Calculation of the electrical of induction heating coils in two dimensional axissymmetric geometry
Energy Technology Data Exchange (ETDEWEB)
Nerg, J.; Partanen, J. [Lappeenranta University of Technology (Finland). Department of Energy Technology, Laboratory of Electrical Engineering
1997-12-31
The effect of the workpiece temperature on the electrical parameters of a plane, spiral inductor is discussed. The effect of workpiece temperature on the electrical efficiency, power transfer to the workpiece and electromagnetic distortion are also presented. Calculation is performed in two dimensional axissymmetric geometry using a FEM program. (orig.) 5 refs.
Structure of six-dimensional microstate geometries
Energy Technology Data Exchange (ETDEWEB)
Lange, Paul de; Mayerson, Daniel R.; Vercnocke, Bert [Institute for Theoretical Physics, University of Amsterdam,Science Park 904, Postbus 94485, 1090 GL Amsterdam (Netherlands)
2015-09-14
We investigate the structure of smooth and horizonless microstate geometries in six dimensions, in the spirit of the five-dimensional analysis of Gibbons and Warner http://arxiv.org/abs/1305.0957 . In six dimensions, which is the natural setting for horizonless geometries with the charges of the D1-D5-P black hole, the natural black objects are strings and there are no Chern-Simons terms for the tensor gauge fields. However, we still find that the same reasoning applies: in absence of horizons, there can be no smooth stationary solutions without non-trivial topology. We use topological arguments to describe the Smarr formula in various examples: the uplift of the five-dimensional minimal supergravity microstates to six dimensions, the two-charge D1-D5 microstates, and the non-extremal JMaRT solution. We also discuss D1-D5-P superstrata and confirm that the Smarr formula gives the same result as for the D1-D5 supertubes which are topologically equivalent.
Structure of six-dimensional microstate geometries
International Nuclear Information System (INIS)
Lange, Paul de; Mayerson, Daniel R.; Vercnocke, Bert
2015-01-01
We investigate the structure of smooth and horizonless microstate geometries in six dimensions, in the spirit of the five-dimensional analysis of Gibbons and Warner http://arxiv.org/abs/1305.0957 . In six dimensions, which is the natural setting for horizonless geometries with the charges of the D1-D5-P black hole, the natural black objects are strings and there are no Chern-Simons terms for the tensor gauge fields. However, we still find that the same reasoning applies: in absence of horizons, there can be no smooth stationary solutions without non-trivial topology. We use topological arguments to describe the Smarr formula in various examples: the uplift of the five-dimensional minimal supergravity microstates to six dimensions, the two-charge D1-D5 microstates, and the non-extremal JMaRT solution. We also discuss D1-D5-P superstrata and confirm that the Smarr formula gives the same result as for the D1-D5 supertubes which are topologically equivalent.
Kashif, Muhammad; Bonnety, Jérôme; Guibert, Philippe; Morin, Céline; Legros, Guillaume
2012-12-17
A Laser Extinction Method has been set up to provide two-dimensional soot volume fraction field time history at a tunable frequency up to 70 Hz inside an axis-symmetric diffusion flame experiencing slow unsteady phenomena preserving the symmetry. The use of a continuous wave laser as the light source enables this repetition rate, which is an incremental advance in the laser extinction technique. The technique is shown to allow a fine description of the soot volume fraction field in a flickering flame exhibiting a 12.6 Hz flickering phenomenon. Within this range of repetition rate, the technique and its subsequent post-processing require neither any method for time-domain reconstruction nor any correction for energy intrusion. Possibly complemented by such a reconstruction method, the technique should support further soot volume fraction database in oscillating flames that exhibit characteristic times relevant to the current efforts in the validation of soot processes modeling.
Higher dimensional uniformisation and W-geometry
International Nuclear Information System (INIS)
Govindarajan, S.
1995-01-01
We formulate the uniformisation problem underlying the geometry of W n -gravity using the differential equation approach to W-algebras. We construct W n -space (analogous to superspace in supersymmetry) as an (n-1)-dimensional complex manifold using isomonodromic deformations of linear differential equations. The W n -manifold is obtained by the quotient of a Fuchsian subgroup of PSL(n,R) which acts properly discontinuously on a simply connected domain in bfCP n-1 . The requirement that a deformation be isomonodromic furnishes relations which enable one to convert non-linear W-diffeomorphisms to (linear) diffeomorphisms on the W n -manifold. We discuss how the Teichmueller spaces introduced by Hitchin can then be interpreted as the space of complex structures or the space of projective structures with real holonomy on the W n -manifold. The projective structures are characterised by Halphen invariants which are appropriate generalisations of the Schwarzian. This construction will work for all ''generic'' W-algebras. (orig.)
Analogy and Dynamic Geometry System Used to Introduce Three-Dimensional Geometry
Mammana, M. F.; Micale, B.; Pennisi, M.
2012-01-01
We present a sequence of classroom activities on Euclidean geometry, both plane and space geometry, used to make three dimensional geometry more catchy and simple. The activity consists of a guided research activity that leads the students to discover unexpected properties of two apparently distant geometrical entities, quadrilaterals and…
Geometry of higher-dimensional black hole thermodynamics
International Nuclear Information System (INIS)
Aaman, Jan E.; Pidokrajt, Narit
2006-01-01
We investigate thermodynamic curvatures of the Kerr and Reissner-Nordstroem (RN) black holes in spacetime dimensions higher than four. These black holes possess thermodynamic geometries similar to those in four-dimensional spacetime. The thermodynamic geometries are the Ruppeiner geometry and the conformally related Weinhold geometry. The Ruppeiner geometry for a d=5 Kerr black hole is curved and divergent in the extremal limit. For a d≥6 Kerr black hole there is no extremality but the Ruppeiner curvature diverges where one suspects that the black hole becomes unstable. The Weinhold geometry of the Kerr black hole in arbitrary dimension is a flat geometry. For the RN black hole the Ruppeiner geometry is flat in all spacetime dimensions, whereas its Weinhold geometry is curved. In d≥5 the Kerr black hole can possess more than one angular momentum. Finally we discuss the Ruppeiner geometry for the Kerr black hole in d=5 with double angular momenta
Low-dimensional geometry from euclidean surfaces to hyperbolic knots
Bonahon, Francis
2009-01-01
The study of 3-dimensional spaces brings together elements from several areas of mathematics. The most notable are topology and geometry, but elements of number theory and analysis also make appearances. In the past 30 years, there have been striking developments in the mathematics of 3-dimensional manifolds. This book aims to introduce undergraduate students to some of these important developments. Low-Dimensional Geometry starts at a relatively elementary level, and its early chapters can be used as a brief introduction to hyperbolic geometry. However, the ultimate goal is to describe the very recently completed geometrization program for 3-dimensional manifolds. The journey to reach this goal emphasizes examples and concrete constructions as an introduction to more general statements. This includes the tessellations associated to the process of gluing together the sides of a polygon. Bending some of these tessellations provides a natural introduction to 3-dimensional hyperbolic geometry and to the theory o...
Higher dimensional homogeneous cosmology in Lyra geometry
Indian Academy of Sciences (India)
1Department of Mathematics, Jadavpur University, Kolkata 700 032, India. 2Khodar ... 1. Introduction. The idea of higher dimensional theory was originated in super string and super gravity .... Equation (7) can easily be integrated to obtain.
Bosonization in a two-dimensional Riemann Cartan geometry
International Nuclear Information System (INIS)
Denardo, G.; Spallucci, E.
1987-01-01
We study the vacuum functional for a Dirac field in a two dimensional Riemann-Cartan geometry. Torsion is treated as a quantum variable while the metric is considered as a classical background field. Decoupling spinors from the non-Riemannian part of the geometry introduces a chiral Jacobian into the vacuum generating functional. We compute this functional Jacobian determinant by means of the Alvarez method. Finally, we show that the effective action for the background geometry is of the Liouville type and does not preserve any memory of the initial torsion field. (author)
Three-dimensional fractal geometry for gas permeation in microchannels
Malankowska, Magdalena; Schlautmann, Stefan; Berenschot, Erwin J.W.; Tiggelaar, Roald M.; Pina, Maria Pilar; Mallada, Reyes; Tas, Niels R.; Gardeniers, Han
2018-01-01
The novel concept of a microfluidic chip with an integrated three-dimensional fractal geometry with nanopores, acting as a gas transport membrane, is presented. The method of engineering the 3D fractal structure is based on a combination of anisotropic etching of silicon and corner lithography. The
Prasolov, V V
2015-01-01
This book provides a systematic introduction to various geometries, including Euclidean, affine, projective, spherical, and hyperbolic geometries. Also included is a chapter on infinite-dimensional generalizations of Euclidean and affine geometries. A uniform approach to different geometries, based on Klein's Erlangen Program is suggested, and similarities of various phenomena in all geometries are traced. An important notion of duality of geometric objects is highlighted throughout the book. The authors also include a detailed presentation of the theory of conics and quadrics, including the theory of conics for non-Euclidean geometries. The book contains many beautiful geometric facts and has plenty of problems, most of them with solutions, which nicely supplement the main text. With more than 150 figures illustrating the arguments, the book can be recommended as a textbook for undergraduate and graduate-level courses in geometry.
Topology as fluid geometry two-dimensional spaces, volume 2
Cannon, James W
2017-01-01
This is the second of a three volume collection devoted to the geometry, topology, and curvature of 2-dimensional spaces. The collection provides a guided tour through a wide range of topics by one of the twentieth century's masters of geometric topology. The books are accessible to college and graduate students and provide perspective and insight to mathematicians at all levels who are interested in geometry and topology. The second volume deals with the topology of 2-dimensional spaces. The attempts encountered in Volume 1 to understand length and area in the plane lead to examples most easily described by the methods of topology (fluid geometry): finite curves of infinite length, 1-dimensional curves of positive area, space-filling curves (Peano curves), 0-dimensional subsets of the plane through which no straight path can pass (Cantor sets), etc. Volume 2 describes such sets. All of the standard topological results about 2-dimensional spaces are then proved, such as the Fundamental Theorem of Algebra (two...
Global geometry of two-dimensional charged black holes
International Nuclear Information System (INIS)
Frolov, Andrei V.; Kristjansson, Kristjan R.; Thorlacius, Larus
2006-01-01
The semiclassical geometry of charged black holes is studied in the context of a two-dimensional dilaton gravity model where effects due to pair-creation of charged particles can be included in a systematic way. The classical mass-inflation instability of the Cauchy horizon is amplified and we find that gravitational collapse of charged matter results in a spacelike singularity that precludes any extension of the spacetime geometry. At the classical level, a static solution describing an eternal black hole has timelike singularities and multiple asymptotic regions. The corresponding semiclassical solution, on the other hand, has a spacelike singularity and a Penrose diagram like that of an electrically neutral black hole. Extremal black holes are destabilized by pair-creation of charged particles. There is a maximally charged solution for a given black hole mass but the corresponding geometry is not extremal. Our numerical data exhibits critical behavior at the threshold for black hole formation
Interactive multimedia-based teaching material for 3-dimensional geometry
Prabowo, A.; Anggoro, R. P.; Astuti, D.; Fahmi, S.
2017-12-01
This study aims to develop the interactive multimedia-based teaching material for 3-dimensional geometry in junior high school. The product was produced through the stages of define, design, develop, and disseminate. Two media experts and two teaching experts had validated it. They judged that the product developed was valid. It had been revised based on their advice. It has been disseminated to 15 mathematics teachers and tried to 30 students of junior high school. Teachers stated that this product gives a new form of teaching material in 3-dimensional geometry. According to the student, the product is interesting. It can motivate them to study mathematics, help them to master the material and increase their interest in mathematics.
Geometry of quantum dynamics in infinite-dimensional Hilbert space
Grabowski, Janusz; Kuś, Marek; Marmo, Giuseppe; Shulman, Tatiana
2018-04-01
We develop a geometric approach to quantum mechanics based on the concept of the Tulczyjew triple. Our approach is genuinely infinite-dimensional, i.e. we do not restrict considerations to finite-dimensional Hilbert spaces, contrary to many other works on the geometry of quantum mechanics, and include a Lagrangian formalism in which self-adjoint (Schrödinger) operators are obtained as Lagrangian submanifolds associated with the Lagrangian. As a byproduct we also obtain results concerning coadjoint orbits of the unitary group in infinite dimensions, embedding of pure states in the unitary group, and self-adjoint extensions of symmetric relations.
Learning 2-Dimensional and 3-Dimensional Geometry with Geogebra: Which Would Students Do Better?
Directory of Open Access Journals (Sweden)
Zaleha Ismail
2017-08-01
Full Text Available The purpose of this study is to examine the geometric thinking of young children who worked with GeoGebra to learn two-dimensional (2-D and three-dimensional (3-D geometry. GeoGebra is an open sourced dynamic mathematics software which is applicable for learning mathematics from primary school to secondary school and to higher education. Thirty pupils studying in second grade (Year 2 at a school located in Pontian, a district in one of the Malaysian state participated in the study. They attended GeoGebra sessions to construct and analyze dynamics of two-dimensional and three-dimensional geometry after learning these topics in the conventional setting. Pretest and posttest on two-dimensional and three-dimensional spatial ability based on Van Hiele level of geometric thinking were administered to the pupils. The comparison between pretest and posttest results demonstrate significant enhancement in visualization and informal deduction for both 2-D and 3-D geometry. Moreover from the intervention, the students benefit most in analyzing 3-D and visualizing 2-D geometry. Interestingly, skills and knowledge acquired through activities using GeoGebra in student-centered learning environment could be successfully transferred to paper and pencil test.
Fractal geometry in an expanding, one-dimensional, Newtonian universe.
Miller, Bruce N; Rouet, Jean-Louis; Le Guirriec, Emmanuel
2007-09-01
Observations of galaxies over large distances reveal the possibility of a fractal distribution of their positions. The source of fractal behavior is the lack of a length scale in the two body gravitational interaction. However, even with new, larger, sample sizes from recent surveys, it is difficult to extract information concerning fractal properties with confidence. Similarly, three-dimensional N-body simulations with a billion particles only provide a thousand particles per dimension, far too small for accurate conclusions. With one-dimensional models these limitations can be overcome by carrying out simulations with on the order of a quarter of a million particles without compromising the computation of the gravitational force. Here the multifractal properties of two of these models that incorporate different features of the dynamical equations governing the evolution of a matter dominated universe are compared. For each model at least two scaling regions are identified. By employing criteria from dynamical systems theory it is shown that only one of them can be geometrically significant. The results share important similarities with galaxy observations, such as hierarchical clustering and apparent bifractal geometry. They also provide insights concerning possible constraints on length and time scales for fractal structure. They clearly demonstrate that fractal geometry evolves in the mu (position, velocity) space. The observed patterns are simply a shadow (projection) of higher-dimensional structure.
Integral Transport Theory in One-dimensional Geometries
Energy Technology Data Exchange (ETDEWEB)
Carlvik, I
1966-06-15
A method called DIT (Discrete Integral Transport) has been developed for the numerical solution of the transport equation in one-dimensional systems. The characteristic features of the method are Gaussian integration over the coordinate as described by Kobayashi and Nishihara, and a particular scheme for the calculation of matrix elements in annular and spherical geometry that has been used for collision probabilities in earlier Flurig programmes. The paper gives a general theory including such things as anisotropic scattering and multi-pole fluxes, and it gives a brief description of the Flurig scheme. Annular geometry is treated in some detail, and corresponding formulae are given for spherical and plane geometry. There are many similarities between DIT and the method of collision probabilities. DIT is in many cases faster, because for a certain accuracy in the fluxes DIT often needs fewer space points than the method of collision probabilities needs regions. Several computer codes using DIT, both one-group and multigroup, have been written. It is anticipated that experience gained in calculations with these codes will be reported in another paper.
Rigid supersymmetry on 5-dimensional Riemannian manifolds and contact geometry
International Nuclear Information System (INIS)
Pan, Yiwen
2014-01-01
In this note we generalize the methods of http://dx.doi.org/10.1007/JHEP08(2012)141, http://dx.doi.org/10.1007/JHEP01(2013)072 and http://dx.doi.org/10.1007/JHEP05(2013)017 to 5-dimensional Riemannian manifolds M. We study the relations between the geometry of M and the number of solutions to a generalized Killing spinor equation obtained from a 5-dimensional supergravity. The existence of 1 pair of solutions is related to almost contact metric structures. We also discuss special cases related to M=S 1 ×M 4 , which leads to M being foliated by submanifolds with special properties, such as Quaternion-Kähler. When there are 2 pairs of solutions, the closure of the isometry sub-algebra generated by the solutions requires M to be S 3 or T 3 -fibration over a Riemann surface. 4 pairs of solutions pin down the geometry of M to very few possibilities. Finally, we propose a new supersymmetric theory for N=1 vector multiplet on K-contact manifold admitting solutions to the Killing spinor equation
Stability analysis of lower dimensional gravastars in noncommutative geometry
Energy Technology Data Exchange (ETDEWEB)
Banerjee, Ayan [Jadavpur University, Department of Mathematics, Kolkata (India); Hansraj, Sudan [University of KwaZulu-Natal, Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics and Computer Science, Durban (South Africa)
2016-11-15
The Banados et al. (Phys. Rev. Lett 69:1849, 1992), black hole solution is revamped from the Einstein field equations in (2 + 1)-dimensional anti-de Sitter spacetime, in a context of noncommutative geometry (Phys. Rev. D 87:084014, 2013). In this article, we explore the exact gravastar solutions in three-dimensional anti-de Sitter space given in the same geometry. As a first step we derive BTZ solution assuming the source of energy density as point-like structures in favor of smeared objects, where the particle mass M, is diffused throughout a region of linear size √(α) and is described by a Gaussian function of finite width rather than a Dirac delta function. We matched our interior solution to an exterior BTZ spacetime at a junction interface situated outside the event horizon. Furthermore, a stability analysis is carried out for the specific case when χ < 0.214 under radial perturbations about the static equilibrium solutions. To give theoretical support we are also trying to explore their physical properties and characteristics. (orig.)
The transmission probability method in one-dimensional cylindrical geometry
International Nuclear Information System (INIS)
Rubin, I.E.
1983-01-01
The collision probability method widely used in solving the problems of neutron transpopt in a reactor cell is reliable for simple cells with small number of zones. The increase of the number of zones and also taking into account the anisotropy of scattering greatly increase the scope of calculations. In order to reduce the time of calculation the transmission probability method is suggested to be used for flux calculation in one-dimensional cylindrical geometry taking into account the scattering anisotropy. The efficiency of the suggested method is verified using the one-group calculations for cylindrical cells. The use of the transmission probability method allows to present completely angular and spatial dependences is neutrons distributions without the increase in the scope of calculations. The method is especially effective in solving the multi-group problems
On wakefields with two-dimensional planar geometry
International Nuclear Information System (INIS)
Chao, A.W.; Bane, K.L.F.
1996-10-01
In order to reach higher acceleration gradients in linear accelerators, it is advantageous to use a higher accelerating RF frequency, which in turn requires smaller accelerating structures. As the structure size becomes smaller, rectangular structures become increasingly interesting because they are easier to construct than cylindrically symmetric ones. One drawback of small structures, however, is that the wakefields generated by the beam in such structures tend to be strong. Recently, it has been suggested that one way of ameliorating this problem is to use rectangular structures that are very flat and to use flat beams. In the limiting case of a very flat planar geometry, the problem resembles a purely two-dimensional (2-D) problem, the wakefields of which have been studied
Ion distributions in a two-dimensional reconnection field geometry
International Nuclear Information System (INIS)
Curran, D.B.; Goertz, C.K.; Whelan, T.A.
1987-01-01
ISEE observations have shown trapped ion distributions in the magnetosphere along with streaming ion distributions in the magnetosheath. The more energetic ion beams are found to exist further away from the magnetopause than lower-energy ion beams. In order to understand these properties of the data, we have taken a simple two-dimensional reconnection model which contains a neutral line and an azimuthal electric field and compared its predictions with the experimental data of September 8, 1978. Our model explains trapped particles in the magnetosphere due to nonadiabatic mirroring in the magnetosheath and streaming ions in the magnetosheath due to energization at the magnetopause. The model also shows the higher-energy ions extending further into the magnetosheath, away from the magnetopause than the lower-energy ions. This suggests the ion data of September 8, 1978 are consistent with a reconnection geometry. Copyright American Geophysical Union 1987
Three-dimensional simulations of magnetic reconnection in slab geometry
International Nuclear Information System (INIS)
Onofri, M.; Primavera, L.; Malara, F.; Veltri, P.
2004-01-01
Magnetic reconnection in an incompressible plasma in three-dimensional slab geometry has been studied through magnetohydrodynamics numerical simulations. Particular attention has been paid to the case in which several unstable modes that correspond to resonant surfaces in different positions of the simulation domain, are excited at the beginning of the simulation. The dynamical evolution of such a system leads to a behavior different than what is expected from the linear theory. In particular the effects of the equilibrium field dissipation and the fact that several resonant surfaces are initially excited both concur in modifying the initial growth rates of the instability. In the nonlinear phase two basic phenomena are observed: first, the rapid transfer of energy to large wave numbers, corresponding to a direct cascade of the energy in the spectrum, which approaches, with increasing time, a power law; second, an energy transfer towards smaller wave numbers, which corresponds in the physical space to a coalescence of magnetic islands. Finally, the spectra in the periodic directions exhibit a strongly anisotropic behavior
RECONSTRUCTING THREE-DIMENSIONAL JET GEOMETRY FROM TWO-DIMENSIONAL IMAGES
Avachat, Sayali; Perlman, Eric S.; Li, Kunyang; Kosak, Katie
2018-01-01
Relativistic jets in AGN are one of the most interesting and complex structures in the Universe. Some of the jets can be spread over hundreds of kilo parsecs from the central engine and display various bends, knots and hotspots. Observations of the jets can prove helpful in understanding the emission and particle acceleration processes from sub-arcsec to kilo parsec scales and the role of magnetic field in it. The M87 jet has many bright knots as well as regions of small and large bends. We attempt to model the jet geometry using the observed 2 dimensional structure. The radio and optical images of the jet show evidence of presence of helical magnetic field throughout. Using the observed structure in the sky frame, our goal is to gain an insight into the intrinsic 3 dimensional geometry in the jets frame. The structure of the bends in jet's frame may be quite different than what we see in the sky frame. The knowledge of the intrinsic structure will be helpful in understanding the appearance of the magnetic field and hence polarization morphology. To achieve this, we are using numerical methods to solve the non-linear equations based on the jet geometry. We are using the Log Likelihood method and algorithm based on Markov Chain Monte Carlo (MCMC) simulations.
International Nuclear Information System (INIS)
Yang Xue; Satvat, Nader
2012-01-01
Highlight: ► A two-dimensional numerical code based on the method of characteristics is developed. ► The complex arbitrary geometries are represented by constructive solid geometry and decomposed by unstructured meshing. ► Excellent agreement between Monte Carlo and the developed code is observed. ► High efficiency is achieved by parallel computing. - Abstract: A transport theory code MOCUM based on the method of characteristics as the flux solver with an advanced general geometry processor has been developed for two-dimensional rectangular and hexagonal lattice and full core neutronics modeling. In the code, the core structure is represented by the constructive solid geometry that uses regularized Boolean operations to build complex geometries from simple polygons. Arbitrary-precision arithmetic is also used in the process of building geometry objects to eliminate the round-off error from the commonly used double precision numbers. Then, the constructed core frame will be decomposed and refined into a Conforming Delaunay Triangulation to ensure the quality of the meshes. The code is fully parallelized using OpenMP and is verified and validated by various benchmarks representing rectangular, hexagonal, plate type and CANDU reactor geometries. Compared with Monte Carlo and deterministic reference solution, MOCUM results are highly accurate. The mentioned characteristics of the MOCUM make it a perfect tool for high fidelity full core calculation for current and GenIV reactor core designs. The detailed representation of reactor physics parameters can enhance the safety margins with acceptable confidence levels, which lead to more economically optimized designs.
Sossinsky, A B
2012-01-01
The book is an innovative modern exposition of geometry, or rather, of geometries; it is the first textbook in which Felix Klein's Erlangen Program (the action of transformation groups) is systematically used as the basis for defining various geometries. The course of study presented is dedicated to the proposition that all geometries are created equal--although some, of course, remain more equal than others. The author concentrates on several of the more distinguished and beautiful ones, which include what he terms "toy geometries", the geometries of Platonic bodies, discrete geometries, and classical continuous geometries. The text is based on first-year semester course lectures delivered at the Independent University of Moscow in 2003 and 2006. It is by no means a formal algebraic or analytic treatment of geometric topics, but rather, a highly visual exposition containing upwards of 200 illustrations. The reader is expected to possess a familiarity with elementary Euclidean geometry, albeit those lacking t...
Indian Academy of Sciences (India)
. In the previous article we looked at the origins of synthetic and analytic geometry. More practical minded people, the builders and navigators, were studying two other aspects of geometry- trigonometry and integral calculus. These are actually ...
Five-dimensional Nernst branes from special geometry
Energy Technology Data Exchange (ETDEWEB)
Dempster, P.; Errington, D. [Department of Mathematical Sciences, University of LiverpoolPeach Street, Liverpool L69 7ZL (United Kingdom); Gutowski, J. [Department of Mathematics, University of Surrey,Guildford, GU2 7XH (United Kingdom); Mohaupt, T. [Department of Mathematical Sciences, University of LiverpoolPeach Street, Liverpool L69 7ZL (United Kingdom)
2016-11-21
We construct Nernst brane solutions, that is black branes with zero entropy density in the extremal limit, of FI-gauged minimal five-dimensional supergravity coupled to an arbitrary number of vector multiplets. While the scalars take specific constant values and dynamically determine the value of the cosmological constant in terms of the FI-parameters, the metric takes the form of a boosted AdS Schwarzschild black brane. This metric can be brought to the Carter-Novotný-Horský form that has previously been observed to occur in certain limits of boosted D3-branes. By dimensional reduction to four dimensions we recover the four-dimensional Nernst branes of arXiv:1501.07863 and show how the five-dimensional lift resolves all their UV singularities. The dynamics of the compactification circle, which expands both in the UV and in the IR, plays a crucial role. At asymptotic infinity, the curvature singularity of the four-dimensional metric and the run-away behaviour of the four-dimensional scalar combine in such a way that the lifted solution becomes asymptotic to AdS{sub 5}. Moreover, the existence of a finite chemical potential in four dimensions is related to fact that the compactification circle has a finite minimal value. While it is not clear immediately how to embed our solutions into string theory, we argue that the same type of dictionary as proposed for boosted D3-branes should apply, although with a lower amount of supersymmetry.
Three dimensional imaging of surface geometry in SEM
International Nuclear Information System (INIS)
Slowko, W.
1997-01-01
A great advantage of scanning electron microscopy (SEM) is its ability of the surface topography in the way as a human eye is accustomed to see lights and shadows on macroobjects. However, SEM's can hardly display vertical dimensions of the structures. One of possible solutions is reconstruction of the surface profiles by directional detection of secondary electrons and proper signal processing. However, the surface profile still gives two dimensional information and the method should be extended to obtain fully three dimensional imaging. The extension consists in a simultaneous reconstruction of the surface profiles in two perpendicular directions (x and y) and their superposition. The solution proposed is based on a quadrupole detector system and a computer or analogue system for signal processing. Quantitative data of the surface topography can be displayed in many manners in the system of two or three co-ordinates with use of pseudo-colour for the altitude coding. (author)
Neutronics code VALE for two-dimensional triagonal (hexagonal) and three-dimensional geometries
International Nuclear Information System (INIS)
Vondy, D.R.; Fowler, T.B.
1981-08-01
This report documents the computer code VALE designed to solve multigroup neutronics problems with the diffusion theory approximation to neutron transport for a triagonal arrangement of mesh points on planes in two- and three-dimensional geometry. This code parallels the VENTURE neutronics code in the local computation system, making exposure and fuel management capabilities available. It uses and generates interface data files adopted in the cooperative effort sponsored by Reactor Physics RRT Division of the US DOE. The programming in FORTRAN is straightforward, although data is transferred in blocks between auxiliary storage devices and main core, and direct access schemes are used. The size of problems which can be handled is essentially limited only by cost of calculation since the arrays are variably dimensioned. The memory requirement is held down while data transfer during iteration is increased only as necessary with problem size. There is provision for the more common boundary conditions including the repeating boundary, 180 0 rotational symmetry, and the rotational symmetry conditions for the 30 0 , 60 0 , and 120 0 triangular grids on planes. A variety of types of problems may be solved: the usual neutron flux eignevalue problem, or a direct criticality search on the buckling, on a reciprocal velocity absorber (prompt mode), or on nuclide concentrations. The adjoint problem and fixed source problem may be solved, as well as the dominating higher harmonic, or the importance problem for an arbitrary fixed source
Interactive three-dimensional visualization and creation of geometries for Monte Carlo calculations
International Nuclear Information System (INIS)
Theis, C.; Buchegger, K.H.; Brugger, M.; Forkel-Wirth, D.; Roesler, S.; Vincke, H.
2006-01-01
The implementation of three-dimensional geometries for the simulation of radiation transport problems is a very time-consuming task. Each particle transport code supplies its own scripting language and syntax for creating the geometries. All of them are based on the Constructive Solid Geometry scheme requiring textual description. This makes the creation a tedious and error-prone task, which is especially hard to master for novice users. The Monte Carlo code FLUKA comes with built-in support for creating two-dimensional cross-sections through the geometry and FLUKACAD, a custom-built converter to the commercial Computer Aided Design package AutoCAD, exists for 3D visualization. For other codes, like MCNPX, a couple of different tools are available, but they are often specifically tailored to the particle transport code and its approach used for implementing geometries. Complex constructive solid modeling usually requires very fast and expensive special purpose hardware, which is not widely available. In this paper SimpleGeo is presented, which is an implementation of a generic versatile interactive geometry modeler using off-the-shelf hardware. It is running on Windows, with a Linux version currently under preparation. This paper describes its functionality, which allows for rapid interactive visualization as well as generation of three-dimensional geometries, and also discusses critical issues regarding common CAD systems
Emergence of geometry: A two-dimensional toy model
International Nuclear Information System (INIS)
Alfaro, Jorge; Espriu, Domene; Puigdomenech, Daniel
2010-01-01
We review the similarities between the effective chiral Lagrangrian, relevant for low-energy strong interactions, and the Einstein-Hilbert action. We use these analogies to suggest a specific mechanism whereby gravitons would emerge as Goldstone bosons of a global SO(D)xGL(D) symmetry broken down to SO(D) by fermion condensation. We propose a two-dimensional toy model where a dynamical zweibein is generated from a topological theory without any preexisting metric structure, the space being endowed only with an affine connection. A metric appears only after the symmetry breaking; thus the notion of distance is an induced effective one. In spite of several nonstandard features this simple toy model appears to be renormalizable and at long distances is described by an effective Lagrangian that corresponds to that of two-dimensional gravity (Liouville theory). The induced cosmological constant is related to the dynamical mass M acquired by the fermion fields in the breaking, which also acts as an infrared regulator. The low-energy expansion is valid for momenta k>M, i.e. for supra-horizon scales. We briefly discuss a possible implementation of a similar mechanism in four dimensions.
The emergence of geometry: a two-dimensional toy model
Alfaro, Jorge; Puigdomenech, Daniel
2010-01-01
We review the similarities between the effective chiral lagrangrian, relevant for low-energy strong interactions, and the Einstein-Hilbert action. We use these analogies to suggest a specific mechanism whereby gravitons would emerge as Goldstone bosons of a global SO(D) X GL(D) symmetry broken down to SO(D) by fermion condensation. We propose a two-dimensional toy model where a dynamical zwei-bein is generated from a topological theory without any pre-existing metric structure, the space being endowed only with an affine connection. A metric appears only after the symmetry breaking; thus the notion of distance is an induced effective one. In spite of several non-standard features this simple toy model appears to be renormalizable and at long distances is described by an effective lagrangian that corresponds to that of two-dimensional gravity (Liouville theory). The induced cosmological constant is related to the dynamical mass M acquired by the fermion fields in the breaking, which also acts as an infrared re...
Secondary Channel Bifurcation Geometry: A Multi-dimensional Problem
Gaeuman, D.; Stewart, R. L.
2017-12-01
The construction of secondary channels (or side channels) is a popular strategy for increasing aquatic habitat complexity in managed rivers. Such channels, however, frequently experience aggradation that prevents surface water from entering the side channels near their bifurcation points during periods of relatively low discharge. This failure to maintain an uninterrupted surface water connection with the main channel can reduce the habitat value of side channels for fish species that prefer lotic conditions. Various factors have been proposed as potential controls on the fate of side channels, including water surface slope differences between the main and secondary channels, the presence of main channel secondary circulation, transverse bed slopes, and bifurcation angle. A quantitative assessment of more than 50 natural and constructed secondary channels in the Trinity River of northern California indicates that bifurcations can assume a variety of configurations that are formed by different processes and whose longevity is governed by different sets of factors. Moreover, factors such as bifurcation angle and water surface slope vary with discharge level and are continuously distributed in space, such that they must be viewed as a multi-dimensional field rather than a single-valued attribute that can be assigned to a particular bifurcation.
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
(3+1)-dimensional topological phases and self-dual quantum geometries encoded on Heegaard surfaces
Energy Technology Data Exchange (ETDEWEB)
Dittrich, Bianca [Perimeter Institute for Theoretical Physics,31 Caroline Street North, Waterloo, Ontario N2L 2Y5 (Canada)
2017-05-22
We apply the recently suggested strategy to lift state spaces and operators for (2+1)-dimensional topological quantum field theories to state spaces and operators for a (3+1)-dimensional TQFT with defects. We start from the (2+1)-dimensional Turaev-Viro theory and obtain a state space, consistent with the state space expected from the Crane-Yetter model with line defects. This work has important applications for quantum gravity as well as the theory of topological phases in (3+1) dimensions. It provides a self-dual quantum geometry realization based on a vacuum state peaked on a homogeneously curved geometry. The state spaces and operators we construct here provide also an improved version of the Walker-Wang model, and simplify its analysis considerably. We in particular show that the fusion bases of the (2+1)-dimensional theory lead to a rich set of bases for the (3+1)-dimensional theory. This includes a quantum deformed spin network basis, which in a loop quantum gravity context diagonalizes spatial geometry operators. We also obtain a dual curvature basis, that diagonalizes the Walker-Wang Hamiltonian. Furthermore, the construction presented here can be generalized to provide state spaces for the recently introduced dichromatic four-dimensional manifold invariants.
Dynamic Three-Dimensional Geometry of the Aortic Valve Apparatus-A Feasibility Study
Khamooshian, Arash; Amador, Yannis; Hai, Ting; Jeganathan, Jelliffe; Saraf, Maria; Mahmood, Eitezaz; Matyal, Robina; Khabbaz, Kamal R.; Mariani, Massimo; Mahmood, Feroze
OBJECTIVE: To provide (1) an overview of the aortic valve (AV) apparatus anatomy and nomenclature, and (2) data regarding the normal AV apparatus geometry and dynamism during the cardiac cycle obtained from three-dimensional transesophageal echocardiography (3D TEE). DESIGN: Retrospective
Instability in near-horizon geometries of even-dimensional Myers–Perry black holes
International Nuclear Information System (INIS)
Tanahashi, Norihiro; Murata, Keiju
2012-01-01
We study the gravitational, electromagnetic and scalar field perturbations on the near-horizon geometries of the even-dimensional extremal Myers–Perry black holes. By dimensional reduction, the perturbation equations are reduced to effective equations of motion in AdS 2 . We find that some modes in the gravitational perturbations violate the Breitenlöhner–Freedman bound in AdS 2 . This result suggests that the even-dimensional (near-)extremal Myers–Perry black holes are unstable against gravitational perturbations. We also discuss implications of our results to the Kerr–CFT correspondence. (paper)
Energy Technology Data Exchange (ETDEWEB)
Liu Guoming [Department of Nuclear Engineering, Xi' an Jiaotong University, Xi' an, Shaanxi 710049 (China)], E-mail: gmliusy@gmail.com; Wu Hongchun; Cao Liangzhi [Department of Nuclear Engineering, Xi' an Jiaotong University, Xi' an, Shaanxi 710049 (China)
2008-09-15
This paper presents a transmission probability method (TPM) to solve the neutron transport equation in three-dimensional triangular-z geometry. The source within the mesh is assumed to be spatially uniform and isotropic. At the mesh surface, the constant and the simplified P{sub 1} approximation are invoked for the anisotropic angular flux distribution. Based on this model, a code TPMTDT is encoded. It was verified by three 3D Takeda benchmark problems, in which the first two problems are in XYZ geometry and the last one is in hexagonal-z geometry, and an unstructured geometry problem. The results of the present method agree well with those of Monte-Carlo calculation method and Spherical Harmonics (P{sub N}) method.
Development of GIFT-PC: the software with multi-drawing functions of three dimensional geometries
International Nuclear Information System (INIS)
Tsuda, Shuichi; Yamaguchi, Yasuhiro
2001-05-01
The Combinatorial Geometry (CG) is a general-purpose geometry package used on radiation transport simulation codes. It is quite useful to illustrate the CG geometries on a simulation code because the visible information of the CG geometries used in a calculation can avoid some mistakes in the case of complicated data, and make it easier to understand the calculation models in the case of presentations. GIFT code (Geographic Information For Target) hsa been developed at Ballistic Research Laboratory, US, for the purpose of illustrating the components of a target from any point of view, calculating a projected area or volume and checking the correctness of the geometry description. Using the drawing functions of GIFT code, perspective or isometric views of a target can be obtained from various points of view. The present report describes the overview of GIFT code and the development of GIFT-PC. GIFT-PC, based on GIFT code, has been developed for easier drawings of three-dimensional geometries using the GUI (Graphical User Interface) system of personal computers, and can be used in various fields as a useful drawing tool for CG geometries. (author)
A new approach for gravity localization in six-dimensional geometries
International Nuclear Information System (INIS)
Santos, Victor Pereira do Nascimento; Almeida, Carlos Alberto Santos de
2011-01-01
Full text: The idea that spacetime may have more than four dimensions is old, originally presented as an attempt to unify Maxwell's theory of Electromagnetism with the brand-new gravitation theory of Einstein. Such extra dimensions are in principle unobservable to the energy scales currently available. However, its effects can be seen in short distance gravity experiments and in observations in cosmology. Also, it is used as a mechanism to explain the difference between the energy scales of the weak force and gravity, which is called the hierarchy problem. The current framework for the extra dimension scenario is consider the four-dimensional known universe as embedded in a higher dimensional space called bulk. The form of this bulk determines how we perceive gravity in our universe; then, the behaviour of gravitational field depends on the geometry of the bulk. Metric solutions were already presented for string-like defect, with and without matter sources, where was shown that the gravity Newtonian potential grows with the inverse cube of distance. Such correction arises from a very particular mass spectrum for the gravitational field, which already contains the orbital angular momentum contributions. In this work we study the behaviour of gravitational field in a extra-dimensional braneworld scenario, using non-factorizable geometries (which preserves Poincare symmetry) and setting suitable matter distributions in order to verify its localization, for several geometries. For such geometries it is possible to find explicit solutions for the tensor fluctuations of the metric. (author)
Non-Euclidean geometry and curvature two-dimensional spaces, volume 3
Cannon, James W
2017-01-01
This is the final volume of a three volume collection devoted to the geometry, topology, and curvature of 2-dimensional spaces. The collection provides a guided tour through a wide range of topics by one of the twentieth century's masters of geometric topology. The books are accessible to college and graduate students and provide perspective and insight to mathematicians at all levels who are interested in geometry and topology. Einstein showed how to interpret gravity as the dynamic response to the curvature of space-time. Bill Thurston showed us that non-Euclidean geometries and curvature are essential to the understanding of low-dimensional spaces. This third and final volume aims to give the reader a firm intuitive understanding of these concepts in dimension 2. The volume first demonstrates a number of the most important properties of non-Euclidean geometry by means of simple infinite graphs that approximate that geometry. This is followed by a long chapter taken from lectures the author gave at MSRI, wh...
Slab1.0: A three-dimensional model of global subduction zone geometries
Hayes, Gavin P.; Wald, David J.; Johnson, Rebecca L.
2012-01-01
We describe and present a new model of global subduction zone geometries, called Slab1.0. An extension of previous efforts to constrain the two-dimensional non-planar geometry of subduction zones around the focus of large earthquakes, Slab1.0 describes the detailed, non-planar, three-dimensional geometry of approximately 85% of subduction zones worldwide. While the model focuses on the detailed form of each slab from their trenches through the seismogenic zone, where it combines data sets from active source and passive seismology, it also continues to the limits of their seismic extent in the upper-mid mantle, providing a uniform approach to the definition of the entire seismically active slab geometry. Examples are shown for two well-constrained global locations; models for many other regions are available and can be freely downloaded in several formats from our new Slab1.0 website, http://on.doi.gov/d9ARbS. We describe improvements in our two-dimensional geometry constraint inversion, including the use of ‘average’ active source seismic data profiles in the shallow trench regions where data are otherwise lacking, derived from the interpolation between other active source seismic data along-strike in the same subduction zone. We include several analyses of the uncertainty and robustness of our three-dimensional interpolation methods. In addition, we use the filtered, subduction-related earthquake data sets compiled to build Slab1.0 in a reassessment of previous analyses of the deep limit of the thrust interface seismogenic zone for all subduction zones included in our global model thus far, concluding that the width of these seismogenic zones is on average 30% larger than previous studies have suggested.
4-dimensional General Relativity from the instrinsic spatial geometry of SO(3) Yang-Mills theory
International Nuclear Information System (INIS)
Ita, Eyo Eyo
2011-01-01
In this paper we derive 4-dimensional General Relativity from three dimensions, using the intrinsic spatial geometry inherent in Yang-Mills theory which has been exposed by previous authors as well as some properties of the Ashtekar variables. We provide various interesting relations, including the fact that General Relativity can be written as a Yang-Mills theory where the antiself-dual Weyl curvature replaces the Yang-Mills coupling constant. We have generalized the results of some previous authors, covering Einstein's spaces, to include more general spacetime geometries.
RTk/SN Solutions of the Two-Dimensional Multigroup Transport Equations in Hexagonal Geometry
International Nuclear Information System (INIS)
Valle, Edmundo del; Mund, Ernest H.
2004-01-01
This paper describes an extension to the hexagonal geometry of some weakly discontinuous nodal finite element schemes developed by Hennart and del Valle for the two-dimensional discrete ordinates transport equation in quadrangular geometry. The extension is carried out in a way similar to the extension to the hexagonal geometry of nodal element schemes for the diffusion equation using a composite mapping technique suggested by Hennart, Mund, and del Valle. The combination of the weakly discontinuous nodal transport scheme and the composite mapping is new and is detailed in the main section of the paper. The algorithm efficiency is shown numerically through some benchmark calculations on classical problems widely referred to in the literature
Energy Technology Data Exchange (ETDEWEB)
Kim, Ha Youn; Park, Sung Tae; Bae, Won Kyoung; Goo, Dong Erk [Dept. of Radiology, Soonchunhyang University Hospital, Seoul (Korea, Republic of)
2014-12-15
We studied the influence of proximal geometry on the results of computational fluid dynamics (CFD). We made five models of different proximal geometry from three dimensional angiography of 63-year-old women with intracranial aneurysm. CFD results were analyzed as peak systolic velocity (PSV) at inlet and outlet as well as flow velocity profile at proximal level of internal carotid artery (ICA) aneurysm. Modified model of cavernous one with proximal tubing showed faster PSV at outlet than that at inlet. The PSV of outlets of other models were slower than that of inlets. The flow velocity profiles at immediate proximal to ICA aneurysm showed similar patterns in all models, suggesting that proximal vessel geometries could affect CFD results.
A numerical method for two-dimensional anisotropic transport problem in cylindrical geometry
International Nuclear Information System (INIS)
Du Mingsheng; Feng Tiekai; Fu Lianxiang; Cao Changshu; Liu Yulan
1988-01-01
The authors deal with the triangular mesh-discontinuous finite element method for solving the time-dependent anisotropic neutron transport problem in two-dimensional cylindrical geometry. A prior estimate of the numerical solution is given. Stability is proved. The authors have computed a two dimensional anisotropic neutron transport problem and a Tungsten-Carbide critical assembly problem by using the numerical method. In comparision with DSN method and the experimental results obtained by others both at home and abroad, the method is satisfactory
Craidon, C. B.
1975-01-01
A computer program that uses a three-dimensional geometric technique for fitting a smooth surface to the component parts of an aircraft configuration is presented. The resulting surface equations are useful in performing various kinds of calculations in which a three-dimensional mathematical description is necessary. Programs options may be used to compute information for three-view and orthographic projections of the configuration as well as cross-section plots at any orientation through the configuration. The aircraft geometry input section of the program may be easily replaced with a surface point description in a different form so that the program could be of use for any three-dimensional surface equations.
Topology and geometry of six-dimensional (1, 0) supergravity black hole horizons
International Nuclear Information System (INIS)
Akyol, M; Papadopoulos, G
2012-01-01
We show that the supersymmetric near horizon black hole geometries of six-dimensional supergravity coupled to any number of scalar and tensor multiplets are either locally AdS 3 x Σ 3 , where Σ 3 is a homology 3-sphere, or R 1,1 )xS 4 , where S 4 is a 4-manifold whose geometry depends on the hypermultiplet scalars. In both cases, we find that the tensorini multiplet scalars are constant and the associated 3-form field strengths vanish. We also demonstrate that the AdS 3 x Σ 3 horizons preserve two, four and eight supersymmetries. For horizons with four supersymmetries, Σ 3 is in addition a non-trivial circle fibration over a topological 2-sphere. The near horizon geometries preserving eight supersymmetries are locally isometric to either AdS 3 x S 3 or R 1, 1 x T 4 . Moreover, we show that the R 1,1 xS horizons preserve one, two and four supersymmetries and the geometry of S is Riemann, Kaehler and hyper-Kaehler, respectively. (paper)
International Nuclear Information System (INIS)
Wu Hongchun; Xie Zhongsheng; Zhu Xuehua
1994-01-01
The nodal discrete-ordinate transport calculating model of anisotropy scattering problem in three-dimensional cartesian geometry is given. The computing code NOTRAN/3D has been encoded and the satisfied conclusion is gained
Salmingo, Remel Alingalan; Tadano, Shigeru; Abe, Yuichiro; Ito, Manabu
2016-05-12
Treatment for severe scoliosis is usually attained when the scoliotic spine is deformed and fixed by implant rods. Investigation of the intraoperative changes of implant rod shape in three-dimensions is necessary to understand the biomechanics of scoliosis correction, establish consensus of the treatment, and achieve the optimal outcome. The objective of this study was to measure the intraoperative three-dimensional geometry and deformation of implant rod during scoliosis corrective surgery.A pair of images was obtained intraoperatively by the dual camera system before rotation and after rotation of rods during scoliosis surgery. The three-dimensional implant rod geometry before implantation was measured directly by the surgeon and after surgery using a CT scanner. The images of rods were reconstructed in three-dimensions using quintic polynomial functions. The implant rod deformation was evaluated using the angle between the two three-dimensional tangent vectors measured at the ends of the implant rod.The implant rods at the concave side were significantly deformed during surgery. The highest rod deformation was found after the rotation of rods. The implant curvature regained after the surgical treatment.Careful intraoperative rod maneuver is important to achieve a safe clinical outcome because the intraoperative forces could be higher than the postoperative forces. Continuous scoliosis correction was observed as indicated by the regain of the implant rod curvature after surgery.
Geometry of lengths, areas, and volumes two-dimensional spaces, volume 1
Cannon, James W
2017-01-01
This is the first of a three volume collection devoted to the geometry, topology, and curvature of 2-dimensional spaces. The collection provides a guided tour through a wide range of topics by one of the twentieth century's masters of geometric topology. The books are accessible to college and graduate students and provide perspective and insight to mathematicians at all levels who are interested in geometry and topology. The first volume begins with length measurement as dominated by the Pythagorean Theorem (three proofs) with application to number theory; areas measured by slicing and scaling, where Archimedes uses the physical weights and balances to calculate spherical volume and is led to the invention of calculus; areas by cut and paste, leading to the Bolyai-Gerwien theorem on squaring polygons; areas by counting, leading to the theory of continued fractions, the efficient rational approximation of real numbers, and Minkowski's theorem on convex bodies; straight-edge and compass constructions, giving c...
International Nuclear Information System (INIS)
Christodoulakis, T; Doulis, G; Terzis, Petros A; Melas, E; Grammenos, Th; Papadopoulos, G O; Spanou, A
2010-01-01
The canonical decomposition of all 3+1 geometries admitting two-dimensional space-like surfaces is exhibited as a generalization of a previous work. A proposal, consisting of a specific renormalization Assumption and an accompanying Requirement, which has been put forward in the 2+1 case is now generalized to 3+1 dimensions. This enables the canonical quantization of these geometries through a generalization of Kuchar's quantization scheme in the case of infinite degrees of freedom. The resulting Wheeler-DeWitt equation is based on a renormalized manifold parameterized by three smooth scalar functionals. The entire space of solutions to this equation is analytically given, a fact that is entirely new to the present case. This is made possible through the exploitation of the residual freedom in the choice of the third functional, which is left by the imposition of the Requirement, and is proven to correspond to a general coordinate transformation in the renormalized manifold.
Visualizing Three-dimensional Slab Geometries with ShowEarthModel
Chang, B.; Jadamec, M. A.; Fischer, K. M.; Kreylos, O.; Yikilmaz, M. B.
2017-12-01
Seismic data that characterize the morphology of modern subducted slabs on Earth suggest that a two-dimensional paradigm is no longer adequate to describe the subduction process. Here we demonstrate the effect of data exploration of three-dimensional (3D) global slab geometries with the open source program ShowEarthModel. ShowEarthModel was designed specifically to support data exploration, by focusing on interactivity and real-time response using the Vrui toolkit. Sixteen movies are presented that explore the 3D complexity of modern subduction zones on Earth. The first movie provides a guided tour through the Earth's major subduction zones, comparing the global slab geometry data sets of Gudmundsson and Sambridge (1998), Syracuse and Abers (2006), and Hayes et al. (2012). Fifteen regional movies explore the individual subduction zones and regions intersecting slabs, using the Hayes et al. (2012) slab geometry models where available and the Engdahl and Villasenor (2002) global earthquake data set. Viewing the subduction zones in this way provides an improved conceptualization of the 3D morphology within a given subduction zone as well as the 3D spatial relations between the intersecting slabs. This approach provides a powerful tool for rendering earth properties and broadening capabilities in both Earth Science research and education by allowing for whole earth visualization. The 3D characterization of global slab geometries is placed in the context of 3D slab-driven mantle flow and observations of shear wave splitting in subduction zones. These visualizations contribute to the paradigm shift from a 2D to 3D subduction framework by facilitating the conceptualization of the modern subduction system on Earth in 3D space.
Application of three-dimensional simulation at lecturing on descriptive geometry
Directory of Open Access Journals (Sweden)
Tel'noy Viktor Ivanovich
2014-05-01
Full Text Available Teaching descriptive geometry has its own characteristics. Need not only to inform students of a certain amount of knowledge on the subject, but also to develop their spatial imagination as well as the right to develop the skills of logical thinking. Practice of teaching the discipline showed that students face serious difficulties in the process of its study. This is due to the relatively low level of their schooling in geometry and technical drawing, and lacking in high spatial imagination. They find it difficult to imagine the geometrical image of the object of study and mentally convert it on the plane. Because of this, there is a need to find ways to effectively teach the discipline «Descriptive Geometry» at university. In the context of global informatization and computerization of the educational process, implementation of graphically programs for the development of design documentation and 3D modeling is one of the most promising applications of information technology in the process of solving these problems. With the help of three-dimensional models the best visibility in the classroom is achieved. When conducting lectures on descriptive geometry it is requested to use three-dimensional modeling not only as didactic means (demonstrativeness means, but also as a method of teaching (learning tool to deal with various graphics tasks. Bearing this in mind, the essence of the implementation of 3D modeling is revealed with the aim of better understanding of the algorithms for solving both positional and metric tasks using spatial representation of graphic constructions. It is shown that the possibility to consider the built model from different angles is of particular importance, as well as the use of transparency properties for illustrating the results of solving geometric problems. Using 3D models together with their display on the plane, as well as text information promotes better assimilation and more lasting memorization of the
The blind student’s interpretation of two-dimensional shapes in geometry
Andriyani; Budayasa, I. K.; Juniati, D.
