
Kandil, Osama A.; Kandil, Hamdy A.; Liu, C. H.
1991-01-01
An extensive computational study of supersonic quasi-axisymmetric vortex breakdown in a configured circular duct is presented. The unsteady, compressible, full Navier-Stokes (NS) equations are used. The NS equations are solved for the quasi-axisymmetric flows using an implicit, upwind, flux difference splitting, finite volume scheme. The quasi-axisymmetric solutions are time accurate and are obtained by forcing the components of the flowfield vector to be equal on two axial planes, which are in close proximity of each other. The effect of Reynolds number, for laminar flows, on the evolution and persistence of vortex breakdown, is studied. Finally, the effect of swirl ration at the duct inlet is investigated.
Iversen, Birger
1992-01-01
Although it arose from purely theoretical considerations of the underlying axioms of geometry, the work of Einstein and Dirac has demonstrated that hyperbolic geometry is a fundamental aspect of modern physics
Energy Technology Data Exchange (ETDEWEB)
Ruiz, H S; BadIa-Majos, A [Departamento de Fisica de la Materia Condensada and Instituto de Ciencia de Materiales de Aragon (ICMA), Universidad de Zaragoza-CSIC, MarIa de Luna 3, E-50018 Zaragoza (Spain); Lopez, C, E-mail: hsruizr@unizar.es [Departamento de Matematicas, Universidad de Alcala de Henares, E-28871 Alcala de Henares (Spain)
2011-11-15
Relying on our theoretical approach for the superconducting critical state problem in 3D magnetic field configurations, we present an exhaustive analysis of the electrodynamic response for the so-called longitudinal transport problem in the slab geometry. A wide set of experimental conditions have been considered, including modulation of the applied magnetic field either perpendicular or parallel (longitudinal) to the transport current density. The main objective of our work was to characterize the role of the macroscopic material law that should properly account for the underlying mechanisms of flux cutting and depinning. The intriguing occurrence of negative current patterns and the enhancement of the transport current flow along the center of the superconducting sample are reproduced as a straightforward consequence of the magnetically induced internal anisotropy. Moreover, we show that, related to a maximal projection of the current density vector onto the local magnetic field, a maximal transport current density occurs somewhere within the sample. The elusive measurement of the flux cutting threshold (critical value of such parallel component J{sub c||}) is suggested on the basis of local measurements of the transport current density. Finally, we show that a high correlation exists between the evolution of the transport current density and the appearance of paramagnetic peak structures in terms of the applied longitudinal magnetic field.
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.
International Nuclear Information System (INIS)
Beckhoff, B.; Ulm, G.; Pepponi, G.; Streli, C.; Wobrauschek, P.; Fabry, L.; Pahlke, S.
2000-01-01
A set of initial TXRF experiments were conducted at the PTB plane grating monochromator beamline for undulator radiation at the electron storage ring BESSY II allowing for exciting energies between 0.1 keV and 1.9 keV. Here, the lower limits of detection of TXRF analysis investigated for some low Z elements such as C, N, 0, Al, Mg and Na in two different detection geometries for various excitation modes. Compared to ordinary XRF geometries involving large incident angles, the TXRF variant offers also at low excitation energies drastically reduced background contributions due to the small penetration depth caused by the total reflection of the incident beam at the polished surface of a flat specimen carrier such as a silicon wafer. For the sake of an application-oriented TXRF approach, droplet samples on Si wafer surfaces were prepared by Wacker Siltronic and investigated in the TXRF irradiation chamber of the Atominstitut offering a semiconductor detector with a thin entrance window that was only 300 nm thick. (author)
Boundary element method for internal axisymmetric flow
Directory of Open Access Journals (Sweden)
Gokhman Alexander
1999-01-01
Full Text Available We present an accurate fast method for the computation of potential internal axisymmetric flow based on the boundary element technique. We prove that the computed velocity field asymptotically satisfies reasonable boundary conditions at infinity for various types of inlet/exit. Computation of internal axisymmetric potential flow is an essential ingredient in the three-dimensional problem of computation of velocity fields in turbomachines. We include the results of a practical application of the method to the computation of flow in turbomachines of Kaplan and Francis types.
Nakonieczna, Anna; Yeom, Dong-han
2016-05-01
Investigating the dynamics of gravitational systems, especially in the regime of quantum gravity, poses a problem of measuring time during the evolution. One of the approaches to this issue is using one of the internal degrees of freedom as a time variable. The objective of our research was to check whether a scalar field or any other dynamical quantity being a part of a coupled multi-component matter-geometry system can be treated as a `clock' during its evolution. We investigated a collapse of a self-gravitating electrically charged scalar field in the Einstein and Brans-Dicke theories using the 2+2 formalism. Our findings concentrated on the spacetime region of high curvature existing in the vicinity of the emerging singularity, which is essential for the quantum gravity applications. We investigated several values of the Brans-Dicke coupling constant and the coupling between the Brans-Dicke and the electrically charged scalar fields. It turned out that both evolving scalar fields and a function which measures the amount of electric charge within a sphere of a given radius can be used to quantify time nearby the singularity in the dynamical spacetime part, in which the apparent horizon surrounding the singularity is spacelike. Using them in this respect in the asymptotic spacetime region is possible only when both fields are present in the system and, moreover, they are coupled to each other. The only nonzero component of the Maxwell field four-potential cannot be used to quantify time during the considered process in the neighborhood of the whole central singularity. None of the investigated dynamical quantities is a good candidate for measuring time nearby the Cauchy horizon, which is also singular due to the mass inflation phenomenon.
Feedback stabilization of axisymmetric modes in tokamaks
International Nuclear Information System (INIS)
Jardin, S.C.; Larrabee, D.A.
1982-01-01
Noncircular tokamak plasmas can be unstable to ideal MHD axisymmetric instabilities. Passive conductors with finite resistivity will at best slow down these instabilities to the resistive (L/R) time of the conductors. An active feedback system far from the plasma which responds on this resistive time can stabilize the system provided its mutual inductance with the passive coils is small enough
Magneto-hydrodynamically stable axisymmetric mirrorsa)
Ryutov, D. D.; Berk, H. L.; Cohen, B. I.; Molvik, A. W.; Simonen, T. C.
2011-09-01
Making axisymmetric mirrors magnetohydrodynamically (MHD) stable opens up exciting opportunities for using mirror devices as neutron sources, fusion-fission hybrids, and pure-fusion reactors. This is also of interest from a general physics standpoint (as it seemingly contradicts well-established criteria of curvature-driven instabilities). The axial symmetry allows for much simpler and more reliable designs of mirror-based fusion facilities than the well-known quadrupole mirror configurations. In this tutorial, after a summary of classical results, several techniques for achieving MHD stabilization of the axisymmetric mirrors are considered, in particular: (1) employing the favorable field-line curvature in the end tanks; (2) using the line-tying effect; (3) controlling the radial potential distribution; (4) imposing a divertor configuration on the solenoidal magnetic field; and (5) affecting the plasma dynamics by the ponderomotive force. Some illuminative theoretical approaches for understanding axisymmetric mirror stability are described. The applicability of the various stabilization techniques to axisymmetric mirrors as neutron sources, hybrids, and pure-fusion reactors are discussed; and the constraints on the plasma parameters are formulated.
Magneto-hydrodynamically stable axisymmetric mirrors
Energy Technology Data Exchange (ETDEWEB)
Ryutov, D. D.; Cohen, B. I.; Molvik, A. W. [Lawrence Livermore National Laboratory, Livermore, California 94551 (United States); Berk, H. L. [University of Texas, Austin, Texas 78712 (United States); Simonen, T. C. [University of California, Berkeley, California 94720 (United States)
2011-09-15
Making axisymmetric mirrors magnetohydrodynamically (MHD) stable opens up exciting opportunities for using mirror devices as neutron sources, fusion-fission hybrids, and pure-fusion reactors. This is also of interest from a general physics standpoint (as it seemingly contradicts well-established criteria of curvature-driven instabilities). The axial symmetry allows for much simpler and more reliable designs of mirror-based fusion facilities than the well-known quadrupole mirror configurations. In this tutorial, after a summary of classical results, several techniques for achieving MHD stabilization of the axisymmetric mirrors are considered, in particular: (1) employing the favorable field-line curvature in the end tanks; (2) using the line-tying effect; (3) controlling the radial potential distribution; (4) imposing a divertor configuration on the solenoidal magnetic field; and (5) affecting the plasma dynamics by the ponderomotive force. Some illuminative theoretical approaches for understanding axisymmetric mirror stability are described. The applicability of the various stabilization techniques to axisymmetric mirrors as neutron sources, hybrids, and pure-fusion reactors are discussed; and the constraints on the plasma parameters are formulated.
The spectrum of axisymmetric torsional Alfven waves
International Nuclear Information System (INIS)
Sy, W.N.
1977-03-01
The spectrum of axisymmetric torsional Alfven waves propagating in a cylindrical, non-uniform, resistive plasma waveguide has been analysed by a method of singular perturbations. A simple condition has been derived which predicts whether the spectrum is continuous or discrete under given physical conditions. Application of this result to resolve an apparent discrepancy in experimental observations is briefly discussed. (Author)
Axisymmetric solution with charge in general relativity
International Nuclear Information System (INIS)
Arutyunyan, G.G.; Papoyan, V.V.
1989-01-01
The possibility of generating solutions to the equations of general relativity from known solutions of the generalized theory of gravitation and vice versa is proved. An electrovac solution to Einstein's equations that describes a static axisymmetric gravitational field is found. 14 refs
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
Energy Technology Data Exchange (ETDEWEB)
Stacey, W. M. [Georgia Institute of Technology, Atlanta, Georgia 30332 (United States); Bae, C. [National Fusion Research Institute, Daejoen (Korea, Republic of)
2015-06-15
A systematic formalism for the calculation of rotation in non-axisymmetric tokamaks with 3D magnetic fields is described. The Braginskii Ωτ-ordered viscous stress tensor formalism, generalized to accommodate non-axisymmetric 3D magnetic fields in general toroidal flux surface geometry, and the resulting fluid moment equations provide a systematic formalism for the calculation of toroidal and poloidal rotation and radial ion flow in tokamaks in the presence of various non-axisymmetric “neoclassical toroidal viscosity” mechanisms. The relation among rotation velocities, radial ion particle flux, ion orbit loss, and radial electric field is discussed, and the possibility of controlling these quantities by producing externally controllable toroidal and/or poloidal currents in the edge plasma for this purpose is suggested for future investigation.
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
From x-ray telescopes to neutron scattering: Using axisymmetric mirrors to focus a neutron beam
International Nuclear Information System (INIS)
Khaykovich, B.; Gubarev, M.V.; Bagdasarova, Y.; Ramsey, B.D.; Moncton, D.E.
2011-01-01
We demonstrate neutron beam focusing by axisymmetric mirror systems based on a pair of mirrors consisting of a confocal ellipsoid and hyperboloid. Such a system, known as a Wolter mirror configuration, is commonly used in X-ray telescopes. The axisymmetric Wolter geometry allows nesting of several mirror pairs to increase collection efficiency. We implemented a system containing four nested Ni mirror pairs, which was tested by the focusing of a polychromatic neutron beam at the MIT Reactor. In addition, we have carried out extensive ray-tracing simulations of the mirrors and their performance in different situations. The major advantages of the Wolter mirrors are nesting for large angular collection and aberration-free performance. We discuss how these advantages can be utilized to benefit various neutron scattering methods, such as imaging, SANS, and time-of-flight spectroscopy.
Numerical description of cavitation on axisymmetric bodies
Energy Technology Data Exchange (ETDEWEB)
Hickox, C.E.; Hailey, C.E.; Wolfe, W.P.; Watts, H.A.; Gross, R.J.; Ingber, M.S.
1988-01-01
This paper reports on ongoing studies which are directed toward the development of predictive techniques for the modeling of steady cavitation on axisymmetric bodies. The primary goal of the modeling effort is the prediction of cavity shape and pressure distribution from which forces and moments can be calculated. Here we present an overview of the modeling techniques developed and compare predictions with experimental data obtained from water tunnel tests for both limited and supercavitation. 14 refs., 4 figs.
Pottmann, Helmut; Eigensatz, Michael; Vaxman, Amir; Wallner, Johannes
2014-01-01
Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural geometry, meanwhile contains a great wealth of individual contributions which are relevant in various fields. For mathematicians, the relation to discrete differential geometry is significant, in particular the integrable system viewpoint. Besides, new application contexts have become available for quite some old-established concepts. Regarding graphics and geometry processing, architectural geometry yields interesting new questions but also new objects, e.g. replacing meshes by other combinatorial arrangements. Numerical optimization plays a major role but in itself would be powerless without geometric understanding. Summing up, architectural geometry has become a rewarding field of study. We here survey the main directions which have been pursued, we show real projects where geometric considerations have played a role, and we outline open problems which we think are significant for the future development of both theory and practice of architectural geometry.
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.
Energy Technology Data Exchange (ETDEWEB)
Rasmussen, N.G. [Nanoscience Center, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen Ø (Denmark); Simeoni, G.G., E-mail: ggsimeoni@outlook.com [Heinz Maier-Leibnitz Zentrum (MLZ) and Physics Department, Technical University of Munich, D-85748 Garching (Germany); Lefmann, K. [Nanoscience Center, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen Ø (Denmark)
2016-04-21
A dedicated beam-focusing device has been designed for the direct geometry thermal-cold neutron time-of-flight spectrometer TOFTOF at the neutron facility FRM II (Garching, Germany). The prototype, based on the compressed Archimedes' mirror concept, benefits from the adaptive-optics technology (adjustable supermirror curvature) and the compact size (only 0.5 m long). We have simulated the neutron transport across the entire guide system. We present a detailed computer characterization of the existing device, along with the study of the factors mostly influencing the future improvement. We have optimized the simulated prototype as a function of the neutron wavelength, accounting also for all relevant features of a real instrument like the non-reflecting side edges. The results confirm the “chromatic” displacement of the focal point (flux density maximum) at fixed supermirror curvature, and the ability of a variable curvature to keep the focal point at the sample position. Our simulations are in excellent agreement with theoretical predictions and the experimentally measured beam profile. With respect to the possibility of a further upgrade, we find that supermirror coatings with m-values higher than 3.5 would have only marginal influence on the optimal behaviour, whereas comparable spectrometers could take advantage of longer focusing segments, with particular impact for the thermal region of the neutron spectrum.
Axisymmetric vibrations of thin shells of revolution
International Nuclear Information System (INIS)
Suzuki, Katsuyoshi; Kikuchi, Norio; Kosawada, Tadashi; Takahashi, Shin
1983-01-01
The problem of free vibration of axisymmetric shells of revolution is important in connection with the design of pressure vessels, chemical equipment, aircrafts, structures and so on. In this study, the axisymmetrical vibration of a thin shell of revolution having a constant curvature in meridian direction was analyzed by thin shell theory. First, the Lagrangian during one period of the vibration of a shell of revolution was determined by the primary approximate theory of Love, and the vibration equations and boundary conditions were derived from its stopping condition. The vibration equations were strictly analyzed by using the series solution. The basic equations for the strain and strain energy of a shell were based on those of Novozhilov. As the examples of numerical calculation, the natural frequency and vibration mode of the symmetrical shells of revolution fixed at both ends and supported at both ends were determined, and their characteristics were clarified. The theory and the numerical calculation ore described. Especially in the frequency curves, the waving phenomena were observed frequently, which were not seen in non-axisymmetric vibration, accordingly also the vibration mode changed in complex state on the frequency curves of same order. The numerical calculation was carried out in the large computer center in Tohoku University. (Kako, I.)
Axisymmetric ideal magnetohydrodynamic equilibria with incompressible flows
International Nuclear Information System (INIS)
Tasso, H.; Throumoulopoulos, G.N.
1997-12-01
It is shown that the ideal MHD equilibrium states of an axisymmetric plasma with incompressible flows are governed by an elliptic partial differential equation for the poloidal magnetic flux function ψ containing five surface quantities along with a relation for the pressure. Exact equilibria are constructed including those with non vanishing poloidal and toroidal flows and differentially varying radial electric fields. Unlike the case in cylindrical incompressible equilibria with isothermal magnetic surfaces which should have necessarily circular cross sections [G. N. Throumoulopoulos and H. Tasso, Phys. Plasmas 4, 1492 (1997)], no restriction appears on the shapes of the magnetic surfaces in the corresponding axisymmetric equilibria. The latter equilibria satisfy a set of six ordinary differential equations which for flows parallel to the magnetic field B can be solved semianalytically. In addition, it is proved the non existence of incompressible axisymmetric equilibria with (a) purely poloidal flows and (b) non-parallel flows with isothermal magnetic surfaces and vertical stroke B vertical stroke = vertical stroke B vertical stroke (ψ) (omnigenous equilibria). (orig.)
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
Kemnitz, Arnfried
Der Grundgedanke der Analytischen Geometrie besteht darin, dass geometrische Untersuchungen mit rechnerischen Mitteln geführt werden. Geometrische Objekte werden dabei durch Gleichungen beschrieben und mit algebraischen Methoden untersucht.
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.
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...
BEYOND THE MALTESE CROSS: GEOMETRY OF TURBULENCE BETWEEN 0.2 AND 1 au
Energy Technology Data Exchange (ETDEWEB)
Verdini, Andrea [Lesia, Observatoire de Paris, Muedon (France); LPP, Ecole Polytechnique, Palaiseau (France); Université Pierre et Marie Curie, Paris (France); Grappin, Roland [LPP, Ecole Polytechnique, Palaiseau (France)
2016-11-10
The spectral anisotropy of turbulent structures has been measured in the solar wind since 1990, relying on the assumption of axisymmetry about the mean magnetic field, B {sub 0}. However, several works indicate that this hypothesis might be partially wrong, thus raising two questions: (i) is it correct to interpret measurements at 1 au (the so-called Maltese cross) in term of a sum of slab and two-dimensional (2D) turbulence; and (ii) what information is really contained in the Maltese cross? We solve direct numerical simulations of the magnetohydrodynamic equations including the transverse stretching exerted by the solar wind flow and study the genuine 3D anisotropy of turbulence as well as that one resulting from the assumption of axisymmetry about B {sub 0}. We show that the evolution of the turbulent spectrum from 0.2 to 1 au depends strongly on its initial anisotropy. An axisymmetric spectrum with respect to B {sub 0} keeps its axisymmetry, i.e., resists stretching perpendicular to radial, while an isotropic spectrum becomes essentially axisymmetric with respect to the radial direction. We conclude that close to the Sun, slow-wind turbulence has a spectrum that is axisymmetric around B {sub 0} and the measured 2D component at 1 au describes the real shape of turbulent structures. In contrast, fast-wind turbulence has a more isotropic spectrum at the source and becomes radially symmetric at 1 au. Such structure is hidden by the symmetrization applied to the data that instead returns a slab geometry.
Low Cost Method of Manufacturing Cooled Axisymmetric Scramjets, Phase I
National Aeronautics and Space Administration — Scramjet engine developers are working on advanced axisymmetric engine concepts that may not be feasible due to limitations of currently available manufacturing...
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
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
Connes, Alain
1994-01-01
This English version of the path-breaking French book on this subject gives the definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics developed by Alain Connes. Profusely illustrated and invitingly written, this book is ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics, quantization, and elementary particles and fields.Key Features* First full treatment of the subject and its applications* Written by the pioneer of this field* Broad applications in mathemat
Reversed straining in axisymmetric compression test
DEFF Research Database (Denmark)
Arentoft, Mogens; Wanheim, Tarras; Lindegren, Maria
2005-01-01
A large group of the cold forging processes is carried out in a thick – walled container with the deformation force transmitted through a punch moving axially in the container. The work piece, being entrapped between punch and container will expand and exert a radial pressure resulting in an expa...... to simulate these conditions a reversed axisymmetrical material tester is designed and constructed. Three different materials were tested, aluminum alloy AA6082, technically pure copper (99.5%) and cold forging steel Ma8, at different temperatures found during cold forging....
An axisymmetric inertia-gravity wave generator
Maurer, P.; Ghaemsaidi, S. J.; Joubaud, S.; Peacock, T.; Odier, P.
2017-10-01
There has been a rich interplay between laboratory experimental studies of internal waves and advancing understanding of their role in the ocean and atmosphere. In this study, we present and demonstrate the concept for a new form of laboratory internal wave generator that can excite axisymmetric wave fields of arbitrary radial structure. The construction and operation of the generator are detailed, and its capabilities are demonstrated through a pair of experiments using a Bessel function and a bourrelet (i.e., ring-shaped) configuration. The results of the experiments are compared with the predictions of an accompanying analytical model.
Calculation of rf fields in axisymmetric cavities
International Nuclear Information System (INIS)
Iwashita, Y.
1985-01-01
A new code, PISCES, has been developed for calculating a complete set of rf electromagnetic modes in an axisymmetric cavity. The finite-element method is used with up to third-order shape functions. Although two components are enough to express these modes, three components are used as unknown variables to take advantage of the symmetry of the element matrix. The unknowns are taken to be either the electric field components or the magnetic field components. The zero-divergence condition will be satisfied by the shape function within each element
Numerical determination of axisymmetric toroidal magnetohydrodynamic equilibria
International Nuclear Information System (INIS)
Johnson, J.L.; Dalhed, H.E.; Greene, J.M.
1978-07-01
Numerical schemes for the determination of stationary axisymmetric toroidal equilibria appropriate for modeling real experimental devices are given. Iterative schemes are used to solve the elliptic nonlinear partial differential equation for the poloidal flux function psi. The principal emphasis is on solving the free boundary (plasma-vacuum interface) equilibrium problem where external current-carrying toroidal coils support the plasma column, but fixed boundary (e.g., conducting shell) cases are also included. The toroidal current distribution is given by specifying the pressure and either the poloidal current or the safety factor profiles as functions of psi. Examples of the application of the codes to tokamak design at PPPL are given
Ideal magnetohydrodynamic stability of axisymmetric mirrors
International Nuclear Information System (INIS)
D'Ippolito, D.A.; Hafizi, B.; Myra, J.R.
1982-01-01
The governing partial differential equation for general mode-number pressure-driven ballooning modes in a long-thin, axisymmetric plasma is derived within the context of ideal magnetohydrodynamics. It is shown that the equation reduces in special limits to the Hain--Luest equation, the high-m diffuse p(psi) ballooning equation, and the low-m sharp-boundary equation. A low-β analytic solution of the full partial differential equation is presented for quasiflute modes in an idealized tandem mirror model to elucidate the relationship of the various limiting cases
Topological fluid mechanics of Axisymmetric Flow
DEFF Research Database (Denmark)
Brøns, Morten
1998-01-01
Topological fluid mechanics in the sense of the present paper is the study and classification of flow patterns close to a critical point. Here we discuss the topology of steady viscous incompressible axisymmetric flows in the vicinity of the axis. Following previous studies the velocity field v...... to the authors knowledge has not been used systematically to high orders in topological fluid mechanics. We compare the general results with experimental and computational results on the Vogel-Ronneberg flow. We show that the topology changes observed when recirculating bubbles on the vortex axis are created...
Static axisymmetric discs and gravitational collapse
Energy Technology Data Exchange (ETDEWEB)
Chamorro, A.; Gregory, R.; Stewart, J.M.
1987-09-08
Regular static axisymmetric vacuum solutions of Einstein's field equations representing the exterior field of a finite thin disc are found. These are used to describe the slow collapse of a disc-like object. If no conditions are placed on the matter, a naked singularity is formed and the cosmic censorship hypothesis would be violated. Imposition of the weak energy condition, however, prevents slow collapse to a singularity and preserves the validity of this hypothesis. The validity of the hoop conjecture is also discussed.
Indian Academy of Sciences (India)
mathematicians are trained to use very precise language, and so find it hard to simplify and state .... thing. If you take a plane on which there are two such triangles which enjoy the above ... within this geometry to simplify things if needed.
Geometry -----------~--------------RESONANCE
Indian Academy of Sciences (India)
Parallel: A pair of lines in a plane is said to be parallel if they do not meet. Mathematicians were at war ... Subsequently, Poincare, Klein, Beltrami and others refined non-. Euclidean geometry. ... plane divides the plane into two half planes and.
Fast axisymmetric stability calculations using variational techniques
International Nuclear Information System (INIS)
Haney, S.W., Pearlstein, L.D.; Bulmer, R.H.
1991-01-01
A procedure for treating the axisymmetric (n = 0) stability of diverted plasmas in the presence of arbitrary, but toroidally symmetric, structures and active feedback circuits has been developed and implemented as a module in the TEQ free-boundary equilibrium code. This procedure is based on a variational solution of the ideal MHD normal mode equations. Inertia is ordered small but provides a constraint to allow the calculation of the poloidal and toroidal components of the plasma displacement. Feedback based on flux loop measurements is handled by introducing an adjoint system into the variational principle. Approximately 200 trial functions for the radial component of the plasma displacement and 200 magnetic surfaces are employed to obtain highly accurate estimates of the passive growth rate and the non-rigid eigenfunction. Nevertheless, the method is extremely fast: typically 10-20 sec of Cray 2 CPU time are required to analyze a realistic tokamak configuration. This speed, along with the direct coupling to the MHD equilibrium solver, allows interactive investigations of tokamak axisymmetric stability. Benchmarks with TSC and GATO are presented along with parameter scans for ITER and BPX. The results emphasize the importance of considering non-rigid mode effects which for ITER, yield higher nominal growth rates (non-rigid: 45 Hz, rigid: 25 Hz) and atypical internal inductance dependence (smaller l i more unstable)
Axisymmetric vibrations of thick shells of revolution
International Nuclear Information System (INIS)
Suzuki, Katsuyoshi; Kosawada, Tadashi; Takahashi, Shin
1983-01-01
Axisymmetric shells of revolution are used for chemical plants, nuclear power plants, aircrafts, structures and so on, and the elucidation of their free vibration is important for the design. In this study, the axisymmetric vibration of a barrel-shaped shell was analyzed by the modified thick shell theory. The Lagrangian during one period of the vibration of a shell of revolution was determined, and from its stopping condition, the vibration equations and the boundary conditions were derived. The vibration equations were analyzed strictly by using the series solution. Moreover, the basic equations for the strain of a shell and others were based on those of Love. As the examples of numerical calculation, the natural frequency and vibration mode of the symmetrical shells of revolution fixed at both ends and supported at both ends were determined, and their characteristics were clarified. By comparing the results of this study with the results by thin shell theory, the effects of shearing deformation and rotary inertia on the natural frequency and vibration mode were clarified. The theoretical analysis and the numerical calculation are described. The effects of shearing deformation and rotary inertia on the natural frequency became larger in the higher order vibration. The vibration mode did not much change in both theories. (Kako, I.)
Multitude scaling laws in axisymmetric turbulent wake
Layek, G. C.; Sunita
2018-03-01
We establish theoretically multitude scaling laws of a self-similar (statistical) axisymmetric turbulent wake. At infinite Reynolds number limit, the flow evolves as general power law and a new exponential law of streamwise distance, consistent with the criterion of equilibrium similarity hypothesis. We found power law scalings for components of the homogeneous dissipation rate (ɛ) obeying the non-Richardson-Kolmogorov cascade as ɛu˜ku3 /2/(l R elm ) , ɛv˜kv3 /2/l , kv˜ku/R el2 m, 0 stress, l is the local length scale, and Rel is the Reynolds number. The Richardson-Kolmogorov cascade corresponds to m = 0. For m ≈ 1, the power law agrees with non-equilibrium scaling laws observed in recent experiments of the axisymmetric wake. On the contrary, the exponential scaling law follows the above dissipation law with different regions of existence for power index m = 3. At finite Reynolds number with kinematic viscosity ν, scalings obey the dissipation laws ɛu ˜ νku/l2 and ɛv ˜ νkv/l2 with kv˜ku/R eln. The value of n is preferably 0 and 2. Different possibilities of scaling laws and symmetry breaking process are discussed at length.
Axisymmetric modeling of prestressing tendons in nuclear containment dome
Energy Technology Data Exchange (ETDEWEB)
Jeon, Se-Jin [DAEWOO E and C, Institute of Construction Technology, 60 Songjook-dong, Jangan-gu, Suwon, Kyonggi 440-210 (Korea, Republic of)]. E-mail: jsj@dwconst.co.kr; Chung, Chul-Hun [Department of Civil and Environmental Engineering, Dankook University, San 8, Hannam-dong, Youngsan-gu, Seoul 140-714 (Korea, Republic of)
2005-12-15
Simple axisymmetric modeling of a nuclear containment building has been often employed in practice to estimate structural behavior for the axisymmetric loadings such as internal pressure. In this case, the prestressing tendons placed in the containment dome should be axisymmetrically approximated, since most dome tendons are not arranged in an axisymmetric manner. Some procedures are proposed that can realistically implement the actual three-dimensional tendon stiffness and prestressing effect into the axisymmetric model. Prestressing tendons, which are arranged in two or three ways depending on a containment type, are converted into the equivalent layer to consider the stiffness contribution in meridional and hoop directions. In order to reflect the prestressing effect, the equivalent load method and the initial stress method are devised, respectively, and the corresponding loads or stresses are derived in terms of the axisymmetric model. The proposed schemes are verified through some numerical examples comparing the results of the axisymmetric models to those of the actual three-dimensional model. The examples show that the proper level of the prestressing in the hoop direction of the axisymmetric dome plays an important role in tracing the actual behavior induced by the prestressing. Finally, some correction factors are discussed that can further improve the analysis results.
Axisymmetric multiphase lattice Boltzmann method for generic equations of state
Reijers, S.A.; Gelderblom, H.; Toschi, F.
2016-01-01
We present an axisymmetric lattice Boltzmann model based on the Kupershtokh et al. multiphase model that is capable of solving liquid–gas density ratios up to 103. Appropriate source terms are added to the lattice Boltzmann evolution equation to fully recover the axisymmetric multiphase conservation
Relativistic equations for axisymmetric gravitational collapse with escaping neutrinos
International Nuclear Information System (INIS)
Patel, M.D.
1979-01-01
Einstein's field equations for the dynamics of a self-gravitating axially symmetric source of a perfect fluid, presented by Chandrasekhar and Friedman (1964), are modified to allow emission of neutrinos. The boundary conditions at the outer surface of the radiating axisymmetric source are obtained by matching to an exterior solution of an axisymmetric rotating, radiating core. (auth.)
Axisymmetric modeling of prestressing tendons in nuclear containment dome
International Nuclear Information System (INIS)
Jeon, Se-Jin; Chung, Chul-Hun
2005-01-01
Simple axisymmetric modeling of a nuclear containment building has been often employed in practice to estimate structural behavior for the axisymmetric loadings such as internal pressure. In this case, the prestressing tendons placed in the containment dome should be axisymmetrically approximated, since most dome tendons are not arranged in an axisymmetric manner. Some procedures are proposed that can realistically implement the actual three-dimensional tendon stiffness and prestressing effect into the axisymmetric model. Prestressing tendons, which are arranged in two or three ways depending on a containment type, are converted into the equivalent layer to consider the stiffness contribution in meridional and hoop directions. In order to reflect the prestressing effect, the equivalent load method and the initial stress method are devised, respectively, and the corresponding loads or stresses are derived in terms of the axisymmetric model. The proposed schemes are verified through some numerical examples comparing the results of the axisymmetric models to those of the actual three-dimensional model. The examples show that the proper level of the prestressing in the hoop direction of the axisymmetric dome plays an important role in tracing the actual behavior induced by the prestressing. Finally, some correction factors are discussed that can further improve the analysis results
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...
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.)
Abbas, S. S.; Nasif, M. S.; Said, M. A. M.; Kadhim, S. K.
2017-10-01
Structural stresses developed in an artificial bileaflet mechanical heart valve (BMHV) due to pulsed blood flow may cause valve failure due to yielding. In this paper, von-Mises stresses are computed and compared for BMHV placed in two types of aortic root geometries that are aortic root with axisymmetric sinuses and with axisymmetric bulb, at different physiological blood flow rates. With BMHV placed in an aortic root with axisymmetric sinuses, the von-Mises stresses developed in the valve were found to be up to 47% higher than BMHV placed in aortic root with axisymmetric bulb under similar physiological conditions. High velocity vectors and therefore high von-Mises stresses have been observed for BMHV placed in aortic root with axisymmetric sinuses, that can lead to valve failure.
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...
Multispecies transport theory for axisymmetric rotating plasmas
International Nuclear Information System (INIS)
Tessarotto, M.; White, R.B.
1992-01-01
A reduced gyrokinetic equation is derived for a multi-species toroidal axisymmetric plasma with arbitrary toroidal differential rotation speeds and in the presence of a finite induced electric field. The kinetic equation obtained, extending previous results obtained by Hinton and Wong and by Catto, Bernstein and Tessarotto, has a form suited for transport applications, via variational techniques; in particular it exhibits the feature that all source terms, including the Spitzer source term, carrying the contribution due to the inductive electric field, appear to be acted upon by the collision operator. Moreover, the equation displays a new contribution due to ''explicit'' velocity perturbations, here proven to be consistent with transport ordering, whose evaluation appears relevant for transport calculations. In addition, general expressions are obtained for the neoclassical fluxes in terms of a variational principle, as well as for the classical ones, retaining, in both cases, the contributions due to the Spitzer's inductive terms
A Compact Quasi-axisymmetric Stellarator Reactor
International Nuclear Information System (INIS)
Ku, L.P.
