Energy Technology Data Exchange (ETDEWEB)
Reynolds, J. M.; Lopez-Bruna, D.
2009-12-11
This report is the first of a series dedicated to the numerical calculation of the evolution of fusion plasmas in general toroidal geometry, including TJ-II plasmas. A kinetic treatment has been chosen: the evolution equation of the distribution function of one or several plasma species is solved in guiding center coordinates. The distribution function is written as a Maxwellian one modulated by polynomial series in the kinetic coordinates with no other approximations than those of the guiding center itself and the computation capabilities. The code allows also for the inclusion of the three-dimensional electrostatic potential in a self-consistent manner, but the initial objective has been set to solving only the neoclassical transport. A high order conservative method (Spectral Difference Method) has been chosen in order to discretized the equation for its numerical solution. In this first report, in addition to justifying the work, the evolution equation and its approximations are described, as well as the baseline of the numerical procedures. (Author) 28 refs.
Magnetic response of certain curved graphitic geometries
International Nuclear Information System (INIS)
Wang, L.; Davids, P.S.; Saxena, A.; Bishop, A.R.
1992-01-01
The quasi-particle energy spectra associated with some members of buckyfamily (curved graphitic geometries), in particular C 50 , C 60 , C 70 and related fullerenes as well as coaxial helical microtubules of graphite, are obtained analytically within the mean-field approximation. These energy spectra are then used to calculate various response functions. Specifically, we calculate the specific heat, magnetization and magnetic susceptibility in the presence of an external magnetic field at low temperatures. For a single microtubule an extra peak superimposed on the first de Haas van Alphen (dHvA) oscillation in magnetic susceptibility is found in the 50--170 Tesla range depending on the radius which is possibly accessible in special (explosive flux compression) experiments. Finally, we point to important potential applications of these novel mesoscopic structures in nanotechnology
UNDERSTANDING THE GEOMETRY OF ASTROPHYSICAL MAGNETIC FIELDS
Energy Technology Data Exchange (ETDEWEB)
Broderick, Avery E [Canadian Institute for Theoretical Astrophysics, 60 St. George St., Toronto, ON M5S 3H8 (Canada); Blandford, Roger D., E-mail: aeb@cita.utoronto.c [Kavli Institute for Particle Astrophysics and Cosmology, 2575 Sand Hill Rd., Menlo Park, CA 94309 (United States)
2010-08-01
Faraday rotation measurements have provided an invaluable technique for probing the properties of astrophysical magnetized plasmas. Unfortunately, typical observations provide information only about the density-weighted average of the magnetic field component parallel to the line of sight. As a result, the magnetic field geometry along the line of sight, and in many cases even the location of the rotating material, is poorly constrained. Frequently, interpretations of Faraday rotation observations are dependent upon underlying models of the magnetic field being probed (e.g., uniform, turbulent, equipartition). However, we show that at sufficiently low frequencies, specifically below roughly 13(RM/1 rad m{sup -2}){sup 1/4}(B/1 G){sup 1/2} MHz, the character of Faraday rotation changes, entering what we term the 'super-adiabatic regime' in which the rotation measure (RM) is proportional to the integrated absolute value of the line-of-sight component of the field. As a consequence, comparing RMs at high frequencies with those in this new regime provides direct information about the geometry of the magnetic field along the line of sight. Furthermore, the frequency defining the transition to this new regime, {nu}{sub SA}, depends directly upon the local electron density and magnetic field strength where the magnetic field is perpendicular to the line of sight, allowing the unambiguous distinction between Faraday rotation within and in front of the emission region. Typical values of {nu}{sub SA} range from 10 kHz (below the ionospheric cutoff, but above the heliospheric cutoff) to 10 GHz, depending upon the details of the Faraday rotating environment. In particular, for resolved active galactic nuclei, including the black holes at the center of the Milky Way (Sgr A*) and M81, {nu}{sub SA} ranges from roughly 10 MHz to 10 GHz, and thus can be probed via existing and up-coming ground-based radio observatories.
UNDERSTANDING THE GEOMETRY OF ASTROPHYSICAL MAGNETIC FIELDS
International Nuclear Information System (INIS)
Broderick, Avery E.; Blandford, Roger D.
2010-01-01
Faraday rotation measurements have provided an invaluable technique for probing the properties of astrophysical magnetized plasmas. Unfortunately, typical observations provide information only about the density-weighted average of the magnetic field component parallel to the line of sight. As a result, the magnetic field geometry along the line of sight, and in many cases even the location of the rotating material, is poorly constrained. Frequently, interpretations of Faraday rotation observations are dependent upon underlying models of the magnetic field being probed (e.g., uniform, turbulent, equipartition). However, we show that at sufficiently low frequencies, specifically below roughly 13(RM/1 rad m -2 ) 1/4 (B/1 G) 1/2 MHz, the character of Faraday rotation changes, entering what we term the 'super-adiabatic regime' in which the rotation measure (RM) is proportional to the integrated absolute value of the line-of-sight component of the field. As a consequence, comparing RMs at high frequencies with those in this new regime provides direct information about the geometry of the magnetic field along the line of sight. Furthermore, the frequency defining the transition to this new regime, ν SA , depends directly upon the local electron density and magnetic field strength where the magnetic field is perpendicular to the line of sight, allowing the unambiguous distinction between Faraday rotation within and in front of the emission region. Typical values of ν SA range from 10 kHz (below the ionospheric cutoff, but above the heliospheric cutoff) to 10 GHz, depending upon the details of the Faraday rotating environment. In particular, for resolved active galactic nuclei, including the black holes at the center of the Milky Way (Sgr A*) and M81, ν SA ranges from roughly 10 MHz to 10 GHz, and thus can be probed via existing and up-coming ground-based radio observatories.
Effects of geometry in itinerant electron magnets
Energy Technology Data Exchange (ETDEWEB)
Nakamura, H [Graduate School of Material Science, University of Hyogo, Kamigori, Ako-gun, Hyogo 678-1297 (Japan); Muro, Y [Graduate School of Material Science, University of Hyogo, Kamigori, Ako-gun, Hyogo 678-1297 (Japan); Kohara, T [Graduate School of Material Science, University of Hyogo, Kamigori, Ako-gun, Hyogo 678-1297 (Japan); Shiga, M [Department of Materials Science and Engineering, Kyoto University, Kyoto 606-8501 (Japan)
2007-04-11
The magnetism of quasi-one-dimensional itinerant electron magnets RMn{sub 4}Al{sub 8} is compared with that of the typical frustrated itinerant electron magnet YMn{sub 2}. The possible formation and observation of the spin pseudogap are discussed in connection with the spin-liquid state in strongly correlated itinerant electron systems.
Comparison of Microinstability Properties for Stellarator Magnetic Geometries
International Nuclear Information System (INIS)
Rewoldt, G.; Ku, L.-P.; Tang, W.M.
2005-01-01
The microinstability properties of seven distinct magnetic geometries corresponding to different operating and planned stellarators with differing symmetry properties are compared. Specifically, the kinetic stability properties (linear growth rates and real frequencies) of toroidal microinstabilities (driven by ion temperature gradients and trapped-electron dynamics) are compared, as parameters are varied. The familiar ballooning representation is used to enable efficient treatment of the spatial variations along the equilibrium magnetic field lines. These studies provide useful insights for understanding the differences in the relative strengths of the instabilities caused by the differing localizations of good and bad magnetic curvature and of the presence of trapped particles. The associated differences in growth rates due to magnetic geometry are large for small values of the temperature gradient parameter n identical to d ln T/d ln n, whereas for large values of n, the mode is strongly unstable for all of the different magnetic geometries
Geometry and magnetism of L10 nanostructures
International Nuclear Information System (INIS)
Sorge, K.D.; Skomski, R.; Daniil, M.; Michalski, S.; Gao, L.; Zhou, J.; Yan, M.; Sui, Y.; Kirby, R.D.; Liou, S.H.; Sellmyer, D.J.
2005-01-01
The fabrication and magnetism of L1 0 nanostructures with different shapes (such as nanoparticles and nanotubes) is investigated. These nanostructures are produced by hydrogen processing and focused ion beam milling. The structures exhibit interesting reversal modes and are of present or potential interest for sensors and imaging, as well as magnetic recording
submitter On Roebel Cable Geometry for Accelerator Magnet
Fleiter, J; Ballarino, A
2016-01-01
Roebel-type cables made of a ReBCO conductor are potential candidates for high-field accelerator magnets. The necessity to promote a large effective transverse section in a Roebel cable to avoid local overstress leading to degradation in electrical performance has been recently addressed. In this paper, a new geometry of meander tapes for a Roebel cable that enhances both the transverse effective section and the current margin at crossing segments is discussed. As Roebel cables are bent at the coil ends, the modulation of the bending radius of strands along the cable pitch leads to a shift of the strands with respect to each other. The shift magnitude is analytically investigated in this paper as a function of both cable features and coil geometry. Finally, the minimum transposition pitch of Roebel cables is determined on the basis of coil characteristics.
Theory for stationary nonlinear wave propagation in complex magnetic geometry
International Nuclear Information System (INIS)
Watanabe, T.; Hojo, H.; Nishikawa, Kyoji.
1977-08-01
We present our recent efforts to derive a systematic calculation scheme for nonlinear wave propagation in the self-consistent plasma profile in complex magnetic-field geometry. Basic assumptions and/or approximations are i) use of the collisionless two-fluid model with an equation of state; ii) restriction to a steady state propagation and iii) existence of modified magnetic surface, modification due to Coriolis' force. We discuss four situations: i) weak-field propagation without static flow, ii) arbitrary field strength with flow in axisymmetric system, iii) weak field limit of case ii) and iv) arbitrary field strength in nonaxisymmetric torus. Except for case iii), we derive a simple variation principle, similar to that of Seligar and Whitham, by introducing appropriate coordinates. In cases i) and iii), we derive explicit results for quasilinear profile modification. (auth.)
An application of differential geometry to SSC magnet end winding
International Nuclear Information System (INIS)
Cook, J.M.
1990-04-01
It is expected that a large fraction of the total cost of the proposed Superconducting Supercollider will be spent on magnets, and, as Leon Lederman has remarked, ''most of the cost of making a magnet is in the ends.'' Among the mechanical problems to be solved there is the construction of an end-configuration for the superconducting cables which will minimize their strain energy. The purpose of this paper is to promote the use of differential geometry in this minimization. The use will be illustrated by a specific application to the winding of dipole ends. The cables are assumed to be clamped so firmly that their strain is not altered by Lorentz stresses. 15 refs
Sossinsky, A B
2012-01-01
The book is an innovative modern exposition of geometry, or rather, of geometries; it is the first textbook in which Felix Klein's Erlangen Program (the action of transformation groups) is systematically used as the basis for defining various geometries. The course of study presented is dedicated to the proposition that all geometries are created equal--although some, of course, remain more equal than others. The author concentrates on several of the more distinguished and beautiful ones, which include what he terms "toy geometries", the geometries of Platonic bodies, discrete geometries, and classical continuous geometries. The text is based on first-year semester course lectures delivered at the Independent University of Moscow in 2003 and 2006. It is by no means a formal algebraic or analytic treatment of geometric topics, but rather, a highly visual exposition containing upwards of 200 illustrations. The reader is expected to possess a familiarity with elementary Euclidean geometry, albeit those lacking t...
Secondary magnetic field harmonics dependence on vacuum beam chamber geometry
Directory of Open Access Journals (Sweden)
S. Y. Shim
2013-08-01
Full Text Available The harmonic magnetic field properties due to eddy currents have been studied with respect to the geometry of the vacuum beam chamber. We derived a generalized formula enabling the precise prediction of any field harmonics generated by eddy currents in beam tubes with different cross-sectional geometries. Applying our model to study the properties of field harmonics in beam tubes with linear dipole magnetic field ramping clearly proved that the circular cross section tube generates only a dipole field from eddy currents. The elliptic tube showed noticeable magnitudes of sextupole and dipole fields. We demonstrate theoretically that it is feasible to suppress the generation of the sextupole field component by appropriately varying the tube wall thickness as a function of angle around the tube circumference. This result indicates that it is possible to design an elliptical-shaped beam tube that generates a dipole field component with zero magnitude of sextupole. In a rectangular-shaped beam tube, one of the selected harmonic fields can be prevented if an appropriate wall thickness ratio between the horizontal and vertical tube walls is properly chosen. Our generalized formalism can be used for optimization of arbitrarily complex-shaped beam tubes, with respect to suppression of detrimental field harmonics.
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 ...
Coil optimisation for transcranial magnetic stimulation in realistic head geometry.
Koponen, Lari M; Nieminen, Jaakko O; Mutanen, Tuomas P; Stenroos, Matti; Ilmoniemi, Risto J
Transcranial magnetic stimulation (TMS) allows focal, non-invasive stimulation of the cortex. A TMS pulse is inherently weakly coupled to the cortex; thus, magnetic stimulation requires both high current and high voltage to reach sufficient intensity. These requirements limit, for example, the maximum repetition rate and the maximum number of consecutive pulses with the same coil due to the rise of its temperature. To develop methods to optimise, design, and manufacture energy-efficient TMS coils in realistic head geometry with an arbitrary overall coil shape. We derive a semi-analytical integration scheme for computing the magnetic field energy of an arbitrary surface current distribution, compute the electric field induced by this distribution with a boundary element method, and optimise a TMS coil for focal stimulation. Additionally, we introduce a method for manufacturing such a coil by using Litz wire and a coil former machined from polyvinyl chloride. We designed, manufactured, and validated an optimised TMS coil and applied it to brain stimulation. Our simulations indicate that this coil requires less than half the power of a commercial figure-of-eight coil, with a 41% reduction due to the optimised winding geometry and a partial contribution due to our thinner coil former and reduced conductor height. With the optimised coil, the resting motor threshold of abductor pollicis brevis was reached with the capacitor voltage below 600 V and peak current below 3000 A. The described method allows designing practical TMS coils that have considerably higher efficiency than conventional figure-of-eight coils. Copyright © 2017 Elsevier Inc. All rights reserved.
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.
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
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
Linear theory of a cold relativistic beam in a strongly magnetized finite-geometry plasma
International Nuclear Information System (INIS)
Gagne, R.R.J.; Shoucri, M.M.
1976-01-01
The linear theory of a finite-geometry cold relativistic beam propagating in a cold homogeneous finite-geometry plasma, is investigated in the case of a strongly magnetized plasma. The beam is assumed to propagate parallel to the external magnetic field. It is shown that the instability which takes place at the Cherenkov resonance ωapprox. =k/subz/v/subb/ is of the convective type. The effect of the finite geometry on the instability growth rate is studied and is shown to decrease the growth rate, with respect to the infinite geometry, by a factor depending on the ratio of the beam-to-plasma radius
Energy Technology Data Exchange (ETDEWEB)
Melendez L, L.; Chavez A, E.; Colunga S, S.; Valencia A, R.; Lopez C, R.; Gaytan G, E
1992-03-15
In a cylindrical magnetic topology. the confined plasma experiences 'classic' collisional transport phenomena. When bending the cylinder with the purpose of forming a toro, the magnetic field that before was uniform now it has a radial gradient which produces an unbalance in the magnetic pressure that is exercised on the plasma in the transverse section of the toro. This gives place to transport phenomena call 'neo-classicist'. In this work the structure of the toroidal magnetic field produced by toroidal coils of triangular form, to which are added even of coils of compensation with form of half moon is analyzed. With this type of coils it is looked for to minimize the radial gradient of the toroidal magnetic field. The values and characteristics of B (magnetic field) in perpendicular planes to the toro in different angular positions in the toroidal direction, looking for to cover all the cases of importance are exhibited. (Author)
Energy Technology Data Exchange (ETDEWEB)
Chavez A, E.; Melendez L, L.; Colunga S, S.; Valencia A, R.; Lopez C, R.; Gaytan G, E
1991-07-15
The charged particles that constitute the plasma in the tokamaks are located in magnetic fields that determine its behavior. The poloidal magnetic field of the plasma current and the toroidal magnetic field of the tokamak possess relatively big gradients, which produce drifts on these particles. These drifts are largely the cause of the continuous lost of particles and of energy of the confinement region. In this work the results of numerical calculations of a modification to the 'traditional' toroidal magnetic field that one waits it diminishes the drifts by gradient and improve the confinement properties of the tokamaks. (Author)
Controlling vortex chirality and polarity by geometry in magnetic nanodots
Agramunt Puig, Sebastià
2014-01-01
The independent control of both vortex chirality and polarity is a significant challenge in magnetic devices based on nano-sized magnetic vortex structures. By micromagnetic simulations here, we show that in soft ferromagnetic nanodots with an adequate modulated thickness, the desired combination of chirality and polarity can be achieved just by changing the direction of the in-plane applied magnetic field. Despite the complex behavior, the vortex chirality and polarity control can be summari...
Energy Technology Data Exchange (ETDEWEB)
Lopez Fraguas, A.; Lopez Bruna, D.; Romero, J. A.
2005-07-01
The properties of the vector magnetic potential and its usefulness to calculate magnetic fluxes in both stationary and time-dependent conditions are p revised in this report. We have adapted to the TJ-II Flexible Heliac efficient numerical expressions to calculate the vector potential, calculating in addition the magnetic flux with this formalism in circumstances whose complexity makes very convenient the use of the vector potential. The result on induced voltages offer theoretical support to the measurements of induced voltage due to the OH coils in the plasma, like the measurements provided by the loop voltage diagnostic installed in the TJ-II, as well as to the cylindrical approximation of the plasma often used to interpret experimental data. (Author) 11 refs.
Geometry dependence of the magnetization reversal process in bridged dots
International Nuclear Information System (INIS)
Escobar, R.A.; Lage, E.; D’Albuquerque e Castro, J.; Altbir, D.; Ross, C.A.
2017-01-01
Based on Monte Carlo numerical simulations: results for the magnetization reversal process in thin circular Ni dots connected by a bridge are presented. The dependence of the process on both the width of the bridge and the orientation of the applied magnetic field has been investigated. It was found that when the applied magnetic field is set parallel to the bridge, the hysteresis curves are weakly dependent on the width of the bridge, being rather close to that of a single dot of the same diameter. On the other hand, when the magnetic field is applied perpendicularly to the bridge, a significant reduction in the coercivity of the system is obtained, even in the case of narrower bridges.
Geometry dependence of the magnetization reversal process in bridged dots
Energy Technology Data Exchange (ETDEWEB)
Escobar, R.A. [Departamento de Física, CEDENNA, Universidad de Santiago de Chile, USACH, Av. Ecuador 3493, Santiago (Chile); Lage, E. [Department of Materials Science and Engineering, Massachusetts Institute of Technology, 02139 Cambridge, MA (United States); D’Albuquerque e Castro, J. [Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, Rio de Janeiro, RJ 21945-970 (Brazil); Altbir, D., E-mail: dora.altbir@usach.cl [Departamento de Física, CEDENNA, Universidad de Santiago de Chile, USACH, Av. Ecuador 3493, Santiago (Chile); Ross, C.A. [Department of Materials Science and Engineering, Massachusetts Institute of Technology, 02139 Cambridge, MA (United States)
2017-06-15
Based on Monte Carlo numerical simulations: results for the magnetization reversal process in thin circular Ni dots connected by a bridge are presented. The dependence of the process on both the width of the bridge and the orientation of the applied magnetic field has been investigated. It was found that when the applied magnetic field is set parallel to the bridge, the hysteresis curves are weakly dependent on the width of the bridge, being rather close to that of a single dot of the same diameter. On the other hand, when the magnetic field is applied perpendicularly to the bridge, a significant reduction in the coercivity of the system is obtained, even in the case of narrower bridges.
Planar Hall effect sensor bridge geometries optimized for magnetic bead detection
DEFF Research Database (Denmark)
Østerberg, Frederik Westergaard; Rizzi, Giovanni; Henriksen, Anders Dahl
2014-01-01
Novel designs of planar Hall effect bridge sensors optimized for magnetic bead detection are presented and characterized. By constructing the sensor geometries appropriately, the sensors can be tailored to be sensitive to an external magnetic field, the magnetic field due to beads being magnetized...... by the sensor self-field or a combination thereof. The sensors can be made nominally insensitive to small external magnetic fields, while being maximally sensitive to magnetic beads, magnetized by the sensor self-field. Thus, the sensor designs can be tailored towards specific applications with minimal...... of the dynamic magnetic response of suspensions of magnetic beads with a nominal diameter of 80 nm are performed. Furthermore, a method to amplify the signal by appropriate combinations of multiple sensor segments is demonstrated....
Reconnection Scaling Experiment (RSX): Magnetic Reconnection in Linear Geometry
Intrator, T.; Sovinec, C.; Begay, D.; Wurden, G.; Furno, I.; Werley, C.; Fisher, M.; Vermare, L.; Fienup, W.
2001-10-01
The linear Reconnection Scaling Experiment (RSX) at LANL is a new experiment that can create MHD relevant plasmas to look at the physics of magnetic reconnection. This experiment can scale many relevant parameters because the guns that generate the plasma and current channels do not depend on equilibrium or force balance for startup. We describe the experiment and initial electrostatic and magnetic probe data. Two parallel current channels sweep down a long plasma column and probe data accumulated over many shots gives 3D movies of magnetic reconnection. Our first data tries to define an operating regime free from kink instabilities that might otherwise confuse the data and shot repeatability. We compare this with MHD 2 fluid NIMROD simulations of the single current channel kink stability boundary for a variety of experimental conditions.
Laser-generated magnetic fields in quasi-hohlraum geometries
Pollock, Bradley; Turnbull, David; Ross, Steven; Hazi, Andrew; Ralph, Joseph; Lepape, Sebastian; Froula, Dustin; Haberberger, Dan; Moody, John
2014-10-01
Laser-generated magnetic fields of 10--40 T have been produced with 100--4000 J laser drives at Omega EP and Titan. The fields are generated using the technique described by Daido et al. [Phys. Rev. Lett. 56, 846 (1986)], which works by directing a laser through a hole in one plate to strike a second plate. Hot electrons generated in the laser-produced plasma on the second plate collect on the first plate. A strap connects the two plates allowing a current of 10 s of kA to flow and generate a solenoidal magnetic field. The magnetic field is characterized using Faraday rotation, b-dot probes, and proton radiography. Further experiments to study the effect of the magnetic field on hohlraum performance are currently scheduled for Omega. This work was performed under the auspices of the United States Department of Energy by the Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA-27344.
Dynamics of post-flare ejections and magnetic loop geometry
International Nuclear Information System (INIS)
Mein, P.; Mein, N.
1982-01-01
Flare-associated mass ejections have been observed at the solar limb on June 29, 1980 in the Hα line, with the Multichannel Subtractive Double Pass spectrograph of the Meudon solar tower. Radial velocities were measured as a function of time in a two dimensional field, and kinematics investigated in one selected fine structure. A simple model of locally dipole-type magnetic field increasing with time can be fitted to the data. It can be checked from extrapolation that the model is consistent with an ejection starting roughly from the same point at the same time. Height of the loops (approx. equal to 135,000 km) is consistent with other determinations. Magnetic field is found to be increasing locally by a factor 1.14 within 10 min. (orig.)
Straight ends for superconducting dipole magnet using constant perimeter geometry
International Nuclear Information System (INIS)
Royet, J.
1989-01-01
The ends of the SSC Dipole magnets are a very critical aspect of the superconducting cable windings needed for this large project. The internal coils, where the radius at the pole is as small as 3/10 of an inch for the first turn, are difficult to form with the very stiff cable, and a high tension is needed. The curing operation on the coils is performed in a heated forming press which applies an important additional stress on the superconducting wire and insulation. A new design of this sensitive region of the magnets was performed at LBL, and several prototypes were built and tested. In this paper the construction method used to solve some of the most critical problems is exposed along with a description of the experimental work in progress. 3 refs., 2 figs
Energy Technology Data Exchange (ETDEWEB)
Rodrigues, Leticia Jenisch
2007-07-01
Accurate analysis of resonance absorption in heterogeneous systems is essential in problems like criticality, breeding ratios and fuel depletion calculations. In compact arrays of fuel rods, resonance absorption is strongly affected by the Dancoff factor, defined in mis study as the probability that a neutron emitted from the surface of a fuel element, enters another fuel element without any collusion in the moderator or cladding. In fact, in the most practical cases of irregular cells, it is observed that inaccuracies in computing both Grey and Black Dancoff factors, i.e. for partially and perfectly absorbing fuel rods, can lead to considerable errors in the calculated values of such integral quantities. For this reason, much effort has been made in the past decades to further improve the models for calculating Dancoff factors, a task that has been accomplished in connection with the development of faster computers. In the WIMS code, Black Dancoff factors based on the above mentioned collusion probability definition are computed in cluster geometry, for each one of the symmetrically distinct fuel pin positions in the cell. Sets of equally-spaced parallel lines are drawn in subroutine PIJ, at a number of discrete equally-incremented azimuthal angles, covering the whole system and forming a mesh over which the in-plane integrations of the Bickley functions are carried out by simple trapezoidal rule, leading to the first-flight collusion matrices. Although fast, the method in PIJ is inefficient, since the constructed mesh does not depended on the system details, so that regions of small relative volumes are crossed out by relatively few lines, which affects the convergence of the calculated probabilities. A new routine (PIJM) was then created to incorporate a more efficient integration scheme considering each system region individually, minimizing convergence problems and reducing the number of neutron track lines required in the in-plane integrations for any given
Energy Technology Data Exchange (ETDEWEB)
Konstantinova, Elena, E-mail: elena.konst@ifsudestemg.edu.br; Sales, José Antonio de
2014-10-01
Creation of magnetic nanodevices leads, in particular, to a growing interest in theoretical investigation of different types of magnetic nanostructures. The purpose of our work is to consider how the properties of such nanomaterials depend on their geometry and on the crystal structure. We report on the Monte Carlo simulation of magnetic nanostructures of different geometric forms, which are based on simple cubic and body-centered cubic cells. The magnetization of spin, magnetic susceptibility and specific heat are investigated for nano-disks, nano-bars and nano-balls of different magnitudes. The combination of dipole and Heisenberg-model interaction are considered for the ferromagnetic case. It is shown that magnetic and thermodynamic properties of nanostructures strongly depend on their geometry. The structures with a body-centered cubic unit cell manifest stronger dependence on size and geometric form. In this case one can interpret the results as an effective reduction of dimension from 3D to 2D for decreasing size of the compound. - Highlights: • Thermodynamic properties of nano-balls are dependent on their size. • Magnetic properties of nano-bars depend on their thickness. • The hysteresis loop is dependent on the geometry of the nanostructure.
DEFF Research Database (Denmark)
Lei, Tian; Engelbrecht, Kurt; Nielsen, Kaspar Kirstein
2017-01-01
Room temperature magnetic refrigeration has attracted substantial attention during the past decades and continuing to increase the performance of active magnetic regenerators (AMR) is of great interest. Optimizing the regenerator geometry and related operating parameters is a practical and effect......Room temperature magnetic refrigeration has attracted substantial attention during the past decades and continuing to increase the performance of active magnetic regenerators (AMR) is of great interest. Optimizing the regenerator geometry and related operating parameters is a practical...... and effective way to obtain the desired cooling performance. To investigate how to choose and optimize the AMR geometry, a quantitative study is presented by simulations based on a one-dimensional (1D) numerical model. Correlations for calculating the friction factor and heat transfer coefficient are reviewed...... and chosen for modeling different geometries. Moreover, the simulated impacts of various parameters on the regenerator efficiency with a constant specific cooling capacity are presented. An analysis based on entropy production minimization reveals how those parameters affect the main losses occurring inside...
LRS Bianchi Type II Massive String Cosmological Models with Magnetic Field in Lyra's Geometry
Directory of Open Access Journals (Sweden)
Raj Bali
2013-01-01
Full Text Available Bianchi type II massive string cosmological models with magnetic field and time dependent gauge function ( in the frame work of Lyra's geometry are investigated. The magnetic field is in -plane. To get the deterministic solution, we have assumed that the shear ( is proportional to the expansion (. This leads to , where and are metric potentials and is a constant. We find that the models start with a big bang at initial singularity and expansion decreases due to lapse of time. The anisotropy is maintained throughout but the model isotropizes when . The physical and geometrical aspects of the model in the presence and absence of magnetic field are also discussed.
Surface geometry of a rotating black hole in a magnetic field
International Nuclear Information System (INIS)
Kulkarni, R.; Dadhich, N.
1986-01-01
We study the intrinsic geometry of the surface of a rotating black hole in a uniform magnetic field, using a metric discovered by Ernst and Wild. Rotating black holes are analogous to material rotating bodies according to Smarr since black holes also tend to become more oblate on being spun up. Our study shows that the presence of a strong magnetic field ensures that a black hole actually becomes increasingly prolate on being spun up. Studying the intrinsic geometry of the black-hole surface also gives rise to an interesting embedding problem. Smarr shows that a Kerr black hole cannot be globally isometrically embedded in R 3 if its specific angular momentum a exceeds (√3 /2)mapprox.0.866. . .m. We show that in the presence of a magnetic field of strength B, satisfying 2- √3 2 m 2 3 for all values of the angular momentum
Magnetic geometry and physics of advanced divertors: The X-divertor and the snowflake
International Nuclear Information System (INIS)
Kotschenreuther, Mike; Valanju, Prashant; Covele, Brent; Mahajan, Swadesh
2013-01-01
Advanced divertors are magnetic geometries where a second X-point is added in the divertor region to address the serious challenges of burning plasma power exhaust. Invoking physical arguments, numerical work, and detailed model magnetic field analysis, we investigate the magnetic field structure of advanced divertors in the physically relevant region for power exhaust—the scrape-off layer. A primary result of our analysis is the emergence of a physical “metric,” the Divertor Index DI, which quantifies the flux expansion increase as one goes from the main X-point to the strike point. It clearly separates three geometries with distinct consequences for divertor physics—the Standard Divertor (DI = 1), and two advanced geometries—the X-Divertor (XD, DI > 1) and the Snowflake (DI < 1). The XD, therefore, cannot be classified as one variant of the Snowflake. By this measure, recent National Spherical Torus Experiment and DIIID experiments are X-Divertors, not Snowflakes
Magnetic geometry and physics of advanced divertors: The X-divertor and the snowflake
Energy Technology Data Exchange (ETDEWEB)
Kotschenreuther, Mike; Valanju, Prashant; Covele, Brent; Mahajan, Swadesh [Institute for Fusion Studies, The University of Texas at Austin, Austin, Texas 78712 (United States)
2013-10-15
Advanced divertors are magnetic geometries where a second X-point is added in the divertor region to address the serious challenges of burning plasma power exhaust. Invoking physical arguments, numerical work, and detailed model magnetic field analysis, we investigate the magnetic field structure of advanced divertors in the physically relevant region for power exhaust—the scrape-off layer. A primary result of our analysis is the emergence of a physical “metric,” the Divertor Index DI, which quantifies the flux expansion increase as one goes from the main X-point to the strike point. It clearly separates three geometries with distinct consequences for divertor physics—the Standard Divertor (DI = 1), and two advanced geometries—the X-Divertor (XD, DI > 1) and the Snowflake (DI < 1). The XD, therefore, cannot be classified as one variant of the Snowflake. By this measure, recent National Spherical Torus Experiment and DIIID experiments are X-Divertors, not Snowflakes.
Magnetic bead micromixer: Influence of magnetic element geometry and field amplitude
DEFF Research Database (Denmark)
Lund-Olesen, Torsten; Buus, Bjarke B.; Howalt, Jakob
2008-01-01
A scheme for the silicon microfabrication of lab-on-a-chip systems with mixing based on dynamic plugs of magnetic beads is presented. The systems consist of a microfluidic channel integrated with a number of soft magnetic elements by the sides of the channel. The elements are magnetized by a homo......A scheme for the silicon microfabrication of lab-on-a-chip systems with mixing based on dynamic plugs of magnetic beads is presented. The systems consist of a microfluidic channel integrated with a number of soft magnetic elements by the sides of the channel. The elements are magnetized...... by a homogeneous external ac magnetic field. The systems are scalable with respect to the number of magnetic bead plugs and number of parallel channels, and thus they have high potential for use in biological separation using functionalized magnetic beads. The mixing efficiency is characterized for two different...
Directory of Open Access Journals (Sweden)
Mei Guo
2018-01-01
Full Text Available The syntheses, structural characterization, and magnetic properties of three lanthanide complexes with formulas [Ln(L13] (Ln = Dy (1Dy; Er (1Er; and [Dy(L22] (2Dy were reported. Complexes 1Dy and 1Er are isostructural with the metal ion in distorted trigonal-prismatic coordination geometry, but exhibit distinct magnetic properties due to the different shapes of electron density for DyIII (oblate and ErIII (prolate ions. Complex 1Dy shows obvious SMM behavior under a zero direct current (dc field with an effective energy barrier of 31.4 K, while complex 1Er only features SMM behavior under a 400 Oe external field with an effective energy barrier of 23.96 K. In stark contrast, complex 2Dy with the octahedral geometry only exhibits the frequency dependence of alternating current (ac susceptibility signals without χ″ peaks under a zero dc field.
Geometry effects on magnetization dynamics in circular cross-section wires
Energy Technology Data Exchange (ETDEWEB)
Sturma, M. [Univ. Grenoble Alpes, INAC-SPINTEC, F-38000 Grenoble (France); CNRS, SPINTEC, F-38000 Grenoble (France); CEA, INAC-SPINTEC, F-38000 Grenoble (France); Univ. Grenoble Alpes, I. Neel, F-38000 Grenoble (France); CNRS, I. Neel, F-38000 Grenoble (France); Toussaint, J.-C., E-mail: jean-christophe.toussaint@neel.cnrs.fr, E-mail: daria.gusakova@cea.fr [Univ. Grenoble Alpes, I. Neel, F-38000 Grenoble (France); CNRS, I. Neel, F-38000 Grenoble (France); Gusakova, D., E-mail: jean-christophe.toussaint@neel.cnrs.fr, E-mail: daria.gusakova@cea.fr [Univ. Grenoble Alpes, INAC-SPINTEC, F-38000 Grenoble (France); CNRS, SPINTEC, F-38000 Grenoble (France); CEA, INAC-SPINTEC, F-38000 Grenoble (France)
2015-06-28
Three-dimensional magnetic memory design based on circular-cross section nanowires with modulated diameter is the emerging field of spintronics. The consequences of the mutual interaction between electron spins and local magnetic moments in such non-trivial geometries are still open to debate. This paper describes the theoretical study of domain wall dynamics within such wires subjected to spin polarized current. We used our home-made finite element software to characterize the variety of domain wall dynamical regimes observed for different constriction to wire diameter ratios d/D. Also, we studied how sizeable geometry irregularities modify the internal micromagnetic configuration and the electron spin spatial distribution in the system, the geometrical reasons underlying the additional contribution to the system's nonadiabaticity, and the specific domain wall width oscillations inherent to fully three-dimensional systems.
The influence of magnetic field geometry on magnetars X-ray spectra
International Nuclear Information System (INIS)
Viganò, D; Pons, J A; Miralles, J A; Parkins, N; Zane, S; Turolla, R
2012-01-01
Nowadays, the analysis of the X-ray spectra of magnetically powered neutron stars or magnetars is one of the most valuable tools to gain insight into the physical processes occurring in their interiors and magnetospheres. In particular, the magnetospheric plasma leaves a strong imprint on the observed X-ray spectrum by means of Compton up-scattering of the thermal radiation coming from the star surface. Motivated by the increased quality of the observational data, much theoretical work has been devoted to develop Monte Carlo (MC) codes that incorporate the effects of resonant Compton scattering (RCS) in the modeling of radiative transfer of photons through the magnetosphere. The two key ingredients in this simulations are the kinetic plasma properties and the magnetic field (MF) configuration. The MF geometry is expected to be complex, but up to now only mathematically simple solutions (self-similar solutions) have been employed. In this work, we discuss the effects of new, more realistic, MF geometries on synthetic spectra. We use new force-free solutions [14] in a previously developed MC code [9] to assess the influence of MF geometry on the emerging spectra. Our main result is that the shape of the final spectrum is mostly sensitive to uncertain parameters of the magnetospheric plasma, but the MF geometry plays an important role on the angle-dependence of the spectra.
Energy Technology Data Exchange (ETDEWEB)
Zapiór, Maciej; Martinez-Gómez, David, E-mail: zapior.maciek@gmail.com [Physics Department, University of the Balearic Islands, Cra. de Valldemossa, km 7.5. Palma (Illes Balears), E-07122 (Spain)
2016-02-01
Based on the data collected by the Vacuum Tower Telescope located in the Teide Observatory in the Canary Islands, we analyzed the three-dimensional (3D) motion of so-called knots in a solar prominence of 2014 June 9. Trajectories of seven knots were reconstructed, giving information of the 3D geometry of the magnetic field. Helical motion was detected. From the equipartition principle, we estimated the lower limit of the magnetic field in the prominence to ≈1–3 G and from the Ampère’s law the lower limit of the electric current to ≈1.2 × 10{sup 9} A.
Zapiór, Maciej; Martínez-Gómez, David
2016-02-01
Based on the data collected by the Vacuum Tower Telescope located in the Teide Observatory in the Canary Islands, we analyzed the three-dimensional (3D) motion of so-called knots in a solar prominence of 2014 June 9. Trajectories of seven knots were reconstructed, giving information of the 3D geometry of the magnetic field. Helical motion was detected. From the equipartition principle, we estimated the lower limit of the magnetic field in the prominence to ≈1-3 G and from the Ampère’s law the lower limit of the electric current to ≈1.2 × 109 A.
Finley, Adam J.; Matt, Sean P.
2018-02-01
During the lifetime of Sun-like or low-mass stars a significant amount of angular momentum is removed through magnetized stellar winds. This process is often assumed to be governed by the dipolar component of the magnetic field. However, observed magnetic fields can host strong quadrupolar and/or octupolar components, which may influence the resulting spin-down torque on the star. In Paper I, we used the MHD code PLUTO to compute steady-state solutions for stellar winds containing a mixture of dipole and quadrupole geometries. We showed the combined winds to be more complex than a simple sum of winds with these individual components. This work follows the same method as Paper I, including the octupole geometry, which not only increases the field complexity but also, more fundamentally, looks for the first time at combining the same symmetry family of fields, with the field polarity of the dipole and octupole geometries reversing over the equator (unlike the symmetric quadrupole). We show, as in Paper I, that the lowest-order component typically dominates the spin-down torque. Specifically, the dipole component is the most significant in governing the spin-down torque for mixed geometries and under most conditions for real stars. We present a general torque formulation that includes the effects of complex, mixed fields, which predicts the torque for all the simulations to within 20% precision, and the majority to within ≈5%. This can be used as an input for rotational evolution calculations in cases where the individual magnetic components are known.
Air core notch-coil magnet with variable geometry for fast-field-cycling NMR.
Kruber, S; Farrher, G D; Anoardo, E
2015-10-01
In this manuscript we present details on the optimization, construction and performance of a wide-bore (71 mm) α-helical-cut notch-coil magnet with variable geometry for fast-field-cycling NMR. In addition to the usual requirements for this kind of magnets (high field-to-power ratio, good magnetic field homogeneity, low inductance and resistance values) a tunable homogeneity and a more uniform heat dissipation along the magnet body are considered. The presented magnet consists of only one machined metallic cylinder combined with two external movable pieces. The optimal configuration is calculated through an evaluation of the magnetic flux density within the entire volume of interest. The magnet has a field-to-current constant of 0.728 mT/A, allowing to switch from zero to 0.125 T in less than 3 ms without energy storage assistance. For a cylindrical sample volume of 35 cm(3) the effective magnet homogeneity is lower than 130 ppm. Copyright © 2015 Elsevier Inc. All rights reserved.
International Nuclear Information System (INIS)
Alnaemi, F.; Moses, A.J.
2003-01-01
FEM modelling of PM motor was carried out to demonstrate the effects of the addition of various types of ferromagnetic tubes (shell) to a rotor of surface mount permanent magnet motor. An enhancement in magnet operating point towards the high field region is obtained. A shell made of amorphous ribbon offers optimum advantages
International Nuclear Information System (INIS)
Isler, R.C.; Aceto, S.; Baylor, L.R.; Bigelow, T.S.; Bell, G.L.; Bell, J.D.; Carreras, B.A.; Colchin, R.J.; Crume, E.C.; Dominguez, N.; Dory, R.A.; Dunlap, J.L.; Dyer, G.R.; England, A.C.; Gandy, R.F.; Glowienka, J.C.; Hanson, G.R.; Harris, J.H.; Hiroe, S.; Horton, L.D.; Jernigan, T.C.; Ji, H.; Langley, R.A.; Lee, D.K.; Likin, K.M.; Lyon, J.F.; Ma, C.H.; Morimoto, S.; Murakami, M.; Okada, H.; Qualls, A.L.; Rasmussen, D.A.; Rome, J.A.; Sato, M.; Schwelberger, J.G.; Shats, M.G.; Simpkins, J.E.; Thomas, C.E.; Uckan, T.; Wade, M.R.; Wilgen, J.B.; Wing, W.R.; Yamada, H.; Zielinski, J.J.