2018-01-01
The blind student’s interpretation of two-dimensional shapes represents the blind student’s mental image of two-dimensional shapes that they can’t visualize directly, which is related to illustration of the characteristics and number of edges and angles. The objective of this research is to identify the blind student’s interpretation of two-dimensional shapes. This research was an exploratory study with qualitative approach. A subject of this research is a sixth-grade student who experiencing total blind from the fifth grade of elementary school. Researchers interviewed the subject about his interpretation of two-dimensional shapes according to his thinking.The findings of this study show the uniqueness of blind students, who have been totally blind since school age, in knowing and illustrating the characteristics of edges and angles of two-dimensional shapes by utilizing visual experiences that were previously obtained before the blind. The result can inspire teachers to design further learning for development of blind student geometry concepts.
Unsteady two-dimensional potential-flow model for thin variable geometry airfoils
DEFF Research Database (Denmark)
Gaunaa, Mac
2010-01-01
In the present work, analytical expressions for distributed and integral unsteady two-dimensional forces on a variable geometry airfoil undergoing arbitrary motion are derived under the assumption of incompressible, irrotational, inviscid flow. The airfoil is represented by its camber line...... in their equivalent state-space form, allowing for use of the present theory in problems employing the eigenvalue approach, such as stability analysis. The analytical expressions for the integral forces can be reduced to Munk's steady and Theodorsen's unsteady results for thin airfoils, and numerical evaluation shows...
Spectral properties of a two dimensional photonic crystal with quasi-integrable geometry
International Nuclear Information System (INIS)
Cruz-Bueno, J J; Méndez-Bermúdez, J A; Arriaga, J
2013-01-01
In this paper we study the statistical properties of the allowed frequencies for electromagnetic waves propagating in two-dimensional photonic crystals with quasi-integrable geometry. We compute the level spacing, group velocity, and curvature distributions (P(s), P(v), and P(c), respectively) and compare them with the corresponding random matrix theory predictions. Due to the quasi-integrability of the crystal we observe signatures of intermediate statistics in P(s) and P(c) for high refractive index contrasts
Landi, Gregorio
2003-01-01
The center of gravity as an algorithm for position measurements is analyzed for a two-dimensional geometry. Several mathematical consequences of discretization for various types of detector arrays are extracted. Arrays with rectangular, hexagonal, and triangular detectors are analytically studied, and tools are given to simulate their discretization properties. Special signal distributions free of discretized error are isolated. It is proved that some crosstalk spreads are able to eliminate the center of gravity discretization error for any signal distribution. Simulations, adapted to the CMS em-calorimeter and to a triangular detector array, are provided for energy and position reconstruction algorithms with a finite number of detectors.
New edge magnetoplasmon for a two-dimensional electron gas in a ring geometry
International Nuclear Information System (INIS)
Proetto, C.R.
1992-09-01
The dynamical response of a classical two-dimensional electron gas confined in a ring geometry under a perpendicular magnetic field is analysed. Within the hydrodynamical approach and in the strong magnetic field limit, a new set of antidot edge magnetoplasmons is obtained, corresponding to density oscillations circulating along the inner boundary of the ring and whose frequency increases with magnetic field. The associated self-induced distribution of densities and currents are presented, together with an analysis of the size dependence of these perimeter waves. (author). 15 refs, 4 figs
One-dimensional transport code for one-group problems in plane geometry
International Nuclear Information System (INIS)
Bareiss, E.H.; Chamot, C.
1970-09-01
Equations and results are given for various methods of solution of the one-dimensional transport equation for one energy group in plane geometry with inelastic scattering and an isotropic source. After considerable investigation, a matrix method of solution was found to be faster and more stable than iteration procedures. A description of the code is included which allows for up to 24 regions, 250 points, and 16 angles such that the product of the number of angles and the number of points is less than 600
Liénard, Jean; Lynn, Kendra; Strigul, Nikolay; Norris, Benjamin K.; Gatziolis, Demetrios; Mullarney, Julia C.; Bryan, Karin, R.; Henderson, Stephen M.
2016-09-01
Aquatic vegetation can shelter coastlines from energetic waves and tidal currents, sometimes enabling accretion of fine sediments. Simulation of flow and sediment transport within submerged canopies requires quantification of vegetation geometry. However, field surveys used to determine vegetation geometry can be limited by the time required to obtain conventional caliper and ruler measurements. Building on recent progress in photogrammetry and computer vision, we present a method for reconstructing three-dimensional canopy geometry. The method was used to survey a dense canopy of aerial mangrove roots, called pneumatophores, in Vietnam's Mekong River Delta. Photogrammetric estimation of geometry required 1) taking numerous photographs at low tide from multiple viewpoints around 1 m2 quadrats, 2) computing relative camera locations and orientations by triangulation of key features present in multiple images and reconstructing a dense 3D point cloud, and 3) extracting pneumatophore locations and diameters from the point cloud data. Step 3) was accomplished by a new 'sector-slice' algorithm, yielding geometric parameters every 5 mm along a vertical profile. Photogrammetric analysis was compared with manual caliper measurements. In all 5 quadrats considered, agreement was found between manual and photogrammetric estimates of stem number, and of number × mean diameter, which is a key parameter appearing in hydrodynamic models. In two quadrats, pneumatophores were encrusted with numerous barnacles, generating a complex geometry not resolved by hand measurements. In remaining cases, moderate agreement between manual and photogrammetric estimates of stem diameter and solid volume fraction was found. By substantially reducing measurement time in the field while capturing in greater detail the 3D structure, photogrammetry has potential to improve input to hydrodynamic models, particularly for simulations of flow through large-scale, heterogenous canopies.
Perez-Alday, Erick A; Thomas, Jason A; Kabir, Muammar; Sedaghat, Golriz; Rogovoy, Nichole; van Dam, Eelco; van Dam, Peter; Woodward, William; Fuss, Cristina; Ferencik, Maros; Tereshchenko, Larisa G
We conducted a prospective clinical study (n=14; 29% female) to assess the accuracy of a three-dimensional (3D) photography-based method of torso geometry reconstruction and body surface electrodes localization. The position of 74 body surface electrocardiographic (ECG) electrodes (diameter 5mm) was defined by two methods: 3D photography, and CT (marker diameter 2mm) or MRI (marker size 10×20mm) imaging. Bland-Altman analysis showed good agreement in X (bias -2.5 [95% limits of agreement (LoA) -19.5 to 14.3] mm), Y (bias -0.1 [95% LoA -14.1 to 13.9] mm), and Z coordinates (bias -0.8 [95% LoA -15.6 to 14.2] mm), as defined by the CT/MRI imaging, and 3D photography. The average Hausdorff distance between the two torso geometry reconstructions was 11.17±3.05mm. Thus, accurate torso geometry reconstruction using 3D photography is feasible. Body surface ECG electrodes coordinates as defined by the CT/MRI imaging, and 3D photography, are in good agreement. Copyright © 2017 Elsevier Inc. All rights reserved.
Gattolin, G.; Franceschi, M.; Breda, A.; Teza, G.; Preto, N.
2012-04-01
At the end of the Early Carnian, the Carnian Pluvial Event (CPE) resulted in a major crisis of carbonate factories. The sharp change in carbonate production lead to a dramatic modifications in depositional geometries. Steep clinoforms of the high-relief pre-crisis carbonate platforms were replaced by low-angle ramps. Spatial characters of depositional geometries can be decisive in identifying the genesis of geological bodies. We here show how 3D modeling techniques can be applied to help in quantifying and highlighting their variations. As case study we considered two outcrops in the Tofane Group (Dolomites, Italy). The first outcrop (bottom of southern walls of Tofana di Rozes) exposes a platform-to-basin transect of pre- and post-crisis platforms, the second (Dibona hut) a clinostratified carbonate body deposited during the Carnian crisis. Outcrop conditions at both sites, with vertical and hardly accessible walls, make the field tracing of depositional geometries particularly challenging. Line drawing on high resolution pictures can help (e.g. for clinoforms), but its use for quantification is hampered by perspective deformation. Three dimensional acquisition and modeling allow to retrieve the true spatial characters of sedimentary bodies in these outcrops. The geometry of the carbonate body at Dibona (~ 15000 sqm) was acquired with terrestrial LiDAR, while for Tofana photogrammetric techniques were applied because of the extension of the outcrop itself (~ 240000 sqm) and the lack of suitable points of view for terrestrial laser scanning. At Tofana, field observations reveal the presence of tens-hundreds m large carbonate mounds grown on a pre-existing inclined surface, intercalated with skeletal carbonates and siltites-arenites. This system rapidly evolves into a carbonate-clastic ramp. Photogrammetric topography acquisition permitted to place and visualize geological features in a three dimensional frame, thus obtaining a conceptual sedimentological model. A 3
D-brane propagation in two-dimensional black hole geometries
International Nuclear Information System (INIS)
Nakayama, Yu; Rey, Soo-Jong; Sugawara, Yuji
2005-01-01
We study propagation of D0-brane in two-dimensional lorentzian black hole backgrounds by the method of boundary conformal field theory of SL(2,R)/U(1) supercoset at level k. Typically, such backgrounds arise as near-horizon geometries of k coincident non-extremal NS5-branes, where 1/k measures curvature of the backgrounds in string unit and hence size of string worldsheet effects. At classical level, string worldsheet effects are suppressed and D0-brane propagation in the lorentzian black hole geometry is simply given by the Wick rotation of D1-brane contour in the euclidean black hole geometry. Taking account of string worldsheet effects, boundary state of the lorentzian D0-brane is formally constructible via Wick rotation from that of the euclidean D1-brane. However, the construction is subject to ambiguities in boundary conditions. We propose exact boundary states describing the D0-brane, and clarify physical interpretations of various boundary states constructed from different boundary conditions. As it falls into the black hole, the D0-brane radiates off to the horizon and to the infinity. From the boundary states constructed, we compute physical observables of such radiative process. We find that part of the radiation to infinity is in effective thermal distribution at the Hawking temperature. We also find that part of the radiation to horizon is in the Hagedorn distribution, dominated by massive, highly non-relativistic closed string states, much like the tachyon matter. Remarkably, such distribution emerges only after string worldsheet effects are taken exactly into account. From these results, we observe that nature of the radiation distribution changes dramatically across the conifold geometry k = 1 (k = 3 for the bosonic case), exposing the 'string - black hole transition' therein
Salmingo, Remel A; Tadano, Shigeru; Fujisaki, Kazuhiro; Abe, Yuichiro; Ito, Manabu
2012-05-01
Scoliosis is defined as a spinal pathology characterized as a three-dimensional deformity of the spine combined with vertebral rotation. Treatment for severe scoliosis is achieved when the scoliotic spine is surgically corrected and fixed using implanted rods and screws. Several studies performed biomechanical modeling and corrective forces measurements of scoliosis correction. These studies were able to predict the clinical outcome and measured the corrective forces acting on screws, however, they were not able to measure the intraoperative three-dimensional geometry of the spinal rod. In effect, the results of biomechanical modeling might not be so realistic and the corrective forces during the surgical correction procedure were intra-operatively difficult to measure. Projective geometry has been shown to be successful in the reconstruction of a three-dimensional structure using a series of images obtained from different views. In this study, we propose a new method to measure the three-dimensional geometry of an implant rod using two cameras. The reconstruction method requires only a few parameters, the included angle θ between the two cameras, the actual length of the rod in mm, and the location of points for curve fitting. The implant rod utilized in spine surgery was used to evaluate the accuracy of the current method. The three-dimensional geometry of the rod was measured from the image obtained by a scanner and compared to the proposed method using two cameras. The mean error in the reconstruction measurements ranged from 0.32 to 0.45 mm. The method presented here demonstrated the possibility of intra-operatively measuring the three-dimensional geometry of spinal rod. The proposed method could be used in surgical procedures to better understand the biomechanics of scoliosis correction through real-time measurement of three-dimensional implant rod geometry in vivo.
Derivation of the low Mach number diphasic system. Numerical simulation in mono-dimensional geometry
International Nuclear Information System (INIS)
Dellacherie, St.
2004-01-01
This work deals with the derivation of a diphasic low Mach number model obtained through a Mach number asymptotic expansion applied to the compressible diphasic Navier Stokes system, expansion which filters out the acoustic waves. This approach is inspired from the work of Andrew Majda giving the equations of low Mach number combustion for thin flame and for perfect gases. When the equations of state verify some thermodynamic hypothesis, we show that the low Mach number diphasic system predicts in a good way the dilatation or the compression of a bubble and has equilibrium convergence properties. Then, we propose an entropic and convergent Lagrangian scheme in mono-dimensional geometry when the fluids are perfect gases and we propose a first approach in Eulerian variables where the interface between the two fluids is captured with a level set technique. (author)
Fourier analysis of cell-wise Block-Jacobi splitting in two-dimensional geometry
International Nuclear Information System (INIS)
Rosa, M.; Warsa, J. S.; Kelley, T. M.
2009-01-01
A Fourier analysis is conducted in two-dimensional (2D) geometry for the discrete ordinates (S N ) approximation of the neutron transport problem solved with Richardson iteration (Source Iteration) using the cell-wise Block-Jacobi (BJ) algorithm. The results of the Fourier analysis show that convergence of cell-wise BJ can degrade, leading to a spectral radius equal to 1, in problems containing optically thin cells. For problems containing cells that are optically thick, instead, the spectral radius tends to 0. Hence, in the optically thick-cell regime, cell-wise BJ is rapidly convergent even for problems that are scattering dominated, with a scattering ratio c close to 1. (authors)
Regional surface geometry of the rat stomach based on three-dimensional curvature analysis
Energy Technology Data Exchange (ETDEWEB)
Liao Donghua [Center of Excellence in Visceral Biomechanics and Pain, Aalborg Hospital, DK-9100 Aalborg (Denmark); Zhao Jingbo [Center of Excellence in Visceral Biomechanics and Pain, Aalborg Hospital, DK-9100 Aalborg (Denmark); Gregersen, Hans [Center of Excellence in Visceral Biomechanics and Pain, Aalborg Hospital, DK-9100 Aalborg (Denmark)
2005-01-21
A better understanding of gastric accommodation and gastric perception requires knowledge of regional gastric geometry and local gastric tension throughout the stomach. An analytic method based on medical imaging data was developed in this study to describe the three-dimensional (3D) rat stomach geometry and tension distribution. The surface principal radii of curvatures were simulated and the surface tension was calculated in the glandular and non-glandular region of the stomach at pressures from 0 Pa to 800 Pa. The radii of curvature and tension distribution in the stomach were non-homogeneous. The radii of curvature in the glandular stomach were larger than those in the non-glandular region at pressures less than 100 Pa (P < 0.001). When the pressure increased to more than 200 Pa, the radii of curvature in the non-glandular stomach was larger than in the glandular stomach (P < 0.05). The curvature and tension distribution mapping using medical imaging technology and 3D models can be used to characterize and distinguish the physical behaviour in separate regions of the stomach.
Regional surface geometry of the rat stomach based on three-dimensional curvature analysis
International Nuclear Information System (INIS)
Liao Donghua; Zhao Jingbo; Gregersen, Hans
2005-01-01
A better understanding of gastric accommodation and gastric perception requires knowledge of regional gastric geometry and local gastric tension throughout the stomach. An analytic method based on medical imaging data was developed in this study to describe the three-dimensional (3D) rat stomach geometry and tension distribution. The surface principal radii of curvatures were simulated and the surface tension was calculated in the glandular and non-glandular region of the stomach at pressures from 0 Pa to 800 Pa. The radii of curvature and tension distribution in the stomach were non-homogeneous. The radii of curvature in the glandular stomach were larger than those in the non-glandular region at pressures less than 100 Pa (P < 0.001). When the pressure increased to more than 200 Pa, the radii of curvature in the non-glandular stomach was larger than in the glandular stomach (P < 0.05). The curvature and tension distribution mapping using medical imaging technology and 3D models can be used to characterize and distinguish the physical behaviour in separate regions of the stomach
Three dimensional range geometry and texture data compression with space-filling curves.
Chen, Xia; Zhang, Song
2017-10-16
This paper presents a novel method to effectively store three-dimensional (3D) data and 2D texture data into a regular 24-bit image. The proposed method uses the Hilbert space-filling curve to map the normalized unwrapped phase map to two 8-bit color channels, and saves the third color channel for 2D texture storage. By further leveraging existing 2D image and video compression techniques, the proposed method can achieve high compression ratios while effectively preserving data quality. Since the encoding and decoding processes can be applied to most of the current 2D media platforms, this proposed compression method can make 3D data storage and transmission available for many electrical devices without requiring special hardware changes. Experiments demonstrate that if a lossless 2D image/video format is used, both original 3D geometry and 2D color texture can be accurately recovered; if lossy image/video compression is used, only black-and-white or grayscale texture can be properly recovered, but much higher compression ratios (e.g., 1543:1 against the ASCII OBJ format) are achieved with slight loss of 3D geometry quality.
International Nuclear Information System (INIS)
Bottoni, M.; Lyczkowski, R.; Ahuja, S.
1995-01-01
Numerical simulation of subcooled boiling in one-dimensional geometry with the Homogeneous Equilibrium Model (HEM) may yield difficulties related to the very low sonic velocity associated with the HEM. These difficulties do not arise with subcritical flow. Possible solutions of the problem include introducing a relaxation of the vapor production rate. Three-dimensional simulations of subcooled boiling in bundle geometry typical of fast reactors can be performed by using two systems of conservation equations, one for the HEM and the other for a Separated Phases Model (SPM), with a smooth transition between the two models
A three-dimensional reconstruction algorithm for an inverse-geometry volumetric CT system
International Nuclear Information System (INIS)
Schmidt, Taly Gilat; Fahrig, Rebecca; Pelc, Norbert J.
2005-01-01
An inverse-geometry volumetric computed tomography (IGCT) system has been proposed capable of rapidly acquiring sufficient data to reconstruct a thick volume in one circular scan. The system uses a large-area scanned source opposite a smaller detector. The source and detector have the same extent in the axial, or slice, direction, thus providing sufficient volumetric sampling and avoiding cone-beam artifacts. This paper describes a reconstruction algorithm for the IGCT system. The algorithm first rebins the acquired data into two-dimensional (2D) parallel-ray projections at multiple tilt and azimuthal angles, followed by a 3D filtered backprojection. The rebinning step is performed by gridding the data onto a Cartesian grid in a 4D projection space. We present a new method for correcting the gridding error caused by the finite and asymmetric sampling in the neighborhood of each output grid point in the projection space. The reconstruction algorithm was implemented and tested on simulated IGCT data. Results show that the gridding correction reduces the gridding errors to below one Hounsfield unit. With this correction, the reconstruction algorithm does not introduce significant artifacts or blurring when compared to images reconstructed from simulated 2D parallel-ray projections. We also present an investigation of the noise behavior of the method which verifies that the proposed reconstruction algorithm utilizes cross-plane rays as efficiently as in-plane rays and can provide noise comparable to an in-plane parallel-ray geometry for the same number of photons. Simulations of a resolution test pattern and the modulation transfer function demonstrate that the IGCT system, using the proposed algorithm, is capable of 0.4 mm isotropic resolution. The successful implementation of the reconstruction algorithm is an important step in establishing feasibility of the IGCT system
Energy Technology Data Exchange (ETDEWEB)
Fathipour, Vala; Jang, Sung Jun; Nia, Iman Hassani; Mohseni, Hooman, E-mail: hmohseni@northwestern.edu [Bio-Inspired Sensors and Optoelectronics Laboratory, Northwestern University, 2145 Sheridan Rd, Evanston, Illinois 60208 (United States)
2015-01-12
We present a quantitative study of the influence of three-dimensional geometry of the isolated electron–injection detectors on their characteristics. Significant improvements in the device performance are obtained as a result of scaling the injector diameter with respect to the trapping/absorbing layer diameters. Devices with about ten times smaller injector area with respect to the trapping/absorbing layer areas show more than an order of magnitude lower dark current, as well as an order of magnitude higher optical gain compared with devices of same size injector and trapping/absorbing layer areas. Devices with 10 μm injector diameter and 30 μm trapping/absorbing layer diameter show an optical gain of ∼2000 at bias voltage of −3 V with a cutoff wavelength of 1700 nm. Analytical expressions are derived for the electron-injection detector optical gain to qualitatively explain the significance of scaling the injector with respect to the absorber.
Solutions of diffusion equations in two-dimensional cylindrical geometry by series expansions
International Nuclear Information System (INIS)
Ohtani, Nobuo
1976-01-01
A solution of the multi-group multi-regional diffusion equation in two-dimensional cylindrical (rho-z) geometry is obtained in the form of a regionwise double series composed of Bessel and trigonometrical functions. The diffusion equation is multiplied by weighting functions, which satisfy the homogeneous part of the diffusion equation, and the products are integrated over the region for obtaining the equations to determine the fluxes and their normal derivatives at the region boundaries. Multiplying the diffusion equation by each function of the set used for the flux expansion, then integrating the products, the coefficients of the double series of the flux inside each region are calculated using the boundary values obtained above. Since the convergence of the series thus obtained is slow especially near the region boundaries, a method for improving the convergence has been developed. The double series of the flux is separated into two parts. The normal derivative at the region boundary of the first part is zero, and that of the second part takes the value which is obtained in the first stage of this method. The second part is replaced by a continuous function, and the flux is represented by the sum of the continuous function and the double series. A sample critical problem of a two-group two-region system is numerically studied. The results show that the present method yields very accurately the flux integrals in each region with only a small number of expansion terms. (auth.)
SIMULATIONS OF VISCOUS ACCRETION FLOW AROUND BLACK HOLES IN A TWO-DIMENSIONAL CYLINDRICAL GEOMETRY
Energy Technology Data Exchange (ETDEWEB)
Lee, Seong-Jae; Hyung, Siek [School of Science Education (Astronomy), Chungbuk National University, Chungbuk 28644 (Korea, Republic of); Chattopadhyay, Indranil; Kumar, Rajiv [ARIES, Manora Peak, Nainital-263002, Uttarakhand (India); Ryu, Dongsu, E-mail: seong@chungbuk.ac.kr [Department of Physics, School of Natural Sciences UNIST, Ulsan 44919 (Korea, Republic of)
2016-11-01
We simulate shock-free and shocked viscous accretion flows onto a black hole in a two-dimensional cylindrical geometry, where initial conditions were chosen from analytical solutions. The simulation code used the Lagrangian total variation diminishing plus remap routine, which enabled us to attain high accuracy in capturing shocks and to handle the angular momentum distribution correctly. The inviscid shock-free accretion disk solution produced a thick disk structure, while the viscous shock-free solution attained a Bondi-like structure, but in either case, no jet activity nor any quasi-periodic oscillation (QPO)-like activity developed. The steady-state shocked solution in the inviscid as well as in the viscous regime matched theoretical predictions well. However, increasing viscosity renders the accretion shock unstable. Large-amplitude shock oscillation is accompanied by intermittent, transient inner multiple shocks. This oscillation of the inner part of the disk is interpreted as the source of QPO in hard X-rays observed in micro-quasars. Strong shock oscillation induces strong episodic jet emission. The jets also show the existence of shocks, which are produced as one shell hits the preceding one. The periodicities of the jets and shock oscillation are similar; the jets for the higher viscosity parameter appear to be stronger and faster.
Energy Technology Data Exchange (ETDEWEB)
Gheisari, R., E-mail: gheisari@pgu.ac.ir [Physics Department, Persian Gulf University, Bushehr 75169 (Iran, Islamic Republic of); Nuclear Energy Research Center, Persian Gulf University, Bushehr 75169 (Iran, Islamic Republic of); Firoozabadi, M. M.; Mohammadi, H. [Department of Physics, University of Birjand, Birjand 97175 (Iran, Islamic Republic of)
2014-01-15
A new idea to calculate ultracold neutron (UCN) production by using Monte Carlo simulation method to calculate the cold neutron (CN) flux and an analytical approach to calculate the UCN production from the simulated CN flux was given. A super-thermal source (UCN source) was modeled based on an arrangement of D{sub 2}O and solid D{sub 2} (sD{sub 2}). The D{sub 2}O was investigated as the neutron moderator, and sD{sub 2} as the converter. In order to determine the required parameters, a two-dimensional (2D) neutron balance equation written in Matlab was combined with the MCNPX simulation code. The 2D neutron-transport equation in cylindrical (ρ − z) geometry was considered for 330 neutron energy groups in the sD{sub 2}. The 2D balance equation for UCN and CN was solved using simulated CN flux as boundary value. The UCN source dimensions were calculated for the development of the next UCN source. In the optimal condition, the UCN flux and the UCN production rate (averaged over the sD{sub 2} volume) equal to 6.79 × 10{sup 6} cm{sup −2}s{sup −1} and 2.20 ×10{sup 5} cm{sup −3}s{sup −1}, respectively.
Diagnosis of 3-dimensional geometry and stress corrosion cracking in steam generator tubes
International Nuclear Information System (INIS)
Lee, D.H.; Choi, M.S.; Hur, D.H.; Kim, K.M.; Han, J.H.; Song, M.H.
2015-01-01
Most of the corrosive degradations in steam generator tubes of nuclear power plants are closely related to the residual stress existing in the local region of a geometric change, that is, an expansion transition, u-bend, dent, bulge, etc. Therefore, accurate information on a geometric anomaly (precursor of degradation) in a tube is a prerequisite to the activity of pre- and in-service non destructive inspection for a precise and earlier detection of a defect in order to prevent a failure during an operation, and also for a root cause analysis of a failure. In this paper, a new diagnostic eddy current probe technology which has simultaneous dual function of a 3-dimensional geometry measurement and defect detection in steam generator tube is introduced. The D-Probe is a rotary type eddy current coil probe equipped with 3 different eddy current coil units (surface riding type plus-point and pancake coils for defect detection, and non-surface riding type shielded high frequency pancake coil for tube profile measurement). A specific data analysis software has been developed. By comparing the eddy current data from the defect with those from the geometric changes, the relationship between the degradation and geometric changes can be revealed. Also, it supplies information on tube location at which defect is most probable and thus, a more efficient detection of earlier degradation. The use of D-probe and analysis software has been demonstrated for steam generator tubes with various geometric anomalies in manufacturing and operating nuclear power plants
International Nuclear Information System (INIS)
Lee, Joo Hee
2006-02-01
There is growing interest in developing pebble bed reactors (PBRs) as a candidate of very high temperature gas-cooled reactors (VHTRs). Until now, most existing methods of nuclear design analysis for this type of reactors are base on old finite-difference solvers or on statistical methods. But for realistic analysis of PBRs, there is strong desire of making available high fidelity nodal codes in three-dimensional (r,θ,z) cylindrical geometry. Recently, the Analytic Function Expansion Nodal (AFEN) method developed quite extensively in Cartesian (x,y,z) geometry and in hexagonal-z geometry was extended to two-group (r,z) cylindrical geometry, and gave very accurate results. In this thesis, we develop a method for the full three-dimensional cylindrical (r,θ,z) geometry and implement the method into a code named TOPS. The AFEN methodology in this geometry as in hexagonal geometry is 'robus' (e.g., no occurrence of singularity), due to the unique feature of the AFEN method that it does not use the transverse integration. The transverse integration in the usual nodal methods, however, leads to an impasse, that is, failure of the azimuthal term to be transverse-integrated over r-z surface. We use 13 nodal unknowns in an outer node and 7 nodal unknowns in an innermost node. The general solution of the node can be expressed in terms of that nodal unknowns, and can be updated using the nodal balance equation and the current continuity condition. For more realistic analysis of PBRs, we implemented em Marshak boundary condition to treat the incoming current zero boundary condition and the partial current translation (PCT) method to treat voids in the core. The TOPS code was verified in the various numerical tests derived from Dodds problem and PBMR-400 benchmark problem. The results of the TOPS code show high accuracy and fast computing time than the VENTURE code that is based on finite difference method (FDM)
DEFF Research Database (Denmark)
Torralba, Marta; Jiménez, Roberto; Yagüe-Fabra, José A.
2018-01-01
micro-geometries as well (i.e., in the sub-mm dimensional range). However, there are different factors that may influence the CT process performance, being one of them the surface extraction technique used. In this paper, two different extraction techniques are applied to measure a complex miniaturized......The number of industrial applications of computed tomography (CT) for dimensional metrology in 100–103 mm range has been continuously increasing, especially in the last years. Due to its specific characteristics, CT has the potential to be employed as a viable solution for measuring 3D complex...... dental file by CT in order to analyze its contribution to the final measurement uncertainty in complex geometries at the mm to sub-mm scales. The first method is based on a similarity analysis: the threshold determination; while the second one is based on a gradient or discontinuity analysis: the 3D...
International Nuclear Information System (INIS)
Matausek, M.V.; Milosevic, M.
1986-01-01
In the present paper a generalization is performed of a procedure to solve multigroup spherical harmonics equations, which has originally been proposed and developed for one-dimensional systems in cylindrical or spherical geometry, and later extended for a special case of a two-dimensional system in r-z geometry. The expressions are derived for the axial and the radial dependence of the group values of the neutron flux moments, in the P-3 approximation of the spherical harmonics method, in a cylindrically symmetrical system with an arbitrary number of material regions in both r- and z-directions. In the special case of an axially homogeneous system, these expressions reduce to the relations derived previously. (author)
International Nuclear Information System (INIS)
Degtyarev, I.I.; Lokhovitskij, A.E.; Maslov, M.A.; Yazynin, I.A.
1994-01-01
The first version of integrative shell of the program complex MARS is written for calculating radiation transfer in the three-dimensional geometries. The integrative shell allows the user to work in convenient form with complex MARS, creat input files data and get graphic visualization of calculated functions. Version 1.0 is adapted for personal computers of types IBM-286,386,486 with operative size memory not smaller than 500K. 5 refs
Micro-tomography based Geometry Modeling of Three-Dimensional Braided Composites
Fang, Guodong; Chen, Chenghua; Yuan, Shenggang; Meng, Songhe; Liang, Jun
2018-06-01
A tracking and recognizing algorithm is proposed to automatically generate irregular cross-sections and central path of braid yarn within the 3D braided composites by using sets of high resolution tomography images. Only the initial cross-sections of braid yarns in a tomography image after treatment are required to be calibrated manually as searching cross-section template. The virtual geometry of 3D braided composites including some detailed geometry information, such as the braid yarn squeezing deformation, braid yarn distortion and braid yarn path deviation etc., can be reconstructed. The reconstructed geometry model can reflect the change of braid configurations during solidification process. The geometry configurations and mechanical properties of the braided composites are analyzed by using the reconstructed geometry model.
Energy Technology Data Exchange (ETDEWEB)
Dellacherie, St
2004-07-01
This work deals with the derivation of a diphasic low Mach number model obtained through a Mach number asymptotic expansion applied to the compressible diphasic Navier Stokes system, expansion which filters out the acoustic waves. This approach is inspired from the work of Andrew Majda giving the equations of low Mach number combustion for thin flame and for perfect gases. When the equations of state verify some thermodynamic hypothesis, we show that the low Mach number diphasic system predicts in a good way the dilatation or the compression of a bubble and has equilibrium convergence properties. Then, we propose an entropic and convergent Lagrangian scheme in mono-dimensional geometry when the fluids are perfect gases and we propose a first approach in Eulerian variables where the interface between the two fluids is captured with a level set technique. (author)
A Comparison of Angular Difference Schemes for One-Dimensional Spherical Geometry SN Equations
International Nuclear Information System (INIS)
Lathrop, K.D.
2000-01-01
To investigate errors caused by angular differencing in approximating the streaming terms of the transport equation, five different approximations are evaluated for three test problems in one-dimensional spherical geometry. The following schemes are compared: diamond, special truncation error minimizing weighted diamond, linear continuous (the original S N scheme), linear discontinuous, and new quadratic continuous. To isolate errors caused by angular differencing, the approximations are derived from the transport equation without spatial differencing, and the resulting coupled ordinary differential equations (ODEs) are solved with an ODE solver. Results from the approximations are compared with analytic solutions derived for two-region purely absorbing spheres. Most of the approximations are derived by taking moments of the conservation form of the transport equation. The quadratic continuous approximation is derived taking the zeroth moment of both the transport equation and the first angular derivative of the transport equation. The advantages of this approach are described. In all of the approximations, the desirability is shown of using an initializing computation of the μ = -1 angular flux to correctly compute the central flux and of having a difference approximation that ensures this central flux is the same for all directions. The behavior of the standard discrete ordinates equations in the diffusion limit is reviewed, and the linear and quadratic continuous approximations are shown to have the correct diffusion limit if an equal interval discrete quadrature is used.In all three test problems, the weighted diamond difference approximation has smaller maximum and average relative flux errors than the diamond or the linear continuous difference approximations. The quadratic continuous approximation and the linear discontinuous approximation are both more accurate than the other approximations, and the quadratic continuous approximation has a decided edge
A comparison of angular difference schemes for one-dimensional spherical geometry SN equations
International Nuclear Information System (INIS)
Lathrop, K.D.
2000-01-01
To investigate errors caused by angular differencing in approximating the streaming terms of the transport equation, five different approximations are evaluated for three test problems in one-dimensional spherical geometry. The following schemes are compared: diamond, special truncation error minimizing weighted diamond, linear continuous (the original S N scheme), linear discontinuous, and new quadratic continuous. To isolate errors caused by angular differencing, the approximations are derived from the transport equation without spatial differencing, and the resulting coupled ordinary differential equations (ODEs) are solved with an ODE solver. Results from the approximations are compared with analytic solutions derived for two-region purely absorbing spheres. Most of the approximations are derived by taking moments of the conservation form of the transport equation. The quadratic continuous approximation is derived taking the zeroth moment of both the transport equation and the first angular derivative of the transport equation. The advantages of this approach are described, In all of the approximations, the desirability is shown of using an initializing computation of the μ = -1 angular flux to correctly compute the central flux and of having a difference approximation that ensures this central flux is the same for all directions. The behavior of the standard discrete ordinates equations in the diffusion limit is reviewed, and the linear and quadratic continuous approximations are shown to have the correct diffusion limit if an equal interval discrete quadrature is used. In all three test problems, the weighted diamond difference approximation has smaller maximum and average relative flux errors than the diamond or the linear continuous difference approximations. The quadratic continuous approximation and the linear discontinuous approximation are both more accurate than the other approximations, and the quadratic continuous approximation has a decided edge
Numerical solution of multigroup diffuse equations of one-dimensional geometry
International Nuclear Information System (INIS)
Pavelesku, M.; Adam, S.
1975-01-01
The one-dimensional diffuse theory is used for reactor physics calculations of fast reactors. Computer program based on the one-dimensional diffuse theory is speedy and not memory consuming. The algorithm is described for the three-zone fast reactor criticality computation in one-dimensional diffusion approximation. This algorithm is realised on IBM 370/135 computer. (I.T.)
Energy Technology Data Exchange (ETDEWEB)
Ukwatta, Eranga, E-mail: eukwatt1@jhu.edu; Arevalo, Hermenegild; Pashakhanloo, Farhad; Prakosa, Adityo; Vadakkumpadan, Fijoy [Institute for Computational Medicine, Johns Hopkins University, Baltimore, Maryland 21205 and Department of Biomedical Engineering, Johns Hopkins University, Baltimore, Maryland 21205 (United States); Rajchl, Martin [Department of Computing, Imperial College London, London SW7 2AZ (United Kingdom); White, James [Stephenson Cardiovascular MR Centre, University of Calgary, Calgary, Alberta T2N 2T9 (Canada); Herzka, Daniel A.; McVeigh, Elliot [Department of Biomedical Engineering, Johns Hopkins University, Baltimore, Maryland 21205 (United States); Lardo, Albert C. [Department of Biomedical Engineering, Johns Hopkins University, Baltimore, Maryland 21205 and Division of Cardiology, Johns Hopkins Institute of Medicine, Baltimore, Maryland 21224 (United States); Trayanova, Natalia A. [Institute for Computational Medicine, Johns Hopkins University, Baltimore, Maryland 21205 (United States); Department of Biomedical Engineering, Johns Hopkins University, Baltimore, Maryland 21205 (United States); Department of Biomedical Engineering, Johns Hopkins Institute of Medicine, Baltimore, Maryland 21205 (United States)
2015-08-15
Purpose: Accurate three-dimensional (3D) reconstruction of myocardial infarct geometry is crucial to patient-specific modeling of the heart aimed at providing therapeutic guidance in ischemic cardiomyopathy. However, myocardial infarct imaging is clinically performed using two-dimensional (2D) late-gadolinium enhanced cardiac magnetic resonance (LGE-CMR) techniques, and a method to build accurate 3D infarct reconstructions from the 2D LGE-CMR images has been lacking. The purpose of this study was to address this need. Methods: The authors developed a novel methodology to reconstruct 3D infarct geometry from segmented low-resolution (Lo-res) clinical LGE-CMR images. Their methodology employed the so-called logarithm of odds (LogOdds) function to implicitly represent the shape of the infarct in segmented image slices as LogOdds maps. These 2D maps were then interpolated into a 3D image, and the result transformed via the inverse of LogOdds to a binary image representing the 3D infarct geometry. To assess the efficacy of this method, the authors utilized 39 high-resolution (Hi-res) LGE-CMR images, including 36 in vivo acquisitions of human subjects with prior myocardial infarction and 3 ex vivo scans of canine hearts following coronary ligation to induce infarction. The infarct was manually segmented by trained experts in each slice of the Hi-res images, and the segmented data were downsampled to typical clinical resolution. The proposed method was then used to reconstruct 3D infarct geometry from the downsampled images, and the resulting reconstructions were compared with the manually segmented data. The method was extensively evaluated using metrics based on geometry as well as results of electrophysiological simulations of cardiac sinus rhythm and ventricular tachycardia in individual hearts. Several alternative reconstruction techniques were also implemented and compared with the proposed method. Results: The accuracy of the LogOdds method in reconstructing 3D
Haj-Ali, Rami; Marom, Gil; Ben Zekry, Sagit; Rosenfeld, Moshe; Raanani, Ehud
2012-09-21
The complex three-dimensional (3D) geometry of the native tricuspid aortic valve (AV) is represented by select parametric curves allowing for a general construction and representation of the 3D-AV structure including the cusps, commissures and sinuses. The proposed general mathematical description is performed by using three independent parametric curves, two for the cusp and one for the sinuses. These curves are used to generate different surfaces that form the structure of the AV. Additional dependent curves are also generated and utilized in this process, such as the joint curve between the cusps and the sinuses. The model's feasibility to generate patient-specific parametric geometry is examined against 3D-transesophageal echocardiogram (3D-TEE) measurements from a non-pathological AV. Computational finite-element (FE) mesh can then be easily constructed from these surfaces. Examples are given for constructing several 3D-AV geometries by estimating the needed parameters from echocardiographic measurements. The average distance (error) between the calculated geometry and the 3D-TEE measurements was only 0.78±0.63mm. The proposed general 3D parametric method is very effective in quantitatively representing a wide range of native AV structures, with and without pathology. It can also facilitate a methodical quantitative investigation over the effect of pathology and mechanical loading on these major AV parameters. Copyright © 2012 Elsevier Ltd. All rights reserved.
Directory of Open Access Journals (Sweden)
Xingwei Wang
2014-01-01
Full Text Available Due to the uneven distribution of pollutions and blur edge of pollutant area, there will exist uncertainty of source term shape in advective-diffusion equation model of contaminant transport. How to generalize those irregular source terms and deal with those uncertainties is very critical but rarely studied in previous research. In this study, the fate and transport of contaminant from rectangular and elliptic source geometry were simulated based on a three-dimensional analytical solute transport model, and the source geometry generalization guideline was developed by comparing the migration of contaminant. The result indicated that the variation of source area size had no effect on pollution plume migration when the plume migrated as far as five times of source side length. The migration of pollution plume became slower with the increase of aquifer thickness. The contaminant concentration was decreasing with scale factor rising, and the differences among various scale factors became smaller with the distance to field increasing.
Chern-Simons forms and four-dimensional N=1 superspace geometry
International Nuclear Information System (INIS)
Girardi, G.; Grimm, R.
1986-12-01
The complete superspace geometry for Yang-Mills, chiral U(1) and Lorentz Chern-Simons forms is constructed. The analysis is completely off-shell and covers the cases of minimal, new minimal and 16-16 supergravity. Supersymmetry is guaranteed by construction. Invariant superfield actions are proposed
Vojak, B. A.; Alley, G. D.
1983-08-01
Two-dimensional numerical simulations are used to compare etched geometry and overgrown Si permeable base transistors (PTBs), considering both the etched collector and etched emitter biasing conditions made possible by the asymmetry of the etched structure. In PTB devices, the two-dimensional nature of the depletion region near the Schottky contact base grating results in a smaller electron barrier and, therefore, a larger collector current in the etched than in the overgrown structure. The parasitic feedback effects which result at high base-to-emitter bias levels lead to a deviation from the square-law behavior found in the collector characteristics of the overgrown PBT. These structures also have lower device capacitances and smaller transconductances at high base-to-emitter voltages. As a result, overgrown and etched structures have comparable predicted maximum values of the small signal unity short-circuit current gain frequency and maximum oscillation frequency.
International Nuclear Information System (INIS)
Shestakov, A.I.; Mirin, A.A.
1984-01-01
A numerical method based on Fourier expansions and finite differences is presented. The method is demonstrated by solving a scalar, three-dimensional elliptic equation arising in MFE research, but has applicability to a wider class of problems. The scheme solves equations whose solutions are expected to be periodic in one or more of the independent variables
Topology Change and the Emergence of Geometry in Two Dimensional Causal Quantum Gravity
Westra, W.
2007-01-01
Despite many attempts, gravity has vigorously resisted a unification with the laws of quantum mechanics. Besides a plethora of technical issues, one is also faced with many interesting conceptual problems. The study of quantum gravity in lower dimensional models ameliorates the technical
Casimir energy in d-dimensional rectangular geometries, under mixed boundary conditions
International Nuclear Information System (INIS)
Silva, J.C. da; Placido, Hebe Q.; Santana, A.E.; M Neto, Arthur
1997-01-01
The Casimir energy and its temperature corrections are presented for the electromagnetic field confined in a d-dimensional hypercavity. The expressions are derived considering Dirichlet boundary conditions for each pair of hyperplanes defining a confined direction (the homogeneous case); or yet, by choosing different boundary conditions (Dirichlet or Neumann) at each hyperplane of the pair (the mixed case). (author)
Levakhina, Yulia
2014-01-01
Yulia Levakhina gives an introduction to the major challenges of image reconstruction in Digital Tomosynthesis (DT), particularly to the connection of the reconstruction problem with the incompleteness of the DT dataset. The author discusses the factors which cause the formation of limited angle artifacts and proposes how to account for them in order to improve image quality and axial resolution of modern DT. The addressed methods include a weighted non-linear back projection scheme for algebraic reconstruction and?novel dual-axis acquisition geometry. All discussed algorithms and methods are supplemented by detailed illustrations, hints for practical implementation, pseudo-code, simulation results and real patient case examples.
Energy Technology Data Exchange (ETDEWEB)
Stark, R.H.
1977-05-01
This report is a non-technical exposition on the ambiguities in conventional specification of the shape of a part to be manufactured and on various alternatives for representing its geometry for computer processing. It touches lightly on wire-frame and bounded surface representations and on the concept of design by volumes. It concludes that no existing computer-aided design system has yet shown its long-range superiority over he spectrum of parts and of uses to which its information base should be applicable. 9 figures.
Yu, Hongyu; Liu, Yajing; Yang, Hongfeng; Ning, Jieyuan
2018-05-01
To assess the potential of catastrophic megathrust earthquakes (MW > 8) along the Manila Trench, the eastern boundary of the South China Sea, we incorporate a 3D non-planar fault geometry in the framework of rate-state friction to simulate earthquake rupture sequences along the fault segment between 15°N-19°N of northern Luzon. Our simulation results demonstrate that the first-order fault geometry heterogeneity, the transitional-segment (possibly related to the subducting Scarborough seamount chain) connecting the steeper south segment and the flatter north segment, controls earthquake rupture behaviors. The strong along-strike curvature at the transitional-segment typically leads to partial ruptures of MW 8.3 and MW 7.8 along the southern and northern segments respectively. The entire fault occasionally ruptures in MW 8.8 events when the cumulative stress in the transitional-segment is sufficiently high to overcome the geometrical inhibition. Fault shear stress evolution, represented by the S-ratio, is clearly modulated by the width of seismogenic zone (W). At a constant plate convergence rate, a larger W indicates on average lower interseismic stress loading rate and longer rupture recurrence period, and could slow down or sometimes stop ruptures that initiated from a narrower portion. Moreover, the modeled interseismic slip rate before whole-fault rupture events is comparable with the coupling state that was inferred from the interplate seismicity distribution, suggesting the Manila trench could potentially rupture in a M8+ earthquake.
Three-Dimensional Geometry of Collagenous Tissues by Second Harmonic Polarimetry.
Reiser, Karen; Stoller, Patrick; Knoesen, André
2017-06-01
Collagen is a biological macromolecule capable of second harmonic generation, allowing label-free detection in tissues; in addition, molecular orientation can be determined from the polarization dependence of the second harmonic signal. Previously we reported that in-plane orientation of collagen fibrils could be determined by modulating the polarization angle of the laser during scanning. We have now extended this method so that out-of-plane orientation angles can be determined at the same time, allowing visualization of the 3-dimensional structure of collagenous tissues. This approach offers advantages compared with other methods for determining out-of-plane orientation. First, the orientation angles are directly calculated from the polarimetry data obtained in a single scan, while other reported methods require data from multiple scans, use of iterative optimization methods, application of fitting algorithms, or extensive post-optical processing. Second, our method does not require highly specialized instrumentation, and thus can be adapted for use in almost any nonlinear optical microscopy setup. It is suitable for both basic and clinical applications. We present three-dimensional images of structurally complex collagenous tissues that illustrate the power of such 3-dimensional analyses to reveal the architecture of biological structures.
Directory of Open Access Journals (Sweden)
Chogo C.N.
2017-12-01
Full Text Available Mathematics is globally valued for use by an individual and society. It plays a significant role in the development of modern science and technology. Despite its importance students motivation to learn and achievement at national examinations globally and at the KCSE mathematics examination in Kenya particularly has been dismal over the years. The learners low achievement in the subject has been attributed to the didactic teaching methods that the teachers use among other factors. The study of geometry in Mathematics poses a number of difficulties to learners which are different in nature from those of arithmetic and algebra. This is because geometry is primarily abstract in nature. The purpose of this study was to determine the effects of Open Ended Teaching and Learning Approach OETLA on Secondary School students mathematics achievement in learning Three Dimensional Geometry 3DG. The study employed Solomon four non-equivalent control group design. The two experimental groups E1amp E2 received OETLA treatment while the control groups C1ampC2 were taught using the conventional teaching and learning methods. Only E1amp C1 took a pre-test and a post test for all the groups. The target population for this study was form four 17 year old students of secondary schools in Marani Sub County in Kisii County. Purposive sampling was used to obtain the four county mixed-sex secondary schools for the study. A total of 152 students formed the sample size. Students Mathematics Achievement Test SMAT was used to collect data. The instruments were validated by three experts from the department of curriculum and instruction of Egerton University and three Secondary School Mathematics Heads of Department. The reliability of the instruments were established using Cronbachs Alpha. A reliability coefficient of 0.92 was obtained and thus considered acceptable. The SMAT was administered to two groups as a pretest before the treatment and as a posttest to all the four
International Nuclear Information System (INIS)
Ceolin, Celina; Vilhena, Marco T.; Petersen, Claudio Z.
2009-01-01
In this work we report an analytical solution for the monoenergetic neutron diffusion kinetic equation in cartesian geometry. Bearing in mind that the equation for the delayed neutron precursor concentration is a first order linear differential equation in the time variable, to make possible the application of the GITT approach to the kinetic equation, we introduce a fictitious diffusion term multiplied by a positive small value ε. By this procedure, we are able to solve this set of equations. Indeed, applying the GITT technique to the modified diffusion kinetic equation, we come out with a matrix differential equation which has a well known analytical solution when ε goes to zero. We report numerical simulations as well study of numerical convergence of the results attained. (author)
A Framework for the Interactive Handling of High-Dimensional Simulation Data in Complex Geometries
Benzina, Amal; Buse, Gerrit; Butnaru, Daniel; Murarasu, Alin; Treib, Marc; Varduhn, Vasco; Mundani, Ralf-Peter
2013-01-01
Flow simulations around building infrastructure models involve large scale complex geometries, which when discretized in adequate detail entail high computational cost. Moreover, tasks such as simulation insight by steering or optimization require many such costly simulations. In this paper, we illustrate the whole pipeline of an integrated solution for interactive computational steering, developed for complex flow simulation scenarios that depend on a moderate number of both geometric and physical parameters. A mesh generator takes building information model input data and outputs a valid cartesian discretization. A sparse-grids-based surrogate model—a less costly substitute for the parameterized simulation—uses precomputed data to deliver approximated simulation results at interactive rates. Furthermore, a distributed multi-display visualization environment shows building infrastructure together with flow data. The focus is set on scalability and intuitive user interaction.
Alekseev, P. S.; Dmitriev, A. P.; Gornyi, I. V.; Kachorovskii, V. Yu.; Narozhny, B. N.; Titov, M.
2018-02-01
Ultrapure conductors may exhibit hydrodynamic transport where the collective motion of charge carriers resembles the flow of a viscous fluid. In a confined geometry (e.g., in ultra-high-quality nanostructures), the electronic fluid assumes a Poiseuille-type flow. Applying an external magnetic field tends to diminish viscous effects leading to large negative magnetoresistance. In two-component systems near charge neutrality, the hydrodynamic flow of charge carriers is strongly affected by the mutual friction between the two constituents. At low fields, the magnetoresistance is negative, however, at high fields the interplay between electron-hole scattering, recombination, and viscosity results in a dramatic change of the flow profile: the magnetoresistance changes its sign and eventually becomes linear in very high fields. This nonmonotonic magnetoresistance can be used as a fingerprint to detect viscous flow in two-component conducting systems.
International Nuclear Information System (INIS)
Bellucci, H.J.
1975-11-01
The report describes the continuation of research into capability for three-dimensional elastic-plastic stress and strain analysis for fracture mechanics. A computer program, MARC-3D, has been completed and was used to analyze a cylindrical pressure vessel with a nozzle insert. A method for generating crack tip elements was developed and a model was created for a cylindrical pressure vessel with a nozzle and an imbedded flaw at the inside nozzle corner. The MARC-3D program was again used to analyze this flawed model. Documentation for the use of the MARC-3D computer program has been included as an appendix
International Nuclear Information System (INIS)
Mikhailova, T V; Berzhansky, V N; Karavainikov, A V; Shaposhnikov, A N; Prokopov, A R; Lyashko, S D
2016-01-01
It is represented the results of modelling of magnetooptical properties in reflection polar geometry of one-dimensional photonic crystal, in which highly Bi-substituted iron garnet defect of composition Bi 1.0 Y 0.5 Gd 1.5 Fe 4.2 A l0.8 O 12 / Bi 2.8 Y 0.2 Fe 5 Oi 2 is located between the dielectric Bragg mirrors (SiO 2 / TiO 2 ) m (were m is number of layer pairs) and buffer SiO 2 and gold top layers of different thicknesses is placed on structure. The modification of spectral line- shapes of microcavity and Tamm plasmon-polariton modes depending on m is found. (paper)
International Nuclear Information System (INIS)
Rosa, M.; Warsa, J. S.; Chang, J. H.
