Efficient Cartesian-grid-based modeling of rotationally symmetric bodies
Shyroki, Dzmitry
2007-01-01
Axially symmetric waveguides, resonators, and scatterers of arbitrary cross section and anisotropy in the cross section can be modeled rigorously with use of 2-D Cartesian-grid based codes by means of mere redefinition of material permittivity and permeability profiles. The method is illustrated...... by the frequencydomain simulations of resonant modes in a circular-cylinder cavity with perfectly conducting walls, a shielded uniaxial anisotropic dielectric cylinder, and an open dielectric sphere for which, after proper implementation of the perfectly matched layer boundary conditions, the radiation quality factor...
Axial symmetric rotation of a partially immersed body in a liquid with a surfactant layer
Sunil Datta; Nidhi Pandya
2001-08-01
This paper gives a simple integral formula to evaluate the torque on a slowly rotating symmetric body partially immersed in a viscous liquid covered by an adsorbed surface ﬁlm. Besides the results known earlier, new results have also been derived for small values of the surface shear viscosity parameter . It is seen that the effect of in all cases is to increase the torque.
Rotationally symmetric viscous gas flows
Weigant, W.; Plotnikov, P. I.
2017-03-01
The Dirichlet boundary value problem for the Navier-Stokes equations of a barotropic viscous compressible fluid is considered. The flow region and the data of the problem are assumed to be invariant under rotations about a fixed axis. The existence of rotationally symmetric weak solutions for all adiabatic exponents from the interval (γ*,∞) with a critical exponent γ* < 4/3 is proved.
Partially locally rotationally symmetric perfect fluid cosmologies
Mustapha, N; Van Elst, H; Marklund, M; Mustapha, Nazeem; Ellis, George F R; Elst, Henk van; Marklund, Mattias
2000-01-01
We show that there are no new consistent perfect fluid cosmologies with the kinematic variables and the electric and magnetic parts of the Weyl curvature all rotationally symmetric about a common axis in an open neighbourhood ${\\cal U}$ of an event. The consistent solutions of this kind are either locally rotationally symmetric, or are subcases of the Szekeres model.
Romano, Marcello
2012-01-01
New exact analytic solutions are introduced for the rotational motion of a rigid body having two equal principal moments of inertia and subjected to an external torque which is constant in magnitude. In particular, the solutions are obtained for the following cases: (1) Torque parallel to the symmetry axis and arbitrary initial angular velocity; (2) Torque perpendicular to the symmetry axis and such that the torque is rotating at a constant rate about the symmetry axis, and arbitrary initial angular velocity; (3) Torque and initial angular velocity perpendicular to the symmetry axis, with the torque being fixed with the body. In addition to the solutions for these three forced cases, an original solution is introduced for the case of torque-free motion, which is simpler than the classical solution as regards its derivation and uses the rotation matrix in order to describe the body orientation. This paper builds upon the recently discovered exact solution for the motion of a rigid body with a spherical ellipso...
Thermophoresis of Axially Symmetric Bodies
2007-11-02
Sweden Abstract. Thermophoresis of axially symmetric bodies is investigated to first order in the Knudsen-mimber, Kn. The study is made in the limit...derived. Asymptotic solutions are studied. INTRODUCTION Thermophoresis as a phenomenon has been known for a long time, and several authors have approached
Rotation Symmetric Bent Boolean Functions for n = 2p
Cusick, T. W.; Sanger, E. M.
2017-01-01
It has been conjectured that there are no homogeneous rotation symmetric bent Boolean functions of degree greater than two. In this paper we begin by proving that sums of short-cycle rotation symmetric bent Boolean functions must contain a specific degree two monomial rotation symmetric Boolean function. We then prove most cases of the conjecture in n=2p, p>2 prime, variables and extend this work to the nonhomogeneous case.
On the symmetrization of rotational spectra for freely rotating linear molecules
Borysow, Aleksandra; Moraldi, Massimo
It is demonstrated that the symmetrization of a quantum mechanical rotational spectrum of freely rotating linear molecules by means of the Egelstaff transformation produces a symmetric spectrum whose first two even moments coincide with the corresponding classical moments.
PELDOR in rotationally symmetric homo-oligomers
Giannoulis, Angeliki; Ward, Richard; Branigan, Emma; Naismith, James H.; Bode, Bela E.
2013-01-01
Nanometre distance measurements by pulsed electron–electron double resonance (PELDOR) spectroscopy have become an increasingly important tool in structural biology. The theoretical underpinning of the experiment is well defined for systems containing two nitroxide spin-labels (spin pairs); however, recently experiments have been reported on homo-oligomeric membrane proteins consisting of up to eight spin-labelled monomers. We have explored the theory behind these systems by examining model systems based on multiple spins arranged in rotationally symmetric polygons. The results demonstrate that with a rising number of spins within the test molecule, increasingly strong distortions appear in distance distributions obtained from an analysis based on the simple spin pair approach. These distortions are significant over a range of system sizes and remain so even when random errors are introduced into the symmetry of the model. We present an alternative approach to the extraction of distances on such systems based on a minimisation that properly treats multi-spin correlations. We demonstrate the utility of this approach on a spin-labelled mutant of the heptameric Mechanosensitive Channel of Small Conductance of E. coli. PMID:24954956
Effects of symmetrically alternative rotating flow on flocculation
徐继润; 张育新; 邢军; 孙永正; 徐海燕; 刘正宁; 康勇
2003-01-01
A symmetrically alternative rotating flow pattern was designed for flocculation process in order to produce large and dense flocs. The special effects of a symmetrically alternative rotating flow on the diameter and density of flocs were investigated. The results show that under the new fluid conditions, the primary particles on the outer part of the formed flocs may be cut down and the flocs contract at the end of the original rotating direction; then fluid changes its rotating direction, an opposite shearing is imposed to the flocs and makes some primary particles slide along the floc surface, leading to a denser floc; meanwhile, the broken and unflocculated particles on the trajectory may have opportunities to penetrate into or cohere to the flocs. Compared with the conventional rotating flow, the new-designed flow pattern can not only keep the floc size (even enlarge the floc diameter if a suitable flow is chosen) but also increase the floc density effectively.
Walsh Spectrum Properties of Rotation Symmetric Boolean Function
WANG Yongjuan; HAN Wenbao; LI Shiqu
2006-01-01
Rotation symmetric function was presented by Pieprzyk. The algebraic configuration of rotation symmetric(RotS) function is special. For a RotS n variables function f(x1,x2,...,xn) we have f(ρkn(x1,x2,...xn))=f(x1,x2,...,xn) for k=0,1,...,n-1. In this paper, useing probability method we find that when the parameters of RotS function is under circular translation of indices, its walsh spectrum is invariant. And we prove the result is both sufficient and necessary.
Classical limits of boot-rotation symmetric spacetimes
Kofron, David
2010-01-01
Boost-rotation symmetric spacetimes are exceptional as they are the only exact asymptotically flat solutions to the Einstein equations describing spatially bounded sources ("point-like" particles, black holes) undergoing non-trivial motion ("uniform acceleration") with radiation. We construct the Newtonian limit of these spacetimes: it yields fields of uniformly accelerated sources in classical mechanics. We also study the special-relativistic limit of the charged rotating C-metric and so find accelerating electromagnetic magic field.
Rotating Symmetrical Piezoelectric Microactuators for Magnetic Head Drives
Kurihara, Kazuaki; Hida, Masaharu; Umemiya, Shigeyoshi; Kondo, Masao; Koganezawa, Shinji
2006-09-01
A unique piezoelectric microactuator for the head-slider drive dual-stage actuator systems in magnetic disk drives has been developed. This microactuator is based on a rotating symmetrical structure and a symmetrical operation. The piezoelectric actuator elements used in the system have a simple rectangular multilayered structure. A prototype model with pico slider and head suspension has been tested to demonstrate 0.86 μm displacement at a dc applied voltage of 30 V and observed main resonant frequency of over 20 kHz. No fluctuation in flying height was observed.
Rotating cylindrically symmetric Kaluza-Klein ﬂuid model
Ramesh Tikekar; L K Patel
2000-09-01
Kaluza-Klein ﬁeld equations for stationary cylindrically symmetric ﬂuid models in standard Einstein theory are formulated and a set of physically viable solutions is reported. This set is believed to be the ﬁrst such Kaluza-Klein solutions and it includes the Kaluza-Klein counterpart of Davidson’s solution describing spacetime of a perfect ﬂuid in rigid rotation about a regular axis.
THE ISOENERGY INEQUALITY FOR HARMONIC MAPS FROM ROTATIONAL SYMMETRIC MANIFOLDS
焦晓祥; 李嘉禹
2002-01-01
Let u be a harmonic map from a rotational symmetric manifold M and B a unit ball in M, let E(u|B) be the energy of the map u|B and E(u| B) the energy of the map u| B, then we obtain the relationship which is called the isoenergy inequality between E(u|B) and E(u| B).
Eccentric error and compensation in rotationally symmetric laser triangulation
Wang Lei; Gao Jun; Wang Xiaojia; Johannes Eckstein; Peter Ott
2007-01-01
Rotationally symmetric triangulation (RST) sensor has more flexibility and less uncertainty limits becauseof the abaxial rotationally symmetric optical system.But if the incident laser is eccentric,the symmetry of the imagewill descend,and it will result in the eccentric error especially when some part of the imaged ring is blocked.Themodel of rotationally symmetric triangulation that meets the Schimpflug condition is presented in this paper.The errorfrom eccentric incident 1aser is analysed.It iS pointed out that the eccentric error is composed of two parts.one is acosine in circumference and proportional to the eccentric departure factor,and the other is a much smaller quadricfactor of the departure.When the ring is complete,the first error factor is zero because it is integrated in whole ring,but if some part of the ring iS blocked,the first factor will be the main error.Simulation verifies the result of the a-nalysis.At last,a compensation method to the error when some part of the ring is lost is presented based on neuralnetwork.The results of experiment show that the compensation will make the absolute maximum error descend tohalf,and the standard deviation of error descends to 1/3.
Static slightly non-spherically symmetric, and slowly rotating linearised vacuum spacetimes
Saw, Vee-Liem
2015-01-01
We apply the general method of constructing manifolds of revolution around a given curve to derive first order perturbations on the Schwarzschild metric. Two different perturbations are carried out separately: 1) Non-rotating 2-spheres are added along a plane curve slightly deviated from the "Schwarzschild line"; 2) Slow-rotating 2-spheres are added along the "Schwarzschild line". For (1), we obtain the first order vacuum solution, representing the exterior region of a static slightly non-spherically symmetric body. No higher order vacuum solution exists. For (2), we find that the first order vacuum solution is equivalent to the slowly rotating Kerr metric. This is hence a much simpler and geometrically insightful derivation as compared to the gravitomagnetic one, where this rotating-shells construction is a direct manifestation of the frame-dragging phenomenon. A (full non-perturbative) generalisation to this method is explored here, by adding rotating 2-ellipsoids. It turns out however, that this cannot pro...
Holder for rotating glass body
Kolleck, Floyd W.
1978-04-04
A device is provided for holding and centering a rotating glass body such as a rod or tube. The device includes a tubular tip holder which may be held in a lathe chuck. The device can utilize a variety of centering tips each adapted for a particular configuration, such as a glass O-ring joint or semi-ball joint.
An Analysis of gravitational redshift from rotating body
Dubey, Anuj Kumar
2014-01-01
Gravitational redshift is generally calculated without considering the rotation of a body. Neglecting the rotation, the geometry of space time can be described by using the spherically symmetric Schwarzschild geometry. Rotation has great effect on general relativity, which gives new challenges on gravitational redshift. When rotation is taken into consideration spherical symmetry is lost and off diagonal terms appear in the metric. The geometry of space time can be then described by using the solutions of Kerr family. In the present paper we discuss the gravitational redshift for rotating body by using Kerr metric. The numerical calculations has been done under Newtonian approximation of angular momentum. It has been found that the value of gravitational redshift is influenced by the direction of spin of central body and also on the position (latitude) on the central body at which the photon is emitted. The variation of gravitational redshift from equatorial to non - equatorial region has been calculated and ...
Rotators for matching non-symmetric ion-therapy beams to rotating gantries
Pavlovič, Márius; Bokor, Jozef; Šagátová, Andrea
2016-09-01
The paper deals with special ion-optical matching sections called “rotators” for matching non-symmetric beams to rotating ion-therapy gantries. General matrix analysis of the problem is formulated resulting in a specific set of ion-optical constraints that must be fulfilled by the rotator transfer matrix. Possible ways of fitting these ion-optical constraints are discussed and illustrated by several examples of suitable rotator lattices. Each lattice is representing a different type of rotator, e.g. point-to-point imaging lattice or parallel-to-point imaging lattice. Optimization of the rotator lattice with respect to its total length is discussed, and the most compact solutions are presented as well.
Deflection of Rotating Symmetric Molecules by Inhomogeneous Fields
Gershnabel, Erez
2011-01-01
We consider deflection of rotating symmetric molecules by inhomogeneous optical and static electric fields, compare results with the case of linear molecules, and find new singularities in the distribution of the scattering angle. Scattering of the prolate/oblate molecules is analyzed in detail, and it is shown that the process can be efficiently controlled by means of short and strong femtosecond laser pulses. In particular, the angular dispersion of the deflected molecules may be dramatically reduced by laser-induced molecular pre-alignment. We first study the problem by using a simple classical model, and then find similar results by means of more sophisticated methods, including the formalism of adiabatic invariants and direct numerical simulation of the Euler-Lagrange equations of motion. The suggested control scheme opens new ways for many applications involving molecular focusing, guiding, and trapping by optical and static fields.
Teleparallel Energy-Momentum Distribution of Locally Rotationally Symmetric Spacetimes
Amir, M Jamil
2014-01-01
In this paper, we explore the energy-momentum distribution of locally rotationally symmetric (LRS) spacetimes in the context of the teleparallel theory of gravity by considering the three metrics, I, II and III, representing the whole class of LRS sapcetimes. In this regard, we use the teleparallel versions of the Einstein, Landau-Lifshitz, Bergmann-Thomson, and M$\\ddot{o}$ller prescriptions. The results show that the momentum density components for the Einstein, Bergmann-Thomson, and M$\\ddot{o}$ller prescriptions turn out to be same in all cases of the metrics I, II and III, but are different from those of the Landau- Lifshitz prescription, while the energy components remain the same for these three prescriptions only in all possible cases of the metrics I and II. We mention here that the M$\\ddot{o}$ller energy-momentum distribution is independent of the coupling constant $\\lambda$; that is, these results are valid for any teleparallel models.
Rotational symmetric HMD with eye-tracking capability
Liu, Fangfang; Cheng, Dewen; Wang, Qiwei; Wang, Yongtian
2016-10-01
As an important auxiliary function of head-mounted displays (HMDs), eye tracking has an important role in the field of intelligent human-machine interaction. In this paper, an eye-tracking HMD system (ET-HMD) is designed based on the rotational symmetric system. The tracking principle in this paper is based on pupil-corneal reflection. The ET-HMD system comprises three optical paths for virtual display, infrared illumination, and eye tracking. The display optics is shared by three optical paths and consists of four spherical lenses. For the eye-tracking path, an extra imaging lens is added to match the image sensor and achieve eye tracking. The display optics provides users a 40° diagonal FOV with a ״ 0.61 OLED, the 19 mm eye clearance, and 10 mm exit pupil diameter. The eye-tracking path can capture 15 mm × 15 mm of the users' eyes. The average MTF is above 0.1 at 26 lp/mm for the display path, and exceeds 0.2 at 46 lp/mm for the eye-tracking path. Eye illumination is simulated using LightTools with an eye model and an 850 nm near-infrared LED (NIR-LED). The results of the simulation show that the illumination of the NIR-LED can cover the area of the eye model with the display optics that is sufficient for eye tracking. The integrated optical system HMDs with eye-tracking feature can help improve the HMD experience of users.
Pfeiffer, F.; Meyer-Koenig, W.
1949-01-01
By means of characteristics theory, formulas for the numerical treatment of stationary compressible supersonic flows for the two-dimensional and rotationally symmetrical cases have been obtained from their differential equations.
Live-Axis Turning for the Fabrication of Non-Rotationally Symmetric Optics Project
National Aeronautics and Space Administration — The goal of this proposal is to develop a new method to create Non-Rotationally Symmetric (NRS) surfaces that overcomes the limitations of the current techniques and...
Rotationally symmetric numerical solutions to the sine-Gordon equation
Olsen, O. H.; Samuelsen, Mogens Rugholm
1981-01-01
We examine numerically the properties of solutions to the spherically symmetric sine-Gordon equation given an initial profile which coincides with the one-dimensional breather solution and refer to such solutions as ring waves. Expanding ring waves either exhibit a return effect or expand towards...
Spherically symmetric steady states of elastic bodies in general relativity
Andréasson, Håkan
2014-01-01
We study the properties of static spherically symmetric elastic bodies in general relativity using both analytical and numerical tools. The materials considered belong to the class of John elastic materials and reduce to perfect fluids when the rigidity parameter is set to zero. We find numerical support that such elastic bodies exist with different possible shapes (balls, single shells and multiple shells) and that their gravitational redshift can be very large ($z\\approx 2.8$) without violating the dominant energy condition. Moreover we show that the elastic body has finite radius even in the case when the constitutive equation of the elastic material is a perturbation of a polytropic fluid without finite radius, thereby concluding that such fluids are structurally unstable within the larger class of elastic matter models under study.
AUTHENTICATED SYMMETRIC-KEY ESTABLISHMENT FOR MEDICAL BODY SENSOR NETWORKS
Bao Shudi; Poon Carmen C.Y.; Shen Lianfeng; Zhang Yuanting
2007-01-01
This study concerns security issues of the emerging Wireless Body Sensor Network(WBSN)formed by biomedical sensors worn on or implanted in the human body for mobile healthcare applications.A novel authenticated symmetric-key establishment scheme is proposed for WBSN,which fully exploits the physiological features obtained by network entities via the body channel available in WBSN but not other wireless networks.The self-defined Intrinsic Shared Secret(ISS)is used to replace the pre-deployment of secrets among network entities,which thus eliminates centralized services or authorities essential in existing protocols,and resolves the key transport problem in the pure symmetric-key cryptosystem for WBSN as well.The security properties of the proposed scheme are demonstrated in terms of its attack complexity and the types of attacks it can resist.Besides,the scheme can be implemented under a light-weight way in WBSN systems.Due to the importance of the ISS concept,the analysis on using false acceptance/false rejection method to evaluate the performance of ISS for its usage in the scheme is also demonstrated.
Axially symmetric equations for differential pulsar rotation with superfluid entrainment
Antonelli, Marco
2016-01-01
We propose an analytical two-components model for pulsar rotational dynamics: the aim is to reduce the 3D hydrodynamical problem to a 1D (radial) problem, using the hypothesis of negligible azimuthal inhomogeneities. The result is the construction of a computationally simple model that takes into account for the non-uniform structure of the star, entrainment effect and differential rotation of the superfluid component. For the first time all these ingredients are treated in a fully consistent way within the picture provided by our initial hypotheses. Our treatment clarifies which are the physical inputs needed to build, to current knowledge, more realistic simulations of rotating neutron stars and gives a neat description of the effect of entrainment when straight vortex lines are considered. Moreover, on this basis, we briefly introduce a new method that can be used to put a constraint to the mass of the pulsars that display very large glitches and to the relative spin up timescales.
Frame-Dragging from Charged Rotating Body
Dubey, Anuj Kumar
2016-01-01
In the present paper, we have considered the three parameters: mass, charge and rotation to discuss their combined effect on frame dragging for a charged rotating body. If we consider the ray of light which is emitted radially outward from a rotating body then the frame dragging shows a periodic nature with respect to coordinate $\\phi$ (azimuthal angle). It has been found that the value of frame dragging obtains a maximum at, $ \\phi =\\frac{\\pi}{2}$ and a minimum at $ \\phi =\\frac{3 \\pi}{2}$.
Deriabine, Mikhail
2003-01-01
We consider the problem of heavy rigid body dynamics in an infinite volume of an ideal incompressible fluid performing a potential motion. If the body is axially-symmetric, then the system admits partial solutions, when the axis of symmetry is vertical, and the body sinks and rotates around its...... symmetry axis. These solutions were found by V.A.Steklov already at the end of the 19th century, and he also pointed out that in general these motions are unstable (as they are uniformly accelerated).Here we consider the more delicate question, namely we derive the conditions for stability of the rotation...
Stationary MHD equilibria describing azimuthal rotations in symmetric plasmas
da Silva, Sidney T.; Viana, Ricardo L.
2016-12-01
We consider the stationary magnetohydrodynamical (MHD) equilibrium equation for an axisymmetric plasma undergoing azimuthal rotations. The case of cylindrical symmetry is treated, and we present two semi-analytical solutions for the stationary MHD equilibrium equations, from which a number of physical properties of the magnetically confined plasma are derived.
Blind Carrier Phase Recovery for General 2{\\pi}/M-rotationally Symmetric Constellations
Slimane, Emna Ben; Bouallègue, Ammar; 10.5121/ijwmn.2012.4104
2012-01-01
This paper introduces a novel blind carrier phase recovery estimator for general 2{\\Pi}/M-rotationally symmetric constellations. This estimation method is a generalization of the non-data-aided (NDA) nonlinear Phase Metric Method (PMM) estimator already designed for general quadrature amplitude constellations. This unbiased estimator is seen here as a fourth order PMM then generalized to Mth order (Mth PMM) in such manner that it covers general 2{\\Pi}/M-rotationally symmetric constellations such as PAM, QAM, PSK. Simulation results demonstrate the good performance of this Mth PMM estimation algorithm against competitive blind phase estimators already published for various modulation systems of practical interest.
Hydroelastic dynamic characteristics of a slender axis-symmetric body
Chen, Weimin; Li, Min; Zheng, Zhongqin; Zhang, Liwu
2010-07-01
The slender axis-symmetric submarine body moving in the vertical plane is the object of our investigation. A coupling model is developed where displacements of a solid body as a Euler beam (consisting of rigid motions and elastic deformations) and fluid pressures are employed as basic independent variables, including the interaction between hydrodynamic forces and structure dynamic forces. Firstly the hydrodynamic forces, depending on and conversely influencing body motions, are taken into account as the governing equations. The expressions of fluid pressure are derived based on the potential theory. The characteristics of fluid pressure, including its components, distribution and effect on structure dynamics, are analyzed. Then the coupling model is solved numerically by means of a finite element method (FEM). This avoids the complicacy, combining CFD (fluid) and FEM (structure), of direct numerical simulation, and allows the body with a non-strict ideal shape so as to be more suitable for practical engineering. An illustrative example is given in which the hydroelastic dynamic characteristics, natural frequencies and modes of a submarine body are analyzed and compared with experimental results. Satisfactory agreement is observed and the model presented in this paper is shown to be valid.
Hydroelastic dynamic characteristics of a slender axis-symmetric body
无
2010-01-01
The slender axis-symmetric submarine body moving in the vertical plane is the object of our investigation.A coupling model is developed where displacements of a solid body as a Euler beam(consisting of rigid motions and elastic deformations) and fluid pressures are employed as basic independent variables,including the interaction between hydrodynamic forces and structure dynamic forces.Firstly the hydrodynamic forces,depending on and conversely influencing body motions,are taken into account as the governing equations.The expressions of fluid pressure are derived based on the potential theory.The characteristics of fluid pressure,including its components,distribution and effect on structure dynamics,are analyzed.Then the coupling model is solved numerically by means of a finite element method(FEM).This avoids the complicacy,combining CFD(fluid) and FEM(structure),of direct numerical simulation,and allows the body with a non-strict ideal shape so as to be more suitable for practical engineering.An illustrative example is given in which the hydroelastic dynamic characteristics,natural frequencies and modes of a submarine body are analyzed and compared with experimental results.Satisfactory agreement is observed and the model presented in this paper is shown to be valid.
Axially symmetric equations for differential pulsar rotation with superfluid entrainment
Antonelli, M.; Pizzochero, P. M.
2017-01-01
In this article we present an analytical two-component model for pulsar rotational dynamics. Under the assumption of axial symmetry, implemented by a paraxial array of straight vortices that thread the entire neutron superfluid, we are able to project exactly the 3D hydrodynamical problem to a 1D cylindrical one. In the presence of density-dependent entrainment the superfluid rotation is non-columnar: we circumvent this by using an auxiliary dynamical variable directly related to the areal density of vortices. The main result is a system of differential equations that take consistently into account the stratified spherical structure of the star, the dynamical effects of non-uniform entrainment, the differential rotation of the superfluid component and its coupling to the normal crust. These equations represent a mathematical framework in which to test quantitatively the macroscopic consequences of the presence of a stable vortex array, a working hypothesis widely used in glitch models. Even without solving the equations explicitly, we are able to draw some general quantitative conclusions; in particular, we show that the reservoir of angular momentum (corresponding to recent values of the pinning forces) is enough to reproduce the largest glitch observed in the Vela pulsar, provided its mass is not too large.
Sums of magnetic eigenvalues are maximal on rotationally symmetric domains
Laugesen, Richard S; Roy, Arindam
2011-01-01
The sum of the first n energy levels of the planar Laplacian with constant magnetic field of given total flux is shown to be maximal among triangles for the equilateral triangle, under normalization of the ratio (moment of inertia)/(area)^3 on the domain. The result holds for both Dirichlet and Neumann boundary conditions, with an analogue for Robin (or de Gennes) boundary conditions too. The square similarly maximizes the eigenvalue sum among parallelograms, and the disk maximizes among ellipses. More generally, a domain with rotational symmetry will maximize the magnetic eigenvalue sum among all linear images of that domain. These results are new even for the ground state energy (n=1).
Spherically Symmetric and Rotating Wormholes Produced by Lightlike Branes
Guendelman, Eduardo; Nissimov, Emil; Pacheva, Svetlana
2009-01-01
Lightlike p-branes (LL-branes) with dynamical (variable) tension allow simple and elegant Polyakov-type and dual to it Nambu-Goto-like world-volume action formulations. Here we first briefly describe the dynamics of LL-branes as test objects in various physically interesting gravitational backgrounds of black hole type, including rotating ones. Next we show that LL-branes are the appropriate gravitational sources that provide proper matter energy momentum tensors in the Einstein equations of motion needed to generate traversable wormhole solutions, in particular, self-consistent cylindrical rotating wormholes, with the LL-branes occupying their throats. Here a major role is being played by the dynamical LL-brane tension which turns out to be negative but may be of arbitrary small magnitude. As a particular solution we obtain traversable wormhole with Schwarzschild geometry generated by a LL-brane positioned at the wormhole throat, which represents the correct consistent realization of the original Einstein-Ro...
Molecular collisions. 11: Semiclassical approximation to atom-symmetric top rotational excitation
Russell, D.; Curtiss, C. F.
1973-01-01
In a paper of this series a distorted wave approximation to the T matrix for atom-symmetric top scattering was developed which is correct to first order in the part of the interaction potential responsible for transitions in the component of rotational angular momentum along the symmetry axis of the top. A semiclassical expression for this T matrix is derived by assuming large values of orbital and rotational angular momentum quantum numbers.
Saccol, Michele Forgiarini; Almeida, Gabriel Peixoto Leão; de Souza, Vivian Lima
2016-08-01
Beach volleyball is a sport with a high demand of shoulder structures that may lead to adaptations in range of motion (ROM) and strength like in other overhead sports. Despite of these possible alterations, no study evaluated the shoulder adaptations in young beach volleyball athletes. The aim of this study was to compare the bilateral ROM and rotation strength in the shoulders of young beach volleyball players. Goniometric passive shoulder ROM of motion and isometric rotational strength were evaluated in 19 male and 14 female asymptomatic athletes. External and internal ROM, total rotation motion, glenohumeral internal rotation deficit (GIRD), external rotation and internal rotation strength, bilateral deficits and external rotation to internal rotation ratio were measured. The statistical analysis included paired Student's t-test and analysis of variance with repeated measures. Significantly lower dominant GIRD was found in both groups (pvolleyball athletes present symmetric rotational strength and shoulder ROM rotational adaptations that can be considered as anatomical. These results indicate that young practitioners of beach volleyball are subject to moderate adaptations compared to those reported for other overhead sports. Copyright © 2015 Elsevier Ltd. All rights reserved.
Proposed New Test of Equivalence Principle from Rotating Bodies
ZHANG Yuan-Zhong; LUO Jun; NIE Yu-Xin
2000-01-01
We study a new kind of equivalence principle for rotating bodies and propose a test of the equivalence principle by comparing free-fall gravitational accelerations of two gyroscopes or a rotating and a non-rotating extended bodies.
Gravitational Waves in Locally Rotationally Symmetric (LRS Class II Cosmologies
Michael Bradley
2017-10-01
Full Text Available In this work we consider perturbations of homogeneous and hypersurface orthogonal cosmological backgrounds with local rotational symmetry (LRS, using a method based on the 1 + 1 + 2 covariant split of spacetime. The backgrounds, of LRS class II, are characterised by that the vorticity, the twist of the 2-sheets, and the magnetic part of the Weyl tensor all vanish. They include the flat Friedmann universe as a special case. The matter contents of the perturbed spacetimes are given by vorticity-free perfect fluids, but otherwise the perturbations are arbitrary and describe gravitational, shear, and density waves. All the perturbation variables can be given in terms of the time evolution of a set of six harmonic coefficients. This set decouples into one set of four coefficients with the density perturbations acting as source terms, and another set of two coefficients describing damped source-free gravitational waves with odd parity. We also consider the flat Friedmann universe, which has been considered by several others using the 1 + 3 covariant split, as a check of the isotropic limit. In agreement with earlier results we find a second-order wavelike equation for the magnetic part of the Weyl tensor which decouples from the density gradient for the flat Friedmann universes. Assuming vanishing vector perturbations, including the density gradient, we find a similar equation for the electric part of the Weyl tensor, which was previously unnoticed.
On the invariant motions of rigid body rotation over the fixed point, via Euler angles
Ershkov, Sergey V
2016-01-01
The generalized Euler case (rigid body rotation over the fixed point) is discussed here: - the center of masses of non-symmetric rigid body is assumed to be located at the equatorial plane on axis Oy which is perpendicular to the main principal axis Ox of inertia at the fixed point. Such a case was presented in the rotating coordinate system, in a frame of reference fixed in the rotating body for the case of rotation over the fixed point (at given initial conditions). In our derivation, we have represented the generalized Euler case in the fixed Cartesian coordinate system; so, the motivation of our ansatz is to elegantly transform the proper components of the previously presented solution from one (rotating) coordinate system to another (fixed) Cartesian coordinates. Besides, we have obtained an elegantly analytical case of general type of rotations; also, we have presented it in the fixed Cartesian coordinate system via Euler angles.
Longhi, Stefano
2017-01-01
We consider wave transport phenomena in a PT -symmetric extension of the periodically kicked quantum rotator model and reveal that dynamical localization assists the unbroken PT phase. In the delocalized (quantum resonance) regime, PT symmetry is always in the broken phase and ratchet acceleration arises as a signature of unidirectional non-Hermitian transport. An optical implementation of the periodically kicked PT -symmetric Hamiltonian, based on transverse beam propagation in a passive optical resonator with combined phase and loss gratings, is suggested to visualize acceleration modes in fractional Talbot cavities.
YRehab F. Abdel-Kader, Rabab M. Ramadan, Fayez W. Zaki , and Emad El-Sayed1
2012-05-01
Full Text Available In this paper a novel rotation-invariant neural-based pattern recognition system is proposed. The system incorporates a new image preprocessing technique to extract rotation-invariant descriptive patterns from the shapes. The proposed system applies a three phase algorithm on the shape image to extract the rotation-invariant pattern. First, the orientation angle of the shape is calculated using a newly developed shape orientation technique. The technique is effective, computationally inexpensive and can be applied to shapes with several non-equally separated axes of symmetry. A simple method to calculate the average angle of the shape’s axes of symmetry is defined. In this technique, only the first moment of inertia is considered to reduce the computational cost. In the second phase, the image is rotated using a simple rotation technique to adapt its orientation angle to any specific reference angle. Finally in the third phase, the image preprocessor creates a symmetrical pattern about the axis with the calculated orientation angle and the perpendicular axis on it. Performing this operation in both the neural network training and application phases, ensures that the test rotated patterns will enter the network in the same position as in the training. Three different approaches were used to create the symmetrical patterns from the shapes. Experimental results indicate that the proposed approach is very effective and provide a recognition rate up to 99.5%.
Entropy bounds for uncollapsed rotating bodies
Abreu, Gabriel
2010-01-01
Entropy bounds in black hole physics, based on a wide variety of different approaches, have had a long and distinguished history. Recently the current authors have turned attention to uncollapsed systems and obtained a robust entropy bound for uncollapsed static spherically symmetric configurations. In the current article we extend this bound to rotating systems. This extension is less simple than one might at first suppose. Purely classically, (using only classical general relativity and basic thermodynamics), it is possible to show that the entropy of uncollapsed matter inside a region enclosed by a surface of area A is bounded from above by S = max kappa(FIDOs) / (2 pi). Thus, using only classical general relativity, basic thermodynamics, and the Unruh effect, we are able to argue that for uncollapsed matter S <= {1/2} A.
Nielsen, Martin Bjerre; Krenk, Steen
2012-01-01
A conservative time integration algorithm for rigid body rotations is presented in a purely algebraic form in terms of the four quaternions components and the four conjugate momentum variables via Hamilton’s equations. The introduction of an extended mass matrix leads to a symmetric set of eight...
Affine Equivalence of Quartic Monomial Rotation Symmetric Boolean Functions in Prime Power Dimension
2015-01-27
ANF. This representation of f (not unique, since one can choose any representative in Gn(x1xi2 . . . xil)) is called the short algebraic normal form ...Affine Equivalence of Quartic Monomial Rotation Symmetric Boolean Functions in Prime Power Dimension Pantelimon Stănică Naval Postgraduate School...Boolean functions, circulant matrices, affine equivalence , permutations, prime powers. Mathematics Subject Classification [2010]: 94A60, 94C10, 06E30 1
Locally Rotationally Symmetric Bianchi Type-I Model with Time Varying (A) Term
R.K.Tiwari; Navin Kumar Jha
2009-01-01
We investigate the locally rotationally symmetric (LRS) Bianchi type-Ⅰ cosmological model for stiff matter and a vacuum solution with a cosmological term proportional to R~(-m) (R is the scale factor and m is a positive constant).The cosmological term decreases with time.We obtain that for both the cases the present universe is accelerating with a large fraction of cosmological density in the form of a cosmological term.
Microscopic derivation of nuclear rotation-vibration model, axially symmetric case
Gulshani, Parviz
2015-01-01
We derive from first principles the successful phenomenological hydrodynamic model of Bohr-Davydov-Faessler-Greiner for rotation-vibration motion of an axially symmetric deformed nucleus. The derivation is not limited to small oscillation amplitude, and provides microscopic expressions for the interaction operators among the rotation, vibration, and intrinsic motions, for the moment of inertia, vibration mass, and for the deformation variables. The method uses canonical transformations to collective co-ordinates, followed by a constrained variational method, with the associated constraints imposed on the wavefunction rather than on the particle co-ordinates. The approach yields three self-consistent, time-reversal invariant, cranking-type Schrodinger equations for the rotation-vibration and intrinsic motions, and a self-consistency equation. For deformed harmonic oscillator mean-field potentials, these equations are solved in closed forms for the energies, moments of inertia, quadrupole moments and transition...
Locally-rotationally-symmetric Bianchi type-V cosmology with heat flow
C P Singh; A Beesham
2009-10-01
In this paper we present a spatially homogeneous locally-rotationally-symmetric (LRS) Bianchi type-V cosmological model with perfect fluid and heat flow. A general approach is introduced to solve Einstein’s field equations using a law of variation for the mean Hubble parameter, which is related to average scale factor of the model that yields a constant value for the deceleration parameter. Exact solutions that correspond to singular and non-singular models are found with heat flow. The physical constraints on the solution and, in particular, the thermodynamical laws that govern such solutions are discussed in some detail.
Moller Energy-Momentum Prescription for a Locally Rotationally Symmetric Space-Time
Aydogdu, O
2006-01-01
The energy distribution in the Locally Rotationally Symmetric (LRS) Bianchi type II space-time is obtained by considering the Moller energy-momentum definition in both Einstein's theory of general relativity and teleparallel theory of relativity. The energy distribution which includes both the matter and gravitational field is found to be zero in both of these different gravitation theories. This result agrees with previous works of Cooperstock and Israelit, Rosen, Johri et al., Banerjee and Sen, Vargas, and Aydogdu and Salti. Our result that the total energy of the universe is zero supports the view points of Albrow and Tryon.
Locally rotationally symmetric Bianchi type I cosmology in f(R, T) gravity
Shamir, M.F. [National University of Computer and Emerging Sciences, Department of Sciences and Humanities, Lahore (Pakistan)
2015-08-15
This manuscript is devoted to the investigation of the Bianchi type I universe in the context of f(R, T) gravity. For this purpose, we explore the exact solutions of locally rotationally symmetric Bianchi type I spacetime. The modified field equations are solved by assuming an expansion scalar θ proportional to the shear scalar σ, which gives A = B{sup n}, where A, B are the metric coefficients and n is an arbitrary constant. In particular, three solutions have been found and physical quantities are calculated in each case. (orig.)
Research on testing method for combined aspheric surface with non-rotational symmetric
Zhou, Wencai; Xu, Feng; Wei, Xiaoxiao
2016-09-01
Non-rotational symmetric aspheric surface has many significant advantages, but it still can not be widely used because the limiting that there is no method can tests it precisely. At present, the coordinate contour measuring machine is the main testing method for the aspheric surface with non-rotational symmetric, but the measurement accuracy of this method is not high. In this paper, the method of diffraction compensator (computed graphic holograph) has been adopted to test the combined aspheric surface, which can compensate the phase caused by tested lens. The sample surface is the combined aspheric surface with diameter of 33.84mm, and the process from optical software simulation design, the fabrication of the computed graphic holograph (CGH) to experimental platform built is given in detail after testing via the CGH technology. The simulation results show that the root mean square (RMS) of remnant wave-front error is 0.004 λ, and the peak to valley (PV) is 0.0245 λ. The free-from surface has been tested by Zygo interferometer, and the experimental results show that the RMS is 0.49 λ, the PV is 4.69 λ. The accuracy of the result is higher than that of coordinate contour measuring machine. The system error caused by optical elements analysed is 0.1149λ. The accurate result means that the CGH technology for testing the combined aspheric surface is realized.
Froessling, Nils
1958-01-01
The fundamental boundary layer equations for the flow, temperature and concentration fields are presented. Two dimensional symmetrical and unsymmetrical and rotationally symmetrical steady boundary layer flows are treated as well as the transfer boundary layer. Approximation methods for the calculation of the transfer layer are discussed and a brief survey of an investigation into the validity of the law that the Nusselt number is proportional to the cube root of the Prandtl number is presented.
Generation of a symmetric magnetic field by thermal convection in a plane rotating layer
Zheligovsky, V
2010-01-01
We investigate numerically magnetic field generation by thermal convection with square periodicity cells in a rotating horizontal layer of electrically-conducting fluid with stress-free electrically perfectly conducting boundaries for Rayleigh numbers in the interval 5100\\le R\\le 5800. Dynamos of three kinds, apparently not encountered before, are presented: 1) Steady and time-periodic regimes, where the flow and magnetic field are symmetric about a vertical axis. In regimes with this symmetry, the global alpha-effect is insignificant, and the complex structure of the system of amplitude equations controlling weakly nonlinear stability of the system to perturbations with large spatial and temporal scales suggests that the perturbations are likely to exhibit uncommon complex patterns of behaviour, to be studied in the future work. 2) Periodic in time regimes, where magnetic field is always concentrated in the interior of the convective layer, in contrast to the behaviour first observed by St Pierre (1993) and ...
Near-equality of the Penrose Inequality for rotationally symmetric Riemannian manifolds
Lee, Dan A
2011-01-01
This article is the sequel to our previous paper [LS] dealing with the near-equality case of the Positive Mass Theorem. We study the near-equality case of the Penrose Inequality for the class of complete asymptotically flat rotationally symmetric Riemannian manifolds with nonnegative scalar curvature whose boundaries are outermost minimal hypersurfaces. Specifically, we prove that if the Penrose Inequality is sufficiently close to being an equality on one of these manifolds, then it must be close to a Schwarzschild space with an appended cylinder, in the sense of Lipschitz Distance. Since the Lipschitz Distance bounds the Intrinsic Flat Distance on compact sets, we also obtain a result for Intrinsic Flat Distance, which is a more appropriate distance for more general near-equality results, as discussed in [LS
Radially Symmetric Motions of Nonlinearly Viscoelastic Bodies Under Live Loads
Stepanov, Alexey B.; Antman, Stuart S.
2017-08-01
This paper treats radially symmetric motions of nonlinearly viscoelastic circular-cylindrical and spherical shells subjected to the live loads of centrifugal force and (time-dependent) hydrostatic pressures. The governing equations are exact versions of those for 3-dimensional continuum mechanics (so shell does not connote an approximate via some shell theory). These motions are governed by quasilinear third-order parabolic-hyperbolic equations having but one independent spatial variable. The principal part of such a partial differential equation is determined by a general family of nonlinear constitutive equations. The presence of strains in two orthogonal directions requires a careful treatment of constitutive restrictions that are physically natural and support the analysis. The interaction of geometrically exact formulations, the compatible use of general constitutive equations for material response, and the presence of live loads show how these factors play crucial roles in the behavior of solutions. In particular, for different kinds of live loads there are thresholds separating materials that produce qualitatively different dynamical behavior. The analysis (using classical methods) covers infinite-time blowup for cylindrical shells subject to centrifugal forces, infinite-time blowup for cylindrical shells subject to steady and time-dependent hydrostatic pressures, finite-time blowup for spherical shells subject to steady and time-dependent hydrostatic pressures, and the preclusion of total compression. This paper concludes with a sketch (using some modern methods) of the existence of regular solutions until the time of blowup.
Stability of rigid body rotation from a bond graph perspective
Breedveld, Peter
2009-01-01
This paper describes the history of the bond graph description of rigid body rotation dynamics and resolves a paradox that resulted from the common Euler Junction Structure (EJS) description of the exterior product in the Newton–Euler equation describing rigid body rotation [D.C. Karnopp, R.C. Rosen
Precession of a Freely Rotating Rigid Body Inelastic Relaxation in the Vicinity of Poles
Efroimsky, M
1999-01-01
When a solid body is freely rotating at an angular velocity ${\\bf \\Omega}$, the ellipsoid of constant angular momentum, in the space $\\Omega_1, \\Omega_2, \\Omega_3$, has poles corresponding to spinning about the minimal-inertia and maximal-inertia axes. The first pole may be considered stable if we neglect the inner dissipation, but becomes unstable if the dissipation is taken into account. This happens because the bodies dissipate energy when they rotate about any axis different from that of the maximal inertia. In the case of an oblate symmetrical body, the angular velocity describes a circular cone about the vector of (conserved) angular momentum. In the course of relaxation, the angle of this cone decreases, so that both the angular velocity and the maximal-inertia axis of the body align along the angular momentum. The generic case of an asymmetric body is far more involved. Even the symmetrical prolate body exhibits a sophisticated behaviour, because an infinitesimally small deviation of the body's shape ...
A symmetric splitting method for rigid body dynamics
E. Celledoni
2006-04-01
Full Text Available It has been known since the time of Jacobi that the solution to the free rigid body (FRB equations of motion is given in terms of a certain type of elliptic functions. Using the Arithmetic-Geometric mean algorithm, (1, these functions can be calculated efficiently and accurately. The overall approach yields a faster and more accurate numerical solution to the FRB equations compared to standard numerical ODE and symplectic solvers. In this paper we investigate the possibility of extending this approach to the case of rigid bodies subject to external forces. By using a splitting strategy similar to the one proposed in (14, we decompose the vector field of our problem in a FRB problem and another completely integrable vector field. We apply the method to the simulation of the heavy top.
Ott, Peter
2003-05-01
Classical triangulation sensors exhibit an orientation depend signal if the scattering properties of the work-piece are not symmetrical like at curved surface locations. This problem is avoided by rotational symmetric triangulation sensors. Due to this attractive property in a lot of applications such a sensor was introduced very recently on the market. This sensor is based on refractive optics and a special PSD detector, both custom made resulting in high costs. Additionally, the existing optical design approach does not offer an optical layout to start with, thus a good amount of trial and error is required and non-optimal solutions are probable. Therefore, there is great interest for a clear optical design strategy that results in layouts that are suitable also to use low cost commercial available detectors, such as CCD or CMOS image detectors. In this paper such a design procedure is presented for optical designs that use reflecting optical surfaces. Several solutions are depicted and discussed. The designs are not only attractive from the optical point of view and from detector considerations, but also from opto-mechanical design issues. For example designs with only one opto-mechanical part are possible. The resulting optical designs consist of aspherical surfaces which are obtained directly by using only some new relations of first order optics for off-axis objects. The designs are validated by exact ray tracing. These ray tracing results show already very good performance. Nevertheless, it was possible to further optimize the optical designs very efficiently using ray tracing software, thus yielding improved optical properties.
Eckstein, Johannes; Lei, Wang; Becker, Jonathan; Jun, Gao; Ott, Peter
2006-04-01
In this paper a distance measurement sensor is introduced, equipped with two integrated optical systems, the first one for rotationally symmetric triangulation and the second one for imaging the object while using only one 2D detector for both purposes. Rotationally symmetric triangulation, introduced in [1], eliminates some disadvantages of classical triangulation sensors, especially at steps or strong curvatures of the object, wherefore the measurement result depends not any longer on the angular orientation of the sensor. This is achieved by imaging the scattered light from an illuminated object point to a centered and sharp ring on a low cost area detector. The diameter of the ring is proportional to the distance of the object. The optical system consists of two off axis aspheric reflecting surfaces. This system allows for integrating a second optical system in order to capture images of the object at the same 2D detector. A mock-up was realized for the first time which consists of the reflecting optics for triangulation manufactured by diamond turning. A commercially available appropriate small lens system for imaging was mechanically integrated in the reflecting optics. Alternatively, some designs of retrofocus lens system for larger field of views were investigated. The optical designs allow overlying the image of the object and the ring for distance measurement in the same plane. In this plane a CCD detector is mounted, centered to the optical axis for both channels. A fast algorithm for the evaluation of the ring is implemented. The characteristics, i.e. the ring diameter versus object distance shows very linear behavior. For illumination of the object point for distance measurement, the beam of a red laser diode system is reflected by a wavelength bandpath filter on the axis of the optical system in. Additionally, the surface of the object is illuminated by LED's in the green spectrum. The LED's are located on the outside rim of the reflecting optics. The
Weak response of cold symmetric nuclear matter at three-body cluster level
Lovato, Alessandro; Benhar, Omar
2012-01-01
We studied the Fermi and Gamow-Teller responses of cold symmetric nuclear matter within a unified dynamical model, suitable to account for both short- and long-range correlation effects. The formalism of correlated basis functions has been used to construct two-body effective interactions and one-body effective weak operators. The inclusion of the three-body cluster term allowed for incorporating in the effective interaction a realistic model of three- nucleon forces, namely the UIX potential. Moreover, the sizable unphysical dependence of the effective weak operator is removed once the three-body cluster term is taken into account.
Scheins, J J; Herzog, H; Shah, N J
2011-03-01
For iterative, fully 3D positron emission tomography (PET) image reconstruction intrinsic symmetries can be used to significantly reduce the size of the system matrix. The precalculation and beneficial memory-resident storage of all nonzero system matrix elements is possible where sufficient compression exists. Thus, reconstruction times can be minimized independently of the used projector and more elaborate weighting schemes, e.g., volume-of-intersection (VOI), are applicable. A novel organization of scanner-independent, adaptive 3D projection data is presented which can be advantageously combined with highly rotation-symmetric voxel assemblies. In this way, significant system matrix compression is achieved. Applications taking into account all physical lines-of-response (LORs) with individual VOI projectors are presented for the Siemens ECAT HR+ whole-body scanner and the Siemens BrainPET, the PET component of a novel hybrid-MR/PET imaging system. Measured and simulated data were reconstructed using the new method with ordered-subset-expectation-maximization (OSEM). Results are compared to those obtained by the sinogram-based OSEM reconstruction provided by the manufacturer. The higher computational effort due to the more accurate image space sampling provides significantly improved images in terms of resolution and noise.