2003-01-01
We report the progress made in assessing the potential of compact, quasi-axisymmetric stellarators as power-producing reactors. Using an aspect ratio A=4.5 configuration derived from NCSX and optimized with respect to the quasi-axisymmetry and MHD stability in the linear regime as an example, we show that a reactor of 1 GW(e) maybe realizable with a major radius *8 m. This is significantly smaller than the designs of stellarator reactors attempted before. We further show the design of modular coils and discuss the optimization of coil aspect ratios in order to accommodate the blanket for tritium breeding and radiation shielding for coil protection. In addition, we discuss the effects of coil aspect ratio on the peak magnetic field in the coils
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
Axisymmetric Eigenmodes of Spheroidal Pure Electron Plasmas
Kawai, Yosuke; Saitoh, Haruhiko; Yoshida, Zensho; Kiwamoto, Yasuhito
2010-11-01
The axisymmetric electrostatic eigenmodes of spheroidal pure electron plasmas have been studied experimentally. It is confirmed that the observed spheroidal plasma attains a theoretically expected equilibrium density distribution, with the exception of a low-density halo distribution surrounding the plasma. When the eigenmode frequency observed for the plasma is compared with the frequency predicted by the dispersion relation derived under ideal conditions wherein the temperature is zero and the boundary is located at an infinite distance from the plasma, it is observed that the absolute value of the observed frequency is systematically higher than the theoretical prediction. Experimental examinations and numerical calculations indicate that the upward shift of the eigenmode frequency cannot be accounted for solely by the finite temperature effect, but is significantly affected by image charges induced on the conducting boundary and the resulting distortion of the density profile from the theoretical expectation.
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
Magnetohydrodynamic equilibria and local stability of axisymmetric tokamak plasmas
International Nuclear Information System (INIS)
Peng, Y.K.M.; Dory, R.A.; Nelson, D.B.; Sayer, R.O.
1976-07-01
Axisymmetric magnetohydrodynamic equilibria are evaluated in terms of the Mercier Stability Criterion. The parameters of interest include poloidal beta (β/sub p/), current and pressure profile widths, D-shaped and doublet plasmas with elongation (sigma) and triangularity (delta), and the aspect ratio (A). For marginal local stability, the critical values of β, plasma current, and the safety factor q with fixed toroidal field at the geometric center of the plasma are obtained. It is shown that for a wide range of profiles in a D-shaped plasma with A = 3, the highest critical β occurs at β/sub p/ = 2.4, sigma = 1.65, and delta = 0.5. If the toroidal field at the coil surface is fixed, the highest critical pressure occurs near A approximately 3 to 4, given reasonable distance between the coils and the plasma edge. Calculations for a Doublet II-A plasma with sigma = 3 show that with similar pressure profile the highest critical β occurs at β/sub p/ = 1 and is 84 percent of the highest critical β for the D-shaped plasmas. Critical values of ohmic heating power density are also found to be comparable for the two plasma shapes. A D-shaped plasma with the above parameters is suggested for use in future high-β tokamak devices
Argyres, Philip C.; Lotito, Matteo; Lü, Yongchao; Martone, Mario
2018-02-01
This is the second in a series of three papers on systematic analysis of rank 1 Coulomb branch geometries of four dimensional N = 2 SCFTs. In [1] we developed a strategy for classifying physical rank-1 CB geometries of N = 2 SCFTs. Here we show how to carry out this strategy computationally to construct the Seiberg-Witten curves and one-forms for all the rank-1 SCFTs. Explicit expressions are given for all 28 cases, with the exception of the N f =4 su(2) gauge theory and the E n SCFTs which were constructed in [2, 3] and [4, 5].
Axisymmetric MHD stability of sharp-boundary Tokamaks
International Nuclear Information System (INIS)
Rebhan, E.; Salat, A.
1976-09-01
For a sharp-boundary, constant pressure plasma model of axisymmetric equilibria the MHD stability problem of axisymmetric perturbations is solved by analytic reduction to a one-dimensional problem on the boundary and subsequent numerical treatment, using the energy principle. The stability boundaries are determined for arbitrary aspect ratio, arbitrary βsub(p) and elliptical, triangular and rectangular plasma cross-sections, wall stabilization not being taken into account. It is found that the axisymmetric stability strongly depends on the plasma shape and is almost independent of the safety factor q. (orig.) [de
Axisymmetric Numerical Modeling of Pulse Detonation Rocket Engines
Morris, Christopher I.
2005-01-01
Pulse detonation rocket engines (PDREs) have generated research interest in recent years as a chemical propulsion system potentially offering improved performance and reduced complexity compared to conventional rocket engines. The detonative mode of combustion employed by these devices offers a thermodynamic advantage over the constant-pressure deflagrative combustion mode used in conventional rocket engines and gas turbines. However, while this theoretical advantage has spurred considerable interest in building PDRE devices, the unsteady blowdown process intrinsic to the PDRE has made realistic estimates of the actual propulsive performance problematic. The recent review article by Kailasanath highlights some of the progress that has been made in comparing the available experimental measurements with analytical and numerical models. In recent work by the author, a quasi-one-dimensional, finite rate chemistry CFD model was utilized to study the gasdynamics and performance characteristics of PDREs over a range of blowdown pressure ratios from 1-1000. Models of this type are computationally inexpensive, and enable first-order parametric studies of the effect of several nozzle and extension geometries on PDRE performance over a wide range of conditions. However, the quasi-one-dimensional approach is limited in that it cannot properly capture the multidimensional blast wave and flow expansion downstream of the PDRE, nor can it resolve nozzle flow separation if present. Moreover, the previous work was limited to single-pulse calculations. In this paper, an axisymmetric finite rate chemistry model is described and utilized to study these issues in greater detail. Example Mach number contour plots showing the multidimensional blast wave and nozzle exhaust plume are shown. The performance results are compared with the quasi-one-dimensional results from the previous paper. Both Euler and Navier-Stokes solutions are calculated in order to determine the effect of viscous
Tearing modes in toroidal geometry
International Nuclear Information System (INIS)
Connor, J.W.; Cowley, S.C.; Hastie, R.J.; Hender, T.C.; Hood, A.; Martin, T.J.
1988-01-01
The separation of the cylindrical tearing mode stability problem into a resistive resonant layer calculation and an external marginal ideal magnetohydrodynamic (MHD) calculation (Δ' calculation) is generalized to axisymmetric toroidal geometry. The general structure of this separation is analyzed and the marginal ideal MHD information (the toroidal generalization of Δ') required to discuss stability is isolated. This can then, in principle, be combined with relevant resonant layer calculations to determine tearing mode growth rates in realistic situations. Two examples are given: the first is an analytic treatment of toroidally coupled (m = 1, n = 1) and (m = 2, n = 1) tearing modes in a large aspect ratio torus; the second, a numerical treatment of the toroidal coupling of three tearing modes through finite pressure effects in a large aspect ratio torus. In addition, the use of a coupling integral approach for determining the stability of coupled tearing modes is discussed. Finally, the possibility of using initial value resistive MHD codes in realistic toroidal geometry to determine the necessary information from the ideal MHD marginal solution is discussed
Computational study of axisymmetric modes in noncircular cross section tokamaks
International Nuclear Information System (INIS)
Johnson, J.L.; Chance, M.S.; Greene, J.M.; Grimm, R.C.; Jardin, S.C.; Kerner, W.; Manickam, J.; Weimer, K.E.
1976-09-01
A major computational program to investigate the MHD equilibrium, stability, and nonlinear evolution properties of realistic tokamak configurations is proceeding. Preliminary application is made to the Princeton PDX device. Both axisymmetric (n = 0) modes and kink (n = 1) modes are found; the growth rates depend sensitively on the configuration. A study of the nonlinear evolution of axisymmetric modes in such a device shows that flux conservation in the vacuum region can limit their growth
Hydrodynamic analysis and shape optimization for vertical axisymmetric wave energy converters
Zhang, Wan-chao; Liu, Heng-xu; Zhang, Liang; Zhang, Xue-wei
2016-12-01
The absorber is known to be vertical axisymmetric for a single-point wave energy converter (WEC). The shape of the wetted surface usually has a great influence on the absorber's hydrodynamic characteristics which are closely linked with the wave power conversion ability. For complex wetted surface, the hydrodynamic coefficients have been predicted traditionally by hydrodynamic software based on the BEM. However, for a systematic study of various parameters and geometries, they are too multifarious to generate so many models and data grids. This paper examines a semi-analytical method of decomposing the complex axisymmetric boundary into several ring-shaped and stepped surfaces based on the boundary discretization method (BDM) which overcomes the previous difficulties. In such case, by using the linear wave theory based on eigenfunction expansion matching method, the expressions of velocity potential in each domain, the added mass, radiation damping and wave excitation forces of the oscillating absorbers are obtained. The good astringency of the hydrodynamic coefficients and wave forces are obtained for various geometries when the discrete number reaches a certain value. The captured wave power for a same given draught and displacement for various geometries are calculated and compared. Numerical results show that the geometrical shape has great effect on the wave conversion performance of the absorber. For absorbers with the same outer radius and draught or displacement, the cylindrical type shows fantastic wave energy conversion ability at some given frequencies, while in the random sea wave, the parabolic and conical ones have better stabilization and applicability in wave power conversion.
Señís, Roger; Brufau, Robert; Sastre, Ramón; Carbajal, Eusebio Carlos
2015-01-01
Congreso celebrado en la Escuela de Arquitectura de la Universidad de Sevilla desde el 24 hasta el 26 de junio de 2015. This study compares flat lattice girders mounted on two supports, based on various design parameters, to determine which have better structural performance and what geometries are more efficient. The fundamental goal is to determine the relationship of performance and structural behaviour of each type of framework structure, with respect to the principle of optimization a...
Axisymmetric thrust-vectoring nozzle performance prediction
International Nuclear Information System (INIS)
Wilson, E. A.; Adler, D.; Bar-Yoseph, P.Z
1998-01-01
Throat-hinged geometrically variable converging-diverging thrust-vectoring nozzles directly affect the jet flow geometry and rotation angle at the nozzle exit as a function of the nozzle geometry, the nozzle pressure ratio and flight velocity. The consideration of nozzle divergence in the effective-geometric nozzle relation is theoretically considered here for the first time. In this study, an explicit calculation procedure is presented as a function of nozzle geometry at constant nozzle pressure ratio, zero velocity and altitude, and compared with experimental results in a civil thrust-vectoring scenario. This procedure may be used in dynamic thrust-vectoring nozzle design performance predictions or analysis for civil and military nozzles as well as in the definition of initial jet flow conditions in future numerical VSTOL/TV jet performance studies
Axisymmetric, Ventilated Supercavitation in Unsteady, Horizontal Flow
Kawakami, Ellison; Lee, Seung-Jae; Arndt, Roger
2012-11-01
Drag reduction and/or speed augmentation of marine vehicles by means of supercavitation is a topic of great interest. During the initial launch of a supercavitating vehicle, an artificial supercavity is required until the vehicle can reach conditions at which a natural supercavity can be sustained. Previous studies at Saint Anthony Falls Laboratory (SAFL) focused on the behavior of ventilated supercavities in steady horizontal flows. In open waters, vehicles can encounter unsteady flows, especially when traveling under waves. A study has been carried out at SAFL to investigate the effects of unsteady flow on axisymmetric supercavities. An attempt is made to duplicate sea states seen in open waters. In an effort to track cavity dimensions throughout a wave cycle, an automated cavity tracking script has been developed. Using a high speed camera and the proper software, it is possible to synchronize cavity dimensions with pressure measurements taken inside the cavity. Results regarding supercavity shape, ventilation demand, cavitation parameters and closure methods are presented. It was found that flow unsteadiness caused a decrease in the overall length of the supercavity while having only a minimal effect on the maximum diameter. The supercavity volume varied with cavitation number and a possible relationship between the two is being explored. (Supported by ONR)
Pressure anisotropy stabilization of axisymmetric mirror machines
International Nuclear Information System (INIS)
Weitzner, H.
1978-01-01
The stability of a two species, anisotropic pressure, axisymmetric plasma is studied using the guiding center plasma model. Successively, asymptotic expansions are applied appropriate to a long, thin plasma, and to a plasma with flux surfaces close to cylinders. The resultant stability problem may be cast as an ordinary differential equation eigenvalue problem or as a problem in the calculus of variations. It is shown that low beta plasmas cannot be confined and be stable although plasmas may be stable in which the pressure gradients are nonzero where the pressure tends to zero. Stable profiles are given; these profiles include the possibility of field reversed regions. These stable profiles require the anisotropic species to be cold near the axis. Rather than absolute stability, a weaker condition is also considered which for fixed azimuthal mode number vertical-barmvertical-bar puts the point of accumulation of the spectrum of modes on the stable side. It is hoped that such a condition may yield systems stable to vertical-barmvertical-bar small modes although not all values of vertical-barmvertical-bar. This condition is more readily satisfied and allows more reasonable profiles near the axis
A steady-state axisymmetric toroidal system
International Nuclear Information System (INIS)
Hirano, K.
1984-01-01
Conditions for achieving a steady state in an axisymmetric toroidal system are studied with emphasis on a very-high-beta field-reversed configuration. The analysis is carried out for the electromotive force produced by the Ohkawa current that is induced by neutral-beam injection. It turns out that, since the perpendicular component of the current j-vectorsub(perpendicular) to the magnetic field can be generated automatically by the diamagnetic effect, only the parallel component j-vectorsub(parallel) must be driven by the electromotive force. The drive of j-vectorsub(parallel) generates shear in the field line so that the pure toroidal field on the magnetic axis is rotated towards the plasma boundary and matched to the external field lines. This matching condition determines the necessary amount of injection beam current and power. It is demonstrated that a very-high-beta field-reversed configuration requires only a small amount of current-driving beam power because almost all the toroidal current except that close to the magnetic axis is carried by the diamagnetic current due to high beta. A low-beta tokamak, on the other hand, needs very high current-driving power since most of the toroidal current is composed of j-vectorsub(parallel) which must be driven by the beam. (author)
Discontinuities in an axisymmetric generalized thermoelastic problem
Directory of Open Access Journals (Sweden)
Moncef Aouadi
2005-06-01
Full Text Available This paper deals with discontinuities analysis in the temperature, displacement, and stress fields of a thick plate whose lower and upper surfaces are traction-free and subjected to a given axisymmetric temperature distribution. The analysis is carried out under three thermoelastic theories. Potential functions together with Laplace and Hankel transform techniques are used to derive the solution in the transformed domain. Exact expressions for the magnitude of discontinuities are computed by using an exact method developed by Boley (1962. It is found that there exist two coupled waves, one of which is elastic and the other is thermal, both propagating with finite speeds with exponential attenuation, and a third which is called shear wave, propagating with constant speed but with no exponential attenuation. The Hankel transforms are inverted analytically. The inversion of the Laplace transforms is carried out using the inversion formula of the transform together with Fourier expansion techniques. Numerical results are presented graphically along with a comparison of the three theories of thermoelasticity.
Pardo-Montero, Juan; Fenwick, John D
2010-06-01
The purpose of this work is twofold: To further develop an approach to multiobjective optimization of rotational therapy treatments recently introduced by the authors [J. Pardo-Montero and J. D. Fenwick, "An approach to multiobjective optimization of rotational therapy," Med. Phys. 36, 3292-3303 (2009)], especially regarding its application to realistic geometries, and to study the quality (Pareto optimality) of plans obtained using such an approach by comparing them with Pareto optimal plans obtained through inverse planning. In the previous work of the authors, a methodology is proposed for constructing a large number of plans, with different compromises between the objectives involved, from a small number of geometrically based arcs, each arc prioritizing different objectives. Here, this method has been further developed and studied. Two different techniques for constructing these arcs are investigated, one based on image-reconstruction algorithms and the other based on more common gradient-descent algorithms. The difficulty of dealing with organs abutting the target, briefly reported in previous work of the authors, has been investigated using partial OAR unblocking. Optimality of the solutions has been investigated by comparison with a Pareto front obtained from inverse planning. A relative Euclidean distance has been used to measure the distance of these plans to the Pareto front, and dose volume histogram comparisons have been used to gauge the clinical impact of these distances. A prostate geometry has been used for the study. For geometries where a blocked OAR abuts the target, moderate OAR unblocking can substantially improve target dose distribution and minimize hot spots while not overly compromising dose sparing of the organ. Image-reconstruction type and gradient-descent blocked-arc computations generate similar results. The Pareto front for the prostate geometry, reconstructed using a large number of inverse plans, presents a hockey-stick shape
Li, Xiaofan; Nie, Qing
2009-07-01
Many applications in materials involve surface diffusion of elastically stressed solids. Study of singularity formation and long-time behavior of such solid surfaces requires accurate simulations in both space and time. Here we present a high-order boundary integral method for an elastically stressed solid with axi-symmetry due to surface diffusions. In this method, the boundary integrals for isotropic elasticity in axi-symmetric geometry are approximated through modified alternating quadratures along with an extrapolation technique, leading to an arbitrarily high-order quadrature; in addition, a high-order (temporal) integration factor method, based on explicit representation of the mean curvature, is used to reduce the stability constraint on time-step. To apply this method to a periodic (in axial direction) and axi-symmetric elastically stressed cylinder, we also present a fast and accurate summation method for the periodic Green's functions of isotropic elasticity. Using the high-order boundary integral method, we demonstrate that in absence of elasticity the cylinder surface pinches in finite time at the axis of the symmetry and the universal cone angle of the pinching is found to be consistent with the previous studies based on a self-similar assumption. In the presence of elastic stress, we show that a finite time, geometrical singularity occurs well before the cylindrical solid collapses onto the axis of symmetry, and the angle of the corner singularity on the cylinder surface is also estimated.
MODFLOW equipped with a new method for the accurate simulation of axisymmetric flow
Samani, N.; Kompani-Zare, M.; Barry, D. A.
2004-01-01
Axisymmetric flow to a well is an important topic of groundwater hydraulics, the simulation of which depends on accurate computation of head gradients. Groundwater numerical models with conventional rectilinear grid geometry such as MODFLOW (in contrast to analytical models) generally have not been used to simulate aquifer test results at a pumping well because they are not designed or expected to closely simulate the head gradient near the well. A scaling method is proposed based on mapping the governing flow equation from cylindrical to Cartesian coordinates, and vice versa. A set of relationships and scales is derived to implement the conversion. The proposed scaling method is then embedded in MODFLOW 2000. To verify the accuracy of the method steady and unsteady flows in confined and unconfined aquifers with fully or partially penetrating pumping wells are simulated and compared with the corresponding analytical solutions. In all cases a high degree of accuracy is achieved.
CASINO, a code for simulation of charged particles in an axisymmetric Tokamak
International Nuclear Information System (INIS)
Dillner, Oe.
1992-01-01
The present report comprises a documentation of CASINO, a simulation code developed as a means for the study of high energy charged particles in an axisymmetric Tokamak. The background of the need for such a numerical tool is presented. In the description of the numerical model used for the orbit integration, the method using constants of motion, the Lao-Hirsman geometry for the flux surfaces and a method for reducing the necessary number of particles is elucidated. A brief outline of the calculational sequence is given as a flow chart. The essential routines and functions as well as the common blocks are briefly described. The input and output routines are shown. Finally the documentation is completed by a short discussion of possible extensions of the code and a test case. (au)
Axisymmetric particle-in-cell simulations of diamagnetic-cavity formation in vacuum
International Nuclear Information System (INIS)
Gisler, G.
1989-01-01
Axisymmetric simulations of the expansion of a hot plasma suddenly introduced into a vacuum containing a weak magnetic field were performed using an electromagnetic particle-in-cell code. Both uniform and gradient fields have been used, with the simulation axis along the principle field direction. The formation of a diamagnetic cavity requires an initial plasma β > 1; as the expansion proceeds, β diminishes, and the field eventually recovers. The maximum spatial extent of the cavity and its duration can be obtained from simple dynamical considerations. Field-aligned ion acceleration behind the electron front is observed in all field geometries and strengths. In the case of expansion into a divergent field, the plasma is found to move down the field gradient by ambipolar diffusion. These simulations are relevant to active release experiments in the Earth's magnetosphere, to pellet ablation experiments, and to the naturally occurring diamagnetic bubbles observed at the Earth's foreshock
International Nuclear Information System (INIS)
Azimi, A.; Hannani, S.K.; Farhanieh, B.
2005-01-01
In this article, a comparison between two iterative inverse techniques to solve simultaneously two unknown functions of axisymmetric transient inverse heat conduction problems in semi complex geometries is presented. The multi-block structured grid together with blocked-interface nodes is implemented for geometric decomposition of physical domain. Numerical scheme for solution of transient heat conduction equation is the finite element method with frontal technique to solve algebraic system of discrete equations. The inverse heat conduction problem involves simultaneous unknown time varying heat generation and time-space varying boundary condition estimation. Two parameter-estimation techniques are considered, Levenberg-Marquardt scheme and conjugate gradient method with adjoint problem. Numerically computed exact and noisy data are used for the measured transient temperature data needed in the inverse solution. The results of the present study for a configuration including two joined disks with different heights are compared to those of exact heat source and temperature boundary condition, and show good agreement. (author)
Impedance Calculations of Non-Axisymmetric Transitions Using the Optical Approximation
International Nuclear Information System (INIS)
Bane, K.L.F.; Stupakov, G.; Zagorodov, I.
2007-01-01
In a companion report, we have derived a method for finding the impedance at high frequencies of vacuum chamber transitions that are short compared to the catch-up distance, in a frequency regime that--in analogy to geometric optics for light--we call the optical regime. In this report we apply the method to various non-axisymmetric geometries such as irises/short collimators in a beam pipe, step-in transitions, step-out transitions, and more complicated transitions of practical importance. Most of our results are analytical, with a few given in terms of a simple one dimensional integral. Our results are compared to wakefield simulations with the time-domain, finite-difference program ECHO, and excellent agreement is found
GATO: an MHD stability code for axisymmetric plasmas with internal separatrices
International Nuclear Information System (INIS)
Bernard, L.C.; Helton, F.J.; Moore, R.W.
1981-07-01
The GATO code computes the growth rate of ideal magnetohydrodynamic instabilities in axisymmetric geometries with internal separatrices such as doublet and expanded spheromak. The basic method, which uses a variational principle and a Galerkin procedure to obtain a matrix eigenvalue problem, is common to the ERATO and PEST codes. A new coordinate system has been developed to handle the internal separatrix. Efficient algorithms have been developed to solve the matrix eigenvalue problem for matrices of rank as large as 40,000. Further improvement is expected using graph theoretical techniques to reorder the matrices. Using judicious mesh repartition, the marginal point can be determined with great precision. The code has been extensively used to optimize doublet and general tokamak plasmas
GATO: An MHD stability code for axisymmetric plasmas with internal separatrices
International Nuclear Information System (INIS)
Bernard, L.C.; Helton, F.J.; Moore, R.W.
1981-01-01
The GATO code computes the growth rate of ideal magnetohydrodynamic instabilities in axisymmetric geometries with internal separatrices such as doublet and expanded spheromak. The basic method, which uses a variational principle and a Galerkin procedure to obtain a matrix eigenvalue problem, is common to the ERATO and PEST codes. A new coordinate system has been developed to handle the internal separatrix. Efficient algorithms have been developed to solve the matrix eigenvalue problem for matrices of rank as large as 40 000. Further improvement is expected using graph theoretical techniques to reorder the matrices. Using judicious mesh repartition, the marginal point can be determined with great precision. The code has been extensively used to optimize doublet and general tokamak plasmas. (orig.)
Impedance calculations of non-axisymmetric transitions using the optical approximation
Energy Technology Data Exchange (ETDEWEB)
Bane, K.L.F.; Stupakov, G. [Stanford Linear Accelerator Center, Menlo Park, CA (United States); Zagorodnov, I. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2007-02-15
In a companion report, we have derived a method for finding the impedance at high frequencies of vacuum chamber transitions that are short compared to the catch-up distance, in a frequency regime that---in analogy to geometric optics for light---we call the optical regime. In this report we apply the method to various non-axisymmetric geometries such as irises/short collimators in a beam pipe, step-in transitions, step-out transitions, and more complicated transitions of practical importance. Most of our results are analytical, with a few given in terms of a simple one dimensional integral. Our results are compared to wakefield simulations with the time-domain, finite-difference program ECHO, and excellent agreement is found. (orig.)
The linear stability analysis of MHD models in axisymmetric toroidal geometry
International Nuclear Information System (INIS)
Manickam, J.; Grimm, R.C.; Dewar, R.L.
1981-01-01
A computational model to analyze the linear stability properties of general toroidal systems in the ideal magnetohydrodynamic limits is presented. This model includes an explicit treatment of the asymptotic singular behaviour at rational surfaces. It is verified through applications to internal kink modes. (orig.)
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.
Integrable motion of a vortex dipole in an axisymmetric flow
International Nuclear Information System (INIS)
Sutyrin, G.G.; Perrot, X.; Carton, X.
2008-01-01
The evolution of a self-propelling vortex dipole, embedded in an external nondivergent flow with constant potential vorticity, is studied in an equivalent-barotropic model commonly used in geophysical, astrophysical and plasma studies. In addition to the conservation of the Hamiltonian for an arbitrary point vortex dipole, it is found that the angular momentum is also conserved when the external flow is axisymmetric. This reduces the original four degrees of freedom to only two, so that the solution is expressed in quadratures. In particular, the scattering of antisymmetric dipoles approaching from the infinity is analyzed in the presence of an axisymmetric oceanic flow typical for the vicinity of isolated seamounts
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
Axisymmetric free convection boundary-layer flow past slender bodies
Kuiken, H.K.
1968-01-01
Radial curvature effects on axisymmetric free convection boundary-layer flow are investigated for vertical cylinders and cones for some special non-uniform temperature differences between the surface and the ambient fluid. The solution is given as a power series expansion, the first term being equal
Vortical motion in the head of an axisymmetric gravity current
Patterson, M.D.; Simpson, J.E.; Dalziel, S.B.; Heijst, van G.J.F.
2006-01-01
A series of experiments that examine the initial development of an axisymmetric gravity current have been carried out. The experiments highlight the growth of a ring vortex that dominates the dynamics of the gravity current's early time propagation. In particular, the experiments show three distinct
The shape of an axisymmetric bubble in uniform motion
Indian Academy of Sciences (India)
Axisymmetric bubble shapes; non-linear free boundary problems; surface singularity methods in potential flows. PACS Nos 47.55.Dz; 47.11.+j; 47.15.Hg. 1. .... should be fast and reasonably accurate, (c) the iterative procedure for determining .... curve while K2 is the other associated principal curvature; K2 can be deduced.
Potential formation in axisymmetrized tandem mirror GAMMA 10
International Nuclear Information System (INIS)
Cho, T.; Ichimura, M.; Inutake, M.
1985-01-01
The paper reports experimental results on potential formation and end plugging in the axisymmetrized tandem mirror GAMMA 10. The plugging at both ends has been achieved by a combination of neutral beams and gyrotrons. The presence of a plug potential with a thermal barrier in an axisymmetric mirror has been confirmed by direct measurement of the axial potential profile. Enhancement of axial particle confinement has been observed during the end plugging. Non-ambipolar radial transport has been greatly reduced in the axisymmetrized magnetic configuration. The potentials measured by beam probes and end loss analysers are 0.7, 0.4 and 1.1 kV in the central, barrier and plug regions, respectively. Strong end plugging is observed when the central-cell density is higher than the densities in the plug and the barrier, and the plug density remains higher than the barrier density. The plug electron temperature is higher than the central temperature. Hot electrons forming a football-shaped profile have been stably produced in the axisymmetric mirror. The beta value and the fraction of the hot electrons reach up to 5% and 0.8, respectively. Central-cell ion-cyclotron resonance heating can sustain a stable plasma with higher density and ion temperature when resonance surfaces exist in both the anchor and the central cells. (author)
Modelling axisymmetric cod-ends made of different mesh types
DEFF Research Database (Denmark)
Priour, D.; Herrmann, Bent; O'Neill, F.G.
2009-01-01
the selectivity process has become more important. This paper presents a model of the deformation of an axisymmetric cod-end. The twine tension and the catch pressure acting on the knots of each mesh along the cod-end profile are calculated, and a Newton-Raphson scheme is used to estimate the equilibrium position...
Decay of passive scalar fluctuations in axisymmetric turbulence
Yoshimatsu, Katsunori; Davidson, Peter A.; Kaneda, Yukio
2016-11-01
Passive scalar fluctuations in axisymmetric Saffman turbulence are examined theoretically and numerically. Theoretical predictions are verified by direct numerical simulation (DNS). According to the DNS, self-similar decay of the turbulence and the persistency of the large-scale anisotropy are found for its fully developed turbulence. The DNS confirms the time-independence of the Corrsin integral.
Non-Axisymmetric Shaping of Tokamaks Preserving Quasi-Axisymmetry
Energy Technology Data Exchange (ETDEWEB)
Long-Poe Ku and Allen H. Boozer
2009-06-05
If quasi-axisymmetry is preserved, non-axisymmetric shaping can be used to design tokamaks that do not require current drive, are resilient to disruptions, and have robust plasma stability without feedback. Suggestions for addressing the critical issues of tokamaks can only be validated when presented with sufficient specificity that validating experiments can be designed. The purpose of this paper is provide that specificity for non-axisymmetric shaping. To our knowledge, no other suggestions for the solution of a number of tokamak issues, such as disruptions, have reached this level of specificity. Sequences of three-field-period quasi-axisymmetric plasmas are studied. These sequences address the questions: (1) What can be achieved at various levels of non-axisymmetric shaping? (2) What simplifications to the coils can be achieved by going to a larger aspect ratio? (3) What range of shaping can be achieved in a single experimental facility? The sequences of plasmas found in this study provide a set of interesting and potentially important configurations.
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
Flux compactifications and generalized geometries
Energy Technology Data Exchange (ETDEWEB)
Grana, Mariana [Service de Physique Theorique, CEA/Saclay, 91191 Gif-sur-Yvette Cedex (France)
2006-11-07
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{sup 6} /(Z{sub 3} x Z{sub 3}) torus in IIA. We finish by studying the effective action and flux vacua for generalized geometries in the context of generalized complex geometry.
International Nuclear Information System (INIS)
Bozic, M.; Zagar, T.; Ravnik, M.
2003-01-01
Neutron fluxes in different spatial locations in biological shield are obtained with TORT code (TORT-Three Dimensional Oak Ridge Discrete Ordinates Neutron/Photon Transport Code). Libraries used with TORT code were BUGLE-96 library (coupled library with 47 neutron groups and 20 gamma groups) and VITAMIN-B6 library (coupled library with 199 neutron groups and 42 gamma groups). BUGLE-96 library is derived from VITAMIN-B6 library. 2-D and 3-D models for homogeneous type of problem (without inserted beam port 4) and problem with asymmetry (non-homogeneous problem; inserted beam port 4, filled with different materials) were of interest for neutron flux calculation. The main purpose is to verify the possibility for using 2-D approximation model instead of large 3-D model in some calculations. Another purpose of this paper was to compare neutron spectral constants obtained from neutron fluxes (3-D model) determined with smaller BUGLE-96 library with new constants obtained from fluxes calculated with bigger VITAMIN-B6 library. These neutron spectral constants are used in isotopic calculation with SCALE code package (ORIGEN-S). In past only neutron spectral constants determined by neutron fluxes from BUGLE-96 library were used. Experimental results used for isotopic composition comparison are available from irradiation experiment with selected type of concrete and other materials in beam port 4 (irradiation channel 4) in TRIGA Mark II reactor. These experimental results were used as a benchmark in this paper. (author)
The lifecycle of axisymmetric internal solitary waves
Directory of Open Access Journals (Sweden)
J. M. McMillan
2010-09-01
Full Text Available The generation and evolution of solitary waves by intrusive gravity currents in an approximate two-layer fluid with equal upper- and lower-layer depths is examined in a cylindrical geometry by way of theory and numerical simulations. The study is limited to vertically symmetric cases in which the density of the intruding fluid is equal to the average density of the ambient. We show that even though the head height of the intrusion decreases, it propagates at a constant speed well beyond 3 lock radii. This is because the strong stratification at the interface supports the formation of a mode-2 solitary wave that surrounds the intrusion head and carries it outwards at a constant speed. The wave and intrusion propagate faster than a linear long wave; therefore, there is strong supporting evidence that the wave is indeed nonlinear. Rectilinear Korteweg-de Vries theory is extended to allow the wave amplitude to decay as r^{-p} with p=½ and the theory is compared to the observed waves to demonstrate that the width of the wave scales with its amplitude. After propagating beyond 7 lock radii the intrusion runs out of fluid. Thereafter, the wave continues to spread radially at a constant speed, however, the amplitude decreases sufficiently so that linear dispersion dominates and the amplitude decays with distance as r^{-1}.
The Role of Axisymmetric Reconnection Events in JET Discharges with Extreme Shear Reversal
Energy Technology Data Exchange (ETDEWEB)
B.C. Stratton; J.A. Breslau; R.V. Budny; S.C. Jardin; W. Park; H.R. Strauss; L.E. Zakharov; B. Alper; V. Drozdov; N.C. Hawkes; S. Reyes-Cortes; and Contributors to the EFDA-JET Work Programme
2001-12-03
Injection of Lower Hybrid Heating and Current Drive into the current ramp-up phase of Joint European Torus (JET) discharges can produce extremely reversed q-profiles characterized by a core region of very small or zero current density (within Motional Stark Effect diagnostic measurement errors) and q(subscript min) > 1. T(subscript e)-profiles show sawtooth-like collapses and the presence of an internal transport barrier. Accurate equilibrium reconstructions of these discharges are obtained using the ESC code, which was recently extended to allow equilibrium reconstructions in which a free boundary solver determines the plasma boundary and a fixed boundary solver provides the magnetic geometry and current density profile. The core current density does not appear to go negative, although current diffusion calculations indicate that sufficient non-inductive current drive to cause this is present. This is explained by nonlinear resistive MHD simulations in toroidal geometry which predict that these discharges undergo n=0 reconnection events (axisymmetric sawteeth) that redistribute the current to hold the core current density near zero.
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...
Indian Academy of Sciences (India)
algebraic geometry but also in related fields like number theory. ... every vector bundle on the affine space is trivial. (equivalently ... les on a compact Riemann surface to unitary rep- ... tial geometry and topology and was generalised in.
