Nguyen, Tien Long; Sansour, Carlo; Hjiaj, Mohammed
2017-05-01
In this paper, an energy-momentum method for geometrically exact Timoshenko-type beam is proposed. The classical time integration schemes in dynamics are known to exhibit instability in the non-linear regime. The so-called Timoshenko-type beam with the use of rotational degree of freedom leads to simpler strain relations and simpler expressions of the inertial terms as compared to the well known Bernoulli-type model. The treatment of the Bernoulli-model has been recently addressed by the authors. In this present work, we extend our approach of using the strain rates to define the strain fields to in-plane geometrically exact Timoshenko-type beams. The large rotational degrees of freedom are exactly computed. The well-known enhanced strain method is used to avoid locking phenomena. Conservation of energy, momentum and angular momentum is proved formally and numerically. The excellent performance of the formulation will be demonstrated through a range of examples.
International Nuclear Information System (INIS)
Saverin, Joseph; Peukert, Juliane; Marten, David; Pechlivanoglou, George; Paschereit, Christian Oliver; Greenblatt, David
2016-01-01
The current paper investigates the aeroelastic modelling of large, flexible multi- MW wind turbine blades. Most current performance prediction tools make use of the Blade Element Momentum (BEM) model, based upon a number of simplifying assumptions that hold only under steady conditions. This is why a lifting line free vortex wake (LLFVW) algorithm is used here to accurately resolve unsteady wind turbine aerodynamics. A coupling to the structural analysis tool BeamDyn, based on geometrically exact beam theory, allows for time-resolved aeroelastic simulations with highly deflected blades including bend-twist, coupling. Predictions of blade loading and deformation for rigid and flexible blades are analysed with reference to different aerodynamic and structural approaches. The emergency shutdown procedure is chosen as an examplary design load case causing large deflections to place emphasis on the influence of structural coupling and demonstrate the necessity of high fidelity structural models. (paper)
Helicopter Rotor Load Prediction Using a Geometrically Exact Beam with Multicomponent Model
DEFF Research Database (Denmark)
Lee, Hyun-Ku; Viswamurthy, S.R.; Park, Sang Chul
2010-01-01
In this paper, an accurate structural dynamic analysis was developed for a helicopter rotor system including rotor control components, which was coupled to various aerodynamic and wake models in order to predict an aeroelastic response and the loads acting on the rotor. Its blade analysis was based...... rotor-blade/control-system model was loosely coupled with various inflow and wake models in order to simulate both hover and forward-flight conditions. The resulting rotor blade response and pitch link loads are in good agreement with those predicted byCAMRADII. The present analysis features both model...... on an intrinsic formulation of moving beams implemented in the time domain. The rotor control system was modeled as a combination of rigid and elastic components. A multicomponent analysis was then developed by coupling the beam finite element model with the rotor control system model to obtain a complete rotor-blade/control...
A geometrically exact beam element based on the absolute nodal coordinate formulation
International Nuclear Information System (INIS)
Gerstmayr, Johannes; Matikainen, Marko K.; Mikkola, Aki M.
2008-01-01
In this study, Reissner's classical nonlinear rod formulation, as implemented by Simo and Vu-Quoc by means of the large rotation vector approach, is implemented into the framework of the absolute nodal coordinate formulation. The implementation is accomplished in the planar case accounting for coupled axial, bending, and shear deformation. By employing the virtual work of elastic forces similarly to Simo and Vu-Quoc in the absolute nodal coordinate formulation, the numerical results of the formulation are identical to those of the large rotation vector formulation. It is noteworthy, however, that the material definition in the absolute nodal coordinate formulation can differ from the material definition used in Reissner's beam formulation. Based on an analytical eigenvalue analysis, it turns out that the high frequencies of cross section deformation modes in the absolute nodal coordinate formulation are only slightly higher than frequencies of common shear modes, which are present in the classical large rotation vector formulation of Simo and Vu-Quoc, as well. Thus, previous claims that the absolute nodal coordinate formulation is inefficient or would lead to ill-conditioned finite element matrices, as compared to classical approaches, could be refuted. In the introduced beam element, locking is prevented by means of reduced integration of certain parts of the elastic forces. Several classical large deformation static and dynamic examples as well as an eigenvalue analysis document the equivalence of classical nonlinear rod theories and the absolute nodal coordinate formulation for the case of appropriate material definitions. The results also agree highly with those computed in commercial finite element codes
International Nuclear Information System (INIS)
Wang, Lin; Liu, Xiongwei; Renevier, Nathalie; Stables, Matthew; Hall, George M.
2014-01-01
Due to the increasing size and flexibility of large wind turbine blades, accurate and reliable aeroelastic modelling is playing an important role for the design of large wind turbines. Most existing aeroelastic models are linear models based on assumption of small blade deflections. This assumption is not valid anymore for very flexible blade design because such blades often experience large deflections. In this paper, a novel nonlinear aeroelastic model for large wind turbine blades has been developed by combining BEM (blade element momentum) theory and mixed-form formulation of GEBT (geometrically exact beam theory). The nonlinear aeroelastic model takes account of large blade deflections and thus greatly improves the accuracy of aeroelastic analysis of wind turbine blades. The nonlinear aeroelastic model is implemented in COMSOL Multiphysics and validated with a series of benchmark calculation tests. The results show that good agreement is achieved when compared with experimental data, and its capability of handling large deflections is demonstrated. Finally the nonlinear aeroelastic model is applied to aeroelastic modelling of the parked WindPACT 1.5 MW baseline wind turbine, and reduced flapwise deflection from the nonlinear aeroelastic model is observed compared to the linear aeroelastic code FAST (Fatigue, Aerodynamics, Structures, and Turbulence). - Highlights: • A novel nonlinear aeroelastic model for wind turbine blades is developed. • The model takes account of large blade deflections and geometric nonlinearities. • The model is reliable and efficient for aeroelastic modelling of wind turbine blades. • The accuracy of the model is verified by a series of benchmark calculation tests. • The model provides more realistic aeroelastic modelling than FAST (Fatigue, Aerodynamics, Structures, and Turbulence)
Exact Solutions for Einstein's Hyperbolic Geometric Flow
International Nuclear Information System (INIS)
He Chunlei
2008-01-01
In this paper we investigate the Einstein's hyperbolic geometric flow and obtain some interesting exact solutions for this kind of flow. Many interesting properties of these exact solutions have also been analyzed and we believe that these properties of Einstein's hyperbolic geometric flow are very helpful to understanding the Einstein equations and the hyperbolic geometric flow
Geometrically exact nonlinear analysis of pre-twisted composite rotor blades
Directory of Open Access Journals (Sweden)
Li'na SHANG
2018-02-01
Full Text Available Modeling of pre-twisted composite rotor blades is very complicated not only because of the geometric non-linearity, but also because of the cross-sectional warping and the transverse shear deformation caused by the anisotropic material properties. In this paper, the geometrically exact nonlinear modeling of a generalized Timoshenko beam with arbitrary cross-sectional shape, generally anisotropic material behavior and large deflections has been presented based on Hodges’ method. The concept of decomposition of rotation tensor was used to express the strain in the beam. The variational asymptotic method was used to determine the arbitrary warping of the beam cross section. The generalized Timoshenko strain energy was derived from the equilibrium equations and the second-order asymptotically correct strain energy. The geometrically exact nonlinear equations of motion were established by Hamilton’s principle. The established modeling was used for the static and dynamic analysis of pre-twisted composite rotor blades, and the analytical results were validated based on experimental data. The influences of the transverse shear deformation on the pre-twisted composite rotor blade were investigated. The results indicate that the influences of the transverse shear deformation on the static deformation and the natural frequencies of the pre-twisted composite rotor blade are related to the length to chord ratio of the blade. Keywords: Geometrically exact, Nonlinear, Pre-twisted composite blade, Transverse shear deformation, Variational asymptotic, Warping
Exact Controllability and Perturbation Analysis for Elastic Beams
International Nuclear Information System (INIS)
Moreles, Miguel Angel
2004-01-01
The Rayleigh beam is a perturbation of the Bernoulli-Euler beam. We establish convergence of the solution of the Exact Controllability Problem for the Rayleigh beam to the corresponding solution of the Bernoulli-Euler beam. Convergence is related to a Singular Perturbation Problem. The main tool in solving this perturbation problem is a weak version of a lower bound for hyperbolic polynomials
Analysis of thin plates with holes by using exact geometrical representation within XFEM.