1992-01-01
Recent experiments in the Advanced Toroidal Facility (ATF) [Fusion Technol. 10, 179 (1986)] have been directed toward investigations of the basic physics mechanisms that control confinement in this device. Measurements of the density fluctuations throughout the plasma volume have provided indications for the existence of theoretically predicted dissipative trapped electron and resistive interchange instabilities. These identifications are supported by results of dynamic configuration scans of the magnetic fields during which the magnetic well volume, shear, and fraction of confined trapped particles are changed continuously. The influence of magnetic islands on the global confinement has been studied by deliberately applying error fields which strongly perturb the nested flux-surface geometry, and the effects of electric fields have been investigated by means of biased limiter experiments
Geometry planning and image registration in magnetic particle imaging using bimodal fiducial markers
International Nuclear Information System (INIS)
Werner, F.; Hofmann, M.; Them, K.; Knopp, T.; Jung, C.; Salamon, J.; Kaul, M. G.; Mummert, T.; Adam, G.; Ittrich, H.; Werner, R.; Säring, D.; Weber, O. M.
2016-01-01
Purpose: Magnetic particle imaging (MPI) is a quantitative imaging modality that allows the distribution of superparamagnetic nanoparticles to be visualized. Compared to other imaging techniques like x-ray radiography, computed tomography (CT), and magnetic resonance imaging (MRI), MPI only provides a signal from the administered tracer, but no additional morphological information, which complicates geometry planning and the interpretation of MP images. The purpose of the authors’ study was to develop bimodal fiducial markers that can be visualized by MPI and MRI in order to create MP–MR fusion images. Methods: A certain arrangement of three bimodal fiducial markers was developed and used in a combined MRI/MPI phantom and also during in vivo experiments in order to investigate its suitability for geometry planning and image fusion. An algorithm for automated marker extraction in both MR and MP images and rigid registration was established. Results: The developed bimodal fiducial markers can be visualized by MRI and MPI and allow for geometry planning as well as automated registration and fusion of MR–MP images. Conclusions: To date, exact positioning of the object to be imaged within the field of view (FOV) and the assignment of reconstructed MPI signals to corresponding morphological regions has been difficult. The developed bimodal fiducial markers and the automated image registration algorithm help to overcome these difficulties.
Geometry planning and image registration in magnetic particle imaging using bimodal fiducial markers
Energy Technology Data Exchange (ETDEWEB)
Werner, F., E-mail: f.werner@uke.de; Hofmann, M.; Them, K.; Knopp, T. [Section for Biomedical Imaging, University Medical Center Hamburg-Eppendorf, Hamburg 20246, Germany and Institute for Biomedical Imaging, Hamburg University of Technology, Hamburg 21073 (Germany); Jung, C.; Salamon, J.; Kaul, M. G.; Mummert, T.; Adam, G.; Ittrich, H. [Department of Diagnostic and Interventional Radiology, University Medical Center Hamburg-Eppendorf, Hamburg 20246 (Germany); Werner, R.; Säring, D. [Institute for Computational Neuroscience, University Medical Center Hamburg-Eppendorf, Hamburg 20246 (Germany); Weber, O. M. [Philips Medical Systems DMC GmbH, Hamburg 22335 (Germany)
2016-06-15
Purpose: Magnetic particle imaging (MPI) is a quantitative imaging modality that allows the distribution of superparamagnetic nanoparticles to be visualized. Compared to other imaging techniques like x-ray radiography, computed tomography (CT), and magnetic resonance imaging (MRI), MPI only provides a signal from the administered tracer, but no additional morphological information, which complicates geometry planning and the interpretation of MP images. The purpose of the authors’ study was to develop bimodal fiducial markers that can be visualized by MPI and MRI in order to create MP–MR fusion images. Methods: A certain arrangement of three bimodal fiducial markers was developed and used in a combined MRI/MPI phantom and also during in vivo experiments in order to investigate its suitability for geometry planning and image fusion. An algorithm for automated marker extraction in both MR and MP images and rigid registration was established. Results: The developed bimodal fiducial markers can be visualized by MRI and MPI and allow for geometry planning as well as automated registration and fusion of MR–MP images. Conclusions: To date, exact positioning of the object to be imaged within the field of view (FOV) and the assignment of reconstructed MPI signals to corresponding morphological regions has been difficult. The developed bimodal fiducial markers and the automated image registration algorithm help to overcome these difficulties.
Influence of the terrestrial magnetic field geometry on the cutoff rigidity of cosmic ray particles
International Nuclear Information System (INIS)
Herbst, K.; Kopp, A.; Heber, B.
2013-01-01
Studies of the propagation of charged energetic particles in the Earth's magnetic field go back to Carl Stoermer. In the end, his investigations finally lead to the definition of the so-called cutoff rigidity RC; that is, the minimum momentum per charge a particle must have in order to reach a certain geographical location. Employing Monte Carlo simulations with the PLANETOCOSMICS code we investigate the correlation between the geomagnetic field structure and the cutoff rigidity. We show that the geometry of the magnetic field has a considerable influence on the resulting cutoff rigidity distribution. Furthermore, we will present a simple geometry-based parameter, δB, which is able to reflect the location-dependent cutoff rigidity. We show that this correlation is also visible in the temporal evolution of the Earth's magnetic field, at least over the last 100 yr. Using latitude scans with neutron monitors, changes of the relative counting rates at different positions are calculated, showing small variations for, e.g., Kiel and Moscow, while large ones occur at Mexico City as well as on the British Virgin Islands.
Detection of electron magnetic circular dichroism signals under zone axial diffraction geometry
Energy Technology Data Exchange (ETDEWEB)
Song, Dongsheng [National Center for Electron Microscopy in Beijing, Key Laboratory of Advanced Materials (MOE) and The State Key Laboratory of New Ceramics and Fine Processing, School of Materials Science and Engineering, Tsinghua University, Beijing 100084 (China); Rusz, Jan [Department of Physics and Astronomy, Uppsala University, Box 516, S-751 20 Uppsala (Sweden); Cai, Jianwang [Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190 (China); Zhu, Jing, E-mail: jzhu@mail.tsinghua.edu.cn [National Center for Electron Microscopy in Beijing, Key Laboratory of Advanced Materials (MOE) and The State Key Laboratory of New Ceramics and Fine Processing, School of Materials Science and Engineering, Tsinghua University, Beijing 100084 (China)
2016-10-15
EMCD (electron magnetic circular dichroism) technique provides us a new opportunity to explore magnetic properties in the transmission electron microscope. However, specific diffraction geometry is the major limitation. Only the two-beam and three-beam case are demonstrated in the experiments until now. Here, we present the more general case of zone axial (ZA) diffraction geometry through which the EMCD signals can be detected even with the very strong sensitivity to dynamical diffraction conditions. Our detailed calculations and well-controlled diffraction conditions lead to experiments in agreement with theory. The effect of dynamical diffraction conditions on EMCD signals are discussed both in theory and experiments. Moreover, with the detailed analysis of dynamical diffraction effects, we experimentally obtain the separate EMCD signals for each crystallographic site in Y{sub 3}Fe{sub 5}O{sub 12}, which is also applicable for other materials and cannot be achieved by site-specific EMCD and XMCD technique directly. Our work extends application of more general diffraction geometries and will further promote the development of EMCD technique. - Highlights: • The zone axial (ZA) diffraction geometry is presented for EMCD technique. • The detailed calculations for EMCD signals under ZA case are conducted. • The EMCD signals are obtained under the ZA case in the experiments. • The effect of dynamical effect on EMCD signals under ZA case is discussed. • Site-specific EMCD signals of Fe in Y{sub 3}Fe{sub 5}O{sub 12} are obtained by specific ZA conditions.
Effect of magnetic island geometry on ECRH/ECCD and consequences to the NTM stabilization dynamics
Chatziantonaki, I.; Tsironis, C.; Isliker, H.; Vlahos, L.
2012-09-01
In the majority of codes that model ECCD-based NTM stabilization, the analysis of the EC propagation and absorption is performed in terms of the axisymmetric magnetic field, ignoring effects due to the island topology. In this paper, we analyze the wave propagation, absorption and current drive in the presence of NTMs, as well as the ECCD-driven island growth, focusing on the effect of the island geometry on the wave de-position. A primary evaluation of the consequences of these effects on the NTM evolution is also made in terms of the modified Rutherford equation.
Intermittent transport in edge plasma with a 3-D magnetic geometry in the Large Helical Device
International Nuclear Information System (INIS)
Tanaka, H.; Masuzaki, S.; Ohno, N.; Morisaki, T.; Tsuji, Y.
2013-01-01
Blobby plasma transport is a universally observed phenomenon in magnetic confinement devices, and it is considered to be closely related to edge plasma physics. We have investigated such an intermittent event observed inside the divertor region of the Large Helical Device by using a fast-scanning Langmuir probe with two electrodes. Ion saturation current fluctuations showed negative spikes in the divertor leg and positive spikes in the private region. Further, the time delay between the two fluctuations followed a unique trajectory in the positive-skewness region. We found common as well as different fluctuation characteristics between the LHD and tokamaks. We discuss the analysis results in relation to the blob-generation and propagation behaviors in the three-dimensional magnetic geometry around the divertor leg. In addition, we quantitatively estimated the blob propagation velocity and size based on a theoretical assumption
Energy Technology Data Exchange (ETDEWEB)
Khatri, Manvendra Singh
2010-07-09
Thin films and nanowires of Co-Pt have been prepared by means of electrodeposition. Composition, structure, microstructure and magnetic properties have been intensively studied using X-ray diffraction, scanning electron microscopy and vibrating sample magnetometry and correlated to the deposition parameters such as electrolyte composition, deposition current and/or potential. Co rich Co-Pt films have been deposited at various current densities. A nearly constant composition of Co{sub 70}Pt{sub 30} was achieved for current densities between 18 and 32 mA/cm{sup 2}. Detailed texture measurements confirmed an increasing fraction of the hexagonal phase with its c-axis aligned perpendicular to the film plane with increasing current density. Accordingly, magnetic properties are strongly affected by the magnetocrystalline anisotropy of the hexagonal phase that competes with the shape anisotropy of the thin film geometry. Co-Pt nanowires have been prepared within alumina templates at different deposition potentials between -0.6 and -0.9 V{sub SCE} changing the composition from nearly pure Pt to Co. The composition Co{sub 80}Pt{sub 20} was observed at a deposition potential of -0.7 V{sub SCE}. Co-Pt nanowires are nanocrystalline in the as-deposited state. Magnetic measurements reveal changing fcc and hcp phase fractions within the wires as the effective anisotropy significantly differs from the expected shape anisotropy for nanowires with high aspect ratio. This change in effective anisotropy is attributed to the preferential alignment of the c-axis of hcp Co-Pt phase perpendicular to the nanowires axis. A promising alternative with much smaller feature sizes is the diblock copolymer template. Electrodeposition of Co and Co-Pt into these templates has been carried out. Inhomogeneities in the template thickness as well as a certain substrate roughness have been identified to be the reasons for inhomogeneous template filling. Thus magnetic properties are dominated by large
Structures of peptide families by nuclear magnetic resonance spectroscopy and distance geometry
Energy Technology Data Exchange (ETDEWEB)
Pease, J.H.
1989-12-01
The three dimensional structures of several small peptides were determined using a combination of {sup 1}H nuclear magnetic resonance (NMR) and distance geometry calculations. These techniques were found to be particularly helpful for analyzing structural differences between related peptides since all of the peptides' {sup 1}H NMR spectra are very similar. The structures of peptides from two separate classes are presented. Peptides in the first class are related to apamin, an 18 amino acid peptide toxin from honey bee venom. The {sup 1}H NMR assignments and secondary structure determination of apamin were done previously. Quantitative NMR measurements and distance geometry calculations were done to calculate apamin's three dimensional structure. Peptides in the second class are 48 amino acid toxins from the sea anemone Radianthus paumotensis. The {sup 1}H NMR assignments of toxin II were done previously. The {sup 1}H NMR assignments of toxin III and the distance geometry calculations for both peptides are presented.
THE EFFECTS OF MAGNETIC-FIELD GEOMETRY ON LONGITUDINAL OSCILLATIONS OF SOLAR PROMINENCES
International Nuclear Information System (INIS)
Luna, M.; Díaz, A. J.; Karpen, J.
2012-01-01
We investigate the influence of the geometry of the solar filament magnetic structure on the large-amplitude longitudinal oscillations. A representative filament flux tube is modeled as composed of a cool thread centered in a dipped part with hot coronal regions on either side. We have found the normal modes of the system and establish that the observed longitudinal oscillations are well described with the fundamental mode. For small and intermediate curvature radii and moderate to large density contrast between the prominence and the corona, the main restoring force is the solar gravity. In this full wave description of the oscillation a simple expression for the oscillation frequencies is derived in which the pressure-driven term introduces a small correction. We have also found that the normal modes are almost independent of the geometry of the hot regions of the tube. We conclude that observed large-amplitude longitudinal oscillations are driven by the projected gravity along the flux tubes and are strongly influenced by the curvature of the dips of the magnetic field in which the threads reside.
The Effects of Magnetic-field Geometry on Longitudinal Oscillaitons of Solar Prominences
Luna, M.; Diaz, A. J.; Karpen, J.
2013-01-01
We investigate the influence of the geometry of the solar filament magnetic structure on the large-amplitude longitudinal oscillations. A representative filament flux tube is modeled as composed of a cool thread centered in a dipped part with hot coronal regions on either side.We have found the normal modes of the system and establish that the observed longitudinal oscillations are well described with the fundamental mode. For small and intermediate curvature radii and moderate to large density contrast between the prominence and the corona, the main restoring force is the solar gravity. In this full wave description of the oscillation a simple expression for the oscillation frequencies is derived in which the pressure-driven term introduces a small correction. We have also found that the normal modes are almost independent of the geometry of the hot regions of the tube. We conclude that observed large-amplitude longitudinal oscillations are driven by the projected gravity along the flux tubes and are strongly influenced by the curvature of the dips of the magnetic field in which the threads reside.
Magnetic behavior of NiCu nanowire arrays: Compositional, geometry and temperature dependence
International Nuclear Information System (INIS)
Palmero, E. M.; Bran, C.; Real, R. P. del; Vázquez, M.; Magén, C.
2014-01-01
Arrays of Ni 100−x Cu x nanowires ranging in composition 0 ≤ x ≤ 75, diameter from 35 to 80 nm, and length from 150 nm to 28 μm have been fabricated by electrochemical co-deposition of Ni and Cu into self-ordered anodic aluminum oxide membranes. As determined by X-ray diffraction and Transmission Electron Microscopy, the crystalline structure shows fcc cubic symmetry with [111] preferred texture and preferential Ni or Cu lattice depending on the composition. Their magnetic properties such as coercivity and squareness have been determined as a function of composition and geometry in a Vibrating Sample Magnetometer in the temperature range from 10 to 290 K for applied magnetic fields parallel and perpendicular to the nanowires axis. Addition of Cu into the NiCu alloy up to 50% enhances both parallel coercivity and squareness. For the higher Cu content, these properties decrease and the magnetization easy axis becomes oriented perpendicular to the wires. In addition, coercivity and squareness increase by decreasing the diameter of nanowires which is ascribed to the increase of shape anisotropy. The temperature dependent measurements reflect a complex behavior of the magnetic anisotropy as a result of energy contributions with different evolution with temperature.
International Nuclear Information System (INIS)
Forkl, A.; Kronmueller, H.
1995-01-01
The distribution of the critical current density j c (r) in hard type-II superconductors depends strongly on their sample geometry. Rules are given for the construction of j c (r). Samples with homogeneous thickness are divided into cakelike regions with a unique current direction. The spatial magnetic flux density distribution and the magnetic polarization of such a cakelike unit cell with homogeneous current density are calculated analytically. The magnetic polarization and magnetic flux density distribution of a superconductor in the mixed state is then given by an adequate superposition of the unit cell solutions. The theoretical results show good agreement with magneto-optically determined magnetic flux density distributions of a quadratic thin superconducting YBa 2 Cu 3 O 7-x film. The current density distribution is discussed for several sample geometries
International Nuclear Information System (INIS)
Alija, A; Sobrado, I; Rodriguez-RodrIguez, G; Velez, M; Alameda, J M; MartIn, J I; Parrondo, J M R
2010-01-01
Micromagnetic simulations have been performed in uniaxial magnetic films with 2D array of asymmetric arrow shape holes. In order to understand the asymmetric pinning potential created by the holes, different boundary geometries conditions are used on the simulations. The depinning fields for forward and backward domain wall propagation have been calculated by the analysis of the energy landscapes as a function of the domain wall position. Domain wall depinning occurs preferentially at the free ends of the domain wall at the film boundaries. We have found that the domain wall propagation is different at the top/bottom boundaries of the simulated film which can be understood in terms of the magnetostatic energy and the chirality of the domain wall.
Effect of drift-acoustic waves on magnetic island stability in slab geometry
International Nuclear Information System (INIS)
Fitzpatrick, R.; Waelbroeck, F.L.
2005-01-01
A mathematical formalism is developed for calculating the ion polarization term in the Rutherford island width evolution equation in the presence of drift-acoustic waves. The calculation is fully nonlinear, includes both ion and electron diamagnetic effects, as well as ion compressibility, but is performed in slab geometry. Magnetic islands propagating in a certain range of phase velocities are found to emit drift-acoustic waves. Wave emission gives rise to rapid oscillations in the ion polarization term as the island phase velocity varies, and also generates a net electromagnetic force acting on the island region. Increasing ion compressibility is found to extend the range of phase velocities over which drift-acoustic wave emission occurs in the electron diamagnetic direction
International Nuclear Information System (INIS)
McMillan, B.F.; Jolliet, S.; Tran, T.M.; Villard, L.; Bottino, A.; Angelino, P.
2010-01-01
Fluctuating quantities in magnetic confinement geometries often inherit a strong anisotropy along the field lines. One technique for describing these structures is the use of a certain set of Fourier components on the tori of nested flux surfaces. We describe an implementation of this approach for solving partial differential equations, like Poisson's equation, where a different set of Fourier components may be chosen on each surface according to the changing safety factor profile. Allowing the resolved components to change to follow the anisotropy significantly reduces the total number of degrees of freedom in the description. This can permit large gains in computational performance. We describe, in particular, how this approach can be applied to rapidly solve the gyrokinetic Poisson equation in a particle code, ORB5 (Jolliet et al. (2007) [5]), with a regular (non-field-aligned) mesh. (authors)
Latitude dependence of the solar wind speed: Influence of the coronal magnetic field geometry
International Nuclear Information System (INIS)
Pneuman, G.W.
1976-01-01
The dependence of solar wind speed on latitude as influenced by the magnetic field configuration of the inner corona is studied. It is found that in general, a dipolelike field geometry characteristic of a minimum-type corona tends to produce a solar wind speed distribution which increases with heliographic latitude, in accordance with observations. At very high coronal base densities and temperatures, however, this effect is minimal or even inverted. Physically, the field affects the wind speed through its area divergence, a larger divergence resulting in correspondingly lower speeds. During solar minimum, eclipse photographs suggest that the field divergence increases from pole to equator, a characteristic not apparent during solar maximum. Hence we expect the latitudinal increase in speed to be most pronounced at the minimum phase of solar activity
Energy Technology Data Exchange (ETDEWEB)
Fang, J [Applied Superconductivity Research Center, Tsinghua University, Beijing 100084 (China); Luo, X M [Applied Superconductivity Research Center, Tsinghua University, Beijing 100084 (China); Chen, D X [ICREA and Grup Electromagnetisme, Departament de Fisica, Universitat Autonoma Barcelona, 08193 Bellaterra (Spain); Alamgir, A K M [Applied Superconductivity Research Center, Tsinghua University, Beijing 100084 (China); Collings, E W [MSE, Ohio State University, Columbus, OH 43210 (United States); Lee, E [MSE, Ohio State University, Columbus, OH 43210 (United States); Sumption, M D [MSE, Ohio State University, Columbus, OH 43210 (United States); Fang, J G [Applied Superconductivity Research Center, Tsinghua University, Beijing 100084 (China); Yi, H P [Applied Superconductivity Research Center, Tsinghua University, Beijing 100084 (China); Song, X H [Innova Superconductor Technology Co., Ltd, 7 Rongchang Dongjie, Longsheng Industrial Park, Beijing Economic and Technological Development Area, 100176 (China); Guo, S Q [Applied Superconductivity Research Center, Tsinghua University, Beijing 100084 (China); Liu, M L [Applied Superconductivity Research Center, Tsinghua University, Beijing 100084 (China); Xin, Y [Innopower Superconductor Cable Co., Ltd, 7 Rongchang Dongjie, Longsheng Industrial Park, Beijing Economic and Technological Development Area, 100176 (China); Han, Z [Applied Superconductivity Research Center, Tsinghua University, Beijing 100084 (China)
2004-10-01
On five Bi-2223/Ag tapes with different aspect ratios from 5 to 26, AC losses have been measured at 77 K while a parallel AC magnetic field or a perpendicular AC magnetic field or a longitudinal AC transport current is applied. It has been found that at any frequency the perpendicular magnetic losses per cycle increase, but the parallel magnetic losses per cycle and the transport losses per cycle decrease as the aspect ratio increases. These experimental results are in accord with theoretical results. Meanwhile, we investigated the geometry dependence of the decay time constant of coupling current and that of full penetration field.
International Nuclear Information System (INIS)
Fang, J; Luo, X M; Chen, D X; Alamgir, A K M; Collings, E W; Lee, E; Sumption, M D; Fang, J G; Yi, H P; Song, X H; Guo, S Q; Liu, M L; Xin, Y; Han, Z
2004-01-01
On five Bi-2223/Ag tapes with different aspect ratios from 5 to 26, AC losses have been measured at 77 K while a parallel AC magnetic field or a perpendicular AC magnetic field or a longitudinal AC transport current is applied. It has been found that at any frequency the perpendicular magnetic losses per cycle increase, but the parallel magnetic losses per cycle and the transport losses per cycle decrease as the aspect ratio increases. These experimental results are in accord with theoretical results. Meanwhile, we investigated the geometry dependence of the decay time constant of coupling current and that of full penetration field
Particle Trapping and Dropouts in Magnetic Turbulence in a Spherical Geometry
Tooprakai, P.; Ruffolo, D.; Matthaeus, W. H.; Chuychai, P.
2006-12-01
The observed dropouts of solar energetic particles from impulsive solar events (i.e., the inhomogeneity and sharp gradients in particle density) indicate the partial filamentation of magnetic connection from small regions of the corona to Earth orbit. This can be understood in terms of persistent trapping of field lines due to small- scale topological structures in the solar wind. We further explore how this turbulence structure should be manifest in particle observations, by evaluating particle trajectories obtained from the Newton-Lorentz equations. By adapting a two-component model of turbulence to spherical geometry, we include the adiabatic focusing of particles. The 2D magnetic field is generated by either 1) a 2D fast Fourier transform, a valid approximation over a small angular region, or 2) a spherical harmonic series with ℓ up to 2000. Dropout features at 1 AU are clearly indicated for low-energy particles, but these features are washed out for E >~ 100 MeV. Different time-intensity profiles are found at locations at 1 AU that are distinct with regard to the small-scale topology. Partially supported by the Thailand Research Fund, the Rachadapisek Sompoj Fund of Chulalongkorn University, and NASA Grant NNG05GG83G.
International Nuclear Information System (INIS)
Piskunov, N.E.
1985-01-01
Mathematical formulation of the inverse problem of determination of magnetic field geometry from the polarization profiles of spectral lines is gven. The solving algorithm is proposed. A set of model calculations has shown the effectiveness of the algorithm, the high precision of magnetic star model parameters obtained and also the advantages of the inverse problem method over the commonly used method of interpretation of effective field curves
Energy Technology Data Exchange (ETDEWEB)
Finley, Adam J.; Matt, Sean P., E-mail: af472@exeter.ac.uk [University of Exeter (UK), Department of Physics and Astronomy, Stoker Road, Devon, Exeter, EX4 4QL (United Kingdom)
2017-08-10
Cool stars with outer convective envelopes are observed to have magnetic fields with a variety of geometries, which on large scales are dominated by a combination of the lowest-order fields such as the dipole, quadrupole, and octupole modes. Magnetized stellar wind outflows are primarily responsible for the loss of angular momentum from these objects during the main sequence. Previous works have shown the reduced effectiveness of the stellar wind braking mechanism with increasingly complex but singular magnetic field geometries. In this paper, we quantify the impact of mixed dipolar and quadrupolar fields on the spin-down torque using 50 MHD simulations with mixed fields, along with 10 each of the pure geometries. The simulated winds include a wide range of magnetic field strength and reside in the slow-rotator regime. We find that the stellar wind braking torque from our combined geometry cases is well described by a broken power-law behavior, where the torque scaling with field strength can be predicted by the dipole component alone or the quadrupolar scaling utilizing the total field strength. The simulation results can be scaled and apply to all main-sequence cool stars. For solar parameters, the lowest-order component of the field (dipole in this paper) is the most significant in determining the angular momentum loss.
Energy Technology Data Exchange (ETDEWEB)
Lee, Hwi Joo; Lee, Hee Gyoun [Korea Polytechnic University, Siheung (Korea, Republic of); Park, Soon Dong; Jun, Bung Hyack; Kim, Chan Joong [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2017-09-15
This study presents that the orientation and the geometry of seed affect on the growth behavior of melt processed single grain REBCO bulk superconductor and its magnetic properties. The effects of seed geometry have been investigated for thin 30mm x 30mm rectangular powder compacts. Single grain REBCO bulk superconductors have been grown successfully by a top seed melt growth method for 8-mm thick vertical thin REBCO slab. Asymmetric structures have been developed at the front surface and at the rear surface of the specimen. Higher magnetic properties have been obtained for the specimen that c-axis is normal to the specimen surface. The relationships between microstructure, grain growth and magnetic properties have been discussed.
Magnetic nanowires and hyperthermia: How geometry and material affect heat production efficiency
Contreras, Maria F.; Zaher, A.; Perez, Jose E.; Ravasi, Timothy; Kosel, Jü rgen
2015-01-01
Magnetic hyperthermia, which refers to the production of heat by magnetic nanostructures under an alternating magnetic field (AMF), has been previously investigated with superparamagnetic nanobeads as a cancer therapy method. Magnetic nanowires (NWs
Nadzharyan, T. A.; Makarova, L. A.; Kazimirova, E. G.; Perov, N. S.; Kramarenko, E. Yu
2018-03-01
We study the effects the geometric configuration has on magnetic interactions between a magnetoactive elastomer (MAE) sample and various systems of permanent magnets for problems with both flat and curved geometry. MAEs consist of a silicone polymer matrix and iron filler microparticles embedded in it. Permanent magnets are cylindrical neodymium magnets arranged in a line on a flat or curved solid surfaces. We use computer simulations, namely the finite element method, in order to study the interaction force and magnetic pressure in a system with an MAE sample and permanent magnets. The model is based on classical Maxwell magnetostatics and two factors taking into account field dependence of MAE’s magnetic properties and inhomogeneities caused by local demagnetization. We calculate magnetic pressure dependences on various geometric parameters of the system, namely, the diameter and the height of permanent magnets, the distance between the magnets and dimensions of MAE samples. This research aims to create a set of guidelines for choosing the geometric configuration of a retina fixator based on MAE seals to be used in eye surgery for retinal detachment treatment.
Energy Technology Data Exchange (ETDEWEB)
Cavia Santos, S; Garcia-Tabares, L
1998-05-01
A new simple theory has been developed for the study of levitation forces between a permanent magnet and a HTc superconductor. This theory is based on the assumption that both, the magnet and the superconductor, can be modelled by an equivalent coil placed on their surface. While the current flowing through the permanent magnet is constant, the equivalent current through the superconductor can be iether corresponding to screen the overall flux or a constant current corresponding to critical current density when the superconductor is saturated. A test facility has been designed and built for measuring levitation forces at variable approaching speeds. Comparison between theoretical and experimental measurements are presented in the report as well as a general description of the test facility. (Author)
Calculation of uncertainties; Calculo de incertidumbres
Energy Technology Data Exchange (ETDEWEB)
Diaz-Asencio, Misael [Centro de Estudios Ambientales de Cienfuegos (Cuba)
2012-07-01
metodologico para la obtencion de informacion (mesurando) de un sistema material (poblacion). Ello supone la necesidad de la definicion del problema, la eleccion de los metodos de muestreo y medicion adecuados y la ejecucion de estas actividades para la obtencion de la informacion. El resultado de una medicion solo es una aproximacion o estimacion del valor del mesurando, el cual se completa solo cuando va acompanado por una estimacion de la incertidumbre del proceso analitico. Segun el 'Vocabulario de Terminos Basicos y Generales de Metrologia' la incertidumbre de medicion 'es el parametro asociado con el resultado de la medicion que caracteriza la dispersion de los valores que razonablemente pudiera ser atribuida al mensurando (o magnitud). Este parametro podria ser una desviacion estandar o un intervalo de confianza'. La evaluacion de la incertidumbre exige que observemos detalladamente todas sus posibles fuentes, pero no de forma desproporcionada. Podemos realizar una buena estimacion de la incertidumbre concentrando el esfuerzo en las mayores contribuciones. Los pasos fundamentales del proceso de determinacion de la incertidumbre en las mediciones son: - la especificacion del mesurando; - la identificacion de las fuentes de incertidumbre; - la cuantificacion de las componentes individuales de la incertidumbre; - el calculo de la incertidumbre estandar combinada; - informe de la incertidumbre.
Energy Technology Data Exchange (ETDEWEB)
Franca, Fernando
1995-12-31
In this work we investigate the local magnetic properties and the electronic structure of HCP Fe, as well introducing transition metals atoms 3d (Cs, Ti, Cr, Mn, Co, Ni, Cu, Zn) in HCP iron matrix. We employed the discrete variational method (DVM), which is an orbital molecular method which incorporate the Hartree-Fock-Slater theory and the linear combination of atomic orbitals (LCAO), in the self-consistent charge approximation and the local density approximation of Von Barth and Hedin to the exchange-correlation potential. We used the embedded cluster model to investigate the electronic structure and the local magnetic properties for the central atom of a cluster of 27 atoms immersed in the microcrystal representing the HCP Fe. (author) 32 refs., 19 figs., 2 tabs.
Energy Technology Data Exchange (ETDEWEB)
Malkov, Victor N.; Rogers, David W.O. [Carleton University (Canada)
2016-08-15
The coupling of MRI and radiation treatment systems for the application of magnetic resonance guided radiation therapy necessitates a reliable magnetic field capable Monte Carlo (MC) code. In addition to the influence of the magnetic field on dose distributions, the question of proper calibration has arisen due to the several percent variation of ion chamber and solid state detector responses in magnetic fields when compared to the 0 T case (Reynolds et al., Med Phys, 2013). In the absence of a magnetic field, EGSnrc has been shown to pass the Fano cavity test (a rigorous benchmarking tool of MC codes) at the 0.1 % level (Kawrakow, Med.Phys, 2000), and similar results should be required of magnetic field capable MC algorithms. To properly test such developing MC codes, the Fano cavity theorem has been adapted to function in a magnetic field (Bouchard et al., PMB, 2015). In this work, the Fano cavity test is applied in a slab and ion-chamber-like geometries to test the transport options of an implemented magnetic field algorithm in EGSnrc. Results show that the deviation of the MC dose from the expected Fano cavity theory value is highly sensitive to the choice of geometry, and the ion chamber geometry appears to pass the test more easily than larger slab geometries. As magnetic field MC codes begin to be used for dose simulations and correction factor calculations, care must be taken to apply the most rigorous Fano test geometries to ensure reliability of such algorithms.
Energy Technology Data Exchange (ETDEWEB)
Reynolds, J. M.; Lopez-Bruna, D.
2009-10-12
In this report we continue with the description of a newly developed numerical method to solve the drift kinetic equation for ions and electrons in toroidal plasmas. Several numerical aspects, already outlined in a previous report [Informes Tecnicos Ciemat 1165, mayo 2009], will be treated now in more detail. Aside from discussing the method in the context of other existing codes, various aspects will be now explained from the viewpoint of numerical methods: the way to solve convection equations, the adopted boundary conditions, the real-space meshing procedures along with a new software developed to build them, and some additional questions related with the parallelization and the numerical integration. (Author) 16 refs.
Energy Technology Data Exchange (ETDEWEB)
Reynolds, J. M.; Lopez-Bruna, D.
2009-12-11
This report is the third of a series [Informes Tecnicos Ciemat 1165 y 1172] devoted to the development of a new numerical code to solve the guiding center equation for electrons and ions in toroidal plasmas. Two calculation meshes corresponding to axisymmetric tokamaks are now prepared and the kinetic equation is expanded so the standard terms of neoclassical theory --fi rst order terms in the Larmor radius expansion-- can be identified, restricting the calculations correspondingly. Using model density and temperature profiles for the plasma, several convergence test are performed depending on the calculation meshes and the expansions of the distribution function; then the results are compared with the theory [Hinton and Hazeltine, Rev. Mod. Phys. (1976)]. (Author) 18 refs.
Magnetic nanowires and hyperthermia: How geometry and material affect heat production efficiency
Contreras, Maria F.
2015-05-01
Magnetic hyperthermia, which refers to the production of heat by magnetic nanostructures under an alternating magnetic field (AMF), has been previously investigated with superparamagnetic nanobeads as a cancer therapy method. Magnetic nanowires (NWs) used in hyperthermia can be very promising, as it has been shown that they have a larger magnetic moment per unit of volume compared to the nanobeads. Moreover, Fe NWs proved to have a higher heating efficiency compared to Fe nanobeads, when exposed to an AMF at the same concentration [1].
International Nuclear Information System (INIS)
Guo, Y.; Ding, M. D.; Liu, Y.; Sun, X. D.; DeRosa, M. L.; Wiegelmann, T.
2012-01-01
We test a nonlinear force-free field (NLFFF) optimization code in spherical geometry using an analytical solution from Low and Lou. Several tests are run, ranging from idealized cases where exact vector field data are provided on all boundaries, to cases where noisy vector data are provided on only the lower boundary (approximating the solar problem). Analytical tests also show that the NLFFF code in the spherical geometry performs better than that in the Cartesian one when the field of view of the bottom boundary is large, say, 20° × 20°. Additionally, we apply the NLFFF model to an active region observed by the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory (SDO) both before and after an M8.7 flare. For each observation time, we initialize the models using potential field source surface (PFSS) extrapolations based on either a synoptic chart or a flux-dispersal model, and compare the resulting NLFFF models. The results show that NLFFF extrapolations using the flux-dispersal model as the boundary condition have slightly lower, therefore better, force-free, and divergence-free metrics, and contain larger free magnetic energy. By comparing the extrapolated magnetic field lines with the extreme ultraviolet (EUV) observations by the Atmospheric Imaging Assembly on board SDO, we find that the NLFFF performs better than the PFSS not only for the core field of the flare productive region, but also for large EUV loops higher than 50 Mm.
Effects of the divertor tile geometries and magnetic field angles on the heat fluxes to the surface
Energy Technology Data Exchange (ETDEWEB)
Hu, Wanpeng; Sang, Chaofeng; Sun, Zhenyue; Wang, Dezhen, E-mail: wangdez@dlut.edu.cn
2017-03-15
Highlights: • Simulation of the plasma behaviors in the divertor gap region is done by using a 2d3 v Particle-In-Cell code. • Heat fluxes on the wall surface in different gap geometries are studied. • The effect of the magnetic field angle on the heat flux is investigated. - Abstract: A two dimension-in-space and three dimension-in-velocity (2d3v) Particle-In-Cell (PIC) code is applied to investigate the plasma behaviors at the divertor gaps region in this work. Electron and D{sup +} ion fluxes to the tile surface in the poloidal and toroidal gaps for different shaped edges are compared to demonstrate the optimized tile geometry. For poloidal gap, shaped edge in the shadowing side makes more ions penetrate into the gap, while shaped edge in the wetted side can mitigate the peak flux value. For toroidal gap, most ions entering the gap impinge on the side tile mainly due to the E × B drift, and shaped wetted edges also can mitigate the peak heat fluxes. In addition, effects of magnetic field inclination angle from toroidal direction on the plasma behaviors are simulated for poloidal and toroidal gaps, respectively. It is found that the magnetic field angles don’t influence the plasma behaviors in poloidal gap; while significant changes have been observed in the toroidal gap.
A holmium(III)-based single-molecule magnet with pentagonal-bipyramidal geometry
Energy Technology Data Exchange (ETDEWEB)
Kajiwara, Takashi [Department of Chemistry, Faculty of Science, Nara Women' s University (Japan)
2017-09-11
The right environment: The remarkable properties of a recently reported holmium(III)-based single-ion magnet have been ascribed to the hyperfine interactions with the half-integer nuclear spin in combination with the pentagonal-bipyramidal coordination environment. These results provide insight into the complicated magnetic properties of nanosized magnetic materials. (copyright 2017 Wiley-VCH Verlag GmbH and Co. KGaA, Weinheim)
Manipulation of magnetic vortex parameters in disk-on-disk nanostructures with various geometry
Directory of Open Access Journals (Sweden)
Maxim E. Stebliy
2015-03-01
Full Text Available Magnetic nanostructures in the form of a sandwich consisting of two permalloy (Py disks with diameters of 600 and 200 nm separated by a nonmagnetic interlayer are studied. Magnetization reversal of the disk-on-disk nanostructures depends on the distance between centers of the small and big disks and on orientation of an external magnetic field applied during measurements. It is found that manipulation of the magnetic vortex chirality and the trajectory of the vortex core in the big disk is only possible in asymmetric nanostructures. Experimentally studied peculiarities of a motion path of the vortex core and vortex parameters by the magneto-optical Kerr effect (MOKE magnetometer are supported by the magnetic force microscopy imaging and micromagnetic simulations.
International Nuclear Information System (INIS)
Du, Hailong; Sang, Chaofeng; Wang, Liang; Bonnin, Xavier; Sun, Jizhong; Wang, Dezhen
2016-01-01
Highlights: • The in-out divertor asymmetry is studied using SOLPS. • The discharge operation and the magnetic filed have a great influence on the divertor asymmetry. • The asymmetry is not obvious in low recycling regime as that in high recycling regime. - Abstract: This paper aims to investigate the reason why the divertor in-out asymmetry was not obvious as experimentally observed in EAST only considering the classical drifts from previous simulations (Guo et al., J. Nucl. Mater. 438 (2013) 280; Du et al., J. Nucl. Mater. 463 (2015) 485). With consideration of the classical drifts, a series of different typical discharge scenarios in EAST in different magnetic field geometries were simulated by using the SOLPS5.2 code package. The simulated results reveal that the classical drifts make a major contribution to the in-out divertor asymmetry in the high recycling regime (HRR) and partial detachment (one divertor target begins to detach, while the other divertor remains attached) regime. In comparison, in low recycling regime the classical drifts play a much smaller role in the contributions to the in-out divertor asymmetry, which can explain reasonably the reason for it in Guo et al. (J. Nucl. Mater. 438 (2013) 280). In addition, the magnetic field geometry also has a great impact on the classical drifts inducing the asymmetry; it is found that for lower single-null, upper single-null and connected double-null topologies, in HRR the classical drifts play an dominant role in the contribution to the in-out divertor asymmetry, while for a disconnected double null magnetic field configuration, they play a minor role, which is the reason why the in-out asymmetry was unobvious by considering the drifts in Du et al. (J. Nucl. Mater. 463 (2015) 485).
