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
Quantum roots in geometry : II
International Nuclear Information System (INIS)
Wanas, M.I.
2006-01-01
The present work is a review of a series of papers, published in the last ten. years, comprising an attempt to find a suitable avenue from geometry to quantum. It shows clearly that, any non-symmetric geometry admits some built-in quantum features. These features disappear completely once the geometry becomes symmetric (torsion-less). It is shown that, torsion of space-time plays an important role in both geometry and physics. It interacts with the spin of the moving particle and with its charge. The first interaction, Spin-Torsion Interaction, has been used to overcome the discrepancy in the results of the COW-experiment. The second interaction, Charge-Torsion Interaction, is similar to the Aharonov-Bohm effect. As a byproduct, a new version of Absolute Parallelism (AP) geometry, the Parameterized Absolute Parallelism (PAP) geometry, has been established and developed. This version can be used to construct field theories that admit some quantum features. Riemannian geometry and conventional AP-geometry are special cases of PAP-geometry
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
Carson, G. T., Jr.; Lee, E. E., Jr.
1981-01-01
Quantitative pressure and force data for five axisymmetric boattail nozzle configurations were examined. These configurations simulate the variable-geometry feature of a single nozzle design operating over a range of engine operating conditions. Five nozzles were tested in the Langley 16-Foot Transonic Tunnel at Mach numbers from 0.60 to 1.30. The experimental data were also compared with theoretical predictions.
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
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
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
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)
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 ...
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.
Modeling axisymmetric flow and transport
Langevin, C.D.
2008-01-01
Unmodified versions of common computer programs such as MODFLOW, MT3DMS, and SEAWAT that use Cartesian geometry can accurately simulate axially symmetric ground water flow and solute transport. Axisymmetric flow and transport are simulated by adjusting several input parameters to account for the increase in flow area with radial distance from the injection or extraction well. Logarithmic weighting of interblock transmissivity, a standard option in MODFLOW, can be used for axisymmetric models to represent the linear change in hydraulic conductance within a single finite-difference cell. Results from three test problems (ground water extraction, an aquifer push-pull test, and upconing of saline water into an extraction well) show good agreement with analytical solutions or with results from other numerical models designed specifically to simulate the axisymmetric geometry. Axisymmetric models are not commonly used but can offer an efficient alternative to full three-dimensional models, provided the assumption of axial symmetry can be justified. For the upconing problem, the axisymmetric model was more than 1000 times faster than an equivalent three-dimensional model. Computational gains with the axisymmetric models may be useful for quickly determining appropriate levels of grid resolution for three-dimensional models and for estimating aquifer parameters from field tests.
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 ...
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
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
Kojima, Yasufumi; Okamoto, Satoki
2018-04-01
A magnetar's magnetosphere gradually evolves by the injection of energy and helicity from the interior. Axisymmetric static solutions for a relativistic force-free magnetosphere with a power-law current model are numerically obtained. They provide information about the configurations in which the stored energy is large. The energy along a sequence of equilibria increases and becomes sufficient to open the magnetic field. A magnetic flux rope, in which a large amount of toroidal field is confined, is formed in the vicinity of the star, for states exceeding the open field energy. These states are energetically metastable, and the excess energy may be ejected as a magnetar outburst.
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 ...
Tam, C. K. W.; Burton, D. E.
1984-01-01
An investigation is conducted of the phenomenon of sound generation by spatially growing instability waves in high-speed flows. It is pointed out that this process of noise generation is most effective when the flow is supersonic relative to the ambient speed of sound. The inner and outer asymptotic expansions corresponding to an excited instability wave in a two-dimensional mixing layer and its associated acoustic fields are constructed in terms of the inner and outer spatial variables. In matching the solutions, the intermediate matching principle of Van Dyke and Cole is followed. The validity of the theory is tested by applying it to an axisymmetric supersonic jet and comparing the calculated results with experimental measurements. Very favorable agreements are found both in the calculated instability-wave amplitude distribution (the inner solution) and the near pressure field level contours (the outer solution) in each case.
DEFF Research Database (Denmark)
Byg din egen boomerang, kast den, se den flyve, forstå hvorfor og hvordan den vender tilbage, og grib den. Det handler om opdriften på vingerne når du flyver, men det handler også og allermest om den mærkværdige gyroskop-effekt, du bruger til at holde balancen, når du kører på cykel. Vi vil bruge...... matematik, geometri, og fysik til at forstå, hvad det er, der foregår....
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...
Li, Yang; Lehmann, Teresa
2012-06-01
The solution structure of Fe(II)-peplomycin was determined from NMR data collected for this molecule. As found previously for Fe(II)- and Co(II)-bound bleomycin; the coordination sphere of the metal is composed of the primary and secondary amines in β-aminoalanine, the pyrimidine and imidazole rings in the pyrimidinylpropionamide, and β-hydroxyhistidine moieties, respectively, the amine nitrogen in β-hydroxyhistidine, and either the carbamoyl group in mannose or a solvent molecule. The two most discussed coordination geometries for the aforementioned ligands in metallo-bleomycins have been tested against the NMR data generated for Fe(II)-peplomycin. The interpretation of the experimental evidence obtained through molecular dynamics indicates that both geometries are equally likely in solution for this compound in the absence of DNA, but arguments are offered to explain why one of these geometries is preferred in the presence of DNA. Published by Elsevier Inc.
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
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.
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 (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. The principles used to provide supplemental shielding to the NSLS-II accelerators and the lessons learned from this process are presented.
Iga, Keita; Yokota, Sho; Watanabe, Shunichi; Ikeda, Takashi; Niino, Hiroshi; Misawa, Nobuhiko
2017-12-01
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.
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
On the variational approach to axisymmetric magnetohydrodynamic equilibria
International Nuclear Information System (INIS)
Andreussi, T.; Pegoraro, F.
2008-01-01
The variational formulation of the axisymmetric magnetohydrodynamic equilibrium equations with plasma flows is addressed and a more comprehensive method is presented that allows, in particular, for open boundary conditions and discontinuous (shock) solutions. A numerical procedure based on the variational formulation is described and a validation test for an open conical geometry, including also hydrodynamic shocks, is investigated.
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
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)
Peng, Yan; Mereacre, Valeriu; Anson, Christopher E; Zhang, Yiquan; Bodenstein, Tilmann; Fink, Karin; Powell, Annie K
2017-06-05
Three air-stable Co(II) mononuclear complexes with different aromatic substituents have been prepared and structurally characterized by single-crystal X-ray diffraction. The mononuclear complexes [Co(H 2 L1) 2 ]·2THF (1), [Co(HL2) 2 ] (2), and [Co(H 2 L3) 2 ]·CH 2 Cl 2 (3) (where H 3 L1, H 2 L2, and H 3 L3 represent 3-hydroxy-naphthalene-2-carboxylic acid (6-hydroxymethyl-pyridin-2-ylmethylene) hydrazide, nicotinic acid (6-hydroxymethyl-pyridin-2-ylmethylene) hydrazide, and 2-hydroxy-benzoic acid (6-hydroxymethyl-pyridin-2-ylmethylene) hydrazide, respectively) feature a distorted mer octahedral coordination geometry. Detailed magnetic studies of 1-3 have been conducted using direct and alternating current magnetic susceptibility data. Field-induced slow magnetic relaxation was observed for these three complexes. There are few examples of such behavior in (distorted) octahedral coordination geometry (OC) Co(II) mononuclear complexes with uniaxial anisotropy. Analysis of the six-coordinate Co(II) mononuclear single-ion magnets (SIMs) in the literature using the SHAPE program revealed that they all show what is best described as distorted trigonal prismatic (TRP) coordination geometry, and in general, these show negative D zero-field splitting (ZFS) values. On the other hand, all the Co(II) mononuclear complexes displaying what is best approximated as distorted octahedral (OC) coordination geometry show positive D values. In the new Co(II) mononuclear complexes we describe here, there is an ambiguity, since the rigid tridentate ligands confer what is best described for an octahedral complex as a mer coordination geometry, but the actual shape of the first coordination sphere is between octahedral and trigonal prismatic. The negative D values observed experimentally and supported by high-level electronic structure calculations are thus in line with a trigonal prismatic geometry. However, a consideration of the rhombicity as indicated by the E value of the ZFS in
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...
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
Axisymmetric finite deformation membrane problems
Energy Technology Data Exchange (ETDEWEB)
Feng, W.W.
1980-12-12
Many biomechanic problems involve the analysis of finite deformation axisymmetric membranes. This paper presents the general formulation for solving a class of axisymmetric membrane problems. The material nonlinearity, as well as the geometric nonlinearity, is considered. Two methods are presented to solve these problems. The first method is solving a set of differential equilibrium equations. The governing equations are reduced to three first-order ordinary-differential equations with explicit derivatives. The second method is the Ritz method where a general potential energy functional valid for all axisymmetric deformed positions is presented. The geometric admissible functions that govern the deformed configuration are written in terms of a series with unknown coefficients. These unknown coefficients are determined by the minimum potential energy principle that of all geometric admissible deformed configurations, the equilibrium configuration minimizes the potential energy. Some examples are presented. A comparison between these two methods is mentioned.
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.
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.
Critical-state magnetization of type-II superconductors in rectangular slab and cylinder geometries
Johansen, T. H.; Bratsberg, H.
1995-04-01
A scheme is described for analytical calculation of critical-state magnetization M of superconductors in the geometry of long rectangular slabs and cylindrical specimens in a parallel magnetic field. The simplicity of the general scheme is demonstrated by deriving compact expressions for the ascending and descending field branches of M in the exponential model Jc=jc0 exp(-B/B0) and in the Kim, Hempstead, and Strnad model [Phys. Rev. 129, 528 (1963)], Jc=jc0/(1+B/B0). The analyses focus on the vertical width ΔM of large field magnetization hysteresis loops. While Bean's result [Phys. Rev. Lett. 8, 250 (1962)], Jc∝ΔM, today is used extensively to infer the critical current, it is well known that the method lacks consistency when a field dependence is seen in ΔM. For the two models it is shown explicitly that in the expansion of the functional relation ΔM(Jc), Bean's result corresponds to the lowest-order term. Also to the next order in the functional expansion we find a unifying form of expressing the model behaviors. This term contains the second derivative of J2c(B) with a prefactor that depends on the sample geometry. A model-independent proof for the two first terms in the expansion of ΔM(Jc) is also given, which allows the significance of size and shape, i.e., thickness and aspect ratio, to be discussed on a general basis. New methods to extract Jc from ΔM data, one of them without having to invoke specific critical-state models, are indicated.
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.
Effect of Annealing on Properties of Carbonaceous Materials. Part II: Porosity and Pore Geometry
Xing, Xing; Zhang, Guangqing; Dell'Amico, Mark; Ciezki, George; Meng, Qingbo; Ostrovski, Oleg
2013-08-01
The pore structure of carbonaceous materials was studied using image analysis. The effect of annealing on the porosity and pore geometry of cokes, chars, and pyrolyzed coals (laboratory chars) was examined in the temperature range of 973 K to 1773 K (700 °C to 1500 °C). The porosity of chars and pyrolyzed coals significantly increased during annealing at temperatures below 1373 K (1100 °C) due to volatile matter release. Further increasing of the annealing temperature from 1373 K to 1773 K (1100 °C to 1500 °C) caused marginal porosity evolution. The porosity of cokes was not affected by annealing at temperatures below 1573 K (1300 °C) and slightly increased in the temperature range 1573 to 1773 K (1300 °C to 1500 °C). The increase in the porosity of chars and pyrolyzed coals during annealing at temperatures 1373 K to 1773 K (1100 °C to 1500 °C), and cokes at 1573 K to 1773 K (1300 °C to 1500 °C), was a result of reactions with oxides of their mineral phases. Annealing had a marginal effect on the pore shape (Feret ratio) of carbonaceous materials, but enlarged the pore size of chars and pyrolyzed coals and decreased their pore density.
Fluid simulations of edge turbulence for stellarators and axisymmetric configurations
Kleiber, R.; Scott, B.
2005-10-01
Nonlinear electromagnetic fluid simulations in a flux tube are used to compute the edge turbulence for a family of axisymmetric configurations with different rotational transform profiles (ι) and the stellarator Wendelstein 7-X (W7-X) [Grieger et al., Plasma Physics and Controlled Nuclear Fusion Research, 1990 (International Atomic Energy Agency, Vienna, 1991), Vol. 3, p. 525]. The influence of the ι profile on anomalous transport and the strength of zonal flows in these axisymmetric equilibria are studied and the results are connected to simulations for the W7-X equilibrium. A strong decrease in transport is found by increasing ι or switching the sign of the shear from tokamak-(ι'0). The effect of pressure-induced changes in the W7-X equilibrium geometry on the transport at fixed parameters is studied and a decrease in the transport following changes in the zonal flows is found.
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
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)
Particle diffusion by magnetic perturbations of axisymmetric geometries
Energy Technology Data Exchange (ETDEWEB)
Mynick, H.E.; Krommes, J.A.
1979-08-01
The quasilinear theory of collisionless test particle diffusion in stochastic magnetic fields is extended to include the effects of finite gyroradius, particle drifts, and magnetic trapping. Runaway confinement is substantially improved relative to earlier estimates which assumed that particles exactly followed field lines. Trapped particles are not expected to be stochastic.
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.
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
2015-03-01
Evaluationmethod employedforthe proposed corridor projects by IndianaDepartment of Transportation(INDOT) considerroad : geometry improvements by a generalized categorization. A newmethod which consi...
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)
Axisymmetric Marangoni convection in microencapsulation
Subramanian, Pravin; Zebib, Abdelfattah; McQuillan, Barry
2005-07-01
Spherical shells used as laser targets in inertial confinement fusion (ICF) experiments are made by microencapsulation. In one phase of manufacturing, the spherical shells contain a solvent (fluorobenzene (FB)) and a solute (polystyrene (PAMS)) in a water-FB environment. Evaporation of the FB results in the desired hardened plastic hollow spherical shells, 1-2 mm in diameter. Perfect sphericity is demanded for efficient fusion ignition and the observed surface roughness maybe driven by Marangoni instabilities due to surface tension dependence on the FB concentration (buoyant forces are negligible in this micro-scale problem). Here we model this drying process and compute nonlinear, time-dependent, axisymmetric, variable viscosity, infinite Schmidt number solutocapillary convection in the shells. Comparison with results from linear theory and available experiments are made.
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.)
SICOS, 2-D Time-Dependent Creep Calculation of Plane or Axisymmetric Concrete Structure
International Nuclear Information System (INIS)
Plettenberg, W.; Schmidt, A.
1984-01-01
1 - Description of problem or function: Two-dimensional program for time-dependent calculation of plane and axisymmetric composite con- crete structures. Assumed material behaviour: - linear viscoelasticity (creep) for the concrete - Hooke's Law for liner and reinforcement The given structure may be represented by: - triangular constant strain concrete elements, plane or axisymmetric - plane or axisymmetric membrane steel elements (liner) - one-dimensional steel elements, in plane or axisymmetric geometry (prestress cables). Transient pressure loads and temperature distributions may be taken into account. Options for mesh generation, calculation of temperature distributions, restart and the representation of results are included. 2 - Method of solution: The program uses the finite-element method. The solution of the linear equation systems is performed either by utilization of the Gauss-Seidel iteration or by direct Gauss elimination possibly with reiteration. The calculation can also be per- formed with double-precision. 3 - Restrictions on the complexity of the problem: Restriction to axisymmetric and plane problems. Only linear-viscoelastic creep behaviour. No possibility of taking into account aging and shrinkage
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
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.
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
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
Energetic Particle Transport in Compact Quasi-axisymmetric Stellarators
International Nuclear Information System (INIS)
Redi, M.H.; Mynick, H.E.; Suewattana, M.; White, R.B.; Zarnstorff, M.C.; Isaev, M.Yu.; Mikhailov, M.I.; Subbotin, A.A.
1999-01-01
Hamiltonian coordinate, guiding-center code calculations of the confinement of suprathermal ions in quasi-axisymmetric stellarator (QAS) designs have been carried out to evaluate the attractiveness of compact configurations which are optimized for ballooning stability. A new stellarator particle-following code is used to predict ion loss rates and particle confinement for thermal and neutral beam ions in a small experiment with R = 145 cm, B = 1-2 T and for alpha particles in a reactor-size device. In contrast to tokamaks, it is found that high edge poloidal flux has limited value in improving ion confinement in QAS, since collisional pitch-angle scattering drives ions into ripple wells and stochastic field regions, where they are quickly lost. The necessity for reduced stellarator ripple fields is emphasized. The high neutral beam ion loss predicted for these configurations suggests that more interesting physics could be explored with an experiment of less constrained size and magnetic field geometry
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.
New Classes of Quasi-Axisymmetric Configurations
International Nuclear Information System (INIS)
Ku, L. P.; Garabedian, P. R.
2005-01-01
Stellarators with quasi-axially symmetric (QA) magnetic field structure have attracted considerable interests in recent years. They are expected to have good particle orbits found in tokamaks and may be made passively stable to MHD perturbations found in conventional stellarators. A proof-of-principle device, the National Compact Stellarator Experiment (NCSX), is being designed and operation is expected to begin in 2008 [1]. In parallel, a reactor studies project (ARIES-CS) is being conducted to examine critical issues of compact stellarators as power producing reactors [2]. It is under the auspices of this project that we made an extensive survey of the aspect ratio-rotational transform space to look for regions endowed with particularly interesting characteristics. We report in this paper the progress made in identifying new configurations with unique features of different emphasis that may be of interest from the standpoint of both power producing reactors and near term physics experiments. NCSX is a highly optimized configuration in both physics and coil properties. The baseline plasma was chosen for its low aspect ratio (A equal 4.5), low non-axisymmetric residues in the magnetic spectrum (<2.5%) and good MHD stability characteristics. The coils were designed with sufficient room to accommodate the scrape-off, vacuum vessel, diagnostics, etc., and with enough flexibility to accommodate a wide variety of operating scenarios. However, the configuration space is vast and complex. Possibilities exist that there are other configurations also having good properties. To look beyond NCSX, we asked ourselves: are there other configurations more attractive and what additional properties will make a quasi-axisymmetric stellarator (QAS) more attractive? We note that recent experimental results from W7AS and LHD showed that, while magnetohydrodynamic (MHD) activities apparently existed in these devices, the plasmas nevertheless were quiescent and remained quasi
Prabhu, Kartik; Wald, Robert M.
2018-01-01
We consider arbitrary stationary and axisymmetric black holes in general relativity in (d +1) dimensions (with d ≥slant 3 ) that satisfy the vacuum Einstein equation and have a non-degenerate horizon. We prove that the canonical energy of axisymmetric electromagnetic perturbations is positive definite. This establishes that all vacuum black holes are stable to axisymmetric electromagnetic perturbations. Our results also hold for asymptotically de Sitter black holes that satisfy the vacuum Einstein equation with a positive cosmological constant. Our results also apply to extremal black holes provided that the initial perturbation vanishes in a neighborhood of the horizon.
Sabolović, Jasmina; Ramek, Michael; Marković, Marijana
2017-09-26
Reliable density functional theory (DFT) calculations can be performed in conjuction with spectroscopic measurements to elucidate the structural properties of physiologically important bis(amino acidato)copper(II) compounds in solutions. They can provide insight into the influence of intermolecular interactions on the molecular geometry in the crystal lattice or solution when compared with a DFT gas-phase minimum. Our previous paper [Marković et al. (2014) Eur J Inorg Chem 198] reported the DFT-determined geometries and Raman spectra for different conformers of physiological bis(L-histidinato)copper(II) with 20 explicit water molecules, as calculated using the B3LYP functional. The present study examined the reliability of those B3LYP results by applying the M06 functional instead, as it should better account for noncovalent interactions. The water molecules were positioned more compactly around the complex by M06 than by B3LYP. The accuracies of the two functionals when compared to relevant experimental data showed that M06 was better at reproducing in-plane Cu-N bond lengths but B3LYP gave more accurate axial Cu-O distances. Both functionals reproduced the experimental Raman spectrum at pH 8 to similar levels of accuracy and provided precise information on the Cu(II) coordination mode and conformation in aqueous solution. Additionally, we assessed several DFT and DFT-D functionals (BP86, B3LYP, B3LYP-D, M06, M06 L, wB97XD, mPW2PLYPD) by using them to model the geometries of experimental bis(L-histidinato)copper(II) crystalline conformations as isolated systems, and then benchmarking the results against those from high-level second-order pertubation Møller-Plesset (MP2) calculations. Although this assessment resulted in an equivocal conclusion because the MP2 results for the isolated complex were inconsistent with the corresponding DFT outcomes, it does provide new information on future benchmark options.
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)
Holme, Audun
1988-01-01
This volume presents selected papers resulting from the meeting at Sundance on enumerative algebraic geometry. The papers are original research articles and concentrate on the underlying geometry of the subject.
van den Broek, P.M.
1984-01-01
The aim of this paper is to give a detailed exposition of the relation between the geometry of twistor space and the geometry of Minkowski space. The paper has a didactical purpose; no use has been made of differential geometry and cohomology.
Directory of Open Access Journals (Sweden)
Jasmina Bogdanović-Jovanović
2017-12-01
Full Text Available One of the most important aims in the turbo pump design is to achieve an optimal design of the pump impeller. The basic assumption in the design procedure of the impeller is that of the axisymmetric fluid flow. It can be confirmed or disputed by using the method presented in the paper, which uses the results of numerical simulation of fluid flow in the pump impeller. The method is actually a procedure for determining averaged axisymmetric flow surfaces and meridian streamlines. Furthermore, according to the obtained streamlines, a correction of the impeller blade geometry can be made (if the streamlines deviate significantly from the assumed axisymmetric ones. It is also possible to calculate the specific works of the elementary stages and compare them with the previous assumptions. The pump impeller torque can be calculated as well.
Hou, Siyuan; Stevenson, Keisean A J M; Harynuk, James J
2018-03-25
The transfer of thermodynamic parameters governing retention of a molecule in gas chromatography from a reference column to a target column is a difficult problem. Successful transfer demands a mechanism whereby the column geometries of both columns can be determined with high accuracy. This is the second part in a series of three papers. In Part I of this work we introduced a new approach to determine the actual effective geometry of a reference column and thermodynamic-based parameters of a suite of compounds on the column. Part II, presented here, illustrates the rapid estimation of the effective inner diameter (or length) and the effective phase ratio of a target column. The estimation model based on the principle of least squares; a fast Quasi-Newton optimization algorithm was developed to provide adequate computational speed. The model and optimization algorithm were tested and validated using simulated and experimental data. This study, together with the work in Parts I and III, demonstrates a method that improves the transferability of thermodynamic models of gas chromatography retention between gas chromatography columns. This article is protected by copyright. All rights reserved. This article is protected by copyright. All rights reserved.
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)
Jana, Subrata; Santra, Ramesh Chandra; Das, Saurabh; Chattopadhyay, Shouvik
2014-09-01
Two new copper(II) complexes, [Cu(L)(OCN)] (1) and [CuL(dca)]n (2), where HL = 2-(-(2-(diethylamino)ethylimino)methyl)naphthalen-1-ol, dca = N(CN)2-, have been synthesized and characterized by elemental analysis, IR, UV-VIS spectroscopy and single crystal X-ray diffraction studies. Complex 1 has square planar and complex 2 square pyramidal geometries in solid state around metal centre. Interactions of the complexes with calf thymus DNA (CT DNA) were studied by UV-VIS spectroscopy. Binding constant and site size of interaction were determined. Binding site size and intrinsic binding constant K revealed complex 1 interacted with calf thymus DNA better than complex 2.
Reimann, Tommy; Schulz, Michael; Mildner, David F. R.; Bleuel, Markus; Brûlet, Annie; Harti, Ralph P.; Benka, Georg; Bauer, Andreas; Böni, Peter; Mühlbauer, Sebastian
2017-10-01
Vortex attraction which can cause a bundling of vortices has been observed in a multitude of type-II superconductors. While its underlying mechanisms have been extensively studied, the morphology of the emerging vortex superstructure has only been rarely considered. Here, we present a comprehensive experimental study on the type-II/1 superconductor niobium which focuses on the transformation of its homogeneous vortex lattice into an inhomogeneous domain structure at the onset of vortex attraction. By means of small-angle neutron scattering, ultra-small-angle neutron scattering, and neutron grating interferometry, the vortex lattice and the micrometer-scale vortex domain structure as well as its distribution could be investigated. In particular, we focus on the transformation of the vortex lattice at the transition to the intermediate mixed state, which is characterized by vortex attraction. We have found that the phase separation of the vortex lattice into an irregular domain structure takes place via a process showing strong similarity to spinodal decomposition. While pinning disorders the domain morphology, the characteristic length scale of the domain structure is governed by an interplay of field distortion energy and domain surface tension. Finally, geometric barriers in the disk-shaped samples provoke an inhomogeneous distribution of domains on the macroscopic scale.
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.)
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
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
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...
Pottmann, Helmut
2014-11-26
Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural geometry, meanwhile contains a great wealth of individual contributions which are relevant in various fields. For mathematicians, the relation to discrete differential geometry is significant, in particular the integrable system viewpoint. Besides, new application contexts have become available for quite some old-established concepts. Regarding graphics and geometry processing, architectural geometry yields interesting new questions but also new objects, e.g. replacing meshes by other combinatorial arrangements. Numerical optimization plays a major role but in itself would be powerless without geometric understanding. Summing up, architectural geometry has become a rewarding field of study. We here survey the main directions which have been pursued, we show real projects where geometric considerations have played a role, and we outline open problems which we think are significant for the future development of both theory and practice of architectural geometry.
Maor, Eli
2014-01-01
If you've ever thought that mathematics and art don't mix, this stunning visual history of geometry will change your mind. As much a work of art as a book about mathematics, Beautiful Geometry presents more than sixty exquisite color plates illustrating a wide range of geometric patterns and theorems, accompanied by brief accounts of the fascinating history and people behind each. With artwork by Swiss artist Eugen Jost and text by acclaimed math historian Eli Maor, this unique celebration of geometry covers numerous subjects, from straightedge-and-compass constructions to intriguing configur
Faulkner, Thomas Ewan
1952-01-01
This text explores the methods of the projective geometry of the plane. Some knowledge of the elements of metrical and analytical geometry is assumed; a rigorous first chapter serves to prepare readers. Following an introduction to the methods of the symbolic notation, the text advances to a consideration of the theory of one-to-one correspondence. It derives the projective properties of the conic and discusses the representation of these properties by the general equation of the second degree. A study of the relationship between Euclidean and projective geometry concludes the presentation. Nu
Haya, Laura; Tavoularis, Stavros
2017-06-01
Flow characteristics past a bileaflet mechanical heart valve were measured under physiological flow conditions in a straight tube with an axisymmetric expansion, similar to vessels used in previous studies, and in an anatomical model of the aorta. We found that anatomical features, including the three-lobed sinus and the aorta's curvature affected significantly the flow characteristics. The turbulent and viscous stresses were presented and discussed as indicators for potential blood damage and thrombosis. Both types of stresses, averaged over the two axial measurement planes, were significantly lower in the anatomical model than in the axisymmetric one. This difference was attributed to the lower height-to-width ratio and more gradual contraction of the anatomical aortic sinus. The curvature of the aorta caused asymmetries in the velocity and stress distributions during forward flow. Secondary flows resulting from the aorta's curvature are thought to have redistributed the fluid stresses transversely, resulting in a more homogeneous stress distribution in the anatomical aortic root than in the axisymmetric root. The results of this study demonstrate the importance of modelling accurately the aortic geometry in experimental and computational studies of prosthetic devices. Moreover, our findings suggest that grafts used for aortic root replacement should approximate as closely as possible the shape of the natural sinuses.
Kinetic theory model predictions compared with low-thrust axisymmetric nozzle plume data
Riley, B. R.; Fuhrman, S. J.; Penko, P. F.
1993-01-01
A system of nonlinear integral equations equivalent to the steady-state Krook kinetic equation was used to model the flow from a low-thrust axisymmetric nozzle. The mathematical model was used to numerically calculate the number density, temperature, and velocity of a simple gas as it expands into a near vacuum. With these quantities the gas pressure and flow directions of the gas near the exit plane were calculated and compared with experimental values for a low-thrust nozzle of the same geometry and mass flow rate.
Dynamical grid method for time dependent simulations of axisymmetric instabilities in tokamaks
International Nuclear Information System (INIS)
Jardin, S.C.; Johnson, J.L.; Greene, J.M.; Grimm, R.C.
1977-07-01
A natural nonorthogonal time-dependent coordinate transformation based on the magnetic field lines is utilized for the numerical integration of the two-dimensional axisymmetric time-dependent ideal MHD equations in tokamak geometry. The finite-difference grid is treated as a dynamical variable, and its equations of motion are integrated simultaneously with those for the fluid and magnetic field. The method is applicable to tokamak systems of arbitrary pressure and cross section. It is particularly useful for the nearly incompressible ideal MHD modes which are of interest in tokamak stability studies
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
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.
Quantitative shearography in axisymmetric gas temperature measurements
VanDerWege, Brad A.; O'Brien, Christopher J.; Hochgreb, Simone
1999-06-01
This paper describes the use of shearing interferometry (shearography) for the quantitative measurement of gas temperatures in axisymmetric systems in which vibration and shock are substantial, and measurement time is limited. The setup and principle of operation of the interferometer are described, as well as Fourier-transform-based fringe pattern analysis, Abel transform, and sensitivity of the phase lead to temperature calculation. A helium jet and a Bunsen burner flame are shown as verification of the diagnostic. The accuracy of the measured temperature profile is shown to be limited by the Abel transform and is critically dependent on the reference temperature used.
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...
Ay, Nihat; Lê, Hông Vân; Schwachhöfer, Lorenz
2017-01-01
The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemannian geometry and Banach space theory. Parametrised measure models are defined as fundamental geometric objects, which can be both finite or infinite dimensional. Based on these models, canonical tensor fields are introduced and further studied, including the Fisher metric and the Amari-Chentsov tensor, and embeddings of statistical manifolds are investigated. This novel foundation then leads to application highlights, such as generalizations and extensions of the classical uniqueness result of Chentsov or the Cramér-Rao inequality. Additionally, several new application fields of information geometry are highlighted, for instance hierarchical and graphical models, complexity theory, population genetics, or Markov Chain Monte Carlo. The book will be of interest to mathematicians who are interested in geometry, inf...
Lefschetz, Solomon
2005-01-01
An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this text for advanced undergraduate students is particularly relevant to those more familiar with analysis than algebra. 1953 edition.
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.)
Near surface stress analysis strategies for axisymmetric fretting
Indian Academy of Sciences (India)
In this paper, we develop design tools for Near Surface Analysis (NSA) for understanding axisymmetric fretting. Axisymmetric Fretting Analysis (AFA) becomes formidable owing to localised tractions that call for Fourier transform techniques. We develop two different NSA strategies based on two-dimensional plane strain ...
Berger, Marcel
2010-01-01
Both classical geometry and modern differential geometry have been active subjects of research throughout the 20th century and lie at the heart of many recent advances in mathematics and physics. The underlying motivating concept for the present book is that it offers readers the elements of a modern geometric culture by means of a whole series of visually appealing unsolved (or recently solved) problems that require the creation of concepts and tools of varying abstraction. Starting with such natural, classical objects as lines, planes, circles, spheres, polygons, polyhedra, curves, surfaces,
Robinson, Gilbert de B
2011-01-01
This brief undergraduate-level text by a prominent Cambridge-educated mathematician explores the relationship between algebra and geometry. An elementary course in plane geometry is the sole requirement for Gilbert de B. Robinson's text, which is the result of several years of teaching and learning the most effective methods from discussions with students. Topics include lines and planes, determinants and linear equations, matrices, groups and linear transformations, and vectors and vector spaces. Additional subjects range from conics and quadrics to homogeneous coordinates and projective geom
Burdette, A C
1971-01-01
Analytic Geometry covers several fundamental aspects of analytic geometry needed for advanced subjects, including calculus.This book is composed of 12 chapters that review the principles, concepts, and analytic proofs of geometric theorems, families of lines, the normal equation of the line, and related matters. Other chapters highlight the application of graphing, foci, directrices, eccentricity, and conic-related topics. The remaining chapters deal with the concept polar and rectangular coordinates, surfaces and curves, and planes.This book will prove useful to undergraduate trigonometric st
Charged particle dynamics in axisymmetric nonconservative beams
International Nuclear Information System (INIS)
Radchenko, V.I.; Nikonov, O.I.
