Institute of Scientific and Technical Information of China (English)
无
1995-01-01
The Random Vortex Method extended to an axisymmetrical flow is used in the study of the flow field inside pipes incorporating an orifice plate with different contraction ratios and different inlet velocity profiles.Three test-cases,each having experimental measurements available in the literature,are studied,.In particular,instantaneous and average velocity fields along with the turbulent statistics for high Reynolds number flows are computed and compared to the corresponding experimental results These comparisons show the ability and the limitations of the method.The results of the numerical simulations are used in the physical analysis of the flow fields and thus allow for a better understanding of the dynamics of the flow in pipes incorporating an orifice plate.
Axisymmetric curvature-driven instability in a model divertor geometry
International Nuclear Information System (INIS)
A model problem is presented which qualitatively describes a pressure-driven instability which can occur near the null-point in the divertor region of a tokamak where the poloidal field becomes small. The model problem is described by a horizontal slot with a vertical magnetic field which plays the role of the poloidal field. Line-tying boundary conditions are applied at the planes defining the slot. A toroidal field lying parallel to the planes is assumed to be very strong, thereby constraining the possible structure of the perturbations. Axisymmetric perturbations which leave the toroidal field unperturbed are analyzed. Ideal magnetohydrodynamics is used, and the instability threshold is determined by the energy principle. Because of the boundary conditions, the Euler equation is, in general, non-separable except at marginal stability. This problem may be useful in understanding the source of heat transport into the private flux region in a snowflake divertor which possesses a large region of small poloidal field, and for code benchmarking as it yields simple analytic results in an interesting geometry
Canonical transformation for trapped/passing guiding-center orbits in axisymmetric tokamak geometry
Energy Technology Data Exchange (ETDEWEB)
Brizard, Alain J. [Department of Physics, Saint Michael' s College, Colchester, Vermont 05439 (United States); Duthoit, François-Xavier [CEA, IRFM, F-13108 Saint-Paul-lez-Durance (France); SNU Division of Graduate Education for Sustainabilization of Foundation Energy, Seoul National University, Seoul 151-742 (Korea, Republic of)
2014-05-15
The generating function for the canonical transformation from the parallel canonical coordinates (s,p{sub ||}) to the action-angle coordinates (ζ, J) for trapped/passing guiding-center orbits in axisymmetric tokamak geometry is presented. Drawing on the analogy between the phase-space portraits of the librating/rotating pendulum and the trapped/passing guiding-center orbits, the generating function is expressed in terms of the Jacobi zeta function, which can then readily be used to obtain an explicit expression for the bounce-center transformation for trapped/passing-particle guiding-center orbits in axisymmetric tokamak geometry.
Compact formulas for bounce/transit averaging in axisymmetric tokamak geometry
International Nuclear Information System (INIS)
Compact formulas for bounce and transit orbit averaging of the fluctuation-amplitude eikonal factor in axisymmetric tokamak geometry, which is frequently encountered in bounce-gyrokinetic description of microturbulence, are given in terms of the Jacobi elliptic functions and elliptic integrals. These formulas are readily applicable to the calculation of the neoclassical susceptibility in the framework of modern bounce-gyrokinetic theory. In the long-wavelength limit for axisymmetric electrostatic perturbations, we recover the expression for the Rosenbluth-Hinton residual zonal flow [M. N. Rosenbluth and F. L. Hinton, Phys. Rev. Lett. 80, 724 (1998)] accurately
Late-time tails in a stationary axisymmetric EMDA black hole geometry
Institute of Scientific and Technical Information of China (English)
Pan Qi-Yuan; Jing Ji-Liang
2005-01-01
The late-time tails of massless and self-interacting (SI) (massive) scalar fields are investigated analytically in a stationary axisymmetric Einstein-Maxwell dilaton-axion (EMDA) black hole geometry. It is shown that the asymptotic behaviour of massless perturbations is dominated by an inverse power-law decaying tail and the intermediate asymptotic behaviour of SI (massive) perturbations is dominated by an oscillatory one.
Bounce-averaged Fokker-Planck solver in non-axisymmetric toroidal geometry
Energy Technology Data Exchange (ETDEWEB)
Ju, M.; Basiuk, V.; Peysson, Y
2001-02-01
It is expected that magnetic ripples can have significant effects on the usual trajectories of particles. This leads to the diffusive losses of particle and energy due to magnetic ripples. For the consistent estimation of these losses on Tore Supra, the Fokker-Planck equation bounce-averaged in the axisymmetric toroidal geometry should be bounce-averaged in the non-axisymmetric toroidal geometry including magnetic ripple effects. The bounce averaged coefficients in the Fokker-Planck equation can be represented by the multiplication with the constants such as {lambda}, S{sup *} and ({delta}){sub {tau}{sub B}}. Therefore, in this work, the new explicit expressions for these constants are developed in nonaxisymmetric toroidal geometry for the circulating particles and trapped particles in the usual banana orbits. From the results, it is found out that for circulating particles, the effects of magnetic ripples on the bounce averaged coefficients are negligible while, for banana trapped particles, those effects can be non-negligible. (authors)
Asymptotic Tails of Massive Scalar Fields in a Stationary Axisymmetric EMDA Black Hole Geometry
Institute of Scientific and Technical Information of China (English)
PAN Qi-Yuan; JING Ji-Liang
2004-01-01
The late-time tail behaviour of massive scalar fields is studied analytically in a stationary axisymmetric EinsteinMaxwell Dilaton-Axion (EMDA) black hole geometry. It is shown that the asymptotic behaviour of massive perturbations is dominated by the oscillatory inverse power-law decaying tail t-(l+3/2) sin(μt) at the intermediate late times, and by the asymptotic tail t-5/6 sin(μt) at asymptotically late times, with μ being field mass. Our result seems to suggest that the intermediate tails t-(l+3/2) sin(μt) and the asymptotically tails t-5/6 sin(μt) may be a quite general feature for evolution of massive scalar fields in any four-dimensional asymptotically flat rotating black hole backgrounds.
Quantum roots in geometry : II
International Nuclear Information System (INIS)
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
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, {\\bf{Spin-Torsion Interaction}}, has been used to overcome the discrepancy in the results of the COW-experiment. The second interaction, {\\bf{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-g...
International Nuclear Information System (INIS)
Two refined axisymmetric finite element models were used for the dynamic seismic analyses of the KKP-II Containment and RPV structures, using a postulated ground motion time history. One model was established primarily for the response of the containment structure, whereas the other was used for the response of the reactor pressure vessel plus internals. (Auth.)
Generalized geometry lectures on type II backgrounds
Tsimpis, Dimitrios
2016-01-01
The first part of these notes is a self-contained introduction to generalized complex geometry. It is intended as a `user manual' for tools used in the study of supersymmetric backgrounds of supergravity. In the second part we review some past and recent results on the generalized complex structure of supersymmetric type II vacua in various dimensions.
Energy Technology Data Exchange (ETDEWEB)
Shapiro, A.B.
1983-08-01
The computer code FACET calculates the radiation geometric view factor (alternatively called shape factor, angle factor, or configuration factor) between surfaces for axisymmetric, two-dimensional planar and three-dimensional geometries with interposed third surface obstructions. FACET was developed to calculate view factors for input to finite-element heat-transfer analysis codes. The first section of this report is a brief review of previous radiation-view-factor computer codes. The second section presents the defining integral equation for the geometric view factor between two surfaces and the assumptions made in its derivation. Also in this section are the numerical algorithms used to integrate this equation for the various geometries. The third section presents the algorithms used to detect self-shadowing and third-surface shadowing between the two surfaces for which a view factor is being calculated. The fourth section provides a user's input guide followed by several example problems.
Perturbation analysis of trapped-particle dynamics in axisymmetric dipole geometry
Duthoit, F -X; Peysson, Y; Decker, J
2010-01-01
The perturbation analysis of the bounce action-angle coordinates $(J,\\zeta)$ for charged particles trapped in an axisymmetric dipole magnetic field is presented. First, the lowest-order bounce action-angle coordinates are derived for deeply-trapped particles in the harmonic-oscillator approximation. Next, the Lie-transform perturbation method is used to derive higher-order anharmonic action-angle corrections. Explicit expressions (with anharmonic corrections) for the canonical parallel coordinates $s(J,\\zeta)$ and $p_{\\|}(J,\\zeta)$ are presented, which satisfy the canonical identity $\\{s,\\; p_{\\|}\\}(J,\\zeta) \\equiv 1$. Lastly, analytical expressions for the bounce and drift frequencies (which include anharmonic corrections) yield excellent agreement with exact numerical results.
Geometry of the TJ-II in Astra 6.0
International Nuclear Information System (INIS)
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
Line geometry and electromagnetism II: wave motion
Delphenich, D H
2013-01-01
The fundamental role of line geometry in the study of wave motion is first introduced in the general context by way of the tangent planes to the instantaneous wave surfaces, in which it is first observed that the possible frequency-wave number 1-forms are typically constrained by a dispersion law that is derived from a constitutive law by way of the field equations. After a general review of the basic concepts that relate to quadratic line complexes, these geometric notions are applied to the study of electromagnetic waves, in particular.
Line geometry and electromagnetism II: wave motion
Delphenich, D. H.
2013-01-01
The fundamental role of line geometry in the study of wave motion is first introduced in the general context by way of the tangent planes to the instantaneous wave surfaces, in which it is first observed that the possible frequency-wave number 1-forms are typically constrained by a dispersion law that is derived from a constitutive law by way of the field equations. After a general review of the basic concepts that relate to quadratic line complexes, these geometric notions are applied to the...
International Nuclear Information System (INIS)
The aim of this paper is to solve axisymmetric problems found in nuclear reactors engineering. Thus, a stabilized finite element formulation for the solution of the Navier-Stokes and energy equations for axisymmetric problems has been developed and tested. This formulation has been implemented in the NSSOLVERMPI2DA 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. The results show the simulation of the mixed convection phenomena that occurs in the downcomer of a PWR nuclear reactor(author)
Generalised geometry and type II supergravity
International Nuclear Information System (INIS)
Ten-dimensional type II supergravity can be reformulated as a generalised geometrical analogue of Einstein gravity, defined by an O(9,1) x O(1,9) is contained in O(10,10) x R + structure on the generalised tangent space. To leading order in the fermion fields, this allow one to rewrite the action, equations of motion and supersymmetry variations in a simple, manifestly Spin(9,1) x Spin(1,9)-covariant form. (Copyright copyright 2012 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
International Nuclear Information System (INIS)
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 NSSOLVERMPI2DA 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)
Geometry of type II common sector N = 2 backgrounds
International Nuclear Information System (INIS)
We describe the geometry of all type II common sector backgrounds with two supersymmetries. In particular, we determine the spacetime geometry of those supersymmetric backgrounds for which each copy of the Killing spinor equations admits a Killing spinor. The stability subgroups of both Killing spinors are Spin(7) x R8, SU(4) x R8 and G2 for IIB backgrounds, and Spin(7), SU(4) and G2 x R8 for IIA backgrounds. We show that the spacetime of backgrounds with spinors that have stability subgroup K x R8 is a pp-wave propagating in an eight-dimensional manifold with a K-structure. The spacetime of backgrounds with K-invariant Killing spinors is a fibre bundle with fibre spanned by the orbits of two commuting null Killing vector fields and base space an eight-dimensional manifold which admits a K-structure. Type II T-duality interchanges the backgrounds with K- and K x R8-invariant Killing spinors. We show that the geometries of the base space of the fibre bundle and the corresponding space in which the pp-wave propagates are the same. The conformal symmetry of the world-sheet action of type II strings propagating in these N = 2 backgrounds can always be fixed in the light-cone gauge
Zhong, Shiyan; Spurzem, Rainer
2015-01-01
Tidal Disruption of stars by supermassive central black holes from dense rotating star clusters is modelled by high-accuracy direct N-body simulation. As in a previous paper on spherical star clusters we study the time evolution of the stellar tidal disruption rate and the origin of tidally disrupted stars, now according to several classes of orbits which only occur in axisymmetric systems (short axis tube and saucer). Compared with that in spherical systems, we found a higher TD rate in axisymmetric systems. The enhancement can be explained by an enlarged loss-cone in phase space which is raised from the fact that total angular momentum $\\bf J$ is not conserved. As in the case of spherical systems, the distribution of the last apocenter distance of tidally accreted stars peaks at the classical critical radius. However, the angular distribution of the origin of the accreted stars reveals interesting features. Inside the influence radius of the supermassive black hole the angular distribution of disrupted star...
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.
International Nuclear Information System (INIS)
Essential data which include the characteristics of soil-structure interaction on Quaternary deposits were obtained from forced vibration tests. The uses of these characteristics in analysis are also discussed. Two analyses have been conducted for G L+18.8 m excitation in the X-direction. The first was a preliminary analysis carried out before forced vibration tests using the axisymmetric finite element (FE) model used in the design procedure. The other was a simulation analysis carried out after the test. This paper describes the Atucha II characteristics, constructed on Quaternary deposits, by axisymmetric FE analysis. (author). 2 refs., 9 figs., 2 tabs
A Particle Simulation for the Axisymmetric Pulsar Magnetosphere: II. the case of dipole field
Wada, Tomohide
2011-01-01
The main issue of the pulsar magnetosphere is how the rotation power is converted into both particle beams which causes pulsed emissions, and a highly relativistic wind of electron-positron plasmas which forms surrounding nebulae shining in X-rays and TeV gamma-rays. As a sequel of the first paper (Wada & Shibata 2007), we carried out a three dimensional particle simulation for the axisymmetric global magnetosphere. We present the results of additional calculations, which are higher resolution model and higher pair creation rate cases, and a detailed analysis for the solution. We confined to demonstrate the cases of low pair creation rate, i.e., the magnetic field is fixed dipole. The radiation drag of the plasma is taken in a form with the curvature radius along the dipole magnetic field. The electrostatic interactions are calculated by a programmable special purpose computer, GRAPE-DR (Makino et al 2007). Once pair creation is onset in the outer gaps, the both signed particles begin to drift across the ...
Shubnikov state in complex geometry Type-II Technetium device
International Nuclear Information System (INIS)
We investigate numerically the flux quantum configurations and some thermodynamic properties of a superconducting Technetium film by using the link variables technique for one shape of circular geometry. The Technetium exhibits superconductivity properties indicated by to an extrapolated critical magnetic field value of Hc(T = 0) = 1410 Oe, a Ginzburg-Landau parameter of κ = 0.92, and a critical temperature Tc = 7.86K, being the magnetic behavior of this material characteristic of a type-II superconductor with a weak-coupling superconductor of the BCS type. The studied sample is a circular sector with angular width θ = 7π/4 surrounded by a dielectric material and submitted to external magnetic field applied perpendicular to its plane. We evaluate the magnetic moment density, Shubnikov state and free Gibbs energy as a function of the external magnetic field
Synthetic line and continuum linear-polarisation signatures of axisymmetric type II supernova ejecta
Dessart, Luc; Hillier, D. John
2011-01-01
We present synthetic single-line and continuum linear-polarisation signatures due to electron scattering in axially-symmetric Type II supernovae (SNe) which we calculate using a Monte Carlo and a long-characteristic radiative-transfer code. Aspherical ejecta are produced by prescribing a latitudinal scaling or stretching of SN ejecta inputs obtained from 1-D non-LTE time-dependent calculations. We study polarisation signatures as a function of inclination, shape factor, wavelength, line ident...
International Nuclear Information System (INIS)
This work determines the dynamic characteristics of the reactor building of the heavy water reactor Atucha II and to checks certain analytical procedures used to validate full-scale vibration tests. Soil-structure interaction effects were incorporated by means of springs and dampers which represent the soil behavior. The full-scale vibration tests were reproduced using a simplified axisymmetric model. (author). 3 refs., 25 figs., 1 tab
Supersymmetric Background of Type II Theories and Generalized Geometry
International Nuclear Information System (INIS)
I will present an outline of generalised geometry and I show how it provides a natural description of supersymmetric backgrounds. The discussion will be in slightly different terms to those appearing in the majority of the literature. It appears that: -) generalized geometry is a natural extension of differential geometry, -) we have brackets, metrics, spinors etc, in generalized geometry, and -) N=1 vacuum equations look more natural in this language. This document is composed of the slides of the presentation. (author)
Synthetic line and continuum linear-polarisation signatures of axisymmetric type II supernova ejecta
Dessart, Luc
2011-01-01
We present synthetic single-line and continuum linear-polarisation signatures due to electron scattering in axially-symmetric Type II supernovae (SNe) which we calculate using a Monte Carlo and a long-characteristic radiative-transfer code. Aspherical ejecta are produced by prescribing a latitudinal scaling or stretching of SN ejecta inputs obtained from 1-D non-LTE time-dependent calculations. We study polarisation signatures as a function of inclination, shape factor, wavelength, line identity, post-explosion time. At early times, cancellation and optical-depth effects make the polarisation intrinsically low, causing complicated sign reversals with inclination or continuum wavelength, and across line profiles. While the line polarisation is positive (negative) for an oblate (prolate) morphology at the peak and in the red wing, the continuum polarisation may be of any sign. These complex polarisation variations are produced not just by the asymmetric distribution of scatterers but also of the flux. Our early...
Incidence Geometry in a Weyl Chamber II: $SL_n$
Esole, Mboyo; Jagadeesan, Ravi; Noël, Alfred G
2016-01-01
We study the polyhedral geometry of the hyperplanes orthogonal to the weights of the first and the second fundamental representations of $sl_n$ inside the dual fundamental Weyl chamber. We obtain generating functions that enumerate the flats and the faces of a fixed dimension. In addition, we describe the extreme rays of the incidence geometry and classify simplicial faces. From the perspective of supersymmetric gauge theories with 8 supercharges in five dimensional spacetime, the poset of flats is isomorphic to the network of mixed Coulomb-Higgs branches. On the other hand, the poset of faces is conjectured to be isomorphic to the network of crepant partial resolutions of an elliptic fibration with gauge algebra $sl_n$ and "matter representation" given by the sum of the first two fundamental representations.
Pedoe, Dan
1988-01-01
""A lucid and masterly survey."" - Mathematics Gazette Professor Pedoe is widely known as a fine teacher and a fine geometer. His abilities in both areas are clearly evident in this self-contained, well-written, and lucid introduction to the scope and methods of elementary geometry. It covers the geometry usually included in undergraduate courses in mathematics, except for the theory of convex sets. Based on a course given by the author for several years at the University of Minnesota, the main purpose of the book is to increase geometrical, and therefore mathematical, understanding and to he
International Nuclear Information System (INIS)
The weighted-sum-of-gray-gases (WSGG) model is widely used in engineering computations of radiative heat transfer due to its relative simplicity, robustness and flexibility. This paper presents the computation of radiative heat transfer in a 2D axisymmetric chamber using two WSGG models to compute radiation in H2O and CO2 mixtures. The first model considers a fixed ratio between the molar concentrations of H2O and CO2, while the second allows the solution for arbitrary ratios. The correlations for both models are based on the HITEMP2010 database. The test case considers typical conditions found in turbulent methane flames, with steep variations in the temperature field as well as in the molar concentrations of the participating species. To assess the accuracy of the WSGG model, the results are compared with a solution obtained by line-by-line integration (LBL) of the spectrum. - Highlights: • The paper presents solutions of radiative heat transfer in a 2D axisymmetric chamber. • The temperature and concentration fields are representative of methane turbulent flames. • Solutions from line-by-line integration of the RTE are presented for evaluation of gas models. • WSGG models considering constant and non-constant pressure ratios of H2O and CO2 are employed. • Solutions from the WSGG models proved to be accurate for the proposed test case
KENO-PLOT, JUNEBUG-II-JR: two- and three-dimensional geometry plotting program
International Nuclear Information System (INIS)
This paper is a user manual of two plotting programs KENO-PLOT and JUNEBUG-II-JR. These programs will be included in the revision of nuclear criticality safety evaluation code system JACS. The KENO-PLOT program plots two-dimensional geometry (cross section) described by the standard KENO-IV input data or the generalized geometry input data. The JUNEBUG-II-JR program based on the JUNEBUG-II program in a modular code system SCALE 3 plots three-dimensional geometry described by not only KENO-IV or KENO-IV/CG input data, but also MULTI-KENO input data, and does not need the DISSPLA graphic software. Two- and three-dimensional pictures plotted by these programs assist KENO-family program users in checking the KENO input data made by themselves. (author)
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....
Zn(II) and Hg(II) binding to a designed peptide that accommodates different coordination geometries.
Szunyogh, Dániel; Gyurcsik, Béla; Larsen, Flemming H; Stachura, Monika; Thulstrup, Peter W; Hemmingsen, Lars; Jancsó, Attila
2015-07-28
Designed metal ion binding peptides offer a variety of applications in both basic science as model systems of more complex metalloproteins, and in biotechnology, e.g. in bioremediation of toxic metal ions, biomining or as artificial enzymes. In this work a peptide (HS: Ac-SCHGDQGSDCSI-NH2) has been specifically designed for binding of both Zn(II) and Hg(II), i.e. metal ions with different preferences in terms of coordination number, coordination geometry, and to some extent ligand composition. It is demonstrated that HS accommodates both metal ions, and the first coordination sphere, metal ion exchange between peptides, and speciation are characterized as a function of pH using UV-absorption-, synchrotron radiation CD-, (1)H-NMR-, and PAC-spectroscopy as well as potentiometry. Hg(II) binds to the peptide with very high affinity in a {HgS2} coordination geometry, bringing together the two cysteinates close to each end of the peptide in a loop structure. Despite the high affinity, Hg(II) is kinetically labile, exchanging between peptides on the subsecond timescale, as indicated by line broadening in (1)H-NMR. The Zn(II)-HS system displays more complex speciation, involving monomeric species with coordinating cysteinates, histidine, and a solvent water molecule, as well as HS-Zn(II)-HS complexes. In summary, the HS peptide displays conformational flexibility, contains many typical metal ion binding groups, and is able to accommodate metal ions with different structural and ligand preferences with high affinity. As such, the HS peptide may be a scaffold offering binding of a variety of metal ions, and potentially serve for metal ion sequestration in biotechnological applications. PMID:26040991
Axisymmetric Coanda-Assisted Vectoring
Allen, Dustin S
2008-01-01
An examination of parameters affecting the control of a jet vectoring technique used in the Coanda-assisted Spray Manipulation (CSM) is presented. The CSM makes use of an enhanced Coanda effect on axisymmetric geometries through the interaction of a high volume primary jet flowing through the center of a collar and a secondary high-momentum jet parallel to the first and adjacent to the convex collar. The control jet attaches to the convex wall and vectors according to known Coanda effect prin...
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.
XAFS study of copper(II) complexes with square planar and square pyramidal coordination geometries
Gaur, A.; Klysubun, W.; Nitin Nair, N.; Shrivastava, B. D.; Prasad, J.; Srivastava, K.