International Nuclear Information System (INIS)
Sloane, Peter
2007-01-01
We adapt the spinorial geometry method introduced in [J. Gillard, U. Gran and G. Papadopoulos, 'The spinorial geometry of supersymmetric backgrounds,' Class. Quant. Grav. 22 (2005) 1033 [ (arXiv:hep-th/0410155)
Energy Technology Data Exchange (ETDEWEB)
Sloane, Peter [Department of Mathematics, King' s College, University of London, Strand, London WC2R 2LS (United Kingdom)
2007-09-15
We adapt the spinorial geometry method introduced in [J. Gillard, U. Gran and G. Papadopoulos, 'The spinorial geometry of supersymmetric backgrounds,' Class. Quant. Grav. 22 (2005) 1033 [ (arXiv:hep-th/0410155)
Experimental and numerical research on cavitating flows around axisymmetric bodies
International Nuclear Information System (INIS)
Haipeng, Wei; Song, Fu; Qin, Wu; Biao, Huang; Guoyu, Wang
2014-01-01
We investigated the cavitating flows around different axisymmetric bodies based on experiments and numerical simulation. In the numerical simulation, the multiphase Reynolds averaged Navier Stokes equations (RANS) were solved via the commercial computational fluid dynamics code CFX. The modified k-wSST turbulence model was used along with the transport equation-based cavitation model. In the experiments, a high-speed video technique was used to observe the unsteady cavitating flow patterns, and the dynamic force measurement system was used to measure the hydrodynamics of the axisymmetric bodies under different cavitation conditions. Results are shown for the hemisphere bodies, conical bodies and blunt bodies. Reasonable agreements were obtained between the computational and experimental results. The results show that for the hemispherical body, the cavity consists of quasi-steady transparent region and unsteady foggy water-vapor mixture region, which contains small-scale vortices and is dominated by bubble clusters, causing irregular disturbances at the cavity interfaces. The curvature at the front of the conical body is larger, resulting in that the flow separates at the shoulder of the axisymmetric body. The cavity stretches downstream and reaches to a fixed cavity length and shape. For blunt bodies, the incipient cavitation number is larger than that for the hemispherical body. A large cloud cavity is formed at the shoulder of the blunt body in the cores of vortices in high shear separation regions and the re-entrant jet does not significantly interact with the cavity interface when it moves upstream. As to the dynamic characteristics of unsteady cavitating flows around the axisymmetric bodies, the pulsation frequency for the hemispherical body is larger than that for the blunt body. For the hemispherical body, the pulsation is mainly caused by the high-frequency, small-scale shedding at the rear end of the cavity, while for the blunt body, the main factor for
Nonconforming axisymmetric elements for the analysis of containment structures
International Nuclear Information System (INIS)
Choi, C.K.; Kim, S.Y.
1989-01-01
In this study, the behaviors of the conforming isoparametric quadrilateral 4-node and triangular 3-nod axisymmetric solid elements are improved by adding nonconforming displacement modes. The convergence tests and the irregular mesh tests have been established through the analyses of a primary shield wall typed structure. For example study, a containment wall with internal pressure of 60 ksi has been analyzed. It shows that the nonconforming elements behave better than the conforming elements, especially, in the structurally discontinuous regions
Axisymmetric MHD equilibrium solver with bicubic Hermite elements
International Nuclear Information System (INIS)
Luetjens, H.; Bondeson, A.; Roy, A.
1990-05-01
A numerical code solving axisymmetric magnetohydrodynamic equilibria with rectangular bicubic Hermite elements has been developed. Two test cases are used for checking the convergence rate of the solution. The mapping of the equilibrium quantities into flux coordinates for magnetohydrodynamic stability calculation is performed by a method which preserves the convergence properties of the cubic Hermite elements. Convergence studies show the behaviour of the stability results when the equilibrium mesh is varied. (author) 13 refs., 3 tabs
RESONANT ABSORPTION OF AXISYMMETRIC MODES IN TWISTED MAGNETIC FLUX TUBES
Energy Technology Data Exchange (ETDEWEB)
Giagkiozis, I.; Verth, G. [Solar Plasma Physics Research Centre, School of Mathematics and Statistics, University of Sheffield, Hounsfield Road, Hicks Building, Sheffield, S3 7RH (United Kingdom); Goossens, M.; Doorsselaere, T. Van [Centre for mathematical Plasma Astrophysics, Mathematics Department, KU Leuven, Celestijnenlaan 200B bus 2400, B-3001 Leuven (Belgium); Fedun, V. [Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, Amy Johnson Building, Sheffield, S1 3JD (United Kingdom)
2016-06-01
It has been shown recently that magnetic twist and axisymmetric MHD modes are ubiquitous in the solar atmosphere, and therefore the study of resonant absorption for these modes has become a pressing issue because it can have important consequences for heating magnetic flux tubes in the solar atmosphere and the observed damping. In this investigation, for the first time, we calculate the damping rate for axisymmetric MHD waves in weakly twisted magnetic flux tubes. Our aim is to investigate the impact of resonant damping of these modes for solar atmospheric conditions. This analytical study is based on an idealized configuration of a straight magnetic flux tube with a weak magnetic twist inside as well as outside the tube. By implementing the conservation laws derived by Sakurai et al. and the analytic solutions for weakly twisted flux tubes obtained recently by Giagkiozis et al. we derive a dispersion relation for resonantly damped axisymmetric modes in the spectrum of the Alfvén continuum. We also obtain an insightful analytical expression for the damping rate in the long wavelength limit. Furthermore, it is shown that both the longitudinal magnetic field and the density, which are allowed to vary continuously in the inhomogeneous layer, have a significant impact on the damping time. Given the conditions in the solar atmosphere, resonantly damped axisymmetric modes are highly likely to be ubiquitous and play an important role in energy dissipation. We also suggest that, given the character of these waves, it is likely that they have already been observed in the guise of Alfvén waves.
Elastoplastic buckling of quasi axisymmetric shells of revolution
International Nuclear Information System (INIS)
Combescure, A.
1987-01-01
This paper gives the formulation of a finite element which allows the computation of quasi axisymmetric shells of revolution. This element has two nodes and the displacement field is developped in Fourier series. In this paper, an emphasis is put on the elastic and plastic buckling formulation. Two examples are developped in details showing the applicability and the interest of such a finite element. (orig.)
Modeling axisymmetric flows dynamics of films, jets, and drops
Middleman, Stanley
1995-01-01
This concise book is intended to fulfill two purposes: to provide an important supplement to classic texts by carrying fluid dynamics students on into the realm of free boundary flows; and to demonstrate the art of mathematical modeling based on knowledge, intuition, and observation. In the authors words, the overall goal is make the complex simple, without losing the essence--the virtue--of the complexity.Modeling Axisymmetric Flows: Dynamics of Films, Jets, and Drops is the first book to cover the topics of axisymmetric laminar flows; free-boundary flows; and dynamics of drops, jets, and films. The text also features comparisons of models to experiments, and it includes a large selection of problems at the end of each chapter.Key Features* Contains problems at the end of each chapter* Compares real-world experimental data to theory* Provides one of the first comprehensive examinations of axisymmetric laminar flows, free-boundary flows, and dynamics of drops, jets, and films* Includes development of basic eq...
Three-Dimensional Electromagnetic High Frequency Axisymmetric Cavity Scars.
Energy Technology Data Exchange (ETDEWEB)
Warne, Larry Kevin; Jorgenson, Roy Eberhardt
2014-10-01
This report examines the localization of high frequency electromagnetic fi elds in three-dimensional axisymmetric cavities along periodic paths between opposing sides of the cavity. The cases where these orbits lead to unstable localized modes are known as scars. This report treats both the case where the opposing sides, or mirrors, are convex, where there are no interior foci, and the case where they are concave, leading to interior foci. The scalar problem is treated fi rst but the approximations required to treat the vector fi eld components are also examined. Particular att ention is focused on the normalization through the electromagnetic energy theorem. Both projections of the fi eld along the scarred orbit as well as point statistics are examined. Statistical comparisons are m ade with a numerical calculation of the scars run with an axisymmetric simulation. This axisymmetric cas eformstheoppositeextreme(wherethetwomirror radii at each end of the ray orbit are equal) from the two -dimensional solution examined previously (where one mirror radius is vastly di ff erent from the other). The enhancement of the fi eldontheorbitaxiscanbe larger here than in the two-dimensional case. Intentionally Left Blank
Options for axisymmetric operation of MFTF-B
International Nuclear Information System (INIS)
Fenstermacher, M.E.; Devoto, R.S.; Thomassen, K.I.
1986-01-01
The flexibility of MFTF-B for axisymmetric experiments has been investigated. Interhcanging the axicell coils and increasing their separation results in an axisymmetric plug cell with 12:1 and 6:1 inner and outer mirror ratios, respectively. For axisymmetric operation, the sloshing-ion neutral beams, ECRH gyrotrons, and the pumping system would be moved to the axicell. Stabilization by E-rings could be explored in this configuration. With the addition of octopole magnets, off-axis multipole stabilization could also be tested. Operating points for octopole and E-ring-stabilized configurations with properties similar to those of the quadrupole MFTF-B, namely T/sub ic/ = 10 - 15 keV and n/sub c/ approx. = 3 x 10 13 cm -3 , have been obtained. Because of the negligible radial transport of central-cell ions, the required neutral-beam power in the central cell has been dramatically reduced. In addition, because MHD stabilization is achieved by off-axis hot electrons in both cases, much lower barrier beta is possible, which aids in reducing the barrier ECRH power. Total ECRH power in the end cell is projected to be approx. =1 MW. Possible operating points for both octopole and E-ring configurations are described along with the stability considerations involved
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
Arithmetic noncommutative geometry
Marcolli, Matilde
2005-01-01
Arithmetic noncommutative geometry denotes the use of ideas and tools from the field of noncommutative geometry, to address questions and reinterpret in a new perspective results and constructions from number theory and arithmetic algebraic geometry. This general philosophy is applied to the geometry and arithmetic of modular curves and to the fibers at archimedean places of arithmetic surfaces and varieties. The main reason why noncommutative geometry can be expected to say something about topics of arithmetic interest lies in the fact that it provides the right framework in which the tools of geometry continue to make sense on spaces that are very singular and apparently very far from the world of algebraic varieties. This provides a way of refining the boundary structure of certain classes of spaces that arise in the context of arithmetic geometry, such as moduli spaces (of which modular curves are the simplest case) or arithmetic varieties (completed by suitable "fibers at infinity"), by adding boundaries...
International Nuclear Information System (INIS)
Simonen, T.; Cohen, R.; Correll, D.; Fowler, K.; Post, D.; Berk, H.; Horton, W.; Hooper, E.B.; Fisch, N.; Hassam, A.; Baldwin, D.; Pearlstein, D.; Logan, G.; Turner, B.; Moir, R.; Molvik, A.; Ryutov, D.; Ivanov, A.A; Kesner, J.; Cohen, B.; McLean, H.; Tamano, T.; Tang, X.Z.; Imai, T.
2008-01-01
Experimental results, theory and innovative ideas now point with increased confidence to the possibility of a Gas Dynamic Trap (GDT) neutron source which would be on the path to an attractively simple Axisymmetric Tandem Mirror (ATM) power plant. Although magnetic mirror research was terminated in the US 20 years ago, experiments continued in Japan (Gamma 10) and Russia (GDT), with a very small US effort. This research has now yielded data, increased understanding, and generated ideas resulting in the new concepts described here. Early mirror research was carried out with circular axisymmetric magnets. These plasmas were MHD unstable due to the unfavorable magnetic curvature near the mid-plane. Then the minimum-B concept emerged in which the field line curvature was everywhere favorable and the plasma was situated in a MHD stable magnetic well (70% average beta in 2XII-B). The Ioffe-bar or baseball-coil became the standard for over 40 years. In the 1980's, driven by success with minimum-B stabilization and the control of ion cyclotron instabilities in PR6 and 2XII-B, mirrors were viewed as a potentially attractive concept with near-term advantages as a lower Q neutron source for applications such as a hybrid fission fuel factory or toxic waste burner. However there are down sides to the minimum-B geometry: coil construction is complex; restraining magnetic forces limit field strength and mirror ratios. Furthermore, the magnetic field lines have geodesic curvature which introduces resonant and neoclassical radial transport as observed in early tandem mirror experiments. So what now leads us to think that simple axisymmetric mirror plasmas can be stable? The Russian GDT experiment achieves on-axis 60% beta by peaking of the kinetic plasma pressure near the mirror throat (where the curvature is favorable) to counter-balance the average unfavorable mid-plane curvature. Then a modest augmentation of plasma pressure in the expander results in stability. The GDT
Energy Technology Data Exchange (ETDEWEB)
Simonen, T; Cohen, R; Correll, D; Fowler, K; Post, D; Berk, H; Horton, W; Hooper, E B; Fisch, N; Hassam, A; Baldwin, D; Pearlstein, D; Logan, G; Turner, B; Moir, R; Molvik, A; Ryutov, D; Ivanov, A A; Kesner, J; Cohen, B; McLean, H; Tamano, T; Tang, X Z; Imai, T
2008-10-24
Experimental results, theory and innovative ideas now point with increased confidence to the possibility of a Gas Dynamic Trap (GDT) neutron source which would be on the path to an attractively simple Axisymmetric Tandem Mirror (ATM) power plant. Although magnetic mirror research was terminated in the US 20 years ago, experiments continued in Japan (Gamma 10) and Russia (GDT), with a very small US effort. This research has now yielded data, increased understanding, and generated ideas resulting in the new concepts described here. Early mirror research was carried out with circular axisymmetric magnets. These plasmas were MHD unstable due to the unfavorable magnetic curvature near the mid-plane. Then the minimum-B concept emerged in which the field line curvature was everywhere favorable and the plasma was situated in a MHD stable magnetic well (70% average beta in 2XII-B). The Ioffe-bar or baseball-coil became the standard for over 40 years. In the 1980's, driven by success with minimum-B stabilization and the control of ion cyclotron instabilities in PR6 and 2XII-B, mirrors were viewed as a potentially attractive concept with near-term advantages as a lower Q neutron source for applications such as a hybrid fission fuel factory or toxic waste burner. However there are down sides to the minimum-B geometry: coil construction is complex; restraining magnetic forces limit field strength and mirror ratios. Furthermore, the magnetic field lines have geodesic curvature which introduces resonant and neoclassical radial transport as observed in early tandem mirror experiments. So what now leads us to think that simple axisymmetric mirror plasmas can be stable? The Russian GDT experiment achieves on-axis 60% beta by peaking of the kinetic plasma pressure near the mirror throat (where the curvature is favorable) to counter-balance the average unfavorable mid-plane curvature. Then a modest augmentation of plasma pressure in the expander results in stability. The GDT
Energy Technology Data Exchange (ETDEWEB)
Browning, R.V.; Anderson, C.A.
1982-02-01
The finite element method is used to determine the temperatures, displacements, stresses, and strains in axisymmetric solids with orthotropic, temperature-dependent material properties under axisymmetric thermal and mechanical loads. The mechanical loads can be surface pressures, surface shears, and nodal point forces as well as an axial or centripetal acceleration. The continuous solid is replaced by a system of ring elements with triangular or quadrilateral cross sections. Accordingly, the method is valid for solids that are composed of many different materials and that have complex geometry. Nonlinear mechanical behavior as typified by plastic, locking, or creeping materials can be approximated. Two dimensional mesh generation, plotting, and editing features allow the computer program to be readily used. In addition to a stress analysis program that is based on a modified version of the SAAS code, TSAAS can carry out a transient thermal analysis with the finite element mesh used in stress analysis. An implicit time differencing scheme allows the use of arbitrary time steps with consequent fast running times. At specified times, the program will return to SAAS for thermal stress analysis. Nonlinear thermal properties and Arrhenius reaction kinetics are also incorporated into TSAAS. Several versions of TSAAS are in use at Los Alamos, running on CDC-7600, CRAY-1 and VAX 11/780 computers. This report describes the nominal TSAAS; other versions may have some unique features.
Self consistent MHD modeling of the solar wind from coronal holes with distinct geometries
Stewart, G. A.; Bravo, S.
1995-01-01
Utilizing an iterative scheme, a self-consistent axisymmetric MHD model for the solar wind has been developed. We use this model to evaluate the properties of the solar wind issuing from the open polar coronal hole regions of the Sun, during solar minimum. We explore the variation of solar wind parameters across the extent of the hole and we investigate how these variations are affected by the geometry of the hole and the strength of the field at the coronal base.
Energy Technology Data Exchange (ETDEWEB)
Balakrishna, C; Sarma, B S [Defence Research and Development Laboratory, Hyderabad (India)
1989-02-01
A formulation for axisymmetric shell analysis under asymmetric load based on Fourier series representation and using field consistent 3 noded curved axisymmetric shell element is presented. Different field inconsistent/consistent interpolations for an element based on shear flexible theory have been studied for thick and thin shells under asymmetric loads. Various examples covering axisymmetric as well as asymmetric loading cases have been analyzed and numerical results show a good agreement with the available results in the case of thin shells. 12 refs.
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.
Clustering in Hilbert simplex geometry
Nielsen, Frank
2017-04-03
Clustering categorical distributions in the probability simplex is a fundamental primitive often met in applications dealing with histograms or mixtures of multinomials. Traditionally, the differential-geometric structure of the probability simplex has been used either by (i) setting the Riemannian metric tensor to the Fisher information matrix of the categorical distributions, or (ii) defining the information-geometric structure induced by a smooth dissimilarity measure, called a divergence. In this paper, we introduce a novel computationally-friendly non-Riemannian framework for modeling the probability simplex: Hilbert simplex geometry. We discuss the pros and cons of those three statistical modelings, and compare them experimentally for clustering tasks.
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
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.
Developments in special geometry
International Nuclear Information System (INIS)
Mohaupt, Thomas; Vaughan, Owen
2012-01-01
We review the special geometry of N = 2 supersymmetric vector and hypermultiplets with emphasis on recent developments and applications. A new formulation of the local c-map based on the Hesse potential and special real coordinates is presented. Other recent developments include the Euclidean version of special geometry, and generalizations of special geometry to non-supersymmetric theories. As applications we discuss the proof that the local r-map and c-map preserve geodesic completeness, and the construction of four- and five-dimensional static solutions through dimensional reduction over time. The shared features of the real, complex and quaternionic version of special geometry are stressed throughout.
Analysis and correction of intrinsic non-axisymmetric magnetic fields in high-β DIII-D plasmas
International Nuclear Information System (INIS)
Garofalo, A.M.; La Haye, R.J.; Scoville, J.T.
2002-01-01
Rapid plasma toroidal rotation, sufficient for stabilization of the n=1 resistive wall mode, can be sustained by improving the axisymmetry of the toroidal magnetic field geometry of DIII-D. The required symmetrization is determined experimentally both by optimizing currents in external n=1 correction coils with respect to the plasma rotation, and by use of the n=1 magnetic feedback to detect and minimize the plasma response to non-axisymmetric fields as β increases. Both methods point to an intrinsic ∼7 G (0.03% of the toroidal field), m/n=2/1 resonant helical field at the q=2 surface as the cause of the plasma rotation slowdown above the no-wall β limit. The drag exerted by this field on the plasma rotation is consistent with the behaviour of 'slipping' in a simple induction motor model. (author)
Axisymmetric Vibration of Piezo-Lemv Composite Hollow Multilayer Cylinder
Directory of Open Access Journals (Sweden)
E. S. Nehru
2012-01-01
Full Text Available Axisymmetric vibration of an infinite piezolaminated multilayer hollow cylinder made of piezoelectric layers of 6 mm class and an isotropic LEMV (Linear Elastic Materials with Voids layers is studied. The frequency equations are obtained for the traction free outer surface with continuity conditions at the interfaces. Numerical results are carried out for the inner, middle, and outer hollow piezoelectric layers bonded by LEMV (It is hypothetical material layers and the dispersion curves are compared with that of a similar 3-layer model and of 3 and 5 layer models with inner, middle, and outer hollow piezoelectric layers bonded by CFRP (Carbon fiber reinforced plastics.
Whether diffusion in axisymmetric confinement systems is intrinsically ambipolar
International Nuclear Information System (INIS)
Kovrizhnykh, L.M.
1997-01-01
The problem of diffusion ambipolarity in axisymmetric magnetic systems is analyzed. The question is discussed of whether diffusion is intrinsically ambipolar (and if so, then in which particular cases) or the ambipolarity constraint is an additional independent condition, which does not follow from the equations of motion and, hence, contains new information. It is shown that the second assertion is correct: strictly speaking, diffusion can never be intrinsically ambipolar, and, in the presence of several different mechanisms causing electron and ion losses across the magnetic field, only the total fluxes, but not the partial ones, should satisfy the ambipolarity constraint. (UK)
Fusion-product transport in axisymmetric tokamaks: losses and thermalization
International Nuclear Information System (INIS)
Hively, L.M.
1980-01-01
High-energy fusion-product losses from an axisymmetric tokamak plasma are studied. Prompt-escape loss fluxes (i.e. prior to slowing down) are calculated including the non-separable dependence of flux as a function of poloidal angle and local angle-of-incidence at the first wall. Fusion-product (fp) thermalization and heating are calculated assuming classical slowing down. The present analytical model describes fast ion orbits and their distribution function in realistic, high-β, non-circular tokamak equilibria. First-orbit losses, trapping effects, and slowing-down drifts are also treated
A high-precision algorithm for axisymmetric flow
Directory of Open Access Journals (Sweden)
A. Gokhman
1995-01-01
Full Text Available We present a new algorithm for highly accurate computation of axisymmetric potential flow. The principal feature of the algorithm is the use of orthogonal curvilinear coordinates. These coordinates are used to write down the equations and to specify quadrilateral elements following the boundary. In particular, boundary conditions for the Stokes' stream-function are satisfied exactly. The velocity field is determined by differentiating the stream-function. We avoid the use of quadratures in the evaluation of Galerkin integrals, and instead use splining of the boundaries of elements to take the double integrals of the shape functions in closed form. This is very accurate and not time consuming.
Preserving spherical symmetry in axisymmetric coordinates for diffusion problems
International Nuclear Information System (INIS)
Brunner, T. A.; Kolev, T. V.; Bailey, T. S.; Till, A. T.
2013-01-01
Persevering symmetric solutions, even in the under-converged limit, is important to the robustness of production simulation codes. We explore the symmetry preservation in both a continuous nodal and a mixed finite element method. In their standard formulation, neither method preserves spherical solution symmetry in axisymmetric (RZ) coordinates. We propose two methods, one for each family of finite elements, that recover spherical symmetry for low-order finite elements on linear or curvilinear meshes. This is a first step toward understanding achieving symmetry for higher-order elements. (authors)
SIGMARZ, Stress Analysis of Axisymmetric or Plane Structures
International Nuclear Information System (INIS)
1978-01-01
1 - Nature of the physical problem solved: Classic stress analysis program for axisymmetric or plane geometric structures. 2 - Method of solution: The finite element method is used. Input are the finite element nodes, the imposed displacements, the applied forces at the nodes and the volumetric distributed forces. The linear equation system is solved by the Cholesky method. 3 - Restrictions on the complexity of the problem: Maximum number of nodes: 800; Maximum number of elements: 1300; Maximum number of displacements: 300; Maximum band width: 72
Modelling Acoustic Wave Propagation in Axisymmetric Varying-Radius Waveguides
DEFF Research Database (Denmark)
Bæk, David; Willatzen, Morten
2008-01-01
A computationally fast and accurate model (a set of coupled ordinary differential equations) for fluid sound-wave propagation in infinite axisymmetric waveguides of varying radius is proposed. The model accounts for fluid heat conduction and fluid irrotational viscosity. The model problem is solved...... by expanding solutions in terms of cross-sectional eigenfunctions following Stevenson’s method. A transfer matrix can be easily constructed from simple model responses of a given waveguide and later used in computing the response to any complex wave input. Energy losses due to heat conduction and viscous...
An axisymmetric PFEM formulation for bottle forming simulation
Ryzhakov, Pavel B.
2017-01-01
A numerical model for bottle forming simulation is proposed. It is based upon the Particle Finite Element Method (PFEM) and is developed for the simulation of bottles characterized by rotational symmetry. The PFEM strategy is adapted to suit the problem of interest. Axisymmetric version of the formulation is developed and a modified contact algorithm is applied. This results in a method characterized by excellent computational efficiency and volume conservation characteristics. The model is validated. An example modelling the final blow process is solved. Bottle wall thickness is estimated and the mass conservation of the method is analysed.
Axisymmetric tandem mirror stabilized by a magnetic limiter
International Nuclear Information System (INIS)
Kesner, J.; Post, R.S.; Lane, B.
1985-06-01
In order to stabilize MHD-like, fast growing m = 1 fluctuations in the central cell of a tandem mirror we propose the introduction of a magnetic limiter. The magnetic limiter would create a ring null in the magnetic field. Electrons which enter the null can stream azimuthally and thereby ''short-circuit'' m = 1 fluctuations. Some pressure could be maintained on the separatrix flux surface by locating the null on a local magnetic maxima or by axial plugging. This scheme introduces the possibility of a fully axisymmetric tandem mirror
Flow in axisymmetric expansion in a catalytic converter
DEFF Research Database (Denmark)
Gotfredsen, Erik; Meyer, Knud Erik
The flow in an axisymmetric expansion (circular diffusor) is used in many different engineering applications, such as heat exchangers, catalytic converters and filters. These applications require a relatively uniform flow at the inlet. To minimise the pressure loss, an ideal solution would...... Velocimetry (PIV) is a unique method that resolve the entire cross flow. This type of flow is expected to have a fluctuating ‘jet’-like structure from the smaller inlet pipe into the larger converter. The fluctuations of the jet are difficult, if not impossible, to capture with standard time averaged models...
Non-axisymmetric SOL-transport study for tokamaks and stellarators
International Nuclear Information System (INIS)
Sardei, F.; Feng, Y.; Kisslinger, J.; Grigull, P.; Kobayashi, M.; Harting, D.; Reiter, D.; Federici, G.; Loarte, A.
2007-01-01
The paper addresses basic features of non-axisymmetric edge transport induced in tokamaks by local limiters or external magnetic perturbations and in low-shear stellarators by the presence of edge magnetic islands. 3D simulations and, if available for comparison, experimental results are presented and discussed for three devices, ITER during start-up operation, TEXTOR-DED and W7-AS, having edge topologies totally different from each other. The modeling is performed with the EMC3/EIRENE code, which treats self-consistently plasma, neutral and impurity transport in a general 3D scrape-off layer (SOL) with arbitrarily complex geometry of magnetic configuration and plasma-facing components. Shown are code predictions of the power load on the ITER start-up limiters as well as modeling results on the transport in the TEXTOR-DED stochastic edge and on the physics of stable detachment in W7-AS. Experimental observations confirming the code simulations are referenced for both TEXTOR-DED and W7-AS, a direct comparison between modeling and experimental results is shown for W7-AS
On the impact of a concave nosed axisymmetric body on a free surface
Mathai, Varghese; Govardhan, Raghuraman N.; Arakeri, Vijay H.
2015-02-01
We report on an experimental study of the vertical impact of a concave nosed axisymmetric body on a free surface. Previous studies have shown that bodies with a convex nose, like a sphere, produce a well defined splash with a relatively large cavity behind the model. In contrast, we find that with a concave nose, there is hardly a splash and the cavity extent is greatly reduced. This may be explained by the fact that in the concave nosed case, the initial impact is between a confined air pocket and the free surface unlike in the convex nosed case. From measurements of the unsteady pressure in the concave nose portion, we show that in this case, the maximum pressures are significantly lower than the classically expected "water hammer" pressures and also lower than those generally measured on other geometries. Thus, the presence of an air pocket in the case of a concave nosed body adds an interesting dimension to the classical problem of impact of solid bodies on to a free surface.
Influence of coherent structures on the evolution of an axisymmetric turbulent jet
Breda, Massimiliano; Buxton, Oliver R. H.
2018-03-01
The role of initial conditions in affecting the evolution toward self-similarity of an axisymmetric turbulent jet is examined. The jet's near-field coherence was manipulated by non-circular exit geometries of identical open area, De2, including a square and a fractal exit, for comparison with a classical round orifice jet. Hot-wire anemometry and 2D-planar particle image velocimetry experiments were performed between the exit and a location 26De downstream, where the Reynolds stress profiles are self-similar. This study shows that a fractal geometry significantly changes the near-field structure of the jet, breaking up the large-scale coherent structures, thereby affecting the entrainment rate of the background fluid into the jet stream. It is found that many of the jet's turbulent characteristics scale with the number of eddy turnover times rather than simply the streamwise coordinate, with the entrainment rate (amongst others) found to be comparable across the different jets after approximately 3-4 eddies have been overturned. The study is concluded by investigating the jet's evolution toward a self-similar state. No differences are found for the large-scale spreading rate of the jets in the weakly self-similar region, so defined as the region for which some, but not all of the terms of the mean turbulent kinetic energy equation are self-similar. However, the dissipation rate of the turbulent kinetic energy was found to vary more gradually in x than predicted according to the classical equilibrium theories of Kolmogorov. Instead, the dissipation was found to vary in a non-equilibrium fashion for all three jets tested.
Nozzle design study for a quasi-axisymmetric scramjet-powered vehicle at Mach 7.9 flight conditions
Tanimizu, Katsuyoshi; Mee, David J.; Stalker, Raymond J.; Jacobs, Peter A.
2013-09-01
A nozzle shape optimization study for a quasi-axisymmetric scramjet has been performed for a Mach 7.9 operating condition with hydrogen fuel, aiming at the application of a hypersonic airbreathing vehicle. In this study, the nozzle geometry which is parameterized by a set of design variables, is optimized for the single objective of maximum net thrust using an in-house CFD solver for inviscid flowfields with a simple force prediction methodology. The combustion is modelled using a simple chemical reaction code. The effects of the nozzle design on the overall vehicle performance are discussed. For the present geometry, net thrust is achieved for the optimized vehicle design. The results of the nozzle-optimization study show that performance is limited by the nozzle area ratio that can be incorporated into the vehicle without leading to too large a base diameter of the vehicle and increasing the external drag of the vehicle. This study indicates that it is very difficult to achieve positive thrust at Mach 7.9 using the basic geometry investigated.
Geometry of multihadron production
Energy Technology Data Exchange (ETDEWEB)
Bjorken, J.D.
1994-10-01
This summary talk only reviews a small sample of topics featured at this symposium: Introduction; The Geometry and Geography of Phase space; Space-Time Geometry and HBT; Multiplicities, Intermittency, Correlations; Disoriented Chiral Condensate; Deep Inelastic Scattering at HERA; and Other Contributions.
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.
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
Morris, Barbara H.
2004-01-01
This article describes a geometry project that used the beauty of stained-glass-window designs to teach middle school students about geometric figures and concepts. Three honors prealgebra teachers and a middle school mathematics gifted intervention specialist created a geometry project that covered the curriculum and also assessed students'…
CSIR Research Space (South Africa)
Shatalov, MY
2010-01-01
Full Text Available artefacts. An elaborate discussion of these artefacts is given by Yenwong-Fai, (Yenwong-Fai, 2008). These artefacts could be simply detected and eliminated from the dispersion plots by program tools.Our algorithm, as it has been implemented, does.... Arthur G. Every and our student Alfred S. Yenwong-Fai participating in the investigation of the non-axisymmetric case of the piezoelectric cylinder vibrations (Shatalov, et al. 2009). I also want to thank Mr. Yuri M. Shatalov who investigated...
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.
Methods of information geometry
Amari, Shun-Ichi
2000-01-01
Information geometry provides the mathematical sciences with a new framework of analysis. It has emerged from the investigation of the natural differential geometric structure on manifolds of probability distributions, which consists of a Riemannian metric defined by the Fisher information and a one-parameter family of affine connections called the \\alpha-connections. The duality between the \\alpha-connection and the (-\\alpha)-connection together with the metric play an essential role in this geometry. This kind of duality, having emerged from manifolds of probability distributions, is ubiquitous, appearing in a variety of problems which might have no explicit relation to probability theory. Through the duality, it is possible to analyze various fundamental problems in a unified perspective. The first half of this book is devoted to a comprehensive introduction to the mathematical foundation of information geometry, including preliminaries from differential geometry, the geometry of manifolds or probability d...
International Nuclear Information System (INIS)
Grotz, Andreas
2011-01-01
In this thesis, a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems is proposed. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal structure. Restricting attention to systems of spin dimension two, we derive the objects of our quantum geometry: the spin space, the tangent space endowed with a Lorentzian metric, connection and curvature. In order to get the correspondence to classical differential geometry, we construct examples of causal fermion systems by regularizing Dirac sea configurations in Minkowski space and on a globally hyperbolic Lorentzian manifold. When removing the regularization, the objects of our quantum geometry reduce to the common objects of spin geometry on Lorentzian manifolds, up to higher order curvature corrections.
Elastic layer under axisymmetric indentation and surface energy effects
Intarit, Pong-in; Senjuntichai, Teerapong; Rungamornrat, Jaroon
2018-04-01
In this paper, a continuum-based approach is adopted to investigate the contact problem of an elastic layer with finite thickness and rigid base subjected to axisymmetric indentation with the consideration of surface energy effects. A complete Gurtin-Murdoch surface elasticity is employed to consider the influence of surface stresses. The indentation problem of a rigid frictionless punch with arbitrary axisymmetric profiles is formulated by employing the displacement Green's functions, derived with the aid of Hankel integral transform technique. The problem is solved by assuming the contact pressure distribution in terms of a linear combination of admissible functions and undetermined coefficients. Those coefficients are then obtained by employing a collocation technique and an efficient numerical quadrature scheme. The accuracy of proposed solution technique is verified by comparing with existing solutions for rigid indentation on an elastic half-space. Selected numerical results for the indenters with flat-ended cylindrical and paraboloidal punch profiles are presented to portray the influence of surface energy effects on elastic fields of the finite layer. It is found that the presence of surface stresses renders the layer stiffer, and the size-dependent behavior of elastic fields is observed in the present solutions. In addition, the surface energy effects become more pronounced with smaller contact area; thus, the influence of surface energy cannot be ignored in the analysis of indentation problem especially when the indenter size is very small such as in the case of nanoindentation.