2007-01-01
A Fourier analysis is conducted in two-dimensional (2D) Cartesian geometry for the discrete-ordinates (SN) approximation of the neutron transport problem solved with Richardson iteration (Source Iteration) and Richardson iteration preconditioned with Transport Synthetic Acceleration (TSA), using the Parallel Block-Jacobi (PBJ) algorithm. The results for the un-accelerated algorithm show that convergence of PBJ can degrade, leading in particular to stagnation of GMRES(m) in problems containing optically thin sub-domains. The results for the accelerated algorithm indicate that TSA can be used to efficiently precondition an iterative method in the optically thin case when implemented in the 'modified' version MTSA, in which only the scattering in the low order equations is reduced by some non-negative factor β<1. (authors)
An algorithm for the calculation of three-dimensional ICRF fields in tokamak geometry
International Nuclear Information System (INIS)
Smithe, D.N.; Kammash, T.
1987-01-01
A computational scheme is developed which permits tractable calculation of three-dimensional full-wave solutions to the Vlasov-Maxwell equations under typical ion cyclotron range of frequencies (ICRF) experimental conditions. The method is unique in that power deposition to the plasma is determined via the anti-Hermitian part of a truncated warm plasma dielectric operator, rather than as the result of an assumed phenomenological collision frequency. The resulting computer code allows arbitrary variation of density, temperature, magnetic field and minority concentration in the poloidal plane by performing a convolution of poloidal modes to produce a coupled system of differential equations in the radial variable. By assuming no inhomogeneity along the toroidal axis, an inverse transform over k parallel is performed, yielding the global three-dimensional fast wave field solutions. The application of the code to TFTR-like plasmas shows a mild resonance structure in antenna loading related to the changing number of wavelengths between the antenna and the resonance layer. (author)
KP solitons and the Grassmannians combinatorics and geometry of two-dimensional wave patterns
Kodama, Yuji
2017-01-01
This is the first book to treat combinatorial and geometric aspects of two-dimensional solitons. Based on recent research by the author and his collaborators, the book presents new developments focused on an interplay between the theory of solitons and the combinatorics of finite-dimensional Grassmannians, in particular, the totally nonnegative (TNN) parts of the Grassmannians. The book begins with a brief introduction to the theory of the Kadomtsev–Petviashvili (KP) equation and its soliton solutions, called the KP solitons. Owing to the nonlinearity in the KP equation, the KP solitons form very complex but interesting web-like patterns in two dimensions. These patterns are referred to as soliton graphs. The main aim of the book is to investigate the detailed structure of the soliton graphs and to classify these graphs. It turns out that the problem has an intimate connection with the study of the TNN part of the Grassmannians. The book also provides an elementary introduction to the recent development of ...
Topological phases of interacting fermions in one-dimensional superconductor - normal metal geometry
Energy Technology Data Exchange (ETDEWEB)
Meidan, Dganit [Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva 84105 (Israel); Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universitaet Berlin, 14195 Berlin (Germany); Romito, Alessandro; Brouwer, Piet W. [Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva 84105 (Israel)
2015-07-01
One-dimensional superconductors can be in non-trivial topological phases harboring Majorana end-states, which possess non-abelian statistics. It has been recently established that in the presence of interactions the classification of topological superconducting phases can be significantly altered. Specifically, for one-dimensional superconductors possessing a time reversal symmetry (BDI class), interactions reduce the infinitely many non-interacting phases (Z topological index) to eight distinct ones (Z{sub 8} topological index). In this talk I will consider multi-mode superconducting wires in such BDI class when probed by an external contact, and discuss their low temperature and voltage bias transport properties. I will first show that the Andreev reflection component of the scattering matrix of the probing lead provides a topological index, r=-4,.., 4, which distinguish the eight topological phases. The two topologically equivalent phases with r= 4,-4 support emergent many-body end states, which are identified to be a topologically protected Kondo-like resonance. The path in phase space that connects these equivalent phases crosses a non-fermi liquid fixed point where a multiple channel Kondo effect develops.
Gap solitons in elongated geometries: The one-dimensional Gross-Pitaevskii equation and beyond
International Nuclear Information System (INIS)
Mateo, A. Munoz; Delgado, V.; Malomed, Boris A.
2011-01-01
We report results of a systematic analysis of matter-wave gap solitons (GSs) in three-dimensional self-repulsive Bose-Einstein condensates (BECs) loaded into a combination of a cigar-shaped trap and axial optical-lattice (OL) potential. Basic cases of the strong, intermediate, and weak radial (transverse) confinement are considered, as well as settings with shallow and deep OL potentials. Only in the case of the shallow lattice combined with tight radial confinement, which actually has little relevance to realistic experimental conditions, does the usual one-dimensional (1D) cubic Gross-Pitaevskii equation (GPE) furnish a sufficiently accurate description of GSs. However, the effective 1D equation with the nonpolynomial nonlinearity, derived in Ref. [Phys. Rev. A 77, 013617 (2008)], provides for quite an accurate approximation for the GSs in all cases, including the situation with weak transverse confinement, when the soliton's shape includes a considerable contribution from higher-order transverse modes, in addition to the usual ground-state wave function of the respective harmonic oscillator. Both fundamental GSs and their multipeak bound states are considered. The stability is analyzed by means of systematic simulations. It is concluded that almost all the fundamental GSs are stable, while their bound states may be stable if the underlying OL potential is deep enough.
International Nuclear Information System (INIS)
Barton, C.C.; Larsen, E.
1985-01-01
Fracture traces exposed on three 214- to 260-m 2 pavements in the same Miocene ash-flow tuff at Yucca Mountain, southwestern Nevada, have been mapped at a scale of 1:50. The maps are two-dimensional sections through the three-dimensional network of strata-bound fractures. All fractures with trace lengths greater than 0.20 m were mapped. The distribution of fracture-trace lengths is log-normal. The fractures do not exhibit well-defined sets based on orientation. Since fractal characterization of such complex fracture-trace networks may prove useful for modeling fracture flow and mechanical responses of fractured rock, an analysis of each of the three maps was done to test whether such networks are fractal. These networks proved to be fractal and the fractal dimensions (D) are tightly clustered (1.12, 1.14, 1.16) for three laterally separated pavements, even though visually the fracture networks appear quite different. The fractal analysis also indicates that the network patterns are scale independent over two orders of magnitude for trace lengths ranging from 0.20 to 25 m. 7 refs., 7 figs
Three-dimensional tracking of cardiac catheters using an inverse geometry x-ray fluoroscopy system
International Nuclear Information System (INIS)
Speidel, Michael A.; Tomkowiak, Michael T.; Raval, Amish N.; Van Lysel, Michael S.
2010-01-01
Purpose: Scanning beam digital x-ray (SBDX) is an inverse geometry fluoroscopic system with high dose efficiency and the ability to perform continuous real-time tomosynthesis at multiple planes. This study describes a tomosynthesis-based method for 3D tracking of high-contrast objects and present the first experimental investigation of cardiac catheter tracking using a prototype SBDX system. Methods: The 3D tracking algorithm utilizes the stack of regularly spaced tomosynthetic planes that are generated by SBDX after each frame period (15 frames/s). Gradient-filtered versions of the image planes are generated, the filtered images are segmented into object regions, and then a 3D coordinate is calculated for each object region. Two phantom studies of tracking performance were conducted. In the first study, an ablation catheter in a chest phantom was imaged as it was pulled along a 3D trajectory defined by a catheter sheath (10, 25, and 50 mm/s pullback speeds). SBDX tip tracking coordinates were compared to the 3D trajectory of the sheath as determined from a CT scan of the phantom after the registration of the SBDX and CT coordinate systems. In the second study, frame-to-frame tracking precision was measured for six different catheter configurations as a function of image noise level (662-7625 photons/mm 2 mean detected x-ray fluence at isocenter). Results: During catheter pullbacks, the 3D distance between the tracked catheter tip and the sheath centerline was 1.0±0.8 mm (mean ±one standard deviation). The electrode to centerline distances were comparable to the diameter of the catheter tip (2.3 mm), the confining sheath (4 mm outside diameter), and the estimated SBDX-to-CT registration error (±0.7 mm). The tip position was localized for all 332 image frames analyzed and 83% of tracked positions were inside the 3D sheath volume derived from CT. The pullback speeds derived from the catheter trajectories were within 5% of the programed pullback speeds. The
On-Orbit 3-Dimensional Electrostatic Detumble for Generic Spacecraft Geometries
Bennett, Trevor J.
In recent years, there is a growing interest in active debris removal and on-orbit servicing of Earth orbiting assets. The growing need for such approaches is often exemplified by the Iridium-Kosmos collision in 2009 that generated thousands of debris fragments. There exists a variety of active debris removal and on-orbit servicing technologies in development. Conventional docking mechanisms and mechanical capture by actuated manipulators, exemplified by NASA's Restore-L mission, require slow target tumble rates or more aggressive circumnavigation rate matching. The tumble rate limitations can be overcome with flexible capture systems such nets, harpoons, or tethers yet these systems require complex deployment, towing, and/or interfacing strategies to avoid servicer and target damage. Alternatively, touchless methods overcome the tumble rate limitations by provide detumble control prior to a mechanical interface. This thesis explores electrostatic detumble technology to touchlessly reduce large target rotation rates of Geostationary satellites and debris. The technical challenges preceding flight implementation largely reside in the long-duration formation flying guidance, navigation, and control of a servicer spacecraft equipped with electrostatic charge transfer capability. Leveraging prior research into the electrostatic charging of spacecraft, electrostatic detumble control formulations are developed for both axisymmetric and generic target geometries. A novel relative position vector and associated relative orbit control approach is created to manage the long-duration proximity operations. Through detailed numerical simulations, the proposed detumble and relative motion control formulations demonstrate detumble of several thousand kilogram spacecraft tumbling at several degrees per second in only several days. The availability, either through modeling or sensing, of the relative attitude, relative position, and electrostatic potential are among key concerns
International Nuclear Information System (INIS)
Sugino, Kazuteru
1998-07-01
As a tool to perform a fast reactor core calculations with high accuracy, NSHEX the nodal transport calculation code for three-dimensional hexagonal-Z geometry is under development. To improve the practical applicability of NSHEX, for instance, in its application to safety analysis and commercial reactor core design studies, we investigated the basic theory used in it, improved the program performance, and evaluated its applicability to the analysis of commercial reactor cores. The current studies show the following: (1) An improvement in the treatment of radial leakage in the radial nodal coupling equation bettered calculational convergence for safety analysis calculation, so the applicability of NSHEX to safety analysis was improved. (2) As a result of comparison of results from NSHEX and the standard core calculation code, it was confirmed that there was consistency between them. (3) According to the evaluation of the effect due to the difference of calculational condition, it was found that the calculation under appropriate nodal expansion orders and Sn orders correspond to the one under most detailed condition. However further investigation is required to reduce the uncertainty in calculational results due to the treatment of high order flux moments. (4) A whole core version of NSHEX enabling calculation for any FBR core geometry has been developed, this improved general applicability of NSHEX. (5) An investigation of the applicability of the rebalance method to acceleration clarified that this improved calculational convergence and it was effective. (J.P.N.)
Huemul: a two dimensional multigroup collision probability code for general geometries
International Nuclear Information System (INIS)
Calabrese, C.R.; Grant, C.R.
1990-01-01
The control rod calculation and the necessity of having a 2-D transport code able to calculate geometries as different as pool reactor or power reactor control rods resulted in the development of a new tool according to these requirements. This new tool permits a 2-D spatial representation, and the calculation mesh is formed by circumferential arcs segments not necessarily parallel to the coordinate axis. It includes the possibility of considering boundary conditions in the form of an albedo matrix (J + /J - ) as well as different external currents for each face of the model. It also allows an arbitrary number of energy groups compatible with computer limitations. These possibilities make HUEMUL a useful tool for a great variety of control rod or supercell type calculations. HUEMUL has been tested with copper activity measurements performed in the Canadian D2O facility ZED-2 with stainless-steel adjuster rods obtaining a very good agreement (better than 2%). Also manganese activity measurements in RA-2 pool reactor were used to compare calculated and measured values inside a MTR fuel element calculations, (better than 1%). Comparisons with results from the WIMS code for a light water cell with 3% enriched UO 2 has also shown a very good agreement in fluxes and multiplication constant (better than 1.5% in fluxes and 50 pcm in k-infinity). (Author) [es
Gyrokinetic Vlasov code including full three-dimensional geometry of experiments
International Nuclear Information System (INIS)
Nunami, Masanori; Watanabe, Tomohiko; Sugama, Hideo
2010-03-01
A new gyrokinetic Vlasov simulation code, GKV-X, is developed for investigating the turbulent transport in magnetic confinement devices with non-axisymmetric configurations. Effects of the magnetic surface shapes in a three-dimensional equilibrium obtained from the VMEC code are accurately incorporated. Linear simulations of the ion temperature gradient instabilities and the zonal flows in the Large Helical Device (LHD) configuration are carried out by the GKV-X code for a benchmark test against the GKV code. The frequency, the growth rate, and the mode structure of the ion temperature gradient instability are influenced by the VMEC geometrical data such as the metric tensor components of the Boozer coordinates for high poloidal wave numbers, while the difference between the zonal flow responses obtained by the GKV and GKV-X codes is found to be small in the core LHD region. (author)
Wei, Jeng; Yin, Wei-Hsian; Lee, Yung-Tsai; Hsiung, Ming C; Tsai, Shen-Kou; Chuang, Yi Cheng; Ou, Ching-Huei; Chou, Yi-Pen
2015-03-01
Paravalvular leaks (PVLs) are a common complication of prosthetic valve replacement. Use of the transcatheter intervention technique is a suitable alternative in high-risk patients who may not tolerate repeat surgery. Common reasons for failure of this demanding intervention include poor imaging quality and unsuitable anatomy. The purpose of this study was to assess the usefulness and the incremental value of real-time three-dimensional (RT 3D) transesophageal echocardiography (TEE) over two-dimensional (2D) TEE findings in the evaluation of the geometry and track of mitral PVLs during transcatheter closure. Five patients with six mitral PVLs at high risk for repeat surgery underwent transcatheter leak closure. Intraoperative RT 3DTEE was used to assess the location, shape, number, and size of the defects. Transapical approaches were used in all cases with fluoroscopic and RT 3D TEE guidance of the wire and catheter, device positioning, and assessment of residual leak after the procedure. In all of the cases, defects with irregular crescent shapes and distorted tracks were clearly delineated by RT 3D TEE. This was compared to those results obtained through 2D TEE, which was unable to characterize the defects. Three cases showed small leaks, which were completely occluded with a patent ductus arteriosus (PDA) device in two cases, and a muscular ventricular septal defect (mVSD) occluder combined with coil devices in one case. One case involved a large leak and early device embolization of the muscular VSD occluder, which was removed surgically, and demonstrated a crescent-shaped defect. One patient had two releaks 2 months subsequent to the procedure due to two new extended leaks at the tails of the crescent-shaped defect. RT 3D TEE can clearly delineate the geometries of defects in their entirety, including shape, size, and location of the defect and track canal. It would also appear that RT 3D TEE is superior to 2D TEE in the process of guiding the wire through the
Saitoh, Takeji; Shiota, Maiko; Izumo, Masaki; Gurudevan, Swaminatha V; Tolstrup, Kirsten; Siegel, Robert J; Shiota, Takahiro
2012-06-01
The present study sought to elucidate the geometry of the left ventricular outflow tract (LVOT) in patients with aortic stenosis and its effect on the accuracy of the continuity equation-based aortic valve area (AVA) estimation. Real-time 3-dimensional transesophageal echocardiography (RT3D-TEE) provides high-resolution images of LVOT in patients with aortic stenosis. Thus, AVA is derived reliably with the continuity equation. Forty patients with aortic stenosis who underwent 2-dimensional transthoracic echocardiography (2D-TTE), 2-dimensional transesophageal echocardiography (2D-TEE), and RT3D-TEE were studied. In 2D-TTE and 2D-TEE, the LVOT areas were calculated as π × (LVOT dimension/2)(2). In RT3D-TEE, the LVOT areas and ellipticity ([diameter of the anteroposterior axis]/[diameter of the medial-lateral axis]) were evaluated by planimetry. The AVA is then determined using planimetry and the continuity equation method. LVOT shape was found to be elliptical (ellipticity of 0.80 ± 0.08). Accordingly, the LVOT areas measured by 2D-TTE (median 3.7 cm(2), interquartile range 3.1 to 4.1) and 2D-TEE (median 3.7 cm(2), interquartile range 3.1 to 4.0) were smaller than those by 3D-TEE (median 4.6 cm(2), interquartile range 3.9 to 5.3; p interquartile range 0.79 to 1.3, p interquartile range 0.64 to 0.94) and 2D-TEE (median 0.76 cm(2), interquartile range 0.62 to 0.95). Additionally, the continuity equation-based AVA by RT3D-TEE was consistent with the planimetry method. In conclusion, RT3D-TEE might allow more accurate evaluation of the elliptical LVOT geometry and continuity equation-based AVA in patients with aortic stenosis than 2D-TTE and 2D-TEE. Copyright © 2012 Elsevier Inc. All rights reserved.
The geometry of percolation fronts in two-dimensional lattices with spatially varying densities
International Nuclear Information System (INIS)
Gastner, Michael T; Oborny, Beáta
2012-01-01
Percolation theory is usually applied to lattices with a uniform probability p that a site is occupied or that a bond is closed. The more general case, where p is a function of the position x, has received less attention. Previous studies with long-range spatial variations in p(x) have only investigated cases where p has a finite, non-zero gradient at the critical point p c . Here we extend the theory to two-dimensional cases in which the gradient can change from zero to infinity. We present scaling laws for the width and length of the hull (i.e. the boundary of the spanning cluster). We show that the scaling exponents for the width and the length depend on the shape of p(x), but they always have a constant ratio 4/3 so that the hull's fractal dimension D = 7/4 is invariant. On this basis, we derive and verify numerically an asymptotic expression for the probability h(x) that a site at a given distance x from p c is on the hull. (paper)
Gikas, Vassilis
2012-01-01
Driven by progress in sensor technology, computer software and data processing capabilities, terrestrial laser scanning has recently proved a revolutionary technique for high accuracy, 3D mapping and documentation of physical scenarios and man-made structures. Particularly, this is of great importance in the underground space and tunnel construction environment as surveying engineering operations have a great impact on both technical and economic aspects of a project. This paper discusses the use and explores the potential of laser scanning technology to accurately track excavation and construction activities of highway tunnels. It provides a detailed overview of the static laser scanning method, its principles of operation and applications for tunnel construction operations. Also, it discusses the planning, execution, data processing and analysis phases of laser scanning activities, with emphasis given on geo-referencing, mesh model generation and cross-section extraction. Specific case studies are considered based on two construction sites in Greece. Particularly, the potential of the method is examined for checking the tunnel profile, producing volume computations and validating the smoothness/thickness of shotcrete layers at an excavation stage and during the completion of excavation support and primary lining. An additional example of the use of the method in the geometric documentation of the concrete lining formwork is examined and comparisons against dimensional tolerances are examined. Experimental comparisons and analyses of the laser scanning method against conventional surveying techniques are also considered. PMID:23112655
Insights into the three-dimensional Lagrangian geometry of the Antarctic polar vortex
Curbelo, Jezabel; José García-Garrido, Víctor; Mechoso, Carlos Roberto; Mancho, Ana Maria; Wiggins, Stephen; Niang, Coumba
2017-07-01
In this paper we study the three-dimensional (3-D) Lagrangian structures in the stratospheric polar vortex (SPV) above Antarctica. We analyse and visualize these structures using Lagrangian descriptor function M. The procedure for calculation with reanalysis data is explained. Benchmarks are computed and analysed that allow us to compare 2-D and 3-D aspects of Lagrangian transport. Dynamical systems concepts appropriate to 3-D, such as normally hyperbolic invariant curves, are discussed and applied. In order to illustrate our approach we select an interval of time in which the SPV is relatively undisturbed (August 1979) and an interval of rapid SPV changes (October 1979). Our results provide new insights into the Lagrangian structure of the vertical extension of the stratospheric polar vortex and its evolution. Our results also show complex Lagrangian patterns indicative of strong mixing processes in the upper troposphere and lower stratosphere. Finally, during the transition to summer in the late spring, we illustrate the vertical structure of two counterrotating vortices, one the polar and the other an emerging one, and the invariant separatrix that divides them.
Mahmood, Feroze; Warraich, Haider J.; Gorman, Joseph H.; Gorman, Robert C.; Chen, Tzong-Huei; Panzica, Peter; Maslow, Andrew; Khabbaz, Kamal
2014-01-01
Background and aim of the study Intraoperative real-time three-dimensional transesophageal echocardiography (RT-3D TEE) was used to examine the geometric changes that occur in the mitral annulus immediately after aortic valve replacement (AVR). Methods A total of 35 patients undergoing elective surgical AVR under cardiopulmonary bypass was enrolled in the study. Intraoperative RT-3D TEE was used prospectively to acquire volumetric echocardiographic datasets immediately before and after AVR. The 3D echocardiographic data were analyzed offline using TomTec® Mitral Valve Assessment software to assess changes in specific mitral annular geometric parameters. Results Datasets were successfully acquired and analyzed for all patients. A significant reduction was noted in the mitral annular area (-16.3%, p <0.001), circumference (-8.9% p <0.001) and the anteroposterior (-6.3%, p = 0.019) and anterolateral-posteromedial (-10.5%, p <0.001) diameters. A greater reduction was noted in the anterior annulus length compared to the posterior annulus length (10.5% versus 62%, p <0.05) after AVR. No significant change was seen in the non-planarity angle, coaptation depth, and closure line length. During the period of data acquisition before and after AVR, no significant change was noted in the central venous pressure or left ventricular end-diastolic diameter. Conclusion The mitral annulus undergoes significant geometric changes immediately after AVR Notably, a 16.3% reduction was observed in the mitral annular area. The anterior annulus underwent a greater reduction in length compared to the posterior annulus, which suggested the existence of a mechanical compression by the prosthetic valve. PMID:23409347
International Nuclear Information System (INIS)
Robinson, I.; Trautman, A.
1988-01-01
The geometry of classical physics is Lorentzian; but weaker geometries are often more appropriate: null geodesics and electromagnetic fields, for example, are well known to be objects of conformal geometry. To deal with a single null congruence, or with the radiative electromagnetic fields associated with it, even less is needed: flag geometry for the first, optical geometry, with which this paper is chiefly concerned, for the second. The authors establish a natural one-to-one correspondence between optical geometries, considered locally, and three-dimensional Cauchy-Riemann structures. A number of Lorentzian geometries are shown to be equivalent from the optical point of view. For example the Goedel universe, the Taub-NUT metric and Hauser's twisting null solution have an optical geometry isomorphic to the one underlying the Robinson congruence in Minkowski space. The authors present general results on the problem of lifting a CR structure to a Lorentz manifold and, in particular, to Minkowski space; and exhibit the relevance of the deviation form to this problem
Directory of Open Access Journals (Sweden)
Hassan Badreddine
2017-01-01
Full Text Available The current work focuses on the development and application of a new finite volume immersed boundary method (IBM to simulate three-dimensional fluid flows and heat transfer around complex geometries. First, the discretization of the governing equations based on the second-order finite volume method on Cartesian, structured, staggered grid is outlined, followed by the description of modifications which have to be applied to the discretized system once a body is immersed into the grid. To validate the new approach, the heat conduction equation with a source term is solved inside a cavity with an immersed body. The approach is then tested for a natural convection flow in a square cavity with and without circular cylinder for different Rayleigh numbers. The results computed with the present approach compare very well with the benchmark solutions. As a next step in the validation procedure, the method is tested for Direct Numerical Simulation (DNS of a turbulent flow around a surface-mounted matrix of cubes. The results computed with the present method compare very well with Laser Doppler Anemometry (LDA measurements of the same case, showing that the method can be used for scale-resolving simulations of turbulence as well.
Energy Technology Data Exchange (ETDEWEB)
Fernandes, Julio Cesar L.; Vilhena, Marco Tullio, E-mail: julio.lombaldo@ufrgs.b, E-mail: vilhena@pq.cnpq.b [Universidade Federal do Rio Grande do Sul (DMPA/UFRGS), Porto Alegre, RS (Brazil). Dept. de Matematica Pura e Aplicada. Programa de Pos Graduacao em Matematica Aplicada; Borges, Volnei; Bodmann, Bardo Ernest, E-mail: bardo.bodmann@ufrgs.b, E-mail: borges@ufrgs.b [Universidade Federal do Rio Grande do Sul (PROMEC/UFRGS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica
2011-07-01
The principal idea of this work, consist on formulate an analytical method to solved problems for diffusion of neutrons with isotropic scattering in one-dimensional cylindrical geometry. In this area were develop many works that study the same problem in different system of coordinates as well as cartesian system, nevertheless using numerical methods to solve the shielding problem. In view of good results in this works, we starting with the idea that we can represent a source in the origin of the cylindrical system by a Delta Dirac distribution, we describe the physical modeling and solved the neutron diffusion equation inside of cylinder of radius R. For the case of transport equation, the formulation of discrete ordinates S{sub N} consists in discretize the angular variables in N directions and in using a quadrature angular set for approximate the sources of scattering, where the Diffusion equation consist on S{sub 2} approximated transport equation in discrete ordinates. We solved the neutron diffusion equation with an analytical form by the finite Hankel transform. Was presented also the build-up factor for the case that we have neutron flux inside the cylinder. (author)
Energy Technology Data Exchange (ETDEWEB)
Lawrence, R.D.
1983-03-01
A nodal method is developed for the solution of the neutron-diffusion equation in two- and three-dimensional hexagonal geometries. The nodal scheme has been incorporated as an option in the finite-difference diffusion-theory code DIF3D, and is intended for use in the analysis of current LMFBR designs. The nodal equations are derived using higher-order polynomial approximations to the spatial dependence of the flux within the hexagonal-z node. The final equations, which are cast in the form of inhomogeneous response-matrix equations for each energy group, involved spatial moments of the node-interior flux distribution plus surface-averaged partial currents across the faces of the node. These equations are solved using a conventional fission-source iteration accelerated by coarse-mesh rebalance and asymptotic source extrapolation. This report describes the mathematical development and numerical solution of the nodal equations, as well as the use of the nodal option and details concerning its programming structure. This latter information is intended to supplement the information provided in the separate documentation of the DIF3D code.
International Nuclear Information System (INIS)
Lawrence, R.D.
1983-03-01
A nodal method is developed for the solution of the neutron-diffusion equation in two- and three-dimensional hexagonal geometries. The nodal scheme has been incorporated as an option in the finite-difference diffusion-theory code DIF3D, and is intended for use in the analysis of current LMFBR designs. The nodal equations are derived using higher-order polynomial approximations to the spatial dependence of the flux within the hexagonal-z node. The final equations, which are cast in the form of inhomogeneous response-matrix equations for each energy group, involved spatial moments of the node-interior flux distribution plus surface-averaged partial currents across the faces of the node. These equations are solved using a conventional fission-source iteration accelerated by coarse-mesh rebalance and asymptotic source extrapolation. This report describes the mathematical development and numerical solution of the nodal equations, as well as the use of the nodal option and details concerning its programming structure. This latter information is intended to supplement the information provided in the separate documentation of the DIF3D code
International Nuclear Information System (INIS)
Fernandes, Julio Cesar L.; Vilhena, Marco Tullio; Borges, Volnei; Bodmann, Bardo Ernest
2011-01-01
The principal idea of this work, consist on formulate an analytical method to solved problems for diffusion of neutrons with isotropic scattering in one-dimensional cylindrical geometry. In this area were develop many works that study the same problem in different system of coordinates as well as cartesian system, nevertheless using numerical methods to solve the shielding problem. In view of good results in this works, we starting with the idea that we can represent a source in the origin of the cylindrical system by a Delta Dirac distribution, we describe the physical modeling and solved the neutron diffusion equation inside of cylinder of radius R. For the case of transport equation, the formulation of discrete ordinates S N consists in discretize the angular variables in N directions and in using a quadrature angular set for approximate the sources of scattering, where the Diffusion equation consist on S 2 approximated transport equation in discrete ordinates. We solved the neutron diffusion equation with an analytical form by the finite Hankel transform. Was presented also the build-up factor for the case that we have neutron flux inside the cylinder. (author)
International Nuclear Information System (INIS)
Ceolin, Celina
2010-01-01
The objective of this work is to obtain an analytical solution of the neutron diffusion kinetic equation in one-dimensional cartesian geometry, to monoenergetic and multigroup problems. These equations are of the type stiff, due to large differences in the orders of magnitude of the time scales of the physical phenomena involved, which make them difficult to solve. The basic idea of the proposed method is applying the spectral expansion in the scalar flux and in the precursor concentration, taking moments and solving the resulting matrix problem by the Laplace transform technique. Bearing in mind that the equation for the precursor concentration is a first order linear differential equation in the time variable, to enable the application of the spectral method we introduce a fictitious diffusion term multiplied by a positive value which tends to zero. This procedure opened the possibility to find an analytical solution to the problem studied. We report numerical simulations and analysis of the results obtained with the precision controlled by the truncation order of the series. (author)
International Nuclear Information System (INIS)
Masahiro, Tatsumi; Akio, Yamamoto
2003-01-01
A production code SCOPE2 was developed based on the fine-grained parallel algorithm by the red/black iterative method targeting parallel computing environments such as a PC-cluster. It can perform a depletion calculation in a few hours using a PC-cluster with the model based on a 9-group nodal-SP3 transport method in 3-dimensional pin-by-pin geometry for in-core fuel management of commercial PWRs. The present algorithm guarantees the identical convergence process as that in serial execution, which is very important from the viewpoint of quality management. The fine-mesh geometry is constructed by hierarchical decomposition with introduction of intermediate management layer as a block that is a quarter piece of a fuel assembly in radial direction. A combination of a mesh division scheme forcing even meshes on each edge and a latency-hidden communication algorithm provided simplicity and efficiency to message passing to enhance parallel performance. Inter-processor communication and parallel I/O access were realized using the MPI functions. Parallel performance was measured for depletion calculations by the 9-group nodal-SP3 transport method in 3-dimensional pin-by-pin geometry with 340 x 340 x 26 meshes for full core geometry and 170 x 170 x 26 for quarter core geometry. A PC cluster that consists of 24 Pentium-4 processors connected by the Fast Ethernet was used for the performance measurement. Calculations in full core geometry gave better speedups compared to those in quarter core geometry because of larger granularity. Fine-mesh sweep and feedback calculation parts gave almost perfect scalability since granularity is large enough, while 1-group coarse-mesh diffusion acceleration gave only around 80%. The speedup and parallel efficiency for total computation time were 22.6 and 94%, respectively, for the calculation in full core geometry with 24 processors. (authors)
Ay, Nihat; Lê, Hông Vân; Schwachhöfer, Lorenz
2017-01-01
The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemannian geometry and Banach space theory. Parametrised measure models are defined as fundamental geometric objects, which can be both finite or infinite dimensional. Based on these models, canonical tensor fields are introduced and further studied, including the Fisher metric and the Amari-Chentsov tensor, and embeddings of statistical manifolds are investigated. This novel foundation then leads to application highlights, such as generalizations and extensions of the classical uniqueness result of Chentsov or the Cramér-Rao inequality. Additionally, several new application fields of information geometry are highlighted, for instance hierarchical and graphical models, complexity theory, population genetics, or Markov Chain Monte Carlo. The book will be of interest to mathematicians who are interested in geometry, inf...
Energy Technology Data Exchange (ETDEWEB)
Tkach, Y., E-mail: Yuri.Tkach@WGIM.com [Department of Civil and Structural Engineering, School of MACE, UMIST/University of Manchester, PO Box 88, Manchester M60 1QD (United Kingdom); Burdekin, F.M., E-mail: mburdekin@aol.com [Department of Civil and Structural Engineering, School of MACE, UMIST/University of Manchester, PO Box 88, Manchester M60 1QD (United Kingdom)
2012-05-15
This paper reports the second stage of an extensive series of detailed three-dimensional elastic-plastic finite element analyses on the influence of fracture mechanics test specimen geometry and different material properties on constraint and triaxiality in the near crack tip region. The specimens studied were pre-cracked plain-sided and side-grooved Charpy sized specimens, plain-sided and side-grooved compact tension specimens of thickness B = 25 mm and plain-sided compact tension specimens of thickness B = 100 mm all with the ratio of the crack length to the specimen width a/W = 0.5. Stress-strain curves of materials of different yield strength and strain hardening behaviour spanning the range of practical interest for typical structural steels were implemented into the finite element models. The level of constraint in the specimens modelled has been characterised in terms of both the Q-stress parameter and the ratio of hydrostatic to the equivalent stress components. It has been established that in-plane constraint in the fracture toughness test pieces is significantly affected by the absolute ligament size of the specimen. It has also been shown that the strain hardening behaviour is one of the major material parameters defining constraint level in the fracture toughness specimen. - Highlights: Black-Right-Pointing-Pointer 3D FE analyses on plain and side-grooved Charpy sized and CT specimens of two sizes. Black-Right-Pointing-Pointer Crack tip constraint analysed for Q-stress and hydrostatic/equivalent stress ratio. Black-Right-Pointing-Pointer In-plane constraint is significantly affected by the absolute ligament size. Black-Right-Pointing-Pointer Constraint level is significantly affected by material strain hardening behaviour.
International Nuclear Information System (INIS)
Tkach, Y.; Burdekin, F.M.
2012-01-01
This paper reports the second stage of an extensive series of detailed three-dimensional elastic-plastic finite element analyses on the influence of fracture mechanics test specimen geometry and different material properties on constraint and triaxiality in the near crack tip region. The specimens studied were pre-cracked plain-sided and side-grooved Charpy sized specimens, plain-sided and side-grooved compact tension specimens of thickness B = 25 mm and plain-sided compact tension specimens of thickness B = 100 mm all with the ratio of the crack length to the specimen width a/W = 0.5. Stress–strain curves of materials of different yield strength and strain hardening behaviour spanning the range of practical interest for typical structural steels were implemented into the finite element models. The level of constraint in the specimens modelled has been characterised in terms of both the Q-stress parameter and the ratio of hydrostatic to the equivalent stress components. It has been established that in-plane constraint in the fracture toughness test pieces is significantly affected by the absolute ligament size of the specimen. It has also been shown that the strain hardening behaviour is one of the major material parameters defining constraint level in the fracture toughness specimen. - Highlights: ► 3D FE analyses on plain and side-grooved Charpy sized and CT specimens of two sizes. ► Crack tip constraint analysed for Q-stress and hydrostatic/equivalent stress ratio. ► In-plane constraint is significantly affected by the absolute ligament size. ► Constraint level is significantly affected by material strain hardening behaviour.
International Nuclear Information System (INIS)
Perez Guerrero, Jesus Salvador
1995-01-01
Laminar developing flow in channels of arbitrary geometry was studied by solving the Navier-Stokes equations in the stream function-only formulation through the Generalized Integral Transform Technique (GITT). The stream function is expanded in an infinite system based on eigenfunctions obtained by considering solely the diffusive terms of the original formulation. The Navier-Stokes equations are transformed into an infinite system of ordinary differential equations, by using the transformation and inversion formulae. For computational purposes, the infinite series is truncated, according to an automatic error control procedure. The ordinary differential is solved through well-established scientific subroutines from widely available mathematical libraries. The classical problem of developing flow between parallel-plates is analysed first, as for both uniform and irrotational inlet conditions. The effect of truncating the duct length in the accuracy of the obtained solution is studied. A convergence analysis of the results obtained by the GITT is performed and compared with results obtained by finite difference and finite element methods, for different values of Reynolds number. The problem of flow over a backward-facing step then follows. Comparisons with experimental results in the literature indicate an excellent agreement. The numerical co-validation was established for a test case, and perfect agreement is reached against results considered as benchmarks in the recent literature. The results were shown to be physically more reasonable than others obtained by purely numerical methods, in particular for situations where three-dimensional effects are identified. Finally, a test problem for an irregular by shoped duct was studied and compared against results found in the literature, with good agreement and excellent convergence rates for the stream function field along the whole channel, for different values of Reynolds number. (author)
International Nuclear Information System (INIS)
Bottoni, M.; Dorr, B.; Homann, C.; Struwe, D.
1983-07-01
The computer programme BACCHUS implemented at KfK includes a steady-state version, a two-dimensional and a three-dimensional transient single-phase flow version describing the thermal-hydraulic behaviour of the coolant (sodium or water) in bundle geometry under nominal or accident conditions. All versions are coupled with a pin model describing the temperature distribution in fuel (or electrical heaters) and cladding. The report describes the programme from the viewpoints of the geometrical model, the mathematical foundations and the numerical treatment of the basic equations. Although emphasis is put on the three-dimensional version, the two-dimensional and the steady state versions are also documented in self-consistent sections. (orig.) [de
DEFF Research Database (Denmark)
Jiménez, Roberto; Torralba, Marta; Yagüe-Fabra, José A.
2017-01-01
The dimensional verification of miniaturized components with 3D complex geometries is particularly challenging. Computed Tomography (CT) can represent a suitable alternative solution to micro metrology tools based on optical and tactile techniques. However, the establishment of CT systems......’ traceability when measuring 3D complex geometries is still an open issue. In this work, an alternative method for the measurement uncertainty assessment of 3D complex geometries by using CT is presented. The method is based on the micro-CT system Maximum Permissible Error (MPE) estimation, determined...... experimentally by using several calibrated reference artefacts. The main advantage of the presented method is that a previous calibration of the component by a more accurate Coordinate Measuring System (CMS) is not needed. In fact, such CMS would still hold all the typical limitations of optical and tactile...
International Nuclear Information System (INIS)
Rakopoulos, C.D.; Kosmadakis, G.M.; Pariotis, E.G.
2010-01-01
The present work investigates the effect of varying the combustion chamber geometry and engine rotational speed on the gas flow and temperature field, using a new quasi-dimensional engine simulation model in conjunction with an in-house developed computational fluid dynamics (CFD) code served to validate the predicted in-cylinder flow field and gas temperature distribution calculated by the quasi-dimensional model, for three alternative piston bowl geometries and three rotational speeds. This CFD code can simulate three-dimensional curvilinear domains using the finite volume method in a collocated grid; it solves the generalized transport equation for the conservation of mass, momentum and energy, and incorporates the standard k-ε turbulence model with some slight modifications to introduce the compressibility of a fluid in generalized coordinates. On the other hand, the quasi-dimensional model solves the general transport equation for the conservation of mass and energy by a finite volume method throughout the entire in-cylinder volume, while for the estimation of the flow field a new simplified three dimensional air motion model is used. To compare these two models the in-cylinder spatial and temporal temperature distribution, the mean cylinder pressure diagram, as well as the mean in-cylinder radial and axial velocity are examined, for the three piston bowl geometries and the three speeds, for a high speed direct injection (HSDI) diesel engine operating under motoring conditions. From the comparison of calculated results, it becomes apparent that the two models predict similar in-cylinder temperature distributions and mean air velocity fields at each crank angle, for all cases examined. Thus, it is shown that the quasi-dimensional model with the proposed simplified air motion model is capable of capturing the physical effect of combustion chamber geometry and speed on the in-cylinder velocity and temperature field, while needing significantly lower computing
Yoshida, M.
2010-12-01
A new numerical simulation model of mantle convection with a compositionally and rheologically heterogeneous, deformable, mobile continental lithosphere is presented for the first time by using three-dimensional regional spherical-shell geometry (Yoshida, 2010, Earth Planet. Sci. Lett.). The numerical results revealed that one of major factor that realizes the supercontinental breakup and subsequent continental drift is a pre-existing, weak (low-viscosity) continental margin (WCM) in the supercontinent. Characteristic tectonic structures such as young orogenic belts and suture zones in a continent are expected to be mechanically weaker than the stable part of the continental lithosphere with the cratonic root (or cratonic lithosphere) and yield lateral viscosity variations in the continental lithosphere. In the present-day Earth's lithosphere, the pre-existing, mechanically weak zones emerge as a diffuse plate boundary. However, the dynamic role of the WCM in the stability of continental lithosphere has not been understood in terms of geophysics. In my numerical model, a compositionally buoyant and highly viscous continental assemblage with pre-existing WCMs, analogous to the past supercontinent, is modeled and imposed on well-developed mantle convection whose vigor of convection, internal heating rate, and rheological parameters are appropriate for the Earth's mantle. The visco-plastic oceanic lithosphere and the associated subduction of oceanic plates are incorporated. The time integration of the advection of continental materials with zero chemical diffusion is performed by a tracer particle method. The time evolution of mantle convection after setting the model supercontinent is followed over 800 Myr. Earth-like continental drift is successfully reproduced, and the characteristic thermal interaction between the mantle and the continent/supercontinent is observed in my new numerical model. Results reveal that the WCM protects the cratonic lithosphere from being
Directory of Open Access Journals (Sweden)
Alexander Burinskii
2013-01-01
Full Text Available The 4D Kerr geometry displays many wonderful relations with quantum world and, in particular, with superstring theory. The lightlike structure of fields near the Kerr singular ring is similar to the structure of Sen solution for a closed heterotic string. Another string, open and complex, appears in the complex representation of the Kerr geometry initiated by Newman. Combination of these strings forms a membrane source of the Kerr geometry which is parallel to the structure of M-theory. In this paper we give one more evidence of this relationship, emergence of the Calabi-Yau twofold (K3 surface in twistorial structure of the Kerr geometry as a consequence of the Kerr theorem. Finally, we indicate that the Kerr stringy system may correspond to a complex embedding of the critical N = 2 superstring.
Spinning geometry = Twisted geometry
International Nuclear Information System (INIS)
Freidel, Laurent; Ziprick, Jonathan
2014-01-01
It is well known that the SU(2)-gauge invariant phase space of loop gravity can be represented in terms of twisted geometries. These are piecewise-linear-flat geometries obtained by gluing together polyhedra, but the resulting geometries are not continuous across the faces. Here we show that this phase space can also be represented by continuous, piecewise-flat three-geometries called spinning geometries. These are composed of metric-flat three-cells glued together consistently. The geometry of each cell and the manner in which they are glued is compatible with the choice of fluxes and holonomies. We first remark that the fluxes provide each edge with an angular momentum. By studying the piecewise-flat geometries which minimize edge lengths, we show that these angular momenta can be literally interpreted as the spin of the edges: the geometries of all edges are necessarily helices. We also show that the compatibility of the gluing maps with the holonomy data results in the same conclusion. This shows that a spinning geometry represents a way to glue together the three-cells of a twisted geometry to form a continuous geometry which represents a point in the loop gravity phase space. (paper)
Energy Technology Data Exchange (ETDEWEB)
Slater, C.O.
1990-07-01
Results are reported for two-dimensional discrete ordinates, X-Y geometry calculations performed for seven Halden Heavy Boiling Water Reactor core configurations. The calculations were performed in support of an effort to reassess the neutron fluence received by the reactor vessel. Nickel foil measurement data indicated considerable underprediction of fluences by the previously used multigroup removal- diffusion method. Therefore, calculations by a more accurate method were deemed appropriate. For each core configuration, data are presented for (1) integral fluxes in the core and near the vessel wall, (2) neutron spectra at selected locations, (3) isoflux contours superimposed on the geometry models, (4) plots of the geometry models, and (5) input for the calculations. The initial calculations were performed with several mesh sizes. Comparisons of the results from these calculations indicated that the uncertainty in the calculated fluxes should be less than 10%. However, three-dimensional effects (such as axial asymmetry in the fuel loading) could contribute to much greater uncertainty in the calculated neutron fluxes. 7 refs., 22 figs., 11 tabs.
International Nuclear Information System (INIS)
Kumar, Jagadeesha; Attridge, Alex; Williams, Mark A; Wood, P K C
2011-01-01
Industrial x-ray computed tomography (CT) scanners are used for non-contact dimensional measurement of small, fragile components and difficult-to-access internal features of castings and mouldings. However, the accuracy and repeatability of measurements are influenced by factors such as cone-beam system geometry, test object configuration, x-ray power, material and size of test object, detector characteristics and data analysis methods. An attempt is made in this work to understand the measurement errors of a CT scanner over the complete scan volume, taking into account only the errors in system geometry and the object configuration within the scanner. A cone-beam simulation model is developed with the radiographic image projection and reconstruction steps. A known amount of errors in geometrical parameters were introduced in the model to understand the effect of geometry of the cone-beam CT system on measurement accuracy for different positions, orientations and sizes of the test object. Simulation analysis shows that the geometrical parameters have a significant influence on the dimensional measurement at specific configurations of the test object. Finally, the importance of system alignment and estimation of correct parameters for accurate CT measurements is outlined based on the analysis
Directory of Open Access Journals (Sweden)
Jeng Wei
2015-03-01
Conclusion: RT 3D TEE can clearly delineate the geometries of defects in their entirety, including shape, size, and location of the defect and track canal. It would also appear that RT 3D TEE is superior to 2D TEE in the process of guiding the wire through the difficult canal anatomy, facilitating the overall procedure. The small mitral PVLs can be completely occluded, but subsequent complications occurred with large defect closures because of embolization or releak. Therefore, transcatheter closure of PVLs seems to be an attractive alternative for these patients, but newer occluder designs that better conform to leak geometry will be required to improve outcomes.
Talebi, A.
2008-01-01
Key words: Hillslope geometry, Hillslope hydrology, Hillslope stability, Complex hillslopes, Modeling shallow landslides, HSB model, HSB-SM model.
The hydrologic response of a hillslope to rainfall involves a complex, transient saturated-unsaturated interaction that usually leads to a
Reilingh, M.L.; Tuijthof, G.J.M.; Van Dijk, C.N.; Blankevoort, L.
2011-01-01
Background: Malalignment of the hindfoot can be corrected with a calcaneal osteotomy (CO). A well-selected osteotomy angle in the sagittal plane will reduce the shear force in the osteotomy plane while walking. The purpose was to determine the presence of a relationship between the foot geometry and
Reilingh, M. L.; Tuijthof, G. J. M.; van Dijk, C. N.; Blankevoort, L.
2011-01-01
Malalignment of the hindfoot can be corrected with a calcaneal osteotomy (CO). A well-selected osteotomy angle in the sagittal plane will reduce the shear force in the osteotomy plane while walking. The purpose was to determine the presence of a relationship between the foot geometry and loading of
Developments in special geometry
International Nuclear Information System (INIS)
Mohaupt, Thomas; Vaughan, Owen
2012-01-01
We review the special geometry of N = 2 supersymmetric vector and hypermultiplets with emphasis on recent developments and applications. A new formulation of the local c-map based on the Hesse potential and special real coordinates is presented. Other recent developments include the Euclidean version of special geometry, and generalizations of special geometry to non-supersymmetric theories. As applications we discuss the proof that the local r-map and c-map preserve geodesic completeness, and the construction of four- and five-dimensional static solutions through dimensional reduction over time. The shared features of the real, complex and quaternionic version of special geometry are stressed throughout.
International Nuclear Information System (INIS)
Matvienko, Anna; Mandelis, Andreas
2006-01-01
The thermal-wave field in a photopyroelectric thermal-wave cavity was calculated with two theoretical approaches: a computationally straightforward, conventional, one-dimensional approach and a three-dimensional experimentally more realistic approach. The calculations show that the dimensionality of the thermal-wave field in the cavity depends on the lateral heat transfer boundary conditions and the relation between the beam size of the laser impinging on the thermal-wave generating metallic film and the diameter of the film itself. The theoretical calculations and the experimental data on the photopyroelectric signal in the cavity were compared. The study resulted in identifying ranges of heat transfer rates, beam sizes, and cavity radii for which accurate quantitative measurements of the thermal diffusivity of intracavity fluids can be made within the far simpler, but only approximate, one-dimensional approach conventionally adopted by users of thermal-wave cavities. It was shown that the major parameters affecting the dimensionality of thermal-wave cavities are the laser beam spot size and the Biot number of the medium comprising the sidewalls of the (cylindrical) cavity
Directory of Open Access Journals (Sweden)
van Buren Simon
2017-01-01
Full Text Available Frost formation is a common, often undesired phenomenon in heat exchanges such as air coolers. Thus, air coolers have to be defrosted periodically, causing significant energy consumption. For the design and optimization, prediction of defrosting by a CFD tool is desired. This paper presents a one-dimensional transient model approach suitable to be used as a zero-dimensional wall-function in CFD for modeling the defrost process at the fin and tube interfaces. In accordance to previous work a multi stage defrost model is introduced (e.g. [1, 2]. In the first instance the multi stage model is implemented and validated using MATLAB. The defrost process of a one-dimensional frost segment is investigated. Fixed boundary conditions are provided at the frost interfaces. The simulation results verify the plausibility of the designed model. The evaluation of the simulated defrost process shows the expected convergent behavior of the three-stage sequence.
International Nuclear Information System (INIS)
Banks, K.M.; Hare, D.R.; Reid, B.R.
1989-01-01
A three-dimensional solution structure for the self-complementary dodecanucleotide [(d-GCCTGATCAGGC)] 2 has been determined by distance geometry with further refinements being performed after back-calculation of the NOESY spectrum. This DNA dodecamer contains the hexamer [d(TGATCA)] 2 recognized and cut by the restriction endonuclease BclI, and its structure was determined in hopes of obtaining a better understanding of the sequence-specific interactions which occur between proteins and DNA. Preliminary examination of the structure indicates the structure is underwound with respect to idealized B-form DNA though some of the local structural parameters (glycosyl torsion angle and pseudorotation angle) suggest a B-family type of structure is present. This research demonstrates the requirements (resonance assignments, interproton distance measurements, distance geometry calculations, and NOESY spectra back-calculation) to generate experimentally self-consistent solution structures for short DNA sequences
Lagomarsino, M.C.; Dogterom, M.; Dijkstra, Marjolein
2003-01-01
We present computer simulations of long, thin, hard spherocylinders in a narrow planar slit. We observe a transition from the isotropic to a nematic phase with quasi-long-range orientational order upon increasing the density. This phase transition is intrinsically two-dimensional and of
International Nuclear Information System (INIS)
Clore, G.M.; Gronenborn, A.M.; Nilges, M.; Ryan, C.A.
1987-01-01
The solution conformation of potato carboxypeptidase inhibitor (CPI) has been investigated by 1 H NMR spectroscopy. The spectrum is assigned in a sequential manner by using two-dimensional NMR techniques to identify through-bond and through-space (<5 A) connectivities. A set of 309 approximate interproton distance restraints is derived from the two-dimensional nuclear Overhauser enhancement spectra and used as the basis of a three-dimensional structure determination by a combination of metric matrix distance geometry and restrained molecular dynamics calculations. A total of 11 converged distance geometry structures were computed and refined by using restrained molecular dynamics. The average atomic root mean square (rms) difference between the final 11 structures and the mean structure obtained by averaging their coordinates is 1.4 +/- 0.3 A for residues 2-39 and 0.9 +/- 0.2 A for residues 5-37. The corresponding values for all atoms are 1.9 +/- 0.3 and 1.4 +/- 0.2 A, respectively. The computed structures are very close to the X-ray structure of CPI in its complex with carboxypeptidase, and the backbone atomic rms difference between the mean of the computed structures and the X-ray structure is only 1.2 A. Nevertheless, there are some real differences present which are evidenced by significant deviations between the experimental upper interproton distance limits and the corresponding interproton distances derived from the X-ray structure. These principally occur in two regions, residues 18-20 and residues 28-30, the latter comprising part of the region of secondary contact between CPI and carboxypeptidase in the X-ray structure
Khan, Farman U; Qamar, Shamsul
2017-05-01
A set of analytical solutions are presented for a model describing the transport of a solute in a fixed-bed reactor of cylindrical geometry subjected to the first (Dirichlet) and third (Danckwerts) type inlet boundary conditions. Linear sorption kinetic process and first-order decay are considered. Cylindrical geometry allows the use of large columns to investigate dispersion, adsorption/desorption and reaction kinetic mechanisms. The finite Hankel and Laplace transform techniques are adopted to solve the model equations. For further analysis, statistical temporal moments are derived from the Laplace-transformed solutions. The developed analytical solutions are compared with the numerical solutions of high-resolution finite volume scheme. Different case studies are presented and discussed for a series of numerical values corresponding to a wide range of mass transfer and reaction kinetics. A good agreement was observed in the analytical and numerical concentration profiles and moments. The developed solutions are efficient tools for analyzing numerical algorithms, sensitivity analysis and simultaneous determination of the longitudinal and transverse dispersion coefficients from a laboratory-scale radial column experiment. © The Author 2017. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.