2016-08-01
X-ray absorption fine structure of six Cu(II) complexes, Cu2(Clna)4 2H2O (1), Cu2(ac)4 2H2O (2), Cu2(phac)4 (pyz) (3), Cu2(bpy)2(na)2 H2O (ClO4) (4), Cu2(teen)4(OH)2(ClO4)2 (5) and Cu2(tmen)4(OH)2(ClO4)2 (6) (where ac, phac, pyz, bpy, na, teen, tmen = acetate, phenyl acetate, pyrazole, bipyridine, nicotinic acid, tetraethyethylenediamine, tetramethylethylenediamine, respectively), which were supposed to have square pyramidal and square planar coordination geometries have been investigated. The differences observed in the X-ray absorption near edge structure (XANES) features of the standard compounds having four, five and six coordination geometry points towards presence of square planar and square pyramidal geometry around Cu centre in the studied complexes. The presence of intense pre-edge feature in the spectra of four complexes, 1-4, indicates square pyramidal coordination. Another important XANES feature, present in complexes 5 and 6, is prominent shoulder in the rising part of edge whose intensity decreases in the presence of axial ligands and thus indicates four coordination in these complexes. Ab initio calculations were carried out for square planar and square pyramidal Cu centres to observe the variation of 4p density of states in the presence and absence of axial ligands. To determine the number and distance of scattering atoms around Cu centre in the complexes, EXAFS analysis has been done using the paths obtained from Cu(II) oxide model and an axial Cu-O path from model of a square pyramidal complex. The results obtained from EXAFS analysis have been reported which confirmed the inference drawn from XANES features. Thus, it has been shown that these paths from model of a standard compound can be used to determine the structural parameters for complexes having unknown structure.
International Nuclear Information System (INIS)
Previously obtained PMR data from an investigation of the complexation of cobalt(II) and nickel(II) with L-histidine have been used to separate overall paramagnetic shifts into their contact and dipolar components. The geometry of the complexes Co(his)2 and Ni(his)2 has been calculated from the latter. Good agreement between the calculated and x-ray structural data has been obtained under the assumption that the magnetic moment remains axially isotropic when its direction is varied. Such correspondence was not obtained for the 1:1 complexes due to the triaxial anisotropy of the magnetic moment, which is possible for these complexes. Conclusions regarding the geometry of the histidine complexes of Co(II) and Ni(II) in aqueous solutions and the solid phase have been drawn
Black holes in the Einstein -Gauss-Bonnet theory and the geometry of their thermodynamics-II
Biswas, Ritabrata; Chakraborty, Subenoy
2009-01-01
In the present work we study (i) charged black hole in Einstein-Gauss-Bonnet (EGB) theory, known as Einstein-Maxwell-Gauss-Bonnet (EMGB) black hole and (ii) black hole in EGB gravity with Yang-Mills field. The thermodynamic geometry of these two black hole solutions has been investigated, using the modified entropy in Gauss-Bonnet theory.
Axisymmetric flows from fluid injection into a confined porous medium
Guo, Bo; Zheng, Zhong; Celia, Michael A.; Stone, Howard A.
2016-02-01
We study the axisymmetric flows generated from fluid injection into a horizontal confined porous medium that is originally saturated with another fluid of different density and viscosity. Neglecting the effects of surface tension and fluid mixing, we use the lubrication approximation to obtain a nonlinear advection-diffusion equation that describes the time evolution of the sharp fluid-fluid interface. The flow behaviors are controlled by two dimensionless groups: M, the viscosity ratio of displaced fluid relative to injected fluid, and Γ, which measures the relative importance of buoyancy and fluid injection. For this axisymmetric geometry, the similarity solution involving R2/T (where R is the dimensionless radial coordinate and T is the dimensionless time) is an exact solution to the nonlinear governing equation for all times. Four analytical expressions are identified as asymptotic approximations (two of which are new solutions): (i) injection-driven flow with the injected fluid being more viscous than the displaced fluid (Γ ≪ 1 and M interface shape; (ii) injection-driven flow with injected and displaced fluids of equal viscosity (Γ ≪ 1 and M = 1), where we find a self-similar solution that predicts a distinct parabolic interface shape; (iii) injection-driven flow with a less viscous injected fluid (Γ ≪ 1 and M > 1) for which there is a rarefaction wave solution, assuming that the Saffman-Taylor instability does not occur at the reservoir scale; and (iv) buoyancy-driven flow (Γ ≫ 1) for which there is a well-known self-similar solution corresponding to gravity currents in an unconfined porous medium [S. Lyle et al. "Axisymmetric gravity currents in a porous medium," J. Fluid Mech. 543, 293-302 (2005)]. The various axisymmetric flows are summarized in a Γ-M regime diagram with five distinct dynamic behaviors including the four asymptotic regimes and an intermediate regime. The implications of the regime diagram are discussed using practical
Axisymmetric Plume Simulations with NASA's DSMC Analysis Code
Stewart, B. D.; Lumpkin, F. E., III
2012-01-01
A comparison of axisymmetric Direct Simulation Monte Carlo (DSMC) Analysis Code (DAC) results to analytic and Computational Fluid Dynamics (CFD) solutions in the near continuum regime and to 3D DAC solutions in the rarefied regime for expansion plumes into a vacuum is performed to investigate the validity of the newest DAC axisymmetric implementation. This new implementation, based on the standard DSMC axisymmetric approach where the representative molecules are allowed to move in all three dimensions but are rotated back to the plane of symmetry by the end of the move step, has been fully integrated into the 3D-based DAC code and therefore retains all of DAC s features, such as being able to compute flow over complex geometries and to model chemistry. Axisymmetric DAC results for a spherically symmetric isentropic expansion are in very good agreement with a source flow analytic solution in the continuum regime and show departure from equilibrium downstream of the estimated breakdown location. Axisymmetric density contours also compare favorably against CFD results for the R1E thruster while temperature contours depart from equilibrium very rapidly away from the estimated breakdown surface. Finally, axisymmetric and 3D DAC results are in very good agreement over the entire plume region and, as expected, this new axisymmetric implementation shows a significant reduction in computer resources required to achieve accurate simulations for this problem over the 3D simulations.
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...
Energy Technology Data Exchange (ETDEWEB)
Souza, Altivo Monteiro de
2008-12-15
The world energy consumption has been increasing strongly in recent years. Nuclear energy has been regarded as a suitable option to supply this growing energy demand in industrial scale. In view of the need of improving the understanding and capacity of analysis of nuclear power plants, modern simulation techniques for flow and heat transfer problems are gaining greater importance. A large number of problems found in nuclear reactor engineering can be dealt assuming axial symmetry. Thus, in this work a stabilized finite element formulation for the solution of the Navier-Stokes and energy equations for axisymmetric problems have been developed and tested. The formulation has been implemented in the NS{sub S}OLVER{sub M}PI{sub 2}D{sub A} program developed at the Parallel Computation Laboratory of the Instituto de Engenharia Nuclear (LCP/IEN) and is now available either for safety analysis or design of nuclear systems. (author)
Axisymmetric multiwormholes revisited
Clément, Gérard
2016-06-01
The construction of stationary axisymmetric multiwormhole solutions to gravitating field theories admitting toroidal reductions to three-dimensional gravitating sigma models is reviewed. We show that, as in the multi-black hole case, strut singularities always appear in this construction, except for very special configurations with an odd number of centers. We also review the analytical continuation of the multicenter solution across the n cuts associated with the wormhole mouths. The resulting Riemann manifold has 2^n sheets interconnected by 2^{n-1}n wormholes. We find that the maximally extended multicenter solution can never be asymptotically locally flat in all the Riemann sheets.
Axisymmetric multiwormholes revisited
Clément, Gérard
2015-01-01
The construction of stationary axisymmetric multiwormhole solutions to gravitating field theories admitting toroidal reductions to three-dimensional gravitating sigma models is reviewed. We show that, as in the multi-black hole case, strut singularities always appear in this construction, except for very special configurations with an odd number of centers. We also review the analytical continuation of the multicenter solution across the $n$ cuts associated with the wormhole mouths. The resulting Riemann manifold has $2^n$ sheets interconnected by $2^{n-1}n$ wormholes. We find that the maximally extended multicenter solution can never be asymptotically locally flat in all the Riemann sheets.
Nonassociative geometry in quasi-Hopf representation categories II: Connections and curvature
Barnes, Gwendolyn E.; Schenkel, Alexander; Szabo, Richard J.
2016-08-01
We continue our systematic development of noncommutative and nonassociative differential geometry internal to the representation category of a quasitriangular quasi-Hopf algebra. We describe derivations, differential operators, differential calculi and connections using universal categorical constructions to capture algebraic properties such as Leibniz rules. Our main result is the construction of morphisms which provide prescriptions for lifting connections to tensor products and to internal homomorphisms. We describe the curvatures of connections within our formalism, and also the formulation of Einstein-Cartan geometry as a putative framework for a nonassociative theory of gravity.
Axisymmetric Coanda-assisted vectoring
Energy Technology Data Exchange (ETDEWEB)
Allen, Dustin; Smith, Barton L. [Utah State University, Mechanical and Aerospace Engineering, Logan, UT (United States)
2009-01-15
An experimental demonstration of a jet vectoring technique used in our novel spray method called Coanda-assisted Spray Manipulation (CSM) is presented. CSM makes use of the Coanda effect on axisymmetric geometries through the interaction of two jets: a primary jet and a control jet. The primary jet has larger volume flow rate but generally a smaller momentum flux than the control jet. The primary jet flows through the center of a rounded collar. The control jet is parallel to the primary and is adjacent to the convex collar. The Reynolds number range for the primary jet at the exit plane was between 20,000 and 80,000. The flow was in the incompressible Mach number range (Mach<0.3). The control jet attaches to the convex wall and vectors according to known Coanda effect principles, entraining and vectoring the primary jet, resulting in controllable r-{theta} directional spraying. Several annular control slots and collar radii were tested over a range of momentum flux ratios to determine the effects of these variables on the vectored jet angle and spreading. Two and Three-component Particle Image Velocimetry systems were used to determine the vectoring angle and the profile of the combined jet in each experiment. The experiments show that the control slot and expansion radius, along with the momentum ratios of the two jets predominantly affected the vectoring angle and profile of the combined jets. (orig.)
Axisymmetric Coanda-assisted vectoring
Allen, Dustin; Smith, Barton L.
2009-01-01
An experimental demonstration of a jet vectoring technique used in our novel spray method called Coanda-assisted Spray Manipulation (CSM) is presented. CSM makes use of the Coanda effect on axisymmetric geometries through the interaction of two jets: a primary jet and a control jet. The primary jet has larger volume flow rate but generally a smaller momentum flux than the control jet. The primary jet flows through the center of a rounded collar. The control jet is parallel to the primary and is adjacent to the convex collar. The Reynolds number range for the primary jet at the exit plane was between 20,000 and 80,000. The flow was in the incompressible Mach number range (Mach Coanda effect principles, entraining and vectoring the primary jet, resulting in controllable r - θ directional spraying. Several annular control slots and collar radii were tested over a range of momentum flux ratios to determine the effects of these variables on the vectored jet angle and spreading. Two and Three-component Particle Image Velocimetry systems were used to determine the vectoring angle and the profile of the combined jet in each experiment. The experiments show that the control slot and expansion radius, along with the momentum ratios of the two jets predominantly affected the vectoring angle and profile of the combined jets.
Axisymmetric control in tokamaks
International Nuclear Information System (INIS)
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 sep = 1.85 can be stabilized robustly with the present control architecture and conductor/sensor configuration
The Influence of Environment Geometry on Injury Outcome: II. Lumbosacral Spine
Shaibani, Saami J.
2006-03-01
It is widely agreed that the type of motor vehicle in which an occupant is situated can sometimes make a noticeable difference in injury potential even when the insult suffered is the same. A simple example might be the same occupant being in a sports car as opposed to a minivan, but such anecdotal experience does not usually help to distinguish the effect of particular features within the same category of vehicle. Other research has addressed the role of environment geometry in neck injury,[1] and this paper adopts the same methodology for the low back. The heights, lengths and angles of the seat cushion and seat back (including head rest) are all examined as descriptors of passenger compartment geometry, and any changes caused by these are determined. Useful results are feasible with the large patient population available even if clear patterns in these are not always present. As in earlier work, there is still the option of finding individual outcomes on a case-by-case basis. [1] The influence of environment geometry on injury outcome: I. Cervical spine, Bull Am Phys Soc, in press (2006).
Optical knots and contact geometry II. From Hopf links to transverse and cosmetic knots
Kholodenko, Arkady L
2014-01-01
In 1985 Moffatt conjectured that in steady incompressible Euler-type fluids the streamlines could have knots/links of all types. Using methods of contact geometry Etnyre and Ghrist in 2000 developed the existence-type proof of the Moffatt conjecture. The alternative proof, also of existence-type, was proposed by Enciso and Peralta -Salas in 2012. In all three papers the Beltrami equation was used as point of departure. However, only work by Etnyre and Ghrist takes full advantage of contact-geometric nature of the Beltrami equation. In this work we propose the constructive proof of the Moffatt conjecture based on ideas and methods of contact geometry. We discuss in sufficient detail various physical processes generating such knotted structures. By employing the correspondence between ideal hydrodynamics and electrodynamics discussed in part I, the Moffatt conjecture is proved for Maxwellian electrodynamics. The potential relevance of the obtained results for source-free Yang-Mills and gravity fields is also br...
On geometry of deformed black holes: II. Schwarzschild hole surrounded by a Bach-Weyl ring
Basovník, M
2016-01-01
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...
Stability of Axisymmetric Liquid Bridges
Rubinstein, Boris
2016-01-01
We study stability of axisymmetric liquid bridges between two axisymmetric solid bodies in the absence of gravity under arbitrary asymmetric perturbations which are expanded into a set of angular Fourier modes. We determine the stability region boundary for every angular mode in case of both fixed and free contact lines. Application of this approach allows us to demonstrate existence of stable convex nodoid menisci between two spheres.
Terzis, Petros A
2010-01-01
Lie group symmetry analysis for systems of coupled, nonlinear ordinary differential equations is performed in order to obtain the entire solution space to Einstein's field equations for vacuum Bianchi spacetime geometries. The symmetries used are the automorphisms of the Lie algebra of the corresponding three- dimensional isometry group acting on the hyper-surfaces of simultaneity for each Bianchi Type, as well as the scaling and the time reparametrization symmetry. The method is applied to Bianchi Types I; II; IV and V. The result is the acquisition, in each case, of the entire solution space of either Lorenzian of Euclidean signature. This includes all the known solutions for each Type and the general solution of Type IV (in terms of sixth Painlev\\'e transcendent PVI).
Supergravity as Generalised Geometry II: $E_{d(d)} \\times \\mathbb{R}^+$ and M theory
Coimbra, André; Waldram, Daniel
2012-01-01
We reformulate eleven-dimensional supergravity, including fermions, in terms of generalised geometry, for spacetimes that are warped products of Minkowski space with a $d$-dimensional manifold $M$ with $d\\leq7$. The reformation has a $E_{d(d)} \\times \\mathbb{R}^+$ structure group and is has a local $\\tilde{H}_d$ symmetry, where $\\tilde{H}_d$ is the double cover of the maximally compact subgroup of $E_{d(d)}$. The bosonic degrees for freedom unify into a generalised metric, and, defining the generalised analogue $D$ of the Levi-Civita connection, one finds that the corresponding equations of motion are the vanishing of the generalised Ricci tensor. To leading order, we show that the fermionic equations of motion, action and supersymmetry variations can all be written in terms of $D$. Although we will not give the detailed decompositions, this reformulation is equally applicable to type IIA or IIB supergravity restricted to a $(d-1)$-dimensional manifold. For completeness we give explicit expressions in terms o...
Axisymmetric annular curtain stability
International Nuclear Information System (INIS)
A temporal stability analysis was carried out to investigate the stability of an axially moving viscous annular liquid jet subject to axisymmetric disturbances in surrounding co-flowing viscous gas media. We investigated in this study the effects of inertia, surface tension, the gas-to-liquid density ratio, the inner-to-outer radius ratio and the gas-to-liquid viscosity ratio on the stability of the jet. With an increase in inertia, the growth rate of the unstable disturbances is found to increase. The dominant (or most unstable) wavenumber decreases with increasing Reynolds number for larger values of the gas-to-liquid viscosity ratio. However, an opposite tendency for the most unstable wavenumber is predicted for small viscosity ratio in the same inertia range. The surrounding gas density, in the presence of viscosity, always reduces the growth rate, hence stabilizing the flow. There exists a critical value of the density ratio above which the flow becomes stable for very small viscosity ratio, whereas for large viscosity ratio, no stable flow appears in the same range of the density ratio. The curvature has a significant destabilizing effect on the thin annular jet, whereas for a relatively thick jet, the maximum growth rate decreases as the inner radius increases, irrespective of the surrounding gas viscosity. The degree of instability increases with Weber number for a relatively large viscosity ratio. In contrast, for small viscosity ratio, the growth rate exhibits a dramatic dependence on the surface tension. There is a small Weber number range, which depends on the viscosity ratio, where the flow is stable. The viscosity ratio always stabilizes the flow. However, the dominant wavenumber increases with increasing viscosity ratio. The range of unstable wavenumbers is affected only by the curvature effect. (paper)
Axisymmetric fretting analysis in coated cylinder
Indian Academy of Sciences (India)
M Ramesh; Satish V Kailas; K R Y Simha
2008-06-01
Fretting is essentially a contact fatigue phenomenon, although bulk stresses and material properties contribute to ﬁnal failure. The near surface state of stress developed under oscillatory contact between machine elements plays a major role in deciding the severity of fretting. It is possible to enhance tribological properties by coating the surface. There is rather scanty literature available on fretting analysis of coated components. Presence of such coatings has a large inﬂuence on the near surface state of stress. The effect of coatings on the severity of fretting is the focus of this paper. Results obtained for both hard and soft coatings are compared with the results obtained for the homogeneous case. The component geometry and loading are chosen to be cylindrical to enable 3D elastic axisymmetric fretting analysis. The results are compared with 2D models (strip and half-plane) to examine their utility and validity for understanding axisymmetric fretting. Contact pressure and frictional shear loading cases are solved separately and superposed appropriately depending on the coefﬁcient of friction considered. Results for different values of coefﬁcient of friction and elastic mismatch are illustrated through contour plots of stresses and strains. These results are expected to be helpful for identifying fretting failure zones and fracture mechanisms in coated components. Analytical results presented here could serve as useful benchmarks for calibrating numerical codes and experimental techniques.
Classification of Stellar Orbits in Axisymmetric Galaxies
Li, Baile; Holley-Bockelmann, Kelly; Khan, Fazeel Mahmood
2015-09-01
It is known that two supermassive black holes (SMBHs) cannot merge in a spherical galaxy within a Hubble time; an emerging picture is that galaxy geometry, rotation, and large potential perturbations may usher the SMBH binary through the critical three-body scattering phase and ultimately drive the SMBH to coalesce. We explore the orbital content within an N-body model of a mildly flattened, non-rotating, SMBH-embedded elliptical galaxy. When used as the foundation for a study on the SMBH binary coalescence, the black holes bypassed the binary stalling often seen within spherical galaxies and merged on gigayear timescales. Using both frequency-mapping and angular momentum criteria, we identify a wealth of resonant orbits in the axisymmetric model, including saucers, that are absent from an otherwise identical spherical system and that can potentially interact with the binary. We quantified the set of orbits that could be scattered by the SMBH binary, and found that the axisymmetric model contained nearly six times the number of these potential loss cone orbits compared to our equivalent spherical model. In this flattened model, the mass of these orbits is more than three times that of the SMBH, which is consistent with what the SMBH binary needs to scatter to transition into the gravitational wave regime.
Classification of Stellar Orbits in Axisymmetric Galaxies
Li, Baile; Khan, Fazeel
2014-01-01
It is known that two supermassive black holes (SMBHs) cannot merge in a spherical galaxy within a Hubble time; an emerging picture is that galaxy geometry, rotation, and large potential perturbations may usher the SMBH binary through the critical three-body scattering phase and ultimately drive the SMBH to coalesce. We explore the orbital content within an N-body model of a mildly- flattened, non-rotating, SMBH-embedded elliptical galaxy. When used as the foundation for a study on the SMBH binary coalescence, the black holes bypassed the binary stalling often seen within spherical galaxies and merged on Gyr timescales (Khan et al. 2013). Using both frequency-mapping and angular momentum criteria, we identify a wealth of resonant orbits in the axisymmetric model, including saucers, that are absent from an otherwise identical spherical system and that can potentially interact with the binary. We quantified the set of orbits that could be scattered by the SMBH binary, and found that the axisymmetric model contai...
Energy Technology Data Exchange (ETDEWEB)
Cambon, S.; Lacoste, P.
2011-07-01
We propose a finite element method to solve the axisymmetric scattering problem posed on a regular bounded domain. Here we shall show how to reduce the initial 3D problem into a truncated sum of 2D independent problems posed into a meridian plane of the object. Each of these problem results in the coupling of a partial differential equation into the interior domain and an integral equation on the surface simulating the free space. Then variational volume and boundary integral formulations of Maxwell's equation on regular surfaces are derived. We introduce some general finite element adapted to cylindrical coordinates and constructed from nodal and mixed finite element both for the interior (volume) and for the integral equation (surface). (authors)
From x-ray telescopes to neutron scattering: using axisymmetric mirrors to focus a neutron beam
Khaykovich, B.; Gubarev, M. V.; Bagdasarova, Y.; Ramsey, B. D.; Moncton, D.E.
2012-01-01
We demonstrate neutron beam focusing by axisymmetric mirror systems based on a pair of mirrors consisting of a confocal ellipsoid and hyperboloid. Such a system, known as a Wolter mirror configuration, is commonly used in x-ray telescopes. The axisymmetric Wolter geometry allows nesting of several mirror pairs to increase collection efficiency. We have implemented a system containing four nested Ni mirror pairs, which was tested by focusing a polychromatic neutron beam at the MIT Reactor. In ...