Perumal, Logah; Tso, C P; Leng, Lim Thong
2016-05-01
This paper presents analysis of thin plates with holes within the context of XFEM. New integration techniques are developed for exact geometrical representation of the holes. Numerical and exact integration techniques are presented, with some limitations for the exact integration technique. Simulation results show that the proposed techniques help to reduce the solution error, due to the exact geometrical representation of the holes and utilization of appropriate quadrature rules. Discussion on minimum order of integration order needed to achieve good accuracy and convergence for the techniques presented in this work is also included.
Computational Contact Mechanics Geometrically Exact Theory for Arbitrary Shaped Bodies
Konyukhov, Alexander
2013-01-01
This book contains a systematical analysis of geometrical situations leading to contact pairs -- point-to-surface, surface-to-surface, point-to-curve, curve-to-curve and curve-to-surface. Each contact pair is inherited with a special coordinate system based on its geometrical properties such as a Gaussian surface coordinate system or a Serret-Frenet curve coordinate system. The formulation in a covariant form allows in a straightforward fashion to consider various constitutive relations for a certain pair such as anisotropy for both frictional and structural parts. Then standard methods well known in computational contact mechanics such as penalty, Lagrange multiplier methods, combination of both and others are formulated in these coordinate systems. Such formulations require then the powerful apparatus of differential geometry of surfaces and curves as well as of convex analysis. The final goals of such transformations are then ready-for-implementation numerical algorithms within the finite e...
Directory of Open Access Journals (Sweden)
Huiqing Fang
2016-01-01
Full Text Available Based on geometrically exact beam theory, a hybrid interpolation is proposed for geometric nonlinear spatial Euler-Bernoulli beam elements. First, the Hermitian interpolation of the beam centerline was used for calculating nodal curvatures for two ends. Then, internal curvatures of the beam were interpolated with a second interpolation. At this point, C1 continuity was satisfied and nodal strain measures could be consistently derived from nodal displacement and rotation parameters. The explicit expression of nodal force without integration, as a function of global parameters, was founded by using the hybrid interpolation. Furthermore, the proposed beam element can be degenerated into linear beam element under the condition of small deformation. Objectivity of strain measures and patch tests are also discussed. Finally, four numerical examples are discussed to prove the validity and effectivity of the proposed beam element.
Exact suppression of depolarisation by beam-beam interaction in an electron ring
International Nuclear Information System (INIS)
Buon, J.
1983-03-01
It is shown that depolarisation due to beam-beam interaction can be exactly suppressed in an electron storage ring. The necessary ''spin matching'' conditions to be fulfilled are derived for a planar ring. They depend on the ring optics, assumed linear, but not on the features of the beam-beam force, like intensity and non-linearity. Extension to a ring equipped with 90 0 spin rotators is straightorward
Exact cone beam CT with a spiral scan
International Nuclear Information System (INIS)
Tam, K.C.; Samarasekera, S.; Sauer, F.
1998-01-01
A method is developed which makes it possible to scan and reconstruct an object with cone beam x-rays in a spiral scan path with area detectors much shorter than the length of the object. The method is mathematically exact. If only a region of interest of the object is to be imaged, a top circle scan at the top level of the region of interest and a bottom circle scan at the bottom level of the region of interest are added. The height of the detector is required to cover only the distance between adjacent turns in the spiral projected at the detector. To reconstruct the object, the Radon transform for each plane intersecting the object is computed from the totality of the cone beam data. This is achieved by suitably combining the cone beam data taken at different source positions on the scan path; the angular range of the cone beam data required at each source position can be determined easily with a mask which is the spiral scan path projected on the detector from the current source position. The spiral scan algorithm has been successfully validated with simulated cone beam data. (author)
Geometrical theory of nonlinear phase distortion of intense laser beams
International Nuclear Information System (INIS)
Glaze, J.A.; Hunt, J.T.; Speck, D.R.
1975-01-01
Phase distortion arising from whole beam self-focusing of intense laser pulses with arbitrary spatial profiles is treated in the limit of geometrical optics. The constant shape approximation is used to obtain the phase and angular distribution of the geometrical rays in the near field. Conditions for the validity of this approximation are discussed. Geometrical focusing of the aberrated beam is treated for the special case of a beam with axial symmetry. Equations are derived that show both the shift of the focus and the distortion of the intensity distribution that are caused by the nonlinear index of refraction of the optical medium. An illustrative example treats the case of beam distortion in a Nd:Glass amplifier
Geometrical and wave optics of paraxial beams.
Meron, M; Viccaro, P J; Lin, B
1999-06-01
Most calculational techniques used to evaluate beam propagation are geared towards either fully coherent or fully incoherent beams. The intermediate partial-coherence regime, while in principle known for a long time, has received comparably little attention so far. The resulting shortage of adequate calculational techniques is currently being felt in the realm of x-ray optics where, with the advent of third generation synchrotron light sources, partially coherent beams become increasingly common. The purpose of this paper is to present a calculational approach which, utilizing a "variance matrix" representation of paraxial beams, allows for a straightforward evaluation of wave propagation through an optical system. Being capable of dealing with an arbitrary degree of coherence, this approach covers the whole range from wave to ray optics, in a seamless fashion.
Auto-focusing accelerating hyper-geometric laser beams
International Nuclear Information System (INIS)
Kovalev, A A; Kotlyar, V V; Porfirev, A P
2016-01-01
We derive a new solution to the paraxial wave equation that defines a two-parameter family of three-dimensional structurally stable vortex annular auto-focusing hyper-geometric (AH) beams, with their complex amplitude expressed via a degenerate hyper-geometric function. The AH beams are found to carry an orbital angular momentum and be auto-focusing, propagating on an accelerating path toward a focus, where the annular intensity pattern is ‘sharply’ reduced in diameter. An explicit expression for the complex amplitude of vortex annular auto-focusing hyper-geometric-Gaussian beams is derived. The experiment has been shown to be in good agreement with theory. (paper)
Geometrical E-beam proximity correction for raster scan systems
Belic, Nikola; Eisenmann, Hans; Hartmann, Hans; Waas, Thomas
1999-04-01
High pattern fidelity is a basic requirement for the generation of masks containing sub micro structures and for direct writing. Increasing needs mainly emerging from OPC at mask level and x-ray lithography require a correction of the e-beam proximity effect. The most part of e-beam writers are raster scan system. This paper describes a new method for geometrical pattern correction in order to provide a correction solution for e-beam system that are not able to apply variable doses.
Geometric calibration method for multiple head cone beam SPECT systems
International Nuclear Information System (INIS)
Rizo, Ph.; Grangeat, P.; Guillemaud, R.; Sauze, R.