Aerodynamics characteristic of axisymmetric surface protuberance in supersonic regime
Qamar, Adnan; Sanghi, Sanjeev
2012-01-01
The present work deals with the problem of an axi-symmetric surface protuberance mounted on a spherical nosed body of revolution. The numerical computations are carried out for laminar supersonic viscous flow for trapezoidal shape axi-symmetric protuberances. A free stream Mach number ranging from 3 to 8 in steps of 1 at a fixed free stream Reynolds number of 1.8x10(4) has been used in the present study. The steady solutions are obtained using a time marching approach. A newly developed Particle Velocity Upwinding (PVU) scheme has been used for the computation. The spatial flow pattern exhibits a strong bow shock in front of the hemispherical nose, which engulfs the entire base body. Near the protuberance, the fluid particle decelerates due to the adverse pressure created by the protuberance and thus the flow separates in front of the protuberance. This point of separation is found to be a function of Mach number and the protuberance shape. A low-pressure expansion region dominates the base region of the obstacle. The reattachment point for the base separation is also a function of Mach number. As the Mach number is increased the reattachment point shifts toward the protuberances base. A weak recompression shock is also seen in the base, which affects the separated zone behind the protuberance. The important design parameters such as skin friction, heat transfer, drag, and surface pressure coefficients are reported extensively.
Application of the Least Squares Method in Axisymmetric Biharmonic Problems
Directory of Open Access Journals (Sweden)
Vasyl Chekurin
2016-01-01
Full Text Available An approach for solving of the axisymmetric biharmonic boundary value problems for semi-infinite cylindrical domain was developed in the paper. On the lateral surface of the domain homogeneous Neumann boundary conditions are prescribed. On the remaining part of the domain’s boundary four different biharmonic boundary pieces of data are considered. To solve the formulated biharmonic problems the method of least squares on the boundary combined with the method of homogeneous solutions was used. That enabled reducing the problems to infinite systems of linear algebraic equations which can be solved with the use of reduction method. Convergence of the solution obtained with developed approach was studied numerically on some characteristic examples. The developed approach can be used particularly to solve axisymmetric elasticity problems for cylindrical bodies, the heights of which are equal to or exceed their diameters, when on their lateral surface normal and tangential tractions are prescribed and on the cylinder’s end faces various types of boundary conditions in stresses in displacements or mixed ones are given.
Identification of multiple modes of axisymmetric or circularly repetitive structures
International Nuclear Information System (INIS)
Kopff, P.
1983-01-01
The axisymmetric structures, or those composed with circularly repetitive elements, often display multiple modes, which are not easy to separate by modal identification of experimental responses. To be able to solve in situ some problems related to the vibrational behaviour of reactor vessels or other such huge structures, ELECTRICITY DE FRANCE developed a few years ago, experimental capabilities providing heavy harmonic driving forces, and elaborate data acquisition, signal processing and modal identification software, self-contained in an integrated mobile test facility. The modal analysis techniques we have developed with the LABORATOIRE DE MECANIQUE Appliquee of University of BESANCON (FRANCE) were especially suited for identification of multiple or separation of quasi-multiple modes, i.e. very close and strongly coupled resonances. Besides, the curve fitting methods involved, compute the same complex eigen-frequencies for all the vibration pick-ups, for better accuracy of the related eigen-vector components. Moreover, the latest extensions of these algorithms give us the means to deal with non-linear behaviour. The performances of these programs are drawn from some experimental results on axisymmetric or circularly repetitive structure, we tested in our laboratory to validate the computational hypothesis used in models for seismic responses of breeder reactor vessels. (orig.)
Stress analysis in a non axisymmetric loaded reactor pressure vessel
International Nuclear Information System (INIS)
Albuquerque, Levi Barcelos; Assis, Gracia Menezes V. de; Miranda, Carlos Alexandre J.; Cruz, Julio Ricardo B.; Mattar Neto, Miguel
1995-01-01
In this work we intend to present the stress analysis of a PWR vessel under postulated concentrated loads. The vessel was modeled with Axisymmetric solid 4 nodes harmonic finite elements with the use of the ANSYS program, version 5.0. The bolts connecting the vessel flanges were modeled with beam elements. Some considerations were made to model the contact between the flanges. The perforated part of the vessel tori spherical head was modeled (with reduced properties due to its holes) to introduce its stiffness and loads but was not within the scope of this work. The loading consists of some usual ones, as pressure, dead weight, bolts preload, seismic load and some postulated ones as concentrated loads, over the vessel, modeled by Fourier Series. The results in the axisymmetric model are taken in terms of linearized stresses, obtained in some circumferential positions and for each position, in some sections along the vessel. Using the ASME Code (Section III, Division 1, Sub-section NB) the stresses are within the allowable limits. In order to draw some conclusions about stress linearization, the membrane plus bending stresses (Pl + Pb) are obtained and compared in some sections, using three different methods. (author)
Hot Wire Measurements in a Axisymmetric Shear Layer with Swirl
Ewing, D.; Pollard, A.
1996-11-01
It is well known that the introduction of swirl in an axisymmetric jet can influence the development of and mixing in the near field of the jet. Recent efforts to compute this flow have demonstrated that the development of the near field is dependent on parameters at the jet outlet other than distribution of the swirl component, such as the distribution the mean radial velocity (Xai, J.L., Smith, B.L., Benim, A. C., Schmidli, J., and Yadigaroglu, G. (1996) Influence of Boundary Conditions on Swirling Flow in Combustors, Proc. ASME Fluid. Eng. Div. Summer Meeting), San Diego, Ca., July 7-11.. An experimental rig has been designed to produce co-axial round and annular swirling jets with uniform outlet conditions in each flow. The flow rate and swirl component from each of these jets can be controlled independently and the rig can be configured to produce both co- and counter-swirling flows. Thus, the rig can be used to carry out an extensive investigation of the effect of swirl on the development of axisymmetric flows. The key design features of the rig and the first sets of hot-wire measurements in the shear layer will be reported here.
Topological Fluid Mechanics with Applications to Free Surfaces and Axisymmetric Flows
DEFF Research Database (Denmark)
Brøns, Morten
1996-01-01
Topological fluid mechanics is the study of qualitative features of fluid patterns. We discuss applications to the flow beneath a stagnant surface film, and to patterns in axisymmetric flow.......Topological fluid mechanics is the study of qualitative features of fluid patterns. We discuss applications to the flow beneath a stagnant surface film, and to patterns in axisymmetric flow....
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
New chemical-DSMC method in numerical simulation of axisymmetric rarefied reactive flow
Zakeri, Ramin; Kamali Moghadam, Ramin; Mani, Mahmoud
2017-04-01
The modified quantum kinetic (MQK) chemical reaction model introduced by Zakeri et al. is developed for applicable cases in axisymmetric reactive rarefied gas flows using the direct simulation Monte Carlo (DSMC) method. Although, the MQK chemical model uses some modifications in the quantum kinetic (QK) method, it also employs the general soft sphere collision model and Stockmayer potential function to properly select the collision pairs in the DSMC algorithm and capture both the attraction and repulsion intermolecular forces in rarefied gas flows. For assessment of the presented model in the simulation of more complex and applicable reacting flows, first, the air dissociation is studied in a single cell for equilibrium and non-equilibrium conditions. The MQK results agree well with the analytical and experimental data and they accurately predict the characteristics of the rarefied flowfield with chemical reaction. To investigate accuracy of the MQK chemical model in the simulation of the axisymmetric flow, air dissociation is also assessed in an axial hypersonic flow around two geometries, the sphere as a benchmark case and the blunt body (STS-2) as an applicable test case. The computed results including the transient, rotational and vibrational temperatures, species concentration in the stagnation line, and also the heat flux and pressure coefficient on the surface are compared with those of the other chemical methods like the QK and total collision energy (TCE) models and available analytical and experimental data. Generally, the MQK chemical model properly simulates the chemical reactions and predicts flowfield characteristics more accurate rather than the typical QK model. Although in some cases, results of the MQK approaches match with those of the TCE method, the main point is that the MQK does not need any experimental data or unrealistic assumption of specular boundary condition as used in the TCE method. Another advantage of the MQK model is the
Development of axisymmetric lattice Boltzmann flux solver for complex multiphase flows
Wang, Yan; Shu, Chang; Yang, Li-Ming; Yuan, Hai-Zhuan
2018-05-01
This paper presents an axisymmetric lattice Boltzmann flux solver (LBFS) for simulating axisymmetric multiphase flows. In the solver, the two-dimensional (2D) multiphase LBFS is applied to reconstruct macroscopic fluxes excluding axisymmetric effects. Source terms accounting for axisymmetric effects are introduced directly into the governing equations. As compared to conventional axisymmetric multiphase lattice Boltzmann (LB) method, the present solver has the kinetic feature for flux evaluation and avoids complex derivations of external forcing terms. In addition, the present solver also saves considerable computational efforts in comparison with three-dimensional (3D) computations. The capability of the proposed solver in simulating complex multiphase flows is demonstrated by studying single bubble rising in a circular tube. The obtained results compare well with the published data.
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.
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
Roe, John
2003-01-01
Coarse geometry is the study of spaces (particularly metric spaces) from a 'large scale' point of view, so that two spaces that look the same from a great distance are actually equivalent. This point of view is effective because it is often true that the relevant geometric properties of metric spaces are determined by their coarse geometry. Two examples of important uses of coarse geometry are Gromov's beautiful notion of a hyperbolic group and Mostow's proof of his famous rigidity theorem. The first few chapters of the book provide a general perspective on coarse structures. Even when only metric coarse structures are in view, the abstract framework brings the same simplification as does the passage from epsilons and deltas to open sets when speaking of continuity. The middle section reviews notions of negative curvature and rigidity. Modern interest in large scale geometry derives in large part from Mostow's rigidity theorem and from Gromov's subsequent 'large scale' rendition of the crucial properties of n...
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...
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...
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.
Tabachnikov, Serge
2005-01-01
Mathematical billiards describe the motion of a mass point in a domain with elastic reflections off the boundary or, equivalently, the behavior of rays of light in a domain with ideally reflecting boundary. From the point of view of differential geometry, the billiard flow is the geodesic flow on a manifold with boundary. This book is devoted to billiards in their relation with differential geometry, classical mechanics, and geometrical optics. The topics covered include variational principles of billiard motion, symplectic geometry of rays of light and integral geometry, existence and nonexistence of caustics, optical properties of conics and quadrics and completely integrable billiards, periodic billiard trajectories, polygonal billiards, mechanisms of chaos in billiard dynamics, and the lesser-known subject of dual (or outer) billiards. The book is based on an advanced undergraduate topics course (but contains more material than can be realistically taught in one semester). Although the minimum prerequisit...
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...
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.
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
Ceresole, Anna; Gnecchi, Alessandra; Marrani, Alessio
2013-01-01
We analyze some properties of the four dimensional supergravity theories which originate from five dimensions upon reduction. They generalize to N>2 extended supersymmetries the d-geometries with cubic prepotentials, familiar from N=2 special K\\"ahler geometry. We emphasize the role of a suitable parametrization of the scalar fields and the corresponding triangular symplectic basis. We also consider applications to the first order flow equations for non-BPS extremal black holes.
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.
Software Geometry in Simulations
Alion, Tyler; Viren, Brett; Junk, Tom
2015-04-01
The Long Baseline Neutrino Experiment (LBNE) involves many detectors. The experiment's near detector (ND) facility, may ultimately involve several detectors. The far detector (FD) will be significantly larger than any other Liquid Argon (LAr) detector yet constructed; many prototype detectors are being constructed and studied to motivate a plethora of proposed FD designs. Whether it be a constructed prototype or a proposed ND/FD design, every design must be simulated and analyzed. This presents a considerable challenge to LBNE software experts; each detector geometry must be described to the simulation software in an efficient way which allows for multiple authors to easily collaborate. Furthermore, different geometry versions must be tracked throughout their use. We present a framework called General Geometry Description (GGD), written and developed by LBNE software collaborators for managing software to generate geometries. Though GGD is flexible enough to be used by any experiment working with detectors, we present it's first use in generating Geometry Description Markup Language (GDML) files to interface with LArSoft, a framework of detector simulations, event reconstruction, and data analyses written for all LAr technology users at Fermilab. Brett is the other of the framework discussed here, the General Geometry Description (GGD).
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
Particle collector scoops for improved exhaust in ''axisymmetric'' devices
International Nuclear Information System (INIS)
Conn, R.W.; Wolf, G.H.
1987-11-01
Application of particle collector scoops in front of the pumping ducts of axisymmetric divertor/magnetic limiter configurations is proposed. These scoops should enclose a significant fraction of the recycling particles. The resulting increase in natural particle pressure in front of the pumping ducts leads to an improved exhaust efficiency. This can permit an extension of the operational margin for density control. Alternatively, aiming at a prescribed exhaust flow in reactor-type devices such as INTOR, the pumping ducts could be reduced in aperture, leaving valuable space for other components. The lay-out of the proposed scheme depends on the heat load on the leading edge in front of the scoop and on the deflector in front of the pumping ducts. 14 refs., 5 figs
Calculation of transport coefficients in an axisymmetric plasma
International Nuclear Information System (INIS)
Shumaker, D.E.
1977-01-01
A method of calculating the transport coefficient in an axisymmetric toroidal plasma is presented. This method is useful in calculating the transport coefficients in a Tokamak plasma confinement device. The particle density and temperature are shown to be a constant on a magnetic flux surface. Transport equations are given for the total particle flux and total energy flux crossing a closed toroidal surface. Also transport equations are given for the toroidal magnetic flux. A computer code was written to calculate the transport coefficients for a three species plasma, electrons and two species of ions. This is useful for calculating the transport coefficients of a plasma which contains impurities. It was found that the particle and energy transport coefficients are increased by a large amount, and the transport coefficients for the toroidal magnetic field are reduced by a small amount
Pressure drop coefficient of laminar Newtonian flow in axisymmetric diffusers
International Nuclear Information System (INIS)
Rosa, S.; Pinho, F.T.
2006-01-01
The laminar flow of Newtonian fluids in axisymmetric diffusers has been numerically investigated to evaluate the pressure-loss coefficient as a function of Reynolds number, diffusion angle and expansion ratio. The numerical simulations were carried out with a finite-volume based code using non-orthogonal collocated grids and second order accurate differencing schemes to discretize all terms of the transport equations. The calculations were carried out for Reynolds numbers between 2 and 200, diffusion angles from 0 deg. to 90 deg. and expansion ratios of 1.5 and 2 and the data are presented in tabular form and as correlations. A simplified 1D theoretical analysis helped explain the various contributions to the loss coefficient and its difference relative to the reversible pressure variation due to differences between the actual and fully developed friction losses, distortions of the velocity profiles and pressure non-uniformity upstream and downstream of the expansion section
Pressure drop coefficient of laminar Newtonian flow in axisymmetric diffusers
Energy Technology Data Exchange (ETDEWEB)
Rosa, S. [Escola Superior de Tecnologia e Gestao, Instituto Politecnico, Campus de Santa Apolonia, 5301-857 Braganca (Portugal)]. E-mail: srosa@ipb.pt; Pinho, F.T. [Centro de Estudos de Fenomenos de Transporte, DEM, Universidade do Minho, Campus de Azurem, 4800-058 Guimaraes (Portugal)]. E-mail: fpinho@fe.up.pt
2006-04-15
The laminar flow of Newtonian fluids in axisymmetric diffusers has been numerically investigated to evaluate the pressure-loss coefficient as a function of Reynolds number, diffusion angle and expansion ratio. The numerical simulations were carried out with a finite-volume based code using non-orthogonal collocated grids and second order accurate differencing schemes to discretize all terms of the transport equations. The calculations were carried out for Reynolds numbers between 2 and 200, diffusion angles from 0 deg. to 90 deg. and expansion ratios of 1.5 and 2 and the data are presented in tabular form and as correlations. A simplified 1D theoretical analysis helped explain the various contributions to the loss coefficient and its difference relative to the reversible pressure variation due to differences between the actual and fully developed friction losses, distortions of the velocity profiles and pressure non-uniformity upstream and downstream of the expansion section.
Development of Compact Quasi-Axisymmetric Stellarator Reactor Configurations
International Nuclear Information System (INIS)
Ku, L.P.; Zarnstorff, M.; White, R.B.; Cooper, W.A.; Sanchez, R.; Neilson, H.; Schmidt, J.A.
2003-01-01
We have started to examine the reactor potential of quasi-axisymmetric (QA) stellarators with an integrated approach that includes systems evaluation, engineering considerations, and plasma and coil optimizations. In this paper, we summarize the progress made so far in developing QA configurations with reduced alpha losses while retaining good MHD stability properties. The minimization of alpha losses is achieved by directly targeting the collisionless orbits to prolong the average resident times. Configurations with an overall energy loss rate of ∼10% or less, including collisional contributions, have been found. To allow remotely maintaining coils and machine components in a reactor environment, there is a desire to simplify to the extent possible the coil design. To this end, finding a configuration that is optimized not only for the alpha confinement and MHD stability but also for the good coil and reactor performance, remains to be a challenging task
Cellular blebs: pressure-driven, axisymmetric, membrane protrusions
Woolley, Thomas E.
2013-07-16
Blebs are cellular protrusions that are used by cells for multiple purposes including locomotion. A mechanical model for the problem of pressure-driven blebs based on force and moment balances of an axisymmetric shell model is proposed. The formation of a bleb is initiated by weakening the shell over a small region, and the deformation of the cellular membrane from the cortex is obtained during inflation. However, simply weakening the shell leads to an area increase of more than 4 %, which is physically unrealistic. Thus, the model is extended to include a reconfiguration process that allows large blebs to form with small increases in area. It is observed that both geometric and biomechanical constraints are important in this process. In particular, it is shown that although blebs are driven by a pressure difference across the cellular membrane, it is not the limiting factor in determining bleb size. © 2013 Springer-Verlag Berlin Heidelberg.
Electron cyclotron current drive efficiency in an axisymmetric tokamak
Energy Technology Data Exchange (ETDEWEB)
Gutierrez-Tapia, C.; Beltran-Plata, M. [Instituto Nacional de Investigaciones Nucleares, Dept. de Fisica, Mexico D.F. (Mexico)
2004-07-01
The neoclassical transport theory is applied to calculate electron cyclotron current drive (ECCD) efficiency in an axisymmetric tokamak in the low-collisionality regime. The tokamak ordering is used to obtain a system of equations that describe the dynamics of the plasma where the nonlinear ponderomotive (PM) force due to high-power radio-frequency (RF) waves is included. The PM force is produced around an electron cyclotron resonant surface at a specific poloidal location. The ECCD efficiency is analyzed in the cases of first and second harmonics (for different impinging angles of the RF waves) and it is validated using experimental parameter values from TCV and T-10 tokamaks. The results are in agreement with those obtained by means of Green's function techniques. (authors)
Stability of axisymmetric plasmas in closed line magnetic fields
International Nuclear Information System (INIS)
Simakov, A.N.; Vernon Wong, H.; Berk, H.L.
2003-01-01
The stability of axisymmetric plasmas confined by closed poloidal magnetic field lines is considered. The results are relevant to plasmas in the dipolar fields of stars and planets, as well as the Levitated Dipole Experiment, multipoles, Z pinches and field reversed configurations. The ideal MHD energy principle is employed to study the stability of pressure driven shear Alfven modes. A point dipole is considered in detail to demonstrate that equilibria exist which are MHD stable for arbitrary beta. Effects of sound waves and plasma resistivity are investigated for Z pinch and point dipole equilibria by means of resistive MHD theory. Kinetic theory is used to study drift frequency modes and their interaction with MHD modes near the ideal stability boundary for different collisionality regimes. Effects of collisional dissipation on drift mode stability are explicitly evaluated and applied to a Z pinch. The role of finite Larmor radius effects and drift reversed particles in modifying ideal stability thresholds is examined. (author)
Theory of plasma confinement in non-axisymmetric magnetic fields.
Helander, Per
2014-08-01
The theory of plasma confinement by non-axisymmetric magnetic fields is reviewed. Such fields are used to confine fusion plasmas in stellarators, where in contrast to tokamaks and reversed-field pinches the magnetic field generally does not possess any continuous symmetry. The discussion is focussed on magnetohydrodynamic equilibrium conditions, collisionless particle orbits, and the kinetic theory of equilbrium and transport. Each of these topics is fundamentally affected by the absence of symmetry in the magnetic field: the field lines need not trace out nested flux surfaces, the particle orbits may not be confined, and the cross-field transport can be very large. Nevertheless, by tailoring the magnetic field appropriately, well-behaved equilibria with good confinement can be constructed, potentially offering an attractive route to magnetic fusion. In this article, the mathematical apparatus to describe stellarator plasmas is developed from first principles and basic elements underlying confinement optimization are introduced.
Nonlinear electromagnetic gyrokinetic equations for rotating axisymmetric plasmas
International Nuclear Information System (INIS)
Artun, M.; Tang, W.M.
1994-03-01
The influence of sheared equilibrium flows on the confinement properties of tokamak plasmas is a topic of much current interest. A proper theoretical foundation for the systematic kinetic analysis of this important problem has been provided here by presented the derivation of a set of nonlinear electromagnetic gyrokinetic equations applicable to low frequency microinstabilities in a rotating axisymmetric plasma. The subsonic rotation velocity considered is in the direction of symmetry with the angular rotation frequency being a function of the equilibrium magnetic flux surface. In accordance with experimental observations, the rotation profile is chosen to scale with the ion temperature. The results obtained represent the shear flow generalization of the earlier analysis by Frieman and Chen where such flows were not taken into account. In order to make it readily applicable to gyrokinetic particle simulations, this set of equations is cast in a phase-space-conserving continuity equation form
Axisymmetric Tornado Simulations with a Semi-Slip Boundary
Directory of Open Access Journals (Sweden)
Brian H. Fiedler
2017-12-01
Full Text Available The structure of natural tornadoes and simulated analogs are sensitive to the lower boundary condition for friction. Three-dimensional numerical simulations of storms require a choice for turbulence parameterizations and resolution of wind near the lower boundary. This article explores some of the consequences of choices of a surface drag coefficient on the structure of a mature simulated tornado, using a conventional axisymmetric model. The surface drag parameterization is explored over the range of the semi-slip condition, including the extremes of no-slip and free-slip. A moderate semi-slip condition allows for an extreme pressure deficit, but without the unrealistic vortex breakdown of the no-slip condition.
Controlled Wake of a Moving Axisymmetric Bluff Body
Lee, E.; Vukasinovic, B.; Glezer, A.
2017-11-01
The aerodynamic loads exerted on a wire-mounted axisymmetric bluff body in prescribed rigid motion are controlled by fluidic manipulation of its near wake. The body is supported by a six-degree of freedom eight-wire traverse and its motion is controlled using a dedicated servo actuator and inline load cell for each wire. The instantaneous aerodynamic forces and moments on the moving body are manipulated by controlled interactions of an azimuthal array of integrated synthetic jet actuators with the cross flow to induce localized flow attachment over the body's aft end and thereby alter the symmetry of the wake. The coupled interactions between the wake structure and the effected aerodynamic loads during prescribed time-periodic and transitory (gust like) motions are investigated with emphasis on enhancing or diminishing the loads for maneuver control, and decoupling the body's motion from its far wake.
Ideal, steady-state, axisymmetric magnetohydrodynamic equations with flow
International Nuclear Information System (INIS)
Baransky, Y.A.
1987-01-01
The motivation of this study is to gain additional understanding of the effect of rotation on the equilibrium of a plasma. The axisymmetric equilibria of ideal magnetohydrodynamics (MHD) with flow have been studied numerically and analytically. A general discussion is provided of previous work on plasmas with flow and comparisons are made to the static model. A variational principle has been derived for the two dimensional problem with comments as to appropriate boundary conditions. An inverse aspect ratio expansion has been used for a study of the toroidal flow equation for both low- and high-β. The inverse aspect ratio expansion has also been used for a study of equations with both poloidal and toroidal flow. An overview is provided of the adaptive finite-difference code which was developed to solve the full equations. (FI)
Numerical study of the axisymmetric ideal MHD stability of Extrap
International Nuclear Information System (INIS)
Benda, M.
1993-04-01
A numerical study of the free-boundary axisymmetric (n=0) ideal magnetohydrodynamical (MHD) motions of the Extrap device is presented. The dependence of stability on current profiles in the plasma and currents in the external conductors is investigated. Results are shown for linear growth-rates and nonlinear saturation amplitudes and their dependence on plasma radius as well as on the conducting shell radius. A method combined of two different algorithms has been developed and tested. The interior region of the plasma is simulated by means of a Lagrangian Finite Element Method (FEM) for ideal magnetohydrodynamics, The method is based on a nonlinear radiation principle for the Lagrangian description of ideal MHD. The Boundary Element Method (BEM) is used together with the Lagrangian FEM to simulate nonlinear motion of an ideal MHD plasma behaviour in a vacuum region under the influence of external magnetic fields. 31 refs
Numerical calculation of axisymmetric non-neutral plasma equilibria
International Nuclear Information System (INIS)
Spencer, R.L.; Rasband, S.N.; Vanfleet, R.R.
1993-01-01
Efficient techniques for computing axisymmetric non-neutral plasma equilibria are described. These equilibria may be obtained either by requiring global thermal equilibrium, by specifying the midplane radial density profile, or by specifying the radial profile of ∫n dz. Both splines and finite-differences are used, and the accuracy of the two is compared by using a new characterization of the thermal equilibrium density profile which gives a simple formula for estimating the radial and axial gradient scale lengths of thermal equilibria. It is found that for global thermal equilibrium 1% accuracy is achieved with splines if the distance between neighboring splines is about two Debye lengths while finite differences require a grid spacing of about one-half Debye length to achieve the same accuracy
The numerical solution of ICRF fields in axisymmetric mirrors
International Nuclear Information System (INIS)
Phillips, M.W.; Todd, A.M.M.
1986-01-01
The numerics of a numerical code called GARFIELD (Grumman Aerospace RF fIELD code) designed to calculate the three-dimensional structure of ICRF fields in axisymmetric mirrors is presented. The code solves the electromagnetic wave equation for the electric field using a cold plasma dispersion relation with a small collision term to simulate absorption. The full wave solution including E.B is computed. The fields are Fourier analyzed in the poloidal direction and solved on a grid in the axial and radial directions. A two-dimensional equilibrium can be used as the source of equilibrium data. This allows us to extend previous studies of ICRF wave propagation and absorption in mirrors to include the effect of axial variation of the magnetic field and density. (orig.)
Axial turbomachine modelling with a 1D axisymmetric approach
International Nuclear Information System (INIS)
Tauveron, Nicolas; Saez, Manuel; Ferrand, Pascal; Leboeuf, Francis
2007-01-01
This work concerns the design and safety analysis of direct cycle gas cooled reactor. The estimation of compressor and turbine performances in transient operations is of high importance for the designer. The first goal of this study is to provide a description of compressor behaviour in unstable conditions with a better understanding than the models based on performance maps ('traditional' 0D approach). A supplementary objective is to provide a coherent description of the turbine behaviour. The turbomachine modelling approach consists in the solution of 1D axisymmetric Navier-Stokes equations on an axial grid inside the turbomachine: mass, axial momentum, circumferential momentum and total-enthalpy balances are written. Blade forces are taken into account by using compressor or turbine blade cascade steady correlations. A particular effort has been developed to generate or test correlations in low mass flow and negative mass flow regimes, based on experimental data. The model is tested on open literature cases of the gas turbine aircraft community. For compressor and turbine, steady situations are fairly described, especially for medium and high mass flow rate. The dynamic behaviour of compressor is also quite well described, even in unstable operation (surge): qualitative tendencies (role of plenum volume and role of throttle) and some quantitative characteristics (frequency) are in a good agreement with experimental data. The application to transient simulations of gas cooled nuclear reactors is concentrated on the hypothetical 10 in. break accident. The results point out the importance of the location of the pipe rupture in a hypothetical break event. In some detailed cases, compressor surge and back flow through the circuit can occur. In order to be used in a design phase, a simplified model of surge has also been developed. This simplified model is applied to the gas fast reactor (GFR) and compared quite favourably with 1D axisymmetric simulation results
Thin circular cylinder under axisymmetrical thermal and mechanical loading
International Nuclear Information System (INIS)
Arnaudeau, F.; Zarka, J.; Gerij, J.
1977-01-01
To assess structural integrity of components subjected to cyclic thermal loadings one must look at thermal ratchetting as a possible failure mode. Considering a thin circular cylinder subjected to constant internal pressure and cyclically varying thermal gradient through the thickness Bree, J. Strain Analysis 2 (1967) No.3, obtained a diagram that serves as a foundation for many design rules (e.g.: ASME code). The upper part of the french LMFBR main vessel is subjected to an axisymmetrical axial thermal loading and an axial load (own weight). Operation of the reactor leads to cyclic variations of the axial thermal loading. The question that arises is whether or not the Bree diagram is realistic for such loading conditions. A special purpose computer code (Ratch) was developed to analyse a thin circular cylinder subjected to axisymmetrical mechanical and thermal loadings. The Mendelson's approach of this problem is followed. Classical Kirchoff-Love hypothesis of thin shells is used and a state of plane stress is assumed. Space integrations are performed by Gaussian quadrature in the axial direction and by Simpson's one third rule throughout the thickness. Thermoelastic-plastic constitutive equations are solved with an implicit scheme (Nguyen). Thermovisco-plastic constitutive equations are solved with an explicit time integration scheme (Treanor's algorithm especially fitted). A Bree type diagram is obtained for an axial step of temperature which varies cyclically and a sustained constant axial load. The material behavior is assumed perfectly plastic and creep effect is not considered. Results show that the domain where no ratchetting occurs is reduced when compared with the domain predicted by the Bree diagram
Secular instability of axisymmetric rotating stars to gravitational radiation reaction
International Nuclear Information System (INIS)
Managan, R.A.
1985-01-01
A generalization of the Eulerian variational principle derived by Ipser and Managan, for nonaxisymmetric neutral modes of axisymmetric fluid configurations, is developed. The principle provides a variational basis for calculating the frequencies of nonaxisymmetric normal modes proportional to e/sup i/(sigmat + mphi). A modified form of this principle, valid for sigma near 0, is also developed. The latter principle is used to locate the points where the frequency of a nonaxisymmetric normal mode of an axisymmetric rotating fluid configuration passes through zero. lt is at these points that the configuration becomes secularly unstable to gravitational radiation reaction (GRR). This is demonstrated directly by including the GRR potential and showing that the imaginary part of sigma passes through zero and becomes negative at these points. The imaginary part of the frequency is used to estimate the e-folding time of the mode. This variational principle is applied to sequences of rotating polytropes. The sequences are constructed using four rotation laws at each value of the polytropic index n = 0.5, 1.0, 1.5, 2.0, and 3.0. The values of (T/W)/sub m/, the ratio of the rotational kinetic energy to the magnitude of the gravitational potential energy at the onset of instability, and timescales for the modes with m = 2, 3, and 4 are estimated for each sequence. The value of (T/W) 2 is largely independent of the equation of state and rotation law. For m > 2, (T/W)/sub m/ decreases as the equation of state becomes softer, i.e., as the polytropic index n increases, and increases as the amount of differential rotation increases. The most striking result of this behavior occurs for uniform rotation
Global aspects of complex geometry
Catanese, Fabrizio; Huckleberry, Alan T
2006-01-01
Present an overview of developments in Complex Geometry. This book covers topics that range from curve and surface theory through special varieties in higher dimensions, moduli theory, Kahler geometry, and group actions to Hodge theory and characteristic p-geometry.
Reedy, Todd Mitchell
decreasing pressure. Implementing an array of eight electric arcs circumferentially around the base near the corner expansion, the LAFPA actuators were shown to produce significant disturbances to the separating shear layer of the base flow and cause modest influences on the base pressure when actuated over a range of high frequencies (O(kHz)), forcing modes, duty cycles, and electrical currents. To tailor the plasma actuator toward the specific flow control application of the separated base flow, several actuator geometries and energy additions were evaluated. Displaying the ability to produce disturbances in the shear layer, an open cavity actuator design outperformed the other geometries consisting of a confined cavity with an exhaust orifice. Increases in duty cycle (between 2% and 6%) and in plasma current (1/4 to 4 amps) were shown to produce large velocity disturbances causing a decrease in average base pressure. At 4 amps and a maximum duty cycle of 6%, the largest measured change in area-weighted base pressure, near -1.5%, was observed for the axisymmetric forcing mode. Positive changes in base pressure were experienced (as much as 1% increase from the no-control) for the vertical and horizontal flapping modes.
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...
International Nuclear Information System (INIS)
Jonsson, Rickard; Westman, Hans
2006-01-01
We show that by employing the standard projected curvature as a measure of spatial curvature, we can make a certain generalization of optical geometry (Abramowicz M A and Lasota J-P 1997 Class. Quantum Grav. A 14 23-30). This generalization applies to any spacetime that admits a hypersurface orthogonal shearfree congruence of worldlines. This is a somewhat larger class of spacetimes than the conformally static spacetimes assumed in standard optical geometry. In the generalized optical geometry, which in the generic case is time dependent, photons move with unit speed along spatial geodesics and the sideways force experienced by a particle following a spatially straight line is independent of the velocity. Also gyroscopes moving along spatial geodesics do not precess (relative to the forward direction). Gyroscopes that follow a curved spatial trajectory precess according to a very simple law of three-rotation. We also present an inertial force formalism in coordinate representation for this generalization. Furthermore, we show that by employing a new sense of spatial curvature (Jonsson R 2006 Class. Quantum Grav. 23 1)) closely connected to Fermat's principle, we can make a more extensive generalization of optical geometry that applies to arbitrary spacetimes. In general this optical geometry will be time dependent, but still geodesic photons move with unit speed and follow lines that are spatially straight in the new sense. Also, the sideways experienced (comoving) force on a test particle following a line that is straight in the new sense will be independent of the velocity
Liu, Jianyong; Lu, Yajun; Li, Zhiping
2010-05-01
Non-axisymmetric wake impact experiments were carried out after the best exciting frequency for a low speed axial compressor had been found by axisymmetric wake impact experiments. When the number and circumferential distribution of inlet guide vanes (IGV) are logical the wakes of non-axisymmetric IGVs can exert beneficial unsteady exciting effect on their downstream rotor flow fields and improve the compressor’s performance. In the present paper, four non-axisymmetric wake impact plans were found working better than the axisymmetric wake impact plan. Compared with the base plan, the best non-axisymmetric plan increased the compressor’s peak efficiency, and the total pressure rise by 1.1 and 2%, and enhanced the stall margin by 4.4%. The main reason why non-axisymmetric plans worked better than the axisymmetric plan was explained as the change of the unsteady exciting signal arising from IGV wakes. Besides the high-frequency components, the non-axisymmetric plan generated a beneficial low-frequency square-wave exciting signal and other secondary frequency components. Compared with the axisymmetric plan, multi-frequency exciting wakes arising from the non-axisymmetric plans are easier to get coupling relation with complex vortices such as clearance vortices, passage vortices and shedding vortices.