EXTINCTION AND DUST GEOMETRY IN M83 H II REGIONS: AN HUBBLE SPACE TELESCOPE/WFC3 STUDY
International Nuclear Information System (INIS)
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 AV 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
Non-axisymmetric flow characteristics in centrifugal compressor
Wang, Leilei; Lao, Dazhong; Liu, Yixiong; Yang, Ce
2015-06-01
The flow field distribution in centrifugal compressor is significantly affected by the non-axisymmetric geometry structure of the volute. The experimental and numerical simulation methods were adopted in this work to study the compressor flow field distribution with different flow conditions. The results show that the pressure distributionin volute is characterized by the circumferential non-uniform phenomenon and the pressure fluctuation on the high static pressure zone propagates reversely to upstream, which results in the non-axisymmetric flow inside the compressor. The non-uniform level of pressure distribution in large flow condition is higher than that in small flow condition, its effect on the upstream flow field is also stronger. Additionally, the non-uniform circumferential pressure distribution in volute brings the non-axisymmetric flow at impeller outlet. In different flow conditions,the circumferential variation of the absolute flow angle at impeller outlet is also different. Meanwhile, the non-axisymmetric flow characteristics in internal impeller can be also reflected by the distribution of the mass flow. The high static pressure region of the volute corresponds to the decrease of mass flow in upstream blade channel, while the low static pressure zone of the volute corresponds to the increase of the mass flow. In small flow condition, the mass flow difference in the blade channel is bigger than that in the large flow condition.
Spinning geometry = Twisted geometry
International Nuclear Information System (INIS)
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)
Modeling the Orion nebula as an axisymmetric blister
Rubin, R. H.; Simpson, J. P.; Haas, M. R.; Erickson, E. F.
1991-01-01
The ionized gas in the Orion nebula is examined by means of axisymmetric modeling that is based on observational data from the ionized, neutral, and molecular regions. Nonsymmetrical features are omitted, radial dependence from the Trapezium is assumed, and azimuthal symmetry in the plane of the sky is used. Stellar properties and abundances of certain elements are described, and these data are used to compare the present axisymmetric-blister model to a previous spherical model. Strong singly-ionized emission that are visible near the Trapezium are found to originate in the ionization-bounded region in the dense Trapezium zone. The model can be more tightly constrained by adding near-IR data on noncentral zones for (Ar II), (AR III), (Ne II), and (S IV). The quadrant with the 'bar' creates an nonsymmetry that influences the observational data, and the model can therefore be improved with the additional data.
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.
Particle stochasticity due to magnetic perturbations of axisymmetric geometries
International Nuclear Information System (INIS)
The quasilinear theory of collisionless test particle diffusion in stochastic magnetic fields is extended to include the effects of finite gyroradius rho and particle drifts (including magnetic trapping). A canonical framework is used, in which both the criterion for onset of stochasticity and the diffusion tensor scale with field-particle coupling coefficients g/sub l/. The g/sub l/ contain all the information about a given particle's unperturbed orbit and the perturbation fields with which it interacts. The modification of transport due to finite rho and drifts is thus found by comparison of the g/sub l/ including these effects to their driftless, rho → o limit
AXISYMMETRIC FLOW THROUGH A PERMEABLE NEAR-SPHERE
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
An analytical approach is described for the axisymmetric flow through a permeable near-sphere with a modification to boundary conditions in order to account permeability. The Stokes equation was solved by a regular perturbation technique up to the second order correction in epsilon representing the deviation from the radius of nondeformed sphere. The drag and the flow rate were calculated and the results were evaluated from the point of geometry and the permeability of the surface. An attempt also was made to apply the theory to the filter feeding problem. The filter appendages of small ecologically important aquatic organisms were modeled as axisymmetric permeable bodies, therefore a rough model for this problem was considered here as an oblate spheroid or near-sphere.
Numerical observation of non-axisymmetric vesicles in fluid membranes
Jie, Y; Ji Xing Liu; Zhong Can Ou Yang; Jie, Yan; Quan-Hui, Liu; Ji-Xing, Liu; Zhong-Can, Ou-Yang
1998-01-01
By means of Surface Evolver (Exp. Math,1,141 1992), a software package of brute-force energy minimization over a triangulated surface developed by the geometry center of University of Minnesota, we have numerically searched the non-axisymmetric shapes under the Helfrich spontaneous curvature (SC) energy model. We show for the first time there are abundant mechanically stable non-axisymmetric vesicles in SC model, including regular ones with intrinsic geometric symmetry and complex irregular ones. We report in this paper several interesting shapes including a corniculate shape with six corns, a quadri-concave shape, a shape resembling sickle cells, and a shape resembling acanthocytes. As far as we know, these shapes have not been theoretically obtained by any curvature model before. In addition, the role of the spontaneous curvature in the formation of irregular crenated vesicles has been studied. The results shows a positive spontaneous curvature may be a necessary condition to keep an irregular crenated shap...
Stationary and Axisymmetric Perfect-Fluid Solutions with Conformal Motion
Mars, Marc; Senovilla, Jose M M
2002-01-01
Stationary and axisymmetric perfect-fluid metrics are studied under the assumption of the existence of a conformal Killing vector field and in the general case of differential rotation. The possible Lie algebras for the conformal group and corresponding canonical line-elements are explicitly given. It turns out that only four different cases appear, the abelian and other three called I, II and III. We explicitly find all the solutions in the abelian and I cases. For the abelian case the gener...
Solar proton exposure of an ICRU sphere within a complex structure part II: Ray-trace geometry
Slaba, Tony C.; Wilson, John W.; Badavi, Francis F.; Reddell, Brandon D.; Bahadori, Amir A.
2016-06-01
A computationally efficient 3DHZETRN code with enhanced neutron and light ion (Z ≤ 2) propagation was recently developed for complex, inhomogeneous shield geometry described by combinatorial objects. Comparisons were made between 3DHZETRN results and Monte Carlo (MC) simulations at locations within the combinatorial geometry, and it was shown that 3DHZETRN agrees with the MC codes to the extent they agree with each other. In the present report, the 3DHZETRN code is extended to enable analysis in ray-trace geometry. This latest extension enables the code to be used within current engineering design practices utilizing fully detailed vehicle and habitat geometries. Through convergence testing, it is shown that fidelity in an actual shield geometry can be maintained in the discrete ray-trace description by systematically increasing the number of discrete rays used. It is also shown that this fidelity is carried into transport procedures and resulting exposure quantities without sacrificing computational efficiency.
Experiments in axisymmetric supersonic jets
Moore, Cyrille Dennis
An experimental study of the effects of exit Mach number and density ratio on the development of axisymmetric jets is described in this thesis. Jet exit Mach numbers of 1.41, 2.0, and 3.0, were studied for jets of helium, argon, and nitrogen. The jets exit into a gas at rest (velocity ratio = 0), in order to better isolate the effects of compressibility and density ratio. Density ratios vary from 0.23 to 5.5.In order to generate shock free-jets, unique nozzles were designed and constructed for each gas and Mach number combination. A plating method for the construction of the nozzles was developed to ensure high-accuracy and a good surface finish at a cost significantly less than direct-machining techniques.The spreading rate of the jet for several downstream locations is measured with a pitot probe. Centerline data are used to characterise the length of the potential core of the jet, which correlates well with the relative spreading rates. Limited frequency data is obtained through the use of piezo-resistive pressure probes. This method is promising for flows that are not conducive to hot-wire probes.Spark shadography is used to visualize both the mean and instantaneous flow, with the minimum spark time being 20 nanoseconds. The convection velocity of large-scale disturbances is estimated from the visible Mach-type acoustic waves emanating from the jet.For a wide range of jet Mach and Reynolds numbers, the convection velocity of the large scale disturbances in the potential core region of the jet is approximately 0.8 times the jet velocity, the approximate velocity of the first helical instability mode of the jet.The main objectives of the present work were to investigate the effects of compressibility and density on the initial development of the axisymmetric jet. Although the data are not sufficient to determine if the convective Mach number concept used in 2-d shear layer research will work in the case of an axisymmetric jet, it is clear that the axisymmetric
Gao, Zhongmei; Shao, Xinyu; Jiang, Ping; Wang, Chunming; Zhou, Qi; Cao, Longchao; Wang, Yilin
2016-06-01
An integrated multi-objective optimization approach combining Kriging model and non-dominated sorting genetic algorithm-II (NSGA-II) is proposed to predict and optimize weld geometry in hybrid fiber laser-arc welding on 316L stainless steel in this paper. A four-factor, five-level experiment using Taguchi L25 orthogonal array is conducted considering laser power ( P), welding current ( I), distance between laser and arc ( D) and traveling speed ( V). Kriging models are adopted to approximate the relationship between process parameters and weld geometry, namely depth of penetration (DP), bead width (BW) and bead reinforcement (BR). NSGA-II is used for multi-objective optimization taking the constructed Kriging models as objective functions and generates a set of optimal solutions with pareto-optimal front for outputs. Meanwhile, the main effects and the first-order interactions between process parameters are analyzed. Microstructure is also discussed. Verification experiments demonstrate that the optimum values obtained by the proposed integrated Kriging model and NSGA-II approach are in good agreement with experimental results.
International Nuclear Information System (INIS)
In this work we explore the possible existence of static, spherically symmetric and stationary, axisymmetric traversable wormholes coupled to nonlinear electrodynamics. Considering static and spherically symmetric (2 + 1)- and (3 + 1)-dimensional wormhole spacetimes, we verify the presence of an event horizon and the non-violation of the null energy condition at the throat. For the former spacetime, the principle of finiteness is imposed, in order to obtain regular physical fields at the throat. Next, we analyse (2 + 1)-dimensional stationary and axisymmetric wormhole, and also verify the presence of an event horizon, rendering the geometry non-traversable. Relative to (3 + 1)-dimensional stationary and axisymmetric wormhole geometry, we find that the field equations impose specific conditions that are incompatible with the properties of wormholes. Thus, we prove the non-existence of the general class of traversable wormhole solutions, outlined above, within the context of nonlinear electrodynamics
Stability of Axisymmetric Pendular Rings
Fel, Leonid G
2014-01-01
Based on the Weierstrass representation of second variation we develop a non-spectral theory of stability for isoperimetric problem with minimized and constrained two-dimensional functionals of general type and free endpoints allowed to move along two given planar curves. We apply this theory to the axisymmetric pendular ring between two solid bodies without gravity to determine the stability of menisci with free contact lines. For catenoid and cylinder menisci and different solid shapes we determine the stability domain. The other menisci (unduloid, nodoid and sphere) are considered in a simple setup between two plates. We find the existence conditions of stable unduloid menisci with and without inflection points.
International Nuclear Information System (INIS)
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 C3 and Stein spaces are finally outlined. given. 111 refs, 2 figs
Ge, Wenjun; Modest, Michael F.; Marquez, Ricardo
2015-05-01
The spherical harmonics (PN) method is a radiative transfer equation solver, which approximates the radiative intensity as a truncated series of spherical harmonics. For general 3-D configurations, N(N + 1) / 2 intensity coefficients must be solved from a system of coupled second-order elliptic PDEs. In 2-D axisymmetric applications, the number of equations and intensity coefficients reduces to (N + 1) 2 / 4 if the geometric relations of the intensity coefficients are taken into account. This paper presents the mathematical details for the transformation and its implementation on the OpenFOAM finite volume based CFD software platform. The transformation and implementation are applicable to any arbitrary axisymmetric geometry, but the examples to test the new formulation are based on a wedge grid, which is the most common axisymmetric geometry in CFD simulations, because OpenFOAM and most other platforms do not have true axisymmetric solvers. Two example problems for the new axisymmetric PN formulation are presented, and the results are verified with that of the general 3-D PN solver, a Photon Monte Carlo solver and exact solutions.
Experimental studies on an axisymmetric divertor in DIVA(JFT-2a)
International Nuclear Information System (INIS)
DIVA(JFT-2a) is the first tokamak with an axisymmetric divertor in the world. Objectives of the experiments were i) Plasma production and confinement in a tokamak with a separatrix magnetic surface, and ii) divertor effects on radiation loss and plasma confinement. The results so far are as follows: i) The equilibrium with a separatrix magnetic surface is stable during the discharge. ii) There is an ergodic region near the separatrix magnetic surface due to non-axisymmetric magnetic perturbations. iii) The divertor reduces radiation loss and increases energy confinement time. iv) The divertor does not affect the transport process in the main plasma. (author)
Radion stability and induced, on-brane geometries in an effective scalar-tensor theory of gravity II
Kar, Sayan; SenGupta, Soumitra
2015-01-01
In our earlier article (Phys.Rev. {\\bf D 88} 083506,(2013)) we had obtained spherically symmetric, static on-brane geometries in the Kanno-Soda effective scalar-tensor theory of gravity. The solution found was the extremal Reissner--Nordstrom black hole (the Majumdar-Papapetrou solution). In this article, we extend our analysis to more general, spherically symmetric, static geometries which are non-extremal in nature. The solution is nothing other than the well-known Reissner--Nordstrom solution. We find the radion field profiles for the various cases and also look into the issue of radion stability. Finally, the energy-momentum tensor for the effective on-brane matter is obtained and we observe that it can satisfy all energy conditions for a certain region of the parameter space of the solution.
Streamline topology of axisymmetric flows
DEFF Research Database (Denmark)
Brøns, Morten
, which 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......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 $v......$ is expanded in a Taylor series at a point on the axis, and the expansion coefficients are considered as bifurcation parameters. After a normal form transformation we easily obtain the most common bifurcations of the flow patterns. The use of non-linear normal forms provide a gross simplification...
Axisymmetric fully spectral code for hyperbolic equations
Macedo, Rodrigo P
2014-01-01
We present a fully pseudo-spectral scheme to solve axisymmetric hyperbolic equations of second order. With the Chebyshev polynomials as basis functions, the numerical grid is based on the Lobbato (for two spatial directions) and Radau (for the time direction) collocation points. The method solves two issues of previous algorithms which were restricted to one spatial dimension, namely, (i) the inversion of a dense matrix and (ii) the acquisition of a sufficiently good initial-guess for non-linear systems of equations. For the first issue, we use the iterative bi-conjugate gradient stabilized method, which we equip with a pre-conditioner based on a singly diagonally implicit Runge-Kutta ("SDIRK"-) method. The SDIRK-method also supplies the code with a good initial-guess. The numerical solutions are correct up to machine precision and we do not observe any restriction concerning the time step in comparison with the spatial resolution. As an application, we solve general-relativistic wave equations on a black-hol...
Stability of perturbed geodesics in $nD$ axisymmetric spacetimes
Coimbra-Araujo, C H
2016-01-01
The effect of self-gravity of a disk matter is evaluated by the simplest modes of oscillation frequencies for perturbed circular geodesics. It is plotted the radial profiles of free oscillations of an equatorial circular geodesic perturbed within the orbital plane or in the vertical direction. The calculation is carried out to geodesics of an axisymmetric $n$-dimensional spacetime. The profiles are computed by examples of disks embeded in five-dimensional or six-dimensional spacetime, where it is studied the motion of free test particles for three axisymmetric cases: (i) the Newtonian limit of a general proposed $5D$ and $6D$ axisymmetric spacetime; (ii) a simple Randall-Sundrum $5D$ spacetime; (iii) general $5D$ and $6D$ Randall-Sundrum spacetime. The equation of motion of such particles is derived and the stability study is computed for both horizontal and vertical directions, to see how extra dimensions could affect the system. In particular, we investigate a disk constructed from Schwarzschild and Chazy-C...
Liszt, H S
2009-01-01
To interpret the galactic center H II region complexes as constituents of a barred galaxy's nuclear star-forming ring, we compare 18cm VLA radiocontinuumm, $8-22\\mu$ MSX IR and 2.6mm BTL and ARO12m CO emission in the inner few hundred pc. Galactic center H II regions are comparable in their IR appearance, luminosity and SED to M17 or N!0, but the IR light distribution is strongly modified by extinction at 8-22$\\mu$, locally and overall. In Sgr B2 at $l > 0.6$\\degr strong radio H II regions are invisible in the IR. In two favorable cases, extinction from individual galactic center molecular clouds is shown to have $\\tau \\ga 1$ at 8-22$\\mu$ independent of wavelength. The gas kinematics are mostly rotational but with systematic $\\pm 30-50$ \\kms non-circular motion. Sgr B and C both show the same shell and high-velocity cap structure. The H II regions lie in a slightly-inclined ring of radius $\\approx$ 180 pc (1.2\\degr) whose near side appears at higher latitude and lower velocity and contains Sgr B. Sgr C is on ...
SICOS, 2-D Time-Dependent Creep Calculation of Plane or Axisymmetric Concrete Structure
International Nuclear Information System (INIS)
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
Li, Jing; Han, Yuan; Cao, Fan; Wei, Rong-Min; Zhang, Yi-Quan; Song, You
2016-05-31
A distorted octahedral Co(II) complex is reported with homoscorpionate ligands. This complex comprised a field-induced single-molecule magnet, showing two slow relaxation processes under a low dc field (magnetic data, we show for the first time that one of the slow relaxation processes in the low dc field originates from intermolecular dipolar interactions. Interestingly, the Raman process is predominant in the spin reversal relaxation process. The origin of the behaviours of the complex was elucidated by ab initio calculations. PMID:27180637
Stability of perturbed geodesics in nD axisymmetric spacetimes
Coimbra-Araújo, C. H.; Anjos, R. C.
2016-09-01
The effect of self-gravity of a disk matter is evaluated by the simplest modes of oscillation frequencies for perturbed circular geodesics. We plotted the radial profiles of free oscillations of an equatorial circular geodesic perturbed within the orbital plane or in the vertical direction. The calculation is carried out to geodesics of an axisymmetric n-dimensional spacetime. The profiles are computed by examples of disks embeded in five-dimensional or six-dimensional spacetime, where we studied the motion of free test particles for three axisymmetric cases: (i) the Newtonian limit of a general proposed 5D and 6D axisymmetric spacetime; (ii) a simple Randall–Sundrum (RS) 5D spacetime; (iii) general 5D and 6D RS spacetime. The equation of motion of such particles is derived and the stability study is computed for both horizontal and vertical directions, to see how extra dimensions could affect the system. In particular, we investigate a disk constructed from Miyamoto–Nagai and Chazy–Curzon with a cut parameter to generate a disk potential. Those solutions have a simple extension for extra dimensions in case (i), and by solving vacuum Einstein field equations for a kind of RS–Weyl metric in cases (ii) and (iii). We find that it is possible to compute a range of possible solutions where such perturbed geodesics are stable. Basically, the stable solutions appear, for the radial direction, in special cases when the system has 5D and in all cases when the system has 6D and, for the axial direction, in all cases when the system has both 5D or 6D.
Terzis, Petros A.; Christodoulakis, T.
2012-12-01
Lie-group symmetry analysis for systems of coupled, nonlinear ordinary differential equations is performed in order to obtain the entire solution space to Einstein’s field equations for vacuum Bianchi spacetime geometries. The symmetries used are the automorphisms of the Lie algebra of the corresponding three-dimensional isometry group acting on the hyper-surfaces of simultaneity for each Bianchi type, as well as the scaling and the time reparametrization symmetry. A detailed application of the method is presented for Bianchi type IV. The result is the acquisition of the general solution of type IV in terms of sixth Painlevé transcendent PVI, along with the known pp-wave solution. For Bianchi types I, II, V the known entire solution space is attained and very briefly listed, along with two new type V solutions of Euclidean and neutral signature and a type I pp-wave metric.
Indian Academy of Sciences (India)
Pradeep Kumar Vishwakarma; Jan Mohammad Mir; Ram Charitra Maurya
2016-04-01
This work deals with the synthesis and characterization of a series of three -Dehydroacetic acid- 4-phenyl-3-thiosemicarbazide (H2dha-ptsc) Schiff base Cu(II) complexes based on combined experimental and theoretical approach, having the general composition formula as [Cu(dha-ptsc)(L-L)], where L-L is H2O, 2,2-bipyridine (bipy) or 1,10-phenanthroline (phen). H2O containing complex acts as origin for the latter two complexes and in due course, the geometry of the complex changes from square planar to square pyramidal. DFT calculations were carried out for both the geometrical forms. B3LYP/LANL2DZ level of theory was used to carry out the required computations. From the overall DFT computations, square pyramidal geometry was found to be more stable as compared to the square planar conformation for the complexes under investigation. Super oxide dismutation, thermal behaviour and electrochemical activity were also studied. The results have shown satisfactory super oxide scavenging potential, high degree of thermal resistance and efficient redox properties for the title complexes. Moreover, charge analysis and nonlinear optical properties were computed to establish a comprehensive note of atomic constituents differing in nature of charge delocalization.
Nakonieczna, Anna
2016-01-01
Investigating the dynamics of gravitational systems, especially in the regime of quantum gravity, poses a problem of measuring time during the evolution. One of the approaches to this issue is using one of the internal degrees of freedom as a time variable. The objective of our research was to check whether a scalar field or any other dynamical quantity being a part of a coupled multi-component matter-geometry system can be treated as a `clock' during its evolution. We investigated a collapse of a self-gravitating electrically charged scalar field in the Einstein and Brans-Dicke theories using the 2+2 formalism. Our findings concentrated on the spacetime region of high curvature existing in the vicinity of the emerging singularity, which is essential for the quantum gravity applications. We investigated several values of the Brans-Dicke coupling constant and the coupling between the Brans-Dicke and the electrically charged scalar fields. It turned out that both evolving scalar fields and a function which meas...
Ruiz, H. S.; Badía-Majós, A.; López, C.
2011-11-01
Relying on our theoretical approach for the superconducting critical state problem in 3D magnetic field configurations, we present an exhaustive analysis of the electrodynamic response for the so-called longitudinal transport problem in the slab geometry. A wide set of experimental conditions have been considered, including modulation of the applied magnetic field either perpendicular or parallel (longitudinal) to the transport current density. The main objective of our work was to characterize the role of the macroscopic material law that should properly account for the underlying mechanisms of flux cutting and depinning. The intriguing occurrence of negative current patterns and the enhancement of the transport current flow along the center of the superconducting sample are reproduced as a straightforward consequence of the magnetically induced internal anisotropy. Moreover, we show that, related to a maximal projection of the current density vector onto the local magnetic field, a maximal transport current density occurs somewhere within the sample. The elusive measurement of the flux cutting threshold (critical value of such parallel component J_{ {c} \\parallel } ) is suggested on the basis of local measurements of the transport current density. Finally, we show that a high correlation exists between the evolution of the transport current density and the appearance of paramagnetic peak structures in terms of the applied longitudinal magnetic field.
Romero-Salazar, C.
2016-04-01
A critical-state model is postulated that incorporates, for the first time, the structural anisotropy and flux-line cutting effect in a type-II superconductor. The model is constructed starting from the theoretical scheme of Romero-Salazar and Pérez-Rodríguez to study the anisotropy induced by flux cutting. Here, numerical calculations of the magnetic induction and static magnetization are presented for samples under an alternating magnetic field, orthogonal to a static dc-bias one. The interplay of the two anisotropies is analysed by comparing the numerical results with available experimental data for an yttrium barium copper oxide (YBCO) plate, and a vanadium-titanium (VTi) strip, subjected to a slowly oscillating field {H}y({H}z) in the presence of a static field {H}z({H}y).