1993-01-01
A method is presented for performing geometric calibration on Single Photon Emission Tomography (SPECT) cone beam systems with multiple cone beam collimators, each having its own orientation parameters. This calibration method relies on the fact that, in tomography, for each head, the relative position of the rotation axis and of the collimator does not change during the acquisition. In order to ensure the method stability, the parameters to be estimated in intrinsic parameters and extrinsic parameters are separated. The intrinsic parameters describe the acquisition geometry and the extrinsic parameters position of the detection system with respect to the rotation axis. (authors) 3 refs
An online interactive geometric database including exact solutions of Einstein's field equations
International Nuclear Information System (INIS)
Ishak, Mustapha; Lake, Kayll
2002-01-01
We describe a new interactive database (GRDB) of geometric objects in the general area of differential geometry. Database objects include, but are not restricted to, exact solutions of Einstein's field equations. GRDB is designed for researchers (and teachers) in applied mathematics, physics and related fields. The flexible search environment allows the database to be useful over a wide spectrum of interests, for example, from practical considerations of neutron star models in astrophysics to abstract space-time classification schemes. The database is built using a modular and object-oriented design and uses several Java technologies (e.g. Applets, Servlets, JDBC). These are platform-independent and well adapted for applications developed for the World Wide Web. GRDB is accompanied by a virtual calculator (GRTensorJ), a graphical user interface to the computer algebra system GRTensorII, used to perform online coordinate, tetrad or basis calculations. The highly interactive nature of GRDB allows systematic internal self-checking and minimization of the required internal records. This new database is now available online at http://grdb.org
Exact computation of the Voronoi Diagram of spheres in 3D, its topology and its geometric invariants
DEFF Research Database (Denmark)
Anton, François; Mioc, Darka; Santos, Marcelo
2011-01-01
In this paper, we are addressing the exact computation of the Delaunay graph (or quasi-triangulation) and the Voronoi diagram of spheres using Wu’s algorithm. Our main contribution is first a methodology for automated derivation of invariants of the Delaunay empty circumcircle predicate for spheres...... and the Voronoi vertex of four spheres, then the application of this methodology to get all geometrical invariants that intervene in this problem and the exact computation of the Delaunay graph and the Voronoi diagram of spheres. To the best of our knowledge, there does not exist a comprehensive treatment...... of the exact computation with geometrical invariants of the Delaunay graph and the Voronoi diagram of spheres. Starting from the system of equations defining the zero-dimensional algebraic set of the problem, we are following Wu’s algorithm to transform the initial system into an equivalent Wu characteristic...
Gradients of geometrically necessary dislocations from white beam microdiffraction
International Nuclear Information System (INIS)
Barabash, R.I.; Ice, G.E.; Pang, J.W.L.
2005-01-01
Variations in the local crystallographic orientation due to the presence of geometrically necessary dislocations and dislocation boundaries smear the distribution of intensity near Laue reflections. Here, some simple model distributions of geometrically necessary dislocations, GNDs, are used to estimate the dislocation tensor field from the intensity distribution of Laue peaks. Streaking of the Laue spots is found to be quantitatively and qualitatively distinct depending on the ratio between the absorption coefficient and the GND density gradient. In addition, different slip systems cause distinctly different Laue-pattern streaking. Experimental Laue patterns are therefore sensitive to stored dislocations and GNDs. As an example, white beam microdiffraction was applied to characterize the dislocation arrangement in a deformed polycrystalline Ni grain during in situ uniaxial tension
Closed-Form Solutions for Gradient Elastic Beams with Geometric Discontinuities by Laplace Transform
Directory of Open Access Journals (Sweden)
Mustafa Özgür Yayli
2013-01-01
Full Text Available The static bending solution of a gradient elastic beam with external discontinuities is presented by Laplace transform. Its utility lies in the ability to switch differential equations to algebraic forms that are more easily solved. A Laplace transformation is applied to the governing equation which is then solved for the static deflection of the microbeam. The exact static response of the gradient elastic beam with external discontinuities is obtained by applying known initial conditions when the others are derived from boundary conditions. The results are given in a series of figures and compared with their classical counterparts. The main contribution of this paper is to provide a closed-form solution for the static deflection of microbeams under geometric discontinuities.
Geometric phase in a split-beam experiment measured with coupled neutron interference loops
International Nuclear Information System (INIS)
Hasegawa, Yuji; Zawisky, M.; Rauch, H.; Ioffe, A.
1996-01-01
A geometric phase factor is derived for a split-beam experiment as an example of cyclic evolutions. The geometric phase is given by one half of the solid angle independent of the spin of the beam. We observe this geometric phase with a two-loop neutron interferometer, where a reference beam can be added to the beam from one interference loop. All the experimental results show complete agreement with our theoretical treatment. (author)
Geometric beam coupling impedance of LHC secondary collimators
Frasciello, Oscar; Tomassini, Sandro; Zobov, Mikhail; Salvant, Benoit; Grudiev, Alexej; Mounet, Nicolas
2016-02-01
The High Luminosity LHC project is aimed at increasing the LHC luminosity by an order of magnitude. One of the key ingredients to achieve the luminosity goal is the beam intensity increase. In order to keep beam instabilities under control and to avoid excessive power losses a careful design of new vacuum chamber components and an improvement of the present LHC impedance model are required. Collimators are among the major impedance contributors. Measurements with beam have revealed that the betatron coherent tune shifts were higher by about a factor of 2 with respect to the theoretical predictions based on the LHC impedance model up to 2012. In that model the resistive wall impedance has been considered as the dominating impedance contribution for collimators. By carefully simulating also their geometric impedance we have contributed to the update of the LHC impedance model, reaching also a better agreement between the measured and simulated betatron tune shifts. During the just ended LHC Long Shutdown I (LSI), TCS/TCT collimators were replaced by new devices embedding BPMs and TT2-111R ferrite blocks. We present here preliminary estimations of their broad-band impedance, showing that an increase of about 20% is expected in the kick factors with respect to previous collimators without BPMs.
International Nuclear Information System (INIS)
Li Liang; Chen Zhiqiang; Xing Yuxiang; Zhang Li; Kang Kejun; Wang Ge
2006-01-01
In recent years, image reconstruction methods for cone-beam computed tomography (CT) have been extensively studied. However, few of these studies discussed computing parallel-beam projections from cone-beam projections. In this paper, we focus on the exact synthesis of complete or incomplete parallel-beam projections from cone-beam projections. First, an extended central slice theorem is described to establish a relationship between the Radon space and the Fourier space. Then, data sufficiency conditions are proposed for computing parallel-beam projection data from cone-beam data. Using these results, a general filtered backprojection algorithm is formulated that can exactly synthesize parallel-beam projection data from cone-beam projection data. As an example, we prove that parallel-beam projections can be exactly synthesized in an angular range in the case of circular cone-beam scanning. Interestingly, this angular range is larger than that derived in the Feldkamp reconstruction framework. Numerical experiments are performed in the circular scanning case to verify our method
Exact fan-beam and 4π-acquisition cone-beam SPECT algorithms with uniform attenuation correction
International Nuclear Information System (INIS)
Tang Qiulin; Zeng, Gengsheng L.; Wu Jiansheng; Gullberg, Grant T.
2005-01-01
This paper presents analytical fan-beam and cone-beam reconstruction algorithms that compensate for uniform attenuation in single photon emission computed tomography. First, a fan-beam algorithm is developed by obtaining a relationship between the two-dimensional (2D) Fourier transform of parallel-beam projections and fan-beam projections. Using this relationship, 2D Fourier transforms of equivalent parallel-beam projection data are obtained from the fan-beam projection data. Then a quasioptimal analytical reconstruction algorithm for uniformly attenuated Radon data, developed by Metz and Pan, is used to reconstruct the image. A cone-beam algorithm is developed by extending the fan-beam algorithm to 4π solid angle geometry. The cone-beam algorithm is also an exact algorithm
Ray, S. Saha
2018-04-01
In this paper, the symmetry analysis and similarity reduction of the (2+1)-dimensional Bogoyavlensky-Konopelchenko (B-K) equation are investigated by means of the geometric approach of an invariance group, which is equivalent to the classical Lie symmetry method. Using the extended Harrison and Estabrook’s differential forms approach, the infinitesimal generators for (2+1)-dimensional B-K equation are obtained. Firstly, the vector field associated with the Lie group of transformation is derived. Then the symmetry reduction and the corresponding explicit exact solution of (2+1)-dimensional B-K equation is obtained.
International Nuclear Information System (INIS)
Brenner, S.E.; Gandyl', E.M.; Podkopaev, A.P.