1998-01-01
Many of ion-beam technologies lead to the requirement of cross-section minimization of a particle beam in the object region acted upon, or to the problem of minimization of charged particle beam emittance (the growth rate of emittance) for a specified segment of the beam formation. In this paper we study the above problem for axisymmetric beams representing a nonconservative system of charged particles. It is shown that under certain assumptions the beam in question can be described by appropriate equations that possess an explicit solution. The latter allows one to study the influence of particle density distribution at the starting point on the future beam evolution. The results are based on approaches developed in J.D. Lawson (1977); V.I. Radchenko, G.D. Ved'manov (1995); O.I. Nikonov (1994). (orig.)
Compact neutron imaging system using axisymmetric mirrors
Khaykovich, Boris; Moncton, David E; Gubarev, Mikhail V; Ramsey, Brian D; Engelhaupt, Darell E
2014-05-27
A dispersed release of neutrons is generated from a source. A portion of this dispersed neutron release is reflected by surfaces of a plurality of nested, axisymmetric mirrors in at least an inner mirror layer and an outer mirror layer, wherein the neutrons reflected by the inner mirror layer are incident on at least one mirror surface of the inner mirror layer N times, wherein N is an integer, and wherein neutrons reflected by the outer mirror are incident on a plurality of mirror surfaces of the outer layer N+i times, where i is a positive integer, to redirect the neutrons toward a target. The mirrors can be formed by a periodically reversed pulsed-plating process.
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
Desseyn, H. O.; And Others
1985-01-01
Compares linear-nonlinear and planar-nonplanar geometry through the valence-shell electron pairs repulsion (V.S.E.P.R.), Mulliken-Walsh, and electrostatic force theories. Indicates that although the V.S.E.P.R. theory has more advantages for elementary courses, an explanation of the best features of the different theories offers students a better…
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 1; Issue 8. Geometry VI - Space-the Final Frontier. Kapil H Paranjape. Series Article Volume 1 Issue 8 August 1996 pp 28-33. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/001/08/0028-0033 ...
Geometry -----------~--------------RESONANCE
Indian Academy of Sciences (India)
Mathematicians were at war with one another because Euclid's axioms for geometry were not entirely acceptable to all. Archi- medes, Pasch and others introduced further axioms as they thought that Euclid had missed a few, while other mathematicians were bothered by the non-elementary nature of the parallel axiom.
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.
International Nuclear Information System (INIS)
Strominger, A.
1990-01-01
A special manifold is an allowed target manifold for the vector multiplets of D=4, N=2 supergravity. These manifolds are of interest for string theory because the moduli spaces of Calabi-Yau threefolds and c=9, (2,2) conformal field theories are special. Previous work has given a local, coordinate-dependent characterization of special geometry. A global description of special geometries is given herein, and their properties are studied. A special manifold M of complex dimension n is characterized by the existence of a holomorphic Sp(2n+2,R)xGL(1,C) vector bundle over M with a nowhere-vanishing holomorphic section Ω. The Kaehler potential on M is the logarithm of the Sp(2n+2,R) invariant norm of Ω. (orig.)
Directory of Open Access Journals (Sweden)
Leonardo Paris
2012-06-01
Full Text Available Lo studio degli ingranaggi si basa sulle geometrie coniugate in cui due curve o due superfici si mantengono costantemente in contatto pur se in movimento reciproco. La teoria geometrica degli ingranaggi fino alla fine del XIX secolo era uno dei molteplici rami nelle applicazioni della Geometria Descrittiva. Lo studio si basa sulla conoscenza delle principali proprietà delle curve piane e gobbe e delle loro derivate. La specificità del tema è che queste geometrie nel momento in cui si devono relazionare con le loro coniugate, devono rispettare dei vincoli che altrimenti non avrebbero. Si vuole evidenziare attraverso casi concreti il ruolo della geometria descrittiva nel passaggio dal teorico al pratico riproponendo in chiave informatica, temi e procedure di indagine spesso passati in secondo piano se non addirittura dimenticati.
Petersen, Peter
2016-01-01
Intended for a one year course, this text serves as a single source, introducing readers to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry. This is one of the few Works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory. The book will appeal to a readership that have a basic knowledge of standard manifold theory, including tensors, forms, and Lie groups. Important revisions to the third edition include: a substantial addition of unique and enriching exercises scattered throughout the text; inclusion of an increased number of coordinate calculations of connection and curvature; addition of general formulas for curvature on Lie Groups and submersions; integration of variational calculus into the text allowing for an early treatment of the Sphere theorem using a proof by Berger; incorporation of several recent results about manifolds with posit...
General Geometry and Geometry of Electromagnetism
Shahverdiyev, Shervgi S.
2002-01-01
It is shown that Electromagnetism creates geometry different from Riemannian geometry. General geometry including Riemannian geometry as a special case is constructed. It is proven that the most simplest special case of General Geometry is geometry underlying Electromagnetism. Action for electromagnetic field and Maxwell equations are derived from curvature function of geometry underlying Electromagnetism. And it is shown that equation of motion for a particle interacting with electromagnetic...
Cervone, A.; Manservisi, S.; Scardovelli, R.
2010-09-01
A multilevel VOF approach has been coupled to an accurate finite element Navier-Stokes solver in axisymmetric geometry for the simulation of incompressible liquid jets with high density ratios. The representation of the color function over a fine grid has been introduced to reduce the discontinuity of the interface at the cell boundary. In the refined grid the automatic breakup and coalescence occur at a spatial scale much smaller than the coarse grid spacing. To reduce memory requirements, we have implemented on the fine grid a compact storage scheme which memorizes the color function data only in the mixed cells. The capillary force is computed by using the Laplace-Beltrami operator and a volumetric approach for the two principal curvatures. Several simulations of axisymmetric jets have been performed to show the accuracy and robustness of the proposed scheme.
bessel functions for axisymmetric elasticity problems of the elastic
African Journals Online (AJOL)
HOD
. ) ( ) r. (. ) ( ). The governing partial differential equation for axisymmetric elasticity problems are the strain- displacement equations, the differential equations of equilibrium and the material constitutive laws, subject to the displacement and ...
Departures from Axisymmetric Balance Dynamics during Secondary Eyewall Formation
2014-10-01
tangential wind tendencies of the mesoscale integration with those diagnosed as the axisymmetric balanced response of a vortex subject to diabatic ...the mesoscale integration with those diagnosed as the axisymmetric balanced response of a vortex subject to diabatic and tangential momentum forcing...secondary circulation will develop to oppose the forcing of diabatic heating and/or friction. After the seminal work of Eliassen (1951), a number of
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
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
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
Rotational Motion of Axisymmetric Marangoni Swimmers
Rothstein, Jonathan; Uvanovic, Nick
2017-11-01
A series of experiments will be presented investigating the motion of millimeter-sized particles on the surface of water. The particles were partially coated with ethanol and carefully placed on a water interface in a series of Petri dishes with different diameters. High speed particle motion was driven by strong surface tension gradients as the ethanol slowly diffuses from the particles into the water resulting in a Marangoni flow. The velocity and acceleration of the particles where measured. In addition to straight line motion, the presence of the bounding walls of the circular Petri dish was found to induce an asymmetric, rotational motion of the axisymmetric Marangoni swimmers. The rotation rate and radius of curvature was found to be a function of the size of the Petri dish and the curvature of the air-water interface near the edge of the dish. For large Petri dishes or small particles, rotation motion was observed far from the bounding walls. In these cases, the symmetry break appears to be the result of the onset of votex shedding. Finally, multiple spherical particles were observed to undergo assembly driven by capillary forces followed by explosive disassembly.
Simmons, Charles J; Stratemeier, Horst; Hitchman, Michael A; Reinen, Dirk; Masters, Vanessa M; Riley, Mark J
2011-06-06
The crystal structures of trans-diaquabis(methoxyacetato)copper(II) and the isostructural nickel(II) complex have been determined over a wide temperature range. In conjunction with the reported behavior of the g-values, the structural data suggest that the copper(II) compound exhibits a thermal equilibrium between three structural forms, two having orthorhombically distorted, tetragonally elongated geometries but with the long and intermediate bonds to different atoms, and the third with a tetragonally compressed geometry. This is apparently the first reported example of a copper(II) complex undergoing an equilibrium between tetragonally elongated and compressed forms. The optical spectrum of single crystals of the copper(II) compound is used to obtain metal-ligand bonding parameters which yield the g-values of the compressed form of the complex and hence the proportions of the complex in each structural form at every temperature. When combined with estimates of the Jahn-Teller distortions of the different forms, the latter produce excellent agreement with the observed temperature dependence of the bond lengths. The behavior of an infrared combination band is consistent with such a thermal equilibrium, as is the temperature dependence of the thermal ellipsoid parameters and the XAFS. The potential surfaces of the different forms of the copper(II) complex have been calculated by a model based upon Jahn-Teller coupling. It is suggested that cooperative effects may cause the development of the population of tetragonally compressed complexes, and the crystal packing is consistent with this hypothesis, though the present model may oversimplify the diversity of structural forms present at high temperature. © 2011 American Chemical Society
Pressure limits of an axisymmetric torus
International Nuclear Information System (INIS)
Yoshikawa, S.
1986-03-01
In order to clarify the pressure limit of a toroidal plasma equilibrium in a three-dimensional geometry, an azimuthally symmetric toroidal plasma was considered. In a tokamak-like plasma, the net toroidal current is necessary for a finite β plasma equilibrium. If external conductors are used to provide the rotational transform, iota, the plasma pressure is limited to β = (iota/2π) 2 /2A, where A is the aspect ratio
Impedance calculations of non-axisymmetric transitions using the optical approximation
International Nuclear Information System (INIS)
Bane, K.L.F.; Stupakov, G.; Zagorodnov, I.
2007-02-01
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. (orig.)
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
Stability of the Shallow Axisymmetric Parabolic-Conic Bimetallic Shell by Nonlinear Theory
Directory of Open Access Journals (Sweden)
M. Jakomin
2011-01-01
Full Text Available In this contribution, we discuss the stress, deformation, and snap-through conditions of thin, axi-symmetric, shallow bimetallic shells of so-called parabolic-conic and plate-parabolic type shells loaded by thermal loading. According to the theory of the third order that takes into account the balance of forces on a deformed body, we present a model with a mathematical description of the system geometry, displacements, stress, and thermoelastic deformations. The equations are based on the large displacements theory. We numerically calculate the deformation curve and the snap-through temperature using the fourth-order Runge-Kutta method and a nonlinear shooting method. We show how the temperature of both snap-through depends on the point where one type of the rotational curve transforms into another.
Drift-kinetic simulations of axisymmetric plasma transport at the edge of a divertor tokamak
Dorf, M.; Dorr, M.; Ghosh, D.; Hittinger, J.; Lee, W.; Cohen, R.
2017-10-01
Eulerian kinetic calculations are presented for the axisymmetric cross-separatrix transport of plasma at the edge of a tokamak. The simulations are performed with a high-order finite-volume code COGENT that solves the full-F drift-kinetic equation for the ion species including the effects of fully-nonlinear Fokker-Plank ion-ion collisions. The ion kinetic response is coupled to two-dimensional self-consistent electrostatic potential variations, which are obtained from the vorticity equation with the isothermal fluid electron model. The paper also presents recent progress toward the full-edge turbulence code. The slab-geometry 5D version has recently become available and is successfully verified in simulations of the collisionless drift-wave instability. Work performed for USDOE, at LLNL under contract DE-AC52-07NA27344.
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...
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
Gmerek, Felix; Stuhlmann, Benjamin; Álvarez-Valtierra, Leonardo; Pratt, David W; Schmitt, Michael
2016-02-28
We determined the changes of the geometries of 2- and 3-tolunitrile upon excitation to the lowest excited singlet states from Franck-Condon fits of the vibronic intensities in several fluorescence emission spectra and of the rotational constant changes upon excitation. These structural changes can be connected to the altered electron distribution in the molecules and are compared to the results of ab initio calculations. We show how the torsional barriers of the methyl groups in both components are used as probe of the molecular changes upon electronic excitation.
Non-Radial Oscillations in an Axisymmetric MHD Incompressible Fluid
Indian Academy of Sciences (India)
2016-01-27
Jan 27, 2016 ... ... oscillations by perturbing the MHD equilibrium solution for an axisymmetric incompressible fluid. The fluid motion and the magnetic field are expressed as scalars , , and , respectively. In deriving the exact solution for the equilibrium state, we neglect the contribution due to meridional circulation.
Modelling axisymmetric cod-ends made of different mesh types
DEFF Research Database (Denmark)
Priour, D.; Herrmann, Bent; O'Neill, F.G.
2009-01-01
Cod-ends are the rearmost part of trawl fishing gears. They collect the catch, and for many important species it is where fish selection takes place. Generally speaking they are axisymmetric, and their shape is influenced by the catch volume, the mesh shape, and the material characteristics. The ...
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.
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)
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.
Modeling MHD Equilibrium and Dynamics with Non-Axisymmetric Resistive Walls in LTX and HBT-EP
Hansen, C.; Levesque, J.; Boyle, D. P.; Hughes, P.
2017-10-01
In experimental magnetized plasmas, currents in the first wall, vacuum vessel, and other conducting structures can have a strong influence on plasma shape and dynamics. These effects are complicated by the 3D nature of these structures, which dictate available current paths. Results from simulations to study the effect of external currents on plasmas in two different experiments will be presented: 1) The arbitrary geometry, 3D extended MHD code PSI-Tet is applied to study linear and non-linear plasma dynamics in the High Beta Tokamak (HBT-EP) focusing on toroidal asymmetries in the adjustable conducting wall. 2) Equilibrium reconstructions of the Lithium Tokamak eXperiment (LTX) in the presence of non-axisymmetric eddy currents. An axisymmetric model is used to reconstruct the plasma equilibrium, using the PSI-Tri code, along with a set of fixed 3D eddy current distributions in the first wall and vacuum vessel [C. Hansen et al., PoP Apr. 2017]. Simulations of detailed experimental geometries are enabled by use of the PSI-Tet code, which employs a high order finite element method on unstructured tetrahedral grids that are generated directly from CAD models. Further development of PSI-Tet and PSI-Tri will also be presented. This work supported by US DOE contract DE-SC0016256.
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
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
Stability of flow over axisymmetric bodies with porous suction strips
Nayfeh, A. H.; Reed, H. L.
1982-01-01
Linear triple deck, closed form solutions for mean-flow quantities are developed for axisymmetric incompressible flow past a body with porous strips. The solutions account for upstream influence and are linear superpositions of the flow past the body without suction plus the perturbations due to the suction strips. Flow past the suctionless body is calculated using the Transition Analysis Program System, and a simple linear optimization scheme to determine number, spacing, and mass flow rate through the strips on an axisymmetric body is developed using the linear, triple-deck, closed-form solutions. The theory is demonstrated by predicting optimal strip distributions, and the effect of various adverse pressure-gradient situations on stability is studied.
Small Engine Technology (SET) - Task 14 Axisymmetric Engine Simulation Environment
Miller, Max J.
1999-01-01
As part of the NPSS (Numerical Propulsion Simulation System) project, NASA Lewis has a goal of developing an U.S. industry standard for an axisymmetric engine simulation environment. In this program, AlliedSignal Engines (AE) contributed to this goal by evaluating the ENG20 software and developing support tools. ENG20 is a NASA developed axisymmetric engine simulation tool. The project was divided into six subtasks which are summarized below: Evaluate the capabilities of the ENG20 code using an existing test case to see how this procedure can capture the component interactions for a full engine. Link AE's compressor and turbine axisymmetric streamline curvature codes (UD0300M and TAPS) with ENG20, which will provide the necessary boundary conditions for an ENG20 engine simulation. Evaluate GE's Global Data System (GDS), attempt to use GDS to do the linking of codes described in Subtask 2 above. Use a turbofan engine test case to evaluate various aspects of the system, including the linkage of UD0300M and TAPS with ENG20 and the GE data storage system. Also, compare the solution results with cycle deck results, axisymmetric solutions (UD0300M and TAPS), and test data to determine the accuracy of the solution. Evaluate the order of accuracy and the convergence time for the solution. Provide a monthly status report and a final formal report documenting AE's evaluation of ENG20. Provide the developed interfaces that link UD0300M and TAPS with ENG20, to NASA. The interface that links UD0300M with ENG20 will be compatible with the industr,, version of UD0300M.
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...
Energy and energy flux in axisymmetric slow and fast waves
Moreels, M. G.; Van Doorsselaere, T.; Grant, S. D. T.; Jess, D. B.; Goossens, M.
2015-06-01
Aims: We aim to calculate the kinetic, magnetic, thermal, and total energy densities and the flux of energy in axisymmetric sausage modes. The resulting equations should contain as few parameters as possible to facilitate applicability for different observations. Methods: The background equilibrium is a one-dimensional cylindrical flux tube model with a piecewise constant radial density profile. This enables us to use linearised magnetohydrodynamic equations to calculate the energy densities and the flux of energy for axisymmetric sausage modes. Results: The equations used to calculate the energy densities and the flux of energy in axisymmetric sausage modes depend on the radius of the flux tube, the equilibrium sound and Alfvén speeds, the density of the plasma, the period and phase speed of the wave, and the radial or longitudinal components of the Lagrangian displacement at the flux tube boundary. Approximate relations for limiting cases of propagating slow and fast sausage modes are also obtained. We also obtained the dispersive first-order correction term to the phase speed for both the fundamental slow body mode under coronal conditions and the slow surface mode under photospheric conditions. Appendix A is available in electronic form at http://www.aanda.org
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
Mahé, Louis; Roy, Marie-Françoise
1992-01-01
Ten years after the first Rennes international meeting on real algebraic geometry, the second one looked at the developments in the subject during the intervening decade - see the 6 survey papers listed below. Further contributions from the participants on recent research covered real algebra and geometry, topology of real algebraic varieties and 16thHilbert problem, classical algebraic geometry, techniques in real algebraic geometry, algorithms in real algebraic geometry, semialgebraic geometry, real analytic geometry. CONTENTS: Survey papers: M. Knebusch: Semialgebraic topology in the last ten years.- R. Parimala: Algebraic and topological invariants of real algebraic varieties.- Polotovskii, G.M.: On the classification of decomposing plane algebraic curves.- Scheiderer, C.: Real algebra and its applications to geometry in the last ten years: some major developments and results.- Shustin, E.L.: Topology of real plane algebraic curves.- Silhol, R.: Moduli problems in real algebraic geometry. Further contribu...
Hancock, Robert D; Reibenspies, Joseph H; Maumela, Hulisani
2004-05-03
The synthesis and structures of [Pb(DOTAM)](ClO4)2.4.5H2O (1) and [Hg(DOTAM)](ClO4)2.0.5CH3OH.1.5H2O (2) are reported, where DOTAM is 1,4,7,10-tetrakis(carbamoylmethyl)-1,4,7,10-tetraazacyclododecane. Compound 1 is triclinic, space group P, a = 12.767(3) A, b = 13.528(2) A, c = 18.385(3) A, alpha = 101.45(2) degrees, beta = 93.32(2) degrees, gamma = 90.53(2) degrees, Z = 4, R = 0.0500. Compound 2 is monoclinic, space group Cc, a = 12.767(3) A, b = 13.528(2) A, c = 18.385(3) A, beta = 101.91(2) degrees, Z = 4, R = 0.0381. The Pb(II) ion in 1 has an average Pb-N = 2.63 A to four N-donors from the macrocyclic ring, and four O-donors (average Pb-O = 2.77 A) from the amide pendant donors of the macrocycle, with a water molecule placed with Pb-O = 3.52 A above the proposed site of the lone pair (Lp) on Pb. The Hg(II) in 2 appears to be only six-coordinate, with four Hg-N bond lengths averaging 2.44 A, and two Hg-O from pendant amide donors at 2.41 A. The other two amide donors appear to be noncoordinating, with Hg-O distances of 2.74 and 2.82 A. A water situated 3.52 A above the proposed site of the lone pair on Pb(II) in 1 is oriented in such a way that it might be thought to be forming a Pb-Lp.H-O-H hydrogen bond. It is concluded that that this is not an H-bond, but that the presence of the lone pair allows a closer approach of the hydrogens to Pb than would be true otherwise. The structural analogy in the VSEPR sense between Pb(II), which has the 5d(10)6s(2) outer electron structure, and the Hg(II) ion, which has the 5d10 structure, is examined. The tendency of Hg(II) toward linear coordination, with two short Hg-L bonds (L = ligand) at 180 degrees to each other, and other donor groups at roughly 90 degrees to this and at much longer bond distances, is paralleled by Pb(II). One of the short Hg-L bonds is replaced in the Pb(II) structures by the lone pair (Lp), which is opposite the short Pb-L bond, or in some cases 2-4 shorter Pb-L bonds.
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)
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...
Chu, Zhaolian; You, Wei; Huang, Wei
2009-02-01
Three dinuclear copper(II) macrocyclic complexes, formulated as [Cu 2L(N 3) 2(0.5H 2O) 2] n ( 1), [Cu 2L(ClO 4) 2(CH 3CH 2OH)] ( 2) and [Cu 2L(CH 3OH) 2](ClO 4) 2 ( 3) (LH 2 = [2+2] Schiff base macrocyclic ligand condensed from 4-chloro-2,6-diformylphenol and 1,3-diaminopropane), have been prepared and determined by X-ray single-crystal diffraction. Complex 1 shows two six-coordinate Cu(II) centers in which two monodentate N3- anions and two half-water molecules are bonded at the apical positions in the trans configuration. Furthermore, the dimeric half-water molecules serve as a μ2-bridge linking adjacent macrocyclic units together with the multiple O sbnd H…N hydrogen bonds with azide anions, forming a novel 1D chain-like coordination polymer. Complexes 2 and 3 are obtained from different solvents (ethanol and methanol) and they can be converted into each other. The molecular structures and packing mode of 2 and 3 are different where six-coordinate and five-coordinate copper(II) centers are present, respectively.
Geometry essentials for dummies
Ryan, Mark
2011-01-01
Just the critical concepts you need to score high in geometry This practical, friendly guide focuses on critical concepts taught in a typical geometry course, from the properties of triangles, parallelograms, circles, and cylinders, to the skills and strategies you need to write geometry proofs. Geometry Essentials For Dummies is perfect for cramming or doing homework, or as a reference for parents helping kids study for exams. Get down to the basics - get a handle on the basics of geometry, from lines, segments, and angles, to vertices, altitudes, and diagonals Conque
Introduction to projective geometry
Wylie, C R
2008-01-01
This lucid introductory text offers both an analytic and an axiomatic approach to plane projective geometry. The analytic treatment builds and expands upon students' familiarity with elementary plane analytic geometry and provides a well-motivated approach to projective geometry. Subsequent chapters explore Euclidean and non-Euclidean geometry as specializations of the projective plane, revealing the existence of an infinite number of geometries, each Euclidean in nature but characterized by a different set of distance- and angle-measurement formulas. Outstanding pedagogical features include w
Thermal optical effect in axisymmetric structural laser resonator
Xu, Yonggen; Li, Yude
2012-02-01
In order to study the thermal optical effect (TOE) resulting from the axisymmetrical sources of thermal energy at the output mirror of CO 2 laser, the Heat Conduction Poisson Equation (HCPE) has been solved in the output mirror. Then the temperature distribution is given. The temperature variations will cause the surface distortion and the phase shift at the output mirror. Therefore, the output laser beam will be subject to thermal optical distortion and phase change. The numerical examples are to confirm our calculated results.
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
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.
Accuracy Improvement in Magnetic Field Modeling for an Axisymmetric Electromagnet
Ilin, Andrew V.; Chang-Diaz, Franklin R.; Gurieva, Yana L.; Il,in, Valery P.
2000-01-01
This paper examines the accuracy and calculation speed for the magnetic field computation in an axisymmetric electromagnet. Different numerical techniques, based on an adaptive nonuniform grid, high order finite difference approximations, and semi-analitical calculation of boundary conditions are considered. These techniques are being applied to the modeling of the Variable Specific Impulse Magnetoplasma Rocket. For high-accuracy calculations, a fourth-order scheme offers dramatic advantages over a second order scheme. For complex physical configurations of interest in plasma propulsion, a second-order scheme with nonuniform mesh gives the best results. Also, the relative advantages of various methods are described when the speed of computation is an important consideration.
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...
Fusion-product transport in axisymmetric tokamaks: losses and thermalization
Energy Technology Data Exchange (ETDEWEB)
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-..beta.., non-circular tokamak equilibria. First-orbit losses, trapping effects, and slowing-down drifts are also treated.
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)
Shao, B. L.; Xu, R. Q.
2009-07-01
Circular piezoelectric bimorph has been successfully used in numerous types of microdevices, such as actuators for flowcontrol applications, transducers for acoustic applications, and in locomotion of robotic systems, energy harvesting and active structural health monitoring applications. Recently, the concept of the functionally graded material (FGM) is introduced to improve properties and increase lifetime by selectively grading the elastic, piezoelectric, and/or dielectric properties along the thickness of a piezoceramic. However, even for the simple case of homogeneous circular piezoelectric geometry, analytical treatments are severely limited. This study established an axisymmetric and isoparametric graded element to model the functionally graded circular piezoelectric plates. All the material properties including elastic coefficients, piezoelectric coefficients, dielectric parameters and mass density are graded in the element and interpolated using the shape functions, which is also used to render the displacements and electric potential distribution in the element. Both static and dynamic cases can be considered in this element. MATLAB is used to implement the whole FEM code and gives some numerical examples to demonstrate the presented method.
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
Passive control of base pressure on an axisymmetric blunt body using a perimetric slit
García de la Cruz, Juan Marcos; Oxlade, Anthony R.; Morrison, Jonathan F.
2017-04-01
The effect on the base pressure of a thin slit located at the base edge of a blunt axisymmetric body, communicating an internal cavity with the external flow, is investigated. A parametric study is performed of the effect on base pressure of changes in slit size and cavity depth. The base pressure increases initially with increasing cavity depth, but saturates at a depth which depends on the slit size. The base pressure increases monotonically up to 5 % with increasing slit size for the geometries tested. An upper limit of base pressure recovery of 20 % is extrapolated from the data. It is observed that the main effect of the slit is to reduce the instantaneous pressure asymmetry, which is linked to the total base pressure in a similar fashion for all the slit sizes. As a second-order effect, for highly asymmetric pressure distributions, the slit produces a base pressure increase not associated with the base pressure asymmetry. The results suggest a global effect of the slit on the wake due to a diametrical flow within the cavity driven by the pressure differences across the slit and regulated by the largest of the pressure drops between the slit and cavity. The slit also reduces the periodic base pressure fluctuations, corresponding mainly to the vortex shedding, and increases the rotational speed of the wake.
Visualizing shear bands in 3-D using axisymmetric sample: An experimental study
Directory of Open Access Journals (Sweden)
W. Khraisat
2017-07-01
Full Text Available In this study a qualitative description of the occurrence of shear bands produced by a sudden impact on an axisymmetric specimen made of medium carbon steel 0.45% C is given. A simple experiment was developed aimed at producing a pinch shear stress in the front side of the test sample in order to visualize shear bands in 3-D. Curve fitting using MATLAB was employed based on the points taken from the images of the front section of the test sample. The predictions of the curve fitting suggests a hyperbolic section leading to the conclusion that within the sample there is a double cone region of material where the shear band region is located on its outer surface. The formation of the shear band is explained by the fact that the interaction of the stress wave front with the free surface of the test sample produces reflection waves that attenuate the incoming stress wave inwards leading to a stress gradient in the plane of the front side of the specimen that causes shear localization. Also, the progressively increasing cross sectional area of the test sample causes the expansion of the wave front, which also results in a stress gradient in the normal direction of the front side of the specimen. So the formation of shear bands depends not only on the impact momentum and strain rates but also on the sample’s geometry.
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.)
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
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.
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)
Uncertainty evaluation method for axi-symmetric measurement machines
Directory of Open Access Journals (Sweden)
Muelaner Jody Emlyn
2016-01-01
Full Text Available This paper describes a method of uncertainty evaluation for axi-symmetric measurement machines. Specialized measuring machines for the inspection of axisymmetric components enable the measurement of properties such as roundness (radial runout, axial runout and coning. These machines typically consist of a rotary table and a number of contact measurement probes located on slideways. Sources of uncertainty include the probe calibration process, probe repeatability, probe alignment, geometric errors in the rotary table, the dimensional stability of the structure holding the probes and form errors in the reference hemisphere which is used to calibrate the system. The generic method is described and an evaluation of an industrial machine is described as a worked example. Expanded uncertainties, at 95% confidence, were then calculated for the measurement of; radial runout (1.2 μm with a plunger probe or 1.7 μm with a lever probe; axial runout (1.2 μm with a plunger probe or 1.5 μm with a lever probe; and coning/swash (0.44 arcseconds with a plunger probe or 0.60 arcseconds with a lever probe.
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.
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.
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....
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.
Euclidean geometry and transformations
Dodge, Clayton W
1972-01-01
This introduction to Euclidean geometry emphasizes transformations, particularly isometries and similarities. Suitable for undergraduate courses, it includes numerous examples, many with detailed answers. 1972 edition.
International Nuclear Information System (INIS)
Hrivnacova, I; Viren, B
2008-01-01
The Virtual Geometry Model (VGM) was introduced at CHEP in 2004 [1], where its concept, based on the abstract interfaces to geometry objects, has been presented. Since then, it has undergone a design evolution to pure abstract interfaces, it has been consolidated and completed with more advanced features. Currently it is used in Geant4 VMC for the support of TGeo geometry definition with Geant4 native geometry navigation and recently it has been used in the validation of the G4Root tool. The implementation of the VGM for a concrete geometry model represents a small layer between the VGM and the particular native geometry. In addition to the implementations for Geant4 and Root TGeo geometry models, there is now added the third one for AGDD, which together with the existing XML exporter makes the VGM the most advanced tool for exchanging geometry formats providing 9 ways of conversions between Geant4, TGeo, AGDD and GDML models. In this presentation we will give the overview and the present status of the tool, we will review the supported features and point to possible limits in converting geometry models
O'Leary, Michael
2010-01-01
Guides readers through the development of geometry and basic proof writing using a historical approach to the topic. In an effort to fully appreciate the logic and structure of geometric proofs, Revolutions of Geometry places proofs into the context of geometry's history, helping readers to understand that proof writing is crucial to the job of a mathematician. Written for students and educators of mathematics alike, the book guides readers through the rich history and influential works, from ancient times to the present, behind the development of geometry. As a result, readers are successfull
Fundamental concepts of geometry
Meserve, Bruce E
1983-01-01
Demonstrates relationships between different types of geometry. Provides excellent overview of the foundations and historical evolution of geometrical concepts. Exercises (no solutions). Includes 98 illustrations.
Algorithms in Algebraic Geometry
Dickenstein, Alicia; Sommese, Andrew J
2008-01-01
In the last decade, there has been a burgeoning of activity in the design and implementation of algorithms for algebraic geometric computation. Some of these algorithms were originally designed for abstract algebraic geometry, but now are of interest for use in applications and some of these algorithms were originally designed for applications, but now are of interest for use in abstract algebraic geometry. The workshop on Algorithms in Algebraic Geometry that was held in the framework of the IMA Annual Program Year in Applications of Algebraic Geometry by the Institute for Mathematics and Its
International Nuclear Information System (INIS)
Xiou, W.J.; Ru, Y.A.; Mo, C.S.; Yi, H.S.
1987-01-01
The heat transfer of enhancement condensation of the vapor over the surface of an axisymmetric cylinder has been first studied theoretically in this paper. The problems of an axisymmetric cylinder are transformed into plate problems. The effects of some parameters on heat transfer coefficients of the vapor condensation over the surface of an axisymmetric cylinder have been discussed here. The heat transfer of the vapor condensation over an elliptical cylinder and an axisymmetric wing-shape cylinder has compared with the heat transfer of the vapor condensation over a tube surface. The conclusion is that the heat transfer of the vapor condensation over an elliptical cylinder and an axisymmetric wing-shape cylinder is greater than that over tubes
Kaufmann, Matthew L.; Bomer, Megan A.; Powell, Nancy Norem
2009-01-01
Students enter the geometry classroom with a strong concept of fairness and a sense of what it means to "play by the rules," yet many students have difficulty understanding the postulates, or rules, of geometry and their implications. Although they may never have articulated the properties of an axiomatic system, they have gained a practical…
Foundations of algebraic geometry
Weil, A
1946-01-01
This classic is one of the cornerstones of modern algebraic geometry. At the same time, it is entirely self-contained, assuming no knowledge whatsoever of algebraic geometry, and no knowledge of modern algebra beyond the simplest facts about abstract fields and their extensions, and the bare rudiments of the theory of ideals.