Nakonieczna, Anna; Yeom, Dong-han
2016-05-01
Investigating the dynamics of gravitational systems, especially in the regime of quantum gravity, poses a problem of measuring time during the evolution. One of the approaches to this issue is using one of the internal degrees of freedom as a time variable. The objective of our research was to check whether a scalar field or any other dynamical quantity being a part of a coupled multi-component matter-geometry system can be treated as a `clock' during its evolution. We investigated a collapse of a self-gravitating electrically charged scalar field in the Einstein and Brans-Dicke theories using the 2+2 formalism. Our findings concentrated on the spacetime region of high curvature existing in the vicinity of the emerging singularity, which is essential for the quantum gravity applications. We investigated several values of the Brans-Dicke coupling constant and the coupling between the Brans-Dicke and the electrically charged scalar fields. It turned out that both evolving scalar fields and a function which measures the amount of electric charge within a sphere of a given radius can be used to quantify time nearby the singularity in the dynamical spacetime part, in which the apparent horizon surrounding the singularity is spacelike. Using them in this respect in the asymptotic spacetime region is possible only when both fields are present in the system and, moreover, they are coupled to each other. The only nonzero component of the Maxwell field four-potential cannot be used to quantify time during the considered process in the neighborhood of the whole central singularity. None of the investigated dynamical quantities is a good candidate for measuring time nearby the Cauchy horizon, which is also singular due to the mass inflation phenomenon.
Nonlinear fluid-structure interaction of axisymmetric systems
International Nuclear Information System (INIS)
Full text: Various numerical procedures, which each have respective merits and drawbacks, are available for the investigation of fluid-structure interaction problems. This paper concentrates on the coupling of the finite element method (FEM) for modeling the structure and the boundary element method (BEM) used to represent the compressible, inviscid fluid. Both methods are formulated in the time domain and a special algorithm is developed to realize the coupling. In particular, nonlinear effects, such as material nonlinearities, large displacements or unilateral boundary conditions, may be taken into account in the structural model, while on infinite expansion of the fluid region is included in the boundary element formulation. For axisymmetric systems, the number of degrees of freedom can be decreased considerably compared to the full three-dimensional situation. Whereas a suitable FE formulation for axisymmetric elastodynamic problems is well-known, the transient fundamental solution for the scalar wave propagation in the BE domain had to be determined numerically up to now. In this contribution an explicit form of this fundamental solution is developed. The numerical results obtained for a simply-shaped geometry and its analytical solution match very well. With this new approach more complicated nonlinear coupled systems like fluid-filled pipes, submerged structures or cylindrical tanks can be simulated without depending too muck on available computer resources. Refs. 3 (author)
SEAWAT-based simulation of axisymmetric heat transport.
Vandenbohede, Alexander; Louwyck, Andy; Vlamynck, Nele
2014-01-01
Simulation of heat transport has its applications in geothermal exploitation of aquifers and the analysis of temperature dependent chemical reactions. Under homogeneous conditions and in the absence of a regional hydraulic gradient, groundwater flow and heat transport from or to a well exhibit radial symmetry, and governing equations are reduced by one dimension (1D) which increases computational efficiency importantly. Solute transport codes can simulate heat transport and input parameters may be modified such that the Cartesian geometry can handle radial flow. In this article, SEAWAT is evaluated as simulator for heat transport under radial flow conditions. The 1971, 1D analytical solution of Gelhar and Collins is used to compare axisymmetric transport with retardation (i.e., as a result of thermal equilibrium between fluid and solid) and a large diffusion (conduction). It is shown that an axisymmetric simulation compares well with a fully three dimensional (3D) simulation of an aquifer thermal energy storage systems. The influence of grid discretization, solver parameters, and advection solution is illustrated. Because of the high diffusion to simulate conduction, convergence criterion for heat transport must be set much smaller (10(-10) ) than for solute transport (10(-6) ). Grid discretization should be considered carefully, in particular the subdivision of the screen interval. On the other hand, different methods to calculate the pumping or injection rate distribution over different nodes of a multilayer well lead to small differences only. PMID:24571415
Generalised Geometry and Flux Vacua
Larfors, Magdalena
2015-01-01
This note discusses the connection between generalised geometry and flux compactifications of string theory. Firstly, we explain in a pedestrian manner how the supersymmetry constraints of type II ${\\mathcal{N}}=1$ flux compactifications can be restated as integrability constraints on certain generalised complex structures. This reformulation uses generalised complex geometry, a mathematical framework that geometrizes the B-field. Secondly, we discuss how exceptional generalised geometry may provide a similar geometrization of the RR fields. Thirdly, we examine the connection between generalised geometry and non-geometry, and finally we present recent developments where generalised geometry is used to construct explicit examples of flux compactifications to flat space.
Light propagation in the field of a moving axisymmetric body: theory and application to JUNO
Van Hees, A; Bertone, S.; Poncin-Lafitte, C. Le
2014-01-01
Given the extreme accuracy of modern space science, a precise relativistic modeling of observations is required. We use the Time Transfer Functions formalism to study light propagation in the field of uniformly moving axisymmetric bodies, which extends the field of application of previous works. We first present a space-time metric adapted to describe the geometry of an ensemble of uniformly moving bodies. Then, we show that the expression of the Time Transfer Functions in the field of a unif...
Stability of the Shallow Axisymmetric Parabolic-Conic Bimetallic Shell by Nonlinear Theory
M. Jakomin; F. Kosel
2011-01-01
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 lar...
Davies, Ben; Sahu, Kailash C
2007-01-01
We present NAOMI/OASIS adaptive-optics assisted integral-field spectroscopy of the transitional massive hypergiant IRC +10420, an extreme mass-losing star apparently in the process of evolving from a Red Supergiant toward the Wolf-Rayet phase. To investigate the present-day mass-loss geometry of the star, we study the appearance of the line-emission from the inner wind as viewed when reflected off the surrounding nebula. We find that, contrary to previous work, there is strong evidence for wind axi-symmetry, based on the equivalent-width and velocity variations of H$\\alpha$ and Fe {\\sc ii} $\\lambda$6516. We attribute this behaviour to the appearance of the complex line-profiles when viewed from different angles. We also speculate that the Ti {\\sc ii} emission originates in the outer nebula in a region analogous to the Strontium Filament of $\\eta$ Carinae, based on the morphology of the line-emission. Finally, we suggest that the present-day axisymmetric wind of IRC +10420, combined with its continued blueward...
Boundary element method for internal axisymmetric flow
Directory of Open Access Journals (Sweden)
Gokhman Alexander
1999-01-01
Full Text Available We present an accurate fast method for the computation of potential internal axisymmetric flow based on the boundary element technique. We prove that the computed velocity field asymptotically satisfies reasonable boundary conditions at infinity for various types of inlet/exit. Computation of internal axisymmetric potential flow is an essential ingredient in the three-dimensional problem of computation of velocity fields in turbomachines. We include the results of a practical application of the method to the computation of flow in turbomachines of Kaplan and Francis types.
Structure of stationary and axisymmetric metrics
International Nuclear Information System (INIS)
We study the structure of stationary and axisymmetric metrics solving the vacuum Einstein equations of general relativity in four and higher dimensions, building on recent work in Phys. Rev. D 70, 124002 (2004). We write the Einstein equations in a new form that naturally identifies the sources for such metrics. The sources live in a one-dimensional subspace and the entire metric is uniquely determined by them. We study in detail the structure of stationary and axisymmetric metrics in four dimensions, and consider as an example the sources of the Kerr black hole
Magneto-hydrodynamically stable axisymmetric mirrors
Energy Technology Data Exchange (ETDEWEB)
Ryutov, D. D.; Cohen, B. I.; Molvik, A. W. [Lawrence Livermore National Laboratory, Livermore, California 94551 (United States); Berk, H. L. [University of Texas, Austin, Texas 78712 (United States); Simonen, T. C. [University of California, Berkeley, California 94720 (United States)
2011-09-15
Making axisymmetric mirrors magnetohydrodynamically (MHD) stable opens up exciting opportunities for using mirror devices as neutron sources, fusion-fission hybrids, and pure-fusion reactors. This is also of interest from a general physics standpoint (as it seemingly contradicts well-established criteria of curvature-driven instabilities). The axial symmetry allows for much simpler and more reliable designs of mirror-based fusion facilities than the well-known quadrupole mirror configurations. In this tutorial, after a summary of classical results, several techniques for achieving MHD stabilization of the axisymmetric mirrors are considered, in particular: (1) employing the favorable field-line curvature in the end tanks; (2) using the line-tying effect; (3) controlling the radial potential distribution; (4) imposing a divertor configuration on the solenoidal magnetic field; and (5) affecting the plasma dynamics by the ponderomotive force. Some illuminative theoretical approaches for understanding axisymmetric mirror stability are described. The applicability of the various stabilization techniques to axisymmetric mirrors as neutron sources, hybrids, and pure-fusion reactors are discussed; and the constraints on the plasma parameters are formulated.
Magneto-hydrodynamically stable axisymmetric mirrorsa)
Ryutov, D. D.; Berk, H. L.; Cohen, B. I.; Molvik, A. W.; Simonen, T. C.
2011-09-01
Making axisymmetric mirrors magnetohydrodynamically (MHD) stable opens up exciting opportunities for using mirror devices as neutron sources, fusion-fission hybrids, and pure-fusion reactors. This is also of interest from a general physics standpoint (as it seemingly contradicts well-established criteria of curvature-driven instabilities). The axial symmetry allows for much simpler and more reliable designs of mirror-based fusion facilities than the well-known quadrupole mirror configurations. In this tutorial, after a summary of classical results, several techniques for achieving MHD stabilization of the axisymmetric mirrors are considered, in particular: (1) employing the favorable field-line curvature in the end tanks; (2) using the line-tying effect; (3) controlling the radial potential distribution; (4) imposing a divertor configuration on the solenoidal magnetic field; and (5) affecting the plasma dynamics by the ponderomotive force. Some illuminative theoretical approaches for understanding axisymmetric mirror stability are described. The applicability of the various stabilization techniques to axisymmetric mirrors as neutron sources, hybrids, and pure-fusion reactors are discussed; and the constraints on the plasma parameters are formulated.
Guggenheimer, Heinrich W
1977-01-01
This is a text of local differential geometry considered as an application of advanced calculus and linear algebra. The discussion is designed for advanced undergraduate or beginning graduate study, and presumes of readers only a fair knowledge of matrix algebra and of advanced calculus of functions of several real variables. The author, who is a Professor of Mathematics at the Polytechnic Institute of New York, begins with a discussion of plane geometry and then treats the local theory of Lie groups and transformation groups, solid differential geometry, and Riemannian geometry, leading to a
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
Rasmussen, N. G.; Simeoni, G. G.; Lefmann, K.
2016-04-01
A dedicated beam-focusing device has been designed for the direct geometry thermal-cold neutron time-of-flight spectrometer TOFTOF at the neutron facility FRM II (Garching, Germany). The prototype, based on the compressed Archimedes' mirror concept, benefits from the adaptive-optics technology (adjustable supermirror curvature) and the compact size (only 0.5 m long). We have simulated the neutron transport across the entire guide system. We present a detailed computer characterization of the existing device, along with the study of the factors mostly influencing the future improvement. We have optimized the simulated prototype as a function of the neutron wavelength, accounting also for all relevant features of a real instrument like the non-reflecting side edges. The results confirm the "chromatic" displacement of the focal point (flux density maximum) at fixed supermirror curvature, and the ability of a variable curvature to keep the focal point at the sample position. Our simulations are in excellent agreement with theoretical predictions and the experimentally measured beam profile. With respect to the possibility of a further upgrade, we find that supermirror coatings with m-values higher than 3.5 would have only marginal influence on the optimal behaviour, whereas comparable spectrometers could take advantage of longer focusing segments, with particular impact for the thermal region of the neutron spectrum.
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
Energy Technology Data Exchange (ETDEWEB)
Stacey, W. M. [Georgia Institute of Technology, Atlanta, Georgia 30332 (United States); Bae, C. [National Fusion Research Institute, Daejoen (Korea, Republic of)
2015-06-15
A systematic formalism for the calculation of rotation in non-axisymmetric tokamaks with 3D magnetic fields is described. The Braginskii Ωτ-ordered viscous stress tensor formalism, generalized to accommodate non-axisymmetric 3D magnetic fields in general toroidal flux surface geometry, and the resulting fluid moment equations provide a systematic formalism for the calculation of toroidal and poloidal rotation and radial ion flow in tokamaks in the presence of various non-axisymmetric “neoclassical toroidal viscosity” mechanisms. The relation among rotation velocities, radial ion particle flux, ion orbit loss, and radial electric field is discussed, and the possibility of controlling these quantities by producing externally controllable toroidal and/or poloidal currents in the edge plasma for this purpose is suggested for future investigation.
International Nuclear Information System (INIS)
A systematic formalism for the calculation of rotation in non-axisymmetric tokamaks with 3D magnetic fields is described. The Braginskii Ωτ-ordered viscous stress tensor formalism, generalized to accommodate non-axisymmetric 3D magnetic fields in general toroidal flux surface geometry, and the resulting fluid moment equations provide a systematic formalism for the calculation of toroidal and poloidal rotation and radial ion flow in tokamaks in the presence of various non-axisymmetric “neoclassical toroidal viscosity” mechanisms. The relation among rotation velocities, radial ion particle flux, ion orbit loss, and radial electric field is discussed, and the possibility of controlling these quantities by producing externally controllable toroidal and/or poloidal currents in the edge plasma for this purpose is suggested for future investigation
Global stability analysis of axisymmetric boundary layers
Vinod, N
2016-01-01
This paper presents the linear global stability analysis of the incompressible axisymmetric boundary layer on a circular cylinder. The base flow is parallel to the axis of the cylinder at inlet. The pressure gradient is zero in the streamwise direction. The base flow velocity profile is fully non-parallel and non-similar in nature. The boundary layer grows continuously in the spatial directions. Linearized Navier-Stokes(LNS) equations are derived for the disturbance flow quantities in the cylindrical polar coordinates. The LNS equations along with homogeneous boundary conditions forms a generalized eigenvalues problem. Since the base flow is axisymmetric, the disturbances are periodic in azimuthal direction. Chebyshev spectral collocation method and Arnoldi's iterative algorithm is used for the solution of the general eigenvalues problem. The global temporal modes are computed for the range of Reynolds numbers and different azimuthal wave numbers. The largest imaginary part of the computed eigenmodes are nega...
The evolution of swirling axisymmetric vortex rings
Gargan-Shingles, C.; Rudman, M.; Ryan, K.
2015-08-01
Swirling vortex rings form in any turbulent flow where a swirling component is present, such as in combustion chambers or the downwash of helicopter blades. Instabilities on initially non-swirling vortex rings result in a localized swirl velocity being generated within the core. The presence of a swirl component of velocity in a vortex ring modifies the relaxation and evolution of numerical Gaussian cores in a manner that is currently unknown. The evolution of Gaussian axisymmetric vortex rings of size 0.2 complete settling of the strain rate within the core does not occur until all sheddings have ceased. Increasing the swirl magnitude past that considered in this paper is expected to result in the original ring losing its structure before the instability can occur. The evolution is found to be qualitatively similar to that of a piston generated axisymmetric vortex ring with swirl, with both cases eventually reaching a similar quasi-steady state.
Orbital effect in the stationary axisymmetric field
International Nuclear Information System (INIS)
This paper uses an elegant mathematical method to calculate the orbital effects in the axisymmetric field created by the spinning mass with electric charge and a large number of magnetic monopoles. In comparison with that in the Reissner–Nordström (R–N) field, the correction terms caused by the spinning mass decrease the advanced effect as the revolution direction of the test particle coincides with that of the Kerr field, however, the correction terms caused by the spinning charged mass increase the advance effect as the revolution direction of the test particle coincides with that of the Kerr–Newman–Kasnya (KNK) field. Generalizing the effect in the axisymmetric field, it obtains interesting results by discussing the parameters of the celestial body, these parameters provide a feasible experimental verification of the general relativity. (general)
An axisymmetric steady state vortex ring model
Wang, Ruo-Qian
2016-01-01
Based on the solution of Atanasiu et al. (2004), a theoretical model for axisymmetric vortex flows is derived in the present study by solving the vorticity transport equation for an inviscid, incompressible fluid in cylindrical coordinates. The model can describe a variety of axisymmetric flows with particular boundary conditions at a moderately high Reynolds number. This paper shows one example: a high Reynolds number laminar vortex ring. The model can represent a family of vortex rings by specifying the modulus function using a Rayleigh distribution function. The characteristics of this vortex ring family are illustrated by numerical methods. For verification, the model results compare well with the recent direct numerical simulations (DNS) in terms of the vorticity distribution and streamline patterns, cross-sectional areas of the vortex core and bubble, and radial vorticity distribution through the vortex center. Most importantly, the asymmetry and elliptical outline of the vorticity profile are well capt...
Orbital effect in the stationary axisymmetric field
Institute of Scientific and Technical Information of China (English)
Gong Tian-Xi; Wang Yong-Jiu
2008-01-01
This paper uses an elegant mathematical method to calculate the orbital effects in the axisymmetric field created by the spinning mass with electric charge and a large number of magnetic monopoles. In comparison with that in the Reissner-Nordstrom (R-N) field, the correction terms caused by the spinning mass decrease the advanced effect as the revolution direction of the test particle coincides with that of the Kerr field, however, the correction terms caused by the spinning charged mass increase the advance effect as the revolution direction of the test particle coincides with that of the Kerr-Newman-Kasnya (KNK) field. Generalizing the effect in the axisymmetric field, it obtains interesting results by discussing the parameters of the celestial body, these parameters provide a feasible experimental verification of the general relativity.
Lefschetz, Solomon
2012-01-01
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.
Collapse of Non-Axisymmetric Cavities
Enriquez, Oscar R.; Peters, Ivo R.; Gekle, Stephan; Schmidt, Laura; Versluis, Michel; van der Meer, Devaraj; Lohse, Detlef
2009-01-01
A round disk with a harmonic disturbance impacts on a water surface and creates a non-axisymmetric cavity which collapses under the influence of hydrostatic pressure. We use disks deformed with mode m=2 to m=6. For all mode numbers we find clear evidence for a phase inversion of the cavity wall during the collapse. We present a fluid dynamics video showing high speed imaging of different modes, pointing out the characteristic features during collapse.
Numerical description of cavitation on axisymmetric bodies
Energy Technology Data Exchange (ETDEWEB)
Hickox, C.E.; Hailey, C.E.; Wolfe, W.P.; Watts, H.A.; Gross, R.J.; Ingber, M.S.
1988-01-01
This paper reports on ongoing studies which are directed toward the development of predictive techniques for the modeling of steady cavitation on axisymmetric bodies. The primary goal of the modeling effort is the prediction of cavity shape and pressure distribution from which forces and moments can be calculated. Here we present an overview of the modeling techniques developed and compare predictions with experimental data obtained from water tunnel tests for both limited and supercavitation. 14 refs., 4 figs.
Axisymmetric stationary solutions as harmonic maps
Matos, T; Tonatiuh Matos; Jerzy Plebanski
1994-01-01
We present a method for generating exact solutions of Einstein equations in vacuum using harmonic maps, when the spacetime possesses two commutating Killing vectors. This method consists in writing the axisymmetric stationry Einstein equations in vacuum as a harmonic map which belongs to the group SL(2,R), and decomposing it in its harmonic "submaps". This method provides a natural classification of the solutions in classes (Weil's class, Lewis' class etc).
Analysis of Axisymmetric Crushing of Frusta
M.M.A. Khan; H. Abbas; N K Gupta
2003-01-01
The paper presents a curved-fold model with variable straight length for the axisymmetric crushing of thin frusta. The folding considered in the model is partly inside and partly outside. The variation of circumferential strain during the formation of a fold has been taken into account. The size of the fold and mean, as well as variation of crushing load, has been computed mathematically. The study is purely analytical and does not involve any empirical constant; and hence, can be used...
AXISYMMETRIC ELASTICITY PROBLEM OF CUBIC QUASICRYSTAL
Institute of Scientific and Technical Information of China (English)
ZHOU WANG-MIN; FAN TIAN-YOU
2000-01-01
A method for analyzing the elasticity problem of cubic quasicrystal is developed. The axisymmetric elasticity problem of cubic quasicrystal is reduced to a single higher-order partial differential equation by introducing a displacement function. As an example, the solutions of elastic field of cubic quasicrystal with a penny-shaped crack are obtained,and the stress intensity factor and strain energy release rate are determined.
Axisymmetric long liquid bridges stability and resonances
Meseguer Ruiz, José; Sanz Andres, Angel Pedro; Perales Perales, José Manuel
1990-01-01
In this paper mathematical expressions for minimum-volume stability limits and resonance frequencies of axisymmetric long liquid bridges are presented. These expressions are valid for a wide range of liquid bridge configurations, accounting for ef-fects like unequal disks and axial microgravity in the case of minimum-volume stability limits,and unequal disks, axial microgravity,non-zero viscosity and liquid bridge volume different from the cylindrical one in the case of resonance frequenc...
Magnetic design of the axisymmetric throttle-coil addition to the tandem mirror experiment-upgrade
International Nuclear Information System (INIS)
The TMX-U magnet set has incorporated new axisymmetric throttle coils and fan-reversing transition magnets. This new magnet geometry, which will allow for the experimental verification of new physics issues related to axicell tandem mirrors, encompasses both engineering and physics considerations. Engineering considerations include structural integrity plus neutral beam and diagnostic access. Physics issues include the stability and radial transport of the confined plasma. We have calculated the magnetic field using the magnetic field code, EFFI, and the plasma stability and surface curvatures using the plasma stability code, TEBASCO. Our magnet design allows the axisymmetric throttle mirror to be varied from the end-cell mirror value of 2 to a peak of 6 T
From x-ray telescopes to neutron scattering: Using axisymmetric mirrors to focus a neutron beam
Energy Technology Data Exchange (ETDEWEB)
Khaykovich, B., E-mail: bkh@mit.ed [Nuclear Reactor Laboratory, Massachusetts Institute of Technology, 138 Albany Street, Cambridge, MA 02139 (United States); Gubarev, M.V. [Marshall Space Flight Center, NASA, VP62, Huntsville, AL 35812 (United States); Bagdasarova, Y. [Department of Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139 (United States); Ramsey, B.D. [Marshall Space Flight Center, NASA, VP62, Huntsville, AL 35812 (United States); Moncton, D.E. [Nuclear Reactor Laboratory, Massachusetts Institute of Technology, 138 Albany Street, Cambridge, MA 02139 (United States); Department of Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139 (United States)
2011-03-01
We demonstrate neutron beam focusing by axisymmetric mirror systems based on a pair of mirrors consisting of a confocal ellipsoid and hyperboloid. Such a system, known as a Wolter mirror configuration, is commonly used in X-ray telescopes. The axisymmetric Wolter geometry allows nesting of several mirror pairs to increase collection efficiency. We implemented a system containing four nested Ni mirror pairs, which was tested by the focusing of a polychromatic neutron beam at the MIT Reactor. In addition, we have carried out extensive ray-tracing simulations of the mirrors and their performance in different situations. The major advantages of the Wolter mirrors are nesting for large angular collection and aberration-free performance. We discuss how these advantages can be utilized to benefit various neutron scattering methods, such as imaging, SANS, and time-of-flight spectroscopy.