International Nuclear Information System (INIS)
Naymeh, L.
2013-01-01
The method of characteristics is a flexible and efficient method solving the transport equation. It has been largely used in two dimension calculations because it enables to study complex geometries and it has a good time/precision ratio. However, despite a great improvement in storage capacities and computing power, a direct three dimension calculation is still unreachable. In the following work, we introduce and analyze several modifications of the method of characteristics (MOC) in order to reduce the memory usage as well as calculation burden. This document aims at studying a higher order spatial approximation for the flux. It steps away from the classical method (constant MOC) by introducing an increase of details of the representation of the flux, which may enable to reduce the size of the grid while keeping a good precision. Numerical results tested on benchmarks show an improvement of time/precision ratio. Regarding the memory storage, the number of trajectories has an influence on the amount of data to be stored. Hence, we study a tracking method based on local tracks defined for all sub-domains having the same geometry. Redundancies happening in a reactor core suggest an important reduction of required memory. Two tracking methods have been studied, the first one being a non-uniform tracking method including sub-domain discontinuities and the other being a method based on periodic and continuous trajectories for a sub-domain to another. (author) [fr
Energy Technology Data Exchange (ETDEWEB)
Liu, S.; Lawton, D. C.; Spratt, D. A. [Calgary Univ., AB (Canada). Dept. of Geology and Geophysics
1996-06-01
Geometry of the triangle zone and its variations in the region lying between the Berland River and the Smoky River in the central Alberta Foothills was described by drawing closely spaced balanced structural cross-sections, constrained by seismic data interpretation and well-log analysis. The stratigraphic sequence (Devonian to Tertiary in the northwest, or Mississipian to Tertiary in the southeast) was found to have been divided into three structural packages by three detachments. In the northwest, the lower detachment lies in the Lower Devonian Woodbend Group, the middle detachment in the Shaftesbury Formation, and the upper detachment in the upper Kaskapau Formation. Each of these detachment combined with the foreland-verging thrust sheet beneath them to form the triangle zone structure. Based on the peculiarities of the geology, it is suspected that the higher triangle zone was formed before the lower triangle zone. 31 refs., 10 figs.
Jiménez, Roberto; Torralba, Marta; Yagüe-Fabra, José A; Ontiveros, Sinué; Tosello, Guido
2017-05-16
The dimensional verification of miniaturized components with 3D complex geometries is particularly challenging. Computed Tomography (CT) can represent a suitable alternative solution to micro metrology tools based on optical and tactile techniques. However, the establishment of CT systems' traceability when measuring 3D complex geometries is still an open issue. In this work, an alternative method for the measurement uncertainty assessment of 3D complex geometries by using CT is presented. The method is based on the micro-CT system Maximum Permissible Error (MPE) estimation, determined experimentally by using several calibrated reference artefacts. The main advantage of the presented method is that a previous calibration of the component by a more accurate Coordinate Measuring System (CMS) is not needed. In fact, such CMS would still hold all the typical limitations of optical and tactile techniques, particularly when measuring miniaturized components with complex 3D geometries and their inability to measure inner parts. To validate the presented method, the most accepted standard currently available for CT sensors, the Verein Deutscher Ingenieure/Verband Deutscher Elektrotechniker (VDI/VDE) guideline 2630-2.1 is applied. Considering the high number of influence factors in CT and their impact on the measuring result, two different techniques for surface extraction are also considered to obtain a realistic determination of the influence of data processing on uncertainty. The uncertainty assessment of a workpiece used for micro mechanical material testing is firstly used to confirm the method, due to its feasible calibration by an optical CMS. Secondly, the measurement of a miniaturized dental file with 3D complex geometry is carried out. The estimated uncertainties are eventually compared with the component's calibration and the micro manufacturing tolerances to demonstrate the suitability of the presented CT calibration procedure. The 2U/T ratios resulting from the
Energy Technology Data Exchange (ETDEWEB)
Fernandes, Julio C.L.; Vilhena, Marco T.; Bodmann, Bardo E.J., E-mail: julio.lombaldo@ufrgs.br, E-mail: mtmbvilhena@gmail.com, E-mail: bardo.bodmann@ufrgs.br [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Dept. de Matematica Pura e Aplicada; Dulla, Sandra; Ravetto, Piero, E-mail: sandra.dulla@polito.it, E-mail: piero.ravetto@polito.it [Dipartimento di Energia, Politecnico di Torino, Piemonte (Italy)
2015-07-01
In this work we generalize the solution of the one-dimensional neutron transport equation to a multi- group approach in planar geometry. The basic idea of this work consists in consider the hierarchical construction of a solution for a generic number G of energy groups, starting from a mono-energetic solution. The hierarchical method follows the reasoning of the decomposition method. More specifically, the additional terms from adding energy groups is incorporated into the recursive scheme as source terms. This procedure leads to an analytical representation for the solution with G energy groups. The recursion depth is related to the accuracy of the solution, that may be evaluated after each recursion step. The authors present a heuristic analysis of stability for the results. Numerical simulations for a specific example with four energy groups and a localized pulsed source. (author)
Negen, James; Roome, Hannah E; Keenaghan, Samantha; Nardini, Marko
2018-06-01
Spatial memory is an important aspect of adaptive behavior and experience, providing both content and context to the perceptions and memories that we form in everyday life. Young children's abilities in this realm shift from mainly egocentric (self-based) to include allocentric (world-based) codings at around 4 years of age. However, information about the cognitive mechanisms underlying acquisition of these new abilities is still lacking. We examined allocentric spatial recall in 4.5- to 8.5-year-olds, looking for continuity with navigation as previously studied in 2- to 4-year-olds and other species. We specifically predicted an advantage for three-dimensional landmarks over two-dimensional ones and for recalling targets "in the middle" versus elsewhere. However, we did not find compelling evidence for either of these effects, and indeed some analyses even support the opposite of each of these conclusions. There were also no significant interactions with age. These findings highlight the incompleteness of our overall theories of the development of spatial cognition in general and allocentric spatial recall in particular. They also suggest that allocentric spatial recall involves processes that have separate behavioral characteristics from other cognitive systems involved in navigation earlier in life and in other species. Copyright © 2018 Elsevier Inc. All rights reserved.
International Nuclear Information System (INIS)
Altın, İsmail; Bilgin, Atilla
2015-01-01
This study builds on a previous parametric investigation using a thermodynamic-based quasi-dimensional (QD) cycle simulation of a spark-ignition (SI) engine with dual-spark plugs. The previous work examined the effects of plug-number and location on some performance parameters considering an engine with a simple cylindrical disc-shaped combustion chamber. In order to provide QD thermodynamic models applicable to complex combustion chamber geometries, a novel approach is considered here: flame-maps, which utilizes a computer aided design (CAD) software (SolidWorks). Flame maps are produced by the CAD software, which comprise all the possible flame radiuses with an increment of one-mm between them, according to the spark plug positions, spark timing, and piston position near the top dead center. The data are tabulated and stored as matrices. Then, these tabulated data are adapted to the previously reported cycle simulation. After testing for simple disc-shaped chamber geometries, the simulation is applied to a real production automobile (Honda-Fit) engine to perform the parametric study. - Highlights: • QD model was applied in dual plug engine with complex realistic combustion chamber. • This method successfully modeled the combustion in the dual-plug Honda-Fit engine. • The same combustion chamber is tested for various spark plug(s) locations. • The centrally located single spark-plug results in the fastest combustion
Arias, Ana; Paqué, Frank; Shyn, Stephanie; Murphy, Sarah; Peters, Ove A
2018-04-01
The purpose of this study was to assess the geometry of non-round root canals after preparation with TRUShape (a novel instrument with s-shaped longitudinal design) in comparison to conventional rotary instrumentation using micro-computed tomography. Twenty distal root canals of mandibular molars were randomly distributed in two groups to be shaped with either TRUShape or Vortex rotaries. Percentages of unprepared surface and volume of dentin removal for the entire canal and for the apical 4 mm were calculated. Canal transportation and the structure model index (SMI) were assessed. Data were compared with Student t-tests. Shaping with both techniques resulted in similar prepared surface and volume of dentin removed, as well as the extent of canal transportation. The SMI shape factor was significantly lower for TRUShape preparations (P = 0.04) suggesting less rounding during rotary preparation. Although both instruments were suitable for the preparation of oval canals, TRUShape appeared to better conform to the original ribbon-shaped anatomy. © 2017 Australian Society of Endodontology Inc.
Energy Technology Data Exchange (ETDEWEB)
Kwon, Ryun-Young [College of Science, George Mason University, 4400 University Drive, Fairfax, VA 22030 (United States); Vourlidas, Angelos [The Johns Hopkins University, Applied Physics Laboratory, Laurel, MD 20723 (United States); Webb, David, E-mail: rkwon@gmu.edu [ISR, Boston College, Chestnut Hill, MA (United States)
2016-07-20
Motivated by the standard flare model, ray-like structures in the wake of coronal mass ejections (CMEs) have been often interpreted as proxies of the reconnecting current sheet connecting the CME with the postflare arcade. We present the three-dimensional properties of a post-CME ray derived from white light images taken from three different viewing perspectives on 2013 September 21. By using a forward modeling method, the direction, cross section, and electron density are determined within the heliocentric distance range of 5–9 R {sub ⊙}. The width and depth of the ray are 0.42 ± 0.08 R {sub ⊙} and 1.24 ± 0.35 R {sub ⊙}, respectively, and the electron density is (2.0 ± 0.5) × 10{sup 4} cm{sup 3}, which seems to be constant with height. Successive blobs moving outward along the ray are observed around 13 hr after the parent CME onset. We model the three-dimensional geometry of the parent CME with the Gradual Cylindrical Shell model and find that the CME and ray are coaxial. We suggest that coaxial post-CME rays, seen in coronagraph images, with successive formation of blobs could be associated with current sheets undergoing magnetic reconnection in the late stage of CMEs.
International Nuclear Information System (INIS)
Tanaka, Masa-aki; Kamide, Hideki
2001-02-01
This investigation deals with the porous blockage in a wire spacer type fuel subassembly in Fast Breeder Reactors (FBR's). Multi-dimensional analysis method for a porous blockage in a fuel subassembly is developed using the standard k-ε turbulence model with the typical correlations in handbooks. The purpose of this analysis method is to evaluate the position and the magnitude of the maximum temperature, and to investigate the thermo-hydraulic phenomena in the porous blockage. Verification of this analysis method was conducted based on the results of 4-subchannel geometry water test. It was revealed that the evaluation of the porosity distribution and the particle diameter in a porous blockage was important to predict the temperature distribution. This analysis method could simulate the spatial characteristic of velocity and temperature distributions in the blockage and evaluate the pin surface temperature inside the porous blockage. Through the verification of this analysis method, it is shown that this multi-dimensional analysis method is useful to predict the thermo-hydraulic field and the highest temperature in a porous blockage. (author)
Nakanishi, A.; Shimomura, N.; Kodaira, S.; Obana, K.; Takahashi, T.; Yamamoto, Y.; Yamashita, M.; Takahashi, N.; Kaneda, Y.
2012-12-01
In the Nankai Trough subduction seismogenic zone, the Nankai and Tonankai earthquakes had often occurred simultaneously, and caused a great event. In order to reduce a great deal of damage to coastal area from both strong ground motion and tsunami generation, it is necessary to understand rupture synchronization and segmentation of the Nankai megathrust earthquake. For a precise estimate of the rupture zone of the Nankai megathrust event based on the knowledge of realistic earthquake cycle and variation of magnitude, it is important to know the geometry and property of the plate boundary of the subduction seismogenic zone. To improve a physical model of the Nankai Trough seismogenic zone, the large-scale high-resolution wide-angle and reflection (MCS) seismic study, and long-term observation has been conducted since 2008. Marine active source seismic data have been acquired along grid two-dimensional profiles having the total length of ~800km every year. A three-dimensional seismic tomography using active and passive seismic data observed both land and ocean bottom stations have been also performed. From those data, we found that several strong lateral variations of the subducting Philippine Sea plate and overriding plate corresponding to margins of coseismic rupture zone of historical large event occurred along the Nankai Trough. Particularly a possible prominent reflector for the forearc Moho is recently imaged in the offshore side in the Kii channel at the depth of ~18km which is shallower than those of other area along the Nankai Trough. Such a drastic variation of the overriding plate might be related to the existence of the segmentation of the Nankai megathrust earthquake. Based on our results derived from seismic studies, we have tried to make a geometrical model of the Philippine Sea plate and a three-dimensional velocity structure model of the Nankai Trough seismogenic zone. In this presentation, we will summarize major results of out seismic studies, and
Ceresole, Anna; Gnecchi, Alessandra; Marrani, Alessio
2013-01-01
We analyze some properties of the four dimensional supergravity theories which originate from five dimensions upon reduction. They generalize to N>2 extended supersymmetries the d-geometries with cubic prepotentials, familiar from N=2 special K\\"ahler geometry. We emphasize the role of a suitable parametrization of the scalar fields and the corresponding triangular symplectic basis. We also consider applications to the first order flow equations for non-BPS extremal black holes.
Iversen, Birger
1992-01-01
Although it arose from purely theoretical considerations of the underlying axioms of geometry, the work of Einstein and Dirac has demonstrated that hyperbolic geometry is a fundamental aspect of modern physics
van den Broek, P.M.
1984-01-01
The aim of this paper is to give a detailed exposition of the relation between the geometry of twistor space and the geometry of Minkowski space. The paper has a didactical purpose; no use has been made of differential geometry and cohomology.
Geometry on the space of geometries
International Nuclear Information System (INIS)
Christodoulakis, T.; Zanelli, J.
1988-06-01
We discuss the geometric structure of the configuration space of pure gravity. This is an infinite dimensional manifold, M, where each point represents one spatial geometry g ij (x). The metric on M is dictated by geometrodynamics, and from it, the Christoffel symbols and Riemann tensor can be found. A ''free geometry'' tracing a geodesic on the manifold describes the time evolution of space in the strong gravity limit. In a regularization previously introduced by the authors, it is found that M does not have the same dimensionality, D, everywhere, and that D is not a scalar, although it is covariantly constant. In this regularization, it is seen that the path integral measure can be absorbed in a renormalization of the cosmological constant. (author). 19 refs
Spacetime and Euclidean geometry
Brill, Dieter; Jacobson, Ted
2006-04-01
Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a two-dimensional spacetime diagram is proportional to the Euclidean area of the corresponding causal domain. We use this relation to derive the Minkowski line element by two geometric proofs of the spacetime Pythagoras theorem.
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
Kollár, János
1997-01-01
This volume contains the lectures presented at the third Regional Geometry Institute at Park City in 1993. The lectures provide an introduction to the subject, complex algebraic geometry, making the book suitable as a text for second- and third-year graduate students. The book deals with topics in algebraic geometry where one can reach the level of current research while starting with the basics. Topics covered include the theory of surfaces from the viewpoint of recent higher-dimensional developments, providing an excellent introduction to more advanced topics such as the minimal model program. Also included is an introduction to Hodge theory and intersection homology based on the simple topological ideas of Lefschetz and an overview of the recent interactions between algebraic geometry and theoretical physics, which involve mirror symmetry and string theory.
Kaehler geometry and SUSY mechanics
International Nuclear Information System (INIS)
Bellucci, Stefano; Nersessian, Armen
2001-01-01
We present two examples of SUSY mechanics related with Kaehler geometry. The first system is the N = 4 supersymmetric one-dimensional sigma-model proposed in hep-th/0101065. Another system is the N = 2 SUSY mechanics whose phase space is the external algebra of an arbitrary Kaehler manifold. The relation of these models with antisymplectic geometry is discussed
Pottmann, Helmut; Eigensatz, Michael; Vaxman, Amir; Wallner, Johannes
2014-01-01
Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural geometry, meanwhile contains a great wealth of individual contributions which are relevant in various fields. For mathematicians, the relation to discrete differential geometry is significant, in particular the integrable system viewpoint. Besides, new application contexts have become available for quite some old-established concepts. Regarding graphics and geometry processing, architectural geometry yields interesting new questions but also new objects, e.g. replacing meshes by other combinatorial arrangements. Numerical optimization plays a major role but in itself would be powerless without geometric understanding. Summing up, architectural geometry has become a rewarding field of study. We here survey the main directions which have been pursued, we show real projects where geometric considerations have played a role, and we outline open problems which we think are significant for the future development of both theory and practice of architectural geometry.
Pottmann, Helmut
2014-11-26
Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural geometry, meanwhile contains a great wealth of individual contributions which are relevant in various fields. For mathematicians, the relation to discrete differential geometry is significant, in particular the integrable system viewpoint. Besides, new application contexts have become available for quite some old-established concepts. Regarding graphics and geometry processing, architectural geometry yields interesting new questions but also new objects, e.g. replacing meshes by other combinatorial arrangements. Numerical optimization plays a major role but in itself would be powerless without geometric understanding. Summing up, architectural geometry has become a rewarding field of study. We here survey the main directions which have been pursued, we show real projects where geometric considerations have played a role, and we outline open problems which we think are significant for the future development of both theory and practice of architectural geometry.
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
Yale, Paul B
2012-01-01
This book is an introduction to the geometry of Euclidean, affine, and projective spaces with special emphasis on the important groups of symmetries of these spaces. The two major objectives of the text are to introduce the main ideas of affine and projective spaces and to develop facility in handling transformations and groups of transformations. Since there are many good texts on affine and projective planes, the author has concentrated on the n-dimensional cases.Designed to be used in advanced undergraduate mathematics or physics courses, the book focuses on ""practical geometry,"" emphasi
Kemnitz, Arnfried
Der Grundgedanke der Analytischen Geometrie besteht darin, dass geometrische Untersuchungen mit rechnerischen Mitteln geführt werden. Geometrische Objekte werden dabei durch Gleichungen beschrieben und mit algebraischen Methoden untersucht.
Lefschetz, Solomon
2005-01-01
An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this text for advanced undergraduate students is particularly relevant to those more familiar with analysis than algebra. 1953 edition.
Introduction to combinatorial geometry
International Nuclear Information System (INIS)
Gabriel, T.A.; Emmett, M.B.
1985-01-01
The combinatorial geometry package as used in many three-dimensional multimedia Monte Carlo radiation transport codes, such as HETC, MORSE, and EGS, is becoming the preferred way to describe simple and complicated systems. Just about any system can be modeled using the package with relatively few input statements. This can be contrasted against the older style geometry packages in which the required input statements could be large even for relatively simple systems. However, with advancements come some difficulties. The users of combinatorial geometry must be able to visualize more, and, in some instances, all of the system at a time. Errors can be introduced into the modeling which, though slight, and at times hard to detect, can have devastating effects on the calculated results. As with all modeling packages, the best way to learn the combinatorial geometry is to use it, first on a simple system then on more complicated systems. The basic technique for the description of the geometry consists of defining the location and shape of the various zones in terms of the intersections and unions of geometric bodies. The geometric bodies which are generally included in most combinatorial geometry packages are: (1) box, (2) right parallelepiped, (3) sphere, (4) right circular cylinder, (5) right elliptic cylinder, (6) ellipsoid, (7) truncated right cone, (8) right angle wedge, and (9) arbitrary polyhedron. The data necessary to describe each of these bodies are given. As can be easily noted, there are some subsets included for simplicity
2002-01-01
Discrete geometry investigates combinatorial properties of configurations of geometric objects. To a working mathematician or computer scientist, it offers sophisticated results and techniques of great diversity and it is a foundation for fields such as computational geometry or combinatorial optimization. This book is primarily a textbook introduction to various areas of discrete geometry. In each area, it explains several key results and methods, in an accessible and concrete manner. It also contains more advanced material in separate sections and thus it can serve as a collection of surveys in several narrower subfields. The main topics include: basics on convex sets, convex polytopes, and hyperplane arrangements; combinatorial complexity of geometric configurations; intersection patterns and transversals of convex sets; geometric Ramsey-type results; polyhedral combinatorics and high-dimensional convexity; and lastly, embeddings of finite metric spaces into normed spaces. Jiri Matousek is Professor of Com...
Burdette, A C
1971-01-01
Analytic Geometry covers several fundamental aspects of analytic geometry needed for advanced subjects, including calculus.This book is composed of 12 chapters that review the principles, concepts, and analytic proofs of geometric theorems, families of lines, the normal equation of the line, and related matters. Other chapters highlight the application of graphing, foci, directrices, eccentricity, and conic-related topics. The remaining chapters deal with the concept polar and rectangular coordinates, surfaces and curves, and planes.This book will prove useful to undergraduate trigonometric st
Berger, Marcel
2010-01-01
Both classical geometry and modern differential geometry have been active subjects of research throughout the 20th century and lie at the heart of many recent advances in mathematics and physics. The underlying motivating concept for the present book is that it offers readers the elements of a modern geometric culture by means of a whole series of visually appealing unsolved (or recently solved) problems that require the creation of concepts and tools of varying abstraction. Starting with such natural, classical objects as lines, planes, circles, spheres, polygons, polyhedra, curves, surfaces,
Robinson, Gilbert de B
2011-01-01
This brief undergraduate-level text by a prominent Cambridge-educated mathematician explores the relationship between algebra and geometry. An elementary course in plane geometry is the sole requirement for Gilbert de B. Robinson's text, which is the result of several years of teaching and learning the most effective methods from discussions with students. Topics include lines and planes, determinants and linear equations, matrices, groups and linear transformations, and vectors and vector spaces. Additional subjects range from conics and quadrics to homogeneous coordinates and projective geom
Connes, Alain
1994-01-01
This English version of the path-breaking French book on this subject gives the definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics developed by Alain Connes. Profusely illustrated and invitingly written, this book is ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics, quantization, and elementary particles and fields.Key Features* First full treatment of the subject and its applications* Written by the pioneer of this field* Broad applications in mathemat
Energy Technology Data Exchange (ETDEWEB)
Fletcher, J K
1973-05-01
CTD is a computer program written in Fortran 4 to solve the multi-group diffusion theory equations in X, Y, Z and triangular Z geometries. A power print- out neutron balance and breeding gain are also produced. 4 references. (auth)
Ng, A.C.; Delgado, V.; Kley, F. van der; Shanks, M.; Veire, N.R. van de; Bertini, M.; Nucifora, G.; Bommel, R.J. van; Tops, L.F.; Weger, A. de; Tavilla, G.; Roos, A. de; Kroft, L.J.; Leung, D.Y.; Schuijf, J.; Schalij, M.J.; Bax, J.J.
2010-01-01
BACKGROUND: 3D transesophageal echocardiography (TEE) may provide more accurate aortic annular and left ventricular outflow tract (LVOT) dimensions and geometries compared with 2D TEE. We assessed agreements between 2D and 3D TEE measurements with multislice computed tomography (MSCT) and changes in
Cosentino Lagomarsino, M.; Tanase, C.; Vos, J.W.; Emons, A.M.C.; Mulder, B.; Dogterom, M.
2007-01-01
Microtubules or microtubule bundles in cells often grow longer than the size of the cell, which causes their shape and organization to adapt to constraints imposed by the cell geometry. We test the reciprocal role of elasticity and confinement in the organization of growing microtubules in a
Sources of hyperbolic geometry
Stillwell, John
1996-01-01
This book presents, for the first time in English, the papers of Beltrami, Klein, and Poincaré that brought hyperbolic geometry into the mainstream of mathematics. A recognition of Beltrami comparable to that given the pioneering works of Bolyai and Lobachevsky seems long overdue-not only because Beltrami rescued hyperbolic geometry from oblivion by proving it to be logically consistent, but because he gave it a concrete meaning (a model) that made hyperbolic geometry part of ordinary mathematics. The models subsequently discovered by Klein and Poincaré brought hyperbolic geometry even further down to earth and paved the way for the current explosion of activity in low-dimensional geometry and topology. By placing the works of these three mathematicians side by side and providing commentaries, this book gives the student, historian, or professional geometer a bird's-eye view of one of the great episodes in mathematics. The unified setting and historical context reveal the insights of Beltrami, Klein, and Po...
Indian Academy of Sciences (India)
mathematicians are trained to use very precise language, and so find it hard to simplify and state .... thing. If you take a plane on which there are two such triangles which enjoy the above ... within this geometry to simplify things if needed.
Geometry -----------~--------------RESONANCE
Indian Academy of Sciences (India)
Parallel: A pair of lines in a plane is said to be parallel if they do not meet. Mathematicians were at war ... Subsequently, Poincare, Klein, Beltrami and others refined non-. Euclidean geometry. ... plane divides the plane into two half planes and.
Energy Technology Data Exchange (ETDEWEB)
Korayem, Moharam Habibnejad, E-mail: hkorayem@iust.ac.ir; Saraie, Maniya B.; Saraee, Mahdieh B.
2017-04-15
An important challenge when using an atomic force microscope (AFM) is to be able to control the force exerted by the AFM for performing various tasks. Nevertheless, the exerted force is proportional to the deflection of the AFM cantilever, which itself is affected by a cantilever's stiffness coefficient. Many papers have been published so far on the methods of obtaining the stiffness coefficients of AFM cantilevers in 2D; however, a comprehensive model is yet to be presented on 3D cantilever motion. The discrepancies between the equations of the 2D and 3D analysis are due to the number and direction of forces and moments that are applied to a cantilever. Moreover, in the 3D analysis, contrary to the 2D analysis, due to the interaction between the forces and moments applied on a cantilever, its stiffness values cannot be separately expressed for each direction; and instead, a stiffness matrix should be used to correctly derive the relevant equations. In this paper, 3D stiffness coefficient matrices have been obtained for three common cantilever geometries including the rectangular, V-shape and dagger-shape cantilevers. The obtained equations are validated by two methods. In the first approach, the Finite Element Method is combined with the cantilever deflection values computed by using the obtained stiffness matrices. In the second approach, by reducing the problem's parameters, the forces applied on a cantilever along different directions are compared with each other in 2D and 3D cases. Then the 3D manipulation of a stiff nanoparticle is modeled and simulated by using the stiffness matrices obtained for the three cantilever geometries. The obtained results indicate that during the manipulation process, the dagger-shaped and rectangular cantilevers exert the maximum and minimum amounts of forces on the stiff nanoparticle, respectively. Also, by examining the effects of different probe tip geometries, it is realized that a probe tip of cylindrical geometry
International Nuclear Information System (INIS)
Korayem, Moharam Habibnejad; Saraie, Maniya B.; Saraee, Mahdieh B.
2017-01-01
An important challenge when using an atomic force microscope (AFM) is to be able to control the force exerted by the AFM for performing various tasks. Nevertheless, the exerted force is proportional to the deflection of the AFM cantilever, which itself is affected by a cantilever's stiffness coefficient. Many papers have been published so far on the methods of obtaining the stiffness coefficients of AFM cantilevers in 2D; however, a comprehensive model is yet to be presented on 3D cantilever motion. The discrepancies between the equations of the 2D and 3D analysis are due to the number and direction of forces and moments that are applied to a cantilever. Moreover, in the 3D analysis, contrary to the 2D analysis, due to the interaction between the forces and moments applied on a cantilever, its stiffness values cannot be separately expressed for each direction; and instead, a stiffness matrix should be used to correctly derive the relevant equations. In this paper, 3D stiffness coefficient matrices have been obtained for three common cantilever geometries including the rectangular, V-shape and dagger-shape cantilevers. The obtained equations are validated by two methods. In the first approach, the Finite Element Method is combined with the cantilever deflection values computed by using the obtained stiffness matrices. In the second approach, by reducing the problem's parameters, the forces applied on a cantilever along different directions are compared with each other in 2D and 3D cases. Then the 3D manipulation of a stiff nanoparticle is modeled and simulated by using the stiffness matrices obtained for the three cantilever geometries. The obtained results indicate that during the manipulation process, the dagger-shaped and rectangular cantilevers exert the maximum and minimum amounts of forces on the stiff nanoparticle, respectively. Also, by examining the effects of different probe tip geometries, it is realized that a probe tip of cylindrical geometry exerts the
Petersen, Peter
2016-01-01
Intended for a one year course, this text serves as a single source, introducing readers to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry. This is one of the few Works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory. The book will appeal to a readership that have a basic knowledge of standard manifold theory, including tensors, forms, and Lie groups. Important revisions to the third edition include: a substantial addition of unique and enriching exercises scattered throughout the text; inclusion of an increased number of coordinate calculations of connection and curvature; addition of general formulas for curvature on Lie Groups and submersions; integration of variational calculus into the text allowing for an early treatment of the Sphere theorem using a proof by Berger; incorporation of several recent results about manifolds with posit...
International Nuclear Information System (INIS)
Strominger, A.
1990-01-01
A special manifold is an allowed target manifold for the vector multiplets of D=4, N=2 supergravity. These manifolds are of interest for string theory because the moduli spaces of Calabi-Yau threefolds and c=9, (2,2) conformal field theories are special. Previous work has given a local, coordinate-dependent characterization of special geometry. A global description of special geometries is given herein, and their properties are studied. A special manifold M of complex dimension n is characterized by the existence of a holomorphic Sp(2n+2,R)xGL(1,C) vector bundle over M with a nowhere-vanishing holomorphic section Ω. The Kaehler potential on M is the logarithm of the Sp(2n+2,R) invariant norm of Ω. (orig.)
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...
Energy Technology Data Exchange (ETDEWEB)
Bore, C; Dandeu, Y; Saint-Amand, Ch [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1965-07-01
MUDE is a nuclear code written in FORTRAN II for IBM 7090-7094. It resolves a system of difference equations approximating to the one-dimensional multigroup neutron scattering problem. More precisely, this code makes it possible to: 1. Calculate the critical condition of a reactor (k{sub eff}, critical radius, critical composition) and the corresponding fluxes; 2. Calculate the associated fluxes and various subsidiary results; 3. Carry out perturbation calculations; 4. Study the propagation of fluxes at a distance; 5. Estimate the relative contributions of the cross sections (macroscopic or microscopic); 6. Study the changes with time of the composition of the reactor. (authors) [French] MUDE est un code nucleaire ecrit en FORTRAN II pour IBM 7090-7094. Il resout un systeme d'equations aux differences approchant le probleme de diffusion neutronique multigroupe a une dimension. Plus precisement ce code permet de: 1. Calculer la condition critique d'un reacteur (k{sub eff}, rayon critique, composition critique) et les flux correspondants; 2. Calculer les flux adjoints et divers resultats connexes; 3. Effectuer des calculs de perturbation; 4. Etudier la propagation des flux a longue distance; 5. Ponderer des sections efficaces (macroscopiques ou microscopiques); 6. Etudier l'evolution de la composition du reacteur au cours du temps. (auteurs)
Energy Technology Data Exchange (ETDEWEB)
Frydrychowicz, Alex [University Hospital Schleswig-Holstein, Clinic for Radiology and Nuclear Medicine, Luebeck (Germany); Berger, Alexander; Russe, Maximilian F.; Bock, Jelena [University Hospital Freiburg, Department of Radiology, Medical Physics, Freiburg (Germany); Munoz del Rio, Alejandro [University of Wisconsin - Madison, Departments of Radiology and Medical Physics, Madison, WI (United States); Harloff, Andreas [University Hospital Freiburg, Department of Neurology and Clinical Neurophysiology, Freiburg (Germany); Markl, Michael [University Hospital Freiburg, Department of Radiology, Medical Physics, Freiburg (Germany); Northwestern University, Departments of Radiology and Biomedical Engineering, Chicago, IL (United States)
2012-05-15
It was the aim to analyse the impact of age, aortic arch geometry, and size on secondary flow patterns such as helix and vortex flow derived from flow-sensitive magnetic resonance imaging (4D PC-MRI). 62 subjects (age range = 20-80 years) without circumscribed pathologies of the thoracic aorta (ascending aortic (AAo) diameter: 3.2 {+-} 0.6 cm [range 2.2-5.1]) were examined by 4D PC-MRI after IRB-approval and written informed consent. Blood flow visualisation based on streamlines and time-resolved 3D particle traces was performed. Aortic diameter, shape (gothic, crook-shaped, cubic), angle, and age were correlated with existence and extent of secondary flow patterns (helicity, vortices); statistical modelling was performed. Helical flow was the typical pattern in standard crook-shaped aortic arches. With altered shapes and increasing age, helicity was less common. AAo diameter and age had the highest correlation (r = 0.69 and 0.68, respectively) with number of detected vortices. None of the other arch geometric or demographic variables (for all, P {>=} 0.177) improved statistical modelling. Substantially different secondary flow patterns can be observed in the normal thoracic aorta. Age and the AAo diameter were the parameters correlating best with presence and amount of vortices. Findings underline the importance of age- and geometry-matched control groups for haemodynamic studies. (orig.)
International Nuclear Information System (INIS)
Frydrychowicz, Alex; Berger, Alexander; Russe, Maximilian F.; Bock, Jelena; Munoz del Rio, Alejandro; Harloff, Andreas; Markl, Michael
2012-01-01
It was the aim to analyse the impact of age, aortic arch geometry, and size on secondary flow patterns such as helix and vortex flow derived from flow-sensitive magnetic resonance imaging (4D PC-MRI). 62 subjects (age range = 20-80 years) without circumscribed pathologies of the thoracic aorta (ascending aortic (AAo) diameter: 3.2 ± 0.6 cm [range 2.2-5.1]) were examined by 4D PC-MRI after IRB-approval and written informed consent. Blood flow visualisation based on streamlines and time-resolved 3D particle traces was performed. Aortic diameter, shape (gothic, crook-shaped, cubic), angle, and age were correlated with existence and extent of secondary flow patterns (helicity, vortices); statistical modelling was performed. Helical flow was the typical pattern in standard crook-shaped aortic arches. With altered shapes and increasing age, helicity was less common. AAo diameter and age had the highest correlation (r = 0.69 and 0.68, respectively) with number of detected vortices. None of the other arch geometric or demographic variables (for all, P ≥ 0.177) improved statistical modelling. Substantially different secondary flow patterns can be observed in the normal thoracic aorta. Age and the AAo diameter were the parameters correlating best with presence and amount of vortices. Findings underline the importance of age- and geometry-matched control groups for haemodynamic studies. (orig.)
Spatial geometry and special relativity
DEFF Research Database (Denmark)
Kneubil, Fabiana Botelho
2016-01-01
In this work, it is shown the interplay of relative and absolute entities, which are present in both spatial geometry and special relativity. In order to strengthen the understanding of special relativity, we discuss firstly an instance of geometry and the existence of both frame......-dependent and frame-independent entities. We depart from a subject well known by students, which is the three-dimensional geometric space in order to compare, afterwards, with the treatment of four-dimensional space in the special relativity. The differences and similarities between these two subjects are also...
Ciarlet, Philippe G
2007-01-01
This book gives the basic notions of differential geometry, such as the metric tensor, the Riemann curvature tensor, the fundamental forms of a surface, covariant derivatives, and the fundamental theorem of surface theory in a selfcontained and accessible manner. Although the field is often considered a classical one, it has recently been rejuvenated, thanks to the manifold applications where it plays an essential role. The book presents some important applications to shells, such as the theory of linearly and nonlinearly elastic shells, the implementation of numerical methods for shells, and
Energy Technology Data Exchange (ETDEWEB)
Couto, Nozimar do
2003-07-01
Diffusion theory is traditionally applied to nuclear reactor global calculations. Based on the good results generated by the one-dimensional spectral nodal diffusion (SND) method for benchmark problems, we offer the SND method for nuclear reactor global calculations in X,Y geometry. In this method, the continuity equation and Flick law are transverse integrated in each spatial direction leading to a system of two 'one-dimensional' equations coupled by the transverse leakage terms. We then apply the SND method to numerically solve this system with constant approximations for the transverse leakage terms. We perform a spectral analysis to determine the local general solution of each 'one-dimensional' nodal equation with flat approximation for the transverse leakages. We used special auxiliary equations with parameters that are to be determined in order to preserve the analytical general solutions in the numerical algorithm. By considering continuity conditions at the node interfaces and appropriate boundary conditions, we obtain a solvable system of discretized equations involving the node-edge average scalar fluxes at each estimate of the dominant eigenvalue (k{sub eff}) in the outer power iterations. As we considered approximations to the transverse leakages, the SND method is not free of spatial truncation errors. Nevertheless, it generated good results for the typical model problems that we considered. (author)
Energy Technology Data Exchange (ETDEWEB)
Couto, Nozimar do
2003-07-01
Diffusion theory is traditionally applied to nuclear reactor global calculations. Based on the good results generated by the one-dimensional spectral nodal diffusion (SND) method for benchmark problems, we offer the SND method for nuclear reactor global calculations in X,Y geometry. In this method, the continuity equation and Flick law are transverse integrated in each spatial direction leading to a system of two 'one-dimensional' equations coupled by the transverse leakage terms. We then apply the SND method to numerically solve this system with constant approximations for the transverse leakage terms. We perform a spectral analysis to determine the local general solution of each 'one-dimensional' nodal equation with flat approximation for the transverse leakages. We used special auxiliary equations with parameters that are to be determined in order to preserve the analytical general solutions in the numerical algorithm. By considering continuity conditions at the node interfaces and appropriate boundary conditions, we obtain a solvable system of discretized equations involving the node-edge average scalar fluxes at each estimate of the dominant eigenvalue (k{sub eff}) in the outer power iterations. As we considered approximations to the transverse leakages, the SND method is not free of spatial truncation errors. Nevertheless, it generated good results for the typical model problems that we considered. (author)
International Nuclear Information System (INIS)
Ondis, L.A. II; Tyburski, L.J.; Moskowitz, B.S.
2000-01-01
The RCP01 Monte Carlo program is used to analyze many geometries of interest in nuclear design and analysis of light water moderated reactors such as the core in its pressure vessel with complex piping arrangement, fuel storage arrays, shipping and container arrangements, and neutron detector configurations. Written in FORTRAN and in use on a variety of computers, it is capable of estimating steady state neutron or photon reaction rates and neutron multiplication factors. The energy range covered in neutron calculations is that relevant to the fission process and subsequent slowing-down and thermalization, i.e., 20 MeV to 0 eV. The same energy range is covered for photon calculations
Energy Technology Data Exchange (ETDEWEB)
Ondis, L.A., II; Tyburski, L.J.; Moskowitz, B.S.
2000-03-01
The RCP01 Monte Carlo program is used to analyze many geometries of interest in nuclear design and analysis of light water moderated reactors such as the core in its pressure vessel with complex piping arrangement, fuel storage arrays, shipping and container arrangements, and neutron detector configurations. Written in FORTRAN and in use on a variety of computers, it is capable of estimating steady state neutron or photon reaction rates and neutron multiplication factors. The energy range covered in neutron calculations is that relevant to the fission process and subsequent slowing-down and thermalization, i.e., 20 MeV to 0 eV. The same energy range is covered for photon calculations.
Buschinelli, Pedro D. V.; Melo, João. Ricardo C.; Albertazzi, Armando; Santos, João. M. C.; Camerini, Claudio S.
2013-04-01
An axis-symmetrical optical laser triangulation system was developed by the authors to measure the inner geometry of long pipes used in the oil industry. It has a special optical configuration able to acquire shape information of the inner geometry of a section of a pipe from a single image frame. A collimated laser beam is pointed to the tip of a 45° conical mirror. The laser light is reflected in such a way that a radial light sheet is formed and intercepts the inner geometry and forms a bright laser line on a section of the inspected pipe. A camera acquires the image of the laser line through a wide angle lens. An odometer-based triggering system is used to shot the camera to acquire a set of equally spaced images at high speed while the device is moved along the pipe's axis. Image processing is done in real-time (between images acquisitions) thanks to the use of parallel computing technology. The measured geometry is analyzed to identify corrosion damages. The measured geometry and results are graphically presented using virtual reality techniques and devices as 3D glasses and head-mounted displays. The paper describes the measurement principles, calibration strategies, laboratory evaluation of the developed device, as well as, a practical example of a corroded pipe used in an industrial gas production plant.
Flux compactifications and generalized geometries
International Nuclear Information System (INIS)
Grana, Mariana
2006-01-01
Following the lectures given at CERN Winter School 2006, we present a pedagogical overview of flux compactifications and generalized geometries, concentrating on closed string fluxes in type II theories. We start by reviewing the supersymmetric flux configurations with maximally symmetric four-dimensional spaces. We then discuss the no-go theorems (and their evasion) for compactifications with fluxes. We analyse the resulting four-dimensional effective theories for Calabi-Yau and Calabi-Yau orientifold compactifications, concentrating on the flux-induced superpotentials. We discuss the generic mechanism of moduli stabilization and illustrate with two examples: the conifold in IIB and a T 6 /(Z 3 x Z 3 ) torus in IIA. We finish by studying the effective action and flux vacua for generalized geometries in the context of generalized complex geometry
Flux compactifications and generalized geometries
Energy Technology Data Exchange (ETDEWEB)
Grana, Mariana [Service de Physique Theorique, CEA/Saclay, 91191 Gif-sur-Yvette Cedex (France)
2006-11-07
Following the lectures given at CERN Winter School 2006, we present a pedagogical overview of flux compactifications and generalized geometries, concentrating on closed string fluxes in type II theories. We start by reviewing the supersymmetric flux configurations with maximally symmetric four-dimensional spaces. We then discuss the no-go theorems (and their evasion) for compactifications with fluxes. We analyse the resulting four-dimensional effective theories for Calabi-Yau and Calabi-Yau orientifold compactifications, concentrating on the flux-induced superpotentials. We discuss the generic mechanism of moduli stabilization and illustrate with two examples: the conifold in IIB and a T{sup 6} /(Z{sub 3} x Z{sub 3}) torus in IIA. We finish by studying the effective action and flux vacua for generalized geometries in the context of generalized complex geometry.
On the 1/N expansion of the two-dimensional non-linear sigma-model: The vestige of chiral geometry
International Nuclear Information System (INIS)
Flume, R.
1978-11-01
We investigate the functioning of the O(N)-symmetry of the non-linear two-dimensional sigma-model using the 1/N expansion. The mechanism of O(N)-symmetry restoration is made explicit. We show that the O(N) invariant operators are in a one to one correspondance with the (c-number) invariants of the classical model. We observe a phenomenon, important in the context of the symmetry restoration, which might be called 'transmutation of anomalies'. That is, an anomaly of the equations of motion appearing before a summation of graphs contributing to the leading order of 1/N as a short distance effect becomes, after the summation, a long-distance effect. (orig.) [de
International Nuclear Information System (INIS)
Hull, C.M.
1993-01-01
The geometric structure of theories with gauge fields of spins two and higher should involve a higher spin generalisation of Riemannian geometry. Such geometries are discussed and the case of W ∝ -gravity is analysed in detail. While the gauge group for gravity in d dimensions is the diffeomorphism group of the space-time, the gauge group for a certain W-gravity theory (which is W ∝ -gravity in the case d=2) is the group of symplectic diffeomorphisms of the cotangent bundle of the space-time. Gauge transformations for W-gravity gauge fields are given by requiring the invariance of a generalised line element. Densities exist and can be constructed from the line element (generalising √detg μν ) only if d=1 or d=2, so that only for d=1,2 can actions be constructed. These two cases and the corresponding W-gravity actions are considered in detail. In d=2, the gauge group is effectively only a subgroup of the symplectic diffeomorphisms group. Some of the constraints that arise for d=2 are similar to equations arising in the study of self-dual four-dimensional geometries and can be analysed using twistor methods, allowing contact to be made with other formulations of W-gravity. While the twistor transform for self-dual spaces with one Killing vector reduces to a Legendre transform, that for two Killing vectors gives a generalisation of the Legendre transform. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Silva, Davi Jose M.; Alves Filho, Hermes; Barros, Ricardo C., E-mail: davijmsilva@yahoo.com.br, E-mail: halves@iprj.uerj.br, E-mail: rcbarros@pq.cnpq.br [Universidade do Estado do Rio de Janeiro (UERJ), Nova Friburgo, RJ (Brazil). Programa de Pos-Graduacao em Modelagem Computacional
2015-07-01
A spectral nodal method is developed for multigroup x,y-geometry discrete ordinates (S{sub N}) eigenvalue problems for nuclear reactor global calculations. This method uses the conventional multigroup SN discretized spatial balance nodal equations with two non-standard auxiliary equations: the spectral diamond (SD) auxiliary equations for the discretization nodes inside the fuel regions, and the spectral Green's function (SGF) auxiliary equations for the non-multiplying regions, such as the baffle and the reactor. This spectral nodal method is derived from the analytical general solution of the SN transverse integrated nodal equations with constant approximations for the transverse leakage terms within each discretization node. The SD and SGF auxiliary equations have parameters, which are determined to preserve the homogeneous and the particular components of these local general solutions. Therefore, we refer to the offered method as the hybrid SD-SGF-Constant Nodal (SD-SGF-CN) method. The S{sub N} discretized spatial balance equations, together with the SD and the SGF auxiliary equations form the SD-SGF-CN equations. We solve the SD-SGF-CN equations by using the one-node block inversion inner iterations (NBI), wherein the most recent estimates for the incoming group node-edge average or prescribed boundary conditions are used to evaluate the outgoing group node-edge average fluxes in the directions of the S{sub N} transport sweeps, for each estimate of the dominant eigenvalue in the conventional Power outer iterations. We show in numerical calculations that the SD-SGF-CN method is very accurate for coarse-mesh multigroup S{sub N} eigenvalue problems, even though the transverse leakage terms are approximated rather simply. (author)
International Nuclear Information System (INIS)
Silva, Davi Jose M.; Alves Filho, Hermes; Barros, Ricardo C.
2015-01-01
A spectral nodal method is developed for multigroup x,y-geometry discrete ordinates (S N ) eigenvalue problems for nuclear reactor global calculations. This method uses the conventional multigroup SN discretized spatial balance nodal equations with two non-standard auxiliary equations: the spectral diamond (SD) auxiliary equations for the discretization nodes inside the fuel regions, and the spectral Green's function (SGF) auxiliary equations for the non-multiplying regions, such as the baffle and the reactor. This spectral nodal method is derived from the analytical general solution of the SN transverse integrated nodal equations with constant approximations for the transverse leakage terms within each discretization node. The SD and SGF auxiliary equations have parameters, which are determined to preserve the homogeneous and the particular components of these local general solutions. Therefore, we refer to the offered method as the hybrid SD-SGF-Constant Nodal (SD-SGF-CN) method. The S N discretized spatial balance equations, together with the SD and the SGF auxiliary equations form the SD-SGF-CN equations. We solve the SD-SGF-CN equations by using the one-node block inversion inner iterations (NBI), wherein the most recent estimates for the incoming group node-edge average or prescribed boundary conditions are used to evaluate the outgoing group node-edge average fluxes in the directions of the S N transport sweeps, for each estimate of the dominant eigenvalue in the conventional Power outer iterations. We show in numerical calculations that the SD-SGF-CN method is very accurate for coarse-mesh multigroup S N eigenvalue problems, even though the transverse leakage terms are approximated rather simply. (author)
Energy Technology Data Exchange (ETDEWEB)
Estrada, Claudio A; Arancibia, Camilo [Centro de Investigacion en Energia UNAM, Temixco, Morelos (Mexico); Hernandez, Nestor [Centro Nacional de Investigacion y Desarrollo Tecnologico, Cuernavaca, Morelos (Mexico)
2000-07-01
The optimal geometry and dimensions for the receiver of a parabolic solar concentrator based on microwave communication antenna are obtained. First, the experiments for the determination of the angular error of the concentrator and the dimensions of its focal region are described. Results are also presented for the ray tracing study, from which the optimal characteristics of the receiver are obtained according to the experimental results. As the aluminum antenna has a rim angle of 90 Celsius degrees, it is necessary to use a cavity receiver to allow external as well as internal absorption of radiative flux. Cylindrical, conical and spherical geometric were considered, as well as combinations of them. The best results are achieved using a conical cavity. Its dimensions are calculated to maximize the radiative transfer efficiency from the aperture of the concentrator to the receiver. [Spanish] Se determinan la geometria y dimensiones optimas del receptor de un concentrador solar parabolico obtenido a partir de una antena de telecomunicaciones para microondas. Primeramente se describen los experimentos realizados para obtener el valor del error angular asociado al concentrador y de las dimensiones de su region focal. Tambien se presentan los resultados del estudio optico de trazado de rayos, que permitio determinar teoricamente las caracteristicas del receptor, de acuerdo a los resultados de los experimentos. Debido a que la antena de aluminio tiene un angulo de borde de 90 grados Celcius, es necesario usar un receptor tipo cavidad que permita la captacion de energia tanto interna como externa. Se consideraron geometrias cilindrica, conica, esferica y combinaciones entre ellas, resultando ser la conica la que da los mejores resultados. Las dimensiones del receptor fueron determinadas maximizando la eficiencia del transporte de radiacion de la apertura del concentrador al receptor.
Pratt, Isaac V; Johnston, James D; Walker, Ernie; Cooper, David M L
2018-06-01
Cortical bone porosity and specifically the orientation of vascular canals is an area of growing interest in biomedical research and comparative/paleontological anatomy. The potential to explain microstructural adaptation is of great interest. However, the determinants of the development of canal orientation remain unclear. Previous studies of birds have shown higher proportions of circumferential canals (called laminarity) in flight bones than in hindlimb bones, and interpreted this as a sign that circumferential canals are a feature for resistance to the torsional loading created by flight. We defined the laminarity index as the percentage of circumferential canal length out of the total canal length. In this study we examined the vascular canal network in the humerus and femur of a sample of 31 bird and 24 bat species using synchrotron micro-computed tomography (micro-CT) to look for a connection between canal orientation and functional loading. The use of micro-CT provides a full three-dimensional (3D) map of the vascular canal network and provides measurements of the 3D orientation of each canal in the whole cross-section of the bone cortex. We measured several cross-sectional geometric parameters and strength indices including principal and polar area moments of inertia, principal and polar section moduli, circularity, buckling ratio, and a weighted cortical thickness index. We found that bat cortices are relatively thicker and poorly vascularized, whereas those of birds are thinner and more highly vascularized, and that according to our cross-sectional geometric parameters, bird bones have a greater resistance to torsional stress than the bats; in particular, the humerus in birds is more adapted to resist torsional stresses than the femur. Our results show that birds have a significantly (P = 0.031) higher laminarity index than bats, with birds having a mean laminarity index of 0.183 in the humerus and 0.232 in the femur, and bats having a mean laminarity
International Nuclear Information System (INIS)
Gutberlet, M.; Grothoff, M.; Roettgen, R.; Lange, P.; Felix, R.; Abdul-Khaliq, H.; Schroeter, J.; Schmitt, B.; Vogel, M.