1995-01-01
The dynamics of high-current relativistic electron beam moving trough the cylindrical drift space has been modelled by the large particles, the shape of which allows to solve the Poisson equations exactly, and in such a way to avoid the linearization being usually used in those problems. The expressions for the components of own electric field of electron beam passing through the cylindrical drift space have been obtained. (author). 11 refs., 1 fig
Exact Stiffness for Beams on Kerr-Type Foundation: The Virtual Force Approach
Directory of Open Access Journals (Sweden)
Suchart Limkatanyu
2013-01-01
Full Text Available This paper alternatively derives the exact element stiffness equation for a beam on Kerr-type foundation. The shear coupling between the individual Winkler-spring components and the peripheral discontinuity at the boundaries between the loaded and the unloaded soil surfaces are taken into account in this proposed model. The element flexibility matrix is derived based on the virtual force principle and forms the core of the exact element stiffness matrix. The sixth-order governing differential compatibility of the problem is revealed using the virtual force principle and solved analytically to obtain the exact force interpolation functions. The matrix virtual force equation is employed to obtain the exact element flexibility matrix based on the exact force interpolation functions. The so-called “natural” element stiffness matrix is obtained by inverting the exact element flexibility matrix. One numerical example is utilized to confirm the accuracy and the efficiency of the proposed beam element on Kerr-type foundation and to show a more realistic distribution of interactive foundation force.
Navas-Montilla, A.; Murillo, J.
2016-07-01
In this work, an arbitrary order HLL-type numerical scheme is constructed using the flux-ADER methodology. The proposed scheme is based on an augmented Derivative Riemann solver that was used for the first time in Navas-Montilla and Murillo (2015) [1]. Such solver, hereafter referred to as Flux-Source (FS) solver, was conceived as a high order extension of the augmented Roe solver and led to the generation of a novel numerical scheme called AR-ADER scheme. Here, we provide a general definition of the FS solver independently of the Riemann solver used in it. Moreover, a simplified version of the solver, referred to as Linearized-Flux-Source (LFS) solver, is presented. This novel version of the FS solver allows to compute the solution without requiring reconstruction of derivatives of the fluxes, nevertheless some drawbacks are evidenced. In contrast to other previously defined Derivative Riemann solvers, the proposed FS and LFS solvers take into account the presence of the source term in the resolution of the Derivative Riemann Problem (DRP), which is of particular interest when dealing with geometric source terms. When applied to the shallow water equations, the proposed HLLS-ADER and AR-ADER schemes can be constructed to fulfill the exactly well-balanced property, showing that an arbitrary quadrature of the integral of the source inside the cell does not ensure energy balanced solutions. As a result of this work, energy balanced flux-ADER schemes that provide the exact solution for steady cases and that converge to the exact solution with arbitrary order for transient cases are constructed.
Jurčišinová, E.; Jurčišin, M.
2018-02-01
The influence of the next-nearest-neighbor interaction on the properties of the geometrically frustrated antiferromagnetic systems is investigated in the framework of the exactly solvable antiferromagnetic spin- 1 / 2 Ising model in the external magnetic field on the square-kagome recursive lattice, where the next-nearest-neighbor interaction is supposed between sites within each elementary square of the lattice. The thermodynamic properties of the model are investigated in detail and it is shown that the competition between the nearest-neighbor antiferromagnetic interaction and the next-nearest-neighbor ferromagnetic interaction changes properties of the single-point ground states but does not change the frustrated character of the basic model. On the other hand, the presence of the antiferromagnetic next-nearest-neighbor interaction leads to the enhancement of the frustration effects with the formation of additional plateau and single-point ground states at low temperatures. Exact expressions for magnetizations and residual entropies of all ground states of the model are found. It is shown that the model exhibits various ground states with the same value of magnetization but different macroscopic degeneracies as well as the ground states with different values of magnetization but the same value of the residual entropy. The specific heat capacity is investigated and it is shown that the model exhibits the Schottky-type anomaly behavior in the vicinity of each single-point ground state value of the magnetic field. The formation of the field-induced double-peak structure of the specific heat capacity at low temperatures is demonstrated and it is shown that its very existence is directly related to the presence of highly macroscopically degenerated single-point ground states in the model.
An improved exact inversion formula for solenoidal fields in cone beam vector tomography
Katsevich, Alexander; Rothermel, Dimitri; Schuster, Thomas
2017-06-01
In this paper we present an improved inversion formula for the 3D cone beam transform of vector fields supported in the unit ball which is exact for solenoidal fields. It is well known that only the solenoidal part of a vector field can be determined from the longitudinal ray transform of a vector field in cone beam geometry. The inversion formula, as it was developed in Katsevich and Schuster (2013 An exact inversion formula for cone beam vector tomography Inverse Problems 29 065013), consists of two parts. The first part is of the filtered backprojection type, whereas the second part is a costly 4D integration and very inefficient. In this article we tackle this second term and obtain an improved formula, which is easy to implement and saves one order of integration. We also show that the first part contains all information about the curl of the field, whereas the second part has information about the boundary values. More precisely, the second part vanishes if the solenoidal part of the original field is tangential at the boundary. A number of numerical tests presented in the paper confirm the theoretical results and the exactness of the formula. Also, we obtain an inversion algorithm that works for general convex domains.
Energy Technology Data Exchange (ETDEWEB)
Sharma, Pankaj, E-mail: psharma@rtu.ac.in; Parashar, Sandeep Kumar, E-mail: parashar2@yahoo.com [Mechanical Engineering Department, Rajasthan Technical University, Kota (India)
2016-05-06
The priority of this paper is to obtain the exact analytical solution for free flexural vibration of FGPM beam actuated using the d{sub 15} effect. In piezoelectric actuators, the potential use of d{sub 15} effect has been of particular interest for engineering applications since shear piezoelectric coefficient d15 is much higher than the other piezoelectric coupling constants d{sub 31} and d{sub 33}. The applications of shear actuators are to induce and control the flexural vibrations of beams and plates. In this study, a modified Timoshenko beam theory is used where electric potential is assumed to vary sinusoidaly along the thickness direction. The material properties are assumed to be graded across the thickness in accordance with power law distribution. Hamilton's principle is employed to obtain the equations of motion along with the associated boundary conditions for FGPM beams. Exact analytical solution is derived thus obtained equations of motion. Results for clamped-clamped and clamped-free boundary conditions are presented. The presented result and method shell serve as benchmark for comparing the results obtained from the other approximate methods.
Stabilization of exact nonlinear Timoshenko beams in space by boundary feedback
Do, K. D.
2018-05-01
Boundary feedback controllers are designed to stabilize Timoshenko beams with large translational and rotational motions in space under external disturbances. The exact nonlinear partial differential equations governing motion of the beams are derived and used in the control design. The designed controllers guarantee globally practically asymptotically (and locally practically exponentially) stability of the beam motions at the reference state. The control design, well-posedness and stability analysis are based on various relationships between the earth-fixed and body-fixed coordinates, Sobolev embeddings, and a Lyapunov-type theorem developed to study well-posedness and stability for a class of evolution systems in Hilbert space. Simulation results are included to illustrate the effectiveness of the proposed control design.
Energy Technology Data Exchange (ETDEWEB)
Coakley, K.J., E-mail: kevin.coakley@nist.go [National Institute of Standards and Technology, 325 Broadway, Boulder, CO 80305 (United States); Dewey, M.S. [National Institute of Standards and Technology, Gaithersburg, MD (United States); Yue, A.T. [University of Tennessee, Knoxville, TN (United States); Laptev, A.B. [Tulane University, New Orleans, LA (United States)
2009-12-11
Many experiments at neutron scattering facilities require nearly monochromatic neutron beams. In such experiments, one must accurately measure the mean wavelength of the beam. We seek to reduce the systematic uncertainty of this measurement to approximately 0.1%. This work is motivated mainly by an effort to improve the measurement of the neutron lifetime determined from data collected in a 2003 in-beam experiment performed at NIST. More specifically, we seek to reduce systematic uncertainty by calibrating the neutron detector used in this lifetime experiment. This calibration requires simultaneous measurement of the responses of both the neutron detector used in the lifetime experiment and an absolute black neutron detector to a highly collimated nearly monochromatic beam of cold neutrons, as well as a separate measurement of the mean wavelength of the neutron beam. The calibration uncertainty will depend on the uncertainty of the measured efficiency of the black neutron detector and the uncertainty of the measured mean wavelength. The mean wavelength of the beam is measured by Bragg diffracting the beam from a nearly perfect silicon analyzer crystal. Given the rocking curve data and knowledge of the directions of the rocking axis and the normal to the scattering planes in the silicon crystal, one determines the mean wavelength of the beam. In practice, the direction of the rocking axis and the normal to the silicon scattering planes are not known exactly. Based on Monte Carlo simulation studies, we quantify systematic uncertainties in the mean wavelength measurement due to these geometric errors. Both theoretical and empirical results are presented and compared.