Energy Technology Data Exchange (ETDEWEB)
Du, Hailong; Sang, Chaofeng [Key Laboratory of Materials Modification by Laser, Ion and Electron Beams (Ministry of Education), School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024 (China); Wang, Liang [Key Laboratory of Materials Modification by Laser, Ion and Electron Beams (Ministry of Education), School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024 (China); Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031 (China); Bonnin, Xavier [LSPM-CNRS, Université Paris 13, Sorbonne Paris Cité, F-93430 Villetaneuse (France); Sun, Jizhong [Key Laboratory of Materials Modification by Laser, Ion and Electron Beams (Ministry of Education), School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024 (China); Wang, Dezhen, E-mail: wangdez@dlut.edu.cn [Key Laboratory of Materials Modification by Laser, Ion and Electron Beams (Ministry of Education), School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024 (China)
2016-11-01
Highlights: • The in-out divertor asymmetry is studied using SOLPS. • The discharge operation and the magnetic filed have a great influence on the divertor asymmetry. • The asymmetry is not obvious in low recycling regime as that in high recycling regime. - Abstract: This paper aims to investigate the reason why the divertor in-out asymmetry was not obvious as experimentally observed in EAST only considering the classical drifts from previous simulations (Guo et al., J. Nucl. Mater. 438 (2013) 280; Du et al., J. Nucl. Mater. 463 (2015) 485). With consideration of the classical drifts, a series of different typical discharge scenarios in EAST in different magnetic field geometries were simulated by using the SOLPS5.2 code package. The simulated results reveal that the classical drifts make a major contribution to the in-out divertor asymmetry in the high recycling regime (HRR) and partial detachment (one divertor target begins to detach, while the other divertor remains attached) regime. In comparison, in low recycling regime the classical drifts play a much smaller role in the contributions to the in-out divertor asymmetry, which can explain reasonably the reason for it in Guo et al. (J. Nucl. Mater. 438 (2013) 280). In addition, the magnetic field geometry also has a great impact on the classical drifts inducing the asymmetry; it is found that for lower single-null, upper single-null and connected double-null topologies, in HRR the classical drifts play an dominant role in the contribution to the in-out divertor asymmetry, while for a disconnected double null magnetic field configuration, they play a minor role, which is the reason why the in-out asymmetry was unobvious by considering the drifts in Du et al. (J. Nucl. Mater. 463 (2015) 485).
Proposal for the award of a contract to measure the geometry of the LHC cryo-magnets
2003-01-01
This document concerns the award of a contract to measure the geometry of the LHC cryo-magnets. Following a market survey carried out among 43 firms in eleven Member States, a call for tenders (IT-2989/EST/LHC) was sent on 10 March 2003 to one firm and three consortia, in seven Member States. By the closing date, CERN had received three tenders from the three consortia in six Member States. The Finance Committee is invited to agree to the negotiation of a contract with the consortium SETAT (FR), INTROTECH (NL) and MAP (CH), the lowest bidder, to measure the geometry of the LHC cryo-magnets, for an amount not exceeding 2 097 582 euros (3 173 347 Swiss francs) covering an initial period of three years starting on 1 October 2003, subject to revision for inflation from 1 October 2004. The rate of exchange used is that stipulated in the tender. The contract will include options for two one-year extensions beyond the initial three-year period. The consortium has indicated the following distribution by country of th...
Effects of magnetic core geometry on false detection in residual current sensor
International Nuclear Information System (INIS)
Colin, Bruno; Chillet, Christian; Kedous-Lebouc, Afef; Mas, Patrick
2006-01-01
Under high-supply current, residual circuit breakers are subject to abnormal tripping, caused by false residual currents. Geometric or magnetic anomalies in the circuit breaker ring core seem to be responsible for these abnormal currents. This paper studies a few anomalies (spiral shape effect, conductor eccentricity, lamination effect) and calculates different contributions using the finite element simulations. The results show that the ring core, made of thin wound magnetic tape, is particularly sensitive to primary conductor eccentricity
Random walks on the braid group B3 and magnetic translations in hyperbolic geometry
International Nuclear Information System (INIS)
Voituriez, Raphaeel
2002-01-01
We study random walks on the three-strand braid group B 3 , and in particular compute the drift, or average topological complexity of a random braid, as well as the probability of trivial entanglement. These results involve the study of magnetic random walks on hyperbolic graphs (hyperbolic Harper-Hofstadter problem), what enables to build a faithful representation of B 3 as generalized magnetic translation operators for the problem of a quantum particle on the hyperbolic plane
Energy Technology Data Exchange (ETDEWEB)
Valle G, E. del; Mugica R, C.A. [IPN, ESFM, Departamento de Ingenieria Nuclear, 07738 Mexico D.F. (Mexico)]. e-mail: cmugica@ipn.mx
2005-07-01
In our country, in last congresses, Gomez et al carried out reactivity calculations based on the solution of the diffusion equation for an energy group using nodal methods in one dimension and the TPL approach (Lineal Perturbation Theory). Later on, Mugica extended the application to the case of multigroup so much so much in one as in two dimensions (X Y geometry) with excellent results. Presently work is carried out similar calculations but this time based on the solution of the neutron transport equation in X Y geometry using nodal methods and again the TPL approximation. The idea is to provide a calculation method that allows to obtain in quick form the reactivity solving the direct problem as well as the enclosed problem of the not perturbed problem. A test problem for the one that results are provided for the effective multiplication factor is described and its are offered some conclusions. (Author)
Magnetic fields, stellar feedback, and the geometry of H II regions
Ferland, Gary J.
2009-04-01
Magnetic pressure has long been known to dominate over gas pressure in atomic and molecular regions of the interstellar medium. Here I review several recent observational studies of the relationships between the H+, H0 and H2 regions in M42 (the Orion complex) and M17. A simple picture results. When stars form they push back surrounding material, mainly through the outward momentum of starlight acting on grains, and field lines are dragged with the gas due to flux freezing. The magnetic field is compressed and the magnetic pressure increases until it is able to resist further expansion and the system comes into approximate magnetostatic equilibrium. Magnetic field lines can be preferentially aligned perpendicular to the long axis of quiescent cloud before stars form. After star formation and pushback occurs ionized gas will be constrained to flow along field lines and escape from the system along directions perpendicular to the long axis. The magnetic field may play other roles in the physics of the H II region and associated PDR. Cosmic rays may be enhanced along with the field and provide additional heating of atomic and molecular material. Wave motions may be associated with the field and contribute a component of turbulence to observed line profiles.
DEFF Research Database (Denmark)
Batra, Tushar; Schaltz, Erik
2014-01-01
Minimizing magnetic field emissions to surroundings is one of the most challenging design criteria for wireless power transfer to vehicles. In this paper, concept of division of the emissions into three zones (primary, secondary, and combined zone) in the vertical direction is introduced. For geo......Minimizing magnetic field emissions to surroundings is one of the most challenging design criteria for wireless power transfer to vehicles. In this paper, concept of division of the emissions into three zones (primary, secondary, and combined zone) in the vertical direction is introduced...... for vertical separation between the coils in range of 100-180 mm. It is observed that lower vertical separation results in higher overlapping of the zones and the coils behave as they are effectively placed close to center of air gap. The analysis in this work provides a better understanding of the space...... profile of magnetic field emissions (with and without ferrite) for wireless power transfer to vehicles....
Punjabi, Alkesh; Ali, Halima
2008-12-01
A new approach to integration of magnetic field lines in divertor tokamaks is proposed. In this approach, an analytic equilibrium generating function (EGF) is constructed in natural canonical coordinates (ψ,θ) from experimental data from a Grad-Shafranov equilibrium solver for a tokamak. ψ is the toroidal magnetic flux and θ is the poloidal angle. Natural canonical coordinates (ψ,θ,φ) can be transformed to physical position (R,Z,φ) using a canonical transformation. (R,Z,φ) are cylindrical coordinates. Another canonical transformation is used to construct a symplectic map for integration of magnetic field lines. Trajectories of field lines calculated from this symplectic map in natural canonical coordinates can be transformed to trajectories in real physical space. Unlike in magnetic coordinates [O. Kerwin, A. Punjabi, and H. Ali, Phys. Plasmas 15, 072504 (2008)], the symplectic map in natural canonical coordinates can integrate trajectories across the separatrix surface, and at the same time, give trajectories in physical space. Unlike symplectic maps in physical coordinates (x,y) or (R,Z), the continuous analog of a symplectic map in natural canonical coordinates does not distort trajectories in toroidal planes intervening the discrete map. This approach is applied to the DIII-D tokamak [J. L. Luxon and L. E. Davis, Fusion Technol. 8, 441 (1985)]. The EGF for the DIII-D gives quite an accurate representation of equilibrium magnetic surfaces close to the separatrix surface. This new approach is applied to demonstrate the sensitivity of stochastic broadening using a set of perturbations that generically approximate the size of the field errors and statistical topological noise expected in a poloidally diverted tokamak. Plans for future application of this approach are discussed.
International Nuclear Information System (INIS)
Punjabi, Alkesh; Ali, Halima
2008-01-01
A new approach to integration of magnetic field lines in divertor tokamaks is proposed. In this approach, an analytic equilibrium generating function (EGF) is constructed in natural canonical coordinates (ψ,θ) from experimental data from a Grad-Shafranov equilibrium solver for a tokamak. ψ is the toroidal magnetic flux and θ is the poloidal angle. Natural canonical coordinates (ψ,θ,φ) can be transformed to physical position (R,Z,φ) using a canonical transformation. (R,Z,φ) are cylindrical coordinates. Another canonical transformation is used to construct a symplectic map for integration of magnetic field lines. Trajectories of field lines calculated from this symplectic map in natural canonical coordinates can be transformed to trajectories in real physical space. Unlike in magnetic coordinates [O. Kerwin, A. Punjabi, and H. Ali, Phys. Plasmas 15, 072504 (2008)], the symplectic map in natural canonical coordinates can integrate trajectories across the separatrix surface, and at the same time, give trajectories in physical space. Unlike symplectic maps in physical coordinates (x,y) or (R,Z), the continuous analog of a symplectic map in natural canonical coordinates does not distort trajectories in toroidal planes intervening the discrete map. This approach is applied to the DIII-D tokamak [J. L. Luxon and L. E. Davis, Fusion Technol. 8, 441 (1985)]. The EGF for the DIII-D gives quite an accurate representation of equilibrium magnetic surfaces close to the separatrix surface. This new approach is applied to demonstrate the sensitivity of stochastic broadening using a set of perturbations that generically approximate the size of the field errors and statistical topological noise expected in a poloidally diverted tokamak. Plans for future application of this approach are discussed.
Geometry optimization of five-phase permanent magnet synchronous motors using Bees algorithm
Directory of Open Access Journals (Sweden)
R Ilka
2015-12-01
Full Text Available Among all types of electrical motors, permanent magnet synchronous motors (PMSMs are reliable and efficient motors in industrial applications. Because of their superiority over other kinds of motors, they are replacing conventional electric motors. On the other hand, high-phase PMSMs are good candidates to be used in certain industrial and military projects such as electric vehicles, spacecrafts, naval systems and etc. In these cases, the motor has to be designed with minimum volume and high torque and efficiency. Design optimization can improve their features noticeably, thus reduce volume and enhance performance of motors. In this paper, a new method for optimum design of a five-phase surface-mounted permanent magnet synchronous motor is presented to achieve minimum permanent magnets (PMs volume with an increased torque and efficiency. Design optimization is performed in search for optimum dimensions of the motor and its permanent magnets using Bees Algorithm (BA. The design optimization results in a motor with great improvement regarding the original motor which is compared with two well-known evolutionary algorithms i.e. GA and PSO. Finally, finite element method simulation is utilized to validate the accuracy of the design.
International Nuclear Information System (INIS)
Sen, P.N.; Andre, A.; Axelrod, S.
1999-01-01
We study the influence of restriction on Carr - Purcell - Meiboom - Gill spin echoes response of magnetization of spins diffusing in a bounded region in the presence of a constant magnetic field gradient. Depending on three main length scales: L S pore size, L G dephasing length and L D diffusion length during half-echo time, three main regimes of decay have been identified: free, localization and motionally averaging regime. In localization regime, the decay exponent depends on a fractional power (2/3) of the gradient, denoting a strong breakdown of the second cumulant or the Gaussian phase approximation (GPA). In the other two regimes, the exponent depends on the gradient squared, and the GPA holds. We find that the transition from the localization to the motionally averaging regime happens when the magnetic field gradients approach special values, corresponding to branch points of the eigenvalues. Transition from one regime to another as a function of echo number for a certain range of parameters is discussed. In this transition region, the signal shows large oscillations with echo number. For large n, asymptotic behavior sets in as a function of n for the decay exponent per echo. This is true for all values of the parameters L S , L G , and L D . copyright 1999 American Institute of Physics
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)
Solution structure of apamin determined by nuclear magnetic resonance and distance geometry
Energy Technology Data Exchange (ETDEWEB)
Pease, J.H.B.; Wemmer, D.E.
1988-11-01
The solution structure of the bee venom neurotoxin apamin has been determined with a distance geometry program using distance constraints derived from NMR. Twenty embedded structures were generated and refined by using the program DSPACE. After error minimization using both conjugate gradient and dynamics algorithms, six structures had very low residual error. Comparisons of these show that the backbone of the peptide is quite well-defined with the largest rms difference between backbone atoms in these structures of 1.34 /Angstrom/. The side chains have far fewer constraints and show greater variability in their positions. The structure derived here is generally consistent with the qualitative model previously described, with most differences occurring in the loop between the ..beta..-turn (residues 2-5) and the C-terminal ..cap alpha..-helix (residues 9-17). Comparisons are made with previously derived models from NMR data and other methods.
Solution structure of apamin determined by nuclear magnetic resonance and distance geometry
International Nuclear Information System (INIS)
Pease, J.H.B.; Wemmer, D.E.
1988-01-01
The solution structure of the bee venom neurotoxin apamin has been determined with a distance geometry program using distance constraints derived from NMR. Twenty embedded structures were generated and refined by using the program DSPACE. After error minimization using both conjugate gradient and dynamics algorithms, six structures had very low residual error. Comparisons of these show that the backbone of the peptide is quite well-defined with the largest rms difference between backbone atoms in these structures of 1.34 /Angstrom/. The side chains have far fewer constraints and show greater variability in their positions. The structure derived here is generally consistent with the qualitative model previously described, with most differences occurring in the loop between the β-turn (residues 2-5) and the C-terminal α-helix (residues 9-17). Comparisons are made with previously derived models from NMR data and other methods
Suppression of excess noise in Transition-Edge Sensors using magnetic field and geometry
International Nuclear Information System (INIS)
Ullom, J.N.; Doriese, W.B.; Hilton, G.C.; Beall, J.A.; Deiker, S.; Irwin, K.D.; Reintsema, C.D.; Vale, L.R.; Xu, Y.
2004-01-01
We report recent progress at NIST on Mo/Cu Transition-Edge Sensors (TESs). While the signal-band noise of our sensors agrees with theory, we observe excess high-frequency noise. We describe this noise and demonstrate that it can be strongly suppressed by a magnetic field perpendicular to the plane of the sensor. Both the excess noise and α=(T/R)(dR/dT) depend strongly on field so our results show that accurate comparisons between devices are only possible when the field is well known or constant. We also present results showing the noise performance of TES designs incorporating parallel and perpendicular normal metal bars, an array of normal metal islands, and in wedge-shaped devices. We demonstrate significant reduction of high-frequency noise with the perpendicular bar devices at the cost of reduced α. Both the bars and the magnetic field are useful noise reduction techniques for bolometers
Patel, Anita; Pulugundla, Gautam; Smolentsev, Sergey; Abdou, Mohamed; Bhattacharyay, Rajendraprasad
2018-04-01
Following the magnetohydrodynamic (MHD) code validation and verification proposal by Smolentsev et al. (Fusion Eng Des 100:65-72, 2015), we perform code to code and code to experiment comparisons between two computational solvers, FLUIDYN and HIMAG, which are presently considered as two of the prospective CFD tools for fusion blanket applications. In such applications, an electrically conducting breeder/coolant circulates in the blanket ducts in the presence of a strong plasma-confining magnetic field at high Hartmann numbers, it{Ha} (it{Ha}^2 is the ratio between electromagnetic and viscous forces) and high interaction parameters, it{N} (it{N} is the ratio of electromagnetic to inertial forces). The main objective of this paper is to provide the scientific and engineering community with common references to assist fusion researchers in the selection of adequate computational means to be used for blanket design and analysis. As an initial validation case, the two codes are applied to the classic problem of a laminar fully developed MHD flows in a rectangular duct. Both codes demonstrate a very good agreement with the analytical solution for it{Ha} up to 15, 000. To address the capabilities of the two codes to properly resolve complex geometry flows, we consider a case of three-dimensional developing MHD flow in a geometry comprising of a series of interconnected electrically conducting rectangular ducts. The computed electric potential distributions for two flows (Case A) it{Ha}=515, it{N}=3.2 and (Case B) it{Ha}=2059, it{N}=63.8 are in very good agreement with the experimental data, while the comparisons for the MHD pressure drop are still unsatisfactory. To better interpret the observed differences, the obtained numerical data are analyzed against earlier theoretical and experimental studies for flows that involve changes in the relative orientation between the flow and the magnetic field.
DEFF Research Database (Denmark)
Petersen, Thomas Frank; Pryds, Nini; Smith, Anders
2007-01-01
We have developed a two-dimensional model of a reciprocating Active Magnetic Regenerator(AMR) with a regenerator made of parallel plates arranged in a stack configuration. The time dependent,two-dimensional model solves the Navier-Stokes equations for the heat transfer fluid and the coupled heat...... transfer equations for the regenerator and the fluid. The model is implemented using the Finite Element Method. The model can be used to study both transient and steady-state phenomena in the AMR for any ratio of regenerator to fluid heat capacity. Results on the AMR performance for different design...
Wu, Yanbing; Huang, Zongyu; Liu, Huating; He, Chaoyu; Xue, Lin; Qi, Xiang; Zhong, Jianxin
2018-06-15
We have studied the stable geometries, band structures and magnetic properties of transition-metal (V, Cr, Mn, Fe, Co and Ni) atoms absorbed on MoS2/h-BN heterostructure systems by first-principles calculations. By comparing the adsorption energies, we find that the adsorbed transition metal (TM) atoms prefer to stay on the top of Mo atoms. The results of the band structure without spin-orbit coupling (SOC) interaction indicate that the Cr-absorbed systems behave in a similar manner to metals, and the Co-absorbed system exhibits a half-metallic state. We also deduce that the V-, Mn-, Fe-absorbed systems are semiconductors with 100% spin polarization at the HOMO level. The Ni-absorbed system is a nonmagnetic semiconductor. In contrast, the Co-absorbed system exhibits metallic state, and the bandgap of V-absorbed system decreases slightly according to the SOC calculations. In addition, the magnetic moments of all the six TM atoms absorbed on the MoS2/h-BN heterostructure systems decrease when compared with those of their free-standing states.
Directory of Open Access Journals (Sweden)
M. A. A. Mohamed
2016-10-01
Full Text Available The focus of this study is to explore the potential use of Polyamide 6 nanocomposite reinforced with nanocrystalline (nc Fe20Ni80 alloy (Fe20Ni80/PA6 PNC in electromagnetic applications and provide understanding of how the alloy particle geometry is controlling the nanocomposite’s physical properties. Thermomechanical rigidity, room-temperature soft magnetic performance and thermal soft magnetic stability of Fe20Ni80/PA6 PNCs based on spherical-sea urchin alloy particles (UMB2-SU and necklace-like alloy chains (UMB2-NC have been investigated. Both PNCs have considerably superior bulk properties compared to neat PA6 and UMB2-SU exhibits the most remarkable overall performance. Morphological observations disclose two relevant phenomena: i improved dispersion and distribution of the SU alloy particles than the NC ones within PA6 matrix, leading to stronger filler-matrix interfacial interactions within the UMB2-SU as compared to the UMB2-NC and ii presence of constraint polymer regions in between alloy segments within the UMB2-SU that provide secondary reinforcing and soft magnetic mechanisms. Such phenomena along with the lower alloy crystallite size and PA6 γ-crystal type content within the UMB2-SU than in the UMB2-NC, are considered the main responsible factors for the distinctive performance of UMB2-SU. Overall, compared to various ferromagnetic nanocrystalline metallic materials, the research proposes the SU nc Fe20Ni80 alloy as a valuable nanofiller in polymers for electromagnetic applications.
Equilibrium geometries, electronic and magnetic properties of small AunNi- (n = 1-9) clusters
Tang, Cui-Ming; Chen, Xiao-Xu; Yang, Xiang-Dong
2014-05-01
Geometrical, electronic and magnetic properties of small AunNi- (n = 1-9) clusters have been investigated based on density functional theory (DFT) at PW91P86 level. An extensive structural search shows that the relative stable structures of AunNi- (n = 1-9) clusters adopt 2D structure for n = 1-5, 7 and 3D structure for n = 6, 8-9. And the substitution of a Ni atom for an Au atom in the Au-n+1 cluster obviously changes the structure of the host cluster. Moreover, an odd-even alternation phenomenon has been found for HOMO-LUMO energy gaps, indicating that the relative stable structures of the AunNi- clusters with odd-numbered gold atoms have a higher relative stability. Finally, the natural population analysis (NPA) and the vertical detachment energies (VDE) are studied, respectively. The theoretical values of VDE are reported for the first time to our best knowledge.
THE INFLUENCE OF MAGNETIC FIELD GEOMETRY ON THE FORMATION OF CLOSE-IN EXOPLANETS
Energy Technology Data Exchange (ETDEWEB)
Simon, Jacob B., E-mail: jbsimon.astro@gmail.com [Department of Space Studies, Southwest Research Institute, Boulder, CO 80302 (United States)
2016-08-20
Approximately half of Sun-like stars harbor exoplanets packed within a radius of ∼0.3 au, but the formation of these planets and why they form in only half of known systems are still not well understood. We employ a one-dimensional steady-state model to gain physical insight into the origin of these close-in exoplanets. We use Shakura and Sunyaev α values extracted from recent numerical simulations of protoplanetary disk accretion processes in which the magnitude of α , and thus the steady-state gas surface density, depend on the orientation of large-scale magnetic fields with respect to the disk’s rotation axis. Solving for the metallicity as a function of radius, we find that for fields anti-aligned with the rotation axis, the inner regions of our model disk often fall within a region of parameter space that is not suitable for planetesimal formation, whereas in the aligned case, the inner disk regions are likely to produce planetesimals through some combination of streaming instability and gravitational collapse, though the degree to which this is true depends on the assumed parameters of our model. More robustly, the aligned field case always produces higher concentrations of solids at small radii compared to the anti-aligned case. In the in situ formation model, this bimodal distribution of solid enhancement leads directly to the observed dichotomy in exoplanet orbital distances.
Energy Technology Data Exchange (ETDEWEB)
Ruiz, Rafael O.; Di Liscia, Marcelo H.; Diaz, Sergio E. [Universidad Simon Bolivar, Sartendejas, Baruta (Venezuela)
2007-11-15
The identification of the dynamic coefficients in air bearings is fundamental for a suitable roto-dynamic analysis. The present paper shows the development of an algorithm that allows the direct obtaining of the dynamic coefficients in hydrodynamic air bearings as much of numerical form as experimental. The testing bench used consists of two magnetic bearings, which support the rotor in their ends and work as well as actuators allowing inducing controlled orbits in the rotor. The test bearing is located between the magnetic bearings. The dynamic forces generated in the air bearing are registered from three load cells. The algorithm was developed in a commercial code of graphical programming, through which the signals can be collected, controlled and processed. The nonlinear behavior of this type of bearings makes difficult the calculation of the dynamic coefficients, therefore the processing of the signals in frequencial space facilitates, in a certain way, its handling. On the other hand, the numerical model was compared with the experimental results obtaining acceptable approaches in magnitude as well as in behavior. The numerical dynamic coefficients calculation was realized solving the Reynolds differential equation for a compressible fluid in the thickness of the gas film, taking into consideration the fluid mass flow that is introduced, as well as the pressure loss suffered by the same in passing through the feeding orifices. The numerical methods utilized include the solution of the differential equation of Reynolds for finite differences, the calculation of the profile realizing successive iterations and the calculation of the hydrodynamics forces through the Simpson numerical integration. The numerical dynamic coefficients were found applying a minimum squared technique to the hydrodynamic stresses generated in simulating an orbit of the rotor at a determined frequency and velocity, allowing in this way the calculation of the synchronous and asynchronous
RA-0 reactor. New neutronic calculations; Reactor RA-0. Nuevos calculos neutronicos
Energy Technology Data Exchange (ETDEWEB)
Rumis, D; Leszczynski, F
1991-12-31
An updating of the neutronic calculations performed at the RA-0 reactor, located at the Natural, Physical and Exact Sciences Faculty of Cordoba National University, are herein described. The techniques used for the calculation of a reactor like the RA-0 allows prediction in detail of the flux behaviour in the core`s interior and in the reflector, which will be helpful for experiments design. In particular, the use of WIMSD4 code to make calculations on the reactor implies a novelty in the possible applications of this code to solve the problems that arise in practice. (Author). [Espanol] En este trabajo se actualizan los calculos neutronicos realizados para el reactor RA-0, instalado en la Facultad de Ciencias Exactas, Fisicas y Naturales de la Universidad Nacional de Cordoba. Se describen los calculos realizados hasta la fecha y los resultados obtenidos. Las tecnicas incorporadas al calculo de un reactor como el RA-0 permiten predecir en detalle el comportamiento del flujo en el interior del nucleo y en el reflector, lo que sera una importante ayuda en el diseno de experimentos. En particular, el empleo del codigo WIMSD4 para calculos del reactor completo constituye una novedad en las posibles aplicaciones de ese codigo para resolver problemas que se presentan en la practica. (Autor).
International Nuclear Information System (INIS)
Ryutov, D. D.; Cohen, R. H.; Rognlien, T. D.; Soukhanovskii, V. A.; Umansky, M. V.
2014-01-01
In the recently published paper “Magnetic geometry and physics of advanced divertors: The X-divertor and the snowflake” [Phys. Plasmas 20, 102507 (2013)], the authors raise interesting and important issues concerning divertor physics and design. However, the paper contains significant errors: (a) The conceptual framework used in it for the evaluation of divertor “quality” is reduced to the assessment of the magnetic field structure in the outer Scrape-Off Layer. This framework is incorrect because processes affecting the pedestal, the private flux region and all of the divertor legs (four, in the case of a snowflake) are an inseparable part of divertor operation. (b) The concept of the divertor index focuses on only one feature of the magnetic field structure and can be quite misleading when applied to divertor design. (c) The suggestion to rename the divertor configurations experimentally realized on NSTX (National Spherical Torus Experiment) and DIII-D (Doublet III-D) from snowflakes to X-divertors is not justified: it is not based on comparison of these configurations with the prototypical X-divertor, and it ignores the fact that the NSTX and DIII-D poloidal magnetic field geometries fit very well into the snowflake “two-null” prescription
Energy Technology Data Exchange (ETDEWEB)
Pereira, Luciano Fabricio Dias
2006-07-01
In this work the magnetic hyperfine field acting on Ce atoms substituting the rare-earths in R Ag compounds (R = Gd e Nd) was studied by means of first-principles electronic structure calculations. The employed method was the Augmented Plane Waves plus local orbitals (APW+lo), embodied in the WIEN2k program, within the framework of the Density Functional Theory (DFT) and with the Generalized Gradient Approximation (GGA) for the exchange and correlation potential. The super-cell approach was utilized in order to simulate for the Ce atoms acting as impurities in the R Ag matrix. In order to improve for correlation effects within the 4f shells, a Hubbard term was added to the DFT Hamiltonian, within a procedure called GGA+U. It was found that the magnetic hyperfine field (MHF) generated by the Ce 4f electron is the main component of the total MHF and that the Ce 4f ground state level is probably a combination of the m{sub l} = -2 and m{sub l} = -1 sub-levels. In addition, the ground-state magnetic structure was determined for Ho Ag and Nd Ag by observing the behavior of the total energy as a function of the lattice volume for several possible magnetic ordering in these compounds, namely, ferromagnetic, and the (0,0,{pi}), ({pi},{pi},0) and (({pi},{pi},{pi}) types of anti-ferromagnetic ordering of rare-earth atoms. It was found that the ground-state magnetic structure is anti-ferromagnetic of type ({pi},{pi},0) for both, the Ho Ag and Nd Ag compounds. The energy difference of the ferromagnetic and antiferromagnetic ordering is very small in the case of the Nd Ag compound. (author)
Iversen, Birger
1992-01-01
Although it arose from purely theoretical considerations of the underlying axioms of geometry, the work of Einstein and Dirac has demonstrated that hyperbolic geometry is a fundamental aspect of modern physics
Energy Technology Data Exchange (ETDEWEB)
Lim-Reinders, S [Sunnybrook Odette Cancer Centre, Toronto (Canada); University of Toronto, Department of Physics (Canada); Keller, B; McCann, C; Sahgal, A; Lee, J; Kim, A [Sunnybrook Odette Cancer Centre, Toronto (Canada); University of Toronto, Department of Radiation Oncology (Canada)
2016-06-15
Purpose: Hypofractionated partial breast irradiation (HPBI) is being used at our clinic to treat inoperable breast cancer patients who have advanced disease. We are investigating how these patients could benefit from being treated in an MRI-linac, where real-time daily MRI tumor imaging and plan adaptation would be possible. As a first step, this study evaluates the dosimetric impact of the magnetic field for different radiation beam geometries on relevant OARs. Methods: Five patients previously treated using HPBI were selected. Six treatment plans were generated for each patient, evaluating three beam geometries (VMAT, IMRT, 3DCRT) with and without B{sub 0}=1.5 T. The Monaco TPS was used with the Elekta MRI-Linac beam model, where the magnetic field is orthogonal to the radiation beam. All plans were re-scaled to the same isocoverage with a prescription of 40Gy/5 to the PTV. Plans were evaluated for the effect of the magnetic field and beam modality on skin V{sub 3} {sub 0}, lung V{sub 2} {sub 0} and mean heart dose. Results: Averaged over all patients, skin V{sub 3} {sub 0}for 3DCRT was higher than VMAT and IMRT (by +22% and +21%, with B{sub 0}-ON). The magnetic field caused larger increases in skin V{sub 3} {sub 0}for 3DCRT (+8%) than VMAT (+3%) and IMRT (+4%) compared with B{sub 0}-OFF. With B{sub 0}-ON, 3DCRT had a markedly lower mean heart dose than VMAT (by 538cGy) and IMRT (by 562cGy); for lung V{sub 2} {sub 0}, 3DCRT had a marginally lower dose than VMAT (by −2.2%) and IMRT (also −2.2%). The magnetic field had minimal effect on the mean heart dose and lung V{sub 2} {sub 0} for all geometries. Conclusion: The decreased skin dose in VMAT and IMRT can potentially mitigate the effects of skin reactions for HPBI in an MRI-linac. This study illustrated that more beam angles may result in lower skin toxicity and better tumor conformality, with the trade-off of elevated heart and lung doses. We are receiving funding support from Elekta.
Enoki, Toshiaki; Kiguchi, Manabu
2018-03-01
This paper is a contribution to the Physical Review Applied collection in memory of Mildred S. Dresselhaus. Nanographenes have important edge geometry dependence in their electronic structures. In armchair edges, electron wave interference works to contribute to energetic stability. Meanwhile, zigzag edges possess an edge-localized and spin-polarized nonbonding edge state, which causes electronic, magnetic, and chemical activities. In addition to the geometry dependence, the electronic structures are seriously affected by edge chemistry details. The edge chemistry dependence together with edge geometries on the electronic structures are discussed with samples of randomly networked nanographenes (microporous activated carbon fibers) in pristine state and under high-temperature annealing. In the pristine sample with the edges oxidized in ambient atmospheric conditions, the edge state, which is otherwise unstable, can be stabilized because of the charge transfer from nanographene to terminating oxygen. Nanographene, whose edges consist of a combination of magnetic zigzag edges and nonmagnetic armchair edges, is found to be ferrimagnetic with a nonzero net magnetic moment created under the interplay between a strong intrazigzag-edge ferromagnetic interaction and intermediate-strength interzigzag-edge antiferromagnetic-ferromagnetic interaction. At heat-treatment temperatures just below the fusion start (approximately 1500 K), the edge-terminating structure is changed from oxygen-containing groups to hydrogen in the nanographene network. Additionally, hydrogen-terminated zigzag edges, which are present as the majority and chemically unstable, play a triggering role in fusion above 1500 K. The fusion start brings about an insulator-to-metal transition at TI -M˜1500 K . Local fusions taking place percolatively between nanographenes work to expand the π -bond network, eventually resulting in the development of antiferromagnetic short-range order toward spin glass in the
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.
Kan, Jinglan; Wang, Hailong; Sun, Wei; Cao, Wei; Tao, Jun; Jiang, Jianzhuang
2013-08-05
Employment of the raise-by-one step method starting from M(TClPP)(acac) (acac = monoanion of acetylacetone) and [Pc(OPh)8]M'[Pc(OPh)8] led to the isolation and free modulation of the two rare-earth ions in the series of four mixed tetrapyrrole dysprosium sandwich complexes {(TClPP)M[Pc(OPh)8]M'[Pc(OPh)8]} [1-4; TClPP = dianion of meso-tetrakis(4-chlorophenyl)porphyrin; Pc(OPh)8 = dianion of 2,3,9,10,16,17,23,24-octa(phenoxyl)phthalocyanine; M-M' = Dy-Dy, Y-Dy, Dy-Y, and Y-Y]. Single-crystal X-ray diffraction analysis reveals different octacoordination geometries for the two metal ions in terms of the twist angle (defined as the rotation angle of one coordination square away from the eclipsed conformation with the other) between the two neighboring tetrapyrrole rings for the three dysprosium-containing isostructural triple-decker compounds, with the metal ion locating between an inner phthalocyanine ligand and an outer porphyrin ligand with a twist angle of 9.64-9.90° and the one between two phthalocyanine ligands of 25.12-25.30°. Systematic and comparative studies over the magnetic properties reveal magnetic-field-induced single-molecule magnet (SMM), SMM, and non-SMM nature for 1-3, respectively, indicating the dominant effect of the coordination geometry of the spin carrier, instead of the f-f interaction, on the magnetic properties. The present result will be helpful for the future design and synthesis of tetrapyrrole lanthanide SMMs with sandwich molecular structures.
International Nuclear Information System (INIS)
Reiter, Gert; Reiter, Ursula; Rienmueller, Rainer; Gagarina, Nina; Ryabikin, Alexander
2004-01-01
Objective: Methodological comparison of ellipsoid model-based approaches and Simpson method to evaluate left ventricular volumetric parameters by magnetic resonance (MR) and electron beam tomography (EBT) and analysis of the origin of possible discrepancies. Methods and material: 100 subjects (87 patients, 13 healthy volunteers) were studied in MR in various cardiac views and EBT long axis view to determine left ventricular volumes and masses by applying (rotational) ellipsoid and Simpson model. Observer variation and method agreement was quantified by means of variance component and Bland-Altman analysis. Results: Simpson approach showed smaller observer variability than all ellipsoid approaches. All geometry-based models gave smaller left ventricular volumes than Simpson approach, the bias in mass determination was minimal. Whereas high correlation coefficients (typically 0.85-0.95) for left ventricular volume and mass measurements indicated satisfying correspondence between methods, large 95% limits of agreement made a transfer of results for single subjects between Simpson and ellipsoid approaches difficult and between different geometry-based models almost impossible. Because 95% limits of agreement and observer variability of geometry-based approaches were of equal order, the latter could be identified as main limiting factor of methodological agreement. Conclusion: MR Simpson approach is superior to all ellipsoid model-based approaches, because observer variability is smaller
International Nuclear Information System (INIS)
Bakshi, P.; Kalman, G.
1976-02-01
A new approach for the solution of the Vlasov equation for complex magnetic field geometries has been developed using operator techniques. The general approach is illustrated by determining the perturbed distribution function and density operator for the problem of shear stabilization of drift waves for transverse and arbitrary directions of propagation. The ensuing corrections to stability criteria of current theories are obtained for certain domains of physical parameters. Preliminary work on the integral equation approach to the dispersion relation has been initiated. As a prelude to the study of particle orbits in complex mirror geometries, the adiabatic and non-adiabatic behavior of a harmonic oscillator has been studied using operator methods. High-β, high shear plasma sheath configurations have been studied with the full ion dynamics taken into account and electrons treated in the zero and first order approximation, in the ratio of the electron Larmor radius to the scale length. The resulting sheath structure equation in the lowest order approximation has been solved for certain entering ion distributions, and prepared for computer analysis for others. In this approximation the electron current parallel to magnetic field lines has to be assumed suppressed or predetermined. Equations in the next order approximation include the finite Larmor radius stress tensor. This equation is under study
Energy Technology Data Exchange (ETDEWEB)
Maruyama, R., E-mail: ryuji.maruyama@j-parc.jp [J-PARC Center, Japan Atomic Energy Agency, 2-4 Shirakata Shirane, Tokai, Ibaraki 319-1195 (Japan); Bigault, T.; Wildes, A.R.; Dewhurst, C.D. [Institut Laue Langevin, 71 avenue des Martyrs, 38042 Grenoble (France); Soyama, K. [J-PARC Center, Japan Atomic Energy Agency, 2-4 Shirakata Shirane, Tokai, Ibaraki 319-1195 (Japan); Courtois, P. [Institut Laue Langevin, 71 avenue des Martyrs, 38042 Grenoble (France)
2016-05-21
The in-plane magnetic structure of a layered system with a polycrystalline grain size less than the ferromagnetic exchange length was investigated using polarized neutron off-specular scattering and grazing incidence small angle scattering measurements to gain insight into the mechanism that controls the magnetic properties which are different from the bulk. These complementary measurements with different length scales and the data analysis based on the distorted wave Born approximation revealed the lateral correlation on a length scale of sub- μm due to the fluctuating orientation of the magnetization in the layer. The obtained in-plane magnetic structure is consistent with the random anisotropy model, i.e. competition between the exchange interactions between neighboring spins and the local magnetocrystalline anisotropy.
International Nuclear Information System (INIS)
Anderson, D.V.; Breazeal, J.; Finan, C.H.; Johnston, B.M.
1976-01-01
ABCXYZ is a computer code for obtaining the Cartesian components of the vector potential and the magnetic field on an observed grid from an arrangement of current-carrying wires. Arbitrary combinations of straight line segments, arcs, and loops are allowed in the specification of the currents. Arbitrary positions and orientations of the current-carrying elements are also allowed. Specification of the wire diameter permits the computation of well-defined fields, even in the interiors of the conductors. An optical feature generates magnetic field lines. Extensive graphical and printed output is available to the user including contour, grid-line, and field-line plots. 12 figures, 1 table
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
Luna, M.; Diaz, A. J.; Oliver, R.; Terradas, J.; Karpen, J.
2016-01-01
Solar prominences are subject to both field-aligned (longitudinal) and transverse oscillatory motions, as evidenced by an increasing number of observations. Large-amplitude longitudinal motions provide valuable information on the geometry of the filament channel magnetic structure that supports the cool prominence plasma against gravity. Our pendulum model, in which the restoring force is the gravity projected along the dipped field lines of the magnetic structure, best explains these oscillations. However, several factors can influence the longitudinal oscillations, potentially invalidating the pendulum model. Aims. The aim of this work is to study the influence of large-scale variations in the magnetic field strength along the field lines, i.e., variations of the cross-sectional area along the flux tubes supporting prominence threads. Methods. We studied the normal modes of several flux tube configurations, using linear perturbation analysis, to assess the influence of different geometrical parameters on the oscillation properties. Results. We found that the influence of the symmetric and asymmetric expansion factors on longitudinal oscillations is small.Conclusions. We conclude that the longitudinal oscillations are not significantly influenced by variations of the cross-section of the flux tubes, validating the pendulum model in this context.
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
Energy Technology Data Exchange (ETDEWEB)
Kallinikos, N.; Isliker, H.; Vlahos, L.; Meletlidou, E. [Department of Physics, Aristotle University of Thessaloniki, GR-54124 Thessaloniki (Greece)
2014-06-15
An analytical description of magnetic islands is presented for the typical case of a single perturbation mode introduced to tokamak plasma equilibrium in the large aspect ratio approximation. Following the Hamiltonian structure directly in terms of toroidal coordinates, the well known integrability of this system is exploited, laying out a precise and practical way for determining the island topology features, as required in various applications, through an analytical and exact flux surface label.
Kallinikos, N.; Isliker, H.; Vlahos, L.; Meletlidou, E.
2014-06-01
An analytical description of magnetic islands is presented for the typical case of a single perturbation mode introduced to tokamak plasma equilibrium in the large aspect ratio approximation. Following the Hamiltonian structure directly in terms of toroidal coordinates, the well known integrability of this system is exploited, laying out a precise and practical way for determining the island topology features, as required in various applications, through an analytical and exact flux surface label.
International Nuclear Information System (INIS)
Kallinikos, N.; Isliker, H.; Vlahos, L.; Meletlidou, E.