Locally-rotationally-symmetric Bianchi type-V cosmology in general relativity
C P Singh
2009-02-01
A spatially homogeneous locally-rotationally-symmetric (LRS) Bianchi type-V cosmological model is considered with a perfect fluid in general relativity. We present two types of cosmologies (power-law and exponential forms) by using a law of variation for the mean Hubble parameter that yields a constant value for the deceleration parameter. We discuss the physical properties of the non-flat and flat models in each cosmology. Exact solutions that correspond to singular and non-singular models are presented. In a generic situation, models can be interpolated between different phases of the Universe. We find that a constant value for the deceleration parameter is reasonable for a description of different phases of the Universe. We arrive at the conclusion that the Universe decelerates when the value of the deceleration parameter is positive whereas it accelerates when the value is negative. The dynamical behaviours of the solutions and kinematical parameters like expansion, shear and the anisotropy parameter are discussed in detail in each section. Exact expressions for look-back time, luminosity distance and event horizon vs. redshift are derived and their significances are discussed in some detail. It has been observed that the solutions are compatible with the results of recent observations.
Longhi, Stefano
2016-01-01
We consider wave transport phenomena in a $\\mathcal{PT}$-symmetric extension of the periodically-kicked quantum rotator model and reveal that dynamical localization assists the unbroken $\\mathcal{PT}$ phase. In the delocalized (quantum resonance) regime, $\\mathcal{PT}$ symmetry is always in the broken phase and ratchet acceleration arises as a signature of unidirectional non-Hermitian transport. An optical implementation of the periodically-kicked $\\mathcal{PT}$-symmetric Hamiltonian, based on transverse beam propagation in a passive optical resonator with combined phase and loss gratings, is suggested to visualize acceleration modes in fractional Talbot cavities.
Effects of asymmetrical stance and movement on body rotation in pushing.
Lee, Yun-Ju; Aruin, Alexander S
2015-01-21
Pushing objects in the presence of body asymmetries could increase the risk of back injury. Furthermore, when the object is heavy, it could exacerbate the effects induced by asymmetrical posture. We investigated how the use of asymmetrical posture and/or upper extremity movement affect vertical torque (Tz) and center of pressure (COP) displacement during pushing. Ten healthy volunteers were instructed to push objects of three different weights using two hands (symmetrical hand use) or one hand (asymmetrical hand use) while standing in symmetrical or asymmetrical foot-positions. The peak values of Tz and COP displacement in the medial-lateral direction (COPML) were analyzed. In cases of isolated asymmetry, changes in the Tz were mainly linked with effects of hand-use whereas effects of foot-position dominated changes in the COPML displacement. In cases of a combined asymmetry, the magnitudes of both Tz and COPML were additive when asymmetrical hand-use and foot-position induced the rotation of the lower and upper body in the same direction or subtractive when asymmetries resulted in the rotation of the body segments in the opposite directions. Moreover, larger Tz and COP displacements were seen when pushing the heavy weight. The results point out the importance of using Tz and COPML to describe the isolated or combined effects of asymmetrical upper extremity movement and asymmetrical posture on body rotation during pushing. Furthermore, it suggests that a proper combination of unilateral arm movement and foot placements could help to reduce body rotation even when pushing heavy objects.
Importance of body rotation during the flight of a butterfly
Fei, Yueh-Han John; Yang, Jing-Tang
2016-03-01
In nature the body motion of a butterfly is clearly observed to involve periodic rotation and varied flight modes. The maneuvers of a butterfly in flight are unique. Based on the flight motion of butterflies (Kallima inachus) recorded in free flight, a numerical model of a butterfly is created to study how its flight relates to body pose; the body motion in a simulation is prescribed and tested with varied initial body angle and rotational amplitude. A butterfly rotates its body to control the direction of the vortex rings generated during flapping flight; the flight modes are found to be closely related to the body motion of a butterfly. When the initial body angle increases, the forward displacement decreases, but the upward displacement increases within a stroke. With increased rotational amplitudes, the jet flows generated by a butterfly eject more downward and further enhance the generation of upward force, according to which a butterfly executes a vertical jump at the end of the downstroke. During this jumping stage, the air relative to the butterfly is moving downward; the butterfly pitches up its body to be parallel to the flow and to decrease the projected area so as to avoid further downward force generated. Our results indicate the importance of the body motion of a butterfly in flight. The inspiration of flight controlled with body motion from the flight of a butterfly might yield an alternative way to control future flight vehicles.
Importance of body rotation during the flight of a butterfly.
Fei, Yueh-Han John; Yang, Jing-Tang
2016-03-01
In nature the body motion of a butterfly is clearly observed to involve periodic rotation and varied flight modes. The maneuvers of a butterfly in flight are unique. Based on the flight motion of butterflies (Kallima inachus) recorded in free flight, a numerical model of a butterfly is created to study how its flight relates to body pose; the body motion in a simulation is prescribed and tested with varied initial body angle and rotational amplitude. A butterfly rotates its body to control the direction of the vortex rings generated during flapping flight; the flight modes are found to be closely related to the body motion of a butterfly. When the initial body angle increases, the forward displacement decreases, but the upward displacement increases within a stroke. With increased rotational amplitudes, the jet flows generated by a butterfly eject more downward and further enhance the generation of upward force, according to which a butterfly executes a vertical jump at the end of the downstroke. During this jumping stage, the air relative to the butterfly is moving downward; the butterfly pitches up its body to be parallel to the flow and to decrease the projected area so as to avoid further downward force generated. Our results indicate the importance of the body motion of a butterfly in flight. The inspiration of flight controlled with body motion from the flight of a butterfly might yield an alternative way to control future flight vehicles.
Ambrus, Victor E
2016-01-01
We consider rigidly rotating states in thermal equilibrium on static spherically symmetric spacetimes. Using the Maxwell-Juttner equilibrium distribution function, onstructed as a solution of the relativistic Boltzmann equation, the equilibrium particle flow four-vector, stress-energy tensor and the transport coefficients in the Marle model are computed. Their properties are discussed in view of the topology of the speed-of-light surface induced by the rotation for two classes of spacetimes: maximally symmetric (Minkowski, de Sitter and anti-de Sitter) and charged (Reissner-Nordstrom) black-hole spacetimes. To facilitate our analysis, we employ a non-holonomic comoving tetrad field, obtained unambiguously by applying a Lorentz boost on a fixed background tetrad.
Nielsen, Martin Bjerre; Krenk, Steen
2012-01-01
A conservative time integration algorithm for rigid body rotations is presented in a purely algebraic form in terms of the four quaternions components and the four conjugate momentum variables via Hamilton’s equations. The introduction of an extended mass matrix leads to a symmetric set of eight...... state-space equations where constraints are embedded without explicit use of Lagrange multipliers. The algorithm is developed by forming a finite increment of the Hamiltonian, which defines the proper selection of increments and mean values that leads to conservation of energy and momentum. The accuracy...... and conservation properties are illustrated by examples....
Narita, Makoto [Department of Mathematics, National Taiwan University, 1, Sec. 4, Roosevelt Rd., Taipei 106, Taiwan (China)
2006-12-21
We discuss the strong cosmic censorship conjecture for cosmological spacetimes in the Einstein-Yang-Mills-dilaton system. Locally rotational symmetric Bianchi I spacetimes are considered. We show local and global existence theorems for the system. Asymptotic behaviour for the spacetimes is also investigated. The curvature invariant is blowup at the initial singularities and the spacetimes are future geodesic complete. Thus, the strong cosmic censorship conjecture for the spacetimes holds.
Babourova, O V; Kudlaev, P E
2016-01-01
On the basis of the Poincare-Weyl gauge theory of gravitation, a new conformal Weyl-Dirac theory of gravitation is proposed, which is a gravitational theory in Cartan-Weyl spacetime with the Dirac scalar field representing the dark matter model. A static approximate axially symmetric solution of the field equations in vacuum is obtained. On the base of this solution in the Newtonian approximation one considers the problem of rotation velocities in spiral components of galaxies.
Pattern Formation Around Interacting Bodies in Rotating Fluids
Karl B(U)HLER
2006-01-01
The interaction of bodies like spheres and disks in rotating fluids leads to novel flow structures. The primary swirling flow in circumferential direction is superimposed by a secondary motion in the meridional plane. The flow is visualized by introducing ink through a hole in the center of the axes and distributed radially in the central plane between the interacting bodies. The flow structure depends on the shape of the bodies, their geometrical arrangement and the Reynolds number given by the rotational speed. The observed flow structures gave rise to further investigations with PIV-measurements and numerical simulations.
On symmetric equilibrium of an isothermal gas with a free boundary and a body force
2006-01-01
Full Text Available The equation of symmetric equilibrium of an isothermal gas with an unknown boundary in the field of a body force is considered. Conditions for solvability and insolvability of the problem as well as for uniqueness and nonuniqueness of solutions are presented. Examples of finite, countable, or continual sets of solutions are constructed including equipotential ones. Static stability of solutions is analyzed too.
Control of fluid-containing rotating rigid bodies
Gurchenkov, Anatoly A
2013-01-01
This book is devoted to the study of the dynamics of rotating bodies with cavities containing liquid. Two basic classes of motions are analyzed: rotation and libration. Cases of complete and partial filling of cavities with ideal liquid and complete filling with viscous liquid are treated. The volume presents a method for obtaining relations between angular velocities perpendicular to main rotation and external force momentums, which are treated as control. The developed models and methods of solving dynamical problems as well as numerical methods for solving problems of optimal control can be
Microscopic Three-Body Force Effect on Nucleon-Nucleon Cross Sections in Symmetric Nuclear Matter
ZHANG Hong-Fei; ZUO Wei; Lombardo Umberto; LI Zeng-Hua; LI Jun-Qing
2008-01-01
We provide a microscopic calculation of neutron-proton and proton-proton cross sections in symmetric nuclear matter at various densities, using the Brueckner-Hartree-Fock approximation scheme with the Argonne V14 potential including the contribution of microscopic three-body force. We investigate separately the effects of three-body force on the effective mass and on the scattering amplitude. In the present calculation, the rearrangement contribution of three-body force is considered, which will reduce the neutron and proton effective mass, and depress the amplitude of cross section. The effect of three body force is shown to be repulsive, especially in high densities and large momenta, which will suppress the cross section markedly.
Earth rotation prevents exact solid body rotation of fluids in the laboratory
Boisson, J; Moisy, F; Cortet, P -P
2012-01-01
We report direct evidence of a secondary flow excited by the Earth rotation in a water-filled spherical container spinning at constant rotation rate. This so-called {\\it tilt-over flow} essentially consists in a rotation around an axis which is slightly tilted with respect to the rotation axis of the sphere. In the astrophysical context, it corresponds to the flow in the liquid cores of planets forced by precession of the planet rotation axis, and it has been proposed to contribute to the generation of planetary magnetic fields. We detect this weak secondary flow using a particle image velocimetry system mounted in the rotating frame. This secondary flow consists in a weak rotation, thousand times smaller than the sphere rotation, around a horizontal axis which is stationary in the laboratory frame. Its amplitude and orientation are in quantitative agreement with the theory of the tilt-over flow excited by precession. These results show that setting a fluid in a perfect solid body rotation in a laboratory exp...
Centripetal focusing of gyrotactic phytoplankton in solid-body rotation
Cencini, M; Santamaria, F; Boffetta, G
2015-01-01
A suspension of gyrotactic microalgae Chlamydomonas augustae swimming in a cylindrical water vessel in solid-body rotation is studied. Our experiments show that swimming algae form an aggregate around the axis of rotation, whose intensity increases with the rotation speed. We explain this phenomenon by the centripetal orientation of the swimming direction towards the axis of rotation. This centripetal focusing is contrasted by diffusive fluxes due to stochastic reorientation of the cells. The competition of the two effects lead to a stationary distribution, which we analytically derive from a refined mathematical model of gyrotactic swimmers. The temporal evolution of the cell distribution, obtained via numerical simulations of the stochastic model, is in quantitative agreement with the experimental measurements in the range of parameters explored.
A new class of symmetric periodic solutions of the spatial elliptic restricted three-body problem
XU XingBo; FU YanNing
2009-01-01
We show that there exists a new class of symmetric periodic solutions of the spatial elliptic restricted three-body problem.In such a solution,the infinitesimal body is confined to the vicinity of a primary and moves on a nearly circular orbit.This orbit is almost perpendicular to the orbital plane of the pri-maries,where the line of symmetry of the orbit lies.The existence is shown by applying a corollary of Arenstorf's fixed point theorem to s periodicity equation system of the problem.And this existence doesn't require any restriction on the mass ratio of the primaries,nor on the eccentricity of their rela-tive elliptic orbit.Potential relevance of this new class of periodic solutions to real celestial body sys-tems and the follow-up studies in this respect are also discussed.
A new class of symmetric periodic solutions of the spatial elliptic restricted three-body problem
无
2009-01-01
We show that there exists a new class of symmetric periodic solutions of the spatial elliptic restricted three-body problem. In such a solution, the infinitesimal body is confined to the vicinity of a primary and moves on a nearly circular orbit. This orbit is almost perpendicular to the orbital plane of the primaries, where the line of symmetry of the orbit lies. The existence is shown by applying a corollary of Arenstorf’s fixed point theorem to a periodicity equation system of the problem. And this existence doesn’t require any restriction on the mass ratio of the primaries, nor on the eccentricity of their relative elliptic orbit. Potential relevance of this new class of periodic solutions to real celestial body systems and the follow-up studies in this respect are also discussed.
Tian, Jiajun; Yao, Yong; Sun, Yunxu; Yu, Xuelian; Chen, Deying
2009-08-17
A new multiwavelength Erbium-doped fiber laser is proposed and demonstrated. The intensity-dependent loss induced by nonlinear polarization rotation in a power-symmetric nonlinear optical loop mirror (NOLM) suppresses the mode competition of an Erbium-doped fiber and ensures stable multiwavelength operation at room temperature. The polarization state and its evolution conditions for stable multiwavelength operation in the ring laser cavity are discussed. The number and spectra region of output wavelength can be controlled by adjusting the work states of NOLM. (c) 2009 Optical Society of America
Gravitational redshift from rotating body having intense magnetic field
Dubey, Anuj Kumar
2016-01-01
It is well known fact that gravitational field can alter the space-time structure and gravitational redshift is its one example. Electromagnetic field can also alter the space-time similar to gravitational field. So electromagnetic field can give rise to an additional effect on gravitational redshift. There are many objects in nature, like neutron stars, magnetars etc which have high amount of rotation and magnetic field. In the present paper we will derive the expression of gravitational redshift from rotating body having intense magnetic field by using the action function of the electromagnetic fields.
R. Mantovani
2002-01-01
Full Text Available This paper presents the analysis of symmetric circulations of a rotating baroclinic flow, forced by a steady thermal wind and dissipated by Laplacian friction. The analysis is performed with numerical time-integration. Symmetric flows, vertically bound by horizontal walls and subject to either periodic or vertical wall lateral boundary conditions, are investigated in the region of parameter-space where unstable small amplitude modes evolve into stable stationary nonlinear solutions. The distribution of solutions in parameter-space is analysed up to the threshold of chaotic behaviour and the physical nature of the nonlinear interaction operating on the finite amplitude unstable modes is investigated. In particular, analysis of time-dependent energy-conversions allows understanding of the physical mechanisms operating from the initial phase of linear instability to the finite amplitude stable state. Vertical shear of the basic flow is shown to play a direct role in injecting energy into symmetric flow since the stage of linear growth. Dissipation proves essential not only in limiting the energy of linearly unstable modes, but also in selecting their dominant space-scales in the finite amplitude stage.
Two Dimensional Subsonic Euler Flows Past a Wall or a Symmetric Body
Chen, Chao; Du, Lili; Xie, Chunjing; Xin, Zhouping
2016-08-01
The existence and uniqueness of two dimensional steady compressible Euler flows past a wall or a symmetric body are established. More precisely, given positive convex horizontal velocity in the upstream, there exists a critical value {ρ_cr} such that if the incoming density in the upstream is larger than {ρ_cr}, then there exists a subsonic flow past a wall. Furthermore, {ρ_cr} is critical in the sense that there is no such subsonic flow if the density of the incoming flow is less than {ρ_cr}. The subsonic flows possess large vorticity and positive horizontal velocity above the wall except at the corner points on the boundary. Moreover, the existence and uniqueness of a two dimensional subsonic Euler flow past a symmetric body are also obtained when the incoming velocity field is a general small perturbation of a constant velocity field and the density of the incoming flow is larger than a critical value. The asymptotic behavior of the flows is obtained with the aid of some integral estimates for the difference between the velocity field and its far field states.
BSK-WBSN: Biometric Symmetric Keys to Secure Wireless Body Sensors Networks
Mesmoudi, Samira
2011-01-01
The Wireless Sensors Network (WSN) is an emergent technology resulting from progress of various fields. Many applications of networks WSN are born. One of the applications which have an operational effectiveness relates to the field of health and allows a medical remote support. Miniature wireless sensors, strategically placed on the human body, create a Wireless Body Sensor Network (WBSN) which allows supervising various essential biological signals (rate of heartbeat, pressure, etc). The sensitivity of medical information requires mechanisms of safety. This performance constitutes a challenge for WBSN because of their limitation in resources energy and data-processing. In this paper we propose a new approach to symmetric cryptographic key establishment, based on biometrics physiology. This approach takes into account WBSN constraints and its topology.
Akbarov, Surkay D.; Cafarova, Fazile I.; Yahnioglu, Nazmiye
2017-02-01
The axisymmetric buckling delamination of the piezoelectric circular sandwich plate with piezoelectric face and elastic (metal) core layers around the interface penny-shaped cracks is investigated. The case is considered where short-circuit conditions with respect to the electrical potential on the upper and lower and also lateral surfaces of face layers are satisfied. It is assumed that the edge surfaces of the cracks have an infinitesimal rotationally symmetric initial imperfection and the development of this imperfection with rotationally symmetric compressive forces acting on the lateral surface of the plate is studied by employing the exact geometrically non-linear field equations and relations of electro-elasticity for piezoelectric materials. Solution to the considered nonlinear problem is reduced to solution of the series boundary value problems derived by applying the linearization procedure with respect to small imperfection of the sought values. Numerical results reveal the effect of piezoelectricity as well as geometrical and material parameters on the critical values are determined numerically by employing finite element method (FEM).
Comparison between formulas of rotational band for axially symmetric deformed nuclei
WU Xi; LEI Yi-An
2008-01-01
The experimental rotational spectra of the deformed nuclei available in even-even and odd-A nuclei in the rare-earth and actinide regions are systematically analyzed with several rotational spectra formulas,including Bohr-Mottelson's I(I+l)-expansion,Harris'w2-expansion,ab and abc formulas.It is shown that the simple 2-parameter ab formula is much better than the widely used 2-parameter Bohr-Mottelson's AB formula and Harris'αβ formula.The available data of the rotational spectra of both ground-state band in even-even nuclei and one-quaasiparticle band in odd-A nuclei can be conveniently and rather accurately reproduced by ab formula and abc formula.The moment of inertia and the variation with rotational frequency of angular momentum can be satisfactorily reproduced by ab and abc formulas.
Rotating and rolling rigid bodies and the "hairy ball" theorem
Bormashenko, Edward; Kazachkov, Alexander
2017-06-01
Rotating and rolling rigid bodies exemplify a fascinating theorem of topology, jokingly called the "hairy ball" theorem, which demands that any continuous tangent vector field on the sphere has at least one point where the field is zero. We demonstrate via a gedanken experiment how drilling through a rotating ball, thereby converting it into a torus, leads to the elimination of zero-velocity points on the ball surface. Using the same reasoning, zero-velocity points can be removed from the surface of a drilled spinning top. We discuss the location of zero-velocity points on the surfaces of rigid bodies rolling with no slip and with slip. Observations made from different reference frames identify various zero-velocity points. Illustrative experiments visualizing zero-velocity points are presented.
Bruijn, Sjoerd M.; Meijer, Onno G.; van Dieën, Jaap H.; Kingma, Idsart; Lamoth, Claudine J.C.
2008-01-01
In walking faster than 3 km/h, transverse pelvic rotation lengthens the step ("pelvic step"). It is often assumed that the thorax then starts to counter rotate to limit total body angular momentum around the vertical. But the relative timing of pelvis and thorax rotation during gait is insufficientl
Balaban, Carey D.; McGee, David M.; Zhou, Jianxun; Scudder, Charles A.
2002-01-01
The caudal aspect of the parabrachial (PBN) and Kolliker-Fuse (KF) nuclei receive vestibular nuclear and visceral afferent information and are connected reciprocally with the spinal cord, hypothalamus, amygdala, and limbic cortex. Hence, they may be important sites of vestibulo-visceral integration, particularly for the development of affective responses to gravitoinertial challenges. Extracellular recordings were made from caudal PBN cells in three alert, adult female Macaca nemestrina through an implanted chamber. Sinusoidal and position trapezoid angular whole body rotation was delivered in yaw, roll, pitch, and vertical semicircular canal planes. Sites were confirmed histologically. Units that responded during rotation were located in lateral and medial PBN and KF caudal to the trochlear nerve at sites that were confirmed anatomically to receive superior vestibular nucleus afferents. Responses to whole-body angular rotation were modeled as a sum of three signals: angular velocity, a leaky integration of angular velocity, and vertical position. All neurons displayed angular velocity and integrated angular velocity sensitivity, but only 60% of the neurons were position-sensitive. These responses to vertical rotation could display symmetric, asymmetric, or fully rectified cosinusoidal spatial tuning about a best orientation in different cells. The spatial properties of velocity and integrated velocity and position responses were independent for all position-sensitive neurons; the angular velocity and integrated angular velocity signals showed independent spatial tuning in the position-insensitive neurons. Individual units showed one of three different orientations of their excitatory axis of velocity rotation sensitivity: vertical-plane-only responses, positive elevation responses (vertical plane plus ipsilateral yaw), and negative elevation axis responses (vertical plane plus negative yaw). The interactions between the velocity and integrated velocity components
Cavitation studies on axi-symmetric underwater body with pumpjet propulsor in cavitation tunnel
Ch. Suryanarayana
2010-12-01
Full Text Available A pumpjet propulsor (PJP was designed for an underwater body (UWB with axi-symmetric configuration. Its performance was predicted through CFD study and models were manufactured. The propulsor design was evaluated for its propulsion characteristics through model tests conducted in a Wind Tunnel (WT. In the concluding part of the study, evaluation of the cavitation performance of the pumpjet was undertaken in a cavitation tunnel (CT. In order to assess the cavitation free operation speeds and depths of the body, cavitation tests of the PJP were carried out in behind condition to determine the inception cavitation numbers for rotor, stator and cowl. The model test results obtained were corrected for full scale Reynolds number and subsequently analyzed for cavitation inception speeds at different operating depths. From model tests it was also found that the cavitation inception of the rotor takes place on the tip face side at higher advance ratios and cavitation shifts towards the suction side as the RPS increases whereas the stator and cowl are free from cavitation.
Kalkan, Erol; ,
2012-01-01
Building codes in the U.S. require at least two horizontal ground motion components for three-dimensional (3D) response history analysis (RHA) of structures. For sites within 5 km of an active fault, these records should be rotated to fault-normal/fault-parallel (FN/FP) directions, and two RHA analyses should be performed separately (when FN and then FP are aligned with transverse direction of the structural axes). It is assumed that this approach will lead to two sets of responses that envelope the range of possible responses over all non-redundant rotation angles. This assumption is examined here using 3D computer models of a single-story structure having symmetric (that is, torsionally-stiff) and asymmetric (that is, torsionally flexible) layouts subjected to an ensemble of bi-directional near-fault strong ground motions with and without apparent velocity pulses. In this parametric study, the elastic vibration period of the structures is varied from 0.2 to 5 seconds, and yield strength reduction factors R is varied from a value that leads to linear-elastic design to 3 and 5. The influence that the rotation angle of the ground motion has on several engineering demand parameters (EDPs) is examined in linear-elastic and nonlinear-inelastic domains to form a benchmark for evaluating the use of the FN/FP directions as well as the maximum-direction (MD) ground motion, a new definition of horizontal ground motions for use in the seismic design of structures according to the 2009 NEHRP Provisions and Commentary.
Second order perturbations of rotating bodies in equilibrium; the exterior vacuum problem
MacCallum, M A H; Vera, R; Callum, Malcolm A. H. Mac; Mars, Marc; Vera, Raul
2005-01-01
We study the exterior vacuum problem for first and second order stationary and axially symmetric perturbations of static bodies. The boundary conditions and their compatibility for the existence of an asymptotically flat exterior solution are discussed.
Modeling Rotating Turbulent Flows with the Body Force Potential Model.
Bhattacharya, Amitabh; Perot, Blair
2000-11-01
Like a Reynolds Stress Transport equation model, the turbulent potential model has an explicit Coriolis acceleration term that appears in the model that accounts for rotation effects. In this work the additional secondary effects that system rotation has on the dissipation rate, return-to-isotropy, and fast pressure strain terms are also included in the model. The resulting model is tested in the context of rotating isotropic turbulence, rotating homogeneous shear flow, rotating channel flow, and swirling pipe flow. Many of the model changes are applicable to Reynolds stress transport equation models. All model modifications are frame indifferent.
Kia, T.; Longuski, J. M.
1984-01-01
Analytic error bounds are presented for the solutions of approximate models for self-excited near-symmetric rigid bodies. The error bounds are developed for analytic solutions to Euler's equations of motion. The results are applied to obtain a simplified analytic solution for Eulerian rates and angles. The results of a sample application of the range and error bound expressions for the case of the Galileo spacecraft experiencing transverse torques demonstrate the use of the bounds in analyses of rigid body spin change maneuvers.
Shatalov, MY
2011-01-01
Full Text Available Standing waves can exist as stable vibrating patterns in perfect structures such as spherical bodies, and inertial rotation of the body causes precession (Bryan’seffect). However, an imperfection such as light mass anisotropy destroys the standing...
Shao, C. G.; Zhang, Y.Z.; Luo, J.; Liu, Z Z
2002-01-01
Owing to Earth's rotation a free-fall body would move in an elliptical orbit rather than along a straight line forward to the center of the Earth. In this paper on the basis of the theory for spin-spin coupling between macroscopic rotating bodies we study violation of the equivalence principle from long-distance free-fall experiments by means of a rotating ball and a non-rotating sell. For the free-fall time of 40 seconds, the difference between the orbits of the two free-fall bodies is of th...
Bound Motion of Bodies and Paticles in the Rotating Systems
Pardy, Miroslav
2007-04-01
The Lagrange theory of particle motion in the noninertial systems is applied to the Foucault pendulum, isosceles triangle pendulum and the general triangle pendulum swinging on the rotating Earth. As an analogue, planet orbiting in the rotating galaxy is considered as the giant galactic gyroscope. The Lorentz equation and the Bargmann-Michel-Telegdi equations are generalized for the rotation system. The knowledge of these equations is inevitable for the construction of LHC where each orbital proton “feels” the Coriolis force caused by the rotation of the Earth.
On the motion of rotating bodies in field gravity theory and general relativity
Baryshev, Yu V
2000-01-01
On the basis of Lagrangian formalism of relativistic field theory post-Newtonian equations of motion for a rotating body are derived in the frame of Feynman's quantum field gravity theory (FGT) and compared with corresponding geodesic equations in general relativity (GR). It is shown that in FGT the trajectory of a rotating test body does not depend on a choice of a coordinate system. The equation of translational motion of a gyroscope is applied to description of laboratory experiments with free falling rotating bodies and rotating bodies on a balance scale. Post-Newtonian relativistic effect of periodical modulation of the orbital motion of a rotating body is discussed for the case of planets of the solar system and for binary pulsars PSR B1913+16 and PSR B1259-63. In the case of binary pulsars with known spin orientations this effect gives a possibility to measure radiuses of neutron stars.
Spectrum generating algebra of the symmetric top
Bijker, R. [Universidad Nacional Autonoma de Mexico, Mexico City (Mexico). Inst. de Ciencias Nucleares; Leviatan, A. [Racah Institute of Physics, The Hebrew University, Jerusalem 91904 (Israel)
1998-03-02
We consider an algebraic treatment of a three-body system. We develop the formalism for a system of three identical objects and show that it provides a simultaneous description of the vibrational and rotational excitations of an oblate symmetric top. (orig.) 8 refs.
Spectrum generating algebra of the symmetric top
Bijker, R
1997-01-01
We consider an algebraic treatment of a three-body system. We develop the formalism for a system of three identical objects and show that it provides a simultaneous description of the vibrational and rotational excitations of an oblate symmetric top.
Numerical simulation of rotating body movement in medium with various densities
Tenenev, Valentin A.; Korolev, Stanislav A.; Rusyak, Ivan G.
2016-10-01
The paper proposes an approach to calculate the motion of rotating bodies in resisting medium by solving the Kirchhoff equations of motion in a coordinate system moving with the body and in determination of aerodynamic characteristics of the body with a given geometry by solving the Navier-Stokes equations. We present the phase trajectories of the perturbed motion of a rotating projectile in media with different densities: gas and liquid.
Radiation from an accelerating neutral body: The case of rotation
Yarman, Tolga; Arik, Metin; Kholmetskii, Alexander L.
2013-11-01
When an object is bound at rest to an attractional field, its rest mass (owing to the law of energy conservation, including the mass and energy equivalence of the Special Theory of Relativity) must decrease. The mass deficiency coming into play indicates a corresponding rest energy discharge. Thus, bringing an object to a rotational motion means that the energy transferred for this purpose serves to extract just as much rest mass (or similarly "rest energy", were the speed of light in empty space taken to be unity) out of it. Here, it is shown that during angular acceleration, photons of fundamental energy are emitted, while the object is kept on being delivered to a more and more intense rotational accelerational field, being the instantaneous angular velocity of the rotating object. This fundamental energy, as seen, does not depend on anything else (such as the mass or charge of the object), and it is in harmony with Bohr's Principle of Correspondence. This means at the same time, that emission will be achieved, as long as the angular velocity keeps on increasing, and will cease right after the object reaches a stationary rotational motion (a constant centrifugal acceleration), but if the object were brought to rotation in vacuum with no friction. By the same token, one can affirm that even the rotation at a macroscopic level is quantized, and can only take on "given angular velocities" (which can only be increased, bit by bit). The rate of emission of photons of concern is, on the other hand, proportional to the angular acceleration of the object, similarly to the derivative of the tangential acceleration with respect to time. It is thus constant for a "constant angular acceleration", although the energy of the emitted photons will increase with increasing , until the rotation reaches a stationary level, after which we expect no emission --let us stress-- if the object is in rotation in vacuum, along with no whatsoever friction (such as the case of a rotating
Bruijn, Sjoerd M; Meijer, Onno G; van Dieën, Jaap H; Kingma, Idsart; Lamoth, Claudine J C
2008-04-01
In walking faster than 3 km/h, transverse pelvic rotation lengthens the step ("pelvic step"). It is often assumed that the thorax then starts to counter rotate to limit total body angular momentum around the vertical. But the relative timing of pelvis and thorax rotation during gait is insufficiently understood. The present study aimed at analysing how transverse pelvis and thorax rotations relate to the movements of the upper leg, and how these patterns contribute to total body angular momentum. Nine healthy male volunteers walked on a treadmill at nine different velocities, ranging from 2.0 km/h to 5.2 km/h. Full body kinematics were recorded. Femur-pelvis, pelvis-thorax, and femur-thorax relative phase were calculated, as well as transverse plane angular momentum of all body segments. The shift in pelvis-thorax coordination from in-phase to out of phase with increasing velocity was found to depend on the pelvis beginning to move in-phase with the femur, while the thorax continued to counter rotate with respect to the femur. Moreover, pelvic and thoracic contributions to total body angular momentum were low (less than 10%), while contributions of the legs and arms were much larger (approximately 90%), suggesting that pelvis-thorax coordination is relatively unimportant to the organisation of total body angular momentum. Taken together, these results may imply that our understanding of the pelvic step need to be changed. Moreover, the alterations in pelvis-thorax relative phase that were reported for different locomotor pathologies may depend on different mechanisms.
COMPUTER SIMULATION OF 3-DIMENSIONAL DYNAMIC ASSEMBLY PROCESS OF MECHANICAL ROTATIONAL BODY
1998-01-01
Focusing on the study of the components of mechanical rotational body,the data structure and algorithm of component model generation are discussed.Some problems in assembly process of 3-dimensional graph of components are studied in great detail.
Pashitskii, E. A.
2017-07-01
On the basis of a two-component (two-fluid) hydrodynamic model, it is shown that the probable phenomenon of solar core rotation with a velocity higher than the average velocity of global rotation of the Sun, discovered by the SOHO mission, can be related to fast solid-body rotation of the light hydrogen component of the solar plasma, which is caused by thermonuclear fusion of hydrogen into helium inside the hot dense solar core. Thermonuclear fusion of four protons into a helium nucleus (α-particle) creates a large free specific volume per unit particle due to the large difference between the densities of the solar plasma and nuclear matter. As a result, an efficient volumetric sink of one of the components of the solar substance—hydrogen—forms inside the solar core. Therefore, a steady-state radial proton flux converging to the center should exist inside the Sun, which maintains a constant concentration of hydrogen as it burns out in the solar core. It is demonstrated that such a converging flux of hydrogen plasma with the radial velocity v r ( r) = -β r creates a convective, v r ∂ v φ/∂ r, and a local Coriolis, v r v φ/ r,φ nonlinear hydrodynamic forces in the solar plasma, rotating with the azimuthal velocity v φ. In the absence of dissipation, these forces should cause an exponential growth of the solid-body rotation velocity of the hydrogen component inside the solar core. However, friction between the hydrogen and helium components of the solar plasma due to Coulomb collisions of protons with α-particles results in a steady-state regime of rotation of the hydrogen component in the solar core with an angular velocity substantially exceeding the global rotational velocity of the Sun. It is suggested that the observed differential (liquid-like) rotation of the visible surface of the Sun (photosphere) with the maximum angular velocity at the equator is caused by sold-body rotation of the solar plasma in the radiation zone and strong turbulence in
Measure of Segments which Intersect a Convex Body from Rotational Formulae
Ximo GUAL-ARNAU; Silena HEROLD-GARC´IA
2015-01-01
Classical problems in integral geometry and geometric probability involve the kinematic measure of congruent segments of fixed length within a convex body in R3. We give this measure from rotational formulae; that is, from isotropic plane sections through a fixed point. From this result we also obtain a new rotational formula for the volume of a convex body;which is proved to be equivalent to the wedge formula for the volume.
Efficiency of Wave-Driven Rigid Body Rotation Toroidal Confinement
Rax, J -M; Fisch, N J
2016-01-01
The compensation of vertical drifts in toroidal magnetic fields through a wave-driven poloidal rotation is compared to compensation through the wave driven toroidal current generation to support the classical magnetic rotational transform. The advantages and drawbacks associated with the sustainment of a radial electric field are compared with those associated with the sustainment of a poloidal magnetic field both in terms of energy content and power dissipation. The energy content of a radial electric field is found to be smaller than the energy content of a poloidal magnetic field for a similar set of orbits. The wave driven radial electric field generation efficiency is similarly shown, at least in the limit of large aspect ratio, to be larger than the efficiency of wave-driven toroidal current generation.
Dynamic analysis on generalized linear elastic body subjected to large scale rigid rotations
刘占芳; 颜世军; 符志
2013-01-01
The dynamic analysis of a generalized linear elastic body undergoing large rigid rotations is investigated. The generalized linear elastic body is described in kine-matics through translational and rotational deformations, and a modified constitutive relation for the rotational deformation is proposed between the couple stress and the curvature tensor. Thus, the balance equations of momentum and moment are used for the motion equations of the body. The floating frame of reference formulation is applied to the elastic body that conducts rotations about a fixed axis. The motion-deformation coupled model is developed in which three types of inertia forces along with their incre-ments are elucidated. The finite element governing equations for the dynamic analysis of the elastic body under large rotations are subsequently formulated with the aid of the constrained variational principle. A penalty parameter is introduced, and the rotational angles at element nodes are treated as independent variables to meet the requirement of C1 continuity. The elastic body is discretized through the isoparametric element with 8 nodes and 48 degrees-of-freedom. As an example with an application of the motion-deformation coupled model, the dynamic analysis on a rotating cantilever with two spatial layouts relative to the rotational axis is numerically implemented. Dynamic frequencies of the rotating cantilever are presented at prescribed constant spin velocities. The maximal rigid rotational velocity is extended for ensuring the applicability of the linear model. A complete set of dynamical response of the rotating cantilever in the case of spin-up maneuver is examined, it is shown that, under the ultimate rigid rotational velocities less than the maximal rigid rotational velocity, the stress strength may exceed the material strength tolerance even though the displacement and rotational angle responses are both convergent. The influence of the cantilever layouts on their responses and
Guruswamy, Guru P.; Tu, Eugene L.
1988-01-01
To accurately study the transonic aeroelastic characteristics, it is important to model the full aircraft configuration, including asymmetry. Recently, an accurate method of computing unsteady transonic flows on full-span wing-body configurations was developed using the transonic potential flow theory. In this work, the method is further developed to account for the aeroelasticity of full-span wing-body configurations. This is accomplished by simultaneously integrating the unsteady aerodynamic forces and modal structural equations of the wing-body configurations. To validate the method, aeroelastic computations are made for a wing-body configuration with a rectangular wing. The aeroelastic responses of this configuration are correlated with the responses of a similar isolated wing. The comparisons are favorable. Aeroelastic computations associated with symmetric and asymmetric modes are also made to study the influence of modal asymmetry on responses. This new development is further illustrated by computing aeroelastic characteristics of a typical fighter aircraft. The results from this study will be useful in accurately computing the transonic flutter boundaries of aircraft, including those associated with asymmetric modes.
Spacecraft motion analysis about rapid rotating small body
史雪岩; 崔祜涛; 崔平远; 栾恩杰
2003-01-01
The orbital dynamics equation of a spacecraft around an irregular sphere small body is established based on the small body' s gravitational potential approximated with a tri-axial ellipsoid. According to the Jacobi integral constant, the spacecraft zero-velocity curves in the vicinity of the small body is described and feasible motion region is analyzed. The limited condition and the periapsis radius corresponding to different eccentricity against impact surface are presented. The stability of direct and retrograde equator orbits is analyzed based on the perturbation solutions of mean orbit elements.
Sowmiya, C.; Kothawala, Ali Arshad; Thittai, Arun K.
2016-04-01
During manual palpation of breast masses, the perception of its stiffness and slipperiness are the two commonly used information by the physician. In order to reliably and quantitatively obtain this information several non-invasive elastography techniques have been developed that seek to provide an image of the underlying mechanical properties, mostly stiffness-related. Very few approaches have visualized the "slip" at the lesion-background boundary that only occurs for a loosely-bonded benign lesion. It has been shown that axial-shear strain distribution provides information about underlying slip. One such feature, referred to as "fill-in" was interpreted as a surrogate of the rotation undergone by an asymmetrically-oriented-loosely bonded-benign-lesion under quasi-static compression. However, imaging and direct visualization of the rotation itself has not been addressed yet. In order to accomplish this, the quality of lateral displacement estimation needs to be improved. In this simulation study, we utilize spatial compounding approach and assess the feasibility to obtain good quality rotation elastogram. The angular axial and lateral displacement estimates were obtained at different insonification angles from a phantom containing an elliptical inclusion oriented at 45°, subjected to 1% compression from the top. A multilevel 2D-block matching algorithm was used for displacement tracking and 2D-least square compounding of angular axial and lateral displacement estimates was employed. By varying the maximum steering angle and incremental angle, the improvement in the lateral motion tracking accuracy and its effects on the quality of rotational elastogram were evaluated. Results demonstrate significantly-improved rotation elastogram using this technique.
Shao, C G; Luo, J; Liu, Z Z
2002-01-01
Owing to Earth's rotation a free-fall body would move in an elliptical orbit rather than along a straight line forward to the center of the Earth. In this paper on the basis of the theory for spin-spin coupling between macroscopic rotating bodies we study violation of the equivalence principle from long-distance free-fall experiments by means of a rotating ball and a non-rotating sell. For the free-fall time of 40 seconds, the difference between the orbits of the two free-fall bodies is of the order of 10^{-9}cm which could be detected by a SQUID magnetometer owing to such a magnetometer can be used to measure displacements as small as 10^{-13} centimeters.
SHAO Cheng-Gang; ZHANG Yuan-Zhong; LUAN En-Jie; LUO Jun; LIU Zhong-Zhu
2003-01-01
Owing to Earth's rotation a free-fall body would move in an elliptical orbit rather than along a straight line forward to the center of the Earth. In this paper on the basis of the theory for spin-spin coupling between macroscopic rotating bodies we study violation of the equivalence principle from long-distance free-fall experiments by means of a rotating ball and a non-rotating shell. For the free-fall time of 40 s, the difference between the orbits of the two free-fall bodies is of the order of 10-9 cm which could be detected by an SQUID magnetometer because such a magnetometer can be used to measure displacements as small as 10-13 cm.
Option selection in whole-body rotation movements in gymnastics
Thomas HEINEN
2016-03-01
Full Text Available Abstract When a gymnast performs a somersault, the linear and angular momentum along with a particular control of inertia during the flight phase constrain the possibilities for action. Given the complexity and dynamic nature of the human moving system, one could argue that there exist a particular amount of stable coordination states when performing somersaults. The goal of this study was to explore the manifold of movement options and coordination states along with their differentiating parameters for a single somersault in gymnastics based on a simple mathematical model reflecting gymnast’s rotation behavior during the flight phase. Biomechanical parameters determining rotation behavior during a somersault were systematically varied with regard to a particular set of biomechanical constraints defining a successful somersault performance. Batch simulations revealed that from 10229760 simulation cycles only 655346 (approximately 6.41% led to successful somersault performance. A subsequent analysis of the movement option landscape for the optimum angular momentum revealed ten coordination states for a single somersault that could be clearly distinguished based on the simulation parameters. Taken the results together, it becomes apparent that it may be most advisable to perform a single somersault with a larger moment of inertia when achieving the tucked position, a longer duration to achieve the tucked position, a longer duration of staying tucked, and an intermediate moment of inertia during landing. This strategy comprises the largest amount of movement options associated with an upright landing and thus the highest probability of success when performing a single somersault.
Elisa Raffaella Ferrè
Full Text Available Vestibular signals are strongly integrated with information from several other sensory modalities. For example, vestibular stimulation was reported to improve tactile detection. However, this improvement could reflect either a multimodal interaction or an indirect interaction driven by vestibular effects on spatial attention and orienting. Here we investigate whether natural vestibular activation induced by passive whole-body rotation influences tactile detection. In particular, we assessed the ability to detect faint tactile stimuli to the fingertips of the left and right hand during spatially congruent or incongruent rotations. We found that passive whole-body rotations significantly enhanced sensitivity to faint shocks, without affecting response bias. Critically, this enhancement of somatosensory sensitivity did not depend on the spatial congruency between the direction of rotation and the hand stimulated. Thus, our results support a multimodal interaction, likely in brain areas receiving both vestibular and somatosensory signals.
Plotnikov, P. K.
2015-05-01
Experimental studies and their results are described for the translation-rotational motion of rolling bodies subjected to forces and elastic deformations of the contact tribological conjunction regions between such bodies and the bases. Most attention is paid to the motion of such bodies outside the contact surfaces in the regions of preliminary displacements and behind these regions. In several experiments, the processes are recorded and analyzed from the very beginning to the termination of the rolling body finite displacements. All displacement stages exhibit oscillations due to variations in the character of motions of the rolling bodies. In the case where the body is only under the action of its weight, the regions of normal strains symmetric with respect to the axis of the weight action are shown as surface indentations outside the region of direct contact between the base and the rolling body. The photographs of the base nonsymmetric deformations due to the additional action of the tangential force on the rolling body are presented. One can see that the indentation slope in the motion or the force action direction is steeper and the indentation depth and length are smaller than those on the opposite side. This suggests that, on the side where the rolling body surface enters the base, the volumes of their deformations and hence the elastic force are greater than on the opposite side. The graphs are constructed for the variation in the values of preliminary and kinematic (in motion) displacements and the arm of rolling friction force for two motor cars, for a solid steel roller, and for a steel roller with two foam rubber wheels. The graphs show that, quantitatively, the displacement values are by one and more orders of magnitude greater than the values of these arms of force. Qualitatively, the arms of rolling friction force, just as the displacements, are characterized by the presence of proportionality and saturation segments of their characteristics. The
Panichi, Roberto; Botti, Fabio Massimo; Ferraresi, Aldo; Faralli, Mario; Kyriakareli, Artemis; Schieppati, Marco; Pettorossi, Vito Enrico
2011-04-01
Self-motion perception and vestibulo-ocular reflex (VOR) were studied during whole body yaw rotation in the dark at different static head positions. Rotations consisted of four cycles of symmetric sinusoidal and asymmetric oscillations. Self-motion perception was evaluated by measuring the ability of subjects to manually track a static remembered target. VOR was recorded separately and the slow phase eye position (SPEP) was computed. Three different head static yaw deviations (active and passive) relative to the trunk (0°, 45° to right and 45° to left) were examined. Active head deviations had a significant effect during asymmetric oscillation: the movement perception was enhanced when the head was kept turned toward the side of body rotation and decreased in the opposite direction. Conversely, passive head deviations had no effect on movement perception. Further, vibration (100 Hz) of the neck muscles splenius capitis and sternocleidomastoideus remarkably influenced perceived rotation during asymmetric oscillation. On the other hand, SPEP of VOR was modulated by active head deviation, but was not influenced by neck muscle vibration. Through its effects on motion perception and reflex gain, head position improved gaze stability and enhanced self-motion perception in the direction of the head deviation.
Body-fixed relativistic molecular Hamiltonian and its application to nuclear spin-rotation tensor.
Xiao, Yunlong; Liu, Wenjian
2013-04-07
A relativistic molecular Hamiltonian that describes electrons fully relativistically and nuclei quasi-relativistically is proposed and transformed from the laboratory to the body-fixed frame of reference. As a first application of the resulting body-fixed relativistic molecular Hamiltonian, the long anticipated relativistic theory of nuclear spin-rotation (NSR) tensor is formulated rigorously. A "relativistic mapping" between experimental NSR and NMR is further proposed, which is of great value in establishing high-precision absolute NMR shielding scales.
Lau, Darryl; Shin, Samuel S.; Patel, Rakesh; Park, Paul
2013-01-01
Cervical fractures can result in severe neurological compromise and even death. One of the most commonly injured segments is the C2 vertebrae, which most frequently involves the odontoid process. In this report, we present the unusual case of a 28-year-old female who sustained a C2 vertebral body fracture (comminuted transverse fracture through the body and both transverse processes) that had both a significant distractive and rotational component, causing the fracture to be highly unstable. ...
On the rotational equations of motion in rigid body dynamics when using Euler parameters.
Sherif, Karim; Nachbagauer, Karin; Steiner, Wolfgang
Many models of three-dimensional rigid body dynamics employ Euler parameters as rotational coordinates. Since the four Euler parameters are not independent, one has to consider the quaternion constraint in the equations of motion. This is usually done by the Lagrange multiplier technique. In the present paper, various forms of the rotational equations of motion will be derived, and it will be shown that they can be transformed into each other. Special attention is hereby given to the value of the Lagrange multiplier and the complexity of terms representing the inertia forces. Particular attention is also paid to the rotational generalized external force vector, which is not unique when using Euler parameters as rotational coordinates.