The completeness condition and source orbits for exact image reconstruction in 3D cone-beam CT
International Nuclear Information System (INIS)
Mao Xiping; Kang Kejun
1997-01-01
The completeness condition for exact image reconstruction in 3D cone-beam CT are carefully analyzed in theory, and discussions about some source orbits which fulfill the completeness condition are followed
Exact free vibration of multi-step Timoshenko beam system with several attachments
Farghaly, S. H.; El-Sayed, T. A.
2016-05-01
This paper deals with the analysis of the natural frequencies, mode shapes of an axially loaded multi-step Timoshenko beam combined system carrying several attachments. The influence of system design and the proposed sub-system non-dimensional parameters on the combined system characteristics are the major part of this investigation. The effect of material properties, rotary inertia and shear deformation of the beam system for each span are included. The end masses are elastically supported against rotation and translation at an offset point from the point of attachment. A sub-system having two degrees of freedom is located at the beam ends and at any of the intermediate stations and acts as a support and/or a suspension. The boundary conditions of the ordinary differential equation governing the lateral deflections and slope due to bending of the beam system including the shear force term, due to the sub-system, have been formulated. Exact global coefficient matrices for the combined modal frequencies, the modal shape and for the discrete sub-system have been derived. Based on these formulae, detailed parametric studies of the combined system are carried out. The applied mathematical model is valid for wide range of applications especially in mechanical, naval and structural engineering fields.
International Nuclear Information System (INIS)
Li Jing; Sun Yi; Zhu Peiping
2013-01-01
Differential phase-contrast computed tomography (DPC-CT) reconstruction problems are usually solved by using parallel-, fan- or cone-beam algorithms. For rod-shaped objects, the x-ray beams cannot recover all the slices of the sample at the same time. Thus, if a rod-shaped sample is required to be reconstructed by the above algorithms, one should alternately perform translation and rotation on this sample, which leads to lower efficiency. The helical cone-beam CT may significantly improve scanning efficiency for rod-shaped objects over other algorithms. In this paper, we propose a theoretically exact filter-backprojection algorithm for helical cone-beam DPC-CT, which can be applied to reconstruct the refractive index decrement distribution of the samples directly from two-dimensional differential phase-contrast images. Numerical simulations are conducted to verify the proposed algorithm. Our work provides a potential solution for inspecting the rod-shaped samples using DPC-CT, which may be applicable with the evolution of DPC-CT equipments. (paper)
Energy Technology Data Exchange (ETDEWEB)
Bundesmann, Carsten; Feder, Rene; Neumann, Horst [Leibniz-Institut fuer Oberflaechenmodifizierung e.V., Leipzig (Germany)
2012-07-01
Ion beam sputtering (IBS) offers, in contrast to other physical vapour deposition techniques, such as magnetron sputtering or electron beam evaporation, the opportunity to change the properties of the layer forming particles (sputtered and scattered particles) by varying ion beam parameters (ion species, ion energy) and geometrical parameters (ion incidence angle, emission angle). Consequently, these effects can be utilized to tailor thin film properties [1]. The goal is to study systematically the correlations between the primary and secondary parameters and, at last, the effects on the properties of Si thin films, such as optical properties, stress, surface topography and composition. First experimental results are presented for Ar-ion sputtering of Si.
Directory of Open Access Journals (Sweden)
Şeref Doğuşcan Akbaş
2013-01-01
Full Text Available Geometrically nonlinear static analysis of edge cracked cantilever Timoshenko beams composed of functionally graded material (FGM subjected to a nonfollower transversal point load at the free end of the beam is studied with large displacements and large rotations. Material properties of the beam change in the height direction according to exponential distributions. The cracked beam is modeled as an assembly of two subbeams connected through a massless elastic rotational spring. In the study, the finite element of the beam is constructed by using the total Lagrangian Timoshenko beam element approximation. The nonlinear problem is solved by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. The convergence study is performed for various numbers of finite elements. In the study, the effects of the location of crack, the depth of the crack, and various material distributions on the nonlinear static response of the FGM beam are investigated in detail. Also, the difference between the geometrically linear and nonlinear analysis of edge cracked FGM beam is investigated in detail.
Structure-preserving geometric algorithms for plasma physics and beam physics
Qin, Hong
2017-10-01
Standard algorithms in the plasma physics and beam physics do not possess the long-term accuracy and fidelity required in the study of multi-scale dynamics, because they do not preserve the geometric structures of the physical systems, such as the local energy-momentum conservation, symplectic structure and gauge symmetry. As a result, numerical errors accumulate coherently with time and long-term simulation results are not reliable. To overcome this difficulty, since 2008 structure-preserving geometric algorithms have been developed. This new generation of algorithms utilizes advanced techniques, such as interpolating differential forms, canonical and non-canonical symplectic integrators, and finite element exterior calculus to guarantee gauge symmetry and charge conservation, and the conservation of energy-momentum and symplectic structure. It is our vision that future numerical capabilities in plasma physics and beam physics will be based on the structure-preserving geometric algorithms.
Accurate technique for complete geometric calibration of cone-beam computed tomography systems
International Nuclear Information System (INIS)
Cho Youngbin; Moseley, Douglas J.; Siewerdsen, Jeffrey H.; Jaffray, David A.
2005-01-01
Cone-beam computed tomography systems have been developed to provide in situ imaging for the purpose of guiding radiation therapy. Clinical systems have been constructed using this approach, a clinical linear accelerator (Elekta Synergy RP) and an iso-centric C-arm. Geometric calibration involves the estimation of a set of parameters that describes the geometry of such systems, and is essential for accurate image reconstruction. We have developed a general analytic algorithm and corresponding calibration phantom for estimating these geometric parameters in cone-beam computed tomography (CT) systems. The performance of the calibration algorithm is evaluated and its application is discussed. The algorithm makes use of a calibration phantom to estimate the geometric parameters of the system. The phantom consists of 24 steel ball bearings (BBs) in a known geometry. Twelve BBs are spaced evenly at 30 deg in two plane-parallel circles separated by a given distance along the tube axis. The detector (e.g., a flat panel detector) is assumed to have no spatial distortion. The method estimates geometric parameters including the position of the x-ray source, position, and rotation of the detector, and gantry angle, and can describe complex source-detector trajectories. The accuracy and sensitivity of the calibration algorithm was analyzed. The calibration algorithm estimates geometric parameters in a high level of accuracy such that the quality of CT reconstruction is not degraded by the error of estimation. Sensitivity analysis shows uncertainty of 0.01 deg. (around beam direction) to 0.3 deg. (normal to the beam direction) in rotation, and 0.2 mm (orthogonal to the beam direction) to 4.9 mm (beam direction) in position for the medical linear accelerator geometry. Experimental measurements using a laboratory bench Cone-beam CT system of known geometry demonstrate the sensitivity of the method in detecting small changes in the imaging geometry with an uncertainty of 0.1 mm in
Exact Reconstruction From Uniformly Attenuated Helical Cone-Beam Projections in SPECT
International Nuclear Information System (INIS)
Gullberg, Grant T.; Huang, Qiu; You, Jiangsheng; Zeng, Gengsheng L.