2014-01-01
An analytical description of magnetic islands is presented for the typical case of a single perturbation mode introduced to tokamak plasma equilibrium in the large aspect ratio approximation. Following the Hamiltonian structure directly in terms of toroidal coordinates, the well known integrability of this system is exploited, laying out a precise and practical way for determining the island topology features, as required in various applications, through an analytical and exact flux surface label
Rotation, spectral variability, magnetic geometry and magnetosphere of the Of?p star CPD -28° 2561
Wade, G. A.; Barba, R. H.; Grunhut, J.; Martins, F.; Petit, V.; Sundqvist, J. O.; Townsend, R. H. D.; Walborn, N. R.; Alecian, E.; Alfaro, E. J.; Maíz Apellaniz, J; Arias, Julia Ines; Gamen, Roberto Claudio; Morrell, Nidia Irene; Naze, Y.
2017-01-01
We report magnetic and spectroscopic observations and modelling of the Of?p star CPD −28° 2561. Using more than 75 new spectra, we have measured the equivalent width variations and examined the dynamic spectra of photospheric and wind-sensitive spectral lines. A period search results in an unambiguous 73.41 d variability period. High-resolution spectropolarimetric data analysed using least-squares deconvolution yield a Zeeman signature detected in the mean Stokes V profile corresponding to ph...
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.)
Directory of Open Access Journals (Sweden)
S. Dubyagin
2013-03-01
Full Text Available We present the results of a coordinated study of the moderate magnetic storm on 22 July 2009. The THEMIS and GOES observations of magnetic field in the inner magnetosphere were complemented by energetic particle observations at low altitude by the six NOAA POES satellites. Observations in the vicinity of geosynchronous orbit revealed a relatively thin (half-thickness of less than 1 RE and intense current sheet in the dusk MLT sector during the main phase of the storm. The total westward current (integrated along the z-direction on the duskside at r ~ 6.6 RE was comparable to that in the midnight sector. Such a configuration cannot be adequately described by existing magnetic field models with predefined current systems (error in B > 60 nT. At the same time, low-altitude isotropic boundaries (IB of > 80 keV protons in the dusk sector were shifted ~ 4° equatorward relative to the IBs in the midnight sector. Both the equatorward IB shift and the current strength on the duskside correlate with the Sym-H* index. These findings imply a close relation between the current intensification and equatorward IB shift in the dusk sector. The analysis of IB dispersion revealed that high-energy IBs (E > 100 keV always exhibit normal dispersion (i.e., that for pitch angle scattering on curved field lines. Anomalous dispersion is sometimes observed in the low-energy channels (~ 30–100 keV. The maximum occurrence rate of anomalous dispersion was observed during the main phase of the storm in the dusk sector.
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.
International Nuclear Information System (INIS)
Reynolds, J. M.; Lopez-Bruna, D.
2009-01-01
This report is the first of a series dedicated to the numerical calculation of the evolution of fusion plasmas in general toroidal geometry, including TJ-II plasmas. A kinetic treatment has been chosen: the evolution equation of the distribution function of one or several plasma species is solved in guiding center coordinates. The distribution function is written as a Maxwellian one modulated by polynomial series in the kinetic coordinates with no other approximations than those of the guiding center itself and the computation capabilities. The code allows also for the inclusion of the three-dimensional electrostatic potential in a self-consistent manner, but the initial objective has been set to solving only the neoclassical transport. A high order conservative method (Spectral Difference Method) has been chosen in order to discretized the equation for its numerical solution. In this first report, in addition to justifying the work, the evolution equation and its approximations are described, as well as the baseline of the numerical procedures. (Author) 28 refs
Maor, Eli
2014-01-01
If you've ever thought that mathematics and art don't mix, this stunning visual history of geometry will change your mind. As much a work of art as a book about mathematics, Beautiful Geometry presents more than sixty exquisite color plates illustrating a wide range of geometric patterns and theorems, accompanied by brief accounts of the fascinating history and people behind each. With artwork by Swiss artist Eugen Jost and text by acclaimed math historian Eli Maor, this unique celebration of geometry covers numerous subjects, from straightedge-and-compass constructions to intriguing configur
Energy Technology Data Exchange (ETDEWEB)
Lusche, Robert; Semenov, Alexey; Huebers, Heinz-Willhelm [DLR, Institut fuer Planetenforschung, Berlin (Germany); Ilin, Konstantin; Siegel, Michael [Karlsruher Institut fuer Technologie (Germany); Korneeva, Yuliya; Trifonov, Andrey; Korneev, Alexander; Goltsman, Gregory [Moscow State Pedagogical University (Russian Federation)
2013-07-01
The interest in single-photon detectors in the near-infrared wavelength regime for applications, e.g. in quantum cryptography has immensely increased in the last years. Superconducting nanowire single-photon detectors (SNSPD) already show quite reasonable detection efficiencies in the NIR which can even be further improved. Novel theoretical approaches including vortex-assisted photon counting state that the detection efficiency in the long wavelength region can be enhanced by the detector geometry and an applied magnetic field. We present spectral measurements in the wavelength range from 350-2500 nm of the detection efficiency of meander-type TaN and NbN SNSPD with varying nanowire line width from 80 to 250 nm. Due to the used experimental setup we can accurately normalize the measured spectra and are able to extract the intrinsic detection efficiency (IDE) of our detectors. The results clearly indicate an improvement of the IDE depending on the wire width according to the theoretic models. Furthermore we experimentally found that the smallest detectable photon-flux can be increased by applying a small magnetic field to the detectors.
Kemnitz, Arnfried
Der Grundgedanke der Analytischen Geometrie besteht darin, dass geometrische Untersuchungen mit rechnerischen Mitteln geführt werden. Geometrische Objekte werden dabei durch Gleichungen beschrieben und mit algebraischen Methoden untersucht.
Lefschetz, Solomon
2005-01-01
An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this text for advanced undergraduate students is particularly relevant to those more familiar with analysis than algebra. 1953 edition.
Ay, Nihat; Lê, Hông Vân; Schwachhöfer, Lorenz
2017-01-01
The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemannian geometry and Banach space theory. Parametrised measure models are defined as fundamental geometric objects, which can be both finite or infinite dimensional. Based on these models, canonical tensor fields are introduced and further studied, including the Fisher metric and the Amari-Chentsov tensor, and embeddings of statistical manifolds are investigated. This novel foundation then leads to application highlights, such as generalizations and extensions of the classical uniqueness result of Chentsov or the Cramér-Rao inequality. Additionally, several new application fields of information geometry are highlighted, for instance hierarchical and graphical models, complexity theory, population genetics, or Markov Chain Monte Carlo. The book will be of interest to mathematicians who are interested in geometry, inf...
Knypiński, Łukasz
2017-12-01
In this paper an algorithm for the optimization of excitation system of line-start permanent magnet synchronous motors will be presented. For the basis of this algorithm, software was developed in the Borland Delphi environment. The software consists of two independent modules: an optimization solver, and a module including the mathematical model of a synchronous motor with a self-start ability. The optimization module contains the bat algorithm procedure. The mathematical model of the motor has been developed in an Ansys Maxwell environment. In order to determine the functional parameters of the motor, additional scripts in Visual Basic language were developed. Selected results of the optimization calculation are presented and compared with results for the particle swarm optimization algorithm.
Energy Technology Data Exchange (ETDEWEB)
Portela, Carlos M. [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia (COPPE); Moreno O, German [Antioquia Univ., Medellin (Colombia). Dept. de Engenharia Eletrica
1995-12-31
The optimization of overhead electric power transmission lines leads to compact projects in which the neighbourhood electric and magnetic field are a critical restriction. The Load Simulation Method enables the reliable calculation of such fields. Presented are equations for the application of such conditions. Results are presented 9 figs., 2 tabs., 10 refs.
Calculo de la Barra Antivuelco de un Vehículo Automotor.
Directory of Open Access Journals (Sweden)
Javier García de la Figal
2005-09-01
Full Text Available El presente trabajo trata acerca del calculo de la barra antivuelco del FORD modelo A, desarrollado por elInstituto de Desarrollo Automotriz, IDA, teniendo en cuenta las fuerzas que la cinta de seguridad de losautomovilistas, ejerce sobre la citada barra, ante un choque que provoca una aceleración de 20 g en elvehículo. El calculo se hace mediante la confección de un modelo de elementos finitos de la barra y lacarrocería, para lo cual se hace uso de un programa profesional de elementos finitos.Se determinan los esfuerzos máximos y los equivalentes, tanto de las partes metálicas del sistema, queson fundamentalmente tubos de acero, como de las partes de material compuesto (poliéster con fibras devidrio E, propios de la carrocería del vehículo. Todo lo cual permite hacer los cálculos y comprobacionesa resistencia de todo el conjunto. Así mismo, se determinan los desplazamientos en todos los sentidos detodos las partes del sistema, para poder realizar los correspondientes análisis de rigidez.El objetivo final de todos los análisis es determinar lo adecuado o no de las soluciones y materialespropuestos para el sistema, bajo la acción de la citada carga de impacto.
DEFF Research Database (Denmark)
Ade, P. A. R.; Aghanim, N.; Alves, M. I. R.
2016-01-01
of the filaments and therefore to provide insight into the structure of their magnetic field (B). We present the polarization maps of three nearby (several parsecs long) star-forming filaments of moderate column density (N-H about 1022 cm-2): Musca, B211, and L1506. These three filaments are detected above...... angles in the three filaments (ψfil) are coherent along their lengths and not the same as in their backgrounds (ψbg). The differences between ψfil and ψbg are 12 degrees and 54 degrees for Musca and L1506, respectively, and only 6 degrees in the case of B211. These differences for Musca and L1506...... (by, e. g., radiative torques) and the structure of the B-field in causing variations in p, but we argue that the decrease in p from the backgrounds to the filaments results in part from depolarization associated with the 3D structure of the B-field: both its orientation in the POS and with respect...
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
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.
Mochalskyy, S.; Wünderlich, D.; Ruf, B.; Franzen, P.; Fantz, U.; Minea, T.
2014-02-01
Decreasing the co-extracted electron current while simultaneously keeping negative ion (NI) current sufficiently high is a crucial issue on the development plasma source system for ITER Neutral Beam Injector. To support finding the best extraction conditions the 3D Particle-in-Cell Monte Carlo Collision electrostatic code ONIX (Orsay Negative Ion eXtraction) has been developed. Close collaboration with experiments and other numerical models allows performing realistic simulations with relevant input parameters: plasma properties, geometry of the extraction aperture, full 3D magnetic field map, etc. For the first time ONIX has been benchmarked with commercial positive ions tracing code KOBRA3D. A very good agreement in terms of the meniscus position and depth has been found. Simulation of NI extraction with different e/NI ratio in bulk plasma shows high relevance of the direct negative ion extraction from the surface produced NI in order to obtain extracted NI current as in the experimental results from BATMAN testbed.
CBM RICH geometry optimization
Energy Technology Data Exchange (ETDEWEB)
Mahmoud, Tariq; Hoehne, Claudia [II. Physikalisches Institut, Giessen Univ. (Germany); Collaboration: CBM-Collaboration
2016-07-01
The Compressed Baryonic Matter (CBM) experiment at the future FAIR complex will investigate the phase diagram of strongly interacting matter at high baryon density and moderate temperatures in A+A collisions from 2-11 AGeV (SIS100) beam energy. The main electron identification detector in the CBM experiment will be a RICH detector with a CO{sub 2} gaseous-radiator, focusing spherical glass mirrors, and MAPMT photo-detectors being placed on a PMT-plane. The RICH detector is located directly behind the CBM dipole magnet. As the final magnet geometry is now available, some changes in the RICH geometry become necessary. In order to guarantee a magnetic field of 1 mT at maximum in the PMT plane for effective operation of the MAPMTs, two measures have to be taken: The PMT plane is moved outwards of the stray field by tilting the mirrors by 10 degrees and shielding boxes have been designed. In this contribution the results of the geometry optimization procedure are presented.
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.)
Dosimetry in intravascular brachytherapy; Calculos dosimetricos em braquiterapia intravascular
Energy Technology Data Exchange (ETDEWEB)
Campos, Laelia Pumilla Botelho
2000-03-01
Among the cardiovascular diseases responsible for deaths in the adult population in almost all countries of the world, the most common is acute myocardial infarction, which generally occurs because of the occlusion of one or more coronary arteries. Several diagnostic techniques and therapies are being tested for the treatment of coronary artery disease. Balloon angioplasty has been a popular treatment which is less invasive than traditional surgeries involving revascularization of the myocardium, thus promising a better quality of life for patients. Unfortunately, the rate of restenosis (re-closing of the vessel) after balloon angioplasty is high (approximately 30-50% within the first year after treatment).Recently, the idea of delivering high radiation doses to coronary arteries to avoid or delay restenosis has been suggested. Known as intravascular brachytherapy, the technique has been used with several radiation sources, and researchers have obtained success in decreasing the rate of restenosis in some patient populations. In order to study the radiation dosimetry in the patient and radiological protection for the attending staff for this therapy, radiation dose distributions for monoenergetic electrons and photons (at nine discrete energies) were calculated for blood vessels of diameter 0.15, o,30 and 0.45 cm with balloon and wire sources using the radiation transport code MCNP4B. Specific calculations were carried out for several candidate radionuclides as well. Two s tent sources (metallic prosthesis that put inside of patient's artery through angioplasty) employing {sup 32} P are also simulated. Advantages and disadvantages of the various radionuclides and source geometries are discussed. The dosimetry developed here will aid in the realization of the benefits obtained in patients for this promising new technology. (author)
Dosimetry in intravascular brachytherapy; Calculos dosimetricos em braquiterapia intravascular
Energy Technology Data Exchange (ETDEWEB)
Campos, Laelia Pumilla Botelho
2000-03-01
Among the cardiovascular diseases responsible for deaths in the adult population in almost all countries of the world, the most common is acute myocardial infarction, which generally occurs because of the occlusion of one or more coronary arteries. Several diagnostic techniques and therapies are being tested for the treatment of coronary artery disease. Balloon angioplasty has been a popular treatment which is less invasive than traditional surgeries involving revascularization of the myocardium, thus promising a better quality of life for patients. Unfortunately, the rate of restenosis (re-closing of the vessel) after balloon angioplasty is high (approximately 30-50% within the first year after treatment).Recently, the idea of delivering high radiation doses to coronary arteries to avoid or delay restenosis has been suggested. Known as intravascular brachytherapy, the technique has been used with several radiation sources, and researchers have obtained success in decreasing the rate of restenosis in some patient populations. In order to study the radiation dosimetry in the patient and radiological protection for the attending staff for this therapy, radiation dose distributions for monoenergetic electrons and photons (at nine discrete energies) were calculated for blood vessels of diameter 0.15, o,30 and 0.45 cm with balloon and wire sources using the radiation transport code MCNP4B. Specific calculations were carried out for several candidate radionuclides as well. Two s tent sources (metallic prosthesis that put inside of patient's artery through angioplasty) employing {sup 32} P are also simulated. Advantages and disadvantages of the various radionuclides and source geometries are discussed. The dosimetry developed here will aid in the realization of the benefits obtained in patients for this promising new technology. (author)
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)
Lasry, J [Commissariat a l' Energie Atomique, Fontenay-aux-Roses (France). Centre d' Etudes Nucleaires
1967-06-15
An hydrogen plasma puff is injected along the lines of a magnetic field with a double curvature geometry. The plasma is produced by a coaxial gun with an annular preionization system. It is shown theoretically that the electric drift of the plasma can be cancelled if a depolarizing current flows along the field lines towards a region of good transverse conductivity. The experiment shows that in these conditions the curvature drift of the ions of the plasma may be used as a very efficient process to purify the fast component of the plasma puff. The depolarizing electron currents are measured and the mutual cancellation of the electric fields developing into the oppositely curved region is demonstrated to be possible. The current densities agree with the values deduced of the curvature drift of the ions. (author) [French] Un plasma d'hydrogene est injecte le long des lignes de force d'un champ magnetique a double courbure. Le plasma est produit par un canon coaxial a preionisation annulaire. Il est montre theoriquement que la derive electrique du plasma peut etre annulee si un courant de depolarisation circule le long des lignes de force vers une region de conductivite transversale elevee. L'experience montre que dans ces conditions, la derive de courbure des ions peut etre utilisee comme un moyen efficace de purification de la composante rapide du plasma. Les courants electroniques de depolarisation sont mesures et l'annulation mutuelle des champs electriques se developpant dans les regions de courbures opposees est demontree. Les densites de courant sont en accord avec les valeurs deduites de la derive de courbure des ions. (auteur)
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)
Silvestre, Larissa Jacome Barros
2016-07-01
Nuclear accidents in the world led to the establishment of rigorous criteria and requirements for nuclear power plant operations by the international regulatory bodies. By using specific computer programs, simulations of various accidents and transients likely to occur at any nuclear power plant are required for certifying and licensing a nuclear power plant. Based on this scenario, some sophisticated computational tools have been used such as the Reactor Excursion and Leak Analysis Program (RELAP5), which is the most widely used code for the thermo-hydraulic analysis of accidents and transients in nuclear reactors in Brazil and worldwide. A major difficulty in the simulation by using RELAP5 code is the amount of information required for the simulation of thermal-hydraulic accidents or transients. The preparation of the input data requires a great number of mathematical operations to calculate the geometry of the components. Thus, for those calculations performance and preparation of RELAP5 input data, a friendly mathematical preprocessor was designed. The Visual Basic for Application (VBA) for Microsoft Excel demonstrated to be an effective tool to perform a number of tasks in the development of the program. In order to meet the needs of RELAP5 users, the RELAP5 Calculation Program (Programa de Calculo do RELAP5 - PCRELAP5) was designed. The components of the code were codified; all entry cards including the optional cards of each one have been programmed. In addition, an English version for PCRELAP5 was provided. Furthermore, a friendly design was developed in order to minimize the time of preparation of input data and errors committed by users. In this work, the final version of this preprocessor was successfully applied for Safety Injection System (SIS) of Angra 2. (author)
Energy Technology Data Exchange (ETDEWEB)
Franco, David; Ambriz, Juan Jose; Romero Paredes, Hernando [Universidad Autonoma Metropolitana-Iztapalapa, Mexico, D. F. (Mexico)
1994-12-31
The efficiency calculation of steam generators is not always simple. The purpose of this paper is to propose an algorithm for the calculation of steam generators efficiency, easy to understand and carry out, in the form of a series of steps to be followed. It takes as starting point that the person in charge of applying these calculations has knowledge of the combustion processes and thermodynamic principles that rule such processes. [Espanol] El calculo de la eficiencia de los generadores de vapor no siempre es sencillo, el presente trabajo tiene como objetivo el de proponer un algoritmo de calculo de eficiencia de generadores de vapor, el cual sea facil de entender y de llevar a cabo, en forma de una serie de pasos a seguir. Se toma como punto de partida, que la persona encargada de aplicar estos calculos tenga el conocimiento de los procesos de combustion y principios termodinamicos que rigen tales procesos.
Mekki, J; Dusseau, Laurent; Roche, Nicolas Jean-Henri; Saigne, Frederic; Mekki, Julien; Glaser, Maurice
2010-01-01
Aiming at evaluating new options for radiation monitoring sensors in LHC/SLHC experiments, the radiation responses of FZ and MCz custom made silicon detectors of different geometry have been studied up to about 4 x 10(14) n(eq)/cm(2). The radiation response of the devices under investigation is discussed in terms of material type, thickness and active area influence.
An experimental study of passive regenerator geometries
DEFF Research Database (Denmark)
Engelbrecht, Kurt; Nielsen, Kaspar Kirstein; Pryds, Nini
2011-01-01
Active magnetic regenerative (AMR) systems are being investigated because they represent a potentially attractive alternative to vapor compression technology. The performance of these systems is dependent on the heat transfer and pressure drop performance of the regenerator geometry. Therefore th...
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.
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
International Nuclear Information System (INIS)
Young, I.R.
1984-01-01
A magnet pole piece for an NMR imaging magnet is made of a plurality of magnetic wires with one end of each wire held in a non-magnetic spacer, the other ends of the wires being brought to a pinch, and connected to a magnetic core. The wires may be embedded in a synthetic resin and the magnetisation and uniformity thereof can be varied by adjusting the density of the wires at the spacer which forms the pole piece. (author)
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
DEFF Research Database (Denmark)
Batra, Tushar; Schaltz, Erik; Ahn, Seungyoung
2014-01-01
Magnetic fields emitted by wireless power transfer to vehicles can potentially affect living organisms. As a result, minimizing the magnetic emissions without compromising with the power transferred is one of the most significant challenges in the success of this technology. Active and passive...... and secondary currents from the standard design. Therefore, a part of the secondary magnetic flux comes in phase opposition with the primary flux and the resultant field is reduced. Operation point is shifted with the new design from the maximum power transfer resonance point and hence the reflected resistance...... is reduced. In order to maintain the same power level, the primary current and voltage have to increased and decreased in the same proportion. Also, the primary capacitor needs to be increased for maintaining unity input power factor in the system. The above statements are provided first with help...
Magnetoelectrostatic thruster physical geometry tests
Ramsey, W. D.
1981-01-01
Inert gas tests are conducted with several magnetoelectrostatic containment discharge chamber geometries. The configurations tested include three discharge chamber lengths; three boundary magnet patterns; two different flux density magnet materials; hemispherical and conical shaped thrusters having different surface-to-volume ratios; and two and three grid ion optics. Argon mass utilizations of 60 to 79% are attained at 210 to 280 eV/ion in different test configurations. Short hemi thruster configurations are found to produce 70 to 92% xenon mass utilization at 185 to 220 eV/ion.
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
DEFF Research Database (Denmark)
Batra, Tushar; Schaltz, Erik
2014-01-01
Magnetic fields in surroundings of wireless power transfer system depends upon the two coil currents, distance from the coils and space angle between the two coil fields in steady state conditions. Increase in value of the secondary capacitor leads to a phase shift between the two currents and as...
International Nuclear Information System (INIS)
Zhang Zhao-Fu; Zhou Tie-Ge; Zhao Hai-Yang; Wei Xiang-Lei
2014-01-01
The geometry, electronic structure and magnetic property of the hexagonal AlN (h-AlN) sheet doped by 5d atoms (Lu, Hf, Ta, W, Re, Os, Ir, Pt, Au and Hg) are investigated by first-principles calculations based on the density functional theory. The influence of symmetry and symmetry-breaking is also studied. There are two types of local symmetries of the doped systems: C 3v and D 3h . The symmetry will deviate from exact C 3v and D 3h for some particular dopants after optimization. The total magnetic moments of the doped systems are 0μ B for Lu, Ta and Ir; 1μ B for Hf, W, Pt and Hg; 2μ B for Re and Au; and 3μ B for Os and Al-vacancy. The total densities of state are presented, where impurity energy levels exist. The impurity energy levels and total magnetic moments can be explained by the splitting of 5d orbitals or molecular orbitals under different symmetries. (condensed matter: structural, mechanical, and thermal properties)
Denton, R.; Sonnerup, B. U. O.; Swisdak, M.; Birn, J.; Drake, J. F.; Heese, M.
2012-01-01
When analyzing data from an array of spacecraft (such as Cluster or MMS) crossing a site of magnetic reconnection, it is desirable to be able to accurately determine the orientation of the reconnection site. If the reconnection is quasi-two dimensional, there are three key directions, the direction of maximum inhomogeneity (the direction across the reconnection site), the direction of the reconnecting component of the magnetic field, and the direction of rough invariance (the "out of plane" direction). Using simulated spacecraft observations of magnetic reconnection in the geomagnetic tail, we extend our previous tests of the direction-finding method developed by Shi et al. (2005) and the method to determine the structure velocity relative to the spacecraft Vstr. These methods require data from four proximate spacecraft. We add artificial noise and calibration errors to the simulation fields, and then use the perturbed gradient of the magnetic field B and perturbed time derivative dB/dt, as described by Denton et al. (2010). Three new simulations are examined: a weakly three-dimensional, i.e., quasi-two-dimensional, MHD simulation without a guide field, a quasi-two-dimensional MHD simulation with a guide field, and a two-dimensional full dynamics kinetic simulation with inherent noise so that the apparent minimum gradient was not exactly zero, even without added artificial errors. We also examined variations of the spacecraft trajectory for the kinetic simulation. The accuracy of the directions found varied depending on the simulation and spacecraft trajectory, but all the directions could be found within about 10 for all cases. Various aspects of the method were examined, including how to choose averaging intervals and the best intervals for determining the directions and velocity. For the kinetic simulation, we also investigated in detail how the errors in the inferred gradient directions from the unmodified Shi et al. method (using the unperturbed gradient
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
Energy Technology Data Exchange (ETDEWEB)
Brumovska, Eva [University of South Bohemia and Biology Centre AS CR v.v.i., Faculty of Science (Czech Republic); Sychrovsky, Vladimir; Vokacova, Zuzana [Institute of Organic Chemistry and Biochemistry, AS CR v.v.i. (Czech Republic); Sponer, Jiri [Institute of Biophysics, AS CR v.v.i. (Czech Republic); Schneider, Bohdan [Biotechnological Institute AS CR (Czech Republic); Trantirek, Lukas [University of South Bohemia and Biology Centre AS CR v.v.i., Faculty of Science (Czech Republic)], E-mail: trant@paru.cas.cz
2008-11-15
Density functional theory was employed to study the dependence of {sup 13}C and {sup 15}N magnetic shielding tensors on the glycosidic torsion angle ({chi}) and conformation of the sugar ring in 2'-deoxyadenosine, 2'-deoxyguanosine, 2'-deoxycytidine, and 2'-deoxythymidine. In general, the magnetic shielding of the glycosidic nitrogens and the sugar carbons was found to depend on both the conformation of the sugar ring and {chi}. Our calculations indicate that the magnetic shielding anisotropy of the C6 atom in pyrimidine and the C8 atom in purine bases depends strongly on {chi}. The remaining base carbons were found to be insensitive to both sugar pucker and {chi} re-orientation. These results call into question the underlying assumptions of currently established methods for interpreting residual chemical shift anisotropies and {sup 13}C and {sup 15}N auto- and cross-correlated relaxation rates and highlight possible limitations of DNA applications of these methods.
Auluck, S. K. H.
2017-11-01
This paper continues earlier discussion [S. K. H. Auluck, Phys. Plasmas 21, 102515 (2014)] concerning the formulation of conservation laws of mass, momentum, and energy in a local curvilinear coordinate system in the dense plasma focus. This formulation makes use of the revised Gratton-Vargas snowplow model [S. K. H. Auluck, Phys. Plasmas 20, 112501 (2013)], which provides an analytically defined imaginary surface in three dimensions which resembles the experimentally determined shape of the plasma. Unit vectors along the local tangent to this surface, along the azimuth, and along the local normal define a right-handed orthogonal local curvilinear coordinate system. The simplifying assumption that physical quantities have significant variation only along the normal enables writing laws of conservation of mass, momentum, and energy in the form of effectively one-dimensional hyperbolic conservation law equations using expressions for various differential operators derived for this coordinate system. This formulation demonstrates the highly non-trivial result that the axial magnetic field and toroidally streaming fast ions, experimentally observed by multiple prestigious laboratories, are natural consequences of conservation of mass, momentum, and energy in the curved geometry of the dense plasma focus current sheath. The present paper continues the discussion in the context of a 3-region shock structure similar to the one experimentally observed: an unperturbed region followed by a hydrodynamic shock containing some current followed by a magnetic piston. Rankine-Hugoniot conditions are derived, and expressions are obtained for the specific volumes and pressures using the mass-flux between the hydrodynamic shock and the magnetic piston and current fraction in the hydrodynamic shock as unknown parameters. For the special case of a magnetic piston that remains continuously in contact with the fluid being pushed, the theory gives closed form algebraic results for the
Czech Academy of Sciences Publication Activity Database
Cahyna, Pavel; Nardon, E.
2011-01-01
Roč. 415, č. 1 (2011), S927-S931 ISSN 0022-3115. [International Conference on Plasma-Surface Interactions in Controlled Fusion Device/19th./. San Diego, 24.05.2010-28.05.2010] R&D Projects: GA MŠk 7G09042; GA MŠk LA08048 Institutional research plan: CEZ:AV0Z20430508 Keywords : tokamaks * ELM control * resonant magnetic perturbations * divertor Subject RIV: BL - Plasma and Gas Discharge Physics Impact factor: 2.052, year: 2011 http://dx.doi.org/10.1016/j.jnucmat.2011.01.117
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)
by B. Curé
2011-01-01
The magnet operation was very satisfactory till the technical stop at the end of the year 2010. The field was ramped down on 5th December 2010, following the successful regeneration test of the turbine filters at full field on 3rd December 2010. This will limit in the future the quantity of magnet cycles, as it is no longer necessary to ramp down the magnet for this type of intervention. This is made possible by the use of the spare liquid Helium volume to cool the magnet while turbines 1 and 2 are stopped, leaving only the third turbine in operation. This obviously requires full availability of the operators to supervise the operation, as it is not automated. The cryogenics was stopped on 6th December 2010 and the magnet was left without cooling until 18th January 2011, when the cryoplant operation resumed. The magnet temperature reached 93 K. The maintenance of the vacuum pumping was done immediately after the magnet stop, when the magnet was still at very low temperature. Only the vacuum pumping of the ma...
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...
Energy Technology Data Exchange (ETDEWEB)
Perez V, Jesus B; Robles G, Saul; Villa M, Hector A; Cabanillas L, Rafael E [Universidad de Sonora, Hermosillo, Sonora (Mexico)
2000-07-01
In this work the development of an interactive software, visible over the World Wide Web, is presented to support the basic calculation required to control the solar gain inside buildings and houses. The site has two main parts: one part describes in a very required parameters to design devices for the control of the illumination inside the buildings, like overhangs and wingwalls for shading. The other part has the routines and procedures to calculate the sun position for any date and position over the earth, and the horizontal and vertical protection angles. The part to implement the calculations has been developed as a Java applet which can run on any platform and let the users, in an interactive way, to get the results. This software makes possible that any Internet user can run the application from his/her own computer without having to compile of use sophisticated procedures as it happens with traditional languages. With this web site it is intended to cover the necessity of having simple and reliable means for architects and civil engineers to support the use of solar energy and the saving of energy in bioclimatic design of buildings. [Spanish] En este trabajo se presenta el desarrollo de un sitio interactivo visible en el World Wide Web (WWW) que pretende servir de apoyo para los calculos basicos de control de asoleamiento en viviendas y edificios. El sitio esta conformado por dos partes principales: una parte cubre el aspecto informativo, donde en forma sencilla y clara, se explican los conceptos y parametros necesarios para disenar los dispositivos de control, alerones y parteluces. La otra parte contiene los procedimientos y las rutinas de calculo para la determinacion de la posicion solar para cualquier fecha del ano desde cualquier punto sobre la tierra, asi como los angulos de sombreado vertical y horizontal. Para la realizacion de los calculos se ha construido un applet de Java, el cual puede ejecutarse desde cualquier plataforma de computacion y
Energy Technology Data Exchange (ETDEWEB)
Kostylev, M., E-mail: mikhail.kostylev@uwa.edu.au [School of Physics, The University of Western Australia, Crawley 6009 (Australia)
2016-01-07
We constructed a quasi-analytical self-consistent model of the stripline-based broadband ferromagnetic resonance (FMR) measurements of ferromagnetic films. Exchange-free description of magnetization dynamics in the films allowed us to obtain simple analytical expressions. They enable quick and efficient numerical simulations of the dynamics. With this model, we studied the contribution of radiation losses to the ferromagnetic resonance linewidth, as measured with the stripline FMR. We found that for films with large conductivity of metals the radiation losses are significantly smaller than for magneto-insulating films. Excitation of microwave eddy currents in these materials contributes to the total microwave impedance of the system. This leads to impedance mismatch with the film environment resulting in decoupling of the film from the environment and, ultimately, to smaller radiation losses. We also show that the radiation losses drop with an increase in the stripline width and when the sample is lifted up from the stripline surface. Hence, in order to eliminate this measurement artefact, one needs to use wide striplines and introduce a spacer between the film and the sample surface. The radiation losses contribution is larger for thicker films.
Benoit Curé
2010-01-01
Operation of the magnet has gone quite smoothly during the first half of this year. The magnet has been at 4.5K for the full period since January. There was an unplanned short stop due to the CERN-wide power outage on May 28th, which caused a slow dump of the magnet. Since this occurred just before a planned technical stop of the LHC, during which access in the experimental cavern was authorized, it was decided to leave the magnet OFF until 2nd June, when magnet was ramped up again to 3.8T. The magnet system experienced a fault also resulting in a slow dump on April 14th. This was triggered by a thermostat on a filter choke in the 20kA DC power converter. The threshold of this thermostat is 65°C. However, no variation in the water-cooling flow rate or temperature was observed. Vibration may have been the root cause of the fault. All the thermostats have been checked, together with the cables, connectors and the read out card. The tightening of the inductance fixations has also been checked. More tem...
B. Curé
2012-01-01
The magnet was energised at the beginning of March 2012 at a low current to check all the MSS safety chains. Then the magnet was ramped up to 3.8 T on 6 March 2012. Unfortunately two days later an unintentional switch OFF of the power converter caused a slow dump. This was due to a misunderstanding of the CCC (CERN Control Centre) concerning the procedure to apply for the CMS converter control according to the beam-mode status at that time. Following this event, the third one since 2009, a discussion was initiated to define possible improvement, not only on software and procedures in the CCC, but also to evaluate the possibility to upgrade the CMS hardware to prevent such discharge from occurring because of incorrect procedure implementations. The magnet operation itself was smooth, and no power cuts took place. As a result, the number of magnetic cycles was reduced to the minimum, with only two full magnetic cycles from 0 T to 3.8 T. Nevertheless the magnet suffered four stops of the cryogeni...
B. Curé
2012-01-01
Following the unexpected magnet stops last August due to sequences of unfortunate events on the services and cryogenics [see CMS internal report], a few more events and initiatives again disrupted the magnet operation. All the magnet parameters stayed at their nominal values during this period without any fault or alarm on the magnet control and safety systems. The magnet was stopped for the September technical stop to allow interventions in the experimental cavern on the detector services. On 1 October, to prepare the transfer of the liquid nitrogen tank on its new location, several control cables had to be removed. One cable was cut mistakenly, causing a digital input card to switch off, resulting in a cold-box (CB) stop. This tank is used for the pre-cooling of the magnet from room temperature down to 80 K, and for this reason it is controlled through the cryogenics control system. Since the connection of the CB was only allowed for a field below 2 T to avoid the risk of triggering a fast d...
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.
Algorithms in Algebraic Geometry
Dickenstein, Alicia; Sommese, Andrew J
2008-01-01
In the last decade, there has been a burgeoning of activity in the design and implementation of algorithms for algebraic geometric computation. Some of these algorithms were originally designed for abstract algebraic geometry, but now are of interest for use in applications and some of these algorithms were originally designed for applications, but now are of interest for use in abstract algebraic geometry. The workshop on Algorithms in Algebraic Geometry that was held in the framework of the IMA Annual Program Year in Applications of Algebraic Geometry by the Institute for Mathematics and Its
O'Leary, Michael
2010-01-01
Guides readers through the development of geometry and basic proof writing using a historical approach to the topic. In an effort to fully appreciate the logic and structure of geometric proofs, Revolutions of Geometry places proofs into the context of geometry's history, helping readers to understand that proof writing is crucial to the job of a mathematician. Written for students and educators of mathematics alike, the book guides readers through the rich history and influential works, from ancient times to the present, behind the development of geometry. As a result, readers are successfull
Fundamental concepts of geometry
Meserve, Bruce E
1983-01-01
Demonstrates relationships between different types of geometry. Provides excellent overview of the foundations and historical evolution of geometrical concepts. Exercises (no solutions). Includes 98 illustrations.
Developments in special geometry
International Nuclear Information System (INIS)
Mohaupt, Thomas; Vaughan, Owen
2012-01-01
We review the special geometry of N = 2 supersymmetric vector and hypermultiplets with emphasis on recent developments and applications. A new formulation of the local c-map based on the Hesse potential and special real coordinates is presented. Other recent developments include the Euclidean version of special geometry, and generalizations of special geometry to non-supersymmetric theories. As applications we discuss the proof that the local r-map and c-map preserve geodesic completeness, and the construction of four- and five-dimensional static solutions through dimensional reduction over time. The shared features of the real, complex and quaternionic version of special geometry are stressed throughout.
B. Curé
2012-01-01
The magnet and its sub-systems were stopped at the beginning of the winter shutdown on 8th December 2011. The magnet was left without cooling during the cryogenics maintenance until 17th January 2012, when the cryoplant operation resumed. The magnet temperature reached 93 K. The vacuum pumping was maintained during this period. During this shutdown, the yearly maintenance was performed on the cryogenics, the vacuum pumps, the magnet control and safety systems, and the power converter and discharge lines. Several preventive actions led to the replacement of the electrovalve command coils, and the 20A DC power supplies of the magnet control system. The filters were cleaned on the demineralised water circuits. The oil of the diffusion pumps was changed. On the cryogenics, warm nitrogen at 343 K was circulated in the cold box to regenerate the filters and the heat exchangers. The coalescing filters have been replaced at the inlet of both the turbines and the lubricant trapping unit. The active cha...
B. Curé
2013-01-01
The magnet was operated without any problem until the end of the LHC run in February 2013, apart from a CERN-wide power glitch on 10 January 2013 that affected the CMS refrigerator, causing a ramp down to 2 T in order to reconnect the coldbox. Another CERN-wide power glitch on 15 January 2013 didn’t affect the magnet subsystems, the cryoplant or the power converter. At the end of the magnet run, the reconnection of the coldbox at 2.5 T was tested. The process will be updated, in particular the parameters of some PID valve controllers. The helium flow of the current leads was reduced but only for a few seconds. The exercise will be repeated with the revised parameters to validate the automatic reconnection process of the coldbox. During LS1, the water-cooling services will be reduced and many interventions are planned on the electrical services. Therefore, the magnet cryogenics and subsystems will be stopped for several months, and the magnet cannot be kept cold. In order to avoid unc...
Benoit Curé
2010-01-01
The magnet was successfully operated at the end of the year 2009 despite some technical problems on the cryogenics. The magnet was ramped up to 3.8 T at the end of November until December 16th when the shutdown started. The magnet operation met a few unexpected stops. The field was reduced to 3.5 T for about 5 hours on December 3rd due to a faulty pressure sensor on the helium compressor. The following day the CERN CCC stopped unintentionally the power converters of the LHC and the experiments, triggering a ramp down that was stopped at 2.7 T. The magnet was back at 3.8 T about 6 hours after CCC sent the CERN-wide command. Three days later, a slow dump was triggered due to a stop of the pump feeding the power converter water-cooling circuit, during an intervention on the water-cooling plant done after several disturbances on the electrical distribution network. The magnet was back at 3.8 T in the evening the same day. On December 10th a break occurred in one turbine of the cold box producing the liquid ...
B. Curé
2011-01-01
The CMS magnet has been running steadily and smoothly since the summer, with no detected flaw. The magnet instrumentation is entirely operational and all the parameters are at their nominal values. Three power cuts on the electrical network affected the magnet run in the past five months, with no impact on the data-taking as the accelerator was also affected at the same time. On 22nd June, a thunderstorm caused a power glitch on the service electrical network. The primary water cooling at Point 5 was stopped. Despite a quick restart of the water cooling, the inlet temperature of the demineralised water on the busbar cooling circuit increased by 5 °C, up to 23.3 °C. It was kept below the threshold of 27 °C by switching off other cooling circuits to avoid the trigger of a slow dump of the magnet. The cold box of the cryogenics also stopped. Part of the spare liquid helium volume was used to maintain the cooling of the magnet at 4.5 K. The operators of the cryogenics quickly restarted ...