Measurements of the Solid-body Rotation of Anisotropic Particles in 3D Turbulence
Marcus, Guy G; Kramel, Stefan; Ni, Rui; Voth, Greg A
2014-01-01
We introduce a new method to measure Lagrangian vorticity and the rotational dynamics of anisotropic particles in a turbulent fluid flow. We use 3D printing technology to fabricate crosses (two perpendicular rods) and jacks (three mutually perpendicular rods). Time-resolved measurements of their orientation and solid-body rotation rate are obtained from stereoscopic video images of their motion in a turbulent flow between oscillating grids with $R_\\lambda$=$91$. The advected particles have a largest dimension of 6 times the Kolmogorov length, making them a good approximation to anisotropic tracer particles. Crosses rotate like disks and jacks rotate like spheres, so these measurements, combined with previous measurements of tracer rods, allow experimental study of ellipsoids across the full range of aspect ratios. The measured mean square tumbling rate, $\\langle \\dot{p}_i \\dot{p}_i \\rangle$, confirms previous direct numerical simulations that indicate that disks tumble much more rapidly than rods. Measurement...
Cao Minsong; Lasley, Foster D.; Das, Indra J.; DesRosiers, Colleen M.; Slessinger, Eric D. [Department of Radiation Oncology, Indiana University School of Medicine, Indianapolis, Indiana (United States); Cardenes, Higinia R., E-mail: hcardene@iupui.edu [Department of Radiation Oncology, Indiana University School of Medicine, Indianapolis, Indiana (United States)
2012-11-01
Purpose: To evaluate the dosimetric impact of rotational setup errors in stereotactic body radiotherapy (SBRT) treatment of liver tumors and to investigate whether translational shifts can compensate for rotation. Methods and Materials: The positioning accuracy in 20 patients with liver malignancies treated with SBRT was reevaluated offline by matching the patients' cone-beam computed tomography (CT) scans (n=75) to the planning CT scans and adjusting the 3 rotational angles (pitch, roll, and yaw). Systematic and random setup errors were calculated. The dosimetric changes caused by rotational setup errors were quantified for both simulated and observed patient rotations. Dose distributions recalculated on the rotated CT scans were compared with the original planned doses. Translational corrections were simulated based on manual translational registration of the rotated images to the original CT scans. The correction efficacy was evaluated by comparing the recalculated plans with the original plans. Results: The systematic rotational setup errors were -0.06 Degree-Sign {+-} 0.68 Degree-Sign , -0.29 Degree-Sign {+-} 0.62 Degree-Sign , and -0.24 Degree-Sign {+-} 0.61 Degree-Sign ; the random setup errors were 0.80 Degree-Sign , 1.05 Degree-Sign , and 0.61 Degree-Sign for pitch, roll, and yaw, respectively. Analysis of CBCT images showed that 56.0%, 14.7%, and 1.3% of treated fractions had rotational errors of >1 Degree-Sign , >2 Degree-Sign , and >3 Degree-Sign , respectively, in any one of the rotational axes. Rotational simulations demonstrated that the reduction of gross tumor volume (GTV) coverage was <2% when rotation was <3 Degree-Sign . Recalculated plans using actual patient roll motions showed similar reduction (<2%) in GTV coverage. Translational corrections improved the GTV coverage to within 3% of the original values. For organs at risk (OAR), the dosimetric impact varied case by case. Conclusion: Actual rotational setup errors in SBRT for liver
Barkin, Yu. V.
New unperturbed motions are suggested for the study of the rotational motion of deformable celestial bodies. This motion describes the rotation of an isolated celestial body deformed by its own rotation. By some natural simplifications and by using special forms of canonical variables (similar to Andoyer's variables) the problem is reduced to the classical Euler-Poinsot problem for a rigid body, but with different moments of inertia. The suggested unpertubed motion describes Chandler's pole motion and we shall call it Chandler or Euler-Chandler motion. The development of the unperturbed theory is described in this paper. The solution of the Chandler problem (Andoyer's variables, components of angular velocity of the body's axes, and their direction cosines) is presented in elliptical and - functions, and in the form of Fourier series in the angle-action variables. Similar Fourier series were obtained for products and squares of the diraction cosines. The coefficients of these series are expressed through full elliptical integrals of the first, second and third kinds with modulus which is the defining function of the action variables. It is the principal peculiarity of these series. As an illustration we give a application of this unperturbed theory to the study of the Earth's rotation (the principal properties of the Earth's rotation and perturbations). So, the unperturbed motion describes the following phenomena of the Earth's rotation: Chandler's motion of the pole of the Earth's axis of rotation; the ellipticity of the trajectory of the Earth's pole; the non-uniformity of the pole motion along the elliptical trajectory; the variation with Chandler's period of the modulus of the Earth's angular velocity. Theory of the perturbed rotational motion of the Earth is constructed on the basis of the special forms of equations of the rotation of a deformable body (in angle-action variables and their modifications for the Chandler-Euler problem). For the construction of
Kirillov, Oleg N.
2008-01-01
Flutter of an elastic body of revolution spinning about its axis of symmetry is prohibited in the subcritical spinning speed range by the Krein theorem for the Hamiltonian perturbations. Indefinite damping creates conical domains of the subcritical flutter (subcritical parametric resonance) bifurcating into the pockets of two Whitney's umbrellas when non-conservative positional forces are additionally taken into account. This explains why in contrast to the common intuition, but in agreement ...
Measurements of the solid-body rotation of anisotropic particles in 3D turbulence
Marcus, Guy G.; Parsa, Shima; Kramel, Stefan; Ni, Rui; Voth, Greg A.
2014-10-01
We introduce a new method to measure Lagrangian vorticity and the rotational dynamics of anisotropic particles in a turbulent fluid flow. We use 3D printing technology to fabricate crosses (two perpendicular rods) and jacks (three mutually perpendicular rods). Time-resolved measurements of their orientation and solid-body rotation rate are obtained from four video images of their motion in a turbulent flow between oscillating grids with {{R}λ } = 91. The advected particles have a largest dimension of 6 times the Kolmogorov length, making them a good approximation to anisotropic tracer particles. Crosses rotate like disks and jacks rotate like spheres, so these measurements, combined with previous measurements of tracer rods, allow experimental study of axisymmetric ellipsoids across the full range of aspect ratios. The measured mean square tumbling rate, , confirms previous direct numerical simulations that indicate that disks tumble much more rapidly than rods. Measurements of the alignment of a unit vector defining the orientation of crosses with the direction of their solid-body rotation rate vector provide the first direct observation of the alignment of anisotropic particles by the velocity gradients in a turbulent flow.
Kirillov, Oleg N
2008-01-01
Flutter of an elastic body of revolution spinning about its axis of symmetry is prohibited in the subcritical spinning speed range by the Krein theorem for the Hamiltonian perturbations. Indefinite damping creates conical domains of the subcritical flutter (subcritical parametric resonance) bifurcating into the pockets of two Whitney's umbrellas when non-conservative positional forces are additionally taken into account. This explains why in contrast to the common intuition, but in agreement with experience, symmetry-breaking stiffness variation can promote subcritical friction-induced oscillations of the rotor rather than inhibit them.
Time-dependent solution for reorientation of rotating tidally deformed visco-elastic bodies
Hu, Haiyang; van der Wal, Wouter; Vermeersen, Bert
2017-04-01
Many icy satellites or planets contain features which suggest a (past) reorientation of the body, such as the tiger stripes on Enceladus and the heart-shaped Sputnik Planum on Pluto. Most of these icy bodies are tidally locked and this creates a large tidal bulge which is about three times of its centrifugal (equatorial) bulge. To study the reorientation of such rotating tidally deformed body is complicated and most previous studies apply the so-called fluid limit method. The fluid limit approach ignores the viscous response of the body and assumes that it immediately reaches its fluid limit when simulating the reorientation due to a changing load. As a result, this method can only simulate cases when the change in the load is much slower than the dominant viscous modes of the body. For other kinds of load, for instance, a Heaviside load due to an impact which creates an instant relocation of mass, it does not give us a prediction of how the reorientation is accomplished (e.g. How fast? Along which path?). We establish a new method which can give an accurate time-dependent solution for reorientation of rotating tidally deformed bodies. Our method can be applied both semi-analytically or numerically (with finite element method) to include features such as lateral heterogeneity or non-linear material. We also present an extension of our method to simulate the e ffect of a fossil bulge. With our method, we show that reorientation of a tidally deformed body driven by a positive mass anomaly near the poles has a preference for rotating around the tidal axis instead of towards it, contrary to predictions in previous studies. References Hu, H., W. van der Wal and L.L.A. Vermeersen (2017). A numerical method for reorientation of rotating tidally deformed visco-elastic bodies. Journal of Geophysical Research: Planets, doi:10.1002/2016JE005114, 2016JE005114. Matsuyama, I. and Nimmo, F. (2007). Rotational stability of tidally deformed planetary bodies. Journal of Geophysical
Ono, Toshiaki; Fushimi, Naomasa; Yamada, Kei; Asada, Hideki
2015-01-01
In terms of Sturm's theorem, we reexamine a marginal stable circular orbit (MSCO) such as the innermost stable circular orbit (ISCO) of a timelike geodesic in any spherically symmetric and static spacetime. MSCOs for some of exact solutions to the Einstein's equation are discussed. Strum's theorem is explicitly applied to the Kottler (often called Schwarzschild-de Sitter) spacetime. Moreover, we analyze MSCOs for a spherically symmetric, static and vacuum solution in Weyl conformal gravity.
Forced convection of power-law fluids flow over a rotating nonisothermal body
Kim, H. W.; Essemyi, A. J.
1993-10-01
Presented is an analysis of steady laminar flow of power-law fluids past a rotating body with nonisothermal surfaces. A coordinate transformation combined with the Merk-type series expansion is employed to transform the governing momentum equations into a set of coupled ordinary differential equations. The equations are numerically integrated to obtain the axial and tangential velocity gradients for determining the friction coefficient. For forced convection, a generalized coordinate transformation is used to analyze the temperature field of the power-law flow. Solutions to the transformed energy equations are obtained in the form of universal functions. The heat transfer coefficients in terms of NuRe(sup 1/(n + 1)) are presented for a rotating sphere. The effects of power-law index, rotation sphere, Prandtl number, and the location of step discontinuity in surface temperature on the local Nusselt number are fully investigated and demonstrated.
Rotation-limited growth of three-dimensional body-centered-cubic crystals.
Tarp, Jens M; Mathiesen, Joachim
2015-07-01
According to classical grain growth laws, grain growth is driven by the minimization of surface energy and will continue until a single grain prevails. These laws do not take into account the lattice anisotropy and the details of the microscopic rearrangement of mass between grains. Here we consider coarsening of body-centered-cubic polycrystalline materials in three dimensions using the phase field crystal model. We observe, as a function of the quenching depth, a crossover between a state where grain rotation halts and the growth stagnates and a state where grains coarsen rapidly by coalescence through rotation and alignment of the lattices of neighboring grains. We show that the grain rotation per volume change of a grain follows a power law with an exponent of -1.25. The scaling exponent is consistent with theoretical considerations based on the conservation of dislocations.
Tidal synchronization of an anelastic multi-layered body: Titan's synchronous rotation
Folonier, Hugo A.; Ferraz-Mello, Sylvio
2017-09-01
Tidal torque drives the rotational and orbital evolution of planet-satellite and star-exoplanet systems. This paper presents one analytical tidal theory for a viscoelastic multi-layered body with an arbitrary number of homogeneous layers. Starting with the static equilibrium figure, modified to include tide and differential rotation, and using the Newtonian creep approach, we find the dynamical equilibrium figure of the deformed body, which allows us to calculate the tidal potential and the forces acting on the tide generating body, as well as the rotation and orbital elements variations. In the particular case of the two-layer model, we study the tidal synchronization when the gravitational coupling and the friction in the interface between the layers is added. For high relaxation factors (low viscosity), the stationary solution of each layer is synchronous with the orbital mean motion (n) when the orbit is circular, but the rotational frequencies increase if the orbital eccentricity increases. This behavior is characteristic in the classical Darwinian theories and in the homogeneous case of the creep tide theory. For low relaxation factors (high viscosity), as in planetary satellites, if friction remains low, each layer can be trapped in different spin-orbit resonances with frequencies n/2,n,3n/2,2n,\\ldots . When the friction increases, attractors with differential rotations are destroyed, surviving only commensurabilities in which core and shell have the same velocity of rotation. We apply the theory to Titan. The main results are: (i) the rotational constraint does not allow us to confirm or reject the existence of a subsurface ocean in Titan; and (ii) the crust-atmosphere exchange of angular momentum can be neglected. Using the rotation estimate based on Cassini's observation (Meriggiola et al. in Icarus 275:183-192, 2016), we limit the possible value of the shell relaxation factor, when a deep subsurface ocean is assumed, to γ _s≲10^{-9} s^{-1} , which
Bang, Do; Awano, Hiroyuki; Tominaga, Junji; Kolobov, Alexander V.; Fons, Paul; Saito, Yuta; Makino, Kotaro; Nakano, Takashi; Hase, Muneaki; Takagaki, Yukihiko; Giussani, Alessandro; Calarco, Raffaella; Murakami, Shuichi
2014-07-01
Interfacial phase change memory (iPCM), that has a structure of a superlattice made of alternating atomically thin GeTe and Sb2Te3 layers, has recently attracted attention not only due to its superior performance compared to the alloy of the same average composition in terms of energy consumption but also due to its strong response to an external magnetic field (giant magnetoresistance) that has been speculated to arise from switching between topological insulator (RESET) and normal insulator (SET) phases. Here we report magneto-optical Kerr rotation loops in the visible range, that have mirror symmetric resonances with respect to the magnetic field polarity at temperatures above 380 K when the material is in the SET phase that has Kramers-pairs in spin-split bands. We further found that this threshold temperature may be controlled if the sample was cooled in a magnetic field. The observed results open new possibilities for use of iPCM beyond phase-change memory applications.
On the polar moment of inertia of a compressible body. [planetary rotational dynamics
Mulholland, J. D.
1980-01-01
The rotational dynamics of a body are governed by the values of its principle moments of inertia. These quantities are not directly observable, but they are related to the harmonic coefficients of the external gravity field and to the density distribution within the body, both of which can be inferred from appropriate observations. It is shown that, for the particular case of a spherical planet whose density varies as a power of the radial distance, the principal moment of inertia has an elegantly simple form. Application of this simplified case to the Jovian planets suggests that the density profiles outside the central core are approximately linear, with the apparent exception of Neptune.
Lau, Darryl; Shin, Samuel S; Patel, Rakesh; Park, Paul
2013-01-01
Cervical fractures can result in severe neurological compromise and even death. One of the most commonly injured segments is the C2 vertebrae, which most frequently involves the odontoid process. In this report, we present the unusual case of a 28-year-old female who sustained a C2 vertebral body fracture (comminuted transverse fracture through the body and both transverse processes) that had both a significant distractive and rotational component, causing the fracture to be highly unstable. Application of halo bracing was unsuccessful. The patient subsequently required a C1-C4 posterior spinal fusion. Follow-up computer tomography imaging confirmed fusion and the patient did well clinically thereafter.
Mantises exchange angular momentum between three rotating body parts to jump precisely to targets.
Burrows, Malcolm; Cullen, Darron A; Dorosenko, Marina; Sutton, Gregory P
2015-03-16
Flightless animals have evolved diverse mechanisms to control their movements in air, whether falling with gravity or propelling against it. Many insects jump as a primary mode of locomotion and must therefore precisely control the large torques generated during takeoff. For example, to minimize spin (angular momentum of the body) at takeoff, plant-sucking bugs apply large equal and opposite torques from two propulsive legs [1]. Interacting gear wheels have evolved in some to give precise synchronization of these legs [2, 3]. Once airborne, as a result of either jumping or falling, further adjustments may be needed to control trajectory and orient the body for landing. Tails are used by geckos to control pitch [4, 5] and by Anolis lizards to alter direction [6, 7]. When falling, cats rotate their body [8], while aphids [9] and ants [10, 11] manipulate wind resistance against their legs and thorax. Falling is always downward, but targeted jumping must achieve many possible desired trajectories. We show that when making targeted jumps, juvenile wingless mantises first rotated their abdomen about the thorax to adjust the center of mass and thus regulate spin at takeoff. Once airborne, they then smoothly and sequentially transferred angular momentum in four stages between the jointed abdomen, the two raptorial front legs, and the two propulsive hind legs to produce a controlled jump with a precise landing. Experimentally impairing abdominal movements reduced the overall rotation so that the mantis either failed to grasp the target or crashed into it head first.
A numerical method for reorientation of rotating tidally deformed viscoelastic bodies
Hu, H.; Wal, W.; Vermeersen, L. L. A.
2017-01-01
Existing approaches for simulating the true polar wander (TPW) of a viscoelastic body can be divided into three categories: (i) a linear dynamic approach which uses the linearized Liouville equation (e.g., Wu and Peltier (1984) and Mitrovica et al. (2005)); (ii) a nonlinear dynamic approach which is based on the quasi-fluid approximation (e.g., Sabadini and Peltier (1981), Ricard et al. (1993), and Cambiotti et al. (2011)); and (iii) a long-term limit approach which only considers the fluid limit of a reorientation (e.g., Matsuyama and Nimmo (2007)). Several limitations of these approaches have not been studied: the range for which the linear approach is accurate, the validity of the quasi-fluid approximation, and the dynamic solution for TPW of a tidally deformed rotating body. We establish a numerical procedure which is able to determine the large-angle reorientation of a viscoelastic celestial body that can be both centrifugally and tidally deformed. We show that the linear approach leads to significant errors for loadings near the poles or the equator. Second, we show that slow relaxation modes can have a significant effect on large-angle TPW of Earth or other planets. Finally, we show that reorientation of a tidally deformed body driven by a positive mass anomaly near the poles has a preference for rotating around the tidal axis instead of toward it. At a tidally deformed body which does not have a remnant bulge, positive mass anomalies are more likely to be found near the equator and the plane perpendicular to the tidal axis, while negative mass anomalies tend to be near the great circle that contains the tidal and rotational axes.
SU-E-J-165: Dosimetric Impact of Liver Rotations in Stereotactic Body Radiation Therapy
Pinnaduwage, D; Paulsson, A; Sudhyadhom, A; Chen, J; Chang, A; Anwar, M; Gottschalk, A; Yom, S S.; Descovich, M [University of California San Francisco, San Francisco, CA (United States)
2015-06-15
Purpose: Often in liver stereotactic body radiotherapy a single fiducial is implanted near the tumor for image-guided treatment delivery. In such cases, rotational corrections are calculated based on the spine. This study quantifies rotational differences between the spine and liver, and investigates the corresponding dosimetric impact. Methods: Seven patients with 3 intrahepatic fiducials and 4DCT scans were identified. The planning CT was separately co-registered with 4 phases of the 4DCT (0%, 50%, 100% inhale and 50% exhale) by 1) rigid registration of the spine, and 2) point-based registration of the 3 fiducials. Rotation vectors were calculated for each registration. Translational differences in fiducial positions between the 2 registrations methods were investigated. Dosimetric impact due to liver rotations and deformations was assessed using critical structures delineated on the 4DCT phases. For dose comparisons, a single fiducial was translationally aligned following spine alignment to represent what is typically done in the clinic. Results: On average, differences between spine and liver rotations during the 0%, 50%, 100% inhale, and 50% exhale phases were 3.23°, 3.27°, 2.26° and 3.11° (pitch), 3.00°, 2.24°, 3.12° and 1.73° (roll), and 1.57°, 1.98°, 2.09° and 1.36° (yaw), respectively. The maximum difference in rotations was 12°, with differences of >3° seen in 14/28 (pitch), 10/28 (roll), and 6/28 (yaw) cases. Average fiducial displacements of 2.73 (craniocaudal), 1.04 (lateral) and 1.82 mm (vertical) were seen. Evaluating percent dose differences for 5 patients at the peaks of the respiratory cycle, the maximum dose to the duodenum, stomach, bowel and esophagus differed on average by 11.4%, 5.3%, 11.2% and 49.1% between the 2 registration methods. Conclusion: Lack of accounting for liver rotation during treatment might Result in clinically significant dose differences to critical structures. Both rotational and translational deviations
Nonlinear evolution of tidally forced inertial waves in rotating fluid bodies
Favier, B; Baruteau, C; Ogilvie, G I
2014-01-01
We perform one of the first studies into the nonlinear evolution of tidally excited inertial waves in a uniformly rotating fluid body, exploring a simplified model of the fluid envelope of a planet (or the convective envelope of a solar-type star) subject to the gravitational tidal perturbations of an orbiting companion. Our model contains a perfectly rigid spherical core, which is surrounded by an envelope of incompressible uniform density fluid. The corresponding linear problem was studied in previous papers which this work extends into the nonlinear regime, at moderate Ekman numbers (the ratio of viscous to Coriolis accelerations). By performing high-resolution numerical simulations, using a combination of pseudo-spectral and spectral element methods, we investigate the effects of nonlinearities, which lead to time-dependence of the flow and the corresponding dissipation rate. Angular momentum is deposited non-uniformly, leading to the generation of significant differential rotation in the initially unifor...
Analysis of the wobbling effect in a lens-shaped body rotation
Kim, Minho
2017-03-01
We discuss the wobbling motion in a lens-shaped body rotation, focusing on the frequencies and the amplitude of nutation by filming the rotational motion and wobbling of the body. The friction coefficient of the surface is altered to examine its influence for two lenses with different curvature radii. MATLAB programs are developed to retrieve the Euler angles, which are graphed according to time. It is shown that the lens with a smaller curvature radius exhibits the wobbling effect in all cases, whereas the lens with a larger curvature radius shows such behaviour in limited circumstances. The study confirms that the friction coefficient has a negative linear correlation with the vertical axis declination amplitude with the R-squared value 0.878, showing that friction gives damping and causes smaller axis declination amplitudes. Negative linear correlation also exists with relation to the number of wobbles before the motion stops, where the R-squared value is 0.938, providing further evidence that friction and wobbling cause higher energy dissipation rates. The frequency of the wobbling motion only has a correlation with the curvature radius of the lens, showing no explicit correlation with the friction coefficient, with its R-squared value being 0.077. No losses of contact were observable in this motion. The overall process does not utilize particularly expensive apparatus and will be applicable for senior undergraduate students to experiment on and analyze the motion of a special situation regarding a rigid body that is both spinning and nutating.
Acoustic equations for a gas stream in rigid-body rotation
Garcia-Ybarra, Pedro L.; Marin-Antuña, Jose M.
2017-02-01
The classical topic of wave propagation in a rotating gas is revisited by deducing scalar wave equations for propagation of acoustic and rotational waves through a plug flow of gas in rigid-body rotation with arbitrary intensities of the radial stratification. In the light of these novel equations, wave propagation is analyzed in two different base gas states: isothermal and homentropic. In both cases, previous findings are recovered that assess the validity of the equations and new results are established. In the non-homentropic but isothermal case, the set of governing equations is reduced to two coupled scalar wave equations with space dependent coefficients for the disturbances of density and pressure. Travelling wave solutions with variable amplitude have been obtained in the limit of weak stratification both for inertial waves as for acoustic waves which, in general, propagate on different frequency bands that overlap in the small wavenumber region. Furthermore, the entropy stratification in the base state is stable and compels the propagation of internal waves, leading to hybrid acoustic-inertial-vortical modes. In the homentropic case, the adiabatic relation between pressure and density disturbances allows to reduce further the governing equations to a single fourth-order scalar wave equation. In this case, the sound propagation velocity depends on the distance to the rotation axis and solutions are found by multiple-scale analyses in the form of waves with slowly varying amplitude and wavenumber. The corresponding eikonal equation shows that acoustic rays are refracted towards the rotation axis, propagating and spinning along and around it. In that way, the swirling gas behaves as an axial waveguide trapping inside any acoustic ray propagating in the vortex with large enough azimuthal and/or vertical wavenumber component.
Generalized flyby trajectories around elongated minor celestial bodies as a rotating mass dipole
Xiangyuan Zeng; Baodong Fang; Junfeng Li; Yang Yu
2016-01-01
The aim of this paper is to understand the com-mon characteristics of the generalized flyby trajectory around natural elongated bodies. Such flyby trajectories provide a short-term mechanism to clear away vicinal objects or temporally capture ejecta into circling orbits. The gravita-tional potential of elongated bodies is described by a unified approximate model, i.e., the rotating mass dipole which is two point masses connected with a constant massless rod. The energy power is used to illustrate the flyby effect in terms of the instantaneous orbital energy. The essential of the single flyby trajectory is studied analytically, and the relationship between the flyby trajectory and its Jacobi integral is also illustrated. Sample trajectories are given to show the varia-tional trend of the energy increment with respect to different orbital periapsides. The distribution of natural ejecting orbits is presented by varying the parameters of the approximate model.
Ultra-relativistic spinning particle and a rotating body in external fields
Deriglazov, Alexei A
2015-01-01
We use the vector model of spinning particle to analyze the influence of spin-field coupling on the particle's trajectory in ultra-relativistic regime. The Lagrangian with minimal spin-gravity interaction yields the equations equivalent to the Mathisson-Papapetrou-Tulczyjew-Dixon (MPTD) equations of a rotating body. We show that they have unsatisfactory behavior in the ultra-relativistic limit. In particular, three-dimensional acceleration of the particle increases with velocity and becomes infinite in the limit. The reason is that in the equation for trajectory emerges the term which can be thought as an effective metric generated by the minimal spin-gravity coupling. Therefore we examine the non-minimal interaction through the gravimagnetic moment $\\kappa$, and show that the theory with $\\kappa=1$ is free of the problems detected in MPTD-equations. Hence the non-minimally interacting theory seem more promising candidate for description of a relativistic rotating body. The Lagrangian for the particle in an a...
Fukushima, Toshio
2017-06-01
Reviewed are recently developed methods of the numerical integration of the gravitational field of general two- or three-dimensional bodies with arbitrary shape and mass density distribution: (i) an axisymmetric infinitely-thin disc (Fukushima 2016a, MNRAS, 456, 3702), (ii) a general infinitely-thin plate (Fukushima 2016b, MNRAS, 459, 3825), (iii) a plane-symmetric and axisymmetric ring-like object (Fukushima 2016c, AJ, 152, 35), (iv) an axisymmetric thick disc (Fukushima 2016d, MNRAS, 462, 2138), and (v) a general three-dimensional body (Fukushima 2016e, MNRAS, 463, 1500). The key techniques employed are (a) the split quadrature method using the double exponential rule (Takahashi and Mori, 1973, Numer. Math., 21, 206), (b) the precise and fast computation of complete elliptic integrals (Fukushima 2015, J. Comp. Appl. Math., 282, 71), (c) Ridder's algorithm of numerical differentiaion (Ridder 1982, Adv. Eng. Softw., 4, 75), (d) the recursive computation of the zonal toroidal harmonics, and (e) the integration variable transformation to the local spherical polar coordinates. These devices succesfully regularize the Newton kernel in the integrands so as to provide accurate integral values. For example, the general 3D potential is regularly integrated as Φ (\\vec{x}) = - G \\int_0^∞ ( \\int_{-1}^1 ( \\int_0^{2π} ρ (\\vec{x}+\\vec{q}) dψ ) dγ ) q dq, where \\vec{q} = q (√{1-γ^2} cos ψ, √{1-γ^2} sin ψ, γ), is the relative position vector referred to \\vec{x}, the position vector at which the potential is evaluated. As a result, the new methods can compute the potential and acceleration vector very accurately. In fact, the axisymmetric integration reproduces the Miyamoto-Nagai potential with 14 correct digits. The developed methods are applied to the gravitational field study of galaxies and protoplanetary discs. Among them, the investigation on the rotation curve of M33 supports a disc-like structure of the dark matter with a double-power-law surface
Understanding symmetrical components for power system modeling
Das, J C
2017-01-01
This book utilizes symmetrical components for analyzing unbalanced three-phase electrical systems, by applying single-phase analysis tools. The author covers two approaches for studying symmetrical components; the physical approach, avoiding many mathematical matrix algebra equations, and a mathematical approach, using matrix theory. Divided into seven sections, topics include: symmetrical components using matrix methods, fundamental concepts of symmetrical components, symmetrical components –transmission lines and cables, sequence components of rotating equipment and static load, three-phase models of transformers and conductors, unsymmetrical fault calculations, and some limitations of symmetrical components.
Dallas, S. S.
1977-01-01
The equations of motion for rotating finite bodies are computed in the perfect fluid metric in the extended parametric post-Newtonian (PPN) formalism of Will and Nordtvedt (1972) and are used to build a model of the solar system consisting of N oblate, homogeneous, stationary, self-gravitating masses of rotating perfect fluid. These equations contain relativistic acceleration terms which are currently observable or may be observable in the future with improved radio and laser ranging techniques.
Instability modes on a solid-body-rotation flow in a finite-length pipe
Feng, Chunjuan; Liu, Feng; Rusak, Zvi; Wang, Shixiao
2017-09-01
Numerical solutions of the incompressible Navier-Stokes equations are obtained to study the time evolution of both axisymmetric and three-dimensional perturbations to a base solid-body-rotation flow in a finite-length pipe with non-periodic boundary conditions imposed at the pipe inlet and outlet. It is found that for a given Reynolds number there exists a critical swirl number beyond which the initial perturbations grow, in contrast to the solid-body rotation flow in an infinitely-long pipe or a finite-length pipe with periodic inlet and exit boundary conditions for which the classical Kelvin analysis and Rayleigh stability criterion affirm neutrally stable for all levels of swirl. This paper uncovers for the first time the detailed evolution of the perturbations in both the axisymmetric and three-dimensional situations. The computations reveal a linear growth stage of the perturbations with a constant growth rate after a brief initial period of decay of the imposed initial perturbations. The fastest growing axisymmetric and three-dimensional instability modes and the associated growth rates are identified numerically for the first time. The computations show that the critical swirl number increases and the growth rate of instability decreases at the same swirl number with decreasing Reynolds number. The growth rate of the axisymmetric mode at high Reynolds number agrees well with previous stability theory for inviscid flow. More importantly, three-dimensional simulations uncover that the most unstable mode is the spiral type m = 1 mode, which appears at a lower critical swirl number than that for the onset of the axisymmetric mode. This spiral mode grows faster than the unstable axisymmetric mode at the same swirl. Moreover, the computations reveal that after the linear growing stage of the perturbation the flow continues to evolve nonlinearly to a saturated axisymmetric vortex breakdown state.
Buksman Hollander, Efrain; de Luca, Jayme
2003-02-01
We find a two-degree-of-freedom Hamiltonian for the time-symmetric problem of straight line motion of two electrons in direct relativistic interaction. This time-symmetric dynamical system appeared 100 years ago and it was popularized in the 1940s by the work of Wheeler and Feynman in electrodynamics, which was left incomplete due to the lack of a Hamiltonian description. The form of our Hamiltonian is such that the action of a Lorentz transformation is explicitly described by a canonical transformation (with rescaling of the evolution parameter). The method is closed and defines the Hamitonian in implicit form without power expansions. We outline the method with an emphasis on the physics of this complex conservative dynamical system. The Hamiltonian orbits are calculated numerically at low energies using a self-consistent steepest-descent method (a stable numerical method that chooses only the nonrunaway solution). The two-degree-of-freedom Hamiltonian suggests a simple prescription for the canonical quantization of the relativistic two-body problem.
2006-01-01
Full Text Available This paper highlights the use of the finite element technique for analyzing stress and displacement distributions in wheels of automotive vehicles when subject to the conjoint influence of inflation pressure and radial load. The most commonly used considerations in the design of the rotating body are elucidated. A potentially viable technique for finite element modeling of radial wheel, subjected to loading, is highlighted. The extrinsic influence of inflation pressure on performance of the rotating body, that is, the wheel, is rationalized.
Rotational kinematics of a rigid body about a fixed axis: development and analysis of an inventory
Mashood, K. K.; Singh, Vijay A.
2015-07-01
We present the development, administration, and analysis of a focused inventory on the rotational kinematics of a rigid body around a fixed axis. The inventory, which is made up of 13 multiple-choice questions, was developed on the basis of interactions with students and teachers. The systematic and iterative aspects of the construction of the inventory are illustrated. The questions, which were validated, were administered to a set of teachers (N = 25) and two groups of preuniversity students (N = 74 and 905) in India. Students, as well as teachers, exhibited difficulties in applying the operational definition of angular velocity to a rigid body. Many erroneously assumed that an angular acceleration cannot exist without a net torque. Patterns of reasoning resulting in errors were identified and categorized under four broad themes. These include inappropriate extensions of familiar procedural practices, reasoning cued by primitive elements in thought, lack of differentiation between related but distinct concepts, and indiscriminate use of equations. The inventory was also administered to introductory-level students (N = 384) at the University of Washington. Popular distractors to most items were similar to the Indian students.
A QUMOND galactic N-body code I: Poisson solver and rotation curve fitting
Angus, Garry W; Famaey, Benoit; Gentile, Gianfranco; McGaugh, Stacy S; de Blok, W J G
2012-01-01
Here we present a new particle-mesh galactic N-body code that uses the full multigrid algorithm for solving the modified Poisson equation of the Quasi Linear formulation of Modified Newtonian Dynamics (QUMOND). A novel approach for handling the boundary conditions using a refinement strategy is implemented and the accuracy of the code is compared with analytical solutions of Kuzmin disks. We then employ the code to compute the predicted rotation curves for a sample of five spiral galaxies from the THINGS sample. We generated static N-body realisations of the galaxies according to their stellar and gaseous surface densities and allowed their distances, mass-to-light ratios (M/L) and both the stellar and gas scale-heights to vary in order to estimate the best fit parameters. We found that NGC 3621, NGC 3521 and DDO 154 are well fit by MOND using expected values of the distance and M/L. NGC 2403 required a moderately larger $M/L$ than expected and NGC 2903 required a substantially larger value. The surprising re...
Kryvohuz, M; Marcus, R A
2010-06-14
A classical theory is proposed to describe the non-RRKM effects in activated asymmetric top triatomic molecules observed numerically in classical molecular dynamics simulations of ozone. The Coriolis coupling is shown to result in an effective diffusive energy exchange between the rotational and vibrational degrees of freedom. A stochastic differential equation is obtained for the K-component of the rotational angular momentum that governs the diffusion.
Gu, X; Hrycushko, B; Lee, H; Lamphier, R; Jiang, S; Abdulrahman, R; Timmerman, R [UT Southwestern Medical Center, Dallas, TX (United States)
2014-06-01
Purpose: Traditional extended SSD total body irradiation (TBI) techniques can be problematic in terms of patient comfort and/or dose uniformity. This work aims to develop a comfortable TBI technique that achieves a uniform dose distribution to the total body while reducing the dose to organs at risk for complications. Methods: To maximize patient comfort, a lazy Susan-like couch top immobilization system which rotates about a pivot point was developed. During CT simulation, a patient is immobilized by a Vac-Lok bag within the body frame. The patient is scanned head-first and then feet-first following 180° rotation of the frame. The two scans are imported into the Pinnacle treatment planning system and concatenated to give a full-body CT dataset. Treatment planning matches multiple isocenter volumetric modulated arc (VMAT) fields of the upper body and multiple isocenter parallel-opposed fields of the lower body. VMAT fields of the torso are optimized to satisfy lung dose constraints while achieving a therapeutic dose to the torso. The multiple isocenter VMAT fields are delivered with an indexed couch, followed by body frame rotation about the pivot point to treat the lower body isocenters. The treatment workflow was simulated with a Rando phantom, and the plan was mapped to a solid water slab phantom for point- and film-dose measurements at multiple locations. Results: The treatment plan of 12Gy over 8 fractions achieved 80.2% coverage of the total body volume within ±10% of the prescription dose. The mean lung dose was 8.1 Gy. All ion chamber measurements were within ±1.7% compared to the calculated point doses. All relative film dosimetry showed at least a 98.0% gamma passing rate using a 3mm/3% passing criteria. Conclusion: The proposed patient comfort-oriented TBI technique provides for a uniform dose distribution within the total body while reducing the dose to the lungs.
Vasiljević, Gorazd
2014-01-01
This BSc thesis deals with certain topics from graph theory. When we talk about studying graphs, we usually mean studying their structure and their structural properties. By doing that, we are often interested in automorphisms of a graph (symmetries), which are permutations of its vertex set, preserving adjacency. There exist graphs, which are symmetric enough, so that automorhism group acts transitively on their vertex set. This means that for any pair of vertices of the graph, there is an a...
Wada, Osamu; Tateuchi, Hiroshige; Ichihashi, Noriaki
2014-01-01
Body rotation is associated with many activities. The concomitant movement of the center of mass (COM) is essential for effective body rotation. This movement is considered to be influenced by kinematic changes in the spine, pelvis, and hip joints. However, there is no research on the association between COM movement and kinematic changes during body rotation. We aimed to investigate the association between COM movement and the kinematics of the spine, pelvis, and hip joints during body rotation in standing. Twenty-four healthy men were included in the study. COM movement during active body rotation in a standing position was measured. We evaluated pelvic shift and changes in the angles of the spine, pelvis, and hip joints. We calculated the Pearson correlation coefficients to analyze the relationship between COM movement and kinematic changes in the spine, pelvis, and hip joints. There were significant correlations between lateral COM movement to the rotational side and pelvic shift to the rotational side, and between posterior COM movement and pelvic shift to the posterior side. In addition, lateral COM movement to the rotational side showed significant and negative correlation with spinal flexion and was significantly and positively correlated with the change in anterior pelvic tilt. Clinicians need to take particular note of both spinal and pelvic motion in the sagittal plane, as well as the pelvic shift, to speculate COM movement during body rotation in standing. Copyright © 2013 Elsevier B.V. All rights reserved.
Symmetrization Selection Rules, 1
Page, P R
1996-01-01
We introduce a category of strong and electromagnetic interaction selection rules for the two-body connected decay and production of exotic J^{PC} = 0^{+-}, 1^{-+}, 2^{+-}, 3^{-+}, ... hybrid and four-quark mesons. The rules arise from symmetrization in states in addition to Bose symmetry and CP invariance. Examples include various decays to \\eta'\\eta, \\eta\\pi, \\eta'\\pi and four-quark interpretations of a 1^{-+} signal.
Symmetrization Selection Rules, 2
Page, P R
1996-01-01
We introduce strong interaction selection rules for the two-body decay and production of hybrid and conventional mesons coupling to two S-wave hybrid or conventional mesons. The rules arise from symmetrization in states in the limit of non-relativistically moving quarks. The conditions under which hybrid coupling to S-wave states is suppressed are determined by the rules, and the nature of their breaking is indicated.
Metric of a Slow Rotating Body with Quadrupole Moment from the Erez-Rosen Metric
Frutos-Alfaro, Francisco; Cordero-García, Iván; Ulloa-Esquivel, Oscar
2012-01-01
A metric representing a slow rotating object with quadrupole moment is obtained using the Newman-Janis formalism to include rotation into the weak limit of the Erez-Rosen metric. This metric is intended to tackle relativistic astrometry and gravitational lensing problems in which a quadrupole moment has to be taken into account.
Xiao, Yunlong; Liu, Wenjian
2013-07-21
The relativistic molecular Hamiltonian written in the body-fixed frame of reference is the basis for high-precision calculations of spectroscopic parameters involving nuclear vibrations and/or rotations. Such a Hamiltonian that describes electrons fully relativistically and nuclei quasi-relativistically is just developed for semi-rigid nonlinear molecules [Y. Xiao and W. Liu, J. Chem. Phys. 138, 134104 (2013)]. Yet, the formulation should somewhat be revised for linear molecules thanks to some unusual features arising from the redundancy of the rotation around the molecular axis. Nonetheless, the resulting isomorphic Hamiltonian is rather similar to that for nonlinear molecules. Consequently, the relativistic formulation of nuclear spin-rotation (NSR) tensor for linear molecules is very much the same as that for nonlinear molecules. So is the relativistic mapping between experimental NSR and NMR.
Bilharz, Herbert; Hoelder, Ernst
1947-01-01
The present report concerns a method of computing the velocity and pressure distributions on bodies of revolution in axially symmetrical flow in the subsonic range. The differential equation for the velocity potential Phi of a compressible fluid motion is linearized tn the conventional manner, and then put in the form Delta(Phi) = 0 by affine transformation. The quantity Phi represents the velocity potential of a fictitious incompressible flow, for which a constant superposition of sources by sections is secured by a method patterned after von Karman which must comply with the boundary condition delta(phi)/delta(n) = 0 at the originally specified contour. This requirement yields for the "pseudo-stream function" psi a differential equation which must be fulfilled for as many points on the contour as source lengths are assumed. In this manner, the problem of defining the still unknown source intensities is reduced to the solution of an inhomogeneous equation system. The pressure distribution is then determined with the aid of Bernoulli's equation and adiabatic equation of state. Lastly, the pressure distributions in compressible and incompressible medium are compared on a model problem.
Strong orientational coordinates and orientational order parameters for symmetric objects
Haji-Akbari, Amir; Glotzer, Sharon C.
2015-12-01
Recent advancements in the synthesis of anisotropic macromolecules and nanoparticles have spurred an immense interest in theoretical and computational studies of self-assembly. The cornerstone of such studies is the role of shape in self-assembly and in inducing complex order. The problem of identifying different types of order that can emerge in such systems can, however, be challenging. Here, we revisit the problem of quantifying orientational order in systems of building blocks with non-trivial rotational symmetries. We first propose a systematic way of constructing orientational coordinates for such symmetric building blocks. We call the arising tensorial coordinates strong orientational coordinates (SOCs) as they fully and exclusively specify the orientation of a symmetric object. We then use SOCs to describe and quantify local and global orientational order, and spatiotemporal orientational correlations in systems of symmetric building blocks. The SOCs and the orientational order parameters developed in this work are not only useful in performing and analyzing computer simulations of symmetric molecules or particles, but can also be utilized for the efficient storage of rotational information in long trajectories of evolving many-body systems.
GONG Yan-Jun; WU Zhen-Sen; WU Jia-Ji
2009-01-01
We present an analytical model of Doppler spectra in backscattering from arbitrary rough convex bodies of revolution rotating around their axes in the global Cartesian coordinate system. This analytical model is applied to analyse Doppler spectra in backscatter from two cones and two cylinders, as well as two ellipsoids of revolution. We numerically analyse the influences of attitude and geometry size of objects on Doppler spectra. The analytical model can give contribution of the surface roughness, attitude and geometry size of convex bodies of revolution to Doppler spectra and may contribute to laser Doppler velocimetry as well as ladar applications.
Dosimetric effect of rotational errors for lung stereotactic body radiation therapy
Park, Jong Min; Lee, Jae Gi; Kim, Hyun Suk; Kim, Jung In; Kim, Hak Jae; Ye, Sung Joon [Radiation Oncology, Seoul National University Hospital, Seoul (Korea, Republic of)
2014-04-15
The aim of this study is to evaluate the dosimetric effects on target volume and organs at risk (OARs) due to roll rotational errors in treatment setup of SBRT for lung cancer delivered with volumetric modulated arc therapy (VMAT) technique. Roll rotational setup errors in lung SBRT significantly influenced the coverage of target volume using VMAT technique. This could be in part compensated by the translational couch correction. However, in spite of the translational correction, the delivered doses to the spinal cord could be more than the calculated doses. Therefore if rotational setup errors exist during lung SBRT using VMAT technique, the rotational correction would rather be considered to prevent over-irradiation of normal tissues than the translational correction.
Bubble motion in a rotating liquid body. [ground based tests for space shuttle experiments
Annamalai, P.; Subramanian, R. S.; Cole, R.
1982-01-01
The behavior of a single gas bubble inside a rotating liquid-filled sphere has been investigated analytically and experimentally as part of ground-based investigations aimed at aiding in the design and interpretation of Shuttle experiments. In the analysis, a quasi-static description of the motion of a bubble was developed in the limit of small values of the Taylor number. A series of rotation experiments using air bubbles and silicone oils were designed to match the conditions specified in the analysis, i.e., the bubble size, sphere rotation rate, and liquid kinematic viscosity were chosen such that the Taylor number was much less than unity. The analytical description predicts the bubble velocity and its asymptotic location. It is shown that the asymptotic position is removed from the axis of rotation.
Krot, A.
The statistical model of the gravitational interaction of particles has been proposed in [1], [2]. Within the framework of this model bodies have fuzzy outlines and are represented by means of spheroidal forms. In the work [3], which is a continuation of the paper [2], it has been investigated a slowly evolving in time process of a gravitational compression of a spheroidal body close to an unstable equilibrium state. In the paper [4] the equation of motion of particles inside the weakly gravitating spheroidal body modeled by means of an ideal liquid has been obtained. It has been derived the equations of hyperbolic type for the gravitational field of a weakly gravitating spheroidal body under observable values of velocities of particles composing it [4]. Using Schwarzschild's and Kerr's metrics, a consistency of the proposed statistical model with the general relativity [5] are shown in this work. This work considers the case of gravitational compression of a spheroidal body with observable values of particles. According to the first approach of this work the field potentials (including the scalar gravitational potential, the potential of centrifugal force and the potential of deformation force along the radial direction) for gravitating spheroidal body with observable velocities of particles are considered. The equations of movement of rotating and gravitating spheroidal body with radial deformation are derived. According to the second approach the distribution function of particles inside weakly rotating spheroidal body is a sum of an isotropic space-homogeneous stationary distribution function and its disturbance under an influence of dynamical gravitational field.The change of initial space-homogeneous stationary distribution function satisfies the Boltzmann kinetic equation. This work shows that if gravitating spheroidal body is rotating uniformly or is being at rest then distribution function of its particles satisfies the Liouville theorem. References: [1] A
Müller, Holger S. P.; Ordu, Matthias H.; Lewen, Frank; Brown, Linda; Drouin, Brian; Pearson, John; Sung, Keeyoon; Kleiner, Isabelle; Sams, Robert
2015-06-01
Rotational and rovibrational spectra of methyl cyanide were recorded to analyze interactions in low-lying vibrational states and to construct line lists for radio astronomical observations as well as for infrared spectroscopic investigations of planetary atmospheres. The rotational spectra cover large portions of the 36-1627~GHz region. In the infrared (IR), a spectrum was recorded for this study in the region of 2ν_8 around 717~cm-1 with assignments covering 684-765~cm-1. Additional spectra in the ν _8 region were used to validate the analysis. Using ν _8 data as well as spectroscopic parameters for v_4 = 1, v_7 = 1, and v_8 = 3 from previous studies, we analyzed rotational data involving v = 0, v_8 = 1, and v_8 = 2 up to high J and K quantum numbers. We analyzed a strong Δ v_8 = ± 1, Δ K = 0, Δ l = ±3 Fermi resonance between v_8 = 1-1 and v_8 = 2+2 at K = 14 and obtained preliminary results for two further Fermi resonances between v_8 = 2 and 3. We also found resonant Δ v_8 = ± 1, Δ K = ∓ 2, Δ l = ± 1 interactions between v_8 = 1 and 2 and present the first detailed analysis of such a resonance between v_8 = 0 and 1. We discuss the impact of this analysis on the v_8 = 1 and 2 as well as on the axial v = 0 parameters and compare selected CH_3CN parameters with those of CH_3CCH and CH_3NC. We evaluated transition dipole moments of ν _8, 2ν _8 - ν _8, and 2ν _8 for remote sensing in the IR. Part of this work was carried out at the Jet Propulsion Laboratory under contract with the National Aeronautics and Space Administration. M. Koivusaari et al., J. Mol. Spectrosc. 152 (1992) 377-388. A.-M. Tolonen et al., J. Mol. Spectrosc. 160 (1993) 554-565.