A time-dependent dusty gas dynamic model of axisymmetric cometary jets
International Nuclear Information System (INIS)
Korosmezey, A.; Gombosi, T.I.
1990-01-01
The present time-dependent, axisymmetric dusty gas dynamical model of inner cometary atmospheres solves the coupled and time-dependent equations of continuity, momentum, and energy for a gas-dust mixture between the surface of the nucleus and 100 km, using an axisymmetric 40 x 40 grid structure. A novel numerical method employing a second-order accurate Godunov-type scheme with dimensional splitting is used to solve the time-dependent pde system. It is established that a subsolar dust spike not predicted by previous calculations is generated by narrow axisymmetric jets, together with a jet cone whose opening angle depends on the jet length. 28 refs
Partial Fourier analysis of time-harmonic Maxwell's equations in axisymmetric domains
International Nuclear Information System (INIS)
Nkemzi, Boniface
2003-01-01
We analyze the Fourier method for treating time-harmonic Maxwell's equations in three-dimensional axisymmetric domains with non-axisymmetric data. The Fourier method reduces the three-dimensional boundary value problem to a system of decoupled two-dimensional boundary value problems on the plane meridian domain of the axisymmetric domain. The reduction process is fully described and suitable weighted spaces are introduced on the meridian domain to characterize the two-dimensional solutions. In particular, existence and uniqueness of solutions of the two-dimensional problems is proved and a priori estimates for the solutions are given. (author)
International Nuclear Information System (INIS)
Choi, S. N.; Kim, H. N.; Jang, K. S.; Kim, H. J.
2000-01-01
The purpose of this paper is to determine a two dimensional axisymmetric model through a comparative study between a three dimensional and an axisymmetric finite element analysis of the reactor coolant piping nozzle subject to internal pressure. The finite element analysis results show that the stress adopting the axisymmetric model with the radius of equivalent spherical vessel are well agree with that adopting the three dimensional model. The radii of equivalent spherical vessel are 3.5 times and 7.3 times of the radius of the reactor coolant piping for the safety injection nozzle and for the residual heat removal nozzle, respectively
International Nuclear Information System (INIS)
Galishin, A.Z.
1995-01-01
The nonaxisymmetric thermoelastic stress-strain state (SSS) of branched laminar orthotropic shells was considered; the axisymmetric thermoviscoelastic SSS of branched laminar orthotropic shells was considered; and the axisymmetric thermoviscoelastoplastic SSS of branched laminar isotropic shells was considered, taking into account of the transverse-shear deformation. In the present work, in contrast, the axisymmetric thermoviscoelastoplastic SSS of branched laminar isotropic shells is considered, taking account of transverse-shear and torsional deformation. Layers that are made from orthotropic materials and deform in the elastic region may be present
International Nuclear Information System (INIS)
Kozlov, A.N.
2010-01-01
This paper reports the results of the numerical studies of the axisymmetric flows in the plasma accelerators with the impenetrable equipotential electrodes of the various geometries. The calculations were performed using the two-dimensional two-fluid magnetohydrodynamic model taking into account the Hall effect and the conductivity tensor of the medium. The numerical experiments have allowed to reveal the influence of the electrode form on effect of occurrence of the current crisis.
Computational synthetic geometry
Bokowski, Jürgen
1989-01-01
Computational synthetic geometry deals with methods for realizing abstract geometric objects in concrete vector spaces. This research monograph considers a large class of problems from convexity and discrete geometry including constructing convex polytopes from simplicial complexes, vector geometries from incidence structures and hyperplane arrangements from oriented matroids. It turns out that algorithms for these constructions exist if and only if arbitrary polynomial equations are decidable with respect to the underlying field. Besides such complexity theorems a variety of symbolic algorithms are discussed, and the methods are applied to obtain new mathematical results on convex polytopes, projective configurations and the combinatorics of Grassmann varieties. Finally algebraic varieties characterizing matroids and oriented matroids are introduced providing a new basis for applying computer algebra methods in this field. The necessary background knowledge is reviewed briefly. The text is accessible to stud...
Discrete and computational geometry
Devadoss, Satyan L
2011-01-01
Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science. This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincaré conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also fe...
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.
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...
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...
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
Conference on Strings, Duality, and Geometry
Phong, Duong; Yau, Shing-Tung; Mirror Symmetry IV
2002-01-01
This book presents contributions of participants of a workshop held at the Centre de Recherches Mathématiques (CRM), University of Montréal. It can be viewed as a sequel to Mirror Symmetry I (1998), Mirror Symmetry II (1996), and Mirror Symmetry III (1999), copublished by the AMS and International Press. The volume presents a broad survey of many of the noteworthy developments that have taken place in string theory, geometry, and duality since the mid 1990s. Some of the topics emphasized include the following: Integrable models and supersymmetric gauge theories; theory of M- and D-branes and noncommutative geometry; duality between strings and gauge theories; and elliptic genera and automorphic forms. Several introductory articles present an overview of the geometric and physical aspects of mirror symmetry and of corresponding developments in symplectic geometry. The book provides an efficient way for a very broad audience of mathematicians and physicists to explore the frontiers of research into this rapi...
Kim, Daejoong; Gil, Y. S.; Chung, TaeWon; Chung, Suk-Ho
2009-01-01
The stabilization characteristics of premixed flames in an axisymmetric curved-wall jet burner have been experimentally investigated. This burner utilized the Coanda effect on top of a burner tip. The initially spherical burner tip was modified to a
International Nuclear Information System (INIS)
Parsa, Z.; Serafini, L.
1992-04-01
This note provides a sketch of the formalism used for the Integration of Transients in Axisymmetrical Cavities for Accelerators, (ITACA). Application to study the BNL Photocathode Gun via the code ITACA is also included
Computation of steady and unsteady compressible quasi-axisymmetric vortex flow and breakdown
Kandil, Osama A.; Kandil, Hamdy A.; Liu, C. H.
1991-01-01
The unsteady, compressible Navier-Stokes equations are used to compute and analyze compressible quasi-axisymmetric isolated vortices. The Navier-Stokes equations are solved using an implicit, upwind, flux-difference splitting finite-volume scheme. The developed three-dimensional solver has been verified by comparing its solution profiles with those of a slender, quasi-axisymmetric vortex solver for a subsonic, isolated quasi-axisymmetric vortex in an unbounded domain. The Navier-Stokes solver is then used to solve for a supersonic quasi-axisymmetric vortex flow in a configured circular duct. Steady and unsteady vortex-shock interactions and breakdown have been captured. The problem has also been calculated using the Euler solver of the same code and the results are compared with those of the Navier-Stokes solver. The effect of the initial swirl has been tentatively studied.
Computation of compressible quasi-axisymmetric slender vortex flow and breakdown
Kandil, Osama A.; Kandil, Hamdy A.
1991-01-01
The unsteady, compressible Navier-Stokes equations are used to compute and analyze compressible quasi-axisymmetric isolated vortices. The Navier-Stokes equations are solved using an implicit, upwind, flux difference splitting finite volume scheme. The developed three dimensional solver was verified by comparing its solution profiles with those of a slender, quasi-axisymmetric vortex solver for a subsonic, quasi-axisymmetric vortex in an unbounded domain. The Navier-Stokes solver is then used to solve for a supersonic, quasi-axisymmetric vortex flow in a configured circular duct. Steady and unsteady vortex-shock interactions and breakdown were captured. The problem was also calculated using the Euler solver of the same code; the results were compared with those of the Navier-Stokes solver. The effect of the initial swirl was investigated.
Elastic-plastic analysis of an axi-symmetric problem by a finite element method
International Nuclear Information System (INIS)
Isozaki, Toshikuni
1984-06-01
Generally speaking, many structures are designed and fabricated on the basis of an axi-symmetric structure. Finite Element Method is the capable method to solve these axi-symmetric problems beyond the elastic limit. As the first step to solve these problems, the computer program for the elastic-plastic analysis of the axi-symmetric problem is composed. The basic program is based upon that described in Zienkiewicz's text book to solve the elastic plane stress problem, taking the plastic stress matrix by Yamada's method into consideration and it is converted to solve the axi-symmetric problem. For the verification of the program, the plane strain problem of a cylindrical tube under internal pressure was solved. The computed results were compared with those shown in ADINA's user's manual. They showed close agreement. (author)
UWMAK-II: a conceptual tokamak reactor design
International Nuclear Information System (INIS)
1975-10-01
This report describes the conceptual design of a Tokamak fusion power reactor, UWMAK-II. The aim of this study is to perform a self consistent and thorough analysis of a probable future fusion power reactor in order to assess the technological problems posed by such a system and to examine feasible solutions. UWMAK-II is a conceptual Tokamak fusion reactor designed to deliver 1716 MWe continuously and to generate 5000 MW(th) during the plasma burn. The structural material is 316 stainless steel and the primary coolant is helium. UWMAK-II is a low aspect ratio, low field design and includes a double null, axisymmetric poloidal field divertor for impurity control. In addition, a carbon curtain, made of two dimensional woven carbon fiber, is mounted on the first vacuum chamber wall to protect the plasma from high Z impurities and to protect the first wall from erosion by charged particle bombardment. The blanket is designed to minimize the inventory of both tritium and lithium while achieving a breeding ratio greater than one. This has led to a blanket design based on the use of a solid breeding material (LiAlO 2 ) with beryllium as a neutron multiplier. The lithium is enriched to 90 percent 6 Li and the blanket coolant is helium at a maximum pressure of 750 psia (5.2 x 10 6 N/m 2 ). A cell of the UWMAK-II blanket design is shown. The breeding ratio is between 1.11 and 1.19 based on one-dimensional discrete ordinates transport calculations, depending on the method of homogenization. Detailed Monte Carlo calculations, which take into account the more complicated geometry, give a breeding ratio of 1.06. The total energy per fusion is 21.56 MeV, which is fairly high
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.
Multiplicity in difference geometry
Tomasic, Ivan
2011-01-01
We prove a first principle of preservation of multiplicity in difference geometry, paving the way for the development of a more general intersection theory. In particular, the fibres of a \\sigma-finite morphism between difference curves are all of the same size, when counted with correct multiplicities.
Spacetime and Euclidean geometry
Brill, Dieter; Jacobson, Ted
2006-04-01
Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a two-dimensional spacetime diagram is proportional to the Euclidean area of the corresponding causal domain. We use this relation to derive the Minkowski line element by two geometric proofs of the spacetime Pythagoras theorem.
International Nuclear Information System (INIS)
Konopleva, N.P.
2009-01-01
The basic ideas of description methods of physical fields and elementary particle interactions are discussed. One of such ideas is the conception of space-time geometry. In this connection experimental measurement methods are analyzed. It is shown that measure procedures are the origin of geometrical axioms. The connection between space symmetry properties and the conservation laws is considered
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…
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)
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...
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.
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.
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.
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.
International Nuclear Information System (INIS)
Ezin, J.P.
1988-08-01
The lectures given at the ''5th Symposium of Mathematics in Abidjan: Differential Geometry and Mechanics'' are presented. They are divided into four chapters: Riemannian metric on a differential manifold, curvature tensor fields on a Riemannian manifold, some classical functionals on Riemannian manifolds and questions. 11 refs
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 ...
Lauriola, I.; Felisa, G.; Petrolo, D.; Di Federico, V.; Longo, S.
2018-05-01
We present an investigation on the combined effect of fluid rheology and permeability variations on the propagation of porous gravity currents in axisymmetric geometry. The fluid is taken to be of power-law type with behaviour index n and the permeability to depend from the distance from the source as a power-law function of exponent β. The model represents the injection of a current of non-Newtonian fluid along a vertical bore hole in porous media with space-dependent properties. The injection is either instantaneous (α = 0) or continuous (α > 0). A self-similar solution describing the rate of propagation and the profile of the current is derived under the assumption of small aspect ratio between the current average thickness and length. The limitations on model parameters imposed by the model assumptions are discussed in depth, considering currents of increasing/decreasing velocity, thickness, and aspect ratio, and the sensitivity of the radius, thickness, and aspect ratio to model parameters. Several critical values of α and β discriminating between opposite tendencies are thus determined. Experimental validation is performed using shear-thinning suspensions and Newtonian mixtures in different regimes. A box filled with ballotini of different diameter is used to reproduce the current, with observations from the side and bottom. Most experimental results for the radius and profile of the current agree well with the self-similar solution except at the beginning of the process, due to the limitations of the 2-D assumption and to boundary effects near the injection zone. The results for this specific case corroborate a general model for currents with constant or time-varying volume of power-law fluids propagating in porous domains of plane or radial geometry, with uniform or varying permeability, and the possible effect of channelization. All results obtained in the present and previous papers for the key parameters governing the dynamics of power-law gravity
Effect of compressibility on the global stability of axisymmetric wake flows
Meliga , Philippe; Sipp , D.; Chomaz , Jean-Marc
2010-01-01
International audience; We study the linear dynamics of global eigenmodes in compressible axisymmetric wake flows, up to the high subsonic regime. We consider both an afterbody flow at zero angle of attack and a sphere, and find that the sequence of bifurcations destabilizing the axisymmetric steady flow is independent of the Mach number and reminiscent of that documented in the incompressible wake past a sphere and a disk (Natarajan & Acrivos, J. Fluid Mech., vol. 254, 1993, p. 323), hence s...
Flock, M.; Ruge, J. P.; Dzyurkevich, N.; Henning, Th.; Klahr, H.; Wolf, S.
2014-01-01
International audience; Aims. Recent observations by the Atacama Large Millimeter/submillimeter Array (ALMA) of disks around young stars revealed distinct asymmetries in the dust continuum emission. In this work we wish to study axisymmetric and non-axisymmetric structures that are generated by the magneto-rotational instability in the outer regions of protoplanetary disks. We combine the results of state-of-the-art numerical simulations with post-processing radiative transfer (RT) to generat...
First integrals of the axisymmetric shape equation of lipid membranes
Zhang, Yi-Heng; McDargh, Zachary; Tu, Zhan-Chun
2018-03-01
The shape equation of lipid membranes is a fourth-order partial differential equation. Under the axisymmetric condition, this equation was transformed into a second-order ordinary differential equation (ODE) by Zheng and Liu (Phys. Rev. E 48 2856 (1993)). Here we try to further reduce this second-order ODE to a first-order ODE. First, we invert the usual process of variational calculus, that is, we construct a Lagrangian for which the ODE is the corresponding Euler–Lagrange equation. Then, we seek symmetries of this Lagrangian according to the Noether theorem. Under a certain restriction on Lie groups of the shape equation, we find that the first integral only exists when the shape equation is identical to the Willmore equation, in which case the symmetry leading to the first integral is scale invariance. We also obtain the mechanical interpretation of the first integral by using the membrane stress tensor. Project supported by the National Natural Science Foundation of China (Grant No. 11274046) and the National Science Foundation of the United States (Grant No. 1515007).
Thin circular cylinder under axisymmetrical thermal and mechanical loading
International Nuclear Information System (INIS)
Arnaudeau, F.; Zarka, J.; Gerij, J.
1977-01-01
A special purpose computer code (Ratch) was developed to analyse a thin circular cylinder subjected to axisymmetrical mechanical and thermal loadings. The Mendelson's approach of this problem is followed. Classical Kirchoff-Love hypothesis of thin shells is used and a state of plane stress is assumed. Space integrations are performed by Gaussian quadrature in the axial direction and by Simpson's one third rule throughout the thickness. Thermoelastic-plastic constitutive equations are solved with an implicit scheme (Nguyen). Thermovisco-plastic constitutive equations are solved with an explicit time integration scheme (Treanor's algorithm especially fitted). A Bree type diagram is obtained for an axial step of temperature which varies cyclically and a sustained constant axial load. The material behavior is assumed perfectly plastic and creep effect is not considered. Results show that the domain where ratchetting occurs is reduced when compared with the domain predicted by the Bree diagram. To investigate the effect of material hardening the authors verify Halphen's Theorem which states that a structure made of material with kinematic hardening behavior and constant properties with temperature will always shake down to a periodic behavior. (Auth.)
Plasma equilibria and stationary flows in axisymmetric systems. Pt. 3
International Nuclear Information System (INIS)
Zelazny, R.; Stankiewicz, R.; Galkowski, A.; Potempski, S.; Pietak, R.
1990-08-01
The problem of the importance of poloidal flows for the behaviour of plasmas in axisymmetric systems has caused a lot of discussion and controversy during the last 15 years. There is no doubt that the mere existence of poloidal flow transforms the elliptic Grad-Shafranov-Schlueter equation into a system of mixed type partial differential equation and an algebraic multivalued Bernoulli equation. This fact leads to the appearance of Bernoulli branches in the solutions. Then, one can come across three branches of elliptic solutions as well as two branches of hyperbolic solutions with the possible appearance of phenomena connected with ''transsonic'' effects. Problems connected with such a mathematical situation have been extensively discussed in the report with the same title, dated May 1988, which we shall call later Part I of our studies on this subject. The present report, considered as Part III, is devoted to the presentation of results of efforts aimed at constructing programmes which allow us to solve the extended Grad-Shafranov-Schlueter equation (EGSS) (with stationary flows) in a more realistic situation relevant to the JET operating conditions. The main problem is to specify for a wider class of profiles the boundary conditions at the magnetic axis for a system of nonlinear ordinary differential equations ODE, resulting from EGSS equation after application of Fourier transformation techniques and of inverse method approach. The present report elaborates a much more general case and describes the computational framework enabling us to derive those boundary conditions. (author)
Linear theory of the tearing instability in axisymmetric toroidal devices
International Nuclear Information System (INIS)
Rogister, A.; Singh, R.
1988-08-01
We derive a very general kinetic equation describing the linear evolution of low m/l modes in axisymmetric toroidal plasmas with arbitrary cross sections. Included are: Ion sound, inertia, diamagnetic drifts, finite poloidal beta, and finite ion Larmor radius effects. Assuming the magnetic surfaces to form a set of nested tori with circular cross sections of shifted centers, and introducing adequate simplifications justified by our knowledge of experimental tokamak plasmas, we then obtain explicitely the sets of equations describing the coupling of the quasimodes 0/1, 1/1, 2/1, and, for m≥2, m/1, (m+1)/1. By keeping finite aspect ratio effects into account when calculating the jump of the derivative of the eigenfunction, it is shown that the theory can explain the rapid evolution, within one sawtooth period, of the growth rate of the sawteeth precursors from resistive values to magnetohydrodynamic ones. The characteristics thus theoretically required from current profiles in sawtoothing discharges have clearly been observed. Other aspects of the full theory could be relevant to the phenomenon of major disruptions. (orig.)
The Poisson equation in axisymmetric domains with conical points
International Nuclear Information System (INIS)
Nkemzi, B.
2003-01-01
This paper analyzes the application of the Fourier-finite-element method (FFEM) for the resolution of the Derichlet problem for the Poisson equation -Δu-circumflex = f-circumflex in axisymmetric domains Ω-circumflex subset of R 3 with conical points on the rotation axis. The FFEM combines the approximate Fourier method with respect to one space direction with the finite element method for the approximate calculation of the Fourier coefficients of the solution. Here, the influence of the conical points on the regularity of the Fourier coefficients of the solution is analyzed and the asymptotic behaviour of the coefficients near the conical points is described by some singularity functions and treated numerically by mesh grading in the two-dimensional meridian of Ω-circumflex. It is proved that for f-circumflex in L 2 (Ω-circumflex), the rate of convergence of the combined approximations in the Sobolev space W 2 1 (Ω-circumflex) is of the order O(h + N -1 ), where h and N represent, respectively, the parameters of the finite-element- and the Fourier-approximation, with h → 0 and n → ∞. (author)
Axisymmetric core collapse simulations using characteristic numerical relativity
International Nuclear Information System (INIS)
Siebel, Florian; Mueller, Ewald; Font, Jose A.; Papadopoulos, Philippos
2003-01-01
We present results from nonrotating axisymmetric stellar core collapse simulations in general relativity. Our hydrodynamics code has proved robust and accurate enough to allow for a detailed analysis of the global dynamics of the collapse. Contrary to traditional approaches based on the 3+1 formulation of the gravitational field equations, our framework uses a foliation based on a family of outgoing light cones, emanating from a regular center, and terminating at future null infinity. Such a coordinate system is well adapted to the study of interesting dynamical spacetimes in relativistic astrophysics such as stellar core collapse and neutron star formation. Perhaps most importantly this procedure allows for the extraction of gravitational waves at future null infinity, along with the commonly used quadrupole formalism for the gravitational wave extraction. Our results concerning the gravitational wave signals show noticeable disagreement when those are extracted by computing the Bondi news at future null infinity on the one hand and by using the quadrupole formula on the other hand. We have a strong indication that for our setup the quadrupole formula on the null cone does not lead to physical gravitational wave signals. The Bondi gravitational wave signals extracted at infinity show typical oscillation frequencies of about 0.5 kHz
Propagation of a hybrid inferior wave in axisymmetrical plasma
International Nuclear Information System (INIS)
Fivaz, M.; Appert, K.; Krlin, L.
1990-05-01
The linear propagation of hybrid inferior waves in an axisymmetrical plasma (magnetohydrodynamic equilibrium of the Soloviev type) has been numerically simulated. The evolution of k // (component of the wave vector k parallel to the magnetic field B), important for current drive modelling, has been studied as a function of the geometric parameters of the equilibrium: aspect ratio, ellipticity and triangularity. The results show that k // depends abruptly on the parameters; the engendered structures are very rich. Two mechanisms by which k // increases have been shown: the 'resonance' occurring in small bands of the space of the parameters and which is associated with trajectories in (R,Z) near stabilization; a stochastic evolution resembling diffusion in equlibriums of very high triangularity. However, a strong increase of k // of a part of the waves, susceptible of engendering a current in the plasma, has only been observed in a minority of cases. In literature current drive experiments have been reported which work and whose parameters are a priori such that our model cannot be expected to show the desired growth of k // . Consequently, our model, which is similar to normally used models, does not explain the current drive. 5 refs., 16 figs
Characterization of axisymmetric disruption dynamics toward VDE avoidance in tokamaks
International Nuclear Information System (INIS)
Nakamura, Y.
2002-01-01
Disruption experiments on Alcator C-Mod and ASDEX-Upgrade tokamaks and axisymmetric MHD simulations using the TSC have explicated the underlying mechanisms of Vertical Displacement Events (VDEs) and a diversity of disruption dynamics. First, the neutral point, which is known as an initial vertical plasma position advantageous to VDE avoidance, is shown to be fairly insensitive to plasma shape and current profile parameters, while the VDE rate significantly depends on those parameters. Secondly, it is clarified that a rapid flattening of the plasma current profile frequently seen at the thermal quench drags a single null-diverted, up-down asymmetric plasma vertically toward divertor, whereas the dragging effect is absent in up-down symmetric limiter discharges. As a consequence, the occurrence of downward-going VDEs predominates over the upward-going ones in bottom-diverted discharges, being consistent with experiments in ASDEX-Upgrade. Together with the attractive force that arises from passive shell currents induced by the current quench and vanishes at the neutral point, the dragging effect explains many details of the VDE dynamics over the whole period of disruptive termination. (author)
Characterization of axisymmetric disruption dynamics toward VDE avoidance in tokamaks
International Nuclear Information System (INIS)
Nakamura, Y.; Yoshino, R.; Granetz, R.S.; Pautasso, G.; Gruber, O.; Jardin, S.C.
2003-01-01
Experiments and axisymmetric MHD simulations on tokamak disruptions have explicated the underlying mechanisms of Vertical Displacement Events (VDEs) and a diversity of disruption dynamics. First, the neutral point, which is known as an advantageous vertical plasma position to avoiding VDEs during the plasma current quench, is shown to be fairly insensitive to plasma shape and current profile parameters. Secondly, a rapid flattening of the plasma current profile frequently seen at thermal quench is newly clarified to play a substantial role in dragging a single null-diverted plasma vertically towards the divertor. As a consequence, the occurrence of downward-going VDEs predominates over the upward-going ones in bottom diverted discharges. This dragging effect is absent in up-down symmetric limiter discharges. These simulation results are consistent with experiments. Together with the attractive force that arises from passive shell currents and essentially vanishes at the neutral point, the dragging effect explains many details of the VDE dynamics over the whole period of the disruptive termination. (author)
Axisymmetric bifurcations of thick spherical shells under inflation and compression
deBotton, G.; Bustamante, R.; Dorfmann, A.
2013-01-01
Incremental equilibrium equations and corresponding boundary conditions for an isotropic, hyperelastic and incompressible material are summarized and then specialized to a form suitable for the analysis of a spherical shell subject to an internal or an external pressure. A thick-walled spherical shell during inflation is analyzed using four different material models. Specifically, one and two terms in the Ogden energy formulation, the Gent model and an I1 formulation recently proposed by Lopez-Pamies. We investigate the existence of local pressure maxima and minima and the dependence of the corresponding stretches on the material model and on shell thickness. These results are then used to investigate axisymmetric bifurcations of the inflated shell. The analysis is extended to determine the behavior of a thick-walled spherical shell subject to an external pressure. We find that the results of the two terms Ogden formulation, the Gent and the Lopez-Pamies models are very similar, for the one term Ogden material we identify additional critical stretches, which have not been reported in the literature before.© 2012 Published by Elsevier Ltd.
Direct numerical simulation of axisymmetric laminar low-density jets
Gomez Lendinez, Daniel; Coenen, Wilfried; Sevilla, Alejandro
2017-11-01
The stability of submerged laminar axisymmetric low-density jets has been investigated experimentally (Kyle & Sreenivasan 1993, Hallberg & Strykowski 2006) and with linear analysis (Jendoubi & Strykowski 1994, Coenen & Sevilla 2012, Coenen et al. 2017). These jets become globally unstable when the Reynolds number is larger than a certain critical value which depends on the density ratio and on the velocity profile at the injector outlet. In this work, Direct Numerical Simulations using FreeFEM + + (Hecht 2012) with P1 elements for pressure and P2 for velocity and density are performed to complement the above mentioned studies. Density and velocity fields are analyzed at long time showing the unforced space-time evolution of nonlinear disturbances propagating along the jet. Using the Stuart-Landau model to fit the numerical results for the self-excited oscillations we have computed a neutral stability curve that shows good agreement with experiments and stability theory. Thanks to Spanish MINECO under projects DPI2014-59292-C3-1-P and DPI2015-71901-REDT for financial support.
Calculation of transport coefficients in an axisymmetric plasma
International Nuclear Information System (INIS)
Shumaker, D.E.
1976-01-01
A method of calculating the transport coefficient in an axisymmetric toroidal plasma is presented. This method is useful in calculating the transport coefficients in a Tokamak plasma confinement device. The particle density and temperature are shown to be a constant on a magnetic flux surface. Transport equations are given for the total particle flux and total energy flux crossing a closed toroidal surface. Also transport equations are given for the toroidal magnetic flux. A computer code was written to calculate the transport coefficients for a three species plasma, electrons and two species of ions. This is useful for calculating the transport coefficients of a plasma which contains impurities. It was found that the particle and energy transport coefficients are increased by a large amount, and the transport coefficients for the toroidal magnetic field are reduced by a small amount. For example, a deuterium plasma with 1.3 percent oxygen, one of the particle transport coefficients is increased by a factor of about four. The transport coefficients for the toroidal magnetic flux are reduced by about 20 percent. The increase in the particle transport coefficient is due to the collisional scattering of the deuterons by the heavy oxygen ions which is larger than the deuteron electron scattering, the normal process for particle transport in a two species plasma. The reduction in the toroidal magnetic flux transport coefficients are left unexplained
Axisymmetric toroidal equilibrium with flow and anisotropic pressure
International Nuclear Information System (INIS)
Iacono, R.; Bondeson, A.; Troyon, F.; Gruber, R.
1989-10-01
Axisymmetric toroidal plasma equilibria with mass flows and anisotropic pressure are investigated. The equilibrium system is derived for a general functional form of the pressures, which includes both fluid models, such as the magnetohydrodynamic (MHD) and the double-adiabatic models, and Grad's guiding centre model. This allows for detailed comparisons between the models and clarifies how the 'first hyperbolic region', occurring in the fluid theory when the poloidal flow is of the order of the poloidal sound speed, can be eliminated in guiding centre theory. In the case of a pure toroidal rotation, macroscopic equations of state are derived from the guiding centre model, characterized by a parallel temperature that is constant on each magnetic surface and a perpendicular temperature that varies with the magnetic field. The outward centrifugal shifts of the magnetic axis and of the mass density profile, due to toroidal rotation, are increased by anisotropy. The guiding centre model shows that poloidal flow produces an inward shift of the density profile, in contrast with the MHD result. (author) 1 fig., 1 tab., 17 refs
Plasma equilibria and stationary flows in axisymmetric systems. Pt. 1
International Nuclear Information System (INIS)
Zelazny, R.; Stankiewicz, R.; Potempski, S.
1988-05-01
During discharges within a tokamak device such as JET fluctuations are observed in the plasma, of plasma density, temperature, electric potential and of the magnetic field. These fluctuations have complicated structure and are linked with different kinds of instabilities. However, it is not clear which instabilities are most important in determining the behaviour of the plasma. A comprehensive numerical theory which can predict the effect of the instabilities on the transport of plasma in axisymmetric systems has been sought using the static Grad-Shafranov-Schlueter (SGSS) equation as a basis. However, the static equation was over simplified for the situation in JET with additional heating giving rise to large toroidal flows, and an extended equation (EGSS) was developed. The results of the study include the discovery of algebraic branches of solutions to the EGSS equation even for very small poloidal flows, solutions to the inverse problem for the SGSS and EGSS equations using Fourier decomposition, classification of the boundary condition at the magnetic axis, demonstration of a visible effect of the poloidal flow on the separation of the density surface and the magnetic surface an indication of the existence of multiple branches of solutions to the EGSS and SGSS equations and their relation to stability properties. (U.K.)
Wave scattering by an axisymmetric ice floe of varying thickness
Bennetts, Luke G.; Biggs, Nicholas R. T.; Porter, David
2009-04-01
The problem of water wave scattering by a circular ice floe, floating in fluid of finite depth, is formulated and solved numerically. Unlike previous investigations of such situations, here we allow the thickness of the floe (and the fluid depth) to vary axisymmetrically and also incorporate a realistic non-zero draught. A numerical approximation to the solution of this problem is obtained to an arbitrary degree of accuracy by combining a Rayleigh-Ritz approximation of the vertical motion with an appropriate variational principle. This numerical solution procedure builds upon the work of Bennets et al. (2007, J. Fluid Mech., 579, 413-443). As part of the numerical formulation, we utilize a Fourier cosine expansion of the azimuthal motion, resulting in a system of ordinary differential equations to solve in the radial coordinate for each azimuthal mode. The displayed results concentrate on the response of the floe rather than the scattered wave field and show that the effects of introducing the new features of varying floe thickness and a realistic draught are significant.
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.
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...
Multilevel geometry optimization
Rodgers, Jocelyn M.; Fast, Patton L.; Truhlar, Donald G.
2000-02-01
Geometry optimization has been carried out for three test molecules using six multilevel electronic structure methods, in particular Gaussian-2, Gaussian-3, multicoefficient G2, multicoefficient G3, and two multicoefficient correlation methods based on correlation-consistent basis sets. In the Gaussian-2 and Gaussian-3 methods, various levels are added and subtracted with unit coefficients, whereas the multicoefficient Gaussian-x methods involve noninteger parameters as coefficients. The multilevel optimizations drop the average error in the geometry (averaged over the 18 cases) by a factor of about two when compared to the single most expensive component of a given multilevel calculation, and in all 18 cases the accuracy of the atomization energy for the three test molecules improves; with an average improvement of 16.7 kcal/mol.
Multilevel geometry optimization
Energy Technology Data Exchange (ETDEWEB)
Rodgers, Jocelyn M. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States); Fast, Patton L. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States); Truhlar, Donald G. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States)
2000-02-15
Geometry optimization has been carried out for three test molecules using six multilevel electronic structure methods, in particular Gaussian-2, Gaussian-3, multicoefficient G2, multicoefficient G3, and two multicoefficient correlation methods based on correlation-consistent basis sets. In the Gaussian-2 and Gaussian-3 methods, various levels are added and subtracted with unit coefficients, whereas the multicoefficient Gaussian-x methods involve noninteger parameters as coefficients. The multilevel optimizations drop the average error in the geometry (averaged over the 18 cases) by a factor of about two when compared to the single most expensive component of a given multilevel calculation, and in all 18 cases the accuracy of the atomization energy for the three test molecules improves; with an average improvement of 16.7 kcal/mol. (c) 2000 American Institute of Physics.
Krauss, Lawrence M.; Turner, Michael S.
1999-01-01
The recognition that the cosmological constant may be non-zero forces us to re-evaluate standard notions about the connection between geometry and the fate of our Universe. An open Universe can recollapse, and a closed Universe can expand forever. As a corollary, we point out that there is no set of cosmological observations we can perform that will unambiguously allow us to determine what the ultimate destiny of the Universe will be.
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....
International Nuclear Information System (INIS)
Lepora, N.; Kibble, T.
1999-01-01
We analyse symmetry breaking in the Weinberg-Salam model paying particular attention to the underlying geometry of the theory. In this context we find two natural metrics upon the vacuum manifold: an isotropic metric associated with the scalar sector, and a squashed metric associated with the gauge sector. Physically, the interplay between these metrics gives rise to many of the non-perturbative features of Weinberg-Salam theory. (author)
International Nuclear Information System (INIS)
Hull, C.M.