From x-ray telescopes to neutron scattering: Using axisymmetric mirrors to focus a neutron beam
International Nuclear Information System (INIS)
We demonstrate neutron beam focusing by axisymmetric mirror systems based on a pair of mirrors consisting of a confocal ellipsoid and hyperboloid. Such a system, known as a Wolter mirror configuration, is commonly used in X-ray telescopes. The axisymmetric Wolter geometry allows nesting of several mirror pairs to increase collection efficiency. We implemented a system containing four nested Ni mirror pairs, which was tested by the focusing of a polychromatic neutron beam at the MIT Reactor. In addition, we have carried out extensive ray-tracing simulations of the mirrors and their performance in different situations. The major advantages of the Wolter mirrors are nesting for large angular collection and aberration-free performance. We discuss how these advantages can be utilized to benefit various neutron scattering methods, such as imaging, SANS, and time-of-flight spectroscopy.
Pinch-off of axisymmetric vortex pairs in the limit of vanishing vortex line curvature
Sadri, V.; Krueger, P. S.
2016-07-01
Pinch-off of axisymmetric vortex pairs generated by flow between concentric cylinders with radial separation ΔR was studied numerically and compared with planar vortex dipole behavior. The axisymmetric case approaches planar vortex dipole behavior in the limit of vanishing ΔR. The flow was simulated at a jet Reynolds number of 1000 (based on ΔR and the jet velocity), jet pulse length-to-gap ratio ( /L Δ R ) in the range 10-20, and gap-to-outer radius ratio ( /Δ R R o ) in the range 0.01-0.1. Contrary to investigations of strictly planar flows, vortex pinch-off was observed for all gap sizes investigated. This difference was attributed to the less constrained geometry considered, suggesting that even very small amounts of vortex line curvature and/or vortex stretching may disrupt the absence of pinch-off observed in strictly planar vortex dipoles.
Energy Technology Data Exchange (ETDEWEB)
Fujisawa, Nobuyuki, E-mail: fujisawa@eng.niigata-u.ac.jp [Visualization Research Center, Niigata University, Niigata (Japan); Kanatani, Nobuaki [Graduate School of Science and Technology, Niigata University, Niigata (Japan); Yamagata, Takayuki, E-mail: yamagata@eng.niigata-u.ac.jp [Visualization Research Center, Niigata University, Niigata (Japan); Takano, Tsuyoshi [Graduate School of Science and Technology, Niigata University, Niigata (Japan)
2015-04-15
Highlights: • Pipe-wall thinning due to flow accelerated corrosion is studied. • Pipeline geometry consists of elbow and orifice in swirling flow. • Velocity field and mass transfer rate are measured in pipeline. • Non-axisymmetric pipe-wall thinning occurs behind orifice. - Abstract: In this study, the mechanism of non-axisymmetric pipe-wall thinning that led to a pipeline break in the Mihama nuclear power plant in 2004 is evaluated in a scale-model experiment in a water tunnel having an elbow and orifice under the influence of swirling flow. The velocity fields are measured by stereo particle image velocimetry, and the mass transfer rate is measured by a benzoic acid dissolution method at Reynolds number Re = 3 × 10{sup 4} with and without swirling flow. The non-axisymmetric swirling flow is found to be generated behind the elbow, even when the axisymmetric swirling flow is supplied in the upstream of the elbow. The secondary flow generated in the elbow is not suppressed in the pipeline 10 diameters downstream of elbow in the swirling flow, and in this flow geometry, the non-axisymmetry of the flow is greatly magnified downstream of the orifice. The measured mass transfer rates downstream of the orifice under the influence of swirling flow indicate that the Sherwood number distribution on one side of the pipe is enhanced and that on the other side is reduced owing to the appearance of the non-axisymmetric swirling flow, which results in the occurrence of non-axisymmetric pipe-wall thinning downstream of the orifice.
International Nuclear Information System (INIS)
Highlights: • Pipe-wall thinning due to flow accelerated corrosion is studied. • Pipeline geometry consists of elbow and orifice in swirling flow. • Velocity field and mass transfer rate are measured in pipeline. • Non-axisymmetric pipe-wall thinning occurs behind orifice. - Abstract: In this study, the mechanism of non-axisymmetric pipe-wall thinning that led to a pipeline break in the Mihama nuclear power plant in 2004 is evaluated in a scale-model experiment in a water tunnel having an elbow and orifice under the influence of swirling flow. The velocity fields are measured by stereo particle image velocimetry, and the mass transfer rate is measured by a benzoic acid dissolution method at Reynolds number Re = 3 × 104 with and without swirling flow. The non-axisymmetric swirling flow is found to be generated behind the elbow, even when the axisymmetric swirling flow is supplied in the upstream of the elbow. The secondary flow generated in the elbow is not suppressed in the pipeline 10 diameters downstream of elbow in the swirling flow, and in this flow geometry, the non-axisymmetry of the flow is greatly magnified downstream of the orifice. The measured mass transfer rates downstream of the orifice under the influence of swirling flow indicate that the Sherwood number distribution on one side of the pipe is enhanced and that on the other side is reduced owing to the appearance of the non-axisymmetric swirling flow, which results in the occurrence of non-axisymmetric pipe-wall thinning downstream of the orifice
Axisymmetric oscillations of magnetic neutron stars
Lee, U
2006-01-01
We calculate axisymmetric oscillations of rotating neutron stars composed of the surface fluid ocean, solid crust, and fluid core, taking account of a dipole magnetic field as strong as $B_S\\sim 10^{15}$G at the surface. The adiabatic oscillation equations for the solid crust threaded by a dipole magnetic field are derived in Newtonian dynamics, on the assumption that the axis of rotation is aligned with the magnetic axis so that perturbations on the equilibrium can be represented by series expansions in terms of spherical harmonic functions $Y_l^m(\\theta,\\phi)$ with different degrees $l$ for a given azimuthal wave number $m$ around the the magnetic axis. Although the three component models can support a rich variety of oscillation modes, axisymmetric ($m=0$) toroidal $_{l}t_n$ and spheroidal $_ls_n$ shear waves propagating in the solid crust are our main concerns, where $l$ and $n$ denote the harmonic degree and the radial order of the modes, respectively. In the absence of rotation, axisymmetric spheroidal ...
Stabilization of the vertical instability by non-axisymmetric coils
Turnbull, A. D.; Reiman, A. H.; Lao, L. L.; Cooper, W. A.; Ferraro, N. M.; Buttery, R. J.
2016-08-01
In a published Physical Review Letter (Reiman 2007 Phys. Rev. Lett. 99 135007), it was shown that axisymmetric (or vertical) stability can be improved by placing a set of parallelogram coils above and below the plasma oriented at an angle to the constant toroidal planes. The physics of this stabilization can be understood as providing an effective additional positive stability index. The original work was based on a simplified model of a straight tokamak and is not straightforwardly applicable to a finite aspect ratio, strongly shaped plasma such as in DIII-D. Numerical calculations were performed in a real DIII-D -like configuration to provide a proof of principal that 3-D fields can, in fact raise the elongation limits as predicted. A four field period trapezioid-shaped coil set was developed in toroidal geometry and 3D equilibria were computed using trapezium coil currents of 10 kA , 100 kA , and 500 kA . The ideal magnetohydrodynamics growth rates were computed as a function of the conformal wall position for the n = 0 symmetry-preserving family. The results show an insignificant relative improvement in the stabilizing wall location for the two lower coil current cases, of the order of 10‑3 and less. In contrast, the marginal wall position is increased by 7% as the coil current is increased to 500 kA , confirming the main prediction from the original study in a real geometry case. In DIII-D the shift in marginal wall position of 7% would correspond to being able to move the existing wall outward by 5 to 10 cm. While the predicted effect on the axisymmetric stability is real, it appears to require higher coil currents than could be provided in an upgrade to existing facilities. Additional optimization over the pitch of the coils, the number of field periods and the coil positions, as well as plasma parameters, such as the internal inductivity {{\\ell}\\text{i}} , β , and {{q}95} would mitigate this but seem unlikely to change the conclusion.
Connes, Alain
1994-01-01
This English version of the path-breaking French book on this subject gives the definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics developed by Alain Connes. Profusely illustrated and invitingly written, this book is ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics, quantization, and elementary particles and fields.Key Features* First full treatment of the subject and its applications* Written by the pioneer of this field* Broad applications in mathemat
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
Levenson, Esther; Tsamir, Pessia
2011-01-01
Recently the issue of early childhood mathematics has come to the fore and with it the importance of teaching geometrical concepts and reasoning from a young age. Geometry is a key domain mentioned in many national curricula and may also support the learning of other mathematical topics, such as number and patterns. This book is based on the rich experience (research and practice) of the authors and is devoted entirely to the learning and teaching of geometry in preschool. The first part of the book is dedicated to children's geometrical thinking, building concept images in line with concept d
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,
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…
Preferential axisymmetric field growth in kinematic geodynamo models
Livermore, Philip W.; Jackson, Andrew
2004-11-01
Earth's magnetic field, generated by fluid motion and inductive processes in Earth's core, has a predominantly axisymmetric dipolar component. Yet indefinite self-excitation of purely axisymmetric fields through any dynamo mechanism is specifically disallowed, begging the question of why the geodynamo sustains this dominant axisymmetric component. By considering a number of different fluid flow models modified from existing studies, we show that axisymmetric fields are consistently the most easily regenerated magnetic fields on short timescales, despite the fact that on long timescales they must die away. We argue that this transient field generation may play an important role in generating Earth's magnetic field, especially in the recovery after reversals.
Low Cost Method of Manufacturing Cooled Axisymmetric Scramjets Project
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...
Axisymmetric instability in a thinning electrified jet
Dharmansh; Chokshi, Paresh
2016-04-01
The axisymmetric stability of an electrified jet is analyzed under electrospinning conditions using the linear stability theory. The fluid is considered Newtonian with a finite electrical conductivity, modeled as a leaky dielectric medium. While the previous studies impose axisymmetric disturbances on a cylindrical jet of uniform radius, referred to as the base state, in the present study the actual thinning jet profile, obtained as the steady-state solution of the one-dimensional slender filament model, is treated as the base state. The analysis takes into account the role of variation in the jet variables like radius, velocity, electric field, and surface charge density along the thinning jet in the stability behavior. The eigenspectrum of the axisymmetric disturbance growth rate is constructed from the linearized disturbance equations discretized using the Chebyshev collocation method. The most unstable growth rate for the thinning jet is significantly different from that for the uniform radius jet. For the same electrospinning conditions, while the uniform radius jet is predicted to be highly unstable, the thinning jet profile is found to be unstable but with a relatively very low growth rate. The stabilizing role of the thinning jet is attributed to the variation in the surface charge density as well as the extensional deformation rate in the fluid ignored in the uniform radius jet analysis. The dominant mode for the thinning jet is an oscillatory conducting mode driven by the field-charge coupling. The disturbance energy balance finds the electric force to be the dominant force responsible for the disturbance growth, potentially leading to bead formation along the fiber. The role of various material and process parameters in the stability behavior is also investigated.
Topological fluid mechanics of Axisymmetric Flow
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 is...... 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...
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...... 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....
Travelling waves in axisymmetric pipe flows
International Nuclear Information System (INIS)
The weakly nonlinear dynamics of axisymmetric Poiseuille pipe flows is investigated. It is shown that small perturbations of the laminar flow with amplitude ε ∼ O(Re−2.5) obey a coupled system of nonlinear Korteweg–de Vries-type equations. To leading order, these support inviscid soliton-type solutions and periodic waves in the form of toroidal vortex tubes that, due to viscous effects, slowly decay in time on a longer time scale t ∼ O(ε−2.5). (paper)
Comment on "Conformally flat stationary axisymmetric metrics"
Barnes, A; Senovilla, José MM
2003-01-01
Garcia and Campuzano claim to have found a previously overlooked family of stationary and axisymmetric conformally flat spacetimes, contradicting an old theorem of Collinson. In both these papers it is tacitly assumed that the isometry group is orthogonally transitive. Under the same assumption, we point out here that Collinson's result still holds if one demands the existence of an axis of symmetry on which the axial Killing vector vanishes. On the other hand if the assumption of orthogonal transitivity is dropped, a wider class of metrics is allowed and it is possible to find explicit counterexamples to Collinson's result.
Detailed Decomposition of Galaxy Images. II. Beyond Axisymmetric Models
Peng, Chien Y; Impey, Chris D; Rix, Hans-Walter
2009-01-01
We present a two-dimensional (2-D) fitting algorithm (GALFIT, Version 3) with new capabilities to study the structural components of galaxies and other astronomical objects in digital images. Our technique improves on previous 2-D fitting algorithms by allowing for irregular, curved, logarithmic and power-law spirals, ring and truncated shapes in otherwise traditional parametric functions like the Sersic, Moffat, King, Ferrer, etc., profiles. One can mix and match these new shape features freely, with or without constraints, apply them to an arbitrary number of model components and of numerous profile types, so as to produce realistic-looking galaxy model images. Yet, despite the potential for extreme complexity, the meaning of the key parameters like the Sersic index, effective radius or luminosity remain intuitive and essentially unchanged. The new features have an interesting potential for use to quantify the degree of asymmetry of galaxies, to quantify low surface brightness tidal features beneath and bey...
Non-axisymmetric wind-accretion simulations. II. Density gradients
Ruffert, M.
1999-01-01
The hydrodynamics of a variant of classical Bondi-Hoyle-Lyttleton accretion is investigated: a totally absorbing sphere moves at various Mach numbers (3 and 10) relative to a medium, which is taken to be an ideal gas having a density gradient (of 3%, 20% or 100% over one accretion radius) perpendicular to the relative motion. Similarly to the 3D models published previously, both with velocity gradients and without, the models with a density gradient presented here exhibit non-stationary flow ...
Snap-through of the system of open shallow axi-symmetric bimetallic shell by non-linear theory
Jakomin, Marko; Kosel, Tadej; Kosel, Franc; Batista, Milan
2015-01-01
The paper deals with stresses, strains and buckling conditions in the thin axi-symmetric shallow bimetallic shells with circular opening at the top of the shell. According to the third order theory by the Czech researcher E. Chawalla, which takes into account the equilibrium state of forces and moments acting on the deformed system, the paper presents a model for mathematical description of the system's geometry, stresses, thermo-elastic strains and displacements. The mathematical formulation...
Stress Analysis of Laminated Composite Cylinders Under Non-Axisymmetric Loading
Energy Technology Data Exchange (ETDEWEB)
Starbuck, J.M.
1999-10-26
The use of thick-walled composite cylinders in structural applications has seen tremendous growth over the last decade. Applications include pressure vessels, flywheels, drive shafts, spoolable tubing, and production risers. In these applications, the geometry of a composite cylinder is axisymmetric but in many cases the applied loads are non-axisymmetric and more rigorous analytical tools are required for an accurate stress analysis. A closed-form solution is presented for determining the layer-by-layer stresses, strains, and displacements and first-ply failure in laminated composite cylinders subjected to non-axisymmetric loads. The applied loads include internal and external pressure, axial force, torque, axial bending moment, uniform temperature change, rotational velocity, and interference fits. The formulation is based on the theory of anisotropic elasticity and a state of generalized plane deformation along the axis of the composite cylinder. Parametric design trade studies can be easily and quickly computed using this closed-form solution. A computer program that was developed for performing the numerical calculations is described and results from specific case studies are presented.
Momentum and Heat Transfer in MHD Axisymmetric Stagnation-Point Flow over a Shrinking Sheet
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T. R. Mahapatra
2013-01-01
Full Text Available In this paper we present a mathematical analysis for the magneto hydrodynamic (MHD axi-symmetric stagnation-point flow and heat transfer over a shrinking sheet which shrinks axi-symmetrically in its own plane. The governing partial differential equations along with the boundary conditions are first cast into a dimensionless form and then these equations are solved numerically by shooting technique. Thermal conductivity is assumed to vary linearly with the temperature. Temperature profiles are obtained for two different types of heating process namely (i the sheet with prescribed surface temperature (PST and (ii the sheet with prescribed surface heat flux (PHF. The effects of various physical parameters on the flow and heat transfer characteristics are presented graphically and discussed.
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...
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.
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...
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.
Axisymmetric arc in a supersonic nozzle
International Nuclear Information System (INIS)
Axisymmetric arc burning in a supersonic nozzle has wide technical applications (eg in gas blast circuit breaker, arc heaters etc.). Mathematical modelling of such an arc is usually based on boundary-layer assumption which assumes a known pressure distribution imposed on the arc or based on the integral method of arc analysis. Thus, the flow outside of the arc's thermal influence is assumed to be one dimensional. In practice, this is not the case as the nozzle is not sufficiently gentle in the axial direction or the presence of the upstream electrode makes the assumption of one-dimensional flow invalid. The purpose of the present investigation is to model the arc based on Navier-Stokes equations which are modified to take into account of electrical power input and radiation transport. The arcing gas is SF6, the transport properties of which (electrical conductivity, viscosity, thermal conductivity etc.) are highly nonlinear functions of temperature but only weakly dependent on the pressure
Lagrangian mixing in an axisymmetric hurricane model
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B. Rutherford
2009-09-01
Full Text Available This paper discusses the extension of established Lagrangian mixing measures to make them applicable to data extracted from a 2-D axisymmetric hurricane simulation. Because of the non-steady and unbounded characteristics of the simulation, the previous measures are extended to a moving frame approach to create time-dependent mixing rates that are dependent upon the initial time of particle integration, and are computed for nonlocal regions. The global measures of mixing derived from finite-time Lyapunov exponents, relative dispersion, and a measured mixing rate are applied to distinct regions representing different characteristic feautures within the model. It is shown that these time-dependent mixing rates exhibit correlations with maximal tangential winds during a quasi-steady state, establishing a connection between mixing and hurricane intensity.
International Nuclear Information System (INIS)
Highlights: • Flow visualizations from experiments and simulations for two axisymmetric bodies. • Improved understanding of mean flow separation topology for hemisphere cylinder. • Modal analysis of unsteady fluid dynamics. • Discussion of possible hydrodynamic instabilities. -- Abstract: The understanding of unsteady three-dimensional separation is lagging behind the understanding of two-dimensional separation due to its greater complexity and the limited amount of data for universal or canonical flow problems. Three-dimensional separation occurs, for example, when low aspect ratio devices such as submarines and torpedoes are operated at large angles of attack, α. Two low aspect ratio geometries, the DARPA Suboff bare hull geometry, which is a prototypical submarine shape, and a hemisphere-cylinder geometry were investigated. Numerical simulations and water tunnel experiments for the Suboff geometry for a Reynolds number based on diameter of Re=10,000 show little flow separation at α=30°. A hemisphere-cylinder geometry was derived by replacing the Suboff forebody with a hemisphere. Simulations and water tunnel experiments were carried out for Re=2000 and 5000. For α=10° a large shedding separation bubble is observed on the leeward side. For α=30° two counter-rotating leeward vortices appear and shedding is reduced. Proper orthogonal decomposition and Fourier analysis in time are employed for investigating the unsteady fluid dynamics. Conclusions are drawn with respect to the mean flow topology and possibly relevant hydrodynamic instabilities
Non-Axisymmetric Equilibrium Reconstruction for Stellarators, Reversed Field Pinches and Tokamaks
International Nuclear Information System (INIS)
Full text: Equilibrium reconstruction is the process of minimizing the mismatch between modeled and observed signals by changing the parameters that specify the equilibrium. While stellarator equilibria are inherently non-axisymmetric, non-axisymmetric effects are also crucial for understanding stability and confinement of high-performance reversed field pinch and tokamak plasmas. Therefore, two-dimensional reconstruction tools are not adequate for fully exploring 3D plasmas. The V3FIT and STELLOPT codes are 3D equilibrium reconstruction codes, both based on the VMEC 3D equilibrium code. VMEC models field-period symmetric 3D flux surface geometry but does not treat magnetic islands and chaotic regions. VMEC requires the specification of the pressure and either rotational transform or toroidal current profiles, as functions of either the toroidal or poloidal flux. VMEC can treat both axisymmetric and non-axisymmetric configurations, both free- and fixed-boundary equilibria, and both stellarator-symmetric and non-stellarator-symmetric equilibria. Both V3FIT and STELLOPT can utilize signals from magnetic diagnostics, soft X-rays (SXR), Thomson scattering, and geometrical information from plasma limiters. STELLOPT can also utilize Motional Stark Effect (MSE) signals. Both calculate a finite difference approximation to a Jacobian for the signal-mismatch minimization. V3FIT and STELLOPT differ in the details of their minimization algorithms, their utilization of auxiliary profiles (like electron density and soft x-ray emissivity), and in their computation of model signals. V3FIT is currently in use on stellarators (HSX, CTH), reversed field pinches (RFX-mod) and tokamaks (DIII-D) for a wide variety of studies: interpretation of Pfirsch-Schliiter and bootstrap currents, design of new magnetic diagnostics, magnetic island generation, vertical instabilities, density-limit disruption activity, conformance of multiple data sources to a single set of flux surfaces, quasi
Axisymmetric Numerical Modeling of Pulse Detonation Rocket Engines
Morris, Christopher I.