A fluid Foucault pendulum: the impossibility of achieving solid-body rotation on Earth
Blum, Robert; Zimmerman, Daniel; Triana, Santiago; Lathrop, Daniel
2012-11-01
Rotating fluid dynamics is key to our understanding of the Earth's atmosphere, oceans, and core, along with a plethora of astrophysical objects. Laboratory study of these natural systems often involves spinning experimental devices, which are assumed to tend to rigid rotation when unstirred. We present results showing that even at the tabletop scale, there is a measurable oscillatory flow driven by the precession of the experiment's axis as the earth rotates. We measure this flow in a rotating cylinder with an adjustable aspect ratio. The horizontal flow in the rotating frame is measured using particle tracking. The steady state is well-described by an inertial mode whose amplitude is maximum when the height to diameter ratio is 0.995, which matches theoretical predictions. We also quantify the resonant amplitude of the inertial mode in the cylinder and estimate the amplitude in other devices. We compare our results to similar studies done in spherical devices. [Triana et al., JGR, 117 (2012), B04103][Boisson et al., EPL, 98 (2012), 59002].
Heinen, Thomas
2013-01-01
Athletes exhibit differences in perceptual-cognitive abilities when compared to non-athletes. Recent theoretical developments focus on the role of the athletes’ body in perceptual-cognitive tasks such as mental rotation tasks. It is assumed that the degree to which stimuli in mental rotation tasks can be embodied facilitates the mental rotation process. The implications of this assumption are discussed and ideas for future research are presented.
Destefino, V J; Reighard, D A; Sugiyama, Y; Suzuki, T; Cotter, L A; Larson, M G; Gandhi, N J; Barman, S M; Yates, B J
2011-06-01
The responses to vestibular stimulation of brain stem neurons that regulate sympathetic outflow and blood flow have been studied extensively in decerebrate preparations, but not in conscious animals. In the present study, we compared the responses of neurons in the rostral ventrolateral medulla (RVLM), a principal region of the brain stem involved in the regulation of blood pressure, to whole body rotations of conscious and decerebrate cats. In both preparations, RVLM neurons exhibited similar levels of spontaneous activity (median of ∼17 spikes/s). The firing of about half of the RVLM neurons recorded in decerebrate cats was modulated by rotations; these cells were activated by vertical tilts in a variety of directions, with response characteristics suggesting that their labyrinthine inputs originated in otolith organs. The activity of over one-third of RVLM neurons in decerebrate animals was altered by stimulation of baroreceptors; RVLM units with and without baroreceptor signals had similar responses to rotations. In contrast, only 6% of RVLM neurons studied in conscious cats exhibited cardiac-related activity, and the firing of just 1% of the cells was modulated by rotations. These data suggest that the brain stem circuitry mediating vestibulosympathetic reflexes is highly sensitive to changes in body position in space but that the responses to vestibular stimuli of neurons in the pathway are suppressed by higher brain centers in conscious animals. The findings also raise the possibility that autonomic responses to a variety of inputs, including those from the inner ear, could be gated according to behavioral context and attenuated when they are not necessary.
Sarah B Wallwork
2013-06-01
Full Text Available We wanted to find out whether people who suffer from dizziness take longer than people who do not, to perform a motor imagery task that involves implicit whole body rotation. Our prediction was that people in the ‘dizzy’ group would take longer at a left/right neck rotation judgment task but not a left/right hand judgment task, because actually performing the former, but not the latter, would exacerbate their dizziness. Secondly, we predicted that when dizzy participants responded to neck rotation images, responses would be greatest when images were in the upside-down orientation; an orientation with greatest dizzy-provoking potential. To test this idea, we used a case-control comparison design. One hundred and eighteen participants who suffered from dizziness and 118 age, gender, arm pain and neck pain matched controls took part in the study. Participants undertook two motor imagery tasks; a left/right neck rotation judgment task and a left/right hand judgment task. The tasks were completed using the Recognise program; an on-line reaction time task program. Images of neck rotation were shown in four different orientations; 0°, 90°, 180° and 270°. Participants were asked to respond to each ‘neck’ image identifying it as either ‘right neck rotation’ or a ‘left neck rotation’, or for hands, a right or a left hand. Results showed that participants in the ‘dizzy’ group were slower than controls at both tasks (p= 0.015, but this was not related to task (p= 0.498. Similarly, ‘dizzy’ participants were not proportionally worse at images of different orientations (p= 0.878. Our findings suggest impaired performance in dizzy people, an impairment that may be confined to motor imagery or may extend more generally.
Golomer, Eveline; Toussaint, Yann; Bouillette, Arnaud; Keller, Jean
2009-04-01
The link between supporting leg stability and individual trunk strategies used during spontaneous whole-body rotations was studied according to visual and kinesthetic imagery styles for classical dancers and untrained female participants. Shoulders-hip angles in the horizontal plane and supporting leg (SL) displacements were analyzed with three-dimensional kinematic at the beginning and end of the four turns, identified according to their SL (left vs. right) and turn direction (clockwise, CW vs. counterclockwise, CCW). To begin a turn in CCW on left SL, all the participants turned shoulders before hips (-25 degrees angle), pdance training, facilitates the en bloc shoulder-hip coordination to maintain equilibrium.
Romano, Marcello
2012-01-01
The exact analytic solution is introduced for the rotational motion of a rigid body having three equal principal moments of inertia and subjected to an external torque vector which is constant for an observer fixed with the body, and to arbitrary initial angular velocity. In the paper a parametrization of the rotation by three complex numbers is used. In particular, the rows of the rotation matrix are seen as elements of the unit sphere and projected, by stereographic projection, onto points on the complex plane. In this representation, the kinematic differential equation reduces to an equation of Riccati type, which is solved through appropriate choices of substitutions, thereby yielding an analytic solution in terms of confluent hypergeometric functions. The rotation matrix is recovered from the three complex rotation variables by inverse stereographic map. The results of a numerical experiment confirming the exactness of the analytic solution are reported. The newly found analytic solution is valid for any...
Reconstructing rotations and rigid body motions from exact point correspondences through reflections
Fontijne, D.; Dorst, L.; Dorst, L.; Lasenby, J.
2011-01-01
We describe a new algorithm to reconstruct a rigid body motion from point correspondences. The algorithm works by constructing a series of reflections which align the points with their correspondences one by one. This is naturally and efficiently implemented in the conformal model of geometric algeb
Rotationally Symmetric Operators for Surface Interpolation
1981-11-01
Uzawa H. Studies in linear and nonlinear programming, Stanford University press, Stanford, 1958. 131 Barrow H. G. and Tenenbaum J. M. "Interpreting...Nonsense Sentences," Machine Intelligence 6, eds. Meltzer B. and Michie D., Edinburgh University Press, 1971. [19] Ikeuchi K. and Horn B. K. P. "Numerical...an object from a single view," Artificial Intelligence 17 (1981), 409-460. [21] Knuth 1). E. "Mathematical typography ," Bull. Amer. Math. Soc. (new
Symmetric Powers of Symmetric Bilinear Forms
Se(a)n McGarraghy
2005-01-01
We study symmetric powers of classes of symmetric bilinear forms in the Witt-Grothendieck ring of a field of characteristic not equal to 2, and derive their basic properties and compute their classical invariants. We relate these to earlier results on exterior powers of such forms.
Kochemasov, , G. G.
2008-09-01
Often observed a sensible difference in appearance and structure between tropical and extra-tropical zones of various heavenly bodies including rocky and gas planets, satellites and Sun compels to look for a common reason of such phenomenon. All bodies rotate and their spherical shape makes zones at different latitudes to have differing angular momenta as a distance to the rotation axis diminishes gradually from the equator to the poles (this is felt particularly when one launches rockets into space -preferable more cheap launches are from the equatorial regions - Kourou is better than Baikonur). One of remarkable changes occurs at tropics. As a single rotating planetary body tends to have angular momenta of its tectonic blocks equilibrated it starts mechanisms leveling this basic physical property. At tropical zones (bulged also due to the rotation ellipsoid) the outer shell - crust as a consequence tends to be destroyed, sunk, subsided and shrunk; a density of crust material changes; the atmosphere reacts changing chemistry and structure; in terrestrial anthroposphere man looses its mass and stature. But according to the Le Chatelier rule mechanisms with an opposing tendency also begin to act. At Earth the wide planetary long tropical zone is marked by destruction of the crust. It is demonstrated by development of numerous islands of the Malay Archipelago (the Sunda Isls., Maluku Isls, Philippines) between the Southeastern Asia and Australia. In Africa and South America huge depressions of the Congo and Amazon Rivers develops where the Archean crust is subsided to depths of more than 2 km. In the Pacific along the equator numerous islands of Micronesia occur. Subsidence of the basaltic oceanic crust is followed by an intensive folding and faulting of basalt and sedimentary layers (Fig. 1) as a larger mass must be held by a smaller space (a planetary radius is diminished). The central Atlantic is very demonstrative in this sense suffering huge transform fault
Ogilvie, Gordon I
2012-01-01
We discuss the linear response to low-frequency tidal forcing of fluid bodies that are slowly and uniformly rotating, are neutrally stratified and may contain a solid or fluid core. This problem may be regarded as a simplified model of astrophysical tides in convective regions of stars and giant planets. The response can be separated into non-wavelike and wavelike parts, where the former is related instantaneously to the tidal potential and the latter may involve resonances or other singularities. The imaginary part of the potential Love number of the body, which is directly related to the rates of energy and angular momentum exchange in the tidal interaction and to the rate of dissipation of energy, may have a complicated dependence on the tidal frequency. However, a certain frequency-average of this quantity is independent of the dissipative properties of the fluid and can be determined by means of an impulse calculation. The result is a strongly increasing function of the size of the core when the tidal po...
Jiang, Haiyong
2016-04-11
We present an automatic algorithm for symmetrizing facade layouts. Our method symmetrizes a given facade layout while minimally modifying the original layout. Based on the principles of symmetry in urban design, we formulate the problem of facade layout symmetrization as an optimization problem. Our system further enhances the regularity of the final layout by redistributing and aligning boxes in the layout. We demonstrate that the proposed solution can generate symmetric facade layouts efficiently. © 2015 IEEE.
Symmetrization of Facade Layouts
Jiang, Haiyong
2016-02-26
We present an automatic approach for symmetrizing urban facade layouts. Our method can generate a symmetric layout through minimally modifying the original input layout. Based on the principles of symmetry in urban design, we formulate facade layout symmetrization as an optimization problem. Our method further enhances the regularity of the final layout by redistributing and aligning elements in the layout. We demonstrate that the proposed solution can effectively generate symmetric facade layouts.
Chambler, A F; Chapman-Sheath, P J; Pearse, M F; Hollingdale, J
1997-10-01
Chronic recurrent multifocal osteomyelitis is often confused with symmetrical Brodie's abscess as it has a similar pathogenesis. We report an otherwise healthy 17-year-old boy presenting with a true symmetrical Brodie's abscess. We conclude that a symmetrical Brodie's abscess presenting in an otherwise healthy patient is a separate clinical condition with a different management protocol.
Konosevich, B. I.
2014-07-01
The error of the Wentzel-Kramers-Brillouin solution of the equations describing the angular motion of the axis of symmetry of rotation of a rigid body (projectile) is estimated. It is established that order of this estimate does not depend on whether the low-frequency oscillations of the axis of symmetry are damped or not
Duran-Matute, M.; Di Nitto, G.; Trieling, R.R.; Kamp, L.P.J.; van Heijst, G.J.F.
2012-01-01
We present an experimental/numerical study of a dipolar flow structure in a shallow layer of electrolyte driven by electromagnetic forcing and subjected to background rotation. The aim of this study is to determine the influence of a non-conservative body force on the range of applicability of the
Duran-Matute, M.; Di Nitto, G.; Trieling, R.R.; Kamp, L.P.J.; van Heijst, G.J.F.
2012-01-01
We present an experimental/numerical study of a dipolar flow structure in a shallow layer of electrolyte driven by electromagnetic forcing and subjected to background rotation. The aim of this study is to determine the influence of a non-conservative body force on the range of applicability of the c
Schmutzer, E
2005-01-01
In a previous paper we treated within the framework of our Projective Unified Field Theory (Schmutzer 2004, Schmutzer 2005a) the 2-body system (e.g. earth-moon system) with a rotating central body in a rather abstract manner. Here a concrete model of the transfer of angular momentum from the rotating central body to the orbital motion of the whole 2-body system is presented, where particularly the transfer is caused by the inhomogeneous gravitational force of the moon acting on the oceanic waters of the earth, being modeled by a spherical shell around the solid earth. The theory is numerically tested. Key words: transfer of angular momentum from earth to moon, action of the gravitational force of the moon on the waters of the earth.
Transport coefficients for rigid spherically symmetric polymers or aggregates
Strating, P.; Wiegel, F.W.
1994-01-01
In this paper we investigate the transport properties for rigid spherically symmetric macromolecules, having a segment density distribution falling off as r- lambda . We calculate the rotational and translational diffusion coefficient for a spherically symmetric polymer and the shear viscosity for a
Canteaut, Anne; Videau, Marion
2005-01-01
http://www.ieee.org/; We present an extensive study of symmetric Boolean functions, especially of their cryptographic properties. Our main result establishes the link between the periodicity of the simplified value vector of a symmetric Boolean function and its degree. Besides the reduction of the amount of memory required for representing a symmetric function, this property has some consequences from a cryptographic point of view. For instance, it leads to a new general bound on the order of...
DÍaz, R.; Rivas, M.
2010-01-01
In order to study Boolean algebras in the category of vector spaces we introduce a prop whose algebras in set are Boolean algebras. A probabilistic logical interpretation for linear Boolean algebras is provided. An advantage of defining Boolean algebras in the linear category is that we are able to study its symmetric powers. We give explicit formulae for products in symmetric and cyclic Boolean algebras of various dimensions and formulate symmetric forms of the inclusion-exclusion principle.
Bach, Rudolf; Weyl, Hermann
2012-03-01
This is the English translation of the third of a series of 3 papers by Hermann Weyl (the third one jointly with Rudolf Bach), first published in 1917-1922, in which the authors derived and discussed the now-famous Weyl two-body static axially symmetric vacuum solution of Einstein's equations. The English translations of the other two papers are published alongside this one. The papers have been selected by the Editors of General Relativity and Gravitation for re-publication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note written by Gernot Neugebauer, David Petroff and Bahram Mashhoon, and by a brief biography of R. Bach, written by H. Goenner.
Inverse Symmetric Inflationary Attractors
Odintsov, S D
2016-01-01
We present a class of inflationary potentials which are invariant under a special symmetry, which depends on the parameters of the models. As we show, in certain limiting cases, the inverse symmetric potentials are qualitatively similar to the $\\alpha$-attractors models, since the resulting observational indices are identical. However, there are some quantitative differences which we discuss in some detail. As we show, some inverse symmetric models always yield results compatible with observations, but this strongly depends on the asymptotic form of the potential at large $e$-folding numbers. In fact when the limiting functional form is identical to the one corresponding to the $\\alpha$-attractors models, the compatibility with the observations is guaranteed. Also we find the relation of the inverse symmetric models with the Starobinsky model and we highlight the differences. In addition, an alternative inverse symmetric model is studied and as we show, not all the inverse symmetric models are viable. Moreove...
Symmetric cryptographic protocols
Ramkumar, Mahalingam
2014-01-01
This book focuses on protocols and constructions that make good use of symmetric pseudo random functions (PRF) like block ciphers and hash functions - the building blocks for symmetric cryptography. Readers will benefit from detailed discussion of several strategies for utilizing symmetric PRFs. Coverage includes various key distribution strategies for unicast, broadcast and multicast security, and strategies for constructing efficient digests of dynamic databases using binary hash trees. • Provides detailed coverage of symmetric key protocols • Describes various applications of symmetric building blocks • Includes strategies for constructing compact and efficient digests of dynamic databases
Tipler, F.J.
1977-08-01
Causally symmetric spacetimes are spacetimes with J/sup +/(S) isometric to J/sup -/(S) for some set S. We discuss certain properties of these spacetimes, showing for example that, if S is a maximal Cauchy surface with matter everywhere on S, then the spacetime has singularities in both J/sup +/(S) and J/sup -/(S). We also consider totally vicious spacetimes, a class of causally symmetric spacetimes for which I/sup +/(p) =I/sup -/(p) = M for any point p in M. Two different notions of stability in general relativity are discussed, using various types of causally symmetric spacetimes as starting points for perturbations.
Symmetrization and Applications
Kesavan, S
2006-01-01
The study of isoperimetric inequalities involves a fascinating interplay of analysis, geometry and the theory of partial differential equations. Several conjectures have been made and while many have been resolved, a large number still remain open.One of the principal tools in the study of isoperimetric problems, especially when spherical symmetry is involved, is Schwarz symmetrization, which is also known as the spherically symmetric and decreasing rearrangement of functions. The aim of this book is to give an introduction to the theory of Schwarz symmetrization and study some of its applicat
Dunajewski, Adam; Dusza, Jacek J.; Rosado Muñoz, Alfredo
2014-11-01
The article presents a proposal for the description of human gait as a periodic and symmetric process. Firstly, the data for researches was obtained in the Laboratory of Group SATI in the School of Engineering of University of Valencia. Then, the periodical model - Mean Double Step (MDS) was made. Finally, on the basis of MDS, the symmetrical models - Left Mean Double Step and Right Mean Double Step (LMDS and RMDS) could be created. The method of various functional extensions was used. Symmetrical gait models can be used to calculate the coefficients of asymmetry at any time or phase of the gait. In this way it is possible to create asymmetry, function which better describes human gait dysfunction. The paper also describes an algorithm for calculating symmetric models, and shows exemplary results based on the experimental data.
Wang, Yue; Xu, Shijie
2014-12-01
The motion of a rigid body in a uniformly rotating second degree and order gravity field is a good model for the gravitationally coupled orbit-attitude motion of a spacecraft in the close proximity of an asteroid. The relative equilibria of this full dynamics model are investigated using geometric mechanics from a global point of view. Two types of relative equilibria are found based on the equilibrium conditions: one is the Lagrangian relative equilibria, at which the circular orbit of the rigid body is in the equatorial plane of the central body; the other is the non-Lagrangian relative equilibria, at which the circular orbit is parallel to but not in the equatorial plane of central body. The existences of the Lagrangian and non-Lagrangian relative equilibria are discussed numerically with respect to the parameters of the gravity field and the rigid body. The effect of the gravitational orbit-attitude coupling is especially assessed. The existence region of the Lagrangian relative equilibria is given on the plane of the system parameters. Numerical results suggest that the negative C 20 with a small absolute value and a negative C 22 with a large absolute value favor the existence of the non-Lagrangian relative equilibria. The effect of the gravitational orbit-attitude coupling of the rigid body on the existence of the non-Lagrangian relative equilibria can be positive or negative, which depends on the harmonics C 20 and C 22, and the angular velocity of the rotation of the gravity field.
Ito, Norie; Takei, Hidetoshi; Chiba, Susumu; Inoue, Kiyoharu; Fukushima, Kikuro
2016-01-01
Although impaired smooth-pursuit in Parkinson's disease (PD) is well known, reports are conflicting on the ability to cancel vestibulo-ocular reflex (VOR) when the target moves with head, requiring gaze-pursuit. To compare visual tracking performance with or without passive whole-body rotation, we examined eye movements of 10 PD patients and 6 age-matched controls during sinusoidal horizontal smooth-pursuit and passive whole-body rotation (0.3 Hz, ± 10°). Three tasks were tested: smooth-pursuit, VOR cancellation, and VORx1 while subjects fixated an earth-stationary spot during whole-body rotation. Mean ± SD eye velocity gains (eye velocities/stimulus velocities) of PD patients during the 3 tasks were 0.32 ± 0.24 0.25 ± 0.22, 0.85 ± 0.20, whereas those of controls were 0.91 ± 0.06, 0.14 ± 0.07, 0.94 ± 0.05, respectively. Difference was significant between the two subject groups only during smooth-pursuit. Plotting eye-velocity gains of individual subjects during VOR cancellation against those during smooth-pursuit revealed significant negative linear correlation between the two parameters in the controls, but no correlation was found in PD patients. Based on the regression equation of the controls, we estimated expected eye velocity gains of individual subjects during VOR cancellation from their smooth-pursuit gains. Estimated gains of PD patients during VOR cancellation were significantly different from their actual gains, suggesting that different neural mechanisms operate during VOR cancellation in the controls and PD.
N>=2 symmetric superpolynomials
Alarie-Vézina, L; Mathieu, P
2015-01-01
The theory of symmetric functions has been extended to the case where each variable is paired with an anticommuting one. The resulting expressions, dubbed superpolynomials, provide the natural N=1 supersymmetric version of the classical bases of symmetric functions. Here we consider the case where two independent anticommuting variables are attached to each ordinary variable. The N=2 super-version of the monomial, elementary, homogeneous symmetric functions, as well as the power sums, are then constructed systematically (using an exterior-differential formalism for the multiplicative bases), these functions being now indexed by a novel type of superpartitions. Moreover, the scalar product of power sums turns out to have a natural N=2 generalization which preserves the duality between the monomial and homogeneous bases. All these results are then generalized to an arbitrary value of N. Finally, for N=2, the scalar product and the homogenous functions are shown to have a one-parameter deformation, a result that...
Counting with symmetric functions
Mendes, Anthony
2015-01-01
This monograph provides a self-contained introduction to symmetric functions and their use in enumerative combinatorics. It is the first book to explore many of the methods and results that the authors present. Numerous exercises are included throughout, along with full solutions, to illustrate concepts and also highlight many interesting mathematical ideas. The text begins by introducing fundamental combinatorial objects such as permutations and integer partitions, as well as generating functions. Symmetric functions are considered in the next chapter, with a unique emphasis on the combinatorics of the transition matrices between bases of symmetric functions. Chapter 3 uses this introductory material to describe how to find an assortment of generating functions for permutation statistics, and then these techniques are extended to find generating functions for a variety of objects in Chapter 4. The next two chapters present the Robinson-Schensted-Knuth algorithm and a method for proving Pólya’s enu...
Symmetric tensor decomposition
Brachat, Jerome; Mourrain, Bernard; Tsigaridas, Elias
2009-01-01
We present an algorithm for decomposing a symmetric tensor, of dimension n and order d as a sum of rank-1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 for binary forms. We recall the correspondence between the decomposition of a homogeneous polynomial in n variables of total degree d as a sum of powers of linear forms (Waring's problem), incidence properties on secant varieties of the Veronese Variety and the representation of linear forms as a linear combination of evaluations at distinct points. Then we reformulate Sylvester's approach from the dual point of view. Exploiting this duality, we propose necessary and sufficient conditions for the existence of such a decomposition of a given rank, using the properties of Hankel (and quasi-Hankel) matrices, derived from multivariate polynomials and normal form computations. This leads to the resolution of polynomial equations of small degree in non-generic cases. We propose a new algorithm for symmetric tensor decomposition, based on th...
Multiparty Symmetric Sum Types
Nielsen, Lasse; Yoshida, Nobuko; Honda, Kohei
2010-01-01
This paper introduces a new theory of multiparty session types based on symmetric sum types, by which we can type non-deterministic orchestration choice behaviours. While the original branching type in session types can represent a choice made by a single participant and accepted by others...... determining how the session proceeds, the symmetric sum type represents a choice made by agreement among all the participants of a session. Such behaviour can be found in many practical systems, including collaborative workflow in healthcare systems for clinical practice guidelines (CPGs). Processes...... with the symmetric sums can be embedded into the original branching types using conductor processes. We show that this type-driven embedding preserves typability, satisfies semantic soundness and completeness, and meets the encodability criteria adapted to the typed setting. The theory leads to an efficient...
Progressive symmetric erythrokeratoderma
Gharpuray Mohan
1990-01-01
Full Text Available Four patients had symmetrically distributed hyperkeratotic plaques on the trunk and extremities; The lesions in all of them had appeared during infancy, and after a brief period of progression, had remained static, All of them had no family history of similar skin lesions. They responded well to topical applications of 6% salicylic acid in 50% propylene glycol. Unusual features in these cases of progressive symmetric erythrokeratoderma were the sparing of palms and soles, involvement of the trunk and absence of erythema.
Topological states in partially-PT-symmetric azimuthal potentials
Kartashov, Yaroslav V; Torner, Lluis
2015-01-01
We introduce partially-parity-time-symmetric (pPT-symmetric) azimuthal potentials composed from individual PT-symmetric cells located on a ring, where two azimuthal directions are nonequivalent in a sense that in such potentials excitations carrying topological dislo-cations exhibit different dynamics for different directions of energy circulation in the initial field distribution. Such non-conservative ratchet-like structures support rich families of stable vortex solitons in cubic nonlinear media, whose properties depend on the sign of the topological charge due to the nonequivalence of azimuthal directions. In contrast, oppositely charged vortex solitons remain equivalent in similar fully PT-symmetric potentials. The vortex solitons in the pPT- and PT-symmetric potentials are shown to feature qualitatively different internal current distributions, which are described by different discrete rotation symmetries of the intensity profiles.
Symmetric Spaces in Supergravity
Ferrara, Sergio
2008-01-01
We exploit the relation among irreducible Riemannian globally symmetric spaces (IRGS) and supergravity theories in 3, 4 and 5 space-time dimensions. IRGS appear as scalar manifolds of the theories, as well as moduli spaces of the various classes of solutions to the classical extremal black hole Attractor Equations. Relations with Jordan algebras of degree three and four are also outlined.
Distributed Searchable Symmetric Encryption
Bösch, Christoph; Peter, Andreas; Leenders, Bram; Lim, Hoon Wei; Tang, Qiang; Wang, Huaxiong; Hartel, Pieter; Jonker, Willem
2014-01-01
Searchable Symmetric Encryption (SSE) allows a client to store encrypted data on a storage provider in such a way, that the client is able to search and retrieve the data selectively without the storage provider learning the contents of the data or the words being searched for. Practical SSE schemes
Amore, Paolo, E-mail: paolo.amore@gmail.com [Facultad de Ciencias, CUICBAS, Universidad de Colima, Bernal Díaz del Castillo 340, Colima, Colima (Mexico); Fernández, Francisco M., E-mail: fernande@quimica.unlp.edu.ar [INIFTA (UNLP, CCT La Plata-CONICET), División Química Teórica, Diag. 113 y 64 (S/N), Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina); Garcia, Javier [INIFTA (UNLP, CCT La Plata-CONICET), División Química Teórica, Diag. 113 y 64 (S/N), Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina); Gutierrez, German [Facultad de Ciencias, CUICBAS, Universidad de Colima, Bernal Díaz del Castillo 340, Colima, Colima (Mexico)
2014-04-15
We study both analytically and numerically the spectrum of inhomogeneous strings with PT-symmetric density. We discuss an exactly solvable model of PT-symmetric string which is isospectral to the uniform string; for more general strings, we calculate exactly the sum rules Z(p)≡∑{sub n=1}{sup ∞}1/E{sub n}{sup p}, with p=1,2,… and find explicit expressions which can be used to obtain bounds on the lowest eigenvalue. A detailed numerical calculation is carried out for two non-solvable models depending on a parameter, obtaining precise estimates of the critical values where pair of real eigenvalues become complex. -- Highlights: •PT-symmetric Hamiltonians exhibit real eigenvalues when PT symmetry is unbroken. •We study PT-symmetric strings with complex density. •They exhibit regions of unbroken PT symmetry. •We calculate the critical parameters at the boundaries of those regions. •There are exact real sum rules for some particular complex densities.
The Nuclear Born Oppenheimer Method and Nuclear Rotations
Zettili, Nouredine
2009-01-01
We deal here with the application of the Nuclear Born Oppenheimer (NBO) method to the description of nuclear rotations. As an edifying illustration, we apply the NBO formalism to study the rotational motion of nuclei which are axially-symmetric and even, but whose shells are not closed. We focus, in particular, on the derivation of expressions for the rotational energy and for the moment of inertia. Additionally, we examine the connection between the NBO method and the self-consistent cranking (SCC) model. Finally, we compare the moment of inertia generated by the NBO method with the Thouless-Valantin formula and hence establish a connection between the NBO method and the large body of experimental data.
Nuclear Rotations and the Born-Oppenheimer Approximation
Zettili, Nouredine
2011-10-01
We deal here with the application of the Nuclear Born Oppenheimer (NBO) method to the description of nuclear rotations. As an edifying illustration, we apply the NBO formalism to study the rotational motion of nuclei which are axially-symmetric and even, but whose shells are not closed. We focus, in particular, on the derivation of expressions for the rotational energy and for the moment of inertia. Additionally, we examine the connection between the NBO method and the self-consistent cranking (SCC) model. Finally, we compare the moment of inertia generated by the NBO method with the Thouless-Valantin formula and hence establish a connection between the NBO method and the large body of experimental data.
Generating functions for symmetric and shifted symmetric functions
Jing, Naihuan; Rozhkovskaya, Natasha
2016-01-01
We describe generating functions for several important families of classical symmetric functions and shifted Schur functions. The approach is originated from vertex operator realization of symmetric functions and offers a unified method to treat various families of symmetric functions and their shifted analogues.
Generating functions for symmetric and shifted symmetric functions
Jing, Naihuan; Rozhkovskaya, Natasha
2016-01-01
We describe generating functions for several important families of classical symmetric functions and shifted Schur functions. The approach is originated from vertex operator realization of symmetric functions and offers a unified method to treat various families of symmetric functions and their shifted analogues.
Thirioux, Berangere; Jorland, Gerard; Bret, Michel; Tramus, Marie-Helene; Berthoz, Alain
2009-01-01
Researchers have recently reintroduced the own-body in the center of the social interaction theory. From the discovery of the mirror neurons in the ventral premotor cortex of the monkey's brain, a human "embodied" model of interindividual relationship based on simulation processes has been advanced, according to which we tend to embody…
Fitzpatrick, P. M.; Harmon, G. R.; Liu, J. J. F.; Cochran, J. E.
1974-01-01
The formalism for studying perturbations of a triaxial rigid body within the Hamilton-Jacobi framework is developed. The motion of a triaxial artificial earth satellite about its center of mass is studied. Variables are found which permit separation, and the Euler angles and associated conjugate momenta are obtained as functions of canonical constants and time.
Thirioux, Berangere; Jorland, Gerard; Bret, Michel; Tramus, Marie-Helene; Berthoz, Alain
2009-01-01
Researchers have recently reintroduced the own-body in the center of the social interaction theory. From the discovery of the mirror neurons in the ventral premotor cortex of the monkey's brain, a human "embodied" model of interindividual relationship based on simulation processes has been advanced, according to which we tend to embody…
Xiaojia Xiang
2015-01-01
Full Text Available The collocation method is extended to the special orthogonal group SO(3 with application to optimal attitude control (OAC of a rigid body. A left-invariant rigid-body attitude dynamical model on SO(3 is established. For the left invariance of the attitude configuration equation in body-fixed frame, a geometrically exact numerical method on SO(3, referred to as the geometric collocation method, is proposed by deriving the equivalent Lie algebra equation in so(3 of the left-invariant configuration equation. When compared with the general Gauss pseudo-spectral method, the explicit RKMK, and Lie group variational integrator having the same order and stepsize in numerical tests for evolving a free-floating rigid-body attitude dynamics, the proposed method is higher in accuracy, time performance, and structural conservativeness. In addition, the numerical method is applied to solve a constrained OAC problem on SO(3. The optimal control problem is transcribed into a nonlinear programming problem, in which the equivalent Lie algebra equation is being considered as the defect constraints instead of the configuration equation. The transcription method is coordinate-free and does not need chart switching or special handling of singularities. More importantly, with the numerical advantage of the geometric collocation method, the proposed OAC method may generate satisfying convergence rate.
EQUIFOCAL HYPERSURFACES IN SYMMETRIC SPACES
无
2000-01-01
This note investigates the multiplicity problem of principal curvatures of equifocal hyper surfaces in simply connected rank 1 symmetric spaces. Using Clifford representation theory, and the author also constructs infinitely many equifocal hypersurfaces in the symmetric spaces.
Homogenous finitary symmetric groups
Otto. H. Kegel
2015-03-01
Full Text Available We characterize strictly diagonal type of embeddings of finitary symmetric groups in terms of cardinality and the characteristic. Namely, we prove the following. Let kappa be an infinite cardinal. If G=underseti=1stackrelinftybigcupG i , where G i =FSym(kappan i , (H=underseti=1stackrelinftybigcupH i , where H i =Alt(kappan i , is a group of strictly diagonal type and xi=(p 1 ,p 2 ,ldots is an infinite sequence of primes, then G is isomorphic to the homogenous finitary symmetric group FSym(kappa(xi (H is isomorphic to the homogenous alternating group Alt(kappa(xi , where n 0 =1,n i =p 1 p 2 ldotsp i .
Chen, Yan; Feng, Huijuan; Ma, Jiayao; Peng, Rui; You, Zhong
2016-06-01
The traditional waterbomb origami, produced from a pattern consisting of a series of vertices where six creases meet, is one of the most widely used origami patterns. From a rigid origami viewpoint, it generally has multiple degrees of freedom, but when the pattern is folded symmetrically, the mobility reduces to one. This paper presents a thorough kinematic investigation on symmetric folding of the waterbomb pattern. It has been found that the pattern can have two folding paths under certain circumstance. Moreover, the pattern can be used to fold thick panels. Not only do the additional constraints imposed to fold the thick panels lead to single degree of freedom folding, but the folding process is also kinematically equivalent to the origami of zero-thickness sheets. The findings pave the way for the pattern being readily used to fold deployable structures ranging from flat roofs to large solar panels.
Symmetric Extended Ockham Algebras
T.S. Blyth; Jie Fang
2003-01-01
The variety eO of extended Ockham algebras consists of those algealgebra with an additional endomorphism k such that the unary operations f and k commute. Here, we consider the cO-algebras which have a property of symmetry. We show that there are thirty two non-isomorphic subdirectly irreducible symmetric extended MS-algebras and give a complete description of them.2000 Mathematics Subject Classification: 06D15, 06D30
Algebraic treatment of the few-body problem
Bijker, R
1998-01-01
We consider an algebraic treatment of a three-body system. We develop the formalism for a system of three identical objects and discuss in more detail an algebraic description of the vibrational and rotational excitations of an oblate symmetric top. A quantum number M_F is introduced, which has a direct connection with the permutation symmetry as well as with the geometric labels of an oblate top.
Matrix calculus for axially symmetric polarized beam.
Matsuo, Shigeki
2011-06-20
The Jones calculus is a well known method for analyzing the polarization of a fully polarized beam. It deals with a beam having spatially homogeneous polarization. In recent years, axially symmetric polarized beams, where the polarization is not homogeneous in its cross section, have attracted great interest. In the present article, we show the formula for the rotation of beams and optical elements on the angularly variant term-added Jones calculus, which is required for analyzing axially symmetric beams. In addition, we introduce an extension of the Jones calculus: use of the polar coordinate basis. With this calculus, the representation of some angularly variant beams and optical elements are simplified and become intuitive. We show definitions, examples, and conversion formulas between different notations.
Castro-Chavez, Fernando
2012-01-01
BACKGROUND: Three binary representations of the genetic code according to the ancient I Ching of Fu-Xi will be presented, depending on their defragging capabilities by pairing based on three biochemical properties of the nucleic acids: H-bonds, Purine/Pyrimidine rings, and the Keto-enol/Amino-imino tautomerism, yielding the last pair a 32/32 single-strand self-annealed genetic code and I Ching tables. METHODS: Our working tool is the ancient binary I Ching's resulting genetic code chromosomes defragged by vertical and by horizontal pairing, reverse engineered into non-binaries of 2D rotating 4×4×4 circles and 8×8 squares and into one 3D 100% symmetrical 16×4 tetrahedron coupled to a functional tetrahedron with apical signaling and central hydrophobicity (codon formula: 4[1(1)+1(3)+1(4)+4(2)]; 5:5, 6:6 in man) forming a stella octangula, and compared to Nirenberg's 16×4 codon table (1965) pairing the first two nucleotides of the 64 codons in axis y. RESULTS: One horizontal and one vertical defragging had the start Met at the center. Two, both horizontal and vertical pairings produced two pairs of 2×8×4 genetic code chromosomes naturally arranged (M and I), rearranged by semi-introversion of central purines or pyrimidines (M' and I') and by clustering hydrophobic amino acids; their quasi-identity was disrupted by amino acids with odd codons (Met and Tyr pairing to Ile and TGA Stop); in all instances, the 64-grid 90° rotational ability was restored. CONCLUSIONS: We defragged three I Ching representations of the genetic code while emphasizing Nirenberg's historical finding. The synthetic genetic code chromosomes obtained reflect the protective strategy of enzymes with a similar function, having both humans and mammals a biased G-C dominance of three H-bonds in the third nucleotide of their most used codons per amino acid, as seen in one chromosome of the i, M and M' genetic codes, while a two H-bond A-T dominance was found in their complementary chromosome, as
Castro-Chavez, Fernando
2012-01-01
Background Three binary representations of the genetic code according to the ancient I Ching of Fu-Xi will be presented, depending on their defragging capabilities by pairing based on three biochemical properties of the nucleic acids: H-bonds, Purine/Pyrimidine rings, and the Keto-enol/Amino-imino tautomerism, yielding the last pair a 32/32 single-strand self-annealed genetic code and I Ching tables. Methods Our working tool is the ancient binary I Ching's resulting genetic code chromosomes defragged by vertical and by horizontal pairing, reverse engineered into non-binaries of 2D rotating 4×4×4 circles and 8×8 squares and into one 3D 100% symmetrical 16×4 tetrahedron coupled to a functional tetrahedron with apical signaling and central hydrophobicity (codon formula: 4[1(1)+1(3)+1(4)+4(2)]; 5:5, 6:6 in man) forming a stella octangula, and compared to Nirenberg's 16×4 codon table (1965) pairing the first two nucleotides of the 64 codons in axis y. Results One horizontal and one vertical defragging had the start Met at the center. Two, both horizontal and vertical pairings produced two pairs of 2×8×4 genetic code chromosomes naturally arranged (M and I), rearranged by semi-introversion of central purines or pyrimidines (M' and I') and by clustering hydrophobic amino acids; their quasi-identity was disrupted by amino acids with odd codons (Met and Tyr pairing to Ile and TGA Stop); in all instances, the 64-grid 90° rotational ability was restored. Conclusions We defragged three I Ching representations of the genetic code while emphasizing Nirenberg's historical finding. The synthetic genetic code chromosomes obtained reflect the protective strategy of enzymes with a similar function, having both humans and mammals a biased G-C dominance of three H-bonds in the third nucleotide of their most used codons per amino acid, as seen in one chromosome of the i, M and M' genetic codes, while a two H-bond A-T dominance was found in their complementary chromosome, as seen
Clabo, D.A. Jr.
1987-04-01
Inclusion of the anharmonicity normal mode vibrations (i.e., the third and fourth (and higher) derivatives of a molecular Born-Oppenheimer potential energy surface) is necessary in order to theoretically reproduce experimental fundamental vibrational frequencies of a molecule. Although ab initio determinations of harmonic vibrational frequencies may give errors of only a few percent by the inclusion of electron correlation within a large basis set for small molecules, in general, molecular fundamental vibrational frequencies are more often available from high resolution vibration-rotation spectra. Recently developed analytic third derivatives methods for self-consistent-field (SCF) wavefunctions have made it possible to examine with previously unavailable accuracy and computational efficiency the anharmonic force fields of small molecules.
On multipartite invariant states III. Rotational symmetry
Chruscinski, D; Chruscinski, Dariusz; Kossakowski, Andrzej
2006-01-01
We construct a class of multipartite states possessing rotational SO(3) symmetry -- these are states of K spin-j_A particles and K spin-j_B particles. The construction of symmetric states follows our two recent papers devoted to unitary and orthogonal multipartite symmetry. We study basic properties of multipartite SO(3) symmetric states: separability criteria and multi-PPT conditions.
Scalar Resonances in Axially Symmetric Spacetimes
Ranea-Sandoval, Ignacio F
2015-01-01
We study properties of resonant solutions to the scalar wave equation in several axially symmetric spacetimes. We prove that non-axial resonant modes do not exist neither in the Lanczos dust cylinder, the $(2+1)$ extreme BTZ spacetime nor in a class of simple rotating wormhole solutions. Moreover, we find unstable solutions to the wave equation in the Lanczos dust cylinder and in the $r^2 <0$ region of the extreme $(2+1)$ BTZ spacetime, two solutions that possess closed timelike curves. Similarities with previous results obtained for the Kerr spacetime are explored.
The Nuclear Born Oppenheimer Method and Nuclear Rotations
Zettili, Nouredine
2008-10-01
In this presentation, we want to discuss how to apply the Nuclear Born Oppenheimer (NBO) formalism to the description of nuclear rotations. This application will be illustrated on nuclei that are axially-symmetric and even (but non-closed shell). We will focus, in particular, on the derivation of expressions for the energy and for the moment of inertia. In addition, we will examine the connection of the NBO method with the self-consistent cranking model. We will compare the moment of inertia generated by the NBO method with the Thouless-Valantin formula and hence establish a connection between the NBO method and the large body of experimental data.
Symmetric Tensor Decomposition
Brachat, Jerome; Comon, Pierre; Mourrain, Bernard
2010-01-01
of polynomial equations of small degree in non-generic cases. We propose a new algorithm for symmetric tensor decomposition, based on this characterization and on linear algebra computations with Hankel matrices. The impact of this contribution is two-fold. First it permits an efficient computation...... of total degree d as a sum of powers of linear forms (Waring’s problem), incidence properties on secant varieties of the Veronese variety and the representation of linear forms as a linear combination of evaluations at distinct points. Then we reformulate Sylvester’s approach from the dual point of view...
Symmetrically Constrained Compositions
Beck, Matthias; Lee, Sunyoung; Savage, Carla D
2009-01-01
Given integers $a_1, a_2, ..., a_n$, with $a_1 + a_2 + ... + a_n \\geq 1$, a symmetrically constrained composition $\\lambda_1 + lambda_2 + ... + lambda_n = M$ of $M$ into $n$ nonnegative parts is one that satisfies each of the the $n!$ constraints ${\\sum_{i=1}^n a_i \\lambda_{\\pi(i)} \\geq 0 : \\pi \\in S_n}$. We show how to compute the generating function of these compositions, combining methods from partition theory, permutation statistics, and lattice-point enumeration.
Fault-tolerant symmetrically-private information retrieval
Wang, Tian-Yin; Cai, Xiao-Qiu; Zhang, Rui-Ling
2016-08-01
We propose two symmetrically-private information retrieval protocols based on quantum key distribution, which provide a good degree of database and user privacy while being flexible, loss-resistant and easily generalized to a large database similar to the precedent works. Furthermore, one protocol is robust to a collective-dephasing noise, and the other is robust to a collective-rotation noise.
Holographic Spherically Symmetric Metrics
Petri, Michael
The holographic principle (HP) conjectures, that the maximum number of degrees of freedom of any realistic physical system is proportional to the system's boundary area. The HP has its roots in the study of black holes. It has recently been applied to cosmological solutions. In this article we apply the HP to spherically symmetric static space-times. We find that any regular spherically symmetric object saturating the HP is subject to tight constraints on the (interior) metric, energy-density, temperature and entropy-density. Whenever gravity can be described by a metric theory, gravity is macroscopically scale invariant and the laws of thermodynamics hold locally and globally, the (interior) metric of a regular holographic object is uniquely determined up to a constant factor and the interior matter-state must follow well defined scaling relations. When the metric theory of gravity is general relativity, the interior matter has an overall string equation of state (EOS) and a unique total energy-density. Thus the holographic metric derived in this article can serve as simple interior 4D realization of Mathur's string fuzzball proposal. Some properties of the holographic metric and its possible experimental verification are discussed. The geodesics of the holographic metric describe an isotropically expanding (or contracting) universe with a nearly homogeneous matter-distribution within the local Hubble volume. Due to the overall string EOS the active gravitational mass-density is zero, resulting in a coasting expansion with Ht = 1, which is compatible with the recent GRB-data.
Sirsi, Swarnamala; Hegde, Subramanya
2011-01-01
Quantum computation on qubits can be carried out by an operation generated by a Hamiltonian such as application of a pulse as in NMR, NQR. Quantum circuits form an integral part of quan- tum computation. We investigate the nonlocal operations generated by a given Hamiltonian. We construct and study the properties of perfect entanglers, that is, the two-qubit operations that can generate maximally entangled states from some suitably chosen initial separable states in terms of their entangling power. Our work addresses the problem of analyzing the quantum evolution in the special case of two qubit symmetric states. Such a symmetric space can be considered to be spanned by the angular momentum states {|j = 1,m>;m = +1, 0,-1}. Our technique relies on the decomposition of a Hamiltonian in terms of newly defined Hermitian operators Mk's (k= 0.....8) which are constructed out of angular momentum operators Jx, Jy, Jz. These operators constitute a linearly independent set of traceless matrices (except for M0). Further...
Giuseppe Di Maio
2008-04-01
Full Text Available The subject of hyperspace topologies on closed or closed and compact subsets of a topological space X began in the early part of the last century with the discoveries of Hausdorff metric and Vietoris hit-and-miss topology. In course of time, several hyperspace topologies were discovered either for solving some problems in Applied or Pure Mathematics or as natural generalizations of the existing ones. Each hyperspace topology can be split into a lower and an upper part. In the upper part the original set inclusion of Vietoris was generalized to proximal set inclusion. Then the topologization of the Wijsman topology led to the upper Bombay topology which involves two proximities. In all these developments the lower topology, involving intersection of finitely many open sets, was generalized to locally finite families but intersection was left unchanged. Recently the authors studied symmetric proximal topology in which proximity was used for the first time in the lower part replacing intersection with its generalization: nearness. In this paper we use two proximities also in the lower part and we obtain the lower Bombay hypertopology. Consequently, a new hypertopology arises in a natural way: the symmetric Bombay topology which is the join of a lower and an upper Bombay topology.
Semenov, Alexander; Babikov, Dmitri
2013-11-07
We formulated the mixed quantum/classical theory for rotationally and vibrationally inelastic scattering process in the diatomic molecule + atom system. Two versions of theory are presented, first in the space-fixed and second in the body-fixed reference frame. First version is easy to derive and the resultant equations of motion are transparent, but the state-to-state transition matrix is complex-valued and dense. Such calculations may be computationally demanding for heavier molecules and/or higher temperatures, when the number of accessible channels becomes large. In contrast, the second version of theory requires some tedious derivations and the final equations of motion are rather complicated (not particularly intuitive). However, the state-to-state transitions are driven by real-valued sparse matrixes of much smaller size. Thus, this formulation is the method of choice from the computational point of view, while the space-fixed formulation can serve as a test of the body-fixed equations of motion, and the code. Rigorous numerical tests were carried out for a model system to ensure that all equations, matrixes, and computer codes in both formulations are correct.
Equilibrium rotation of semiliquid exoplanets and satellites
Makarov, Valeri V
2015-01-01
A wide range of exoplanet and exomoon models are characterized by a finite average rigidity and a viscosity much lower than the typical values for terrestrials. Such semiliquid bodies may or may not have rigid crusts with permanent figures. Unlike planets with solid mantles and Earth-like rheology, semiliquid bodies can be captured into stable pseudosynchronous spin resonance, where the average rate of rotation is higher than the synchronous 1:1 resonance. Two basic conditions are derived for capture of planets with a triaxial figure into pseudosynchronous rotation, one related to the characteristic tidal wave number (the product of the tidal frequency by the Maxwell time), and the other to the orbital eccentricity. If a semiliquid object does not satisfy either of the two conditions, it is captured into the synchronous resonance. For nearly axially symmetric bodies, only the first condition is in place, and the other is much relaxed, so they should predominantly be pseudosynchronous. It is also pointed out t...
The Symmetricity of Normal Modes in Symmetric Complexes
Song, Guang
2016-01-01
In this work, we look at the symmetry of normal modes in symmetric structures, particularly structures with cyclic symmetry. We show that normal modes of symmetric structures have different levels of symmetry, or symmetricity. One novel theoretical result of this work is that, for a ring structure with $m$ subunits, the symmetricity of the normal modes falls into $m$ groups of equal size, with normal modes in each group having the same symmetricity. The normal modes in each group can be computed separately, using a much smaller amount of memory and time (up to $m^3$ less), thus making it applicable to larger complexes. We show that normal modes with perfect symmetry or anti-symmetry have no degeneracy while the rest of the modes have a degeneracy of two. We show also how symmetry in normal modes correlates with symmetry in structure. While a broken symmetry in structure generally leads to a loss of symmetricity in symmetric normal modes, the symmetricity of some symmetric normal modes is preserved even when s...