Supersymmetric Sigma Model Geometry
Directory of Open Access Journals (Sweden)
Ulf Lindström
2012-08-01
Full Text Available This is a review of how sigma models formulated in Superspace have become important tools for understanding geometry. Topics included are: The (hyperkähler reduction; projective superspace; the generalized Legendre construction; generalized Kähler geometry and constructions of hyperkähler metrics on Hermitian symmetric spaces.
Geometry of multihadron production
International Nuclear Information System (INIS)
Bjorken, J.D.
1994-10-01
This summary talk only reviews a small sample of topics featured at this symposium: Introduction; The Geometry and Geography of Phase space; Space-Time Geometry and HBT; Multiplicities, Intermittency, Correlations; Disoriented Chiral Condensate; Deep Inelastic Scattering at HERA; and Other Contributions
1996-01-01
Designs and Finite Geometries brings together in one place important contributions and up-to-date research results in this important area of mathematics. Designs and Finite Geometries serves as an excellent reference, providing insight into some of the most important research issues in the field.
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.
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.
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.
Numerical calculation of axisymmetric non-neutral plasma equilibria
Spencer, Ross L.; Rasband, S. N.; Vanfleet, Richard R.
1993-12-01
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.
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...... for a specific local flow rate and a non-uniform inflow to the catalyst will severely reduce the efficiency of the process. Since each ship will have a unique design the flow system, it is desirable to be able to design the system using Computational Fluid Dynamics (CFD). However, CFD fails to predict flow......-scaled model of the catalytic converter is constructed, see figure 1. The experiments are performed at laboratory conditions, with lower pressure, temperature and velocity than the full-scale catalytic converter. The Reynolds number based on the velocity in the inlet pipe and the diameter of the converter...
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)
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
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
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
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
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.
Kulczycki, Stefan
2008-01-01
This accessible approach features two varieties of proofs: stereometric and planimetric, as well as elementary proofs that employ only the simplest properties of the plane. A short history of geometry precedes a systematic exposition of the principles of non-Euclidean geometry.Starting with fundamental assumptions, the author examines the theorems of Hjelmslev, mapping a plane into a circle, the angle of parallelism and area of a polygon, regular polygons, straight lines and planes in space, and the horosphere. Further development of the theory covers hyperbolic functions, the geometry of suff
Complex and symplectic geometry
Medori, Costantino; Tomassini, Adriano
2017-01-01
This book arises from the INdAM Meeting "Complex and Symplectic Geometry", which was held in Cortona in June 2016. Several leading specialists, including young researchers, in the field of complex and symplectic geometry, present the state of the art of their research on topics such as the cohomology of complex manifolds; analytic techniques in Kähler and non-Kähler geometry; almost-complex and symplectic structures; special structures on complex manifolds; and deformations of complex objects. The work is intended for researchers in these areas.
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)
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)
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
Busemann, Herbert
2005-01-01
A comprehensive approach to qualitative problems in intrinsic differential geometry, this text examines Desarguesian spaces, perpendiculars and parallels, covering spaces, the influence of the sign of the curvature on geodesics, more. 1955 edition. Includes 66 figures.
Introduction to tropical geometry
Maclagan, Diane
2015-01-01
Tropical geometry is a combinatorial shadow of algebraic geometry, offering new polyhedral tools to compute invariants of algebraic varieties. It is based on tropical algebra, where the sum of two numbers is their minimum and the product is their sum. This turns polynomials into piecewise-linear functions, and their zero sets into polyhedral complexes. These tropical varieties retain a surprising amount of information about their classical counterparts. Tropical geometry is a young subject that has undergone a rapid development since the beginning of the 21st century. While establishing itself as an area in its own right, deep connections have been made to many branches of pure and applied mathematics. This book offers a self-contained introduction to tropical geometry, suitable as a course text for beginning graduate students. Proofs are provided for the main results, such as the Fundamental Theorem and the Structure Theorem. Numerous examples and explicit computations illustrate the main concepts. Each of t...
Melzak, Z A
2008-01-01
Intended for students of many different backgrounds with only a modest knowledge of mathematics, this text features self-contained chapters that can be adapted to several types of geometry courses. 1983 edition.
Rudiments of algebraic geometry
Jenner, WE
2017-01-01
Aimed at advanced undergraduate students of mathematics, this concise text covers the basics of algebraic geometry. Topics include affine spaces, projective spaces, rational curves, algebraic sets with group structure, more. 1963 edition.
Kollár, János
1997-01-01
This volume contains the lectures presented at the third Regional Geometry Institute at Park City in 1993. The lectures provide an introduction to the subject, complex algebraic geometry, making the book suitable as a text for second- and third-year graduate students. The book deals with topics in algebraic geometry where one can reach the level of current research while starting with the basics. Topics covered include the theory of surfaces from the viewpoint of recent higher-dimensional developments, providing an excellent introduction to more advanced topics such as the minimal model program. Also included is an introduction to Hodge theory and intersection homology based on the simple topological ideas of Lefschetz and an overview of the recent interactions between algebraic geometry and theoretical physics, which involve mirror symmetry and string theory.
DEFF Research Database (Denmark)
Kokkendorff, Simon Lyngby
2002-01-01
The subject of this Ph.D.-thesis is somewhere in between continuous and discrete geometry. Chapter 2 treats the geometry of finite point sets in semi-Riemannian hyperquadrics,using a matrix whose entries are a trigonometric function of relative distances in a given point set. The distance...... to the geometry of a simplex in a semi-Riemannian hyperquadric. In chapter 3 we study which finite metric spaces that are realizable in a hyperbolic space in the limit where curvature goes to -∞. We show that such spaces are the so called leaf spaces, the set of degree 1 vertices of weighted trees. We also...... establish results on the limiting geometry of such an isometrically realized leaf space simplex in hyperbolic space, when curvature goes to -∞. Chapter 4 discusses negative type of metric spaces. We give a measure theoretic treatment of this concept and related invariants. The theory developed...
Lectures on Symplectic Geometry
Silva, Ana Cannas
2001-01-01
The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and cl...
Energy Technology Data Exchange (ETDEWEB)
B.C. Lyons, S.C. Jardin, and J.J. Ramos
2012-06-28
A new code, the Neoclassical Ion-Electron Solver (NIES), has been written to solve for stationary, axisymmetric distribution functions (f ) in the conventional banana regime for both ions and elec trons using a set of drift-kinetic equations (DKEs) with linearized Fokker-Planck-Landau collision operators. Solvability conditions on the DKEs determine the relevant non-adiabatic pieces of f (called h ). We work in a 4D phase space in which Ψ defines a flux surface, θ is the poloidal angle, v is the total velocity referenced to the mean flow velocity, and λ is the dimensionless magnetic moment parameter. We expand h in finite elements in both v and λ . The Rosenbluth potentials, φ and ψ, which define the integral part of the collision operator, are expanded in Legendre series in cos χ , where χ is the pitch angle, Fourier series in cos θ , and finite elements in v . At each ψ , we solve a block tridiagonal system for hi (independent of fe ), then solve another block tridiagonal system for he (dependent on fi ). We demonstrate that such a formulation can be accurately and efficiently solved. NIES is coupled to the MHD equilibrium code JSOLVER [J. DeLucia, et al., J. Comput. Phys. 37 , pp 183-204 (1980).] allowing us to work with realistic magnetic geometries. The bootstrap current is calculated as a simple moment of the distribution function. Results are benchmarked against the Sauter analytic formulas and can be used as a kinetic closure for an MHD code (e.g., M3D-C1 [S.C. Jardin, et al ., Computational Science & Discovery, 4 (2012).]).
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
Osborne, I.; Brownson, E.; Eulisse, G.; Jones, C. D.; Lange, D. J.; Sexton-Kennedy, E.
2014-06-01
CMS faces real challenges with upgrade of the CMS detector through 2020 and beyond. One of the challenges, from the software point of view, is managing upgrade simulations with the same software release as the 2013 scenario. We present the CMS geometry description software model, its integration with the CMS event setup and core software. The CMS geometry configuration and selection is implemented in Python. The tools collect the Python configuration fragments into a script used in CMS workflow. This flexible and automated geometry configuration allows choosing either transient or persistent version of the same scenario and specific version of the same scenario. We describe how the geometries are integrated and validated, and how we define and handle different geometry scenarios in simulation and reconstruction. We discuss how to transparently manage multiple incompatible geometries in the same software release. Several examples are shown based on current implementation assuring consistent choice of scenario conditions. The consequences and implications for multiple/different code algorithms are discussed.
Introduction to combinatorial geometry
International Nuclear Information System (INIS)
Gabriel, T.A.; Emmett, M.B.
1985-01-01
The combinatorial geometry package as used in many three-dimensional multimedia Monte Carlo radiation transport codes, such as HETC, MORSE, and EGS, is becoming the preferred way to describe simple and complicated systems. Just about any system can be modeled using the package with relatively few input statements. This can be contrasted against the older style geometry packages in which the required input statements could be large even for relatively simple systems. However, with advancements come some difficulties. The users of combinatorial geometry must be able to visualize more, and, in some instances, all of the system at a time. Errors can be introduced into the modeling which, though slight, and at times hard to detect, can have devastating effects on the calculated results. As with all modeling packages, the best way to learn the combinatorial geometry is to use it, first on a simple system then on more complicated systems. The basic technique for the description of the geometry consists of defining the location and shape of the various zones in terms of the intersections and unions of geometric bodies. The geometric bodies which are generally included in most combinatorial geometry packages are: (1) box, (2) right parallelepiped, (3) sphere, (4) right circular cylinder, (5) right elliptic cylinder, (6) ellipsoid, (7) truncated right cone, (8) right angle wedge, and (9) arbitrary polyhedron. The data necessary to describe each of these bodies are given. As can be easily noted, there are some subsets included for simplicity
International Nuclear Information System (INIS)
Osborne, I; Brownson, E; Eulisse, G; Jones, C D; Sexton-Kennedy, E; Lange, D J
2014-01-01
CMS faces real challenges with upgrade of the CMS detector through 2020 and beyond. One of the challenges, from the software point of view, is managing upgrade simulations with the same software release as the 2013 scenario. We present the CMS geometry description software model, its integration with the CMS event setup and core software. The CMS geometry configuration and selection is implemented in Python. The tools collect the Python configuration fragments into a script used in CMS workflow. This flexible and automated geometry configuration allows choosing either transient or persistent version of the same scenario and specific version of the same scenario. We describe how the geometries are integrated and validated, and how we define and handle different geometry scenarios in simulation and reconstruction. We discuss how to transparently manage multiple incompatible geometries in the same software release. Several examples are shown based on current implementation assuring consistent choice of scenario conditions. The consequences and implications for multiple/different code algorithms are discussed.
Comment on the Exterior Solutions and Their Geometry in Scalar-Tensor Theories of Gravity
Tsuchida, T.; Watanabe, K.
1999-01-01
We study series of stationary solutions with asymptotic flatness properties in the Einstein-Maxwell-free scalar system because they are locally equivalent to the exterior solutions in some class of scalar-tensor theories of gravity. First, we classify spherical exterior solutions into two types of solutions, an apparently black hole type solution and an apparently worm hole type solution. The solutions contain three parameters, and we clarify their physical significance. Second, we reduce the field equations for the axisymmetric exterior solutions. We find that the reduced equations are partially the same as the Ernst equations. As simple examples, we derive new series of static, axisymmetric exterior solutions, which correspond to Voorhees's solutions. We then establish a non-trivial relation between the spherical exterior solutions and our new solutions. Finally, since null geodesics have conformally invariant properties, we study the local geometry of the exterior solutions by using the optical scalar equations and find some anomalous behavior of the null geodesics.
National Research Council Canada - National Science Library
Reeder, D
2002-01-01
... laboratory acoustic measurements. A general acoustic scattering model is developed that is accurate and numerically efficient for a wide range of frequencies, angles of orientation, irregular axisymmetric shapes and boundary...
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.
Experiences with the use of axisymmetric elements in cosmic NASTRAN for static analysis
Cooper, Michael J.; Walton, William C.
1991-01-01
Discussed here are some recent finite element modeling experiences using the axisymmetric elements CONEAX, TRAPAX, and TRIAAX, from the COSMIC NASTRAN element library. These experiences were gained in the practical application of these elements to the static analysis of helicopter rotor force measuring systems for two design projects for the NASA Ames Research Center. These design projects were the Rotor Test Apparatus and the Large Rotor Test Apparatus, which are dedicated to basic helicopter research. Here, a genetic axisymmetric model is generated for illustrative purposes. Modeling considerations are discussed, and the advantages and disadvantages of using axisymmetric elements are presented. Asymmetric mechanical and thermal loads are applied to the structure, and single and multi-point constraints are addressed. An example that couples the axisymmetric model to a non-axisymmtric model is demonstrated, complete with DMAP alters. Recommendations for improving the elements and making them easier to use are offered.
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
EFFECTS OF LARGE-SCALE NON-AXISYMMETRIC PERTURBATIONS IN THE MEAN-FIELD SOLAR DYNAMO
Energy Technology Data Exchange (ETDEWEB)
Pipin, V. V. [Institute of Solar-Terrestrial Physics, Russian Academy of Sciences (Russian Federation); Kosovichev, A. G. [W.W. Hansen Experimental Physics Laboratory, Stanford University, Stanford, CA 94305 (United States)
2015-11-10
We explore the response of a nonlinear non-axisymmetric mean-field solar dynamo model to shallow non-axisymmetric perturbations. After a relaxation period, the amplitude of the non-axisymmetric field depends on the initial condition, helicity conservation, and the depth of perturbation. It is found that a perturbation that is anchored at 0.9 R{sub ⊙} has a profound effect on the dynamo process, producing a transient magnetic cycle of the axisymmetric magnetic field, if it is initiated at the growing phase of the cycle. The non-symmetric, with respect to the equator, perturbation results in a hemispheric asymmetry of the magnetic activity. The evolution of the axisymmetric and non-axisymmetric fields depends on the turbulent magnetic Reynolds number R{sub m}. In the range of R{sub m} = 10{sup 4}–10{sup 6} the evolution returns to the normal course in the next cycle, in which the non-axisymmetric field is generated due to a nonlinear α-effect and magnetic buoyancy. In the stationary state, the large-scale magnetic field demonstrates a phenomenon of “active longitudes” with cyclic 180° “flip-flop” changes of the large-scale magnetic field orientation. The flip-flop effect is known from observations of solar and stellar magnetic cycles. However, this effect disappears in the model, which includes the meridional circulation pattern determined by helioseismology. The rotation rate of the non-axisymmetric field components varies during the relaxation period and carries important information about the dynamo process.
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...
Dielectric tensor operator of hot plasmas in toroidal axisymmetric systems
International Nuclear Information System (INIS)
Brunner, S.; Vaclavik, J.
1992-08-01
Kinetic theory is used to develop equations describing dynamics of small-amplitude electromagnetic perturbations in toroidal axisymmetric plasmas. The closed Vlasov-Maxwell equations are first solved for a hot stationary plasma using the expansion in the small parameter ε e =ρ/L, where ρ is the Larmor radius and L a characteristic length scale of the stationary state. The ordering and additional assumptions are specified so as to obtain the well-known Grad-Shafranov equation. The dielectric tensor of such a plasma is then derived. The Vlasov equation for the perturbed distribution function is solved by the expansion in the small parameters ε e and ε p =ρ/λ, where λ is a characteristic wavelength of the perturbing electromagnetic field. The solution is obtained up to the first order in ε e and the second order in ε p . By integrating the resulting distribution function over velocity space, an explicit expression for the tensor is derived in the form of a two-dimensional partial differential operator. The operator is shown to possess the proper symmetry corresponding to the energy conservation law. (author) 6 refs
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
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.)
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.
Adhesion and detachment of a capsule in axisymmetric flow
Keh, M. P.; Leal, L. G.
2016-05-01
The adhesion and detachment of a capsule on a solid boundary surface is studied via a combination of scaling theory and numerical simulation and the behavior is compared and contrasted with a vesicle. It is shown that the dominant physical property for both capsules and vesicles is the area dilation modulus Ks of the membrane. The nonzero shear modulus Gs for capsules increases the resistance to deformation and thus decreases slightly the equilibrium contact radius for an adhered capsule compared to an adhered vesicle. The detachment process in this study is due to an external axisymmetric flow. Unlike a rigid body that must be pulled away without change of shape, capsules (and vesicles) almost always detach dominantly by peeling in which the contact radius decreases but the minimum separation distance does not change until the final moments of detachment. Compared to a vesicle with the same Ks, a capsule maintains a more compact shape and is harder to elongate under a given external flow. Hence, the detachment process is slower for capsules compared to vesicles with the same Ks.
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)
Uniformly rotating, axisymmetric, and triaxial quark stars in general relativity
Zhou, Enping; Tsokaros, Antonios; Rezzolla, Luciano; Xu, Renxin; UryÅ«, KÅji
2018-01-01
Quasiequilibrium models of uniformly rotating axisymmetric and triaxial quark stars are computed in a general-relativistic gravity scenario. The Isenberg-Wilson-Mathews (IWM) formulation is employed and the Compact Object Calculator (cocal) code is extended to treat rotating stars with finite surface density and new equations of state (EOSs). Besides the MIT bag model for quark matter which is composed of deconfined quarks, we examine a new EOS proposed by Lai and Xu that is based on quark clustering and results in a stiff EOS that can support masses up to 3.3 M⊙ in the case we considered. We perform convergence tests for our new code to evaluate the effect of finite surface density in the accuracy of our solutions and construct sequences of solutions for both small and high compactness. The onset of secular instability due to viscous dissipation is identified and possible implications are discussed. An estimate of the gravitational wave amplitude and luminosity based on quadrupole formulas is presented and comparison with neutron stars is discussed.
Turbulent contributions to Ohm's law in axisymmetric magnetized plasmas
Chavdarovski, I.; Gatto, R.
2017-07-01
The effect of magnetic turbulence in shaping the current density in axisymmetric magnetized plasmas is analyzed using a turbulent extension of Ohm's law derived from the self-consistent action-angle transport theory. Besides the well-known hyper-resistive (helicity-conserving) contribution, the generalized Ohm's law contains an anomalous resistivity term and a turbulent bootstrap-like term proportional to the current density derivative. The numerical solution of the equation for equilibrium and turbulence profiles characteristic of conventional and advanced scenarios shows that, through the "turbulent bootstrap" effect and anomalous resistivity, power and parallel current can be generated which are a sizable portion (about 20%-25%) of the corresponding effects associated with the neoclassical bootstrap effect. The degree of alignment of the turbulence peak and the pressure gradient plays an important role in defining the steady-state regime. In a fully bootstrapped tokamak, the hyper-resistivity is essential in overcoming the intrinsic limitation of the hollow current profile.
Transverse linear dynamics in an axisymmetric ionization cooling channel
Directory of Open Access Journals (Sweden)
G. Dugan
2001-10-01
Full Text Available This paper outlines a formalism for the description of the linear transverse dynamics of charged particles in an axisymmetric ionization cooling channel. The particle trajectories in the absence of Coulomb scattering are described in terms of lattice functions à la Courant and Snyder, which depend only on the electric and magnetic fields in the channel. The process of multiple Coulomb scattering, which introduces stochastic terms into the particle equations of motion, is treated (in Gaussian approximation by obtaining the distribution function in phase space as a solution of a Fokker-Planck equation. The distribution function is then used to obtain moment equations for the transverse variables and for combinations of variables such as the emittance and angular momentum. The distribution function is also used to obtain an expression for the peak four-dimensional phase space density and for the fraction of the beam that is within a certain area in phase space. The special case of a periodic channel is then considered and expressions for the asymptotic rms emittance and peak phase space density are obtained. Finally, the application of the general formalism to a numerical example, based on the reported design of a cooling channel for a neutrino source, is considered, and comparisons are made with numerical simulations of that channel.
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).
Axisymmetric bifurcations of thick spherical shells under inflation and compression
deBotton, G.
2013-01-01
Incremental equilibrium equations and corresponding boundary conditions for an isotropic, hyperelastic and incompressible material are summarized and then specialized to a form suitable for the analysis of a spherical shell subject to an internal or an external pressure. A thick-walled spherical shell during inflation is analyzed using four different material models. Specifically, one and two terms in the Ogden energy formulation, the Gent model and an I1 formulation recently proposed by Lopez-Pamies. We investigate the existence of local pressure maxima and minima and the dependence of the corresponding stretches on the material model and on shell thickness. These results are then used to investigate axisymmetric bifurcations of the inflated shell. The analysis is extended to determine the behavior of a thick-walled spherical shell subject to an external pressure. We find that the results of the two terms Ogden formulation, the Gent and the Lopez-Pamies models are very similar, for the one term Ogden material we identify additional critical stretches, which have not been reported in the literature before.© 2012 Published by Elsevier Ltd.
Students Discovering Spherical Geometry Using Dynamic Geometry Software
Guven, Bulent; Karatas, Ilhan
2009-01-01
Dynamic geometry software (DGS) such as Cabri and Geometers' Sketchpad has been regularly used worldwide for teaching and learning Euclidean geometry for a long time. The DGS with its inductive nature allows students to learn Euclidean geometry via explorations. However, with respect to non-Euclidean geometries, do we need to introduce them to…
2002-01-01
Discrete geometry investigates combinatorial properties of configurations of geometric objects. To a working mathematician or computer scientist, it offers sophisticated results and techniques of great diversity and it is a foundation for fields such as computational geometry or combinatorial optimization. This book is primarily a textbook introduction to various areas of discrete geometry. In each area, it explains several key results and methods, in an accessible and concrete manner. It also contains more advanced material in separate sections and thus it can serve as a collection of surveys in several narrower subfields. The main topics include: basics on convex sets, convex polytopes, and hyperplane arrangements; combinatorial complexity of geometric configurations; intersection patterns and transversals of convex sets; geometric Ramsey-type results; polyhedral combinatorics and high-dimensional convexity; and lastly, embeddings of finite metric spaces into normed spaces. Jiri Matousek is Professor of Com...
Ochiai, T.; Nacher, J. C.
2011-09-01
Recently, the application of geometry and conformal mappings to artificial materials (metamaterials) has attracted the attention in various research communities. These materials, characterized by a unique man-made structure, have unusual optical properties, which materials found in nature do not exhibit. By applying the geometry and conformal mappings theory to metamaterial science, it may be possible to realize so-called "Harry Potter cloaking device". Although such a device is still in the science fiction realm, several works have shown that by using such metamaterials it may be possible to control the direction of the electromagnetic field at will. We could then make an object hidden inside of a cloaking device. Here, we will explain how to design invisibility device using differential geometry and conformal mappings.
Zheng, Fangyang
2002-01-01
The theory of complex manifolds overlaps with several branches of mathematics, including differential geometry, algebraic geometry, several complex variables, global analysis, topology, algebraic number theory, and mathematical physics. Complex manifolds provide a rich class of geometric objects, for example the (common) zero locus of any generic set of complex polynomials is always a complex manifold. Yet complex manifolds behave differently than generic smooth manifolds; they are more coherent and fragile. The rich yet restrictive character of complex manifolds makes them a special and interesting object of study. This book is a self-contained graduate textbook that discusses the differential geometric aspects of complex manifolds. The first part contains standard materials from general topology, differentiable manifolds, and basic Riemannian geometry. The second part discusses complex manifolds and analytic varieties, sheaves and holomorphic vector bundles, and gives a brief account of the surface classifi...
Cecil, Thomas E
2015-01-01
This exposition provides the state-of-the art on the differential geometry of hypersurfaces in real, complex, and quaternionic space forms. Special emphasis is placed on isoparametric and Dupin hypersurfaces in real space forms as well as Hopf hypersurfaces in complex space forms. The book is accessible to a reader who has completed a one-year graduate course in differential geometry. The text, including open problems and an extensive list of references, is an excellent resource for researchers in this area. Geometry of Hypersurfaces begins with the basic theory of submanifolds in real space forms. Topics include shape operators, principal curvatures and foliations, tubes and parallel hypersurfaces, curvature spheres and focal submanifolds. The focus then turns to the theory of isoparametric hypersurfaces in spheres. Important examples and classification results are given, including the construction of isoparametric hypersurfaces based on representations of Clifford algebras. An in-depth treatment of Dupin hy...
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...
MacKeown, P. K.
1984-01-01
Clarifies two concepts of gravity--those of a fictitious force and those of how space and time may have geometry. Reviews the position of Newton's theory of gravity in the context of special relativity and considers why gravity (as distinct from electromagnetics) lends itself to Einstein's revolutionary interpretation. (JN)
Implosions and hypertoric geometry
DEFF Research Database (Denmark)
Dancer, A.; Kirwan, F.; Swann, A.
2013-01-01
The geometry of the universal hyperkahler implosion for SU (n) is explored. In particular, we show that the universal hyperkahler implosion naturally contains a hypertoric variety described in terms of quivers. Furthermore, we discuss a gauge theoretic approach to hyperkahler implosion....
Boyer, Carl B
2012-01-01
Designed as an integrated survey of the development of analytic geometry, this study presents the concepts and contributions from before the Alexandrian Age through the eras of the great French mathematicians Fermat and Descartes, and on through Newton and Euler to the "Golden Age," from 1789 to 1850.
Hartshorne, Robin
2000-01-01
In recent years, I have been teaching a junior-senior-level course on the classi cal geometries. This book has grown out of that teaching experience. I assume only high-school geometry and some abstract algebra. The course begins in Chapter 1 with a critical examination of Euclid's Elements. Students are expected to read concurrently Books I-IV of Euclid's text, which must be obtained sepa rately. The remainder of the book is an exploration of questions that arise natu rally from this reading, together with their modern answers. To shore up the foundations we use Hilbert's axioms. The Cartesian plane over a field provides an analytic model of the theory, and conversely, we see that one can introduce coordinates into an abstract geometry. The theory of area is analyzed by cutting figures into triangles. The algebra of field extensions provides a method for deciding which geometrical constructions are possible. The investigation of the parallel postulate leads to the various non-Euclidean geometries. And ...
Wares, Arsalan; Elstak, Iwan
2017-01-01
The purpose of this paper is to describe the mathematics that emanates from the construction of an origami box. We first construct a simple origami box from a rectangular sheet and then discuss some of the mathematical questions that arise in the context of geometry and algebra. The activity can be used as a context for illustrating how algebra…
DEFF Research Database (Denmark)
Frisvad, Jeppe Revall
2008-01-01
, whether the shape of the material should be coupled to the appearance model or not, etc. A generalised concept of shape and geometry is presented to provide a framework for handling these many degrees of freedom. Constraints between input and output parameters are modelled as multidimensional shapes...
Diophantine geometry an introduction
Hindry, Marc
2000-01-01
This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and professional mathematicians. In each part of the book, the reader will find numerous exercises.
Metrics for Probabilistic Geometries
DEFF Research Database (Denmark)
Tosi, Alessandra; Hauberg, Søren; Vellido, Alfredo
2014-01-01
We investigate the geometrical structure of probabilistic generative dimensionality reduction models using the tools of Riemannian geometry. We explicitly define a distribution over the natural metric given by the models. We provide the necessary algorithms to compute expected metric tensors where...
Towards relativistic quantum geometry
Energy Technology Data Exchange (ETDEWEB)
Ridao, Luis Santiago [Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina); Bellini, Mauricio, E-mail: mbellini@mdp.edu.ar [Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350, C.P. 7600, Mar del Plata (Argentina); Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina)
2015-12-17
We obtain a gauge-invariant relativistic quantum geometry by using a Weylian-like manifold with a geometric scalar field which provides a gauge-invariant relativistic quantum theory in which the algebra of the Weylian-like field depends on observers. An example for a Reissner–Nordström black-hole is studied.
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.
Hsü, K J; Hsü, A J
1990-01-01
Music critics have compared Bach's music to the precision of mathematics. What "mathematics" and what "precision" are the questions for a curious scientist. The purpose of this short note is to suggest that the mathematics is, at least in part, Mandelbrot's fractal geometry and the precision is the deviation from a log-log linear plot.
Cooper, Brett D.; Barger, Rita
2009-01-01
The many connections between music and mathematics are well known. The length of a plucked string determines its tone, the time signature of a piece of music is a ratio, and note durations are measured in fractions. One connection commonly overlooked is that between music and geometry--specifically, geometric transformations, including…
Atiyah, M.; Dijkgraaf, R.; Hitchin, N.
2010-01-01
We review the remarkably fruitful interactions between mathematics and quantum physics in the past decades, pointing out some general trends and highlighting several examples, such as the counting of curves in algebraic geometry, invariants of knots and four-dimensional topology.
Martin, John
2010-01-01
The cycloid has been called the Helen of Geometry, not only because of its beautiful properties but also because of the quarrels it provoked between famous mathematicians of the 17th century. This article surveys the history of the cycloid and its importance in the development of the calculus.
Sliding vane geometry turbines
Sun, Harold Huimin; Zhang, Jizhong; Hu, Liangjun; Hanna, Dave R
2014-12-30
Various systems and methods are described for a variable geometry turbine. In one example, a turbine nozzle comprises a central axis and a nozzle vane. The nozzle vane includes a stationary vane and a sliding vane. The sliding vane is positioned to slide in a direction substantially tangent to an inner circumference of the turbine nozzle and in contact with the stationary vane.
DEFF Research Database (Denmark)
Booss-Bavnbek, Bernhelm
2011-01-01
This paper applies I.M. Gelfand's distinction between adequate and non-adequate use of mathematical language in different contexts to the newly opened window of model-based measurements of intracellular dynamics. The specifics of geometry and dynamics on the mesoscale of cell physiology are elabo...
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.
Energy Technology Data Exchange (ETDEWEB)
Kennedy, J. M.; Pfeiffer, P. A.; Marchertas, A. H.
1989-01-01
TEMP-STRESS has been developed to improve the understanding of the behavior of concrete subjected to mechanical loadings and high temperatures simulating the effects of coolant spills, molten debris, etc. The capability to model concrete structures subjected to static and dynamic overpressures, such as LWR and LMR containments with complex axisymmetric geometries, can be solved. The computer code is a finite element program which has a weakly coupled thermomechanical formulation. It can handle transient and steady state problems through the use of explicit time integration and dynamic relaxation. There is a plane or axisymmetric continuum element and flexural beam and shell elements for concrete discretization. The continuum element is a four node quadrilateral using numerical integration and elastic hourglass control. Variable material properties as a function of temperature are available. Thermal and/or mechanical loading can be handled. The concrete material model has the following characteristics: (a) elastic-plastic response, (b) variable loading surface capability, (c) cracking normal to maximum principal strain at specified failure surface, (d) post-failure element treatment, and (e) variable temperature dependence. Concrete can be reinforced and/or prestressed. 15 refs., 33 figs., 24 tabs.
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
Large Deformation and Adhesive Contact Studies of Axisymmetric Membranes
Laprade, Evan J.; Long, Rong; Pham, Jonathan; Lawrence, Jimmy; Emrick, Todd; Crosby, Alfred; Hui, Chung-Yuen; Shull, Kenneth R.
2013-01-01
A model membrane contact system consisting of an acrylic copolymer membrane and polydimethyl-siloxane substrate was utilized to evaluate a recently developed nonlinear large-deformation adhesive contact analysis. Direct measurements of the local membrane apex strain during non-contact inflation indicated that the neo-Hookean model provides an accurate measure of membrane strain and supports its use as the strain energy function for the analysis. A time dependent modulus emerges from the analysis, with principal tensions obtained from a comparison of predicted and experimental membrane profiles. A displacement controlled geometry was more easily modeled than the pressure controlled geometry, the applicability of the analysis was limited by wrinkling instabilities. The substantial viscoelastic behavior of these membranes made it difficult to describe the entire membrane with a single modulus, given the nonuniform deformation history of the membranes. Given the difficulty in determining membrane tension from the measured pressure and profile fits using the model, the peel energy was used as a simpler measure of adhesion. Using an analytical balance in the displacement controlled geometry, the membrane tension at the contact line was directly measured. Coupled with contact angle imaging, the peel energy was determined. For the model membranes studied, this peel energy described the membrane/substrate adhesive interactions quite well, giving well-defined peel energies that were independent of the detailed strain state of the membrane. PMID:23289644
Transformational plane geometry
Umble, Ronald N
2014-01-01
Axioms of Euclidean Plane Geometry The Existence and Incidence Postulates The Distance and Ruler Postulates The Plane Separation Postulate The Protractor Postulate The Side-Angle-Side Postulate and the Euclidean Parallel Postulate Theorems of Euclidean Plane Geometry The Exterior Angle Theorem Triangle Congruence Theorems The Alternate Interior Angles Theorem and the Angle Sum Theorem Similar Triangles Introduction to Transformations, Isometries, and Similarities Transformations Isometries and SimilaritiesAppendix: Proof of Surjectivity Translations, Rotations, and Reflections Translations Rotations Reflections Appendix: Geometer's Sketchpad Commands Required by Exploratory Activities Compositions of Translations, Rotations, and Reflections The Three Points Theorem Rotations as Compositions of Two Reflections Translations as Compositions of Two Halfturns or Two Reflections The Angle Addition Theorem Glide Reflections Classification of Isometries The Fundamental Theorem and Congruence Classification of Isometr...