2003-01-01
Purpose: To assess the new method of 3-dimensional echocardiography in comparison to the 'gold standard' MRI as to its ability to calculate left ventricular volumes in patients with congenital heart disease. Materials and methods: Eighteen patients between the ages of 3.9 to 37.3 years (mean: 12.8±9.7) with a geometrically abnormal left ventricle were examined using a 1.5 T scanner with a fast gradient-echo sequence (TR=14 ms, TE=2.6-2.9 ms, FOV=300-400 mm, flip angle=20 , matrix=128:256, slice thickness=5 mm, retrospective gating) in multislice-multiphase technique. Transthoracic 3D-echocardiography was performed with a 3.5 MHz transducer and a Tomtec trademark (Munich, Germany) system for 3D reconstruction. Results: Volume calculation was possible in all patients with 3D-echocardiography, but the muscle mass calculation only succeeded in 11 to 18 patients (61%) due to inadequate visualization of the entire myocardium. Comparing MRI and 3D-echocardiography, the correlation was r=0.97 for the end-systolic volumes, r=0.98 for the end-diastolic volumes, r=0.79 for the end-systolic muscle mass and r=0.77 for the end-diastolic muscle mass. The agreement between both methods was considered good for the calculated end-diastolic volumes and sufficient for the calculated end-systolic volumes. The muscle mass calculations showed larger differences especially for the end-systolic mass. Mean intraobserver variability was 18.6% for end-systolic and 8.3% for end-diastolic volumes. Conclusion: In patients with an abnormal left ventricular configuration due to congenital heart disease, the new method of 3D-echocardiography is sufficient for volume calculations in preselected patients. The high intraobserver variability is still a limitation of transthoracic 3D-echocardiography in comparison to MRI. (orig.) [de
International Nuclear Information System (INIS)
Li, Ke-Zeng; Gao, Yuan; Zhang, Ru; Hu, Tao; Guo, Bin
2011-01-01
Together with diagnosis and treatment planning, a good knowledge of the root canal system and its frequent variations is a necessity for successful root canal therapy. The selection of instrumentation techniques for variants in internal anatomy of teeth has significant effects on the shaping ability and cleaning effectiveness. The aim of this study was to reveal the differences made by including variations in the internal anatomy of premolars into the study protocol for investigation of a single instrumentation technique (hand ProTaper instruments) assessed by microcomputed tomography and three-dimensional reconstruction. Five single-root premolars, whose root canal systems were classified into one of five types, were scanned with micro-CT before and after preparation with a hand ProTaper instrument. Instrumentation characteristics were measured quantitatively in 3-D using a customized application framework based on MeVisLab. Numeric values were obtained for canal surface area, volume, volume changes, percentage of untouched surface, dentin wall thickness, and the thickness of dentin removed. Preparation errors were also evaluated using a color-coded reconstruction. Canal volumes and surface areas were increased after instrumentation. Prepared canals of all five types were straightened, with transportation toward the inner aspects of S-shaped or multiple curves. However, a ledge was formed at the apical third curve of the type II canal system and a wide range in the percentage of unchanged canal surfaces (27.4-83.0%) was recorded. The dentin walls were more than 0.3 mm thick except in a 1 mm zone from the apical surface and the hazardous area of the type II canal system after preparation with an F3 instrument. The 3-D color-coded images showed different morphological changes in the five types of root canal systems shaped with the same hand instrumentation technique. Premolars are among the most complex teeth for root canal treatment and instrumentation techniques
Directory of Open Access Journals (Sweden)
Hu Tao
2011-06-01
Full Text Available Abstract Background Together with diagnosis and treatment planning, a good knowledge of the root canal system and its frequent variations is a necessity for successful root canal therapy. The selection of instrumentation techniques for variants in internal anatomy of teeth has significant effects on the shaping ability and cleaning effectiveness. The aim of this study was to reveal the differences made by including variations in the internal anatomy of premolars into the study protocol for investigation of a single instrumentation technique (hand ProTaper instruments assessed by microcomputed tomography and three-dimensional reconstruction. Methods Five single-root premolars, whose root canal systems were classified into one of five types, were scanned with micro-CT before and after preparation with a hand ProTaper instrument. Instrumentation characteristics were measured quantitatively in 3-D using a customized application framework based on MeVisLab. Numeric values were obtained for canal surface area, volume, volume changes, percentage of untouched surface, dentin wall thickness, and the thickness of dentin removed. Preparation errors were also evaluated using a color-coded reconstruction. Results Canal volumes and surface areas were increased after instrumentation. Prepared canals of all five types were straightened, with transportation toward the inner aspects of S-shaped or multiple curves. However, a ledge was formed at the apical third curve of the type II canal system and a wide range in the percentage of unchanged canal surfaces (27.4-83.0% was recorded. The dentin walls were more than 0.3 mm thick except in a 1 mm zone from the apical surface and the hazardous area of the type II canal system after preparation with an F3 instrument. Conclusions The 3-D color-coded images showed different morphological changes in the five types of root canal systems shaped with the same hand instrumentation technique. Premolars are among the most
Stochastic geometry and its applications
Chiu, Sung Nok; Kendall, Wilfrid S; Mecke, Joseph
2013-01-01
An extensive update to a classic text Stochastic geometry and spatial statistics play a fundamental role in many modern branches of physics, materials sciences, engineering, biology and environmental sciences. They offer successful models for the description of random two- and three-dimensional micro and macro structures and statistical methods for their analysis. The previous edition of this book has served as the key reference in its field for over 18 years and is regarded as the best treatment of the subject of stochastic geometry, both as a subject with vital a
SABRINA, Geometry Plot Program for MCNP
International Nuclear Information System (INIS)
SEIDL, Marcus
2003-01-01
1 - Description of program or function: SABRINA is an interactive, three-dimensional, geometry-modeling code system, primarily for use with CCC-200/MCNP. SABRINA's capabilities include creation, visualization, and verification of three-dimensional geometries specified by either surface- or body-base combinatorial geometry; display of particle tracks are calculated by MCNP; and volume fraction generation. 2 - Method of solution: Rendering is performed by ray tracing or an edge and intersection algorithm. Volume fraction calculations are made by ray tracing. 3 - Restrictions on the complexity of the problem: A graphics display with X Window capability is required
Functional integration over geometries
International Nuclear Information System (INIS)
Mottola, E.
1995-01-01
The geometric construction of the functional integral over coset spaces M/G is reviewed. The inner product on the cotangent space of infinitesimal deformations of M defines an invariant distance and volume form, or functional integration measure on the full configuration space. Then, by a simple change of coordinates parameterizing the gauge fiber G, the functional measure on the coset space M/G is deduced. This change of integration variables leads to a Jacobian which is entirely equivalent to the Faddeev--Popov determinant of the more traditional gauge fixed approach in non-abelian gauge theory. If the general construction is applied to the case where G is the group of coordinate reparameterizations of spacetime, the continuum functional integral over geometries, i.e. metrics modulo coordinate reparameterizations may be defined. The invariant functional integration measure is used to derive the trace anomaly and effective action for the conformal part of the metric in two and four dimensional spacetime. In two dimensions this approach generates the Polyakov--Liouville action of closed bosonic non-critical string theory. In four dimensions the corresponding effective action leads to novel conclusions on the importance of quantum effects in gravity in the far infrared, and in particular, a dramatic modification of the classical Einstein theory at cosmological distance scales, signaled first by the quantum instability of classical de Sitter spacetime. Finite volume scaling relations for the functional integral of quantum gravity in two and four dimensions are derived, and comparison with the discretized dynamical triangulation approach to the integration over geometries are discussed. Outstanding unsolved problems in both the continuum definition and the simplicial approach to the functional integral over geometries are highlighted
Silva, Alessandro
1993-01-01
The papers in this wide-ranging collection report on the results of investigations from a number of linked disciplines, including complex algebraic geometry, complex analytic geometry of manifolds and spaces, and complex differential geometry.
Eisenhart, Luther Pfahler
2005-01-01
This concise text by a prominent mathematician deals chiefly with manifolds dominated by the geometry of paths. Topics include asymmetric and symmetric connections, the projective geometry of paths, and the geometry of sub-spaces. 1927 edition.
The odd side of torsion geometry
DEFF Research Database (Denmark)
Conti, Diego; Madsen, Thomas Bruun
2014-01-01
We introduce and study a notion of `Sasaki with torsion structure' (ST) as an odd-dimensional analogue of Kähler with torsion geometry (KT). These are normal almost contact metric manifolds that admit a unique compatible connection with 3-form torsion. Any odd-dimensional compact Lie group is sho...
Connecting Functions in Geometry and Algebra
Steketee, Scott; Scher, Daniel
2016-01-01
One goal of a mathematics education is that students make significant connections among different branches of mathematics. Connections--such as those between arithmetic and algebra, between two-dimensional and three-dimensional geometry, between compass-and-straight-edge constructions and transformations, and between calculus and analytic…
International Nuclear Information System (INIS)
Gurevich, L.Eh.; Gliner, Eh.B.
1978-01-01
Problems of investigating the Universe space-time geometry are described on a popular level. Immediate space-time geometries, corresponding to three cosmologic models are considered. Space-time geometry of a closed model is the spherical Riemann geonetry, of an open model - is the Lobachevskij geometry; and of a plane model - is the Euclidean geometry. The Universe real geometry in the contemporary epoch of development is based on the data testifying to the fact that the Universe is infinitely expanding
Convection in Slab and Spheroidal Geometries
Porter, David H.; Woodward, Paul R.; Jacobs, Michael L.
2000-01-01
Three-dimensional numerical simulations of compressible turbulent thermally driven convection, in both slab and spheroidal geometries, are reviewed and analyzed in terms of velocity spectra and mixing-length theory. The same ideal gas model is used in both geometries, and resulting flows are compared. The piecewise-parabolic method (PPM), with either thermal conductivity or photospheric boundary conditions, is used to solve the fluid equations of motion. Fluid motions in both geometries exhibit a Kolmogorov-like k(sup -5/3) range in their velocity spectra. The longest wavelength modes are energetically dominant in both geometries, typically leading to one convection cell dominating the flow. In spheroidal geometry, a dipolar flow dominates the largest scale convective motions. Downflows are intensely turbulent and up drafts are relatively laminar in both geometries. In slab geometry, correlations between temperature and velocity fluctuations, which lead to the enthalpy flux, are fairly independent of depth. In spheroidal geometry this same correlation increases linearly with radius over the inner 70 percent by radius, in which the local pressure scale heights are a sizable fraction of the radius. The effects from the impenetrable boundary conditions in the slab geometry models are confused with the effects from non-local convection. In spheroidal geometry nonlocal effects, due to coherent plumes, are seen as far as several pressure scale heights from the lower boundary and are clearly distinguishable from boundary effects.
Energy Technology Data Exchange (ETDEWEB)
Perez Guerrero, Jesus Salvador
1996-12-31
Laminar developing flow in channels of arbitrary geometry was studied by solving the Navier-Stokes equations in the stream function-only formulation through the Generalized Integral Transform Technique (GITT). The stream function is expanded in an infinite system based on eigenfunctions obtained by considering solely the diffusive terms of the original formulation. The Navier-Stokes equations are transformed into an infinite system of ordinary differential equations, by using the transformation and inversion formulae. For computational purposes, the infinite series is truncated, according to an automatic error control procedure. The ordinary differential is solved through well-established scientific subroutines from widely available mathematical libraries. The classical problem of developing flow between parallel-plates is analysed first, as for both uniform and irrotational inlet conditions. The effect of truncating the duct length in the accuracy of the obtained solution is studied. A convergence analysis of the results obtained by the GITT is performed and compared with results obtained by finite difference and finite element methods, for different values of Reynolds number. The problem of flow over a backward-facing step then follows. Comparisons with experimental results in the literature indicate an excellent agreement. The numerical co-validation was established for a test case, and perfect agreement is reached against results considered as benchmarks in the recent literature. The results were shown to be physically more reasonable than others obtained by purely numerical methods, in particular for situations where three-dimensional effects are identified. Finally, a test problem for an irregular by shoped duct was studied and compared against results found in the literature, with good agreement and excellent convergence rates for the stream function field along the whole channel, for different values of Reynolds number. (author) 78 refs., 24 figs., 14 tabs.
Energy Technology Data Exchange (ETDEWEB)
Perez Guerrero, Jesus Salvador
1995-12-31
Laminar developing flow in channels of arbitrary geometry was studied by solving the Navier-Stokes equations in the stream function-only formulation through the Generalized Integral Transform Technique (GITT). The stream function is expanded in an infinite system based on eigenfunctions obtained by considering solely the diffusive terms of the original formulation. The Navier-Stokes equations are transformed into an infinite system of ordinary differential equations, by using the transformation and inversion formulae. For computational purposes, the infinite series is truncated, according to an automatic error control procedure. The ordinary differential is solved through well-established scientific subroutines from widely available mathematical libraries. The classical problem of developing flow between parallel-plates is analysed first, as for both uniform and irrotational inlet conditions. The effect of truncating the duct length in the accuracy of the obtained solution is studied. A convergence analysis of the results obtained by the GITT is performed and compared with results obtained by finite difference and finite element methods, for different values of Reynolds number. The problem of flow over a backward-facing step then follows. Comparisons with experimental results in the literature indicate an excellent agreement. The numerical co-validation was established for a test case, and perfect agreement is reached against results considered as benchmarks in the recent literature. The results were shown to be physically more reasonable than others obtained by purely numerical methods, in particular for situations where three-dimensional effects are identified. Finally, a test problem for an irregular by shoped duct was studied and compared against results found in the literature, with good agreement and excellent convergence rates for the stream function field along the whole channel, for different values of Reynolds number. (author) 78 refs., 24 figs., 14 tabs.
Application of Tessellation in Architectural Geometry Design
Chang, Wei
2018-06-01
Tessellation plays a significant role in architectural geometry design, which is widely used both through history of architecture and in modern architectural design with the help of computer technology. Tessellation has been found since the birth of civilization. In terms of dimensions, there are two- dimensional tessellations and three-dimensional tessellations; in terms of symmetry, there are periodic tessellations and aperiodic tessellations. Besides, some special types of tessellations such as Voronoi Tessellation and Delaunay Triangles are also included. Both Geometry and Crystallography, the latter of which is the basic theory of three-dimensional tessellations, need to be studied. In history, tessellation was applied into skins or decorations in architecture. The development of Computer technology enables tessellation to be more powerful, as seen in surface control, surface display and structure design, etc. Therefore, research on the application of tessellation in architectural geometry design is of great necessity in architecture studies.
Geometry and topology of wild translation surfaces
Randecker, Anja
2016-01-01
A translation surface is a two-dimensional manifold, equipped with a translation structure. It can be obtained by considering Euclidean polygons and identifying their edges via translations. The vertices of the polygons form singularities if the translation structure can not be extended to them. We study translation surfaces with wild singularities, regarding the topology (genus and space of ends), the geometry (behavior of the singularities), and how the topology and the geometry are related.
Perspectives in Analysis, Geometry, and Topology
Itenberg, I V; Passare, Mikael
2012-01-01
The articles in this volume are invited papers from the Marcus Wallenberg symposium and focus on research topics that bridge the gap between analysis, geometry, and topology. The encounters between these three fields are widespread and often provide impetus for major breakthroughs in applications. Topics include new developments in low dimensional topology related to invariants of links and three and four manifolds; Perelman's spectacular proof of the Poincare conjecture; and the recent advances made in algebraic, complex, symplectic, and tropical geometry.
Meyer, Walter J
2006-01-01
Meyer''s Geometry and Its Applications, Second Edition, combines traditional geometry with current ideas to present a modern approach that is grounded in real-world applications. It balances the deductive approach with discovery learning, and introduces axiomatic, Euclidean geometry, non-Euclidean geometry, and transformational geometry. The text integrates applications and examples throughout and includes historical notes in many chapters. The Second Edition of Geometry and Its Applications is a significant text for any college or university that focuses on geometry''s usefulness in other disciplines. It is especially appropriate for engineering and science majors, as well as future mathematics teachers.* Realistic applications integrated throughout the text, including (but not limited to): - Symmetries of artistic patterns- Physics- Robotics- Computer vision- Computer graphics- Stability of architectural structures- Molecular biology- Medicine- Pattern recognition* Historical notes included in many chapters...
Indian Academy of Sciences (India)
algebraic geometry but also in related fields like number theory. ... every vector bundle on the affine space is trivial. (equivalently ... les on a compact Riemann surface to unitary rep- ... tial geometry and topology and was generalised in.
International Nuclear Information System (INIS)
Sloane, Peter
2007-01-01
We adapt the spinorial geometry method introduced in [J. Gillard, U. Gran and G. Papadopoulos, 'The spinorial geometry of supersymmetric backgrounds,' Class. Quant. Grav. 22 (2005) 1033 [ (arXiv:hep-th/0410155)
Energy Technology Data Exchange (ETDEWEB)
Sloane, Peter [Department of Mathematics, King' s College, University of London, Strand, London WC2R 2LS (United Kingdom)
2007-09-15
We adapt the spinorial geometry method introduced in [J. Gillard, U. Gran and G. Papadopoulos, 'The spinorial geometry of supersymmetric backgrounds,' Class. Quant. Grav. 22 (2005) 1033 [ (arXiv:hep-th/0410155)
Physical meaning of the optical reference geometry
International Nuclear Information System (INIS)
Abramowicz, M.A.
1990-09-01
I show that contrary to a popular misconception the optical reference geometry, introduced a few years ago as a formally possible metric of a 3-space corresponding to a static spacetime, is quite satisfactory also from the physical point of view. The optical reference geometry has a clear physical meaning, as it may be constructed experimentally by measuring light round travel time between static observers. Distances and directions in the optical reference geometry are more strongly connected to experiment than distances and directions in the widely used directly projected metric (discussed e.g. in Landau and Lifshitz textbook. In addition, the optical reference geometry is more natural and convenient than the directly projected one in application to dynamics. In the optical geometry dynamical behaviour of matter is described by concepts and formulae identical to those well known in Newtonian dynamics on a given two dimensional (curved) surface. (author). 22 refs
Differential geometry and topology of curves
Animov, Yu
2001-01-01
Differential geometry is an actively developing area of modern mathematics. This volume presents a classical approach to the general topics of the geometry of curves, including the theory of curves in n-dimensional Euclidean space. The author investigates problems for special classes of curves and gives the working method used to obtain the conditions for closed polygonal curves. The proof of the Bakel-Werner theorem in conditions of boundedness for curves with periodic curvature and torsion is also presented. This volume also highlights the contributions made by great geometers. past and present, to differential geometry and the topology of curves.
Nonperturbative quantum geometries
International Nuclear Information System (INIS)
Jacobson, T.; California Univ., Santa Barbara; Smolin, L.; California Univ., Santa Barbara
1988-01-01
Using the self-dual representation of quantum general relativity, based on Ashtekar's new phase space variables, we present an infinite dimensional family of quantum states of the gravitational field which are exactly annihilated by the hamiltonian constraint. These states are constructed from Wilson loops for Ashtekar's connection (which is the spatial part of the left handed spin connection). We propose a new regularization procedure which allows us to evaluate the action of the hamiltonian constraint on these states. Infinite linear combinations of these states which are formally annihilated by the diffeomorphism constraints as well are also described. These are explicit examples of physical states of the gravitational field - and for the compact case are exact zero eigenstates of the hamiltonian of quantum general relativity. Several different approaches to constructing diffeomorphism invariant states in the self dual representation are also described. The physical interpretation of the states described here is discussed. However, as we do not yet know the physical inner product, any interpretation is at this stage speculative. Nevertheless, this work suggests that quantum geometry at Planck scales might be much simpler when explored in terms of the parallel transport of left-handed spinors than when explored in terms of the three metric. (orig.)
Quantification of Porcine Vocal Fold Geometry.
Stevens, Kimberly A; Thomson, Scott L; Jetté, Marie E; Thibeault, Susan L
2016-07-01
The aim of this study was to quantify porcine vocal fold medial surface geometry and three-dimensional geometric distortion induced by freezing the larynx, especially in the region of the vocal folds. The medial surface geometries of five excised porcine larynges were quantified and reported. Five porcine larynges were imaged in a micro-CT scanner, frozen, and rescanned. Segmentations and three-dimensional reconstructions were used to quantify and characterize geometric features. Comparisons were made with geometry data previously obtained using canine and human vocal folds as well as geometries of selected synthetic vocal fold models. Freezing induced an overall expansion of approximately 5% in the transverse plane and comparable levels of nonuniform distortion in sagittal and coronal planes. The medial surface of the porcine vocal folds was found to compare reasonably well with other geometries, although the compared geometries exhibited a notable discrepancy with one set of published human female vocal fold geometry. Porcine vocal folds are qualitatively geometrically similar to data available for canine and human vocal folds, as well as commonly used models. Freezing of tissue in the larynx causes distortion of around 5%. The data can provide direction in estimating uncertainty due to bulk distortion of tissue caused by freezing, as well as quantitative geometric data that can be directly used in developing vocal fold models. Copyright © 2016 The Voice Foundation. Published by Elsevier Inc. All rights reserved.
Geometry of isotropic convex bodies
Brazitikos, Silouanos; Valettas, Petros; Vritsiou, Beatrice-Helen
2014-01-01
The study of high-dimensional convex bodies from a geometric and analytic point of view, with an emphasis on the dependence of various parameters on the dimension stands at the intersection of classical convex geometry and the local theory of Banach spaces. It is also closely linked to many other fields, such as probability theory, partial differential equations, Riemannian geometry, harmonic analysis and combinatorics. It is now understood that the convexity assumption forces most of the volume of a high-dimensional convex body to be concentrated in some canonical way and the main question is whether, under some natural normalization, the answer to many fundamental questions should be independent of the dimension. The aim of this book is to introduce a number of well-known questions regarding the distribution of volume in high-dimensional convex bodies, which are exactly of this nature: among them are the slicing problem, the thin shell conjecture and the Kannan-Lov�sz-Simonovits conjecture. This book prov...
Network geometry with flavor: From complexity to quantum geometry
Bianconi, Ginestra; Rahmede, Christoph
2016-03-01
Network geometry is attracting increasing attention because it has a wide range of applications, ranging from data mining to routing protocols in the Internet. At the same time advances in the understanding of the geometrical properties of networks are essential for further progress in quantum gravity. In network geometry, simplicial complexes describing the interaction between two or more nodes play a special role. In fact these structures can be used to discretize a geometrical d -dimensional space, and for this reason they have already been widely used in quantum gravity. Here we introduce the network geometry with flavor s =-1 ,0 ,1 (NGF) describing simplicial complexes defined in arbitrary dimension d and evolving by a nonequilibrium dynamics. The NGF can generate discrete geometries of different natures, ranging from chains and higher-dimensional manifolds to scale-free networks with small-world properties, scale-free degree distribution, and nontrivial community structure. The NGF admits as limiting cases both the Bianconi-Barabási models for complex networks, the stochastic Apollonian network, and the recently introduced model for complex quantum network manifolds. The thermodynamic properties of NGF reveal that NGF obeys a generalized area law opening a new scenario for formulating its coarse-grained limit. The structure of NGF is strongly dependent on the dimensionality d . In d =1 NGFs grow complex networks for which the preferential attachment mechanism is necessary in order to obtain a scale-free degree distribution. Instead, for NGF with dimension d >1 it is not necessary to have an explicit preferential attachment rule to generate scale-free topologies. We also show that NGF admits a quantum mechanical description in terms of associated quantum network states. Quantum network states evolve by a Markovian dynamics and a quantum network state at time t encodes all possible NGF evolutions up to time t . Interestingly the NGF remains fully classical but
Geometry essentials for dummies
Ryan, Mark
2011-01-01
Just the critical concepts you need to score high in geometry This practical, friendly guide focuses on critical concepts taught in a typical geometry course, from the properties of triangles, parallelograms, circles, and cylinders, to the skills and strategies you need to write geometry proofs. Geometry Essentials For Dummies is perfect for cramming or doing homework, or as a reference for parents helping kids study for exams. Get down to the basics - get a handle on the basics of geometry, from lines, segments, and angles, to vertices, altitudes, and diagonals Conque
Arithmetic noncommutative geometry
Marcolli, Matilde
2005-01-01
Arithmetic noncommutative geometry denotes the use of ideas and tools from the field of noncommutative geometry, to address questions and reinterpret in a new perspective results and constructions from number theory and arithmetic algebraic geometry. This general philosophy is applied to the geometry and arithmetic of modular curves and to the fibers at archimedean places of arithmetic surfaces and varieties. The main reason why noncommutative geometry can be expected to say something about topics of arithmetic interest lies in the fact that it provides the right framework in which the tools of geometry continue to make sense on spaces that are very singular and apparently very far from the world of algebraic varieties. This provides a way of refining the boundary structure of certain classes of spaces that arise in the context of arithmetic geometry, such as moduli spaces (of which modular curves are the simplest case) or arithmetic varieties (completed by suitable "fibers at infinity"), by adding boundaries...
International Nuclear Information System (INIS)
Atiyah, M.F.
1978-01-01
In this talk I shall explain how information about classical solutions of Yang-Mills equations can be obtained, rather surprisingly, from algebraic geometry. Although direct physical interest is restricted to the case of four dimensions I shall begin by discussing the two-dimensional case. Besides preparing the ground for the four-dimensional problem this has independent mathematical (and possible physical) interest, and very complete results can be obtained. (orig.) [de
Conformal geometry and quasiregular mappings
Vuorinen, Matti
1988-01-01
This book is an introduction to the theory of spatial quasiregular mappings intended for the uninitiated reader. At the same time the book also addresses specialists in classical analysis and, in particular, geometric function theory. The text leads the reader to the frontier of current research and covers some most recent developments in the subject, previously scatterd through the literature. A major role in this monograph is played by certain conformal invariants which are solutions of extremal problems related to extremal lengths of curve families. These invariants are then applied to prove sharp distortion theorems for quasiregular mappings. One of these extremal problems of conformal geometry generalizes a classical two-dimensional problem of O. Teichmüller. The novel feature of the exposition is the way in which conformal invariants are applied and the sharp results obtained should be of considerable interest even in the two-dimensional particular case. This book combines the features of a textbook an...
The causal structure of spacetime is a parameterized Randers geometry
Energy Technology Data Exchange (ETDEWEB)
Skakala, Jozef; Visser, Matt, E-mail: jozef.skakala@msor.vuw.ac.nz, E-mail: matt.visser@msor.vuw.ac.nz [School of Mathematics, Statistics and Operations Research, Victoria University of Wellington, PO Box 600, Wellington (New Zealand)
2011-03-21
There is a well-established isomorphism between stationary four-dimensional spacetimes and three-dimensional purely spatial Randers geometries-these Randers geometries being a particular case of the more general class of three-dimensional Finsler geometries. We point out that in stably causal spacetimes, by using the (time-dependent) ADM decomposition, this result can be extended to general non-stationary spacetimes-the causal structure (conformal structure) of the full spacetime is completely encoded in a parameterized (t-dependent) class of Randers spaces, which can then be used to define a Fermat principle, and also to reconstruct the null cones and causal structure.
The causal structure of spacetime is a parameterized Randers geometry
International Nuclear Information System (INIS)
Skakala, Jozef; Visser, Matt
2011-01-01
There is a well-established isomorphism between stationary four-dimensional spacetimes and three-dimensional purely spatial Randers geometries-these Randers geometries being a particular case of the more general class of three-dimensional Finsler geometries. We point out that in stably causal spacetimes, by using the (time-dependent) ADM decomposition, this result can be extended to general non-stationary spacetimes-the causal structure (conformal structure) of the full spacetime is completely encoded in a parameterized (t-dependent) class of Randers spaces, which can then be used to define a Fermat principle, and also to reconstruct the null cones and causal structure.
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.
Geometry and the Design of Product Packaging
Cherico, Cindy M.
2011-01-01
The most common question the author's students ask is, "When will I ever use this in real life?" To address this question in her geometry classes, the author sought to create a project that would incorporate a real-world business situation with their lesson series on the surface area and volume of three-dimensional objects--specifically, prisms,…
Monte Carlo simulation of fully Markovian stochastic geometries
International Nuclear Information System (INIS)
Lepage, Thibaut; Delaby, Lucie; Malvagi, Fausto; Mazzolo, Alain
2010-01-01
The interest in resolving the equation of transport in stochastic media has continued to increase these last years. For binary stochastic media it is often assumed that the geometry is Markovian, which is never the case in usual environments. In the present paper, based on rigorous mathematical theorems, we construct fully two-dimensional Markovian stochastic geometries and we study their main properties. In particular, we determine a percolation threshold p c , equal to 0.586 ± 0.0015 for such geometries. Finally, Monte Carlo simulations are performed through these geometries and the results compared to homogeneous geometries. (author)
Index theory for locally compact noncommutative geometries
Carey, A L; Rennie, A; Sukochev, F A
2014-01-01
Spectral triples for nonunital algebras model locally compact spaces in noncommutative geometry. In the present text, the authors prove the local index formula for spectral triples over nonunital algebras, without the assumption of local units in our algebra. This formula has been successfully used to calculate index pairings in numerous noncommutative examples. The absence of any other effective method of investigating index problems in geometries that are genuinely noncommutative, particularly in the nonunital situation, was a primary motivation for this study and the authors illustrate this point with two examples in the text. In order to understand what is new in their approach in the commutative setting the authors prove an analogue of the Gromov-Lawson relative index formula (for Dirac type operators) for even dimensional manifolds with bounded geometry, without invoking compact supports. For odd dimensional manifolds their index formula appears to be completely new.
Algorithms in Algebraic Geometry
Dickenstein, Alicia; Sommese, Andrew J
2008-01-01
In the last decade, there has been a burgeoning of activity in the design and implementation of algorithms for algebraic geometric computation. Some of these algorithms were originally designed for abstract algebraic geometry, but now are of interest for use in applications and some of these algorithms were originally designed for applications, but now are of interest for use in abstract algebraic geometry. The workshop on Algorithms in Algebraic Geometry that was held in the framework of the IMA Annual Program Year in Applications of Algebraic Geometry by the Institute for Mathematics and Its
O'Leary, Michael
2010-01-01
Guides readers through the development of geometry and basic proof writing using a historical approach to the topic. In an effort to fully appreciate the logic and structure of geometric proofs, Revolutions of Geometry places proofs into the context of geometry's history, helping readers to understand that proof writing is crucial to the job of a mathematician. Written for students and educators of mathematics alike, the book guides readers through the rich history and influential works, from ancient times to the present, behind the development of geometry. As a result, readers are successfull
Fundamental concepts of geometry
Meserve, Bruce E
1983-01-01
Demonstrates relationships between different types of geometry. Provides excellent overview of the foundations and historical evolution of geometrical concepts. Exercises (no solutions). Includes 98 illustrations.
International Nuclear Information System (INIS)
Gervais, J.L.
1993-01-01
By analyzing the extrinsic geometry of two dimensional surfaces chirally embedded in C P n (the C P n W-surface), we give exact treatments in various aspects of the classical W-geometry in the conformal gauge: First, the basis of tangent and normal vectors are defined at regular points of the surface, such that their infinitesimal displacements are given by connections which coincide with the vector potentials of the (conformal) A n -Toda Lax pair. Since the latter is known to be intrinsically related with the W symmetries, this gives the geometrical meaning of the A n W-Algebra. Second, W-surfaces are put in one-to-one correspondence with solutions of the conformally-reduced WZNW model, which is such that the Toda fields give the Cartan part in the Gauss decomposition of its solutions. Third, the additional variables of the Toda hierarchy are used as coordinates of C P n . This allows us to show that W-transformations may be extended as particular diffeomorphisms of this target-space. Higher-dimensional generalizations of the WZNW equations are derived and related with the Zakharov-Shabat equations of the Toda hierarchy. Fourth, singular points are studied from a global viewpoint, using our earlier observation that W-surfaces may be regarded as instantons. The global indices of the W-geometry, which are written in terms of the Toda fields, are shown to be the instanton numbers for associated mappings of W-surfaces into the Grassmannians. The relation with the singularities of W-surface is derived by combining the Toda equations with the Gauss-Bonnet theorem. (orig.)
Quantum groups and algebraic geometry in conformal field theory
International Nuclear Information System (INIS)
Smit, T.J.H.
1989-01-01
The classification of two-dimensional conformal field theories is described with algebraic geometry and group theory. This classification is necessary in a consistent formulation of a string theory. (author). 130 refs.; 4 figs.; schemes
Geometry of multihadron production
Energy Technology Data Exchange (ETDEWEB)
Bjorken, J.D.
1994-10-01
This summary talk only reviews a small sample of topics featured at this symposium: Introduction; The Geometry and Geography of Phase space; Space-Time Geometry and HBT; Multiplicities, Intermittency, Correlations; Disoriented Chiral Condensate; Deep Inelastic Scattering at HERA; and Other Contributions.
1996-01-01
Designs and Finite Geometries brings together in one place important contributions and up-to-date research results in this important area of mathematics. Designs and Finite Geometries serves as an excellent reference, providing insight into some of the most important research issues in the field.
Geometry of multihadron production
International Nuclear Information System (INIS)
Bjorken, J.D.
1994-10-01
This summary talk only reviews a small sample of topics featured at this symposium: Introduction; The Geometry and Geography of Phase space; Space-Time Geometry and HBT; Multiplicities, Intermittency, Correlations; Disoriented Chiral Condensate; Deep Inelastic Scattering at HERA; and Other Contributions
Morris, Barbara H.
2004-01-01
This article describes a geometry project that used the beauty of stained-glass-window designs to teach middle school students about geometric figures and concepts. Three honors prealgebra teachers and a middle school mathematics gifted intervention specialist created a geometry project that covered the curriculum and also assessed students'…
Energy Technology Data Exchange (ETDEWEB)
Grotz, Andreas
2011-10-07
In this thesis, a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems is proposed. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal structure. Restricting attention to systems of spin dimension two, we derive the objects of our quantum geometry: the spin space, the tangent space endowed with a Lorentzian metric, connection and curvature. In order to get the correspondence to classical differential geometry, we construct examples of causal fermion systems by regularizing Dirac sea configurations in Minkowski space and on a globally hyperbolic Lorentzian manifold. When removing the regularization, the objects of our quantum geometry reduce to the common objects of spin geometry on Lorentzian manifolds, up to higher order curvature corrections.
Methods of information geometry
Amari, Shun-Ichi
2000-01-01
Information geometry provides the mathematical sciences with a new framework of analysis. It has emerged from the investigation of the natural differential geometric structure on manifolds of probability distributions, which consists of a Riemannian metric defined by the Fisher information and a one-parameter family of affine connections called the \\alpha-connections. The duality between the \\alpha-connection and the (-\\alpha)-connection together with the metric play an essential role in this geometry. This kind of duality, having emerged from manifolds of probability distributions, is ubiquitous, appearing in a variety of problems which might have no explicit relation to probability theory. Through the duality, it is possible to analyze various fundamental problems in a unified perspective. The first half of this book is devoted to a comprehensive introduction to the mathematical foundation of information geometry, including preliminaries from differential geometry, the geometry of manifolds or probability d...
International Nuclear Information System (INIS)
Grotz, Andreas
2011-01-01
In this thesis, a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems is proposed. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal structure. Restricting attention to systems of spin dimension two, we derive the objects of our quantum geometry: the spin space, the tangent space endowed with a Lorentzian metric, connection and curvature. In order to get the correspondence to classical differential geometry, we construct examples of causal fermion systems by regularizing Dirac sea configurations in Minkowski space and on a globally hyperbolic Lorentzian manifold. When removing the regularization, the objects of our quantum geometry reduce to the common objects of spin geometry on Lorentzian manifolds, up to higher order curvature corrections.
Cloaking of 2D particle geometries in a surface medium
Energy Technology Data Exchange (ETDEWEB)
Alexopoulos, A., E-mail: Aris.Alexopoulos@dsto.defence.gov.au [Electronic Warfare and Radar Division, Defence Science and Technology Organisation (DSTO), PO Box 1500, Edinburgh 5111 (Australia); Yau, K.S.B. [Electronic Warfare and Radar Division, Defence Science and Technology Organisation (DSTO), PO Box 1500, Edinburgh 5111 (Australia)
2013-06-17
We theoretically examine the cloaking condition for two-dimensional particles with varying geometry embedded inside a surface medium. General solutions are obtained for multi-layer particle configurations with either all positive or partially negative constitutive parameters respectively. Cloaking of particle geometries that are large relative to the incident wavelength is demonstrated. Theoretical predictions are compared to full-wave numerical simulations for arrays of particles consisting of different geometries.
Capillary condensation in a square geometry with surface fields.
Zubaszewska, M; Gendiar, A; Drzewiński, A
2012-12-01
We study the influence of wetting on capillary condensation for a simple fluid in a square geometry with surface fields, where the reference system is an infinitely long slit. The corner transfer matrix renormalization group method has been extended to study a two-dimensional Ising model confined in an L × L geometry with equal surface fields. Our results have confirmed that in both geometries the coexistence line shift is governed by the same scaling powers, but their prefactors are different.
A Statistical Model for Synthesis of Detailed Facial Geometry
Golovinskiy, Aleksey; Matusik, Wojciech; Pfister, Hanspeter; Rusinkiewicz, Szymon; Funkhouser, Thomas
2006-01-01
Detailed surface geometry contributes greatly to the visual realism of 3D face models. However, acquiring high-resolution face geometry is often tedious and expensive. Consequently, most face models used in games, virtual reality, or computer vision look unrealistically smooth. In this paper, we introduce a new statistical technique for the analysis and synthesis of small three-dimensional facial features, such as wrinkles and pores. We acquire high-resolution face geometry for people across ...
Exact solution of the neutron transport equation in spherical geometry
Energy Technology Data Exchange (ETDEWEB)
Anli, Fikret; Akkurt, Abdullah; Yildirim, Hueseyin; Ates, Kemal [Kahramanmaras Suetcue Imam Univ. (Turkey). Faculty of Sciences and Letters
2017-03-15
Solution of the neutron transport equation in one dimensional slab geometry construct a basis for the solution of neutron transport equation in a curvilinear geometry. Therefore, in this work, we attempt to derive an exact analytical benchmark solution for both neutron transport equations in slab and spherical medium by using P{sub N} approximation which is widely used in neutron transport theory.
Complex and symplectic geometry
Medori, Costantino; Tomassini, Adriano
2017-01-01
This book arises from the INdAM Meeting "Complex and Symplectic Geometry", which was held in Cortona in June 2016. Several leading specialists, including young researchers, in the field of complex and symplectic geometry, present the state of the art of their research on topics such as the cohomology of complex manifolds; analytic techniques in Kähler and non-Kähler geometry; almost-complex and symplectic structures; special structures on complex manifolds; and deformations of complex objects. The work is intended for researchers in these areas.
Kulczycki, Stefan
2008-01-01
This accessible approach features two varieties of proofs: stereometric and planimetric, as well as elementary proofs that employ only the simplest properties of the plane. A short history of geometry precedes a systematic exposition of the principles of non-Euclidean geometry.Starting with fundamental assumptions, the author examines the theorems of Hjelmslev, mapping a plane into a circle, the angle of parallelism and area of a polygon, regular polygons, straight lines and planes in space, and the horosphere. Further development of the theory covers hyperbolic functions, the geometry of suff
Energy Technology Data Exchange (ETDEWEB)
Candelore, N R; Gast, R C; Ondis, II, L A
1978-08-01
The RCP01 Monte Carlo program for the CDC-7600 and CDC-6600 performs fixed source or eigenfunction neutron reaction rate calculations, or photon reaction rate calculations, for complex geometries. The photon calculations may be linked to the neutron reaction rate calculations. For neutron calculations, the full energy range is treated as required for neutron birth by the fission process and the subsequent neutron slowing down and thermalization, i.e., 10 MeV to 0 eV; for photon calculations the same energy range is treated. The detailed cross sections required for the neutron or photon collision processes are provided by RCPL1. This report provides details of the various types of neutron and photon starts and collisions, the common geometry tracking, and the input required. 37 figures, 1 table.
Roe, John
2003-01-01
Coarse geometry is the study of spaces (particularly metric spaces) from a 'large scale' point of view, so that two spaces that look the same from a great distance are actually equivalent. This point of view is effective because it is often true that the relevant geometric properties of metric spaces are determined by their coarse geometry. Two examples of important uses of coarse geometry are Gromov's beautiful notion of a hyperbolic group and Mostow's proof of his famous rigidity theorem. The first few chapters of the book provide a general perspective on coarse structures. Even when only metric coarse structures are in view, the abstract framework brings the same simplification as does the passage from epsilons and deltas to open sets when speaking of continuity. The middle section reviews notions of negative curvature and rigidity. Modern interest in large scale geometry derives in large part from Mostow's rigidity theorem and from Gromov's subsequent 'large scale' rendition of the crucial properties of n...
Lectures on Symplectic Geometry
Silva, Ana Cannas
2001-01-01
The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and cl...
DEFF Research Database (Denmark)
Kokkendorff, Simon Lyngby
2002-01-01
The subject of this Ph.D.-thesis is somewhere in between continuous and discrete geometry. Chapter 2 treats the geometry of finite point sets in semi-Riemannian hyperquadrics,using a matrix whose entries are a trigonometric function of relative distances in a given point set. The distance...... to the geometry of a simplex in a semi-Riemannian hyperquadric. In chapter 3 we study which finite metric spaces that are realizable in a hyperbolic space in the limit where curvature goes to -∞. We show that such spaces are the so called leaf spaces, the set of degree 1 vertices of weighted trees. We also...... establish results on the limiting geometry of such an isometrically realized leaf space simplex in hyperbolic space, when curvature goes to -∞. Chapter 4 discusses negative type of metric spaces. We give a measure theoretic treatment of this concept and related invariants. The theory developed...
Busemann, Herbert
2005-01-01
A comprehensive approach to qualitative problems in intrinsic differential geometry, this text examines Desarguesian spaces, perpendiculars and parallels, covering spaces, the influence of the sign of the curvature on geodesics, more. 1955 edition. Includes 66 figures.
Tabachnikov, Serge
2005-01-01
Mathematical billiards describe the motion of a mass point in a domain with elastic reflections off the boundary or, equivalently, the behavior of rays of light in a domain with ideally reflecting boundary. From the point of view of differential geometry, the billiard flow is the geodesic flow on a manifold with boundary. This book is devoted to billiards in their relation with differential geometry, classical mechanics, and geometrical optics. The topics covered include variational principles of billiard motion, symplectic geometry of rays of light and integral geometry, existence and nonexistence of caustics, optical properties of conics and quadrics and completely integrable billiards, periodic billiard trajectories, polygonal billiards, mechanisms of chaos in billiard dynamics, and the lesser-known subject of dual (or outer) billiards. The book is based on an advanced undergraduate topics course (but contains more material than can be realistically taught in one semester). Although the minimum prerequisit...
Introduction to tropical geometry
Maclagan, Diane
2015-01-01
Tropical geometry is a combinatorial shadow of algebraic geometry, offering new polyhedral tools to compute invariants of algebraic varieties. It is based on tropical algebra, where the sum of two numbers is their minimum and the product is their sum. This turns polynomials into piecewise-linear functions, and their zero sets into polyhedral complexes. These tropical varieties retain a surprising amount of information about their classical counterparts. Tropical geometry is a young subject that has undergone a rapid development since the beginning of the 21st century. While establishing itself as an area in its own right, deep connections have been made to many branches of pure and applied mathematics. This book offers a self-contained introduction to tropical geometry, suitable as a course text for beginning graduate students. Proofs are provided for the main results, such as the Fundamental Theorem and the Structure Theorem. Numerous examples and explicit computations illustrate the main concepts. Each of t...
Rudiments of algebraic geometry
Jenner, WE
2017-01-01
Aimed at advanced undergraduate students of mathematics, this concise text covers the basics of algebraic geometry. Topics include affine spaces, projective spaces, rational curves, algebraic sets with group structure, more. 1963 edition.
Implosions and hypertoric geometry
DEFF Research Database (Denmark)
Dancer, A.; Kirwan, F.; Swann, A.
2013-01-01
The geometry of the universal hyperkahler implosion for SU (n) is explored. In particular, we show that the universal hyperkahler implosion naturally contains a hypertoric variety described in terms of quivers. Furthermore, we discuss a gauge theoretic approach to hyperkahler implosion.......The geometry of the universal hyperkahler implosion for SU (n) is explored. In particular, we show that the universal hyperkahler implosion naturally contains a hypertoric variety described in terms of quivers. Furthermore, we discuss a gauge theoretic approach to hyperkahler implosion....
Intermediate algebra & analytic geometry
Gondin, William R
1967-01-01
Intermediate Algebra & Analytic Geometry Made Simple focuses on the principles, processes, calculations, and methodologies involved in intermediate algebra and analytic geometry. The publication first offers information on linear equations in two unknowns and variables, functions, and graphs. Discussions focus on graphic interpretations, explicit and implicit functions, first quadrant graphs, variables and functions, determinate and indeterminate systems, independent and dependent equations, and defective and redundant systems. The text then examines quadratic equations in one variable, system
More on microstate geometries of 4d black holes
International Nuclear Information System (INIS)
Bianchi, M.; Morales, J.F.; Pieri, L.; Zinnato, N.
2017-01-01
We construct explicit examples of microstate geometries of four-dimensional black holes that lift to smooth horizon-free geometries in five dimensions. Solutions consist of half-BPS D-brane atoms distributed in ℝ 3 . Charges and positions of the D-brane centers are constrained by the bubble equations and boundary conditions ensuring the regularity of the metric and the match with the black hole geometry. In the case of three centers, we find that the moduli spaces of solutions includes disjoint one-dimensional components of (generically) finite volume.
More on microstate geometries of 4d black holes
Energy Technology Data Exchange (ETDEWEB)
Bianchi, M. [Università di Roma Tor Vergata and I.N.F.N, Dipartimento di Fisica,Via della Ricerca Scientifica, I-00133 Rome (Italy); Morales, J.F. [I.N.F.N. - Sezione di Roma 2 and Università di Roma Tor Vergata, Dipartimento di Fisica,Via della Ricerca Scientifica, I-00133 Roma (Italy); Pieri, L. [Università di Roma Tor Vergata and I.N.F.N, Dipartimento di Fisica,Via della Ricerca Scientifica, I-00133 Rome (Italy); Center for Research in String Theory, School of Physics and Astronomy,Queen Mary University of London, Mile End Road, London, E1 4NS (United Kingdom); Zinnato, N. [Università di Roma Tor Vergata and I.N.F.N, Dipartimento di Fisica,Via della Ricerca Scientifica, I-00133 Rome (Italy)
2017-05-29
We construct explicit examples of microstate geometries of four-dimensional black holes that lift to smooth horizon-free geometries in five dimensions. Solutions consist of half-BPS D-brane atoms distributed in ℝ{sup 3}. Charges and positions of the D-brane centers are constrained by the bubble equations and boundary conditions ensuring the regularity of the metric and the match with the black hole geometry. In the case of three centers, we find that the moduli spaces of solutions includes disjoint one-dimensional components of (generically) finite volume.
International Nuclear Information System (INIS)
Osborne, I; Brownson, E; Eulisse, G; Jones, C D; Sexton-Kennedy, E; Lange, D J
2014-01-01
CMS faces real challenges with upgrade of the CMS detector through 2020 and beyond. One of the challenges, from the software point of view, is managing upgrade simulations with the same software release as the 2013 scenario. We present the CMS geometry description software model, its integration with the CMS event setup and core software. The CMS geometry configuration and selection is implemented in Python. The tools collect the Python configuration fragments into a script used in CMS workflow. This flexible and automated geometry configuration allows choosing either transient or persistent version of the same scenario and specific version of the same scenario. We describe how the geometries are integrated and validated, and how we define and handle different geometry scenarios in simulation and reconstruction. We discuss how to transparently manage multiple incompatible geometries in the same software release. Several examples are shown based on current implementation assuring consistent choice of scenario conditions. The consequences and implications for multiple/different code algorithms are discussed.
Software Geometry in Simulations
Alion, Tyler; Viren, Brett; Junk, Tom
2015-04-01
The Long Baseline Neutrino Experiment (LBNE) involves many detectors. The experiment's near detector (ND) facility, may ultimately involve several detectors. The far detector (FD) will be significantly larger than any other Liquid Argon (LAr) detector yet constructed; many prototype detectors are being constructed and studied to motivate a plethora of proposed FD designs. Whether it be a constructed prototype or a proposed ND/FD design, every design must be simulated and analyzed. This presents a considerable challenge to LBNE software experts; each detector geometry must be described to the simulation software in an efficient way which allows for multiple authors to easily collaborate. Furthermore, different geometry versions must be tracked throughout their use. We present a framework called General Geometry Description (GGD), written and developed by LBNE software collaborators for managing software to generate geometries. Though GGD is flexible enough to be used by any experiment working with detectors, we present it's first use in generating Geometry Description Markup Language (GDML) files to interface with LArSoft, a framework of detector simulations, event reconstruction, and data analyses written for all LAr technology users at Fermilab. Brett is the other of the framework discussed here, the General Geometry Description (GGD).
The Use of Geometry Learning Media Based on Augmented Reality for Junior High School Students
Rohendi, D.; Septian, S.; Sutarno, H.
2018-02-01
Understanding the geometry especially of three-dimensional space is still considered difficult by some students. Therefore, a learning innovation is required to overcome students’ difficulties in learning geometry. In this research, we developed geometry learning media based on augmented reality in android flatform’s then it was implemented in teaching three-dimensional objects for some junior high school students to find out: how is the students response in using this new media in geometry and is this media can solve the student’s difficulties in understanding geometry concept. The results showed that the use of geometry learning media based on augmented reality in android flatform is able to get positive responses from the students in learning geometry concepts especially three-dimensional objects and students more easy to understand concept of diagonal in geometry than before using this media.
Introduction to global variational geometry
Krupka, Demeter
2015-01-01
The book is devoted to recent research in the global variational theory on smooth manifolds. Its main objective is an extension of the classical variational calculus on Euclidean spaces to (topologically nontrivial) finite-dimensional smooth manifolds; to this purpose the methods of global analysis of differential forms are used. Emphasis is placed on the foundations of the theory of variational functionals on fibered manifolds - relevant geometric structures for variational principles in geometry, physical field theory and higher-order fibered mechanics. The book chapters include: - foundations of jet bundles and analysis of differential forms and vector fields on jet bundles, - the theory of higher-order integral variational functionals for sections of a fibred space, the (global) first variational formula in infinitesimal and integral forms- extremal conditions and the discussion of Noether symmetries and generalizations,- the inverse problems of the calculus of variations of Helmholtz type- variational se...
Seesaw mechanism in warped geometry
International Nuclear Information System (INIS)
Huber, S.J.; Shafi, Q.
2003-09-01
We show how the seesaw mechanism for neutrino masses can be realized within a five dimensional (5D) warped geometry framework. Intermediate scale standard model (SM) singlet neutrino masses, needed to explain the atmospheric and solar neutrino oscillations, are shown to be proportional to M P1 .exp((2c-1)πkR), where c denotes the coefficient of the 5D Dirac mass term for the singlet neutrino which also has a Planck scale Majorana mass localized on the Planck-brane, and kR∼11 in order to resolve the gauge hierarchy problem. The case with a bulk 5D Majorana mass term for the singlet neutrino is briefly discussed. (orig.)
Seesaw mechanism in warped geometry
International Nuclear Information System (INIS)
Huber, Stephan J.; Shafi, Qaisar
2004-01-01
We show how the seesaw mechanism for neutrino masses can be realized within a five-dimensional (5D) warped geometry framework. Intermediate scale standard model (SM) singlet neutrino masses, needed to explain the atmospheric and solar neutrino oscillations, are shown to be proportional to M Pl exp((2c-1)πkR), where c denotes the coefficient of the 5D Dirac mass term for the singlet neutrino which also has a Planck scale Majorana mass localized on the Planck-brane, and kR∼11 in order to resolve the gauge hierarchy problem. The case with a bulk 5D Majorana mass term for the singlet neutrino is briefly discussed
Global aspects of complex geometry
Catanese, Fabrizio; Huckleberry, Alan T
2006-01-01
Present an overview of developments in Complex Geometry. This book covers topics that range from curve and surface theory through special varieties in higher dimensions, moduli theory, Kahler geometry, and group actions to Hodge theory and characteristic p-geometry.