Plane symmetric cosmological models
Yadav, Anil Kumar; Ray, Saibal; Mallick, A
2016-01-01
In this work, we perform the Lie symmetry analysis on the Einstein-Maxwell field equations in plane symmetric spacetime. Here Lie point symmetries and optimal system of one dimensional subalgebras are determined. The similarity reductions and exact solutions are obtained in connection to the evolution of universe. The present study deals with the electromagnetic energy of inhomogeneous universe where $F_{12}$ is the non-vanishing component of electromagnetic field tensor. To get a deterministic solution, it is assumed that the free gravitational field is Petrov type-II non-degenerate. The electromagnetic field tensor $F_{12}$ is found to be positive and increasing function of time. As a special case, to validate the solution set, we discuss some physical and geometric properties of a specific sub-model.
傅育熙
1998-01-01
An alternative presentation of the π－calculus is given.This version of the π-calculus is symmetric in the sense that communications are symmetric and there is no difference between input and output prefixes.The point of the symmetric π-calculus is that it has no abstract names.The set of closed names is therefore homogeneous.The π－calculus can be fully embedded into the symmetric π-calculus.The symmetry changes the emphasis of the communication mechanism of the π-calculus and opens up possibility for further variations.
Representation of Fuzzy Symmetric Relations
1986-03-19
Std Z39-18 REPRESENTATION OF FUZZY SYMMETRIC RELATIONS L. Valverde Dept. de Matematiques i Estadistica Universitat Politecnica de Catalunya Avda...REPRESENTATION OF FUZZY SYMMETRIC RELATIONS L. "Valverde* Dept. de Matematiques i Estadistica Universitat Politecnica de Catalunya Avda. Diagonal, 649
Parallel Symmetric Eigenvalue Problem Solvers
2015-05-01
Plemmons G. Golub and A. Sameh. High-speed computing : scientific appli- cations and algorithm design. University of Illinois Press, Champaign, Illinois , 1988...16. SECURITY CLASSIFICATION OF: Sparse symmetric eigenvalue problems arise in many computational science and engineering applications such as...Eigenvalue Problem Solvers Report Title Sparse symmetric eigenvalue problems arise in many computational science and engineering applications such as
EQUIVARIANT COHOMOLOGY AND REPRESENTATIONS OF THE SYMMETRIC GROUP
M.ATIYAH
2001-01-01
In a recent paper the author constructed a continuous map from the configuration space of n distinct ordered points in 3-space to the flag manifold of the unitary group U(n), which is compatible with the action of the symmetric group. This map is also compatible with appropriate actions of the rotation group SO(3). In this paper the author studies the induced homomorphism in SO(3)-equivariant cohomology and shows that this contains much interesting information involving representations of the symmetric group.
Color-symmetric superconductivity in a phenomenological QCD model
Bohr, Henrik; Providencia, C.; Providencia, J. da
2009-01-01
In this paper, we construct a theory of the NJL type where superconductivity is present, and yet the superconducting state remains, in the average, color symmetric. This shows that the present approach to color superconductivity is consistent with color singletness. Indeed, quarks are free...... in the deconfined phase, but the deconfined phase itself is believed to be a color singlet. The usual description of the color superconducting state violates color singletness. On the other hand, the color superconducting state here proposed is color symmetric in the sense that an arbitrary color rotation leads...
Rotational spectra and molecular structure
Wollrab, James E
1967-01-01
Physical Chemistry, A Series of Monographs: Rotational Spectra and Molecular Structure covers the energy levels and rotational transitions. This book is divided into nine chapters that evaluate the rigid asymmetric top molecules and the nuclear spin statistics for asymmetric tops. Some of the topics covered in the book are the asymmetric rotor functions; rotational transition intensities; classes of molecules; nuclear spin statistics for linear molecules and symmetric tops; and classical appearance of centrifugal and coriolis forces. Other chapters deal with the energy levels and effects of ce
Plasma Control in Symmetric Mirror Machines
Horton, W.; Rowan, W. L.; Alvarado, Igor; Fu, X. R.; Beklemishev, A. D.
2014-10-01
Plasma confinement in the symmetric rotating mirror plasma at the Budker Institute shows enhanced confinement with high electron temperatures with end plates biasing. Improved confinement is achieved by biasing end plate cells in the expansion tanks so as to achieve an inward pointing radial electric field. The negative potential well produces vortex plasma rotation similar to that in the negative potential well of Ohmic heated tokamaks. This plasma state has similarity with the lower turbulence level regimes documented in the Helimak where negative biasing of the end plates produces an inward radial electric field. To understand this vortex confinement we carry out 3D simulations with nonlinear partial differential equations for the electric potential and density in plasmas with an axially localized region of unfavorable and favorable magnetic curvature. The simulations show that the plasma density rapidly adjusts to be higher in the region of favorable curvature regions and remains relatively well confined while rapidly rotating. The results support the concept of using plasma-biasing electrodes in large expander tanks to achieve enhanced mirror plasma confinement. Supported by US-DoE grant to UT, LANL and the Budker Institute for Nuclear Physics.
MINIMIZATION PROBLEM FOR SYMMETRIC ORTHOGONAL ANTI-SYMMETRIC MATRICES
Yuan Lei; Anping Liao; Lei Zhang
2007-01-01
By applying the generalized singular value decomposition and the canonical correlation decomposition simultaneously, we derive an analytical expression of the optimal approximate solution (X), which is both a least-squares symmetric orthogonal anti-symmetric solution of the matrix equation ATXA ＝ B and a best approximation to a given matrix X*.Moreover, a numerical algorithm for finding this optimal approximate solution is described in detail, and a numerical example is presented to show the validity of our algorithm.
Di Maso, L [Chicago, IL (United States); Forbang, R Teboh; Zhang, Y; Herman, J; Lee, J [John Hopkins University, Baltimore, MD (United States)
2015-06-15
Purpose: To explore the dosimetric consequences of uncorrected rotational setup errors during SBRT for pancreatic cancer patients. Methods: This was a retrospective study utilizing data from ten (n=10) previously treated SBRT pancreas patients. For each original planning CT, we applied rotational transformations to derive additional CT images representative of possible rotational setup errors. This resulted in 6 different sets of rotational combinations, creating a total of 60 CT planning images. The patients’ clinical dosimetric plans were then applied to their corresponding rotated CT images. The 6 rotation sets encompassed a 3, 2 and 1-degree rotation in each rotational direction and a 3-degree in just the pitch, a 3-degree in just the yaw and a 3-degree in just the roll. After the dosimetric plan was applied to the rotated CT images, the resulting plan was then evaluated and compared with the clinical plan for tumor coverage and normal tissue sparing. Results: PTV coverage, defined here by V33 throughout all of the patients’ clinical plans, ranged from 92–98%. After an n degree rotation in each rotational direction that range decreased to 68–87%, 85–92%, and 88– 94% for n=3, 2 and 1 respectively. Normal tissue sparing defined here by the proximal stomach V15 throughout all of the patients’ clinical plans ranged from 0–8.9 cc. After an n degree rotation in each rotational direction that range increased to 0–17 cc, 0–12 cc, and 0–10 cc for n=3, 2, and 1 respectively. Conclusion: For pancreatic SBRT, small rotational setup errors in the pitch, yaw and roll direction on average caused under dosage to PTV and over dosage to proximal normal tissue. The 1-degree rotation was on average the least detrimental to the normal tissue and the coverage of the PTV. The 3-degree yaw created on average the lowest increase in volume coverage to normal tissue. This research was sponsored by the AAPM Education Council through the AAPM Education and Research
Sums of Laplace eigenvalues - rotationally symmetric maximizers in the plane
Laugesen, R S
2010-01-01
The sum of the first $n \\geq 1$ eigenvalues of the Laplacian is shown to be maximal among triangles for the equilateral triangle, maximal among parallelograms for the square, and maximal among ellipses for the disk, provided the ratio $\\text{(area)}^3/\\text{(moment of inertia)}$ for the domain is fixed. This result holds for both Dirichlet and Neumann eigenvalues, and similar conclusions are derived for Robin boundary conditions and Schr\\"odinger eigenvalues of potentials that grow at infinity. A key ingredient in the method is the tight frame property of the roots of unity. For general convex plane domains, the disk is conjectured to maximize sums of Neumann eigenvalues.
Maximum likelihood characterization of rotationally symmetric distributions on the sphere
Duerinckx, Mitia; Ley, Christophe
2012-01-01
A classical characterization result, which can be traced back to Gauss, states that the maximum likelihood estimator (MLE) of the location parameter equals the sample mean for any possible univariate samples of any possible sizes n if and only if the samples are drawn from a Gaussian population. A similar result, in the two-dimensional case, is given in von Mises (1918) for the Fisher-von Mises-Langevin (FVML) distribution, the equivalent of the Gaussian law on the unit circle. Half a century...
Maximum likelihood characterization of rotationally symmetric distributions on the sphere
Duerinckx, Mitia; Ley, Christophe
2012-01-01
A classical characterization result, which can be traced back to Gauss, states that the maximum likelihood estimator (MLE) of the location parameter equals the sample mean for any possible univariate samples of any possible sizes n if and only if the samples are drawn from a Gaussian population. A similar result, in the two-dimensional case, is given in von Mises (1918) for the Fisher-von Mises-Langevin (FVML) distribution, the equivalent of the Gaussian law on the unit circle. Half a century...
Determination of Star Bodies from -Centroid Bodies
Lujun Guo; Gangsong Leng
2013-11-01
In this paper, we prove that an origin-symmetric star body is uniquely determined by its -centroid body. Furthermore, using spherical harmonics, we establish a result for non-symmetric star bodies. As an application, we show that there is a unique member of $_p\\langle K \\rangle$ characterized by having larger volume than any other member, for all real ≥ 1 that are not even natural numbers, where $_p\\langle K \\rangle$ denotes the -centroid equivalence class of the star body .
New Classes of Quasi-helically Symmetric Stellarators
L.P. Ku and A.H. Boozer
2010-08-09
New classes of quasi-helically symmetric stellarators with aspect ratios ≤ 10 have been found which are stable to the perturbation of magnetohydrodynamic modes at plasma pressures of practical interest. These configurations have large rotational transform and good quality of flux surfaces. Characteristics of some selected examples are discussed in detail. The feasibility of using modular coils for these stellarators has been investigated. It is shown that practical designs for modular coils can be achieved.
The group theory for solving electromagnetic scattering problems with geometric symmetric structure
朱峰; 杨海川; 任朗
1997-01-01
It is a very important issue to reduce computer storage and calculation time for matrix in solving scattering field by making use of geometric and physical symmetric features of a scattering body. A general definition for the symmetric and anti-symmetric structure is given by applying the group theory in mathematics and a general method for treating the electromagnetic scattering problems with symmetry is proposed. An example for applying the theory mentioned above is also given.
Exact Spherically Symmetric Solutions in Massive Gravity
Berezhiani, Z; Nesti, F; Pilo, L
2008-01-01
A phase of massive gravity free from pathologies can be obtained by coupling the metric to an additional spin-two field. We study the gravitational field produced by a static spherically symmetric body, by finding the exact solution that generalizes the Schwarzschild metric to the case of massive gravity. Besides the usual 1/r term, the main effects of the new spin-two field are a shift of the total mass of the body and the presence of a new power-like term, with sizes determined by the mass and the shape (the radius) of the source. These modifications, being source dependent, give rise to a dynamical violation of the Strong Equivalence Principle. Depending on the details of the coupling of the new field, the power-like term may dominate at large distances or even in the ultraviolet. The effect persists also when the dynamics of the extra field is decoupled.
Analysis of steady-state and dynamical radially-symmetric problems of nonlinear viscoelasticity
Stepanov, Alexey B.
This thesis treats radially symmetric steady states and radially symmetric motions of nonlinearly elastic and viscoelastic plates and shells subject to dead-load and hydrostatic pressures on their boundaries and with the plate subject to centrifugal force. The plates and shells are described by specializations of the exact (nonlinear) equations of three-dimensional continuum mechanics. The treatment in every case is very general and encompasses large classes of constitutive functions (characterizing the material response). We first treat the radially symmetric steady states of plates and shells and the radially symmetric steady rotations of plates. We show that the existence, multiplicity, and qualitative behavior of solutions for problems accounting for the live loads due to hydrostatic pressure and centrifugal force depend critically on the material properties of the bodies, physically reasonable refined descriptions of which are given and examined here with great care, and on the nature of boundary conditions. he treatment here, giving new and sharp results, employs several different mathematical tools, ranging from phase-plane analysis to the mathematically more sophisticated direct methods of the Calculus of Variations, fixed-point theorems, and global continuation methods, each of which has different strengths and weaknesses for handling intrinsic difficulties in the mechanics. We then treat the initial-boundary-value problems for the radially symmetric motions of annular plates and spherical shells that consist of a nonlinearly viscoelastic material of strain-rate type. We discuss a range of physically natural constitutive equations. We first show that when the material is strong in a suitable sense relative to externally applied loads, solutions exist for all time, depend continuously on the data, and consequently are unique. We study the role of the constitutive restrictions and that of the regularity of the data in ensuring the preclusion of a total
Particle-vortex symmetric liquid
Mulligan, Michael
2016-01-01
We introduce an effective theory with manifest particle-vortex symmetry for disordered thin films undergoing a magnetic field-tuned superconductor-insulator transition. The theory may enable one to access both the critical properties of the strong-disorder limit, which has recently been confirmed [Breznay et al., PNAS 113, 280 (2016)] to exhibit particle-vortex symmetric electrical response, and the metallic phase discovered earlier [Mason and Kapitulnik, Phys. Rev. Lett. 82, 5341 (1999)] in less disordered samples. Within the effective theory, the Cooper-pair and field-induced vortex degrees of freedom are simultaneously incorporated into an electrically-neutral Dirac fermion minimally coupled to an (emergent) Chern-Simons gauge field. A derivation of the theory follows upon mapping the superconductor-insulator transition to the integer quantum Hall plateau transition and the subsequent use of Son's particle-hole symmetric composite Fermi liquid. Remarkably, particle-vortex symmetric response does not requir...
Harmonic analysis on symmetric spaces
Terras, Audrey
This text explores the geometry and analysis of higher rank analogues of the symmetric spaces introduced in volume one. To illuminate both the parallels and differences of the higher rank theory, the space of positive matrices is treated in a manner mirroring that of the upper-half space in volume one. This concrete example furnishes motivation for the general theory of noncompact symmetric spaces, which is outlined in the final chapter. The book emphasizes motivation and comprehensibility, concrete examples and explicit computations (by pen and paper, and by computer), history, and, above all, applications in mathematics, statistics, physics, and engineering. The second edition includes new sections on Donald St. P. Richards’s central limit theorem for O(n)-invariant random variables on the symmetric space of GL(n, R), on random matrix theory, and on advances in the theory of automorphic forms on arithmetic groups.
Symmetric autocompensating quantum key distribution
Walton, Zachary D.; Sergienko, Alexander V.; Levitin, Lev B.; Saleh, Bahaa E. A.; Teich, Malvin C.
2004-08-01
We present quantum key distribution schemes which are autocompensating (require no alignment) and symmetric (Alice and Bob receive photons from a central source) for both polarization and time-bin qubits. The primary benefit of the symmetric configuration is that both Alice and Bob may have passive setups (neither Alice nor Bob is required to make active changes for each run of the protocol). We show that both the polarization and the time-bin schemes may be implemented with existing technology. The new schemes are related to previously described schemes by the concept of advanced waves.
Are effects of the symmetric and asymmetric tonic neck reflexes still visible in healthy adults?
Bruijn, S M; Massaad, F; Maclellan, M J; Van Gestel, L; Ivanenko, Y P; Duysens, J
2013-11-27
When a cat's head is rotated in a transverse plane to one side, the legs on that side of the body extend, while on the other side, they flex (asymmetric tonic neck reflexes ATNR). On the contrary, when the head is rotated in a sagittal plane both legs flex when the head flexes, and extend when the head extends (symmetric tonic neck reflexes STNR). These reflexes have also been found in newborn babies and are thought to be a motor primitive, which is suppressed later in life. Still, using a test in which children sit on hand and knees, the ATNR and STNR can be found in children up to 9 years of age. This may suggest that these reflexes may still be involved in motor control in these children. Whether this is also the case in full-grown adults has thus far only been studied using coarse methods. Thus, for the current study, we set out to measure in detail whether the ATNR/STNR can still be evoked in healthy adult subjects. We measured 10 subjects who were asked to sit on their hands and knees while (1) their head was rotated left and right by an experimenter, (2) their head was flexed and extended by an experimenter. Kinematics was registered using a Vicon system. Elbow and head angles were detrended, and a regression analysis was performed, to investigate the effects of head angle on elbow angle. Results clearly showed the existence of the ATNR and STNR in adult subjects. A next step will be to assess the effects of the ATNR and STNR during everyday motor control tasks, such as making head rotations while driving a bike. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.
Research on the Rotational Inertia of Several Categories of Rigid - Body%对几种刚体转动惯量的研究
周瑞雪
2011-01-01
According to the definition of moment of inertia, this paper counted the rotational inertia of ring, including the thin - rods with both uniform and the non - uniform quality. It analyzed the rotational inertia of the disk, which axis is in different site, and others＂ rotational inertia such as oval- plate, cylinder and sphere as well. This paper also discussed the Hexahedral -rotational -inertia by the projection. It researched the rotational inertia in detail from the theory and computation.%文章根据转动惯量的定义，计算了圆环的转动惯量及质量均匀细棒和质量不均匀细棒的转动惯量；研究了圆盘轴在不同位置时的转动惯量和椭圆盘以及圆柱和球体的转动惯量；采用了投影法研究了六面体的转动惯量。从理论和计算上对刚体的转动惯量进行一个详细的研究。
RT-Symmetric Laplace Operators on Star Graphs: Real Spectrum and Self-Adjointness
Maria Astudillo
2015-01-01
Full Text Available How ideas of PT-symmetric quantum mechanics can be applied to quantum graphs is analyzed, in particular to the star graph. The class of rotationally symmetric vertex conditions is analyzed. It is shown that all such conditions can effectively be described by circulant matrices: real in the case of odd number of edges and complex having particular block structure in the even case. Spectral properties of the corresponding operators are discussed.
Rotational spectroscopy of interstellar PAHs
Ali-Haïmoud, Yacine
2013-01-01
Polycyclic aromatic hydrocarbons (PAHs) have long been part of the standard model of the interstellar medium, and are believed to play important roles in its physics and chemistry. Yet, up to now it has not been possible to identify any specific molecule among them. In this paper, a new observational avenue is suggested to detect individual PAHs, using their rotational line emission at radio frequencies. Previous PAH searches based on rotational spectroscopy have only targeted the bowl-shaped corannulene molecule, with the underlying assumption that other polar PAHs are triaxial and as a consequence their rotational emission is diluted over a very large number of lines and unusable for detection purposes. In this paper the rotational spectrum of quasi-symmetric PAHs is computed analytically, as a function of the level of triaxiality. It is shown that the asymmetry of planar, nitrogen-substituted symmetric PAHs is small enough that their rotational spectrum, when observed with a resolution of about a MHz, has ...
Axially Symmetric, Spatially Homothetic Spacetimes
Wagh, S M; Wagh, Sanjay M.; Govinder, Keshlan S.
2002-01-01
We show that the existence of appropriate spatial homothetic Killing vectors is directly related to the separability of the metric functions for axially symmetric spacetimes. The density profile for such spacetimes is (spatially) arbitrary and admits any equation of state for the matter in the spacetime. When used for studying axisymmetric gravitational collapse, such solutions do not result in a locally naked singularity.
Shearfree Spherically Symmetric Fluid Models
Sharif, M
2013-01-01
We try to find some exact analytical models of spherically symmetric spacetime of collapsing fluid under shearfree condition. We consider two types of solutions: one is to impose a condition on the mass function while the other is to restrict the pressure. We obtain totally of five exact models, and some of them satisfy the Darmois conditions.
Particle-vortex symmetric liquid
Mulligan, Michael
2017-01-01
We introduce an effective theory with manifest particle-vortex symmetry for disordered thin films undergoing a magnetic field-tuned superconductor-insulator transition. The theory may enable one to access both the critical properties of the strong-disorder limit, which has recently been confirmed by Breznay et al. [Proc. Natl. Acad. Sci. USA 113, 280 (2016), 10.1073/pnas.1522435113] to exhibit particle-vortex symmetric electrical response, and the nearby metallic phase discovered earlier by Mason and Kapitulnik [Phys. Rev. Lett. 82, 5341 (1999), 10.1103/PhysRevLett.82.5341] in less disordered samples. Within the effective theory, the Cooper-pair and field-induced vortex degrees of freedom are simultaneously incorporated into an electrically neutral Dirac fermion minimally coupled to a (emergent) Chern-Simons gauge field. A derivation of the theory follows upon mapping the superconductor-insulator transition to the integer quantum Hall plateau transition and the subsequent use of Son's particle-hole symmetric composite Fermi liquid. Remarkably, particle-vortex symmetric response does not require the introduction of disorder; rather, it results when the Dirac fermions exhibit vanishing Hall effect. The theory predicts approximately equal (diagonal) thermopower and Nernst signal with a deviation parameterized by the measured electrical Hall response at the symmetric point.
Symmetric relations of finite negativity
Kaltenbaeck, M.; Winkler, H.; Woracek, H.; Forster, KH; Jonas, P; Langer, H
2006-01-01
We construct and investigate a space which is related to a symmetric linear relation S of finite negativity on an almost Pontryagin space. This space is the indefinite generalization of the completion of dom S with respect to (S.,.) for a strictly positive S on a Hilbert space.
Vassiliev Invariants from Symmetric Spaces
Biswas, Indranil; Gammelgaard, Niels Leth
We construct a natural framed weight system on chord diagrams from the curvature tensor of any pseudo-Riemannian symmetric space. These weight systems are of Lie algebra type and realized by the action of the holonomy Lie algebra on a tangent space. Among the Lie algebra weight systems, they are ......, they are exactly characterized by having the symmetries of the Riemann curvature tensor....
Axiomatizations of symmetrically weighted solutions
Kleppe, John; Reijnierse, Hans; Sudhölter, P.
2013-01-01
If the excesses of the coalitions in a transferable utility game are weighted, then we show that the arising weighted modifications of the well-known (pre)nucleolus and (pre)kernel satisfy the equal treatment property if and only if the weight system is symmetric in the sense that the weight of a su
Computationally Efficient Searchable Symmetric Encryption
Liesdonk, van Peter; Sedghi, Saeed; Doumen, Jeroen; Hartel, Pieter; Jonker, Willem; Jonker, Willem; Petkovic, Milan
2010-01-01
Searchable encryption is a technique that allows a client to store documents on a server in encrypted form. Stored documents can be retrieved selectively while revealing as little information as possible to the server. In the symmetric searchable encryption domain, the storage and the retrieval are
Symmetrical progressive erythro-keratoderma
Sunil Gupta
1999-01-01
Full Text Available A 13-year-old male child had gradually progressive, bilaterall, symmetrical, erythematous hyperkeratotic plaques over knees, elbows, natal cleft, dorsa of hands and feet with palmoplantar keratoderma. High arched palate, fissured tongue and sternal depression (pectus-excavatum were unusual associations.
顾国庆; 王开福; 许星
2012-01-01
基于刚体面内微小转动测量在实验力学测量中的必要性和重要性,开展了利用数字图像相关方法(DICM)定量测量转动角度和准确定位转动中心的研究.从理论上分析了刚体面内转动角度与面内位移分量之间的关系,运用计算机仿真散斑图进行数值模拟研究,得到的转动角度和转动中心位置测量误差都在2％以内,模拟结果验证了数字图像相关法进行刚体面内微小转动定量测量的可行性.运用数字图像相关法对刚体面内未知微小转动进行了实测,并与几何光学实验方法所得到的结果进行了比较,两者结果误差为3.1％,符合较好.实验结果表明数字图像相关方法可以作为定量测量刚体面内微小转动的有效方法.%Due to the necessity and importance of the measurement of in-plane micro-rotations of a rigid body in the field of experimental mechanics < an investigation of quantitative measurement of rotation angle and rotation-center location is developed with digital image correlation method (DICM). The relation between the rotation angle and the in-plane displacement components is analyzed through theoretical analysis. The study of numerical simulation is carried out by specklegram produced by computer simulation. The measurement errors of both rotation angle and rotation-center location are within 2%. It shows that digital image correlation method is quite competent for the quantitative measurement of in-plane micro-rotations. The unknown in-plane rotation of a rigid body is practically measured by using digital image correlation method. The obtained rotation angle is compared with the result obtained from the geometrical optics experiment. The relative error is 3. 1%. It shows that they are in good agreement. Experimental results indicate that digital image correlation method can be regarded as an efficient method to measure in-plane micro-rotations of a rigid body quantitatively.
Moes, C.C.M.
2007-01-01
The pressure distribution and the location of the points of maximum pressure, usually below the ischial tuberosities, was measured for subjects sitting on a flat, hard and horizontal support, and varying angle of the rotation of the pelvis. The pressure data were analyzed for force- and pressure-rel
Amel'kin, N. I.
2009-01-01
The set of steady motions of the system named in the title is represented parametrically via the gyro gimbal rotation angle for an arbitrary position of the gimbal axis. We study the set of steady motions for a system in which the gyro gimbal axis is parallel to a principal plane of inertia as well
Moes, C.C.M.
2007-01-01
The pressure distribution and the location of the points of maximum pressure, usually below the ischial tuberosities, was measured for subjects sitting on a flat, hard and horizontal support, and varying angle of the rotation of the pelvis. The pressure data were analyzed for force- and
Scars of Invariant Manifolds in Interacting Few-Body Systems
Papenbrock, T; Weidenmüller, H A
1997-01-01
We present a novel extension of the concept of scars for the wave functions of classically chaotic few--body systems of identical particles with rotation and permutation symmetry. Generically there exist manifolds in classical phase space which are invariant under the action of a common subgroup of these two symmetries. Such manifolds are associated with highly symmetric configurations and, if sufficiently stable, support quantum resonances. Although not directly associated to individual periodic orbits, the resonances nevertheless cause scars which signify collective motion on the quantum level and which should be experimentally observable.
Differentially-rotating neutron star models with a parametrized rotation profile
Galeazzi, Filippo; Eriguchi, Yoshiharu
2011-01-01
We analyze the impact of the choice rotation law on equilibrium sequences of relativistic differentially-rotating neutron stars in axisymmetry. The maximum allowed mass for each model is strongly affected by the distribution of angular velocity along the radial direction and by the consequent degree of differential rotation. In order to study the wide parameter space implied by the choice of rotation law, we introduce a functional form that generalizes the so called "j-const. law" adopted in all previous work. Using this new rotation law we reproduce the angular velocity profile of differentially-rotating remnants from the coalescence of binary neutron stars in various 3-dimensional dynamical simulations. We compute equilibrium sequences of differentially rotating stars with a polytropic equation of state starting from the spherically symmetric static case. By analyzing the sequences at constant ratio, T/|W|, of rotational kinetic energy to gravitational binding energy, we find that the parameters that best d...
Modelling non-symmetric collagen fibre dispersion in arterial walls.
Holzapfel, Gerhard A; Niestrawska, Justyna A; Ogden, Ray W; Reinisch, Andreas J; Schriefl, Andreas J
2015-05-06
New experimental results on collagen fibre dispersion in human arterial layers have shown that the dispersion in the tangential plane is more significant than that out of plane. A rotationally symmetric dispersion model is not able to capture this distinction. For this reason, we introduce a new non-symmetric dispersion model, based on the bivariate von Mises distribution, which is used to construct a new structure tensor. The latter is incorporated in a strain-energy function that accommodates both the mechanical and structural features of the material, extending our rotationally symmetric dispersion model (Gasser et al. 2006 J. R. Soc. Interface 3, 15-35. (doi:10.1098/rsif.2005.0073)). We provide specific ranges for the dispersion parameters and show how previous models can be deduced as special cases. We also provide explicit expressions for the stress and elasticity tensors in the Lagrangian description that are needed for a finite-element implementation. Material and structural parameters were obtained by fitting predictions of the model to experimental data obtained from human abdominal aortic adventitia. In a finite-element example, we analyse the influence of the fibre dispersion on the homogeneous biaxial mechanical response of aortic strips, and in a final example the non-homogeneous stress distribution is obtained for circumferential and axial strips under fixed extension. It has recently become apparent that this more general model is needed for describing the mechanical behaviour of a variety of fibrous tissues.
Childs, Peter R N
2010-01-01
Rotating flow is critically important across a wide range of scientific, engineering and product applications, providing design and modeling capability for diverse products such as jet engines, pumps and vacuum cleaners, as well as geophysical flows. Developed over the course of 20 years' research into rotating fluids and associated heat transfer at the University of Sussex Thermo-Fluid Mechanics Research Centre (TFMRC), Rotating Flow is an indispensable reference and resource for all those working within the gas turbine and rotating machinery industries. Traditional fluid and flow dynamics
Symmetric Satellite Swarms and Choreographic Crystals.
Boyle, Latham; Khoo, Jun Yong; Smith, Kendrick
2016-01-08
In this Letter, we introduce a natural dynamical analogue of crystalline order, which we call choreographic order. In an ordinary (static) crystal, a high degree of symmetry may be achieved through a careful arrangement of the fundamental repeated elements. In the dynamical analogue, a high degree of symmetry may be achieved by having the fundamental elements perform a carefully choreographed dance. For starters, we show how to construct and classify all symmetric satellite constellations. Then we explain how to generalize these ideas to construct and classify choreographic crystals more broadly. We introduce a quantity, called the "choreography" of a given configuration. We discuss the possibility that some (naturally occurring or artificial) many-body or condensed-matter systems may exhibit choreographic order, and suggest natural experimental signatures that could be used to identify and characterize such systems.
The antipodal sets of compact symmetric spaces
Liu, Xingda; Deng, Shaoqiang
2014-01-01
We study the antipodal set of a point in a compact Riemannian symmetric space. It turns out that we can give an explicit description of the antipodal set of a point in any connected simply connected compact Riemannian symmetric space...
Symmetric normalisation for intuitionistic logic
Guenot, Nicolas; Straßburger, Lutz
2014-01-01
, but using a non-local rewriting. The second system is the symmetric completion of the first, as normally given in deep inference for logics with a DeMorgan duality: all inference rules have duals, as cut is dual to the identity axiom. We prove a generalisation of cut elimination, that we call symmetric...... normalisation, where all rules dual to standard ones are permuted up in the derivation. The result is a decomposition theorem having cut elimination and interpolation as corollaries.......We present two proof systems for implication-only intuitionistic logic in the calculus of structures. The first is a direct adaptation of the standard sequent calculus to the deep inference setting, and we describe a procedure for cut elimination, similar to the one from the sequent calculus...
Symmetric two-coordinate photodiode
Dobrovolskiy Yu. G.
2008-12-01
Full Text Available The two-coordinate photodiode is developed and explored on the longitudinal photoeffect, which allows to get the coordinate descriptions symmetric on the steepness and longitudinal resistance great exactness. It was shown, that the best type of the coordinate description is observed in the case of scanning by the optical probe on the central part of the photosensitive element. The ways of improvement of steepness and linear of its coordinate description were analyzed.
Thermodynamic Volume Product in Spherically Symmetric and Axisymmetric Spacetime
Pradhan, Parthapratim
2016-01-01
In this Letter, we compute particularly thermodynamic \\emph{volume product, volume sum, volume minus and volume division} for wide variety of spherically symmetric spacetime and axisymmetric spacetime in the frame work of \\emph{extended phase space}. We consider Einstein gravity as well as other than Einstein gravity i.e. \\emph{Ho\\v{r}ava Lifshitz} gravity. We speculate that for spherically symmetric black holes the volume product is mass-independent both in Einstein gravity as well as Ho\\v{r}ava Lifshitz gravity while the other combination is mass-dependent. For axisymmetric black hole spacetime in Einstein gravity all the combination is \\emph{mass-dependent}. There has been no chance to generate any combination of volume product is mass-independent. Interestingly, \\emph{only rotating BTZ black hole} in 3D provides the volume product formula is mass-independent i.e. \\emph{universal} and hence it is quantized.
PT-symmetric phase in kagome photonic lattices
Chern, Gia-Wei
2015-01-01
Kagome lattice is a two-dimensional network of corner-sharing triangles and is often associated with geometrical frustration. In particular, the frustrated coupling between waveguide modes in a kagome array leads to a dispersionless flat band consisting of spatially localized modes. Here we propose a complex photonic lattice by placing $\\mathcal{PT}$-symmetric dimers at the kagome lattice points. Each dimer corresponds to a pair of strongly coupled waveguides. With balanced arrangement of gain and loss on individual dimers, the system exhibits a $\\mathcal{PT}$-symmetric phase for finite gain/loss parameter up to a critical value. The beam evolution in this complex kagome waveguide array exhibits a novel oscillatory rotation of optical power along the propagation distance. Long-lived local chiral structures originating from the nearly flat bands of the kagome structure are observed when the lattice is subject to a narrow beam excitation.
PT-symmetric phase in kagome-based photonic lattices.
Chern, Gia-Wei; Saxena, Avadh
2015-12-15
The kagome lattice is a two-dimensional network of corner-sharing triangles and is often associated with geometrical frustration. In particular, the frustrated coupling between waveguide modes in a kagome array leads to a dispersionless flat band consisting of spatially localized modes. Here we propose a complex photonic lattice by placing PT-symmetric dimers at the kagome lattice points. Each dimer corresponds to a pair of strongly coupled waveguides. With balanced arrangement of gain and loss on individual dimers, the system exhibits a PT-symmetric phase for finite gain/loss parameter up to a critical value. The beam evolution in this complex kagome waveguide array exhibits a novel oscillatory rotation of optical power along the propagation distance. Long-lived local chiral structures originating from the nearly flat bands of the kagome structure are observed when the lattice is subject to a narrow beam excitation.
Bender, Carl M.
2015-07-01
The average quantum physicist on the street would say that a quantum-mechanical Hamiltonian must be Dirac Hermitian (invariant under combined matrix transposition and complex conjugation) in order to guarantee that the energy eigenvalues are real and that time evolution is unitary. However, the Hamiltonian H = p2 + ix3, which is obviously not Dirac Hermitian, has a positive real discrete spectrum and generates unitary time evolution, and thus it defines a fully consistent and physical quantum theory. Evidently, the axiom of Dirac Hermiticity is too restrictive. While H = p2 + ix3 is not Dirac Hermitian, it is PT symmetric; that is, invariant under combined parity P (space reflection) and time reversal T. The quantum mechanics defined by a PT-symmetric Hamiltonian is a complex generalization of ordinary quantum mechanics. When quantum mechanics is extended into the complex domain, new kinds of theories having strange and remarkable properties emerge. In the past few years, some of these properties have been verified in laboratory experiments. A particularly interesting PT-symmetric Hamiltonian is H = p2 - x4, which contains an upside-down potential. This potential is discussed in detail, and it is explained in intuitive as well as in rigorous terms why the energy levels of this potential are real, positive, and discrete. Applications of PT-symmetry in quantum field theory are also discussed.
李子丰
2013-01-01
在旋转问题中，坐标系的选取至关重要，否则会因角速度测量不准而出现错误。旋转问题一级近似惯性坐标系，应该选取比被绕行物体高一级的天体引力场：（1）一般的旋转问题--固定在地球上的直角坐标系；（2）卫星绕地球旋转问题--日心-地心直角坐标系；（3）地球绕太阳旋转问题--银河系心-日心直角坐标系。在天体物理学中，质量计算不准和旋转角速度测量不准导致黑洞猜想。%Selection of the coordinate system is essential for rotate problem.Otherwise,mistakes may occur due to inaccurate measurement of angular speed. Approximate inertial coordinate system selections for rotate problems should be the gravitational field of a celestial body higher than the object being rotated:(1) the earth fixed Cartesian coordinate system for normal rotation problem;(2) heliocentric-geocentric Cartesian coordinate system for satellites orbiting the earth;(3) the Galaxy Heart-heliocentric Cartesian coordinates for Earth's rotation around the sun.In astrophysics,mass calculation error and angular velocity measurement error lead to a black hole conjecture.
Lekner, John
2008-01-01
Any free-particle wavepacket solution of Schrodinger's equation can be converted by differentiations to wavepackets rotating about the original direction of motion. The angular momentum component along the motion associated with this rotation is an integral multiple of [h-bar]. It is an "intrinsic" angular momentum: independent of origin and…
Vassiliev, Dmitri
2017-04-01
We consider an infinite three-dimensional elastic continuum whose material points experience no displacements, only rotations. This framework is a special case of the Cosserat theory of elasticity. Rotations of material points are described mathematically by attaching to each geometric point an orthonormal basis that gives a field of orthonormal bases called the coframe. As the dynamical variables (unknowns) of our theory, we choose the coframe and a density. We write down the general dynamic variational functional for our rotational theory of elasticity, assuming our material to be physically linear but the kinematic model geometrically nonlinear. Allowing geometric nonlinearity is natural when dealing with rotations because rotations in dimension three are inherently nonlinear (rotations about different axes do not commute) and because there is no reason to exclude from our study large rotations such as full turns. The main result of the talk is an explicit construction of a class of time-dependent solutions that we call plane wave solutions; these are travelling waves of rotations. The existence of such explicit closed-form solutions is a non-trivial fact given that our system of Euler-Lagrange equations is highly nonlinear. We also consider a special case of our rotational theory of elasticity which in the stationary setting (harmonic time dependence and arbitrary dependence on spatial coordinates) turns out to be equivalent to a pair of massless Dirac equations. The talk is based on the paper [1]. [1] C.G.Boehmer, R.J.Downes and D.Vassiliev, Rotational elasticity, Quarterly Journal of Mechanics and Applied Mathematics, 2011, vol. 64, p. 415-439. The paper is a heavily revised version of preprint https://arxiv.org/abs/1008.3833
Periodic Orbits of Radially Symmetric Keplerian-Like Systems with a Singularity
Shengjun Li
2016-01-01
Full Text Available We study planar radially symmetric Keplerian-like systems with repulsive singularities near the origin and with some semilinear growth near infinity. By the use of topological degree theory, we prove the existence of two distinct families of periodic orbits; one rotates around the origin with small angular momentum, and the other one rotates around the origin with both large angular momentum and large amplitude.
Axially Symmetric Post-Newtonian Stellar Systems
Camilo Akímushkin
2010-06-01
Full Text Available We introduce a method to obtain self-consistent, axially symmetric disklike stellar models in the first post-Newtonian (1PN approximation. By using in the field equations of the 1PN approximation a distribution function (DF corresponding to a Newtonian model, two fundamental equations determining the 1PN corrections are obtained. The rotation curves of the corrected models differs from the classical ones and the corrections are clearly appreciable with values of the mass and radius of a typical galaxy. On the other hand, the relativistic mass correction can be ignored for all models. Resumen. Presentamos un método para obtener modelos estelares discoidales, axialmente simétricos, auto-consistentes en la primera aproximación post-Newtoniana (1PN. Usando en las ecuaciones de campo de la aproximación 1PN una función de distribución conocida (DF que corresponde a un modelo Newtoniano, se obtienen dos ecuaciones fundamentales para determinar las correcciones 1PN. Las curvas de rotación de los modelos corregidos difieren de las clásicas y las correcciones son claramente apreciables con los valores de la masa y el radio de una galaxia típica. Por otro lado, la corrección relativista de la masa se puede ignorar para todos los modelos.
Symmetric products of mixed Hodge modules
Maxim, Laurentiu; Schuermann, Joerg
2010-01-01
Generalizing a theorem of Macdonald, we show a formula for the mixed Hodge structure on the cohomology of the symmetric products of bounded complexes of mixed Hodge modules by showing the existence of the canonical action of the symmetric group on the multiple external self-products of complexes of mixed Hodge modules. We also generalize a theorem of Hirzebruch and Zagier on the signature of the symmetric products of manifolds to the case of the symmetric products of symmetric parings on bounded complexes with constructible cohomology sheaves where the pairing is not assumed to be non-degenerate.
Singular Value Decomposition for Unitary Symmetric Matrix
ZOUHongxing; WANGDianjun; DAIQionghai; LIYanda
2003-01-01
A special architecture called unitary sym-metric matrix which embodies orthogonal, Givens, House-holder, permutation, and row (or column) symmetric ma-trices as its special cases, is proposed, and a precise corre-spondence of singular values and singular vectors between the unitary symmetric matrix and its mother matrix is de-rived. As an illustration of potential, it is shown that, for a class of unitary symmetric matrices, the singular value decomposition (SVD) using the mother matrix rather than the unitary symmetric matrix per se can save dramatically the CPU time and memory without loss of any numerical precision.
Numerical Study on Fixed-Axis Rotation of Rigid Body under Variable Moment Inertia%变转动惯量刚体定轴转动的数值研究
唐军杰; 王爱军; 赵昆; 张鹏
2012-01-01
Given a model of variable moment inertia of rigid body,a numerical method with Matlab has been applied to study the fixed-axis rotation of rigid body under variable moment inertia and constant external torque. Because at the initial stage the changes in variable moment inertia are very small , the movement of rigid body is similar to that when moment inertia is constant. As the changes in moment inertia become greater,the angular velocity of rigid body changes periodically under the impact of elastic restoring forces.%给出一个变转动惯量刚体模型,用数值方法研究了在恒力矩作用下变转动惯量刚体的定轴转动问题.在开始阶段由于转动惯量变化很小,刚体运动与刚体转动惯量不变的情况相似,随着转动惯量变化增大,在弹性恢复力的作用下,刚体角速度呈周期性变化.
Rotational nuclear models and electron scattering
Moya de Guerra, E.
1986-05-01
A review is made of the basic formalism involved in the application of nuclear rotational models to the problem of electron scattering from axially symmetric deformed nuclei. Emphasis is made on the use of electron scattering to extract information on the nature of the collective rotational model. In this respect, the interest of using polarized beam and target is discussed with the help of illustrative examples. Concerning the nuclear structure four rotational models are considered: Two microscopic models, namely the Projected Hartree-Fock (PHF) and cranking models; and two collective models, the rigid rotor and the irrotational flow models. The problem of current conservation within the different models is also discussed.
Discrete Torsion and Symmetric Products
Dijkgraaf, R
1999-01-01
In this note we point out that a symmetric product orbifold CFT can be twisted by a unique nontrivial two-cocycle of the permutation group. This discrete torsion changes the spins and statistics of corresponding second-quantized string theory making it essentially ``supersymmetric.'' The long strings of even length become fermionic (or ghosts), those of odd length bosonic. The partition function and elliptic genus can be described by a sum over stringy spin structures. The usual cubic interaction vertex is odd and nilpotent, so this construction gives rise to a DLCQ string theory with a leading quartic interaction.
A charged spherically symmetric solution
K Moodley; S D Maharaj; K S Govinder
2003-09-01
We ﬁnd a solution of the Einstein–Maxwell system of ﬁeld equations for a class of accelerating, expanding and shearing spherically symmetric metrics. This solution depends on a particular ansatz for the line element. The radial behaviour of the solution is fully speciﬁed while the temporal behaviour is given in terms of a quadrature. By setting the charge contribution to zero we regain an (uncharged) perfect ﬂuid solution found previously with the equation of state =+ constant, which is a generalisation of a stiff equation of state. Our class of charged shearing solutions is characterised geometrically by a conformal Killing vector.
Spherically symmetric scalar field collapse
Koyel Ganguly; Narayan Banerjee
2013-03-01
It is shown that a scalar field, minimally coupled to gravity, may have collapsing modes even when the energy condition is violated, that is, for ( + 3) < 0. This result may be useful in the investigation of the possible clustering of dark energy. All the examples dealt with have apparent horizons formed before the formation of singularity. The singularities formed are shell focussing in nature. The density of the scalar field distribution is seen to diverge at singularity. The Ricci scalar also diverges at the singularity. The interior spherically symmetric metric is matched with exterior Vaidya metric at the hypersurface and the appropriate junction conditions are obtained.
Immanant Conversion on Symmetric Matrices
Purificação Coelho M.
2014-01-01
Full Text Available Letr Σn(C denote the space of all n χ n symmetric matrices over the complex field C. The main objective of this paper is to prove that the maps Φ : Σn(C -> Σn (C satisfying for any fixed irre- ducible characters X, X' -SC the condition dx(A +aB = dχ·(Φ(Α + αΦ(Β for all matrices A,В ε Σ„(С and all scalars a ε C are automatically linear and bijective. As a corollary of the above result we characterize all such maps Φ acting on ΣИ(С.
Rotating Polygons on a Fluid Surface
Bohr, Tomas; Jansson, Thomas; Haspang, Martin
The free surface of a rotating fluid will, due to the centrifugal force, be pressed radially outward. If the fluid rotates as a rigid body in a cylindrical container the surface will assume a parabolic shape. If, however, the flow is driven by rotating the bottom plate, the axial symmetry can break...
Motor Processes in Children's Mental Rotation
Frick, Andrea; Daum, Moritz M.; Walser, Simone; Mast, Fred W.
2009-01-01
Previous studies with adult human participants revealed that motor activities can influence mental rotation of body parts and abstract shapes. In this study, we investigated the influence of a rotational hand movement on mental rotation performance from a developmental perspective. Children at the age of 5, 8, and 11 years and adults performed a…
Rotational symmetry breaking in baby Skyrme models
Hen, Itay
2007-01-01
We consider multisolitons with charges 1 =< B =< 5 in the baby Skyrme model for the one-parametric family of potentials U=\\mu^2 (1-\\phi_3)^s with 0rotationally-symmetric. For higher charges, stable solutions exist only below s \\approx 2. In the charge-two sector the stable solutions are always rotationally-symmetric and ring-like. For charge three and above, rotational symmetry is exhibited only in the small s region; above a certain critical value of s, this symmetry is broken and a strong repulsion between the constituent one-Skyrmions becomes apparent. We also compute the spatial energy distributions of these solutions.
Josipovic, Mirjana; Persson, Gitte Fredberg; Logadottir, Ashildur;
2012-01-01
Implementation of cone beam computed tomography (CBCT) in frameless stereotactic body radiotherapy (SBRT) of lung tumours enables setup correction based on tumour position. The aim of this study was to compare setup accuracy with daily soft tissue matching to bony anatomy matching and evaluate...
The Nuclear Born Oppenheimer Method and Nuclear Rotations
Zettili, Nouredine
2009-01-01
We deal here with the application of the Nuclear Born Oppenheimer (NBO) method to the description of nuclear rotations. As an edifying illustration, we apply the NBO formalism to study the rotational motion of nuclei which are axially-symmetric and even, but whose shells are not closed. We focus, in particular, on the derivation of expressions for the rotational energy and for the moment of inertia. Additionally, we examine the connection between the NBO method and the self-consistent crankin...
Schwarz Methods: To Symmetrize or Not to Symmetrize
Holst, Michael
2010-01-01
A preconditioning theory is presented which establishes sufficient conditions for multiplicative and additive Schwarz algorithms to yield self-adjoint positive definite preconditioners. It allows for the analysis and use of non-variational and non-convergent linear methods as preconditioners for conjugate gradient methods, and it is applied to domain decomposition and multigrid. It is illustrated why symmetrizing may be a bad idea for linear methods. It is conjectured that enforcing minimal symmetry achieves the best results when combined with conjugate gradient acceleration. Also, it is shown that absence of symmetry in the linear preconditioner is advantageous when the linear method is accelerated by using the Bi-CGstab method. Numerical examples are presented for two test problems which illustrate the theory and conjectures.