International Nuclear Information System (INIS)
Kotschenreuther, Mike; Valanju, Prashant; Covele, Brent; Mahajan, Swadesh
2014-01-01
Relying on coil positions relative to the plasma, the “Comment on ‘Magnetic geometry and physics of advanced divertors: The X-divertor and the snowflake’ ” [Phys. Plasmas 21, 054701 (2014)], emphasizes a criterion for divertor characterization that was critiqued to be ill posed [M. Kotschenreuther et al., Phys. Plasmas 20, 102507 (2013)]. We find that no substantive physical differences flow from this criteria. However, using these criteria, the successful NSTX experiment by Ryutov et al. [Phys. Plasmas 21, 054701 (2014)] has the coil configuration of an X-divertor (XD), rather than a snowflake (SF). On completing the divertor index (DI) versus distance graph for this NSTX shot (which had an inexplicably missing region), we find that the DI is like an XD for most of the outboard wetted divertor plate. Further, the “proximity condition,” used to define an SF [M. Kotschenreuther et al., Phys. Plasmas 20, 102507 (2013)], does not have a substantive physics basis to override metrics based on flux expansion and line length. Finally, if the criteria of the comment are important, then the results of NSTX-like experiments could have questionable applicability to reactors
Energy Technology Data Exchange (ETDEWEB)
Kotschenreuther, Mike; Valanju, Prashant; Covele, Brent; Mahajan, Swadesh [Institute for Fusion Studies, The University of Texas at Austin, Austin, Texas 78712 (United States)
2014-05-15
Relying on coil positions relative to the plasma, the “Comment on ‘Magnetic geometry and physics of advanced divertors: The X-divertor and the snowflake’ ” [Phys. Plasmas 21, 054701 (2014)], emphasizes a criterion for divertor characterization that was critiqued to be ill posed [M. Kotschenreuther et al., Phys. Plasmas 20, 102507 (2013)]. We find that no substantive physical differences flow from this criteria. However, using these criteria, the successful NSTX experiment by Ryutov et al. [Phys. Plasmas 21, 054701 (2014)] has the coil configuration of an X-divertor (XD), rather than a snowflake (SF). On completing the divertor index (DI) versus distance graph for this NSTX shot (which had an inexplicably missing region), we find that the DI is like an XD for most of the outboard wetted divertor plate. Further, the “proximity condition,” used to define an SF [M. Kotschenreuther et al., Phys. Plasmas 20, 102507 (2013)], does not have a substantive physics basis to override metrics based on flux expansion and line length. Finally, if the criteria of the comment are important, then the results of NSTX-like experiments could have questionable applicability to reactors.
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'…
B. Curé
2011-01-01
The magnet ran smoothly in the last few months until a fast dump occurred on 9th May 2011. Fortunately, this occurred in the afternoon of the first day of the technical stop. The fast dump was due to a valve position controller that caused the sudden closure of a valve. This valve is used to regulate the helium flow on one of the two current leads, which electrically connects the coil at 4.5 K to the busbars at room temperature. With no helium flow on the lead, the voltage drop and the temperatures across the leads increase up to the defined thresholds, triggering a fast dump through the Magnet Safety System (MSS). The automatic reaction triggered by the MSS worked properly. The helium release was limited as the pressure rise was just at the limit of the safety valve opening pressure. The average temperature of the magnet reached 72 K. It took four days to recover the temperature and refill the helium volumes. The faulty valve controller was replaced by a spare one before the magnet ramp-up resumed....
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.
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
Methods in nuclear reactors calculations; Metodos de calculo en reactores nucleares
Energy Technology Data Exchange (ETDEWEB)
Velarde, G
1966-07-01
Studies are made of the neutron transport equation corresponding to the the real and virtual reactors, as well as the starting hypotheses. Methods are developed to solve the transport equation in slab geometry, and P{sub l}; B{sub l}; M{sub l}; S{sub n} and discrete ordinates approximations. (Author)
Benoit Curé
2010-01-01
The magnet worked very well at 3.8 T as expected, despite a technical issue that manifested twice in the cryogenics since June. All the other magnet sub-systems worked without flaw. The issue in the cryogenics was with the cold box: it could be observed that the cold box was getting progressively blocked, due to some residual humidity and air accumulating in the first thermal exchanger and in the adsorber at 65 K. This was later confirmed by the analysis during the regeneration phases. An increase in the temperature difference between the helium inlet and outlet across the heat exchanger and a pressure drop increase on the filter of the adsorber were observed. The consequence was a reduction of the helium flow, first compensated by the automatic opening of the regulation valves. But once they were fully opened, the flow and refrigeration power reduced as a consequence. In such a situation, the liquid helium level in the helium Dewar decreased, eventually causing a ramp down of the magnet current and a field...
B. Curé
MAGNET During the winter shutdown, the magnet subsystems went through a full maintenance. The magnet was successfully warmed up to room temperature beginning of December 2008. The vacuum was broken later on by injecting nitrogen at a pressure just above one atmosphere inside the vacuum tank. This was necessary both to prevent any accidental humidity ingress, and to allow for a modification of the vacuum gauges on the vacuum tank and maintenance of the diffusion pumps. The vacuum gauges had to be changed, because of erratic variations on the measurements, causing spurious alarms. The new type of vacuum gauges has been used in similar conditions on the other LHC experiments and without problems. They are shielded against the stray field. The lubricants of the primary and diffusion pumps have been changed. Several minor modifications were also carried out on the equipment in the service cavern, with the aim to ease the maintenance and to allow possible intervention during operation. Spare sensors have been bough...
Benoit Curé.
The magnet operation restarted end of June this year. Quick routine checks of the magnet sub-systems were performed at low current before starting the ramps up to higher field. It appeared clearly that the end of the field ramp down to zero was too long to be compatible with the detector commissioning and operations plans. It was decided to perform an upgrade to keep the ramp down from 3.8T to zero within 4 hours. On July 10th, when a field of 1.5T was reached, small movements were observed in the forward region support table and it was decided to fix this problem before going to higher field. At the end of July the ramps could be resumed. On July 28th, the field was at 3.8T and the summer CRAFT exercise could start. This run in August went smoothly until a general CERN wide power cut took place on August 3rd, due to an insulation fault on the high voltage network outside point 5. It affected the magnet powering electrical circuit, as it caused the opening of the main circuit breakers, resulting in a fast du...
B. Curé
2013-01-01
The magnet is fully stopped and at room temperature. The maintenance works and consolidation activities on the magnet sub-systems are progressing. To consolidate the cryogenic installation, two redundant helium compressors will be installed as ‘hot spares’, to avoid the risk of a magnet downtime in case of a major failure of a compressor unit during operation. The screw compressors, their motors, the mechanical couplings and the concrete blocks are already available and stored at P5. The metallic structure used to access the existing compressors in SH5 will be modified to allow the installation of the two redundant ones. The plan is to finish the installation and commissioning of the hot spare compressors before the summer 2014. In the meantime, a bypass on the high-pressure helium piping will be installed for the connection of a helium drier unit later during the Long Shutdown 1, keeping this installation out of the schedule critical path. A proposal is now being prepared for the con...
Complex and symplectic geometry
Medori, Costantino; Tomassini, Adriano
2017-01-01
This book arises from the INdAM Meeting "Complex and Symplectic Geometry", which was held in Cortona in June 2016. Several leading specialists, including young researchers, in the field of complex and symplectic geometry, present the state of the art of their research on topics such as the cohomology of complex manifolds; analytic techniques in Kähler and non-Kähler geometry; almost-complex and symplectic structures; special structures on complex manifolds; and deformations of complex objects. The work is intended for researchers in these areas.
Kulczycki, Stefan
2008-01-01
This accessible approach features two varieties of proofs: stereometric and planimetric, as well as elementary proofs that employ only the simplest properties of the plane. A short history of geometry precedes a systematic exposition of the principles of non-Euclidean geometry.Starting with fundamental assumptions, the author examines the theorems of Hjelmslev, mapping a plane into a circle, the angle of parallelism and area of a polygon, regular polygons, straight lines and planes in space, and the horosphere. Further development of the theory covers hyperbolic functions, the geometry of suff
Roe, John
2003-01-01
Coarse geometry is the study of spaces (particularly metric spaces) from a 'large scale' point of view, so that two spaces that look the same from a great distance are actually equivalent. This point of view is effective because it is often true that the relevant geometric properties of metric spaces are determined by their coarse geometry. Two examples of important uses of coarse geometry are Gromov's beautiful notion of a hyperbolic group and Mostow's proof of his famous rigidity theorem. The first few chapters of the book provide a general perspective on coarse structures. Even when only metric coarse structures are in view, the abstract framework brings the same simplification as does the passage from epsilons and deltas to open sets when speaking of continuity. The middle section reviews notions of negative curvature and rigidity. Modern interest in large scale geometry derives in large part from Mostow's rigidity theorem and from Gromov's subsequent 'large scale' rendition of the crucial properties of n...
Lectures on Symplectic Geometry
Silva, Ana Cannas
2001-01-01
The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and cl...
Kollár, János
1997-01-01
This volume contains the lectures presented at the third Regional Geometry Institute at Park City in 1993. The lectures provide an introduction to the subject, complex algebraic geometry, making the book suitable as a text for second- and third-year graduate students. The book deals with topics in algebraic geometry where one can reach the level of current research while starting with the basics. Topics covered include the theory of surfaces from the viewpoint of recent higher-dimensional developments, providing an excellent introduction to more advanced topics such as the minimal model program. Also included is an introduction to Hodge theory and intersection homology based on the simple topological ideas of Lefschetz and an overview of the recent interactions between algebraic geometry and theoretical physics, which involve mirror symmetry and string theory.
DEFF Research Database (Denmark)
Kokkendorff, Simon Lyngby
2002-01-01
The subject of this Ph.D.-thesis is somewhere in between continuous and discrete geometry. Chapter 2 treats the geometry of finite point sets in semi-Riemannian hyperquadrics,using a matrix whose entries are a trigonometric function of relative distances in a given point set. The distance...... to the geometry of a simplex in a semi-Riemannian hyperquadric. In chapter 3 we study which finite metric spaces that are realizable in a hyperbolic space in the limit where curvature goes to -∞. We show that such spaces are the so called leaf spaces, the set of degree 1 vertices of weighted trees. We also...... establish results on the limiting geometry of such an isometrically realized leaf space simplex in hyperbolic space, when curvature goes to -∞. Chapter 4 discusses negative type of metric spaces. We give a measure theoretic treatment of this concept and related invariants. The theory developed...
Busemann, Herbert
2005-01-01
A comprehensive approach to qualitative problems in intrinsic differential geometry, this text examines Desarguesian spaces, perpendiculars and parallels, covering spaces, the influence of the sign of the curvature on geodesics, more. 1955 edition. Includes 66 figures.
Tabachnikov, Serge
2005-01-01
Mathematical billiards describe the motion of a mass point in a domain with elastic reflections off the boundary or, equivalently, the behavior of rays of light in a domain with ideally reflecting boundary. From the point of view of differential geometry, the billiard flow is the geodesic flow on a manifold with boundary. This book is devoted to billiards in their relation with differential geometry, classical mechanics, and geometrical optics. The topics covered include variational principles of billiard motion, symplectic geometry of rays of light and integral geometry, existence and nonexistence of caustics, optical properties of conics and quadrics and completely integrable billiards, periodic billiard trajectories, polygonal billiards, mechanisms of chaos in billiard dynamics, and the lesser-known subject of dual (or outer) billiards. The book is based on an advanced undergraduate topics course (but contains more material than can be realistically taught in one semester). Although the minimum prerequisit...
Introduction to tropical geometry
Maclagan, Diane
2015-01-01
Tropical geometry is a combinatorial shadow of algebraic geometry, offering new polyhedral tools to compute invariants of algebraic varieties. It is based on tropical algebra, where the sum of two numbers is their minimum and the product is their sum. This turns polynomials into piecewise-linear functions, and their zero sets into polyhedral complexes. These tropical varieties retain a surprising amount of information about their classical counterparts. Tropical geometry is a young subject that has undergone a rapid development since the beginning of the 21st century. While establishing itself as an area in its own right, deep connections have been made to many branches of pure and applied mathematics. This book offers a self-contained introduction to tropical geometry, suitable as a course text for beginning graduate students. Proofs are provided for the main results, such as the Fundamental Theorem and the Structure Theorem. Numerous examples and explicit computations illustrate the main concepts. Each of t...
Rudiments of algebraic geometry
Jenner, WE
2017-01-01
Aimed at advanced undergraduate students of mathematics, this concise text covers the basics of algebraic geometry. Topics include affine spaces, projective spaces, rational curves, algebraic sets with group structure, more. 1963 edition.
Implosions and hypertoric geometry
DEFF Research Database (Denmark)
Dancer, A.; Kirwan, F.; Swann, A.
2013-01-01
The geometry of the universal hyperkahler implosion for SU (n) is explored. In particular, we show that the universal hyperkahler implosion naturally contains a hypertoric variety described in terms of quivers. Furthermore, we discuss a gauge theoretic approach to hyperkahler implosion.......The geometry of the universal hyperkahler implosion for SU (n) is explored. In particular, we show that the universal hyperkahler implosion naturally contains a hypertoric variety described in terms of quivers. Furthermore, we discuss a gauge theoretic approach to hyperkahler implosion....
Intermediate algebra & analytic geometry
Gondin, William R
1967-01-01
Intermediate Algebra & Analytic Geometry Made Simple focuses on the principles, processes, calculations, and methodologies involved in intermediate algebra and analytic geometry. The publication first offers information on linear equations in two unknowns and variables, functions, and graphs. Discussions focus on graphic interpretations, explicit and implicit functions, first quadrant graphs, variables and functions, determinate and indeterminate systems, independent and dependent equations, and defective and redundant systems. The text then examines quadratic equations in one variable, system
Ceresole, Anna; Gnecchi, Alessandra; Marrani, Alessio
2013-01-01
We analyze some properties of the four dimensional supergravity theories which originate from five dimensions upon reduction. They generalize to N>2 extended supersymmetries the d-geometries with cubic prepotentials, familiar from N=2 special K\\"ahler geometry. We emphasize the role of a suitable parametrization of the scalar fields and the corresponding triangular symplectic basis. We also consider applications to the first order flow equations for non-BPS extremal black holes.
International Nuclear Information System (INIS)
Osborne, I; Brownson, E; Eulisse, G; Jones, C D; Sexton-Kennedy, E; Lange, D J
2014-01-01
CMS faces real challenges with upgrade of the CMS detector through 2020 and beyond. One of the challenges, from the software point of view, is managing upgrade simulations with the same software release as the 2013 scenario. We present the CMS geometry description software model, its integration with the CMS event setup and core software. The CMS geometry configuration and selection is implemented in Python. The tools collect the Python configuration fragments into a script used in CMS workflow. This flexible and automated geometry configuration allows choosing either transient or persistent version of the same scenario and specific version of the same scenario. We describe how the geometries are integrated and validated, and how we define and handle different geometry scenarios in simulation and reconstruction. We discuss how to transparently manage multiple incompatible geometries in the same software release. Several examples are shown based on current implementation assuring consistent choice of scenario conditions. The consequences and implications for multiple/different code algorithms are discussed.
Software Geometry in Simulations
Alion, Tyler; Viren, Brett; Junk, Tom
2015-04-01
The Long Baseline Neutrino Experiment (LBNE) involves many detectors. The experiment's near detector (ND) facility, may ultimately involve several detectors. The far detector (FD) will be significantly larger than any other Liquid Argon (LAr) detector yet constructed; many prototype detectors are being constructed and studied to motivate a plethora of proposed FD designs. Whether it be a constructed prototype or a proposed ND/FD design, every design must be simulated and analyzed. This presents a considerable challenge to LBNE software experts; each detector geometry must be described to the simulation software in an efficient way which allows for multiple authors to easily collaborate. Furthermore, different geometry versions must be tracked throughout their use. We present a framework called General Geometry Description (GGD), written and developed by LBNE software collaborators for managing software to generate geometries. Though GGD is flexible enough to be used by any experiment working with detectors, we present it's first use in generating Geometry Description Markup Language (GDML) files to interface with LArSoft, a framework of detector simulations, event reconstruction, and data analyses written for all LAr technology users at Fermilab. Brett is the other of the framework discussed here, the General Geometry Description (GGD).
Introduction to combinatorial geometry
International Nuclear Information System (INIS)
Gabriel, T.A.; Emmett, M.B.
1985-01-01
The combinatorial geometry package as used in many three-dimensional multimedia Monte Carlo radiation transport codes, such as HETC, MORSE, and EGS, is becoming the preferred way to describe simple and complicated systems. Just about any system can be modeled using the package with relatively few input statements. This can be contrasted against the older style geometry packages in which the required input statements could be large even for relatively simple systems. However, with advancements come some difficulties. The users of combinatorial geometry must be able to visualize more, and, in some instances, all of the system at a time. Errors can be introduced into the modeling which, though slight, and at times hard to detect, can have devastating effects on the calculated results. As with all modeling packages, the best way to learn the combinatorial geometry is to use it, first on a simple system then on more complicated systems. The basic technique for the description of the geometry consists of defining the location and shape of the various zones in terms of the intersections and unions of geometric bodies. The geometric bodies which are generally included in most combinatorial geometry packages are: (1) box, (2) right parallelepiped, (3) sphere, (4) right circular cylinder, (5) right elliptic cylinder, (6) ellipsoid, (7) truncated right cone, (8) right angle wedge, and (9) arbitrary polyhedron. The data necessary to describe each of these bodies are given. As can be easily noted, there are some subsets included for simplicity
Benoit Curé
The magnet subsystems resumed operation early this spring. The vacuum pumping was restarted mid March, and the cryogenic power plant was restarted on March 30th. Three and a half weeks later, the magnet was at 4.5 K. The vacuum pumping system is performing well. One of the newly installed vacuum gauges had to be replaced at the end of the cool-down phase, as the values indicated were not coherent with the other pressure measurements. The correction had to be implemented quickly to be sure no helium leak could be at the origin of this anomaly. The pressure measurements have been stable and coherent since the change. The cryogenics worked well, and the cool-down went quite smoothly, without any particular difficulty. The automated start of the turbines had to be fine-tuned to get a smooth transition, as it was observed that the cooling power delivered by the turbines was slightly higher than needed, causing the cold box to stop automatically. This had no consequence as the cold box safety system acts to keep ...
B. Curé
During the winter shutdown, the magnet subsystems went through a full maintenance. The magnet was successfully warmed up to room temperature beginning of December 2008. The vacuum was broken later on by injecting nitrogen at a pressure just above one atmosphere inside the vacuum tank. This was necessary both to prevent any accidental humidity ingress, and to allow for a modification of the vacuum gauges on the vacuum tank and maintenance of the diffusion pumps. The vacuum gauges had to be changed, because of erratic variations on the measurements, causing spurious alarms. The new type of vacuum gauges has been used in similar conditions on the other LHC experiments and without problems. They are shielded against the stray field. The lubricants of the primary and diffusion pumps have been changed. Several minor modifications were also carried out on the equipment in the service cavern, with the aim to ease the maintenance and to allow possible intervention during operation. Spare sensors have been bought. Th...
Energy Technology Data Exchange (ETDEWEB)
Duran, I; Martinez-Laso, L
1989-07-01
We present here the methods we used to analyse the characteristic parameters of drift chambers. The algorithms to calculate the electric potential in any point for any drift chamber geometry are presented. We include the description of the programs used to calculate the electric field, the drift paths, the drift velocity and the drift time. The results and the errors are discussed. (Author) 7 refs.
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.
Sources of hyperbolic geometry
Stillwell, John
1996-01-01
This book presents, for the first time in English, the papers of Beltrami, Klein, and Poincaré that brought hyperbolic geometry into the mainstream of mathematics. A recognition of Beltrami comparable to that given the pioneering works of Bolyai and Lobachevsky seems long overdue-not only because Beltrami rescued hyperbolic geometry from oblivion by proving it to be logically consistent, but because he gave it a concrete meaning (a model) that made hyperbolic geometry part of ordinary mathematics. The models subsequently discovered by Klein and Poincaré brought hyperbolic geometry even further down to earth and paved the way for the current explosion of activity in low-dimensional geometry and topology. By placing the works of these three mathematicians side by side and providing commentaries, this book gives the student, historian, or professional geometer a bird's-eye view of one of the great episodes in mathematics. The unified setting and historical context reveal the insights of Beltrami, Klein, and Po...
International Nuclear Information System (INIS)
Jonsson, Rickard; Westman, Hans
2006-01-01
We show that by employing the standard projected curvature as a measure of spatial curvature, we can make a certain generalization of optical geometry (Abramowicz M A and Lasota J-P 1997 Class. Quantum Grav. A 14 23-30). This generalization applies to any spacetime that admits a hypersurface orthogonal shearfree congruence of worldlines. This is a somewhat larger class of spacetimes than the conformally static spacetimes assumed in standard optical geometry. In the generalized optical geometry, which in the generic case is time dependent, photons move with unit speed along spatial geodesics and the sideways force experienced by a particle following a spatially straight line is independent of the velocity. Also gyroscopes moving along spatial geodesics do not precess (relative to the forward direction). Gyroscopes that follow a curved spatial trajectory precess according to a very simple law of three-rotation. We also present an inertial force formalism in coordinate representation for this generalization. Furthermore, we show that by employing a new sense of spatial curvature (Jonsson R 2006 Class. Quantum Grav. 23 1)) closely connected to Fermat's principle, we can make a more extensive generalization of optical geometry that applies to arbitrary spacetimes. In general this optical geometry will be time dependent, but still geodesic photons move with unit speed and follow lines that are spatially straight in the new sense. Also, the sideways experienced (comoving) force on a test particle following a line that is straight in the new sense will be independent of the velocity
Computational synthetic geometry
Bokowski, Jürgen
1989-01-01
Computational synthetic geometry deals with methods for realizing abstract geometric objects in concrete vector spaces. This research monograph considers a large class of problems from convexity and discrete geometry including constructing convex polytopes from simplicial complexes, vector geometries from incidence structures and hyperplane arrangements from oriented matroids. It turns out that algorithms for these constructions exist if and only if arbitrary polynomial equations are decidable with respect to the underlying field. Besides such complexity theorems a variety of symbolic algorithms are discussed, and the methods are applied to obtain new mathematical results on convex polytopes, projective configurations and the combinatorics of Grassmann varieties. Finally algebraic varieties characterizing matroids and oriented matroids are introduced providing a new basis for applying computer algebra methods in this field. The necessary background knowledge is reviewed briefly. The text is accessible to stud...
Discrete and computational geometry
Devadoss, Satyan L
2011-01-01
Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science. This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincaré conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also fe...
Ochiai, T.; Nacher, J. C.
2011-09-01
Recently, the application of geometry and conformal mappings to artificial materials (metamaterials) has attracted the attention in various research communities. These materials, characterized by a unique man-made structure, have unusual optical properties, which materials found in nature do not exhibit. By applying the geometry and conformal mappings theory to metamaterial science, it may be possible to realize so-called "Harry Potter cloaking device". Although such a device is still in the science fiction realm, several works have shown that by using such metamaterials it may be possible to control the direction of the electromagnetic field at will. We could then make an object hidden inside of a cloaking device. Here, we will explain how to design invisibility device using differential geometry and conformal mappings.
2002-01-01
Discrete geometry investigates combinatorial properties of configurations of geometric objects. To a working mathematician or computer scientist, it offers sophisticated results and techniques of great diversity and it is a foundation for fields such as computational geometry or combinatorial optimization. This book is primarily a textbook introduction to various areas of discrete geometry. In each area, it explains several key results and methods, in an accessible and concrete manner. It also contains more advanced material in separate sections and thus it can serve as a collection of surveys in several narrower subfields. The main topics include: basics on convex sets, convex polytopes, and hyperplane arrangements; combinatorial complexity of geometric configurations; intersection patterns and transversals of convex sets; geometric Ramsey-type results; polyhedral combinatorics and high-dimensional convexity; and lastly, embeddings of finite metric spaces into normed spaces. Jiri Matousek is Professor of Com...
Zheng, Fangyang
2002-01-01
The theory of complex manifolds overlaps with several branches of mathematics, including differential geometry, algebraic geometry, several complex variables, global analysis, topology, algebraic number theory, and mathematical physics. Complex manifolds provide a rich class of geometric objects, for example the (common) zero locus of any generic set of complex polynomials is always a complex manifold. Yet complex manifolds behave differently than generic smooth manifolds; they are more coherent and fragile. The rich yet restrictive character of complex manifolds makes them a special and interesting object of study. This book is a self-contained graduate textbook that discusses the differential geometric aspects of complex manifolds. The first part contains standard materials from general topology, differentiable manifolds, and basic Riemannian geometry. The second part discusses complex manifolds and analytic varieties, sheaves and holomorphic vector bundles, and gives a brief account of the surface classifi...
Yale, Paul B
2012-01-01
This book is an introduction to the geometry of Euclidean, affine, and projective spaces with special emphasis on the important groups of symmetries of these spaces. The two major objectives of the text are to introduce the main ideas of affine and projective spaces and to develop facility in handling transformations and groups of transformations. Since there are many good texts on affine and projective planes, the author has concentrated on the n-dimensional cases.Designed to be used in advanced undergraduate mathematics or physics courses, the book focuses on ""practical geometry,"" emphasi
Aboud, Essam; El-Masry, Nabil; Qaddah, Atef; Alqahtani, Faisal; Moufti, Mohammed R. H.
2015-06-01
The Rahat volcanic field represents one of the widely distributed Cenozoic volcanic fields across the western regions of the Arabian Peninsula. Its human significance stems from the fact that its northern fringes, where the historical eruption of 1256 A.D. took place, are very close to the holy city of Al-Madinah Al-Monawarah. In the present work, we analyzed aeromagnetic data from the northern part of Rahat volcanic field as well as carried out a ground gravity survey. A joint interpretation and inversion of gravity and magnetic data were used to estimate the thickness of the lava flows, delineate the subsurface structures of the study area, and estimate the depth to basement using various geophysical methods, such as Tilt Derivative, Euler Deconvolution and 2D modeling inversion. Results indicated that the thickness of the lava flows in the study area ranges between 100 m (above Sea Level) at the eastern and western boundaries of Rahat Volcanic field and getting deeper at the middle as 300-500 m. It also showed that, major structural trend is in the NW direction (Red Sea trend) with some minor trends in EW direction.
Benoit Curé
The cooling down to the nominal temperature of 4.5 K was achieved at the beginning of August, in conjunction with the completion of the installation work of the connection between the power lines and the coil current leads. The temperature gradient on the first exchanger of the cold box is now kept within the nominal range. A leak of lubricant on a gasket of the helium compressor station installed at the surface was observed and several corrective actions were necessary to bring the situation back to normal. The compressor had to be refilled with lubricant and a regeneration of the filters and adsorbers was necessary. The coil cool down was resumed successfully, and the cryogenics is running since then with all parameters being nominal. Preliminary tests of the 20kA coil power supply were done earlier at full current through the discharge lines into the dump resistors, and with the powering busbars from USC5 to UXC5 without the magnet connected. On Monday evening August 25th, at 8pm, the final commissionin...
B. Curé
The first phase of the commissioning ended in August by a triggered fast dump at 3T. All parameters were nominal, and the temperature recovery down to 4.5K was carried out in two days by the cryogenics. In September, series of ramps were achieved up to 3 and finally 3.8T, while checking thoroughly the detectors in the forward region, measuring any movement of and around the HF. After the incident of the LHC accelerator on September 19th, corrective actions could be undertaken in the forward region. When all these displacements were fully characterized and repetitive, with no sign of increments in displacement at each field ramp, it was possible to start the CRAFT, Cosmic Run at Four Tesla (which was in fact at 3.8T). The magnet was ramped up to 18.16kA and the 3 week run went smoothly, with only 4 interruptions: due to the VIP visits on 21st October during the LHC inauguration day; a water leak on the cooling demineralized water circuit, about 1 l/min, that triggered a stop of the cooling pumps, and resulte...
Benoit Curé
2013-01-01
Maintenance work and consolidation activities on the magnet cryogenics and its power distribution are progressing according to the schedules. The manufacturing of the two new helium compressor frame units has started. The frame units support the valves, all the sensors and the compressors with their motors. This activity is subcontracted. The final installation and the commissioning at CERN are scheduled for March–April 2014. The overhauls of existing cryogenics equipment (compressors, motors) are in progress. The reassembly of the components shall start in early 2014. The helium drier, to be installed on the high-pressure helium piping, has been ordered and will be delivered in the first trimester of 2014. The power distribution for the helium compressors in SH5 on the 3.3kV network is progressing. The 3.3kV switches, between each compressor and its hot spare compressor, are being installed, together with the power cables for the new compressors. The 3.3kV electrical switchboards in SE5 will ...
Towards relativistic quantum geometry
Energy Technology Data Exchange (ETDEWEB)
Ridao, Luis Santiago [Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina); Bellini, Mauricio, E-mail: mbellini@mdp.edu.ar [Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350, C.P. 7600, Mar del Plata (Argentina); Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina)
2015-12-17
We obtain a gauge-invariant relativistic quantum geometry by using a Weylian-like manifold with a geometric scalar field which provides a gauge-invariant relativistic quantum theory in which the algebra of the Weylian-like field depends on observers. An example for a Reissner–Nordström black-hole is studied.
Multiplicity in difference geometry
Tomasic, Ivan
2011-01-01
We prove a first principle of preservation of multiplicity in difference geometry, paving the way for the development of a more general intersection theory. In particular, the fibres of a \\sigma-finite morphism between difference curves are all of the same size, when counted with correct multiplicities.
Spacetime and Euclidean geometry
Brill, Dieter; Jacobson, Ted
2006-04-01
Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a two-dimensional spacetime diagram is proportional to the Euclidean area of the corresponding causal domain. We use this relation to derive the Minkowski line element by two geometric proofs of the spacetime Pythagoras theorem.
International Nuclear Information System (INIS)
Konopleva, N.P.
2009-01-01
The basic ideas of description methods of physical fields and elementary particle interactions are discussed. One of such ideas is the conception of space-time geometry. In this connection experimental measurement methods are analyzed. It is shown that measure procedures are the origin of geometrical axioms. The connection between space symmetry properties and the conservation laws is considered
Wares, Arsalan; Elstak, Iwan
2017-01-01
The purpose of this paper is to describe the mathematics that emanates from the construction of an origami box. We first construct a simple origami box from a rectangular sheet and then discuss some of the mathematical questions that arise in the context of geometry and algebra. The activity can be used as a context for illustrating how algebra…
MacKeown, P. K.
1984-01-01
Clarifies two concepts of gravity--those of a fictitious force and those of how space and time may have geometry. Reviews the position of Newton's theory of gravity in the context of special relativity and considers why gravity (as distinct from electromagnetics) lends itself to Einstein's revolutionary interpretation. (JN)
DEFF Research Database (Denmark)
Booss-Bavnbek, Bernhelm
2011-01-01
This paper applies I.M. Gelfand's distinction between adequate and non-adequate use of mathematical language in different contexts to the newly opened window of model-based measurements of intracellular dynamics. The specifics of geometry and dynamics on the mesoscale of cell physiology are elabo...
Diophantine geometry an introduction
Hindry, Marc
2000-01-01
This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and professional mathematicians. In each part of the book, the reader will find numerous exercises.
Sliding vane geometry turbines
Sun, Harold Huimin; Zhang, Jizhong; Hu, Liangjun; Hanna, Dave R
2014-12-30
Various systems and methods are described for a variable geometry turbine. In one example, a turbine nozzle comprises a central axis and a nozzle vane. The nozzle vane includes a stationary vane and a sliding vane. The sliding vane is positioned to slide in a direction substantially tangent to an inner circumference of the turbine nozzle and in contact with the stationary vane.
Boyer, Carl B
2012-01-01
Designed as an integrated survey of the development of analytic geometry, this study presents the concepts and contributions from before the Alexandrian Age through the eras of the great French mathematicians Fermat and Descartes, and on through Newton and Euler to the "Golden Age," from 1789 to 1850.
Coxeter, HSM
1965-01-01
This textbook introduces non-Euclidean geometry, and the third edition adds a new chapter, including a description of the two families of 'mid-lines' between two given lines and an elementary derivation of the basic formulae of spherical trigonometry and hyperbolic trigonometry, and other new material.
International Nuclear Information System (INIS)
Ezin, J.P.
1988-08-01
The lectures given at the ''5th Symposium of Mathematics in Abidjan: Differential Geometry and Mechanics'' are presented. They are divided into four chapters: Riemannian metric on a differential manifold, curvature tensor fields on a Riemannian manifold, some classical functionals on Riemannian manifolds and questions. 11 refs
Hartshorne, Robin
2000-01-01
In recent years, I have been teaching a junior-senior-level course on the classi cal geometries. This book has grown out of that teaching experience. I assume only high-school geometry and some abstract algebra. The course begins in Chapter 1 with a critical examination of Euclid's Elements. Students are expected to read concurrently Books I-IV of Euclid's text, which must be obtained sepa rately. The remainder of the book is an exploration of questions that arise natu rally from this reading, together with their modern answers. To shore up the foundations we use Hilbert's axioms. The Cartesian plane over a field provides an analytic model of the theory, and conversely, we see that one can introduce coordinates into an abstract geometry. The theory of area is analyzed by cutting figures into triangles. The algebra of field extensions provides a method for deciding which geometrical constructions are possible. The investigation of the parallel postulate leads to the various non-Euclidean geometries. And ...
Un error en los calculos matematicos destroza el acelerador de particulas del CERN
Cernuda, Olalla
2007-01-01
The most famous particle accelerator in the world, who is at CERN, has suffered a catastrophic damage after a great explosion took place in its depths. This explosion has an absolutely scientific explanation: a mathematical mistake in the design of the anchorages of great magnets. (1 page)
Energy Technology Data Exchange (ETDEWEB)
Hernandez R, Alejandro; Garcia I, Rafael; Mazur C, Zdislaw [Instituto de Investigaciones Electricas, Cuernavaca, Morelos (Mexico)
2004-07-01
The analysis begins with the generation of a computational geometric model of the gas turbine nozzle using reverse engineering techniques. For the obtaining of the original geometry of the blade, a measurement machine by coordinates and computerized numerical control was used. Next, the computational model is converted into a three-dimensional mesh. In advance, a study of boundary conditions was made of the nozzle material as well as of the turbine operating conditions during non-operating cycles, start-ups and shut-downs. On the other hand, with the boundary conditions imposed to the model, the distributions of the temperature and pressures on the aerofoil profile of the nozzle blade were calculated. These results had to be manipulated to be exported to a finite element software (ANSYS); at this point, another nozzle model was elaborated to be able to import the temperature distribution. With the temperatures correctly imported, the simulations for the calculation of the thermal stresses were made in the nozzle. [Spanish] El analisis inicia con la generacion de un modelo geometrico computacional de la tobera de la turbina de gas utilizando tecnicas de ingenieria inversa. Para la obtencion de la geometria original del alabe, se utilizo una maquina de medicion por coordenadas y control numerico computarizado. A continuacion, el modelo computacional es convertido en una malla tridimensional. Con antelacion, se realizo un estudio de las condiciones de frontera, tanto del material de la tobera como de las condiciones de operacion de la turbina, durante ciclos de paro, arranque y disparo. Por otra parte, con las condiciones de frontera impuestas al modelo, se calcularon las distribuciones de las temperaturas y presiones sobre el perfil aerodinamico de la paleta de la tobera. Estos resultados tuvieron que ser manipulados para ser exportados a un software de elemento finito (ANSYS); en este punto, se elaboro otro modelo de la tobera para poder importar la distribucion de
Multivariate calculus and geometry
Dineen, Seán
2014-01-01
Multivariate calculus can be understood best by combining geometric insight, intuitive arguments, detailed explanations and mathematical reasoning. This textbook has successfully followed this programme. It additionally provides a solid description of the basic concepts, via familiar examples, which are then tested in technically demanding situations. In this new edition the introductory chapter and two of the chapters on the geometry of surfaces have been revised. Some exercises have been replaced and others provided with expanded solutions. Familiarity with partial derivatives and a course in linear algebra are essential prerequisites for readers of this book. Multivariate Calculus and Geometry is aimed primarily at higher level undergraduates in the mathematical sciences. The inclusion of many practical examples involving problems of several variables will appeal to mathematics, science and engineering students.
Transformational plane geometry
Umble, Ronald N
2014-01-01
Axioms of Euclidean Plane Geometry The Existence and Incidence Postulates The Distance and Ruler Postulates The Plane Separation Postulate The Protractor Postulate The Side-Angle-Side Postulate and the Euclidean Parallel Postulate Theorems of Euclidean Plane Geometry The Exterior Angle Theorem Triangle Congruence Theorems The Alternate Interior Angles Theorem and the Angle Sum Theorem Similar Triangles Introduction to Transformations, Isometries, and Similarities Transformations Isometries and SimilaritiesAppendix: Proof of Surjectivity Translations, Rotations, and Reflections Translations Rotations Reflections Appendix: Geometer's Sketchpad Commands Required by Exploratory Activities Compositions of Translations, Rotations, and Reflections The Three Points Theorem Rotations as Compositions of Two Reflections Translations as Compositions of Two Halfturns or Two Reflections The Angle Addition Theorem Glide Reflections Classification of Isometries The Fundamental Theorem and Congruence Classification of Isometr...
Multilevel geometry optimization
Rodgers, Jocelyn M.; Fast, Patton L.; Truhlar, Donald G.
2000-02-01
Geometry optimization has been carried out for three test molecules using six multilevel electronic structure methods, in particular Gaussian-2, Gaussian-3, multicoefficient G2, multicoefficient G3, and two multicoefficient correlation methods based on correlation-consistent basis sets. In the Gaussian-2 and Gaussian-3 methods, various levels are added and subtracted with unit coefficients, whereas the multicoefficient Gaussian-x methods involve noninteger parameters as coefficients. The multilevel optimizations drop the average error in the geometry (averaged over the 18 cases) by a factor of about two when compared to the single most expensive component of a given multilevel calculation, and in all 18 cases the accuracy of the atomization energy for the three test molecules improves; with an average improvement of 16.7 kcal/mol.
Multilevel geometry optimization
Energy Technology Data Exchange (ETDEWEB)
Rodgers, Jocelyn M. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States); Fast, Patton L. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States); Truhlar, Donald G. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States)
2000-02-15
Geometry optimization has been carried out for three test molecules using six multilevel electronic structure methods, in particular Gaussian-2, Gaussian-3, multicoefficient G2, multicoefficient G3, and two multicoefficient correlation methods based on correlation-consistent basis sets. In the Gaussian-2 and Gaussian-3 methods, various levels are added and subtracted with unit coefficients, whereas the multicoefficient Gaussian-x methods involve noninteger parameters as coefficients. The multilevel optimizations drop the average error in the geometry (averaged over the 18 cases) by a factor of about two when compared to the single most expensive component of a given multilevel calculation, and in all 18 cases the accuracy of the atomization energy for the three test molecules improves; with an average improvement of 16.7 kcal/mol. (c) 2000 American Institute of Physics.
Krauss, Lawrence M.; Turner, Michael S.
1999-01-01
The recognition that the cosmological constant may be non-zero forces us to re-evaluate standard notions about the connection between geometry and the fate of our Universe. An open Universe can recollapse, and a closed Universe can expand forever. As a corollary, we point out that there is no set of cosmological observations we can perform that will unambiguously allow us to determine what the ultimate destiny of the Universe will be.
DEFF Research Database (Denmark)
Tamke, Martin; Ramsgaard Thomsen, Mette; Riiber Nielsen, Jacob
2009-01-01
The versatility of wood constructions and traditional wood joints for the production of non standard elements was in focus of a design based research. Herein we established a seamless process from digital design to fabrication. A first research phase centered on the development of a robust...... parametric model and a generic design language a later explored the possibilities to construct complex shaped geometries with self registering joints on modern wood crafting machines. The research was carried out as collaboration with industrial partners....
International Nuclear Information System (INIS)
Lepora, N.; Kibble, T.
1999-01-01
We analyse symmetry breaking in the Weinberg-Salam model paying particular attention to the underlying geometry of the theory. In this context we find two natural metrics upon the vacuum manifold: an isotropic metric associated with the scalar sector, and a squashed metric associated with the gauge sector. Physically, the interplay between these metrics gives rise to many of the non-perturbative features of Weinberg-Salam theory. (author)
International Nuclear Information System (INIS)
Hull, C.M.
1993-01-01
The geometric structure of theories with gauge fields of spins two and higher should involve a higher spin generalisation of Riemannian geometry. Such geometries are discussed and the case of W ∝ -gravity is analysed in detail. While the gauge group for gravity in d dimensions is the diffeomorphism group of the space-time, the gauge group for a certain W-gravity theory (which is W ∝ -gravity in the case d=2) is the group of symplectic diffeomorphisms of the cotangent bundle of the space-time. Gauge transformations for W-gravity gauge fields are given by requiring the invariance of a generalised line element. Densities exist and can be constructed from the line element (generalising √detg μν ) only if d=1 or d=2, so that only for d=1,2 can actions be constructed. These two cases and the corresponding W-gravity actions are considered in detail. In d=2, the gauge group is effectively only a subgroup of the symplectic diffeomorphisms group. Some of the constraints that arise for d=2 are similar to equations arising in the study of self-dual four-dimensional geometries and can be analysed using twistor methods, allowing contact to be made with other formulations of W-gravity. While the twistor transform for self-dual spaces with one Killing vector reduces to a Legendre transform, that for two Killing vectors gives a generalisation of the Legendre transform. (orig.)