1993-01-01
The geometric structure of theories with gauge fields of spins two and higher should involve a higher spin generalisation of Riemannian geometry. Such geometries are discussed and the case of W ∝ -gravity is analysed in detail. While the gauge group for gravity in d dimensions is the diffeomorphism group of the space-time, the gauge group for a certain W-gravity theory (which is W ∝ -gravity in the case d=2) is the group of symplectic diffeomorphisms of the cotangent bundle of the space-time. Gauge transformations for W-gravity gauge fields are given by requiring the invariance of a generalised line element. Densities exist and can be constructed from the line element (generalising √detg μν ) only if d=1 or d=2, so that only for d=1,2 can actions be constructed. These two cases and the corresponding W-gravity actions are considered in detail. In d=2, the gauge group is effectively only a subgroup of the symplectic diffeomorphisms group. Some of the constraints that arise for d=2 are similar to equations arising in the study of self-dual four-dimensional geometries and can be analysed using twistor methods, allowing contact to be made with other formulations of W-gravity. While the twistor transform for self-dual spaces with one Killing vector reduces to a Legendre transform, that for two Killing vectors gives a generalisation of the Legendre transform. (orig.)
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...
CBM RICH geometry optimization
Energy Technology Data Exchange (ETDEWEB)
Mahmoud, Tariq; Hoehne, Claudia [II. Physikalisches Institut, Giessen Univ. (Germany); Collaboration: CBM-Collaboration
2016-07-01
The Compressed Baryonic Matter (CBM) experiment at the future FAIR complex will investigate the phase diagram of strongly interacting matter at high baryon density and moderate temperatures in A+A collisions from 2-11 AGeV (SIS100) beam energy. The main electron identification detector in the CBM experiment will be a RICH detector with a CO{sub 2} gaseous-radiator, focusing spherical glass mirrors, and MAPMT photo-detectors being placed on a PMT-plane. The RICH detector is located directly behind the CBM dipole magnet. As the final magnet geometry is now available, some changes in the RICH geometry become necessary. In order to guarantee a magnetic field of 1 mT at maximum in the PMT plane for effective operation of the MAPMTs, two measures have to be taken: The PMT plane is moved outwards of the stray field by tilting the mirrors by 10 degrees and shielding boxes have been designed. In this contribution the results of the geometry optimization procedure are presented.
Golbedaghi, Reza; Alavipour, Ehsan
2015-11-01
Three new binuclear Cu(II), Mn(II), Co(II) complexes [Cu2(L) (ClO4)](ClO4)2 (1), [Mn2(L) (ClO4)](ClO4)2 (2), and [Co2(L) (ClO4)](ClO4)2 (3), {L = 1,3-bis(2-((Z)-(2-aminopropylimino)methyl)phenoxy)propan-2-ol} have been synthesized. Single crystal X-ray structure analysis of complex 1 showed that the complex is binuclear and all nitrogen and oxygen atoms of ligand (N4O3) are coordinated to two Cu(II) center ions. In addition, the crystal structure studying shows, a perchlorate ion has been bridged to the Cu(II) metal centers. However, two distorted square pyramidal Cu(II) ions are bridged asymmetrically by a perchlorate ion and oxygen of hydroxyl group of Schiff base ligand. In addition, the conductometry behaviors of all complexes were studied in acetonitrile solution.
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.
Simulations of ion beams for NDCX-II
Energy Technology Data Exchange (ETDEWEB)
Grote, D.P., E-mail: dpgrote@lbl.gov [LBNL MS47-112, 1 Cyclotron Rd, Bekerley, CA 94720 (United States); Lawrence Livermore National Lab, Livermore, CA 94550 (United States); Friedman, A., E-mail: afriedman@lbl.gov [Lawrence Livermore National Lab, Livermore, CA 94550 (United States); Sharp, W.M. [Lawrence Livermore National Lab, Livermore, CA 94550 (United States)
2014-01-01
NDCX-II, the second neutralized drift compression experiment, is a moderate energy, high current accelerator designed to drive targets for warm dense matter and IFE-relevant energy coupling studies, and to serve as a testbed for high current accelerator physics. As part of the design process, studies were carried out to assess the sensitivities of the accelerator to errors, and to further optimize the design in concert with the evolving pulsed power engineering. The Warp code was used to carry out detailed simulations in both axisymmetric and full 3-D geometry. Ensembles of simulations were carried out to characterize the effects of errors, such as timing jitter and noise on the accelerator waveforms, noise on the source waveform, and solenoid and source offsets. In some cases, the ensemble studies resulted in better designs, revealing operating points with improved performance and showing possible means for further improvement. These studies also revealed a new non-paraxial effect of the final focus solenoid on the beam, which must be taken into account in designing an optimal final focusing system.
Two lectures on D-geometry and noncommutative geometry
International Nuclear Information System (INIS)
Douglas, M.R.
1999-01-01
This is a write-up of lectures given at the 1998 Spring School at the Abdus Salam ICTP. We give a conceptual introduction to D-geometry, the study of geometry as seen by D-branes in string theory, and to noncommutative geometry as it has appeared in D-brane and Matrix theory physics. (author)
Forcing scheme analysis for the axisymmetric lattice Boltzmann method under incompressible limit.
Zhang, Liangqi; Yang, Shiliang; Zeng, Zhong; Chen, Jie; Yin, Linmao; Chew, Jia Wei
2017-04-01
Because the standard lattice Boltzmann (LB) method is proposed for Cartesian Navier-Stokes (NS) equations, additional source terms are necessary in the axisymmetric LB method for representing the axisymmetric effects. Therefore, the accuracy and applicability of the axisymmetric LB models depend on the forcing schemes adopted for discretization of the source terms. In this study, three forcing schemes, namely, the trapezium rule based scheme, the direct forcing scheme, and the semi-implicit centered scheme, are analyzed theoretically by investigating their derived macroscopic equations in the diffusive scale. Particularly, the finite difference interpretation of the standard LB method is extended to the LB equations with source terms, and then the accuracy of different forcing schemes is evaluated for the axisymmetric LB method. Theoretical analysis indicates that the discrete lattice effects arising from the direct forcing scheme are part of the truncation error terms and thus would not affect the overall accuracy of the standard LB method with general force term (i.e., only the source terms in the momentum equation are considered), but lead to incorrect macroscopic equations for the axisymmetric LB models. On the other hand, the trapezium rule based scheme and the semi-implicit centered scheme both have the advantage of avoiding the discrete lattice effects and recovering the correct macroscopic equations. Numerical tests applied for validating the theoretical analysis show that both the numerical stability and the accuracy of the axisymmetric LB simulations are affected by the direct forcing scheme, which indicate that forcing schemes free of the discrete lattice effects are necessary for the axisymmetric LB method.
Computer Aided Process Planning for Non-Axisymmetric Deep Drawing Products
Park, Dong Hwan; Yarlagadda, Prasad K. D. V.
2004-06-01
In general, deep drawing products have various cross-section shapes such as cylindrical, rectangular and non-axisymmetric shapes. The application of the surface area calculation to non-axisymmetric deep drawing process has not been published yet. In this research, a surface area calculation for non-axisymmetric deep drawing products with elliptical shape was constructed for a design of blank shape of deep drawing products by using an AutoLISP function of AutoCAD software. A computer-aided process planning (CAPP) system for rotationally symmetric deep drawing products has been developed. However, the application of the system to non-axisymmetric components has not been reported yet. Thus, the CAPP system for non-axisymmetric deep drawing products with elliptical shape was constructed by using process sequence design. The system developed in this work consists of four modules. The first is recognition of shape module to recognize non-axisymmetric products. The second is a three-dimensional (3-D) modeling module to calculate the surface area for non-axisymmetric products. The third is a blank design module to create an oval-shaped blank with the identical surface area. The forth is a process planning module based on the production rules that play the best important role in an expert system for manufacturing. The production rules are generated and upgraded by interviewing field engineers. Especially, the drawing coefficient, the punch and die radii for elliptical shape products are considered as main design parameters. The suitability of this system was verified by applying to a real deep drawing product. This CAPP system constructed would be very useful to reduce lead-time for manufacturing and improve an accuracy of products.
Kinetic extensions of magnetohydrodynamic models for axisymmetric toroidal plasmas
International Nuclear Information System (INIS)
Cheng, C.Z.
1989-04-01
A nonvariational kinetic-MHD stability code (NOVA-K) has been developed to integrate a set of non-Hermitian integro-differential eigenmode equations due to energetic particles for axisymmetric toroidal plasmas in a general flux coordinate system with an arbitrary Jacobian. The NOVA-K code employs the Galerkin method involving Fourier expansions in the generalized poloidal angle θ and generalized toroidal angle /zeta/ directions, and cubic-B spline finite elements in the radial /Psi/ direction. Extensive comparisons with the existing variational ideal MHD codes show that the ideal MHD version of the NOVA-K code converges faster and gives more accurate results. The NOVA-K code is employed to study the effects of energetic particles on MHD-type modes: the stabilization of ideal MHD internal kink modes and the excitation of ''fishbone'' internal kink modes; and the alpha particle destabilization of toroidicity-induced Alfven eigenmodes (TAE) via transit resonances. Analytical theories are also presented to help explain the NOVA-K results. For energetic trapped particles generated by neutral beam injection (NBI) or ion cyclotron resonant heating (ICRH), a stability window for the n = 1 internal kink mode in the hot particle beta space exists even in the absence of the core ion finite Larmor radius effect. On the other hand, the trapped alpha particles are found to have negligible effects on the stability of the n = 1 internal kink mode, but the circulating alpha particles can strongly destabilize TAE modes via inverse Landau damping associated with the spatial gradient of the alpha particle pressure. 60 refs., 24 figs., 1 tab
Effect of magnetic island geometry on ECRH/ECCD and consequences to the NTM stabilization dynamics
Chatziantonaki, I.; Tsironis, C.; Isliker, H.; Vlahos, L.
2012-09-01
In the majority of codes that model ECCD-based NTM stabilization, the analysis of the EC propagation and absorption is performed in terms of the axisymmetric magnetic field, ignoring effects due to the island topology. In this paper, we analyze the wave propagation, absorption and current drive in the presence of NTMs, as well as the ECCD-driven island growth, focusing on the effect of the island geometry on the wave de-position. A primary evaluation of the consequences of these effects on the NTM evolution is also made in terms of the modified Rutherford equation.
International Nuclear Information System (INIS)
Shibata, Masaru
2003-01-01
We report a new implementation for axisymmetric simulation in full general relativity. In this implementation, the Einstein equations are solved using the Nakamura-Shibata formulation with the so-called cartoon method to impose an axisymmetric boundary condition, and the general relativistic hydrodynamic equations are solved using a high-resolution shock-capturing scheme based on an approximate Riemann solver. As tests, we performed the following simulations: (i) long-term evolution of nonrotating and rapidly rotating neutron stars, (ii) long-term evolution of neutron stars of a high-amplitude damping oscillation accompanied with shock formation, (iii) collapse of unstable neutron stars to black holes, and (iv) stellar collapses to neutron stars. Tests (i)-(iii) were carried out with the Γ-law equation of state, and test (iv) with a more realistic parametric equation of state for high-density matter. We found that this new implementation works very well: It is possible to perform the simulations for stable neutron stars for more than 10 dynamical time scales, to capture strong shocks formed at stellar core collapses, and to accurately compute the mass of black holes formed after the collapse and subsequent accretion. In conclusion, this implementation is robust enough to apply to astrophysical problems such as stellar core collapse of massive stars to a neutron star, and black hole, phase transition of a neutron star to a high-density star, and accretion-induced collapse of a neutron star to a black hole. The result for the first simulation of stellar core collapse to a neutron star started from a realistic initial condition is also presented
International Nuclear Information System (INIS)
Hook, D W
2008-01-01
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 framework, and
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
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
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.
Torsional heterotic geometries
International Nuclear Information System (INIS)
Becker, Katrin; Sethi, Savdeep
2009-01-01
We construct new examples of torsional heterotic backgrounds using duality with orientifold flux compactifications. We explain how duality provides a perturbative solution to the type I/heterotic string Bianchi identity. The choice of connection used in the Bianchi identity plays an important role in the construction. We propose the existence of a much larger landscape of compact torsional geometries using string duality. Finally, we present some quantum exact metrics that correspond to NS5-branes placed on an elliptic space. These metrics describe how torus isometries are broken by NS flux.
Geometrie verstehen: statisch - kinematisch
Kroll, Ekkehard
Dem Allgemeinen steht begrifflich das Besondere gegenüber. In diesem Sinne sind allgemeine Überlegungen zum Verstehen von Mathematik zu ergänzen durch Untersuchungen hinsichtlich des Verstehens der einzelnen mathematischen Disziplinen, insbesondere der Geometrie. Hier haben viele Schülerinnen und Schüler Probleme. Diese rühren hauptsächlich daher, dass eine fertige geometrische Konstruktion in ihrer statischen Präsentation auf Papier nicht mehr die einzelnen Konstruktionsschritte erkennen lässt; zum Nachvollzug müssen sie daher ergänzend in einer Konstruktionsbeschreibung festgehalten werden.
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
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
Akopyan, A V
2007-01-01
The book is devoted to the properties of conics (plane curves of second degree) that can be formulated and proved using only elementary geometry. Starting with the well-known optical properties of conics, the authors move to less trivial results, both classical and contemporary. In particular, the chapter on projective properties of conics contains a detailed analysis of the polar correspondence, pencils of conics, and the Poncelet theorem. In the chapter on metric properties of conics the authors discuss, in particular, inscribed conics, normals to conics, and the Poncelet theorem for confoca
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
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
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
A variational principle for the axisymmetric stability of rotating relativistic stars
International Nuclear Information System (INIS)
Prabhu, Kartik; Wald, Robert M; Schiffrin, Joshua S
2016-01-01
It is well known that all rotating perfect fluid stars in general relativity are unstable to certain non-axisymmetric perturbations via the Chandrasekhar–Friedman–Schutz (CFS) instability. However, the mechanism of the CFS instability requires, in an essential way, the loss of angular momentum by gravitational radiation and, in many instances, it acts on too long a timescale to be physically/astrophysically relevant. It is therefore of interest to examine the stability of rotating, relativistic stars to axisymmetric perturbations, where the CFS instability does not occur. In this paper, we provide a Rayleigh–Ritz-type variational principle for testing the stability of perfect fluid stars to axisymmetric perturbations, which generalizes to axisymmetric perturbations of rotating stars a variational principle given by Chandrasekhar for spherical perturbations of static, spherical stars. Our variational principle provides a lower bound to the rate of exponential growth in the case of instability. The derivation closely parallels the derivation of a recently obtained variational principle for analyzing the axisymmetric stability of black holes. (paper)
1979-10-01
total pressures and the model static pressures were converted to a d-c electrical signal by one of two Scanivalve ®, Druck Model PDCR22, 0- to l0...31 3d 33 3+ 3’:, 3~ 3~ ~d ~ 4 4 b 4 h ,.,.9 50 0 , 0 0 + 0 . 0 9 9 n . 0 1 4 0.019 0 , 0 ~ 4 0 . 0 2 9 C . 0 3 ~ ~ . 0 3...1 ° 5 8 5 £ 02 0 .322 - 1 ° 2 5 b £ O~ 0,3~2 - 9 . f i ~ 3 £ t)l 0 ,36~ - 7 , b P ~ £ 01 0 . 3d ~ - 5 , ~ 3 9 £ Ol 0 , ~ 0 ~ - ~ ° 5 1
Ma, Xinxing; Ennis, D. A.; Hanson, J. D.; Hartwell, G. J.; Knowlton, S. F.; Maurer, D. A.
2017-10-01
Non-axisymmetric equilibrium reconstructions have been routinely performed with the V3FIT code in the Compact Toroidal Hybrid (CTH), a stellarator/tokamak hybrid. In addition to 50 external magnetic measurements, 160 SXR emissivity measurements are incorporated into V3FIT to reconstruct the magnetic flux surface geometry and infer the current distribution within the plasma. Improved reconstructions of current and q profiles provide insight into understanding the physics of density limit disruptions observed in current-carrying discharges in CTH. It is confirmed that the final scenario of the density limit of CTH plasmas is consistent with classic observations in tokamaks: current profile shrinkage leads to growing MHD instabilities (tearing modes) followed by a loss of MHD equilibrium. It is also observed that the density limit at a given current linearly increases with increasing amounts of 3D shaping fields. Consequently, plasmas with densities up to two times the Greenwald limit are attained. Equilibrium reconstructions show that addition of 3D fields effectively moves resonance surfaces towards the edge of the plasma where the current profile gradient is less, providing a stabilizing effect. This work is supported by US Department of Energy Grant No. DE-FG02-00ER54610.
Nemeth, Michael P.; Schultz, Marc R.
2012-01-01
A detailed exact solution is presented for laminated-composite circular cylinders with general wall construction and that undergo axisymmetric deformations. The overall solution is formulated in a general, systematic way and is based on the solution of a single fourth-order, nonhomogeneous ordinary differential equation with constant coefficients in which the radial displacement is the dependent variable. Moreover, the effects of general anisotropy are included and positive-definiteness of the strain energy is used to define uniquely the form of the basis functions spanning the solution space of the ordinary differential equation. Loading conditions are considered that include axisymmetric edge loads, surface tractions, and temperature fields. Likewise, all possible axisymmetric boundary conditions are considered. Results are presented for five examples that demonstrate a wide range of behavior for specially orthotropic and fully anisotropic cylinders.
Conference on Complex Geometry and Mirror Symmetry
Vinet, Luc; Yau, Shing-Tung; Mirror Symmetry III
1999-01-01
This book presents surveys from a workshop held during the theme year in geometry and topology at the Centre de recherches mathématiques (CRM, University of Montréal). The volume is in some sense a sequel to Mirror Symmetry I (1998) and Mirror Symmetry II (1996), copublished by the AMS and International Press. Included are recent developments in the theory of mirror manifolds and the related areas of complex and symplectic geometry. The long introductory articles explain the key physical ideas and motivation, namely conformal field theory, supersymmetry, and string theory. Open problems are emphasized. Thus the book provides an efficient way for a very broad audience of mathematicians and physicists to reach the frontier of research in this fast expanding area. - See more at: http://bookstore.ams.org/amsip-10#sthash.DbxEFJDx.dpuf
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.
Critique of information geometry
International Nuclear Information System (INIS)
Skilling, John
2014-01-01
As applied to probability, information geometry fails because probability distributions do not form a metric space. Probability theory rests on a compelling foundation of elementary symmetries, which also support information (aka minus entropy, Kullback-Leibler) H(p;q) as the unique measure of divergence from source probability distribution q to destination p. Because the only compatible connective H is from≠to asymmetric, H(p;q)≠H(q;p), there can be no compatible geometrical distance (which would necessarily be from=to symmetric). Hence there is no distance relationship compatible with the structure of probability theory. Metrics g and densities sqrt(det(g)) interpreted as prior probabilities follow from the definition of distance, and must fail likewise. Various metrics and corresponding priors have been proposed, Fisher's being the most popular, but all must behave unacceptably. This is illustrated with simple counter-examples
International Nuclear Information System (INIS)
Correa, Diego H.; Silva, Guillermo A.
2008-01-01
We discuss how geometrical and topological aspects of certain (1/2)-BPS type IIB geometries are captured by their dual operators in N = 4 Super Yang-Mills theory. The type IIB solutions are characterized by arbitrary droplet pictures in a plane and we consider, in particular, axially symmetric droplets. The 1-loop anomalous dimension of the dual gauge theory operators probed with single traces is described by some bosonic lattice Hamiltonians. These Hamiltonians are shown to encode the topology of the droplets. In appropriate BMN limits, the Hamiltonians spectrum reproduces the spectrum of near-BPS string excitations propagating along each of the individual edges of the droplet. We also study semiclassical regimes for the Hamiltonians. For droplets having disconnected constituents, the Hamiltonian admits different complimentary semiclassical descriptions, each one replicating the semiclassical description for closed strings extending in each of the constituents
Emergent geometry of membranes
Energy Technology Data Exchange (ETDEWEB)
Badyn, Mathias Hudoba de; Karczmarek, Joanna L.; Sabella-Garnier, Philippe; Yeh, Ken Huai-Che [Department of Physics and Astronomy, University of British Columbia,6224 Agricultural Road, Vancouver (Canada)
2015-11-13
In work http://dx.doi.org/10.1103/PhysRevD.86.086001, a surface embedded in flat ℝ{sup 3} is associated to any three hermitian matrices. We study this emergent surface when the matrices are large, by constructing coherent states corresponding to points in the emergent geometry. We find the original matrices determine not only shape of the emergent surface, but also a unique Poisson structure. We prove that commutators of matrix operators correspond to Poisson brackets. Through our construction, we can realize arbitrary noncommutative membranes: for example, we examine a round sphere with a non-spherically symmetric Poisson structure. We also give a natural construction for a noncommutative torus embedded in ℝ{sup 3}. Finally, we make remarks about area and find matrix equations for minimal area surfaces.
Non-axisymmetric line-driven disc winds - I. Disc perturbations
Dyda, Sergei; Proga, Daniel
2018-04-01
We study mass outflows driven from accretion discs by radiation pressure due to spectral lines. To investigate non-axisymmetric effects, we use the ATHENA++ code and develop a new module to account for radiation pressure driving. In 2D, our new simulations are consistent with previous 2D axisymmetric solutions by Proga et al., who used the ZEUS 2D code. Specifically, we find that the disc winds are time dependent, characterized by a dense stream confined to ˜45° relative to the disc mid-plane and bounded on the polar side by a less dense, fast stream. In 3D, we introduce a vertical, ϕ-dependent, subsonic velocity perturbation in the disc mid-plane. The perturbation does not change the overall character of the solution but global outflow properties such as the mass, momentum, and kinetic energy fluxes are altered by up to 100 per cent. Non-axisymmetric density structures develop and persist mainly at the base of the wind. They are relatively small, and their densities can be a few times higher than the azimuthal average. The structure of the non-axisymmetric and axisymmetric solutions differ also in other ways. Perhaps most importantly from the observational point of view are the differences in the so-called clumping factors, that serve as a proxy for emissivity due to two body processes. In particular, the spatially averaged clumping factor over the entire fast stream, while it is of a comparable value in both solutions, it varies about 10 times faster in the non-axisymmetric case.
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...
Linear wave propagation in a hot axisymmetric toroidal plasma
International Nuclear Information System (INIS)
Jaun, A.
1995-03-01
Kinetic effects on the propagation of the Alfven wave are studied for the first time in a toroidal plasma relevant for experiments. This requires the resolution of a set of coupled partial differential equations whose coefficients depend locally on the plasma parameters. For this purpose, a numerical wave propagation code called PENN has been developed using either a bilinear or a bicubic Hermite finite element discretization. It solves Maxwell's equations in toroidal geometry, with a dielectric tensor operator that takes into account the linear response of the plasma. Two different models have been implemented and can be used comparatively to describe the same physical case: the first treats the plasma as resistive fluids and gives results which are in good agreement with toroidal fluid codes. The second is a kinetic model and takes into account the finite size of the Larmor radii; it has successfully been tested against a kinetic plasma model in cylindrical geometry. New results have been obtained when studying kinetic effects in toroidal geometry. Two different conversion mechanisms to the kinetic Alfven wave have been described: one occurs at toroidally coupled resonant surfaces and is the kinetic counterpart of the fluid models' resonance absorption. The other has no such correspondence and results directly from the toroidal coupling between the kinetic Alfven wave and the global wavefield. An analysis of a heating scenario suggests that it might be difficult to heat a plasma with Alfven waves up to temperatures that are relevant for a tokamak reactor. Kinetic effects are studied for three types of global Alfven modes (GAE, TAE, BAE) and a new class of kinetic eigenmodes is described which appear inside the fluid gap: it could be related to recent observations in the JET (Joint European Torus) tokamak. (author) 56 figs., 6 tabs., 58 refs
Linear wave propagation in a hot axisymmetric toroidal plasma
Energy Technology Data Exchange (ETDEWEB)
Jaun, A [Ecole Polytechnique Federale, Lausanne (Switzerland). Centre de Recherche en Physique des Plasma (CRPP)
1995-03-01
Kinetic effects on the propagation of the Alfven wave are studied for the first time in a toroidal plasma relevant for experiments. This requires the resolution of a set of coupled partial differential equations whose coefficients depend locally on the plasma parameters. For this purpose, a numerical wave propagation code called PENN has been developed using either a bilinear or a bicubic Hermite finite element discretization. It solves Maxwell`s equations in toroidal geometry, with a dielectric tensor operator that takes into account the linear response of the plasma. Two different models have been implemented and can be used comparatively to describe the same physical case: the first treats the plasma as resistive fluids and gives results which are in good agreement with toroidal fluid codes. The second is a kinetic model and takes into account the finite size of the Larmor radii; it has successfully been tested against a kinetic plasma model in cylindrical geometry. New results have been obtained when studying kinetic effects in toroidal geometry. Two different conversion mechanisms to the kinetic Alfven wave have been described: one occurs at toroidally coupled resonant surfaces and is the kinetic counterpart of the fluid models` resonance absorption. The other has no such correspondence and results directly from the toroidal coupling between the kinetic Alfven wave and the global wavefield. An analysis of a heating scenario suggests that it might be difficult to heat a plasma with Alfven waves up to temperatures that are relevant for a tokamak reactor. Kinetic effects are studied for three types of global Alfven modes (GAE, TAE, BAE) and a new class of kinetic eigenmodes is described which appear inside the fluid gap: it could be related to recent observations in the JET (Joint European Torus) tokamak. (author) 56 figs., 6 tabs., 58 refs.
ASCOT-1, Thermohydraulics of Axisymmetric PWR Core with Homogeneous Flow During LOCA
International Nuclear Information System (INIS)
1978-01-01
1 - Nature of the physical problem solved: ASCOT-1 is used to analyze the thermo-hydraulic behaviour in a PWR core during a loss-of-coolant accident. 2 - Method of solution: The core is assumed to be axisymmetric two-dimensional and the conservation laws are solved by the method of characteristics. For the temperature response of fuel in the annular regions into which the core is divided, the heat conduction equations are solved by an explicit method with averaged flow conditions. 3 - Restrictions on the complexity of the problem: Axisymmetric two-dimensional homogeneous flows
Asymptotic properties of axisymmetric Stokes flow of a viscous liquid with intersecting boundaries
International Nuclear Information System (INIS)
Voinov, O.V.
2004-01-01
The general axisymmetric problem on the liquid flow by the low Reynolds number when the boundary surfaces (both of the solid body and free one) are intersecting at the certain angle on the moving line, is considered. The work is aimed at establishing the asymptotic regularities of the behavior of the current function and voltages in the small vicinity of the intersection (contact) line of the boundary surfaces. The asymptotic analysis makes it possible to consider the arbitrary axisymmetric Stokes flow with the intersecting boundaries [ru
Stable operation of an effectively axisymmetric neutral beam driven tandem mirror
International Nuclear Information System (INIS)
Molvik, A.W.; Barter, J.D.; Buchenauer, D.A.; Casper, T.A.; Correll, D.L.; Dimonte, G.; Falabella, S.; Foote, J.H.; Pincosy, P.A.
1990-01-01
A quiescent plasma is sustained for 80 energy confinement times by only gas fuelling and neutral beam heating in an axisymmetric region of the Tandem Mirror Experiment Upgrade (TMX-U). This plasma should be unstable because of the bad magnetic curvature and the absence of ion cyclotron heating which previously provided ponderomotive stabilization to sustain plasmas in bad-curvature regions of other axisymmetric mirror experiments. The TMX-U data are consistent with stabilization by a symbiosis between two mechanisms - line tying, which reduces the growth rate, and finite Larmor radius edge stabilization, which can result in quiescent operation. (author). 42 refs, 8 figs, 1 tab
Numerical Investigation of Pressure Losses in Axisymmetric Sudden Expansion with a Chamfer
Energy Technology Data Exchange (ETDEWEB)
Bae, Youngmin; Kim, Youngin; Kim, Keung Koo [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2014-05-15
In this paper, the pressure losses through axisymmetric sudden expansions with a chamfer are analyzed by means of numerical simulation, with an emphasis on the effect of the Reynolds number. In this study, we investigate numerically the turbulent flow in axisymmetric sudden expansions having a slight chamfer on the edge. With the aim of investigating the impact of Reynolds number on the expansion losses in a time-averaged sense, an extensive set of simulations is carried out. On the basis of numerical results, we also propose a general correlation to estimate the local loss coefficient in sudden expansions with a chamfer.
Numerical Investigation of Pressure Losses in Axisymmetric Sudden Expansion with a Chamfer
International Nuclear Information System (INIS)
Bae, Youngmin; Kim, Youngin; Kim, Keung Koo
2014-01-01
In this paper, the pressure losses through axisymmetric sudden expansions with a chamfer are analyzed by means of numerical simulation, with an emphasis on the effect of the Reynolds number. In this study, we investigate numerically the turbulent flow in axisymmetric sudden expansions having a slight chamfer on the edge. With the aim of investigating the impact of Reynolds number on the expansion losses in a time-averaged sense, an extensive set of simulations is carried out. On the basis of numerical results, we also propose a general correlation to estimate the local loss coefficient in sudden expansions with a chamfer
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
Thin accretion disks in stationary axisymmetric wormhole spacetimes
International Nuclear Information System (INIS)
Harko, Tiberiu; Kovacs, Zoltan; Lobo, Francisco S. N.
2009-01-01
In this paper, we study the physical properties and the equilibrium thermal radiation emission characteristics of matter forming thin accretion disks in stationary axially symmetric wormhole spacetimes. The thin disk models are constructed by taking different values of the wormhole's angular velocity, and the time averaged energy flux, the disk temperature, and the emission spectra of the accretion disks are obtained. Comparing the mass accretion in a rotating wormhole geometry with the one of a Kerr black hole, we verify that the intensity of the flux emerging from the disk surface is greater for wormholes than for rotating black holes with the same geometrical mass and accretion rate. We also present the conversion efficiency of the accreting mass into radiation, and show that the rotating wormholes provide a much more efficient engine for the transformation of the accreting mass into radiation than the Kerr black holes. Therefore specific signatures appear in the electromagnetic spectrum of thin disks around rotating wormholes, thus leading to the possibility of distinguishing wormhole geometries by using astrophysical observations of the emission spectra from accretion disks.
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...
International Nuclear Information System (INIS)
Buescher, R.
2005-01-01
Casimir interactions are interactions induced by quantum vacuum fluctuations and thermal fluctuations of the electromagnetic field. Using a path integral quantization for the gauge field, an effective Gaussian action will be derived which is the starting point to compute Casimir forces between macroscopic objects analytically and numerically. No assumptions about the independence of the material and shape dependent contributions to the interaction are made. We study the limit of flat surfaces in further detail and obtain a concise derivation of Lifshitz' theory of molecular forces. For the case of ideally conducting boundaries, the Gaussian action will be calculated explicitly. Both limiting cases are also discussed within the framework of a scalar field quantization approach, which is applicable for translationally invariant geometries. We develop a non-perturbative approach to calculate the Casimir interaction from the Gaussian action for periodically deformed and ideally conducting objects numerically. The obtained results reveal two different scaling regimes for the Casimir force as a function of the distance between the objects, their deformation wavelength and -amplitude. The results confirm that the interaction is non-additive, especially in the presence of strong geometric deformations. Furthermore, the numerical approach is extended to calculate lateral Casimir forces. The results are consistent with the results of the proximity-force approximation for large deformation wavelengths. A qualitatively different behaviour between the normal and lateral force is revealed. We also establish a relation between the boundary induced change of the of the density of states for the scalar Helmholtz equation and the Casimir interaction using the path integral method. For statically deformed boundaries, this relation can be expressed as a novel trace formula, which is formally similar to the so-called Krein-Friedel-Lloyd formula. While the latter formula describes the
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
Plasma equilibria and stationary flows in axisymmetric systems. Pt. 2
International Nuclear Information System (INIS)
Zelazny, R.; Stankiewicz, R.; Potempski, S.
1988-05-01
Part I of this report described the computational problems connected with the bifurcating solutions to static and extended Grad-Shafranov-Schlueter equations (with stationary flows). Part II is a listing of the computer program for solving the extended Grad-Shafranov-Schlueter equations developed in Part I. (author)
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
Directory of Open Access Journals (Sweden)
C. SPÎNU
2008-04-01
Full Text Available Iron(II, cobalt(II, nickel (II, copper (II, zinc(II and cadmium(II complexes of the type ML2Cl2, where M is a metal and L is the Schiff base N-(2-thienylmethylenemethanamine (TNAM formed by the condensation of 2-thiophenecarboxaldehyde and methylamine, were prepared and characterized by elemental analysis as well as magnetic and spectroscopic measurements. The elemental analyses suggest the stoichiometry to be 1:2 (metal:ligand. Magnetic susceptibility data coupled with electronic, ESR and Mössbauer spectra suggest a distorted octahedral structure for the Fe(II, Co(II and Ni(II complexes, a square-planar geometry for the Cu(II compound and a tetrahedral geometry for the Zn(II and Cd(II complexes. The infrared and NMR spectra of the complexes agree with co-ordination to the central metal atom through nitrogen and sulphur atoms. Conductance measurements suggest the non-electrolytic nature of the complexes, except for the Cu(II, Zn(II and Cd(II complexes, which are 1:2 electrolytes. The Schiff base and its metal chelates were screened for their biological activity against Escherichia coli, Staphylococcus aureus and Pseudomonas aeruginosa and the metal chelates were found to possess better antibacterial activity than that of the uncomplexed Schiff base.
DEFF Research Database (Denmark)
Frisvad, Jeppe Revall
Interaction of light and matter produces the appearance of materials. To deal with the immense complexity of nature, light and matter is modelled at a macroscopic level in computer graphics. This work is the first to provide the link between the microscopic physical theories of light and matter...... of a material and determine the contents of the material. The book is in four parts. Part I provides the link between microscopic and macroscopic theories of light. Part II describes how to use the properties of microscopic particles to compute the macroscopic properties of materials. Part III illustrates...