2005-01-01
Pulse detonation rocket engines (PDREs) have generated research interest in recent years as a chemical propulsion system potentially offering improved performance and reduced complexity compared to conventional rocket engines. The detonative mode of combustion employed by these devices offers a thermodynamic advantage over the constant-pressure deflagrative combustion mode used in conventional rocket engines and gas turbines. However, while this theoretical advantage has spurred considerable interest in building PDRE devices, the unsteady blowdown process intrinsic to the PDRE has made realistic estimates of the actual propulsive performance problematic. The recent review article by Kailasanath highlights some of the progress that has been made in comparing the available experimental measurements with analytical and numerical models. In recent work by the author, a quasi-one-dimensional, finite rate chemistry CFD model was utilized to study the gasdynamics and performance characteristics of PDREs over a range of blowdown pressure ratios from 1-1000. Models of this type are computationally inexpensive, and enable first-order parametric studies of the effect of several nozzle and extension geometries on PDRE performance over a wide range of conditions. However, the quasi-one-dimensional approach is limited in that it cannot properly capture the multidimensional blast wave and flow expansion downstream of the PDRE, nor can it resolve nozzle flow separation if present. Moreover, the previous work was limited to single-pulse calculations. In this paper, an axisymmetric finite rate chemistry model is described and utilized to study these issues in greater detail. Example Mach number contour plots showing the multidimensional blast wave and nozzle exhaust plume are shown. The performance results are compared with the quasi-one-dimensional results from the previous paper. Both Euler and Navier-Stokes solutions are calculated in order to determine the effect of viscous
Asymmetric and axisymmetric dynamics of tropical cyclones
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J. Persing
2013-05-01
Full Text Available We present the results of idealized numerical experiments to examine the difference between tropical cyclone evolution in three-dimensional (3-D and axisymmetric (AX model configurations. We focus on the prototype problem for intensification, which considers the evolution of an initially unsaturated AX vortex in gradient-wind balance on an f-plane. Consistent with findings of previous work, the mature intensity in the 3-D model is reduced relative to that in the AX model. In contrast with previous interpretations invoking barotropic instability and related horizontal mixing processes as a mechanism detrimental to the spin-up process, the results indicate that 3-D eddy processes associated with vortical plume structures can assist the intensification process by contributing to a radial contraction of the maximum tangential velocity and to a vertical extension of tangential winds through the depth of the troposphere. These plumes contribute significantly also to the azimuthally-averaged heating rate and the corresponding azimuthal-mean overturning circulation. The comparisons show that the resolved 3-D eddy momentum fluxes above the boundary layer exhibit counter-gradient characteristics and are generally not represented properly by the subgrid-scale parameterizations in the AX configuration. The resolved eddy fluxes act to support the contraction and intensification of the maximum tangential winds. The comparisons indicate fundamental differences between convective organization in the 3-D and AX configurations for meteorologically relevant forecast time scales. While the radial and vertical gradients of the system-scale angular rotation provide a hostile environment for deep convection in the 3-D model, with a corresponding tendency to strain the convective elements in the tangential direction, deep convection in the AX model does not suffer this tendency. Also, since during the 3-D intensification process the convection has not yet organized
Non-axisymmetric, scale-free, razor-thin discs
Syer, D; Syer, Dave; Tremaine, Scott
1996-01-01
Galaxies exhibit a variety of non-axisymmetric structure (bars, spiral structure, lopsided structure, etc.). These suggest the following general problem: what are the possible stationary configurations of a two-dimensional self-gravitating fluid other than an axisymmetric razor-thin disc? We address a modest component of this problem: we seek non-axisymmetric razor-thin discs of two-dimensional barotropic fluid that are stationary in an inertial frame. We distinguish between `razor-thin' and `two-dimensional,' applying the latter term to the equation of state. Furthermore we assume that our systems are scale-free, which reduces the partial differential equations describing the system to ordinary differential equations. We also allow for the presence of an axisymmetric background potential. This simple and highly idealized problem already exhibits a rich variety of solutions, the richest being for m=1 symmetry.
Axisymmetric thrust-vectoring nozzle performance prediction
International Nuclear Information System (INIS)
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
Lu, Zhumin; Dou, Hua-Shu; Phan-Thien, Nhan; Yeo, Khoon Seng
2008-01-01
In this paper, the finite element method is combined with the Brownian Configuration Field (BFC) method to simulate the fibre suspension flow in axisymmetric contraction and expansion passages. In order to solve for the high stress at high concentration, the Discrete Adaptive Viscoelastic Stress Splitting (DAVSS) method is employed. For the axisymmetric contraction and expansion passages with different geometry ratios, the results obtained are compared to available constitutive models and experiments. The predicted vortex length for dilute suspensions agrees well with experimental data in literature. Our numerical results show clearly the effect on vortex enhancement with increase of the volume fractions and the aspect ratios. Effect of aspect ratio of fibres on the vortex length is also studied. It is found that for the lower expansion ratio flows the vortex dimension in the corner region is fairly independent of fibre concentration and aspect ratio of fibres while the said vortex dimension increases with th...
Parametric study of axisymmetric fusion devices
International Nuclear Information System (INIS)
Three different axisymmetric magnetic mirror fusion machines are examined in order to optimize the ratio the fusion power produced by them to the power injected into them to maintain the plasma. These three devices were chosen to study the continuum between a simple mirror and a tandem mirror. This allowed the evolutionary process leading from the simple to the tandem mirror to be examined in detail. The Kelley mirror, which corresponds to the middle step, was examined in depth for the first time. A computer code that models the plasma in these machines was written to investigate the steady-state operation of these machines. The balance equations are solved by using an ordinary differential equation solver, LSODE, to numerically solve the system of differential equations. The computer model was used to examine parameter space to optimize Q for each of the three machines. When feasible, a comparison with a Fokker-Planck code was made for the optimal Q case for each machine. Finally, the possible roles these devices might fill was discussed
Axisymmetric Vortex Simulations with Various Turbulence Models
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Brian Howard Fiedler
2010-10-01
Full Text Available The CFD code FLUENT^{TM} has been applied to a vortex within an updraft above a frictional lower boundary. The sensitivity of vortex intensity and structure to the choice of turbulent model is explored. A high Reynolds number of 10^{8} is employed to make the investigation relevant to the atmospheric vortex known as a tornado. The simulations are axisymmetric and are integrated forward in time to equilibrium. In a variety of turbulence models tested, the Reynolds Stress Model allows for the greatest intensification of the vortex, with the azimuthal wind speed near the surface being 2.4 times the speed of the updraft, consistent with the destructive nature of tornadoes. The Standard k-e Model, which is simpler than the Reynolds Stress Model but still more detailed than what is commonly available in numerical weather prediction models, produces an azimuthal wind speed near the surface of at most 0.6 times the updraft speed.
Magnetic surfaces in an axisymmetric torus
International Nuclear Information System (INIS)
A method is developed for specifying the boundary equilibrium magnetic surface in an axially symmetric torus by using the absolute values of the magnetic field B = Bs(θ) and the gradient of the poloidal flux vertical bar vertical bar ∇Ψ vertical bar = vertical bar ∇Ψ vertical bar s(θ) in a special flux coordinate system. By setting two surface constants (e.g., the safety factor q and dp/dΨ) and matching the absolute values of the magnetic field and the flux gradient on a closed magnetic surface, it is possible to find all equilibrium magnetic functions (including n · ∇ ln B and the local shear s) and all constants (including the toroidal current J and the shear dμ/dΨ) on this surface. Such a non-traditional formulation of the boundary conditions in solving the stability problem in an axisymmetric torus allows one to impose intentional conditions on plasma confinement and MHD stability at the periphery of the system.
Axisymmetric, Ventilated Supercavitation in Unsteady, Horizontal Flow
Kawakami, Ellison; Lee, Seung-Jae; Arndt, Roger
2012-11-01
Drag reduction and/or speed augmentation of marine vehicles by means of supercavitation is a topic of great interest. During the initial launch of a supercavitating vehicle, an artificial supercavity is required until the vehicle can reach conditions at which a natural supercavity can be sustained. Previous studies at Saint Anthony Falls Laboratory (SAFL) focused on the behavior of ventilated supercavities in steady horizontal flows. In open waters, vehicles can encounter unsteady flows, especially when traveling under waves. A study has been carried out at SAFL to investigate the effects of unsteady flow on axisymmetric supercavities. An attempt is made to duplicate sea states seen in open waters. In an effort to track cavity dimensions throughout a wave cycle, an automated cavity tracking script has been developed. Using a high speed camera and the proper software, it is possible to synchronize cavity dimensions with pressure measurements taken inside the cavity. Results regarding supercavity shape, ventilation demand, cavitation parameters and closure methods are presented. It was found that flow unsteadiness caused a decrease in the overall length of the supercavity while having only a minimal effect on the maximum diameter. The supercavity volume varied with cavitation number and a possible relationship between the two is being explored. (Supported by ONR)
Numerical Strategies for Stroke Optimization of Axisymmetric Microswimmers
Alouges, François; Heltai, Luca
2009-01-01
We propose a computational method to solve optimal swimming problems, based on the boundary integral formulation of the hydrodynamic interaction between swimmer and surrounding fluid and direct constrained minimization of the energy consumed by the swimmer. We apply our method to axisymmetric model examples. We consider a classical model swimmer (the three-sphere swimmer of Golestanian et al.) as well as a novel axisymmetric swimmer inspired by the observation of biological micro-organisms.
Artificial boundary conditions for axisymmetric eddy current probe problems
Haddar, Houssem; Jiang, Zixian; Lechleiter, Armin
2015-01-01
We study different strategies for the truncation of computational domains in the simulation of eddy current probes of elongated axisymmetric tubes. For axial fictitious boundaries, an exact Dirichlet-to-Neumann map is proposed and mathematically analyzed via a non-selfadjoint spectral problem: under general assumptions we show convergence of the solution to an eddy current problem involving a truncated Dirichlet-to-Neumann map to the solution on the entire, unbounded axisymmetric domain as th...
Some aspects of the axisymmetric wall-jet analysis
Czech Academy of Sciences Publication Activity Database
Kolář, Václav
Istanbul : WSEAS Press, 2012 - (Mastny, P.; Perminov, V.), s. 317-320 ISBN 978-1-61804-114-2. ISSN 2227-4596. - (Recent Advances in Mechanical Engineering Series. 1). [WSEAS International Conference on Fluid Mechanics & Aerodynamics /10./ (FMA '12). Istanbul (TR), 21.08.2012-23.08.2012] R&D Projects: GA AV ČR IAA200600801 Institutional support: RVO:67985874 Keywords : axisymmetric wall jets * flow past axisymmetric bodies * similarity solution * swirl Subject RIV: BK - Fluid Dynamics
Axisymmetric Control in Alcator C-Mod
Tinios, Gerasimos
1995-01-01
This thesis investigates the degree to which linear axisymmetric modeling of the response of a tokamak plasma can reproduce observed experimental behavior. The emphasis is on the vertical instability. The motivation for this work lies in the fact that, once dependable models have been developed, modern control theory methods can be used to design feedback laws for more effective and efficient tokamak control. The models are tested against experimental data from the Alcator C-Mod tokamak. A linear model for each subsystem of the closed-loop system constituting an Alcator C-Mod discharge under feedback control has been constructed. A non-rigid, approximately flux-conserving, perturbed equilibrium plasma response model is used in the comparison to experiment. A detailed toroidally symmetric model of the vacuum vessel and the supporting superstructure is used. Modeling of the power supplies feeding the active coils has been included. Experiments have been conducted with vertically unstable plasmas where the feedback was turned off and the plasma response was observed in an open -loop configuration. The closed-loop behavior has been examined by injecting step perturbations into the desired vertical position of the plasma. The agreement between theory and experiment in the open-loop configuration was very satisfactory, proving that the perturbed equilibrium plasma response model and a toroidally symmetric electromagnetic model of the vacuum vessel and the structure can be trusted for the purpose of calculations for control law design. When the power supplies and the feedback computer hardware are added to the system, however, as they are in the closed-loop configuration, they introduce nonlinearities that make it difficult to explain observed behavior with linear theory. Nonlinear simulation of the time evolution of the closed-loop experiments was able to account for the discrepancies between linear theory and experiment. (Copies available exclusively from MIT Libraries
Extreme Black Holes and Near-Horizon Geometries
Li, Ka Ki; Li, Carmen
2016-01-01
In this thesis we study near-horizon geometries of extreme black holes. We first consider stationary extreme black hole solutions to the Einstein-Yang-Mills theory with a compact semi-simple gauge group in four dimensions, allowing for a negative cosmological constant. We prove that any axisymmetric black hole of this kind possesses a near-horizon AdS2 symmetry and deduce its near-horizon geometry must be that of the abelian embedded extreme Kerr-Newman (AdS) black hole. We sho...
Brooker, B. Tyler
A new nose shape that was determined using the penetration mechanics to have the least penetration drag has been tested in the supersonic wind tunnel of the University of Alabama to determine the aerodynamic characteristics of this nose shape. The aerodynamic drag measured on the new nose shape and on four additional nose shapes are compared to each other. The results show that the new nose shape has the least aerodynamic drag. The measurements were made at Mach numbers ranging from 1.85 to 3.1. This study also required the maintenance of several components of the University of Alabama's 6-inch by 6-inch supersonic wind tunnel and modification of the existing data acquisition programs. These repairs and modifications included the repair and recalibration of the supersonic wind tunnel, repair of the four component force balance, and the modification of the tunnel's control program.
Light propagation in the field of a moving axisymmetric body: theory and application to Juno
Hees, A; Poncin-Lafitte, C Le
2014-01-01
Given the extreme accuracy of modern space science, a precise relativistic modeling of observations is required. We use the Time Transfer Functions formalism to study light propagation in the field of moving axisymmetric bodies, which extends the field of application of previous works. We first derive a space-time metric adapted to describe the geometry of an ensemble of moving bodies. Then, we show that the expression of the Time Transfer Functions in the field of a uniformly moving body can be easily derived from its well-known expression in a stationary field by using a change of variables. We also give a general expression of the Time Transfer Function in the case where the motion of the body is arbitrary. This result is given in the form of an integral easily computable numerically. We also provide the derivatives of the Time Transfer Function in this case, which are mandatory to compute Doppler and astrometric observables. We particularize our results in the case of moving axisymmetric bodies. Finally, ...
Resonance and cut-off surfaces in the ion cyclotron frequency range in toroidal geometry
International Nuclear Information System (INIS)
Resonances and cut-offs of the fast Alfven and ion-cyclotron waves have been studied for a multicomponent plasma in a toroidal axisymmetric geometry. The resonance and cut-off frequencies are given by eigenvalues of ordinary differential equations on the rosonance and cut-off sufaces, respectively. These surfaces coincide with magnetic surfaces. (author)
Waychunas, G.A.; Fuller, C.C.; Davis, J.A.
2002-01-01
"Two-line" ferrihydrite samples precipitated and then exposed to a range of aqueous Zn solutions (10-5 to 10-3 M), and also coprecipitated in similar Zn solutions (pH 6.5), have been examined by Zn and Fe K-edge X-ray absorption spectroscopy. Typical Zn complexes on the surface have Zn-O distances of 1.97(0.2) A?? and coordination numbers of about 4.0(0.5), consistent with tetrahedral oxygen coordination. This contrasts with Zn-O distances of 2.11(.02) A?? and coordination numbers of 6 to 7 in the aqueous Zn solutions used in sample preparation. X-ray absorption extended fine structure spectroscopy (EXAFS) fits to the second shell of cation neighbors indicate as many as 4 Zn-Fe neighbors at 3.44(.04) A?? in coprecipitated samples, and about two Zn-Fe neighbors at the same distance in adsorption samples. In both sets of samples, the fitted coordination number of second shell cations decreases as sorption density increases, indicating changes in the number and type of available complexing sites or the onset of competitive precipitation processes. Comparison of our results with the possible geometries for surface complexes and precipitates suggests that the Zn sorption complexes are inner sphere and at lowest adsorption densities are bidentate, sharing apical oxygens with adjacent edge-sharing Fe(O,OH)6 octahedra. Coprecipitation samples have complexes with similar geometry, but these are polydentate, sharing apices with more than two adjacent edge-sharing Fe(O,OH)6 polyhedra. The results are inconsistent with Zn entering the ferrihydrite structure (i.e., solid solution formation) or formation of other Zn-Fe precipitates. The fitted Zn-Fe coordination numbers drop with increasing Zn density with a minimum of about 0.8(.2) at Zn/(Zn + Fe) of 0.08 or more. This change appears to be attributable to the onset of precipitation of zinc hydroxide polymers with mainly tetrahedral Zn coordination. At the highest loadings studied, the nature of the complexes changes further
Axisymmetric modes of rotating relativistic stars in the cowling approximation
International Nuclear Information System (INIS)
Axisymmetric pulsations of rotating neutron stars can be excited in several scenarios, such as core-collapse, crust and core-quakes and binary mergers and could become detectable either in gravitational waves or high-energy radiation. Here, we present a comprehensive study of all low-order axisymmetric modes of uniformly and rapidly rotating relativistic stars. Initial stationary configurations are appropriately perturbed and are numerically evolved using an axisymmetric, nonlinear relativistic hydrodynamics code, assuming time-independence of the gravitational field (Cowling approximation). The simulations are performed using a high-resolution shock-capturing finite-difference scheme accurate enough to maintain the initial rotation law for a large number of rotational periods, even for stars at the mass-shedding limit. Through Fourier transforms of the time evolution of selected fluid variables, we compute the frequencies of quasi-radial and non-radial modes with spherical harmonic indices l=0, 1, 2 and 3, for a sequence of rotating stars from the non-rotating limit to the mass-shedding limit. The frequencies of the axisymmetric modes are affected significantly by rotation only when the rotation rate exceeds about 50% of the maximum allowed. As expected, at large rotation rates, apparent mode crossings between different modes appear. In addition to the above modes, several axisymmetric inertial modes are also excited in our numerical evolutions. (orig.)
Stationary and axisymmetric solutions of higher-dimensional general relativity
International Nuclear Information System (INIS)
We study stationary and axisymmetric solutions of General Relativity, i.e., pure gravity, in four or higher dimensions. D-dimensional stationary and axisymmetric solutions are defined as having D-2 commuting Killing vector fields. We derive a canonical form of the metric for such solutions that effectively reduces the Einstein equations to a differential equation on an axisymmetric D-2 by D-2 matrix field living in three-dimensional flat space (apart from a subclass of solutions that instead reduce to a set of equations on a D-2 by D-2 matrix field living in two-dimensional flat space). This generalizes the Papapetrou form of the metric for stationary and axisymmetric solutions in four dimensions, and furthermore generalizes the work on Weyl solutions in four and higher dimensions. We analyze then the sources for the solutions, which are in the form of thin rods along a line in the three-dimensional flat space that the matrix field can be seen to live in. As examples of stationary and axisymmetric solutions, we study the five-dimensional rotating black hole and the rotating black ring, write the metrics in the canonical form and analyze the structure of the rods for each solution
Axisymmetric Tandem Mirrors: Stabilization and Confinement Studies
International Nuclear Information System (INIS)
The 'Kinetic Stabilizer' has been proposed as a means of MHD stabilizing an axisymmetric tandem mirror system. The K-S concept is based on theoretical studies by Ryutov, confirmed experimentally in the Gas Dynamic Trap experiment in Novosibirsk. In the K-S beams of ions are directed into the end of an 'expander' region outside the outer mirror of a tandem mirror. These ions, slowed, stagnated, and reflected as they move up the magnetic gradient, produce a low-density stabilizing plasma.At the Lawrence Livermore National Laboratory we have been conducting theoretical and computational studies of the K-S Tandem Mirror. These studies have employed a low-beta code written especially to analyze the beam injection/stabilization process,and a new code SYMTRAN (by Hua and Fowler)that solves the coupled radial and axial particle and energy transport in a K-S T-M. Also, a 'legacy' MHD stability code, FLORA, has been upgraded and employed to benchmark the injection/stabilization code and to extend its results to high beta values.The FLORA code studies so far have confirmed the effectiveness of the K-S in stabilizing high-beta (40%) plasmas with stabilizer plasmas the peak pressures of which are several orders of magnitude smaller than those of the confined plasma.Also the SYMTRAN code has shown D-T plasma ignition from alpha particle energy deposition in T-M regimes with strong end plugging.Our studies have confirmed the viability of the K-S T-M concept with respect to MHD stability and radial and axial confinement. We are continuing these studies in order to optimize the parameters and to examine means for the stabilization of possible residual instability modes, such as drift modes and 'trapped-particle' modes. These modes may in principle be controlled by tailoring the stabilizer plasma distribution and/or the radial potential distribution.In the paper the results to date of our studies are summarized and projected to scope out possible fusion-power versions of the K-S T-M
Axisymmetric Tandem Mirrors: Stabilization and Confinement Studies
International Nuclear Information System (INIS)
The 'Kinetic Stabilizer' has been proposed as a means of MHD stabilizing an axisymmetric tandem mirror system. The K-S concept is based on theoretical studies by Ryutov, confirmed experimentally in the Gas Dynamic Trap experiment in Novosibirsk. In the K-S beams of ions are directed into the end of an 'expander' region outside the outer mirror of a tandem mirror. These ions, slowed, stagnated, and reflected as they move up the magnetic gradient, produce a low-density stabilizing plasma. At the Lawrence Livermore National Laboratory we have been conducting theoretical and computational studies of the K-S Tandem Mirror. These studies have employed a low-beta code written especially to analyze the beam injection/stabilization process, and a new code SYMTRAN (by Hua and Fowler) that solves the coupled radial and axial particle and energy transport in a K-S TM. Also, a 'legacy' MHD stability code, FLORA, has been upgraded and employed to benchmark the injection/stabilization code and to extend its results to high beta values. The FLORA code studies so far have confirmed the effectiveness of the K-S in stabilizing high-beta (40%) plasmas with stabilizer plasmas the peak pressures of which are several orders of magnitude smaller than those of the confined plasma. Also the SYMTRAN code has shown D-T plasma ignition from alpha particle energy deposition in T-M regimes with strong end plugging. Our studies have confirmed the viability of the K-S-T-M concept with respect to MHD stability and radial and axial confinement. We are continuing these studies in order to optimize the parameters and to examine means for the stabilization of possible residual instability modes, such as drift modes and 'trapped-particle' modes. These modes may in principle be controlled by tailoring the stabilizer plasma distribution and/or the radial potential distribution. In the paper the results to date of our studies are summarized and projected to scope out possible fusion-power versions of the K
Impedance calculations of non-axisymmetric transitions using the optical approximation
International Nuclear Information System (INIS)
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.)
ECOM: a fast and accurate solver for toroidal axisymmetric MHD equilibria
Lee, Jungpyo
2014-01-01
We present ECOM (Equilibrium solver via COnformal Mapping), a fast and accurate fixed boundary solver for toroidally axisymmetric magnetohydrodynamic equilibria with or without a toroidal flow. ECOM combines conformal mapping and Fourier and integral equation methods on the unit disk to achieve exponential convergence for the poloidal flux function as well as its first and second partial derivatives. As a consequence of its high order accuracy, for dense grids and tokamak-like elongations ECOM computes key quantities such as the safety factor and the magnetic shear with higher accuracy than the finite element based code CHEASE [H. L\\"utjens \\textit{et al.}, Computer physics communications 97, 219 (1996)] at equal run time. ECOM has been developed to provide equilibrium quantities and details of the flux contour geometry as inputs to stability, wave propagation and transport codes.
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.
International Nuclear Information System (INIS)
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)
Near surface stress analysis strategies for axisymmetric fretting
Indian Academy of Sciences (India)
M Ramesh; Satish V Kailas; K R Y Simha
2008-06-01
Fretting is essentially a surface phenomenon, but bulk stresses and material properties contribute to subsequent failure. This feature of fretting demands a thorough understanding of near surface stresses under the joint action of normal, shear and thermal loading. Axisymmetric fretting is of great concern in piping and coupling design. 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 models: 2D strip model (2DS) and half-plane Flamant model (2DF). We compare the results of 2DS and 2DF with the exact results for AFA obtained using Love’s stress function in conjunction with Fourier transform. There is a good correspondence between stress components obtained from 2D-models.