Integral geometry and valuations
Solanes, Gil
2014-01-01
Valuations are finitely additive functionals on the space of convex bodies. Their study has become a central subject in convexity theory, with fundamental applications to integral geometry. In the last years there has been significant progress in the theory of valuations, which in turn has led to important achievements in integral geometry. This book originated from two courses delivered by the authors at the CRM and provides a self-contained introduction to these topics, covering most of the recent advances. The first part, by Semyon Alesker, is devoted to the theory of convex valuations, with emphasis on the latest developments. A special focus is put on the new fundamental structures of the space of valuations discovered after Alesker's irreducibility theorem. Moreover, the author describes the newly developed theory of valuations on manifolds. In the second part, Joseph H. G. Fu gives a modern introduction to integral geometry in the sense of Blaschke and Santaló, based on the notions and tools presented...
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.
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)
Energy Technology Data Exchange (ETDEWEB)
Espinoza Garza, Jesus; Garcia Tinoco, Guillermo J; Martinez Flores, Jose Oscar [Instituto de Investigaciones Electricas, Cuernavaca (Mexico)
1990-12-31
For boiler soot blowing converging-diverging nozzles are employed, whose function is to convert thermal energy of a gas into kinetic energy to remove the deposits that adhere to the heat exchanger surfaces. In this paper are described the experimental equipment and the methods for flow, dynamic pressure, discharge velocity and air expansion factor calculation in each nozzle, as a function of its design geometry, utilizing air from a five stage centrifugal compressor. The graphic analysis of the results, concludes that the most efficient nozzles are not the ones than develop the greatest velocity, but the ones of highest dynamic pressure at the outlet. The nozzle geometry that allows obtaining the maximum dynamic air pressure at the discharge is A{sub 2}/A{sub g}=1.3676 [Espanol] Para el deshollinado de calderas se utilizan las toberas convergentes-divergentes, cuya funcion es convertir la energia termica de un gas en energia cinetica para remover los depositos que se adhieren a las superficies de intercambio de calor. En este trabajo se describen el equipo experimental y los metodos de calculo para flujo, presion dinamica, velocidad a la descarga y factor de expansion del aire en cada tobera, como funcion de su geometria de diseno. Durante la experimentacion se evaluaron siete disenos diferentes de toberas, empleando aire de un compresor centrifugo de cinco etapas. Del analisis grafico de los resultados, se concluye que las toberas mas eficientes no son las que desarrollan mayor velocidad sino las de mayor presion dinamica de la salida. La geometria de tobera que permite obtener la maxima presion dinamica del aire a la descarga es A{sub 2}/A{sub g} = 1.3676.
Energy Technology Data Exchange (ETDEWEB)
Espinoza Garza, Jesus; Garcia Tinoco, Guillermo J.; Martinez Flores, Jose Oscar [Instituto de Investigaciones Electricas, Cuernavaca (Mexico)
1989-12-31
For boiler soot blowing converging-diverging nozzles are employed, whose function is to convert thermal energy of a gas into kinetic energy to remove the deposits that adhere to the heat exchanger surfaces. In this paper are described the experimental equipment and the methods for flow, dynamic pressure, discharge velocity and air expansion factor calculation in each nozzle, as a function of its design geometry, utilizing air from a five stage centrifugal compressor. The graphic analysis of the results, concludes that the most efficient nozzles are not the ones than develop the greatest velocity, but the ones of highest dynamic pressure at the outlet. The nozzle geometry that allows obtaining the maximum dynamic air pressure at the discharge is A{sub 2}/A{sub g}=1.3676 [Espanol] Para el deshollinado de calderas se utilizan las toberas convergentes-divergentes, cuya funcion es convertir la energia termica de un gas en energia cinetica para remover los depositos que se adhieren a las superficies de intercambio de calor. En este trabajo se describen el equipo experimental y los metodos de calculo para flujo, presion dinamica, velocidad a la descarga y factor de expansion del aire en cada tobera, como funcion de su geometria de diseno. Durante la experimentacion se evaluaron siete disenos diferentes de toberas, empleando aire de un compresor centrifugo de cinco etapas. Del analisis grafico de los resultados, se concluye que las toberas mas eficientes no son las que desarrollan mayor velocidad sino las de mayor presion dinamica de la salida. La geometria de tobera que permite obtener la maxima presion dinamica del aire a la descarga es A{sub 2}/A{sub g} = 1.3676.
International Nuclear Information System (INIS)
Hook, D W
2008-01-01
A geometric framework for quantum mechanics arose during the mid 1970s when authors such as Cantoni explored the notion of generalized transition probabilities, and Kibble promoted the idea that the space of pure quantum states provides a natural quantum mechanical analogue for classical phase space. This central idea can be seen easily since the projection of Schroedinger's equation from a Hilbert space into the space of pure spaces is a set of Hamilton's equations. Over the intervening years considerable work has been carried out by a variety of authors and a mature description of quantum mechanics in geometric terms has emerged with many applications. This current offering would seem ideally placed to review the last thirty years of progress and relate this to the most recent work in quantum entanglement. Bengtsson and Zyczkowski's beautifully illustrated volume, Geometry of Quantum States (referred to as GQS from now on) attempts to cover considerable ground in its 466 pages. Its topics range from colour theory in Chapter 1 to quantum entanglement in Chapter 15-to say that this is a whirlwind tour is, perhaps, no understatement. The use of the work 'introduction' in the subtitle of GQS, might suggest to the reader that this work be viewed as a textbook and I think that this interpretation would be incorrect. The authors have chosen to present a survey of different topics with the specific aim to introduce entanglement in geometric terms-the book is not intended as a pedagogical introduction to the geometric approach to quantum mechanics. Each of the fifteen chapters is a short, and mostly self-contained, essay on a particular aspect or application of geometry in the context of quantum mechanics with entanglement being addressed specifically in the final chapter. The chapters fall into three classifications: those concerned with the mathematical background, those which discuss quantum theory and the foundational aspects of the geometric framework, and
Functional integration over geometries
International Nuclear Information System (INIS)
Mottola, E.
1995-01-01
The geometric construction of the functional integral over coset spaces M/G is reviewed. The inner product on the cotangent space of infinitesimal deformations of M defines an invariant distance and volume form, or functional integration measure on the full configuration space. Then, by a simple change of coordinates parameterizing the gauge fiber G, the functional measure on the coset space M/G is deduced. This change of integration variables leads to a Jacobian which is entirely equivalent to the Faddeev--Popov determinant of the more traditional gauge fixed approach in non-abelian gauge theory. If the general construction is applied to the case where G is the group of coordinate reparameterizations of spacetime, the continuum functional integral over geometries, i.e. metrics modulo coordinate reparameterizations may be defined. The invariant functional integration measure is used to derive the trace anomaly and effective action for the conformal part of the metric in two and four dimensional spacetime. In two dimensions this approach generates the Polyakov--Liouville action of closed bosonic non-critical string theory. In four dimensions the corresponding effective action leads to novel conclusions on the importance of quantum effects in gravity in the far infrared, and in particular, a dramatic modification of the classical Einstein theory at cosmological distance scales, signaled first by the quantum instability of classical de Sitter spacetime. Finite volume scaling relations for the functional integral of quantum gravity in two and four dimensions are derived, and comparison with the discretized dynamical triangulation approach to the integration over geometries are discussed. Outstanding unsolved problems in both the continuum definition and the simplicial approach to the functional integral over geometries are highlighted
In-situ magnetization of NdFeB magnets for permanent magnet machines
International Nuclear Information System (INIS)
Chang, L.; Eastham, T.R.; Dawson, G.E.
1991-01-01
In-situ magnetizers are needed to facilitate the assembly of permanent magnet machines and to remagnetize the magnets after weakening due to a fault condition. The air-core magnetizer in association with the silicon steel lamination structure of the rotor has advantages over its iron-core counterpart. This novel method has been used to magnetize the NdFeB magnets in a 30-hp permanent magnet synchronous motor. The magnetizing capability for different magnetizer geometries was investigated for the magnetization of NdFeB material. The design, testing, and operation of this magnetizer are reported in this paper
Super magnets for interaction regions
International Nuclear Information System (INIS)
Biallas, G.; Fowler, W.; Diebold, R.
1977-01-01
The feasibility of using superconducting magnets in the beam interaction regions of particle accelerators is discussed. These higher field magnets can be shorter, leaving more room for detectors, but also must have a large aperture and magnetic shielding. The ''kissing geometry'' was investigated, and design and scaling considerations are given. A rough estimate of the cost of such superconducting magnets is given as an aid to the selection of interaction geometry
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
Crossing geometry for Main Ring on Doubler collisions
International Nuclear Information System (INIS)
Diebold, R.
1977-01-01
There are two basic methods for bringing about Main Ring on Doubler collisions: the transposed, and kissing geometries. Examples of both are discussed assuming maximum momenta of 250 on 1000 GeV/c. The magnets required to bring the beams into small-angle collision are substantial in both cases. Detailed engineering work will be required to distinguish a substantial cost advantage of one geometry over the other
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...
Geometry of hyperbolic monopoles
International Nuclear Information System (INIS)
Nash, C.
1986-01-01
The hyperbolic monopoles of Atiyah [M. F. Atiyah, Commun. Math. Phys. 93, 471 (1984); ''Magnetic monopoles in hyperbolic space,'' in Proceedings of the International Colloquium on Vector Bundles (Tata Institute, Bombay, 1984)] and Chakrabarti [A. Chakrabarti, J. Math. Phys. 27, 340 (1986)] are introduced and their geometric properties and relations to instantons and ordinary monopoles clarified. A key tool is the use of the ball model of hyperbolic space to construct and examine solutions
International Nuclear Information System (INIS)
Marks, N.
1994-01-01
The design and construction of conventional, steel-cored, direct-current magnets are discussed. Laplace's equation and the associated cylindrical harmonic solutions in two dimensions are established. The equations are used to define the ideal pole shapes and required excitation for dipole, quadrupole and sextupole magnets. Standard magnet geometries are then considered and criteria determining the coil design are presented. The use of codes for predicting flux density distributions and the iterative techniques used for pole face design are then discussed. This includes a description of the use of two-dimensional codes to generate suitable magnet end geometries. Finally, standard constructional techniques for cores and coils are described. (orig.)
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
Unstable drift eigenmode in slab geometry
International Nuclear Information System (INIS)
Tsotsonis, S.; Hirose, A.
1986-01-01
The unstable Pearlstein-Berk mode of drift waves in plane, sheared slab geometry has later been shown to be stable when electron Landau resonance is rigorously treated. Based on the variational method previously developed the authors have found that in addition to the absolutely stable Pearlstein-Berk mode, there exists an absolutely unstable eigenfunction characterized by ω ≤ ω/sub chemical bonde/, and weak ''radial'' dependence. Also, the growth rate, only weakly depends on the magnetic shear and ion/electron temperature ratio
An introduction to incidence geometry
De Bruyn, Bart
2016-01-01
This book gives an introduction to the field of Incidence Geometry by discussing the basic families of point-line geometries and introducing some of the mathematical techniques that are essential for their study. The families of geometries covered in this book include among others the generalized polygons, near polygons, polar spaces, dual polar spaces and designs. Also the various relationships between these geometries are investigated. Ovals and ovoids of projective spaces are studied and some applications to particular geometries will be given. A separate chapter introduces the necessary mathematical tools and techniques from graph theory. This chapter itself can be regarded as a self-contained introduction to strongly regular and distance-regular graphs. This book is essentially self-contained, only assuming the knowledge of basic notions from (linear) algebra and projective and affine geometry. Almost all theorems are accompanied with proofs and a list of exercises with full solutions is given at the end...
International Nuclear Information System (INIS)
Buescher, R.
2005-01-01
Casimir interactions are interactions induced by quantum vacuum fluctuations and thermal fluctuations of the electromagnetic field. Using a path integral quantization for the gauge field, an effective Gaussian action will be derived which is the starting point to compute Casimir forces between macroscopic objects analytically and numerically. No assumptions about the independence of the material and shape dependent contributions to the interaction are made. We study the limit of flat surfaces in further detail and obtain a concise derivation of Lifshitz' theory of molecular forces. For the case of ideally conducting boundaries, the Gaussian action will be calculated explicitly. Both limiting cases are also discussed within the framework of a scalar field quantization approach, which is applicable for translationally invariant geometries. We develop a non-perturbative approach to calculate the Casimir interaction from the Gaussian action for periodically deformed and ideally conducting objects numerically. The obtained results reveal two different scaling regimes for the Casimir force as a function of the distance between the objects, their deformation wavelength and -amplitude. The results confirm that the interaction is non-additive, especially in the presence of strong geometric deformations. Furthermore, the numerical approach is extended to calculate lateral Casimir forces. The results are consistent with the results of the proximity-force approximation for large deformation wavelengths. A qualitatively different behaviour between the normal and lateral force is revealed. We also establish a relation between the boundary induced change of the of the density of states for the scalar Helmholtz equation and the Casimir interaction using the path integral method. For statically deformed boundaries, this relation can be expressed as a novel trace formula, which is formally similar to the so-called Krein-Friedel-Lloyd formula. While the latter formula describes the
Planetary Image Geometry Library
Deen, Robert C.; Pariser, Oleg
2010-01-01
The Planetary Image Geometry (PIG) library is a multi-mission library used for projecting images (EDRs, or Experiment Data Records) and managing their geometry for in-situ missions. A collection of models describes cameras and their articulation, allowing application programs such as mosaickers, terrain generators, and pointing correction tools to be written in a multi-mission manner, without any knowledge of parameters specific to the supported missions. Camera model objects allow transformation of image coordinates to and from view vectors in XYZ space. Pointing models, specific to each mission, describe how to orient the camera models based on telemetry or other information. Surface models describe the surface in general terms. Coordinate system objects manage the various coordinate systems involved in most missions. File objects manage access to metadata (labels, including telemetry information) in the input EDRs and RDRs (Reduced Data Records). Label models manage metadata information in output files. Site objects keep track of different locations where the spacecraft might be at a given time. Radiometry models allow correction of radiometry for an image. Mission objects contain basic mission parameters. Pointing adjustment ("nav") files allow pointing to be corrected. The object-oriented structure (C++) makes it easy to subclass just the pieces of the library that are truly mission-specific. Typically, this involves just the pointing model and coordinate systems, and parts of the file model. Once the library was developed (initially for Mars Polar Lander, MPL), adding new missions ranged from two days to a few months, resulting in significant cost savings as compared to rewriting all the application programs for each mission. Currently supported missions include Mars Pathfinder (MPF), MPL, Mars Exploration Rover (MER), Phoenix, and Mars Science Lab (MSL). Applications based on this library create the majority of operational image RDRs for those missions. A
Initiation to global Finslerian geometry
Akbar-Zadeh, Hassan
2006-01-01
After a brief description of the evolution of thinking on Finslerian geometry starting from Riemann, Finsler, Berwald and Elie Cartan, the book gives a clear and precise treatment of this geometry. The first three chapters develop the basic notions and methods, introduced by the author, to reach the global problems in Finslerian Geometry. The next five chapters are independent of each other, and deal with among others the geometry of generalized Einstein manifolds, the classification of Finslerian manifolds of constant sectional curvatures. They also give a treatment of isometric, affine, p
Directory of Open Access Journals (Sweden)
Šárka Nedomová
2013-01-01
Full Text Available Precise quantification of the profile of egg can provide a powerful tool for the analysis of egg shape for various biological problems. A new approach to the geometry of a Ostrich’s egg profile is presented here using an analysing the egg’s digital photo by edge detection techniques. The obtained points on the eggshell counter are fitted by the Fourier series. The obtained equations describing an egg profile have been used to calculate radii of curvature. The radii of the curvature at the important point of the egg profile (sharp end, blunt end and maximum thickness are independent on the egg shape index. The exact values of the egg surface and the egg volume have been obtained. These quantities are also independent on the egg shape index. These quantities can be successively estimated on the basis of simplified equations which are expressed in terms of the egg length, L¸ and its width, B. The surface area of the eggshells also exhibits good correlation with the egg long circumference length. Some limitations of the most used procedures have been also shown.
Nonperturbative quantum geometries
International Nuclear Information System (INIS)
Jacobson, T.; California Univ., Santa Barbara; Smolin, L.; California Univ., Santa Barbara
1988-01-01
Using the self-dual representation of quantum general relativity, based on Ashtekar's new phase space variables, we present an infinite dimensional family of quantum states of the gravitational field which are exactly annihilated by the hamiltonian constraint. These states are constructed from Wilson loops for Ashtekar's connection (which is the spatial part of the left handed spin connection). We propose a new regularization procedure which allows us to evaluate the action of the hamiltonian constraint on these states. Infinite linear combinations of these states which are formally annihilated by the diffeomorphism constraints as well are also described. These are explicit examples of physical states of the gravitational field - and for the compact case are exact zero eigenstates of the hamiltonian of quantum general relativity. Several different approaches to constructing diffeomorphism invariant states in the self dual representation are also described. The physical interpretation of the states described here is discussed. However, as we do not yet know the physical inner product, any interpretation is at this stage speculative. Nevertheless, this work suggests that quantum geometry at Planck scales might be much simpler when explored in terms of the parallel transport of left-handed spinors than when explored in terms of the three metric. (orig.)
Bhatia, Rajendra
2013-01-01
This book is an outcome of the Indo-French Workshop on Matrix Information Geometries (MIG): Applications in Sensor and Cognitive Systems Engineering, which was held in Ecole Polytechnique and Thales Research and Technology Center, Palaiseau, France, in February 23-25, 2011. The workshop was generously funded by the Indo-French Centre for the Promotion of Advanced Research (IFCPAR). During the event, 22 renowned invited french or indian speakers gave lectures on their areas of expertise within the field of matrix analysis or processing. From these talks, a total of 17 original contribution or state-of-the-art chapters have been assembled in this volume. All articles were thoroughly peer-reviewed and improved, according to the suggestions of the international referees. The 17 contributions presented are organized in three parts: (1) State-of-the-art surveys & original matrix theory work, (2) Advanced matrix theory for radar processing, and (3) Matrix-based signal processing applications.
Energy Technology Data Exchange (ETDEWEB)
Takahashi, K., E-mail: t2216017@iwate-u.ac.jp [Department of Physical Science and Materials Engineering, Faculty of Science and Engineering, Iwate University, 4-3-5 Ueda, Morioka 020-8551 (Japan); Ainslie, M.D. [Bulk Superconductivity Group, Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ (United Kingdom); Fujishiro, H.; Naito, T. [Department of Physical Science and Materials Engineering, Faculty of Science and Engineering, Iwate University, 4-3-5 Ueda, Morioka 020-8551 (Japan); Shi, Y-H.; Cardwell, D.A. [Bulk Superconductivity Group, Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ (United Kingdom)
2017-05-15
Highlights: • The trapped field characteristics of a standard Y–Ba–Cu–O bulk magnetized by PFM was investigated using a split coil with three kinds of iron yokes inserted in the bores of coil,both experimentally and numerically. • Numerical results encourage better understanding of the role of yoke, including the typical behavior of the magnetic flux, such as a flux jump during PFM. • A higher saturation magnetic flux density of the yoke material was effective to reduce flux flow in the descending stage of the pulsed field. • A conductivity of the yoke material also acts to reduce the velocity of the flux intruding the bulk because of eddy currents that flow in the yoke that oppose the magnetization, which reduces the temperature rise in the bulk. - Abstract: We have investigated, both experimentally and numerically, the trapped field characteristics of a standard Y–Ba–Cu–O bulk of 30 mm in diameter and 14 mm in thickness magnetized by pulsed field magnetization (PFM) using a split coil, in which three kinds of iron yoke are inserted in the bore of the coil: soft iron with a flat surface, soft iron with a taper, and permendur (50Fe + 50Co alloy) with a flat surface. The highest trapped field, B{sub Tmax}, of 2.93 T was achieved at 40 K in the case of the permendur yoke, which was slightly higher than that obtained for the flat soft iron or the tapered soft iron yokes, and was much higher than 2.20 T in the case without the yoke. The insertion effect of the yoke on the trapped field characteristics was also investigated using numerical simulations. The results suggest that the saturation magnetic flux density, B{sub sat}, of the yoke acts to reduce the flux flow due to its hysteretic magnetization curve and the higher electrical conductivity, σ, of the yoke material also acts to suppress the flux increase rate. A flux jump (or flux leap) can be reproduced in the ascending stage of PFM using numerical simulation, using an assumption of relatively
GPS: Geometry, Probability, and Statistics
Field, Mike
2012-01-01
It might be said that for most occupations there is now less of a need for mathematics than there was say fifty years ago. But, the author argues, geometry, probability, and statistics constitute essential knowledge for everyone. Maybe not the geometry of Euclid, but certainly geometrical ways of thinking that might enable us to describe the world…
Surrogate Modeling for Geometry Optimization
DEFF Research Database (Denmark)
Rojas Larrazabal, Marielba de la Caridad; Abraham, Yonas; Holzwarth, Natalie
2009-01-01
A new approach for optimizing the nuclear geometry of an atomic system is described. Instead of the original expensive objective function (energy functional), a small number of simpler surrogates is used.......A new approach for optimizing the nuclear geometry of an atomic system is described. Instead of the original expensive objective function (energy functional), a small number of simpler surrogates is used....
Kaehler geometry and SUSY mechanics
International Nuclear Information System (INIS)
Bellucci, Stefano; Nersessian, Armen
2001-01-01
We present two examples of SUSY mechanics related with Kaehler geometry. The first system is the N = 4 supersymmetric one-dimensional sigma-model proposed in hep-th/0101065. Another system is the N = 2 SUSY mechanics whose phase space is the external algebra of an arbitrary Kaehler manifold. The relation of these models with antisymplectic geometry is discussed
A prediction for bubbling geometries
Okuda, Takuya
2007-01-01
We study the supersymmetric circular Wilson loops in N=4 Yang-Mills theory. Their vacuum expectation values are computed in the parameter region that admits smooth bubbling geometry duals. The results are a prediction for the supergravity action evaluated on the bubbling geometries for Wilson loops.
Molecular motion in restricted geometries
Indian Academy of Sciences (India)
Molecular dynamics in restricted geometries is known to exhibit anomalous behaviour. Diffusion, translational or rotational, of molecules is altered significantly on confinement in restricted geometries. Quasielastic neutron scattering (QENS) offers a unique possibility of studying molecular motion in such systems. Both time ...
Parametric excitation of drift waves in a sheared slab geometry
International Nuclear Information System (INIS)
Vranjes, J.; Weiland, J.
1992-01-01
The threshold for parametric excitation of drift waves in a sheared slab geometry is calculated for a pump wave that is a standing wave along the magnetic field, using the Hasegawa-Mima nonlinearity. The shear damping is counteracted by the parametric coupling and the eigenvalue problem is solved analytically using Taylor's strong coupling approximation. (au)
Using Dance to Deepen Student Understanding of Geometry
Moore, Candice; Linder, Sandra M.
2012-01-01
This article provides an example of a collaborative effort between a dance specialist and four third-grade classroom teachers at an arts magnet school. They developed a dance and geometry integration project including implementation strategies, assessment tools, and reflections completed by both the classroom teacher and the third-grade students.…
Pulsar Emission Geometry and Accelerating Field Strength
DeCesar, Megan E.; Harding, Alice K.; Miller, M. Coleman; Kalapotharakos, Constantinos; Parent, Damien
2012-01-01
The high-quality Fermi LAT observations of gamma-ray pulsars have opened a new window to understanding the generation mechanisms of high-energy emission from these systems, The high statistics allow for careful modeling of the light curve features as well as for phase resolved spectral modeling. We modeled the LAT light curves of the Vela and CTA I pulsars with simulated high-energy light curves generated from geometrical representations of the outer gap and slot gap emission models. within the vacuum retarded dipole and force-free fields. A Markov Chain Monte Carlo maximum likelihood method was used to explore the phase space of the magnetic inclination angle, viewing angle. maximum emission radius, and gap width. We also used the measured spectral cutoff energies to estimate the accelerating parallel electric field dependence on radius. under the assumptions that the high-energy emission is dominated by curvature radiation and the geometry (radius of emission and minimum radius of curvature of the magnetic field lines) is determined by the best fitting light curves for each model. We find that light curves from the vacuum field more closely match the observed light curves and multiwavelength constraints, and that the calculated parallel electric field can place additional constraints on the emission geometry
Energy Technology Data Exchange (ETDEWEB)
Lusche, Robert
2015-06-24
The aim of this thesis is to a gain deeper understanding of the single photon detection process in superconducting nanowire single-photon detectors (SNSPDs). A detailed knowledge of the physical principles and mechanisms which the detection process is based on helps to improve specific detector parameters and hence the suitability of such detectors for various applications. Several theoretical models of the detection process have been compared to the results of measurements of photon and dark count rates in meander-type TaN- and NbN-SNSPDs with different wire-widths in a broad range of wavelengths, transport currents and magnetic fields. In the first part of the thesis, measurements of the photon and dark count rates of TaN- and NbN-SNSPDs with varying wire width are described. For each meander spectra of the intrinsic detection efficiency (IDE) were derived. The IDE represents the probability that the SNSPD generates a measurable voltage pulse upon absorption of a photon. The recorded IDE spectra have shown a characteristic cut-off wavelength up to which photons were detected with a probability of 100 per cent. Furthermore it was found that the cut-off wavelengths increases linearly with the increase in the inverse wire width. This observation is best explained by the refined hot spot model. The second part of the thesis describes the influence of magnetic field on the photon and dark count rates of NbN-SNSPDs. In order to apply magnetic fields to the meanders a continuous-flow inset for mobile 4He storage dewars was constructed. It was shown for the first time, that the photon count rate exhibits a magnetic field dependence. Furthermore it could be shown that the measured dependence of the photon and dark count rate on the magnetic field is in good agreement with the theoretical model of vortex-assisted photon detection in narrow superconducting lines. Hence, within this thesis it could be confirmed that magnetic vortices are involved in the single photon
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
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.
Dengg, S; Kneissl, S
2013-01-01
Ferromagnetic material in microchips, used for animal identification, causes local signal increase, signal void or distortion (susceptibility artifact) on MR images. To measure the impact of microchip geometry on the artifact's size, an MRI phantom study was performed. Microchips of the labels Datamars®, Euro-I.D.® and Planet-ID® (n = 15) were placed consecutively in a phantom and examined with respect to the ASTM Standard Test Method F2119-07 using spin echo (TR 500 ms, TE 20 ms), gradient echo (TR 300 ms, TE 15 ms, flip angel 30°) and otherwise constant imaging parameters (slice thickness 3 mm, field of view 250 x 250 mm, acquisition matrix 256 x 256 pixel, bandwidth 32 kHz) at 1.5 Tesla. Image acquisition was undertaken with a microchip positioned in the x- and z-direction and in each case with a phase-encoding direction in the y- and z-direction. The artifact size was determined with a) a measurement according to the test method F2119-07 using a homogeneous point operation, b) signal intensity measurement according to Matsuura et al. and c) pixel counts in the artifact according to Port and Pomper. There was a significant difference in artifact size between the three microchips tested (Wilcoxon p = 0.032). A two- to three-fold increase in microchip volume generated an up to 76% larger artifact, depending on the sequence type, phase-encoding direction and chip position to B0. The smaller the microchip geometry, the less is the susceptibility artifact. Spin echoes (SE) generated smaller artifacts than gradient echoes (GE). In relation to the spatial measurement of the artifact, the switch in phase-encoding direction had less influence on the artifact size in GE- than in SE-sequences. However, the artifact shape and direction of SE-sequences can be changed by altering the phase. The artifact size, caused by the microchip, plays a major clinical role in the evaluation of MRI from the head, shoulder and neck regions.
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)
THE TOPOLOGY OF CANONICAL FLUX TUBES IN FLARED JET GEOMETRY
Energy Technology Data Exchange (ETDEWEB)
Lavine, Eric Sander; You, Setthivoine, E-mail: Slavine2@uw.edu, E-mail: syou@aa.washington.edu [University of Washington, 4000 15th Street, NE Aeronautics and Astronautics 211 Guggenheim Hall, Box 352400, Seattle, WA 98195 (United States)
2017-01-20
Magnetized plasma jets are generally modeled as magnetic flux tubes filled with flowing plasma governed by magnetohydrodynamics (MHD). We outline here a more fundamental approach based on flux tubes of canonical vorticity, where canonical vorticity is defined as the circulation of the species’ canonical momentum. This approach extends the concept of magnetic flux tube evolution to include the effects of finite particle momentum and enables visualization of the topology of plasma jets in regimes beyond MHD. A flared, current-carrying magnetic flux tube in an ion-electron plasma with finite ion momentum is thus equivalent to either a pair of electron and ion flow flux tubes, a pair of electron and ion canonical momentum flux tubes, or a pair of electron and ion canonical vorticity flux tubes. We examine the morphology of all these flux tubes for increasing electrical currents, different radial current profiles, different electron Mach numbers, and a fixed, flared, axisymmetric magnetic geometry. Calculations of gauge-invariant relative canonical helicities track the evolution of magnetic, cross, and kinetic helicities in the system, and show that ion flow fields can unwind to compensate for an increasing magnetic twist. The results demonstrate that including a species’ finite momentum can result in a very long collimated canonical vorticity flux tube even if the magnetic flux tube is flared. With finite momentum, particle density gradients must be normal to canonical vorticities, not to magnetic fields, so observations of collimated astrophysical jets could be images of canonical vorticity flux tubes instead of magnetic flux tubes.
Confinement and related transport in Extrap geometry
International Nuclear Information System (INIS)
Tendler, M.
1983-01-01
The properties of the plasma dynamic equilibrium are investigated for the Extrap magnetic confinement geometry. The temperatures achieved so far in the high-#betta# pinches are much lower than the predicted values. Here, it is shown that the particle containment in Extrap may be improved as compared to the other pinches due to the electrostatic confinement. An analytic solution for the profiles of the plasma parameters are found under the assumption that the energy is lost primarily in the radial direction by heat conduction and convection. An estimate of the radial particle confinement time is given, showing favourable scaling with plasma density and temperature. The conventional assumption of a uniform current density is shown to be unjustified in the case of an inhomogeneous electron temperature. An analytical expression is found for the pinch radius at different mechanisms of the heat transport. (orig.)
The analysis and geometry of Hardy's inequality
Balinsky, Alexander A; Lewis, Roger T
2015-01-01
This volume presents advances that have been made over recent decades in areas of research featuring Hardy's inequality and related topics. The inequality and its extensions and refinements are not only of intrinsic interest but are indispensable tools in many areas of mathematics and mathematical physics. Hardy inequalities on domains have a substantial role and this necessitates a detailed investigation of significant geometric properties of a domain and its boundary. Other topics covered in this volume are Hardy- Sobolev-Maz’ya inequalities; inequalities of Hardy-type involving magnetic fields; Hardy, Sobolev and Cwikel-Lieb-Rosenbljum inequalities for Pauli operators; the Rellich inequality. The Analysis and Geometry of Hardy’s Inequality provides an up-to-date account of research in areas of contemporary interest and would be suitable for a graduate course in mathematics or physics. A good basic knowledge of real and complex analysis is a prerequisite.
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)
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.
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.
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...
DOGBONE GEOMETRY FOR RECIRCULATING ACCELERATORS
International Nuclear Information System (INIS)
BERG, J.S.; JOHNSTONE, C.; SUMMERS, D.
2001-01-01
Most scenarios for accelerating muons require recirculating acceleration. A racetrack shape for the accelerator requires particles with lower energy in early passes to traverse almost the same length of arc as particles with the highest energy. This extra arc length may lead to excess decays and excess cost. Changing the geometry to a dogbone shape, where there is a single linac and the beam turns completely around at the end of the linac, returning to the same end of the linac from which it exited, addresses this problem. In this design, the arc lengths can be proportional to the particle's momentum. This paper proposes an approximate cost model for a recirculating accelerator, attempts to make cost-optimized designs for both racetrack and dogbone geometries, and demonstrates that the dogbone geometry does appear to be more cost effective
Geometric Transformations in Engineering Geometry
Directory of Open Access Journals (Sweden)
I. F. Borovikov
2015-01-01
Full Text Available Recently, for business purposes, in view of current trends and world experience in training engineers, research and faculty staff there has been a need to transform traditional courses of descriptive geometry into the course of engineering geometry in which the geometrical transformations have to become its main section. On the basis of critical analysis the paper gives suggestions to improve a presentation technique of this section both in the classroom and in academic literature, extend an application scope of geometrical transformations to solve the position and metric tasks and simulation of surfaces, as well as to design complex engineering configurations, which meet a number of pre-specified conditions.The article offers to make a number of considerable amendments to the terms and definitions used in the existing courses of descriptive geometry. It draws some conclusions and makes the appropriate proposals on feasibility of coordination in teaching the movement transformation in the courses of analytical and descriptive geometry. This will provide interdisciplinary team teaching and allow students to be convinced that a combination of analytical and graphic ways to solve geometric tasks is useful and reasonable.The traditional sections of learning courses need to be added with a theory of projective and bi-rational transformations. In terms of application simplicity and convenience it is enough to consider the central transformations when solving the applied tasks. These transformations contain a beam of sub-invariant (low-invariant straight lines on which the invariant curve induces non-involution and involution projectivities. The expediency of nonlinear transformations application is shown in the article by a specific example of geometric modeling of the interfacing surface "spar-blade".Implementation of these suggestions will contribute to a real transformation of a traditional course of descriptive geometry to the engineering geometry
Surface magnetic structures in amorphous ferromagnetic microwires
Energy Technology Data Exchange (ETDEWEB)
Usov, N.A., E-mail: usov@obninsk.ru [National University of Science and Technology «MISIS», 119049 Moscow (Russian Federation); Pushkov Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation, Russian Academy of Sciences, IZMIRAN, 108840 Troitsk, Moscow (Russian Federation); Serebryakova, O.N.; Gudoshnikov, S.A. [National University of Science and Technology «MISIS», 119049 Moscow (Russian Federation); Pushkov Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation, Russian Academy of Sciences, IZMIRAN, 108840 Troitsk, Moscow (Russian Federation); Tarasov, V.P. [National University of Science and Technology «MISIS», 119049 Moscow (Russian Federation)
2017-05-01
The spatial period of magnetization perturbations that occur near the surface of magnetic nanotube or nanowire under the influence of surface magnetic anisotropy is determined by means of numerical simulation as a function of the sample geometry and material parameters. The surface magnetization distribution obtained is then used to estimate the period of the surface magnetic texture in amorphous microwire of several micrometers in diameter by means of appropriate variational procedure. The period of the surface magnetic texture in amorphous microwire is found to be significantly smaller than the wire diameter. - Highlights: • Magnetic structure may arise near the magnetic nanotube surface under the influence of surface magnetic anisotropy. • The period of the surface magnetization pattern is calculated as a function of the sample geometry. • Similar magnetic structure may exist in amorphous microwire of several micrometers in diameter. • The period of the surface magnetic structure in amorphous wire is found to be significantly smaller than the wire diameter.
KEMAJUAN BELAJAR SISWA PADA GEOMETRI TRANSFORMASI MENGGUNAKAN AKTIVITAS REFLEKSI GEOMETRI
Directory of Open Access Journals (Sweden)
Irkham Ulil Albab
2014-10-01
Full Text Available Abstrak: Penelitian ini bertujuan untuk mendeskripsikan kemajuan belajar siswa pada materi geometri transformasi yang didukung dengan serangkaian aktivitas belajar berdasarkan Pendidikan Matematika Realistik Indonesia. Penelitian didesain melalui tiga tahap, yaitu tahapan perancangan desain awal, pengujian desain melalui pembelajaran awal dan pembelajaran eksperimental, dan tahap analisis retrospektif. Dalam penelitian ini, Hypothetical Learning Trajectory, HLT (HLT berperan penting sebagai desain pembelajaran sekaligus instrumen penelitian. HLT diujikan terhadap 26 siswa kelas VII. Data dikumpulkan dengan teknik wawancara, pengamatan, dan catatan lapangan. Hasil penelitian menunjukkan bahwa desain pembelajaran ini mampu menstimulasi siswa untuk memberikan karakteristik refleksi dan transformasi geometri lainnya secara informal, mengklasifikasikannya dalam transformasi isometri pada level kedua, dan menemukan garis bantuan refleksi pada level yang lebih formal. Selain itu, garis bantuan refleksi digunakan oleh siswa untuk menggambar bayangan refleksi dan pola pencerminan serta memahami bentuk rotasi dan translasi sebagai kombinasi refleksi adalah level tertinggi. Keyword: transformasi geometri, kombinasi refleksi, rotasi, translasi, design research, HLT STUDENTS’ LEARNING PROGRESS ON TRANSFORMATION GEOMETRY USING THE GEOMETRY REFLECTION ACTIVITIES Abstract: This study was aimed at describing the students’ learning progress on transformation geometry supported by a set of learning activities based on Indonesian Realistic Mathematics Education. The study was designed into three stages, that is, the preliminary design stage, the design testing through initial instruction and experiment, and the restrospective analysis stage. In this study, Hypothetical Learning Trajectory (HLT played an important role as an instructional design and a research instrument. HLT was tested to 26 seventh grade students. The data were collected through interviews
Graphical debugging of combinational geometry
International Nuclear Information System (INIS)
Burns, T.J.; Smith, M.S.
1992-01-01
A graphical debugger for combinatorial geometry being developed at Oak Ridge National Laboratory is described. The prototype debugger consists of two parts: a FORTRAN-based ''view'' generator and a Microsoft Windows application for displaying the geometry. Options and features of both modules are discussed. Examples illustrating the various options available are presented. The potential for utilizing the images produced using the debugger as a visualization tool for the output of the radiation transport codes is discussed as is the future direction of the development
Lectures on Algebraic Geometry I
Harder, Gunter
2012-01-01
This book and the following second volume is an introduction into modern algebraic geometry. In the first volume the methods of homological algebra, theory of sheaves, and sheaf cohomology are developed. These methods are indispensable for modern algebraic geometry, but they are also fundamental for other branches of mathematics and of great interest in their own. In the last chapter of volume I these concepts are applied to the theory of compact Riemann surfaces. In this chapter the author makes clear how influential the ideas of Abel, Riemann and Jacobi were and that many of the modern metho
Combinatorial geometry in the plane
Hadwiger, Hugo; Klee, Victor
2014-01-01
Geared toward advanced undergraduates familiar with analysis and college geometry, this concise book discusses theorems on topics restricted to the plane such as convexity, coverings, and graphs. In addition to helping students cultivate rigorous thought, the text encourages the development of mathematical intuition and clarifies the nature of mathematical research.The two-part treatment begins with specific topics including integral distances, covering problems, point set geometry and convexity, simple paradoxes involving point sets, and pure combinatorics, among other subjects. The second pa
Modern differential geometry for physicists
Isham, C J
1989-01-01
These notes are the content of an introductory course on modern, coordinate-free differential geometry which is taken by the first-year theoretical physics PhD students, or by students attending the one-year MSc course "Fundamental Fields and Forces" at Imperial College. The book is concerned entirely with mathematics proper, although the emphasis and detailed topics have been chosen with an eye to the way in which differential geometry is applied these days to modern theoretical physics. This includes not only the traditional area of general relativity but also the theory of Yang-Mills fields
Comparison theorems in Riemannian geometry
Cheeger, Jeff
2008-01-01
The central theme of this book is the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry. The first five chapters are preparatory in nature. They begin with a very concise introduction to Riemannian geometry, followed by an exposition of Toponogov's theorem-the first such treatment in a book in English. Next comes a detailed presentation of homogeneous spaces in which the main goal is to find formulas for their curvature. A quick chapter of Morse theory is followed by one on the injectivity radius. Chapters 6-9 deal with many of the most re
Geometry, topology, and string theory
Energy Technology Data Exchange (ETDEWEB)
Varadarajan, Uday [Univ. of California, Berkeley, CA (United States)
2003-01-01
A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect. In particular, situations in which extra dimensions, non-commutative geometries as well as other non-local structures emerge are explored in detail. Further, a preliminary exploration of such issues in Lorentzian space-times with non-trivial causal structures within string theory is initiated.