Directory of Open Access Journals (Sweden)
Šárka Nedomová
2013-01-01
Full Text Available Precise quantification of the profile of egg can provide a powerful tool for the analysis of egg shape for various biological problems. A new approach to the geometry of a Ostrich’s egg profile is presented here using an analysing the egg’s digital photo by edge detection techniques. The obtained points on the eggshell counter are fitted by the Fourier series. The obtained equations describing an egg profile have been used to calculate radii of curvature. The radii of the curvature at the important point of the egg profile (sharp end, blunt end and maximum thickness are independent on the egg shape index. The exact values of the egg surface and the egg volume have been obtained. These quantities are also independent on the egg shape index. These quantities can be successively estimated on the basis of simplified equations which are expressed in terms of the egg length, L¸ and its width, B. The surface area of the eggshells also exhibits good correlation with the egg long circumference length. Some limitations of the most used procedures have been also shown.
Nonperturbative quantum geometries
International Nuclear Information System (INIS)
Jacobson, T.; California Univ., Santa Barbara; Smolin, L.; California Univ., Santa Barbara
1988-01-01
Using the self-dual representation of quantum general relativity, based on Ashtekar's new phase space variables, we present an infinite dimensional family of quantum states of the gravitational field which are exactly annihilated by the hamiltonian constraint. These states are constructed from Wilson loops for Ashtekar's connection (which is the spatial part of the left handed spin connection). We propose a new regularization procedure which allows us to evaluate the action of the hamiltonian constraint on these states. Infinite linear combinations of these states which are formally annihilated by the diffeomorphism constraints as well are also described. These are explicit examples of physical states of the gravitational field - and for the compact case are exact zero eigenstates of the hamiltonian of quantum general relativity. Several different approaches to constructing diffeomorphism invariant states in the self dual representation are also described. The physical interpretation of the states described here is discussed. However, as we do not yet know the physical inner product, any interpretation is at this stage speculative. Nevertheless, this work suggests that quantum geometry at Planck scales might be much simpler when explored in terms of the parallel transport of left-handed spinors than when explored in terms of the three metric. (orig.)
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.
Axisymmetric polydimethysiloxane microchannels for in vitro hemodynamic studies
International Nuclear Information System (INIS)
Lima, Rui; Oliveira, Monica S N; Ishikawa, Takuji; Kaji, Hirokazu; Nishizawa, Matsuhiko; Tanaka, Shuji; Yamaguchi, Takami
2009-01-01
The current microdevices used for biomedical research are often manufactured using microelectromechanical systems (MEMS) technology. Although it is possible to fabricate precise and reproducible rectangular microchannels using soft lithography techniques, this kind of geometry may not reflect the actual physiology of the microcirculation. Here, we present a simple method to fabricate circular polydimethysiloxane (PDMS) microchannels aiming to mimic an in vivo microvascular environment and suitable for state-of-the-art microscale flow visualization techniques, such as confocal μPIV/PTV. By using a confocal μPTV system individual red blood cells (RBCs) were successfully tracked trough a 75 μm circular PDMS microchannel. The results show that RBC lateral dispersion increases with the volume fraction of RBCs in the solution, i.e. with the hematocrit.
VANDERVEGT, W; VANDERMEI, HC; BUSSCHER, HJ
Axisymmetric drop shape analysis by profile (ADSA-P) is a technique developed in colloid and surface science to simultaneously determine the contact angle and liquid surface tension from the profile of a droplet resting on a solid surface. In this paper is described how ADSA-P can be employed to
International Nuclear Information System (INIS)
Zhong, Z.
1985-01-01
A new approach to the solution of certain differential equations, the double complex function method, is developed, combining ordinary complex numbers and hyperbolic complex numbers. This method is applied to the theory of stationary axisymmetric Einstein equations in general relativity. A family of exact double solutions, double transformation groups, and n-soliton double solutions are obtained
Dynamic analysis of reactor containment building using axisymmetric finite element model
International Nuclear Information System (INIS)
Thakkar, S.K.; Dubey, R.N.
1989-01-01
The structural safety of nuclear reactor building during earthquake is of great importance in view of possibility of radiation hazards. The rational evaluation of forces and displacements in various portions of structure and foundation during strong ground motion is most important for safe performance and economic design of the reactor building. The accuracy of results of dynamic analysis is naturally dependent on the type of mathematical model employed. Three types of mathematical models are employed for dynamic analysis of reactor building beam model axisymmetric finite element model and three dimensional model. In this paper emphasis is laid on axisymmetric model. This model of containment building is considered a reinfinement over conventional beam model of the structure. The nuclear reactor building on a rocky foundation is considered herein. The foundation-structure interaction is relatively less in this condition. The objective of the paper is to highlight the significance of modelling of non-axisymmetric portion of building, such as reactor internals by equivalent axisymmetric body, on the structural response of the building
Material density measurements from dynamic flash x-ray radiographs using axisymmetric tomography
International Nuclear Information System (INIS)
Fugelso, E.
1981-03-01
The axisymmetric version of the tomographic x-ray reconstruction procedures has been utilized to determine the material density for the impact of a cylinder on a steel plate. Derivations of the reconstruction algorithms relating x-ray radiographic intensities to the material densities are presented. Effects of noise, point spread functions, and motion blur are minimized
On the impact of a concave nosed axisymmetric body on a free surface
Mathai, Varghese; Govardhan, R.N.; Arakeri, V.H.
2015-01-01
We report on an experimental study of the vertical impact of a concave nosed axisymmetric body on a free surface. Previous studies have shown that bodies with a convex nose, like a sphere, produce a well defined splash with a relatively large cavity behind the model. In contrast, we find that with a
Quantum cosmology of a Bianchi III LRS geometry coupled to a source free electromagnetic field
Karagiorgos, A.; Pailas, T.; Dimakis, N.; Terzis, Petros A.; Christodoulakis, T.
2018-03-01
We consider a Bianchi type III axisymmetric geometry in the presence of an electromagnetic field. A first result at the classical level is that the symmetry of the geometry need not be applied on the electromagnetic tensor Fμν the algebraic restrictions, implied by the Einstein field equations to the stress energy tensor Tμν, suffice to reduce the general Fμν to the appropriate form. The classical solution thus found contains a time dependent electric and a constant magnetic charge. The solution is also reachable from the corresponding mini-superspace action, which is strikingly similar to the Reissner-Nordstr{öm one. This points to a connection between the black hole geometry and the cosmological solution here found, which is the analog of the known correlation between the Schwarzschild and the Kantowski-Sachs metrics. The configuration space is drastically modified by the presence of the magnetic charge from a 3D flat to a 3D pp wave geometry. We map the emerging linear and quadratic classical integrals of motion, to quantum observables. Along with the Wheeler-DeWitt equation these observables provide unique, up to constants, wave functions. The employment of a Bohmian interpretation of these quantum states results in deterministic (semi-classical) geometries most of which are singularity free.
GPS: Geometry, Probability, and Statistics
Field, Mike
2012-01-01
It might be said that for most occupations there is now less of a need for mathematics than there was say fifty years ago. But, the author argues, geometry, probability, and statistics constitute essential knowledge for everyone. Maybe not the geometry of Euclid, but certainly geometrical ways of thinking that might enable us to describe the world…
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....
Kaehler geometry and SUSY mechanics
International Nuclear Information System (INIS)
Bellucci, Stefano; Nersessian, Armen
2001-01-01
We present two examples of SUSY mechanics related with Kaehler geometry. The first system is the N = 4 supersymmetric one-dimensional sigma-model proposed in hep-th/0101065. Another system is the N = 2 SUSY mechanics whose phase space is the external algebra of an arbitrary Kaehler manifold. The relation of these models with antisymplectic geometry is discussed
A prediction for bubbling geometries
Okuda, Takuya
2007-01-01
We study the supersymmetric circular Wilson loops in N=4 Yang-Mills theory. Their vacuum expectation values are computed in the parameter region that admits smooth bubbling geometry duals. The results are a prediction for the supergravity action evaluated on the bubbling geometries for Wilson loops.
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 ...
Surface pressure drag for hydrostatic two-layer flow over axisymmetric mountains
Energy Technology Data Exchange (ETDEWEB)
Leutbecher, M.
2000-07-01
The effect of partial reflections on surface pressure drag is investigated for hydrostatic gravity waves in two-layer flow with piecewise constant buoyancy frequency. The variation of normalized surface pressure drag with interface height is analyzed for axisymmetric mountains. The results are compared with the familiar solution for infinitely long ridges. The drag for the two-layer flow is normalized with the drag of one-layer flow, which has the buoyancy frequency of the lower layer. An analytical expression for the normalized drag of axisymmetric mountains is derived from linear theory of steady flow. Additionally, two-layer flow over finite-height axisymmetric mountains is simulated numerically for flow with higher stability in the upper layer. The temporal evolution of the surface pressure drag is examined in a series of experiments with different interface and mountain heights. The focus is on the linear regime and the nonlinear regime of nonbreaking gravity waves. The dispersion of gravity waves in flow over isolated mountains prevents that the entire wave spectrum is in resonance at the same interface height, which is the case in hydrostatic flow over infinitely long ridges. In consequence, the oscillation of the normalized drag with interface height is smaller for axisymmetric mountains than for infinitely long ridges. However, even for a reflection coefficient as low as 1/3 the drag of an axisymmetric mountain can be amplified by 50% and reduced by 40%. The nonlinear drag becomes steady in the numerical experiments in which no wave breaking occurs. The steady state nonlinear drag agrees quite well with the prediction of linear theory if the linear drag is computed for a slightly lowered interface. (orig.)
Numerical simulation of the generation mechanism of axisymmetric supersonic jet screech tones
Li, X. D.; Gao, J. H.
2005-08-01
In this paper an axisymmetric computational aeroacoustic procedure is developed to investigate the generation mechanism of axisymmetric supersonic jet screech tones. The axisymmetric Navier-Stokes equations and the two equations standard k-ɛ turbulence model modified by Turpin and Troyes ["Validation of a two-equation turbulence model for axisymmetric reacting and non-reaction flows," AIAA Paper No. 2000-3463 (2000)] are solved in the generalized curvilinear coordinate system. A generalized wall function is applied in the nozzle exit wall region. The dispersion-relation-preserving scheme is applied for space discretization. The 2N storage low-dissipation and low-dispersion Runge-Kutta scheme is employed for time integration. Much attention is paid to far-field boundary conditions and turbulence model. The underexpanded axisymmetric supersonic jet screech tones are simulated over the Mach number from 1.05 to 1.2. Numerical results are presented and compared with the experimental data by other researchers. The simulated wavelengths of A0, A1, A2, and B modes and part of simulated amplitudes agree very well with the measurement data by Ponton and Seiner ["The effects of nozzle exit lip thickness on plume resonance," J. Sound Vib. 154, 531 (1992)]. In particular, the phenomena of modes jumping have been captured correctly although the numerical procedure has to be improved to predict the amplitudes of supersonic jet screech tones more accurately. Furthermore, the phenomena of shock motions are analyzed. The predicted splitting and combination of shock cells are similar with the experimental observations of Panda ["Shock oscillation in underexpanded screeching jets," J. Fluid. Mech. 363, 173 (1998)]. Finally, the receptivity process is numerically studied and analyzed. It is shown that the receptivity zone is associated with the initial thin shear layer, and the incoming and reflected sound waves.
Ferlemann, Paul G.; Gollan, Rowan J.
2010-01-01
Computational design and analysis of three-dimensional hypersonic inlets with shape transition has been a significant challenge due to the complex geometry and grid required for three-dimensional viscous flow calculations. Currently, the design process utilizes an inviscid design tool to produce initial inlet shapes by streamline tracing through an axisymmetric compression field. However, the shape is defined by a large number of points rather than a continuous surface and lacks important features such as blunt leading edges. Therefore, a design system has been developed to parametrically construct true CAD geometry and link the topology of a structured grid to the geometry. The Adaptive Modeling Language (AML) constitutes the underlying framework that is used to build the geometry and grid topology. Parameterization of the CAD geometry allows the inlet shapes produced by the inviscid design tool to be generated, but also allows a great deal of flexibility to modify the shape to account for three-dimensional viscous effects. By linking the grid topology to the parametric geometry, the GridPro grid generation software can be used efficiently to produce a smooth hexahedral multiblock grid. To demonstrate the new capability, a matrix of inlets were designed by varying four geometry parameters in the inviscid design tool. The goals of the initial design study were to explore inviscid design tool geometry variations with a three-dimensional analysis approach, demonstrate a solution rate which would enable the use of high-fidelity viscous three-dimensional CFD in future design efforts, process the results for important performance parameters, and perform a sample optimization.
Shafarevich, Igor Rostislavovich
1994-01-01
Shafarevich Basic Algebraic Geometry 2 The second edition of Shafarevich's introduction to algebraic geometry is in two volumes. The second volume covers schemes and complex manifolds, generalisations in two different directions of the affine and projective varieties that form the material of the first volume. Two notable additions in this second edition are the section on moduli spaces and representable functors, motivated by a discussion of the Hilbert scheme, and the section on Kähler geometry. The book ends with a historical sketch discussing the origins of algebraic geometry. From the Zentralblatt review of this volume: "... one can only respectfully repeat what has been said about the first part of the book (...): a great textbook, written by one of the leading algebraic geometers and teachers himself, has been reworked and updated. As a result the author's standard textbook on algebraic geometry has become even more important and valuable. Students, teachers, and active researchers using methods of al...
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
Gong, Lunkun; Chen, Xiong; Musa, Omer; Yang, Haitao; Zhou, Changsheng
2017-12-01
Numerical and experimental investigation on the solid-fuel ramjet was carried out to study the effect of geometry on combustion characteristics. The two-dimensional axisymmetric program developed in the present study adopted finite rate chemistry and second-order moment turbulence-chemistry models, together with k-ω shear stress transport (SST) turbulence model. Experimental data were obtained by burning cylindrical polyethylene using a connected pipe facility. The simulation results show that a fuel-rich zone near the solid fuel surface and an air-rich zone in the core exist in the chamber, and the chemical reactions occur mainly in the interface of this two regions; The physical reasons for the effect of geometry on regression rate is the variation of turbulent viscosity due to the geometry change. Port-to-inlet diameter ratio is the main parameter influencing the turbulent viscosity, and a linear relationship between port-to-inlet diameter and regression rate were obtained. The air mass flow rate and air-fuel ratio are the main influencing factors on ramjet performances. Based on the simulation results, the correlations between geometry and air-fuel ratio were obtained, and the effect of geometry on ramjet performances was analyzed according to the correlation. Three-dimensional regression rate contour obtained experimentally indicates that the regression rate which shows axisymmetric distribution due to the symmetry structure increases sharply, followed by slow decrease in axial direction. The radiation heat transfer in recirculation zone cannot be ignored. Compared with the experimental results, the deviations of calculated average regression rate and characteristic velocity are about 5%. Concerning the effect of geometry on air-fuel ratio, the deviations between experimental and theoretical results are less than 10%.
Detonation Propagation in Slabs and Axisymmetric Rate Sticks
Romick, Christopher; Aslam, Tariq
Insensitive high explosives (IHE) have many benefits; however, these IHEs exhibit longer reaction zones than more conventional high explosives (HE). This makes IHEs less ideal explosives and more susceptible to edge effects as well as other performance degradation issues. Thus, there is a resulting reduction in the detonation speed within the explosive. Many HE computational models, e. g. WSD, SURF, CREST, have shock-dependent reaction rates. This dependency places a high value on having an accurate shock speed. In the common practice of shock-capturing, there is ambiguity in the shock-state due to smoothing of the shock-front. Moreover, obtaining an accurate shock speed with shock-capturing becomes prohibitively computationally expensive in multiple dimensions. The use of shock-fitting removes the ambiguity of the shock-state as it is one of the boundaries. As such, the required resolution for a given error in the detonation speed is less than with shock-capturing. This allows for further insight into performance degradation. A two-dimensional shock-fitting scheme has been developed for unconfined slabs and rate sticks of HE. The HE modeling is accomplished by Euler equations utilizing several models with single-step irreversible kinetics in slab and rate stick geometries. Department of Energy - LANL.
Complex analysis and CR geometry
Zampieri, Giuseppe
2008-01-01
Cauchy-Riemann (CR) geometry is the study of manifolds equipped with a system of CR-type equations. Compared to the early days when the purpose of CR geometry was to supply tools for the analysis of the existence and regularity of solutions to the \\bar\\partial-Neumann problem, it has rapidly acquired a life of its own and has became an important topic in differential geometry and the study of non-linear partial differential equations. A full understanding of modern CR geometry requires knowledge of various topics such as real/complex differential and symplectic geometry, foliation theory, the geometric theory of PDE's, and microlocal analysis. Nowadays, the subject of CR geometry is very rich in results, and the amount of material required to reach competence is daunting to graduate students who wish to learn it. However, the present book does not aim at introducing all the topics of current interest in CR geometry. Instead, an attempt is made to be friendly to the novice by moving, in a fairly relaxed way, f...
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
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
Differential geometry curves, surfaces, manifolds
Kohnel, Wolfgang
2002-01-01
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. Special topics that are explored include Frenet frames, ruled surfaces, minimal surfaces and the Gauss-Bonnet theorem. The second part is an introduction to the geometry of general manifolds, with particular emphasis on connections and curvature. The final two chapters are insightful examinations of the special cases of spaces of constant curvature and Einstein manifolds. The text is illustrated with many figures and examples. The prerequisites are undergraduate analysis and linear algebra.
Honda, M.; Satake, S.; Suzuki, Y.; Shinohara, K.; Yoshida, M.; Narita, E.; Nakata, M.; Aiba, N.; Shiraishi, J.; Hayashi, N.; Matsunaga, G.; Matsuyama, A.; Ide, S.
2017-11-01
Capabilities of the integrated framework consisting of TOPICS, OFMC, VMEC and FORTEC-3D, have been extended to calculate toroidal rotation in fully non-axisymmetric perturbed magnetic fields for demonstrating operation scenarios in actual tokamak geometry and conditions. The toroidally localized perturbed fields due to the test blanket modules and the tangential neutral beam ports in ITER augment the neoclassical toroidal viscosity (NTV) substantially, while do not significantly influence losses of beam ions and alpha particles in an ITER L-mode discharge. The NTV takes up a large portion of total torque in ITER and fairly decelerates toroidal rotation, but the change in toroidal rotation may have limited effectiveness against turbulent heat transport. The error field correction coils installed in JT-60SA can externally apply the perturbed fields, which may alter the NTV and the resultant toroidal rotation profiles. However, the non-resonant n=18 components of the magnetic fields arising from the toroidal field ripple mainly contribute to the NTV, regardless of the presence of the applied field by the coil current of 10 kA , where n is the toroidal mode number. The theoretical model of the intrinsic torque due to the fluctuation-induced residual stress is calibrated by the JT-60U data. For five JT-60U discharges, the sign of the calibration factor conformed to the gyrokinetic linear stability analysis and a range of the amplitude thereof was revealed. This semi-empirical approach opens up access to an attempt on predicting toroidal rotation in H-mode plasmas.
Zuffada, Cinzia; Crisp, David
1997-01-01
Reliable descriptions of the optical properties of clouds and aerosols are essential for studies of radiative transfer in planetary atmospheres. The scattering algorithms provide accurate estimates of these properties for spherical particles with a wide range of sizes and refractive indices, but these methods are not valid for non-spherical particles (e.g., ice crystals, mineral dust, and smoke). Even though a host of methods exist for deriving the optical properties of nonspherical particles that are very small or very large compared with the wavelength, only a few methods are valid in the resonance regime, where the particle dimensions are comparable with the wavelength. Most such methods are not ideal for particles with sharp edges or large axial ratios. We explore the utility of an integral equation approach for deriving the single-scattering optical properties of axisymmetric particles with large axial ratios. The accuracy of this technique is shown for spheres of increasing size parameters and an ensemble of randomly oriented prolate spheroids of size parameter equal to 10.079368. In this last case our results are compared with published results obtained with the T-matrix approach. Next we derive cross sections, single-scattering albedos, and phase functions for cylinders, disks, and spheroids of ice with dimensions extending from the Rayleigh to the geometric optics regime. Compared with those for a standard surface integral equation method, the storage requirement and the computer time needed by this method are reduced, thus making it attractive for generating databases to be used in multiple-scattering calculations. Our results show that water ice disks and cylinders are more strongly absorbing than equivalent volume spheres at most infrared wavelengths. The geometry of these particles also affects the angular dependence of the scattering. Disks and columns with maximum linear dimensions larger than the wavelength scatter much more radiation in the forward
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, ...
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...
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.
Symplectic geometry and Fourier analysis
Wallach, Nolan R
2018-01-01
Suitable for graduate students in mathematics, this monograph covers differential and symplectic geometry, homogeneous symplectic manifolds, Fourier analysis, metaplectic representation, quantization, Kirillov theory. Includes Appendix on Quantum Mechanics by Robert Hermann. 1977 edition.
Topology and geometry for physicists
Nash, Charles
1983-01-01
Differential geometry and topology are essential tools for many theoretical physicists, particularly in the study of condensed matter physics, gravity, and particle physics. Written by physicists for physics students, this text introduces geometrical and topological methods in theoretical physics and applied mathematics. It assumes no detailed background in topology or geometry, and it emphasizes physical motivations, enabling students to apply the techniques to their physics formulas and research. ""Thoroughly recommended"" by The Physics Bulletin, this volume's physics applications range fr
Spectral dimension of quantum geometries
International Nuclear Information System (INIS)
Calcagni, Gianluca; Oriti, Daniele; Thürigen, Johannes
2014-01-01
The spectral dimension is an indicator of geometry and topology of spacetime and a tool to compare the description of quantum geometry in various approaches to quantum gravity. This is possible because it can be defined not only on smooth geometries but also on discrete (e.g., simplicial) ones. In this paper, we consider the spectral dimension of quantum states of spatial geometry defined on combinatorial complexes endowed with additional algebraic data: the kinematical quantum states of loop quantum gravity (LQG). Preliminarily, the effects of topology and discreteness of classical discrete geometries are studied in a systematic manner. We look for states reproducing the spectral dimension of a classical space in the appropriate regime. We also test the hypothesis that in LQG, as in other approaches, there is a scale dependence of the spectral dimension, which runs from the topological dimension at large scales to a smaller one at short distances. While our results do not give any strong support to this hypothesis, we can however pinpoint when the topological dimension is reproduced by LQG quantum states. Overall, by exploring the interplay of combinatorial, topological and geometrical effects, and by considering various kinds of quantum states such as coherent states and their superpositions, we find that the spectral dimension of discrete quantum geometries is more sensitive to the underlying combinatorial structures than to the details of the additional data associated with them. (paper)
Investigating the Problem Solving Competency of Pre Service Teachers in Dynamic Geometry Environment
Haja, Shajahan
2005-01-01
This study investigated the problem-solving competency of four secondary pre service teachers (PSTs) of University of London as they explored geometry problems in dynamic geometry environment (DGE) in 2004. A constructivist experiment was designed in which dynamic software Cabri-Geometre II (hereafter Cabri) was used as an interactive medium.…
FLEXURAL STRESS ANALYSIS OF RIGID PAVEMENTS USING AXI-SYMMETRIC AND PLANE STRAIN FEM
Directory of Open Access Journals (Sweden)
V.A. Sawant
2017-11-01
Full Text Available The design of pavement involves a study of soils and paving materials, their response under load for different climatic conditions. In the present study, an attempt has been made to compare stresses predicted using two finite element analyses. First analysis is based on the twodimensional plane strain assumption where as in second approach axi-symmetric condition is assumed to consider three-dimensional behavior of rigid pavement. The results are compared with flexural stresses obtained from conventional Portland Cement Association method. The computed flexural stresses obtained from axi-symmetric condition are found to be in close agreement with PCA method. Results of plane strain analysis show a fair agreement after application of an appropriate multiplication factor
Non-Axisymmetric Oscillation of Acoustically Levitated Water Drops at Specific Frequencies
International Nuclear Information System (INIS)
Chang-Le, Shen; Wen-Jun, Xie; Bing-Bo, Wei
2010-01-01
A category of non-axisymmetric oscillations of acoustically levitated water drops was observed. These oscillations can be qualitatively described by superposing a sectorial oscillating term upon the initial oblate shape resulting from the effect of acoustic radiation pressure. The oscillation frequencies are around 25 Hz for the 2-lobed mode and exactly 50 Hz for the 3- and 4-lobed modes. These oscillations were excited by the disturbance from the power supply. For the same water drop, higher mode oscillations were observed with more oblate initial shape, indicating that the eigenfrequencies of these non-axisymmetric oscillations decrease with increasing initial distortion. The maximum velocity and acceleration within the oscillating drop can attain 0.3m·s −1 and 98.7m·s −2 respectively, resulting in strong fluid convection and enhanced heat and mass transfer. (condensed matter: structure, mechanical and thermal properties)
On Perturbation Solutions for Axisymmetric Bending Boundary Values of a Deep Thin Spherical Shell
Directory of Open Access Journals (Sweden)
Rong Xiao
2014-01-01
Full Text Available On the basis of the general theory of elastic thin shells and the Kirchhoff-Love hypothesis, a fundamental equation for a thin shell under the moment theory is established. In this study, the author derives Reissner’s equation with a transverse shear force Q1 and the displacement component w. These basic unknown quantities are derived considering the axisymmetry of the deep, thin spherical shell and manage to constitute a boundary value question of axisymmetric bending of the deep thin spherical shell under boundary conditions. The asymptotic solution is obtained by the composite expansion method. At the end of this paper, to prove the correctness and accuracy of the derivation, an example is given to compare the numerical solution by ANSYS and the perturbation solution. Meanwhile, the effects of material and geometric parameters on the nonlinear response of axisymmetric deep thin spherical shell under uniform external pressure are also analyzed in this paper.
Marginal Stability Boundaries for Infinite-n Ballooning Modes in a Quasi-axisymmetric Stellarator
International Nuclear Information System (INIS)
Hudson, S.R.; Hegna, C.C.
2003-01-01
A method for computing the ideal-MHD stability boundaries in three-dimensional equilibria is employed. Following Hegna and Nakajima [Phys. Plasmas 5 (May 1998) 1336], a two-dimensional family of equilibria are constructed by perturbing the pressure and rotational-transform profiles in the vicinity of a flux surface for a given stellarator equilibrium. The perturbations are constrained to preserve the magnetohydrodynamic equilibrium condition. For each perturbed equilibrium, the infinite-n ballooning stability is calculated. Marginal stability diagrams are thus constructed that are analogous to (s; a) diagrams for axisymmetric configurations. A quasi-axisymmetric stellarator is considered. Calculations of stability boundaries generally show regions of instability can occur for either sign of the average magnetic shear. Additionally, regions of second-stability are present
On solution of Maxwell's equations in axisymmetric domains with edges. Part I: Theoretical aspects
International Nuclear Information System (INIS)
Nkemzi, Boniface
2003-10-01
In this paper we present the basic mathematical tools for treating boundary value problems for the Maxwell's equations in three-dimensional axisymmetric domains with reentrant edges by means of partial Fourier analysis. We consider the decomposition of the classical and regularized time-harmonic three-dimensional Maxwell's equations into variational equations in the plane meridian domain of the axisymmetric domain and define suitable weighted Sobolev spaces for their treatment. The trace properties of these spaces on the rotational axis and some properties of the solutions are proved, which are important for further numerical treatment, e.g. by the finite-element method. Particularly, a priori estimates of the solutions of the reduced system are given and the asymptotic behavior of these solutions near reentrant corners of the meridian domain is explicitly described by suitable singular functions. (author)
Shtemler, Yu.; Mond, M.; Liverts, E.
2018-02-01
The excitation of nonaxisymmetric quasi-resonant triads by clustering around a dominant axisymmetric explosively unstable magnetorotational instability (MRI) in Keplerian discs is investigated. Clustering, namely, the mutual interactions of a large number of quasi-resonant triads that are connected by a single dominant explosively unstable axisymmetric triad, is invoked in order to provide a viable mechanism for the stabilization of the explosive nature of the latter. The results, however, are of wider scope as the proposed clustering scenario also provides a strong mechanism for the excitation of high-amplitude nonaxisymmetric perturbations. The latter play a major role in the nonlinear evolution of the MRI on the route to fully developed turbulence.
Effect of Axisymmetric Aft Wall Angle Cavity in Supersonic Flow Field
Jeyakumar, S.; Assis, Shan M.; Jayaraman, K.
2018-03-01
Cavity plays a significant role in scramjet combustors to enhance mixing and flame holding of supersonic streams. In this study, the characteristics of axisymmetric cavity with varying aft wall angles in a non-reacting supersonic flow field are experimentally investigated. The experiments are conducted in a blow-down type supersonic flow facility. The facility consists of a supersonic nozzle followed by a circular cross sectional duct. The axisymmetric cavity is incorporated inside the duct. Cavity aft wall is inclined with two consecutive angles. The performance of the aft wall cavities are compared with rectangular cavity. Decreasing aft wall angle reduces the cavity drag due to the stable flow field which is vital for flame holding in supersonic combustor. Uniform mixing and gradual decrease in stagnation pressure loss can be achieved by decreasing the cavity aft wall angle.
Application of Quasi-Newton methods to the analysis of axisymmetric pressure vessels
International Nuclear Information System (INIS)
Parisi, D.A.C.
1987-01-01
This work studies the application of Quasi-Newton techniques to material nonlinear analysis of axisymmetrical pressure vessels by the finite element method. In the formulation the material bahavior is described by an isotropic elastoplastic model with strain hardening. The continum is discretized through triangular finite elements of axisymmetrical solids with linear interpolation of the displacement field. The incremental governing equations are derived by the virtual work. The solution of the system of simultaneous nonlinear equations is solved iteratively by the Quasi-Newton method employing the BFGS update. The numerical performance of the proposed method is compared with the Newton-Raphson method and some of its variants through some selected examples. (author) [pt
Approximations to the non-adiabatic particle response in toroidal geometry
International Nuclear Information System (INIS)
Schep, T.J.; Braams, B.J.
1981-08-01
The non-adiabatic part of the particle response to low-frequency electromagnetic modes with long parallel wavelengths is discussed. Analytic approximations to the kernels of the integrals that relate the amplitudes of the perturbed potentials to the non-adiabatic part of the perturbed density in an axisymmetric toroidal configuration are presented and the results are compared with numerical calculations. It is shown that both in the plane slab and in toroidal geometry the kernel contains a logarithmic singularity. This singularity is associated with particles with vanishing parallel velocity so that, in toroidal geometry, it is related with the behaviour of trapped particles near their turning points. In contrast to the plane slab, in toroidal geometry this logarithmic singularity is mainly real and associated with non-resonant particles. Apart from this logarithmic term, the kernel contains a complex regular part arising from resonant as well as from non-resonant particles. The analytic approximations that will be presented make the dispersion relation of drift-type modes in toroidal geometry amenable to analytic as well as to simpler numerical calculation of the growth rate and of the spatial mode structure
Emergent Geometry from Entropy and Causality
Engelhardt, Netta
generalizations are discussed, both at the classical and perturbatively quantum limits. In particular, several No Go Theorems are proven, indicative of a conclusion that supplementary approaches or information may be necessary to recover the full spacetime geometry. Part II of this thesis involves the relation between geometry and causality, the property that information cannot travel faster than light. Requiring this of any quantum field theory results in constraints on string theory setups that are dual to quantum field theories via the AdS/CFT correspondence. At the level of perturbative quantum gravity, it is shown that causality in the field theory constraints the causal structure in the bulk. At the level of nonperturbative quantum string theory, we find that constraints on causal signals restrict the possible ways in which curvature singularities can be resolved in string theory. Finally, a new program of research is proposed for the construction of bulk geometry from the divergences of correlation functions in the dual field theory. This divergence structure is linked to the causal structure of the bulk and of the field theory.
Berloff, Natalia G.; Roberts, Paul H.
2004-01-01
The stability of the axisymmetric solitary waves of the Gross-Pitaevskii (GP) equation is investigated. The Implicitly Restarted Arnoldi Method for banded matrices with shift-invert was used to solve the linearised spectral stability problem. The rarefaction solitary waves on the upper branch of the Jones-Roberts dispersion curve are shown to be unstable to axisymmetric infinitesimal perturbations, whereas the solitary waves on the lower branch and all two-dimensional solitary waves are linea...
International Nuclear Information System (INIS)
Cintra Filho, J. de S.
1981-01-01
The fluctuating temperature field structure is studied for the case of turbulent circular pipe flow. Experimentally determined integral length scales are used in modeling this structure in terms of axisymmetric forms. It is found that the appropriate angle of axisymmetry is larger than the one for modeling the large scale velocity structure. The axisymmetric model is then used to examine the validity and the prediction capability of the Tyldesley and Silver's non-spherical eddy diffusivity theory. (Author) [pt
Global regularity for a family of 3D models of the axi-symmetric Navier–Stokes equations
Hou, Thomas Y.; Liu, Pengfei; Wang, Fei
2018-05-01
We consider a family of three-dimensional models for the axi-symmetric incompressible Navier–Stokes equations. The models are derived by changing the strength of the convection terms in the axisymmetric Navier–Stokes equations written using a set of transformed variables. We prove the global regularity of the family of models in the case that the strength of convection is slightly stronger than that of the original Navier–Stokes equations, which demonstrates the potential stabilizing effect of convection.
SPECTROPOLARIMETRY OF SUPERLUMINOUS SUPERNOVAE: INSIGHT INTO THEIR GEOMETRY
Energy Technology Data Exchange (ETDEWEB)
Inserra, C.; Bulla, M.; Sim, S. A.; Smartt, S. J., E-mail: c.inserra@qub.ac.uk [Astrophysics Research Centre, School of Mathematics and Physics, Queens University Belfast, Belfast BT7 1NN (United Kingdom)
2016-11-01
We present the first spectropolarimetric observations of a hydrogen-free superluminous supernova (SLSN) at z = 0.1136, namely SN 2015bn. The transient shows significant polarization at both of the observed epochs: one 24 days before maximum light in the rest-frame, and the other at 27 days after peak luminosity. Analysis of the Q – U plane suggests the presence of a dominant axis and no physical departure from the main axis at either epoch. The polarization spectrum along the dominant axis is characterized by a strong wavelength dependence and an increase in the signal from the first to the second epoch. We use a Monte Carlo code to demonstrate that these properties are consistent with a simple toy model that adopts an axisymmetric ellipsoidal configuration for the ejecta. We find that the wavelength dependence of the polarization is possibly due to a strong wavelength dependence in the line opacity, while the higher level of polarization at the second epoch is a consequence of the increase in the asphericity of the inner layers of the ejecta or the fact that the photosphere recedes into less spherical layers. The geometry of the SLSN is similar to that of stripped-envelope core-collapse SNe connected to GRB, while the overall evolution of the ejecta shape could be consistent with a central engine.