2008-01-01
In recent years the development of cone-beam reconstruction algorithms has been an active research area in x-ray computed tomography (CT), and significant progress has been made in the advancement of algorithms. Theoretically exact and computationally efficient analytical algorithms can be found in the literature. However, in single photon emission computed tomography (SPECT), published cone-beam reconstruction algorithms are either approximate or involve iterative methods. The SPECT reconstruction problem is more complicated due to degradations in the imaging detection process, one of which is the effect of attenuation of gamma ray photons. Attenuation should be compensated for to obtain quantitative results. In this paper, an analytical reconstruction algorithm for uniformly attenuated cone-beam projection data is presented for SPECT imaging. The algorithm adopts the DBH method, a procedure consisting of differentiation and backprojection followed by a finite inverse cosh-weighted Hilbert transform. The significance of the proposed approach is that a selected region of interest can be reconstructed even with a detector with a reduced field of view. The algorithm is designed for a general trajectory. However, to validate the algorithm, a numerical study was performed using a helical trajectory. The implementation is efficient and the simulation result is promising
Generation of equal-intensity coherent optical beams by binary geometrical phase on metasurface
Energy Technology Data Exchange (ETDEWEB)
Wang, Zheng-Han; Jiang, Shang-Chi; Xiong, Xiang; Peng, Ru-Wen, E-mail: rwpeng@nju.edu.cn, E-mail: muwang@nju.edu.cn; Wang, Mu, E-mail: rwpeng@nju.edu.cn, E-mail: muwang@nju.edu.cn [National Laboratory of Solid State Microstructures and School of Physics, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093 (China)
2016-06-27
We report here the design and realization of a broadband, equal-intensity optical beam splitter with a dispersion-free binary geometric phase on a metasurface with unit cell consisting of two mirror-symmetric elements. We demonstrate experimentally that two identical beams can be efficiently generated with incidence of any polarization. The efficiency of the device reaches 80% at 1120 nm and keeps larger than 70% in the range of 1000–1400 nm. We suggest that this approach for generating identical, coherent beams have wide applications in diffraction optics and in entangled photon light source for quantum communication.
Douglas, David R [York County, VA
2012-01-10
A method of using off-axis particle beam injection in energy-recovering linear accelerators that increases operational efficiency while eliminating the need to merge the high energy re-circulating beam with an injected low energy beam. In this arrangement, the high energy re-circulating beam and the low energy beam are manipulated such that they are within a predetermined distance from one another and then the two immerged beams are injected into the linac and propagated through the system. The configuration permits injection without geometric beam merging as well as decelerated beam extraction without the use of typical beamline elements.
Yang, Guang; Lin, Qingyu; Ding, Yu; Tian, Di; Duan, Yixiang
2015-01-01
A new laser induced breakdown spectroscopy (LIBS) based on single-beam-splitting (SBS) and proper optical geometric configuration has been initially explored in this work for effective signal enhancement. In order to improve the interaction efficiency of laser energy with the ablated material, a laser beam operated in pulse mode was divided into two streams to ablate/excite the target sample in different directions instead of the conventional one beam excitation in single pulse LIBS (SP-LIBS). In spatial configuration, the laser beam geometry plays an important role in the emission signal enhancement. Thus, an adjustable geometric configuration with variable incident angle between the two splitted laser beams was constructed for achieving maximum signal enhancement. With the optimized angles of 60° and 70° for Al and Cu atomic emission lines at 396.15 nm and 324.75 nm respectively, about 5.6- and 4.8-folds signal enhancements were achieved for aluminum alloy and copper alloy samples compared to SP-LIBS. Furthermore, the temporal analysis, in which the intensity of atomic lines in SP-LIBS decayed at least ten times faster than the SBS-LIBS, proved that the energy coupling efficiency of SBS-LIBS was significantly higher than that of SP-LIBS. PMID:25557721
Vacaru, Sergiu I.; Yazici, Enis
2014-01-01
We show that a geometric techniques can be elaborated and applied for constructing generic off-diagonal exact solutions in $f(R,T)$--modified gravity for systems of gravitational-Yang-Mills-Higgs equations. The corresponding classes of metrics and generalized connections are determined by generating and integration functions which depend, in general, on all space and time coordinates and may possess, or not, Killing symmetries. For nonholonomic constraints resulting in Levi-Civita configurations, we can extract solutions of the Einstein-Yang-Mills-Higgs equations. We show that the constructions simplify substantially for metrics with at least one Killing vector. There are provided and analyzed some examples of exact solutions describing generic off-diagonal modifications to black hole/ellipsoid and solitonic configurations.
DEFF Research Database (Denmark)
Lee, Daniel Sang-Hoon; Naboni, Emanuele
2017-01-01
mass effect (and the implication on thermal comfort) and the given geometrical parameters of exposed soffit reinforced concrete beams are explored. The geometrical parameters of the beams are initially defined in means of structural optimisation. The beams consist of flange and web in likeness of T...... the resultant heat exchange behaviour, and the implication on thermal comfort indoor environment. However, the current paper presents the thermal mass characteristics of one geometrical type. The study is based on results derived from computational fluid dynamics (CFD) analysis, where Rhino 3D is used......The paper presents a research exploring the thermal mass effect of reinforced concrete beams with structurally optimised geometrical forms. Fully exposed concrete soffits in architectural contexts create more than just visual impacts on the indoor climate through their possible interferences...
Directory of Open Access Journals (Sweden)
Litesh N. Sulbhewar
Full Text Available Abstract The conventional Timoshenko piezoelectric beam finite elements based on First-order Shear Deformation Theory (FSDT do not maintain the accuracy and convergence consistently over the applicable range of material and geometric properties. In these elements, the inaccuracy arises due to the induced potential effects in the transverse direction and inefficiency arises due to the use of independently assumed linear polynomial interpolation of the field variables in the longitudinal direction. In this work, a novel FSDT-based piezoelectric beam finite element is proposed which is devoid of these deficiencies. A variational formulation with consistent through-thickness potential is developed. The governing equilibrium equations are used to derive the coupled field relations. These relations are used to develop a polynomial interpolation scheme which properly accommodates the bending-extension, bending-shear and induced potential couplings to produce accurate results in an efficient manner. It is noteworthy that this consistently accurate and efficient beam finite element uses the same nodal variables as of conventional FSDT formulations available in the literature. Comparison of numerical results proves the consistent accuracy and efficiency of the proposed formulation irrespective of geometric and material configurations, unlike the conventional formulations.
International Nuclear Information System (INIS)
Leng Shuai; Zhuang Tingliang; Nett, Brian E; Chen Guanghong
2005-01-01
In this paper, we present a new algorithm designed for a specific data truncation problem in fan-beam CT. We consider a scanning configuration in which the fan-beam projection data are acquired from an asymmetrically positioned half-sized detector. Namely, the asymmetric detector only covers one half of the scanning field of view. Thus, the acquired fan-beam projection data are truncated at every view angle. If an explicit data rebinning process is not invoked, this data acquisition configuration will reek havoc on many known fan-beam image reconstruction schemes including the standard filtered backprojection (FBP) algorithm and the super-short-scan FBP reconstruction algorithms. However, we demonstrate that a recently developed fan-beam image reconstruction algorithm which reconstructs an image via filtering a backprojection image of differentiated projection data (FBPD) survives the above fan-beam data truncation problem. Namely, we may exactly reconstruct the whole image object using the truncated data acquired in a full scan mode (2π angular range). We may also exactly reconstruct a small region of interest (ROI) using the truncated projection data acquired in a short-scan mode (less than 2π angular range). The most important characteristic of the proposed reconstruction scheme is that an explicit data rebinning process is not introduced. Numerical simulations were conducted to validate the new reconstruction algorithm
Geometrical correction of the e-beam proximity effect for raster scan systems
Belic, Nikola; Eisenmann, Hans; Hartmann, Hans; Waas, Thomas
1999-06-01
Increasing demands on pattern fidelity and CD accuracy in e- beam lithography require a correction of the e-beam proximity effect. The new needs are mainly coming from OPC at mask level and x-ray lithography. The e-beam proximity limits the achievable resolution and affects neighboring structures causing under- or over-exposion depending on the local pattern densities and process settings. Methods to compensate for this unequilibrated does distribution usually use a dose modulation or multiple passes. In general raster scan systems are not able to apply variable doses in order to compensate for the proximity effect. For system of this kind a geometrical modulation of the original pattern offers a solution for compensation of line edge deviations due to the proximity effect. In this paper a new method for the fast correction of the e-beam proximity effect via geometrical pattern optimization is described. The method consists of two steps. In a first step the pattern dependent dose distribution caused by back scattering is calculated by convolution of the pattern with the long range part of the proximity function. The restriction to the long range part result in a quadratic sped gain in computing time for the transformation. The influence of the short range part coming from forward scattering is not pattern dependent and can therefore be determined separately in a second step. The second calculation yields the dose curve at the border of a written structure. The finite gradient of this curve leads to an edge displacement depending on the amount of underground dosage at the observed position which was previously determined in the pattern dependent step. This unintended edge displacement is corrected by splitting the line into segments and shifting them by multiples of the writers address grid to the opposite direction.