Axisymmetric Modes of Rotating Relativistic Stars in the Cowling Approximation
Font, J A; Sen-Gupta, A; Stergioulas, N; Font, Jose A.; Dimmelmeier, Harald; Gupta, Anshu; Stergioulas, Nikolaos
2001-01-01
Axisymmetric pulsations of rotating neutron stars can be excited in several scenarios, such as core-collapse, crust and core-quakes and binary mergers and could become detectable either in gravitational waves or high-energy radiation. Here, we present a comprehensive study of all low-order axisymmetric modes of uniformly and rapidly rotating relativistic stars. Initial stationary configurations are appropriately perturbed and are numerically evolved using an axisymmetric, nonlinear relativistic hydrodynamics code, assuming time-independence of the gravitational field (Cowling approximation). The simulations are performed using a high-resolution shock-capturing finite-difference scheme accurate enough to maintain the initial rotation law for a large number of rotational periods, even for stars at the mass-shedding limit. Through Fourier transforms of the time evolution of selected fluid variables, we compute the frequencies of quasi-radial and non-radial modes with spherical harmonic indices l=0,1,2 and 3, for...
Transient axial solution for plane and axisymmetric waves focused by a paraboloidal reflector.
Tsai, Yi-Te; Zhu, Jinying; Haberman, Michael R
2013-04-01
A time domain analytical solution is presented to calculate the pressure response along the axis of a paraboloidal reflector for a normally incident plane wave. This work is inspired by Hamilton's axial solution for an ellipsoidal mirror and the same methodology is employed in this paper. Behavior of the reflected waves along reflector axis is studied, and special interest is placed on focusing gain obtained at the focal point. This analytical solution indicates that the focusing gain is affected by reflector geometry and the time derivative of the input signal. In addition, focused pressure response in the focal zone given by various reflector geometries and input frequencies are also investigated. This information is useful for selecting appropriate reflector geometry in a specific working environment to achieve the best signal enhancement. Numerical simulation employing the finite element method is used to validate the analytical solution, and visualize the wave field to provide a better understanding of the propagation of reflected waves. This analytical solution can be modified to apply to non-planar incident waves with axisymmetric wavefront and non-uniform pressure distribution. An example of incident waves with conical-shaped wavefront is presented. PMID:23556573
Study of axisymmetric flow problems by Hele-Shaw models
Rao, P. V.; Sachan, J. S.
1980-05-01
Hele-Shaw models have been applied for solving two-dimensional, irrotational flow problems such as flow past bodies or radial seepage flow. The gap between the two plates is varied as a cubic parabola in the radial direction. Results are presented for seven axisymmetric models, including a cylindrical body with 60-deg conical head forms, an axisymmetric sluice entrance with a compound elliptical transition and radial flow to a well with a free surface. Pressure distributions were computed and compared with water-tunnel data, wind-tunnel data, finite-differential solutions and exact solutions.
Axisymmetric solitary waves on the surface of a ferrofluid
Bourdin, Elise; Falcon, Eric
2010-01-01
We report the first observation of axisymmetric solitary waves on the surface of a cylindrical magnetic fluid layer surrounding a current-carrying metallic tube. According to the ratio between the magnetic and capillary forces, both elevation and depression solitary waves are observed with profiles in good agreement with theoretical predictions based on the magnetic analogue of the Korteweg-deVries equation. We also report the first measurements of the velocity and the dispersion relation of axisymmetric linear waves propagating on the cylindrical ferrofluid layer that are found in good agreement with theoretical predictions.
Axisymmetric multiphase Lattice Boltzmann method for generic equations of state
Reijers, Sten A; Toschi, Federico
2015-01-01
We present an axisymmetric lattice Boltzmann model based on the Kupershtokh et al. multiphase model that is capable of solving liquid-gas density ratios up to $10^3$. Appropriate source terms are added to the lattice Boltzmann evolution equation to fully recover the axisymmetric multiphase conservation equations. We validate the model by showing that a stationary droplet obeys the Young-Laplace law, comparing the second oscillation mode of a droplet with respect to an analytical solution and showing correct mass conservation of a propagating density wave.
Analytical calculation of boozer magnetic coordinates for axisymmetric MHD equilibria
International Nuclear Information System (INIS)
A new analytical technique for extracting the Boozer magnetic coordinates in axisymmetric MHD equilibria is described. The method is based upon the correspondence between the expansion of the flux function in toroidal multipolar moments and the expansion in toroidal axisymmetric harmonics of the magnetic scalar potential χ0, which appears in the covariant representation B=∇χ0+β∇ψ-T of the magnetic field. An example of calculation of Boozer magnetic coordinates is given for an experimental highly shaped high β equilibrium of DIIID
Potential flow past axisymmetric bodies at angle of attack
Kuhlman, J. M.; Shu, J.-Y.
1984-01-01
The Karamcheti (1966) suggestion concerning the use of higher order singularity techniques has been developed for the calculation of incompressible flow past an axisymmetric body at angle of attack. Attention is given to the results of a convergence study using this axial singularity method, where solution accuracy has been investigated for ellipsoids of slenderness ratio in the 1-10 range for both axial and inclined flow. Effects of singularity type, element number and size distribution, and singularity line inset distance, are noted, and a paneling scheme is developed which yields accurate results for the class of axisymmetric bodies having continuous body slopes with discontinuous curvature jumps.
Local Axisymmetric Instability Criterion in the Thin, Rotating, Multicomponent Disk
Rafikov, R R
2000-01-01
Purely gravitational perturbations are considered in a thin rotating disk composed of several gas and stellar components. The dispersion relation for the axisymmetric density waves propagating through the disk is found and the criterion for the local axisymmetric stability of the whole system is formulated. In the appropriate limit of two-component gas we confirm the findings of Jog & Solomon (1984) and extend consideration to the case when one component is collisionless. Gravitational stability of the Galactic disk in the Solar neighborhood based on the multicomponent instability condition is explored using recent measurements of the stellar composition and kinematics in the local Galactic disk obtained by Hipparcos satellite.
A regularity criterion for the angular velocity component in axisymmetric Navier-Stokes equations
Ondrej Kreml; Milan Pokorny
2007-01-01
We study the non-stationary Navier-Stokes equations in the entire three-dimensional space under the assumption that the data are axisymmetric. We extend the regularity criterion for axisymmetric weak solutions given in [10].
A regularity criterion for the angular velocity component in axisymmetric Navier-Stokes equations
Directory of Open Access Journals (Sweden)
Ondrej Kreml
2007-01-01
Full Text Available We study the non-stationary Navier-Stokes equations in the entire three-dimensional space under the assumption that the data are axisymmetric. We extend the regularity criterion for axisymmetric weak solutions given in [10].
Li, X; K. Suzuki; Kanaori, K; Tajima, K; Kashiwada, A.; Hiroaki, H; Kohda, D; Tanaka, T
2000-01-01
We previously reported the de novo design of an amphiphilic peptide [YGG(IEKKIEA)4] that forms a native-like, parallel triple-stranded coiled coil. Starting from this peptide, we sought to regulate the assembly of the peptide by a metal ion. The replacement of the Ile18 and Ile22 residues with Ala and Cys residues, respectively, in the hydrophobic positions disrupted of the triple-stranded alpha-helix structure. The addition of Cd(II), however, resulted in the reconstitution of the triple-str...
Bär, Christian; Schwarz, Matthias
2012-01-01
This volume contains a collection of well-written surveys provided by experts in Global Differential Geometry to give an overview over recent developments in Riemannian Geometry, Geometric Analysis and Symplectic Geometry. The papers are written for graduate students and researchers with a general interest in geometry, who want to get acquainted with the current trends in these central fields of modern mathematics.
Consistent lattice Boltzmann methods for incompressible axisymmetric flows
Zhang, Liangqi; Yang, Shiliang; Zeng, Zhong; Yin, Linmao; Zhao, Ya; Chew, Jia Wei
2016-08-01
In this work, consistent lattice Boltzmann (LB) methods for incompressible axisymmetric flows are developed based on two efficient axisymmetric LB models available in the literature. In accord with their respective original models, the proposed axisymmetric models evolve within the framework of the standard LB method and the source terms contain no gradient calculations. Moreover, the incompressibility conditions are realized with the Hermite expansion, thus the compressibility errors arising in the existing models are expected to be reduced by the proposed incompressible models. In addition, an extra relaxation parameter is added to the Bhatnagar-Gross-Krook collision operator to suppress the effect of the ghost variable and thus the numerical stability of the present models is significantly improved. Theoretical analyses, based on the Chapman-Enskog expansion and the equivalent moment system, are performed to derive the macroscopic equations from the LB models and the resulting truncation terms (i.e., the compressibility errors) are investigated. In addition, numerical validations are carried out based on four well-acknowledged benchmark tests and the accuracy and applicability of the proposed incompressible axisymmetric LB models are verified.
Non-Axisymmetric Shaping of Tokamaks Preserving Quasi-Axisymmetry
International Nuclear Information System (INIS)
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.
Unified characteristics line theory of spacial axisymmetric plastic problem
Institute of Scientific and Technical Information of China (English)
俞茂宏; 李建春; 张永强
2001-01-01
The unified strength theory proposed by Yu in 1991 is extended to spacial axisymmetric problem. A unified spacial axismymmetric characteristics line theory based on the unified strength theory is proposed. This theory takes account of different effects of intermediate principal stress on yielding or failure and the SD effect (tensile-compression strength difference) of materials. Various conventional axisymmetric characteristics line theories, whihc are based on the Haar-von Karman plastic condition, Szczepinski hypothesis, Tresca criterion, von Mises criterion and Mohr-Coulomb theory, are special cases of the new theory. Besides, a series of new spacial axisymmetric characteristics fields for different materials can be introduced. It forms a unified spacial axisymmetric characteristics theory. Two examples are calculated with the new theory, the results are compared with those obtained by the finite element program UEPP and those based on the Mohr-Coulomb strength theory. It is shown that the new theory is reliable and feasible. The economic benefit can be obtained from the engineering application of the new theory.
Stability analysis of axisymmetric supersonic wakes using various basic states
International Nuclear Information System (INIS)
Two-dimensional stability analyses are conducted of turbulent axisymmetric supersonic wakes at M = 2.46. The aim is to investigate which azimuthal modes are dominant and how the stability behaviour is influenced by the choice of basic state. To that end, axisymmetric (two dimensional) and three dimensional direct numerical simulations (DNS) with either laminar or turbulent inflow conditions were conducted of supersonic wakes to provide the respective basic states for the stability analysis. The global stability analyses were then performed by computing the temporal pulse response using forced Navier-Stokes simulations for each basic state. Using the time- and azimuthally-averaged data from the 3D DNS with turbulent inflow as basic state, an absolute instability of the axisymmetric mode at a Reynolds number, based on wake-generating body diameter and freestream velocity, ReD = 100,000 was found. This is in contrast to results obtained earlier using an axisymmetric flow solution as the basic state. The linear stability analysis for all basic states is presented showing the temporal growth of various azimuthal modes and the respective radial mode shapes. The results are also contrasted to those obtained from nonlinear DNS.
Stability of a compound sessile drop at the axisymmetric configuration.
Zhang, Ying; Chatain, Dominique; Anna, Shelley L; Garoff, Stephen
2016-01-15
The equilibrium configuration of compound sessile drops has been calculated previously in the absence of gravity. Using the Laplace equations, we establish seven dimensionless parameters describing the axisymmetric configuration in the presence of gravity. The equilibrium axisymmetric configuration can be either stable or unstable depending on the fluid properties. A stability criterion is established by calculating forces on a perturbed Laplacian shape. In the zero Bond number limit, the stability criterion depends on the density ratio, two ratios of interfacial tensions, the volume ratio of the two drops, and the contact angle. We use Surface Evolver to examine the stability of compound sessile drops at small and large Bond numbers and compare with the zero Bond number approximation. Experimentally, we realize a stable axisymmetric compound sessile drop in air, where the buoyancy force exerted by the air is negligible. Finally, using a pair of fluids in which the density ratio can be tuned nearly independently of the interfacial tensions, the stability transition is verified for the axisymmetric configuration. Even though the perturbations are different for the theory, simulations and experiments, both simulations and experiments agree closely with the zero Bond number approximation, exhibiting a small discrepancy at large Bond number. PMID:26433481
ON INTEGRITY ASSESSMENT OF AXISYMMETRIC COMPONENTS OPERATING WITHIN CREEP REGIME
Institute of Scientific and Technical Information of China (English)
ZARRABI K; LAWRENCE Ng
2006-01-01
A multiaxial paradigm for predicting creep damage/lives of components is described. Although in principle the paradigm is general, it is verified using axisymmetric experimental data. It is shown that the proposed paradigm is capable of predicting creep lives with an error of less than 2%. It is also shown that the proposed paradigm is more accurate than the reference stress method.
Hawking radiation via tunnelling from general stationary axisymmetric black holes
Institute of Scientific and Technical Information of China (English)
Zhang Jing-Yi; Fan Jun-Hui
2007-01-01
Hawking radiation is viewed as a tunnelling process. In this way the emission rates of massless particles and massive particles tunnelling across the event horizon of general stationary axisymmetric black holes are calculated,separately. The emission spectra of these two different kinds of outgoing particles have the same functional form and both are consistent with an underlying unitary theory.
Motion of charged particle in axisymmetric electromagnetic fields
Energy Technology Data Exchange (ETDEWEB)
Robouch, B.V. [ENEA, Frascati (Italy). Dipartimento Energia; Gratreau, P.
1995-05-01
A previous work is now extended to cover toroidal or corrugated (periodically perturbed) axisymmetric fields. Coordinate surfaces are defined as being coincident with the magnetic surfaces. Scale factors are determined. Equations of motion are obtained in their exact form. This allows a direct numerical treatment instead of having to resort to iterative methods of successive approximations.
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 solv...
Potential formation in axisymmetrized tandem mirror GAMMA 10
International Nuclear Information System (INIS)
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)
The lifecycle of axisymmetric internal solitary waves
Directory of Open Access Journals (Sweden)
J. M. McMillan
2010-09-01
Full Text Available The generation and evolution of solitary waves by intrusive gravity currents in an approximate two-layer fluid with equal upper- and lower-layer depths is examined in a cylindrical geometry by way of theory and numerical simulations. The study is limited to vertically symmetric cases in which the density of the intruding fluid is equal to the average density of the ambient. We show that even though the head height of the intrusion decreases, it propagates at a constant speed well beyond 3 lock radii. This is because the strong stratification at the interface supports the formation of a mode-2 solitary wave that surrounds the intrusion head and carries it outwards at a constant speed. The wave and intrusion propagate faster than a linear long wave; therefore, there is strong supporting evidence that the wave is indeed nonlinear. Rectilinear Korteweg-de Vries theory is extended to allow the wave amplitude to decay as r^{-p} with p=½ and the theory is compared to the observed waves to demonstrate that the width of the wave scales with its amplitude. After propagating beyond 7 lock radii the intrusion runs out of fluid. Thereafter, the wave continues to spread radially at a constant speed, however, the amplitude decreases sufficiently so that linear dispersion dominates and the amplitude decays with distance as r^{-1}.
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...
Digital Differential Geometry Processing
Institute of Scientific and Technical Information of China (English)
Xin-Guo Liu; Hu-Jun Bao; Qun-Sheng Peng
2006-01-01
The theory and methods of digital geometry processing has been a hot research area in computer graphics, as geometric models serves as the core data for 3D graphics applications. The purpose of this paper is to introduce some recent advances in digital geometry processing, particularly mesh fairing, surface parameterization and mesh editing, that heavily use differential geometry quantities. Some related concepts from differential geometry, such as normal, curvature, gradient,Laplacian and their counterparts on digital geometry are also reviewed for understanding the strength and weakness of various digital geometry processing methods.
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...... are solved using extended boundary conditions that account for: i) negligible temperature fluctuations at the boundary, and ii) normal and tangential matching of the boundary’s particle velocity. The proposed model does not require constructing a special mesh for the viscous and thermal boundary layers...... 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....
Emergent Geometry of KP Hierarchy. II
Zhou, Jian
2015-01-01
We elaborate on a construction of quantum LG superpotential associated to a tau-function of the KP hierarchy in the case that resulting quantum spectral curve lies in the quantum two-torus. This construction is applied to Hurwitz numbers, one-legged topological vertex and resolved conifold with external D-brane to give a natural explanation of some earlier work on the relevant quantum curves.
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...
Axi-symmetric forward spiral extrusion, a kinematic and experimental study
International Nuclear Information System (INIS)
Research highlights: → The accumulated strain in AFSE, a new extrusion process, is the result of circumferential velocity gradient along extrusion axis. → The effective strain depends on the radius and helix angle only while independent of the chamfer geometry. → Embedded wires were used to verify the validity of the derived velocity field during AFSE. → The velocity field and the observations conform well and the proposed kinematics is a reliable model for AFSE. - Abstract: A modified axi-symmetric forward spiral extrusion process has been proposed here to allow for a near zero area reduction process. The axi-symmetric forward spiral extrusion, AFSE, can be carried out through a die with a number of engraved spiral grooves. This paper investigates the kinematics of the AFSE process. A velocity field is derived using principle of mass conservation along the extrusion axis. The proposed model has been developed to calculate strain components in the deformation zone during the process. An experimental method has been designed which uses composite lead samples with embedded copper wires to trace the strain path to verify the proposed velocity field. A good agreement between experimental results and the proposed analytical model was observed. The proposed velocity field, verified by experimental results, shows that the deformation develops away from the AFSE die-sample interface. A linear gradient of velocity in the radial direction was observed which is in good agreement with the proposed velocity field. Based on the estimated strains, velocity gradient, and nearly no change in sample cross section during AFSE, the process seems to have good potential for application as a new severe plastic deformation process in both continuous and batch modes.
Taylor, M
2006-01-01
Two charge BPS horizon free supergravity geometries are important in proposals for understanding black hole microstates. In this paper we construct a new class of geometries in the NS1-P system, corresponding to solitonic strings carrying fermionic as well as bosonic condensates. Such geometries are required to account for the full microscopic entropy of the NS1-P system. We then briefly discuss the properties of the corresponding geometries in the dual D1-D5 system.
Bis(thiosemicarbazonato) chelates of Co(II), Ni(II), Cu(II), Pd(II) and Pt(II)
Chandra, Sulekh; Singh, R.
1985-01-01
Bis chelates of Co(II), Ni(II), Cu(II), Pd(II) and Pt(II) with the enolic form of diethyl ketone and methyl n-propyl thiosemicarbazones were synthesized and characterized by elemental analyses, magnetic moments, i.r. and electronic and electron spin resonance spectral studies. All the complexes were found to have the composition ML 2 [where M = Co(II), Ni(II), Cu(II), Pd(ii) and Pt(II) and L = thiosemicarbazones of diethyl ketone and methyl n-propyl ketone]. Co(II) and Cu(II) complexes are paramagnetic and may have polymeric six-coordinate octahedral and square planar geometries, respectively. The Ni(II), Pd(II) and Pt(II) complexes are diamagnetic and may have square planar geometries. Pyridine adducts (ML 2·2Py) of Ni(II) and Cu(II) complexes were also prepared and characterized.
Application of the PTT model to axisymmetric free surface flows
Merejolli, R.; Paulo, G. S.; Tomé, M. F.
2013-10-01
This work is concerned with numerical simulation of axisymmetric viscoelastic free surface flows using the Phan-Thien-Tanner (PTT) constitutive equation. A finite difference technique for solving the governing equations for unsteady incompressible flows written in Cylindrical coordinates on a staggered grid is described. The fluid is modelled by a Marker-and-Cell type method and an accurate representation of the fluid surface is employed. The full free surface stress conditions are applied. The numerical method is verified by comparing numerical predictions of fully developed flow in a pipe with the corresponding analytic solutions. To demonstrate that the numerical method can simulate axisymmetric free surface flows governed by the PTT model, numerical results of the flow evolution of a drop impacting on a rigid dry plate are presented. In these simulations, the rheological effects of the parameters ɛ and ξ are investigated.
Axisymmetric large eddy simulation of a circular source of buoyancy
Energy Technology Data Exchange (ETDEWEB)
Nihous, Gerard C., E-mail: nihous@hawaii.ed [University of Hawaii, Hawaii Natural Energy Institute, 1680 East-West Road, POST 109, Honolulu, HI 96822 (United States)
2009-12-15
Axisymmetric large-eddy simulations (LES) of published experiments on vertical mixing above a circular source of buoyancy are performed. Numerical results confirm the existence of a mixing boundary layer just above the buoyancy source (freshwater injected into saline water). As experiments suggested, the calculated normalized shape of the boundary layer seems independent of source size, freshwater injection rate and background solute concentration. This validates a restrictive but numerically efficient assumption of axisymmetric turbulence for the LES calculations. It also lends additional credibility to the theoretical boundary-layer analysis of Epstein and Burelbach [Epstein, M., Burelbach, J.P., 2001. Vertical mixing above a steady circular source of buoyancy. Int. J. Heat Mass Trans. 44, 525-536], even at marginally high Froude numbers.
Axisymmetric large eddy simulation of a circular source of buoyancy
International Nuclear Information System (INIS)
Axisymmetric large-eddy simulations (LES) of published experiments on vertical mixing above a circular source of buoyancy are performed. Numerical results confirm the existence of a mixing boundary layer just above the buoyancy source (freshwater injected into saline water). As experiments suggested, the calculated normalized shape of the boundary layer seems independent of source size, freshwater injection rate and background solute concentration. This validates a restrictive but numerically efficient assumption of axisymmetric turbulence for the LES calculations. It also lends additional credibility to the theoretical boundary-layer analysis of Epstein and Burelbach [Epstein, M., Burelbach, J.P., 2001. Vertical mixing above a steady circular source of buoyancy. Int. J. Heat Mass Trans. 44, 525-536], even at marginally high Froude numbers.
Stable photon orbits in stationary axisymmetric electrovacuum spacetimes
Dolan, Sam R
2016-01-01
We investigate the existence and phenomenology of stable photon orbits (SPOs) in stationary axisymmetric electrovacuum spacetimes in four dimensions. First, we classify the equatorial circular photon orbits of Kerr-Newman spacetimes in the charge-spin plane. Second, using a Hamiltonian formulation, we show that Reissner-Nordstr\\"om di-holes (a family encompassing the Majumdar-Papapetrou and Weyl-Bach special cases) admit SPOs, in a certain parameter regime that we investigate. Third, we explore the transition from order to chaos for typical SPOs bounded within a torus around a di-hole, via a selection of Poincar\\'e sections. Finally, for general axisymmetric stationary spacetimes, we show that the Einstein-Maxwell field equations allow for the existence of SPOs in electrovacuum; but not in pure vacuum.