Foundations of arithmetic differential geometry
Buium, Alexandru
2017-01-01
The aim of this book is to introduce and develop an arithmetic analogue of classical differential geometry. In this new geometry the ring of integers plays the role of a ring of functions on an infinite dimensional manifold. The role of coordinate functions on this manifold is played by the prime numbers. The role of partial derivatives of functions with respect to the coordinates is played by the Fermat quotients of integers with respect to the primes. The role of metrics is played by symmetric matrices with integer coefficients. The role of connections (respectively curvature) attached to metrics is played by certain adelic (respectively global) objects attached to the corresponding matrices. One of the main conclusions of the theory is that the spectrum of the integers is "intrinsically curved"; the study of this curvature is then the main task of the theory. The book follows, and builds upon, a series of recent research papers. A significant part of the material has never been published before.
Dimensional control of die castings
Karve, Aniruddha Ajit
The demand for net shape die castings, which require little or no machining, is steadily increasing. Stringent customer requirements are forcing die casters to deliver high quality castings in increasingly short lead times. Dimensional conformance to customer specifications is an inherent part of die casting quality. The dimensional attributes of a die casting are essentially dependent upon many factors--the quality of the die and the degree of control over the process variables being the two major sources of dimensional error in die castings. This study focused on investigating the nature and the causes of dimensional error in die castings. The two major components of dimensional error i.e., dimensional variability and die allowance were studied. The major effort of this study was to qualitatively and quantitatively study the effects of casting geometry and process variables on die casting dimensional variability and die allowance. This was accomplished by detailed dimensional data collection at production die casting sites. Robust feature characterization schemes were developed to describe complex casting geometry in quantitative terms. Empirical modeling was utilized to quantify the effects of the casting variables on dimensional variability and die allowance for die casting features. A number of casting geometry and process variables were found to affect dimensional variability in die castings. The dimensional variability was evaluated by comparisons with current published dimensional tolerance standards. The casting geometry was found to play a significant role in influencing the die allowance of the features measured. The predictive models developed for dimensional variability and die allowance were evaluated to test their effectiveness. Finally, the relative impact of all the components of dimensional error in die castings was put into perspective, and general guidelines for effective dimensional control in the die casting plant were laid out. The results of
Geometric Monte Carlo and black Janus geometries
Energy Technology Data Exchange (ETDEWEB)
Bak, Dongsu, E-mail: dsbak@uos.ac.kr [Physics Department, University of Seoul, Seoul 02504 (Korea, Republic of); B.W. Lee Center for Fields, Gravity & Strings, Institute for Basic Sciences, Daejeon 34047 (Korea, Republic of); Kim, Chanju, E-mail: cjkim@ewha.ac.kr [Department of Physics, Ewha Womans University, Seoul 03760 (Korea, Republic of); Kim, Kyung Kiu, E-mail: kimkyungkiu@gmail.com [Department of Physics, Sejong University, Seoul 05006 (Korea, Republic of); Department of Physics, College of Science, Yonsei University, Seoul 03722 (Korea, Republic of); Min, Hyunsoo, E-mail: hsmin@uos.ac.kr [Physics Department, University of Seoul, Seoul 02504 (Korea, Republic of); Song, Jeong-Pil, E-mail: jeong_pil_song@brown.edu [Department of Chemistry, Brown University, Providence, RI 02912 (United States)
2017-04-10
We describe an application of the Monte Carlo method to the Janus deformation of the black brane background. We present numerical results for three and five dimensional black Janus geometries with planar and spherical interfaces. In particular, we argue that the 5D geometry with a spherical interface has an application in understanding the finite temperature bag-like QCD model via the AdS/CFT correspondence. The accuracy and convergence of the algorithm are evaluated with respect to the grid spacing. The systematic errors of the method are determined using an exact solution of 3D black Janus. This numerical approach for solving linear problems is unaffected initial guess of a trial solution and can handle an arbitrary geometry under various boundary conditions in the presence of source fields.
International Nuclear Information System (INIS)
Jonsson, Rickard; Westman, Hans
2006-01-01
We show that by employing the standard projected curvature as a measure of spatial curvature, we can make a certain generalization of optical geometry (Abramowicz M A and Lasota J-P 1997 Class. Quantum Grav. A 14 23-30). This generalization applies to any spacetime that admits a hypersurface orthogonal shearfree congruence of worldlines. This is a somewhat larger class of spacetimes than the conformally static spacetimes assumed in standard optical geometry. In the generalized optical geometry, which in the generic case is time dependent, photons move with unit speed along spatial geodesics and the sideways force experienced by a particle following a spatially straight line is independent of the velocity. Also gyroscopes moving along spatial geodesics do not precess (relative to the forward direction). Gyroscopes that follow a curved spatial trajectory precess according to a very simple law of three-rotation. We also present an inertial force formalism in coordinate representation for this generalization. Furthermore, we show that by employing a new sense of spatial curvature (Jonsson R 2006 Class. Quantum Grav. 23 1)) closely connected to Fermat's principle, we can make a more extensive generalization of optical geometry that applies to arbitrary spacetimes. In general this optical geometry will be time dependent, but still geodesic photons move with unit speed and follow lines that are spatially straight in the new sense. Also, the sideways experienced (comoving) force on a test particle following a line that is straight in the new sense will be independent of the velocity
Virial theorem and hypervirial theorem in a spherical geometry
International Nuclear Information System (INIS)
Li Yan; Chen Jingling; Zhang Fulin
2011-01-01
The virial theorem in the one- and two-dimensional spherical geometry are presented in both classical and quantum mechanics. Choosing a special class of hypervirial operators, the quantum hypervirial relations in the spherical spaces are obtained. With the aid of the Hellmann-Feynman theorem, these relations can be used to formulate a perturbation theorem without wavefunctions, corresponding to the hypervirial-Hellmann-Feynman theorem perturbation theorem of Euclidean geometry. The one-dimensional harmonic oscillator and two-dimensional Coulomb system in the spherical spaces are given as two sample examples to illustrate the perturbation method. (paper)
Comparison of selected dynamic geometry software
Lahajner, Sonja
2012-01-01
Mathematical software is an important means for increasing motivation and for promoting activities for developing mathematical thinking. One of the main purposes in this respect is improving the level of geometric thinking. The diploma thesis starts with a description of Van Hiele theory, which is considered to be the best description of pupils’ understanding of two-dimensional geometry. The theory aims to improving pupils’ level of geometric thinking, which can be achieved also by combin...
Algorithms and file structures for computational geometry
International Nuclear Information System (INIS)
Hinrichs, K.; Nievergelt, J.
1983-01-01
Algorithms for solving geometric problems and file structures for storing large amounts of geometric data are of increasing importance in computer graphics and computer-aided design. As examples of recent progress in computational geometry, we explain plane-sweep algorithms, which solve various topological and geometric problems efficiently; and we present the grid file, an adaptable, symmetric multi-key file structure that provides efficient access to multi-dimensional data along any space dimension. (orig.)
Computational synthetic geometry
Bokowski, Jürgen
1989-01-01
Computational synthetic geometry deals with methods for realizing abstract geometric objects in concrete vector spaces. This research monograph considers a large class of problems from convexity and discrete geometry including constructing convex polytopes from simplicial complexes, vector geometries from incidence structures and hyperplane arrangements from oriented matroids. It turns out that algorithms for these constructions exist if and only if arbitrary polynomial equations are decidable with respect to the underlying field. Besides such complexity theorems a variety of symbolic algorithms are discussed, and the methods are applied to obtain new mathematical results on convex polytopes, projective configurations and the combinatorics of Grassmann varieties. Finally algebraic varieties characterizing matroids and oriented matroids are introduced providing a new basis for applying computer algebra methods in this field. The necessary background knowledge is reviewed briefly. The text is accessible to stud...
Discrete and computational geometry
Devadoss, Satyan L
2011-01-01
Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science. This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincaré conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also fe...
Ochiai, T.; Nacher, J. C.
2011-09-01
Recently, the application of geometry and conformal mappings to artificial materials (metamaterials) has attracted the attention in various research communities. These materials, characterized by a unique man-made structure, have unusual optical properties, which materials found in nature do not exhibit. By applying the geometry and conformal mappings theory to metamaterial science, it may be possible to realize so-called "Harry Potter cloaking device". Although such a device is still in the science fiction realm, several works have shown that by using such metamaterials it may be possible to control the direction of the electromagnetic field at will. We could then make an object hidden inside of a cloaking device. Here, we will explain how to design invisibility device using differential geometry and conformal mappings.
Zheng, Fangyang
2002-01-01
The theory of complex manifolds overlaps with several branches of mathematics, including differential geometry, algebraic geometry, several complex variables, global analysis, topology, algebraic number theory, and mathematical physics. Complex manifolds provide a rich class of geometric objects, for example the (common) zero locus of any generic set of complex polynomials is always a complex manifold. Yet complex manifolds behave differently than generic smooth manifolds; they are more coherent and fragile. The rich yet restrictive character of complex manifolds makes them a special and interesting object of study. This book is a self-contained graduate textbook that discusses the differential geometric aspects of complex manifolds. The first part contains standard materials from general topology, differentiable manifolds, and basic Riemannian geometry. The second part discusses complex manifolds and analytic varieties, sheaves and holomorphic vector bundles, and gives a brief account of the surface classifi...
Assigned and unassigned distance geometry: applications to biological molecules and nanostructures
Energy Technology Data Exchange (ETDEWEB)
Billinge, Simon J. L. [Columbia Univ., New York, NY (United States). Applied Physics and Applied Mathematics; Brookhaven National Lab. (BNL), Upton, NY (United States). X-ray Scattering Group; Duxbury, Phillip M. [Michigan State Univ., East Lansing, MI (United States). Dept. of Physics and Astronomy; Gonçalves, Douglas S. [Univ. Federal de Santa Catarina,; Lavor, Carlile [Univ. of Campinas (UNICAMP), Sao Paulo (Brazil). Dept. of Applied Mathematics (IMECC-UNICAMP); Mucherino, Antonio [Univ. de Rennes, Rennes (France). Institut de Recherche en Informatique et Systemes Aleatoires
2016-04-04
Here, considering geometry based on the concept of distance, the results found by Menger and Blumenthal originated a body of knowledge called distance geometry. This survey covers some recent developments for assigned and unassigned distance geometry and focuses on two main applications: determination of three-dimensional conformations of biological molecules and nanostructures.
Towards relativistic quantum geometry
Energy Technology Data Exchange (ETDEWEB)
Ridao, Luis Santiago [Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina); Bellini, Mauricio, E-mail: mbellini@mdp.edu.ar [Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350, C.P. 7600, Mar del Plata (Argentina); Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina)
2015-12-17
We obtain a gauge-invariant relativistic quantum geometry by using a Weylian-like manifold with a geometric scalar field which provides a gauge-invariant relativistic quantum theory in which the algebra of the Weylian-like field depends on observers. An example for a Reissner–Nordström black-hole is studied.
Multiplicity in difference geometry
Tomasic, Ivan
2011-01-01
We prove a first principle of preservation of multiplicity in difference geometry, paving the way for the development of a more general intersection theory. In particular, the fibres of a \\sigma-finite morphism between difference curves are all of the same size, when counted with correct multiplicities.
International Nuclear Information System (INIS)
Konopleva, N.P.
2009-01-01
The basic ideas of description methods of physical fields and elementary particle interactions are discussed. One of such ideas is the conception of space-time geometry. In this connection experimental measurement methods are analyzed. It is shown that measure procedures are the origin of geometrical axioms. The connection between space symmetry properties and the conservation laws is considered
Wares, Arsalan; Elstak, Iwan
2017-01-01
The purpose of this paper is to describe the mathematics that emanates from the construction of an origami box. We first construct a simple origami box from a rectangular sheet and then discuss some of the mathematical questions that arise in the context of geometry and algebra. The activity can be used as a context for illustrating how algebra…
MacKeown, P. K.
1984-01-01
Clarifies two concepts of gravity--those of a fictitious force and those of how space and time may have geometry. Reviews the position of Newton's theory of gravity in the context of special relativity and considers why gravity (as distinct from electromagnetics) lends itself to Einstein's revolutionary interpretation. (JN)
DEFF Research Database (Denmark)
Booss-Bavnbek, Bernhelm
2011-01-01
This paper applies I.M. Gelfand's distinction between adequate and non-adequate use of mathematical language in different contexts to the newly opened window of model-based measurements of intracellular dynamics. The specifics of geometry and dynamics on the mesoscale of cell physiology are elabo...
Diophantine geometry an introduction
Hindry, Marc
2000-01-01
This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and professional mathematicians. In each part of the book, the reader will find numerous exercises.
Sliding vane geometry turbines
Sun, Harold Huimin; Zhang, Jizhong; Hu, Liangjun; Hanna, Dave R
2014-12-30
Various systems and methods are described for a variable geometry turbine. In one example, a turbine nozzle comprises a central axis and a nozzle vane. The nozzle vane includes a stationary vane and a sliding vane. The sliding vane is positioned to slide in a direction substantially tangent to an inner circumference of the turbine nozzle and in contact with the stationary vane.
Boyer, Carl B
2012-01-01
Designed as an integrated survey of the development of analytic geometry, this study presents the concepts and contributions from before the Alexandrian Age through the eras of the great French mathematicians Fermat and Descartes, and on through Newton and Euler to the "Golden Age," from 1789 to 1850.
Coxeter, HSM
1965-01-01
This textbook introduces non-Euclidean geometry, and the third edition adds a new chapter, including a description of the two families of 'mid-lines' between two given lines and an elementary derivation of the basic formulae of spherical trigonometry and hyperbolic trigonometry, and other new material.
International Nuclear Information System (INIS)
Ezin, J.P.
1988-08-01
The lectures given at the ''5th Symposium of Mathematics in Abidjan: Differential Geometry and Mechanics'' are presented. They are divided into four chapters: Riemannian metric on a differential manifold, curvature tensor fields on a Riemannian manifold, some classical functionals on Riemannian manifolds and questions. 11 refs
Hartshorne, Robin
2000-01-01
In recent years, I have been teaching a junior-senior-level course on the classi cal geometries. This book has grown out of that teaching experience. I assume only high-school geometry and some abstract algebra. The course begins in Chapter 1 with a critical examination of Euclid's Elements. Students are expected to read concurrently Books I-IV of Euclid's text, which must be obtained sepa rately. The remainder of the book is an exploration of questions that arise natu rally from this reading, together with their modern answers. To shore up the foundations we use Hilbert's axioms. The Cartesian plane over a field provides an analytic model of the theory, and conversely, we see that one can introduce coordinates into an abstract geometry. The theory of area is analyzed by cutting figures into triangles. The algebra of field extensions provides a method for deciding which geometrical constructions are possible. The investigation of the parallel postulate leads to the various non-Euclidean geometries. And ...
Higher (odd dimensional quantum Hall effect and extended dimensional hierarchy
Directory of Open Access Journals (Sweden)
Kazuki Hasebe
2017-07-01
Full Text Available We demonstrate dimensional ladder of higher dimensional quantum Hall effects by exploiting quantum Hall effects on arbitrary odd dimensional spheres. Non-relativistic and relativistic Landau models are analyzed on S2k−1 in the SO(2k−1 monopole background. The total sub-band degeneracy of the odd dimensional lowest Landau level is shown to be equal to the winding number from the base-manifold S2k−1 to the one-dimension higher SO(2k gauge group. Based on the chiral Hopf maps, we clarify the underlying quantum Nambu geometry for odd dimensional quantum Hall effect and the resulting quantum geometry is naturally embedded also in one-dimension higher quantum geometry. An origin of such dimensional ladder connecting even and odd dimensional quantum Hall effects is illuminated from a viewpoint of the spectral flow of Atiyah–Patodi–Singer index theorem in differential topology. We also present a BF topological field theory as an effective field theory in which membranes with different dimensions undergo non-trivial linking in odd dimensional space. Finally, an extended version of the dimensional hierarchy for higher dimensional quantum Hall liquids is proposed, and its relationship to quantum anomaly and D-brane physics is discussed.
Introduction to Louis Michel's lattice geometry through group action
Zhilinskii, Boris
2015-01-01
Group action analysis developed and applied mainly by Louis Michel to the study of N-dimensional periodic lattices is the central subject of the book. Different basic mathematical tools currently used for the description of lattice geometry are introduced and illustrated through applications to crystal structures in two- and three-dimensional space, to abstract multi-dimensional lattices and to lattices associated with integrable dynamical systems. Starting from general Delone sets the authors turn to different symmetry and topological classifications including explicit construction of orbifolds for two- and three-dimensional point and space groups. Voronoï and Delone cells together with positive quadratic forms and lattice description by root systems are introduced to demonstrate alternative approaches to lattice geometry study. Zonotopes and zonohedral families of 2-, 3-, 4-, 5-dimensional lattices are explicitly visualized using graph theory approach. Along with crystallographic applications, qualitative ...
HKT geometry and de Sitter supergravity
International Nuclear Information System (INIS)
Grover, Jai; Gutowski, Jan B.; Herdeiro, Carlos A.R.; Sabra, Wafic
2009-01-01
Solutions of five-dimensional minimal de Sitter supergravity admitting Killing spinors are considered. It is shown that the 'timelike' solutions are determined in terms of a four-dimensional hyper-Kaehler torsion (HKT) manifold. If the HKT manifold is conformally hyper-Kaehler the most general solution can be obtained from a sub-class of supersymmetric solutions of minimal N=2 ungauged supergravity, by means of a simple transformation. Examples include a multi-BMPV de Sitter solution, describing multiple rotating black holes co-moving with the expansion of the universe. If the HKT manifold is not conformally hyper-Kaehler, examples admitting a tri-holomorphic Killing vector field are constructed in terms of certain solutions of three-dimensional Einstein-Weyl geometry
Multivariate calculus and geometry
Dineen, Seán
2014-01-01
Multivariate calculus can be understood best by combining geometric insight, intuitive arguments, detailed explanations and mathematical reasoning. This textbook has successfully followed this programme. It additionally provides a solid description of the basic concepts, via familiar examples, which are then tested in technically demanding situations. In this new edition the introductory chapter and two of the chapters on the geometry of surfaces have been revised. Some exercises have been replaced and others provided with expanded solutions. Familiarity with partial derivatives and a course in linear algebra are essential prerequisites for readers of this book. Multivariate Calculus and Geometry is aimed primarily at higher level undergraduates in the mathematical sciences. The inclusion of many practical examples involving problems of several variables will appeal to mathematics, science and engineering students.
Transformational plane geometry
Umble, Ronald N
2014-01-01
Axioms of Euclidean Plane Geometry The Existence and Incidence Postulates The Distance and Ruler Postulates The Plane Separation Postulate The Protractor Postulate The Side-Angle-Side Postulate and the Euclidean Parallel Postulate Theorems of Euclidean Plane Geometry The Exterior Angle Theorem Triangle Congruence Theorems The Alternate Interior Angles Theorem and the Angle Sum Theorem Similar Triangles Introduction to Transformations, Isometries, and Similarities Transformations Isometries and SimilaritiesAppendix: Proof of Surjectivity Translations, Rotations, and Reflections Translations Rotations Reflections Appendix: Geometer's Sketchpad Commands Required by Exploratory Activities Compositions of Translations, Rotations, and Reflections The Three Points Theorem Rotations as Compositions of Two Reflections Translations as Compositions of Two Halfturns or Two Reflections The Angle Addition Theorem Glide Reflections Classification of Isometries The Fundamental Theorem and Congruence Classification of Isometr...
Multilevel geometry optimization
Rodgers, Jocelyn M.; Fast, Patton L.; Truhlar, Donald G.
2000-02-01
Geometry optimization has been carried out for three test molecules using six multilevel electronic structure methods, in particular Gaussian-2, Gaussian-3, multicoefficient G2, multicoefficient G3, and two multicoefficient correlation methods based on correlation-consistent basis sets. In the Gaussian-2 and Gaussian-3 methods, various levels are added and subtracted with unit coefficients, whereas the multicoefficient Gaussian-x methods involve noninteger parameters as coefficients. The multilevel optimizations drop the average error in the geometry (averaged over the 18 cases) by a factor of about two when compared to the single most expensive component of a given multilevel calculation, and in all 18 cases the accuracy of the atomization energy for the three test molecules improves; with an average improvement of 16.7 kcal/mol.
Multilevel geometry optimization
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Rodgers, Jocelyn M. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States); Fast, Patton L. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States); Truhlar, Donald G. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States)
2000-02-15
Geometry optimization has been carried out for three test molecules using six multilevel electronic structure methods, in particular Gaussian-2, Gaussian-3, multicoefficient G2, multicoefficient G3, and two multicoefficient correlation methods based on correlation-consistent basis sets. In the Gaussian-2 and Gaussian-3 methods, various levels are added and subtracted with unit coefficients, whereas the multicoefficient Gaussian-x methods involve noninteger parameters as coefficients. The multilevel optimizations drop the average error in the geometry (averaged over the 18 cases) by a factor of about two when compared to the single most expensive component of a given multilevel calculation, and in all 18 cases the accuracy of the atomization energy for the three test molecules improves; with an average improvement of 16.7 kcal/mol. (c) 2000 American Institute of Physics.
Krauss, Lawrence M.; Turner, Michael S.
1999-01-01
The recognition that the cosmological constant may be non-zero forces us to re-evaluate standard notions about the connection between geometry and the fate of our Universe. An open Universe can recollapse, and a closed Universe can expand forever. As a corollary, we point out that there is no set of cosmological observations we can perform that will unambiguously allow us to determine what the ultimate destiny of the Universe will be.
DEFF Research Database (Denmark)
Tamke, Martin; Ramsgaard Thomsen, Mette; Riiber Nielsen, Jacob
2009-01-01
The versatility of wood constructions and traditional wood joints for the production of non standard elements was in focus of a design based research. Herein we established a seamless process from digital design to fabrication. A first research phase centered on the development of a robust...... parametric model and a generic design language a later explored the possibilities to construct complex shaped geometries with self registering joints on modern wood crafting machines. The research was carried out as collaboration with industrial partners....
International Nuclear Information System (INIS)
Lepora, N.; Kibble, T.
1999-01-01
We analyse symmetry breaking in the Weinberg-Salam model paying particular attention to the underlying geometry of the theory. In this context we find two natural metrics upon the vacuum manifold: an isotropic metric associated with the scalar sector, and a squashed metric associated with the gauge sector. Physically, the interplay between these metrics gives rise to many of the non-perturbative features of Weinberg-Salam theory. (author)
Integral geometry and valuations
Solanes, Gil
2014-01-01
Valuations are finitely additive functionals on the space of convex bodies. Their study has become a central subject in convexity theory, with fundamental applications to integral geometry. In the last years there has been significant progress in the theory of valuations, which in turn has led to important achievements in integral geometry. This book originated from two courses delivered by the authors at the CRM and provides a self-contained introduction to these topics, covering most of the recent advances. The first part, by Semyon Alesker, is devoted to the theory of convex valuations, with emphasis on the latest developments. A special focus is put on the new fundamental structures of the space of valuations discovered after Alesker's irreducibility theorem. Moreover, the author describes the newly developed theory of valuations on manifolds. In the second part, Joseph H. G. Fu gives a modern introduction to integral geometry in the sense of Blaschke and Santaló, based on the notions and tools presented...
CBM RICH geometry optimization
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Mahmoud, Tariq; Hoehne, Claudia [II. Physikalisches Institut, Giessen Univ. (Germany); Collaboration: CBM-Collaboration
2016-07-01
The Compressed Baryonic Matter (CBM) experiment at the future FAIR complex will investigate the phase diagram of strongly interacting matter at high baryon density and moderate temperatures in A+A collisions from 2-11 AGeV (SIS100) beam energy. The main electron identification detector in the CBM experiment will be a RICH detector with a CO{sub 2} gaseous-radiator, focusing spherical glass mirrors, and MAPMT photo-detectors being placed on a PMT-plane. The RICH detector is located directly behind the CBM dipole magnet. As the final magnet geometry is now available, some changes in the RICH geometry become necessary. In order to guarantee a magnetic field of 1 mT at maximum in the PMT plane for effective operation of the MAPMTs, two measures have to be taken: The PMT plane is moved outwards of the stray field by tilting the mirrors by 10 degrees and shielding boxes have been designed. In this contribution the results of the geometry optimization procedure are presented.
Introducing geometry concept based on history of Islamic geometry
Maarif, S.; Wahyudin; Raditya, A.; Perbowo, K. S.
2018-01-01
Geometry is one of the areas of mathematics interesting to discuss. Geometry also has a long history in mathematical developments. Therefore, it is important integrated historical development of geometry in the classroom to increase’ knowledge of how mathematicians earlier finding and constructing a geometric concept. Introduction geometrical concept can be started by introducing the Muslim mathematician who invented these concepts so that students can understand in detail how a concept of geometry can be found. However, the history of mathematics development, especially history of Islamic geometry today is less popular in the world of education in Indonesia. There are several concepts discovered by Muslim mathematicians that should be appreciated by the students in learning geometry. Great ideas of mathematicians Muslim can be used as study materials to supplement religious character values taught by Muslim mathematicians. Additionally, by integrating the history of geometry in teaching geometry are expected to improve motivation and geometrical understanding concept.
A short course in computational geometry and topology
Edelsbrunner, Herbert
2014-01-01
With the aim to bring the subject of Computational Geometry and Topology closer to the scientific audience, this book is written in thirteen ready-to-teach sections organized in four parts: tessellations, complexes, homology, persistence. To speak to the non-specialist, detailed formalisms are often avoided in favor of lively 2- and 3-dimensional illustrations. The book is warmly recommended to everybody who loves geometry and the fascinating world of shapes.
Quantum groups: Geometry and applications
International Nuclear Information System (INIS)
Chu, C.S.
1996-01-01
The main theme of this thesis is a study of the geometry of quantum groups and quantum spaces, with the hope that they will be useful for the construction of quantum field theory with quantum group symmetry. The main tool used is the Faddeev-Reshetikhin-Takhtajan description of quantum groups. A few content-rich examples of quantum complex spaces with quantum group symmetry are treated in details. In chapter 1, the author reviews some of the basic concepts and notions for Hopf algebras and other background materials. In chapter 2, he studies the vector fields of quantum groups. A compact realization of these vector fields as pseudodifferential operators acting on the linear quantum spaces is given. In chapter 3, he describes the quantum sphere as a complex quantum manifold by means of a quantum stereographic projection. A covariant calculus is introduced. An interesting property of this calculus is the existence of a one-form realization of the exterior differential operator. The concept of a braided comodule is introduced and a braided algebra of quantum spheres is constructed. In chapter 4, the author considers the more general higher dimensional quantum complex projective spaces and the quantum Grassman manifolds. Differential calculus, integration and braiding can be introduced as in the one dimensional case. Finally, in chapter 5, he studies the framework of quantum principal bundle and construct the q-deformed Dirac monopole as a quantum principal bundle with a quantum sphere as the base and a U(1) with non-commutative calculus as the fiber. The first Chern class can be introduced and integrated to give the monopole charge
Two lectures on D-geometry and noncommutative geometry
International Nuclear Information System (INIS)
Douglas, M.R.
1999-01-01
This is a write-up of lectures given at the 1998 Spring School at the Abdus Salam ICTP. We give a conceptual introduction to D-geometry, the study of geometry as seen by D-branes in string theory, and to noncommutative geometry as it has appeared in D-brane and Matrix theory physics. (author)
International Nuclear Information System (INIS)
Hook, D W
2008-01-01
A geometric framework for quantum mechanics arose during the mid 1970s when authors such as Cantoni explored the notion of generalized transition probabilities, and Kibble promoted the idea that the space of pure quantum states provides a natural quantum mechanical analogue for classical phase space. This central idea can be seen easily since the projection of Schroedinger's equation from a Hilbert space into the space of pure spaces is a set of Hamilton's equations. Over the intervening years considerable work has been carried out by a variety of authors and a mature description of quantum mechanics in geometric terms has emerged with many applications. This current offering would seem ideally placed to review the last thirty years of progress and relate this to the most recent work in quantum entanglement. Bengtsson and Zyczkowski's beautifully illustrated volume, Geometry of Quantum States (referred to as GQS from now on) attempts to cover considerable ground in its 466 pages. Its topics range from colour theory in Chapter 1 to quantum entanglement in Chapter 15-to say that this is a whirlwind tour is, perhaps, no understatement. The use of the work 'introduction' in the subtitle of GQS, might suggest to the reader that this work be viewed as a textbook and I think that this interpretation would be incorrect. The authors have chosen to present a survey of different topics with the specific aim to introduce entanglement in geometric terms-the book is not intended as a pedagogical introduction to the geometric approach to quantum mechanics. Each of the fifteen chapters is a short, and mostly self-contained, essay on a particular aspect or application of geometry in the context of quantum mechanics with entanglement being addressed specifically in the final chapter. The chapters fall into three classifications: those concerned with the mathematical background, those which discuss quantum theory and the foundational aspects of the geometric framework, and
Graph-drawing algorithms geometries versus molecular mechanics in fullereness
Kaufman, M.; Pisanski, T.; Lukman, D.; Borštnik, B.; Graovac, A.
1996-09-01
The algorithms of Kamada-Kawai (KK) and Fruchterman-Reingold (FR) have been recently generalized (Pisanski et al., Croat. Chem. Acta 68 (1995) 283) in order to draw molecular graphs in three-dimensional space. The quality of KK and FR geometries is studied here by comparing them with the molecular mechanics (MM) and the adjacency matrix eigenvectors (AME) algorithm geometries. In order to compare different layouts of the same molecule, an appropriate method has been developed. Its application to a series of experimentally detected fullerenes indicates that the KK, FR and AME algorithms are able to reproduce plausible molecular geometries.
Vanishing theorems and effective results in algebraic geometry
International Nuclear Information System (INIS)
Demailly, J.P.; Goettsche, L.; Lazarsfeld, R.
2001-01-01
The School on Vanishing Theorems and Effective Results in Algebraic Geometry took place in ICTP, Trieste from 25 April 2000 to 12 May 2000. It was organized by J. P. Demailly (Universite de Grenoble I) and R. Lazarsfeld (University of Michigan). The main topics considered were vanishing theorems, multiplyer ideal sheaves and effective results in algebraic geometry, tight closure, geometry of higher dimensional projective and Kahler manifolds, hyperbolic algebraic varieties. The school consisted of two weeks of lectures and one week of conference. This volume contains the lecture notes of most of the lectures in the first two weeks
Vanishing theorems and effective results in algebraic geometry
Energy Technology Data Exchange (ETDEWEB)
Demailly, J P [Universite de Grenoble (France); Goettsche, L [Abdus Salam International Centre for Theoretical Physics, Trieste (Italy); Lazarsfeld, R [University of Michigan (United States)
2001-12-15
The School on Vanishing Theorems and Effective Results in Algebraic Geometry took place in ICTP, Trieste from 25 April 2000 to 12 May 2000. It was organized by J. P. Demailly (Universite de Grenoble I) and R. Lazarsfeld (University of Michigan). The main topics considered were vanishing theorems, multiplyer ideal sheaves and effective results in algebraic geometry, tight closure, geometry of higher dimensional projective and Kahler manifolds, hyperbolic algebraic varieties. The school consisted of two weeks of lectures and one week of conference. This volume contains the lecture notes of most of the lectures in the first two weeks.
Differential geometry in string models
International Nuclear Information System (INIS)
Alvarez, O.
1986-01-01
In this article the author reviews the differential geometric approach to the quantization of strings. A seminal paper demonstrates the connection between the trace anomaly and the critical dimension. The role played by the Faddeev-Popov ghosts has been instrumental in much of the subsequent work on the quantization of strings. This paper discusses the differential geometry of two dimensional surfaces and its importance in the quantization of strings. The path integral quantization approach to strings will be carefully analyzed to determine the correct effective measure for string theories. The choice of measure for the path integral is determined by differential geometric considerations. Once the measure is determined, the manifest diffeomorphism invariance of the theory will have to be broken by using the Faddeev-Popov ansatz. The gauge fixed theory is studied in detail with emphasis on the role of conformal and gravitational anomalies. In the analysis, the path integral formulation of the gauge fixed theory requires summing over all the distinct complex structures on the manifold
Scanlon, Regina M.
2003-01-01
Describes an engaging project in which students have to design and construct a three-dimensional candy box that would appeal to children. Requires students to make the box out of prisms, pyramids, or cylinders, determine the surface area and volume of the solids, and write a persuasive business letter. (YDS)
International Nuclear Information System (INIS)
Marmo, G.; Morandi, G.
1995-01-01
In this lecture some mathematical problems that arise when one deals with low-dimensional field theories, such as homotopy and topological invariants, differential calculus on Lie groups and coset spaces, fiber spaces and parallel transport, differential calculus on fiber bundles, sequences on principal bundles and Chern-Simons terms are discussed
Dooner, David B
2012-01-01
Building on the first edition published in 1995 this new edition of Kinematic Geometry of Gearing has been extensively revised and updated with new and original material. This includes the methodology for general tooth forms, radius of torsure', cylinder of osculation, and cylindroid of torsure; the author has also completely reworked the '3 laws of gearing', the first law re-written to better parallel the existing 'Law of Gearing" as pioneered by Leonard Euler, expanded from Euler's original law to encompass non-circular gears and hypoid gears, the 2nd law of gearing describing a unique relat
Flegg, H Graham
2001-01-01
This excellent introduction to topology eases first-year math students and general readers into the subject by surveying its concepts in a descriptive and intuitive way, attempting to build a bridge from the familiar concepts of geometry to the formalized study of topology. The first three chapters focus on congruence classes defined by transformations in real Euclidean space. As the number of permitted transformations increases, these classes become larger, and their common topological properties become intuitively clear. Chapters 4-12 give a largely intuitive presentation of selected topics.
Torsional heterotic geometries
International Nuclear Information System (INIS)
Becker, Katrin; Sethi, Savdeep
2009-01-01
We construct new examples of torsional heterotic backgrounds using duality with orientifold flux compactifications. We explain how duality provides a perturbative solution to the type I/heterotic string Bianchi identity. The choice of connection used in the Bianchi identity plays an important role in the construction. We propose the existence of a much larger landscape of compact torsional geometries using string duality. Finally, we present some quantum exact metrics that correspond to NS5-branes placed on an elliptic space. These metrics describe how torus isometries are broken by NS flux.
Geometrie verstehen: statisch - kinematisch
Kroll, Ekkehard
Dem Allgemeinen steht begrifflich das Besondere gegenüber. In diesem Sinne sind allgemeine Überlegungen zum Verstehen von Mathematik zu ergänzen durch Untersuchungen hinsichtlich des Verstehens der einzelnen mathematischen Disziplinen, insbesondere der Geometrie. Hier haben viele Schülerinnen und Schüler Probleme. Diese rühren hauptsächlich daher, dass eine fertige geometrische Konstruktion in ihrer statischen Präsentation auf Papier nicht mehr die einzelnen Konstruktionsschritte erkennen lässt; zum Nachvollzug müssen sie daher ergänzend in einer Konstruktionsbeschreibung festgehalten werden.
Kendig, Keith
2015-01-01
Designed to make learning introductory algebraic geometry as easy as possible, this text is intended for advanced undergraduates and graduate students who have taken a one-year course in algebra and are familiar with complex analysis. This newly updated second edition enhances the original treatment's extensive use of concrete examples and exercises with numerous figures that have been specially redrawn in Adobe Illustrator. An introductory chapter that focuses on examples of curves is followed by a more rigorous and careful look at plane curves. Subsequent chapters explore commutative ring th
Abhyankar, Shreeram Shankar
1964-01-01
This book provides, for use in a graduate course or for self-study by graduate students, a well-motivated treatment of several topics, especially the following: (1) algebraic treatment of several complex variables; (2) geometric approach to algebraic geometry via analytic sets; (3) survey of local algebra; (4) survey of sheaf theory. The book has been written in the spirit of Weierstrass. Power series play the dominant role. The treatment, being algebraic, is not restricted to complex numbers, but remains valid over any complete-valued field. This makes it applicable to situations arising from
Akopyan, A V
2007-01-01
The book is devoted to the properties of conics (plane curves of second degree) that can be formulated and proved using only elementary geometry. Starting with the well-known optical properties of conics, the authors move to less trivial results, both classical and contemporary. In particular, the chapter on projective properties of conics contains a detailed analysis of the polar correspondence, pencils of conics, and the Poncelet theorem. In the chapter on metric properties of conics the authors discuss, in particular, inscribed conics, normals to conics, and the Poncelet theorem for confoca
2015-01-01
This stimulating volume offers a broad collection of the principles of geometry and trigonometry and contains colorful diagrams to bring mathematical principles to life. Subjects are enriched by references to famous mathematicians and their ideas, and the stories are presented in a very comprehensible way. Readers investigate the relationships of points, lines, surfaces, and solids. They study construction methods for drawing figures, a wealth of facts about these figures, and above all, methods to prove the facts. They learn about triangle measure for circular motion, sine and cosine, tangent
REA, The Editors of
2012-01-01
REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Geometry I includes methods of proof, points, lines, planes, angles, congruent angles and line segments, triangles, parallelism, quadrilaterals, geometric inequalities, and geometric
Graded geometry and Poisson reduction
Cattaneo, A S; Zambon, M
2009-01-01
The main result of [2] extends the Marsden-Ratiu reduction theorem [4] in Poisson geometry, and is proven by means of graded geometry. In this note we provide the background material about graded geometry necessary for the proof in [2]. Further, we provide an alternative algebraic proof for the main result. ©2009 American Institute of Physics
Fourier rebinning algorithm for inverse geometry CT.
Mazin, Samuel R; Pele, Norbert J
2008-11-01
Inverse geometry computed tomography (IGCT) is a new type of volumetric CT geometry that employs a large array of x-ray sources opposite a smaller detector array. Volumetric coverage and high isotropic resolution produce very large data sets and therefore require a computationally efficient three-dimensional reconstruction algorithm. The purpose of this work was to adapt and evaluate a fast algorithm based on Defrise's Fourier rebinning (FORE), originally developed for positron emission tomography. The results were compared with the average of FDK reconstructions from each source row. The FORE algorithm is an order of magnitude faster than the FDK-type method for the case of 11 source rows. In the center of the field-of-view both algorithms exhibited the same resolution and noise performance. FORE exhibited some resolution loss (and less noise) in the periphery of the field-of-view. FORE appears to be a fast and reasonably accurate reconstruction method for IGCT.
Lectures on fractal geometry and dynamical systems
Pesin, Yakov
2009-01-01
Both fractal geometry and dynamical systems have a long history of development and have provided fertile ground for many great mathematicians and much deep and important mathematics. These two areas interact with each other and with the theory of chaos in a fundamental way: many dynamical systems (even some very simple ones) produce fractal sets, which are in turn a source of irregular "chaotic" motions in the system. This book is an introduction to these two fields, with an emphasis on the relationship between them. The first half of the book introduces some of the key ideas in fractal geometry and dimension theory--Cantor sets, Hausdorff dimension, box dimension--using dynamical notions whenever possible, particularly one-dimensional Markov maps and symbolic dynamics. Various techniques for computing Hausdorff dimension are shown, leading to a discussion of Bernoulli and Markov measures and of the relationship between dimension, entropy, and Lyapunov exponents. In the second half of the book some examples o...
Metamaterial Electromagnetic Superabsorber with Arbitrary Geometries
Directory of Open Access Journals (Sweden)
Jingjing Yang
2010-06-01
Full Text Available The electromagnetic superabsorber that has larger absorption cross section than its real size may be a novel photothermal device with improved solar energy conversion rates. Based on a transformation optical approach, the material parameters for a two-dimensional (2D metamaterial-assisted electromagnetic superabsorber with arbitrary geometries are derived and validated by numerical simulation. We find that for the given geometry size, the absorption cross section of the superabsorber using nonlinear transformation is larger than that using linear transformation. These transformations can also be specialized to the designing the N-sided regular polygonal superabsorber just by changing the contour equation. All theoretical and numerical results validate the material parameters for the 2D electromagnetic superabsorber we have developed.
International Nuclear Information System (INIS)
Heckman, Jonathan J.; Morrison, David R.; Rudelius, Tom; Vafa, Cumrun
2015-01-01
We study renormalization group flows between six-dimensional superconformal field theories (SCFTs) using their geometric realizations as singular limits of F-theory compactified on elliptically fibered Calabi-Yau threefolds. There are two general types of flows: one corresponds to giving expectation values to scalars in the tensor multiplets (tensor branch flow) realized as resolving the base of the geometry. The other corresponds to giving expectation values to hypermultiplets (Higgs branch flow) realized as complex structure deformations of the geometry. To corroborate this physical picture we calculate the change in the anomaly polynomial for these theories, finding strong evidence for a flow from a UV fixed point to an IR fixed point. Moreover, we find evidence against non-trivial dualities for 6D SCFTs. In addition we find non-trivial RG flows for theories realizing small E 8 instantons on ALE spaces.
Stages as models of scene geometry.
Nedović, Vladimir; Smeulders, Arnold W M; Redert, André; Geusebroek, Jan-Mark
2010-09-01
Reconstruction of 3D scene geometry is an important element for scene understanding, autonomous vehicle and robot navigation, image retrieval, and 3D television. We propose accounting for the inherent structure of the visual world when trying to solve the scene reconstruction problem. Consequently, we identify geometric scene categorization as the first step toward robust and efficient depth estimation from single images. We introduce 15 typical 3D scene geometries called stages, each with a unique depth profile, which roughly correspond to a large majority of broadcast video frames. Stage information serves as a first approximation of global depth, narrowing down the search space in depth estimation and object localization. We propose different sets of low-level features for depth estimation, and perform stage classification on two diverse data sets of television broadcasts. Classification results demonstrate that stages can often be efficiently learned from low-dimensional image representations.
c-Extremization from toric geometry
Amariti, Antonio; Cassia, Luca; Penati, Silvia
2018-04-01
We derive a geometric formulation of the 2d central charge cr from infinite families of 4d N = 1 superconformal field theories topologically twisted on constant curvature Riemann surfaces. They correspond to toric quiver gauge theories and are associated to D3 branes probing five dimensional Sasaki-Einstein geometries in the AdS/CFT correspondence. We show that cr can be expressed in terms of the areas of the toric diagram describing the moduli space of the 4d theory, both for toric geometries with smooth and singular horizons. We also study the relation between a-maximization in 4d and c-extremization in 2d, giving further evidences of the mixing of the baryonic symmetries with the exact R-current in two dimensions.
Distance Adaptive Tensor Discriminative Geometry Preserving Projection for Face Recognition
Directory of Open Access Journals (Sweden)
Ziqiang Wang
2012-09-01
Full Text Available There is a growing interest in dimensionality reduction techniques for face recognition, however, the traditional dimensionality reduction algorithms often transform the input face image data into vectors before embedding. Such vectorization often ignores the underlying data structure and leads to higher computational complexity. To effectively cope with these problems, a novel dimensionality reduction algorithm termed distance adaptive tensor discriminative geometry preserving projection (DATDGPP is proposed in this paper. The key idea of DATDGPP is as follows: first, the face image data are directly encoded in high-order tensor structure so that the relationships among the face image data can be preserved; second, the data-adaptive tensor distance is adopted to model the correlation among different coordinates of tensor data; third, the transformation matrix which can preserve discrimination and local geometry information is obtained by an iteration algorithm. Experimental results on three face databases show that the proposed algorithm outperforms other representative dimensionality reduction algorithms.
Geometry and conformal theories
International Nuclear Information System (INIS)
Vafa, C.
1991-01-01
In this paper, the authors indicate how simplest types of string vacua arise from a class of two dimensional superconformal theories. These superconformal theories are characterized, using the universality of renormalization group flow, by the superpotential. Many questions of phenomenological interest can be answered from the structure of the superpotential alone. These include the number of generations and some of the Yukawa couplings. The material in this lecture can be found in the listed references below
Calibrated geometries and non perturbative superpotentials in M-theory
International Nuclear Information System (INIS)
Hernandez, R.
1999-12-01
We consider non perturbative effects in M-theory compactifications on a seven-manifold of G 2 holonomy arising from membranes wrapped on supersymmetric three-cycles. When membranes are wrapped on associative submanifolds they induce a superpotential that can be calculated using calibrated geometry. This superpotential is also derived from compactification on a seven-manifold, to four dimensional Anti-de Sitter spacetime, of eleven dimensional supergravity with non vanishing expectation value of the four-form field strength. (author)
The BTZ black hole as a Lorentz-flat geometry
Energy Technology Data Exchange (ETDEWEB)
Alvarez, Pedro D., E-mail: alvarez@physics.ox.ac.uk [Rudolf Peierls Centre for Theoretical Physics, University of Oxford (United Kingdom); Pais, Pablo, E-mail: pais@cecs.cl [Centro de Estudios Científicos (CECs), Av. Arturo Prat 514, Valdivia (Chile); Universidad Andrés Bello, Av. República 440, Santiago (Chile); Rodríguez, Eduardo, E-mail: eduarodriguezsal@unal.edu.co [Departamento de Matemática y Física Aplicadas, Universidad Católica de la Santísima Concepción, Concepción (Chile); Salgado-Rebolledo, Patricio, E-mail: pasalgado@udec.cl [Centro de Estudios Científicos (CECs), Av. Arturo Prat 514, Valdivia (Chile); Departamento de Física, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Physique Théorique et Mathématique, Université Libre de Bruxelles and International Solvay Institutes, Campus Plaine C.P. 231, B-1050 Bruxelles (Belgium); Zanelli, Jorge, E-mail: z@cecs.cl [Centro de Estudios Científicos (CECs), Av. Arturo Prat 514, Valdivia (Chile); Universidad Andrés Bello, Av. República 440, Santiago (Chile)
2014-11-10
It is shown that 2+1 dimensional anti-de Sitter spacetimes are Lorentz-flat. This means, in particular, that any simply-connected patch of the BTZ black hole solution can be endowed with a Lorentz connection that is locally pure gauge. The result can be naturally extended to a wider class of black hole geometries and point particles in three-dimensional spacetime.
Bochnak, Jacek; Roy, Marie-Françoise
1998-01-01
This book is a systematic treatment of real algebraic geometry, a subject that has strong interrelation with other areas of mathematics: singularity theory, differential topology, quadratic forms, commutative algebra, model theory, complexity theory etc. The careful and clearly written account covers both basic concepts and up-to-date research topics. It may be used as text for a graduate course. The present edition is a substantially revised and expanded English version of the book "Géometrie algébrique réelle" originally published in French, in 1987, as Volume 12 of ERGEBNISSE. Since the publication of the French version the theory has made advances in several directions. Many of these are included in this English version. Thus the English book may be regarded as a completely new treatment of the subject.
Critique of information geometry
International Nuclear Information System (INIS)
Skilling, John
2014-01-01
As applied to probability, information geometry fails because probability distributions do not form a metric space. Probability theory rests on a compelling foundation of elementary symmetries, which also support information (aka minus entropy, Kullback-Leibler) H(p;q) as the unique measure of divergence from source probability distribution q to destination p. Because the only compatible connective H is from≠to asymmetric, H(p;q)≠H(q;p), there can be no compatible geometrical distance (which would necessarily be from=to symmetric). Hence there is no distance relationship compatible with the structure of probability theory. Metrics g and densities sqrt(det(g)) interpreted as prior probabilities follow from the definition of distance, and must fail likewise. Various metrics and corresponding priors have been proposed, Fisher's being the most popular, but all must behave unacceptably. This is illustrated with simple counter-examples
International Nuclear Information System (INIS)
Correa, Diego H.; Silva, Guillermo A.
2008-01-01
We discuss how geometrical and topological aspects of certain (1/2)-BPS type IIB geometries are captured by their dual operators in N = 4 Super Yang-Mills theory. The type IIB solutions are characterized by arbitrary droplet pictures in a plane and we consider, in particular, axially symmetric droplets. The 1-loop anomalous dimension of the dual gauge theory operators probed with single traces is described by some bosonic lattice Hamiltonians. These Hamiltonians are shown to encode the topology of the droplets. In appropriate BMN limits, the Hamiltonians spectrum reproduces the spectrum of near-BPS string excitations propagating along each of the individual edges of the droplet. We also study semiclassical regimes for the Hamiltonians. For droplets having disconnected constituents, the Hamiltonian admits different complimentary semiclassical descriptions, each one replicating the semiclassical description for closed strings extending in each of the constituents
Emergent geometry of membranes
Energy Technology Data Exchange (ETDEWEB)
Badyn, Mathias Hudoba de; Karczmarek, Joanna L.; Sabella-Garnier, Philippe; Yeh, Ken Huai-Che [Department of Physics and Astronomy, University of British Columbia,6224 Agricultural Road, Vancouver (Canada)
2015-11-13
In work http://dx.doi.org/10.1103/PhysRevD.86.086001, a surface embedded in flat ℝ{sup 3} is associated to any three hermitian matrices. We study this emergent surface when the matrices are large, by constructing coherent states corresponding to points in the emergent geometry. We find the original matrices determine not only shape of the emergent surface, but also a unique Poisson structure. We prove that commutators of matrix operators correspond to Poisson brackets. Through our construction, we can realize arbitrary noncommutative membranes: for example, we examine a round sphere with a non-spherically symmetric Poisson structure. We also give a natural construction for a noncommutative torus embedded in ℝ{sup 3}. Finally, we make remarks about area and find matrix equations for minimal area surfaces.
Geometry through history Euclidean, hyperbolic, and projective geometries
Dillon, Meighan I
2018-01-01
Presented as an engaging discourse, this textbook invites readers to delve into the historical origins and uses of geometry. The narrative traces the influence of Euclid’s system of geometry, as developed in his classic text The Elements, through the Arabic period, the modern era in the West, and up to twentieth century mathematics. Axioms and proof methods used by mathematicians from those periods are explored alongside the problems in Euclidean geometry that lead to their work. Students cultivate skills applicable to much of modern mathematics through sections that integrate concepts like projective and hyperbolic geometry with representative proof-based exercises. For its sophisticated account of ancient to modern geometries, this text assumes only a year of college mathematics as it builds towards its conclusion with algebraic curves and quaternions. Euclid’s work has affected geometry for thousands of years, so this text has something to offer to anyone who wants to broaden their appreciation for the...
Real symplectic formulation of local special geometry
Ferrara, Sergio; Ferrara, Sergio; Macia, Oscar
2006-01-01
We consider a formulation of local special geometry in terms of Darboux special coordinates $P^I=(p^i,q_i)$, $I=1,...,2n$. A general formula for the metric is obtained which is manifestly $\\mathbf{Sp}(2n,\\mathbb{R})$ covariant. Unlike the rigid case the metric is not given by the Hessian of the real function $S(P)$ which is the Legendre transform of the imaginary part of the holomorphic prepotential. Rather it is given by an expression that contains $S$, its Hessian and the conjugate momenta $S_I=\\frac{\\partial S}{\\partial P^I}$. Only in the one-dimensional case ($n=1$) is the real (two-dimensional) metric proportional to the Hessian with an appropriate conformal factor.
On organizing principles of discrete differential geometry. Geometry of spheres
International Nuclear Information System (INIS)
Bobenko, Alexander I; Suris, Yury B
2007-01-01
Discrete differential geometry aims to develop discrete equivalents of the geometric notions and methods of classical differential geometry. This survey contains a discussion of the following two fundamental discretization principles: the transformation group principle (smooth geometric objects and their discretizations are invariant with respect to the same transformation group) and the consistency principle (discretizations of smooth parametrized geometries can be extended to multidimensional consistent nets). The main concrete geometric problem treated here is discretization of curvature-line parametrized surfaces in Lie geometry. Systematic use of the discretization principles leads to a discretization of curvature-line parametrization which unifies circular and conical nets.