Beam heat load due to geometrical and resistive wall impedance in COLDDIAG
Casalbuoni, S.; Migliorati, M.; Mostacci, A.; Palumbo, L.; Spataro, B.
2012-11-01
One of the still open issues for the development of superconductive insertion devices is the understanding of the heat intake from the electron beam. With the aim of measuring the beam heat load to a cold bore and the hope to gain a deeper understanding in the underlying mechanisms, a cold vacuum chamber for diagnostics (COLDDIAG) was built. It is equipped with the following instrumentation: retarding field analyzers to measure the electron flux, temperature sensors to measure the beam heat load, pressure gauges, and mass spectrometers to measure the gas content. Possible beam heat load sources are: synchrotron radiation, wakefield effects due to geometrical and resistive wall impedance and electron/ion bombardment. The flexibility of the engineering design will allow the installation of the cryostat in different synchrotron light sources. COLDDIAG was first installed in the Diamond Light Source (DLS) in 2011. Due to a mechanical failure of the thermal transition of the cold liner, the cryostat had to be removed after one week of operation. After having implemented design changes in the thermal liner transition, COLDDIAG has been reinstalled in the DLS at the end of August 2012. In order to understand the beam heat load mechanism it is important to compare the measured COLDDIAG parameters with theoretical expectations. In this paper we report on the analytical and numerical computation of the COLDDIAG beam heat load due to coupling impedances deriving from unavoidable step transitions, ports used for pumping and diagnostics, surface roughness, and resistive wall. The results might have an important impact on future technological solutions to be applied to cold bore devices.
Quan, Wei-cai; Zhang, Zhu-ying; Zhang, Ai-qun; Zhang, Qi-feng; Tian, Yu
2015-04-01
This paper proposes a geometrically exact formulation for three-dimensional static and dynamic analyses of the umbilical cable in a deep-sea remotely operated vehicle (ROV) system. The presented formulation takes account of the geometric nonlinearities of large displacement, effects of axial load and bending stiffness for modeling of slack cables. The resulting nonlinear second-order governing equations are discretized spatially by the finite element method and solved temporally by the generalized- α implicit time integration algorithm, which is adapted to the case of varying coefficient matrices. The ability to consider three-dimensional union action of ocean current and ship heave motion upon the umbilical cable is the key feature of this analysis. The presented formulation is firstly validated, and then three numerical examples for the umbilical cable in a deep-sea ROV system are demonstrated and discussed, including the steady configurations only under the action of depth-dependent ocean current, the dynamic responses in the case of the only ship heave motion, and in the case of the combined action of the ship heave motion and ocean current.
Directory of Open Access Journals (Sweden)
Francisco Casesnoves
2014-08-01
Full Text Available Purpose: Static wedge filters (WF are commonly used in radiation therapy, forward and/or inverse planning. We calculated the exact 2D/3D geometrical pathway of the photon-beam through the usual alloy WF, in order to get a better dose related to the beam intensity attenuation factor(s, after the beam has passed through the WF. The objective was to provide general formulation into the Anisotropic Analytical Algorithm (AAA model coordinates system (depending on collimator/wedge angles that also can be applied to other models. Additionally, second purpose of this study was to develop integral formulation for 3D wedge exponential factor with statistical approximations, with introduction for the limit angle/conformal wedge.Methods: The radiotherapy model used to develop this mathematical task is the classical superposition-convolution algorithm, AAA (developed by Ulmer and Harder. We worked with optimal geometrical approximations to make the computational IMRT calculations quicker/reduce the planning-system time. Analytic geometry/computational-techniques to carry out simulations (for standard wedges are detailed/developed sharply. Integral developments/integral-statistical approximations are explained. Beam-divergence limit Angle for optimal wedge filtration formulas is calculated/sketched, with geometrical approximations. Fundamental trigonometry is used for this purpose.Results: Extent simulation tables for WF of 15º, 30º, 45º, and 60º are shown with errors. As a result, it is possible to determine the best individual treatment dose distribution for each patient. We presented these basic simulations/numerical examples for standard manufacturing WF of straight sloping surface, to check the accuracy/errors of the calculations. Simulations results give low RMS/Relative Error values (formulated for WF of 15º, 30º, 45º, and 60º.Conclusion: We obtained a series of formulas of analytic geometry for WF that can be applied for any particular dose
Nonlinear focal shift beyond the geometrical focus in moderately focused acoustic beams.
Camarena, Francisco; Adrián-Martínez, Silvia; Jiménez, Noé; Sánchez-Morcillo, Víctor
2013-08-01
The phenomenon of the displacement of the position along the axis of the pressure, intensity, and radiation force maxima of focused acoustic beams under increasing driving voltages (nonlinear focal shift) is studied for the case of a moderately focused beam. The theoretical and experimental results show the existence of this shift along the axis when the initial pressure in the transducer increases until the acoustic field reaches the fully developed nonlinear regime of propagation. Experimental data show that at high amplitudes and for moderate focusing, the position of the on-axis pressure maximum and radiation force maximum can surpass the geometrical focal length. On the contrary, the on-axis pressure minimum approaches the transducer under increasing driving voltages, increasing the distance between the positive and negative peak pressure in the beam. These results are in agreement with numerical KZK model predictions and the existed data of other authors and can be explained according to the effect of self-refraction characteristic of the nonlinear regime of propagation.
An exact dynamic stiffness matrix for axially loaded double-beam ...
Indian Academy of Sciences (India)
identical beams and the effects of shear deformation and rotary inertia. Further, even fewer papers about the free vibration of the double-beam systems considering the effects of the axial force, shear defor- mation and rotary inertia in a unitary ...
Geometric Parameters Estimation and Calibration in Cone-Beam Micro-CT
Directory of Open Access Journals (Sweden)
Jintao Zhao
2015-09-01
Full Text Available The quality of Computed Tomography (CT images crucially depends on the precise knowledge of the scanner geometry. Therefore, it is necessary to estimate and calibrate the misalignments before image acquisition. In this paper, a Two-Piece-Ball (TPB phantom is used to estimate a set of parameters that describe the geometry of a cone-beam CT system. Only multiple projections of the TPB phantom at one position are required, which can avoid the rotation errors when acquiring multi-angle projections. Also, a corresponding algorithm is derived. The performance of the method is evaluated through simulation and experimental data. The results demonstrated that the proposed method is valid and easy to implement. Furthermore, the experimental results from the Micro-CT system demonstrate the ability to reduce artifacts and improve image quality through geometric parameter calibration.
Energy Technology Data Exchange (ETDEWEB)
Xie, M. [Lawrence Berkeley Lab., CA (United States)
1995-12-31
I present an exact calculation of free-electron-laser (FEL) eigenmodes (fundamental as well as higher order modes) in the exponential-gain regime. These eigenmodes specify transverse profiles and exponential growth rates of the laser field, and they are self-consistent solutions of the coupled Maxwell-Vlasov equations describing the FEL interaction taking into account the effects due to energy spread, emittance and betatron oscillations of the electron beam, and diffraction and guiding of the laser field. The unperturbed electron distribution is assumed to be of Gaussian shape in four dimensional transverse phase space and in the energy variable, but uniform in longitudinal coordinate. The focusing of the electron beam is assumed to be matched to the natural wiggler focusing in both transverse planes. With these assumptions the eigenvalue problem can be reduced to a numerically manageable integral equation and solved exactly with a kernel iteration method. An approximate, but more efficient solution of the integral equation is also obtained for the fundamental mode by a variational technique, which is shown to agree well with the exact results. Furthermore, I present a handy formula, obtained from interpolating the numerical results, for a quick calculation of FEL exponential growth rate. Comparisons with simulation code TDA will also be presented. Application of these solutions to the design and multi-dimensional parameter space optimization for an X-ray free electron laser driven by SLAC linac will be demonstrated. In addition, a rigorous analysis of transverse mode degeneracy and hence the transverse coherence of the X-ray FEL will be presented based on the exact solutions of the higher order guided modes.