Multivariate calculus and geometry
Dineen, Seán
2014-01-01
Multivariate calculus can be understood best by combining geometric insight, intuitive arguments, detailed explanations and mathematical reasoning. This textbook has successfully followed this programme. It additionally provides a solid description of the basic concepts, via familiar examples, which are then tested in technically demanding situations. In this new edition the introductory chapter and two of the chapters on the geometry of surfaces have been revised. Some exercises have been replaced and others provided with expanded solutions. Familiarity with partial derivatives and a course in linear algebra are essential prerequisites for readers of this book. Multivariate Calculus and Geometry is aimed primarily at higher level undergraduates in the mathematical sciences. The inclusion of many practical examples involving problems of several variables will appeal to mathematics, science and engineering students.
Algebra, Arithmetic, and Geometry
Tschinkel, Yuri
2009-01-01
The two volumes of "Algebra, Arithmetic, and Geometry: In Honor of Y.I. Manin" are composed of invited expository articles and extensions detailing Manin's contributions to the subjects, and are in celebration of his 70th birthday. The well-respected and distinguished contributors include: Behrend, Berkovich, Bost, Bressler, Calaque, Carlson, Chambert-Loir, Colombo, Connes, Consani, Dabrowski, Deninger, Dolgachev, Donaldson, Ekedahl, Elsenhans, Enriques, Etingof, Fock, Friedlander, Geemen, Getzler, Goncharov, Harris, Iskovskikh, Jahnel, Kaledin, Kapranov, Katz, Kaufmann, Kollar, Kont
DEFF Research Database (Denmark)
Tamke, Martin; Ramsgaard Thomsen, Mette; Riiber Nielsen, Jacob
2009-01-01
The versatility of wood constructions and traditional wood joints for the production of non standard elements was in focus of a design based research. Herein we established a seamless process from digital design to fabrication. A first research phase centered on the development of a robust...... parametric model and a generic design language a later explored the possibilities to construct complex shaped geometries with self registering joints on modern wood crafting machines. The research was carried out as collaboration with industrial partners....
DEFF Research Database (Denmark)
Tamke, Martin; Ramsgaard Thomsen, Mette; Riiber Nielsen, Jacob
2009-01-01
The versatility of wood constructions and traditional wood joints for the production of non standard elements was in focus of a design based research. Herein we established a seamless process from digital design to fabrication. A first research phase centered on the development of a robust parame...... parametric model and a generic design language a later explored the possibilities to construct complex shaped geometries with self registering joints on modern wood crafting machines. The research was carried out as collaboration with industrial partners....
Introducing geometry concept based on history of Islamic geometry
Maarif, S.; Wahyudin; Raditya, A.; Perbowo, K. S.
2018-01-01
Geometry is one of the areas of mathematics interesting to discuss. Geometry also has a long history in mathematical developments. Therefore, it is important integrated historical development of geometry in the classroom to increase’ knowledge of how mathematicians earlier finding and constructing a geometric concept. Introduction geometrical concept can be started by introducing the Muslim mathematician who invented these concepts so that students can understand in detail how a concept of geometry can be found. However, the history of mathematics development, especially history of Islamic geometry today is less popular in the world of education in Indonesia. There are several concepts discovered by Muslim mathematicians that should be appreciated by the students in learning geometry. Great ideas of mathematicians Muslim can be used as study materials to supplement religious character values taught by Muslim mathematicians. Additionally, by integrating the history of geometry in teaching geometry are expected to improve motivation and geometrical understanding concept.
Integral geometry and valuations
Solanes, Gil
2014-01-01
Valuations are finitely additive functionals on the space of convex bodies. Their study has become a central subject in convexity theory, with fundamental applications to integral geometry. In the last years there has been significant progress in the theory of valuations, which in turn has led to important achievements in integral geometry. This book originated from two courses delivered by the authors at the CRM and provides a self-contained introduction to these topics, covering most of the recent advances. The first part, by Semyon Alesker, is devoted to the theory of convex valuations, with emphasis on the latest developments. A special focus is put on the new fundamental structures of the space of valuations discovered after Alesker's irreducibility theorem. Moreover, the author describes the newly developed theory of valuations on manifolds. In the second part, Joseph H. G. Fu gives a modern introduction to integral geometry in the sense of Blaschke and Santaló, based on the notions and tools presented...
Integral geometry and holography
Energy Technology Data Exchange (ETDEWEB)
Czech, Bartłomiej; Lamprou, Lampros; McCandlish, Samuel [Stanford Institute for Theoretical Physics, Department of Physics, Stanford University,Stanford, CA 94305 (United States); Sully, James [Theory Group, SLAC National Accelerator Laboratory,Menlo Park, CA 94025 (United States)
2015-10-27
We present a mathematical framework which underlies the connection between information theory and the bulk spacetime in the AdS{sub 3}/CFT{sub 2} correspondence. A key concept is kinematic space: an auxiliary Lorentzian geometry whose metric is defined in terms of conditional mutual informations and which organizes the entanglement pattern of a CFT state. When the field theory has a holographic dual obeying the Ryu-Takayanagi proposal, kinematic space has a direct geometric meaning: it is the space of bulk geodesics studied in integral geometry. Lengths of bulk curves are computed by kinematic volumes, giving a precise entropic interpretation of the length of any bulk curve. We explain how basic geometric concepts — points, distances and angles — are reflected in kinematic space, allowing one to reconstruct a large class of spatial bulk geometries from boundary entanglement entropies. In this way, kinematic space translates between information theoretic and geometric descriptions of a CFT state. As an example, we discuss in detail the static slice of AdS{sub 3} whose kinematic space is two-dimensional de Sitter space.
Vorticity dynamics of a bileaflet mechanical heart valve in an axisymmetric aorta
Dasi, L. P.; Ge, L.; Simon, H. A.; Sotiropoulos, F.; Yoganathan, A. P.
2007-06-01
We present comprehensive particle image velocimetry measurements and direct numerical simulation (DNS) of physiological, pulsatile flow through a clinical quality bileaflet mechanical heart valve mounted in an idealized axisymmetric aorta geometry with a sudden expansion modeling the aortic sinus region. Instantaneous and ensemble-averaged velocity measurements as well as the associated statistics of leaflet kinematics are reported and analyzed in tandem to elucidate the structure of the velocity and vorticity fields of the ensuing flow-structure interaction. The measurements reveal that during the first half of the acceleration phase, the flow is laminar and repeatable from cycle to cycle. The valve housing shear layer rolls up into the sinus and begins to extract vorticity of opposite sign from the sinus wall. A start-up vortical structure is shed from the leaflets and is advected downstream as the leaflet shear layers become wavy and oscillatory. In the second half of flow acceleration the leaflet shear layers become unstable and break down into two von Karman-like vortex streets. The onset of vortex shedding from the valve leaflets is responsible for the growth of significant cycle-to-cycle vorticity oscillations. At peak flow, the housing and leaflet shear layers undergo secondary instabilities and break down rapidly into a chaotic, turbulent-like state with multiple small-scale vortical structures emerging in the flow. During the deceleration and closing phases all large-scale coherent flow features disappear and a chaotic small-scale vorticity field emerges, which persists even after the valve has closed. Probability density functions of the leaflet position during opening and closing phases show that the leaflet position fluctuates from cycle to cycle with larger fluctuations evident during valve closure. The DNS is carried out by prescribing the leaflet kinematics from the experimental data. The computed instantaneous vorticity fields are in very good
Tieng, S. M.; Lai, W. Z.
Because of the importance of the temperature scalar measurements in combination diagonostics, application of phase shift holographic interferometry to temperature measurement of an axisymmetrically premixed flame was experimentally investigated. The test apparatus is an axisymmetric Bunsen burner. Propane of 99 percent purity is used as the gaseous fuel. A fast Fourier transform, a more efficient and accurate approach for Abel inversion, is used for reconstructed the axisymmetric temperature field from the interferometric data. The temperature distribution is compared with the thermocouple-measured values. The comparison shows that the proposed technique is satisfactory. The result errors are analyzed in detail. It is shown that this technique overcomes most of the earlier problems and limitations detrimental to the conventional holographic interferometry.
Introductory non-Euclidean geometry
Manning, Henry Parker
1963-01-01
This fine and versatile introduction begins with the theorems common to Euclidean and non-Euclidean geometry, and then it addresses the specific differences that constitute elliptic and hyperbolic geometry. 1901 edition.
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.
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.
Non-conventional laser surface hardening for axisymmetric components
Liverani, Erica; Battiato, Nadine; Ascari, Alessandro; Fortunato, Alessandro
2014-02-01
A new process, based on ring spot geometry, is presented for laser surface hardening of large cylindrical com-ponents. The proposed technique leads to a very hard, deep and uniform treated area along the entire work piece surface without introducing a tempered zone, making the process very attractive compared to conventional induction hardening that exhibits both low energy efficiency and poor flexibility. A complete physical model is presented for the process, together with a study of the influence of process parameters on the final outcome. The results of an extensive validation campaign, carried out following the AISI1040 standard, are also reported.
Matter in toy dynamical geometries
International Nuclear Information System (INIS)
Konopka, Tomasz
2009-01-01
One of the objectives of theories describing quantum dynamical geometry is to compute expectation values of geometrical observables. The results of such computations can be affected by whether or not matter is taken into account. It is thus important to understand to what extent and to what effect matter can affect dynamical geometries. Using a simple model, it is shown that matter can effectively mold a geometry into an isotropic configuration. Implications for 'atomistic' models of quantum geometry are briefly discussed.
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
Flow of Polymer Melts in Plane- and Axi-symmetric Converging Dies
DEFF Research Database (Denmark)
Lauridsen, Carsten Linding; Kjær, Erik Michael; Haudrum, Jan
1997-01-01
The extensional flow has considerable influence on the pressure loss in converging flows, which are present in both extrusion and injection moulding. Both plane- and axi-symmetric converging flows have been studied with LDPE, HDPE and PS. The transient extensional viscosities are determined in all...... cases. The extensional viscous description used is the one proposed by Cogswell (3). The extensional viscosities in the two now different flow fields ate compared. The plane-symmetric extensional viscosity is found to be larger than the axi-symmetric for the HDPE melt. The two viscosities are comparable...
Energy Technology Data Exchange (ETDEWEB)
Hook, D W [Blackett Laboratory, Imperial College of Science Technology and Medicine, University of London, Prince Consort Road, London, SW7 2BW (United Kingdom)
2008-01-11
A geometric framework for quantum mechanics arose during the mid 1970s when authors such as Cantoni explored the notion of generalized transition probabilities, and Kibble promoted the idea that the space of pure quantum states provides a natural quantum mechanical analogue for classical phase space. This central idea can be seen easily since the projection of Schroedinger's equation from a Hilbert space into the space of pure spaces is a set of Hamilton's equations. Over the intervening years considerable work has been carried out by a variety of authors and a mature description of quantum mechanics in geometric terms has emerged with many applications. This current offering would seem ideally placed to review the last thirty years of progress and relate this to the most recent work in quantum entanglement. Bengtsson and Zyczkowski's beautifully illustrated volume, Geometry of Quantum States (referred to as GQS from now on) attempts to cover considerable ground in its 466 pages. Its topics range from colour theory in Chapter 1 to quantum entanglement in Chapter 15-to say that this is a whirlwind tour is, perhaps, no understatement. The use of the work 'introduction' in the subtitle of GQS, might suggest to the reader that this work be viewed as a textbook and I think that this interpretation would be incorrect. The authors have chosen to present a survey of different topics with the specific aim to introduce entanglement in geometric terms-the book is not intended as a pedagogical introduction to the geometric approach to quantum mechanics. Each of the fifteen chapters is a short, and mostly self-contained, essay on a particular aspect or application of geometry in the context of quantum mechanics with entanglement being addressed specifically in the final chapter. The chapters fall into three classifications: those concerned with the mathematical background, those which discuss quantum theory and the foundational aspects of the geometric
Teaching of Geometry in Bulgaria
Bankov, Kiril
2013-01-01
Geometry plays an important role in the school mathematics curriculum all around the world. Teaching of geometry varies a lot (Hoyls, Foxman, & Kuchemann, 2001). Many countries revise the objectives, the content, and the approaches to the geometry in school. Studies of the processes show that there are not common trends of these changes…
Graded geometry and Poisson reduction
Cattaneo, A S; Zambon, M
2009-01-01
The main result of [2] extends the Marsden-Ratiu reduction theorem [4] in Poisson geometry, and is proven by means of graded geometry. In this note we provide the background material about graded geometry necessary for the proof in [2]. Further, we provide an alternative algebraic proof for the main result. ©2009 American Institute of Physics
Functional integration over geometries
International Nuclear Information System (INIS)
Mottola, E.
1995-01-01
The geometric construction of the functional integral over coset spaces M/G is reviewed. The inner product on the cotangent space of infinitesimal deformations of M defines an invariant distance and volume form, or functional integration measure on the full configuration space. Then, by a simple change of coordinates parameterizing the gauge fiber G, the functional measure on the coset space M/G is deduced. This change of integration variables leads to a Jacobian which is entirely equivalent to the Faddeev--Popov determinant of the more traditional gauge fixed approach in non-abelian gauge theory. If the general construction is applied to the case where G is the group of coordinate reparameterizations of spacetime, the continuum functional integral over geometries, i.e. metrics modulo coordinate reparameterizations may be defined. The invariant functional integration measure is used to derive the trace anomaly and effective action for the conformal part of the metric in two and four dimensional spacetime. In two dimensions this approach generates the Polyakov--Liouville action of closed bosonic non-critical string theory. In four dimensions the corresponding effective action leads to novel conclusions on the importance of quantum effects in gravity in the far infrared, and in particular, a dramatic modification of the classical Einstein theory at cosmological distance scales, signaled first by the quantum instability of classical de Sitter spacetime. Finite volume scaling relations for the functional integral of quantum gravity in two and four dimensions are derived, and comparison with the discretized dynamical triangulation approach to the integration over geometries are discussed. Outstanding unsolved problems in both the continuum definition and the simplicial approach to the functional integral over geometries are highlighted
Gillespie, Ronald J; Robinson, Edward A
2005-05-01
Although the structure of almost any molecule can now be obtained by ab initio calculations chemists still look for simple answers to the question "What determines the geometry of a given molecule?" For this purpose they make use of various models such as the VSEPR model and qualitative quantum mechanical models such as those based on the valence bond theory. The present state of such models, and the support for them provided by recently developed methods for analyzing calculated electron densities, are reviewed and discussed in this tutorial review.
2015-01-01
This stimulating volume offers a broad collection of the principles of geometry and trigonometry and contains colorful diagrams to bring mathematical principles to life. Subjects are enriched by references to famous mathematicians and their ideas, and the stories are presented in a very comprehensible way. Readers investigate the relationships of points, lines, surfaces, and solids. They study construction methods for drawing figures, a wealth of facts about these figures, and above all, methods to prove the facts. They learn about triangle measure for circular motion, sine and cosine, tangent
Abhyankar, Shreeram Shankar
1964-01-01
This book provides, for use in a graduate course or for self-study by graduate students, a well-motivated treatment of several topics, especially the following: (1) algebraic treatment of several complex variables; (2) geometric approach to algebraic geometry via analytic sets; (3) survey of local algebra; (4) survey of sheaf theory. The book has been written in the spirit of Weierstrass. Power series play the dominant role. The treatment, being algebraic, is not restricted to complex numbers, but remains valid over any complete-valued field. This makes it applicable to situations arising from
Flegg, H Graham
2001-01-01
This excellent introduction to topology eases first-year math students and general readers into the subject by surveying its concepts in a descriptive and intuitive way, attempting to build a bridge from the familiar concepts of geometry to the formalized study of topology. The first three chapters focus on congruence classes defined by transformations in real Euclidean space. As the number of permitted transformations increases, these classes become larger, and their common topological properties become intuitively clear. Chapters 4-12 give a largely intuitive presentation of selected topics.
Kendig, Keith
2015-01-01
Designed to make learning introductory algebraic geometry as easy as possible, this text is intended for advanced undergraduates and graduate students who have taken a one-year course in algebra and are familiar with complex analysis. This newly updated second edition enhances the original treatment's extensive use of concrete examples and exercises with numerous figures that have been specially redrawn in Adobe Illustrator. An introductory chapter that focuses on examples of curves is followed by a more rigorous and careful look at plane curves. Subsequent chapters explore commutative ring th
Gruber, Peter M
1987-01-01
This volume contains a fairly complete picture of the geometry of numbers, including relations to other branches of mathematics such as analytic number theory, diophantine approximation, coding and numerical analysis. It deals with convex or non-convex bodies and lattices in euclidean space, etc.This second edition was prepared jointly by P.M. Gruber and the author of the first edition. The authors have retained the existing text (with minor corrections) while adding to each chapter supplementary sections on the more recent developments. While this method may have drawbacks, it has the definit
REA, The Editors of
2012-01-01
REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Geometry I includes methods of proof, points, lines, planes, angles, congruent angles and line segments, triangles, parallelism, quadrilaterals, geometric inequalities, and geometric
Dooner, David B
2012-01-01
Building on the first edition published in 1995 this new edition of Kinematic Geometry of Gearing has been extensively revised and updated with new and original material. This includes the methodology for general tooth forms, radius of torsure', cylinder of osculation, and cylindroid of torsure; the author has also completely reworked the '3 laws of gearing', the first law re-written to better parallel the existing 'Law of Gearing" as pioneered by Leonard Euler, expanded from Euler's original law to encompass non-circular gears and hypoid gears, the 2nd law of gearing describing a unique relat
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.
Non-commutative geometry, non-associative geometry and the standard model of particle physics
International Nuclear Information System (INIS)
Boyle, Latham; Farnsworth, Shane
2014-01-01
Connes’ notion of non-commutative geometry (NCG) generalizes Riemannian geometry and yields a striking reinterepretation of the standard model of particle physics, coupled to Einstein gravity. We suggest a simple reformulation with two key mathematical advantages: (i) it unifies many of the traditional NCG axioms into a single one; and (ii) it immediately generalizes from non-commutative to non-associative geometry. Remarkably, it also resolves a long-standing problem plaguing the NCG construction of the standard model, by precisely eliminating from the action the collection of seven unwanted terms that previously had to be removed by an extra, non-geometric, assumption. With this problem solved, the NCG algorithm for constructing the standard model action is tighter and more explanatory than the traditional one based on effective field theory. (paper)
Zamuraev, V. P.; Kalinina, A. P.
2017-10-01
This work concerns the process of deceleration of supersonic flow up to the transonic velocities in the channel. This process is connected with the problem of combustion organizing of fuels in the various ramjet engines. The influence of mode of energy supply and the type of channel geometry (axisymmetric or planar channel) is studied as well as the other factors. The similarity of gas dynamic structure formed under hydrogen burning and under pulse periodic energy supply is studied.
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.
Axisymmetric polydimethysiloxane microchannels for in vitro hemodynamic studies
Energy Technology Data Exchange (ETDEWEB)
Lima, Rui [Department of Mechanical Technology, ESTiG, Braganca Polyt., C. Sta. Apolonia, 5301-857 Braganca (Portugal); Oliveira, Monica S N [Departamento de Engenharia Quimica, CEFT, Faculdade de Engenharia da Universidade do Porto, Rua Dr Roberto Frias, 4200-465 Porto (Portugal); Ishikawa, Takuji; Kaji, Hirokazu; Nishizawa, Matsuhiko [Department of Bioengineering and Robotics, Graduate School of Engineering, Tohoku University, 6-6-01 Aoba, 980-8579 Sendai (Japan); Tanaka, Shuji [Department of Nanomechanics, Graduate School of Engineering, Tohoku University, 6-6-01 Aoba, 980-8579 Sendai (Japan); Yamaguchi, Takami, E-mail: ruimec@ipb.p [Department of Biomedical Engineering, Graduate School of Biomedical Engineering, Tohoku University, 6-6-01 Aoba, 980-8579 Sendai (Japan)
2009-09-15
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 muPIV/PTV. By using a confocal muPTV system individual red blood cells (RBCs) were successfully tracked trough a 75 mum 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.
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
Numerical analyses of radiative heat transfer in any arbitrarily-shaped axisymmetric enclosures
International Nuclear Information System (INIS)
Ben Salah, M.; Askri, F; Jemni, A.; Nasrallah, S. Ben
2006-01-01
A numerical approach for the treatment of radiative heat transfer in any irregularly-shaped axisymmetric enclosure filled with absorbing, emitting and scattering gray media is developed. Radiative transfer equation (RTE) is formulated for a general axisymmetric geometrical configurations, and the discretized equation is conducted using an unstructured meshes, generated by an appropriate computer algorithm, and the control volume finite element method which frequently adopted in CFD problems. A computer procedure has been done to solve the discretized RTE and to examine the accuracy and the computational efficiency of the proposed numerical approach. By using this computer algorithm, five test cases, a cylindrical enclosure with absorbing and emitting medium, a diffuser shaped axisymmetric enclosure, a finite axisymmetric cylindrical enclosure with a curved wall, a furnace with axially varying medium temperature and a rocket nozzle, are treated and the obtained results agree very well with other published works. Furthermore, the developed computer procedure has an accurate CPU time and it can be coupled easily with CFD codes
Axi-Symmetric Simulation of the Slump Flow Test for Self-Compacting
DEFF Research Database (Denmark)
Thrane, Lars Nyholm; Szabo, Peter; Geiker, Mette Rica
2004-01-01
. This paper presents a numerical axi-symmetric approach for simulation of the slump flow test. Simulations are compared to experimental test results on the rheological properties and slump flow. Former rheological investigations on SCC indicate a non-Newtonian behaviour according to the Bingham model....
Flow of Polymer Melts in Plane- and Axi-symmetric Converging Dies
DEFF Research Database (Denmark)
Lauridsen, Carsten Linding; Kjær, Erik Michael; Haudrum, Jan
1997-01-01
The extensional flow has considerable influence on the pressure loss in converging flows, which are present in both extrusion and injection moulding. Both plane- and axi-symmetric converging flows have been studied with LDPE, HDPE and PS. The transient extensional viscosities are determined in all...
Gavrilyuk, I.; Hermann, M.; Trotsenko, Yu.; Timokha, A.
2013-10-01
Employing the virtual work variational principle and the linear multimodal method for the liquid sloshing in an axisymmetric tank, we study coupled eigenoscillations of a tower and an elevated tank partially filled by a liquid. An emphasis is placed on the case of an upright circular cylindrical tank. Theoretical results are compared with known experimental data.
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
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
Low-frequency behavior of the turbulent axisymmetric near-wake
Gentile, V.; Schrijer, F.F.J.; van Oudheusden, B.W.; Scarano, F.
2016-01-01
The turbulent wake past an axisymmetric body is investigated with time-resolved stereoscopic particle image velocimetry (PIV) at a Reynolds number ReD = 6.7 × 104 based on the object diameter. The azimuthal organization of the near-wake is studied at different locations downstream of the trailing
Experimental investigation into the unsteady effects on non-axisymmetric turbine endwall contouring
CSIR Research Space (South Africa)
Dunn, Dwain I
2010-01-01
Full Text Available Turbine manufacturers are striving to develop turbines that are more efficient. One area of focus has been the control of secondary flows through the use of non-axisymmetric endwalls. The majority of development has been performed in cascades...
Corrections and comments on the multipole moments of axisymmetric electrovacuum spacetimes
Energy Technology Data Exchange (ETDEWEB)
Sotiriou, Thomas P; Apostolatos, Theocharis A [Section of Astrophysics, Astronomy, and Mechanics Department of Physics, National and Kapodistrian University of Athens, Panepistimiopolis, Zografos GR-15783, Athens (Greece)
2004-12-21
Following the method of Hoenselaers and Perjes, we present a new corrected and dimensionally consistent set of multipole gravitational and electromagnetic moments for stationary axisymmetric spacetimes. Furthermore, we use our results to compute the multipole moments, both gravitational and electromagnetic, of a Kerr-Newman black hole.
2016-01-22
Electromagnetic Simulations for an Axisymmetric Gregorian Reflector System for a Space-Deployed Inflatable Antenna Alan J. Fenn Lincoln...system for potential space deployment is explored. The antenna utilizes a planar array located near the vertex of the primary reflector. Numerical...electromagnetic simulations based on the multilevel fast multipole method (MLFMM) were used to analyze and optimize the antenna parameters for
Emerson, Benjamin; Lieuwen, Tim
2017-11-01
This study investigates the forced response characteristics of axisymmetric structures in density-stratified swirling jets. The reacting, swirling jet is an important canonical flow field for modern combustion systems. This work is motivated by the combustion instability problem for such systems, where acoustically excited vortical structures may drive oscillatory heat release of combustion. Previous hydrodynamics studies have shown that the stability of helical structures is highly sensitive to the swirl number. However, the combustion literature has shown that axisymmetric structures (in contrast to helical structures) are often responsible for most of the heat release response. Therefore, this work performs a spatial stability analysis to study the swirl number sensitivity of the forced response of the axisymmetric mode. A spatio-temporal analysis is conducted in tandem to investigate the swirl number sensitivity of the impulse response of this mode. The results show that at low values of the swirl number, the axisymmetric mode stability is a weak function of the swirl number, but that new modes and stability bifurcations appear at high swirl numbers.
Flow of Polymer Melts in Plane- and Axi-Symmetric Converging Dies
DEFF Research Database (Denmark)
Lauridsen, Carsten Linding; Kjær, Erik Michael; Haudrum, Jan
1998-01-01
The extensional flow has considerable influence on the pressure loss in converging flows, which are present in both extrusion and injection moulding. Both plane- and axi-symmetric converging flows have been studied with LDPE, HDPE and PS. The transient extensional viscosities are determined in al...
Geometry through history Euclidean, hyperbolic, and projective geometries
Dillon, Meighan I
2018-01-01
Presented as an engaging discourse, this textbook invites readers to delve into the historical origins and uses of geometry. The narrative traces the influence of Euclid’s system of geometry, as developed in his classic text The Elements, through the Arabic period, the modern era in the West, and up to twentieth century mathematics. Axioms and proof methods used by mathematicians from those periods are explored alongside the problems in Euclidean geometry that lead to their work. Students cultivate skills applicable to much of modern mathematics through sections that integrate concepts like projective and hyperbolic geometry with representative proof-based exercises. For its sophisticated account of ancient to modern geometries, this text assumes only a year of college mathematics as it builds towards its conclusion with algebraic curves and quaternions. Euclid’s work has affected geometry for thousands of years, so this text has something to offer to anyone who wants to broaden their appreciation for the...
Geometry through history euclidean, hyperbolic, and projective geometries
Dillon, Meighan I
2018-01-01
Presented as an engaging discourse, this textbook invites readers to delve into the historical origins and uses of geometry. The narrative traces the influence of Euclid’s system of geometry, as developed in his classic text The Elements, through the Arabic period, the modern era in the West, and up to twentieth century mathematics. Axioms and proof methods used by mathematicians from those periods are explored alongside the problems in Euclidean geometry that lead to their work. Students cultivate skills applicable to much of modern mathematics through sections that integrate concepts like projective and hyperbolic geometry with representative proof-based exercises. For its sophisticated account of ancient to modern geometries, this text assumes only a year of college mathematics as it builds towards its conclusion with algebraic curves and quaternions. Euclid’s work has affected geometry for thousands of years, so this text has something to offer to anyone who wants to broaden their appreciation for the...
Bochnak, Jacek; Roy, Marie-Françoise
1998-01-01
This book is a systematic treatment of real algebraic geometry, a subject that has strong interrelation with other areas of mathematics: singularity theory, differential topology, quadratic forms, commutative algebra, model theory, complexity theory etc. The careful and clearly written account covers both basic concepts and up-to-date research topics. It may be used as text for a graduate course. The present edition is a substantially revised and expanded English version of the book "Géometrie algébrique réelle" originally published in French, in 1987, as Volume 12 of ERGEBNISSE. Since the publication of the French version the theory has made advances in several directions. Many of these are included in this English version. Thus the English book may be regarded as a completely new treatment of the subject.
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
Langohr, G Daniel G; Willing, Ryan; Medley, John B; King, Graham J W; Johnson, James A
2015-05-01
Radial head (RH) implants are manufactured from stiff materials, resulting in reduced radiocapitellar contact area that may lead to cartilage degeneration. Although the native RH is nonaxisymmetric, most implants are axisymmetric, potentially contributing to altered contact mechanics. This study compared the joint contact area (Ac) and maximum contact stress (σmax) of axisymmetric and nonaxisymmetric RH implants to the native radiocapitellar joint. The contact mechanics of intact elbows derived from cadaveric computed tomography data (n = 15) were compared with axisymmetric (size: 18, 20, 22 mm) and nonaxisymmetric (size: 16 × 18, 18 × 20, 20 × 22 mm) RH hemiarthroplasty reconstructed elbows using Abaqus finite element software. Under a 100 N load, Ac and σmax were computed for ±90° pronation-supination and 0°, 45°, 90°, and 135° flexion. Compared with native, both hemiarthroplasty models produced significantly lower Ac and higher σmax (P < .001). In the best orientation, the nonaxisymmetric RH provided significantly larger Ac at 0° and 135° flexion (P = .03, P = .007) and reduced levels of σmax at 45° and 90° flexion (P = .003, P < .001). However, there was also a worst orientation that reduced Ac and increased σmax for all flexion angles (P < .003 for all). The native RH was less sensitive to rotation than the nonaxisymmetric RH in terms of σmax (P < .001). The axisymmetric RH was not sensitive to rotation. Whereas a nonaxisymmetric RH can provide improved contact mechanics at certain forearm rotations and flexions, there are also orientations where Ac is reduced and σmax is increased. Axisymmetric designs are more consistent throughout forearm rotation and therefore may be more forgiving than the nonaxisymmetric RH implant design used in this study. Copyright © 2015 Journal of Shoulder and Elbow Surgery Board of Trustees. Published by Elsevier Inc. All rights reserved.
Geodesics in supersymmetric microstate geometries
International Nuclear Information System (INIS)
Eperon, Felicity C
2017-01-01
It has been argued that supersymmetric microstate geometries are classically unstable. One argument for instability involves considering the motion of a massive particle near the ergosurface of such a spacetime. It is shown that the instability can be triggered by a particle that starts arbitrarily far from the ergosurface. Another argument for instability is related to the phenomenon of stable trapping of null geodesics in these geometries. Such trapping is studied in detail for the most symmetrical microstate geometries. It is found that there are several distinct types of trapped null geodesic, both prograde and retrograde. Several important differences between geodesics in microstate geometries and black hole geometries are noted. The Penrose process for energy extraction in these geometries is discussed. (paper)
An introduction to incidence geometry
De Bruyn, Bart
2016-01-01
This book gives an introduction to the field of Incidence Geometry by discussing the basic families of point-line geometries and introducing some of the mathematical techniques that are essential for their study. The families of geometries covered in this book include among others the generalized polygons, near polygons, polar spaces, dual polar spaces and designs. Also the various relationships between these geometries are investigated. Ovals and ovoids of projective spaces are studied and some applications to particular geometries will be given. A separate chapter introduces the necessary mathematical tools and techniques from graph theory. This chapter itself can be regarded as a self-contained introduction to strongly regular and distance-regular graphs. This book is essentially self-contained, only assuming the knowledge of basic notions from (linear) algebra and projective and affine geometry. Almost all theorems are accompanied with proofs and a list of exercises with full solutions is given at the end...
Self-designing parametric geometries
Sobester, Andras
2015-01-01
The thesis of this paper is that script-based geometry modelling offers the possibility of building `self-designing' intelligence into parametric airframe geometries. We show how sophisticated heuristics (such as optimizers and complex decision structures) can be readily integrated into the parametric geometry model itself using a script-driven modelling architecture. The result is an opportunity for optimization with the scope of conceptual design and the fidelity of preliminary design. Addi...
Large deformation and adhesive contact studies of axisymmetric membranes.