通用三维转动机构测试系统研究与设计%Research and Design of General Three-dimensional Rotating Body Test System
孙弋; 董延杰; 刘涵君
2011-01-01
随着空间科学技术和航天设备的不断发展,对测试系统的自动化程度要求越来越高,通过对航天测试标准和对通用三维转动机构的研究,提出了一种基于LabVIEW和工业控制计算机的可视化空间三维转动机构控制的测试系统方案;该方案采用工业控制计算机作为控制台,用高精度双通道旋变解调模块对双余度步进电机的角度位移信号进行测量,来获取天线转动的位置信息;操作系统平台采用Windows XP,采用NI公司虚拟测试软件LabVIEW进行人机界面的设计,可以直观的对三维转动机构进行位置变化控制和获取各种参数信息,并可以对数据进行分析、报警、存储、查询等操作,以及进行定时转动控制;经测试,该系统能满足要求,且稳定可靠.%As the continuous development of space sciencc and technology and aerospace equipment, the degree of automation of the test system have become increasingly demanding in this field, according to test standards and the general space three-dimensional rotating body research, proposes a three-dimensional rotation of the control of the space program based on LabVIEW and industrial control computer visualization.The program uses industrial control computer as the console, using high-precision dual-channel rotary variable demodulation module redundant pairs of angle stepper motor displacement signal measured to obtain the location information of the rotating antenna.Operating system platform, using Windows XP, uses NIs LabVIEW virtual test software to conduct human-computer interface design, intuitive three-dimensional rotation of the position change institutions to control and access to information on various parameters, and can analyze the data, alarm, storage, queries and other operations, as well as regular rotation control.After testing, the system can meet the requirements,and reliable.
刘静; 张建民
2008-01-01
采用改进分析型嵌入原子法(modified analytical embedded atom method,MAEAM),从原子尺度对体心立方(body-centered cubic,BCC)金属Li在以[001]为旋转轴的对称倾斜晶界(symmetrical tilt grain boundary,STGB)中的结构和能量进行了计算机模拟.结果表明,刚性结合的对称倾斜晶界面附近的原子距离非常近,从而导致能量异常高.所研究的27个晶界面两晶粒间的相对平移均可降低晶界能,最小晶界能出现在特定的平移距离处,且随重合密度倒数∑增加而振荡增加,随相对面间距d/a增加而减小,3个最低能量的晶界面依次对应于(310)、(530)和(510).由能量最小化原理知这些晶界面将依次择优出现.
Testing whether and when abstract symmetric patterns produce affective responses.
Marco Bertamini
Full Text Available Symmetry has a central role in visual art, it is often linked to beauty, and observers can detect it efficiently in the lab. We studied what kind of fast and automatic responses are generated by visual presentation of symmetrical patterns. Specifically, we tested whether a brief presentation of novel symmetrical patterns engenders positive affect using a priming paradigm. The abstract patterns were used as primes in a pattern-word interference task. To ensure that familiarity was not a factor, no pattern and no word was ever repeated within each experiment. The task was to classify words that were selected to have either positive or negative valence. We tested irregular patterns, patterns containing vertical and horizontal reflectional symmetry, and patterns containing a 90 deg rotation. In a series of 7 experiments we found that the effect of affective congruence was present for both types of regularity but only when observers had to classify the regularity of the pattern after responding to the word. The findings show that processing abstract symmetrical shapes or random pattern can engender positive or negative affect as long as the regularity of the pattern is a feature that observers have to attend to and classify.
Carbon-13 and tin-119 relaxation studies of some axially symmetrical organotin compounds
Chapelle, S.; Granger, P.
We have studied a variety of axially symmetrical tin compounds by 119Sn and 13C NMR. Tin was observed at two field strengths and, except for Ph 3SnCl, T1 is field independent and governed mainly by spin-rotation. A chemical-shift anisotropy of 136 ppm is observed for 119Sn in Ph 3SnCl. Deverell's relationship provides a good estimate of the values of the spin-rotational constants and the theory of Woessner, Snowden, and Huntress leads to the values of the rotational diffusion constants.
Fine Spectra of Symmetric Toeplitz Operators
Muhammed Altun
2012-01-01
Full Text Available The fine spectra of 2-banded and 3-banded infinite Toeplitz matrices were examined by several authors. The fine spectra of n-banded triangular Toeplitz matrices and tridiagonal symmetric matrices were computed in the following papers: Altun, “On the fine spectra of triangular toeplitz operators” (2011 and Altun, “Fine spectra of tridiagonal symmetric matrices” (2011. Here, we generalize those results to the (2+1-banded symmetric Toeplitz matrix operators for arbitrary positive integer .
Classification of symmetric toroidal orbifolds
Fischer, Maximilian; Ratz, Michael; Torrado, Jesus [Technische Univ. Muenchen, Garching (Germany). Physik-Department; Vaudrevange, Patrick K.S. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2012-09-15
We provide a complete classification of six-dimensional symmetric toroidal orbifolds which yield N{>=}1 supersymmetry in 4D for the heterotic string. Our strategy is based on a classification of crystallographic space groups in six dimensions. We find in total 520 inequivalent toroidal orbifolds, 162 of them with Abelian point groups such as Z{sub 3}, Z{sub 4}, Z{sub 6}-I etc. and 358 with non-Abelian point groups such as S{sub 3}, D{sub 4}, A{sub 4} etc. We also briefly explore the properties of some orbifolds with Abelian point groups and N=1, i.e. specify the Hodge numbers and comment on the possible mechanisms (local or non-local) of gauge symmetry breaking.
Classification of symmetric toroidal orbifolds
Fischer, Maximilian; Ratz, Michael; Torrado, Jesus [Technische Univ. Muenchen, Garching (Germany). Physik-Department; Vaudrevange, Patrick K.S. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2012-09-15
We provide a complete classification of six-dimensional symmetric toroidal orbifolds which yield N{>=}1 supersymmetry in 4D for the heterotic string. Our strategy is based on a classification of crystallographic space groups in six dimensions. We find in total 520 inequivalent toroidal orbifolds, 162 of them with Abelian point groups such as Z{sub 3}, Z{sub 4}, Z{sub 6}-I etc. and 358 with non-Abelian point groups such as S{sub 3}, D{sub 4}, A{sub 4} etc. We also briefly explore the properties of some orbifolds with Abelian point groups and N=1, i.e. specify the Hodge numbers and comment on the possible mechanisms (local or non-local) of gauge symmetry breaking.
Symmetric functions and Hall polynomials
MacDonald, Ian Grant
1998-01-01
This reissued classic text is the acclaimed second edition of Professor Ian Macdonald's groundbreaking monograph on symmetric functions and Hall polynomials. The first edition was published in 1979, before being significantly expanded into the present edition in 1995. This text is widely regarded as the best source of information on Hall polynomials and what have come to be known as Macdonald polynomials, central to a number of key developments in mathematics and mathematical physics in the 21st century Macdonald polynomials gave rise to the subject of double affine Hecke algebras (or Cherednik algebras) important in representation theory. String theorists use Macdonald polynomials to attack the so-called AGT conjectures. Macdonald polynomials have been recently used to construct knot invariants. They are also a central tool for a theory of integrable stochastic models that have found a number of applications in probability, such as random matrices, directed polymers in random media, driven lattice gases, and...
A Minimally Symmetric Higgs Boson
Low, Ian
2014-01-01
Models addressing the naturalness of a light Higgs boson typically employ symmetries, either bosonic or fermionic, to stabilize the Higgs mass. We consider a setup with the minimal amount of symmetries: four shift symmetries acting on the four components of the Higgs doublet, subject to the constraints of linearly realized SU(2)xU(1) electroweak symmetry. Up to terms that explicitly violate the shift symmetries, the effective lagrangian can be derived, irrespective of the spontaneously broken group G in the ultraviolet, and is universal in all models where the Higgs arises as a pseudo-Nambu-Goldstone boson (PNGB). Very high energy scatterings of vector bosons could provide smoking gun signals of a minimally symmetric Higgs boson.
Computing symmetric colorings of the dihedral group
Zelenyuk, Yuliya
2016-06-01
A symmetry on a group G is a mapping G ∋ x ↦ gx-1 g ∈ G, where g ∈ G. A subset A ⊆ G is symmetric if it is invariant under some symmetry, that is, A = gA-1g. The notion of symmetry has interesting relations to enumerative combinatorics. A coloring is symmetric if χ(gx-1g) = χ(x) for some g ∈ G. We discuss an approach how to compute the number of symmetric r-colorings for any finite group. Using this approach we derive the formula for the number of symmetric r-colorings of the dihedral group D3.
Nobili, A. M.; Bramanti, D.; Polacco, E.; Catastini, G.; Anselmi, A.; Portigliotti, S.; Lenti, A.; di Giamberardino, P.; Monaco, S.; Ronchini, R.
1999-04-01
Test masses coupled by weak mechanical suspensions are sensitive to differential forces such as the force due to a possible violation of the equivalence principle (EP). If in addition they are put in rapid rotation, the differential signal is modulated at high frequency, which is beneficial for noise reduction. Galileo Galilei (GG) is a proposed space experiment for testing the equivalence principle to 1 part in 0264-9381/16/4/032/img8 based on these concepts. A recent paper by Jafry and Weinberger (1998 Class. Quantum Grav. 15 481-500) claims that GG can only reach 0264-9381/16/4/032/img9. We show that the analysis of this paper is flawed (by several orders of magnitude) because of two misconceptions: one on the physical nature of mechanical damping and the other on active control methods for the stabilization of spinning bodies.
Automorphism groups of causal symmetric spaces of Cayley type and bounded symmetric domains
Soji; Kaneyuki
2005-01-01
Symmetric spaces of Cayley type are a higher dimensional analogue of a onesheeted hyperboloid in R3. They form an important class of causal symmetric spaces. To a symmetric space of Cayley type M, one can associate a bounded symmetric domain of tube type D. We determine the full causal automorphism group of M. This clarifies the relation between the causal automorphism group and the holomorphic automorphism group of D.
Stability of spherically symmetric, charged black holes and multipole moments for stationary systems
Gursel, H.Y.
1983-01-01
This dissertation is written in two parts. Part I deals with the question of stability of a spherically symmetric, charged black hole against scalar, electromagnetic, and gravitational perturbations. It consists of two papers written in collaboration with Igor D. Novikov, Vernon D. Sandberg and A.A. Starobinsky. In these papers the dynamical evolution of these perturbations on the interior of a Reissner-Nordstrom black hole is described. The instability of the hole's Cauchy horizon is discussed in detail in terms of the energy densities of the test fields as measured by a freely falling observer approaching the Cauchy horizon. It is concluded that the Cauchy horizon of the analytically extended Reissner-Nordstrom solution is highly unstable and not a physical feature of a realistic gravitational collapse. Part II of this dissertation addresses two problems closely connected with multipole structure of stationary, asymptotically flat spacetimes. It consists of two papers written in collaboration with Kip S. Thorne. The first one shows the equivalence of the moments defined by Kip S. Thorne and the moments defined by Robert Geroch and Richard Hansen. The second proves a conjecture by Kip S. Thorne: In the limit of ''slow'' motion, general relativistic gravity produces no changes whatsoever in the classical Euler equations of rigid body motion. This conjecture is proved by giving an algorithm for generating rigidly rotating solutions of Einstein's equation from nonrotating, static solutions.
Hydrodynamic Instabilities in Rotating Fluids
KarlBuehler
2000-01-01
Rotating flow systems are often used to study stability phenomena and structure developments.The closed spherical gap prblem is generalized into an open flow system by superimposing a mass flux in meridional direction.The basic solutions at low Reynolds numbers are described by analytical methods.The nonlinear supercritical solutions are simulated numerically and realized in experiments.Novel steady and time-dependent modes of flows are obtained.The extensive results concern the stability behaviour.non-uniqueness of supercritical solutions,symmetry behaviour and transitions between steady and time-dependent solutions.The experimental investigations concern the visualization of the various instabilities and the quatitative description of the flow structures including the laminar-turbulent transition.A Comparison between theoretical and experimental results shows good agreement within the limit of rotational symmetric solutions from the theory.
Whirling skirts and rotating cones
Guven, Jemal; Müller, Martin Michael
2013-01-01
Steady, dihedrally symmetric patterns with sharp peaks may be observed on a spinning skirt, lagging behind the material flow of the fabric. These qualitative features are captured with a minimal model of traveling waves on an inextensible, flexible, generalized-conical sheet rotating about a fixed axis. Conservation laws are used to reduce the dynamics to a quadrature describing a particle in a three-parameter family of potentials. One parameter is associated with the stress in the sheet, the second is the Noether current associated with rotational invariance, and the third is a Rossby number which indicates the relative strength of Coriolis forces. Solutions are quantized by enforcing a topology appropriate to a skirt and a particular choice of dihedral symmetry. A perturbative analysis of nearly axisymmetric cones shows that Coriolis effects are essential in establishing skirt-like solutions. Fully non-linear solutions with three-fold symmetry are presented, which bear a suggestive resemblance to the observ...
CANONICAL EXTENSIONS OF SYMMETRIC LINEAR RELATIONS
Sandovici, Adrian; Davidson, KR; Gaspar, D; Stratila, S; Timotin, D; Vasilescu, FH
2006-01-01
The concept of canonical extension of Hermitian operators has been recently introduced by A. Kuzhel. This paper deals with a generalization of this notion to the case of symmetric linear relations. Namely, canonical regular extensions of symmetric linear relations in Hilbert spaces are studied. The
Symmetric products, permutation orbifolds and discrete torsion
Bántay, P
2000-01-01
Symmetric product orbifolds, i.e. permutation orbifolds of the full symmetric group S_{n} are considered by applying the general techniques of permutation orbifolds. Generating functions for various quantities, e.g. the torus partition functions and the Klein-bottle amplitudes are presented, as well as a simple expression for the discrete torsion coefficients.
Inversion-symmetric topological insulators
Hughes, Taylor L.; Prodan, Emil; Bernevig, B. Andrei
2011-06-01
We analyze translationally invariant insulators with inversion symmetry that fall outside the current established classification of topological insulators. These insulators exhibit no edge or surface modes in the energy spectrum and hence they are not edge metals when the Fermi level is in the bulk gap. However, they do exhibit protected modes in the entanglement spectrum localized on the cut between two entangled regions. Their entanglement entropy cannot be made to vanish adiabatically, and hence the insulators can be called topological. There is a direct connection between the inversion eigenvalues of the Hamiltonian band structure and the midgap states in the entanglement spectrum. The classification of protected entanglement levels is given by an integer N, which is the difference between the negative inversion eigenvalues at inversion symmetric points in the Brillouin zone, taken in sets of 2. When the Hamiltonian describes a Chern insulator or a nontrivial time-reversal invariant topological insulator, the entirety of the entanglement spectrum exhibits spectral flow. If the Chern number is zero for the former, or time reversal is broken in the latter, the entanglement spectrum does not have spectral flow, but, depending on the inversion eigenvalues, can still exhibit protected midgap bands similar to impurity bands in normal semiconductors. Although spectral flow is broken (implying the absence of real edge or surface modes in the original Hamiltonian), the midgap entanglement bands cannot be adiabatically removed, and the insulator is “topological.” We analyze the linear response of these insulators and provide proofs and examples of when the inversion eigenvalues determine a nontrivial charge polarization, a quantum Hall effect, an anisotropic three-dimensional (3D) quantum Hall effect, or a magnetoelectric polarization. In one dimension, we establish a link between the product of the inversion eigenvalues of all occupied bands at all inversion
Motor processes in mental rotation
Wexler, Mark; Kosslyn, Stephen; Berthoz, Alain
1997-01-01
Much indirect evidence supports the hypothesis that transformations of mental images are at least in part guided by motor processes, even in the case of images of abstract objects rather than of body parts. For example, rotation may be guided by processes that also prime one to see results of a specific motor action. We directly test the hypothesis by means of a dual-task paradigm in which subjects perform the Cooper-Shepard mental rotation task while executing an unseen motor rotation in a g...
Joglekar, Yogesh N
2010-01-01
We study the properties of a parity- and time-reversal- (PT) symmetric tight-binding chain of size N with position-dependent hopping amplitude. In contrast to the fragile PT-symmetric phase of a chain with constant hopping and imaginary impurity potentials, we show that, under very general conditions, our model is {\\it always} in the PT-symmetric phase. We numerically obtain the energy spectrum and the density of states of such a chain, and show that they are widely tunable. By studying the size-dependence of inverse participation ratios, we show that although the chain is not translationally invariant, most of its eigenstates are extended. Our results indicate that tight-binding models with non-Hermitian PT-symmetric hopping have a robust PT-symmetric phase and rich dynamics.
Classification of Entanglement in Symmetric States
Aulbach, Martin
2011-01-01
Quantum states that are symmetric with respect to permutations of their subsystems appear in a wide range of physical settings, and they have a variety of promising applications in quantum information science. In this thesis the entanglement of symmetric multipartite states is categorised, with a particular focus on the pure multi-qubit case and the geometric measure of entanglement. An essential tool for this analysis is the Majorana representation, a generalisation of the single-qubit Bloch sphere representation, which allows for a unique representation of symmetric n qubit states by n points on the surface of a sphere. Here this representation is employed to search for the maximally entangled symmetric states of up to 12 qubits in terms of the geometric measure, and an intuitive visual understanding of the upper bound on the maximal symmetric entanglement is given. Furthermore, it will be seen that the Majorana representation facilitates the characterisation of entanglement equivalence classes such as Stoc...
Modeling rigid magnetically rotated microswimmers: rotation axes, bistability, and controllability.
Meshkati, Farshad; Fu, Henry Chien
2014-12-01
Magnetically actuated microswimmers have recently attracted attention due to many possible biomedical applications. In this study we investigate the dynamics of rigid magnetically rotated microswimmers with permanent magnetic dipoles. Our approach uses a boundary element method to calculate a mobility matrix, accurate for arbitrary geometries, which is then used to identify the steady periodically rotating orbits in a co-rotating body-fixed frame. We evaluate the stability of each of these orbits. We map the magnetoviscous behavior as a function of dimensionless Mason number and as a function of the angle that the magnetic field makes with its rotation axis. We describe the wobbling motion of these swimmers by investigating how the rotation axis changes as a function of experimental parameters. We show that for a given magnetic field strength and rotation frequency, swimmers can have more than one stable periodic orbit with different rotation axes. Finally, we demonstrate that one can improve the controllability of these types of microswimmers by adjusting the relative angle between the magnetic field and its axis of rotation.
Wu, Bin; Ji, Denggao; Guo, Zhenxi; Shen, Haibin; Zhang, Jianfei
2016-11-01
This article proposes a type of proportional navigation law design of plane-symmetrical vehicle with terminal attack angle constraint for over target flight. Firstly, the line of sight rotating rate and the velocity rotating rate model of the vehicle are expressed. Then, the attitude of the vehicle is constructed by the acceleration vector requirement of proportional navigation law. Accordingly, the guidance command uncertain issue can be avoided for plane-symmetrical vehicle over target flight. It guarantees high precision to hit the target. The effect and efficiency of the guidance law are shown by simulations of characteristic trajectories.
Baryon symmetric big bang cosmology
Stecker, F. W.
1978-01-01
Both the quantum theory and Einsteins theory of special relativity lead to the supposition that matter and antimatter were produced in equal quantities during the big bang. It is noted that local matter/antimatter asymmetries may be reconciled with universal symmetry by assuming (1) a slight imbalance of matter over antimatter in the early universe, annihilation, and a subsequent remainder of matter; (2) localized regions of excess for one or the other type of matter as an initial condition; and (3) an extremely dense, high temperature state with zero net baryon number; i.e., matter/antimatter symmetry. Attention is given to the third assumption, which is the simplest and the most in keeping with current knowledge of the cosmos, especially as pertains the universality of 3 K background radiation. Mechanisms of galaxy formation are discussed, whereby matter and antimatter might have collided and annihilated each other, or have coexisted (and continue to coexist) at vast distances. It is pointed out that baryon symmetric big bang cosmology could probably be proved if an antinucleus could be detected in cosmic radiation.
Symmetric Structure in Logic Programming
Jin-Zhao Wu; Harald Fecher
2004-01-01
It is argued that some symmetric structure in logic programs could be taken into account when implementing semantics in logic programming. This may enhance the declarative ability or expressive power of the semantics. The work presented here may be seen as representative examples along this line. The focus is on the derivation of negative information and some other classic semantic issues. We first define a permutation group associated with a given logic program. Since usually the canonical models used to reflect the common sense or intended meaning are minimal or completed models of the program, we expose the relationships between minimal models and completed models of the original program and its so-called G-reduced form newly-derived via the permutation group defined. By means of this G-reduced form, we introduce a rule to assume negative information termed G-CWA, which is actually a generalization of the GCWA. We also develop the notions of G-definite, G-hierarchical and G-stratified logic programs, which are more general than definite, hierarchical and stratified programs, and extend some well-known declarative and procedural semantics to them, respectively.
PT-Symmetric Quantum Electrodynamics
Bender, C M; Milton, K A; Shajesh, K V; Bender, Carl M.; Cavero-Pelaez, Ines; Milton, Kimball A.
2005-01-01
The Hamiltonian for quantum electrodynamics becomes non-Hermitian if the unrenormalized electric charge $e$ is taken to be imaginary. However, if one also specifies that the potential $A^\\mu$ in such a theory transforms as a pseudovector rather than a vector, then the Hamiltonian becomes PT symmetric. The resulting non-Hermitian theory of electrodynamics is the analog of a spinless quantum field theory in which a pseudoscalar field $\\phi$ has a cubic self-interaction of the form $i\\phi^3$. The Hamiltonian for this cubic scalar field theory has a positive spectrum, and it has recently been demonstrated that the time evolution of this theory is unitary. The proof of unitarity requires the construction of a new operator called C, which is then used to define an inner product with respect to which the Hamiltonian is self-adjoint. In this paper the corresponding C operator for non-Hermitian quantum electrodynamics is constructed perturbatively. This construction demonstrates the unitarity of the theory. Non-Hermit...
Substring-Searchable Symmetric Encryption
Chase Melissa
2015-06-01
Full Text Available In this paper, we consider a setting where a client wants to outsource storage of a large amount of private data and then perform substring search queries on the data – given a data string s and a search string p, find all occurrences of p as a substring of s. First, we formalize an encryption paradigm that we call queryable encryption, which generalizes searchable symmetric encryption (SSE and structured encryption. Then, we construct a queryable encryption scheme for substring queries. Our construction uses suffix trees and achieves asymptotic efficiency comparable to that of unencrypted suffix trees. Encryption of a string of length n takes O(λn time and produces a ciphertext of size O(λn, and querying for a substring of length m that occurs k times takes O(λm+k time and three rounds of communication. Our security definition guarantees correctness of query results and privacy of data and queries against a malicious adversary. Following the line of work started by Curtmola et al. (ACM CCS 2006, in order to construct more efficient schemes we allow the query protocol to leak some limited information that is captured precisely in the definition. We prove security of our substring-searchable encryption scheme against malicious adversaries, where the query protocol leaks limited information about memory access patterns through the suffix tree of the encrypted string.
Rotated balance in humans due to repetitive rotational movement.
Zakynthinaki, M S; Milla, J Madera; De Durana, A López Diaz; Martínez, C A Cordente; Romo, G Rodríguez; Quintana, M Sillero; Molinuevo, J Sampedro
2010-03-01
We show how asymmetries in the movement patterns during the process of regaining balance after perturbation from quiet stance can be modeled by a set of coupled vector fields for the derivative with respect to time of the angles between the resultant ground reaction forces and the vertical in the anteroposterior and mediolateral directions. In our model, which is an adaption of the model of Stirling and Zakynthinaki (2004), the critical curve, defining the set of maximum angles one can lean to and still correct to regain balance, can be rotated and skewed so as to model the effects of a repetitive training of a rotational movement pattern. For the purposes of our study a rotation and a skew matrix is applied to the critical curve of the model. We present here a linear stability analysis of the modified model, as well as a fit of the model to experimental data of two characteristic "asymmetric" elite athletes and to a "symmetric" elite athlete for comparison. The new adapted model has many uses not just in sport but also in rehabilitation, as many work place injuries are caused by excessive repetition of unaligned and rotational movement patterns.
Symmetric Partial Derivatives%对称偏导数
徐永平
2001-01-01
In this paper, symmetric partial derivatives and symmetric total differential of a function of several variables are defined. The relationship between partial derivative and the symmetric partial derivative, the total differential and the symmetric total derivative are discussed. By means of the concept of symmetric partial derivatives, the existence theorem of the total differential of a function of several is obtained.
侯刚; 陈明娟; 戎利民; 陈建庭; 陈昌燕
2011-01-01
Objective To explore the relationship between the physiological rotation of vertebral body and individual development by measuring of rotation angle of normal spine. Methods Pectoral CT data from 150 cases without clinical or radiologic evidence of scoliosis were used to measure vertebral axial rotation from T2 to T12. The data were divided into 3 groups based on different ages: infants (0～3y), juvenile (3～11y) and young(11-16y). The angle, defined between two lines that connected the junction of each lamina and the pedicle of the posterior junction of the two laminae, was firstly bisected by the third line. The angle of axial vertebral rotation was then measured as the angle between the obtained line and the reference sagittal plane. The reference sagittal line was defined as zero degrees rotation. Rotation to the right was defined as a positive angle,to the left as a negative angle. Results The average rotation angle ranged from(-1.24±1.80)° to (1.72±1.01)°in group infants, (-1.38±0.97)° to (1.18±1.36)° in group juvenile, and (-1.52±1.23)° to (2.03±1.22)° in group young. The rotation angle in group juvenile significantly less than that of group infants on T6(P＜0.01 ), and that of group juvenile significantly less than that of group youny on T7 (P=0.03). Conclusions It is revealed that the physiological rotation of vertebral occurred for the nonnal and nonscoliotic spine, and tends to be stable with the age increasing.%目的 研究椎体生理性旋转与个体发育之间的关系.方法 以150例因肺部或纵隔内疾病在我院行胸部CT检查的被证实无脊柱侧凸畸形的患者的CT图像为研究对象.分三个组,各50例,幼儿组年龄为0～3岁,少儿年组为3～11岁,青年组为11～16岁.各组男女比例为1/1.椎体旋转角度的测量采用HO等人提出的角平分线法进行测量.分别对各个年龄组T2～12椎体旋转度进行测量.结果 幼儿组椎体旋转角度为(-1.24±1.80)°～(1.72±1.01)°.少
The symmetric extendibility of quantum states
Nowakowski, Marcin L.
2016-09-01
Studies on the symmetric extendibility of quantum states have become particularly important in the context of the analysis of one-way quantum measures of entanglement, and the distillability and security of quantum protocols. In this paper we analyze composite systems containing a symmetric extendible part, with particular attention devoted to the one-way security of such systems. Further, we introduce a new one-way entanglement monotone based on the best symmetric approximation of a quantum state and the extendible number of a quantum state. We underpin these results with geometric observations about the structures of multi-party settings which posses substantial symmetric extendible components in their subspaces. The impossibility of reducing the maximal symmetric extendibility by means of the one-way local operations and classical communication method is pointed out on multiple copies. Finally, we state a conjecture linking symmetric extendibility with the one-way distillability and security of all quantum states, analyzing the behavior of a private key in the neighborhood of symmetric extendible states.
Random matrix theory and symmetric spaces
Caselle, M.; Magnea, U
2004-05-01
In this review we discuss the relationship between random matrix theories and symmetric spaces. We show that the integration manifolds of random matrix theories, the eigenvalue distribution, and the Dyson and boundary indices characterizing the ensembles are in strict correspondence with symmetric spaces and the intrinsic characteristics of their restricted root lattices. Several important results can be obtained from this identification. In particular the Cartan classification of triplets of symmetric spaces with positive, zero and negative curvature gives rise to a new classification of random matrix ensembles. The review is organized into two main parts. In Part I the theory of symmetric spaces is reviewed with particular emphasis on the ideas relevant for appreciating the correspondence with random matrix theories. In Part II we discuss various applications of symmetric spaces to random matrix theories and in particular the new classification of disordered systems derived from the classification of symmetric spaces. We also review how the mapping from integrable Calogero-Sutherland models to symmetric spaces can be used in the theory of random matrices, with particular consequences for quantum transport problems. We conclude indicating some interesting new directions of research based on these identifications.
Wada, Yoshiro; Nishiike, Suetaka; Kitahara, Tadashi; Yamanaka, Toshiaki; Imai, Takao; Ito, Taeko; Sato, Go; Matsuda, Kazunori; Kitamura, Yoshiaki; Takeda, Noriaki
2016-11-01
After repeated snowboard exercises in the virtual reality (VR) world with increasing time lags in trials 3-8, it is suggested that the adaptation to repeated visual-vestibulosomatosensory conflict in the VR world improved dynamic posture control and motor performance in the real world without the development of motion sickness. The VR technology was used and the effects of repeated snowboard exercise examined in the VR world with time lags between visual scene and body rotation on the head stability and slalom run performance during exercise in healthy subjects. Forty-two healthy young subjects participated in the study. After trials 1 and 2 of snowboard exercise in the VR world without time lag, trials 3-8 were conducted with 0.1, 0.2, 0.3, 0.4, 0.5, and 0.6 s time lags of the visual scene that the computer creates behind board rotation, respectively. Finally, trial 9 was conducted without time lag. Head linear accelerations and subjective slalom run performance were evaluated. The standard deviations of head linear accelerations in inter-aural direction were significantly increased in trial 8, with a time lag of 0.6 s, but significantly decreased in trial 9 without a time lag, compared with those in trial 2 without a time lag. The subjective scores of slalom run performance were significantly decreased in trial 8, with a time lag of 0.6 s, but significantly increased in trial 9 without a time lag, compared with those in trial 2 without a time lag. Motion sickness was not induced in any subjects.
A new family of exact and rotating solutions of fireball hydrodynamics
Csörgő, T
2013-01-01
A new class of analytic, exact, rotating, self-similar and surprisingly simple solutions of non-relativistic hydrodynamics are presented for a three-dimensionally expanding, spheroidally symmetric fireball. These results generalize earlier, non-rotating solutions for ellipsoidally symmetric fireballs with directional, three-dimensional Hubble flows. The solutions are presented for a general class of equations of state that includes the lattice QCD equations of state and may feature inhomogeneous temperature and corresponding density profiles.
Invalidity of Geometrical Interpretation of F-Spin Structure of Nuclear Rotations by Otsuka's View
Long, Guilu
1995-06-01
In Otsuka's view of nuclear rotations neutrons and protons are not rotating around a common axis, but rather around separate axis. In this letter, we pointed out that this invalidates the geometrical interpretation of F-spin structure of the neutron-proton interacting boson model, where the angle between the axis of symmetries of neutron ellipsoid and proton ellipsoid is used to determine whether a state is F-spin symmetric or mixed symmetric.
Mode-Coupling in Realistic Rotating Gravitational Collapse
Hod, S
2000-01-01
We analyze the mode-coupling phenomena in realistic rotating gravitational collapse. Physically, this phenomena is caused by the dragging of reference frames, due to the black-hole (or star's) rotation. It is shown that different modes become coupled during the rotating collapse. As a consequence, the asymptotic late-time tails are dominated by modes which, in general, have an angular distribution different from the original one. We show that a rotating Kerr black hole becomes ``bald'' slower than a spherically-symmetric Schwarzschild black hole. This paper considers gravitational, electromagnetic and neutrino fields propagating on a Kerr background.
Asymmetrical Body Perception: A Possible Role for Neural Body Representations
2009-01-01
Perception of one's body is related not only to the physical appearance of the body, but also to the neural representation of the body. The brain contains many body maps that systematically differ between right- and left-handed people. In general, the cortical representations of the right arm and right hand tend to be of greater area in the left hemisphere than in the right hemisphere for right-handed people, whereas these cortical representations tend to be symmetrical across hemispheres for...
A class of symmetric controlled quantum operations
Vaccaro, J A; Huelga, S F; Vaccaro, John A.
2001-01-01
Certain quantum gates, such as the controlled-NOT gate, are symmetric in terms of the operation of the control system upon the target system and vice versa. However, no operational criteria yet exist for establishing whether or not a given quantum gate is symmetrical in this sense. We consider a restricted, yet broad, class of two-party controlled gate operations for which the gate transforms a reference state of the target into one of an orthogonal set of states. We show that for this class of gates it is possible to establish a simple necessary and sufficient condition for the gate operation to be symmetric.
A class of symmetric controlled quantum operations
Vaccaro, John A.; Steuernagel, O.; Huelga, S.F. [Division of Physics and Astronomy, Department of Physical Sciences, University of Hertfordshire, Hatfield (United Kingdom)
2001-09-07
Certain quantum gates, such as the controlled-NOT gate, are symmetric in terms of the operation of the control system upon the target system and vice versa. However, no operational criteria yet exist for establishing whether or not a given quantum gate is symmetrical in this sense. We consider a restricted, yet broad, class of two-party controlled gate operations for which the gate transforms a reference state of the target into one of an orthogonal set of states. We show that for this class of gates it is possible to establish a simple necessary and sufficient condition for the gate operation to be symmetric. (author)
Nilpotent orbits in real symmetric pairs
Dietrich, Heiko; Ruggeri, Daniele; Trigiante, Mario
2016-01-01
In the classification of stationary solutions in extended supergravities with symmetric scalar manifolds, the nilpotent orbits of a real symmetric pair play an important role. In this paper we discuss two approaches to determining the nilpotent orbits of a real symmetric pair. We apply our methods to an explicit example, and thereby classify the nilpotent orbits of SL_2(R)^4 acting on the fourth tensor power of the natural 2-dimensional SL_2(R)-module. This makes it possible to classify all stationary solutions of the so-called STU-supergravity model.
A symmetric positive definite formulation for monolithic fluid structure interaction
Robinson-Mosher, Avi
2011-02-01
In this paper we consider a strongly coupled (monolithic) fluid structure interaction framework for incompressible flow, as opposed to a loosely coupled (partitioned) method. This requires solving a single linear system that combines the unknown velocities of the structure with the unknown pressures of the fluid. In our previous work, we were able to obtain a symmetric formulation of this coupled system; however, it was also indefinite, making it more difficult to solve. In fact in practice there have been cases where we have been unable to invert the system. In this paper we take a novel approach that consists of factoring the damping matrix of deformable structures and show that this can be used to obtain a symmetric positive definite system, at least to the extent that the uncoupled systems were symmetric positive definite. We use a traditional MAC grid discretization of the fluid and a fully Lagrangian discretization of the structures for the sake of exposition, noting that our procedure can be generalized to other scenarios. For the special case of rigid bodies, where there are no internal damping forces, we exactly recover the system of Batty et al. (2007) [4]. © 2010 Elsevier Inc.
Symmetrization in jellyfish: reorganization to regain function, and not lost parts.
Abrams, Michael J; Goentoro, Lea
2016-02-01
We recently reported a previously unidentified strategy of self-repair in the moon jellyfish Aurelia aurita. Rather than regenerating lost parts, juvenile Aurelia reorganize remaining parts to regain essential body symmetry. This process that we called symmetrization is rapid and frequent, and is not driven by cell proliferation or cell death. Instead, the swimming machinery generates mechanical forces that drive symmetrization. We found evidence for symmetrization across three other species of jellyfish (Chrysaora pacifica, Mastigias sp., and Cotylorhiza tuberculata). We propose reorganization to regain function without recovery of initial morphology as a potentially broad class of self-repair strategy beyond radially symmetrical animals, and discuss the implications of this finding on the evolution of self-repair strategies in animals.
Rotational spin Hall effect in a uniaxial crystal
Fadeyeva, Tatyana A.; Alexeyev, Constantine N.; Rubass, Alexander F.; Ivanov, Maksym O.; Zinov'ev, Alexey O.; Konovalenko, Victor L.; Volyar, Alexander V.
2012-04-01
We have considered the propagation process of the phase-matched array of singular beams through a uniaxial crystal. We have revealed that local beams in the array are rotated when propagating. However the right and left rotations are unequal. There are at least two processes responsible for the array rotation: the interference of local beams and the spatial depolarization. The interference takes place in the vortex birth and annihilation events forming the symmetrical part of the rotation. The depolarization process contributes to the asymmetry of the rotation that is called the rotational spin Hall effect. It can be brought to light due to the difference between the envelopes of the dependences of the angular displacement on the inclination angle of the local beams or the crystal length reaching the value some angular degree. The direction of the additional array rotation is exclusively defined by the handedness of the circular polarization in the initial beam array.
Continuation of periodic orbits in symmetric Hamiltonian and conservative systems
Galan-Vioque, J.; Almaraz, F. J. M.; Macías, E. F.
2014-12-01
We present and review results on the continuation and bifurcation of periodic solutions in conservative, reversible and Hamiltonian systems in the presence of symmetries. In particular we show how two-point boundary value problem continuation software can be used to compute families of periodic solutions of symmetric Hamiltonian systems. The technique is introduced with a very simple model example (the mathematical pendulum), justified with a theoretical continuation result and then applied to two non trivial examples: the non integrable spring pendulum and the continuation of the figure eight solution of the three body problem.
PT-Symmetric Quantum Field Theory
Milton, K A
2003-01-01
In the context of the PT-symmetric version of quantum electrodynamics, it is argued that the C operator introduced in order to define a unitary inner product has nothing to do with charge conjugation.
Symmetric centres of braided monoidal categories
无
2000-01-01
This paper introduces the concept of‘symmetric centres' of braided monoidal categories. Let H be a Hopf algebra with bijective antipode over a field k. We address the symmetric centre of the Yetter-Drinfel'd module category HH(yD) and show that a left Yetter-Drinfel'd module M belongs to the symmetric centre of HH(yD) if and only if M is trivial. We also study the symmetric centres of categories of representations of quasitriangular Hopf algebras and give a sufficient and necessary condition for the braid of H(M) to induce the braid of (H(H)(A),(○)A,A,φ,l,r), or equivalently, the braid of (A#H(H),(○)A,A,φ,l,r), where A is a quantum commutative H-module algebra.
Martingale Rosenthal inequalities in symmetric spaces
Astashkin, S V [Samara State University, Samara (Russian Federation)
2014-12-31
We establish inequalities similar to the classical Rosenthal inequalities for sequences of martingale differences in general symmetric spaces; a central role is played here by the predictable quadratic characteristic of a martingale. Bibliography: 26 titles.
Resistor Networks based on Symmetrical Polytopes
Moody, Jeremy; Aravind, P.K
2015-01-01
This paper shows how a method developed by Van Steenwijk can be generalized to calculate the resistance between any two vertices of a symmetrical polytope all of whose edges are identical resistors...
Spherically symmetric brane spacetime with bulk gravity
Chakraborty, Sumanta; SenGupta, Soumitra
2015-01-01
Introducing term in the five-dimensional bulk action we derive effective Einstein's equation on the brane using Gauss-Codazzi equation. This effective equation is then solved for different conditions on dark radiation and dark pressure to obtain various spherically symmetric solutions. Some of these static spherically symmetric solutions correspond to black hole solutions, with parameters induced from the bulk. Specially, the dark pressure and dark radiation terms (electric part of Weyl curvature) affect the brane spherically symmetric solutions significantly. We have solved for one parameter group of conformal motions where the dark radiation and dark pressure terms are exactly obtained exploiting the corresponding Lie symmetry. Various thermodynamic features of these spherically symmetric space-times are studied, showing existence of second order phase transition. This phenomenon has its origin in the higher curvature term with gravity in the bulk.
The limiting form of symmetric instability in geophysical flows
Griffiths, Stephen
2017-04-01
The stability of parallel flow with vertical shear, density stratification and background rotation is of fundamental importance in geophysical fluid dynamics. For a flow with vertical shear Uz and buoyancy frequency N, the dominant instability is typically a symmetric instability (sometimes known as slantwise convection) when 1/4 linear stability problem has been well studied for the case of constant Uz and N, and has some interesting mathematical properties (e.g., non-separable governing PDE, an absence of normal mode solutions in rectangular domains). Here, for the first time, a general theory of symmetric instability is given when Ri varies smoothly with height, thinking of the more realistic case where an unstable layer with Ri 1. The mathematical theory is developed for horizontally periodic disturbances to a basic state with arbitrary smooth N(z), but constant Uz. An asymptotic analysis is used to derive expressions for the most unstable mode, which occurs in the limit of large cross-isentropic wavenumber and takes the form of solutions trapped within the unstable layer; the same result is derived using an interesting generalised parcel dynamics argument, which explicitly shows how the trapping is linked to vertical variations of the potential vorticity. A separate asymptotic analysis is given for the small wavenumber limit, where only one such trapped mode may exist, as expected from the spectral theory of the Schrödinger equation. These two limiting results are shown to be consistent with an exact solution of the linear stability problem that can be obtained for a special choice of N(z). The asymptotic analysis can be extended to allow for weak diffusion at arbitrary Prandtl number, yielding an explicit diffusive scale selection at large wavenumber. Numerical simulations show that these weakly diffusive modes dominate the early stages of the nonlinear evolution of the symmetric instability.
Symmetric states: Their nonlocality and entanglement
Wang, Zizhu; Markham, Damian [CNRS LTCI, Département Informatique et Réseaux, Telecom ParisTech, 23 avenue d' Italie, CS 51327, 75214 Paris CEDEX 13 (France)
2014-12-04
The nonlocality of permutation symmetric states of qubits is shown via an extension of the Hardy paradox and the extension of the associated inequality. This is achieved by using the Majorana representation, which is also a powerful tool in the study of entanglement properties of symmetric states. Through the Majorana representation, different nonlocal properties can be linked to different entanglement properties of a state, which is useful in determining the usefulness of different states in different quantum information processing tasks.
Success and decisiveness on proper symmetric games
Freixas Bosch, Josep; Pons Vallès, Montserrat
2015-01-01
The final publication is available at Springer via http://dx.doi.org/10.1007/s10100-013-0332-5 This paper provides a complete study for the possible rankings of success and decisiveness for individuals in symmetric voting systems, assuming anonymous and independent probability distributions. It is proved that for any pair of symmetric voting systems it is always possible to rank success and decisiveness in opposite order whenever the common probability of voting for “acceptance...
Jian WANG
2009-01-01
The study of symmetric property in the L2-sense for the non-positive definite operator is motivated by the theory of probability and analysis. This paper presents some sufficient conditions for the existence of symmetric measure for Lévy type operator. Some new examples are illustrated. The present study is an important step for considering various ergodic properties and functional inequalities of Lévy type operator.
Scattering properties of PT-symmetric objects
Miri, Mohammad-Ali; Facao, Margarida; Abouraddy, Ayman F; Bakry, Ahmed; Razvi, Mir A N; Alshahrie, Ahmed; Alù, Andrea; Christodoulides, Demetrios N
2016-01-01
We investigate the scattering response of parity-time (PT) symmetric structures. We show that, due to the local flow of energy between gain and loss regions, such systems can deflect light in unusual ways, as a function of the gain/loss contrast. Such structures are highly anisotropic and their scattering patterns can drastically change as a function of the angle of incidence. In addition, we derive a modified optical theorem for PT-symmetric scattering systems, and discuss its ramifications.
Novel C3-symmetric molecular scaffolds with potential facial differentiation.
Hennrich, Gunther; Lynch, Vincent M; Anslyn, Eric V
2002-05-17
The conversion of 1,3,5-substituted benzene and mesitylene by electrophilic aromatic substitution and Sonogashira cross-coupling, respectively, furnished the C3-symmetric, hexasubstituted benzene derivatives 1 and 2 with an alternating substitution pattern. Based on the molecular scaffolds obtained, the two systems serve as model compounds for novel receptor molecules with distinct geometric features. X-ray structures have been obtained for 1 and 2, which are discussed in regard to their aptitude as receptor platforms or supramolecular building blocks. By looking at the rotational barriers for the functional groups placed around the molecular scaffolds by variable temperature 1H NMR spectroscopy, 1 and 2 turn out to exist in rapidly interconverting conformations. The alignment of these potential binding groups around the molecular scaffolds should be strongly biased by specific interactions with suitable guest molecules.
Mirror-Symmetric Matrices and Their Application
李国林; 冯正和
2002-01-01
The well-known centrosymmetric matrices correctly reflect mirror-symmetry with no component or only one component on the mirror plane. Mirror-symmetric matrices defined in this paper can represent mirror-symmetric structures with various components on the mirror plane. Some basic properties of mirror-symmetric matrices were studied and applied to interconnection analysis. A generalized odd/even-mode decomposition scheme was developed based on the mirror reflection relationship for mirror-symmetric multiconductor transmission lines (MTLs). The per-unit-length (PUL) impedance matrix Z and admittance matrix Y can be divided into odd-mode and even-mode PUL matrices. Thus the order of the MTL system is reduced from n to k and k+p, where p(≥0)is the conductor number on the mirror plane. The analysis of mirror-symmetric matrices is related to the theory of symmetric group, which is the most effective tool for the study of symmetry.
Can zonally symmetric inertial waves drive an oscillating mean flow?
Seelig, Torsten; Harlander, Uwe
2016-04-01
In the presentation [5] zonal mean flow excitation by inertial waves is studied in analogy to mean flow excitation by gravity waves [3] that plays an important role for the quasi-biennial oscillation in the equatorial atmosphere. In geophysical flows that are stratified and rotating, pure gravity and inertial waves correspond to the two limiting cases: gravity waves neglect rotation, inertial waves neglect stratification. The former are more relevant for fluids like the atmosphere, where stratification is dominant, the latter for the deep oceans or planet cores, where rotation dominates. In the present study a hierarchy of simple analytical and numerical models of zonally symmetric inertial wave-mean flow interactions is considered and the results are compared with data from a laboratory experiment [4]. The main findings can be summarised as follows: (i) when the waves are decoupled from the mean flow they just drive a retrograde (eastward) zonal mean flow, independent of the sign of the meridional phase speed; (ii) when coupling is present and the zonal mean flow is assumed to be steady, the waves can drive vertically alternating jets, but still, in contrast to the gravity wave case, the structure is independent of the sign of the meridional phase speed; (iii) when coupling is present and time-dependent zonal mean flows are considered the waves can drive vertically and temporarily oscillating mean flows. The comparison with laboratory data from a rotating annulus experiment shows a qualitative agreement. It appears that the experiment captures the basic elements of the inertial wave mean flow coupling. The results might be relevant to understand how the Equatorial Deep Jets can be maintained against dissipation [1, 2], a process currently discussed controversially. [1] Greatbatch, R., Brandt, P., Claus, M., Didwischus, S., Fu, Y.: On the width of the equatorial deep jets. J. Phys. Oceanogr. 42, 1729-1740 (2012) [2] Muench, J.E., Kunze, E.: Internal wave
Axially Symmetric Shear-free Fluids in $f(R,T)$ Gravity
Noureen, Ifra
2016-01-01
In this work we have discussed the implications of shear-free condition on axially symmetric anisotropic gravitating objects in $f(R,T)$ theory. Restricted axial symmetry ignoring rotation and reflection enteries is taken into account for establishment of instability range. Implementation of linear perturbation on constitutive modified dynamical equations yield evolution equation. This equation associates adiabatic index $\\Gamma$ with material and dark source components defining stable and unstable regions in Newtonian (N) and post-Newtonian (pN) approximations.
Bioreactor rotating wall vessel
2001-01-01
The NASA Bioreactor provides a low turbulence culture environment which promotes the formation of large, three-dimensional cell clusters. Due to their high level of cellular organization and specialization, samples constructed in the bioreactor more closely resemble the original tumor or tissue found in the body. The work is sponsored by NASA's Office of Biological and Physical Research. The bioreactor is managed by the Biotechnology Cell Science Program at NASA's Johnson Space Center (JSC). NASA-sponsored bioreactor research has been instrumental in helping scientists to better understand normal and cancerous tissue development. In cooperation with the medical community, the bioreactor design is being used to prepare better models of human colon, prostate, breast and ovarian tumors. Cartilage, bone marrow, heart muscle, skeletal muscle, pancreatic islet cells, liver and kidney are just a few of the normal tissues being cultured in rotating bioreactors by investigators. Cell constructs grown in a rotating bioreactor on Earth (left) eventually become too large to stay suspended in the nutrient media. In the microgravity of orbit, the cells stay suspended. Rotation then is needed for gentle stirring to replenish the media around the cells.