Spatial geometry and special relativity
DEFF Research Database (Denmark)
Kneubil, Fabiana Botelho
2016-01-01
In this work, it is shown the interplay of relative and absolute entities, which are present in both spatial geometry and special relativity. In order to strengthen the understanding of special relativity, we discuss firstly an instance of geometry and the existence of both frame......-dependent and frame-independent entities. We depart from a subject well known by students, which is the three-dimensional geometric space in order to compare, afterwards, with the treatment of four-dimensional space in the special relativity. The differences and similarities between these two subjects are also...
Stochastic geometry and its applications
Chiu, Sung Nok; Kendall, Wilfrid S; Mecke, Joseph
2013-01-01
An extensive update to a classic text Stochastic geometry and spatial statistics play a fundamental role in many modern branches of physics, materials sciences, engineering, biology and environmental sciences. They offer successful models for the description of random two- and three-dimensional micro and macro structures and statistical methods for their analysis. The previous edition of this book has served as the key reference in its field for over 18 years and is regarded as the best treatment of the subject of stochastic geometry, both as a subject with vital a
Introduction to topology and geometry
Stahl, Saul
2014-01-01
An easily accessible introduction to over three centuries of innovations in geometry Praise for the First Edition ". . . a welcome alternative to compartmentalized treatments bound to the old thinking. This clearly written, well-illustrated book supplies sufficient background to be self-contained." -CHOICE This fully revised new edition offers the most comprehensive coverage of modern geometry currently available at an introductory level. The book strikes a welcome balance between academic rigor and accessibility, providing a complete and cohesive picture of the science with an unparallele
Algebraic geometry and theta functions
Coble, Arthur B
1929-01-01
This book is the result of extending and deepening all questions from algebraic geometry that are connected to the central problem of this book: the determination of the tritangent planes of a space curve of order six and genus four, which the author treated in his Colloquium Lecture in 1928 at Amherst. The first two chapters recall fundamental ideas of algebraic geometry and theta functions in such fashion as will be most helpful in later applications. In order to clearly present the state of the central problem, the author first presents the better-known cases of genus two (Chapter III) and
Geometry, topology, and string theory
International Nuclear Information System (INIS)
Varadarajan, Uday
2003-01-01
A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect. In particular, situations in which extra dimensions, non-commutative geometries as well as other non-local structures emerge are explored in detail. Further, a preliminary exploration of such issues in Lorentzian space-times with non-trivial causal structures within string theory is initiated
Energy Technology Data Exchange (ETDEWEB)
Portillo Jimenez, Canek [Universidad Autonoma de Sinaloa, Culiacan, Sinaloa (Mexico)]. E-mail: cnk@uas.uasnet.mx
2010-11-15
It is presented a software application for calculating the thickness of the thermal insulation used in various facilities where there are thermal systems using solar energy. The software facilitates the calculation of the thermal cover thickness over components such as pipes (flat or round), storage and other devices that require thermal protection, installed in outdoors or indoors. The software was programmed in Visual Basic by following the technical specifications of the current regulations in the field. Application examples are performed, obtaining certain results that are discussed briefly. [Spanish] Se presenta un software de aplicacion para el calculo de los espesores de los aislantes termicos, utilizados en diferentes instalaciones donde existen sistemas de aprovechamiento termico de energia solar. El software facilita el calculo del grosor del recubrimiento termico en componentes tales como: tuberias (planas o circulares), depositos acumuladores y otros aparatos que necesiten proteccion termica, instalados en exteriores o en interiores. El software fue programado en Visual Basic siguiendo las especificaciones tecnicas de la normatividad vigente en la materia. Se realizan ejemplos de aplicacion, donde se obtienen ciertos resultados de los cuales se hace una breve discusion.
Almost-commutative geometries beyond the standard model
International Nuclear Information System (INIS)
Stephan, Christoph A
2006-01-01
In Iochum et al (2004 J. Math. Phys. 45 5003), Jureit and Stephan (2005 J. Math. Phys. 46 043512), Schuecker T (2005 Preprint hep-th/0501181) and Jureit et al (2005 J. Math. Phys. 46 072303), a conjecture is presented that almost-commutative geometries, with respect to sensible physical constraints, allow only the standard model of particle physics and electro-strong models as Yang-Mills-Higgs theories. In this paper, a counter-example will be given. The corresponding almost-commutative geometry leads to a Yang-Mills-Higgs model which consists of the standard model of particle physics and two new fermions of opposite electro-magnetic charge. This is the second Yang-Mills-Higgs model within noncommutative geometry, after the standard model, which could be compatible with experiments. Combined to a hydrogen-like composite particle, these new particles provide a novel dark matter candidate
Non commutative geometry and super Yang-Mills theory
International Nuclear Information System (INIS)
Bigatti, D.
1999-01-01
We aim to connect the non commutative geometry 'quotient space' viewpoint with the standard super Yang Mills theory approach in the spirit of Connes-Douglas-Schwartz and Douglas-Hull description of application of noncommutative geometry to matrix theory. This will result in a relation between the parameters of a rational foliation of the torus and the dimension of the group U(N). Namely, we will be provided with a prescription which allows to study a noncommutative geometry with rational parameter p/N by means of a U(N) gauge theory on a torus of size Σ/N with the boundary conditions given by a system with p units of magnetic flux. The transition to irrational parameter can be obtained by letting N and p tend to infinity with fixed ratio. The precise meaning of the limiting process will presumably allow better clarification. (Copyright (c) 1999 Elsevier Science B.V., Amsterdam. All rights reserved.)
Theoretical aspects of magnetic helicity
International Nuclear Information System (INIS)
Hammer, J.H.
1985-01-01
The magnetic helicity, usually defined as K=integralA.Bdv, where A is the vector potential and B the magnetic field, measures the topological linkage of magnetic fluxes. Helicity manifests itself in the twistedness and knottedness of flux tubes. Its significance is that it is an ideal MHD invariant. While the helicity formalism has proven very useful in understanding reversed field pinch and spheromak behavior, some problems exist in applying the method consistently for complex (e.g., toroidal) conductor geometries or in situations where magnetic flux penetrates conducting walls. Recent work has attempted to generalize K to allow for all possible geometries
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...
Energy Technology Data Exchange (ETDEWEB)
Gutierrez Delgado, Wilson; Kubiak, Janusz; Serrano Romero, Luis Enrique [Instituto de Investigaciones Electricas, Cuernavaca (Mexico)
1990-12-31
In the preliminary design and diagnosis of rotary machines is very common to utilize simple calculation methods for the mechanical and thermal stresses, dynamic and thermodynamic analysis and flow of fluids in this machines (Gutierrez et al., 1989). The analysis with these methods provides the necessary results for the project initial stage of the machine. Later on, more complex tools are employed to refine the design of some machine components. In the Gutierrez report et al., (1989) 34 programs were developed for the preliminary design and diagnosis of rotating equipment; in this article, one of them is presented in which a method for the analysis of mechanical and thermal stresses is applied in discs of uniform or variable thickness that are normally found in turbomachines and rotary equipment. [Espanol] En el diseno preliminar y diagnostico de maquinas rotatorias es muy comun emplear metodos de calculo sencillos para el analisis de esfuerzos mecanicos y termicos, analisis dinamico y termodinamico y de flujo de fluidos en estas maquinas (Gutierrez et al., 1989). El analisis con estos metodos proporcionan los resultados necesarios para la etapa del proyecto inicial de la maquina. Posteriormente, para refinar el diseno de algunos componentes de la maquina, se aplican las herramientas mas complejas. En el informe de Gutierrez et al., (1989) se desarrollan 34 programas para el diseno preliminar y diagnostico de equipo rotatorio; en este articulo, se presenta uno de ellos, en el que se emplea un metodo para el analisis de esfuerzos mecanicos y termicos en discos de espesor constante o variable que se encuentran comunmente en turbomaquinas y en equipos rotatorios.
Energy Technology Data Exchange (ETDEWEB)
Gutierrez Delgado, Wilson; Kubiak, Janusz; Serrano Romero, Luis Enrique [Instituto de Investigaciones Electricas, Cuernavaca (Mexico)
1991-12-31
In the preliminary design and diagnosis of rotary machines is very common to utilize simple calculation methods for the mechanical and thermal stresses, dynamic and thermodynamic analysis and flow of fluids in this machines (Gutierrez et al., 1989). The analysis with these methods provides the necessary results for the project initial stage of the machine. Later on, more complex tools are employed to refine the design of some machine components. In the Gutierrez report et al., (1989) 34 programs were developed for the preliminary design and diagnosis of rotating equipment; in this article, one of them is presented in which a method for the analysis of mechanical and thermal stresses is applied in discs of uniform or variable thickness that are normally found in turbomachines and rotary equipment. [Espanol] En el diseno preliminar y diagnostico de maquinas rotatorias es muy comun emplear metodos de calculo sencillos para el analisis de esfuerzos mecanicos y termicos, analisis dinamico y termodinamico y de flujo de fluidos en estas maquinas (Gutierrez et al., 1989). El analisis con estos metodos proporcionan los resultados necesarios para la etapa del proyecto inicial de la maquina. Posteriormente, para refinar el diseno de algunos componentes de la maquina, se aplican las herramientas mas complejas. En el informe de Gutierrez et al., (1989) se desarrollan 34 programas para el diseno preliminar y diagnostico de equipo rotatorio; en este articulo, se presenta uno de ellos, en el que se emplea un metodo para el analisis de esfuerzos mecanicos y termicos en discos de espesor constante o variable que se encuentran comunmente en turbomaquinas y en equipos rotatorios.
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...
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 ...
Comparative analysis of linear motor geometries for Stirling coolers
R, Rajesh V.; Kuzhiveli, Biju T.
2017-12-01
Compared to rotary motor driven Stirling coolers, linear motor coolers are characterized by small volume and long life, making them more suitable for space and military applications. The motor design and operational characteristics have a direct effect on the operation of the cooler. In this perspective, ample scope exists in understanding the behavioural description of linear motor systems. In the present work, the authors compare and analyze different moving magnet linear motor geometries to finalize the most favourable one for Stirling coolers. The required axial force in the linear motors is generated by the interaction of magnetic fields of a current carrying coil and that of a permanent magnet. The compact size, commercial availability of permanent magnets and low weight requirement of the system are quite a few constraints for the design. The finite element analysis performed using Maxwell software serves as the basic tool to analyze the magnet movement, flux distribution in the air gap and the magnetic saturation levels on the core. A number of material combinations are investigated for core before finalizing the design. The effect of varying the core geometry on the flux produced in the air gap is also analyzed. The electromagnetic analysis of the motor indicates that the permanent magnet height ought to be taken in such a way that it is under the influence of electromagnetic field of current carrying coil as well as the outer core in the balanced position. This is necessary so that sufficient amount of thrust force is developed by efficient utilisation of the air gap flux density. Also, the outer core ends need to be designed to facilitate enough room for the magnet movement under the operating conditions.
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)
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.
International Nuclear Information System (INIS)
Suess, S.T.
1987-01-01
Magnetic clouds are a carefully defined subclass of all interplanetary signatures of coronal mass ejections whose geometry is thought to be that of a cylinder embedded in a plane. It has been found that the total magnetic pressure inside the clouds is higher than the ion pressure outside, and that the clouds are expanding at 1 AU at about half the local Alfven speed. The geometry of the clouds is such that even though the magnetic pressure inside is larger than the total pressure outside, expansion will not occur because the pressure is balanced by magnetic tension - the pinch effect. The evidence for expansion of clouds at 1 AU is nevertheless quite strong so another reason for its existence must be found. It is demonstrated that the observations can be reproduced by taking into account the effects of geometrical distortion of the low plasma beta clouds as they move away from the Sun
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
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.
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
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
ONIX results: Comparison of grid geometry (BATMAN - ELISE - flat grid)
Revel, Adrien; Mochalskyy, Serhiy; Wünderlich, Dirk; Fantz, Ursel; Minea, Tiberiu
2017-08-01
The 3D PIC-MCC code ONIX is dedicated to the modelling of negative hydrogen or deuterium ion extraction and the co-extracted electrons from the plasma in radio-frequency driven sources. The extraction process highly depends on the plasma characteristics close to the plasma grid where it is difficult to obtain experimental data. ONIX brings valuable insights on the plasma behavior in this area. In the code, the numerical treatment of the boundaries have been improved in order to describe with more accuracy the potential and the electric field in this vicinity. The computation time has been reduced by a factor of 2 and the parallelization efficiency has been highly improved. The influence of the magnetic field in BATMAN on the plasma behaviour has been investigated by comparing two different configurations of the magnet bars producing the filter field (internal magnets: x = 3 cm; external magnets: x = 9 cm). A flat grid geometry for the PG instead of the usual conical grid geometry has been studied to evaluate its impact on the extracted current, especially for the negative ions emitted from the surface of the PG. Finally, the ONIX code has been used for the first 3D PIC calculations ever performed for the ELISE experiment.
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.
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.)
Energy Technology Data Exchange (ETDEWEB)
Castillo Diaz, Ramon
2002-06-15
In this work the method of the finite element is applied to the bi-dimensional analysis of the induction motor in operation in steady state, excited by sine sources of laminar currents and sine sources of voltage. The analysis is focused mainly in the calculation of the electromagnetic torque. The topics of electromagnetic theory are covered and in an idealized model of the induction motor, analytically and numerically with the method of the finite element, in the variant method of Galerkin, the vectorial potential and the torque are calculated. The results obtained with the analytical and numerical methods are compared. Three formulations are developed to calculate the torque with the method of the finite element, using triangular elements of first order, based in the equation of force of Lorentz, the Maxwell tensor and the principle of the virtual work. Finally, a motor of induction of real characteristics is simulated, assuming it is connected to a three-phase voltage source. In this motor it is analyzed the convergence and the evolution in the results obtained of the torque with different discretions, and the torque-velocity performance curve is calculated. [Spanish] En este trabajo se aplica el metodo del elemento finito al analisis bidimensional del motor de induccion en operacion en estado estable, excitado por fuentes de corriente laminar senoidales y fuentes de voltaje senoidales. El analisis se enfoca principalmente en el calculo del par electromagnetico. Se tratan los topicos de teoria electromagnetica involucrados y en un modelo idealizado del motor de induccion, se calculan analitica y numericamente con el metodo del elemento finito, en la variante metodo de Galerkin, el potencial vectorial y el par. Se comparan resultados obtenidos con los metodos analiticos y numericos. Se desarrollan tres formulaciones para calcular el par con el metodo del elemento finito, utilizando elementos triangulares de primer orden, basadas en la ecuacion de fuerza de
Stochastic geometry for image analysis
Descombes, Xavier
2013-01-01
This book develops the stochastic geometry framework for image analysis purpose. Two main frameworks are described: marked point process and random closed sets models. We derive the main issues for defining an appropriate model. The algorithms for sampling and optimizing the models as well as for estimating parameters are reviewed. Numerous applications, covering remote sensing images, biological and medical imaging, are detailed. This book provides all the necessary tools for developing an image analysis application based on modern stochastic modeling.
Programming system for analytic geometry
International Nuclear Information System (INIS)
Raymond, Jacques
1970-01-01
After having outlined the characteristics of computing centres which do not comply with engineering tasks, notably the time required by all different tasks to be performed when developing a software (assembly, compilation, link edition, loading, run), and identified constraints specific to engineering, the author identifies the characteristics a programming system should have to suit engineering tasks. He discussed existing conversational systems and their programming language, and their main drawbacks. Then, he presents a system which aims at facilitating programming and addressing problems of analytic geometry and trigonometry
The geometry of special relativity
International Nuclear Information System (INIS)
Parizet, Jean
2008-01-01
This book for students in mathematics or physics shows the interest of geometry to understand special relativity as a consequence of invariance of Maxwell equations and of constancy of the speed of light. Space-time is actually provided with a geometrical structure and a physical interpretation: at each observer are associated his own time and his own physical space in which occur events he is concerned with. This leads to a natural approach to special relativity. The Lorentz group and its algebra are then studied by using matrices and the Pauli algebra. Quaternions are also addressed
Moduli spaces in algebraic geometry
International Nuclear Information System (INIS)
Goettsche, L.
2000-01-01
This volume of the new series of lecture notes of the Abdus Salam International Centre for Theoretical Physics contains the lecture notes of the School on Algebraic Geometry which took place at the Abdus Salam International Centre for Theoretical Physics from 26 July to 13 August 1999. The school consisted of 2 weeks of lecture courses and one week of conference. The topic of the school was moduli spaces. More specifically the lectures were divided into three subtopics: principal bundles on Riemann surfaces, moduli spaces of vector bundles and sheaves on projective varieties, and moduli spaces of curves
Worldsheet geometries of ambitwistor string
Energy Technology Data Exchange (ETDEWEB)
Ohmori, Kantaro [Department of Physics, the University of Tokyo,Hongo, Bunkyo-ku, Tokyo 133-0022 (Japan)
2015-06-12
Mason and Skinner proposed the ambitwistor string theory which directly reproduces the formulas for the amplitudes of massless particles proposed by Cachazo, He and Yuan. In this paper we discuss geometries of the moduli space of worldsheets associated to the bosonic or the RNS ambitwistor string. Further, we investigate the factorization properties of the amplitudes when an internal momentum is near on-shell in the abstract CFT language. Along the way, we propose the existence of the ambitwistor strings with three or four fermionic worldsheet currents.
Porous media geometry and transports
Adler, Pierre
1992-01-01
The goal of ""Porous Media: Geometry and Transports"" is to provide the basis of a rational and modern approach to porous media. This book emphasizes several geometrical structures (spatially periodic, fractal, and random to reconstructed) and the three major single-phase transports (diffusion, convection, and Taylor dispersion).""Porous Media"" serves various purposes. For students it introduces basic information on structure and transports. Engineers will find this book useful as a readily accessible assemblage of al the major experimental results pertaining to single-phase tr
Geometry of physical dispersion relations
International Nuclear Information System (INIS)
Raetzel, Dennis; Rivera, Sergio; Schuller, Frederic P.
2011-01-01
To serve as a dispersion relation, a cotangent bundle function must satisfy three simple algebraic properties. These conditions are derived from the inescapable physical requirements that local matter field dynamics must be predictive and allow for an observer-independent notion of positive energy. Possible modifications of the standard relativistic dispersion relation are thereby severely restricted. For instance, the dispersion relations associated with popular deformations of Maxwell theory by Gambini-Pullin or Myers-Pospelov are not admissible. Dispersion relations passing the simple algebraic checks derived here correspond to physically admissible Finslerian refinements of Lorentzian geometry.
Projective geometry and projective metrics
Busemann, Herbert
2005-01-01
The basic results and methods of projective and non-Euclidean geometry are indispensable for the geometer, and this book--different in content, methods, and point of view from traditional texts--attempts to emphasize that fact. Results of special theorems are discussed in detail only when they are needed to develop a feeling for the subject or when they illustrate a general method. On the other hand, an unusual amount of space is devoted to the discussion of the fundamental concepts of distance, motion, area, and perpendicularity.Topics include the projective plane, polarities and conic sectio
Tropical geometry of statistical models.
Pachter, Lior; Sturmfels, Bernd
2004-11-16
This article presents a unified mathematical framework for inference in graphical models, building on the observation that graphical models are algebraic varieties. From this geometric viewpoint, observations generated from a model are coordinates of a point in the variety, and the sum-product algorithm is an efficient tool for evaluating specific coordinates. Here, we address the question of how the solutions to various inference problems depend on the model parameters. The proposed answer is expressed in terms of tropical algebraic geometry. The Newton polytope of a statistical model plays a key role. Our results are applied to the hidden Markov model and the general Markov model on a binary tree.
Geometry of supersymmetric gauge theories
International Nuclear Information System (INIS)
Gieres, F.
1988-01-01
This monograph gives a detailed and pedagogical account of the geometry of rigid superspace and supersymmetric Yang-Mills theories. While the core of the text is concerned with the classical theory, the quantization and anomaly problem are briefly discussed following a comprehensive introduction to BRS differential algebras and their field theoretical applications. Among the treated topics are invariant forms and vector fields on superspace, the matrix-representation of the super-Poincare group, invariant connections on reductive homogeneous spaces and the supermetric approach. Various aspects of the subject are discussed for the first time in textbook and are consistently presented in a unified geometric formalism
Clustering in Hilbert simplex geometry
Nielsen, Frank
2017-04-03
Clustering categorical distributions in the probability simplex is a fundamental primitive often met in applications dealing with histograms or mixtures of multinomials. Traditionally, the differential-geometric structure of the probability simplex has been used either by (i) setting the Riemannian metric tensor to the Fisher information matrix of the categorical distributions, or (ii) defining the information-geometric structure induced by a smooth dissimilarity measure, called a divergence. In this paper, we introduce a novel computationally-friendly non-Riemannian framework for modeling the probability simplex: Hilbert simplex geometry. We discuss the pros and cons of those three statistical modelings, and compare them experimentally for clustering tasks.
An invitation to noncommutative geometry
Marcolli, Matilde
2008-01-01
This is the first existing volume that collects lectures on this important and fast developing subject in mathematics. The lectures are given by leading experts in the field and the range of topics is kept as broad as possible by including both the algebraic and the differential aspects of noncommutative geometry as well as recent applications to theoretical physics and number theory. Sample Chapter(s). A Walk in the Noncommutative Garden (1,639 KB). Contents: A Walk in the Noncommutative Garden (A Connes & M Marcolli); Renormalization of Noncommutative Quantum Field Theory (H Grosse & R Wulke
Trends and developments in computational geometry
Berg, de M.
1997-01-01
This paper discusses some trends and achievements in computational geometry during the past five years, with emphasis on problems related to computer graphics. Furthermore, a direction of research in computational geometry is discussed that could help in bringing the fields of computational geometry
Global affine differential geometry of hypersurfaces
Li, An-Min; Zhao, Guosong; Hu, Zejun
2015-01-01
This book draws a colorful and widespread picture of global affine hypersurface theory up to the most recent state. Moreover, the recent development revealed that affine differential geometry- as differential geometry in general- has an exciting intersection area with other fields of interest, like partial differential equations, global analysis, convex geometry and Riemann surfaces.
"WGL," a Web Laboratory for Geometry
Quaresma, Pedro; Santos, Vanda; Maric, Milena
2018-01-01
The role of information and communication technologies (ICT) in education is nowadays well recognised. The "Web Geometry Laboratory," is an e-learning, collaborative and adaptive, Web environment for geometry, integrating a well known dynamic geometry system. In a collaborative session, teachers and students, engaged in solving…
Control of flow geometry using electromagnetic body forcing
International Nuclear Information System (INIS)
Rossi, L.; Bocquet, S.; Ferrari, S.; Garcia de la Cruz, J.M.; Lardeau, S.
2009-01-01
This paper presents conceptual experiments and simulations aiming at controlling flow geometries. Such flow design is performed by driving electromagnetically a shallow layer of brine, the forcing being generated by a transverse electrical current and different combinations of permanent magnets placed underneath the brine supporting wall. It is shown how different basic flow characteristics can be obtained with a single pair of magnets, by varying the angle with the electrical current. These basic flows are proposed as potential building blocks for advanced and complex flows studies. Three typical flow structures are presented to illustrate these building blocks. The discussion is then extended to multi-scale geometry by using blocks of various sizes. The flow is analysed using complementary experiments and numerical simulations. A good agreement is found between the 3D simulations and the experiments for both velocity and acceleration fields, which allows a higher degree of confidence in designing and modelling such flows. As the control of the flow geometry is important for mixing, in particular at low Reynolds number, we also illustrate the different stirring properties of the electromagnetically forced flows by comparing visualisations of passive scalars. They reveal complementary mixing properties for each of the building blocks.
Computational geometry algorithms and applications
de Berg, Mark; Overmars, Mark; Schwarzkopf, Otfried
1997-01-01
Computational geometry emerged from the field of algorithms design and anal ysis in the late 1970s. It has grown into a recognized discipline with its own journals, conferences, and a large community of active researchers. The suc cess of the field as a research discipline can on the one hand be explained from the beauty of the problems studied and the solutions obtained, and, on the other hand, by the many application domains--computer graphics, geographic in formation systems (GIS), robotics, and others-in which geometric algorithms play a fundamental role. For many geometric problems the early algorithmic solutions were either slow or difficult to understand and implement. In recent years a number of new algorithmic techniques have been developed that improved and simplified many of the previous approaches. In this textbook we have tried to make these modem algorithmic solutions accessible to a large audience. The book has been written as a textbook for a course in computational geometry, but it can ...
Tearing modes in toroidal geometry
International Nuclear Information System (INIS)
Connor, J.W.; Cowley, S.C.; Hastie, R.J.; Hender, T.C.; Hood, A.; Martin, T.J.
1988-01-01
The separation of the cylindrical tearing mode stability problem into a resistive resonant layer calculation and an external marginal ideal magnetohydrodynamic (MHD) calculation (Δ' calculation) is generalized to axisymmetric toroidal geometry. The general structure of this separation is analyzed and the marginal ideal MHD information (the toroidal generalization of Δ') required to discuss stability is isolated. This can then, in principle, be combined with relevant resonant layer calculations to determine tearing mode growth rates in realistic situations. Two examples are given: the first is an analytic treatment of toroidally coupled (m = 1, n = 1) and (m = 2, n = 1) tearing modes in a large aspect ratio torus; the second, a numerical treatment of the toroidal coupling of three tearing modes through finite pressure effects in a large aspect ratio torus. In addition, the use of a coupling integral approach for determining the stability of coupled tearing modes is discussed. Finally, the possibility of using initial value resistive MHD codes in realistic toroidal geometry to determine the necessary information from the ideal MHD marginal solution is discussed
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.
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...
Differential geometry of group lattices
International Nuclear Information System (INIS)
Dimakis, Aristophanes; Mueller-Hoissen, Folkert
2003-01-01
In a series of publications we developed ''differential geometry'' on discrete sets based on concepts of noncommutative geometry. In particular, it turned out that first-order differential calculi (over the algebra of functions) on a discrete set are in bijective correspondence with digraph structures where the vertices are given by the elements of the set. A particular class of digraphs are Cayley graphs, also known as group lattices. They are determined by a discrete group G and a finite subset S. There is a distinguished subclass of ''bicovariant'' Cayley graphs with the property ad(S)S subset of S. We explore the properties of differential calculi which arise from Cayley graphs via the above correspondence. The first-order calculi extend to higher orders and then allow us to introduce further differential geometric structures. Furthermore, we explore the properties of ''discrete'' vector fields which describe deterministic flows on group lattices. A Lie derivative with respect to a discrete vector field and an inner product with forms is defined. The Lie-Cartan identity then holds on all forms for a certain subclass of discrete vector fields. We develop elements of gauge theory and construct an analog of the lattice gauge theory (Yang-Mills) action on an arbitrary group lattice. Also linear connections are considered and a simple geometric interpretation of the torsion is established. By taking a quotient with respect to some subgroup of the discrete group, generalized differential calculi associated with so-called Schreier diagrams are obtained
Geometry of anisotropic CO outflows
International Nuclear Information System (INIS)
Liseau, R.; Sandell, G.; Helsinki Univ., Observatory, Finland)
1986-01-01
A simple geometrical model for the space motions of the bipolar high-velocity CO outflows in regions of recent, active star formation is proposed. It is assumed that the velocity field of the neutral gas component can be represented by large-scale uniform motions. From observations of the spatial distribution and from the characteristics of the line shape of the high-velocity molecular gas emission the geometry of the line-emitting regions can be inferred, i.e., the direction in space and the collimating angle of the flow. The model has been applied to regions where a check on presently obtained results is provided by independent optical determinations of the motions of Herbig-Haro objects associated with the CO flows. These two methods are in good agreement and, furthermore, the results obtained provide convincingly strong evidence for the physical association of CO outflows and Herbig-Haro objects. This also supports the common view that a young stellar central source is responsible for the active phenomena observed in its environmental neighborhood. It is noteworthy that within the framework of the model the determination of the flow geometry of the high-velocity gas from CO measurements is independent of the distance to the source and, furthermore, can be done at relatively low spatial resolution. 32 references
Current deposition profiles in advanced geometries
International Nuclear Information System (INIS)
Wright, J.C.; Phillips, C.K.; Bonoli, P.T.
1997-01-01
In advanced toroidal devices, plasma shaping can have a significant effect on quantities of interest, including the radio frequency (RF) deposited power and current. Most 2D RF modeling codes use a parameterization of current drive efficiencies to calculate fast wave driven currents. This parameterization is derived from a ray-tracing model in a low-beta model equilibrium. There are difficulties in applying it to a spectrum of waves, and it cannot account for multiple resonances and coherency effects between the electrons and the waves. By evaluating a formulation of the quasilinear diffusion coefficient in an arbitrary inhomogenous geometry with the fields from a full wave code, we address the effects of wave spectra, plasma inhomogeneity, and plasma profile on the evaluation of current deposition profiles. Current profiles are calculated directly from the quasilinear diffusion using the adjoint formulation, with the magnetic equilibrium specified consistently in both the adjoint routine and the full wave code. Results are benchmarked by comparing a power deposition calculation from conductivity to one from the quasilinear expression. RF driven current profiles for various devices, including tokamaks with different aspect ratios, will be presented. copyright 1997 American Institute of Physics
Canonical differential geometry of string backgrounds
International Nuclear Information System (INIS)
Schuller, Frederic P.; Wohlfarth, Mattias N.R.
2006-01-01
String backgrounds and D-branes do not possess the structure of Lorentzian manifolds, but that of manifolds with area metric. Area metric geometry is a true generalization of metric geometry, which in particular may accommodate a B-field. While an area metric does not determine a connection, we identify the appropriate differential geometric structure which is of relevance for the minimal surface equation in such a generalized geometry. In particular the notion of a derivative action of areas on areas emerges naturally. Area metric geometry provides new tools in differential geometry, which promise to play a role in the description of gravitational dynamics on D-branes
Stationary metrics and optical Zermelo-Randers-Finsler geometry
International Nuclear Information System (INIS)
Gibbons, G. W.; Warnick, C. M.; Herdeiro, C. A. R.; Werner, M. C.
2009-01-01
We consider a triality between the Zermelo navigation problem, the geodesic flow on a Finslerian geometry of Randers type, and spacetimes in one dimension higher admitting a timelike conformal Killing vector field. From the latter viewpoint, the data of the Zermelo problem are encoded in a (conformally) Painleve-Gullstrand form of the spacetime metric, whereas the data of the Randers problem are encoded in a stationary generalization of the usual optical metric. We discuss how the spacetime viewpoint gives a simple and physical perspective on various issues, including how Finsler geometries with constant flag curvature always map to conformally flat spacetimes and that the Finsler condition maps to either a causality condition or it breaks down at an ergo surface in the spacetime picture. The gauge equivalence in this network of relations is considered as well as the connection to analogue models and the viewpoint of magnetic flows. We provide a variety of examples.
Separation of attractors in 1-modulus quantum corrected special geometry
Bellucci, S; Marrani, A; Shcherbakov, A
2008-01-01
We study the solutions to the N=2, d=4 Attractor Equations in a dyonic, extremal, static, spherically symmetric and asymptotically flat black hole background, in the simplest case of perturbative quantum corrected cubic Special Kahler geometry consistent with continuous axion-shift symmetry, namely in the 1-modulus Special Kahler geometry described (in a suitable special symplectic coordinate) by the holomorphic Kahler gauge-invariant prepotential F=t^3+i*lambda, with lambda real. By performing computations in the ``magnetic'' charge configuration, we find evidence for interesting phenomena (absent in the classical limit of vanishing lambda). Namely, for a certain range of the quantum parameter lambda we find a ``splitting'' of attractors, i.e. the existence of multiple solutions to the Attractor Equations for fixed supporting charge configuration. This corresponds to the existence of ``area codes'' in the radial evolution of the scalar t, determined by the various disconnected regions of the moduli space, wh...
Ambient Occlusion Effects for Combined Volumes and Tubular Geometry
Schott, M.
2013-06-01
This paper details a method for interactive direct volume rendering that computes ambient occlusion effects for visualizations that combine both volumetric and geometric primitives, specifically tube-shaped geometric objects representing streamlines, magnetic field lines or DTI fiber tracts. The algorithm extends the recently presented the directional occlusion shading model to allow the rendering of those geometric shapes in combination with a context providing 3D volume, considering mutual occlusion between structures represented by a volume or geometry. Stream tube geometries are computed using an effective spline-based interpolation and approximation scheme that avoids self-intersection and maintains coherent orientation of the stream tube segments to avoid surface deforming twists. Furthermore, strategies to reduce the geometric and specular aliasing of the stream tubes are discussed.
Ambient Occlusion Effects for Combined Volumes and Tubular Geometry
Schott, M.; Martin, T.; Grosset, A. V. P.; Smith, S. T.; Hansen, C. D.
2013-01-01
This paper details a method for interactive direct volume rendering that computes ambient occlusion effects for visualizations that combine both volumetric and geometric primitives, specifically tube-shaped geometric objects representing streamlines, magnetic field lines or DTI fiber tracts. The algorithm extends the recently presented the directional occlusion shading model to allow the rendering of those geometric shapes in combination with a context providing 3D volume, considering mutual occlusion between structures represented by a volume or geometry. Stream tube geometries are computed using an effective spline-based interpolation and approximation scheme that avoids self-intersection and maintains coherent orientation of the stream tube segments to avoid surface deforming twists. Furthermore, strategies to reduce the geometric and specular aliasing of the stream tubes are discussed.
Differential Geometry Based Multiscale Models
Wei, Guo-Wei
2010-01-01
Large chemical and biological systems such as fuel cells, ion channels, molecular motors, and viruses are of great importance to the scientific community and public health. Typically, these complex systems in conjunction with their aquatic environment pose a fabulous challenge to theoretical description, simulation, and prediction. In this work, we propose a differential geometry based multiscale paradigm to model complex macromolecular systems, and to put macroscopic and microscopic descriptions on an equal footing. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum mechanical description of the aquatic environment with the microscopic discrete atom-istic description of the macromolecule. Multiscale free energy functionals, or multiscale action functionals are constructed as a unified framework to derive the governing equations for the dynamics of different scales and different descriptions. Two types of aqueous macromolecular complexes, ones that are near equilibrium and others that are far from equilibrium, are considered in our formulations. We show that generalized Navier–Stokes equations for the fluid dynamics, generalized Poisson equations or generalized Poisson–Boltzmann equations for electrostatic interactions, and Newton's equation for the molecular dynamics can be derived by the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. Comparison is given to classical descriptions of the fluid and electrostatic interactions without geometric flow based micro-macro interfaces. The detailed balance of forces is emphasized in the present work. We further extend the proposed multiscale paradigm to micro-macro analysis of electrohydrodynamics, electrophoresis, fuel cells, and ion channels. We derive generalized Poisson–Nernst–Planck equations that
Differential geometry based multiscale models.
Wei, Guo-Wei
2010-08-01
Large chemical and biological systems such as fuel cells, ion channels, molecular motors, and viruses are of great importance to the scientific community and public health. Typically, these complex systems in conjunction with their aquatic environment pose a fabulous challenge to theoretical description, simulation, and prediction. In this work, we propose a differential geometry based multiscale paradigm to model complex macromolecular systems, and to put macroscopic and microscopic descriptions on an equal footing. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum mechanical description of the aquatic environment with the microscopic discrete atomistic description of the macromolecule. Multiscale free energy functionals, or multiscale action functionals are constructed as a unified framework to derive the governing equations for the dynamics of different scales and different descriptions. Two types of aqueous macromolecular complexes, ones that are near equilibrium and others that are far from equilibrium, are considered in our formulations. We show that generalized Navier-Stokes equations for the fluid dynamics, generalized Poisson equations or generalized Poisson-Boltzmann equations for electrostatic interactions, and Newton's equation for the molecular dynamics can be derived by the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. Comparison is given to classical descriptions of the fluid and electrostatic interactions without geometric flow based micro-macro interfaces. The detailed balance of forces is emphasized in the present work. We further extend the proposed multiscale paradigm to micro-macro analysis of electrohydrodynamics, electrophoresis, fuel cells, and ion channels. We derive generalized Poisson-Nernst-Planck equations that are
Hopf algebras in noncommutative geometry
International Nuclear Information System (INIS)
Varilly, Joseph C.
2001-10-01
We give an introductory survey to the use of Hopf algebras in several problems of non- commutative geometry. The main example, the Hopf algebra of rooted trees, is a graded, connected Hopf algebra arising from a universal construction. We show its relation to the algebra of transverse differential operators introduced by Connes and Moscovici in order to compute a local index formula in cyclic cohomology, and to the several Hopf algebras defined by Connes and Kreimer to simplify the combinatorics of perturbative renormalization. We explain how characteristic classes for a Hopf module algebra can be obtained from the cyclic cohomology of the Hopf algebra which acts on it. Finally, we discuss the theory of non- commutative spherical manifolds and show how they arise as homogeneous spaces of certain compact quantum groups. (author)
Integrable systems, geometry, and topology
Terng, Chuu-Lian
2006-01-01
The articles in this volume are based on lectures from a program on integrable systems and differential geometry held at Taiwan's National Center for Theoretical Sciences. As is well-known, for many soliton equations, the solutions have interpretations as differential geometric objects, and thereby techniques of soliton equations have been successfully applied to the study of geometric problems. The article by Burstall gives a beautiful exposition on isothermic surfaces and their relations to integrable systems, and the two articles by Guest give an introduction to quantum cohomology, carry out explicit computations of the quantum cohomology of flag manifolds and Hirzebruch surfaces, and give a survey of Givental's quantum differential equations. The article by Heintze, Liu, and Olmos is on the theory of isoparametric submanifolds in an arbitrary Riemannian manifold, which is related to the n-wave equation when the ambient manifold is Euclidean. Mukai-Hidano and Ohnita present a survey on the moduli space of ...
Tarski Geometry Axioms. Part III
Directory of Open Access Journals (Sweden)
Coghetto Roland
2017-12-01
Full Text Available In the article, we continue the formalization of the work devoted to Tarski’s geometry - the book “Metamathematische Methoden in der Geometrie” by W. Schwabhäuser, W. Szmielew, and A. Tarski. After we prepared some introductory formal framework in our two previous Mizar articles, we focus on the regular translation of underlying items faithfully following the abovementioned book (our encoding covers first seven chapters. Our development utilizes also other formalization efforts of the same topic, e.g. Isabelle/HOL by Makarios, Metamath or even proof objects obtained directly from Prover9. In addition, using the native Mizar constructions (cluster registrations the propositions (“Satz” are reformulated under weaker conditions, i.e. by using fewer axioms or by proposing an alternative version that uses just another axioms (ex. Satz 2.1 or Satz 2.2.
Applied geometry and discrete mathematics
Sturm; Gritzmann, Peter; Sturmfels, Bernd
1991-01-01
This volume, published jointly with the Association for Computing Machinery, comprises a collection of research articles celebrating the occasion of Victor Klee's sixty-fifth birthday in September 1990. During his long career, Klee has made contributions to a wide variety of areas, such as discrete and computational geometry, convexity, combinatorics, graph theory, functional analysis, mathematical programming and optimization, and theoretical computer science. In addition, Klee made important contributions to mathematics education, mathematical methods in economics and the decision sciences, applications of discrete mathematics in the biological and social sciences, and the transfer of knowledge from applied mathematics to industry. In honor of Klee's achievements, this volume presents more than forty papers on topics related to Klee's research. While the majority of the papers are research articles, a number of survey articles are also included. Mirroring the breadth of Klee's mathematical contributions, th...
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...
Some Progress in Conformal Geometry
Directory of Open Access Journals (Sweden)
Sun-Yung A. Chang
2007-12-01
Full Text Available This is a survey paper of our current research on the theory of partial differential equations in conformal geometry. Our intention is to describe some of our current works in a rather brief and expository fashion. We are not giving a comprehensive survey on the subject and references cited here are not intended to be complete. We introduce a bubble tree structure to study the degeneration of a class of Yamabe metrics on Bach flat manifolds satisfying some global conformal bounds on compact manifolds of dimension 4. As applications, we establish a gap theorem, a finiteness theorem for diffeomorphism type for this class, and diameter bound of the $sigma_2$-metrics in a class of conformal 4-manifolds. For conformally compact Einstein metrics we introduce an eigenfunction compactification. As a consequence we obtain some topological constraints in terms of renormalized volumes.
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
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...