THE TOPOLOGY OF CANONICAL FLUX TUBES IN FLARED JET GEOMETRY
Energy Technology Data Exchange (ETDEWEB)
Lavine, Eric Sander; You, Setthivoine, E-mail: Slavine2@uw.edu, E-mail: syou@aa.washington.edu [University of Washington, 4000 15th Street, NE Aeronautics and Astronautics 211 Guggenheim Hall, Box 352400, Seattle, WA 98195 (United States)
2017-01-20
Magnetized plasma jets are generally modeled as magnetic flux tubes filled with flowing plasma governed by magnetohydrodynamics (MHD). We outline here a more fundamental approach based on flux tubes of canonical vorticity, where canonical vorticity is defined as the circulation of the species’ canonical momentum. This approach extends the concept of magnetic flux tube evolution to include the effects of finite particle momentum and enables visualization of the topology of plasma jets in regimes beyond MHD. A flared, current-carrying magnetic flux tube in an ion-electron plasma with finite ion momentum is thus equivalent to either a pair of electron and ion flow flux tubes, a pair of electron and ion canonical momentum flux tubes, or a pair of electron and ion canonical vorticity flux tubes. We examine the morphology of all these flux tubes for increasing electrical currents, different radial current profiles, different electron Mach numbers, and a fixed, flared, axisymmetric magnetic geometry. Calculations of gauge-invariant relative canonical helicities track the evolution of magnetic, cross, and kinetic helicities in the system, and show that ion flow fields can unwind to compensate for an increasing magnetic twist. The results demonstrate that including a species’ finite momentum can result in a very long collimated canonical vorticity flux tube even if the magnetic flux tube is flared. With finite momentum, particle density gradients must be normal to canonical vorticities, not to magnetic fields, so observations of collimated astrophysical jets could be images of canonical vorticity flux tubes instead of magnetic flux tubes.
Stationary axisymmetric four dimensional space-time endowed with Einstein metric
International Nuclear Information System (INIS)
Hasanuddin; Azwar, A.; Gunara, B. E.
2015-01-01
In this paper, we construct Ernst equation from vacuum Einstein field equation for both zero and non-zero cosmological constant. In particular, we consider the case where the space-time admits axisymmetric using Boyer-Lindquist coordinates. This is called Kerr-Einstein solution describing a spinning black hole. Finally, we give a short discussion about the dynamics of photons on Kerr-Einstein space-time
International Nuclear Information System (INIS)
Jardin, S.C.; Schmidt, J.A.
1998-01-01
The Tokamak Simulation Code (TSC) has been used to model a new method of feedback stabilization of the axisymmetric instability in tokamaks using driven halo (or scrape-off layer) currents. The method appears to be feasible for a wide range of plasma edge parameters. It may offer advantages over the more conventional method of controlling this instability when applied in a reactor environment. (author)
Numerical analysis of laser ablation using the axisymmetric two-temperature model
Dziatkiewicz, Jolanta; Majchrzak, Ewa
2018-01-01
Laser ablation of the axisymmetric micro-domain is analyzed. To describe the thermal processes occurring in the micro-domain the two-temperature hyperbolic model supplemented by the boundary and initial conditions is used. This model takes into account the phase changes of material (solid-liquid and liquid-vapour) and the ablation process. At the stage of numerical computations the finite difference method with staggered grid is used. In the final part the results of computations are shown.
MHD stability calculations of high-β quasi-axisymmetric stellarators
International Nuclear Information System (INIS)
Fu, G.Y.; Ku, L.P.; Pomphrey, N.; Redi, M.H.; Kessel, C.; Monticello, D.A.; Reiman, A.; Hughes, M.; Cooper, W.A.; Nuehrenberg, C.
1999-01-01
The MHD stability of quasi-axisymmetric compact stellarators is investigated. It is shown that bootstrap current driven external kink modes can be stabilized by a combination of edge magnetic shear and appropriate 3D plasma boundary shaping while maintaining good quasi-axisymmetry. The results demonstrate that there exists a new class of stellarators with quasi-axisymmetry, large bootstrap current, high MHD beta limit, and compact size. (author)
MHD Stability Calculations of High-Beta Quasi-Axisymmetric Stellarators
International Nuclear Information System (INIS)
Kessel, C.; Fu, G.Y.; Ku, L.P.; Redi, M.H.; Pomphrey, N.
1999-01-01
The MHD stability of quasi-axisymmetric compact stellarators is investigated. It is shown that bootstrap current driven external kink modes can be stabilized by a combination of edge magnetic shear and appropriate 3D plasma boundary shaping while maintaining good quasi-axisymmetry. The results demonstrate that there exists a new class of stellarators with quasi-axisymmetry, large bootstrap current, high MHD beta limit, and compact size
NOVA: a nonvariational code for solving MHD stability of axisymmetric toroidal plasmas
International Nuclear Information System (INIS)
Cheng, C.Z.; Chance, M.S.
1986-04-01
A nonvariational approach for determining the ideal MHD stability of axisymmetric toroidal confinement systems is presented. The code (NOVA) employs cubic B-spline finite elements and Fourier expansion in a general flux coordinate (psi, theta, zeta) system. Better accuracy and faster convergence were obtained in comparison with the variational PEST and ERATO codes. The nonvariational approach can be extended to problems having non-Hermitian eigenmode equations where variational energy principles cannot be obtained
MHD stability calculations of high-β quasi-axisymmetric stellarators
International Nuclear Information System (INIS)
Fu, G.Y.; Ku, L.P.; Pomphrey, N.; Redi, M.; Kessel, C.; Monticello, D.; Reiman, A.; Hughes, M.; Cooper, W.A.; Nuehrenberg, C.
2001-01-01
The MHD stability of quasi-axisymmetric compact stellarators is investigated. It is shown that bootstrap current driven external kink modes can be stabilized by a combination of edge magnetic shear and appropriate 3D plasma boundary shaping while maintaining good quasi-axisymmetry. The results demonstrate that there exists a new class of stellarators with quasi-axisymmetry, large bootstrap current, high MHD beta limit, and compact size. (author)
Axisymmetric modeling of ultrashort-pulse laser interactions with thin metal film
Directory of Open Access Journals (Sweden)
E. Majchrzak
2011-10-01
Full Text Available The hyperbolic two-temperature model is used in order to describe the heat propagation in metal film subjected to an ultrashort-pulse laser heating. An axisymmetric heat soureceewith Gaussian temporeal and spatial distributions has been taken into account. At the stage of numerical computations the finite difference method is used. In the final part of the paper the examples of computations are shown.
An Axisymmetric View of Concentric Eyewall Evolution in Hurricane Rita (2005)
2012-08-01
of Hurricane Hugo (1989). Mon. Wea. Rev., 136, 1237–1259. Martinez, Y., G. Brunet, and M. K. Yau, 2010: On the dynamics of two-dimensional hurricane ...An Axisymmetric View of Concentric Eyewall Evolution in Hurricane Rita (2005) MICHAEL M. BELL Naval Postgraduate School, Monterey, California, and... Hurricane Research Division, Miami, Florida WEN-CHAU LEE National Center for Atmospheric Research,* Boulder, Colorado (Manuscript received 23 June 2011, in
Nonlinear full two-fluid study of m=0 sausage instabilities in an axisymmetric Z pinch
International Nuclear Information System (INIS)
Loverich, J.; Shumlak, U.
2006-01-01
A nonlinear full five-moment two-fluid model is used to study axisymmetric instabilities in a Z pinch. When the electron velocity due to the current J is greater than the ion acoustic speed, high wave-number sausage instabilities develop that initiate shock waves in the ion fluid. This condition corresponds to a pinch radius on the order of a few ion Larmor radii
International Nuclear Information System (INIS)
Saha, S.; Dasgupta, A.; Basu, P.C.
1993-01-01
Seismic analysis of a Reactor Building is performed idealising the system as a beam model (BM) and also an Axi-symmetric model (ASM) and the results compared. In both the cases effect of Soil-Structure Interaction have been taken Into account. Since the lower boundary of the ASM was at a depth much lower than that of the BM, deconvolution of the specified Free-Field Motion (FFM) was necessary. The deconvolution has been performed using frequency domain approach. (author)
Axisymmetric force-free states and relaxation of a spheroidal spheromak
International Nuclear Information System (INIS)
Throumoulopoulos, G.N.; Pantis, G.
1990-01-01
Axisymmetric force-free equilibrium eigenstates for a prolate as well as an oblate spheroidal Spheromak with arbitrary elongation are obtained. In the framework of the Woltjer-Taylor relaxation theory the relaxed states are also identified. A simple hypothesis for the relaxation process is introduced, which implies that the plasma relaxes from multitoroidal formations to a singly toroidal configuration, in qualitative agreement with experimental results. (author)
Kalantarian, Ali; Ninomiya, Hiromasa; Saad, Sameh M.I.; David, Robert; Winklbauer, Rudolf; Neumann, A. Wilhelm
2009-01-01
Biological tissues behave in certain respects like liquids. Consequently, the surface tension concept can be used to explain aspects of the in vitro and in vivo behavior of multicellular aggregates. Unfortunately, conventional methods of surface tension measurement cannot be readily applied to small cell aggregates. This difficulty can be overcome by an experimentally straightforward method consisting of centrifugation followed by axisymmetric drop shape analysis (ADSA). Since the aggregates ...
Effects of shape and stroke parameters on the propulsion performance of an axisymmetric swimmer.
Peng, Jifeng; Alben, Silas
2012-03-01
In nature, there exists a special group of aquatic animals which have an axisymmetric body and whose primary swimming mechanism is to use periodic body contractions to generate vortex rings in the surrounding fluid. Using jellyfish medusae as an example, this study develops a mathematical model of body kinematics of an axisymmetric swimmer and uses a computational approach to investigate the induced vortex wakes. Wake characteristics are identified for swimmers using jet propulsion and rowing, two mechanisms identified in previous studies of medusan propulsion. The parameter space of body kinematics is explored through four quantities: a measure of body shape, stroke amplitude, the ratio between body contraction duration and extension duration, and the pulsing frequency. The effects of these parameters on thrust, input power requirement and circulation production are quantified. Two metrics, cruising speed and energy cost of locomotion, are used to evaluate the propulsion performance. The study finds that a more prolate-shaped swimmer with larger stroke amplitudes is able to swim faster, but its cost of locomotion is also higher. In contrast, a more oblate-shaped swimmer with smaller stroke amplitudes uses less energy for its locomotion, but swims more slowly. Compared with symmetric strokes with equal durations of contraction and extension, faster bell contractions increase the swimming speed whereas faster bell extensions decrease it, but both require a larger energy input. This study shows that besides the well-studied correlations between medusan body shape and locomotion, stroke variables also affect the propulsion performance. It provides a framework for comparing the propulsion performance of axisymmetric swimmers based on their body kinematics when it is difficult to measure and analyze their wakes empirically. The knowledge from this study is also useful for the design of robotic swimmers that use axisymmetric body contractions for propulsion.
Effects of shape and stroke parameters on the propulsion performance of an axisymmetric swimmer
International Nuclear Information System (INIS)
Peng Jifeng; Alben, Silas
2012-01-01
In nature, there exists a special group of aquatic animals which have an axisymmetric body and whose primary swimming mechanism is to use periodic body contractions to generate vortex rings in the surrounding fluid. Using jellyfish medusae as an example, this study develops a mathematical model of body kinematics of an axisymmetric swimmer and uses a computational approach to investigate the induced vortex wakes. Wake characteristics are identified for swimmers using jet propulsion and rowing, two mechanisms identified in previous studies of medusan propulsion. The parameter space of body kinematics is explored through four quantities: a measure of body shape, stroke amplitude, the ratio between body contraction duration and extension duration, and the pulsing frequency. The effects of these parameters on thrust, input power requirement and circulation production are quantified. Two metrics, cruising speed and energy cost of locomotion, are used to evaluate the propulsion performance. The study finds that a more prolate-shaped swimmer with larger stroke amplitudes is able to swim faster, but its cost of locomotion is also higher. In contrast, a more oblate-shaped swimmer with smaller stroke amplitudes uses less energy for its locomotion, but swims more slowly. Compared with symmetric strokes with equal durations of contraction and extension, faster bell contractions increase the swimming speed whereas faster bell extensions decrease it, but both require a larger energy input. This study shows that besides the well-studied correlations between medusan body shape and locomotion, stroke variables also affect the propulsion performance. It provides a framework for comparing the propulsion performance of axisymmetric swimmers based on their body kinematics when it is difficult to measure and analyze their wakes empirically. The knowledge from this study is also useful for the design of robotic swimmers that use axisymmetric body contractions for propulsion. (paper)
WKB theory for high-n modes in axisymmetric toroidal plasmas
International Nuclear Information System (INIS)
Dewar, R.L.; Chance, M.S.; Glasser, A.H.; Greene, J.M.; Frieman, E.A.
1979-09-01
It is demonstrated that the low-frequency, k/sub parallel//k/sub perpendicular/ approx. = 0 normal modes of an axisymmetric plasma, at large but finite toroidal mode number n, can be obtained by solving a novel WKB problem involving an infinite number of branches. Formulae for the frequencies of periodic normal modes are derived. The analysis is performed in the context of an ideal MHD model, and comparison is made with numerical ballooning mode results
CFD Validation Experiment of a Mach 2.5 Axisymmetric Shock-Wave/Boundary-Layer Interaction
Davis, David Owen
2015-01-01
Preliminary results of an experimental investigation of a Mach 2.5 two-dimensional axisymmetric shock-wave/ boundary-layer interaction (SWBLI) are presented. The purpose of the investigation is to create a SWBLI dataset specifically for CFD validation purposes. Presented herein are the details of the facility and preliminary measurements characterizing the facility and interaction region. These results will serve to define the region of interest where more detailed mean and turbulence measurements will be made.
Axisymmetric force-free states and relaxation of a spheroidal spheromak
International Nuclear Information System (INIS)
Throumoulopoulos, G.N.; Pantis, G.
1990-01-01
Axisymmetric force-free equilibrium eigenstates for a prolate as well as an oblate spheroidal spheromak with arbitrary elongation are obtained. In the framework of the Woltjer-Taylor relaxation theory the relaxed states are also identified. A simple hypothesis for the relaxation process is introduced which implies that the plasma relaxes from multitoroidal formations to a singly toroidal configuration in qualitative agreement with experimental results. (Author)
International Nuclear Information System (INIS)
Shibata, Masaru; Sekiguchi, Yu-ichirou
2004-01-01
Axisymmetric numerical simulations of rotating stellar core collapse to a neutron star are performed in the framework of full general relativity. The so-called Cartoon method, in which the Einstein field equations are solved in Cartesian coordinates and the axisymmetric condition is imposed around the y=0 plane, is adopted. The hydrodynamic equations are solved in cylindrical coordinates (on the y=0 plane in Cartesian coordinates) using a high-resolution shock-capturing scheme with maximum grid size (2500,2500). A parametric equation of state is adopted to model collapsing stellar cores and neutron stars following Dimmelmeier, Font, and Mueller. It is found that the evolution of the central density during the collapse, bounce, and formation of protoneutron stars agrees well with that in the work of Dimmelmeier, Font, and Mueller in which an approximate general relativistic formulation is adopted. This indicates that such an approximation is appropriate for following axisymmetric stellar core collapses and the subsequent formation of protoneutron stars. Gravitational waves are computed using a quadrupole formula. It is found that the waveforms are qualitatively in good agreement with those by Dimmelmeier, Font, and Mueller. However, quantitatively, two waveforms do not agree well. The possible reasons for the disagreement are discussed
Gildfind, D. E.; Jacobs, P. A.; Morgan, R. G.; Chan, W. Y. K.; Gollan, R. J.
2017-11-01
This paper presents the second part of a study aiming to accurately characterise a Mach 10 scramjet test flow generated using a large free-piston-driven expansion tube. Part 1 described the experimental set-up, the quasi-one-dimensional simulation of the full facility, and the hybrid analysis technique used to compute the nozzle exit test flow properties. The second stage of the hybrid analysis applies the computed 1-D shock tube flow history as an inflow to a high-fidelity two-dimensional-axisymmetric analysis of the acceleration tube. The acceleration tube exit flow history is then applied as an inflow to a further refined axisymmetric nozzle model, providing the final nozzle exit test flow properties and thereby completing the analysis. This paper presents the results of the axisymmetric analyses. These simulations are shown to closely reproduce experimentally measured shock speeds and acceleration tube static pressure histories, as well as nozzle centreline static and impact pressure histories. The hybrid scheme less successfully predicts the diameter of the core test flow; however, this property is readily measured through experimental pitot surveys. In combination, the full test flow history can be accurately determined.
Global stability analysis of axisymmetric boundary layer over a circular cylinder
Bhoraniya, Ramesh; Vinod, Narayanan
2018-05-01
This paper presents a linear global stability analysis of the incompressible axisymmetric boundary layer on a circular cylinder. The base flow is parallel to the axis of the cylinder at inflow boundary. The pressure gradient is zero in the streamwise direction. The base flow velocity profile is fully non-parallel and non-similar in nature. The boundary layer grows continuously in the spatial directions. Linearized Navier-Stokes (LNS) equations are derived for the disturbance flow quantities in the cylindrical polar coordinates. The LNS equations along with homogeneous boundary conditions forms a generalized eigenvalues problem. Since the base flow is axisymmetric, the disturbances are periodic in azimuthal direction. Chebyshev spectral collocation method and Arnoldi's iterative algorithm is used for the solution of the general eigenvalues problem. The global temporal modes are computed for the range of Reynolds numbers and different azimuthal wave numbers. The largest imaginary part of the computed eigenmodes is negative, and hence, the flow is temporally stable. The spatial structure of the eigenmodes shows that the disturbance amplitudes grow in size and magnitude while they are moving towards downstream. The global modes of axisymmetric boundary layer are more stable than that of 2D flat-plate boundary layer at low Reynolds number. However, at higher Reynolds number they approach 2D flat-plate boundary layer. Thus, the damping effect of transverse curvature is significant at low Reynolds number. The wave-like nature of the disturbance amplitudes is found in the streamwise direction for the least stable eigenmodes.
Axisymmetrical separator for separating particulate matter from a fluid carrying medium
Linhardt, Hans D.
1984-09-04
A separator for separating particles carried in a fluid carrying medium is disclosed. The separator includes an elongated duct and associated openings incorporated in a solid body. The duct is axisymmetrical relative to its longitudinal axis, and includes a curved wall portion having a curved cross-section taken along the longitudinal axis. An axisymmetrical opening located downstream of the curved wall portion leads from the duct into an axisymmetrical channel which is substantially radially disposed relative to the longitudinal axis. Continuation of the duct downstream of the opening is a discharge portion which is substantially colinear with the longitudinal axis. In operation, a substantial majority of the fluid carrying medium leaves the duct radially through the opening and channel in a state substantially free of particles. A remaining small portion of the fluid carrying medium and a substantial majority of the particles are channelled into the discharge portion by centrifugal forces arising due to travel of the particles along the curved walls. For industrial scale separation of particles from a fluid carrying medium, such as for the clean-up of stack gases, an array of several hundred to several thousand of the separators is provided.
Directory of Open Access Journals (Sweden)
Monika Tyagi
2014-01-01
Full Text Available Complexes of Mn(II, Co(II, Ni(II, Pd(II and Pt(II were synthesized with the macrocyclic ligand, i.e., 2,3,9,10-tetraketo-1,4,8,11-tetraazacycoletradecane. The ligand was prepared by the [2 + 2] condensation of diethyloxalate and 1,3-diamino propane and characterized by elemental analysis, mass, IR and 1H NMR spectral studies. All the complexes were characterized by elemental analysis, molar conductance, magnetic susceptibility measurements, IR, electronic and electron paramagnetic resonance spectral studies. The molar conductance measurements of Mn(II, Co(II and Ni(II complexes in DMF correspond to non electrolyte nature, whereas Pd(II and Pt(II complexes are 1:2 electrolyte. On the basis of spectral studies an octahedral geometry has been assigned for Mn(II, Co(II and Ni(II complexes, whereas square planar geometry assigned for Pd(II and Pt(II. In vitro the ligand and its metal complexes were evaluated against plant pathogenic fungi (Fusarium odum, Aspergillus niger and Rhizoctonia bataticola and some compounds found to be more active as commercially available fungicide like Chlorothalonil.
Black Holes and Large Order Quantum Geometry
Huang, Min-xin; Mariño, Marcos; Tavanfar, Alireza
2009-01-01
We study five-dimensional black holes obtained by compactifying M theory on Calabi-Yau threefolds. Recent progress in solving topological string theory on compact, one-parameter models allows us to test numerically various conjectures about these black holes. We give convincing evidence that a microscopic description based on Gopakumar-Vafa invariants accounts correctly for their macroscopic entropy, and we check that highly nontrivial cancellations -which seem necessary to resolve the so-called entropy enigma in the OSV conjecture- do in fact occur. We also study analytically small 5d black holes obtained by wrapping M2 branes in the fiber of K3 fibrations. By using heterotic/type II duality we obtain exact formulae for the microscopic degeneracies in various geometries, and we compute their asymptotic expansion for large charges.
Energy Technology Data Exchange (ETDEWEB)
El-Amin, M.F.; Kanayama, H. [Department of Mechanical Engineering, Faculty of Engineering, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395 (Japan)
2009-02-15
As hydrogen leaks into a partially open space with a ceiling wall, a boundary layer of hydrogen can be constructed under that wall due to the impingement on the wall and the buoyancy force. The resulting boundary layer can be divided into two regions, namely the stagnation-point region and the far region. When the geometry of the source of the hydrogen leak is circular, such as a pinhole or an o-ring, the behavior of leakage flow will be axisymmetric due to the resulting radial jet. In contrast, when the geometry of the source of the hydrogen leak is planar, such as a crack, the behavior of leakage flow will be planar due to the resulting planar jet. Previously, we studied the planar case in the context of both the stagnation-point flow region [El-Amin MF, Kanayama H. Boundary layer theory approach to the concentration layer adjacent to a ceiling wall at impinging region of a hydrogen leakage. Int J Hydrogen Energy 2008; 33(21): 6393-00] and the far region [El-Amin MF, Inoue M, Kanayama H. Boundary layer theory approach to the concentration layer adjacent to a ceiling wall of a hydrogen leakage: far region. Int J Hydrogen Energy 2008; 33(24):7642-7]. This paper is concerned with both the stagnation-point flow region and the far region of the axisymmetric concentration boundary layer adjacent to a ceiling wall. Flow in the stagnation-point region is treated as Hiemenz flow, while it is treated as Blasius flow in the far region. The current results are compared with the planar cases [El-Amin MF, Kanayama H. Boundary layer theory approach to the concentration layer adjacent to a ceiling wall at impinging region of a hydrogen leakage. Int J Hydrogen Energy 2008; 33(21): 6393-00; El-Amin MF, Inoue M, Kanayama H. Boundary layer theory approach to the concentration layer adjacent to a ceiling wall of a hydrogen leakage: far region. Int J Hydrogen Energy 2008; 33(24):7642-7] for both stagnation-point flow and far regions. Both momentum and concentration boundary layer
Advanced geometries for ballistic neutron guides
International Nuclear Information System (INIS)
Schanzer, Christian; Boeni, Peter; Filges, Uwe; Hils, Thomas
2004-01-01
Sophisticated neutron guide systems take advantage of supermirrors being used to increase the neutron flux. However, the finite reflectivity of supermirrors becomes a major loss mechanism when many reflections occur, e.g. in long neutron guides and for long wavelengths. In order to reduce the number of reflections, ballistic neutron guides have been proposed. Usually linear tapered sections are used to enlarge the cross-section and finally, focus the beam to the sample. The disadvantages of linear tapering are (i) an inhomogeneous phase space at the sample position and (ii) a decreasing flux with increasing distance from the exit of the guide. We investigate the properties of parabolic and elliptic tapering for ballistic neutron guides, using the Monte Carlo program McStas with a new guide component dedicated for such geometries. We show that the maximum flux can indeed be shifted away from the exit of the guide. In addition we explore the possibilities of parabolic and elliptic geometries to create point like sources for dedicated experimental demands
Variable geometry Darrieus wind machine
Pytlinski, J. T.; Serrano, D.
1983-08-01
A variable geometry Darrieus wind machine is proposed. The lower attachment of the blades to the rotor can move freely up and down the axle allowing the blades of change shape during rotation. Experimental data for a 17 m. diameter Darrieus rotor and a theoretical model for multiple streamtube performance prediction were used to develop a computer simulation program for studying parameters that affect the machine's performance. This new variable geometry concept is described and interrelated with multiple streamtube theory through aerodynamic parameters. The computer simulation study shows that governor behavior of a Darrieus turbine can not be attained by a standard turbine operating within normally occurring rotational velocity limits. A second generation variable geometry Darrieus wind turbine which uses a telescopic blade is proposed as a potential improvement on the studied concept.
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...
Guide to Computational Geometry Processing
DEFF Research Database (Denmark)
Bærentzen, Jakob Andreas; Gravesen, Jens; Anton, François
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...... to the theoretical and mathematical underpinnings of each technique, enabling the reader to not only implement a given method, but also to understand the ideas behind it, its limitations and its advantages. Topics and features: Presents an overview of the underlying mathematical theory, covering vector spaces......, metric space, affine spaces, differential geometry, and finite difference methods for derivatives and differential equations Reviews geometry representations, including polygonal meshes, splines, and subdivision surfaces Examines techniques for computing curvature from polygonal meshes Describes...
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.
Dayside merging and cusp geometry
International Nuclear Information System (INIS)
Crooker, N.U.
1979-01-01
Geometrical considerations are presented to show that dayside magnetic merging when constrained to act only where the fields are antiparallel results in lines of merging that converge at the polar cusps. An important consequence of this geometry is that no accelerated flows are predicted across the dayside magnetopause. Acceleration owing to merging acts in opposition to the magnetosheath flow at the merging point and produces the variably directed, slower-than-magnetosheath flows observed in the entry layer. Another consequence of the merging geometry is that much of the time closed field lines constitute the subsolar region of the magnetopause. The manner in which the polar cap convection patterns predicted by the proposed geometry change as the interplanetary field is rotated through 360 0 provides a unifying description of how the observed single circular vortex and the crescent-shaped double vortex patterns mutually evolve under the influence of a single operating principle
DOGBONE GEOMETRY FOR RECIRCULATING ACCELERATORS
International Nuclear Information System (INIS)
BERG, J.S.; JOHNSTONE, C.; SUMMERS, D.
2001-01-01
Most scenarios for accelerating muons require recirculating acceleration. A racetrack shape for the accelerator requires particles with lower energy in early passes to traverse almost the same length of arc as particles with the highest energy. This extra arc length may lead to excess decays and excess cost. Changing the geometry to a dogbone shape, where there is a single linac and the beam turns completely around at the end of the linac, returning to the same end of the linac from which it exited, addresses this problem. In this design, the arc lengths can be proportional to the particle's momentum. This paper proposes an approximate cost model for a recirculating accelerator, attempts to make cost-optimized designs for both racetrack and dogbone geometries, and demonstrates that the dogbone geometry does appear to be more cost effective
Geometric Transformations in Engineering Geometry
Directory of Open Access Journals (Sweden)
I. F. Borovikov
2015-01-01
Full Text Available Recently, for business purposes, in view of current trends and world experience in training engineers, research and faculty staff there has been a need to transform traditional courses of descriptive geometry into the course of engineering geometry in which the geometrical transformations have to become its main section. On the basis of critical analysis the paper gives suggestions to improve a presentation technique of this section both in the classroom and in academic literature, extend an application scope of geometrical transformations to solve the position and metric tasks and simulation of surfaces, as well as to design complex engineering configurations, which meet a number of pre-specified conditions.The article offers to make a number of considerable amendments to the terms and definitions used in the existing courses of descriptive geometry. It draws some conclusions and makes the appropriate proposals on feasibility of coordination in teaching the movement transformation in the courses of analytical and descriptive geometry. This will provide interdisciplinary team teaching and allow students to be convinced that a combination of analytical and graphic ways to solve geometric tasks is useful and reasonable.The traditional sections of learning courses need to be added with a theory of projective and bi-rational transformations. In terms of application simplicity and convenience it is enough to consider the central transformations when solving the applied tasks. These transformations contain a beam of sub-invariant (low-invariant straight lines on which the invariant curve induces non-involution and involution projectivities. The expediency of nonlinear transformations application is shown in the article by a specific example of geometric modeling of the interfacing surface "spar-blade".Implementation of these suggestions will contribute to a real transformation of a traditional course of descriptive geometry to the engineering geometry
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
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
Lectures on Algebraic Geometry I
Harder, Gunter
2012-01-01
This book and the following second volume is an introduction into modern algebraic geometry. In the first volume the methods of homological algebra, theory of sheaves, and sheaf cohomology are developed. These methods are indispensable for modern algebraic geometry, but they are also fundamental for other branches of mathematics and of great interest in their own. In the last chapter of volume I these concepts are applied to the theory of compact Riemann surfaces. In this chapter the author makes clear how influential the ideas of Abel, Riemann and Jacobi were and that many of the modern metho
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
Comparison theorems in Riemannian geometry
Cheeger, Jeff
2008-01-01
The central theme of this book is the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry. The first five chapters are preparatory in nature. They begin with a very concise introduction to Riemannian geometry, followed by an exposition of Toponogov's theorem-the first such treatment in a book in English. Next comes a detailed presentation of homogeneous spaces in which the main goal is to find formulas for their curvature. A quick chapter of Morse theory is followed by one on the injectivity radius. Chapters 6-9 deal with many of the most re
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.
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 frame-independent entities. We depart from a subject well known by students, which is the three-dimensional geometric space in order to compare, afterwards, with the treatment of four-dimensional space in the special relativity. The differences and similarities between these two subjects are also...
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
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
Photogrammetric computer vision statistics, geometry, orientation and reconstruction
Förstner, Wolfgang
2016-01-01
This textbook offers a statistical view on the geometry of multiple view analysis, required for camera calibration and orientation and for geometric scene reconstruction based on geometric image features. The authors have backgrounds in geodesy and also long experience with development and research in computer vision, and this is the first book to present a joint approach from the converging fields of photogrammetry and computer vision. Part I of the book provides an introduction to estimation theory, covering aspects such as Bayesian estimation, variance components, and sequential estimation, with a focus on the statistically sound diagnostics of estimation results essential in vision metrology. Part II provides tools for 2D and 3D geometric reasoning using projective geometry. This includes oriented projective geometry and tools for statistically optimal estimation and test of geometric entities and transformations and their relations, tools that are useful also in the context of uncertain reasoning in po...
African Journals Online (AJOL)
DR. AMINU
Department of Chemistry Bayero University, P. M. B. 3011, Kano, Nigeria. E-mail: hnuhu2000@yahoo.com. ABSTRACT. The manganese (II), cobalt (II), nickel (II) and .... water and common organic solvents, but are readily soluble in acetone. The molar conductance measurement [Table 3] of the complex compounds in.
Flow, transport and diffusion in random geometries II: applications
Asinari, Pietro
2015-01-07
Multilevel Monte Carlo (MLMC) is an efficient and flexible solution for the propagation of uncertainties in complex models, where an explicit parametrization of the input randomness is not available or too expensive. We present several applications of our MLMC algorithm for flow, transport and diffusion in random heterogeneous materials. The absolute permeability and effective diffusivity (or formation factor) of micro-scale porous media samples are computed and the uncertainty related to the sampling procedures is studied. The algorithm is then extended to the transport problems and multiphase flows for the estimation of dispersion and relative permeability curves. The impact of water drops on random stuctured surfaces, with microfluidics applications to self-cleaning materials, is also studied and simulated. Finally the estimation of new drag correlation laws for poly-dispersed dilute and dense suspensions is presented.
Flow, transport and diffusion in random geometries II: applications
Asinari, Pietro; Ceglia, Diego; Icardi, Matteo; Prudhomme, Serge; Tempone, Raul
2015-01-01
Multilevel Monte Carlo (MLMC) is an efficient and flexible solution for the propagation of uncertainties in complex models, where an explicit parametrization of the input randomness is not available or too expensive. We present several applications of our MLMC algorithm for flow, transport and diffusion in random heterogeneous materials. The absolute permeability and effective diffusivity (or formation factor) of micro-scale porous media samples are computed and the uncertainty related to the sampling procedures is studied. The algorithm is then extended to the transport problems and multiphase flows for the estimation of dispersion and relative permeability curves. The impact of water drops on random stuctured surfaces, with microfluidics applications to self-cleaning materials, is also studied and simulated. Finally the estimation of new drag correlation laws for poly-dispersed dilute and dense suspensions is presented.
Geometry of Kaluza-Klein theory. II. Field equations
International Nuclear Information System (INIS)
Maia, M.D.
1985-01-01
In the preceding paper a geometric formulation of Kaluza-Klein theory was presented with the basic assumption that the space-time is locally and isometrically embedded in the high-dimensional space which emerged at the big bang. In the present note the Gauss-Codazzi-Ricci equations which are the integrability equations for the embedding are interpreted as the dynamical equations for a low-energy observer. The second quadratic form which results from the embedding is interpreted as a fundamental spin-two massless field. The dynamics for an observer with high-energy probes is described as usual by the Einstein-Hilbert action defined in the high-dimensional space and dimensionally reduced by integration over the internal space. The behavior of fermion masses under different gravitational field strengths is implemented by use of the mass operator defined with the second-order Casimir operator of the embedding symmetry group
Discrete Geometry Toolkit for Shape Optimization, Phase II
National Aeronautics and Space Administration — Simulation-based design optimization has been steadily maturing over the past two decades, but not without its own unique and persistent challenges. The proposed...