Bioreactor rotating wall vessel
2001-01-01
The NASA Bioreactor provides a low turbulence culture environment which promotes the formation of large, three-dimensional cell clusters. Due to their high level of cellular organization and specialization, samples constructed in the bioreactor more closely resemble the original tumor or tissue found in the body. The work is sponsored by NASA's Office of Biological and Physical Research. The bioreactor is managed by the Biotechnology Cell Science Program at NASA's Johnson Space Center (JSC). NASA-sponsored bioreactor research has been instrumental in helping scientists to better understand normal and cancerous tissue development. In cooperation with the medical community, the bioreactor design is being used to prepare better models of human colon, prostate, breast and ovarian tumors. Cartilage, bone marrow, heart muscle, skeletal muscle, pancreatic islet cells, liver and kidney are just a few of the normal tissues being cultured in rotating bioreactors by investigators. Cell constructs grown in a rotating bioreactor on Earth (left) eventually become too large to stay suspended in the nutrient media. In the microgravity of orbit, the cells stay suspended. Rotation then is needed for gentle stirring to replenish the media around the cells.
Deflection of light ray due to a charged body using Material Medium Approach
Roy, Saswati
2015-01-01
The gravitational deflection of light ray is an important prediction of General Theory of Relativity. In this paper we develop analytical expression of the deflection of light ray without any weak field approximation due to a charged gravitational body represented by Reissner_Nordstr\\"om (RN) and Janis-Newman-Winicour (JNW) space time geometry, using material medium approach. It is concluded that although both the geometries represent the charged, non-rotating, spherically symmetric gravitating body, but the effect of charge on the gravitational deflection is just opposite to each other. The gravitational deflection decreases with charge in the RN geometry and increases with charge in the JNW geometry. The calculations obtained here are compared with other methods done by different authors. The formalism is applied to an arbitrary selected pulsar PSRB1937+21 as a gravitating body, as a test case.
Wang, Fang; Chang, Chih-Hsuan; Nesbitt, David
2014-06-01
Hydroxymethyl radical (CH_2OH) plays an important role in combustion and environmental chemistry as a reactive intermediate. Reisler's group published the first rotationally resolved spectroscopy of CH_2OH with determined band origins for fundamental CH symmetric stretch state, CH asymmetric stretch state and OH stretch state, respectively. Here CH_2OH was first studied via sub-Doppler infrared spectroscopy in a slit-jet supersonic discharge expansion source. Rotationally resolved direct absorption spectra in the CH symmetric stretching mode were recorded. As a result of the low rotational temperature and sub-Doppler linewidths, the tunneling splittings due to the large amplitude of COH torsion slightly complicate the spectra. Each of the ground vibration state and the CH symmetric stretch state includes two levels. One level, with a 3:1 nuclear spin statistic ratio for Ka=0+/Ka=1+, is labeled as ``+". The other tunneling level, labeled as ``-", has Ka=0-/Ka=1- states with 1:3 nuclear spin statistics. Except for the Ka=0+ ← 0+ band published before, more bands (Ka=1+ ← 1+, Ka=0- ← 0- and Ka=1- ← 1-) were identified. The assigned transitions were fit to a Watson A-reduced symmetric top Hamiltonian to improve the accuracy of the band origin of CH symmetric state. The rotational parameters for both ground and CH symmetric stretch state were well determined. L. Feng, J. Wei and H. Reisler, J. Phys. Chem. A, Vol. 108. M. A. Roberts, E. N. Sharp-Williams and D. J. Nesbitt, J. Phys. Chem. A 2013, 117, 7042-7049
Rotation Axis Variation Due To Spin Orbit Resonance
Gallavotti, G
1993-01-01
Abstract: rotation axis variation due to spin orbit resonance: conference report; keywords: planetary precession, rigid body, chaos, KAM, Arnold diffusion, averaging, celestial mechanics, classical mechanics, large deviations
Generation of zonal flows in rotating fluids and magnetized plasmas
Juul Rasmussen, J.; Garcia, O.E.; Naulin, V.
2006-01-01
contribution the generation of zonal flows will be illustrated in a simple fluid experiment performed in a rotating container with radial symmetric bottom topography. An effective mixing that homogenizes the potential vorticity in the fluid layer will lead to the replacement of the high-potential vorticity...
Lagrange mesh, relativistic flux tube, and rotating string
Buisseret, F.; Semay, C.
2004-01-01
The Lagrange mesh method is a very accurate and simple procedure to compute eigenvalues and eigenfunctions of nonrelativistic and semirelativistic Hamiltonians. We show here that it can be used successfully to solve the equations of both the relativistic flux tube model and the rotating string model, in the symmetric case. Verifications of the convergence of the method are given.
Lagrange mesh, relativistic flux tube, and rotating string.
Buisseret, Fabien; Semay, Claude
2005-02-01
The Lagrange mesh method is a very accurate and simple procedure to compute eigenvalues and eigenfunctions of nonrelativistic and semirelativistic Hamiltonians. We show here that it can be used successfully to solve the equations of both the relativistic flux tube model and the rotating string model, in the symmetric case. Verifications of the convergence of the method are given.
Nutational Oscillatory Effect of the Test Body in Space Equivalence Principle Experiments
SHAO Cheng-Gang; ZHANG Yuan-Zhong; LUO Jun
2004-01-01
The significance of quadrupole gravitational force is discussed for test .mass in equivalence principle (EP),and the angular moment acting on a cylindrically symmetrical body due to quadrupole force is calculated, which will result in nutational oscillatory effect. The oscillations contain a perturbation with the same frequency of EP violation signal, which is mitigated by two different methods as in Galileo Galilei (GG) mission and μSCOPE. In GG the sensor for readout is sensitive to differential forces in the orbital plane perpendicular to spin axis of test cylinders. In order to mitigate the nutational oscillatory effect, test mass should be rapidly rotated with the spin axis. However, in μSCOPE,the readout sensitive axis is the symmetry axis in the orbital plane. This nutational oscillation will produce a second order effect in the rotation amplitude at twice the signal frequency, and could be subtracted easily, too.
Calculating pure rotational transitions of water molecule with a simple Lanczos method
Pranab Sarkar
2001-04-01
We have calculated pure rotational transitions of water molecule from a kinetic energy operator (KEO) with the -axis perpendicular to the molecular plane. We have used rotational basis functions which are linear combinations of symmetric top functions so that all matrix elements are real. The calculated spectra agree well with the observed values.
Symmetric cryptographic protocols for extended millionaires' problem
LI ShunDong; WANG DaoShun; DAI YiQi
2009-01-01
Yao's millionaires' problem is a fundamental problem in secure multiparty computation, and its solutions have become building blocks of many secure multiparty computation solutions. Unfortunately,most protocols for millionaires' problem are constructed based on public cryptography, and thus are inefficient. Furthermore, all protocols are designed to solve the basic millionaires' problem, that is,to privately determine which of two natural numbers is greater. If the numbers are real, existing solutions do not directly work. These features limit the extensive application of the existing protocols. This study introduces and refines the first symmetric cryptographic protocol for the basic millionaires' problem, and then extends the symmetric cryptographic protocol to privately determining which of two real numbers is greater, which are called the extended millionaires' problem, and proposes corresponding Constructed based on symmetric cryptography, these protocols are very efficient.
Chiral light by symmetric optical antennas
Mekonnen, Addis; Zubritskaya, Irina; Jönsson, Gustav Edman; Dmitriev, Alexandre
2014-01-01
Chirality is at the origin of life and is ubiquitous in nature. An object is deemed chiral if it is non-superimposable with its own mirror image. This relates to how circularly polarized light interacts with such object, a circular dichroism, the differential absorption of right and left circularly polarized light. According to the common understanding in biology, chemistry and physics, the circular dichroism results from an internal chiral structure or external symmetry breaking by illumination. We show that circular dichroism is possible with simple symmetric optical nanoantennas at symmetric illumination. We experimentally and theoretically demonstrate that two electromagnetic dipole-like modes with a phase lag, in principle, suffice to produce circular dichroism in achiral structure. Examples of the latter are all visible spectrum optical nanoantennas, symmetric nanoellipses and nanodimers. The simplicity and generality of this finding reveal a whole new significance of the electromagnetic design at a nan...
The Robust Assembly of Small Symmetric Nanoshells.
Wagner, Jef; Zandi, Roya
2015-09-01
Highly symmetric nanoshells are found in many biological systems, such as clathrin cages and viral shells. Many studies have shown that symmetric shells appear in nature as a result of the free-energy minimization of a generic interaction between their constituent subunits. We examine the physical basis for the formation of symmetric shells, and by using a minimal model, demonstrate that these structures can readily grow from the irreversible addition of identical subunits. Our model of nanoshell assembly shows that the spontaneous curvature regulates the size of the shell while the mechanical properties of the subunit determine the symmetry of the assembled structure. Understanding the minimum requirements for the formation of closed nanoshells is a necessary step toward engineering of nanocontainers, which will have far-reaching impact in both material science and medicine.
INERTIA SETS OF SYMMETRIC SIGN PATTERN MATRICES
无
2001-01-01
A sign pattern matrix is a matrixwhose entries are from the set {+ ,- ,0}. The symmetric sign pattern matrices that require unique inertia have recently been characterized. The purpose of this paper is to more generally investigate the inertia sets of symmetric sign pattern matrices. In particular, nonnegative fri-diagonal sign patterns and the square sign pattern with all + entries are examined. An algorithm is given for generating nonnegative real symmetric Toeplitz matrices with zero diagonal of orders n≥3 which have exactly two negative eigenvalues. The inertia set of the square pattern with all + off-diagonal entries and zero diagonal entries is then analyzed. The types of inertias which can be in the inertia set of any sign pattern are also obtained in the paper. Specifically, certain compatibility and consecutiveness properties are established.
Symmetric States on the Octonionic Bloch Ball
Graydon, Matthew
2012-02-01
Finite-dimensional homogeneous self-dual cones arise as natural candidates for convex sets of states and effects in a variety of approaches towards understanding the foundations of quantum theory in terms of information-theoretic concepts. The positive cone of the ten-dimensional Jordan-algebraic spin factor is one particular instantiation of such a convex set in generalized frameworks for quantum theory. We consider a projection of the regular 9-simplex onto the octonionic projective line to form a highly symmetric structure of ten octonionic quantum states on the surface of the octonionic Bloch ball. A uniform subnormalization of these ten symmetric states yields a symmetric informationally complete octonionic quantum measurement. We discuss a Quantum Bayesian reformulation of octonionic quantum formalism for the description of two-dimensional physical systems. We also describe a canonical embedding of the octonionic Bloch ball into an ambient space for states in usual complex quantum theory.
Local neighborliness of the symmetric moment curve
Lee, Seung Jin
2011-01-01
A centrally symmetric analogue of the cyclic polytope, the bicyclic polytope, was defined in [BN08]. The bicyclic polytope is defined by the convex hull of finitely many points on the symmetric moment curve where the set of points has a symmetry about the origin. In this paper, we study the Barvinok-Novik orbitope, the convex hull of the symmetric moment curve. It was proven in [BN08] that the orbitope is locally $k$-neighborly, that is, the convex hull of any set of $k$ distinct points on an arc of length not exceeding $\\phi_k$ in $\\mathbb{S}^1$ is a $(k-1)$-dimensional face of the orbitope for some positive constant $\\phi_k$. We prove that we can choose $\\phi_k $ bigger than $\\gamma k^{-3/2} $ for some positive constant $\\gamma$.
Revisiting the Optical PT-Symmetric Dimer
José Delfino Huerta Morales
2016-08-01
Full Text Available Optics has proved a fertile ground for the experimental simulation of quantum mechanics. Most recently, optical realizations of PT -symmetric quantum mechanics have been shown, both theoretically and experimentally, opening the door to international efforts aiming at the design of practical optical devices exploiting this symmetry. Here, we focus on the optical PT -symmetric dimer, a two-waveguide coupler where the materials show symmetric effective gain and loss, and provide a review of the linear and nonlinear optical realizations from a symmetry-based point of view. We go beyond a simple review of the literature and show that the dimer is just the smallest of a class of planar N-waveguide couplers that are the optical realization of the Lorentz group in 2 + 1 dimensions. Furthermore, we provide a formulation to describe light propagation through waveguide couplers described by non-Hermitian mode coupling matrices based on a non-Hermitian generalization of the Ehrenfest theorem.
Revisiting the optical $PT$-symmetric dimer
Morales, J D Huerta; López-Aguayo, S; Rodríguez-Lara, B M
2016-01-01
Optics has proved a fertile ground for the experimental simulation of quantum mechanics. Most recently, optical realizations of $\\mathcal{PT}$-symmetric quantum mechanics have been shown, both theoretically and experimentally, opening the door to international efforts aiming at the design of practical optical devices exploiting this symmetry. Here, we focus on the optical $\\mathcal{PT}$-symmetric dimer, a two-waveguide coupler were the materials show symmetric effective gain and loss, and provide a review of the linear and nonlinear optical realizations from a symmetry based point of view. We go beyond a simple review of the literature and show that the dimer is just the smallest of a class of planar $N$-waveguide couplers that are the optical realization of Lorentz group in 2+1 dimensions. Furthermore, we provide a formulation to describe light propagation through waveguide couplers described by non-Hermitian mode coupling matrices based on a non-Hermitian generalization of Ehrenfest theorem.
PT-Symmetric Optomechanically-Induced Transparency
Jing, H; Özdemir, S K; Zhang, J; Lü, X -Y; Peng, B; Yang, L; Nori, F
2014-01-01
Optomechanically-induced transparency (OMIT) and the associated slow-light propagation provide the basis for storing photons in nanofabricated phononic devices. Here we study OMIT in parity-time (PT)-symmetric microresonators with a tunable gain-to-loss ratio. This system features a reversed, non-amplifying transparency: inverted-OMIT. When the gain-to-loss ratio is steered, the system exhibits a transition from the PT-symmetric phase to the broken-PT-symmetric phase. We show that by tuning the pump power at fixed gain-to-loss ratio or the gain-to-loss ratio at fixed pump power, one can switch from slow to fast light and vice versa. Moreover, the presence of PT-phase transition results in the reversal of the pump and gain dependence of transmission rates. These features provide new tools for controlling light propagation using optomechanical devices.
Radiative corrections in symmetrized classical electrodynamics
Van Meter JR; Kerman; Chen; Hartemann
2000-12-01
The physics of radiation reaction for a point charge is discussed within the context of classical electrodynamics. The fundamental equations of classical electrodynamics are first symmetrized to include magnetic charges: a double four-potential formalism is introduced, in terms of which the field tensor and its dual are employed to symmetrize Maxwell's equations and the Lorentz force equation in covariant form. Within this framework, the symmetrized Dirac-Lorentz equation is derived, including radiation reaction (self-force) for a particle possessing both electric and magnetic charge. The connection with electromagnetic duality is outlined, and an in-depth discussion of nonlocal four-momentum conservation for the wave-particle system is given.
Symmetry theorems via the continuous steiner symmetrization
L. Ragoub
2000-06-01
Full Text Available Using a new approach due to F. Brock called the Steiner symmetrization, we show first that if $u$ is a solution of an overdetermined problem in the divergence form satisfying the Neumann and non-constant Dirichlet boundary conditions, then $Omega$ is an N-ball. In addition, we show that we can relax the condition on the value of the Dirichlet boundary condition in the case of superharmonicity. Finally, we give an application to positive solutions of some semilinear elliptic problems in symmetric domains for the divergence case.
Synthesis of cyclically symmetric five-ports
Guldbrandsen, Tom
1994-01-01
A class of matched, symmetric five-ports have been synthesized by solving the circular cylindrical wave equation. Among the solutions are chosen those for which the match condition is fulfilled over the broadest bandwidth. Bandwidths up to +/-20% have been found......A class of matched, symmetric five-ports have been synthesized by solving the circular cylindrical wave equation. Among the solutions are chosen those for which the match condition is fulfilled over the broadest bandwidth. Bandwidths up to +/-20% have been found...
Active Sound Localization in a Symmetric Environment
Jordan Brindza
2013-07-01
Full Text Available Localization for humanoid robots becomes difficult when events that disrupt robot positioning information occur. This holds especially true in symmetric environments because landmark data may not be sufficient to determine orientation. We propose a system of localizing humanoid robots in a known, symmetric environment using a Rao-Blackwellized particle filter and a sound localization system. This system was used in the RoboCup Standard Platform League, and has been found to reduce the amount of own-goals scored as compared with the previously used localization system without sound.
Time-Symmetric Approach to Gravity
Chu, S Y
1998-01-01
Quantization of the time symmetric system of interacting strings requires that gravity, just as electromagnetism in Wheeler-Feynman's time symmetric electro- dynamics, also be an "adjunct field" instead of an independent entity. The "adjunct field" emerges, at a scale large compared to that of the strings, as a "statistic" that summarizes how the string positions in the underlying space- time are "compactified" into those in Minkowski space. We are able to show, WITHOUT adding a scalar curvature term to the string action, that the "adjunct gravitational field" satisfies Einstein's equation with no cosmological term.
Benign symmetric lipomatosis of the knees
Zhiqiang Yin; Di Wu; Yixin Ge; Meihua Zhang; Zhigang Bi; Dan Luo
2008-01-01
Benign symmetric lipomatosis(BSL) is a rare disease characterized by the presence of multiple, symmetric and nonencapsulated fat masses in the face, neck and other areas. It is commonly seen in middle-aged Caucasian Mediterranean males, while its etiology is still not clear. The majority of the patients with BSL have a history of alcohol abuse and hepatopathy. BSL of the limbs is very rare. This article reports a unique case of a 60-year-old Chinese woman with involvement of the knees confirmed by the results of magnetic resonance imaging(MRI) and histopathology, which was not described previously in published literatures.
Inflation in spherically symmetric inhomogeneous models
Stein-Schabes, J.A.
1986-11-01
Exact analytical solutions of Einstein's equations are found for a spherically symmetric inhomogeneous metric in the presence of a massless scalar field with a flat potential. The process of isotropization and homogenization is studied in detail. It is found that the time dependence of the metric becomes de Sitter for large times. Two cases are studied. The first deals with a homogeneous scalar field, while the second with a spherically symmetric inhomogeneous scalar field. In the former case the metric is of the Robertson-Walker form, while the latter is intrinsically inhomogeneous. 16 refs.
... this page: //medlineplus.gov/ency/patientinstructions/000357.htm Rotator cuff exercises To use the sharing features on this ... gov/pubmed/25560729 . Read More Frozen shoulder Rotator cuff problems Rotator cuff repair Shoulder arthroscopy Shoulder CT scan Shoulder ...
Ivanovski, S. L.; Zakharov, V. V.; Della Corte, V.; Crifo, J.-F.; Rotundi, A.; Fulle, M.
2017-01-01
In-situ measurements of individual dust grain parameters in the immediate vicinity of a cometary nucleus are being carried by the Rosetta spacecraft at comet 67P/Churyumov-Gerasimenko. For the interpretations of these observational data, a model of dust grain motion as realistic as possible is requested. In particular, the results of the Stardust mission and analysis of samples of interplanetary dust have shown that these particles are highly aspherical, which should be taken into account in any credible model. The aim of the present work is to study the dynamics of ellipsoidal shape particles with various aspect ratios introduced in a spherically symmetric expanding gas flow and to reveal the possible differences in dynamics between spherical and aspherical particles. Their translational and rotational motion under influence of the gravity and of the aerodynamic force and torque is numerically integrated in a wide range of physical parameters values including those of comet 67P/Churyumov-Gerasimenko. The main distinctions of the dynamics of spherical and ellipsoidal particles are discussed. The aerodynamic characteristics of the ellipsoidal particles, and examples of their translational and rotational motion in the postulated gas flow are presented.
The Boltzmann equation near a rotational local Maxwellian
Kim, Chanwoo
2011-01-01
In rotationally symmetric domains, the Boltzmann equation with specular reflection boundary condition has a special type of equilibrium states called the rotational local Maxwellian which, unlike the uniform Maxwellian, has an additional term related to the angular momentum of the gas. In this paper, we consider the initial boundary value problem of the Boltzmann equation near the rotational local Maxwellian. Based on the L2-L1 framework of [12], we establish the global well-posedness and the convergence toward such equilibrium states.
Stability of spherically symmetric, charged black holes and multipole moments for stationary systems
Gursel, Yekta
This dissertation is written in two parts. Part I deals with the question of stability of a spherically symmetric, charged black hole against scalar, electromagnetic, and gravitational perturbations. It consists of two papers written in collaboration with Igor D. NoVikov, Vernon D. Sandberg and A. A. Starobinsky. In these papers we describe the dynamical evolution of these perturbations on the interior of a Reissner-Nordstrom black hole. The instability of the hole's Cauchy horizon is discussed in detail in terms of the energy densities of the test fields as measured by a freely falling observer approaching the Cauchy horizon. We conclude that the Cauchy horizon of the analytically extended Reissner-Nordstrom solution is highly unstable and not a physical feature of a realistic gravitational collapse. Part II of this dissertation addresses two problems closely connected with muitipole structure of stationary, asymptotically flat spacetimes. It consists of two papers written in collaboration with Kip S. Thorne despite the fact that his name does not appear on one of them. The first one (Paper III in this thesis) shows the equivalence of the moments defined by Kip S. Thorne and the moments defined by Robert Geroch and Richard Hansen. The second (Paper IV in this thesis) proves a conjecture by Kip S. Thorne: In the limit of "slow" motion, general relativistic gravity produces no changes whatsoever in the classical Euler equations of rigid body motion. We prove this conjecture by giving an algorithm for generating rigidly rotating solutions of Einstein's equations from nonrotating, static solutions.
Magnetic damping of rotation. [in satellites
Opik, E. J.
1977-01-01
Based on Wilson's (1977) article on the magnetic effects on space vehicles and other celestial bodies, the magnetic damping of rotation is considered. The inadequacy of the interstellar magnetic field in overcoming solar wind shielding and thus influencing the rotation of bodies is described. The ionospheric shielding of the interstellar field is discussed along with the permeability and magnetic damping by the solar or stellar wind. Star formation and angular momentum is discussed and attention is given to the magnetic damping of unshielded small bodies. Calculations of the rate for damping through random particle impact are made. Theories concerning the rotation of asteroids and the origin of meteorites are reviewed. The shielding process of ionospheric plasmas is outlined and the damping effect of the geomagnetic field on the rotation of artificial satellites is evaluated.
Rotating Cavitation Supression Project
National Aeronautics and Space Administration — FTT proposes development of a rotating cavitation (RC) suppressor for liquid rocket engine turbopump inducers. Cavitation instabilities, such as rotating...
Design of a deployment rotation mechanism for microsatellite
Abdelal, G.F.; Bakr Elhady, A.; Kassab, M.
2009-01-01
Solar array rotation mechanism provides a hinged joint between the solar panel and satellite body, smooth rotation of the solar array into deployed position and its fixation in this position. After unlocking of solar panel (while in orbit), rotation bracket turns towards ready-to-work position under
Design of a deployment rotation mechanism for microsatellite
Abdelal, G.F.; Bakr Elhady, A.; Kassab, M.
2009-01-01
Solar array rotation mechanism provides a hinged joint between the solar panel and satellite body, smooth rotation of the solar array into deployed position and its fixation in this position. After unlocking of solar panel (while in orbit), rotation bracket turns towards ready-to-work position under
Degenerative full thickness rotator cuff tears : Towards optimal management
Lambers Heerspink, Frederik
2016-01-01
The shoulder is one of the most complex joints in the body. Besides a wide range of motion it also has to be stable. The rotator cuff is a major stabiliser of the glenohumoral joint. With increasing age rotator cuff tears are common. Successful treatment is described following surgical (rotator cuff
Luo, Shao-Kai; Dai, Yun; Zhang, Xiao-Tian; He, Jin-Man
2016-10-01
In this paper, we present the fractional Mei symmetrical method of finding conserved quantity and explore its applications to physics. For the fractional generalized Hamiltonian system, we introduce the fractional infinitesimal transformation of Lie groups and, under the transformation, give the fractional Mei symmetrical definition, criterion and determining equation. Then, we present the fractional Mei symmetrical theorem of finding conserved quantity. As the fractional Mei symmetrical method's applications, we respectively find the conserved quantities of a fractional general relativistic Buchduhl model, a fractional three-body model and a fractional Robbins-Lorenz model.
Superdeformed rotational bands in the presence of Y44 deformation
Hamamoto, Ikuko; Mottelson, Ben
1994-08-01
The observation of ΔI = 4 staggering in the rotational spectra of superdeformed nuclei suggests the occurence of Y44 deformations in the nuclear shape with associated C4 v point-symmetry for the rotational Hamiltonian. We have investigated the general class of Hamiltonians with such symmetry. In addition, we require the axially symmetric terms to favour rotation about an axis that is perpendicular to the long axis of nuclear shape. The δI = 4 staggering can indeed result from the tunneling between the four equivalent minima that occur in the plane perpendicular to the superdeformation symmetry axis, but the occurence of this effect is a subtle matter depending sensitively on the axially symmetric terms in the Hamiltonian.
Fields, Strings, Matrices and Symmetric Products
Dijkgraaf, R.
1999-01-01
In these notes we review the role played by the quantum mechanics and sigma models of symmetric product spaces in the light-cone quantization of quantum field theories, string theory and matrix theory. Lectures given at the Institute for Theoretical Physics, UC Santa Barbara, January 1998 and the Spring School on String Theory and Mathematics, Harvard University, May 1998.
How Symmetrical Assumptions Advance Strategic Management Research
Foss, Nicolai Juul; Hallberg, Hallberg
2014-01-01
We develop the case for symmetrical assumptions in strategic management theory. Assumptional symmetry obtains when assumptions made about certain actors and their interactions in one of the application domains of a theory are also made about this set of actors and their interactions in other appl...
Noncommutative spherically symmetric spacetimes at semiclassical order
Fritz, Christopher
2016-01-01
Working within the recent formalism of Poisson-Riemannian geometry, we completely solve the case of generic spherically symmetric metric and spherically symmetric Poisson-bracket to find a unique answer for the quantum differential calculus, quantum metric and quantum Levi-Civita connection at semiclassical order $O(\\lambda)$. Here $\\lambda$ is the deformation parameter, plausibly the Planck scale. We find that $r,t,dr,dt$ are all forced to be central, i.e. undeformed at order $\\lambda$, while for each value of $r,t$ we are forced to have a fuzzy sphere of radius $r$ with a unique differential calculus which is necessarily nonassociative at order $\\lambda^2$. We give the spherically symmetric quantisation of the FLRW cosmology in detail and also recover a previous analysis for the Schwarzschild black hole, now showing that the quantum Ricci tensor for the latter vanishes at order $\\lambda$. The quantum Laplace-Beltrami operator for spherically symmetric models turns out to be undeformed at order $\\lambda$ whi...
efficient and convenient synthesis of symmetrical carboxylic ...
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An efficient and convenient procedure for the synthesis of symmetrical .... solution was stirred for 16 h at 35 °C followed by filtration and washing with ... obtained hydrous zirconia sample was ground to fine powder and immersed in 1 M H2SO4 ..... Ullmann's Encyclopedia of Industrial Chemistry, Wiley-VCH: Weinheim; 2002.
Designing new symmetrical facial oligothiophene amphiphiles
Janeliunas, Dainius; Eelkema, Rienk; Nieto-Ortega, Belén; Ramírez Aguilar, Francisco J; López Navarrete, Juan T; van der Mee, Lars; Stuart, Marc C A; Casado, Juan; van Esch, Jan H
2013-01-01
In this study we designed a new class of symmetrical facial oligothiophene amphiphiles, which could be obtained in fewer steps than for previously reported analogues, but still possess the specific substituent sequence to control their backbone curvature. This novel design allows the late-stage intr
Tautological Integrals on Symmetric Products of Curves
Zhi Lan WANG
2016-01-01
We propose a conjecture on the generating series of Chern numbers of tautological bundles on symmetric products of curves and establish the rank 1 and rank −1 case of this conjecture. Thus we compute explicitly the generating series of integrals of Segre classes of tautological bundles of line bundles on curves, which has a similar structure as Lehn’s conjecture for surfaces.
Jordan algebraic approach to symmetric optimization
Vieira, M.V.C.
2007-01-01
In this thesis we present a generalization of interior-point methods for linear optimization based on kernel functions to symmetric optimization. It covers the three standard cases of conic optimization: linear optimization, second-order cone optimization and semi-definite optimization. We give an
Symmetrized solutions for nonlinear stochastic differential equations
G. Adomian
1981-01-01
Full Text Available Solutions of nonlinear stochastic differential equations in series form can be put into convenient symmetrized forms which are easily calculable. This paper investigates such forms for polynomial nonlinearities, i.e., equations of the form Ly+ym=x where x is a stochastic process and L is a linear stochastic operator.
Fourier inversion on a reductive symmetric space
Ban, E.P. van den
2001-01-01
Let X be a semisimple symmetric space. In previous papers, [8] and [9], we have dened an explicit Fourier transform for X and shown that this transform is injective on the space C 1 c (X) ofcompactly supported smooth functions on X. In the present paper, which is a continuation of these papers, we e
The Symmetric Rudin-Shapiro Transform
Harbo, Anders La-Cour
2003-01-01
A method for constructing spread spectrum sequences is presented. The method is based on a linear, orthogonal, symmetric transform, the Rudin-Shapiro transform (RST), which is in many respects quite similar to the Haar wavelet packet transform. The RST provides the means for generating large sets...
The Symmetric Rudin-Shapiro Transform
Harbo, Anders La-Cour
2003-01-01
A method for constructing spread spectrum sequences is presented. The method is based on a linear, orthogonal, and symmetric transform given as the Rudin-Shapiro transform (RST), which is in many respects quite similar to the Haar wavelet packet transform. The RST provides the means for generating...
Unary self-verifying symmetric difference automata
Marais, Laurette
2016-07-01
Full Text Available We investigate self-verifying nondeterministic finite automata, in the case of unary symmetric difference nondeterministic finite automata (SV-XNFA). We show that there is a family of languages Ln=2 which can always be represented non...
Exterior Powers of Symmetric Bilinear Forms
Seán McGarraghy
2002-01-01
We study exterior powers of classes of symmetric bilinear forms in the Witt-Grothendieck ring of a field of characteristic not equal to 2, and derive their basic properties. The exterior powers are used to obtain annihilating polynomials for quadratic forms in the Witt ring.
PT -symmetric model of immune response
Bender, Carl M.; Ghatak, Ananya; Gianfreda, Mariagiovanna
2017-01-01
The study of PT -symmetric physical systems began in 1998 as a complex generalization of conventional quantum mechanics, but beginning in 2007 experiments began to be published in which the predicted PT phase transition was clearly observed in classical rather than in quantum-mechanical systems. This paper examines the classical PT phase transition in dynamical-system models that are moderately accurate representations of antigen-antibody systems. A surprising conclusion that can be drawn from these models is that it might be possible treat a serious disease in which the antigen concentration grows out of bounds (and the host dies) by injecting a small dose of a second (different) antigen. In this case a PT -symmetric analysis shows there are two possible favorable outcomes. In the unbroken-PT -symmetric phase the disease becomes chronic and is no longer lethal, while in the appropriate broken-PT -symmetric phase the concentration of lethal antigen goes to zero and the disease is completely cured.
Realizability of stationary spherically symmetric transonic accretion
Ray, A K; Ray, Arnab K.
2002-01-01
The spherically symmetric stationary transonic (Bondi) flow is considered a classic example of an accretion flow. This flow, however, is along a separatrix, which is usually not physically realizable. We demonstrate, using a pedagogical example, that it is the dynamics which selects the transonic flow.
Adaptively Secure Computationally Efficient Searchable Symmetric Encryption
Sedghi, S.; Liesdonk, van P.; Doumen, J.M.; Hartel, P.H.; Jonker, W.
2009-01-01
Searchable encryption is a technique that allows a client to store documents on a server in encrypted form. Stored documents can be retrieved selectively while revealing as little information as possible to the server. In the symmetric searchable encryption domain, the storage and the retrieval are
On balanced truncation for symmetric nonlinear systems
Fujimoto, K.; Scherpen, Jacqueline M.A.
2014-01-01
This paper is concerned with model order reduction based on balanced realization for symmetric nonlinear systems. A new notion of symmetry for nonlinear systems was characterized recently. It plays an important role in linear systems theory and is expected to provide new insights to nonlinear system
Fundamental group of locally symmetric varieties
Sankaran, G K
1995-01-01
Take a bounded symmetric domain D and an arithmetic subgroup \\Gamma of {\\rm Aut}(D). Take the quotient D/\\Gamma, compactify and resolve the singularities. We study the fundamental group of the compact complex manifolds that result from this procedure, and in particular the case of Siegel modular threefolds.
Qp-spaces on bounded symmetric domains
Jonathan Arazy
2008-01-01
Full Text Available We generalize the theory of Qp spaces, introduced on the unit disc in 1995 by Aulaskari, Xiao and Zhao, to bounded symmetric domains in Cd, as well as to analogous Moebius-invariant function spaces and Bloch spaces defined using higher order derivatives; the latter generalization contains new results even in the original context of the unit disc.
Onthe static and spherically symmetric gravitational field
Gottlieb, Ioan; Maftei, Gheorghe; Mociutchi, Cleopatra
Starting from a generalization of Einstein 's theory of gravitation, proposed by one of the authors (Cleopatra Mociutchi), the authors study a particular spherical symmetric case. Among other one obtain the compatibility conditions for the existence of the static and spherically symmetruic gravitational filed in the case of extended Einstein equation.
Some aspects of symmetric Gamma process mixtures
Naulet, Zacharie; Barat, Eric
2015-01-01
In this article, we present some specific aspects of symmetric Gamma process mixtures for use in regression models. We propose a new Gibbs sampler for simulating the posterior and we establish adaptive posterior rates of convergence related to the Gaussian mean regression problem.
Super-symmetric informationally complete measurements
Zhu, Huangjun, E-mail: hzhu@pitp.ca
2015-11-15
Symmetric informationally complete measurements (SICs in short) are highly symmetric structures in the Hilbert space. They possess many nice properties which render them an ideal candidate for fiducial measurements. The symmetry of SICs is intimately connected with the geometry of the quantum state space and also has profound implications for foundational studies. Here we explore those SICs that are most symmetric according to a natural criterion and show that all of them are covariant with respect to the Heisenberg–Weyl groups, which are characterized by the discrete analog of the canonical commutation relation. Moreover, their symmetry groups are subgroups of the Clifford groups. In particular, we prove that the SIC in dimension 2, the Hesse SIC in dimension 3, and the set of Hoggar lines in dimension 8 are the only three SICs up to unitary equivalence whose symmetry groups act transitively on pairs of SIC projectors. Our work not only provides valuable insight about SICs, Heisenberg–Weyl groups, and Clifford groups, but also offers a new approach and perspective for studying many other discrete symmetric structures behind finite state quantum mechanics, such as mutually unbiased bases and discrete Wigner functions.
Convexity and symmetrization in relativistic theories
Ruggeri, T.
1990-09-01
There is a strong motivation for the desire to have symmetric hyperbolic field equations in thermodynamics, because they guarantee well-posedness of Cauchy problems. A generic quasi-linear first order system of balance laws — in the non-relativistic case — can be shown to be symmetric hyperbolic, if the entropy density is concave with respect to the variables. In relativistic thermodynamics this is not so. This paper shows that there exists a scalar quantity in relativistic thermodynamics whose concavity guarantees a symmetric hyperbolic system. But that quantity — we call it —bar h — is not the entropy, although it is closely related to it. It is formed by contracting the entropy flux vector — ha with a privileged time-like congruencebar ξ _α . It is also shown that the convexity of h plus the requirement that all speeds be smaller than the speed of light c provide symmetric hyperbolic field equations for all choices of the direction of time. At this level of generality the physical meaning of —h is unknown. However, in many circumstances it is equal to the entropy. This is so, of course, in the non-relativistic limit but also in the non-dissipative relativistic fluid and even in relativistic extended thermodynamics for a non-degenerate gas.
Dai, Yanyan; Kim, YoonGu; Wee, SungGil; Lee, DongHa; Lee, SukGyu
2016-01-01
In this paper, the problem of object caging and transporting is considered for multiple mobile robots. With the consideration of minimizing the number of robots and decreasing the rotation of the object, the proper points are calculated and assigned to the multiple mobile robots to allow them to form a symmetric caging formation. The caging formation guarantees that all of the Euclidean distances between any two adjacent robots are smaller than the minimal width of the polygonal object so that the object cannot escape. In order to avoid collision among robots, the parameter of the robots radius is utilized to design the caging formation, and the A⁎ algorithm is used so that mobile robots can move to the proper points. In order to avoid obstacles, the robots and the object are regarded as a rigid body to apply artificial potential field method. The fuzzy sliding mode control method is applied for tracking control of the nonholonomic mobile robots. Finally, the simulation and experimental results show that multiple mobile robots are able to cage and transport the polygonal object to the goal position, avoiding obstacles.
Design of Stable Circularly Symmetric Two-Dimensional GIC Digital Filters Using PLSI Polynomials
K. Ramar
2007-01-01
Full Text Available A method for designing stable circularly symmetric two-dimensional digital filters is presented. Two-dimensional discrete transfer functions of the rotated filters are obtained from stable one-dimensional analog-filter transfer functions by performing rotation and then applying the double bilinear transformation. The resulting filters which may be unstable due to the presence of nonessential singularities of the second kind are stabilized by using planar least-square inverse polynomials. The stabilized rotated filters are then realized by using the concept of generalized immittance converter. The proposed method is simple and straight forward and it yields stable digital filter structures possessing many salient features such as low noise, low sensitivity, regularity, and modularity which are attractive for VLSI implementation.
Symmetric key structural residues in symmetric proteins with beta-trefoil fold.
Jianhui Feng
Full Text Available To understand how symmetric structures of many proteins are formed from asymmetric sequences, the proteins with two repeated beta-trefoil domains in Plant Cytotoxin B-chain family and all presently known beta-trefoil proteins are analyzed by structure-based multi-sequence alignments. The results show that all these proteins have similar key structural residues that are distributed symmetrically in their structures. These symmetric key structural residues are further analyzed in terms of inter-residues interaction numbers and B-factors. It is found that they can be distinguished from other residues and have significant propensities for structural framework. This indicates that these key structural residues may conduct the formation of symmetric structures although the sequences are asymmetric.
A Numerical Comparison of Symmetric and Asymmetric Supersonic Wind Tunnels
Clark, Kylen D.
Supersonic wind tunnels are a vital aspect to the aerospace industry. Both the design and testing processes of different aerospace components often include and depend upon utilization of supersonic test facilities. Engine inlets, wing shapes, and body aerodynamics, to name a few, are aspects of aircraft that are frequently subjected to supersonic conditions in use, and thus often require supersonic wind tunnel testing. There is a need for reliable and repeatable supersonic test facilities in order to help create these vital components. The option of building and using asymmetric supersonic converging-diverging nozzles may be appealing due in part to lower construction costs. There is a need, however, to investigate the differences, if any, in the flow characteristics and performance of asymmetric type supersonic wind tunnels in comparison to symmetric due to the fact that asymmetric configurations of CD nozzle are not as common. A computational fluid dynamics (CFD) study has been conducted on an existing University of Michigan (UM) asymmetric supersonic wind tunnel geometry in order to study the effects of asymmetry on supersonic wind tunnel performance. Simulations were made on both the existing asymmetrical tunnel geometry and two axisymmetric reflections (of differing aspect ratio) of that original tunnel geometry. The Reynolds Averaged Navier Stokes equations are solved via NASAs OVERFLOW code to model flow through these configurations. In this way, information has been gleaned on the effects of asymmetry on supersonic wind tunnel performance. Shock boundary layer interactions are paid particular attention since the test section integrity is greatly dependent upon these interactions. Boundary layer and overall flow characteristics are studied. The RANS study presented in this document shows that the UM asymmetric wind tunnel/nozzle configuration is not as well suited to producing uniform test section flow as that of a symmetric configuration, specifically one
Turbulent skin-friction drag on a slender body of revolution and Gray's Paradox
Nesteruk, Igor [Institute of Hydromechanics, National Academy of Sciences of Ukraine, Kyiv (Ukraine); Cartwright, Julyan H E [Instituto Andaluz de Ciencias de la Tierra, CSIC-Universidad de Granada (Spain)
2011-12-22
The boundary layer on a slender body of revolution differs considerably from that on a flat plate, but these two cases can be connected by the Mangler-Stepanov transformations. The presented analysis shows that turbulent frictional drag on a slender rotationally symmetric body is much smaller than the flat-plate concept gives and the flow can remain laminar at larger Reynolds numbers. Both facts are valid for an unseparated flow pattern and enable us to revise the turbulent drag estimation of a dolphin, presented by Gray 74 years ago, and to resolve his paradox, since experimental data testify that dolphins can achieve flow without separation. The small values of turbulent skin-friction drag on slender bodies of revolution have additional interest for further experimental investigations and for applications of shapes without boundary-layer separation to diminish the total drag and noise of air- and hydrodynamic hulls.
Phillion, D W; Sommargren, G E; Johnson, M A; Decker, T A; Taylor, J S; Gomie, Y; Kakuchi, O; Takeuchi, S
2005-06-29
The azimuthal Zernike coefficients for shells of Zernike functions with shell numbers n
Gravitational Faraday Rotation of the Earth and Its Possible Test
LIU Lin-Xia; SHAO Cheng-Gang; LUO Jun
2005-01-01
@@ It is shown that the rotation of the polarization plane of rays induced by a rotating body can be accumulated by means of a long baseline optical cavity. Theoretical analysis shows that the presently proposal experimental scheme is possible to test this gravitational Faraday rotation effect on the Earth, especially including how to effectively suppress the dominant part of the Sagnac effect due to the rotation of the Earth with a reasonable experimental configuration.
Rotating black hole and quintessence
Ghosh, Sushant G. [Jamia Millia Islamia, Centre for Theoretical Physics, New Delhi (India); University of KwaZulu-Natal, Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics and Computer Science, Private Bag 54001, Durban (South Africa)
2016-04-15
We discuss spherically symmetric exact solutions of the Einstein equations for quintessential matter surrounding a black hole, which has an additional parameter (ω) due to the quintessential matter, apart from the mass (M). In turn, we employ the Newman-Janis complex transformation to this spherical quintessence black hole solution and present a rotating counterpart that is identified, for α = -e{sup 2} ≠ 0 and ω = 1/3, exactly as the Kerr-Newman black hole, and as the Kerr black hole when α = 0. Interestingly, for a given value of parameter ω, there exists a critical rotation parameter (a = a{sub E}), which corresponds to an extremal black hole with degenerate horizons, while for a < a{sub E}, it describes a nonextremal black hole with Cauchy and event horizons, and no black hole for a > a{sub E}. We find that the extremal value a{sub E} is also influenced by the parameter ω and so is the ergoregion. (orig.)
Reconstruction of symmetric models composed of analytic curves and surfaces from point cloud
Qing WANG; Wei-dong ZHU; Ying-lin KE
2008-01-01
This paper presents a method to reconstruct symmetric geometric models from point cloud with inherent symmetric structure. Symmetry types commonly found in engineering parts, I.e., translational, reflectional and rotational symmetries are considered. The reconstruction problem is formulated as a constrained optimization, where the objective function is the sum of squared distances of points to the model, and constraints are enforced to keep geometric relationships in the model. First, the explicit representations of symmetric models are presented. Then, by using the concept of parameterized points (where the coor-dinate components are represented as functions rather than constants), the distances of points to symmetric models are deduced.With these distance functions, symmetry information, for both 2D and 3D models, is uniformly represented in the process of reconstruction. The constrained optimization problem is solved by a standard nonlinear optimization method. Owing to the explicit representation of symmetry information, the computational complexity of our method is reduced greatly. Finally, examples are given to demonstrate the application of the proposed method.
Properties of hyperon stars rotating at Keplerian frequency
Wen De-Hua; Chen Wei
2011-01-01
The structure and properties of a Keplerian rotating hyperon star with an equation of state (BOS) investigated using the relativistic σ-ω-ρ model are examined by employing an accurate numerical scheme. It is shown that there is a clear rotating effect on the structure and properties, and that hyperon star matter cannot support a star with a mass larger than 1.9 M☉, even a star rotating at the fastest allowed frequency. The constraints of the two known fastest rotating frequencies (716 Hz and 1122 Hz) on the mass and radius of a hyperon star are also explored. Furthermore, our results indicate that the imprint of the rapid rotation of a hyperon star on the moment of inertia is clear; the backward equatorial redshift, the forward equatorial redshift and the polar redshift can be distinguished clearly, the forward equatorial redshift is always negative; and its figuration is far from a spherical symmetric shape.
Electrovacuum Static Counter-Rotating Relativistic Dust Disks
González, G A
2002-01-01
A detailed study of the Counter-Rotating Model (CRM) for generic electrostatic (magnetostatic) axially symmetric thin disks without radial pressure is presented. We find a general constraint over the counter-rotating tangential velocities needed to cast the surface energy-momentum tensor of the disk as the superposition of two counter-rotating charged dust fluids. We then show that this constraint is satisfied if we take the two counter-rotating streams as circulating along electrogeodesics with equal and opposite tangential velocities. We also find explicit expressions for the energy densities, electrostatic (magnetostatic) charge densities and velocities of the counter-rotating fluids. Three specific examples are considered where we obtain some CRM well behaved based in simple solutions to the Einstein-Maxwell equations. The considered solutions are Reissner-Nordstrom in the electrostatic case, its magnetostatic counterpart and two solutions obtained from Taub-NUT and Kerr solutions.
On the convex hull of symmetric stable processes
Kampf, Jürgen
2010-01-01
Let alpha \\in (1, 2] and X be an R^d-valued alpha-stable process with independent and symmetric components starting in 0. We consider the closure S_t of the path described by X on the interval [0, t] and its convex hull Z_t. The first result of this paper provides a formula for certain mean mixed volumes of Z_t and in particular for the expected first intrinsic volume of Z_t. The second result deals with the asymptotics of the expected volume of the stable sausage Z_t+B (where B is an arbitrary convex body with interior points) as t \\to 0.
Multiple Symmetric Lipomatosis: A Review of 3 Cases
Emilio Mevio
2012-01-01
Full Text Available Multiple symmetrical lipomatosis, or Madelung's disease, is a rare disease of unknown etiology. It is characterized by the presence of loose adipose tissue deposits localized in the cervical region and in the upper body. The neoformations grow slowly and their initial consequence is purely esthetic. They can, however, lead to compression of the laryngotacheal area and of the esophagus. This disease usually affects middle-aged males from the Mediterranean area with a history of alcohol abuse. Although most cases have been sporadic, a few authors have indicated that the disorder may be hereditary. It is thought that this pathology originates from an alteration in lipid metabolism. Since the patients were asymptomatic temperance and diet was proposed, surgical removal of the lipomatose mass is the treatment of choice in case of complications due to fat mass compression on upper aerodigestive tract. The authors present three cases of Madelung's disease with different and particular manifestations.
Dynamic rotation and stretch tensors from a dynamic polar decomposition
Haller, George
2016-01-01
The local rigid-body component of continuum deformation is typically characterized by the rotation tensor, obtained from the polar decomposition of the deformation gradient. Beyond its well-known merits, the polar rotation tensor also has a lesser known dynamical inconsistency: it does not satisfy the fundamental superposition principle of rigid-body rotations over adjacent time intervals. As a consequence, the polar rotation diverts from the observed mean material rotation of fibers in fluids, and introduces a purely kinematic memory effect into computed material rotation. Here we derive a generalized polar decomposition for linear processes that yields a unique, dynamically consistent rotation component, the dynamic rotation tensor, for the deformation gradient. The left dynamic stretch tensor is objective, and shares the principal strain values and axes with its classic polar counterpart. Unlike its classic polar counterpart, however, the dynamic stretch tensor evolves in time without spin. The dynamic rotation tensor further decomposes into a spatially constant mean rotation tensor and a dynamically consistent relative rotation tensor that is objective for planar deformations. We also obtain simple expressions for dynamic analogues of Cauchy's mean rotation angle that characterize a deforming body objectively.