Quantization of the Schwarzschild geometry
International Nuclear Information System (INIS)
Melas, Evangelos
2013-01-01
The conditional symmetries of the reduced Einstein-Hilbert action emerging from a static, spherically symmetric geometry are used as supplementary conditions on the wave function. Based on their integrability conditions, only one of the three existing symmetries can be consistently imposed, while the unique Casimir invariant, being the product of the remaining two symmetries, is calculated as the only possible second condition on the wave function. This quadratic integral of motion is identified with the reparametrization generator, as an implication of the uniqueness of the dynamical evolution, by fixing a suitable parametrization of the r-lapse function. In this parametrization, the determinant of the supermetric plays the role of the mesure. The combined Wheeler – DeWitt and linear conditional symmetry equations are analytically solved. The solutions obtained depend on the product of the two ''scale factors''.
Eliashberg, Yakov; Maeda, Yoshiaki; Symplectic, Poisson, and Noncommutative geometry
2014-01-01
Symplectic geometry originated in physics, but it has flourished as an independent subject in mathematics, together with its offspring, symplectic topology. Symplectic methods have even been applied back to mathematical physics. Noncommutative geometry has developed an alternative mathematical quantization scheme based on a geometric approach to operator algebras. Deformation quantization, a blend of symplectic methods and noncommutative geometry, approaches quantum mechanics from a more algebraic viewpoint, as it addresses quantization as a deformation of Poisson structures. This volume contains seven chapters based on lectures given by invited speakers at two May 2010 workshops held at the Mathematical Sciences Research Institute: Symplectic and Poisson Geometry in Interaction with Analysis, Algebra and Topology (honoring Alan Weinstein, one of the key figures in the field) and Symplectic Geometry, Noncommutative Geometry and Physics. The chapters include presentations of previously unpublished results and ...
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.
Geometrical protection of topological magnetic solitons in microprocessed chiral magnets
Mito, Masaki; Ohsumi, Hiroyuki; Tsuruta, Kazuki; Kotani, Yoshinori; Nakamura, Tetsuya; Togawa, Yoshihiko; Shinozaki, Misako; Kato, Yusuke; Kishine, Jun-ichiro; Ohe, Jun-ichiro; Kousaka, Yusuke; Akimitsu, Jun; Inoue, Katsuya
2018-01-01
A chiral soliton lattice stabilized in a monoaxial chiral magnet CrNb3S6 is a magnetic superlattice consisting of magnetic kinks with a ferromagnetic background. The magnetic kinks are considered to be topological magnetic solitons (TMSs). Changes in the TMS number yield discretized responses in magnetization and electrical conductivity, and this effect is more prominent in smaller crystals. We demonstrate that, in microprocessed CrNb3S6 crystals, TMSs are geometrically protected through element-selected micromagnetometry using soft x-ray magnetic circular dichroism (MCD). A series of x-ray MCD data is supported by mean-field and micromagnetic analyses. By designing the microcrystal geometry, TMS numbers can be successfully changed and fixed over a wide range of magnetic fields.
Rational design of the exchange-spring permanent magnet.
Jiang, J S; Bader, S D
2014-02-12
The development of the optimal exchange-spring permanent magnet balances exchange hardening, magnetization enhancement, and the feasibility of scalable fabrication. These requirements can be met with a rational design of the microstructural characteristics. The magnetization processes in several model exchange-spring structures with different geometries have been analyzed with both micromagnetic simulations and nucleation theory. The multilayer geometry and the soft-cylinders-in-hard-matrix geometry have the highest achievable figure of merit (BH)max, while the soft-spheres-in-hard-matrix geometry has the lowest upper limit for (BH)max. The cylindrical geometry permits the soft phase to be larger and does not require strict size control. Exchange-spring permanent magnets based on the cylindrical geometry may be amenable to scaled-up fabrication.
Rational design of the exchange-spring permanent magnet
International Nuclear Information System (INIS)
Jiang, J S; Bader, S D
2014-01-01
The development of the optimal exchange-spring permanent magnet balances exchange hardening, magnetization enhancement, and the feasibility of scalable fabrication. These requirements can be met with a rational design of the microstructural characteristics. The magnetization processes in several model exchange-spring structures with different geometries have been analyzed with both micromagnetic simulations and nucleation theory. The multilayer geometry and the soft-cylinders-in-hard-matrix geometry have the highest achievable figure of merit (BH) max , while the soft-spheres-in-hard-matrix geometry has the lowest upper limit for (BH) max . The cylindrical geometry permits the soft phase to be larger and does not require strict size control. Exchange-spring permanent magnets based on the cylindrical geometry may be amenable to scaled-up fabrication. (paper)
Magnetic matrices used in high gradient magnetic separation (HGMS: A review
Directory of Open Access Journals (Sweden)
Wei Ge
Full Text Available HGMS is effective in separating or filtering fine and weakly magnetic particles and widely applied in mineral processing, water treatment, cell and protein purification. The magnetic matrix is a crucial device used in magnetic separator to generate high magnetic field gradient and provide surface sites for capturing magnetic particles. The material, geometry, size and arrangement of the matrix elements can significantly affect the gradient and distribution of the magnetic field, and the separating or filtrating performance. In this paper, the researches and developments of magnetic matrices used in HGMS are reviewed. Keywords: Magnetic matrix, HGMS, Review
Connections between algebra, combinatorics, and geometry
Sather-Wagstaff, Sean
2014-01-01
Commutative algebra, combinatorics, and algebraic geometry are thriving areas of mathematical research with a rich history of interaction. Connections Between Algebra, Combinatorics, and Geometry contains lecture notes, along with exercises and solutions, from the Workshop on Connections Between Algebra and Geometry held at the University of Regina from May 29-June 1, 2012. It also contains research and survey papers from academics invited to participate in the companion Special Session on Interactions Between Algebraic Geometry and Commutative Algebra, which was part of the CMS Summer Meeting at the University of Regina held June 2–3, 2012, and the meeting Further Connections Between Algebra and Geometry, which was held at the North Dakota State University, February 23, 2013. This volume highlights three mini-courses in the areas of commutative algebra and algebraic geometry: differential graded commutative algebra, secant varieties, and fat points and symbolic powers. It will serve as a useful resou...
Second International workshop Geometry and Symbolic Computation
Walczak, Paweł; Geometry and its Applications
2014-01-01
This volume has been divided into two parts: Geometry and Applications. The geometry portion of the book relates primarily to geometric flows, laminations, integral formulae, geometry of vector fields on Lie groups, and osculation; the articles in the applications portion concern some particular problems of the theory of dynamical systems, including mathematical problems of liquid flows and a study of cycles for non-dynamical systems. This Work is based on the second international workshop entitled "Geometry and Symbolic Computations," held on May 15-18, 2013 at the University of Haifa and is dedicated to modeling (using symbolic calculations) in differential geometry and its applications in fields such as computer science, tomography, and mechanics. It is intended to create a forum for students and researchers in pure and applied geometry to promote discussion of modern state-of-the-art in geometric modeling using symbolic programs such as Maple™ and Mathematica®, as well as presentation of new results. ...
Superconducting dipole magnet for the UTSI MHD facility
International Nuclear Information System (INIS)
Wang, S.T.; Niemann, R.C.; Turner, L.R.
1978-01-01
The Argonne National Laboratory is designing and will build a large superconducting dipole magnet system for use in the Coal Fired Flow MHD Research Facility at the University of Tennessee Space Institute (UTSI). Presented in detail are the conceptual design of the magnet geometry, conductor design, cryostability evaluation, magnetic pressure computation, structural design, cryostat design, the cryogenics system design, and magnet instrumentations and control
A vector space approach to geometry
Hausner, Melvin
2010-01-01
The effects of geometry and linear algebra on each other receive close attention in this examination of geometry's correlation with other branches of math and science. In-depth discussions include a review of systematic geometric motivations in vector space theory and matrix theory; the use of the center of mass in geometry, with an introduction to barycentric coordinates; axiomatic development of determinants in a chapter dealing with area and volume; and a careful consideration of the particle problem. 1965 edition.
Classical geometry Euclidean, transformational, inversive, and projective
Leonard, I E; Liu, A C F; Tokarsky, G W
2014-01-01
Features the classical themes of geometry with plentiful applications in mathematics, education, engineering, and science Accessible and reader-friendly, Classical Geometry: Euclidean, Transformational, Inversive, and Projective introduces readers to a valuable discipline that is crucial to understanding bothspatial relationships and logical reasoning. Focusing on the development of geometric intuitionwhile avoiding the axiomatic method, a problem solving approach is encouraged throughout. The book is strategically divided into three sections: Part One focuses on Euclidean geometry, which p
submitter Optimization of Nb$_{3}$Sn Rutherford Cables Geometry for the High Luminosity LHC
Fleiter, Jerome; Bonasia, Angelo; Bordini, Bernardo; Richter, David
2017-01-01
The quadrupole and dipole magnets for the LHC High Luminosity (HL-LHC) upgrade will be based on Nb$_{3}$Sn Rutherford cables that operate at 1.9 K and experience magnetic fields of up to about 12 T. An important step in the design of these magnets is the development of the high aspect ratio Nb$_{3}$Sn cables to achieve the nominal field with sufficient margin. The strong plastic deformation of unreacted $Nb_3Sn$ strands during the Rutherford cabling process may induce non negligible $I_c$ and RRR degradation. In this paper, the cabling degradation is investigated as a function of the cable geometry for both PIT and RRP conductors. Based on this analysis, new baseline geometries for both 11 T and QXF magnets of HL-LHC are proposed.
submitter Optimization of Nb$_{3}$Sn Rutherford Cables Geometry for the High Luminosity LHC
Fleiter, Jerome; Bonasia, Angelo; Bordini, Bernardo; Richter, David
2017-01-01
The quadrupole and dipole magnets for the LHC High Luminosity (HL-LHC) upgrade will be based on Nb3Sn Rutherford cables that operate at 1.9 K and experience magnetic fields of up to about 12 T. An important step in the design of these magnets is the development of the high aspect ratio Nb3Sn cables to achieve the nominal field with sufficient margin. The strong plastic deformation of unreacted $Nb_3Sn$ strands during the Rutherford cabling process may induce non negligible $I_c$ and RRR degradation. In this paper, the cabling degradation is investigated as a function of the cable geometry for both PIT and RRP conductors. Based on this analysis, new baseline geometries for both 11 T and QXF magnets of HL-LHC are proposed.
Introduction to non-Euclidean geometry
Wolfe, Harold E
2012-01-01
One of the first college-level texts for elementary courses in non-Euclidean geometry, this concise, readable volume is geared toward students familiar with calculus. A full treatment of the historical background explores the centuries-long efforts to prove Euclid's parallel postulate and their triumphant conclusion. Numerous original exercises form an integral part of the book.Topics include hyperbolic plane geometry and hyperbolic plane trigonometry, applications of calculus to the solutions of some problems in hyperbolic geometry, elliptic plane geometry and trigonometry, and the consistenc
Disformal transformation in Newton-Cartan geometry
Energy Technology Data Exchange (ETDEWEB)
Huang, Peng [Zhejiang Chinese Medical University, Department of Information, Hangzhou (China); Sun Yat-Sen University, School of Physics and Astronomy, Guangzhou (China); Yuan, Fang-Fang [Nankai University, School of Physics, Tianjin (China)
2016-08-15
Newton-Cartan geometry has played a central role in recent discussions of the non-relativistic holography and condensed matter systems. Although the conformal transformation in non-relativistic holography can easily be rephrased in terms of Newton-Cartan geometry, we show that it requires a nontrivial procedure to arrive at the consistent form of anisotropic disformal transformation in this geometry. Furthermore, as an application of the newly obtained transformation, we use it to induce a geometric structure which may be seen as a particular non-relativistic version of the Weyl integrable geometry. (orig.)
Applications of Affine and Weyl geometry
García-Río, Eduardo; Nikcevic, Stana
2013-01-01
Pseudo-Riemannian geometry is, to a large extent, the study of the Levi-Civita connection, which is the unique torsion-free connection compatible with the metric structure. There are, however, other affine connections which arise in different contexts, such as conformal geometry, contact structures, Weyl structures, and almost Hermitian geometry. In this book, we reverse this point of view and instead associate an auxiliary pseudo-Riemannian structure of neutral signature to certain affine connections and use this correspondence to study both geometries. We examine Walker structures, Riemannia
Special Geometry and Automorphic Forms
Berglund, P; Wyllard, N; Berglund, Per; Henningson, Mans; Wyllard, Niclas
1997-01-01
We consider special geometry of the vector multiplet moduli space in compactifications of the heterotic string on $K3 \\times T^2$ or the type IIA string on $K3$-fibered Calabi-Yau threefolds. In particular, we construct a modified dilaton that is invariant under $SO(2, n; Z)$ T-duality transformations at the non-perturbative level and regular everywhere on the moduli space. The invariant dilaton, together with a set of other coordinates that transform covariantly under $SO(2, n; Z)$, parameterize the moduli space. The construction involves a meromorphic automorphic function of $SO(2, n; Z)$, that also depends on the invariant dilaton. In the weak coupling limit, the divisor of this automorphic form is an integer linear combination of the rational quadratic divisors where the gauge symmetry is enhanced classically. We also show how the non-perturbative prepotential can be expressed in terms of meromorphic automorphic forms, by expanding a T-duality invariant quantity both in terms of the standard special coord...
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
Geometry of lattice field theory
International Nuclear Information System (INIS)
Honan, T.J.
1986-01-01
Using some tools of algebraic topology, a general formalism for lattice field theory is presented. The lattice is taken to be a simplicial complex that is also a manifold and is referred to as a simplicial manifold. The fields on this lattice are cochains, that are called lattice forms to emphasize the connections with differential forms in the continuum. This connection provides a new bridge between lattice and continuum field theory. A metric can be put onto this simplicial manifold by assigning lengths to every link or I-simplex of the lattice. Regge calculus is a way of defining general relativity on this lattice. A geometric discussion of Regge calculus is presented. The Regge action, which is a discrete form of the Hilbert action, is derived from the Hilbert action using distribution valued forms. This is a new derivation that emphasizes the underlying geometry. Kramers-Wannier duality in statistical mechanics is discussed in this general setting. Nonlinear field theories, which include gauge theories and nonlinear sigma models are discussed in the continuum and then are put onto a lattice. The main new result here is the generalization to curved spacetime, which consists of making the theory compatible with Regge calculus
Latent geometry of bipartite networks
Kitsak, Maksim; Papadopoulos, Fragkiskos; Krioukov, Dmitri
2017-03-01
Despite the abundance of bipartite networked systems, their organizing principles are less studied compared to unipartite networks. Bipartite networks are often analyzed after projecting them onto one of the two sets of nodes. As a result of the projection, nodes of the same set are linked together if they have at least one neighbor in common in the bipartite network. Even though these projections allow one to study bipartite networks using tools developed for unipartite networks, one-mode projections lead to significant loss of information and artificial inflation of the projected network with fully connected subgraphs. Here we pursue a different approach for analyzing bipartite systems that is based on the observation that such systems have a latent metric structure: network nodes are points in a latent metric space, while connections are more likely to form between nodes separated by shorter distances. This approach has been developed for unipartite networks, and relatively little is known about its applicability to bipartite systems. Here, we fully analyze a simple latent-geometric model of bipartite networks and show that this model explains the peculiar structural properties of many real bipartite systems, including the distributions of common neighbors and bipartite clustering. We also analyze the geometric information loss in one-mode projections in this model and propose an efficient method to infer the latent pairwise distances between nodes. Uncovering the latent geometry underlying real bipartite networks can find applications in diverse domains, ranging from constructing efficient recommender systems to understanding cell metabolism.
Fractal Geometry and Stochastics V
Falconer, Kenneth; Zähle, Martina
2015-01-01
This book brings together leading contributions from the fifth conference on Fractal Geometry and Stochastics held in Tabarz, Germany, in March 2014. The book is divided into five sections covering different facets of this fast developing area: geometric measure theory, self-similar fractals and recurrent structures, analysis and algebra on fractals, multifractal theory, and random constructions. There are state-of-the-art surveys as well as papers highlighting more specific recent advances. The authors are world-experts who present their topics comprehensibly and attractively. The book provides an accessible gateway to the subject for newcomers as well as a reference for recent developments for specialists. Authors include: Krzysztof Barański, Julien Barral, Kenneth Falconer, De-Jun Feng, Peter J. Grabner, Rostislav Grigorchuk, Michael Hinz, Stéphane Jaffard, Maarit Järvenpää, Antti Käenmäki, Marc Kesseböhmer, Michel Lapidus, Klaus Mecke, Mark Pollicott, Michał Rams, Pablo Shmerkin, and András Te...
Stochastic geometry in PRIZMA code
International Nuclear Information System (INIS)
Malyshkin, G. N.; Kashaeva, E. A.; Mukhamadiev, R. F.
2007-01-01
The paper describes a method used to simulate radiation transport through random media - randomly placed grains in a matrix material. The method models the medium consequently from one grain crossed by particle trajectory to another. Like in the Limited Chord Length Sampling (LCLS) method, particles in grains are tracked in the actual grain geometry, but unlike LCLS, the medium is modeled using only Matrix Chord Length Sampling (MCLS) from the exponential distribution and it is not necessary to know the grain chord length distribution. This helped us extend the method to media with randomly oriented arbitrarily shaped convex grains. Other extensions include multicomponent media - grains of several sorts, and polydisperse media - grains of different sizes. Sort and size distributions of crossed grains were obtained and an algorithm was developed for sampling grain orientations and positions. Special consideration was given to medium modeling at the boundary of the stochastic region. The method was implemented in the universal 3D Monte Carlo code PRIZMA. The paper provides calculated results for a model problem where we determine volume fractions of modeled components crossed by particle trajectories. It also demonstrates the use of biased sampling techniques implemented in PRIZMA for solving a problem of deep penetration in model random media. Described are calculations for the spectral response of a capacitor dose detector whose anode was modeled with account for its stochastic structure. (authors)
The geometry of population genetics
Akin, Ethan
1979-01-01
The differential equations which model the action of selection and recombination are nonlinear equations which are impossible to It is even difficult to describe in general the solve explicitly. Recently, Shahshahani began using qualitative behavior of solutions. differential geometry to study these equations [28]. with this mono graph I hope to show that his ideas illuminate many aspects of pop ulation genetics. Among these are his proof and clarification of Fisher's Fundamental Theorem of Natural Selection and Kimura's Maximum Principle and also the effect of recombination on entropy. We also discover the relationship between two classic measures of 2 genetic distance: the x measure and the arc-cosine measure. There are two large applications. The first is a precise definition of the biological concept of degree of epistasis which applies to general (i.e. frequency dependent) forms of selection. The second is the unexpected appearance of cycling. We show that cycles can occur in the two-locus-two-allele...
Topics in Cubic Special Geometry
Bellucci, Stefano; Roychowdhury, Raju
2011-01-01
We reconsider the sub-leading quantum perturbative corrections to N=2 cubic special Kaehler geometries. Imposing the invariance under axion-shifts, all such corrections (but the imaginary constant one) can be introduced or removed through suitable, lower unitriangular symplectic transformations, dubbed Peccei-Quinn (PQ) transformations. Since PQ transformations do not belong to the d=4 U-duality group G4, in symmetric cases they generally have a non-trivial action on the unique quartic invariant polynomial I4 of the charge representation R of G4. This leads to interesting phenomena in relation to theory of extremal black hole attractors; namely, the possibility to make transitions between different charge orbits of R, with corresponding change of the supersymmetry properties of the supported attractor solutions. Furthermore, a suitable action of PQ transformations can also set I4 to zero, or vice versa it can generate a non-vanishing I4: this corresponds to transitions between "large" and "small" charge orbit...
Resistance transition assisted geometry enhanced magnetoresistance in semiconductors
International Nuclear Information System (INIS)
Luo, Zhaochu; Zhang, Xiaozhong
2015-01-01
Magnetoresistance (MR) reported in some non-magnetic semiconductors (particularly silicon) has triggered considerable interest owing to the large magnitude of the effect. Here, we showed that MR in lightly doped n-Si can be significantly enhanced by introducing two diodes and proper design of the carrier path [Wan, Nature 477, 304 (2011)]. We designed a geometrical enhanced magnetoresistance (GEMR) device whose room-temperature MR ratio reaching 30% at 0.065 T and 20 000% at 1.2 T, respectively, approaching the performance of commercial MR devices. The mechanism of this GEMR is: the diodes help to define a high resistive state (HRS) and a low resistive state (LRS) in device by their openness and closeness, respectively. The ratio of apparent resistance between HRS and LRS is determined by geometry of silicon wafer and electrodes. Magnetic field could induce a transition from LRS to HRS by reshaping potential and current distribution among silicon wafer, resulting in a giant enhancement of intrinsic MR. We expect that this GEMR could be also realized in other semiconductors. The combination of high sensitivity to low magnetic fields and large high-field response should make this device concept attractive to the magnetic field sensing industry. Moreover, because this MR device is based on a conventional silicon/semiconductor platform, it should be possible to integrate this MR device with existing silicon/semiconductor devices and so aid the development of silicon/semiconductor-based magnetoelectronics. Also combining MR devices and semiconducting devices in a single Si/semiconductor chip may lead to some novel devices with hybrid function, such as electric-magnetic-photonic properties. Our work demonstrates that the charge property of semiconductor can be used in the magnetic sensing industry, where the spin properties of magnetic materials play a role traditionally
Solar wind acceleration in a prescribed flow geometry
International Nuclear Information System (INIS)
Biernat, H.; Koemle, N.; Lichtenegger, H.
1985-01-01
It is known that the flow tubes above coronal holes diverge stronger than radial and that the magnetic field lines may be considerably curved near the border of the holes. The authors investigate the consequences of such a magnetic field geometry on the flow of the solar wind plasma in the vicinity of the Sun. For this purpose the one-dimensional conservation equations are solved along prescribed flow tubes. A temperature profile based on observational data (EUV rocket-observations) is used in the calculations. In an alternative approach the temperature is determined by a polytropic index, which is assumed to be variable. The authors study how both curvature and non-radial divergence of the flow tubes modify the velocity, the density, and the energy balance of the solar wind plasma. (Auth.)
Sieve Tube Geometry in Relation to Phloem Flow
Mullendore, Daniel L.; Windt, Carel W.; Van As, Henk; Knoblauch, Michael
2010-01-01
Sieve elements are one of the least understood cell types in plants. Translocation velocities and volume flow to supply sinks with photoassimilates greatly depend on the geometry of the microfluidic sieve tube system and especially on the anatomy of sieve plates and sieve plate pores. Several models for phloem translocation have been developed, but appropriate data on the geometry of pores, plates, sieve elements, and flow parameters are lacking. We developed a method to clear cells from cytoplasmic constituents to image cell walls by scanning electron microscopy. This method allows high-resolution measurements of sieve element and sieve plate geometries. Sieve tube–specific conductivity and its reduction by callose deposition after injury was calculated for green bean (Phaseolus vulgaris), bamboo (Phyllostachys nuda), squash (Cucurbita maxima), castor bean (Ricinus communis), and tomato (Solanum lycopersicum). Phloem sap velocity measurements by magnetic resonance imaging velocimetry indicate that higher conductivity is not accompanied by a higher velocity. Studies on the temporal development of callose show that small sieve plate pores might be occluded by callose within minutes, but plants containing sieve tubes with large pores need additional mechanisms. PMID:20354199
Investigation of Surface Phenomena in Shocked Tin in Converging Geometry
Energy Technology Data Exchange (ETDEWEB)
Rousculp, Christopher L. [Los Alamos National Laboratory; Oro, David Michael [Los Alamos National Laboratory; Griego, Jeffrey Randall [Los Alamos National Laboratory; Turchi, Peter John [Los Alamos National Laboratory; Reinovsky, Robert Emil [Los Alamos National Laboratory; Bradley, Joseph Thomas [Los Alamos National Laboratory; Cheng, Baolian [Los Alamos National Laboratory; Freeman, Matthew Stouten [Los Alamos National Laboratory; Patten, Austin Randall [Los Alamos National Laboratory
2016-03-21
There is great interest in the behavior of the free surface of tin under shock loading. While it is known that meso-scale surface imperfections can seed the Richtmyer- Meshkov Instability (RMI) for a surface that is melted on release, much less is known about a tin surface that is solid, but plastically deforming. Here material properties such as shear and yield strength come into play especially in converging geometry. Previous experiments have been driven by direct contact HE. Usually a thin, flat target coupon is fielded with various single-mode, sinusoidal, machined, profiles on the free surface. The free surface is adjacent to either vacuum or an inert receiver gas. Most of these previous driver/target configurations have been nominal planer geometry. With modern HE it has been straightforward to shock tin into melt on release. However it has been challenging to achieve a low enough pressure for solid state on release. Here we propose to extend the existing base of knowledge to include the behavior of the free surface of tin in cylindrical converging geometry. By shock loading a cylindrical tin shell with a magnetically driven cylindrical liner impactor, the free surface evolution can be diagnosed with proton radiography. With the PHELIX capacitor bank, the drive can easily be varied to span the pressure range to achieve solid, mixed, and liquid states on release. A conceptual cylindrical liner and target is shown in Figure 1.
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
The geometry of elementary particles
International Nuclear Information System (INIS)
Lov, T.R.
1987-01-01
A new model of elementary particles based on the geometry of Quantum deSitter space QdS = SU (3,2)/(SU(3,1) x U(1)) is introduced and studied. QdS is a complexification of quantization of anti-de Sitter space, AdS = SO(3,2)/SO(3,1), which in recent years had played a pivotal role in supergravity. The nontrival principle fiber bundle has total space SU(3,2), fiber SU(3,1) x U(1) and base QdS. In this setting, the standard recipes for Yang-Mills fields don't work. These require connections and the associated covariant derivatives. Here it is shown that the Lie derivatives, not the covariant derivatives are important in quantization. In this setting, the no-go theorems are not valid. This new quantum mechanics leads to a model of elementary particles as vertical vector fields in the bundle with interaction via the Lie bracket. There are five physical interactions modelled by the bracket interaction. The quantum numbers are identified as the roots of su(3,2) and are preserved under the bracket interaction. The model explains conservation of charge, baryon number, lepton number, parity and the heirarchy problem. Since the bracket is the curvature of a homogeneous space, particles are then the curvature of QdS. This model for particles is consistent with the requirements of General Relativity. Furthermore, since the curvature tensor is built from the quantized wave functions, the curvature tensor is quantized and this is quantum theory of gravity
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
Description of SSG Geometry - phase 1
DEFF Research Database (Denmark)
Margheritini, Lucia; Kofoed, Jens Peter
The purpose of the study is to define the optimized geometry for the SSG in Svaheia, Norway and to provide the responsible for the turbines with useful information to their work.......The purpose of the study is to define the optimized geometry for the SSG in Svaheia, Norway and to provide the responsible for the turbines with useful information to their work....
Increasing insightful thinking in analytic geometry
Timmer, Mark; Verhoef, Neeltje Cornelia
Elsewhere in this issue Ferdinand Verhulst described the discussion of the interaction of analysis and geometry in the 19th century. In modern times such discussions come up again and again. As of 2014, synthetic geometry will not be part of the Dutch 'vwo - mathematics B' programme anymore.
Symposium on Differential Geometry and Differential Equations
Berger, Marcel; Bryant, Robert
1987-01-01
The DD6 Symposium was, like its predecessors DD1 to DD5 both a research symposium and a summer seminar and concentrated on differential geometry. This volume contains a selection of the invited papers and some additional contributions. They cover recent advances and principal trends in current research in differential geometry.
Curvature tensor copies in affine geometry
International Nuclear Information System (INIS)
Srivastava, P.P.
1981-01-01
The sets of space-time and spin-connections which give rise to the same curvature tensor are constructed. The corresponding geometries are compared. Results are illustrated by an explicit calculation and comment on the copies in Einstein-Cartan and Weyl-Cartan geometries. (Author) [pt
Fractal geometry of high temperature superconductors
International Nuclear Information System (INIS)
Mosolov, A.B.
1989-01-01
Microstructural geometry of superconducting structural composites of Ag-Yba 2 Cu 3 O x system with a volumetric shave of silver from 0 to 60% is investigated by light and electron microscopy methods. It is ascertained that the structure of cermets investigated is characterized by fractal geometry which is sufficient for describing the electrical and mechanical properties of these materials
Quantification of variability in bedform geometry
van der Mark, C.F.; Blom, Astrid; Hulscher, Suzanne J.M.H.
2008-01-01
We analyze the variability in bedform geometry in laboratory and field studies. Even under controlled steady flow conditions in laboratory flumes, bedforms are irregular in size, shape, and spacing, also in case of well-sorted sediment. Our purpose is to quantify the variability in bedform geometry.
Random geometry and Yang-Mills theory
International Nuclear Information System (INIS)
Froehlich, J.
1981-01-01
The author states various problems and discusses a very few preliminary rigorous results in a branch of mathematics and mathematical physics which one might call random (or stochastic) geometry. Furthermore, he points out why random geometry is important in the quantization of Yang-Mills theory. (Auth.)
The Geometry of the Universe: Part 2
Francis, Stephanie
2009-01-01
Hyperbolic geometry occurs on hyperbolic planes--the most commonly cited one being a saddle shape. In this article, the author explores negative hyperbolic curvature, and provides a detailed description of how she constructed two hyperbolic paraboloids. Hyperbolic geometry occurs on surfaces that have negative curvature. (Contains 11 figures and 4…
Poisson geometry from a Dirac perspective
Meinrenken, Eckhard
2018-03-01
We present proofs of classical results in Poisson geometry using techniques from Dirac geometry. This article is based on mini-courses at the Poisson summer school in Geneva, June 2016, and at the workshop Quantum Groups and Gravity at the University of Waterloo, April 2016.
An approach for management of geometry data
Dube, R. P.; Herron, G. J.; Schweitzer, J. E.; Warkentine, E. R.
1980-01-01
The strategies for managing Integrated Programs for Aerospace Design (IPAD) computer-based geometry are described. The computer model of geometry is the basis for communication, manipulation, and analysis of shape information. IPAD's data base system makes this information available to all authorized departments in a company. A discussion of the data structures and algorithms required to support geometry in IPIP (IPAD's data base management system) is presented. Through the use of IPIP's data definition language, the structure of the geometry components is defined. The data manipulation language is the vehicle by which a user defines an instance of the geometry. The manipulation language also allows a user to edit, query, and manage the geometry. The selection of canonical forms is a very important part of the IPAD geometry. IPAD has a canonical form for each entity and provides transformations to alternate forms; in particular, IPAD will provide a transformation to the ANSI standard. The DBMS schemas required to support IPAD geometry are explained.
Transformasi Geometri Rotasi Berbantuan Software Geogebra
Directory of Open Access Journals (Sweden)
Muhamad Hanafi
2018-02-01
Full Text Available Penelitian ini bertujuan untuk membantu visualisasi dan menemukan konsep pada Transformasi geometri Rotasi di titik Pusat dengan menggunakan software GeoGebra. Penelitian ini mengulas tentang Koordinat Kartesius dan Polar, dan selanjutntya Transformasi geometri Rotasi di titik Pusat .
Muhassanah, Nuraini; Sujadi, Imam; Riyadi, Riyadi
2014-01-01
The objective of this research was to describe the VIII grade students geometry skills atSMP N 16 Surakarta in the level 0 (visualization), level 1 (analysis), and level 2 (informaldeduction) van Hiele level of thinking in solving the geometry problem. This research was aqualitative research in the form of case study analyzing deeply the students geometry skill insolving the geometry problem based on van Hiele level of thingking. The subject of this researchwas nine students of VIII grade at ...
The design of geometry teaching: learning from the geometry textbooks of Godfrey and Siddons
Fujita, Taro; Jones, Keith
2002-01-01
Deciding how to teach geometry remains a demanding task with one of major arguments being about how to combine the intuitive and deductive aspects of geometry into an effective teaching design. In order to try to obtain an insight into tackling this issue, this paper reports an analysis of innovative geometry textbooks which were published in the early part of the 20th Century, a time when significant efforts were being made to improve the teaching and learning of geometry. The analysis sugge...
International Nuclear Information System (INIS)
Toepfer, J.; Pawlowski, B.; Beer, H.; Ploetner, K.; Hofmann, P.; Herrfurth, J.
2004-01-01
Multi-pole magnetization of NdFeB plate magnets of thickness between 0.25 and 2 mm with a stripe pattern and a pole pitch of 2 or 1 mm was performed by pulse magnetization. The experimental conditions of the magnetization process were optimized to give a maximum surface flux density at the poles. The magnetic field distribution above the magnets was measured with a field mapping device that automatically scans the surface of the magnet with a Hall probe. It is demonstrated for different magnet geometries that the field mapping system is a useful device to study the magnetic surface pole structure. The characterization of the pole flux density of multi-pole NdFeB flat magnets is an important prerequisite for the application of these magnets in miniature actuators
Some simulation aspects, from molecular systems to stochastic geometries of pebble bed reactors
International Nuclear Information System (INIS)
Mazzolo, A.
2009-06-01
After a brief presentation of his teaching and supervising activities, the author gives an overview of his research activities: investigation of atoms under high intensity magnetic field (investigation of the electronic structure under these fields), studies of theoretical and numerical electrochemistry (simulation coupling molecular dynamics and quantum calculations, comprehensive simulations of molecular dynamics), and studies relating stochastic geometry and neutron science
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
FINAL REPORT: GEOMETRY AND ELEMENTARY PARTICLE PHYSICS
Energy Technology Data Exchange (ETDEWEB)
Singer, Isadore M.
2008-03-04
The effect on mathematics of collaborations between high-energy theoretical physics and modern mathematics has been remarkable. Mirror symmetry has revolutionized enumerative geometry, and Seiberg-Witten invariants have greatly simplified the study of four manifolds. And because of their application to string theory, physicists now need to know cohomology theory, characteristic classes, index theory, K-theory, algebraic geometry, differential geometry, and non-commutative geometry. Much more is coming. We are experiencing a deeper contact between the two sciences, which will stimulate new mathematics essential to the physicists’ quest for the unification of quantum mechanics and relativity. Our grant, supported by the Department of Energy for twelve years, has been instrumental in promoting an effective interaction between geometry and string theory, by supporting the Mathematical Physics seminar, postdoc research, collaborations, graduate students and several research papers.
Machine learning spatial geometry from entanglement features
You, Yi-Zhuang; Yang, Zhao; Qi, Xiao-Liang
2018-02-01
Motivated by the close relations of the renormalization group with both the holography duality and the deep learning, we propose that the holographic geometry can emerge from deep learning the entanglement feature of a quantum many-body state. We develop a concrete algorithm, call the entanglement feature learning (EFL), based on the random tensor network (RTN) model for the tensor network holography. We show that each RTN can be mapped to a Boltzmann machine, trained by the entanglement entropies over all subregions of a given quantum many-body state. The goal is to construct the optimal RTN that best reproduce the entanglement feature. The RTN geometry can then be interpreted as the emergent holographic geometry. We demonstrate the EFL algorithm on a 1D free fermion system and observe the emergence of the hyperbolic geometry (AdS3 spatial geometry) as we tune the fermion system towards the gapless critical point (CFT2 point).
Final Report: Geometry And Elementary Particle Physics
International Nuclear Information System (INIS)
Singer, Isadore M.
2008-01-01
The effect on mathematics of collaborations between high-energy theoretical physics and modern mathematics has been remarkable. Mirror symmetry has revolutionized enumerative geometry, and Seiberg-Witten invariants have greatly simplified the study of four manifolds. And because of their application to string theory, physicists now need to know cohomology theory, characteristic classes, index theory, K-theory, algebraic geometry, differential geometry, and non-commutative geometry. Much more is coming. We are experiencing a deeper contact between the two sciences, which will stimulate new mathematics essential to the physicists quest for the unification of quantum mechanics and relativity. Our grant, supported by the Department of Energy for twelve years, has been instrumental in promoting an effective interaction between geometry and string theory, by supporting the Mathematical Physics seminar, postdoc research, collaborations, graduate students and several research papers.
Special metrics and group actions in geometry
Fino, Anna; Musso, Emilio; Podestà, Fabio; Vezzoni, Luigi
2017-01-01
The volume is a follow-up to the INdAM meeting “Special metrics and quaternionic geometry” held in Rome in November 2015. It offers a panoramic view of a selection of cutting-edge topics in differential geometry, including 4-manifolds, quaternionic and octonionic geometry, twistor spaces, harmonic maps, spinors, complex and conformal geometry, homogeneous spaces and nilmanifolds, special geometries in dimensions 5–8, gauge theory, symplectic and toric manifolds, exceptional holonomy and integrable systems. The workshop was held in honor of Simon Salamon, a leading international scholar at the forefront of academic research who has made significant contributions to all these subjects. The articles published here represent a compelling testimony to Salamon’s profound and longstanding impact on the mathematical community. Target readership includes graduate students and researchers working in Riemannian and complex geometry, Lie theory and mathematical physics.
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…
Drawing Dynamic Geometry Figures Online with Natural Language for Junior High School Geometry
Wong, Wing-Kwong; Yin, Sheng-Kai; Yang, Chang-Zhe
2012-01-01
This paper presents a tool for drawing dynamic geometric figures by understanding the texts of geometry problems. With the tool, teachers and students can construct dynamic geometric figures on a web page by inputting a geometry problem in natural language. First we need to build the knowledge base for understanding geometry problems. With the…
Primes, Geometry and Condensed Matter
Directory of Open Access Journals (Sweden)
Al Rabeh R. H.
2009-07-01
Full Text Available Fascination with primes dates back to the Greeks and before. Primes are named by some "the elementary particles of arithmetic" as every nonprime integer is made of a unique set of primes. In this article we point to new connections between primes, geometry and physics which show that primes could be called "the elementary particles of physics" too. This study considers the problem of closely packing similar circles/spheres in 2D/3D space. This is in effect a discretization process of space and the allowable number in a pack is found to lead to some unexpected cases of prime configurations which is independent of the size of the constituents. We next suggest that a non-prime can be considered geometrically as a symmetric collection that is separable (factorable into similar parts- six is two threes or three twos for example. A collection that has no such symmetry is a prime. As a result, a physical prime aggregate is more difficult to split symmetrically resulting in an inherent stability. This "number/physical" stability idea applies to bigger collections made from smaller (prime units leading to larger stable prime structures in a limitless scaling up process. The distribution of primes among numbers can be understood better using the packing ideas described here and we further suggest that differing numbers (and values of distinct prime factors making a nonprime collection is an important factor in determining the probability and method of possible and subsequent disintegration. Disintegration is bound by energy conservation and is closely related to symmetry by Noether theorems. Thinking of condensed matter as the packing of identical elements, we examine plots of the masses of chemical elements of the periodic table, and also those of the elementary particles of physics, and show that prime packing rules seem to play a role in the make up of matter. The plots show convincingly that the growth of prime numbers and that of the masses of
Primes, Geometry and Condensed Matter
Directory of Open Access Journals (Sweden)
Al Rabeh R. H.
2009-07-01
Full Text Available Fascination with primes dates back to the Greeks and before. Primes are named by some “the elementary particles of arithmetic” as every nonprime integer is made of a unique set of primes. In this article we point to new connections between primes, geometry and physics which show that primes could be called “the elementary particles of physics” too. This study considers the problem of closely packing similar circles / spheres in 2D / 3D space. This is in effect a discretization process of space and the allowable num- ber in a pack is found to lead to some unexpected cases of prime configurations which is independent of the size of the constituents. We next suggest that a non-prime can be considered geometrically as a symmetric collection that is separable (factorable into similar parts- six is two threes or three twos for example. A collection that has no such symmetry is a prime. As a result, a physical prime aggregate is more difficult to split symmetrically resulting in an inherent stability. This “number / physical” stability idea applies to bigger collections made from smaller (prime units leading to larger sta- ble prime structures in a limitless scaling up process. The distribution of primes among numbers can be understood better using the packing ideas described here and we further suggest that differing numbers (and values of distinct prime factors making a nonprime collection is an important factor in determining the probability and method of possible and subsequent disintegration. Disintegration is bound by energy conservation and is closely related to symmetry by Noether theorems. Thinking of condensed matter as the packing of identical elements, we examine plots of the masses of chemical elements of the periodic table, and also those of the elementary particles of physics, and show that prime packing rules seem to play a role in the make up of matter. The plots show con- vincingly that the growth of prime numbers and that
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
Ultra-high-field magnets for future hadron colliders
International Nuclear Information System (INIS)
McIntyre, P.M.; Shen, W.
1997-01-01
Several new concepts in magnetic design and coil fabrication are being incorporated into designs for ultra-high field collider magnets: a 16 Tesla block-coil dual dipole, also using Nb 3 Sn cable, featuring simple pancake coil construction and face-loaded prestress geometry; a 330 T/m block-coil quadrupole; and a ∼ 20 Tesla pipe-geometry dual dipole, using A15 or BSCCO tape. Field design and fabrication issues are discussed for each magnet