Laprade, Evan J; Long, Rong; Pham, Jonathan T; Lawrence, Jimmy; Emrick, Todd; Crosby, Alfred J; Hui, Chung-Yuen; Shull, Kenneth R
2013-02-05
A model membrane contact system consisting of an acrylic copolymer membrane and a PDMS substrate was utilized to evaluate a recently developed nonlinear large-deformation adhesive contact analysis. Direct measurements of the local membrane apex strain during noncontact inflation indicated that the neo-Hookean model provides an accurate measure of membrane strain and supports its use as the strain energy function for the analysis. Two membrane contact geometries, exhibiting significantly different strain distributions during withdrawal, were investigated. The first examines the wet contact of an air pressurized membrane. The second looks at the dry contact of a fluid deformed membrane in which a stepper motor controls membrane-substrate separation. A time-dependent modulus emerges from the analysis, with principal tensions obtained from a comparison of predicted and experimental membrane profiles. The applicability of this numerical analysis for determining membrane tension, however, is limited by wrinkling instabilities and viscoelasticity. For this reason, a conceptually simpler method, based on the direct measurement of the membrane tension and contact angle, was also utilized. The traditional peel energy defined with this direct measurement accurately described the membrane/substrate adhesive interactions, giving well-defined peel energies that were independent of the detailed strain state of the membrane.
Initiation to global Finslerian geometry
Akbar-Zadeh, Hassan
2006-01-01
After a brief description of the evolution of thinking on Finslerian geometry starting from Riemann, Finsler, Berwald and Elie Cartan, the book gives a clear and precise treatment of this geometry. The first three chapters develop the basic notions and methods, introduced by the author, to reach the global problems in Finslerian Geometry. The next five chapters are independent of each other, and deal with among others the geometry of generalized Einstein manifolds, the classification of Finslerian manifolds of constant sectional curvatures. They also give a treatment of isometric, affine, p
Planetary Image Geometry Library
Deen, Robert C.; Pariser, Oleg
2010-01-01
The Planetary Image Geometry (PIG) library is a multi-mission library used for projecting images (EDRs, or Experiment Data Records) and managing their geometry for in-situ missions. A collection of models describes cameras and their articulation, allowing application programs such as mosaickers, terrain generators, and pointing correction tools to be written in a multi-mission manner, without any knowledge of parameters specific to the supported missions. Camera model objects allow transformation of image coordinates to and from view vectors in XYZ space. Pointing models, specific to each mission, describe how to orient the camera models based on telemetry or other information. Surface models describe the surface in general terms. Coordinate system objects manage the various coordinate systems involved in most missions. File objects manage access to metadata (labels, including telemetry information) in the input EDRs and RDRs (Reduced Data Records). Label models manage metadata information in output files. Site objects keep track of different locations where the spacecraft might be at a given time. Radiometry models allow correction of radiometry for an image. Mission objects contain basic mission parameters. Pointing adjustment ("nav") files allow pointing to be corrected. The object-oriented structure (C++) makes it easy to subclass just the pieces of the library that are truly mission-specific. Typically, this involves just the pointing model and coordinate systems, and parts of the file model. Once the library was developed (initially for Mars Polar Lander, MPL), adding new missions ranged from two days to a few months, resulting in significant cost savings as compared to rewriting all the application programs for each mission. Currently supported missions include Mars Pathfinder (MPF), MPL, Mars Exploration Rover (MER), Phoenix, and Mars Science Lab (MSL). Applications based on this library create the majority of operational image RDRs for those missions. A
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.
Bhatia, Rajendra
2013-01-01
This book is an outcome of the Indo-French Workshop on Matrix Information Geometries (MIG): Applications in Sensor and Cognitive Systems Engineering, which was held in Ecole Polytechnique and Thales Research and Technology Center, Palaiseau, France, in February 23-25, 2011. The workshop was generously funded by the Indo-French Centre for the Promotion of Advanced Research (IFCPAR). During the event, 22 renowned invited french or indian speakers gave lectures on their areas of expertise within the field of matrix analysis or processing. From these talks, a total of 17 original contribution or state-of-the-art chapters have been assembled in this volume. All articles were thoroughly peer-reviewed and improved, according to the suggestions of the international referees. The 17 contributions presented are organized in three parts: (1) State-of-the-art surveys & original matrix theory work, (2) Advanced matrix theory for radar processing, and (3) Matrix-based signal processing applications.
Guijosa, A
1999-01-01
This thesis explores some aspects of the recently uncovered connection between gauge theories and gravity, known as the AdS/CFT, or bulk-boundary, correspondence. This is a remarkable statement of equivalence between string or M-theory on certain backgrounds and field theories living on the boundaries of the corresponding spacetimes. Under the duality between four-dimensional N = 4 SU(N) superYang-Mills (SYM) and Type IIB string theory on AdS5 × S5, a baryon is mapped onto N fundamental strings terminating on a wrapped D5-brane. We examine the structure and energetics of this system from the vantage point of the fivebrane worldvolume action, making use of the Born-Infeld string approach. We construct supersymmetric fivebrane embeddings which correspond to gauge theory configurations with n external quarks, 0 ≤ n ≤ N. The extension of these solutions to the full asymptotically flat geometry of N D3-branes provides a detailed description of the creation of strings as the fivebrane is...
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.
Positive geometries and canonical forms
Arkani-Hamed, Nima; Bai, Yuntao; Lam, Thomas
2017-11-01
Recent years have seen a surprising connection between the physics of scattering amplitudes and a class of mathematical objects — the positive Grassmannian, positive loop Grassmannians, tree and loop Amplituhedra — which have been loosely referred to as "positive geometries". The connection between the geometry and physics is provided by a unique differential form canonically determined by the property of having logarithmic singularities (only) on all the boundaries of the space, with residues on each boundary given by the canonical form on that boundary. The structures seen in the physical setting of the Amplituhedron are both rigid and rich enough to motivate an investigation of the notions of "positive geometries" and their associated "canonical forms" as objects of study in their own right, in a more general mathematical setting. In this paper we take the first steps in this direction. We begin by giving a precise definition of positive geometries and canonical forms, and introduce two general methods for finding forms for more complicated positive geometries from simpler ones — via "triangulation" on the one hand, and "push-forward" maps between geometries on the other. We present numerous examples of positive geometries in projective spaces, Grassmannians, and toric, cluster and flag varieties, both for the simplest "simplex-like" geometries and the richer "polytope-like" ones. We also illustrate a number of strategies for computing canonical forms for large classes of positive geometries, ranging from a direct determination exploiting knowledge of zeros and poles, to the use of the general triangulation and push-forward methods, to the representation of the form as volume integrals over dual geometries and contour integrals over auxiliary spaces. These methods yield interesting representations for the canonical forms of wide classes of positive geometries, ranging from the simplest Amplituhedra to new expressions for the volume of arbitrary convex
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.
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%.
Surrogate Modeling for Geometry Optimization
DEFF Research Database (Denmark)
Rojas Larrazabal, Marielba de la Caridad; Abraham, Yonas; Holzwarth, Natalie
2009-01-01
A new approach for optimizing the nuclear geometry of an atomic system is described. Instead of the original expensive objective function (energy functional), a small number of simpler surrogates is used.......A new approach for optimizing the nuclear geometry of an atomic system is described. Instead of the original expensive objective function (energy functional), a small number of simpler surrogates is used....
Enumerative Geometry of Hyperplane Arrangements
2012-05-11
NUMBER 6. AUTHOR(SI 5d. PROJECT NUMBER Paul, Thomas Joseph 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS! ESl ...Smith and Bernd Sturmfels. Teaching the geometry of schemes. In Computations in algebraic geometry with Macaulay 2, volume 8 of Algorithms Comput
Spatial geometry and special relativity
DEFF Research Database (Denmark)
Kneubil, Fabiana Botelho
2016-01-01
In this work, it is shown the interplay of relative and absolute entities, which are present in both spatial geometry and special relativity. In order to strengthen the understanding of special relativity, we discuss firstly an instance of geometry and the existence of both frame-dependent and fr...
Molecular motion in restricted geometries
Indian Academy of Sciences (India)
Molecular dynamics in restricted geometries is known to exhibit anomalous behaviour. Diffusion, translational or rotational, of molecules is altered significantly on confinement in restricted geometries. Quasielastic neutron scattering (QENS) offers a unique possibility of studying molecular motion in such systems. Both time ...
Conformal Lorentz geometry revisited
Teleman, Kostake
1996-02-01
. We also show that Mach's principle on inertial motions receives an explanation in our theory by considering the particular geodesic paths, for which one of the partners of an interacting pair is fixed and sent to infinity. In fact we study a dynamical system (W,L) which presents some formal and topological similarities with a system of two particles interacting gravitationally. (W,L) is the only conformally invariant relativistic two-point dynamical system. At the end we show that W can be naturally regarded as the base of a principal GL(2,C)-bundle which comes with a natural connection. We study this bundle from differential geometric point of view. Physical interpretations will be discussed in a future paper. This text is an improvement of a previous version, which was submitted under the title ``Hypertwistor Geometry.'' [See, K. Teleman, ``Hypertwistor Geometry (abstract),'' 14th International Conference on General Relativity and Gravitation, Florence, Italy, 1995.] The change of the title and many other improvements are due to the valuable comments of the referee, who also suggested the author to avoid hazardous interpretations.
Magnetism in curved geometries
Streubel, Robert
Deterministically bending and twisting two-dimensional structures in the three-dimensional (3D) space provide means to modify conventional or to launch novel functionalities by tailoring curvature and 3D shape. The recent developments of 3D curved magnetic geometries, ranging from theoretical predictions over fabrication to characterization using integral means as well as advanced magnetic tomography, will be reviewed. Theoretical works predict a curvature-induced effective anisotropy and effective Dzyaloshinskii-Moriya interaction resulting in a vast of novel effects including magnetochiral effects (chirality symmetry breaking) and topologically induced magnetization patterning. The remarkable development of nanotechnology, e.g. preparation of high-quality extended thin films, nanowires and frameworks via chemical and physical deposition as well as 3D nano printing, has granted first insights into the fundamental properties of 3D shaped magnetic objects. Optimizing magnetic and structural properties of these novel 3D architectures demands new investigation methods, particularly those based on vector tomographic imaging. Magnetic neutron tomography and electron-based 3D imaging, such as electron holography and vector field electron tomography, are well-established techniques to investigate macroscopic and nanoscopic samples, respectively. At the mesoscale, the curved objects can be investigated using the novel method of magnetic X-ray tomography. In spite of experimental challenges to address the appealing theoretical predictions of curvature-induced effects, those 3D magnetic architectures have already proven their application potential for life sciences, targeted delivery, realization of 3D spin-wave filters, and magneto-encephalography devices, to name just a few. DOE BES MSED (DE-AC02-05-CH11231).
On spin dependence of relativistic acoustic geometry
International Nuclear Information System (INIS)
Pu, Hung-Yi; Chang, Hsiang-Kuang; Maity, Ishita; Das, Tapas Kumar
2012-01-01
This work makes the first ever attempt to understand the influence of the black hole background spacetime in determining the fundamental properties of the embedded relativistic acoustic geometry. To accomplish such task, we investigate the role of the spin angular momentum of the astrophysical black hole (the Kerr parameter a—a representative feature of the background black hole metric) in estimating the value of the acoustic surface gravity (the representative feature of the corresponding analogue spacetime). Since almost all astrophysical black holes are supposed to posses some degree of intrinsic rotation, the influence of the Kerr parameter on classical analogue models is very important to understand. We study the general relativistic, axially symmetric, non-self-gravitating inflow of the hydrodynamic fluid onto a rotating astrophysical black hole from the dynamical systems point of view. In this work the location of the acoustic horizon inside such fluid flow is identified and the associated acoustic surface gravity is estimated. We study the dependence of such surface gravity as a function of the Kerr parameter as well as with other dynamical and thermodynamic variables governing the fluid flow under strong gravity, and demonstrate that for retrograde flow, the surface gravity (and hence the associated analogue Hawking temperature) correlates with the black hole spin in general, whereas for the prograde flow, the surface gravity as well as the analogue temperature correlates with the black hole spin for slow to moderately rotating holes, but anti-correlates with the spin for fast to extremely rotating holes. We found that for certain values of the initial boundary conditions, more than one acoustic horizons, namely two black hole types and one white hole type, may form, and the surface gravity may become formally infinite at the acoustic white hole. We discuss the possible connection between the corresponding analogue Hawking temperature and astrophysically
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
Essid, Idris; Soudani, Sarra; Lefebvre, Frédéric; Kaminsky, Werner; Fujita, Wataru; Ben Nasr, Cherif; Touil, Soufiane
2017-12-01
We report efficient and green syntheses of two α-hydroxyphosphonates, C17H21O4P (I) and C19H25O4P (II), obtained by the reaction of dialkylphosphites with 1,3-diphenylacetone, on magnesia support, under solvent-free conditions. Their structures were determined by single crystal X-ray diffraction. Compound (I) crystallizes in the monoclinic system and P21/c space group with a = 10.2656(4), b = 7.0539(3), c = 23.3340(1) Å, β = 100.514(2)°, V = 1661.72(12) Å3 with Z = 4. The structure was refined to R = 0.044, wR(F2) = 0.101. Compound (II) belongs also to the monoclinic system, space group P21/c with the following parameters: a = 11.8110 (13), b = 16.0285 (17), c = 10.0691 (12) Å, β = 103.254(3)°, V = 1855.4 (4)Å3 and Z = 4. The structure was refined to R = 0.061, wR(F2) = 0.173. The molecular properties of these two compounds were characterized by multinuclear solid state (13C and 31P) CP-MAS-NMR. Intermolecular interactions were investigated by Hirshfeld surfaces. Electronic properties such as HOMO and LUMO energies were derived.
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.
Fernández-Trincado, J. G.; Robin, A. C.; Bienaymé, O.; Reylé, C.; Valenzuela, O.; Pichardo, B.
2014-07-01
In this contributed poster we present a preliminary attempt to compute a non-axisymmetric potential together with previous axisymmetric potential of the Besançon galaxy model. The contribution by non-axisymmetric components are modeled by the superposition of inhomogeneous ellipsoids to approximate the triaxial bar and superposition of homogeneous oblate spheroids for a stellar halo, possibly triaxial. Finally, we have computed the potential and force field for these non-axisymmetric components in order to constraint the total mass of the Milky Way. We present preliminary results for the rotation curve and the contribution of the bar to it. This approach will allow future studies of dynamical constraints from comparisons of kinematical simulations with upcoming surveys such as RAVE, BRAVA, APOGEE, and GAIA in the near future. More details, are presented in https://gaia.ub.edu/Twiki/pub/GREATITNFC/ProgramFinalconference/Poster_JG.Fern%e1ndez.pdf.
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.
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
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.
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.
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
Axisymmetric solid-of-revolution finite elements with rotational degrees of freedom
CSIR Research Space (South Africa)
Long, CS
2009-01-01
Full Text Available of the axis of radial symmetry. Weissman and Taylor [23] introduced two elements based on the Hellinger- Reissner functional. Their elements employ the popular Pian and Sumihara interpolation, modified to obtain correct rank for the axisymmetric case... option however. Essentially, we adopt the procedure suggested by Jog and Annabat- tula [25], who proposed the selection of interpolation functions such that zero- energy modes (associated with reduced integrations schemes) are captured. In their paper...
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
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.
AxisSPH:devising and validating an axisymmetric smoothed particle hydrodynamics code
Relaño Castillo, Antonio
2012-01-01
A two-dimensional axisymmetric implementation of the smoothed particle hydrodynamics (SPH) technique, called for short AxisSPH, has been described in this thesis, along with a number of basic tests and realistic applications. The main goal of this work was to fill a gap on a topic which has been scarcely addressed in the published literature concerning SPH. Although the application of AxisSPH to the simulation of real problems is restricted to those systems which display the appropriate ...
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)
Preliminary summary of particle transport effects in non-axisymmetric tandem mirrors
International Nuclear Information System (INIS)
Baldwin, D.E.
1978-01-01
This report reviews the physical basis for the theory of enhanced transport in non-axisymmetric tandem mirror systems recently published by Ryutov, et al. For TMX and thermal ions in a reactor, the radial loss is estimated to be somewhat less than the axial loss; energetic alphas in reactors are susceptible to rapid loss. A number of variations of current magnetic field designs are suggested for reducing this transport
Solving the Axisymmetric Inverse Heat Conduction Problem by a Wavelet Dual Least Squares Method
Directory of Open Access Journals (Sweden)
Fu Chu-Li
2009-01-01
Full Text Available We consider an axisymmetric inverse heat conduction problem of determining the surface temperature from a fixed location inside a cylinder. This problem is ill-posed; the solution (if it exists does not depend continuously on the data. A special project method—dual least squares method generated by the family of Shannon wavelet is applied to formulate regularized solution. Meanwhile, an order optimal error estimate between the approximate solution and exact solution is proved.
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)
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
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)
The nonlinear behaviour of axisymmetric hydromagnetic waves in a partially ionized plasma
International Nuclear Information System (INIS)
Sawley, M.
1977-10-01
Finite amplitude effects in the propagation of axisymmetric hydromagnetic waves in a cylindrical, magnetized plasma are considered. The influence of the Hall term and the presence of neutral atoms on the resulting second order fields is examined. The combined effect of these two factors is to produce a substantial secord order azimuthal field, in addition to the axial field predicted by earlier work which neglected these factors. In some circumstances this azimuthal field is much larger than the axial field. (Author)
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
Differential geometry and symmetric spaces
Helgason, Sigurdur
2001-01-01
Sigurdur Helgason's Differential Geometry and Symmetric Spaces was quickly recognized as a remarkable and important book. For many years, it was the standard text both for Riemannian geometry and for the analysis and geometry of symmetric spaces. Several generations of mathematicians relied on it for its clarity and careful attention to detail. Although much has happened in the field since the publication of this book, as demonstrated by Helgason's own three-volume expansion of the original work, this single volume is still an excellent overview of the subjects. For instance, even though there
Differential geometry curves, surfaces, manifolds
Kühnel, Wolfgang
2015-01-01
This carefully written book is an introduction to the beautiful ideas and results of differential geometry. The first half covers the geometry of curves and surfaces, which provide much of the motivation and intuition for the general theory. The second part studies the geometry of general manifolds, with particular emphasis on connections and curvature. The text is illustrated with many figures and examples. The prerequisites are undergraduate analysis and linear algebra. This new edition provides many advancements, including more figures and exercises, and-as a new feature-a good number of so
Fallow), Stray
2009-01-01
Having trouble with geometry? Do Pi, The Pythagorean Theorem, and angle calculations just make your head spin? Relax. With Head First 2D Geometry, you'll master everything from triangles, quads and polygons to the time-saving secrets of similar and congruent angles -- and it'll be quick, painless, and fun. Through entertaining stories and practical examples from the world around you, this book takes you beyond boring problems. You'll actually use what you learn to make real-life decisions, like using angles and parallel lines to crack a mysterious CSI case. Put geometry to work for you, and
Walsh, Edward T
2014-01-01
This introductory text is designed to help undergraduate students develop a solid foundation in geometry. Early chapters progress slowly, cultivating the necessary understanding and self-confidence for the more rapid development that follows. The extensive treatment can be easily adapted to accommodate shorter courses. Starting with the language of mathematics as expressed in the algebra of logic and sets, the text covers geometric sets of points, separation and angles, triangles, parallel lines, similarity, polygons and area, circles, space geometry, and coordinate geometry. Each chapter incl
Energy Technology Data Exchange (ETDEWEB)
Hogan, Craig
2013-03-24
Standard particle theory is based on quantized matter embedded in a classical geometry. Here, a complementary model is proposed, based on classical matter -- massive bodies, without quantum properties -- embedded in a quantum geometry. It does not describe elementary particles, but may be a better, fully consistent quantum description for position states in laboratory-scale systems. Gravitational theory suggests that the geometrical quantum system has an information density of about one qubit per Planck length squared. If so, the model here predicts that the quantum uncertainty of geometry creates a new form of noise in the position of massive bodies, detectable by interferometers.
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
An introduction to differential geometry
Willmore, T J
2012-01-01
This text employs vector methods to explore the classical theory of curves and surfaces. Topics include basic theory of tensor algebra, tensor calculus, calculus of differential forms, and elements of Riemannian geometry. 1959 edition.
Hyperbolic Metamaterials with Complex Geometry
DEFF Research Database (Denmark)
Lavrinenko, Andrei; Andryieuski, Andrei; Zhukovsky, Sergei
2016-01-01
We investigate new geometries of hyperbolic metamaterialssuch as highly corrugated structures, nanoparticle monolayer assemblies, super-structured or vertically arranged multilayersand nanopillars. All structures retain basic propertiesof hyperbolic metamaterials, but have functionality improved...
Advances in discrete differential geometry
2016-01-01
This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. The authors take a closer look at discrete models in differential geometry and dynamical systems. Their curves are polygonal, surfaces are made from triangles and quadrilaterals, and time is discrete. Nevertheless, the difference between the corresponding smooth curves, surfaces and classical dynamical systems with continuous time can hardly be seen. This is the paradigm of structure-preserving discretizations. Current advances in this field are stimulated to a large extent by its relevance for computer graphics and mathematical physics. This book is written by specialists working together on a common research project. It is about differential geometry and dynamical systems, smooth and discrete theories, ...
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.
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.
Cell geometry dictates TNFα-induced genome response.
Mitra, Aninda; Venkatachalapathy, Saradha; Ratna, Prasuna; Wang, Yejun; Jokhun, Doorgesh Sharma; Shivashankar, G V
2017-05-16
Cells in physiology integrate local soluble and mechanical signals to regulate genomic programs. Whereas the individual roles of these signals are well studied, the cellular responses to the combined chemical and physical signals are less explored. Here, we investigated the cross-talk between cellular geometry and TNFα signaling. We stabilized NIH 3T3 fibroblasts into rectangular anisotropic or circular isotropic geometries and stimulated them with TNFα and analyzed nuclear translocation of transcription regulators -NFκB (p65) and MKL and downstream gene-expression patterns. We found that TNFα induces geometry-dependent actin depolymerization, which enhances IκB degradation, p65 nuclear translocation, nuclear exit of MKL, and sequestration of p65 at the RNA-polymerase-II foci. Further, global transcription profile of cells under matrix-TNFα interplay reveals a geometry-dependent gene-expression pattern. At a functional level, we find cell geometry affects TNFα-induced cell proliferation. Our results provide compelling evidence that fibroblasts, depending on their geometries, elicit distinct cellular responses for the same cytokine.
A Comment on Molecular Geometry
Gomba, Frank J.
1999-12-01
A method of determining the correct molecular geometry of simple molecules and ions with one central atom is proposed. While the usual method of determining the molecular geometry involves first drawing the Lewis structure, this method can be used without doing so. In fact, the Lewis structure need not be drawn at all. The Lewis structure may be drawn as the final step, with the geometry of the simple molecule or ion already established. In the case of diatomic molecules, any atom may be used as the central atom. When hydrogen is present in a multiatom molecule or ion, this method "naturally" eliminates choosing hydrogen; but, any other atom may be used as the central atom to determine the correct geometry. The Lewis structure can then be used to determine the formal charges on the atoms. In this way there is a check on the selection of the central atom, should the correct Lewis structure be desired. Thus, it assumes that one is familiar with both Lewis structures and the valence shell electron pair repulsion (VSEPR) approach to bonding. The approach suggested in this paper will give rapid and accurate molecular geometries, and it is fun !!!
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
Electrodynamics and Spacetime Geometry: Foundations
Cabral, Francisco; Lobo, Francisco S. N.
2017-02-01
We explore the intimate connection between spacetime geometry and electrodynamics. This link is already implicit in the constitutive relations between the field strengths and excitations, which are an essential part of the axiomatic structure of electromagnetism, clearly formulated via integration theory and differential forms. We review the foundations of classical electromagnetism based on charge and magnetic flux conservation, the Lorentz force and the constitutive relations. These relations introduce the conformal part of the metric and allow the study of electrodynamics for specific spacetime geometries. At the foundational level, we discuss the possibility of generalizing the vacuum constitutive relations, by relaxing the fixed conditions of homogeneity and isotropy, and by assuming that the symmetry properties of the electro-vacuum follow the spacetime isometries. The implications of this extension are briefly discussed in the context of the intimate connection between electromagnetism and the geometry (and causal structure) of spacetime.
Euclidean geometry and its subgeometries
Specht, Edward John; Calkins, Keith G; Rhoads, Donald H
2015-01-01
In this monograph, the authors present a modern development of Euclidean geometry from independent axioms, using up-to-date language and providing detailed proofs. The axioms for incidence, betweenness, and plane separation are close to those of Hilbert. This is the only axiomatic treatment of Euclidean geometry that uses axioms not involving metric notions and that explores congruence and isometries by means of reflection mappings. The authors present thirteen axioms in sequence, proving as many theorems as possible at each stage and, in the process, building up subgeometries, most notably the Pasch and neutral geometries. Standard topics such as the congruence theorems for triangles, embedding the real numbers in a line, and coordinatization of the plane are included, as well as theorems of Pythagoras, Desargues, Pappas, Menelaus, and Ceva. The final chapter covers consistency and independence of axioms, as well as independence of definition properties. There are over 300 exercises; solutions to many of the...
Guide to Computational Geometry Processing
DEFF Research Database (Denmark)
Bærentzen, Jakob Andreas; Gravesen, Jens; Anton, François
Optical scanning is rapidly becoming ubiquitous. From industrial laser scanners to medical CT, MR and 3D ultrasound scanners, numerous organizations now have easy access to optical acquisition devices that provide huge volumes of image data. However, the raw geometry data acquired must first...... be processed before it is useful. This Guide to Computational Geometry Processing reviews the algorithms for processing geometric data, with a practical focus on important techniques not covered by traditional courses on computer vision and computer graphics. This is balanced with an introduction...... Provides additional material at a supplementary website Includes self-study exercises throughout the text Graduate students will find this text a valuable, hands-on guide to developing key skills in geometry processing. The book will also serve as a useful reference for professionals wishing to improve...
Takeda, M; Hiratsuka, T; Ito, K; Finsterle, S
2011-04-25
Diffusion anisotropy is a critical property in predicting migration of substances in sedimentary formations with very low permeability. The diffusion anisotropy of sedimentary rocks has been evaluated mainly from laboratory diffusion experiments, in which the directional diffusivities are separately estimated by through-diffusion experiments using different rock samples, or concurrently by in-diffusion experiments in which only the tracer profile in a rock block is measured. To estimate the diffusion anisotropy from a single rock sample, this study proposes an axisymmetric diffusion test, in which tracer diffuses between a cylindrical rock sample and a surrounding solution reservoir. The tracer diffusion between the sample and reservoir can be monitored from the reservoir tracer concentrations, and the tracer profile could also be obtained after dismantling the sample. Semi-analytical solutions are derived for tracer concentrations in both the reservoir and sample, accounting for an anisotropic diffusion tensor of rank two as well as the dilution effects from sampling and replacement of reservoir solution. The transient and steady-state analyses were examined experimentally and numerically for different experimental configurations, but without the need for tracer profiling. These experimental configurations are tested for in- and out-diffusion experiments using Koetoi and Wakkanai mudstones and Shirahama sandstone, and are scrutinized by a numerical approach to identify favorable conditions for parameter estimation. The analysis reveals the difficulty in estimating diffusion anisotropy; test configurations are proposed for enhanced identifiability of diffusion anisotropy. Moreover, it is demonstrated that the axisymmetric diffusion test is efficient in obtaining the sorption parameter from both steady-state and transient data, and in determining the effective diffusion coefficient if isotropic diffusion is assumed. Moreover, measuring reservoir concentrations in an
Copper (II) complexes with aroylhydrazones
Indian Academy of Sciences (India)
Copper(II) complexes with aroylhydrazones ... The coordination chemistry of copper(II) with tridentate aroylhydrazones is briefly discussed in this article. ... EPR spectroscopy and variable temperature magnetic susceptibility measurements have been used to reveal the nature of the coordination geometry and magnetic ...
Realism, positivism, instrumentalism, and quantum geometry
Prugovečki, Eduard
1992-02-01
The roles of classical realism, logical positivism, and pragmatic instrumentalism in the shaping of fundamental ideas in quantum physics are examined in the light of some recent historical and sociological studies of the factors that influenced their development. It is shown that those studies indicate that the conventionalistic form of instrumentalism that has dominated all the major post-World War II developments in quantum physics is not an outgrowth of the Copenhagen school, and that despite the “schism” in twentieth century physics created by the Bohr-Einstein “disagreements” on foundational issues in quantum theory, both their philosophical stands were very much opposed to those of conventionalistic instrumentalism. Quotations from the writings of Dirac, Heisenberg, Popper, Russell, and other influential thinkers, are provided, illustrating the fact that, despite the various divergencies in their opinions, they all either opposed the instrumentalist concept of “truth” in general, or its conventionalistic version in post-World War II quantum physics in particular. The basic epistemic ideas of a quantum geometry approach to quantum physics are reviewed and discussed from the point of view of a quantum realism that seeks to reconcile Bohr's “positivism” with Einstein's “realism” by emphasizing the existence of an underlying quantum reality, in which they both believed. This quantum geometry framework seeks to introduce geometro-stochastic concepts that are specifically designed for the systematic description of that underlying quantum reality, by developing the conceptual and mathematical tools that are most appropriate for such a use.
International Nuclear Information System (INIS)
Kondaiah, P; Shankar, K; Ganesan, N
2013-01-01
In this paper, a multiphase magneto–electro–elastic (MEE) cylindrical shell is investigated under thermal environments using semi-analytical finite element procedures. The main aim of this paper is to study the pyroelectric and pyromagnetic effects on multiphase MEE cylindrical shells subjected to a uniform axisymmetric temperature of 50 K under different boundary conditions. This numerical study is mainly focused on the pyroelectric and pyromagnetic effects on system parameters such as thermal displacements, thermal stresses, electric potential, magnetic potential, electric displacements and magnetic flux densities. It is found that there is a significant increase in electric potential due to the pyroelectric and pyromagnetic effects under clamped–free boundary conditions. (paper)
A numerical study of two-phase Stokes flow in an axisymmetric flow-focusing device
DEFF Research Database (Denmark)
Jensen, Mads Jakob; Stone, H.A.; Bruus, Henrik
2006-01-01
We present a numerical investigation of the time-dependent dynamics of the creation of gas bubbles in an axisymmetric flow-focusing device. The liquid motion is treated as a Stokes flow, and using a generic framework we implement a second-order time-integration scheme and a free-surface model...... in MATLAB, which interfaces with the finite-element software FEMLAB. We derive scaling laws for the volume of a created bubble and for the gas flow rate, and confirm them numerically. Our results are consistent with existing experimental results by Garstecki et al. [Phys. Rev. Lett. 94, 164501 (2005...
Vortex breakdown simulation - A circumspect study of the steady, laminar, axisymmetric model
Salas, M. D.; Kuruvila, G.
1989-01-01
The incompressible axisymmetric steady Navier-Stokes equations are written using the streamfunction-vorticity formulation. The resulting equations are discretized using a second-order central-difference scheme. The discretized equations are linearized and then solved using an exact LU decomposition, Gaussian elimination, and Newton iteration. Solutions are presented for Reynolds numbers (based on vortex core radius) 100-1800 and swirl parameter 0.9-1.1. The effects of inflow boundary conditions, the location of farfield and outflow boundaries, and mesh refinement are examined. Finally, the stability of the steady solutions is investigated by solving the time-dependent equations.
Directory of Open Access Journals (Sweden)
Ap Kuiroukidis
2018-01-01
Full Text Available We consider a generalized Grad–Shafranov equation (GGSE in a triangularity-deformed axisymmetric toroidal coordinate system and solve it numerically for the generic case of ITER-like and JET-like equilibria with non-parallel flow. It turns out that increase of the triangularity improves confinement by leading to larger values of the toroidal beta and the safety factor. This result is supported by the application of a criterion for linear stability valid for equilibria with flow parallel to the magnetic field. Also, the parallel flow has a weaker stabilizing effect.
DUGDALE-MAUGIS ADHESIVE NORMAL CONTACT OF AXISYMMETRIC POWER-LAW GRADED ELASTIC BODIES
Directory of Open Access Journals (Sweden)
Emanuel Willert
2018-02-01
Full Text Available A closed-form general analytic solution is presented for the adhesive normal contact of convex axisymmetric power-law graded elastic bodies using a Dugdale-Maugis model for the adhesive stress. The case of spherical contacting bodies is studied in detail. The known JKR- and DMT-limits can be derived from the general solution, whereas the transition between both can be captured introducing a generalized Tabor parameter depending on the material grading. The influence of the Tabor parameter and the material grading is studied.