Higher geometry an introduction to advanced methods in analytic geometry
Woods, Frederick S
2005-01-01
For students of mathematics with a sound background in analytic geometry and some knowledge of determinants, this volume has long been among the best available expositions of advanced work on projective and algebraic geometry. Developed from Professor Woods' lectures at the Massachusetts Institute of Technology, it bridges the gap between intermediate studies in the field and highly specialized works.With exceptional thoroughness, it presents the most important general concepts and methods of advanced algebraic geometry (as distinguished from differential geometry). It offers a thorough study
Curvature perturbations from dimensional decoupling
Giovannini, Massimo
2005-01-01
The scalar modes of the geometry induced by dimensional decoupling are investigated. In the context of the low energy string effective action, solutions can be found where the spatial part of the background geometry is the direct product of two maximally symmetric Euclidean manifolds whose related scale factors evolve at a dual rate so that the expanding dimensions first accelerate and then decelerate while the internal dimensions always contract. After introducing the perturbative treatment of the inhomogeneities, a class of five-dimensional geometries is discussed in detail. Quasi-normal modes of the system are derived and the numerical solution for the evolution of the metric inhomogeneities shows that the fluctuations of the internal dimensions provide a term that can be interpreted, in analogy with the well-known four-dimensional situation, as a non-adiabatic pressure density variation. Implications of this result are discussed with particular attention to string cosmological scenarios.
An introduction to incidence geometry
De Bruyn, Bart
2016-01-01
This book gives an introduction to the field of Incidence Geometry by discussing the basic families of point-line geometries and introducing some of the mathematical techniques that are essential for their study. The families of geometries covered in this book include among others the generalized polygons, near polygons, polar spaces, dual polar spaces and designs. Also the various relationships between these geometries are investigated. Ovals and ovoids of projective spaces are studied and some applications to particular geometries will be given. A separate chapter introduces the necessary mathematical tools and techniques from graph theory. This chapter itself can be regarded as a self-contained introduction to strongly regular and distance-regular graphs. This book is essentially self-contained, only assuming the knowledge of basic notions from (linear) algebra and projective and affine geometry. Almost all theorems are accompanied with proofs and a list of exercises with full solutions is given at the end...
The Geometry Of The Zygapophysial ("Paravertebral") Joints By Biostereometric Measurement
Adams, L. P.; Driver-Jowitt, J. P.
1986-07-01
Precise three dimensional measurements were made on a normal, dried adult vertebral column, using the recently developed reflex microscope. Preliminary conclusions are drawn from these measurements regarding the geometry of the lumbar and thoracic vertebrae. Subsequent measurements were made on a number of unrelated fifth lumbar and first sacral vertebrae and comparisons were made with the findings of the "master model".
Neutron flux in a periodical slab geometry (1960)
International Nuclear Information System (INIS)
Lamare, J. de; Mathelot, P.; Cadhilac, M.
1960-01-01
In the present report, we explain an original method to perform exact calculations of neutron flux in either of two geometries: a slab surrounded by an infinite multiplying medium or a periodical, one dimensional array of two different media. (author) [fr
International Nuclear Information System (INIS)
Buescher, R.
2005-01-01
Casimir interactions are interactions induced by quantum vacuum fluctuations and thermal fluctuations of the electromagnetic field. Using a path integral quantization for the gauge field, an effective Gaussian action will be derived which is the starting point to compute Casimir forces between macroscopic objects analytically and numerically. No assumptions about the independence of the material and shape dependent contributions to the interaction are made. We study the limit of flat surfaces in further detail and obtain a concise derivation of Lifshitz' theory of molecular forces. For the case of ideally conducting boundaries, the Gaussian action will be calculated explicitly. Both limiting cases are also discussed within the framework of a scalar field quantization approach, which is applicable for translationally invariant geometries. We develop a non-perturbative approach to calculate the Casimir interaction from the Gaussian action for periodically deformed and ideally conducting objects numerically. The obtained results reveal two different scaling regimes for the Casimir force as a function of the distance between the objects, their deformation wavelength and -amplitude. The results confirm that the interaction is non-additive, especially in the presence of strong geometric deformations. Furthermore, the numerical approach is extended to calculate lateral Casimir forces. The results are consistent with the results of the proximity-force approximation for large deformation wavelengths. A qualitatively different behaviour between the normal and lateral force is revealed. We also establish a relation between the boundary induced change of the of the density of states for the scalar Helmholtz equation and the Casimir interaction using the path integral method. For statically deformed boundaries, this relation can be expressed as a novel trace formula, which is formally similar to the so-called Krein-Friedel-Lloyd formula. While the latter formula describes the
Planetary Image Geometry Library
Deen, Robert C.; Pariser, Oleg
2010-01-01
The Planetary Image Geometry (PIG) library is a multi-mission library used for projecting images (EDRs, or Experiment Data Records) and managing their geometry for in-situ missions. A collection of models describes cameras and their articulation, allowing application programs such as mosaickers, terrain generators, and pointing correction tools to be written in a multi-mission manner, without any knowledge of parameters specific to the supported missions. Camera model objects allow transformation of image coordinates to and from view vectors in XYZ space. Pointing models, specific to each mission, describe how to orient the camera models based on telemetry or other information. Surface models describe the surface in general terms. Coordinate system objects manage the various coordinate systems involved in most missions. File objects manage access to metadata (labels, including telemetry information) in the input EDRs and RDRs (Reduced Data Records). Label models manage metadata information in output files. Site objects keep track of different locations where the spacecraft might be at a given time. Radiometry models allow correction of radiometry for an image. Mission objects contain basic mission parameters. Pointing adjustment ("nav") files allow pointing to be corrected. The object-oriented structure (C++) makes it easy to subclass just the pieces of the library that are truly mission-specific. Typically, this involves just the pointing model and coordinate systems, and parts of the file model. Once the library was developed (initially for Mars Polar Lander, MPL), adding new missions ranged from two days to a few months, resulting in significant cost savings as compared to rewriting all the application programs for each mission. Currently supported missions include Mars Pathfinder (MPF), MPL, Mars Exploration Rover (MER), Phoenix, and Mars Science Lab (MSL). Applications based on this library create the majority of operational image RDRs for those missions. A
KENO-IV/CG, the combinatorial geometry version of the KENO Monte Carlo criticality safety program
International Nuclear Information System (INIS)
West, J.T.; Petrie, L.M.; Fraley, S.K.
1979-09-01
KENO-IV/CG was developed to merge the simple geometry input description utilized by combinatorial geometry with the repeating lattice feature of the original KENO geometry package. The result is a criticality code with the ability to model a complex system of repeating rectangular lattices inside a complicated three-dimensional geometry system. Furthermore, combinatorial geometry was modified to differentiate between combinatorial zones describing a particular KENO BOX to be repeated in a KENO array and those combinatorial zones describing geometry external to an array. This allows the user to maintain a simple coordinate system without any geometric conflict due to spatial overlap. Several difficult criticality design problems have been solved with the new geometry package in KENO-IV/CG, thus illustrating the power of the code to model difficult geometries with a minimum of effort
Initiation to global Finslerian geometry
Akbar-Zadeh, Hassan
2006-01-01
After a brief description of the evolution of thinking on Finslerian geometry starting from Riemann, Finsler, Berwald and Elie Cartan, the book gives a clear and precise treatment of this geometry. The first three chapters develop the basic notions and methods, introduced by the author, to reach the global problems in Finslerian Geometry. The next five chapters are independent of each other, and deal with among others the geometry of generalized Einstein manifolds, the classification of Finslerian manifolds of constant sectional curvatures. They also give a treatment of isometric, affine, p
Holographic free energy and thermodynamic geometry
Ghorai, Debabrata; Gangopadhyay, Sunandan
2016-12-01
We obtain the free energy and thermodynamic geometry of holographic superconductors in 2+1 dimensions. The gravitational theory in the bulk dual to this 2+1-dimensional strongly coupled theory lives in the 3+1 dimensions and is that of a charged AdS black hole together with a massive charged scalar field. The matching method is applied to obtain the nature of the fields near the horizon using which the holographic free energy is computed through the gauge/gravity duality. The critical temperature is obtained for a set of values of the matching point of the near horizon and the boundary behaviour of the fields in the probe limit approximation which neglects the back reaction of the matter fields on the background spacetime geometry. The thermodynamic geometry is then computed from the free energy of the boundary theory. From the divergence of the thermodynamic scalar curvature, the critical temperature is obtained once again. We then compare this result for the critical temperature with that obtained from the matching method.
Holographic free energy and thermodynamic geometry
International Nuclear Information System (INIS)
Ghorai, Debabrata; Gangopadhyay, Sunandan
2016-01-01
We obtain the free energy and thermodynamic geometry of holographic superconductors in 2 + 1 dimensions. The gravitational theory in the bulk dual to this 2 + 1-dimensional strongly coupled theory lives in the 3 + 1 dimensions and is that of a charged AdS black hole together with a massive charged scalar field. The matching method is applied to obtain the nature of the fields near the horizon using which the holographic free energy is computed through the gauge/gravity duality. The critical temperature is obtained for a set of values of the matching point of the near horizon and the boundary behaviour of the fields in the probe limit approximation which neglects the back reaction of the matter fields on the background spacetime geometry. The thermodynamic geometry is then computed from the free energy of the boundary theory. From the divergence of the thermodynamic scalar curvature, the critical temperature is obtained once again. We then compare this result for the critical temperature with that obtained from the matching method. (orig.)
Holographic free energy and thermodynamic geometry
Energy Technology Data Exchange (ETDEWEB)
Ghorai, Debabrata [S.N. Bose National Centre for Basic Sciences, Kolkata (India); Gangopadhyay, Sunandan [Indian Institute of Science Education and Research, Kolkata, Nadia (India); West Bengal State University, Department of Physics, Barasat (India); Inter University Centre for Astronomy and Astrophysics, Pune (India)
2016-12-15
We obtain the free energy and thermodynamic geometry of holographic superconductors in 2 + 1 dimensions. The gravitational theory in the bulk dual to this 2 + 1-dimensional strongly coupled theory lives in the 3 + 1 dimensions and is that of a charged AdS black hole together with a massive charged scalar field. The matching method is applied to obtain the nature of the fields near the horizon using which the holographic free energy is computed through the gauge/gravity duality. The critical temperature is obtained for a set of values of the matching point of the near horizon and the boundary behaviour of the fields in the probe limit approximation which neglects the back reaction of the matter fields on the background spacetime geometry. The thermodynamic geometry is then computed from the free energy of the boundary theory. From the divergence of the thermodynamic scalar curvature, the critical temperature is obtained once again. We then compare this result for the critical temperature with that obtained from the matching method. (orig.)
The Finsler spacetime framework. Backgrounds for physics beyond metric geometry
Energy Technology Data Exchange (ETDEWEB)
Pfeifer, Christian
2013-11-15
The fundamental structure on which physics is described is the geometric spacetime background provided by a four dimensional manifold equipped with a Lorentzian metric. Most importantly the spacetime manifold does not only provide the stage for physical field theories but its geometry encodes causality, observers and their measurements and gravity simultaneously. This threefold role of the Lorentzian metric geometry of spacetime is one of the key insides of general relativity. During this thesis we extend the background geometry for physics from the metric framework of general relativity to our Finsler spacetime framework and ensure that the threefold role of the geometry of spacetime in physics is not changed. The geometry of Finsler spacetimes is determined by a function on the tangent bundle and includes metric geometry. In contrast to the standard formulation of Finsler geometry our Finsler spacetime framework overcomes the differentiability and existence problems of the geometric objects in earlier attempts to use Finsler geometry as an extension of Lorentzian metric geometry. The development of our nonmetric geometric framework which encodes causality is one central achievement of this thesis. On the basis of our well-defined Finsler spacetime geometry we are able to derive dynamics for the non-metric Finslerian geometry of spacetime from an action principle, obtained from the Einstein-Hilbert action, for the first time. We can complete the dynamics to a non-metric description of gravity by coupling matter fields, also formulated via an action principle, to the geometry of our Finsler spacetimes. We prove that the combined dynamics of the fields and the geometry are consistent with general relativity. Furthermore we demonstrate how to define observers and their measurements solely through the non-metric spacetime geometry. Physical consequence derived on the basis of our Finsler spacetime are: a possible solution to the fly-by anomaly in the solar system; the
The Finsler spacetime framework. Backgrounds for physics beyond metric geometry
International Nuclear Information System (INIS)
Pfeifer, Christian
2013-11-01
The fundamental structure on which physics is described is the geometric spacetime background provided by a four dimensional manifold equipped with a Lorentzian metric. Most importantly the spacetime manifold does not only provide the stage for physical field theories but its geometry encodes causality, observers and their measurements and gravity simultaneously. This threefold role of the Lorentzian metric geometry of spacetime is one of the key insides of general relativity. During this thesis we extend the background geometry for physics from the metric framework of general relativity to our Finsler spacetime framework and ensure that the threefold role of the geometry of spacetime in physics is not changed. The geometry of Finsler spacetimes is determined by a function on the tangent bundle and includes metric geometry. In contrast to the standard formulation of Finsler geometry our Finsler spacetime framework overcomes the differentiability and existence problems of the geometric objects in earlier attempts to use Finsler geometry as an extension of Lorentzian metric geometry. The development of our nonmetric geometric framework which encodes causality is one central achievement of this thesis. On the basis of our well-defined Finsler spacetime geometry we are able to derive dynamics for the non-metric Finslerian geometry of spacetime from an action principle, obtained from the Einstein-Hilbert action, for the first time. We can complete the dynamics to a non-metric description of gravity by coupling matter fields, also formulated via an action principle, to the geometry of our Finsler spacetimes. We prove that the combined dynamics of the fields and the geometry are consistent with general relativity. Furthermore we demonstrate how to define observers and their measurements solely through the non-metric spacetime geometry. Physical consequence derived on the basis of our Finsler spacetime are: a possible solution to the fly-by anomaly in the solar system; the
New geometries for black hole horizons
Energy Technology Data Exchange (ETDEWEB)
Armas, Jay [Physique Théorique et Mathématique,Université Libre de Bruxelles and International Solvay Institutes, ULB-Campus Plaine CP231, B-1050 Brussels (Belgium); Blau, Matthias [Albert Einstein Center for Fundamental Physics, University of Bern,Sidlerstrasse 5, 3012 Bern (Switzerland)
2015-07-10
We construct several classes of worldvolume effective actions for black holes by integrating out spatial sections of the worldvolume geometry of asymptotically flat black branes. This provides a generalisation of the blackfold approach for higher-dimensional black holes and yields a map between different effective theories, which we exploit by obtaining new hydrodynamic and elastic transport coefficients via simple integrations. Using Euclidean minimal surfaces in order to decouple the fluid dynamics on different sections of the worldvolume, we obtain local effective theories for ultraspinning Myers-Perry branes and helicoidal black branes, described in terms of a stress-energy tensor, particle currents and non-trivial boost vectors. We then study in detail and present novel compact and non-compact geometries for black hole horizons in higher-dimensional asymptotically flat space-time. These include doubly-spinning black rings, black helicoids and helicoidal p-branes as well as helicoidal black rings and helicoidal black tori in D≥6.
Directory of Open Access Journals (Sweden)
Šárka Nedomová
2013-01-01
Full Text Available Precise quantification of the profile of egg can provide a powerful tool for the analysis of egg shape for various biological problems. A new approach to the geometry of a Ostrich’s egg profile is presented here using an analysing the egg’s digital photo by edge detection techniques. The obtained points on the eggshell counter are fitted by the Fourier series. The obtained equations describing an egg profile have been used to calculate radii of curvature. The radii of the curvature at the important point of the egg profile (sharp end, blunt end and maximum thickness are independent on the egg shape index. The exact values of the egg surface and the egg volume have been obtained. These quantities are also independent on the egg shape index. These quantities can be successively estimated on the basis of simplified equations which are expressed in terms of the egg length, L¸ and its width, B. The surface area of the eggshells also exhibits good correlation with the egg long circumference length. Some limitations of the most used procedures have been also shown.
Bhatia, Rajendra
2013-01-01
This book is an outcome of the Indo-French Workshop on Matrix Information Geometries (MIG): Applications in Sensor and Cognitive Systems Engineering, which was held in Ecole Polytechnique and Thales Research and Technology Center, Palaiseau, France, in February 23-25, 2011. The workshop was generously funded by the Indo-French Centre for the Promotion of Advanced Research (IFCPAR). During the event, 22 renowned invited french or indian speakers gave lectures on their areas of expertise within the field of matrix analysis or processing. From these talks, a total of 17 original contribution or state-of-the-art chapters have been assembled in this volume. All articles were thoroughly peer-reviewed and improved, according to the suggestions of the international referees. The 17 contributions presented are organized in three parts: (1) State-of-the-art surveys & original matrix theory work, (2) Advanced matrix theory for radar processing, and (3) Matrix-based signal processing applications.
Unit cell geometry of 3-D braided structures
Du, Guang-Wu; Ko, Frank K.
1993-01-01
The traditional approach used in modeling of composites reinforced by three-dimensional (3-D) braids is to assume a simple unit cell geometry of a 3-D braided structure with known fiber volume fraction and orientation. In this article, we first examine 3-D braiding methods in the light of braid structures, followed by the development of geometric models for 3-D braids using a unit cell approach. The unit cell geometry of 3-D braids is identified and the relationship of structural parameters such as yarn orientation angle and fiber volume fraction with the key processing parameters established. The limiting geometry has been computed by establishing the point at which yarns jam against each other. Using this factor makes it possible to identify the complete range of allowable geometric arrangements for 3-D braided preforms. This identified unit cell geometry can be translated to mechanical models which relate the geometrical properties of fabric preforms to the mechanical responses of composite systems.
Radiography geometry principle
International Nuclear Information System (INIS)
Abdul Nassir Ibrahim; Azali Muhammad; Ab. Razak Hamzah; Abd. Aziz Mohamed; Mohamad Pauzi Ismail
2008-01-01
If one object placed in the field under the sun, we can see the shadow of that object in two dimensional where that object was placed. Nevertheless, the sun cannot penetrate deeply so that it will produce the shadow with same object. This principal also same as radiography, however, with ionizing radiation, it can penetrate through the object so that the image that produced not only the shadow of the object but also what are inside the object. So this can give advantages for the radiographer to make inspection what are inside this object. The images that produce depend with the shape, density, thickness and distance between the object, film and source. The reader also will introduce with some term such as Distance source to film, distance source to object, and distance object to film also some basic on DIN standard and API 1104 Standard.
The intrinsic geometry of the human brain connectome.
Ye, Allen Q; Ajilore, Olusola A; Conte, Giorgio; GadElkarim, Johnson; Thomas-Ramos, Galen; Zhan, Liang; Yang, Shaolin; Kumar, Anand; Magin, Richard L; G Forbes, Angus; Leow, Alex D
2015-12-01
This paper describes novel methods for constructing the intrinsic geometry of the human brain connectome using dimensionality-reduction techniques. We posit that the high-dimensional, complex geometry that represents this intrinsic topology can be mathematically embedded into lower dimensions using coupling patterns encoded in the corresponding brain connectivity graphs. We tested both linear and nonlinear dimensionality-reduction techniques using the diffusion-weighted structural connectome data acquired from a sample of healthy subjects. Results supported the nonlinearity of brain connectivity data, as linear reduction techniques such as the multidimensional scaling yielded inferior lower-dimensional embeddings. To further validate our results, we demonstrated that for tractography-derived structural connectome more influential regions such as rich-club members of the brain are more centrally mapped or embedded. Further, abnormal brain connectivity can be visually understood by inspecting the altered geometry of these three-dimensional (3D) embeddings that represent the topology of the human brain, as illustrated using simulated lesion studies of both targeted and random removal. Last, in order to visualize brain's intrinsic topology we have developed software that is compatible with virtual reality technologies, thus allowing researchers to collaboratively and interactively explore and manipulate brain connectome data.
CHOLESK, Diffusion Calculation with 2-D Source in X-Y or R-Z Geometry
International Nuclear Information System (INIS)
1988-01-01
1 - Description of problem or function: Solution of the diffusion equation with source in two-dimensional geometries x-y or r-z. 2 - Method of solution: The finite-element method of Ritz-Galerkin is applied
INEXTENSIBLE FLOWS OF CURVES IN THE EQUIFORM GEOMETRY OF THE PSEUDO-GALILEAN SPACE G13
Directory of Open Access Journals (Sweden)
HANDAN OZTEKIN
2016-12-01
Full Text Available In this paper, we study inextensible ows of curves in 3-dimensional pseudo- Galilean space. We give necessary and sucient conditions for inextensible ows of curves according to equiform geometry in pseudo-Galilean space.
GPS: Geometry, Probability, and Statistics
Field, Mike
2012-01-01
It might be said that for most occupations there is now less of a need for mathematics than there was say fifty years ago. But, the author argues, geometry, probability, and statistics constitute essential knowledge for everyone. Maybe not the geometry of Euclid, but certainly geometrical ways of thinking that might enable us to describe the world…
Surrogate Modeling for Geometry Optimization
DEFF Research Database (Denmark)
Rojas Larrazabal, Marielba de la Caridad; Abraham, Yonas; Holzwarth, Natalie
2009-01-01
A new approach for optimizing the nuclear geometry of an atomic system is described. Instead of the original expensive objective function (energy functional), a small number of simpler surrogates is used.......A new approach for optimizing the nuclear geometry of an atomic system is described. Instead of the original expensive objective function (energy functional), a small number of simpler surrogates is used....
A prediction for bubbling geometries
Okuda, Takuya
2007-01-01
We study the supersymmetric circular Wilson loops in N=4 Yang-Mills theory. Their vacuum expectation values are computed in the parameter region that admits smooth bubbling geometry duals. The results are a prediction for the supergravity action evaluated on the bubbling geometries for Wilson loops.
Molecular motion in restricted geometries
Indian Academy of Sciences (India)
Molecular dynamics in restricted geometries is known to exhibit anomalous behaviour. Diffusion, translational or rotational, of molecules is altered significantly on confinement in restricted geometries. Quasielastic neutron scattering (QENS) offers a unique possibility of studying molecular motion in such systems. Both time ...
Shafarevich, Igor Rostislavovich
1994-01-01
Shafarevich Basic Algebraic Geometry 2 The second edition of Shafarevich's introduction to algebraic geometry is in two volumes. The second volume covers schemes and complex manifolds, generalisations in two different directions of the affine and projective varieties that form the material of the first volume. Two notable additions in this second edition are the section on moduli spaces and representable functors, motivated by a discussion of the Hilbert scheme, and the section on Kähler geometry. The book ends with a historical sketch discussing the origins of algebraic geometry. From the Zentralblatt review of this volume: "... one can only respectfully repeat what has been said about the first part of the book (...): a great textbook, written by one of the leading algebraic geometers and teachers himself, has been reworked and updated. As a result the author's standard textbook on algebraic geometry has become even more important and valuable. Students, teachers, and active researchers using methods of al...
Optical geometry across the horizon
International Nuclear Information System (INIS)
Jonsson, Rickard
2006-01-01
In a recent paper (Jonsson and Westman 2006 Class. Quantum Grav. 23 61), a generalization of optical geometry, assuming a non-shearing reference congruence, is discussed. Here we illustrate that this formalism can be applied to (a finite four-volume) of any spherically symmetric spacetime. In particular we apply the formalism, using a non-static reference congruence, to do optical geometry across the horizon of a static black hole. While the resulting geometry in principle is time dependent, we can choose the reference congruence in such a manner that an embedding of the geometry always looks the same. Relative to the embedded geometry the reference points are then moving. We discuss the motion of photons, inertial forces and gyroscope precession in this framework
Geometry and physics of branes
International Nuclear Information System (INIS)
Gal'tsov, D V
2003-01-01
The book brings together the contents of lecture courses delivered at the school 'Geometry and Physics of Branes' which took place at the Center 'Alessandro Volta' (Como, Italy) in the spring of 2001. The purpose of the school was to provide an introduction to some lines of research, related to the notion of branes in superstring theory, which are in the focus of attention both in the physical and mathematical communities. The book is structured into three parts: the first contains an elementary introduction to branes, the second is devoted to physical aspects (conformal field theory on open and unoriented surfaces and topics in string tachyon dynamics), and the last contains some more formal mathematical developments. An introduction to branes is given in a remarkably lucid contribution by A Lerda. It opens with a construction of p-brane solutions in classical IIA and IIB supergravities with particular emphasis on the 'fundamental string' solution, the NS5-brane and the D3-brane. Then, the quantum description of D-branes is discussed in terms of boundary states of the closed superstring, which is an alternative to the more common description in terms of open strings with Dirichlet boundary conditions in the transverse to the brane directions. When a constant gauge field is present in the D-brane worldvolume, the boundary states are coherent states of the string oscillators depending on the field strength tensor. The couplings of the brane to the bulk fields - the graviton, the dilaton, and the Kalb-Ramond fields - are then extracted and shown to be precisely the ones that are produced by the Dirac-Born-Infeld action governing the low-energy dynamics of the D-brane derived using the open strings formalism. It is also shown that in the classical limit, the boundary states correctly reproduce the parameters of the corresponding classical solutions. The second part of the book starts with a contribution by Y S Stanev devoted to the two-dimensional conformal field
Three-dimensional modelling of thermal stress in floating zone silicon crystal growth
Plate, Matiss; Krauze, Armands; Virbulis, Jānis
2018-05-01
During the growth of large diameter silicon single crystals with the industrial floating zone method, undesirable level of thermal stress in the crystal is easily reached due to the inhomogeneous expansion as the crystal cools down. Shapes of the phase boundaries, temperature field and elastic material properties determine the thermal stress distribution in the solid mono crystalline silicon during cylindrical growth. Excessive stress can lead to fracture, generation of dislocations and altered distribution of intrinsic point defects. Although appearance of ridges on the crystal surface is the decisive factor of a dislocation-free growth, the influence of these ridges on the stress field is not completely clear. Here we present the results of thermal stress analysis for 4” and 5” diameter crystals using a quasi-stationary three dimensional mathematical model including the material anisotropy and the presence of experimentally observed ridges which cannot be addressed with axis-symmetric models. The ridge has a local but relatively strong influence on thermal stress therefore its relation to the origin of fracture is hypothesized. In addition, thermal stresses at the crystal rim are found to increase for a particular position of the crystal radiation reflector.
A new concept in biometric identification 3-dimensional hand geometry
International Nuclear Information System (INIS)
Sidlauskas, D.P.
1987-01-01
A new type of biometric identifier which utilizes hand outline measurements made in three dimensions is described. This device uses solid state imaging with no moving parts. The important characteristics of accuracy, speed, user tolerability, small template size, low power, portability and reliability are discussed. A complete stand-alone biometric access control station with sufficient memory for 10,000 users and weighing less than 10 pounds has been built and tested. A test was conducted involving daily use by 112 users over a seven week period during which over 6300 access attempts were made. The single try equal error rate was found to be 0.4%. There were no false rejects when three tries were allowed before access was denied. Defeat with an artifact is difficult because the hand must be copied in all three dimensions
Higher-dimensional string theory in Lyra geometry
Indian Academy of Sciences (India)
Cosmic strings as source of gravitational field in general relativity was discussed by ... tensor theory of gravitation and constructed an analog of Einstein field ... As string concept is useful before the particle creation and can explain galaxy for-.
Two-dimensional fractal geometry, critical phenomena and conformal invariance
International Nuclear Information System (INIS)
Duplantier, B.
1988-01-01
The universal properties of critical geometrical systems in two-dimensions (2D) like the O (n) and Potts models, are described in the framework of Coulomb gas methods and conformal invariance. The conformal spectrum of geometrical critical systems obtained is made of a discrete infinite series of scaling dimensions. Specific applications involve the fractal properties of self-avoiding walks, percolation clusters, and also some non trivial critical exponents or fractal dimensions associated with subsets of the planar Brownian motion. The statistical mechanics of the same critical models on a random 2D lattice (namely in presence of a critically-fluctuating metric, in the so-called 2D quantum gravity) is also addressed, and the above critical geometrical systems are shown to be exactly solvable in this case. The new ''gravitational'' conformal spectrum so derived is found to satisfy the recent Knizhnik, Polyakov and Zamolodchikov quadratic relation which links it to the standard conformal spectrum in the plane
Complex analysis and CR geometry
Zampieri, Giuseppe
2008-01-01
Cauchy-Riemann (CR) geometry is the study of manifolds equipped with a system of CR-type equations. Compared to the early days when the purpose of CR geometry was to supply tools for the analysis of the existence and regularity of solutions to the \\bar\\partial-Neumann problem, it has rapidly acquired a life of its own and has became an important topic in differential geometry and the study of non-linear partial differential equations. A full understanding of modern CR geometry requires knowledge of various topics such as real/complex differential and symplectic geometry, foliation theory, the geometric theory of PDE's, and microlocal analysis. Nowadays, the subject of CR geometry is very rich in results, and the amount of material required to reach competence is daunting to graduate students who wish to learn it. However, the present book does not aim at introducing all the topics of current interest in CR geometry. Instead, an attempt is made to be friendly to the novice by moving, in a fairly relaxed way, f...
The geometry description markup language
International Nuclear Information System (INIS)
Chytracek, R.
2001-01-01
Currently, a lot of effort is being put on designing complex detectors. A number of simulation and reconstruction frameworks and applications have been developed with the aim to make this job easier. A very important role in this activity is played by the geometry description of the detector apparatus layout and its working environment. However, no real common approach to represent geometry data is available and such data can be found in various forms starting from custom semi-structured text files, source code (C/C++/FORTRAN), to XML and database solutions. The XML (Extensible Markup Language) has proven to provide an interesting approach for describing detector geometries, with several different but incompatible XML-based solutions existing. Therefore, interoperability and geometry data exchange among different frameworks is not possible at present. The author introduces a markup language for geometry descriptions. Its aim is to define a common approach for sharing and exchanging of geometry description data. Its requirements and design have been driven by experience and user feedback from existing projects which have their geometry description in XML
Fallow), Stray
2009-01-01
Having trouble with geometry? Do Pi, The Pythagorean Theorem, and angle calculations just make your head spin? Relax. With Head First 2D Geometry, you'll master everything from triangles, quads and polygons to the time-saving secrets of similar and congruent angles -- and it'll be quick, painless, and fun. Through entertaining stories and practical examples from the world around you, this book takes you beyond boring problems. You'll actually use what you learn to make real-life decisions, like using angles and parallel lines to crack a mysterious CSI case. Put geometry to work for you, and
Walsh, Edward T
2014-01-01
This introductory text is designed to help undergraduate students develop a solid foundation in geometry. Early chapters progress slowly, cultivating the necessary understanding and self-confidence for the more rapid development that follows. The extensive treatment can be easily adapted to accommodate shorter courses. Starting with the language of mathematics as expressed in the algebra of logic and sets, the text covers geometric sets of points, separation and angles, triangles, parallel lines, similarity, polygons and area, circles, space geometry, and coordinate geometry. Each chapter incl
Differential geometry curves, surfaces, manifolds
Kohnel, Wolfgang
2002-01-01
This carefully written book is an introduction to the beautiful ideas and results of differential geometry. The first half covers the geometry of curves and surfaces, which provide much of the motivation and intuition for the general theory. Special topics that are explored include Frenet frames, ruled surfaces, minimal surfaces and the Gauss-Bonnet theorem. The second part is an introduction to the geometry of general manifolds, with particular emphasis on connections and curvature. The final two chapters are insightful examinations of the special cases of spaces of constant curvature and Einstein manifolds. The text is illustrated with many figures and examples. The prerequisites are undergraduate analysis and linear algebra.
Advances in discrete differential geometry
2016-01-01
This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. The authors take a closer look at discrete models in differential geometry and dynamical systems. Their curves are polygonal, surfaces are made from triangles and quadrilaterals, and time is discrete. Nevertheless, the difference between the corresponding smooth curves, surfaces and classical dynamical systems with continuous time can hardly be seen. This is the paradigm of structure-preserving discretizations. Current advances in this field are stimulated to a large extent by its relevance for computer graphics and mathematical physics. This book is written by specialists working together on a common research project. It is about differential geometry and dynamical systems, smooth and discrete theories, ...
Hyperbolic Metamaterials with Complex Geometry
DEFF Research Database (Denmark)
Lavrinenko, Andrei; Andryieuski, Andrei; Zhukovsky, Sergei
2016-01-01
We investigate new geometries of hyperbolic metamaterialssuch as highly corrugated structures, nanoparticle monolayer assemblies, super-structured or vertically arranged multilayersand nanopillars. All structures retain basic propertiesof hyperbolic metamaterials, but have functionality improved...
An introduction to differential geometry
Willmore, T J
2012-01-01
This text employs vector methods to explore the classical theory of curves and surfaces. Topics include basic theory of tensor algebra, tensor calculus, calculus of differential forms, and elements of Riemannian geometry. 1959 edition.
Symplectic geometry and Fourier analysis
Wallach, Nolan R
2018-01-01
Suitable for graduate students in mathematics, this monograph covers differential and symplectic geometry, homogeneous symplectic manifolds, Fourier analysis, metaplectic representation, quantization, Kirillov theory. Includes Appendix on Quantum Mechanics by Robert Hermann. 1977 edition.
Geometry and physics of branes
Energy Technology Data Exchange (ETDEWEB)
Gal' tsov, D V
2003-03-21
The book brings together the contents of lecture courses delivered at the school 'Geometry and Physics of Branes' which took place at the Center 'Alessandro Volta' (Como, Italy) in the spring of 2001. The purpose of the school was to provide an introduction to some lines of research, related to the notion of branes in superstring theory, which are in the focus of attention both in the physical and mathematical communities. The book is structured into three parts: the first contains an elementary introduction to branes, the second is devoted to physical aspects (conformal field theory on open and unoriented surfaces and topics in string tachyon dynamics), and the last contains some more formal mathematical developments. An introduction to branes is given in a remarkably lucid contribution by A Lerda. It opens with a construction of p-brane solutions in classical IIA and IIB supergravities with particular emphasis on the 'fundamental string' solution, the NS5-brane and the D3-brane. Then, the quantum description of D-branes is discussed in terms of boundary states of the closed superstring, which is an alternative to the more common description in terms of open strings with Dirichlet boundary conditions in the transverse to the brane directions. When a constant gauge field is present in the D-brane worldvolume, the boundary states are coherent states of the string oscillators depending on the field strength tensor. The couplings of the brane to the bulk fields - the graviton, the dilaton, and the Kalb-Ramond fields - are then extracted and shown to be precisely the ones that are produced by the Dirac-Born-Infeld action governing the low-energy dynamics of the D-brane derived using the open strings formalism. It is also shown that in the classical limit, the boundary states correctly reproduce the parameters of the corresponding classical solutions. The second part of the book starts with a contribution by Y S Stanev devoted to the two-dimensional
Topology and geometry for physicists
Nash, Charles
1983-01-01
Differential geometry and topology are essential tools for many theoretical physicists, particularly in the study of condensed matter physics, gravity, and particle physics. Written by physicists for physics students, this text introduces geometrical and topological methods in theoretical physics and applied mathematics. It assumes no detailed background in topology or geometry, and it emphasizes physical motivations, enabling students to apply the techniques to their physics formulas and research. ""Thoroughly recommended"" by The Physics Bulletin, this volume's physics applications range fr
Spectral dimension of quantum geometries
International Nuclear Information System (INIS)
Calcagni, Gianluca; Oriti, Daniele; Thürigen, Johannes
2014-01-01
The spectral dimension is an indicator of geometry and topology of spacetime and a tool to compare the description of quantum geometry in various approaches to quantum gravity. This is possible because it can be defined not only on smooth geometries but also on discrete (e.g., simplicial) ones. In this paper, we consider the spectral dimension of quantum states of spatial geometry defined on combinatorial complexes endowed with additional algebraic data: the kinematical quantum states of loop quantum gravity (LQG). Preliminarily, the effects of topology and discreteness of classical discrete geometries are studied in a systematic manner. We look for states reproducing the spectral dimension of a classical space in the appropriate regime. We also test the hypothesis that in LQG, as in other approaches, there is a scale dependence of the spectral dimension, which runs from the topological dimension at large scales to a smaller one at short distances. While our results do not give any strong support to this hypothesis, we can however pinpoint when the topological dimension is reproduced by LQG quantum states. Overall, by exploring the interplay of combinatorial, topological and geometrical effects, and by considering various kinds of quantum states such as coherent states and their superpositions, we find that the spectral dimension of discrete quantum geometries is more sensitive to the underlying combinatorial structures than to the details of the additional data associated with them. (paper)
Spinor calculus on 5-dimensional spacetimes
International Nuclear Information System (INIS)
Gomez-Lobo, Alfonso Garcia-Parrado; Martin-Garcia, Jose M
2010-01-01
We explain how Penrose's spinor calculus of 4-dimensional Lorentzian geometry is implemented in a 5-dimensional Lorentzian manifold. A number of issues, such as the essential spin algebra, the spin covariant derivative and the algebro-differential properties of the curvature spinors are discussed.
Elastocapillary fabrication of three-dimensional microstructures
van Honschoten, J.W.; Berenschot, Johan W.; Ondarcuhu, T.; Sanders, Remco G.P.; Sundaram, J.; Elwenspoek, Michael Curt; Tas, Niels Roelof
2010-01-01
We describe the fabrication of three-dimensional microstructures by means of capillary forces. Using an origami-like technique, planar silicon nitride structures of various geometries are folded to produce three-dimensional objects of 50–100 m. Capillarity is a particularly effective mechanism since
Instanton strings and hyper-Kaehler geometry
International Nuclear Information System (INIS)
Dijkgraaf, Robbert
1999-01-01
We discuss two-dimensional sigma models on moduli spaces of instantons on K3 surfaces. These N = (4, 4) superconformal field theories describe the near-horizon dynamics of the D1-D5-brane system and are dual to string theory on AdS 3 . We derive a precise map relating the moduli of the K3 type 1113 string compactification to the moduli of these conformal field theories and the corresponding classical hyper-Kahler geometry. We conclude that in the absence of background gauge fields, the metric on the instanton moduli spaces degenerates exactly to the orbifold symmetric product of K3. Turning on a self-dual NS B-field deforms this symmetric product to a manifold that is diffeomorphic to the Hilbert scheme. We also comment on the mathematical applications of string duality to the global issues of deformations of hyper-Kaehler manifolds
Black Holes and Large Order Quantum Geometry
Huang, Min-xin; Mariño, Marcos; Tavanfar, Alireza
2009-01-01
We study five-dimensional black holes obtained by compactifying M theory on Calabi-Yau threefolds. Recent progress in solving topological string theory on compact, one-parameter models allows us to test numerically various conjectures about these black holes. We give convincing evidence that a microscopic description based on Gopakumar-Vafa invariants accounts correctly for their macroscopic entropy, and we check that highly nontrivial cancellations -which seem necessary to resolve the so-called entropy enigma in the OSV conjecture- do in fact occur. We also study analytically small 5d black holes obtained by wrapping M2 branes in the fiber of K3 fibrations. By using heterotic/type II duality we obtain exact formulae for the microscopic degeneracies in various geometries, and we compute their asymptotic expansion for large charges.
Differential geometry of curves and surfaces
Banchoff, Thomas F
2010-01-01
Students and professors of an undergraduate course in differential geometry will appreciate the clear exposition and comprehensive exercises in this book that focuses on the geometric properties of curves and surfaces, one- and two-dimensional objects in Euclidean space. The problems generally relate to questions of local properties (the properties observed at a point on the curve or surface) or global properties (the properties of the object as a whole). Some of the more interesting theorems explore relationships between local and global properties. A special feature is the availability of accompanying online interactive java applets coordinated with each section. The applets allow students to investigate and manipulate curves and surfaces to develop intuition and to help analyze geometric phenomena.
Algorithmic algebraic geometry and flux vacua
International Nuclear Information System (INIS)
Gray, James; He Yanghui; Lukas, Andre
2006-01-01
We develop a new and efficient method to systematically analyse four dimensional effective supergravities which descend from flux compactifications. The issue of finding vacua of such systems, both supersymmetric and non-supersymmetric, is mapped into a problem in computational algebraic geometry. Using recent developments in computer algebra, the problem can then be rapidly dealt with in a completely algorithmic fashion. Two main results are (1) a procedure for calculating constraints which the flux parameters must satisfy in these models if any given type of vacuum is to exist; (2) a stepwise process for finding all of the isolated vacua of such systems and their physical properties. We illustrate our discussion with several concrete examples, some of which have eluded conventional methods so far
Microfluidic step-emulsification in axisymmetric geometry.
Chakraborty, I; Ricouvier, J; Yazhgur, P; Tabeling, P; Leshansky, A M
2017-10-25
Biphasic step-emulsification (Z. Li et al., Lab Chip, 2015, 15, 1023) is a promising microfluidic technique for high-throughput production of μm and sub-μm highly monodisperse droplets. The step-emulsifier consists of a shallow (Hele-Shaw) microchannel operating with two co-flowing immiscible liquids and an abrupt expansion (i.e., step) to a deep and wide reservoir. Under certain conditions the confined stream of the disperse phase, engulfed by the co-flowing continuous phase, breaks into small highly monodisperse droplets at the step. Theoretical investigation of the corresponding hydrodynamics is complicated due to the complex geometry of the planar device, calling for numerical approaches. However, direct numerical simulations of the three dimensional surface-tension-dominated biphasic flows in confined geometries are computationally expensive. In the present paper we study a model problem of axisymmetric step-emulsification. This setup consists of a stable core-annular biphasic flow in a cylindrical capillary tube connected co-axially to a reservoir tube of a larger diameter through a sudden expansion mimicking the edge of the planar step-emulsifier. We demonstrate that the axisymmetric setup exhibits similar regimes of droplet generation to the planar device. A detailed parametric study of the underlying hydrodynamics is feasible via inexpensive (two dimensional) simulations owing to the axial symmetry. The phase diagram quantifying the different regimes of droplet generation in terms of governing dimensionless parameters is presented. We show that in qualitative agreement with experiments in planar devices, the size of the droplets generated in the step-emulsification regime is independent of the capillary number and almost insensitive to the viscosity ratio. These findings confirm that the step-emulsification regime is solely controlled by surface tension. The numerical predictions are in excellent agreement with in-house experiments with the axisymmetric
The analytic nodal method in cylindrical geometry
International Nuclear Information System (INIS)
Prinsloo, Rian H.; Tomasevic, Djordje I.
2008-01-01
Nodal diffusion methods have been used extensively in nuclear reactor calculations, specifically for their performance advantage, but also for their superior accuracy. More specifically, the Analytic Nodal Method (ANM), utilising the transverse integration principle, has been applied to numerous reactor problems with much success. In this work, a nodal diffusion method is developed for cylindrical geometry. Application of this method to three-dimensional (3D) cylindrical geometry has never been satisfactorily addressed and we propose a solution which entails the use of conformal mapping. A set of 1D-equations with an adjusted, geometrically dependent, inhomogeneous source, is obtained. This work describes the development of the method and associated test code, as well as its application to realistic reactor problems. Numerical results are given for the PBMR-400 MW benchmark problem, as well as for a 'cylindrisized' version of the well-known 3D LWR IAEA benchmark. Results highlight the improved accuracy and performance over finite-difference core solutions and investigate the applicability of nodal methods to 3D PBMR type problems. Results indicate that cylindrical nodal methods definitely have a place within PBMR applications, yielding performance advantage factors of 10 and 20 for 2D and 3D calculations, respectively, and advantage factors of the order of 1000 in the case of the LWR problem
The algebraic geometry of Harper operators
Li, Dan
2011-10-01
Following an approach developed by Gieseker, Knörrer and Trubowitz for discretized Schrödinger operators, we study the spectral theory of Harper operators in dimensions 2 and 1, as a discretized model of magnetic Laplacians, from the point of view of algebraic geometry. We describe the geometry of an associated family of Bloch varieties and compute their density of states. Finally, we also compute some spectral functions based on the density of states. We discuss the difference between the cases with rational or irrational parameters: for the two-dimensional Harper operator, the compactification of the Bloch variety is an ordinary variety in the rational case and an ind-pro-variety in the irrational case. This gives rise, at the algebro-geometric level of Bloch varieties, to a phenomenon similar to the Hofstadter butterfly in the spectral theory. In dimension 2, the density of states can be expressed in terms of period integrals over Fermi curves, where the resulting elliptic integrals are independent of the parameters. In dimension 1, for the almost Mathieu operator, with a similar argument, we find the usual dependence of the spectral density on the parameter, which gives rise to the well-known Hofstadter butterfly picture.
The algebraic geometry of Harper operators
International Nuclear Information System (INIS)
Li, Dan
2011-01-01
Following an approach developed by Gieseker, Knoerrer and Trubowitz for discretized Schroedinger operators, we study the spectral theory of Harper operators in dimensions 2 and 1, as a discretized model of magnetic Laplacians, from the point of view of algebraic geometry. We describe the geometry of an associated family of Bloch varieties and compute their density of states. Finally, we also compute some spectral functions based on the density of states. We discuss the difference between the cases with rational or irrational parameters: for the two-dimensional Harper operator, the compactification of the Bloch variety is an ordinary variety in the rational case and an ind-pro-variety in the irrational case. This gives rise, at the algebro-geometric level of Bloch varieties, to a phenomenon similar to the Hofstadter butterfly in the spectral theory. In dimension 2, the density of states can be expressed in terms of period integrals over Fermi curves, where the resulting elliptic integrals are independent of the parameters. In dimension 1, for the almost Mathieu operator, with a similar argument, we find the usual dependence of the spectral density on the parameter, which gives rise to the well-known Hofstadter butterfly picture. (paper)
Tensor analysis and elementary differential geometry for physicists and engineers
Nguyen-Schäfer, Hung
2017-01-01
This book comprehensively presents topics, such as Dirac notation, tensor analysis, elementary differential geometry of moving surfaces, and k-differential forms. Additionally, two new chapters of Cartan differential forms and Dirac and tensor notations in quantum mechanics are added to this second edition. The reader is provided with hands-on calculations and worked-out examples at which he will learn how to handle the bra-ket notation, tensors, differential geometry, and differential forms; and to apply them to the physical and engineering world. Many methods and applications are given in CFD, continuum mechanics, electrodynamics in special relativity, cosmology in the Minkowski four-dimensional spacetime, and relativistic and non-relativistic quantum mechanics. Tensors, differential geometry, differential forms, and Dirac notation are very useful advanced mathematical tools in many fields of modern physics and computational engineering. They are involved in special and general relativity physics, quantum m...
Hypermultiplets and hypercomplex geometry from six to three dimensions
International Nuclear Information System (INIS)
Rosseel, Jan; Proeyen, Antoine van
2004-01-01
The formulation of hypermultiplets that has been developed for five-dimensional matter multiplets is by dimensional reductions translated into the appropriate spinor language for six and four dimensions. We also treat the theories without actions that have the geometrical structure of hypercomplex geometry. The latter is the generalization of hyper-Kaehler geometry that does not require a Hermitian metric and hence corresponds to field equations without action. The translation tables of this paper allow the direct application of superconformal tensor calculus for the hypermultiplets using the available Weyl multiplets in six and four dimensions. Furthermore, the hypermultiplets in three dimensions that result from reduction of vector multiplets in four dimensions are considered, leading to a superconformal formulation of the c-map and an expression for the main geometric quantities of the hyper-Kaehler manifolds in the image of this map
Buoyancy-driven mixing of fluids in a confined geometry
International Nuclear Information System (INIS)
Hallez, Y.
2007-12-01
The present work based on Direct Numerical Simulations is devoted to the study of mixing between two miscible fluids of different densities. The movement of these fluids is induced by buoyancy. Three geometries are considered: a cylindrical tube, a square channel and a plane two-dimensional flow. For cylindrical tubes, the results of numerical simulations fully confirm previous experimental findings by Seon et al., especially regarding the existence of three different flow regimes, depending on the tilt angle. The comparison of the various geometries shows that tridimensional flows in tubes or channels are similar, whereas the two-dimensional model fails to give reliable information about real 3D flows, either from a quantitative point of view or for a phenomenological understanding. A peculiar attention is put on a joint analysis of the concentration and vorticity fields and allows us to explain several subtle aspects of the mixing dynamics. (author)
Anomalies free E-infinity from von Neumann's continuous geometry
International Nuclear Information System (INIS)
El Naschie, M.S.
2008-01-01
Von Neumann's continuous geometry has been considerably developed by Connes and is characterized by two fundamental concepts. First it is formulated without any direct reference to points and second it possesses a dimensional function. The present work explores the relevance of these two points to string theory as well as E-infinity theory. In particular we show that point-lessness and dimensional function implies fractality. In turn fractality leads to the concept of average or fuzzy symmetry and the elimination of gauge anomalies
Fuzzy Geometry of Commutative Spaces and Quantum Dynamics
International Nuclear Information System (INIS)
Mayburov, S.N.
2016-01-01
Fuzzy topology and geometry considered as the possible mathematical framework for novel quantum-mechanical formalism. In such formalism the states of massive particle m correspond to the elements of fuzzy manifold called fuzzy points. Due to the manifold weak topology, m space coordinate x acquires principal uncertainty σ_x and described by the positive, normalized density w(r-vector , t) in 3-dimensional case. It’s shown that the evolution of m state on such 3-dimensional manifold corresponds to Shroedinger dynamics of massive quantum particle
The SUSY oscillator from local geometry: Dynamics and coherent states
International Nuclear Information System (INIS)
Thienel, H.P.
1994-01-01
The choice of a coordinate chart on an analytical R n (R a n ) provides a representation of the n-dimensional SUSY oscillator. The corresponding Hilbert space is Cartan's exterior algebra endowed with a suitable scalar product. The exterior derivative gives rise to the algebra of the n-dimensional SUSY oscillator. Its euclidean dynamics is an inherent consequence of the geometry imposed by the Lie derivative generating the dilations, i.e. evolution of the quantum system corresponds to parametrization of a sequence of charts by euclidean time. Coherent states emerge as a natural structure related to the Lie derivative generating the translations. (orig.)
International Nuclear Information System (INIS)
Blakeman, E.D.
2000-01-01
A software system, GRAVE (Geometry Rendering and Visual Editor), has been developed at the Oak Ridge National Laboratory (ORNL) to perform interactive visualization and development of models used as input to the TORT three-dimensional discrete ordinates radiation transport code. Three-dimensional and two-dimensional visualization displays are included. Display capabilities include image rotation, zoom, translation, wire-frame and translucent display, geometry cuts and slices, and display of individual component bodies and material zones. The geometry can be interactively edited and saved in TORT input file format. This system is an advancement over the current, non-interactive, two-dimensional display software. GRAVE is programmed in the Java programming language and can be implemented on a variety of computer platforms. Three- dimensional visualization is enabled through the Visualization Toolkit (VTK), a free-ware C++ software library developed for geometric and data visual display. Future plans include an extension of the system to read inputs using binary zone maps and combinatorial geometry models containing curved surfaces, such as those used for Monte Carlo code inputs. Also GRAVE will be extended to geometry visualization/editing for the DORT two-dimensional transport code and will be integrated into a single GUI-based system for all of the ORNL discrete ordinates transport codes
System theory as applied differential geometry. [linear system
Hermann, R.
1979-01-01
The invariants of input-output systems under the action of the feedback group was examined. The approach used the theory of Lie groups and concepts of modern differential geometry, and illustrated how the latter provides a basis for the discussion of the analytic structure of systems. Finite dimensional linear systems in a single independent variable are considered. Lessons of more general situations (e.g., distributed parameter and multidimensional systems) which are increasingly encountered as technology advances are presented.
Background geometries in string and M-theory
International Nuclear Information System (INIS)
Jeschek, C.