New cylindrical gravitational soliton waves and gravitational Faraday rotation
Tomizawa, Shinya
2013-01-01
In terms of gravitational solitons, we study gravitational non-linear effects of gravitational solitary waves such as Faraday rotation. Applying the Pomeransky's procedure for inverse scattering method, which has been recently used for constructing stationary black hole solutions in five dimensions to a cylindrical spacetime in four dimensions, we construct a new cylindrically symmetric soliton solution. This is the first example to be applied to the cylindrically symmetric case. In particular, we clarify the difference from the Tomimatsu's single soliton solution, which was constructed by the Belinsky-Zakharov's procedure.
REPRESENTATION OF SYMMETRIC SUPER-MARTINGALE MULTIPLICATIVE FUNCTIONALS
金蒙为; 应坚刚
2002-01-01
The authors introduce concepts of even and odd additive functionals and prove that an even martingale continuous additive functional of a symmetric Markov process vanishes identically.A representation for symmetric super-martingale multiplicative functionals are also given.
The Symmetric Solutions of Affiliated Value Model
Che Ka-jia; Li Zhi-chen
2004-01-01
In a symmetric affiliated value model, this paper analyses High-Technology industrial firms' competitive strategy in research and development (R&D). We obtain the symmetric Bayesian Nash Equilibrium functions with or without government's prize:b1(x)=v(x,x)Fn-1(x|x)-∫x0Fn-1(y|y)dv(y,y), b2(x)=∫x0[v(y,y)+v0]dFn-1(y|y), and b3(x)=∫x0v(y,y)(fn-1(y|y))/(1-Fn-1(y|y))dy. We find the firm's investment level will increase in prize, only when the constant prize v0≥v(y,y)(Fn-1(y|y))/(1-Fn-1(y|y)), does the firm invest more aggressively with constant prize than with variable prize.
Representations of the infinite symmetric group
Borodin, Alexei
2016-01-01
Representation theory of big groups is an important and quickly developing part of modern mathematics, giving rise to a variety of important applications in probability and mathematical physics. This book provides the first concise and self-contained introduction to the theory on the simplest yet very nontrivial example of the infinite symmetric group, focusing on its deep connections to probability, mathematical physics, and algebraic combinatorics. Following a discussion of the classical Thoma's theorem which describes the characters of the infinite symmetric group, the authors describe explicit constructions of an important class of representations, including both the irreducible and generalized ones. Complete with detailed proofs, as well as numerous examples and exercises which help to summarize recent developments in the field, this book will enable graduates to enhance their understanding of the topic, while also aiding lecturers and researchers in related areas.
Four-qubit PPT entangled symmetric states
Tura, J; Hyllus, P; Kuś, M; Samsonowicz, J; Lewenstein, M
2012-01-01
We solve an open question of the existence of four-qubit entangled symmetric states with positive partial transpositions (PPT states). We reach this goal with two different approaches. First, we propose a half-analytical-half-numerical method that allows to construct multipartite PPT entangled symmetric states (PPTESS) from the qubit-qudit PPT entangled states. Second, we adapt the algorithm allowing to search for extremal elements in the convex set of bipartite PPT states [J. M. Leinaas, J. Myrheim, and E. Ovrum, Phys. Rev. A 76, 034304 (2007)] to the multipartite scenario. With its aid we search for extremal four-qubit PPTESS and show that generically they have ranks (5,7,8). Finally, we provide an exhaustive characterization of these states with respect to their separability properties.
Nonlinear electrodynamics as a symmetric hyperbolic system
Abalos, Fernando; Goulart, Érico; Reula, Oscar
2015-01-01
Nonlinear theories generalizing Maxwell's electromagnetism and arising from a Lagrangian formalism have dispersion relations in which propagation planes factor into null planes corresponding to two effective metrics which depend on the point-wise values of the electromagnetic field. These effective Lorentzian metrics share the null (generically two) directions of the electromagnetic field. We show that, the theory is symmetric hyperbolic if and only if the cones these metrics give rise to have a non-empty intersection. Namely that there exist families of symmetrizers in the sense of Geroch which are positive definite for all covectors in the interior of the cones intersection. Thus, for these theories, the initial value problem is well-posed. We illustrate the power of this approach with several nonlinear models of physical interest such as Born-Infeld, Gauss-Bonnet and Euler-Heisenberg.
Replica symmetric spin glass field theory
Temesvari, T. [Research Group for Theoretical Physics of the Hungarian Academy of Sciences, Eoetvoes University, Pazmany Peter setany 1/A, H-1117 Budapest (Hungary)]. E-mail: temtam@helios.elte.hu
2007-06-18
A new powerful method to test the stability of the replica symmetric spin glass phase is proposed by introducing a replicon generator function g(v). Exact symmetry arguments are used to prove that its extremum is proportional to the inverse spin glass susceptibility. By the idea of independent droplet excitations a scaling form for g(v) can be derived, whereas it can be exactly computed in the mean field Sherrington-Kirkpatrick model. It is shown by a first order perturbative treatment that the replica symmetric phase is unstable down to dimensions d < or approx. 6, and the mean field scaling function proves to be very robust. Although replica symmetry breaking is escalating for decreasing dimensionality, a mechanism caused by the infrared divergent replicon propagator may destroy the mean field picture at some low enough dimension.
Replica symmetric spin glass field theory
Temesvári, T.
2007-06-01
A new powerful method to test the stability of the replica symmetric spin glass phase is proposed by introducing a replicon generator function g(v). Exact symmetry arguments are used to prove that its extremum is proportional to the inverse spin glass susceptibility. By the idea of independent droplet excitations a scaling form for g(v) can be derived, whereas it can be exactly computed in the mean field Sherrington-Kirkpatrick model. It is shown by a first order perturbative treatment that the replica symmetric phase is unstable down to dimensions d≲6, and the mean field scaling function proves to be very robust. Although replica symmetry breaking is escalating for decreasing dimensionality, a mechanism caused by the infrared divergent replicon propagator may destroy the mean field picture at some low enough dimension.
Leptogenesis in left-right symmetric theories
Joshipura, A S; Rodejohann, W
2001-01-01
The masses and mixing of the light left-handed neutrinos can be related to those of the heavy right-handed neutrinos in left-right symmetric theories. Properties of the light neutrinos are measured in terrestrial experiments and the CP-violating decays of their heavy counterparts produce a baryon asymmetry via the well-known leptogenesis mechanism. The left-handed Higgs triplet, present in left-right symmetric theories, modifies the usual see-saw formula. It is possible to relate the lepton asymmetry to the light neutrino parameters when the triplet and the top quark through the usual see-saw mechanism give dominant contribution to the neutrino mass matrix. We find that in this situation the small angle MSW and vacuum solutions produce reasonable asymmetry, whereas the large angle MSW case requires extreme fine-tuning of the three phases in the mixing matrix.
Polymer-based symmetric electrochromic devices
Arbizzani, Catia; Cerroni, Maria Grazia [Department of Chemistry `G. Ciamician`, University of Bologna, via Selmi 2, 40126 Bologna (Italy); Mastragostino, Marina [Department of Physical Chemistry, University of Palermo, via Archirafi 26, 20123 Palermo (Italy)
1998-12-30
The fact that conjugated polymers repeatedly undergo electrochemical doping/undoping processes, which are accompanied by color changes, makes these materials very attractive, and much effort has been devoted to their use in advanced devices. There is renewed interest in electroactive polymers that reversibly undergo both p- and n-doping because of their potential application in symmetric electrochemical devices. We employed fused molecules, dithienothiophenes, as monomers to obtain polymers with a narrow band gap suitable for n- and p-doping. The performance results of two symmetric electrochromic devices having as electrodes both poly(dithieno[3,4-b:3`,4`-d]thiophene) (pDTT1) and poly(dithieno[3,4-b:2`,3`-d]thiophene) (pDTT3) are reported and discussed
Factored Facade Acquisition using Symmetric Line Arrangements
Ceylan, Duygu
2012-05-01
We introduce a novel framework for image-based 3D reconstruction of urban buildings based on symmetry priors. Starting from image-level edges, we generate a sparse and approximate set of consistent 3D lines. These lines are then used to simultaneously detect symmetric line arrangements while refining the estimated 3D model. Operating both on 2D image data and intermediate 3D feature representations, we perform iterative feature consolidation and effective outlier pruning, thus eliminating reconstruction artifacts arising from ambiguous or wrong stereo matches. We exploit non-local coherence of symmetric elements to generate precise model reconstructions, even in the presence of a significant amount of outlier image-edges arising from reflections, shadows, outlier objects, etc. We evaluate our algorithm on several challenging test scenarios, both synthetic and real. Beyond reconstruction, the extracted symmetry patterns are useful towards interactive and intuitive model manipulations.
Maximally Symmetric Spacetimes emerging from thermodynamic fluctuations
Bravetti, A; Quevedo, H
2015-01-01
In this work we prove that the maximally symmetric vacuum solutions of General Relativity emerge from the geometric structure of statistical mechanics and thermodynamic fluctuation theory. To present our argument, we begin by showing that the pseudo-Riemannian structure of the Thermodynamic Phase Space is a solution to the vacuum Einstein-Gauss-Bonnet theory of gravity with a cosmological constant. Then, we use the geometry of equilibrium thermodynamics to demonstrate that the maximally symmetric vacuum solutions of Einstein's Field Equations -- Minkowski, de-Sitter and Anti-de-Sitter spacetimes -- correspond to thermodynamic fluctuations. Moreover, we argue that these might be the only possible solutions that can be derived in this manner. Thus, the results presented here are the first concrete examples of spacetimes effectively emerging from the thermodynamic limit over an unspecified microscopic theory without any further assumptions.
Leptogenesis in left-right symmetric theories
Joshipura, Anjan S. E-mail: anjan@prl.ernet.in; Paschos, Emmanuel A. E-mail: paschos@physik.uni-dortmund.de; Rodejohann, Werner E-mail: rodejoha@xena.physik.uni-dortmund.de
2001-09-17
The masses and mixing of the light left-handed neutrinos can be related to those of the heavy right-handed neutrinos in left-right symmetric theories. Properties of the light neutrinos are measured in terrestrial experiments and the CP-violating decays of their heavy counterparts produce a baryon asymmetry via the well-known leptogenesis mechanism. The left-handed Higgs triplet, present in left-right symmetric theories, modifies the usual see-saw formula. It is possible to relate the lepton asymmetry to the light neutrino parameters when the triplet and the top quark through the usual see-saw mechanism give the dominant contribution to the neutrino mass matrix. We find that in this situation the small angle MSW and vacuum solutions produce reasonable asymmetry, whereas the large angle MSW case requires extreme fine-tuning of the three phases in the mixing matrix.
Chirally symmetric strong and electroweak interactions
Rajpoot, Subhash
1988-07-01
Strong and electroweak interactions may be a relic of the spontaneous breakdown of a chirally symmetric colour-flavour gauge group. The minimum possibility of such a structure that is symmetric between left and right is SU(3) L×SU(3) R×SU(2) L×SU(2) R×U(1) B- L where quantum chromodynamics originates in the chiral colour group SU(3) L×SU(3) R and the electroweak interaction originates in the ambidextrous electroweak interaction group SU L×SU(2) R×U(1) B- L. The chiral anomalies are cancelled by adding a set of fermions that transform as singlets under the weak interaction group SU(2) L×SU(2) R. This model requires only three Higgs representations to break the proposed gauge symmetry to SU(3) C×U(1) em and give masses to all the quarks and leptons of the theory. All fermion masses are “see-saw” masses.
Cusped Wilson lines in symmetric representations
Correa, Diego H; Trancanelli, Diego
2015-01-01
We study the cusped Wilson line operators and Bremsstrahlung functions associated to particles transforming in the rank-$k$ symmetric representation of the gauge group $U(N)$ for ${\\cal N} = 4$ super Yang-Mills. We find the holographic D3-brane description for Wilson loops with internal cusps in two different limits: small cusp angle and $k\\sqrt{\\lambda}\\gg N$. This allows for a non-trivial check of a conjectured relation between the Bremsstrahlung function and the expectation value of the 1/2 BPS circular loop in the case of a representation other than the fundamental. Moreover, we observe that in the limit of $k\\gg N$, the cusped Wilson line expectation value is simply given by the exponential of the 1-loop diagram. Using group theory arguments, this eikonal exponentiation is conjectured to take place for all Wilson loop operators in symmetric representations with large $k$, independently of the contour on which they are supported.
The quantum capacity with symmetric side channels
Smith, G; Winter, A; Smith, Graeme; Smolin, John A.; Winter, Andreas
2006-01-01
We present an upper bound for the quantum channel capacity that is both additive and convex. Our bound can be interpreted as the capacity of a channel for high-fidelity communication when assisted by the family of all channels mapping symmetrically to their output and environment. The bound seems to be quite tight, and for degradable quantum channels it coincides with the unassisted channel capacity. Using this symmetric side channel capacity, we find new upper bounds on the capacity of the depolarizing channel. We also briefly indicate an analogous notion for distilling entanglement using the same class of (one-way) channels, yielding one of the few genuinely 1-LOCC monotonic entanglement measures.
Static spherically symmetric wormholes with isotropic pressure
Cataldo, Mauricio; Rodríguez, Pablo
2016-01-01
In this paper we study static spherically symmetric wormhole solutions sustained by matter sources with isotropic pressure. We show that such spherical wormholes do not exist in the framework of zero-tidal-force wormholes. On the other hand, it is shown that for the often used power-law shape function there is no spherically symmetric traversable wormholes sustained by sources with a linear equation of state $p=\\omega \\rho$ for the isotropic pressure, independently of the form of the redshift function $\\phi(r)$. We consider a solution obtained by Tolman at 1939 for describing static spheres of isotropic fluids, and show that it also may describe wormhole spacetimes with a power-law redshift function, which leads to a polynomial shape function, generalizing a power-law shape function, and inducing a solid angle deficit.
Horizon quantum mechanics of rotating black holes
Casadio, Roberto [Universita di Bologna, Dipartimento di Fisica e Astronomia, Bologna (Italy); I.N.F.N., Sezione di Bologna, I.S. FLAG, Bologna (Italy); Giugno, Andrea [Ludwig-Maximilians-Universitaet, Arnold Sommerfeld Center, Munich (Germany); Giusti, Andrea [Universita di Bologna, Dipartimento di Fisica e Astronomia, Bologna (Italy); I.N.F.N., Sezione di Bologna, I.S. FLAG, Bologna (Italy); Ludwig-Maximilians-Universitaet, Arnold Sommerfeld Center, Munich (Germany); Micu, Octavian [Institute of Space Science, Bucharest, P.O. Box MG-23, Bucharest-Magurele (Romania)
2017-05-15
The horizon quantum mechanics is an approach that was previously introduced in order to analyze the gravitational radius of spherically symmetric systems and compute the probability that a given quantum state is a black hole. In this work, we first extend the formalism to general space-times with asymptotic (ADM) mass and angular momentum. We then apply the extended horizon quantum mechanics to a harmonic model of rotating corpuscular black holes. We find that simple configurations of this model naturally suppress the appearance of the inner horizon and seem to disfavor extremal (macroscopic) geometries. (orig.)
Spherically Symmetric, Self-Similar Spacetimes
Wagh, S M; Wagh, Sanjay M.; Govinder, Keshlan S.
2001-01-01
Self-similar spacetimes are of importance to cosmology and to gravitational collapse problems. We show that self-similarity or the existence of a homothetic Killing vector field for spherically symmetric spacetimes implies the separability of the spacetime metric in terms of the co-moving coordinates and that the metric is, uniquely, the one recently reported in [cqg1]. The spacetime, in general, has non-vanishing energy-flux and shear. The spacetime admits matter with any equation of state.
Expansion-free Cylindrically Symmetric Models
Sharif, M
2013-01-01
This paper investigates cylindrically symmetric distribution of an-isotropic fluid under the expansion-free condition, which requires the existence of vacuum cavity within the fluid distribution. We have discussed two family of solutions which further provide two exact models in each family. Some of these solutions satisfy Darmois junction condition while some show the presence of thin shell on both boundary surfaces. We also formulate a relation between the Weyl tensor and energy density.
Irreducible complexity of iterated symmetric bimodal maps
J. P. Lampreia
2005-01-01
Full Text Available We introduce a tree structure for the iterates of symmetric bimodal maps and identify a subset which we prove to be isomorphic to the family of unimodal maps. This subset is used as a second factor for a ∗-product that we define in the space of bimodal kneading sequences. Finally, we give some properties for this product and study the ∗-product induced on the associated Markov shifts.
Quantum unharmonic symmetrical oscillators using elliptic functions
Sanchez, A.M.; Bejarano, J.d.
1986-04-21
The authors study in the JWKB approximation the energy levels of the symmetric anharmonic oscillators V(x) Ax/sup 2/ + Bx/sup 4/ for different signs and values of A and B. Comparisons are made with published results for specific cases and with numerical calculations. An additional example is given of exact value, to add to the very rare catalogue of known examples.
Resistor Networks based on Symmetrical Polytopes
Jeremy Moody
2015-03-01
Full Text Available This paper shows how a method developed by Van Steenwijk can be generalized to calculate the resistance between any two vertices of a symmetrical polytope all of whose edges are identical resistors. The method is applied to a number of cases that have not been studied earlier such as the Archimedean polyhedra and their duals in three dimensions, the regular polytopes in four dimensions and the hypercube in any number of dimensions.
Symmetrical peripheral gangrene associated with peripartum cardiomyopathy
Ajay Jaryal
2013-01-01
Full Text Available Symmetrical peripheral gangrene (SPG is a rare clinical entity. It was first described in late 19 th century and since then has been reported with array of medical conditions mainly those complicated with shock, sepsis, and disseminated intravascular coagulation (DIC. Here in, we describe a parturient with peripartum cardiomyopathy (PPCM and SPG. Clinicians should be aware of this entity as early recognition can help in reducing morbidity and mortality.
On integrability of strings on symmetric spaces
Wulff, Linus [Blackett Laboratory, Imperial College,London SW7 2AZ (United Kingdom)
2015-09-17
In the absence of NSNS three-form flux the bosonic string on a symmetric space is described by a symmetric space coset sigma-model. Such models are known to be classically integrable. We show that the integrability extends also to cases with non-zero NSNS flux (respecting the isometries) provided that the flux satisfies a condition of the form H{sub abc}H{sup cde}∼R{sub ab}{sup de}. We then turn our attention to the type II Green-Schwarz superstring on a symmetric space. We prove that if the space preserves some supersymmetry there exists a truncation of the full superspace to a supercoset space and derive the general form of the superisometry algebra. In the case of vanishing NSNS flux the corresponding supercoset sigma-model for the string is known to be integrable. We prove that the integrability extends to the full string by augmenting the supercoset Lax connection with terms involving the fermions which are not captured by the supercoset model. The construction is carried out to quadratic order in these fermions. This proves the integrability of strings on symmetric spaces supported by RR flux which preserve any non-zero amount of supersymmetry. Finally we also construct Lax connections for some supercoset models with non-zero NSNS flux describing strings in AdS{sub 2,3}×S{sup 2,3}×S{sup 2,3}×T{sup 2,3,4} backgrounds preserving eight supersymmetries.
Coefficients of symmetric square L-functions
LAU; Yuk-Kam
2010-01-01
Let λsym2f(n) be the n-th coefficient in the Dirichlet series of the symmetric square L-function associated with a holomorphic primitive cusp form f.We prove Ω± results for λsym2f(n) and evaluate the number of positive(resp.,negative) λsym2f(n) in some intervals.
Time-symmetric electrodynamics and quantum measurement
Pegg, D. T.
The application of the Wheeler-Feynman theory of time-symmetric electrodynamics to obtain definite answers to questions concerning the objective existence of quantum states in an optical EPR type of experiment is discussed. This theory allows the influence of the detector on the system being studied to be taken into account. The result is an entirely fresh understanding of experiments of the Kocher-Commins type.
Symmetric Wilson Loops beyond leading order
Chen-Lin, Xinyi
2016-01-01
We study the circular Wilson loop in the symmetric representation of U(N) in $\\mathcal{N} = 4$ super-Yang-Mills (SYM). In the large N limit, we computed the exponentially-suppressed corrections for strong coupling, which suggests non-perturbative physics in the dual holographic theory. We also computed the next-to-leading order term in 1/N, and the result matches with the exact result from the k-fundamental representation.
Symmetric categorial grammar: residuation and Galois connections
Moortgat, Michael
2010-01-01
The Lambek-Grishin calculus is a symmetric extension of the Lambek calculus: in addition to the residuated family of product, left and right division operations of Lambek's original calculus, one also considers a family of coproduct, right and left difference operations, related to the former by an arrow-reversing duality. Communication between the two families is implemented in terms of linear distributivity principles. The aim of this paper is to complement the symmetry between (dual) resid...
Entropy, subentropy and the elementary symmetric functions
Jozsa, Richard; Mitchison, Graeme
2013-01-01
We use complex contour integral techniques to study the entropy H and subentropy Q as functions of the elementary symmetric polynomials, revealing a series of striking properties. In particular for these variables, derivatives of -Q are equal to derivatives of H of one higher order and the first derivatives of H and Q are seen to be completely monotone functions. It then follows that exp (-H) and exp(-Q) are Laplace transforms of infinitely divisible probability distributions.
Compensator configurations for load currents' symmetrization
Rusinaru, D.; Manescu, L. G.; Dinu, R. C.
2016-02-01
This paper approaches aspects regarding the mitigation effects of asymmetries in 3-phase 3-wire networks. The measure consisting in connecting of load current symmetrization devices at the load coupling point is presented. A time-variation of compensators parameters is determined as a function of the time-recorded electrical values. The general sizing principle of the load current symmetrization reactive components is based on a simple equivalent model of the unbalanced 3-phase loads. By using these compensators a certain control of the power components transits is ensured in the network. The control is based on the variations laws of the compensators parameters as functions of the recorded electrical values: [B] = [T]·[M]. The link between compensator parameters and measured values is ensured by a transformation matrix [T] for each operation conditions of the supply network. Additional conditions for improving of energy and efficiency performance of the compensator are considered: i.e. reactive power compensation. The compensator sizing algorithm was implemented into a MATLAB environment software, which generate the time-evolution of the parameters of load current symmetrization device. The input data of application takes into account time-recording of the electrical values. By using the compensator sizing software, some results were achieved for the case of a consumer connected at 20 kV busbar of a distribution substation, during 24 hours measurement session. Even the sizing of the compensators aimed some additional network operation aspects (power factor correction) correlated with the total or major load symmetrizations, the harmonics aspects of the network values were neglected.
Classification Models for Symmetric Key Cryptosystem Identification
Shri Kant
2012-01-01
Full Text Available The present paper deals with the basic principle and theory behind prevalent classification models and their judicious application for symmetric key cryptosystem identification. These techniques have been implemented and verified on varieties of known and simulated data sets. After establishing the techniques the problems of cryptosystem identification have been addressed.Defence Science Journal, 2012, 62(1, pp.38-45, DOI:http://dx.doi.org/10.14429/dsj.62.1440
SVD row or column symmetric matrix
无
2000-01-01
A new architecture for row or column symmetric matrix called extended matrix is defined, and a precise correspondence of the singular values and singular vectors between the extended matrix and its original (namely, the mother matrix) is derived. As an illustration of potential, we show that, for a class of extended matrices, the singular value decomposition using the mother matrix rather than the extended matrix per se can save the CPU time and memory without loss of numerical precision.
Differential rotation of geomagnetic field
WEI Zigang; XU Wenyao
2003-01-01
The latitudinal dependence of the westward drift in the main geomagnetic field is examined by using the correlation analysis of moving random pattern. The study reveals the characteristics in the differential rotation of the main field. The results show that the global geomagnetic field drifts westward with an average speed of 0.18°/a during 1900-2000. The westward drift rate is not symmetrical with respect to the equator. The maximum westward drift rate, 0.31°/a, occurs at the latitude --= -15°, forming a Rapid Westward Drift Belt (RDB) around this latitude. Going northward and southward from this belt, the drift rate decreases and reaches the minimum (0.12°/a) at --= 50° and the minimum (0.14°/a) at --= -56°, forming a Northern Hemisphere Slow Westward Drift Belt (N-SDB) and a Southern Hemisphere Slow Westward Drift Belt (S-SDB). Three phases can be detected in the evolution of the westward drift. In the first phase (1900-1940), the RDB dominates the global drift pattern. The westward drifts in this belt are much faster than those in other areas. In the second phase (1940-1960), the drift rates in the RDB are less than those in the first phase, while the drifts in the N-SDB and S-SDB are relatively large. In this phase, the differential rotation becomes less obvious. In the third phase (1960-2000), the westward drift in the RDB increases again and the differential rotation gradually becomes apparent.
Static spherically symmetric solutions in the IR limit of nonrelativistic quantum gravity
Harada, Tomohiro; Tsukamoto, Naoki
2009-01-01
We investigate static spherically symmetric vacuum solutions in the IR limit of projectable nonrelativistic quantum gravity, including the renormalisable quantum gravity recently proposed by Ho\\v{r}ava. It is found that the projectability condition plays an important role. Without the cosmological constant, the spacetime is uniquely given by the Schwarzschild solution. With the cosmological constant, the spacetime is uniquely given by the Kottler (Schwarzschild-(anti) de Sitter) solution for the entirely vacuum spacetime. However, the ``ultra-static'' metric of spherical and hyperbolic spaces can be also admissible for the locally empty region, for the positive and negative cosmological constants, respectively, if its nonvanishing contribution to the global Hamiltonian constraint can be compensated by that from the nonempty or nonstatic region. This implies that static spherically symmetric entirely vacuum solutions would not admit the freedom to reproduce the observed flat rotation curves of galaxies. On the...
QR factorization for row or column symmetric matrix
ZOU; Hongxing(邹红星); WANG; Dianjun(王殿军); DAI; Qionghai(戴琼海); LI; Yanda(李衍达)
2003-01-01
The problem of fast computing the QR factorization of row or column symmetric matrix isconsidered. We address two new algorithms based on a correspondence of Q and R matrices between the rowor column symmetric matrix and its mother matrix. Theoretical analysis and numerical evidence show that, fora class of row or column symmetric matrices, the QR factorization using the mother matrix rather than therow or column symmetric matrix per se can save dramatically the CPU time and memory without loss of anynumerical precision.
Distal symmetrical polyneuropathy: definition for clinical research.
England, J D; Gronseth, G S; Franklin, G; Miller, R G; Asbury, A K; Carter, G T; Cohen, J A; Fisher, M A; Howard, J F; Kinsella, L J; Latov, N; Lewis, R A; Low, P A; Sumner, A J
2005-01-01
The objective of this report was to develop a case definition of "distal symmetrical polyneuropathy" to standardize and facilitate clinical research and epidemiological studies. A formalized consensus process was employed to reach agreement after a systematic review and classification of evidence from the literature. The literature indicates that symptoms alone have relatively poor diagnostic accuracy in predicting the presence of polyneuropathy; signs are better predictors of polyneuropathy than symptoms; and single abnormalities on examination are less sensitive than multiple abnormalities in predicting the presence of polyneuropathy. The combination of neuropathic symptoms, signs, and electrodiagnostic findings provides the most accurate diagnosis of distal symmetrical polyneuropathy. A set of case definitions was rank ordered by likelihood of disease. The highest likelihood of polyneuropathy (useful for clinical trials) occurs with a combination of multiple symptoms, multiple signs, and abnormal electrodiagnostic studies. A modest likelihood of polyneuropathy (useful for field or epidemiological studies) occurs with a combination of multiple symptoms and multiple signs when the results of electrodiagnostic studies are not available. A lower likelihood of polyneuropathy occurs when electrodiagnostic studies and signs are discordant. For research purposes, the best approach for defining distal symmetrical polyneuropathy is a set of case definitions rank ordered by estimated likelihood of disease. The inclusion of this formalized case definition in clinical and epidemiological research studies will ensure greater consistency of case selection.
Neutrino Mass Matrix Predicted From Symmetric Texture
Bando, M; Bando, Masako; Obara, Midori
2003-01-01
Within the framework of grand unified theories, we make full analysis of symmetric texture to see if such texture can reproduce large neutrino mixings, which have recently been confirmed by the observed solar and atmospheric neutrino oscillation experiments. It is found that so-called symmetric texture with anomalous U(1) family symmetry with Froggatt-Nielsen mechanism does not provide a natural explanation of two large mixing angles. On the contrary we should adopt "zero texture" which have been extensively studied by many authors and only this scenario can reproduce two large mixing angles naturally. Under such "zero texture" with minimal symmetric Majorana matrix, all the neutrino masses and mixing angles, 6 quantities, are expressed in terms of up-quark masses, $m_t,m_c,m_u$ with two adjustable parameters. This provides interesting relations among neutrio mixing angles, $\\tan^2 2\\theta_{12} \\simeq \\frac{144m_c}{m_t} \\tan^2 2\\theta_{23} \\cos^2 \\theta_{23}, \\quad \\sin^2 \\theta_{13} \\simeq \\frac{4m_c}{m_t}\\s...
Instability of counter-rotating stellar disks
Hohlfeld, R. G.; Lovelace, R. V. E.
2015-09-01
We use an N-body simulation, constructed using GADGET-2, to investigate an accretion flow onto an astrophysical disk that is in the opposite sense to the disk's rotation. In order to separate dynamics intrinsic to the counter-rotating flow from the impact of the flow onto the disk, we consider an initial condition in which the counter-rotating flow is in an annular region immediately exterior the main portion of the astrophysical disk. Such counter-rotating flows are seen in systems such as NGC 4826 (known as the "Evil Eye Galaxy"). Interaction between the rotating and counter-rotating components is due to two-stream instability in the boundary region. A multi-armed spiral density wave is excited in the astrophysical disk and a density distribution with high azimuthal mode number is excited in the counter-rotating flow. Density fluctuations in the counter-rotating flow aggregate into larger clumps and some of the material in the counter-rotating flow is scattered to large radii. Accretion flow processes such as this are increasingly seen to be of importance in the evolution of multi-component galactic disks.
The Exponent Set of Central Symmetric Primitive Matrices
陈佘喜; 胡亚辉
2004-01-01
This paper first establishes a distance inequality of the associated diagraph of a central symmetric primitive matrix, then characters the exponent set of central symmetric primitive matrices, and proves that the exponent set of central symmetric primitive matrices of order n is {1, 2,… ,n-1}. There is no gap in it.
Kashiwara-Vergne-Rouviere methods for symmetric spaces
Torossian, Charles
2002-01-01
This article follows our previous work on Campbell-Hausdorff formula. We study the case of symmetric spaces. We recover, by using a Kontsevich's deformation of the Baker-Campbell-Hausdorff formula, Rouviere's results on the convolution of invariant distributions, for solvable symmetric spaces and "very symmetric spaces".
Kashiwara-Vergne-Rouviere methods for symmetric spaces
Torossian, Charles
2002-01-01
This article follows our previous work on Campbell-Hausdorff formula. We study the case of symmetric spaces. We recover, by using a Kontsevich's deformation of the Baker-Campbell-Hausdorff formula, Rouviere's results on the convolution of invariant distributions, for solvable symmetric spaces and "very symmetric spaces".
Magnetism and domain formation in SU(3)-symmetric multi-species Fermi mixtures
Titvinidze, I; Privitera, A; Hofstetter, W [Institut fuer Theoretische Physik, Johann Wolfgang Goethe-Universitaet, 60438 Frankfurt am Main (Germany); Chang, S-Y; Diehl, S; Baranov, M A; Daley, A, E-mail: irakli@itp.uni-frankfurt.de [Institute for Quantum Optics and Quantum information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria, Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck (Austria)
2011-03-15
We study the phase diagram of an SU(3)-symmetric mixture of three-component ultracold fermions with attractive interactions in an optical lattice, including the additional effect on the mixture of an effective three-body constraint induced by three-body losses. We address the properties of the system in D{>=}2 by using dynamical mean-field theory and variational Monte Carlo techniques. The phase diagram of the model shows a strong interplay between magnetism and superfluidity. In the absence of the three-body constraint (no losses), the system undergoes a phase transition from a color superfluid (c-SF) phase to a trionic phase, which shows additional particle density modulations at half-filling. Away from the particle-hole symmetric point the c-SF phase is always spontaneously magnetized, leading to the formation of different c-SF domains in systems where the total number of particles of each species is conserved. This can be seen as the SU(3) symmetric realization of a more general tendency for phase separation in three-component Fermi mixtures. The three-body constraint strongly disfavors the trionic phase, stabilizing a (fully magnetized) c-SF also at strong coupling. With increasing temperature we observe a transition to a non-magnetized SU(3) Fermi liquid phase.
Shell model for warm rotating nuclei
Matsuo, M.; Yoshida, K. [Kyoto Univ. (Japan); Dossing, T. [Univ. of Copenhagen (Denmark)] [and others
1996-12-31
Utilizing a shell model which combines the cranked Nilsson mean-field and the residual surface and volume delta two-body forces, the authors discuss the onset of rotational damping in normal- and super-deformed nuclei. Calculation for a typical normal deformed nucleus {sup 168}Yb indicates that the rotational damping sets in at around 0.8 MeV above the yrast line, and about 30 rotational bands of various length exists at a given rotational frequency, in overall agreement with experimental findings. It is predicted that the onset of rotational damping changes significantly in different superdeformed nuclei due to the variety of the shell gaps and single-particle orbits associated with the superdeformed mean-field.
Shapes of rotating superfluid helium nanodroplets
Bernando, Charles; Tanyag, Rico Mayro P.; Jones, Curtis; Bacellar, Camila; Bucher, Maximilian; Ferguson, Ken R.; Rupp, Daniela; Ziemkiewicz, Michael P.; Gomez, Luis F.; Chatterley, Adam S.; Gorkhover, Tais; Müller, Maria; Bozek, John; Carron, Sebastian; Kwok, Justin; Butler, Samuel L.; Möller, Thomas; Bostedt, Christoph; Gessner, Oliver; Vilesov, Andrey F.
2017-02-01
Rotating superfluid He droplets of approximately 1 μm in diameter were obtained in a free nozzle beam expansion of liquid He in vacuum and were studied by single-shot coherent diffractive imaging using an x-ray free electron laser. The formation of strongly deformed droplets is evidenced by large anisotropies and intensity anomalies (streaks) in the obtained diffraction images. The analysis of the images shows that in addition to previously described axially symmetric oblate shapes, some droplets exhibit prolate shapes. Forward modeling of the diffraction images indicates that the shapes of rotating superfluid droplets are very similar to their classical counterparts, giving direct access to the droplet angular momenta and angular velocities. The analyses of the radial intensity distribution and appearance statistics of the anisotropic images confirm the existence of oblate metastable superfluid droplets with large angular momenta beyond the classical bifurcation threshold.
Observational properties of rigidly rotating dust configurations
Ilyas, Batyr; Yang, Jinye
2016-01-01
We study the observational properties of a class of exact solutions of Einstein's field equations describing stationary, axially symmetric, rigidly rotating dust. We ask the question whether such solutions can describe astrophysical rotating dark matter clouds and we probe the possibility that they may constitute an alternative to supermassive black holes at the center of galaxies. We show that light emission from accretion disks in this space-time has several differences with respect to the emission of light from accretion disks around black holes. The shape of the iron K{\\alpha} line in the reflection spectrum of accretion disks can potentially distinguish this class of solution from the Kerr metric, but this may not be possible with current X-ray missions.
State reconstruction of molecular spatial rotation
Qin Xiao; Gao Jun-Yi
2012-01-01
We establish a reconstruction approach for the rotational quantum state of linear molecules possessing a magnetic manifold.Our approximate method contains an iteration with generalized matrix inverses,processing the tomographic integral of the time-dependent molecular-axis distribution in a polar angle.As shown in a simulated example for an alignment state,the density matrix is determined in a high fidelity.An analytic tomographic formula is also derived for the symmetric top rotation.The state coherent in the quantun space of both the angular momentum and its magnetic projection can be approximately retrieved from the observable time-resolved solid-angle distribution of the molecular.
Ideal magnetohydrodynamic equilibrium in a non-symmetric topological torus
Weitzner, Harold [Courant Institute of Mathematical Sciences, New York University, New York, New York 10012 (United States)
2014-02-15
An alternative representation of an ideal magnetohydrodynamic equilibrium is developed. The representation is a variation of one given by A. Salat, Phys. Plasmas 2, 1652 (1995). The system of equations is used to study the possibility of non-symmetric equilibria in a topological torus, here an approximate rectangular parallelopiped, with periodicity in two of the three rectangular coordinates. An expansion is carried out in the deviation of pressure surfaces from planes. Resonances are manifest in the process. Nonetheless, provided the magnetic shear is small, it is shown that it is possible to select the magnetic fields and flux surfaces in such a manner that no singularities appear on resonant surfaces. One boundary surface of the parallelopiped is not arbitrary but is dependent on the equilibrium in question. A comparison of the solution sets of axisymmetric and non-axisymmetric equilibria suggests that the latter have a wider class of possible boundary shapes but more restrictive rotational transform profiles. No proof of convergence of the series is given.
Modelling Submesoscale Dynamics: A New Parameterization for Symmetric Instability
Bachman, S.; Thomas, L. N.; Taylor, J. R.; Fox-Kemper, B.
2016-02-01
Next-generation ocean models are expected to routinely resolve dynamics at 1/4 degree or smaller, offering new challenges in modelling subgridscale physics. These models are entering a regime where the unresolved turbulence is less constrained by planetary rotation, requiring a paradigm shift in the way modellers construct turbulence closures. Of particular importance is the representation of submesoscale turbulence, occupying O(1-10) km scales, which plays a leading role in setting the stratification of the surface mixed layer and mediating air-sea fluxes. This talk will introduce the submesoscale parameterization problem by presenting a few extant parameterizations, and will focus on a special type of fluid instability for which no parameterization has previously been developed: symmetric instability (SI). The theory and dynamics of SI will be discussed, from which a new parameterization will be proposed. This parameterization is dependent on external forcing by either surface buoyancy loss or down-front winds, which reduce potential vorticity (PV) and lead to conditions favorable for SI. Preliminary testing of the parameterization using a set of idealized models shows that the induced vertical fluxes of passive tracers and momentum are consistent with those from SI-resolving Large Eddy Simulations.
Functional decor in the International Space Station: Body orientation cues and picture perception
Coss, Richard G.; Clearwater, Yvonne A.; Barbour, Christopher G.; Towers, Steven R.
1989-01-01
Subjective reports of American astronauts and their Soviet counterparts suggest that homogeneous, often symmetrical, spacecraft interiors can contribute to motion sickness during the earliest phase of a mission and can also engender boredom. Two studies investigated the functional aspects of Space Station interior aesthetics. One experiment examined differential color brightnesses as body orientation cues; the other involved a large survey of photographs and paintings that might enhance the interior aesthetics of the proposed International Space Station. Ninety male and female college students reclining on their backs in the dark were disoriented by a rotating platform and inserted under a slowly rotating disk that filled their entire visual field. The entire disk was painted the same color but one half had a brightness value that was about 69 percent higher than the other. The effects of red, blue, and yellow were examined. Subjects wearing frosted goggles opened their eyes to view the rotating, illuminated disk, which was stopped when they felt that they were right-side up. For all three colors, significant numbers of subjects said they felt right-side up when the brighter side of the disk filled their upper visual field. These results suggest that color brightness could provide Space Station crew members with body orientation cues as they move about. It was found that subjects preferred photographs and paintings with the greatest depths of field, irrespective of picture topic.
Rotating blade vibration analysis using shells
Leissa, A. W.; Lee, J. K.; Wang, A. J.
1981-01-01
Shallow shell theory and the Ritz method are employed to determine the frequencies and mode shapes of turbomachinery blades having both camber and twist, rotating with non-zero angles of attack. Frequencies obtained for different degrees of shallowness and thickness are compared with results available in the literature, obtained from finite element analyses of nonrotating blades. Frequencies are also determined for a rotating blade, showing the effects of changing the (1) angular velocity of rotation, (2) disk radius and (3) angle of attack, as well as the significance of the most important body force terms.
Finite rotation and nonlinear beam kinematics
Hodges, Dewey H.
1987-01-01
Standard means of representing finite rotation in rigid-body kinematics, including orientation angles, Euler parameters, and Rodrigues parameters, are reviewed and compared. General kinematical relations for a beam theory that treats arbitrarily large rotation are then presented. The standard methods of representing finite rotations are applied to these kinematical expressions, and comparison is made among the standard methods and additional methods found in the literature, such as quasi-coordinates and linear combinations of projection angles. The method of Rodrigues parameters is shown to stand out for both its simplicity and generality when applied to beam kinematics, a result that is really missing from the literature.
Rotator cuff repair - slideshow
... this page: //medlineplus.gov/ency/presentations/100229.htm Rotator cuff repair - series—Normal anatomy To use the sharing ... to slide 4 out of 4 Overview The rotator cuff is a group of muscles and tendons that ...
Experimental demonstration of PT-symmetric stripe lasers
Gu, Zhiyuan; Lyu, Quan; Li, Meng; Xiao, Shumin; Song, Qinghai
2015-01-01
Recently, the coexistence of parity-time (PT) symmetric laser and absorber has gained tremendous research attention. While the PT symmetric absorber has been observed in microwave metamaterials, the experimental demonstration of PT symmetric laser is still absent. Here we experimentally study PT-symmetric laser absorber in stripe waveguide. Using the concept of PT symmetry to exploit the light amplification and absorption, PT-symmetric laser absorbers have been successfully obtained. Different from the single-mode PT symmetric lasers, the PT-symmetric stripe lasers have been experimentally confirmed by comparing the relative wavelength positions and mode spacing under different pumping conditions. When the waveguide is half pumped, the mode spacing is doubled and the lasing wavelengths shift to the center of every two initial lasing modes. All these observations are consistent with the theoretical predictions and confirm the PT-symmetry breaking well.
Gramkow, Claus
1999-01-01
In this article two common approaches to averaging rotations are compared to a more advanced approach based on a Riemannian metric. Very offten the barycenter of the quaternions or matrices that represent the rotations are used as an estimate of the mean. These methods neglect that rotations belong...... approximations to the Riemannian metric, and that the subsequent corrections are inherient in the least squares estimation. Keywords: averaging rotations, Riemannian metric, matrix, quaternion...
Symmetric Euler orientation representations for orientational averaging.
Mayerhöfer, Thomas G
2005-09-01
A new kind of orientation representation called symmetric Euler orientation representation (SEOR) is presented. It is based on a combination of the conventional Euler orientation representations (Euler angles) and Hamilton's quaternions. The properties of the SEORs concerning orientational averaging are explored and compared to those of averaging schemes that are based on conventional Euler orientation representations. To that aim, the reflectance of a hypothetical polycrystalline material with orthorhombic crystal symmetry was calculated. The calculation was carried out according to the average refractive index theory (ARIT [T.G. Mayerhöfer, Appl. Spectrosc. 56 (2002) 1194]). It is shown that the use of averaging schemes based on conventional Euler orientation representations leads to a dependence of the result from the specific Euler orientation representation that was utilized and from the initial position of the crystal. The latter problem can be overcome partly by the introduction of a weighing factor, but only for two-axes-type Euler orientation representations. In case of a numerical evaluation of the average, a residual difference remains also if a two-axes type Euler orientation representation is used despite of the utilization of a weighing factor. In contrast, this problem does not occur if a symmetric Euler orientation representation is used as a matter of principle, while the result of the averaging for both types of orientation representations converges with increasing number of orientations considered in the numerical evaluation. Additionally, the use of a weighing factor and/or non-equally spaced steps in the numerical evaluation of the average is not necessary. The symmetrical Euler orientation representations are therefore ideally suited for the use in orientational averaging procedures.
1981-08-01
ten-diode lossless X-band combiner indicates a l-d-B locking bandwidth of 300 MHz and 10 dB gain , while the millimeter-wave DD 1AN731473 j ~ cjj... over the lossless case while still retaining rotating mode suppression properties. The penalty is typically an increase in combiner size and stored...resrerse side it necessary and identify b) tsock numnber) Power combining~ Lossless , radial-symmetric, TEM-line combiners Res-istive-stabilized radial
Rozgacheva, I K
2016-01-01
A precise solution of the general relativity equations for centrally symmetric distribution of a pseudoscalar field with U(1) symmetry is presented. It is found that energy density of the field is restricted in the symmetry center and falls with radial distance at a much slower rate than in numerical simulations of dark matter haloes. This result can solve the cusp problem for galaxies and the problem of rotation curves for galaxy exteriors.
Rotations with Rodrigues' Vector
Pina, E.
2011-01-01
The rotational dynamics was studied from the point of view of Rodrigues' vector. This vector is defined here by its connection with other forms of parametrization of the rotation matrix. The rotation matrix was expressed in terms of this vector. The angular velocity was computed using the components of Rodrigues' vector as coordinates. It appears…
Gramkow, Claus
2001-01-01
In this paper two common approaches to averaging rotations are compared to a more advanced approach based on a Riemannian metric. Very often the barycenter of the quaternions or matrices that represent the rotations are used as an estimate of the mean. These methods neglect that rotations belong...
Clinostat exposure and symmetrization of frog eggs
Nace, G. W.; Tremor, J. W.
1982-01-01
Since the orientation of unfertilized eggs and the righting of eggs after grey crescent formation do not affect the axes, attention here is directed toward a comparative study of the initial rotation of the fertilized egg, the so-called rotation of orientation (R-of-O). The goal of the investigation is to determine the timing and dynamics of the R-of-O (as distinct from inversion rotations), to confirm prior observations, and to examine the influence of gravity compensation at periods that might be crucial. Gravity compensation for 1 hr during the R-of-O is found to yield fewer abnormalities. It is hypothesized that it changes the axes and that return to normal conditions permits regulation. Longer exposure is found to yield more abnormalities, perhaps by perturbing both the action of the aster and regulation.
Communities and classes in symmetric fractals
Krawczyk, M J
2014-01-01
Two aspects of fractal networks are considered: the community structure and the class structure, where classes of nodes appear as a consequence of a local symmetry of nodes. The analysed systems are the networks constructed for two selected symmetric fractals: the Sierpinski triangle and the Koch curve. Communities are searched for by means of a set of differential equations. Overlapping nodes which belong to two different communities are identified by adding some noise to the initial connectivity matrix. Then, a node can be characterized by a spectrum of probabilities of belonging to different communities. Our main goal is that the overlapping nodes with the same spectra belong to the same class.
Quantum asymmetric cryptography with symmetric keys
Gao, Fei; Wen, Qiaoyan; Qin, Sujuan; Zhu, Fuchen
2009-12-01
Based on quantum encryption, we present a new idea for quantum public-key cryptography (QPKC) and construct a whole theoretical framework of a QPKC system. We show that the quantum-mechanical nature renders it feasible and reasonable to use symmetric keys in such a scheme, which is quite different from that in conventional public-key cryptography. The security of our scheme is analyzed and some features are discussed. Furthermore, the state-estimation attack to a prior QPKC scheme is demonstrated.
Quantum asymmetric cryptography with symmetric keys
Gao, Fei; Wen, Qiao-Yan; Qin, Su-Juan; Zhu, Fu-Chen
2008-01-01
Based on quantum encryption, we present a new idea for quantum public-key cryptography (QPKC) and construct a whole theoretical framework of a QPKC system. We show that the quantum-mechanical nature renders it feasible and reasonable to use symmetric keys in such a scheme, which is quite different from that in conventional public-key cryptography. The security of our scheme is analyzed and some features are discussed. Furthermore, the state-estimation attack to a prior QPKC scheme is demonstr...
Quantum asymmetric cryptography with symmetric keys
无
2009-01-01
Based on quantum encryption,we present a new idea for quantum public-key cryptography (QPKC) and construct a whole theoretical framework of a QPKC system. We show that the quantum-mechanical nature renders it feasible and reasonable to use symmetric keys in such a scheme,which is quite different from that in conventional public-key cryptography. The security of our scheme is analyzed and some features are discussed. Furthermore,the state-estimation attack to a prior QPKC scheme is demonstrated.