On the blow-up problem for the axisymmetric 3D Euler equations
International Nuclear Information System (INIS)
Chae, Dongho
2008-01-01
In this paper we study the finite time blow-up problem for the axisymmetric 3D incompressible Euler equations with swirl. The evolution equations for the deformation tensor and the vorticity are reduced considerably in this case. Under the assumption of local minima for the pressure on the axis of symmetry with respect to the radial variations we show that the solution blows up in finite time. If we further assume that the second radial derivative vanishes on the axis, then the system reduces to the form of Constantin–Lax–Majda equations and can be integrated explicitly
International Nuclear Information System (INIS)
Frater, J.; Lestingi, J.; Padovan, J.
1977-01-01
This paper describes the development of an improved semi-analytical finite element for the stress analysis of anisotropic axisymmetric solids subjected to nonsymmetric loads. Orthogonal functions in the form of finite Fourier exponential transforms, which satisfy the equations of equilibrium of the theory of elasticity for an anisotropic solid of revolution, are used to expand the imposed loadings and displacement field. It is found that the orthogonality conditions for the assumed solution reduce the theta-dependency, thus reducing the three dimensional problem to an infinite series of two dimensional problems. (Auth.)
Qayyum, Mubashir; Khan, Hamid; Rahim, M Tariq; Ullah, Inayat
2015-01-01
The aim of this article is to model and analyze an unsteady axisymmetric flow of non-conducting, Newtonian fluid squeezed between two circular plates passing through porous medium channel with slip boundary condition. A single fourth order nonlinear ordinary differential equation is obtained using similarity transformation. The resulting boundary value problem is solved using Homotopy Perturbation Method (HPM) and fourth order Explicit Runge Kutta Method (RK4). Convergence of HPM solution is verified by obtaining various order approximate solutions along with absolute residuals. Validity of HPM solution is confirmed by comparing analytical and numerical solutions. Furthermore, the effects of various dimensionless parameters on the longitudinal and normal velocity profiles are studied graphically.
Analysis of Unsteady Axisymmetric Squeezing Fluid Flow with Slip and No-Slip Boundaries Using OHAM
Directory of Open Access Journals (Sweden)
Mubashir Qayyum
2015-01-01
Full Text Available In this manuscript, An unsteady axisymmetric flow of nonconducting, Newtonian fluid squeezed between two circular plates is studied with slip and no-slip boundaries. Using similarity transformation, the system of nonlinear partial differential equations is reduced to a single fourth order ordinary differential equation. The resulting boundary value problems are solved by optimal homotopy asymptotic method (OHAM and fourth order explicit Runge-Kutta method (RK4. It is observed that the results obtained from OHAM are in good agreement with numerical results by means of residuals. Furthermore, the effects of various dimensionless parameters on the velocity profiles are investigated graphically.
The surface effect on axisymmetric wave propagation in piezoelectric cylindrical shells
Directory of Open Access Journals (Sweden)
Yunying Zhou
2015-02-01
Full Text Available Based on the surface piezoelectricity theory and first-order shear deformation theory, the surface effect on the axisymmetric wave propagating in piezoelectric cylindrical shells is analyzed. The Gurtin–Murdoch theory is utilized to get the nontraditional boundary conditions and constitutive equations of the surface, in company with classical governing equations of the bulk, from which the basic formulations are obtained. Numerical results show that the surface layer has a profound effect on wave characteristics in nanostructure at a higher mode.
Enhanced understanding of non-axisymmetric intrinsic and controlled field impacts in tokamaks
In, Y.; Park, J.-K.; Jeon, Y. M.; Kim, J.; Park, G. Y.; Ahn, J.-W.; Loarte, A.; Ko, W. H.; Lee, H. H.; Yoo, J. W.; Juhn, J. W.; Yoon, S. W.; Park, H.; Physics Task Force in KSTAR, 3D
2017-11-01
An extensive study of intrinsic and controlled non-axisymmetric field (δB) impacts in KSTAR has enhanced the understanding about non-axisymmetric field physics and its implications, in particular, on resonant magnetic perturbation (RMP) physics and power threshold (P th) for L-H transition. The n = 1 intrinsic non-axisymmetric field in KSTAR was measured to remain as low as δB/B 0 ~ 4 × 10-5 even at high-beta plasmas (β N ~ 2), which corresponds to approximately 20% below the targeted ITER tolerance level. As for the RMP edge-localized-modes (ELM) control, robust n = 1 RMP ELM-crash-suppression has been not only sustained for more than ~90 τ E, but also confirmed to be compatible with rotating RMP. An optimal window of radial position of lower X-point (i.e. R x = 1.44+/- 0.02 m) proved to be quite critical to reach full n = 1 RMP-driven ELM-crash-suppression, while a constraint of the safety factor could be relaxed (q 95 = 5 +/- 0.25). A more encouraging finding was that even when R x cannot be positioned in the optimal window, another systematic scan in the vicinity of the previously optimal R x allows for a new optimal window with relatively small variations of plasma parameters. Also, we have addressed the importance of optimal phasing (i.e. toroidal phase difference between adjacent rows) for n = 1 RMP-driven ELM control, consistent with an ideal plasma response modeling which could predict phasing-dependent ELM suppression windows. In support of ITER RMP study, intentionally misaligned RMPs have been found to be quite effective during ELM-mitigation stage in lowering the peaks of divertor heat flux, as well as in broadening the ‘wet’ areas. Besides, a systematic survey of P th dependence on non-axisymmetric field has revealed the potential limit of the merit of low intrinsic non-axisymmetry. Considering that the ITER RMP coils are composed of 3-rows, just like in KSTAR, further 3D
Numerical study of stress concentration in localized axisymmetric thinnings in shells and plates
International Nuclear Information System (INIS)
Neoberdin, Yu.A.; Maslenok, B.A.; Borintsev, A.B.; Egorov, M.F.; Shvetsov, A.V.
1981-01-01
Based on the method of finite elements and that of central composition orthogonal planning, regression equations are obtained for stress concentration coefficients for three different forms of localized thinning of a ring plate subjected to axisymmetric tension. The equations obtained allow the stress concentration coefficients to be determined in a plate and with a sufficient accuracy for practice, in shells over a wide range of changes in the hollow depth, grinding spot diameter and the plate or shell thickness. Recommendations are given as to the hollow shape securing the least stress concentration
Antenna design for microwave hepatic ablation using an axisymmetric electromagnetic model
Directory of Open Access Journals (Sweden)
Converse Mark C
2006-02-01
Full Text Available Abstract Background An axisymmetric finite element method (FEM model was employed to demonstrate important techniques used in the design of antennas for hepatic microwave ablation (MWA. To effectively treat deep-seated hepatic tumors, these antennas should produce a highly localized specific absorption rate (SAR pattern and be efficient radiators at approved generator frequencies. Methods and results As an example, a double slot choked antenna for hepatic MWA was designed and implemented using FEMLAB™ 3.0. Discussion This paper emphasizes the importance of factors that can affect simulation accuracy, which include boundary conditions, the dielectric properties of liver tissue, and mesh resolution.
Two-point boundary value and Cauchy formulations in an axisymmetrical MHD equilibrium problem
International Nuclear Information System (INIS)
Atanasiu, C.V.; Subbotin, A.A.
1999-01-01
In this paper we present two equilibrium solvers for axisymmetrical toroidal configurations, both based on the expansion in poloidal angle method. The first one has been conceived as a two-point boundary value solver in a system of coordinates with straight field lines, while the second one uses a well-conditioned Cauchy formulation of the problem in a general curvilinear coordinate system. In order to check the capability of our moment methods to describe equilibrium accurately, a comparison of the moment solutions with analytical solutions obtained for a Solov'ev equilibrium has been performed. (author)
Turbulent properties of axisymmetric shock-wave/boundary-layer interaction flows
Brown, J. L.; Kussoy, M. I.; Coakley, T. J.
1986-01-01
A combined experimental and computational investigation of an axisymmetric turbulent shock-wave boundary-layer interaction flow is presented. Experimental measurements include both mean and fluctuating data obtained by LDV techniques and identify large scale unsteady motions associated with shock induced separation. Computations using the compressible Navier-Stokes equations, and a two-equation turbulence model are in relatively good agreement with experimental measurements. It is found that the large scale unsteady motions do not appear to have a critical impact on the ability to compute the mean properties of the flows investigated in this paper.
Adverse consequences of a moving vacuum-plasma boundary on axisymmetric ac helicity injection
International Nuclear Information System (INIS)
Bellan, P.M.
1986-01-01
The recent prediction of Liewer, Gould, and Bellan that a moving plasma-vacuum boundary significantly lowers the effectiveness of ac helicity injection is generalized by resolution of the apparent discrepancy between the helicity-conservation equations of Jensen and Chu and of Moffatt. It is shown that, if there are axisymmetric circular flux surfaces and a moving vacuum-plasma boundary, the helicity injected by oscillating fields (if net injection occurs) is simply consumed by an increase in helicity dissipation due to the same oscillating fields
Axisymmetric thermoviscoelastoplastic state of thin laminated shells made of a damageable material
Galishin, A. Z.
2008-04-01
A technique for the determination of the axisymmetric thermoviscoelastoplastic state of laminated thin shells made of a damageable material is developed. The technique is based on the kinematic equations of the theory of thin shells that account for transverse shear strains. The thermoviscoplastic equations, which describe the deformation of a shell element along paths of small curvature, are used as the constitutive equations. The equivalent stress that appears in the kinetic equations of damage and creep is determined from a failure criterion that accounts for the stress mode. The thermoviscoplastic deformation of a two-layer shell that models an element of a rocket engine nozzle is considered as an example
An axisymmetric evolution code for the Einstein equations on hyperboloidal slices
International Nuclear Information System (INIS)
Rinne, Oliver
2010-01-01
We present the first stable dynamical numerical evolutions of the Einstein equations in terms of a conformally rescaled metric on hyperboloidal hypersurfaces extending to future null infinity. Axisymmetry is imposed in order to reduce the computational cost. The formulation is based on an earlier axisymmetric evolution scheme, adapted to time slices of constant mean curvature. Ideas from a previous study by Moncrief and the author are applied in order to regularize the formally singular evolution equations at future null infinity. Long-term stable and convergent evolutions of Schwarzschild spacetime are obtained, including a gravitational perturbation. The Bondi news function is evaluated at future null infinity.
KEMAJUAN BELAJAR SISWA PADA GEOMETRI TRANSFORMASI MENGGUNAKAN AKTIVITAS REFLEKSI GEOMETRI
Directory of Open Access Journals (Sweden)
Irkham Ulil Albab
2014-10-01
Full Text Available Abstrak: Penelitian ini bertujuan untuk mendeskripsikan kemajuan belajar siswa pada materi geometri transformasi yang didukung dengan serangkaian aktivitas belajar berdasarkan Pendidikan Matematika Realistik Indonesia. Penelitian didesain melalui tiga tahap, yaitu tahapan perancangan desain awal, pengujian desain melalui pembelajaran awal dan pembelajaran eksperimental, dan tahap analisis retrospektif. Dalam penelitian ini, Hypothetical Learning Trajectory, HLT (HLT berperan penting sebagai desain pembelajaran sekaligus instrumen penelitian. HLT diujikan terhadap 26 siswa kelas VII. Data dikumpulkan dengan teknik wawancara, pengamatan, dan catatan lapangan. Hasil penelitian menunjukkan bahwa desain pembelajaran ini mampu menstimulasi siswa untuk memberikan karakteristik refleksi dan transformasi geometri lainnya secara informal, mengklasifikasikannya dalam transformasi isometri pada level kedua, dan menemukan garis bantuan refleksi pada level yang lebih formal. Selain itu, garis bantuan refleksi digunakan oleh siswa untuk menggambar bayangan refleksi dan pola pencerminan serta memahami bentuk rotasi dan translasi sebagai kombinasi refleksi adalah level tertinggi. Keyword: transformasi geometri, kombinasi refleksi, rotasi, translasi, design research, HLT STUDENTS’ LEARNING PROGRESS ON TRANSFORMATION GEOMETRY USING THE GEOMETRY REFLECTION ACTIVITIES Abstract: This study was aimed at describing the students’ learning progress on transformation geometry supported by a set of learning activities based on Indonesian Realistic Mathematics Education. The study was designed into three stages, that is, the preliminary design stage, the design testing through initial instruction and experiment, and the restrospective analysis stage. In this study, Hypothetical Learning Trajectory (HLT played an important role as an instructional design and a research instrument. HLT was tested to 26 seventh grade students. The data were collected through interviews
Geometry, topology, and string theory
Energy Technology Data Exchange (ETDEWEB)
Varadarajan, Uday [Univ. of California, Berkeley, CA (United States)
2003-01-01
A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect. In particular, situations in which extra dimensions, non-commutative geometries as well as other non-local structures emerge are explored in detail. Further, a preliminary exploration of such issues in Lorentzian space-times with non-trivial causal structures within string theory is initiated.
Stochastic geometry and its applications
Chiu, Sung Nok; Kendall, Wilfrid S; Mecke, Joseph
2013-01-01
An extensive update to a classic text Stochastic geometry and spatial statistics play a fundamental role in many modern branches of physics, materials sciences, engineering, biology and environmental sciences. They offer successful models for the description of random two- and three-dimensional micro and macro structures and statistical methods for their analysis. The previous edition of this book has served as the key reference in its field for over 18 years and is regarded as the best treatment of the subject of stochastic geometry, both as a subject with vital a
Introduction to topology and geometry
Stahl, Saul
2014-01-01
An easily accessible introduction to over three centuries of innovations in geometry Praise for the First Edition ". . . a welcome alternative to compartmentalized treatments bound to the old thinking. This clearly written, well-illustrated book supplies sufficient background to be self-contained." -CHOICE This fully revised new edition offers the most comprehensive coverage of modern geometry currently available at an introductory level. The book strikes a welcome balance between academic rigor and accessibility, providing a complete and cohesive picture of the science with an unparallele
Graphical debugging of combinational geometry
International Nuclear Information System (INIS)
Burns, T.J.; Smith, M.S.
1992-01-01
A graphical debugger for combinatorial geometry being developed at Oak Ridge National Laboratory is described. The prototype debugger consists of two parts: a FORTRAN-based ''view'' generator and a Microsoft Windows application for displaying the geometry. Options and features of both modules are discussed. Examples illustrating the various options available are presented. The potential for utilizing the images produced using the debugger as a visualization tool for the output of the radiation transport codes is discussed as is the future direction of the development
Combinatorial geometry in the plane
Hadwiger, Hugo; Klee, Victor
2014-01-01
Geared toward advanced undergraduates familiar with analysis and college geometry, this concise book discusses theorems on topics restricted to the plane such as convexity, coverings, and graphs. In addition to helping students cultivate rigorous thought, the text encourages the development of mathematical intuition and clarifies the nature of mathematical research.The two-part treatment begins with specific topics including integral distances, covering problems, point set geometry and convexity, simple paradoxes involving point sets, and pure combinatorics, among other subjects. The second pa
Modern differential geometry for physicists
Isham, C J
1989-01-01
These notes are the content of an introductory course on modern, coordinate-free differential geometry which is taken by the first-year theoretical physics PhD students, or by students attending the one-year MSc course "Fundamental Fields and Forces" at Imperial College. The book is concerned entirely with mathematics proper, although the emphasis and detailed topics have been chosen with an eye to the way in which differential geometry is applied these days to modern theoretical physics. This includes not only the traditional area of general relativity but also the theory of Yang-Mills fields
Algebraic geometry and theta functions
Coble, Arthur B
1929-01-01
This book is the result of extending and deepening all questions from algebraic geometry that are connected to the central problem of this book: the determination of the tritangent planes of a space curve of order six and genus four, which the author treated in his Colloquium Lecture in 1928 at Amherst. The first two chapters recall fundamental ideas of algebraic geometry and theta functions in such fashion as will be most helpful in later applications. In order to clearly present the state of the central problem, the author first presents the better-known cases of genus two (Chapter III) and
Geometry, topology, and string theory
International Nuclear Information System (INIS)
Varadarajan, Uday
2003-01-01
A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect. In particular, situations in which extra dimensions, non-commutative geometries as well as other non-local structures emerge are explored in detail. Further, a preliminary exploration of such issues in Lorentzian space-times with non-trivial causal structures within string theory is initiated
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...
Teaching Activity-Based Taxicab Geometry
Ada, Tuba
2013-01-01
This study aimed on the process of teaching taxicab geometry, a non-Euclidean geometry that is easy to understand and similar to Euclidean geometry with its axiomatic structure. In this regard, several teaching activities were designed such as measuring taxicab distance, defining a taxicab circle, finding a geometric locus in taxicab geometry, and…
VARR2 VARRLXSG, 2-D Transient Fluid Flow and Heat Transfer in X-Y and Cylindrical Geometry
International Nuclear Information System (INIS)
Cook, J. L.; Nakayama, P. I.; Andreychek, T.
1980-01-01
1 - Description of problem or function: VARR2 is a two-dimensional transient slightly-compressible fluid dynamics program. It solves the complete unsteady Navier-Stokes equation, the energy equation, and the continuity equation in either Cartesian or axisymmetric cylindrical geometry. Slight density variations are accounted for by use of the Boussinesq approximation, which couples the energy and momentum equations. At a cell face, the normal velocity component may be inward, outward, or zero; the tangential velocity component may specify free slip, no slip, or no slip with a turbulent velocity profile. For heat transfer problems, adiabatic or constant heat flux boundary conditions can be specified. By specifying the totality of cell-face boundary conditions in a self-consistent manner, the user can specify a wide spectrum of overall boundary conditions; for example, those called rigid, continuative, periodic, inflow/outflow, or derived. 2 - Method of solution: The governing differential equations are replaced by finite difference equations of explicit type and solved over a region of fixed rectangular cells by using the simplified marker and cell technique (SMAC) of Amsden and Harlow. The continuity equation is solved through a successive over- relaxation (SOR) iterative process on a Poisson equation for pressure. 3 - Restrictions on the complexity of the problem: With current dimensioning, the maximum number of cells is about 1600; roughly a 40 x 40 mesh. The problem geometry must be reasonably approximated by a two-dimensional net of rectangular cells, either in Cartesian geometry or transformed from axisymmetric cylindrical geometry. Interior obstacles are allowed. The working fluid may be specified as either sodium or water if the built-in material property coefficients are used. Otherwise, the properties of the working fluid may be entered as part of the problem input
African Journals Online (AJOL)
DR. AMINU
ABSTRACT. The manganese (II), cobalt (II), nickel (II) and copper (II) complexes of N, N' – bis(benzoin)ethylenediiminato have been prepared and characterized by infrared, elemental analysis, conductivity measurements and solubility. The potentiometric, and elemental analyses studies of the complexes revealed 1:1 ...
Non-Ideal ELM Stability and Non-Axisymmetric Field Penetration Calculations with M3D-C1
Ferraro, N. M.; Chu, M. S.; Snyder, P. B.; Jardin, S. C.; Luo, X.
2009-11-01
Numerical studies of ELM stability and non-axisymmetric field penetration in diverted DIII-D and NSTX equilibria are presented, with resistive and finite Larmor radius effects included. These results are obtained with the nonlinear two-fluid code M3D-C1, which has recently been extended to allow linear non-axisymmetric calculations. Benchmarks of M3D-C1 with ideal codes ELITE and GATO show good agreement for the linear stability of peeling-ballooning modes in the ideal limit. New calculations of the resistive stability of ideally stable DIII-D equilibria are presented. M3D-C1 has also been used to calculate the linear response to non-axisymmetric external fields; these calculations are benchmarked with Surfmn and MARS-F. New numerical methods implemented in M3D-C1 are presented, including the treatment of boundary conditions with C^1 elements in a non-rectangular mesh.
Axiomatic characterization of physical geometry
International Nuclear Information System (INIS)
Schmidt, H.J.
1979-01-01
This book deals with the foundations of a theory which can be considered as the most ancient part of physics, namely Euclidean geometry. It may be viewed as a partial realization of a program set up by G. Ludwig who suggested to formulate geometry explicity as a theory of possible operations with practically rigid bodies, using as basic concepts 'region', 'inclusion' and 'transport'. After an introduction to the problems, in which we sketch also the historical development, we develop a pre-theory with respect to the geometry with the aim to give an interpretation of the above-mentioned basic geometrical concepts in terms of notions which are closely related to experimental situations. The passage from a pure topological analysis of physical space to the differential geometrical view is made in the next section where we use the prerequisites established in the previous chapter to apply the Tits/Freudenthal solution of the Helmholtz-Lie problem. The main theorem of this book is stated in the last section by a characterization of Euclidean geometry. It turns out that two additional postulates are necessary whose empirical meaning we stress by referring to the axiom of dimension. The book might be of interest to scientist working in the field of axiomatics. Unfamiliar readers will be required to have a sound knowledge of topology and group theory. (HJ) 891 HJ/HJ 892 MB
Algebraic Methods in Plane Geometry
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 13; Issue 10. Algebraic Methods in Plane Geometry - The Use of Conic Sections. Shailesh A Shirali. General Article Volume 13 Issue 10 October 2008 pp 916-928. Fulltext. Click here to view fulltext PDF. Permanent link:
Multivariable calculus and differential geometry
Walschap, Gerard
2015-01-01
This text is a modern in-depth study of the subject that includes all the material needed from linear algebra. It then goes on to investigate topics in differential geometry, such as manifolds in Euclidean space, curvature, and the generalization of the fundamental theorem of calculus known as Stokes' theorem.
Stochastic Modelling of River Geometry
DEFF Research Database (Denmark)
Sørensen, John Dalsgaard; Schaarup-Jensen, K.
1996-01-01
Numerical hydrodynamic river models are used in a large number of applications to estimate critical events for rivers. These estimates are subject to a number of uncertainties. In this paper, the problem to evaluate these estimates using probabilistic methods is considered. Stochastic models for ...... for river geometries are formulated and a coupling between hydraulic computational methods and numerical reliability methods is presented....
GEOMETRY AND COMPLEXITY IN ARCHITECTURE
Directory of Open Access Journals (Sweden)
RUSU Maria Ana
2015-06-01
Full Text Available As Constantin Brancuși (1876-1956 said „Simplicity is complexity itself“, simplicity and regularity through the use of basic geometric forms has always played a central role in architectural design, during the 20th century. A diachronic perspective, shows as the use of geometry and mathematics to describe built form provided a common basis for communication between the processes of design, fabrication and stability. Classic ways of representing geometry, based on descriptive methods, favor precise language of bidimensionality easy to represent in a rectangular coordinate system. In recent years, the importance of geometry has been re-emphasized by significant advances in the digital age, where computers are increasingly used in design, fabrication and construction to explore the art of the possible. Contemporary architecture transcend the limitations of Euclidean geometry and create new forms that are emerging through the convergence of complex systems, computational design and robotic fabrication devices, but which can also achieve higher levels of performance. Freeform architectural shapes and structures play an increasingly important role in 21st century architectural design. Through a series of examples, the paper relates to contemporary architectural explorations of complex, curvilinear surfaces in the digital age and discusses how it has required rethinking the mode in which we traditionally operate as architects. The analysis creates the possibility of comparisons between original and current design.
Signature geometry and quantum engineering
Samociuk, Stefan
2013-09-01
As the operating frequency of electromagnetic based devices increase, physical design geometry is playing an ever more important role. Evidence is considered in support of a relationship between the dimensionality of primitive geometric forms, such as transistors, and corresponding electromagnetic coupling efficiency. The industry of electronics is defined as the construction of devices by the patterning of primitive forms to physical materials. Examples are given to show the evolution of these primitives, down to nano scales, are requiring exacting geometry and three dimensional content. Consideration of microwave monolithic integrated circuits,(MMIC), photonics and metamaterials,(MM), support this trend and also add new requirements of strict geometric periodicity and multiplicity. Signature geometries,(SG), are characterized by distinctive attributes and examples are given. The transcendent form transcode algorithm, (TTA) is introduced as a multi dimensional SG and its use in designing photonic integrated circuits and metamaterials is discussed . A creative commons licensed research database, TRANSFORM, containing TTA geometries in OASIS file formats is described. An experimental methodology for using the database is given. Multidimensional SG and extraction of three dimensional cross sections as primitive forms is discussed as a foundation for quantum engineering and the exploitation of phenomena other than the electromagnetic.
Exploring Bundling Theory with Geometry
Eckalbar, John C.
2006-01-01
The author shows how instructors might successfully introduce students in principles and intermediate microeconomic theory classes to the topic of bundling (i.e., the selling of two or more goods as a package, rather than separately). It is surprising how much students can learn using only the tools of high school geometry. To be specific, one can…
Generative CAI in Analytical Geometry.
Uttal, William R.; And Others
A generative computer-assisted instruction system is being developed to tutor students in analytical geometry. The basis of this development is the thesis that a generative teaching system can be developed by establishing and then stimulating a simplified, explicit model of the human tutor. The goal attempted is that of a computer environment…
Stochastic Modelling of River Geometry
DEFF Research Database (Denmark)
Sørensen, John Dalsgaard; Schaarup-Jensen, K.
1996-01-01
Numerical hydrodynamic river models are used in a large number of applications to estimate critical events for rivers. These estimates are subject to a number of uncertainties. In this paper, the problem to evaluate these estimates using probabilistic methods is considered. Stochastic models...... for river geometries are formulated and a coupling between hydraulic computational methods and numerical reliability methods is presented....
M. Deza; M. Laurent (Monique)
1997-01-01
htmlabstractCuts and metrics are well-known objects that arise - independently, but with many deep and fascinating connections - in diverse fields: in graph theory, combinatorial optimization, geometry of numbers, combinatorial matrix theory, statistical physics, VLSI design etc. This book offers a
Analogical Reasoning in Geometry Education
Magdas, Ioana
2015-01-01
The analogical reasoning isn't used only in mathematics but also in everyday life. In this article we approach the analogical reasoning in Geometry Education. The novelty of this article is a classification of geometrical analogies by reasoning type and their exemplification. Our classification includes: analogies for understanding and setting a…
Matter in toy dynamical geometries
Konopka, T.J.
2009-01-01
One of the objectives of theories describing quantum dynamical geometry is to compute expectation values of geometrical observables. The results of such computations can be affected by whether or not matter is taken into account. It is thus important to understand to what extent and to what effect
Complex Numbers and Plane Geometry
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 13; Issue 1. Complex Numbers and Plane Geometry. Anant R Shastri. General Article Volume 13 Issue 1 January 2008 pp 35-53. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/013/01/0035-0053. Keywords.
Learners engaging with transformation geometry
African Journals Online (AJOL)
Grade 12, learners would have been exposed to both visual and analytical strategies. The visual approach is one ... movement), dynamic imagery, memory images and pattern imagery. She found that concrete .... the visual and analytic modes of thinking when working with transformation geometry? We hope then to set out ...
General Relativity: Geometry Meets Physics
Thomsen, Dietrick E.
1975-01-01
Observing the relationship of general relativity and the geometry of space-time, the author questions whether the rest of physics has geometrical explanations. As a partial answer he discusses current research on subatomic particles employing geometric transformations, and cites the existence of geometrical definitions of physical quantities such…
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.
Nonlinear to Linear Elastic Code Coupling in 2-D Axisymmetric Media.
Energy Technology Data Exchange (ETDEWEB)
Preston, Leiph [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2017-08-01
Explosions within the earth nonlinearly deform the local media, but at typical seismological observation distances, the seismic waves can be considered linear. Although nonlinear algorithms can simulate explosions in the very near field well, these codes are computationally expensive and inaccurate at propagating these signals to great distances. A linearized wave propagation code, coupled to a nonlinear code, provides an efficient mechanism to both accurately simulate the explosion itself and to propagate these signals to distant receivers. To this end we have coupled Sandia's nonlinear simulation algorithm CTH to a linearized elastic wave propagation code for 2-D axisymmetric media (axiElasti) by passing information from the nonlinear to the linear code via time-varying boundary conditions. In this report, we first develop the 2-D axisymmetric elastic wave equations in cylindrical coordinates. Next we show how we design the time-varying boundary conditions passing information from CTH to axiElasti, and finally we demonstrate the coupling code via a simple study of the elastic radius.
Directory of Open Access Journals (Sweden)
XING Junhua
2017-12-01
Full Text Available [Objectives] In order to study the underwater jet noise characteristics,[Methods] the Lighthill acoustic analogy is carried out to compute the underwater free jet flow sound field characteristic of axisymmetric nozzle, with applying of FLUENT simulation software and large eddy simulation, the real flow field of submerged axisymmetric nozzle is simulated, and the jet noise is measured by the reverberation method.[Results] The results show that the core length of steady flow field is independent of flow rate, and the length is about 8 times the diameter of the nozzle. The radiation power of jet noise is proportional to the velocity of eight times. The power spectrum of jet noise is different with the flow velocity in the low frequency. In the high frequency, the difference is significantly reduced. The radiated noise energy is mainly concentrated in the low frequency. With the increase of flow velocity, the main contribution of jet noise moves to high frequency.[Conclusions] In terms of computing simulation of jet noise, the large eddy simulation and Lighthill acoustic analogy combined analysis is an effective means.
Topologically nontrivial solutions to Yang-Mills equations with axisymmetric external sources
Isidro Filho, M. P.; Kerman, A. K.; Trottier, Howard D.
1989-12-01
We present a new set of solutions to Yang-Mills equations with axially symmetric external charge sources. Our solutions for the gauge fields are not explicitly axisymmetric, but the noninvariance of the fields under a rotation about the symmetry axis can be compensated by a gauge transformation about a symmetry axis in gauge space. All gauge-invariant quantities are therefore axisymmetric. Our solutions are characterized by a gauge-invariant integer winding number n, and all winding numbers are allowed. We prove that the total gauge-invariant charge of the system (source plus gauge fields) vanishes identically in our solutions for n≠0, even if the source has net charge. We explicitly solve the equations of motion for a spherical shell of charge. The solution depends on the gauge coupling g, the total charge of the shell QS, and the topological number n. We use perturbative methods to obtain the solution in closed form for α¯==g2QS/(4π)g2Q2S/(8πa)]×1/(2+1), where a is the radius of the shell. Using relaxation methods to find the exact solution to the equations of motion numerically for arbitrary α¯, we establish that this bound is satisfied for all g, QS, and n.
Characterization of a medium-sized washer-gun for an axisymmetric mirror
Yi, Hongshen; Liu, Ming; Shi, Peiyun; Yang, Zhida; Zhu, Guanghui; Lu, Quanming; Sun, Xuan
2018-04-01
A new medium-sized washer gun is developed for a plasma start-up in a fully axisymmetric mirror. The gun is positioned at the east end of the Keda Mirror with AXisymmetricity facility and operated in the pulsed mode with an arc discharging time of 1.2 ms and a typical arc current of 8.5 kA with 1.5 kV discharge voltage. To optimize the operation, a systematic scan of the neutral pressure, the arc voltage, the bias voltage on a mesh grid 6 cm in front of the gun and an end electrode located on the west end of mirror, and the mirror ratio was performed. The streaming plasma was measured with triple probes in the three mirror cells and a diamagnetic loop in the central cell. Floating potential measurements suggest that the plasma could be divided into streaming and mirror-confined plasmas. The floating potential for the streaming plasma is negative, with an electric field pointing inwards. The mirror-confined plasma has a typical lifetime of 0.5 ms.
Equilibrium and ballooning mode stability of an axisymmetric tensor pressure tokamak
International Nuclear Information System (INIS)
Cooper, W.A.; Bateman, G.; Nelson, D.B.; Kammash, T.