Dynamics and thermodynamics of axisymmetric flows: I. Theory
Leprovost, N; Chavanis, P H; Leprovost, Nicolas; Chavanis, Pierre-Henri
2005-01-01
We develop new variational principles to study stability and equilibrium of axisymmetric flows. We show that there is an infinite number of steady state solutions. We show that these steady states maximize a (non-universal) $H$-function. We derive relaxation equations which can be used as numerical algorithm to construct stable stationary solutions of axisymmetric flows. In a second part, we develop a thermodynamical approach to the equilibrium states at some fixed coarse-grained scale. We show that the resulting distribution can be divided in a universal part coming from the conservation of robust invariants and one non-universal determined by the initial conditions through the fragile invariants (for freely evolving systems) or by a prior distribution encoding non-ideal effects such as viscosity, small-scale forcing and dissipation (for forced systems). Finally, we derive a parameterization of inviscid mixing to describe the dynamics of the system at the coarse-grained scale.
Axisymmetric solitary waves on the surface of a ferrofluid
Bourdin, Elise; Bacri, Jean-Claude; Falcon, Eric
2010-01-01
We report the first observation of axisymmetric solitary waves on the surface of a cylindrical magnetic fluid layer surrounding a current-carrying metallic tube. According to the ratio between the magnetic and capillary forces, both elevation and depression solitary waves are observed with profiles in good agreement with theoretical predictions based on the magnetic analogue of the Korteweg-deVries equation. We also report the first measurements of the velocity and the dispersion relation of ...
Axisymmetric smoothed particle hydrodynamics with self-gravity
García Senz, Domingo; Relano, A.; Cabezón Gómez, Rubén Martín; Bravo Guil, Eduardo
2008-01-01
The axisymmetric form of the hydrodynamic equations within the smoothed particle hydrodynamics (SPH) formalism is presented and checked using idealized scenarios taken from astrophysics (free fall collapse, implosion and further pulsation of a Sun-like star), gas dynamics (wall heating problem, collision of two streams of gas) and inertial confinement fusion (ablative implosion of a small capsule). New material concerning the standard SPH formalism is given. That includes the numerical handli...
Axisymmetric and triaxial MOND density-potential pairs
Ciotti, L.; Londrillo, P.; Nipoti, C.
2005-01-01
We present a simple method, based on the deformation of spherically symmetric potentials, to construct explicit axisymmetric and triaxial MOND density-potential pairs. General guidelines to the choice of suitable deformations, so that the resulting density distribution is nowhere negative, are presented. This flexible method offers for the first time the possibility to study the MOND gravitational field for sufficiently general and realistic density distributions without resorting to sophisti...
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 ...... of the netting. The software package developed to solve this problem is freely available. Comparisons are carried out with a previous model and experimental data....
Non-axisymmetric oscillations of differentially rotating relativistic stars
Passamonti, Andrea; Stavridis, Adamantios; Kokkotas, Kostas
2007-01-01
Non-axisymmetric oscillations of differentially rotating stars are studied using both slow rotation and Cowling approximation. The equilibrium stellar models are relativistic polytropes where differential rotation is described by the relativistic j-constant rotation law. The oscillation spectrum is studied versus three main parameters: the stellar compactness $M/R$, the degree of differential rotation $A$ and the number of maximun couplings $\\ell_{\\rm max}$. It is shown that the rotational sp...
Study on the Interaction of Non-axisymmetric Binary Vortices
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
In the context of advection dynamics, 19 experiments (Exps.) are performed using a quasi-geostrophic barotropic vorticity equation model to explore the condition for the mergence of binary vortices and the self-organization of the larger scale vortex. Results show that the initial distance between the centers of binary vortices and the non-axisymmetric distributions of their initial vorticity are two factors affecting the mergence of binary vortices. There is a critical distance for the mergence of initial symmetric binary vortices, however, the mergence of initial non-axisymmetric binary vortices is also affected by the asymmetric structure of initial vortices. The self-organization processes in 19 experiments can be classified into two types: one is the merging of identical, axisymmetric binary vortices in which the interaction of the two vortices undergoes slowly change, rapid change, and the formation, stretching, and development of the filaments of vorticity, and the two vortices merge into a symmetric vortex, with its vorticity piled up in the inner region coming from the two initial vortices, and the vorticity of the spiral band in the outer region from the stretching of the filaments of the two initial vortices. And the other type is the merging of the two non-axisymmetric initial vortices of an elliptic vortex and an eccentric vortex hi which the elliptic vortex, on the one hand, mutually rotates, and on the other hand moves towards the center of the computational domain, at the same time expands its vorticity area, and at last forms the inner core of resultant state vortex; and the eccentric vortex mutually rotates, meanwhile continuously stretches, and finally forms the spiral band of resultant state vortex. The interaction process is characteristic of the vorticity piled up in the inner core region of resultant state vortex originating from the elliptic vortex and the vorticity in spiral band mainly from the successive stretch and rupture of the
Resonant Absorption of Axisymmetric Modes in Twisted Magnetic Flux Tubes
Giagkiozis, I.; Goossens, M.; Verth, G.; Fedun, V.; Van Doorsselaere, T.
2016-06-01
It has been shown recently that magnetic twist and axisymmetric MHD modes are ubiquitous in the solar atmosphere, and therefore the study of resonant absorption for these modes has become a pressing issue because it can have important consequences for heating magnetic flux tubes in the solar atmosphere and the observed damping. In this investigation, for the first time, we calculate the damping rate for axisymmetric MHD waves in weakly twisted magnetic flux tubes. Our aim is to investigate the impact of resonant damping of these modes for solar atmospheric conditions. This analytical study is based on an idealized configuration of a straight magnetic flux tube with a weak magnetic twist inside as well as outside the tube. By implementing the conservation laws derived by Sakurai et al. and the analytic solutions for weakly twisted flux tubes obtained recently by Giagkiozis et al. we derive a dispersion relation for resonantly damped axisymmetric modes in the spectrum of the Alfvén continuum. We also obtain an insightful analytical expression for the damping rate in the long wavelength limit. Furthermore, it is shown that both the longitudinal magnetic field and the density, which are allowed to vary continuously in the inhomogeneous layer, have a significant impact on the damping time. Given the conditions in the solar atmosphere, resonantly damped axisymmetric modes are highly likely to be ubiquitous and play an important role in energy dissipation. We also suggest that, given the character of these waves, it is likely that they have already been observed in the guise of Alfvén waves.
Dynamical system properties of an axisymmetric convective tropical cyclone model
Schönemann, Daria; Frisius, Thomas
2014-01-01
The dynamical system behaviour of tropical cyclones and their potential intensity with a view to sea surface temperature, tropospheric temperature stratification and tropospheric moisture content is investigated in the axisymmetric convective model HURMOD. The model results exhibit the existence of a fixed-point attractor associated with a strong tropical cyclone. Moreover, the initial vortex strength forms an amplitude threshold to cyclogenesis. Above this threshold, the size of the tropical...
AXISYMMETRIC MHD INSTABILITIES IN SOLAR/STELLAR TACHOCLINES
International Nuclear Information System (INIS)
Extensive studies over the past decade showed that HD and MHD nonaxisymmetric instabilities exist in the solar tachocline for a wide range of toroidal field profiles, amplitudes, and latitude locations. Axisymmetric instabilities (m = 0) do not exist in two dimensions, and are excited in quasi-three-dimensional shallow-water systems only for very high field strengths (2 mG). We investigate here MHD axisymmetric instabilities in a three-dimensional thin-shell model of the solar/stellar tachocline, employing a hydrostatic, non-Boussinesq system of equations. We deduce a number of general properties of the instability by use of an integral theorem, as well as finding detailed numerical solutions for unstable modes. Toroidal bands become unstable to axisymmetric perturbations for solar-like field strengths (100 kG). The e-folding time can be months down to a few hours if the field strength is 1 mG or higher, which might occur in the solar core, white dwarfs, or neutron stars. These instabilities exist without rotation, with rotation, and with differential rotation, although both rotation and differential rotation have stabilizing effects. Broad toroidal fields are stable. The instability for modes with m = 0 is driven from the poleward shoulder of banded profiles by a perturbation magnetic curvature stress that overcomes the stabilizing Coriolis force. The nonaxisymmetric instability tips or deforms a band; with axisymmetric instability, the fluid can roll in latitude and radius, and can convert bands into tubes stacked in radius. The velocity produced by this instability in the case of low-latitude bands crosses the equator, and hence can provide a mechanism for interhemispheric coupling.
Viscosity Effects on the Dynamics of Long Axisymmetric Liquid Bridges
Meseguer Ruiz, José; Perales Perales, José Manuel
1992-01-01
In this paper the dynamics of axisymmetric liquid columns held by capillary forces between two circular, concentric, solid disks is considered. The problem has been solved by using an one-dimensional model known in the literature as the Cosserat model, which includes viscosity effects, where the axial velocity is considered constant in each section of the liquid bridge. The dynamic response of the bridge to an excitation consisting of a small amplitude vibration of the supporting disks has be...
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
Affine and Projective Geometry
Bennett, M K
1995-01-01
An important new perspective on AFFINE AND PROJECTIVE GEOMETRY. This innovative book treats math majors and math education students to a fresh look at affine and projective geometry from algebraic, synthetic, and lattice theoretic points of view. Affine and Projective Geometry comes complete with ninety illustrations, and numerous examples and exercises, covering material for two semesters of upper-level undergraduate mathematics. The first part of the book deals with the correlation between synthetic geometry and linear algebra. In the second part, geometry is used to introduce lattice theory
Three-Dimensional Electromagnetic High Frequency Axisymmetric Cavity Scars.
Energy Technology Data Exchange (ETDEWEB)
Warne, Larry Kevin; Jorgenson, Roy Eberhardt
2014-10-01
This report examines the localization of high frequency electromagnetic fi elds in three-dimensional axisymmetric cavities along periodic paths between opposing sides of the cavity. The cases where these orbits lead to unstable localized modes are known as scars. This report treats both the case where the opposing sides, or mirrors, are convex, where there are no interior foci, and the case where they are concave, leading to interior foci. The scalar problem is treated fi rst but the approximations required to treat the vector fi eld components are also examined. Particular att ention is focused on the normalization through the electromagnetic energy theorem. Both projections of the fi eld along the scarred orbit as well as point statistics are examined. Statistical comparisons are m ade with a numerical calculation of the scars run with an axisymmetric simulation. This axisymmetric cas eformstheoppositeextreme(wherethetwomirror radii at each end of the ray orbit are equal) from the two -dimensional solution examined previously (where one mirror radius is vastly di ff erent from the other). The enhancement of the fi eldontheorbitaxiscanbe larger here than in the two-dimensional case. Intentionally Left Blank
Options for axisymmetric operation of MFTF-B
International Nuclear Information System (INIS)
The flexibility of MFTF-B for axisymmetric experiments has been investigated. Interhcanging the axicell coils and increasing their separation results in an axisymmetric plug cell with 12:1 and 6:1 inner and outer mirror ratios, respectively. For axisymmetric operation, the sloshing-ion neutral beams, ECRH gyrotrons, and the pumping system would be moved to the axicell. Stabilization by E-rings could be explored in this configuration. With the addition of octopole magnets, off-axis multipole stabilization could also be tested. Operating points for octopole and E-ring-stabilized configurations with properties similar to those of the quadrupole MFTF-B, namely T/sub ic/ = 10 - 15 keV and n/sub c/ approx. = 3 x 1013 cm-3, have been obtained. Because of the negligible radial transport of central-cell ions, the required neutral-beam power in the central cell has been dramatically reduced. In addition, because MHD stabilization is achieved by off-axis hot electrons in both cases, much lower barrier beta is possible, which aids in reducing the barrier ECRH power. Total ECRH power in the end cell is projected to be approx. =1 MW. Possible operating points for both octopole and E-ring configurations are described along with the stability considerations involved
International Nuclear Information System (INIS)
Full text: This work will present a new technology for modeling the geometry of pressure vessels, using thin axi-symmetrical shells. An ObjectARX application is being developed based on the ObjectARX programming environment, which provides an object oriented C++ programming interface for developers to use, customize and extend AutoCAD. The application will perform the modeling and the discretization of vessels into axi-symmetrical finite elements for limit and shakedown analysis of pressure vessels. It uses AutoCAD as a graphical platform, taking advantage of AutoCAD's open architecture, which provides direct access to AutoCAD graphic system, database structures and native command definition. The application customized entities; objects and commands can be ordered by command line, toolbars or menu and will be virtually indistinguishable from built-in AutoCAD's related. Modeling the geometry required the construction of a mother class denominated shell, from which the following primitives were derived: spherical, toroidal, conical and cylindrical. For the discretization of the shell geometry two entities were created, element and node. The class constraint imposes restrictions on displacements to the element nodes at the edges of the vessel. The mother class load contains the characteristics of the entities ring load and pressure load. Finally, the class material is derived from AutoCAD object and has only numerical data and no graphical representation. All data are saved into AutoCAD database and can be easily exported to analysis in a text format through an appropriate interface. Further, the work will present advances on the development of the technique proposed by Franco and Ponter for the finite element formulation of shakedown problems in symmetrically loaded shells of revolution. An upper bound formulation for estimating limit and shakedown loads for pressure vessels is recounted. The error estimator using the energy norm and adaptive strategies for remeshing
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.
Osborne, Ianna
2013-01-01
CMS faces real challenges with upgrade of the CMS detector through 2020. 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, 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...
Energy Technology Data Exchange (ETDEWEB)
Simonen, T; Cohen, R; Correll, D; Fowler, K; Post, D; Berk, H; Horton, W; Hooper, E B; Fisch, N; Hassam, A; Baldwin, D; Pearlstein, D; Logan, G; Turner, B; Moir, R; Molvik, A; Ryutov, D; Ivanov, A A; Kesner, J; Cohen, B; McLean, H; Tamano, T; Tang, X Z; Imai, T
2008-10-24
Experimental results, theory and innovative ideas now point with increased confidence to the possibility of a Gas Dynamic Trap (GDT) neutron source which would be on the path to an attractively simple Axisymmetric Tandem Mirror (ATM) power plant. Although magnetic mirror research was terminated in the US 20 years ago, experiments continued in Japan (Gamma 10) and Russia (GDT), with a very small US effort. This research has now yielded data, increased understanding, and generated ideas resulting in the new concepts described here. Early mirror research was carried out with circular axisymmetric magnets. These plasmas were MHD unstable due to the unfavorable magnetic curvature near the mid-plane. Then the minimum-B concept emerged in which the field line curvature was everywhere favorable and the plasma was situated in a MHD stable magnetic well (70% average beta in 2XII-B). The Ioffe-bar or baseball-coil became the standard for over 40 years. In the 1980's, driven by success with minimum-B stabilization and the control of ion cyclotron instabilities in PR6 and 2XII-B, mirrors were viewed as a potentially attractive concept with near-term advantages as a lower Q neutron source for applications such as a hybrid fission fuel factory or toxic waste burner. However there are down sides to the minimum-B geometry: coil construction is complex; restraining magnetic forces limit field strength and mirror ratios. Furthermore, the magnetic field lines have geodesic curvature which introduces resonant and neoclassical radial transport as observed in early tandem mirror experiments. So what now leads us to think that simple axisymmetric mirror plasmas can be stable? The Russian GDT experiment achieves on-axis 60% beta by peaking of the kinetic plasma pressure near the mirror throat (where the curvature is favorable) to counter-balance the average unfavorable mid-plane curvature. Then a modest augmentation of plasma pressure in the expander results in stability. The GDT
International Nuclear Information System (INIS)
Experimental results, theory and innovative ideas now point with increased confidence to the possibility of a Gas Dynamic Trap (GDT) neutron source which would be on the path to an attractively simple Axisymmetric Tandem Mirror (ATM) power plant. Although magnetic mirror research was terminated in the US 20 years ago, experiments continued in Japan (Gamma 10) and Russia (GDT), with a very small US effort. This research has now yielded data, increased understanding, and generated ideas resulting in the new concepts described here. Early mirror research was carried out with circular axisymmetric magnets. These plasmas were MHD unstable due to the unfavorable magnetic curvature near the mid-plane. Then the minimum-B concept emerged in which the field line curvature was everywhere favorable and the plasma was situated in a MHD stable magnetic well (70% average beta in 2XII-B). The Ioffe-bar or baseball-coil became the standard for over 40 years. In the 1980's, driven by success with minimum-B stabilization and the control of ion cyclotron instabilities in PR6 and 2XII-B, mirrors were viewed as a potentially attractive concept with near-term advantages as a lower Q neutron source for applications such as a hybrid fission fuel factory or toxic waste burner. However there are down sides to the minimum-B geometry: coil construction is complex; restraining magnetic forces limit field strength and mirror ratios. Furthermore, the magnetic field lines have geodesic curvature which introduces resonant and neoclassical radial transport as observed in early tandem mirror experiments. So what now leads us to think that simple axisymmetric mirror plasmas can be stable? The Russian GDT experiment achieves on-axis 60% beta by peaking of the kinetic plasma pressure near the mirror throat (where the curvature is favorable) to counter-balance the average unfavorable mid-plane curvature. Then a modest augmentation of plasma pressure in the expander results in stability. The GDT
Fundamental concepts of geometry
Meserve, Bruce E
2014-01-01
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.
Split Special Lagrangian Geometry
Harvey, F. Reese; Lawson Jr, H. Blaine
2010-01-01
One purpose of this article is to draw attention to the seminal work of J. Mealy in 1989 on calibrations in semi-riemannian geometry where split SLAG geometry was first introduced. The natural setting is provided by doing geometry with the complex numbers C replaced by the double numbers D, where i with i^2 = -1 is replaced by tau with tau^2 = 1. A rather surprising amount of complex geometry carries over, almost untouched, and this has been the subject of many papers. We briefly review this ...
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
Emission-Line Profiles of Accretion Disks with a Non-Axisymmetric Pattern
SANBUICHI, Kiyotaka; FUKUE, Jun; Kojima, Yasufumi
1994-01-01
In several cases, accretion disks may have non-axisymmetric patterns, such as one-armed oscillations and spiral shock waves. In such cases the line emissivity may also become non-axisymmetric. We examined the emission-line profiles for geometrically thin/thick, (non-) relativistic accretion disks while taking acount of the non-axisymmetric emissivity. The emission-line profiles were calculated numerically using a code based on the ray-tracing method. The emission-line profiles are usually ...
International Nuclear Information System (INIS)
Snap-through buckling of shallow clamped spherical shells made of functionally graded material (FGM) and surface-bonded piezoelectric actuators under the thermo-electro-mechanical loading is studied in this paper. The governing equations are based on the classical shell theory and the Sanders nonlinear kinematics equations. It is assumed that the property of the functionally graded materials vary continuously through the thickness of the shell according to a power law distribution of the volume fraction of the constituent materials. The constituent materials of the functionally graded shell are assumed to be mixture of ceramic and metal. The results show that the axisymmetric buckling of Piezo-FGM shallow clamped spherical shells under thermo-electro-mechanical loading is of snap-through type. The intensity of buckling is dependent on the geometry of the shell, value of thermo-electro-mechanical loading and type of thermal loading. - Highlights: • Finite diff erence method is adopted to analyze behavior of Piezo-FGM shallow spherical shell. • The eff ect of electrical loading on the behavior of Piezo-FGM shell isn't considerable. • Mechanical and thermal loading have great e ect on the axisymmetric response of shell. • Geometric dimension of shell has considerable eff ect on the response of spherical shell
Genetic algorithm optimisation of load cell geometry by finite element analysis
Robinson, Gordon M.
1995-01-01
The objective of the work described in this thesis was to numerically model the influence of end-loading conditions on column strain gauge load cells and to develop the model into a program for optimising the geometry of column load cells. It is shown that, for most practical loading conditions, load celis with large numbers of equispaced strain gauges are only sensitive to the axisymmetric components of contact stress distribution. The problem of cylindrical load celis subject to frictio...
Geometry of multihadron production
International Nuclear Information System (INIS)
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
A Generalization of Abel Inversion to non axisymmetric density distribution
Tomassini, P
2001-01-01
Abel Inversion is currently used in laser-plasma studies in order to estimate the electronic density $n_e$ from the phase-shift map $\\delta \\phi$ obtained via interferometry. The main limitation of the Abel method is due to the assumption of axial symmetry of the electronic density, which is often hardly fulfilled. In this paper we present an improvement to the Abel inversion technique in which the axial symmetry condition is relaxed by means of a truncated Legendre Polinomial expansion in the azimutal angle. With the help of simulated interferograms, we will show that the generalized Abel inversion generates accurate densities maps when applied to non axisymmetric density sources.
Angle-action estimation in a general axisymmetric potential
Sanders, Jason
2012-01-01
The usefulness of angle-action variables in galaxy dynamics is well known, but their use is limited due to the difficulty of their calculation in realistic galaxy potentials. Here we present a method for estimating angle-action variables in a realistic Milky Way axisymmetric potential by locally fitting a St\\"ackel potential over the region an orbit probes. The quality of the method is assessed by comparison with other known methods for estimating angle-action variables of a range of disc and...
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.
Frequency spectrum of axisymmetric horizontal oscillations in accretion disks
Giussani, L; Mishra, B
2015-01-01
We present the spectrum of eigenfrequencies of axisymmetric acoustic-inertial oscillations of thin accretion disks for a Schwarzschild black hole modeled with a pseudo-potential. There are nine discrete frequencies, corresponding to trapped modes. Eigenmodes with nine or more radial nodes in the inner disk belong to the continuum, whose frequency range starts somewhat below the maximum value of the radial epicyclic frequency. The results are derived under the assumption that the oscillatory motion is parallel to the midplane of the disk.
Note on reflection symmetry in stationary axisymmetric electrovacuum spacetimes
Energy Technology Data Exchange (ETDEWEB)
Pachon, Leonardo A [Laboratorio de Astronomia y Fisica Teorica (LAFT), Departamento de Fisica, Facultad de Ciencias, La Universidad del Zulia, Maracaibo, 4004 (Venezuela); Sanabria-Gomez, Jose D [Escuela de Fisica, Universidad Industrial de Santander. A.A. 678, Bucaramanga (Colombia)
2006-05-07
Recently, Kordas (1995 Class. Quantum Grav. 12 2037) and Meinel and Neugebauer (1995 Class. Quantum Grav. 12 2045) studied the conditions for reflection symmetry in stationary axisymmetric spacetimes in vacuum. They found that a solution to the Einstein field equations is reflectionally symmetric if their Ernst potential E ({rho} = 0, z) = e(z) on a portion of the positive z-axis extending to infinity satisfies the condition e{sub +}(z)e*{sub +}(-z) = 1. In this note, we formulate analogous conditions for two complex Ernst potentials in electrovacuum. We also present the special case of rational axis potentials. (comments, replies and notes)