2005-01-01
In this thesis we consider background geometries resulting from string theory compactifications. In particular, we investigate supersymmetric vacuum spaces of supergravity theories and topological twisted sigma models by means of classical and generalised G-structures. In the first part we compactify 11d supergravity on seven-dimensional manifolds due to phenomenological reasons. A certain amount of supersymmetry forces the internal background to admit a classical SU(3)- or G 2 -structure. Especially, in the case that the four-dimensional space is maximally symmetric and four form fluxes are present we calculate the relation to the intrinsic torsion. The second and main part is two-fold. Firstly, we realise that generalised geometries on six-dimensional manifolds are a natural framework to study T-duality and mirror symmetry, in particular if the B-field is non-vanishing. An explicit mirror map is given and we apply this idea to the generalised formulation of a topological twisted sigma model. Implications of mirror symmetry are studied, e.g. observables and topological A- and B-branes. Secondly, we show that seven-dimensional NS-NS backgrounds in type II supergravity theories can be described by generalised G 2 -geometries. A compactification on six manifolds leads to a new structure. We call this geometry a generalised SU(3)-structure. We study the relation between generalised SU(3)- and G 2 -structures on six- and seven-manifolds and generalise the Hitchin-flow equations. Finally, we further develop the generalised SU(3)- and G 2 -structures via a constrained variational principle to incorporate also the remaining physical R-R fields. (Orig.)
BCS @ 50: derivation of gap equations in different lattice geometries
International Nuclear Information System (INIS)
Saurabh Basu
2007-07-01
We rigorously derive BCS gap equations for a square, triangular and a honeycomb lattice using a two-dimensional t-J model. The gap equations in all the three lattice geometries look usual, with band indices appearing and a minor modification in the separable pair potential for the (two band) honeycomb lattice. In each case, the gap equation is solved (self consistently with the number equation) at low densities assuming singlet pairing. (author)
Empirical intrinsic geometry for nonlinear modeling and time series filtering.
Talmon, Ronen; Coifman, Ronald R
2013-07-30
In this paper, we present a method for time series analysis based on empirical intrinsic geometry (EIG). EIG enables one to reveal the low-dimensional parametric manifold as well as to infer the underlying dynamics of high-dimensional time series. By incorporating concepts of information geometry, this method extends existing geometric analysis tools to support stochastic settings and parametrizes the geometry of empirical distributions. However, the statistical models are not required as priors; hence, EIG may be applied to a wide range of real signals without existing definitive models. We show that the inferred model is noise-resilient and invariant under different observation and instrumental modalities. In addition, we show that it can be extended efficiently to newly acquired measurements in a sequential manner. These two advantages enable us to revisit the Bayesian approach and incorporate empirical dynamics and intrinsic geometry into a nonlinear filtering framework. We show applications to nonlinear and non-Gaussian tracking problems as well as to acoustic signal localization.
A systematic construction of microstate geometries with low angular momentum
Bena, Iosif; Heidmann, Pierre; Ramírez, Pedro F.
2017-10-01
We outline a systematic procedure to obtain horizonless microstate geometries that have the same charges as three-charge five-dimensional black holes with a macroscopically-large horizon area and an arbitrarily-small angular momentum. There are two routes through which such solutions can be constructed: using multi-center Gibbons-Hawking (GH) spaces or using superstratum technology. So far the only solutions corre-sponding to microstate geometries for black holes with no angular momentum have been obtained via superstrata [1], and multi-center Gibbons-Hawking spaces have been believed to give rise only to microstate geometries of BMPV black holes with a large angular mo-mentum [2]. We perform a thorough search throughout the parameter space of smooth horizonless solutions with four GH centers and find that these have an angular momentum that is generally larger than 80% of the cosmic censorship bound. However, we find that solutions with three GH centers and one supertube (which are smooth in six-dimensional supergravity) can have an arbitrarily-low angular momentum. Our construction thus gives a recipe to build large classes of microstate geometries for zero-angular-momentum black holes without resorting to superstratum technology.
Three theorems on near horizon extremal vanishing horizon geometries
Directory of Open Access Journals (Sweden)
S. Sadeghian
2016-02-01
Full Text Available EVH black holes are Extremal black holes with Vanishing Horizon area, where vanishing of horizon area is a result of having a vanishing one-cycle on the horizon. We prove three theorems regarding near horizon geometry of EVH black hole solutions to generic Einstein gravity theories in diverse dimensions. These generic gravity theories are Einstein–Maxwell-dilaton-Λ theories, and gauged or ungauged supergravity theories with U(1 Maxwell fields. Our three theorems are: (1 The near horizon geometry of any EVH black hole has a three dimensional maximally symmetric subspace. (2 If the energy momentum tensor of the theory satisfies strong energy condition either this 3d part is an AdS3, or the solution is a direct product of a locally 3d flat space and a d−3 dimensional part. (3 These results extend to the near horizon geometry of near-EVH black holes, for which the AdS3 part is replaced with BTZ geometry.
Variable geometry Darrieus wind machine
Pytlinski, J. T.; Serrano, D.
1983-08-01
A variable geometry Darrieus wind machine is proposed. The lower attachment of the blades to the rotor can move freely up and down the axle allowing the blades of change shape during rotation. Experimental data for a 17 m. diameter Darrieus rotor and a theoretical model for multiple streamtube performance prediction were used to develop a computer simulation program for studying parameters that affect the machine's performance. This new variable geometry concept is described and interrelated with multiple streamtube theory through aerodynamic parameters. The computer simulation study shows that governor behavior of a Darrieus turbine can not be attained by a standard turbine operating within normally occurring rotational velocity limits. A second generation variable geometry Darrieus wind turbine which uses a telescopic blade is proposed as a potential improvement on the studied concept.
Euclidean geometry and its subgeometries
Specht, Edward John; Calkins, Keith G; Rhoads, Donald H
2015-01-01
In this monograph, the authors present a modern development of Euclidean geometry from independent axioms, using up-to-date language and providing detailed proofs. The axioms for incidence, betweenness, and plane separation are close to those of Hilbert. This is the only axiomatic treatment of Euclidean geometry that uses axioms not involving metric notions and that explores congruence and isometries by means of reflection mappings. The authors present thirteen axioms in sequence, proving as many theorems as possible at each stage and, in the process, building up subgeometries, most notably the Pasch and neutral geometries. Standard topics such as the congruence theorems for triangles, embedding the real numbers in a line, and coordinatization of the plane are included, as well as theorems of Pythagoras, Desargues, Pappas, Menelaus, and Ceva. The final chapter covers consistency and independence of axioms, as well as independence of definition properties. There are over 300 exercises; solutions to many of the...
Guide to Computational Geometry Processing
DEFF Research Database (Denmark)
Bærentzen, Jakob Andreas; Gravesen, Jens; Anton, François
be processed before it is useful. This Guide to Computational Geometry Processing reviews the algorithms for processing geometric data, with a practical focus on important techniques not covered by traditional courses on computer vision and computer graphics. This is balanced with an introduction...... to the theoretical and mathematical underpinnings of each technique, enabling the reader to not only implement a given method, but also to understand the ideas behind it, its limitations and its advantages. Topics and features: Presents an overview of the underlying mathematical theory, covering vector spaces......, metric space, affine spaces, differential geometry, and finite difference methods for derivatives and differential equations Reviews geometry representations, including polygonal meshes, splines, and subdivision surfaces Examines techniques for computing curvature from polygonal meshes Describes...
Electrodynamics and Spacetime Geometry: Foundations
Cabral, Francisco; Lobo, Francisco S. N.
2017-02-01
We explore the intimate connection between spacetime geometry and electrodynamics. This link is already implicit in the constitutive relations between the field strengths and excitations, which are an essential part of the axiomatic structure of electromagnetism, clearly formulated via integration theory and differential forms. We review the foundations of classical electromagnetism based on charge and magnetic flux conservation, the Lorentz force and the constitutive relations. These relations introduce the conformal part of the metric and allow the study of electrodynamics for specific spacetime geometries. At the foundational level, we discuss the possibility of generalizing the vacuum constitutive relations, by relaxing the fixed conditions of homogeneity and isotropy, and by assuming that the symmetry properties of the electro-vacuum follow the spacetime isometries. The implications of this extension are briefly discussed in the context of the intimate connection between electromagnetism and the geometry (and causal structure) of spacetime.
Dayside merging and cusp geometry
International Nuclear Information System (INIS)
Crooker, N.U.
1979-01-01
Geometrical considerations are presented to show that dayside magnetic merging when constrained to act only where the fields are antiparallel results in lines of merging that converge at the polar cusps. An important consequence of this geometry is that no accelerated flows are predicted across the dayside magnetopause. Acceleration owing to merging acts in opposition to the magnetosheath flow at the merging point and produces the variably directed, slower-than-magnetosheath flows observed in the entry layer. Another consequence of the merging geometry is that much of the time closed field lines constitute the subsolar region of the magnetopause. The manner in which the polar cap convection patterns predicted by the proposed geometry change as the interplanetary field is rotated through 360 0 provides a unifying description of how the observed single circular vortex and the crescent-shaped double vortex patterns mutually evolve under the influence of a single operating principle
DOGBONE GEOMETRY FOR RECIRCULATING ACCELERATORS
International Nuclear Information System (INIS)
BERG, J.S.; JOHNSTONE, C.; SUMMERS, D.
2001-01-01
Most scenarios for accelerating muons require recirculating acceleration. A racetrack shape for the accelerator requires particles with lower energy in early passes to traverse almost the same length of arc as particles with the highest energy. This extra arc length may lead to excess decays and excess cost. Changing the geometry to a dogbone shape, where there is a single linac and the beam turns completely around at the end of the linac, returning to the same end of the linac from which it exited, addresses this problem. In this design, the arc lengths can be proportional to the particle's momentum. This paper proposes an approximate cost model for a recirculating accelerator, attempts to make cost-optimized designs for both racetrack and dogbone geometries, and demonstrates that the dogbone geometry does appear to be more cost effective
Energy Technology Data Exchange (ETDEWEB)
Hallez, Y
2007-12-15
The present work based on Direct Numerical Simulations is devoted to the study of mixing between two miscible fluids of different densities. The movement of these fluids is induced by buoyancy. Three geometries are considered: a cylindrical tube, a square channel and a plane two-dimensional flow. For cylindrical tubes, the results of numerical simulations fully confirm previous experimental findings by Seon et al., especially regarding the existence of three different flow regimes, depending on the tilt angle. The comparison of the various geometries shows that tridimensional flows in tubes or channels are similar, whereas the two-dimensional model fails to give reliable information about real 3D flows, either from a quantitative point of view or for a phenomenological understanding. A peculiar attention is put on a joint analysis of the concentration and vorticity fields and allows us to explain several subtle aspects of the mixing dynamics. (author)
Geometric Transformations in Engineering Geometry
Directory of Open Access Journals (Sweden)
I. F. Borovikov
2015-01-01
Full Text Available Recently, for business purposes, in view of current trends and world experience in training engineers, research and faculty staff there has been a need to transform traditional courses of descriptive geometry into the course of engineering geometry in which the geometrical transformations have to become its main section. On the basis of critical analysis the paper gives suggestions to improve a presentation technique of this section both in the classroom and in academic literature, extend an application scope of geometrical transformations to solve the position and metric tasks and simulation of surfaces, as well as to design complex engineering configurations, which meet a number of pre-specified conditions.The article offers to make a number of considerable amendments to the terms and definitions used in the existing courses of descriptive geometry. It draws some conclusions and makes the appropriate proposals on feasibility of coordination in teaching the movement transformation in the courses of analytical and descriptive geometry. This will provide interdisciplinary team teaching and allow students to be convinced that a combination of analytical and graphic ways to solve geometric tasks is useful and reasonable.The traditional sections of learning courses need to be added with a theory of projective and bi-rational transformations. In terms of application simplicity and convenience it is enough to consider the central transformations when solving the applied tasks. These transformations contain a beam of sub-invariant (low-invariant straight lines on which the invariant curve induces non-involution and involution projectivities. The expediency of nonlinear transformations application is shown in the article by a specific example of geometric modeling of the interfacing surface "spar-blade".Implementation of these suggestions will contribute to a real transformation of a traditional course of descriptive geometry to the engineering geometry
KEMAJUAN BELAJAR SISWA PADA GEOMETRI TRANSFORMASI MENGGUNAKAN AKTIVITAS REFLEKSI GEOMETRI
Directory of Open Access Journals (Sweden)
Irkham Ulil Albab
2014-10-01
Full Text Available Abstrak: Penelitian ini bertujuan untuk mendeskripsikan kemajuan belajar siswa pada materi geometri transformasi yang didukung dengan serangkaian aktivitas belajar berdasarkan Pendidikan Matematika Realistik Indonesia. Penelitian didesain melalui tiga tahap, yaitu tahapan perancangan desain awal, pengujian desain melalui pembelajaran awal dan pembelajaran eksperimental, dan tahap analisis retrospektif. Dalam penelitian ini, Hypothetical Learning Trajectory, HLT (HLT berperan penting sebagai desain pembelajaran sekaligus instrumen penelitian. HLT diujikan terhadap 26 siswa kelas VII. Data dikumpulkan dengan teknik wawancara, pengamatan, dan catatan lapangan. Hasil penelitian menunjukkan bahwa desain pembelajaran ini mampu menstimulasi siswa untuk memberikan karakteristik refleksi dan transformasi geometri lainnya secara informal, mengklasifikasikannya dalam transformasi isometri pada level kedua, dan menemukan garis bantuan refleksi pada level yang lebih formal. Selain itu, garis bantuan refleksi digunakan oleh siswa untuk menggambar bayangan refleksi dan pola pencerminan serta memahami bentuk rotasi dan translasi sebagai kombinasi refleksi adalah level tertinggi. Keyword: transformasi geometri, kombinasi refleksi, rotasi, translasi, design research, HLT STUDENTS’ LEARNING PROGRESS ON TRANSFORMATION GEOMETRY USING THE GEOMETRY REFLECTION ACTIVITIES Abstract: This study was aimed at describing the students’ learning progress on transformation geometry supported by a set of learning activities based on Indonesian Realistic Mathematics Education. The study was designed into three stages, that is, the preliminary design stage, the design testing through initial instruction and experiment, and the restrospective analysis stage. In this study, Hypothetical Learning Trajectory (HLT played an important role as an instructional design and a research instrument. HLT was tested to 26 seventh grade students. The data were collected through interviews
Graphical debugging of combinational geometry
International Nuclear Information System (INIS)
Burns, T.J.; Smith, M.S.
1992-01-01
A graphical debugger for combinatorial geometry being developed at Oak Ridge National Laboratory is described. The prototype debugger consists of two parts: a FORTRAN-based ''view'' generator and a Microsoft Windows application for displaying the geometry. Options and features of both modules are discussed. Examples illustrating the various options available are presented. The potential for utilizing the images produced using the debugger as a visualization tool for the output of the radiation transport codes is discussed as is the future direction of the development
Lectures on Algebraic Geometry I
Harder, Gunter
2012-01-01
This book and the following second volume is an introduction into modern algebraic geometry. In the first volume the methods of homological algebra, theory of sheaves, and sheaf cohomology are developed. These methods are indispensable for modern algebraic geometry, but they are also fundamental for other branches of mathematics and of great interest in their own. In the last chapter of volume I these concepts are applied to the theory of compact Riemann surfaces. In this chapter the author makes clear how influential the ideas of Abel, Riemann and Jacobi were and that many of the modern metho
Combinatorial geometry in the plane
Hadwiger, Hugo; Klee, Victor
2014-01-01
Geared toward advanced undergraduates familiar with analysis and college geometry, this concise book discusses theorems on topics restricted to the plane such as convexity, coverings, and graphs. In addition to helping students cultivate rigorous thought, the text encourages the development of mathematical intuition and clarifies the nature of mathematical research.The two-part treatment begins with specific topics including integral distances, covering problems, point set geometry and convexity, simple paradoxes involving point sets, and pure combinatorics, among other subjects. The second pa
Modern differential geometry for physicists
Isham, C J
1989-01-01
These notes are the content of an introductory course on modern, coordinate-free differential geometry which is taken by the first-year theoretical physics PhD students, or by students attending the one-year MSc course "Fundamental Fields and Forces" at Imperial College. The book is concerned entirely with mathematics proper, although the emphasis and detailed topics have been chosen with an eye to the way in which differential geometry is applied these days to modern theoretical physics. This includes not only the traditional area of general relativity but also the theory of Yang-Mills fields
Comparison theorems in Riemannian geometry
Cheeger, Jeff
2008-01-01
The central theme of this book is the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry. The first five chapters are preparatory in nature. They begin with a very concise introduction to Riemannian geometry, followed by an exposition of Toponogov's theorem-the first such treatment in a book in English. Next comes a detailed presentation of homogeneous spaces in which the main goal is to find formulas for their curvature. A quick chapter of Morse theory is followed by one on the injectivity radius. Chapters 6-9 deal with many of the most re
Geometry, topology, and string theory
Energy Technology Data Exchange (ETDEWEB)
Varadarajan, Uday [Univ. of California, Berkeley, CA (United States)
2003-01-01
A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect. In particular, situations in which extra dimensions, non-commutative geometries as well as other non-local structures emerge are explored in detail. Further, a preliminary exploration of such issues in Lorentzian space-times with non-trivial causal structures within string theory is initiated.
Introduction to topology and geometry
Stahl, Saul
2014-01-01
An easily accessible introduction to over three centuries of innovations in geometry Praise for the First Edition ". . . a welcome alternative to compartmentalized treatments bound to the old thinking. This clearly written, well-illustrated book supplies sufficient background to be self-contained." -CHOICE This fully revised new edition offers the most comprehensive coverage of modern geometry currently available at an introductory level. The book strikes a welcome balance between academic rigor and accessibility, providing a complete and cohesive picture of the science with an unparallele
Algebraic geometry and theta functions
Coble, Arthur B
1929-01-01
This book is the result of extending and deepening all questions from algebraic geometry that are connected to the central problem of this book: the determination of the tritangent planes of a space curve of order six and genus four, which the author treated in his Colloquium Lecture in 1928 at Amherst. The first two chapters recall fundamental ideas of algebraic geometry and theta functions in such fashion as will be most helpful in later applications. In order to clearly present the state of the central problem, the author first presents the better-known cases of genus two (Chapter III) and
Geometry, topology, and string theory
International Nuclear Information System (INIS)
Varadarajan, Uday
2003-01-01
A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect. In particular, situations in which extra dimensions, non-commutative geometries as well as other non-local structures emerge are explored in detail. Further, a preliminary exploration of such issues in Lorentzian space-times with non-trivial causal structures within string theory is initiated
Momentum-space cigar geometry in topological phases
Palumbo, Giandomenico
2018-01-01
In this paper, we stress the importance of momentum-space geometry in the understanding of two-dimensional topological phases of matter. We focus, for simplicity, on the gapped boundary of three-dimensional topological insulators in class AII, which are described by a massive Dirac Hamiltonian and characterized by an half-integer Chern number. The gap is induced by introducing a magnetic perturbation, such as an external Zeeman field or a ferromagnet on the surface. The quantum Bures metric acquires a central role in our discussion and identifies a cigar geometry. We first derive the Chern number from the cigar geometry and we then show that the quantum metric can be seen as a solution of two-dimensional non-Abelian BF theory in momentum space. The gauge connection for this model is associated to the Maxwell algebra, which takes into account the Lorentz symmetries related to the Dirac theory and the momentum-space magnetic translations connected to the magnetic perturbation. The Witten black-hole metric is a solution of this gauge theory and coincides with the Bures metric. This allows us to calculate the corresponding momentum-space entanglement entropy that surprisingly carries information about the real-space conformal field theory describing the defect lines that can be created on the gapped boundary.
Sums over geometries and improvements on the mean field approximation
International Nuclear Information System (INIS)
Sacksteder, Vincent E. IV
2007-01-01
The saddle points of a Lagrangian due to Efetov are analyzed. This Lagrangian was originally proposed as a tool for calculating systematic corrections to the Bethe approximation, a mean-field approximation which is important in statistical mechanics, glasses, coding theory, and combinatorial optimization. Detailed analysis shows that the trivial saddle point generates a sum over geometries reminiscent of dynamically triangulated quantum gravity, which suggests new possibilities to design sums over geometries for the specific purpose of obtaining improved mean-field approximations to D-dimensional theories. In the case of the Efetov theory, the dominant geometries are locally treelike, and the sum over geometries diverges in a way that is similar to quantum gravity's divergence when all topologies are included. Expertise from the field of dynamically triangulated quantum gravity about sums over geometries may be able to remedy these defects and fulfill the Efetov theory's original promise. The other saddle points of the Efetov Lagrangian are also analyzed; the Hessian at these points is nonnormal and pseudo-Hermitian, which is unusual for bosonic theories. The standard formula for Gaussian integrals is generalized to nonnormal kernels
On spinor geometry: A genesis of extended supersymmetry
International Nuclear Information System (INIS)
Budini, P.
1980-08-01
It is conjectured that euclidean geometry should be derived from spinor geometry through the equivalence of simple semispinor with isotropic semi n-vectors. The only tensors of complex 2n dimensional Euclidean space Esub(c)sup(2n) should then be: isotropic n - vectors and their intersections. Esub(c) 4 spinor geometry generates two isotropic semi bivectors equivalent to the semispinors of Esub(c) 4 (their geometrical properties are those of light propagating in vacuum), and their intersection: an isotropic vector (possibly representing momenta of massless particle and/or light rays); but no scalar, pseudoscalar or pseudovector is generated. In order to generate vectors outside the light cone in Msup(3.1) one needs not less than Esub(c) 6 spinor geometry which also generates Lorentz pseudoscalars and non isotropic pseudovectors and tensors. Besides, Dirac spinor should then always appear in doublets in Msup(3.1). Furthermore the mere geometrical structure of Esub(c) 6 spinor geometry seems to suggest formally, both Poincare (extended) and conformal supersymmetry. The suggested spinor-geometrical approach privileges the elementary role of semispinors. Its relevance for the real world should be manifested by the privileged role of semispinors in elementary interactions as in fact seems to be the case with Lorentz semispinors in weak interactions (and could perhaps also be the case for strong ones where conformal semispinors (or twistors) could be the interacting spinor fields). (author)
The Idea of Order at Geometry Class.
Rishel, Thomas
The idea of order in geometry is explored using the experience of assignments given to undergraduates in a college geometry course "From Space to Geometry." Discussed are the definition of geometry, and earth measurement using architecture, art, and common experience. This discussion concludes with a consideration of the question of whether…
Teaching Spatial Geometry in a Virtual World
DEFF Research Database (Denmark)
Förster, Klaus-Tycho
2017-01-01
Spatial geometry is one of the fundamental mathematical building blocks of any engineering education. However, it is overshadowed by planar geometry in the curriculum between playful early primary education and later analytical geometry, leaving a multi-year gap where spatial geometry is absent...
Analogical Reasoning in Geometry Education
Magdas, Ioana
2015-01-01
The analogical reasoning isn't used only in mathematics but also in everyday life. In this article we approach the analogical reasoning in Geometry Education. The novelty of this article is a classification of geometrical analogies by reasoning type and their exemplification. Our classification includes: analogies for understanding and setting a…
Normal forms in Poisson geometry
Marcut, I.T.
2013-01-01
The structure of Poisson manifolds is highly nontrivial even locally. The first important result in this direction is Conn's linearization theorem around fixed points. One of the main results of this thesis (Theorem 2) is a normal form theorem in Poisson geometry, which is the Poisson-geometric
Exploring Bundling Theory with Geometry
Eckalbar, John C.
2006-01-01
The author shows how instructors might successfully introduce students in principles and intermediate microeconomic theory classes to the topic of bundling (i.e., the selling of two or more goods as a package, rather than separately). It is surprising how much students can learn using only the tools of high school geometry. To be specific, one can…
Stochastic Modelling of River Geometry
DEFF Research Database (Denmark)
Sørensen, John Dalsgaard; Schaarup-Jensen, K.
1996-01-01
Numerical hydrodynamic river models are used in a large number of applications to estimate critical events for rivers. These estimates are subject to a number of uncertainties. In this paper, the problem to evaluate these estimates using probabilistic methods is considered. Stochastic models for ...... for river geometries are formulated and a coupling between hydraulic computational methods and numerical reliability methods is presented....
Matter in toy dynamical geometries
Konopka, T.J.
2009-01-01
One of the objectives of theories describing quantum dynamical geometry is to compute expectation values of geometrical observables. The results of such computations can be affected by whether or not matter is taken into account. It is thus important to understand to what extent and to what effect
Ca??adas, Mar??a C.; Molina, Marta; Gallardo, Sandra; Mart??nez-Santaolalla, Manuel J.; Pe??as, Mar??a
2010-01-01
In this work we present an activity for High School students in which various mathematical concepts of plane and spatial geometry are involved. The final objective of the proposed tasks is constructing a particular polyhedron, the cube, by using a modality of origami called modular origami.
Granular flows in constrained geometries
Murthy, Tejas; Viswanathan, Koushik
Confined geometries are widespread in granular processing applications. The deformation and flow fields in such a geometry, with non-trivial boundary conditions, determine the resultant mechanical properties of the material (local porosity, density, residual stresses etc.). We present experimental studies of deformation and plastic flow of a prototypical granular medium in different nontrivial geometries- flat-punch compression, Couette-shear flow and a rigid body sliding past a granular half-space. These geometries represent simplified scaled-down versions of common industrial configurations such as compaction and dredging. The corresponding granular flows show a rich variety of flow features, representing the entire gamut of material types, from elastic solids (beam buckling) to fluids (vortex-formation, boundary layers) and even plastically deforming metals (dead material zone, pile-up). The effect of changing particle-level properties (e.g., shape, size, density) on the observed flows is also explicitly demonstrated. Non-smooth contact dynamics particle simulations are shown to reproduce some of the observed flow features quantitatively. These results showcase some central challenges facing continuum-scale constitutive theories for dynamic granular flows.
General Relativity: Geometry Meets Physics
Thomsen, Dietrick E.
1975-01-01
Observing the relationship of general relativity and the geometry of space-time, the author questions whether the rest of physics has geometrical explanations. As a partial answer he discusses current research on subatomic particles employing geometric transformations, and cites the existence of geometrical definitions of physical quantities such…
Learners engaging with transformation geometry
African Journals Online (AJOL)
participants engaged in investigative semi-structured interviews with the resear- chers. ... Keywords: analysis; conversions; transformation geometry; transformations; treatments .... semiotic systems of representation is not only to designate mathematical objects or to com- municate but also to ... Research design. We believe ...
Multivariable calculus and differential geometry
Walschap, Gerard
2015-01-01
This text is a modern in-depth study of the subject that includes all the material needed from linear algebra. It then goes on to investigate topics in differential geometry, such as manifolds in Euclidean space, curvature, and the generalization of the fundamental theorem of calculus known as Stokes' theorem.
College geometry a unified development
Kay, David C
2011-01-01
""The book is a comprehensive textbook on basic geometry. … Key features of the book include numerous figures and many problems, more than half of which come with hints or even complete solutions. Frequent historical comments add to making the reading a pleasant one.""-Michael Joswig, Zentralblatt MATH 1273
Mahaffey, Michael L.
One of a series of experimental units for children at the preschool level, this booklet deals with geometric concepts. A unit on volume and a unit on linear measurement are covered; for each unit a discussion of mathematical objectives, a list of materials needed, and a sequence of learning activities are provided. Directions are specified for the…
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...
Ferlemann, Paul G.; Gollan, Rowan J.
2010-01-01
Computational design and analysis of three-dimensional hypersonic inlets with shape transition has been a significant challenge due to the complex geometry and grid required for three-dimensional viscous flow calculations. Currently, the design process utilizes an inviscid design tool to produce initial inlet shapes by streamline tracing through an axisymmetric compression field. However, the shape is defined by a large number of points rather than a continuous surface and lacks important features such as blunt leading edges. Therefore, a design system has been developed to parametrically construct true CAD geometry and link the topology of a structured grid to the geometry. The Adaptive Modeling Language (AML) constitutes the underlying framework that is used to build the geometry and grid topology. Parameterization of the CAD geometry allows the inlet shapes produced by the inviscid design tool to be generated, but also allows a great deal of flexibility to modify the shape to account for three-dimensional viscous effects. By linking the grid topology to the parametric geometry, the GridPro grid generation software can be used efficiently to produce a smooth hexahedral multiblock grid. To demonstrate the new capability, a matrix of inlets were designed by varying four geometry parameters in the inviscid design tool. The goals of the initial design study were to explore inviscid design tool geometry variations with a three-dimensional analysis approach, demonstrate a solution rate which would enable the use of high-fidelity viscous three-dimensional CFD in future design efforts, process the results for important performance parameters, and perform a sample optimization.
Discrete differential geometry. Consistency as integrability
Bobenko, Alexander I.; Suris, Yuri B.
2005-01-01
A new field of discrete differential geometry is presently emerging on the border between differential and discrete geometry. Whereas classical differential geometry investigates smooth geometric shapes (such as surfaces), and discrete geometry studies geometric shapes with finite number of elements (such as polyhedra), the discrete differential geometry aims at the development of discrete equivalents of notions and methods of smooth surface theory. Current interest in this field derives not ...
Numerically robust geometry engine for compound solid geometries
International Nuclear Information System (INIS)
Vlachoudis, V.; Sinuela-Pastor, D.
2013-01-01
Monte Carlo programs heavily rely on a fast and numerically robust solid geometry engines. However the success of solid modeling, depends on facilities for specifying and editing parameterized models through a user-friendly graphical front-end. Such a user interface has to be fast enough in order to be interactive for 2D and/or 3D displays, but at the same time numerically robust in order to display possible modeling errors at real time that could be critical for the simulation. The graphical user interface Flair for FLUKA currently employs such an engine where special emphasis has been given on being fast and numerically robust. The numerically robustness is achieved by a novel method of estimating the floating precision of the operations, which dynamically adapts all the decision operations accordingly. Moreover a predictive caching mechanism is ensuring that logical errors in the geometry description are found online, without compromising the processing time by checking all regions. (authors)
Classification of digital affine noncommutative geometries
Majid, Shahn; Pachoł, Anna
2018-03-01
It is known that connected translation invariant n-dimensional noncommutative differentials dxi on the algebra k[x1, …, xn] of polynomials in n-variables over a field k are classified by commutative algebras V on the vector space spanned by the coordinates. These data also apply to construct differentials on the Heisenberg algebra "spacetime" with relations [xμ, xν] = λΘμν, where Θ is an antisymmetric matrix, as well as to Lie algebras with pre-Lie algebra structures. We specialise the general theory to the field k =F2 of two elements, in which case translation invariant metrics (i.e., with constant coefficients) are equivalent to making V a Frobenius algebra. We classify all of these and their quantum Levi-Civita bimodule connections for n = 2, 3, with partial results for n = 4. For n = 2, we find 3 inequivalent differential structures admitting 1, 2, and 3 invariant metrics, respectively. For n = 3, we find 6 differential structures admitting 0, 1, 2, 3, 4, 7 invariant metrics, respectively. We give some examples for n = 4 and general n. Surprisingly, not all our geometries for n ≥ 2 have zero quantum Riemann curvature. Quantum gravity is normally seen as a weighted "sum" over all possible metrics but our results are a step towards a deeper approach in which we must also "sum" over differential structures. Over F2 we construct some of our algebras and associated structures by digital gates, opening up the possibility of "digital geometry."
Contact Geometry of Hyperbolic Equations of Generic Type
Directory of Open Access Journals (Sweden)
Dennis The
2008-08-01
Full Text Available We study the contact geometry of scalar second order hyperbolic equations in the plane of generic type. Following a derivation of parametrized contact-invariants to distinguish Monge-Ampère (class 6-6, Goursat (class 6-7 and generic (class 7-7 hyperbolic equations, we use Cartan's equivalence method to study the generic case. An intriguing feature of this class of equations is that every generic hyperbolic equation admits at most a nine-dimensional contact symmetry algebra. The nine-dimensional bound is sharp: normal forms for the contact-equivalence classes of these maximally symmetric generic hyperbolic equations are derived and explicit symmetry algebras are presented. Moreover, these maximally symmetric equations are Darboux integrable. An enumeration of several submaximally symmetric (eight and seven-dimensional generic hyperbolic structures is also given.
Physical model of dimensional regularization
Energy Technology Data Exchange (ETDEWEB)
Schonfeld, Jonathan F.
2016-12-15
We explicitly construct fractals of dimension 4-ε on which dimensional regularization approximates scalar-field-only quantum-field theory amplitudes. The construction does not require fractals to be Lorentz-invariant in any sense, and we argue that there probably is no Lorentz-invariant fractal of dimension greater than 2. We derive dimensional regularization's power-law screening first for fractals obtained by removing voids from 3-dimensional Euclidean space. The derivation applies techniques from elementary dielectric theory. Surprisingly, fractal geometry by itself does not guarantee the appropriate power-law behavior; boundary conditions at fractal voids also play an important role. We then extend the derivation to 4-dimensional Minkowski space. We comment on generalization to non-scalar fields, and speculate about implications for quantum gravity. (orig.)
Code subspaces for LLM geometries
Berenstein, David; Miller, Alexandra
2018-03-01
We consider effective field theory around classical background geometries with a gauge theory dual, specifically those in the class of LLM geometries. These are dual to half-BPS states of N= 4 SYM. We find that the language of code subspaces is natural for discussing the set of nearby states, which are built by acting with effective fields on these backgrounds. This work extends our previous work by going beyond the strict infinite N limit. We further discuss how one can extract the topology of the state beyond N→∞ and find that, as before, uncertainty and entanglement entropy calculations provide a useful tool to do so. Finally, we discuss obstructions to writing down a globally defined metric operator. We find that the answer depends on the choice of reference state that one starts with. Therefore, within this setup, there is ambiguity in trying to write an operator that describes the metric globally.
Euclidean distance geometry an introduction
Liberti, Leo
2017-01-01
This textbook, the first of its kind, presents the fundamentals of distance geometry: theory, useful methodologies for obtaining solutions, and real world applications. Concise proofs are given and step-by-step algorithms for solving fundamental problems efficiently and precisely are presented in Mathematica®, enabling the reader to experiment with concepts and methods as they are introduced. Descriptive graphics, examples, and problems, accompany the real gems of the text, namely the applications in visualization of graphs, localization of sensor networks, protein conformation from distance data, clock synchronization protocols, robotics, and control of unmanned underwater vehicles, to name several. Aimed at intermediate undergraduates, beginning graduate students, researchers, and practitioners, the reader with a basic knowledge of linear algebra will gain an understanding of the basic theories of distance geometry and why they work in real life.
Fractal geometry and computer graphics
Sakas, Georgios; Peitgen, Heinz-Otto; Englert, Gabriele
1992-01-01
Fractal geometry has become popular in the last 15 years, its applications can be found in technology, science, or even arts. Fractal methods and formalism are seen today as a general, abstract, but nevertheless practical instrument for the description of nature in a wide sense. But it was Computer Graphics which made possible the increasing popularity of fractals several years ago, and long after their mathematical formulation. The two disciplines are tightly linked. The book contains the scientificcontributions presented in an international workshop in the "Computer Graphics Center" in Darmstadt, Germany. The target of the workshop was to present the wide spectrum of interrelationships and interactions between Fractal Geometry and Computer Graphics. The topics vary from fundamentals and new theoretical results to various applications and systems development. All contributions are original, unpublished papers.The presentations have been discussed in two working groups; the discussion results, together with a...
The geometry of celestial mechanics
Geiges, Hansjörg
2016-01-01
Celestial mechanics is the branch of mathematical astronomy devoted to studying the motions of celestial bodies subject to the Newtonian law of gravitation. This mathematical introductory textbook reveals that even the most basic question in celestial mechanics, the Kepler problem, leads to a cornucopia of geometric concepts: conformal and projective transformations, spherical and hyperbolic geometry, notions of curvature, and the topology of geodesic flows. For advanced undergraduate and beginning graduate students, this book explores the geometric concepts underlying celestial mechanics and is an ideal companion for introductory courses. The focus on the history of geometric ideas makes it perfect supplementary reading for students in elementary geometry and topology. Numerous exercises, historical notes and an extensive bibliography provide all the contextual information required to gain a solid grounding in celestial mechanics.
Differential geometry and mathematical physics
Rudolph, Gerd
Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and symplectic geometry, • Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous d...
Grassmannian geometry of scattering amplitudes
Arkani-Hamed, Nima; Cachazo, Freddy; Goncharov, Alexander; Postnikov, Alexander; Trnka, Jaroslav
2016-01-01
Outlining a revolutionary reformulation of the foundations of perturbative quantum field theory, this book is a self-contained and authoritative analysis of the application of this new formulation to the case of planar, maximally supersymmetric Yang–Mills theory. The book begins by deriving connections between scattering amplitudes and Grassmannian geometry from first principles before introducing novel physical and mathematical ideas in a systematic manner accessible to both physicists and mathematicians. The principle players in this process are on-shell functions which are closely related to certain sub-strata of Grassmannian manifolds called positroids - in terms of which the classification of on-shell functions and their relations becomes combinatorially manifest. This is an essential introduction to the geometry and combinatorics of the positroid stratification of the Grassmannian and an ideal text for advanced students and researchers working in the areas of field theory, high energy physics, and the...
Foliation theory in algebraic geometry
McKernan, James; Pereira, Jorge
2016-01-01
Featuring a blend of original research papers and comprehensive surveys from an international team of leading researchers in the thriving fields of foliation theory, holomorphic foliations, and birational geometry, this book presents the proceedings of the conference "Foliation Theory in Algebraic Geometry," hosted by the Simons Foundation in New York City in September 2013. Topics covered include: Fano and del Pezzo foliations; the cone theorem and rank one foliations; the structure of symmetric differentials on a smooth complex surface and a local structure theorem for closed symmetric differentials of rank two; an overview of lifting symmetric differentials from varieties with canonical singularities and the applications to the classification of AT bundles on singular varieties; an overview of the powerful theory of the variety of minimal rational tangents introduced by Hwang and Mok; recent examples of varieties which are hyperbolic and yet the Green-Griffiths locus is the whole of X; and a classificati...
Groups and Geometries : Siena Conference
Kantor, William; Lunardon, Guglielmo; Pasini, Antonio; Tamburini, Maria
1998-01-01
On September 1-7, 1996 a conference on Groups and Geometries took place in lovely Siena, Italy. It brought together experts and interested mathematicians from numerous countries. The scientific program centered around invited exposi tory lectures; there also were shorter research announcements, including talks by younger researchers. The conference concerned a broad range of topics in group theory and geometry, with emphasis on recent results and open problems. Special attention was drawn to the interplay between group-theoretic methods and geometric and combinatorial ones. Expanded versions of many of the talks appear in these Proceedings. This volume is intended to provide a stimulating collection of themes for a broad range of algebraists and geometers. Among those themes, represented within the conference or these Proceedings, are aspects of the following: 1. the classification of finite simple groups, 2. the structure and properties of groups of Lie type over finite and algebraically closed fields of f...
Needle decompositions in Riemannian geometry
Klartag, Bo'az
2017-01-01
The localization technique from convex geometry is generalized to the setting of Riemannian manifolds whose Ricci curvature is bounded from below. In a nutshell, the author's method is based on the following observation: When the Ricci curvature is non-negative, log-concave measures are obtained when conditioning the Riemannian volume measure with respect to a geodesic foliation that is orthogonal to the level sets of a Lipschitz function. The Monge mass transfer problem plays an important role in the author's analysis.
Systematics of IIB spinorial geometry
Gran, U.; Gutowski, J.; Papadopoulos, G.; Roest, D.
2005-01-01
We reduce the classification of all supersymmetric backgrounds of IIB supergravity to the evaluation of the Killing spinor equations and their integrability conditions, which contain the field equations, on five types of spinors. This extends the work of [hep-th/0503046] to IIB supergravity. We give the expressions of the Killing spinor equations on all five types of spinors. In this way, the Killing spinor equations become a linear system for the fluxes, geometry and spacetime derivatives of...
Geometry Dependence of Stellarator Turbulence
International Nuclear Information System (INIS)
Mynick, H.E.; Xanthopoulos, P.; Boozer, A.H.
2009-01-01
Using the nonlinear gyrokinetic code package GENE/GIST, we study the turbulent transport in a broad family of stellarator designs, to understand the geometry-dependence of the microturbulence. By using a set of flux tubes on a given flux surface, we construct a picture of the 2D structure of the microturbulence over that surface, and relate this to relevant geometric quantities, such as the curvature, local shear, and effective potential in the Schrodinger-like equation governing linear drift modes
Superbanana orbits in stellarator geometries
International Nuclear Information System (INIS)
Derr, J.A.; Shohet, J.L.
1979-04-01
The presence of superbanana orbit types localized to either the interior or the exterior of stellarators and torsatrons is numerically investigated for 3.5 MeV alpha particles. The absence of the interior superbanana in both geometries is found to be due to non-conservation of the action. Exterior superbananas are found in the stellarator only, as a consequence of the existence of closed helical magnetic wells. No superbananas of either type are found in the torsatron
Turtle geometry the Python way
Battle, S.
2014-01-01
An introduction to coding using Python’s on-screen ‘turtle’ that can be commanded with a few simple instructions including forward, backward, left and right. The turtle leaves a trace that can be used to draw geometric figures. This workshop is aimed at beginners of all ages. The aim is to learn a smattering of programming and a little bit of geometry in a fun way.
Topics in modern differential geometry
Verstraelen, Leopold
2017-01-01
A variety of introductory articles is provided on a wide range of topics, including variational problems on curves and surfaces with anisotropic curvature. Experts in the fields of Riemannian, Lorentzian and contact geometry present state-of-the-art reviews of their topics. The contributions are written on a graduate level and contain extended bibliographies. The ten chapters are the result of various doctoral courses which were held in 2009 and 2010 at universities in Leuven, Serbia, Romania and Spain.
COGEDIF - automatic TORT and DORT input generation from MORSE combinatorial geometry models
International Nuclear Information System (INIS)
Castelli, R.A.; Barnett, D.A.
1992-01-01
COGEDIF is an interactive utility which was developed to automate the preparation of two and three dimensional geometrical inputs for the ORNL-TORT and DORT discrete ordinates programs from complex three dimensional models described using the MORSE combinatorial geometry input description. The program creates either continuous or disjoint mesh input based upon the intersections of user defined meshing planes and the MORSE body definitions. The composition overlay of the combinatorial geometry is used to create the composition mapping of the discretized geometry based upon the composition found at the centroid of each of the mesh cells. This program simplifies the process of using discrete orthogonal mesh cells to represent non-orthogonal geometries in large models which require mesh sizes of the order of a million cells or more. The program was specifically written to take advantage of the new TORT disjoint mesh option which was developed at ORNL
Computational geometry for reactor applications
International Nuclear Information System (INIS)
Brown, F.B.; Bischoff, F.G.
1988-01-01
Monte Carlo codes for simulating particle transport involve three basic computational sections: a geometry package for locating particles and computing distances to regional boundaries, a physics package for analyzing interactions between particles and problem materials, and an editing package for determining event statistics and overall results. This paper describes the computational geometry methods in RACER, a vectorized Monte Carlo code used for reactor physics analysis, so that comparisons may be made with techniques used in other codes. The principal applications for RACER are eigenvalue calculations and power distributions associated with reactor core physics analysis. Successive batches of neutrons are run until convergence and acceptable confidence intervals are obtained, with typical problems involving >10 6 histories. As such, the development of computational geometry methods has emphasized two basic needs: a flexible but compact geometric representation that permits accurate modeling of reactor core details and efficient geometric computation to permit very large numbers of histories to be run. The current geometric capabilities meet these needs effectively, supporting a variety of very large and demanding applications
Number theory III Diophantine geometry
1991-01-01
From the reviews of the first printing of this book, published as Volume 60 of the Encyclopaedia of Mathematical Sciences: "Between number theory and geometry there have been several stimulating influences, and this book records of these enterprises. This author, who has been at the centre of such research for many years, is one of the best guides a reader can hope for. The book is full of beautiful results, open questions, stimulating conjectures and suggestions where to look for future developments. This volume bears witness of the broad scope of knowledge of the author, and the influence of several people who have commented on the manuscript before publication ... Although in the series of number theory, this volume is on diophantine geometry, and the reader will notice that algebraic geometry is present in every chapter. ... The style of the book is clear. Ideas are well explained, and the author helps the reader to pass by several technicalities. Reading and rereading this book I noticed that the topics ...
Riemannian geometry and geometric analysis
Jost, Jürgen
2017-01-01
This established reference work continues to provide its readers with a gateway to some of the most interesting developments in contemporary geometry. It offers insight into a wide range of topics, including fundamental concepts of Riemannian geometry, such as geodesics, connections and curvature; the basic models and tools of geometric analysis, such as harmonic functions, forms, mappings, eigenvalues, the Dirac operator and the heat flow method; as well as the most important variational principles of theoretical physics, such as Yang-Mills, Ginzburg-Landau or the nonlinear sigma model of quantum field theory. The present volume connects all these topics in a systematic geometric framework. At the same time, it equips the reader with the working tools of the field and enables her or him to delve into geometric research. The 7th edition has been systematically reorganized and updated. Almost no page has been left unchanged. It also includes new material, for instance on symplectic geometry, as well as the B...
Donaldson invariants in algebraic geometry
International Nuclear Information System (INIS)
Goettsche, L.
2000-01-01
In these lectures I want to give an introduction to the relation of Donaldson invariants with algebraic geometry: Donaldson invariants are differentiable invariants of smooth compact 4-manifolds X, defined via moduli spaces of anti-self-dual connections. If X is an algebraic surface, then these moduli spaces can for a suitable choice of the metric be identified with moduli spaces of stable vector bundles on X. This can be used to compute Donaldson invariants via methods of algebraic geometry and has led to a lot of activity on moduli spaces of vector bundles and coherent sheaves on algebraic surfaces. We will first recall the definition of the Donaldson invariants via gauge theory. Then we will show the relation between moduli spaces of anti-self-dual connections and moduli spaces of vector bundles on algebraic surfaces, and how this makes it possible to compute Donaldson invariants via algebraic geometry methods. Finally we concentrate on the case that the number b + of positive eigenvalues of the intersection form on the second homology of the 4-manifold is 1. In this case the Donaldson invariants depend on the metric (or in the algebraic geometric case on the polarization) via a system of walls and chambers. We will study the change of the invariants under wall-crossing, and use this in particular to compute the Donaldson invariants of rational algebraic surfaces. (author)
Aspects of differential geometry II
Gilkey, Peter
2015-01-01
Differential Geometry is a wide field. We have chosen to concentrate upon certain aspects that are appropriate for an introduction to the subject; we have not attempted an encyclopedic treatment. Book II deals with more advanced material than Book I and is aimed at the graduate level. Chapter 4 deals with additional topics in Riemannian geometry. Properties of real analytic curves given by a single ODE and of surfaces given by a pair of ODEs are studied, and the volume of geodesic balls is treated. An introduction to both holomorphic and Kähler geometry is given. In Chapter 5, the basic properties of de Rham cohomology are discussed, the Hodge Decomposition Theorem, Poincaré duality, and the Künneth formula are proved, and a brief introduction to the theory of characteristic classes is given. In Chapter 6, Lie groups and Lie algebras are dealt with. The exponential map, the classical groups, and geodesics in the context of a bi-invariant metric are discussed. The de Rham cohomology of compact Lie groups an...
Algebraic Geometry and Number Theory Summer School
Sarıoğlu, Celal; Soulé, Christophe; Zeytin, Ayberk
2017-01-01
This lecture notes volume presents significant contributions from the “Algebraic Geometry and Number Theory” Summer School, held at Galatasaray University, Istanbul, June 2-13, 2014. It addresses subjects ranging from Arakelov geometry and Iwasawa theory to classical projective geometry, birational geometry and equivariant cohomology. Its main aim is to introduce these contemporary research topics to graduate students who plan to specialize in the area of algebraic geometry and/or number theory. All contributions combine main concepts and techniques with motivating examples and illustrative problems for the covered subjects. Naturally, the book will also be of interest to researchers working in algebraic geometry, number theory and related fields.
Geometry success in 20 minutes a day
LLC, LearningExpress
2014-01-01
Whether you're new to geometry or just looking for a refresher, Geometry Success in 20 Minutes a Day offers a 20-step lesson plan that provides quick and thorough instruction in practical, critical skills. Stripped of unnecessary math jargon but bursting with geometry essentials, Geometry Success in 20 Minutes a Day: Covers all vital geometry skills, from the basic building blocks of geometry to ratio, proportion, and similarity to trigonometry and beyond Provides hundreds of practice exercises in test format Applies geometr
Formation of classical crystals of dipolar particles in a helical geometry
DEFF Research Database (Denmark)
K. Pedersen, J.; V. Fedorov, D.; S. Jensen, A.
2014-01-01
We consider crystal formation of particles with dipole-dipole interactions that are confined to move in a one-dimensional helical geometry with their dipole moments oriented along the symmetry axis of the confining helix. The stable classical lowest energy configurations are found to be chain......-to-tail attraction in the system. The speed of sound propagates along the chains. It is independent of the number of chains although depending on geometry....
Lattice gas simulations of dynamical geometry in two dimensions.
Klales, Anna; Cianci, Donato; Needell, Zachary; Meyer, David A; Love, Peter J
2010-10-01
We present a hydrodynamic lattice gas model for two-dimensional flows on curved surfaces with dynamical geometry. This model is an extension to two dimensions of the dynamical geometry lattice gas model previously studied in one dimension. We expand upon a variation of the two-dimensional flat space Frisch-Hasslacher-Pomeau (FHP) model created by Frisch [Phys. Rev. Lett. 56, 1505 (1986)] and independently by Wolfram, and modified by Boghosian [Philos. Trans. R. Soc. London, Ser. A 360, 333 (2002)]. We define a hydrodynamic lattice gas model on an arbitrary triangulation whose flat space limit is the FHP model. Rules that change the geometry are constructed using the Pachner moves, which alter the triangulation but not the topology. We present results on the growth of the number of triangles as a function of time. Simulations show that the number of triangles grows with time as t(1/3), in agreement with a mean-field prediction. We also present preliminary results on the distribution of curvature for a typical triangulation in these simulations.
Charged fluid distribution in higher dimensional spheroidal space-time
Indian Academy of Sciences (India)
A general solution of Einstein field equations corresponding to a charged fluid distribution on the background of higher dimensional spheroidal space-time is obtained. The solution generates several known solutions for superdense star having spheroidal space-time geometry.
A Whirlwind Tour of Computational Geometry.
Graham, Ron; Yao, Frances
1990-01-01
Described is computational geometry which used concepts and results from classical geometry, topology, combinatorics, as well as standard algorithmic techniques such as sorting and searching, graph manipulations, and linear programing. Also included are special techniques and paradigms. (KR)
Optimizing solar-cell grid geometry
Crossley, A. P.
1969-01-01
Trade-off analysis and mathematical expressions calculate optimum grid geometry in terms of various cell parameters. Determination of the grid geometry provides proper balance between grid resistance and cell output to optimize the energy conversion process.
Mathematical model of geometry and fibrous structure of the heart.
Nielsen, P M; Le Grice, I J; Smaill, B H; Hunter, P J
1991-04-01
We developed a mathematical representation of ventricular geometry and muscle fiber organization using three-dimensional finite elements referred to a prolate spheroid coordinate system. Within elements, fields are approximated using basis functions with associated parameters defined at the element nodes. Four parameters per node are used to describe ventricular geometry. The radial coordinate is interpolated using cubic Hermite basis functions that preserve slope continuity, while the angular coordinates are interpolated linearly. Two further nodal parameters describe the orientation of myocardial fibers. The orientation of fibers within coordinate planes bounded by epicardial and endocardial surfaces is interpolated linearly, with transmural variation given by cubic Hermite basis functions. Left and right ventricular geometry and myocardial fiber orientations were characterized for a canine heart arrested in diastole and fixed at zero transmural pressure. The geometry was represented by a 24-element ensemble with 41 nodes. Nodal parameters fitted using least squares provided a realistic description of ventricular epicardial [root mean square (RMS) error less than 0.9 mm] and endocardial (RMS error less than 2.6 mm) surfaces. Measured fiber fields were also fitted (RMS error less than 17 degrees) with a 60-element, 99-node mesh obtained by subdividing the 24-element mesh. These methods provide a compact and accurate anatomic description of the ventricles suitable for use in finite element stress analysis, simulation of cardiac electrical activation, and other cardiac field modeling problems.