1980-08-01
A force balance relation, a representation for the poloidal beta (β/sub p/), and expressions for the current densities are derived from the MHD equilibrium relations for an axisymmetric tensor pressure tokamak. Perpendicular and parallel beam pressure components are evaluated from a distribution function that models high energy neutral particle injection. A double adiabatic energy principle is derived from that of Kruskal and Oberman, with correction terms added. The energy principle is then applied to an arbitrary cross-section axisymmetric tokamak to examine ballooning instabilities of large toroidal mode number. The resulting Euler equation is remarkably similar to that of ideal MHD. Although the field-bending term is virtually unaltered, the driving term is modified because the pressures are no longer constant on a flux surface. Either a necessary or a sufficient marginal stability criterion for a guiding center plasma can be derived from this equation whenever an additional stabilizing element unique to the double adiabatic theory is either kept or neglected, respectively
Developing 1D MM of Axisymmetric Transient Quenched Chromium Steel to Determine LHP
Directory of Open Access Journals (Sweden)
Abdlmanam S. A. Elmaryami
2012-01-01
Full Text Available The modelling of an axisymmetric industrial quenched chromium steel bar AISI-SAE 8650H based on finite element method has been produced to investigate the impact of process history on metallurgical and material properties. Mathematical modelling of 1-dimensional line (radius element axisymmetric model has been adopted to predict temperature history and consequently the hardness of the quenched steel bar at any point (node. The lowest hardness point (LHP is determined. In this paper hardness in specimen points was calculated by the conversion of calculated characteristic cooling time for phase transformation t8/5 to hardness. The model can be employed as a guideline to design cooling approach to achieve desired microstructure and mechanical properties such as hardness. The developed mathematical model is converted to a computer program. This program can be used independently or incorporated into a temperature history calculator to continuously calculate and display temperature history of the industrial quenched steel bar and thereby calculate LHP. The developed program from the mathematical model has been verified and validated by comparing its hardness results with commercial finite element software results.
MHD stability analysis of axisymmetric surface current model tokamaks close to the spheromak regime
International Nuclear Information System (INIS)
Honma, Toshihisa; Kaji, Ikuo; Fukai, Ichiro; Kito, Masafumi.
1984-01-01
In the toroidal coordinates, a stability analysis is presented for very low-aspect-ratio tokamaks with circular cross section which is described by a surface current model (SCM) of axisymmetric equilibria. The energy principle determining the stability of plasma is treated without any expansion of aspect ratio. Numerical results show that, owing to the occurrence of the non-axisymmetric (n=1) unstable modes, there exists no MHD-stable ideal SCM spheromak characterized by zero external toroidal vacuum field. Instead, a stable spheromak-type plasma which comes to the ideal SCM spheromak is provided by the configuration with a very weak external toroidal field. Close to the spheromak regime (1.0 1 aspect ratio< = 1.1), the minimum safety factor and the critical β-values increase mo notonically with aspect ratio decreasing from a large value, and curves of βsub(p) versus β in the marginal stability approach to an ideal SCM spheromak line βsub(p)=β. (author)
Jet flow issuing from an axisymmetric pipe-cavity-orifice nozzle
Directory of Open Access Journals (Sweden)
Broučková Zuzana
2016-01-01
Full Text Available An axisymmetric air jet flow is experimentally investigated under passive flow control. The jet issues from a pipe of the inner diameter and length of 10 mm and 150 mm which is equipped with an axisymmetric cavity at the pipe end. The cavity operates as a resonator creating self-sustained acoustic excitations of the jet flow. A mechanism of excitations is rather complex – in comparison with a common Helmholtz resonator. The experiments were performed using flow visualization, microphone measurements and time-mean velocity measurements by the Pitot probe. The power spectral density (PSD and the sound pressure level (SPL were evaluated from microphone measurements. The jet Reynolds number ranged Re = 1600–18 000. Distinguishable peaks in PSD indicated a function of the resonator. Because the most effective acoustic response was found at higher Re, a majority of experiments focused on higher Re regime. The results demonstrate effects of the passive control on the jet behavior. Fluid mixing and velocity decay along the axis is intensified. It causes shortening of the jet transition region. On the other hand, an inverse proportionality of the velocity decay (u ~ 1/x in the fully developed region is not changed. The momentum and kinetic energy fluxes decrease more intensively in the controlled jets in comparison with common jets.
Finite analytic numerical solution axisymmetric Navier-Stokes and energy equations
International Nuclear Information System (INIS)
Chen, C.; Yoon, Y.H.
1983-01-01
Convective heat transfer for steady-state laminar flow in axisymmetric coordinates is considered. Numerical solutions for flow pattern and temperature distribution are obtained by the finite analytic numerical method applied to the Navier-Stokes equations expressed in terms of vorticity and stream function, and the energy equation. The finite analytic numerical method differs from other numerical methods in that it utilizes a local analytic solution in an element of the problem to construct the total numerical solution. Finite analytic solutions of vorticity, stream function, temperature, and heat transfer coefficients for flow with Reynolds numbers of 5, 100, 1000, and 2000, and Prandtl numbers of 0.1, 1.0, and 10.0 with uniform grid sizes, are reported for an axisymmetric pipe with a sudden expansion and contraction. The wall temperature is considered to be isothermal and differs from the inlet temperature. It is shown that the finite analytic is stable converges rapidly, and simulates the convection of fluid flow accurately, since the local analytic solution is capable of simulating automatically the influence of skewed convection through the element boundary on the interior nodal values, thereby minimizing the false numerical diffusion
International Nuclear Information System (INIS)
Hsieh, B.J.
1977-01-01
The instability of axisymmetric shells has been used in engineering fields as a safety device such as the rupture discs used in the LMFBR (Liquid Metal Fast Breeder Reactor) design to relieve the excessive pressure caused by the water and sodium reaction when there is a leak in the piping system. Hence, the analysis of the instability of shells under time varying loading is becoming more and more important. However, notorious discrepancy has been observed between various analytical predications and experimental results for the buckling of shells. Various theories have been proposed to explain these discrepancies. Most of these theories are concerned with two aspects: initial imperfections and asymmetric responses. Both theories do narrow the gap between theoretical and experimental results; however, the remaining discrepancy is still not small. Other possible causes of this discrepancy have to be studied- among them, the boundary conditions. It has been pointed out that the slip at the boundary may have noticeable effect on the transient behavior of a plate. In this paper, the effect of various boundary conditions on the dynamic instability of axisymmetric shells is studied using the numerical discretization technique--convective finite element method
Axisymmetric flow and heat transfer to modified second grade fluid over a radially stretching sheet
Directory of Open Access Journals (Sweden)
Masood Khan
Full Text Available In the present work, an analysis is made to the two-dimensional axisymmetric flow and heat transfer of a modified second grade fluid over an isothermal non-linear radially stretching sheet. The momentum and energy equations are modelled and the boundary layer equations are derived. The governing equations for velocity and temperature are turned down into a system of ordinary differential equations by invoking appropriate transformations which are then solved numerically via fourth and fifth order Runge-Kutta Fehlberg method. Moreover, the influence of the pertinent parameters namely the generalized second grade parameter, stretching parameter, the power-law index and the generalized Prandtl number is graphically portrayed. It is inferred that the generalized second grade parameter uplifted the momentum boundary layer while lessened the thermal boundary layer. Furthermore, the impact of stretching parameter is more pronounced for the second grade fluid (m = 0 in contrast with the power-law fluid (k = 0. For some special cases, comparisons are made with previously reported results and an excellent agreement is established. Keywords: Modified second grade fluid, Axisymmetric flow, Heat transfer, Non-linear stretching sheet
Field simulation of axisymmetric plasma screw pinches by alternating-direction-implicit methods
International Nuclear Information System (INIS)
Lambert, M.A.
1996-06-01
An axisymmetric plasma screw pinch is an axisymmetric column of ionized gaseous plasma radially confined by forces from axial and azimuthal currents driven in the plasma and its surroundings. This dissertation is a contribution to detailed, high resolution computer simulation of dynamic plasma screw pinches in 2-d rz-coordinates. The simulation algorithm combines electron fluid and particle-in-cell (PIC) ion models to represent the plasma in a hybrid fashion. The plasma is assumed to be quasineutral; along with the Darwin approximation to the Maxwell equations, this implies application of Ampere's law without displacement current. Electron inertia is assumed negligible so that advective terms in the electron momentum equation are ignored. Electrons and ions have separate scalar temperatures, and a scalar plasma electrical resistivity is assumed. Altemating-direction-implicit (ADI) methods are used to advance the electron fluid drift velocity and the magnetic fields in the simulation. The ADI methods allow time steps larger than allowed by explicit methods. Spatial regions where vacuum field equations have validity are determined by a cutoff density that invokes the quasineutral vacuum Maxwell equations (Darwin approximation). In this dissertation, the algorithm was first checked against ideal MM stability theory, and agreement was nicely demonstrated. However, such agreement is not a new contribution to the research field. Contributions to the research field include new treatments of the fields in vacuum regions of the pinch simulation. The new treatments predict a level of magnetohydrodynamic turbulence near the bulk plasma surface that is higher than predicted by other methods
Indian Academy of Sciences (India)
Limit: (of a sequence) A point such that the points of the sequence eventually approach it to within any previously specified distance. Some of the Greek mathematicians were quite confused! For example, let us take an empty cup and put it under a tap. Assume that it is half full in a minute. It is then 3/4-th full in another half.
Indian Academy of Sciences (India)
Huygens, Leibnitz and Newton. (independently) formulated the notion of curvature of a curve. (This was developed by Serret-Frenet into a multiplicity of invariants for curves in higher dimensions. We will concentrate on the curvature defined by Huygens et al). A line then becomes a curve of curvature zero. It is always ...
Indian Academy of Sciences (India)
As in art, understanding is enhanced by doing. Readers are encour- aged to attempt the exercises scattered in the text. The Origin (s). Origin: the starting point of a .... role to play In modem mathematics. Address {or correspondence. Kapil H Paranjape,. Indian Statistical Institute,. 8th Mile, Mysore Road,. Bangalore 560 059 ...
Indian Academy of Sciences (India)
In the previous article the author examined curves and surfaces. One might hope to continue by analogy in many dimensions. The concept of working in many dimensions is so bewildering (yet today so matter-of-course) that it needed the genius ofBemhard Riemann to show us exactly how it can be done. In just one lecture ...
Argatov, Ivan I.; Popov, Valentin L.
2016-08-01
The method of dimensionality reduction (MDR) is extended for the axisymmetric frictionless unilateral Hertz-type contact problem for a viscoelastic half-space and an arbitrary axisymmetric rigid indenter under the assumption that an arbitrarily evolving in time circular contact area remains singly connected during the whole process of indentation. In particular, the MDR is applied to study in detail the so-called rebound indentation problem, where the contact radius has a single maximum. It is shown that the obtained closed-form analytical solution for the rebound indentation displacement (recorded in the recovery phase, when the contact force vanishes) does not depend on the indenter shape.
CSIR Research Space (South Africa)
Snedden, Glen C
2010-06-01
Full Text Available The application of non-axisymmetric end walls in turbine stages has gained wide spread acceptance as a means to improve the performance of turbines in both power generation and aero-derivative applications. Non-axisymmetric end walls are aimed...
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.
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...
Coordinate geometry method for capturing and evaluating crown preparation geometry.
Tiu, Janine; Waddell, J Neil; Al-Amleh, Basil; Jansen van Vuuren, Wendy-Ann; Swain, Michael V
2014-09-01
A validated universal method requiring no human input is needed to capture and evaluate preparation geometries in a manner that can be used to see the correlation of different parameters. The purpose of this study was to present a method of capturing and evaluating crown preparation geometry. One manually machined acrylic resin block and 9 randomly selected preparations for ceramic complete crowns prepared by general dentists were selected and prepared. The specimens were scanned (3D scanner; Nobel Biocare), and buccolingual and mesiodistal cross section images were collected. The images were imported into digitizing software (Engauge Digitizer 4.1) to convert the outlines into x and y coordinates. Six points were chosen by using a set of algorithms, and the resulting parameters were calculated. The acrylic resin block was milled with a 12 degree total occlusal convergence (TOC) instrument producing a 12.83 degree TOC. For the other specimens, average TOC values ranged from 18 degrees to 52 degrees. The mean average margin width was 0.70 mm, and the mean average base dimension was 6.23 mm. The surface area/volume ratio, resistance length, and limiting taper were also calculated. The method described provides a basis for accurately evaluating preparation geometry without human input. Copyright © 2014 Editorial Council for the Journal of Prosthetic Dentistry. Published by Elsevier Inc. All rights reserved.
Fractal geometry and computer graphics
Sakas, Georgios; Peitgen, Heinz-Otto; Englert, Gabriele
1992-01-01
Fractal geometry has become popular in the last 15 years, its applications can be found in technology, science, or even arts. Fractal methods and formalism are seen today as a general, abstract, but nevertheless practical instrument for the description of nature in a wide sense. But it was Computer Graphics which made possible the increasing popularity of fractals several years ago, and long after their mathematical formulation. The two disciplines are tightly linked. The book contains the scientificcontributions presented in an international workshop in the "Computer Graphics Center" in Darmstadt, Germany. The target of the workshop was to present the wide spectrum of interrelationships and interactions between Fractal Geometry and Computer Graphics. The topics vary from fundamentals and new theoretical results to various applications and systems development. All contributions are original, unpublished papers.The presentations have been discussed in two working groups; the discussion results, together with a...
Groups and Geometries : Siena Conference
Kantor, William; Lunardon, Guglielmo; Pasini, Antonio; Tamburini, Maria
1998-01-01
On September 1-7, 1996 a conference on Groups and Geometries took place in lovely Siena, Italy. It brought together experts and interested mathematicians from numerous countries. The scientific program centered around invited exposi tory lectures; there also were shorter research announcements, including talks by younger researchers. The conference concerned a broad range of topics in group theory and geometry, with emphasis on recent results and open problems. Special attention was drawn to the interplay between group-theoretic methods and geometric and combinatorial ones. Expanded versions of many of the talks appear in these Proceedings. This volume is intended to provide a stimulating collection of themes for a broad range of algebraists and geometers. Among those themes, represented within the conference or these Proceedings, are aspects of the following: 1. the classification of finite simple groups, 2. the structure and properties of groups of Lie type over finite and algebraically closed fields of f...
Code subspaces for LLM geometries
Berenstein, David; Miller, Alexandra
2018-03-01
We consider effective field theory around classical background geometries with a gauge theory dual, specifically those in the class of LLM geometries. These are dual to half-BPS states of N= 4 SYM. We find that the language of code subspaces is natural for discussing the set of nearby states, which are built by acting with effective fields on these backgrounds. This work extends our previous work by going beyond the strict infinite N limit. We further discuss how one can extract the topology of the state beyond N→∞ and find that, as before, uncertainty and entanglement entropy calculations provide a useful tool to do so. Finally, we discuss obstructions to writing down a globally defined metric operator. We find that the answer depends on the choice of reference state that one starts with. Therefore, within this setup, there is ambiguity in trying to write an operator that describes the metric globally.
Differential geometry and mathematical physics
Rudolph, Gerd
Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and symplectic geometry, • Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous d...
Grassmannian geometry of scattering amplitudes
Arkani-Hamed, Nima; Cachazo, Freddy; Goncharov, Alexander; Postnikov, Alexander; Trnka, Jaroslav
2016-01-01
Outlining a revolutionary reformulation of the foundations of perturbative quantum field theory, this book is a self-contained and authoritative analysis of the application of this new formulation to the case of planar, maximally supersymmetric Yang–Mills theory. The book begins by deriving connections between scattering amplitudes and Grassmannian geometry from first principles before introducing novel physical and mathematical ideas in a systematic manner accessible to both physicists and mathematicians. The principle players in this process are on-shell functions which are closely related to certain sub-strata of Grassmannian manifolds called positroids - in terms of which the classification of on-shell functions and their relations becomes combinatorially manifest. This is an essential introduction to the geometry and combinatorics of the positroid stratification of the Grassmannian and an ideal text for advanced students and researchers working in the areas of field theory, high energy physics, and the...
Foliation theory in algebraic geometry
McKernan, James; Pereira, Jorge
2016-01-01
Featuring a blend of original research papers and comprehensive surveys from an international team of leading researchers in the thriving fields of foliation theory, holomorphic foliations, and birational geometry, this book presents the proceedings of the conference "Foliation Theory in Algebraic Geometry," hosted by the Simons Foundation in New York City in September 2013. Topics covered include: Fano and del Pezzo foliations; the cone theorem and rank one foliations; the structure of symmetric differentials on a smooth complex surface and a local structure theorem for closed symmetric differentials of rank two; an overview of lifting symmetric differentials from varieties with canonical singularities and the applications to the classification of AT bundles on singular varieties; an overview of the powerful theory of the variety of minimal rational tangents introduced by Hwang and Mok; recent examples of varieties which are hyperbolic and yet the Green-Griffiths locus is the whole of X; and a classificati...
Hyperbolic geometry for colour metrics.
Farup, Ivar
2014-05-19
It is well established from both colour difference and colour order perpectives that the colour space cannot be Euclidean. In spite of this, most colour spaces still in use today are Euclidean, and the best Euclidean colour metrics are performing comparably to state-of-the-art non-Euclidean metrics. In this paper, it is shown that a transformation from Euclidean to hyperbolic geometry (i.e., constant negative curvature) for the chromatic plane can significantly improve the performance of Euclidean colour metrics to the point where they are statistically significantly better than state-of-the-art non-Euclidean metrics on standard data sets. The resulting hyperbolic geometry nicely models both qualitatively and quantitatively the hue super-importance phenomenon observed in colour order systems.
Euclidean distance geometry an introduction
Liberti, Leo
2017-01-01
This textbook, the first of its kind, presents the fundamentals of distance geometry: theory, useful methodologies for obtaining solutions, and real world applications. Concise proofs are given and step-by-step algorithms for solving fundamental problems efficiently and precisely are presented in Mathematica®, enabling the reader to experiment with concepts and methods as they are introduced. Descriptive graphics, examples, and problems, accompany the real gems of the text, namely the applications in visualization of graphs, localization of sensor networks, protein conformation from distance data, clock synchronization protocols, robotics, and control of unmanned underwater vehicles, to name several. Aimed at intermediate undergraduates, beginning graduate students, researchers, and practitioners, the reader with a basic knowledge of linear algebra will gain an understanding of the basic theories of distance geometry and why they work in real life.
Holographic thermalization in noncommutative geometry
Directory of Open Access Journals (Sweden)
Xiao-Xiong Zeng
2015-05-01
Full Text Available Gravitational collapse of a shell of dust in noncommutative geometry is probed by the renormalized geodesic length, which is dual to probe the thermalization by the two-point correlation function in the dual conformal field theory. We find that the larger the noncommutative parameter is, the longer the thermalization time is, which implies that the large noncommutative parameter delays the thermalization process. We also investigate how the noncommutative parameter affects the thermalization velocity and thermalization acceleration.
Needle decompositions in Riemannian geometry
Klartag, Bo'az
2017-01-01
The localization technique from convex geometry is generalized to the setting of Riemannian manifolds whose Ricci curvature is bounded from below. In a nutshell, the author's method is based on the following observation: When the Ricci curvature is non-negative, log-concave measures are obtained when conditioning the Riemannian volume measure with respect to a geodesic foliation that is orthogonal to the level sets of a Lipschitz function. The Monge mass transfer problem plays an important role in the author's analysis.
Systematics of IIB spinorial geometry
Gran, U.; Gutowski, J.; Papadopoulos, G.; Roest, D.
2005-01-01
We reduce the classification of all supersymmetric backgrounds of IIB supergravity to the evaluation of the Killing spinor equations and their integrability conditions, which contain the field equations, on five types of spinors. This extends the work of [hep-th/0503046] to IIB supergravity. We give the expressions of the Killing spinor equations on all five types of spinors. In this way, the Killing spinor equations become a linear system for the fluxes, geometry and spacetime derivatives of...
Needle decompositions in riemannian geometry
Klartag, Bo'az
2017-01-01
The localization technique from convex geometry is generalized to the setting of Riemannian manifolds whose Ricci curvature is bounded from below. In a nutshell, the author's method is based on the following observation: When the Ricci curvature is non-negative, log-concave measures are obtained when conditioning the Riemannian volume measure with respect to a geodesic foliation that is orthogonal to the level sets of a Lipschitz function. The Monge mass transfer problem plays an important role in the author's analysis.
Turtle geometry the Python way
Battle, S.
2014-01-01
An introduction to coding using Python’s on-screen ‘turtle’ that can be commanded with a few simple instructions including forward, backward, left and right. The turtle leaves a trace that can be used to draw geometric figures. This workshop is aimed at beginners of all ages. The aim is to learn a smattering of programming and a little bit of geometry in a fun way.
Topics in modern differential geometry
Verstraelen, Leopold
2017-01-01
A variety of introductory articles is provided on a wide range of topics, including variational problems on curves and surfaces with anisotropic curvature. Experts in the fields of Riemannian, Lorentzian and contact geometry present state-of-the-art reviews of their topics. The contributions are written on a graduate level and contain extended bibliographies. The ten chapters are the result of various doctoral courses which were held in 2009 and 2010 at universities in Leuven, Serbia, Romania and Spain.
Geometry success in 20 minutes a day
LLC, LearningExpress
2014-01-01
Whether you're new to geometry or just looking for a refresher, Geometry Success in 20 Minutes a Day offers a 20-step lesson plan that provides quick and thorough instruction in practical, critical skills. Stripped of unnecessary math jargon but bursting with geometry essentials, Geometry Success in 20 Minutes a Day: Covers all vital geometry skills, from the basic building blocks of geometry to ratio, proportion, and similarity to trigonometry and beyond Provides hundreds of practice exercises in test format Applies geometr
Algebraic Geometry and Number Theory Summer School
Sarıoğlu, Celal; Soulé, Christophe; Zeytin, Ayberk
2017-01-01
This lecture notes volume presents significant contributions from the “Algebraic Geometry and Number Theory” Summer School, held at Galatasaray University, Istanbul, June 2-13, 2014. It addresses subjects ranging from Arakelov geometry and Iwasawa theory to classical projective geometry, birational geometry and equivariant cohomology. Its main aim is to introduce these contemporary research topics to graduate students who plan to specialize in the area of algebraic geometry and/or number theory. All contributions combine main concepts and techniques with motivating examples and illustrative problems for the covered subjects. Naturally, the book will also be of interest to researchers working in algebraic geometry, number theory and related fields.
Number theory III Diophantine geometry
1991-01-01
From the reviews of the first printing of this book, published as Volume 60 of the Encyclopaedia of Mathematical Sciences: "Between number theory and geometry there have been several stimulating influences, and this book records of these enterprises. This author, who has been at the centre of such research for many years, is one of the best guides a reader can hope for. The book is full of beautiful results, open questions, stimulating conjectures and suggestions where to look for future developments. This volume bears witness of the broad scope of knowledge of the author, and the influence of several people who have commented on the manuscript before publication ... Although in the series of number theory, this volume is on diophantine geometry, and the reader will notice that algebraic geometry is present in every chapter. ... The style of the book is clear. Ideas are well explained, and the author helps the reader to pass by several technicalities. Reading and rereading this book I noticed that the topics ...
Introduction to geometry and relativity
2013-01-01
This book provides a lucid introduction to both modern differential geometry and relativity for advanced undergraduates and first-year graduate students of applied mathematics and physical sciences. This book meets an overwhelming need for a book on modern differential geometry and relativity that is student-friendly, and which is also suitable for self-study. The book presumes a minimal level of mathematical maturity so that any student who has completed the standard Calculus sequence should be able to read and understand the book. The key features of the book are: Detailed solutions are provided to the Exercises in each chapter; Many of the missing steps that are often omitted from standard mathematical derivations have been provided to make the book easier to read and understand; A detailed introduction to Electrodynamics is provided so that the book is accessible to students who have not had a formal course in this area; In its treatment of modern differential geometry, the book employs both a modern, c...
Riemannian geometry and geometric analysis
Jost, Jürgen
2017-01-01
This established reference work continues to provide its readers with a gateway to some of the most interesting developments in contemporary geometry. It offers insight into a wide range of topics, including fundamental concepts of Riemannian geometry, such as geodesics, connections and curvature; the basic models and tools of geometric analysis, such as harmonic functions, forms, mappings, eigenvalues, the Dirac operator and the heat flow method; as well as the most important variational principles of theoretical physics, such as Yang-Mills, Ginzburg-Landau or the nonlinear sigma model of quantum field theory. The present volume connects all these topics in a systematic geometric framework. At the same time, it equips the reader with the working tools of the field and enables her or him to delve into geometric research. The 7th edition has been systematically reorganized and updated. Almost no page has been left unchanged. It also includes new material, for instance on symplectic geometry, as well as the B...
Computational geometry for reactor applications
International Nuclear Information System (INIS)
Brown, F.B.; Bischoff, F.G.
1988-01-01
Monte Carlo codes for simulating particle transport involve three basic computational sections: a geometry package for locating particles and computing distances to regional boundaries, a physics package for analyzing interactions between particles and problem materials, and an editing package for determining event statistics and overall results. This paper describes the computational geometry methods in RACER, a vectorized Monte Carlo code used for reactor physics analysis, so that comparisons may be made with techniques used in other codes. The principal applications for RACER are eigenvalue calculations and power distributions associated with reactor core physics analysis. Successive batches of neutrons are run until convergence and acceptable confidence intervals are obtained, with typical problems involving >10 6 histories. As such, the development of computational geometry methods has emphasized two basic needs: a flexible but compact geometric representation that permits accurate modeling of reactor core details and efficient geometric computation to permit very large numbers of histories to be run. The current geometric capabilities meet these needs effectively, supporting a variety of very large and demanding applications
DEFF Research Database (Denmark)
Brøns, Morten; Voigt, Lars Peter Køllgaard; Sørensen, Jens Nørkær
1998-01-01
Using a combination of bifurcation theory for two-dimensional dynamical systems and numerical simulations, we systematically determine the possible flow topologies of the steady vortex breakdown in axisymmetric flow in a cylindrical container with rotating end-covers. For fixed values...
DEFF Research Database (Denmark)
Brøns, Morten; Voigt, Lars Peter Kølgaard; Sørensen, Jens Nørkær
1999-01-01
Using a combination of bifurcation theory for two-dimensional dynamical systems and numerical simulations, we systematically determine the possible flow topologies of the steady vortex breakdown in axisymmetric flow in a cylindrical container with rotating end-covers. For fixed values of the ratio...
Mokhov, A. V.; Bennett, B. A. V.; Levinsky, H.B.; Smooke, M. D.
2007-01-01
Raman measurements of C2H2 and CO mole fractions in a laminar axisymmetric methane-air diffusion flame are compared with numerical predictions. A high-repetition-rate, high-average-power laser is used to increase signal-to-noise ratio to measure these minor flame species. Computationally, the system
Nakiboglu, G.; Manders, H.B.M.; Hirschberg, Abraham
2012-01-01
Aeroacoustic power generation due to a self-sustained oscillation by an axisymmetric compact cavity exposed to a low-Mach-number grazing flow is studied both experimentally and numerically. The feedback effect is produced by the velocity fluctuations resulting from a coupling with acoustic standing
Directory of Open Access Journals (Sweden)
J. Comer
Full Text Available The technique of tracing along magnetic field lines is widely used in magnetospheric physics to provide a "magnetic frame of reference'' that facilitates both the planning of experiments and the interpretation of observations. The precision of any such magnetic frame of reference depends critically on the accurate representation of the various sources of magnetic field in the magnetosphere. In order to consider this important problem systematically, a study is initiated to estimate first the uncertainties in magnetic-field-line tracing in the magnetosphere that arise solely from the published (standard errors in the specification of the geomagnetic field of internal origin. Because of the complexity in computing these uncertainties for the complete geomagnetic field of internal origin, attention is focused in this preliminary paper on the uncertainties in magnetic-field-line tracing that result from the standard errors in just the axisymmetric part of the internal geomagnetic field. An exact analytic equation exists for the magnetic field lines of an arbitrary linear combination of axisymmetric multipoles. This equation is used to derive numerical estimates of the uncertainties in magnetic-field-line tracing that are due to the published standard errors in the axisymmetric spherical harmonic coefficients (i.e. gn0 ± δgn0. Numerical results determined from the analytic equation are compared with computational results based on stepwise numerical integration along magnetic field lines. Excellent agreement is obtained between the analytical and computational methods in the axisymmetric case, which provides great confidence in the accuracy of the computer program used for stepwise numerical integration along magnetic field lines. This computer program is then used in the following paper to estimate the uncertainties in magnetic-field-line tracing in the magnetosphere that arise from the published standard errors in the full set of spherical
Thermal-hydraulic analysis techniques for axisymmetric pebble bed nuclear reactor cores
International Nuclear Information System (INIS)
Stroh, K.R.
1979-03-01
The pebble bed reactor's cylindrical core volume contains a random bed of small, spherical fuel-moderator elements. These graphite spheres, containing a central region of dispersed coated-particle fissile and fertile material, are cooled by high pressure helium flowing through the connected interstitial voids. A mathematical model and numerical solution technique have been developed which allow calculation of macroscopic values of thermal-hydraulic variables in an axisymmetric pebble bed nuclear reactor core. The computer program PEBBLE is based on a mathematical model which treats the bed macroscopically as a generating, conducting porous medium. The steady-state model uses a nonlinear Forchheimer-type relation between the coolant pressure gradient and mass flux, with newly derived coefficients for the linear and quadratic resistance terms. The remaining equations in the model make use of mass continuity, and thermal energy balances for the solid and fluid phases
Analytic axisymmetric equilibria with pressure anisotropy and non-parallel flow
Kuiroukidis, A.; Evangelias, A.; Throumoulopoulos, G. N.
2017-10-01
We extend previous work by two of the authors [Evangelias and Throumoulopoulos 2016 Plasma Phys. Control. Fusion 58 045022] and find analytic solutions to a generalized Grad-Shafranov equation (GGSE) with pressure anisotropy, hollow toroidal current density and incompressible flow of arbitrary direction. By specifying the surface-function terms involved in the GGSE as quadratic functions of the poloidal magnetic flux function, we derive analytic tokamak pertinent equilibria. It turns out that, irrespective of the shape of the toroidal current density profile, which is noticeably affected by the pressure anisotropy, this anisotropy has a paramagnetic effect for {p}\\parallel > {p}\\perp and a diamagnetic one for {p}\\parallel < {p}\\perp . In addition, the parallel flow induces paramagnetism, while the residual toroidal flow associated with the electric field induces diamagnetism. The analytic results obtained here contribute to the physics understanding of axisymmetric equilibria with pressure anisotropy and flow, and can be employed for validating equilibrium codes.
Energy Technology Data Exchange (ETDEWEB)
Stroh, K.R.
1979-03-01
The pebble bed reactor's cylindrical core volume contains a random bed of small, spherical fuel-moderator elements. These graphite spheres, containing a central region of dispersed coated-particle fissile and fertile material, are cooled by high pressure helium flowing through the connected interstitial voids. A mathematical model and numerical solution technique have been developed which allow calculation of macroscopic values of thermal-hydraulic variables in an axisymmetric pebble bed nuclear reactor core. The computer program PEBBLE is based on a mathematical model which treats the bed macroscopically as a generating, conducting porous medium. The steady-state model uses a nonlinear Forchheimer-type relation between the coolant pressure gradient and mass flux, with newly derived coefficients for the linear and quadratic resistance terms. The remaining equations in the model make use of mass continuity, and thermal energy balances for the solid and fluid phases.
A Family of Vortices to Study Axisymmetric Vortex Breakdown and Reconnection
Young, Larry A.
2007-01-01
A new analytic model describing a family of vortices has been developed to study some of the axisymmetric vortex breakdown and reconnection fluid dynamic processes underlying body-vortex interactions that are frequently manifested in rotorcraft and propeller-driven fixed-wing aircraft wakes. The family of vortices incorporates a wide range of prescribed initial vorticity distributions -- including single or dual-core vorticity distributions. The result is analytical solutions for the vorticity and velocities for each member of the family of vortices. This model is of sufficient generality to further illustrate the dependence of vortex reconnection and breakdown on initial vorticity distribution as was suggested by earlier analytical work. This family of vortices, though laminar in nature, is anticipated to provide valuable insight into the vortical evolution of large-scale rotor and propeller wakes.
Influence of Initial Vorticity Distribution on Axisymmetric Vortex Breakdown and Reconnection
Young, Larry A.
2007-01-01
An analytical treatment has been developed to study some of the axisymmetric vortex breakdown and reconnection fluid dynamic processes underlying body-vortex interactions that are frequently manifested in rotorcraft and propeller-driven fixed-wing aircraft wakes. In particular, the presence of negative vorticity in the inner core of a vortex filament (one example of which is examined in this paper) subsequent to "cutting" by a solid body has a profound influence on the vortex reconnection, leading to analog flow behavior similar to vortex breakdown phenomena described in the literature. Initial vorticity distributions (three specific examples which are examined) without an inner core of negative vorticity do not exhibit vortex breakdown and instead manifest diffusion-like properties while undergoing vortex reconnection. Though this work focuses on laminar vortical flow, this work is anticipated to provide valuable insight into rotary-wing aerodynamics as well as other types of vortical flow phenomena.
Physical modeling of flow over an axisymmetric knoll under neutral atmospheric conditions
International Nuclear Information System (INIS)
Cliff, W.C.; Smith, J.D.
1980-02-01
A glass-walled hydraulic (water) flume was used to model physically air flow near an axisymmetric knoll in a neutral atmospheric boundary layer. The knoll was a 1:250 scale model. An upstream velocity profile (1/7 power law), characteristic of a neutral atmospheric boundary layer, was produced by locating a 10-cm-high (4-in.) trip near the flume entrance and by appropriately roughening the flume floor. Mean velocity, rms velocity, and turbulence intensity profiles were measured at locations near the knoll using an existing laser Doppler anemometer system. The flow accelerated over the knoll and produced a relatively uniform velocity profile at the crest. The measured velocity profile was in close agreement with a theoretical velocity profile developed using potential flow theory and an upstream power law velocity profile. The turbulence intensity decreased at the crest of the knoll as a result of the flow acceleration
Axisymmetrical impulsive responses of an infinite circular cylindrical shell filled with liquid
International Nuclear Information System (INIS)
Ujihashi, Sadayuki; Matsumoto, Hiroyuki; Nakahara, Ichiro; Shigeta, Masayuki.
1986-01-01
In this paper, dynamic interaction phenomena on solid and liquid interfaces are discussed. Axisymmetrical responses of an infinite circular cylindrical shell perfectly filled with liquid are analyzed, based on Fluegge's theory for a circular cylindrical shell and the potential theory for the ideal fluid under conditions of the impulsive external band pressure given on the outer surface of the shell. The deflection and the moment of the shell and the pressure in the fluid are evaluated by using the numerical inversion of the Laplace transformation method. The approximate solution for the shell with an equivalent mass on it is analyzed and is evaluated, based on the solution for the solid and liquid interaction. (author)
Axisymmetric accretion flows very near black holes and Rosen-collapsed objects
International Nuclear Information System (INIS)
Stoeger, W.R.
1979-01-01
Motivated by the need for stronger observational leverage on the black hole hypothesis and for a more detailed characterization of axisymmetric accretion flows across the marginally stable circular orbit rsub(ms), a general approach for describing the non-Keplerian accretion in the region rsub(H) 0 , where rsub(H) = radius of the event horizon and r 0 > = rsub(ms) is developed. The procedure possesses many advantages, including easily imposed consistency with the Keplerian for r > rsub(o), the avoidance of ad hoc boundary conditions at rsub(ms) and/or at rsub(H) and its application also to accretion in Rosen's bimetric theory, whose spherically symmetric solution has the same qualitative orbital topography as that of general relativity. It becomes apparent, furthermore, that the particular viscosity law chosen in this procedure will have a crucial bearing on the flow in the region rsub(ms) 0 . (author)
Experimental and numerical studies on super-cavitating flow of axisymmetric cavitators
Directory of Open Access Journals (Sweden)
Byoung-Kwon Ahn
2010-03-01
Full Text Available Recently underwater systems moving at high speed such as a super-cavitating torpedo have been studied for their practical advantage of the dramatic drag reduction. In this study we are focusing our attention on super-cavitating flows around axisymmetric cavitators. A numerical method based on inviscid flow is developed and the results for several shapes of the cavitator are presented. First using a potential based boundary element method, we find the shape of the cavitator yielding a sufficiently large enough cavity to surround the body. Second, numerical predictions of supercavity are validated by comparing with experimental observations carried out in a high speed cavitation tunnel at Chungnam National University (CNU CT.
International Nuclear Information System (INIS)
Prakash, B.; Gupta, S.; Malik, P.; Mishra, K.K.; Jha, M.N.; Kandaswamy, E.; Martin, M.
2015-01-01
Electron beam melting gun with indirectly heated axi-symmetric solid cathode was designed, fabricated and characterized experimentally. The thermal simulation and optical analysis of the electron gun was carried out to estimate the power required to achieve the emission temperature of the solid cathode, to obtain the temperature distribution in the assembly and the beam transportation. On the basis of the thermal simulation and electron optics, the electron gun design was finalised. The electron gun assembly was fabricated and installed in the vacuum chamber for carrying out the experiment to find the actual temperature distribution. Thermocouple and two colour pyrometer were used to measure the temperature at various locations in the electron gun. The attenuation effect of the viewing port glass of the vacuum chamber was compensated in the final reading of the temperature measured by the pyrometer. The temperature of solid cathode obtained by the experiment was found to be 2800K which is the emission temperature of solid cathode. (author)
Low-speed aerodynamic test of an axisymmetric supersonic inlet with variable cowl slot
Powell, A. G.; Welge, H. R.; Trefny, C. J.
1985-01-01
The experimental low-speed aerodynamic characteristics of an axisymmetric mixed-compression supersonic inlet with variable cowl slot are described. The model consisted of the NASA P-inlet centerbody and redesigned cowl with variable cowl slot powered by the JT8D single-stage fan simulator and driven by an air turbine. The model was tested in the NASA Lewis Research Center 9- by 15-foot low-speed tunnel at Mach numbers of 0, 0.1, and 0.2 over a range of flows, cowl slot openings, centerbody positions, and angles of attack. The variable cowl slot was effective in minimizing lip separation at high velocity ratios, showed good steady-state and dynamic distortion characteristics, and had good angle-of-attack tolerance.
Modified k-l model and its ability to simulate supersonic axisymmetric turbulent flows
International Nuclear Information System (INIS)
Ahmadikia, H.; Shirani, E.
2001-05-01
The k-l turbulence model is a promising two-equation model. In this paper, the k and l model equations were derived from k-kl incompressible and one-equation turbulent models. Then the model was modified for compressible and transitional flows, and was applied to simulate supersonic axisymmetric flows over Hollow cylinder flare an hyperboloid flare bodies. The results were compared with the results obtained for the same flows experimentally as well as k-ε, k-ω and Baldwin-Lomax models. It was shown that the k-l model produces good results compared with experimental data and numerical data obtained when other turbulence models were used. It gives better results than k-ω and k-ε models in some cases. (author)
Calculation of an axisymmetric current coil field with the bounding contour integration method
Energy Technology Data Exchange (ETDEWEB)
Telegin, Alexander P.; Klevets, Nickolay I. E-mail: pmsolution@mail.ru
2004-06-01
Method for the economic and stable (in the sense of calculation errors) analysis of an induction of a magnetic field created with axisymmetric coils in arbitrary points of space, including points located inside a coil or on its border, is obtained. The basic idea of the method is to replace a current coil with continuous distribution of current density by magnetization distributed in the volume of the coil and creating the equivalent magnetic field. This allows to use field surface sources at calculation of the fields. Consequently, the range of integration is reduced resulting in reduction of calculation volume by an order in most cases. Besides, the calculation of improper integrals in internal points and on the border is completely excluded.
Calculation of an axisymmetric current coil field with the bounding contour integration method
International Nuclear Information System (INIS)
Telegin, Alexander P.; Klevets, Nickolay I.
2004-01-01
Method for the economic and stable (in the sense of calculation errors) analysis of an induction of a magnetic field created with axisymmetric coils in arbitrary points of space, including points located inside a coil or on its border, is obtained. The basic idea of the method is to replace a current coil with continuous distribution of current density by magnetization distributed in the volume of the coil and creating the equivalent magnetic field. This allows to use field surface sources at calculation of the fields. Consequently, the range of integration is reduced resulting in reduction of calculation volume by an order in most cases. Besides, the calculation of improper integrals in internal points and on the border is completely excluded
Directory of Open Access Journals (Sweden)
S.M. Moawad
Full Text Available In this paper, the equilibrium properties of some ideal and resistive magnetohydrodynamics (MHD are investigated. The governing equations are taken in the steady state for parallel and non-parallel flow to magnetic filed. The governing equations are reduced to Bernoulli-Grad-Shafranov system. The problem of finding exact equilibria to the governing equations in the presence of incompressible mass flows is studied. Several nonlinear equilibria of the governing equations are obtained with aid of constructed constraints. The obtained results cover several previously configurations and include new considerations about the nonlinearity of magnetic flux stream variables. The possibility of applying the obtained results to magnetic confinement devices are discussed. Keywords: Magnetohydrodynamics, Axisymmetric plasma, Resistivity, Incompressible flows, Exact equilibria, Magnetic confinement devices
Directory of Open Access Journals (Sweden)
Liu Ming
2017-11-01
Full Text Available The wave energy, as a clean and non-pollution renewable energy sources, has become a hot research topic at home and abroad and is likely to become a new industry in the future. In this article, to effectively extract and maximize the energy from ocean waves, a vertical axisymmetric wave energy converter (WEC was presented according to investigating of the advantages and disadvantages of the current WEC. The linear and quadratic equations in frequency-domain for the reactive controlled single-point converter property under regular waves condition are proposed for an efficient power take-off (PTO. A method of damping coefficients, theoretical added mass and exciting force are calculated with the analytical method which is in use of the series expansion of eigen functions. The loads of optimal reactive and resistive, the amplitudes of corresponding oscillation, and the width ratios of energy capture are determined approximately and discussed in numerical results.
Energy Technology Data Exchange (ETDEWEB)
Cook, G.O. Jr.
1982-12-01
The Topolotron is an axisymmetric, toroidal magnetic fusion concept in which two-dimensional effects are important, as well as all three magnetic field components. The particular MHD model employed is basically the one-fluid, two-temperature model using classical Braginskii transport with viscous effects ignored. The model is augmented by Saha-Boltzmann dissociation and partial ionization physics, a simple radiation loss mechanism, and an additional resistivity due to electron-neutral collisions. While retaining all velocity and magnetic field components, the assumption of axisymmetry is made, and the resulting equations are expanded in cylindrical coordinates. The major approximation technique is then applied: spline collocation, which reduces these equations to a set of ordinary differential equations.
DEFF Research Database (Denmark)
Cutanda Henriquez, Vicente; Juhl, Peter Møller
2013-01-01
The formulation presented in this paper is based on the Boundary Element Method (BEM) and implements Kirchhoff’s decomposition into viscous, thermal and acoustic components, which can be treated independently everywhere in the domain except on the boundaries. The acoustic variables with losses ar...... as is the case with the existing Finite Element Method (FEM) implementations with losses. The suitability of this approach is demonstrated using an axisymmetrical BEM and two test cases where the numerical results are compared with analytical solutions.......The formulation presented in this paper is based on the Boundary Element Method (BEM) and implements Kirchhoff’s decomposition into viscous, thermal and acoustic components, which can be treated independently everywhere in the domain except on the boundaries. The acoustic variables with losses...
Tokamak equilibria with non field-aligned axisymmetric divergence-free rotational flows
Energy Technology Data Exchange (ETDEWEB)
Tsui, K. H.; Navia, C. E.; Serbeto, A.; Shigueoka, H. [Instituto de Fisica, Universidade Federal Fluminense, Campus da Praia Vermelha, Av. General Milton Tavares de Souza s/n, Gragoata, 24.210-346, Niteroi, Rio de Janeiro (Brazil)
2011-07-15
Rotational ideal divergence-free magnetohydrodynamic (MHD) equations are expressed in terms of transformed variables w-vector{sub *}=({mu}{rho}){sup 1/2}v-vector and {mu}p{sub *} = ({mu}p + w{sub *}{sup 2}/2), where v-vector, p, and {rho} are plasma velocity, pressure, and mass density, respectively. With divergence-free flows, {nabla}{center_dot}v-vector=0, the plasma density {rho} does not appear in the MHD equations written in terms of w-vector{sub *} and {mu}p{sub *}. The non field-aligned rotational Grad-Shafranov equation is represented in spherical coordinates. Tokamak-like axisymmetric equilibria with v-vector perpendicular {nabla}{rho} are obtained analytically by solving for torus solutions under only three source functions.
Directory of Open Access Journals (Sweden)
Freidooni Mehr N.
2012-01-01
Full Text Available In this paper, the semi-analytical/numerical technique known as the homotopy analysis method (HAM is employed to derive solutions for the laminar axisymmetric mixed convection boundary-layer nanofluid flow past a vertical cylinder. The similarity solutions are employed to transform the parabolic partial differential conservation equations into system of nonlinear, coupled ordinary differential equations, subject to appropriate boundary conditions. A comparison has been done to verify the obtained results with the purely numerical results of Grosan and Pop (2011 with excellent correlation achieved. The effects of nanoparticle volume fraction, curvature parameter and mixed convection or buoyancy parameter on the dimensionless velocity and temperature distributions, skin friction and wall temperature gradients are illustrated graphically. HAM is found to demonstrate excellent potential for simulating nanofluid dynamics problems. Applications of the study include materials processing and also thermal enhancement of energy systems.
International Nuclear Information System (INIS)
Méchi, Rachid; Farhat, Habib; Said, Rachid
2016-01-01
Nongray radiation calculations are carried out for a case problem available in the literature. The problem is a non-isothermal and inhomogeneous CO 2 -H 2 O- N 2 gas mixture confined within an axisymmetric cylindrical furnace. The numerical procedure is based on the zonal method associated with the weighted sum of gray gases (WSGG) model. The effect of the wall emissivity on the heat flux losses is discussed. It is shown that this property affects strongly the furnace efficiency and that the most important heat fluxes are those leaving through the circumferential boundary. The numerical procedure adopted in this work is found to be effective and may be relied on to simulate coupled turbulent combustion-radiation in fired furnaces. (paper)
Input-output analysis of high-speed axisymmetric isothermal jet noise
Jeun, Jinah; Nichols, Joseph W.; Jovanović, Mihailo R.
2016-04-01
We use input-output analysis to predict and understand the aeroacoustics of high-speed isothermal turbulent jets. We consider axisymmetric linear perturbations about Reynolds-averaged Navier-Stokes solutions of ideally expanded turbulent jets with jet Mach numbers 0.6 parabolized stability equations (PSE), and this mode dominates the response. For subsonic jets, however, the singular values indicate that the contributions of sub-optimal modes to noise generation are nearly equal to that of the optimal mode, explaining why the PSE do not fully capture the far-field sound in this case. Furthermore, high-fidelity large eddy simulation (LES) is used to assess the prevalence of sub-optimal modes in the unsteady data. By projecting LES source term data onto input modes and the LES acoustic far-field onto output modes, we demonstrate that sub-optimal modes of both types are physically relevant.
Peng, Y.; Shu, C.; Chew, Y. T.; Qiu, J.
2003-03-01
An alternative new method called lattice Boltzmann method (LBM) is applied in this work to simulate the flows in Czochralski crystal growth, which is one of the widely used prototypical systems for melt-crystal growth. The standard LBM can only be used in Cartesian coordinate system and we extend it to be applicable to this axisymmetric thermal flow problem, avoiding the use of three-dimensional LBM on Cartesian coordinate system. The extension is based on the following idea. By inserting position and time dependent source terms into the evolution equation of standard LBM, the continuity and NS equations on the cylindrical coordinate system [1] can be recovered. Our extension is validated by its application to the benchmark problem suggested by Wheeler [2].
Peng, Y; Chew, Y T; Qiu, J
2003-01-01
An alternative new method called lattice Boltzmann method (LBM) is applied in this work to simulate the flows in Czochralski crystal growth, which is one of the widely used prototypical systems for melt-crystal growth. The standard LBM can only be used in Cartesian coordinate system and we extend it to be applicable to this axisymmetric thermal flow problem, avoiding the use of three-dimensional LBM on Cartesian coordinate system. The extension is based on the following idea. By inserting position and time dependent source terms into the evolution equation of standard LBM, the continuity and NS equations on the cylindrical coordinate system can be recovered. Our extension is validated by its application to the benchmark problem suggested by Wheeler .
International Nuclear Information System (INIS)
Peng, Y.; Shu, C.; Chew, Y.T.; Qiu, J.
2003-01-01
An alternative new method called lattice Boltzmann method (LBM) is applied in this work to simulate the flows in Czochralski crystal growth, which is one of the widely used prototypical systems for melt-crystal growth. The standard LBM can only be used in Cartesian coordinate system and we extend it to be applicable to this axisymmetric thermal flow problem, avoiding the use of three-dimensional LBM on Cartesian coordinate system. The extension is based on the following idea. By inserting position and time dependent source terms into the evolution equation of standard LBM, the continuity and NS equations on the cylindrical coordinate system can be recovered. Our extension is validated by its application to the benchmark problem suggested by Wheeler
Khine, Y. Y.; Walker, J. S.
1996-08-01
Centrifugal pumping flows are produced in the melt by the rotations of crystal and crucible during the Czochralski growth of silicon crystals. This paper treats the centrifugal pumping effects with a steady, strong, non-uniform axisymmetric magnetic field. We consider a family of magnetic fields ranging from a uniform axial field to a "cusp" field, which has a purely radial field at the crystal-melt interface and free surface. We present the numerical solutions for the centrifugal pumping flows as the magnetic field is changed continuously from a uniform axial field to a cusp one, and for arbitrary Hartmann number. Since the perfect alignment between the local magnetic field vector and the crystal-melt interface or free surface is not likely, we also investigate the effects of a slight misalignment.
Khine, Y. Y.; Walker, J. S.
1995-02-01
This paper treats the buoyant convection during the Czochralski growth of silicon crystals with a steady, strong, non-uniform, axisymmetric magnetic field. We consider a family of magnetic fields which includes a uniform axial magnetic field and a "cusp" field which is produced by identical solenoids placed symmetrically above and below the plane of the crystal-melt interface and free surface. We investigate the evolution of the buoyant convection as the magnetic field is changed continuously from a uniform axial field to a cusp field, with a constant value of the root-mean-squared magnetic flux density in the melt. We also investigate changes as the magnetic flux density is increased. While the cusp field appears very promising, perfect alignment between the local magnetic field vector and the crystal-melt interface or free surface is not possible, so the effects of a slight misalignment are also investigated.
International Nuclear Information System (INIS)
Cook, G.O. Jr.
1982-12-01
The Topolotron is an axisymmetric, toroidal magnetic fusion concept in which two-dimensional effects are important, as well as all three magnetic field components. The particular MHD model employed is basically the one-fluid, two-temperature model using classical Braginskii transport with viscous effects ignored. The model is augmented by Saha-Boltzmann dissociation and partial ionization physics, a simple radiation loss mechanism, and an additional resistivity due to electron-neutral collisions. While retaining all velocity and magnetic field components, the assumption of axisymmetry is made, and the resulting equations are expanded in cylindrical coordinates. The major approximation technique is then applied: spline collocation, which reduces these equations to a set of ordinary differential equations
Axisymmetric electromagnetic field influence on the characteristic velocity of an arc-jet
Oggero, M.; Gennuso, D.
1984-01-01
Tests for determining the influence of an axisymmetric EM field on the characteristic velocity of an arc jet are presented. The experimental set up is briefly described. Tests were performed with rotation induced by the centrifugal and magnetic fields in the same sense. The fuels used were HE and N2 and the results are discussed. It is found that by variation of the induction, current, and arc jet strength, the behavior is determined essentially by the shape of the cathodic and anodic blobs on the electrodes together with their movement under the combined effect of the aerodynamic and magnetic fields. In view of the different characteristics of He and N2 in respect to the dissociation heat and ionization, it is expected that the regime of the arc jet when used with H2 fuel will be similar to that with He.
Eddy currents in a nonperiodic vacuum vessel induced by axisymmetric plasma motion
International Nuclear Information System (INIS)
DeLucia, J.
1985-12-01
A method is described for calculating the two-dimensional trajectory of a vertically or horizontally unstable axisymmetric tokamak plasma in the presence of a resistive vacuum vessel. The vessel is not assumed to have toroidal symmetry. The plasma is represented by a current-filament loop that is free to move vertically and to change its major radius. Its position is evolved in time self-consistently with the vacuum vessel eddy currents. The plasma current, internal inductance, and poloidal beta can be specified functions of time so that eddy currents resulting from a disruption can be modeled. The vacuum vessel is represented by a set of current-filaments whose positions and orientations are chosen to model the dominant eddy current paths. Although the specific application is to TFTR, the present model is of general applicability. 7 refs., 4 figs., 2 tabs
Feedback stabilization of the axisymmetric instability of a deformable tokamak plasma
International Nuclear Information System (INIS)
Pomphrey, N.; Jardin, S.C.
1987-09-01
We analyze the magnetohydrodynamic (MHD) stability of the axisymmetric system consisting of a free boundary, non-circular cross-section tokamak plasma, finite resistivity passive conductors, and an active feedback system with magnetic flux pickup loops, a proportional amplifier with gain G, and current carrying poloidal field coils. Numerical simulation of a system that is unstable with G = 0 shows that for some placements of the pickup loops, the system will remain unstable for all values of G, while for other placements of the loops, the system will be stable for G > G/sub crit/. This behavior is explained by analysis using an extended energy principle, and it is shown to result from the deformability of the plasma cross section. 9 refs., 5 figs
An axisymmetric method of creep analysis for primary and secondary creep
International Nuclear Information System (INIS)
Jahed, Hamid; Bidabadi, Jalal
2003-01-01
A general axisymmetric method for elastic-plastic analysis was previously proposed by Jahed and Dubey [ASME J Pressure Vessels Technol 119 (1997) 264]. In the present work the method is extended to the time domain. General rate type governing equations are derived and solved in terms of rate of change of displacement as a function of rate of change in loading. Different types of loading, such as internal and external pressure, centrifugal loading and temperature gradient, are considered. To derive specific equations and employ the proposed formulation, the problem of an inhomogeneous non-uniform rotating disc is worked out. Primary and secondary creep behaviour is predicted using the proposed method and results are compared to FEM results. The problem of creep in pressurized vessels is also solved. Several numerical examples show the effectiveness and robustness of the proposed method
Optimal cloning of qubits given by an arbitrary axisymmetric distribution on the Bloch sphere
International Nuclear Information System (INIS)
Bartkiewicz, Karol; Miranowicz, Adam
2010-01-01
We find an optimal quantum cloning machine, which clones qubits of arbitrary symmetrical distribution around the Bloch vector with the highest fidelity. The process is referred to as phase-independent cloning in contrast to the standard phase-covariant cloning for which an input qubit state is a priori better known. We assume that the information about the input state is encoded in an arbitrary axisymmetric distribution (phase function) on the Bloch sphere of the cloned qubits. We find analytical expressions describing the optimal cloning transformation and fidelity of the clones. As an illustration, we analyze cloning of qubit state described by the von Mises-Fisher and Brosseau distributions. Moreover, we show that the optimal phase-independent cloning machine can be implemented by modifying the mirror phase-covariant cloning machine for which quantum circuits are known.
Minimal inductance for axisymmetric transmission lines with radially dependent anode-cathode gap
Directory of Open Access Journals (Sweden)
Eduardo M. Waisman
2009-09-01
Full Text Available We extend the variational calculus technique for inductance minimization of constant gap axisymmetric transmission lines (TL, introduced by Hurricane [J. Appl. Phys. 95, 4503 (2004JAPIAU0021-897910.1063/1.1687986], to the case in which the anode-cathode gap is a linear function of the midgap radius. The full analytic optimal midgap solution curve z(r yielding minimum inductance is obtained in terms of a single parameter ρ_{0}, determined numerically by imposing that z(r goes through prescribed end points. The radius of curvature ρ(r of the optimal curve is obtained everywhere the function is defined, even outside of the end point range, and it is shown that a convenient choice is ρ_{0}=ρ(0. The value of the transmission line inductance is calculated by 1D numerical quadrature. A simple numerical technique is introduced for TL with nonlinear radial gap dependence.
Reversed field Vlasov equilibria and orbits in 2D axisymmetric 2XIIB configurations
International Nuclear Information System (INIS)
Anderson, D.V.; Rensink, M.E.; Post, R.F.
1977-01-01
The details of the ion distribution function are important in determining the volume of and degree of field reversal. To show some of these dependencies the double delta function distribution function f = delta(E - E 0 )delta(P/sub c/ - P/sub co/) is used where E and P/sub c/ are the particle energy and canonical angular momentum, respectively. Electrons are ignored except for providing charge neutrality. Results of a parameter study from the 2D axisymmetric equilibrium code CYLEQ 1 will show how field reversal is related to the radius, length, rotation, total number and energy of the plasma ions. Optimal injection strategies are presented which lead to plasma distributions with good reversal. Particle orbits conforming to this distribution function are displayed
Feedback stabilization of the axisymmetric instability of a deformable tokamak plasma
International Nuclear Information System (INIS)
Pomphrey, N.; Jardin, S.C.; Ward, D.J.
1989-01-01
The paper presents an analysis of the magnetohydrodynamic stability of the axisymmetric system consisting of a free boundary tokamak plasma with non-circular cross-section, finite resistivity passive conductors, and an active feedback system with magnetic flux pickup loops, a proportional amplifier with gain G and current carrying poloidal field coils. A numerical simulation of the system when G is set to zero identifies flux loop locations which correctly sense the plasma motion. However, when certain of these locations are incorporated into an active feedback scheme, the plasma fails to be stabilized, no matter what value of the gain is chosen. Analysis on the basis of an extended energy principle indicates that this failure is due to the deformability of the plasma cross-section. (author). 14 refs, 7 figs
Nonlinear focusing of ultrasonic waves by an axisymmetric diffraction grating embedded in water
Energy Technology Data Exchange (ETDEWEB)
Jiménez, N.; Picó, R. [Instituto de Investigación para la Gestión Integrada de zonas Costeras, Universitat Politècnica de València, Paranimf 1, 46730 Grao de Gandia, València (Spain); Romero-García, V. [LUNAM Université, Université du Maine, LAUM UMR CNRS 6613, Av. O. Messiaen, 72085 Le Mans (France); Garcia-Raffi, L. M. [Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camino de Vera s/n, 46022 València (Spain); Staliunas, K. [ICREA, Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya, Colom, 11, E-08222 Terrassa, Barcelona (Spain)
2015-11-16
We report the nonlinear focusing of ultrasonic waves by an axisymmetric diffraction grating immersed in water. In the linear regime, the system presents high focal gain (32 dB), with a narrow beam-width and intense side lobes as it is common in focusing by Fresnel-like lenses. Activating the nonlinearity of the host medium by using high amplitude incident waves, the focusing properties of the lens dramatically change. Theoretical predictions show that the focal gain of the system extraordinary increases in the strongly nonlinear regime (Mach number of 6.1 × 10{sup −4}). Particularly, the harmonic generation is locally activated at the focal spot, and the second harmonic beam is characterized by strongly reduced side-lobes and an excellent beam profile as experiments show in agreement with theory. The results can motivate applications in medical therapy or second harmonic imaging.
Regimes of Axisymmetric Flow and Scaling Laws in a Rotating Annulus with Local Convective Forcing
Directory of Open Access Journals (Sweden)
Susie Wright
2017-07-01
Full Text Available We present a numerical study of axisymmetric flow in a rotating annulus in which local thermal forcing, via a heated annular ring on the outside of the base and a cooled circular disk in the centre of the top surface, drives convection. This new configuration is a variant of the classical thermally-driven annulus, where uniform heating and cooling are applied through the outer and inner sidewalls respectively. The annulus provides an analogue to a planetary circulation and the new configuration, with its more relaxed vertical thermal boundary conditions, is expected to better emulate vigorous convection in the tropics and polar regions as well as baroclinic instability in the mid-latitude baroclinic zone. Using the Met Office/Oxford Rotating Annulus Laboratory (MORALS code, we have investigated a series of equilibrated, two dimensional axisymmetric flows across a large region of parameter space. These are characterized in terms of their velocity and temperature fields. When rotation is applied several distinct flow regimes may be identified for different rotation rates and strengths of differential heating. These regimes are defined as a function of the ratio of the horizontal Ekman layer thickness to the non-rotating thermal boundary layer thickness and are found to be similar to those identified in previous annulus experiments. Convection without rotation is also considered and the scaling of the heat transport with Rayleigh number is calculated. This is then compared with existing work on the classical annulus as well as horizontal and Rayleigh-Bénard convection. As with previous studies on both rotating and non-rotating convection the system’s behaviour is found to be aspect ratio dependent. This dependence is seen in the scaling of the non-rotating Nusselt number and in transitions between regimes in the rotating case although further investigation is required to fully explain these observations.
International Nuclear Information System (INIS)
Nelson, E.M.
1993-12-01
Some two-dimensional finite element electromagnetic field solvers are described and tested. For TE and TM modes in homogeneous cylindrical waveguides and monopole modes in homogeneous axisymmetric structures, the solvers find approximate solutions to a weak formulation of the wave equation. Second-order isoparametric lagrangian triangular elements represent the field. For multipole modes in axisymmetric structures, the solver finds approximate solutions to a weak form of the curl-curl formulation of Maxwell's equations. Second-order triangular edge elements represent the radial (ρ) and axial (z) components of the field, while a second-order lagrangian basis represents the azimuthal (φ) component of the field weighted by the radius ρ. A reduced set of basis functions is employed for elements touching the axis. With this basis the spurious modes of the curl-curl formulation have zero frequency, so spurious modes are easily distinguished from non-static physical modes. Tests on an annular ring, a pillbox and a sphere indicate the solutions converge rapidly as the mesh is refined. Computed eigenvalues with relative errors of less than a few parts per million are obtained. Boundary conditions for symmetric, periodic and symmetric-periodic structures are discussed and included in the field solver. Boundary conditions for structures with inversion symmetry are also discussed. Special corner elements are described and employed to improve the accuracy of cylindrical waveguide and monopole modes with singular fields at sharp corners. The field solver is applied to three problems: (1) cross-field amplifier slow-wave circuits, (2) a detuned disk-loaded waveguide linear accelerator structure and (3) a 90 degrees overmoded waveguide bend. The detuned accelerator structure is a critical application of this high accuracy field solver. To maintain low long-range wakefields, tight design and manufacturing tolerances are required
Directory of Open Access Journals (Sweden)
Bogdanović-Jovanović Jasmina B.
2012-01-01
Full Text Available In the increasing need for energy saving worldwide, the designing process of turbomachinery, as an essential part of thermal and hydroenergy systems, goes in the direction of enlarging efficiency. Therefore, the optimization of turbomachinery designing strongly affects the energy efficiency of the entire system. In the designing process of turbomachinery blade profiling, the model of axisymmetric fluid flows is commonly used in technical practice, even though this model suits only the profile cascades with infinite number of infinitely thin blades. The actual flow in turbomachinery profile cascades is not axisymmetric, and it can be fictively derived into the axisymmetric flow by averaging flow parameters in the blade passages according to the circular coordinate. Using numerical simulations of flow in turbomachinery runners, its operating parameters can be preliminarily determined. Furthermore, using the numerically obtained flow parameters in the blade passages, averaged axisymmetric flow surfaces in blade profile cascades can also be determined. The method of determination of averaged flow parameters and averaged meridian streamlines is presented in this paper, using the integral continuity equation for averaged flow parameters. With thus obtained results, every designer can be able to compare the obtained averaged flow surfaces with axisymmetric flow surfaces, as well as the specific work of elementary stages, which are used in the procedure of blade designing. Numerical simulations of flow in an exemplary axial flow pump, used as a part of the thermal power plant cooling system, were performed using Ansys CFX. [Projekat Ministarstva nauke Republike Srbije, br. TR33040: Revitalization of existing and designing new micro and mini hydropower plants (from 100 kW to 1000 kW in the territory of South and Southeast Serbia
Geometry in the Early Years: A Commentary
Dindyal, Jaguthsing
2015-01-01
The primary goal of this paper is to provide a commentary on the teaching and learning of geometry in the early years of schooling with the set of papers in this issue as a guiding factor. It is structured around issues about geometry education of young learners, such as: what should we teach in geometry and why; representation of geometrical…
Blow-Ups in Generalized Complex Geometry
van der Leer Duran, J.L.
2016-01-01
Generalized complex geometry is a theory that unifies complex geometry and symplectic geometry into one single framework. It was introduced by Hitchin and Gualtieri around 2002. In this thesis we address the following question: given a generalized complex manifold together with a submanifold, does
Global affine differential geometry of hypersurfaces
Li, An-Min; Zhao, Guosong; Hu, Zejun
2015-01-01
This book draws a colorful and widespread picture of global affine hypersurface theory up to the most recent state. Moreover, the recent development revealed that affine differential geometry- as differential geometry in general- has an exciting intersection area with other fields of interest, like partial differential equations, global analysis, convex geometry and Riemann surfaces.
Students' Misconceptions and Errors in Transformation Geometry
Ada, Tuba; Kurtulus, Aytac
2010-01-01
This study analyses the students' performances in two-dimensional transformation geometry and explores the mistakes made by the students taking the analytic geometry course given by researchers. An examination was given to students of Education Faculties who have taken the analytic geometry course at Eskisehir Osmangazi University in Turkey. The…