Energy Technology Data Exchange (ETDEWEB)
Dobranskis, R. R.; Zharkova, V. V., E-mail: valentina.zharkova@northumbria.ac.uk [Department of Mathematics and Information Sciences, University of Northumbria, Newcastle upon Tyne NE1 2XP (United Kingdom)
2014-06-10
The original continuity equation (CE) used for the interpretation of the power law energy spectra of beam electrons in flares was written and solved for an electron beam flux while ignoring an additional free term with an electron density. In order to remedy this omission, the original CE for electron flux, considering beam's energy losses in Coulomb collisions, was first differentiated by the two independent variables: depth and energy leading to partial differential equation for an electron beam density instead of flux with the additional free term. The analytical solution of this partial differential continuity equation (PDCE) is obtained by using the method of characteristics. This solution is further used to derive analytical expressions for mean electron spectra for Coulomb collisions and to carry out numeric calculations of hard X-ray (HXR) photon spectra for beams with different parameters. The solutions revealed a significant departure of electron densities at lower energies from the original results derived from the CE for the flux obtained for Coulomb collisions. This departure is caused by the additional exponential term that appeared in the updated solutions for electron differential density leading to its faster decrease at lower energies (below 100 keV) with every precipitation depth similar to the results obtained with numerical Fokker-Planck solutions. The effects of these updated solutions for electron densities on mean electron spectra and HXR photon spectra are also discussed.
Xu, Feng; Ren, Kuan Fang; Cai, Xiaoshu
2006-07-10
The geometrical-optics approximation of light scattering by a transparent or absorbing spherical particle is extended from plane wave to Gaussian beam incidence. The formulas for the calculation of the phase of each ray and the divergence factor are revised, and the interference of all the emerging rays is taken into account. The extended geometrical-optics approximation (EGOA) permits one to calculate the scattering diagram in all directions from 0 degrees to 180 degrees. The intensities of the scattered field calculated by the EGOA are compared with those calculated by the generalized Lorenz-Mie theory, and good agreement is found. The surface wave effect in Gaussian beam scattering is also qualitatively analyzed by introducing a flux ratio factor. The approach proposed is particularly important to the further extension of the geometrical-optics approximation to the scattering of large spheroidal particles.
An optimization-based method for geometrical calibration in cone-beam CT without dedicated phantoms
International Nuclear Information System (INIS)
Panetta, D; Belcari, N; Guerra, A Del; Moehrs, S
2008-01-01
In this paper we present a new method for the determination of geometrical misalignments in cone-beam CT scanners, from the analysis of the projection data of a generic object. No a priori knowledge of the object shape and positioning is required. We show that a cost function, which depends on the misalignment parameters, can be defined using the projection data and that such a cost function has a local minimum in correspondence to the actual parameters of the system. Hence, the calibration of the scanner can be carried out by minimizing the cost function using standard optimization techniques. The method is developed for a particular class of 3D object functions, for which the redundancy of the fan beam sinogram in the transaxial midplane can be extended to cone-beam projection data, even at wide cone angles. The method has an approximated validity for objects which do not belong to that class; in that case, a suitable subset of the projection data can be selected in order to compute the cost function. We show by numerical simulations that our method is capable to determine with high accuracy the most critical misalignment parameters of the scanner, i.e., the transversal shift and the skew of the detector. Additionally, the detector slant can be determined. Other parameters such as the detector tilt, the longitudinal shift and the error in the source-detector distance cannot be determined with our method, as the proposed cost function has a very weak dependence on them. However, due to the negligible influence of these latter parameters in the reconstructed image quality, they can be kept fixed at estimated values in both calibration and reconstruction processes without compromising the final result. A trade-off between computational cost and calibration accuracy must be considered when choosing the data subset used for the computation of the cost function. Results on real data of a mouse femur as obtained with a small animal micro-CT are shown as well, proving
Directory of Open Access Journals (Sweden)
Edgar Husser
2017-03-01
Full Text Available The mechanical behavior of single crystalline, micro-sized copper is investigated in the context of cantilever beam bending experiments. Particular focus is on the role of geometrically necessary dislocations (GNDs during bending-dominated load conditions and their impact on the characteristic bending size effect. Three different sample sizes are considered in this work with main variation in thickness. A gradient extended crystal plasticity model is presented and applied in a three-dimensional finite-element (FE framework considering slip system-based edge and screw components of the dislocation density vector. The underlying mathematical model contains non-standard evolution equations for GNDs, crystal-specific interaction relations, and higher-order boundary conditions. Moreover, two element formulations are examined and compared with respect to size-independent as well as size-dependent bending behavior. The first formulation is based on a linear interpolation of the displacement and the GND density field together with a full integration scheme whereas the second is based on a mixed interpolation scheme. While the GND density fields are treated equivalently, the displacement field is interpolated quadratically in combination with a reduced integration scheme. Computational results indicate that GND storage in small cantilever beams strongly influences the evolution of statistically stored dislocations (SSDs and, hence, the distribution of the total dislocation density. As a particular example, the mechanical bending behavior in the case of a physically motivated limitation of GND storage is studied. The resulting impact on the mechanical bending response as well as on the predicted size effect is analyzed. Obtained results are discussed and related to experimental findings from the literature.
International Nuclear Information System (INIS)
Li Qing; Wang Tianshu; Ma Xingrui
2009-01-01
Flexible-body modeling with geometric nonlinearities remains a hot topic of research by applications in multibody system dynamics undergoing large overall motions. However, the geometric nonlinear effects on the impact dynamics of flexible multibody systems have attracted significantly less attention. In this paper, a point-surface impact problem between a rigid ball and a pivoted flexible beam is investigated. The Hertzian contact law is used to describe the impact process, and the dynamic equations are formulated in the floating frame of reference using the assumed mode method. The two important geometric nonlinear effects of the flexible beam are taken into account, i.e., the longitudinal foreshortening effect due to the transverse deformation, and the stress stiffness effect due to the axial force. The simulation results show that good consistency can be obtained with the nonlinear finite element program ABAQUS/Explicit if proper geometric nonlinearities are included in the floating frame formulation. Specifically, only the foreshortening effect should be considered in a pure transverse impact for efficiency, while the stress stiffness effect should be further considered in an oblique case with much more computational effort. It also implies that the geometric nonlinear effects should be considered properly in the impact dynamic analysis of more general flexible multibody systems
Geometric calibration method for multiple-head cone-beam SPECT system
International Nuclear Information System (INIS)
Rizo, P.; Grangeat, P.; Guillemaud, R.
1994-01-01
A method is presented for estimating the geometrical parameters of cone beam systems with multiple heads, each head having its own orientation. In tomography, for each head, the relative position of the rotation axis and f the collimator do not change during the data acquisition. The authors thus can separate the parameters into intrinsic parameters and extrinsic parameters. The intrinsic parameters describe the detection system geometry and the extrinsic parameters the position of the detection system with respect to the rotation axis. Intrinsic parameters must be estimated each time the acquisition geometry is modified. Extrinsic parameters are estimated by minimizing the distances between the measured position of a point source projection and the computed position obtained using the estimated extrinsic parameters. The main advantage of this method is that the extrinsic parameters are only weakly correlated when the intrinsic parameters are known. Thus the authors can use any simple least square error minimization method to perform the estimation of the extrinsic parameters. Giving a fixed value to the distance between the point source and the rotation axis in the estimation process, ensures the coherence of the extrinsic parameters between each head. They show that with this calibration method, the full width at half maximum measured with point sources is very close to the theoretical one, and remains almost unchanged when more than one head is used. Simulation results and reconstructions on a Jaszczak phantom are presented that show the capabilities of this method
Loce, R P; Jodoin, R E
1990-09-10
Using the tools of Fourier analysis, a sampling requirement is derived that assures that sufficient information is contained within the samples of a distribution to calculate accurately geometric moments of that distribution. The derivation follows the standard textbook derivation of the Whittaker-Shannon sampling theorem, which is used for reconstruction, but further insight leads to a coarser minimum sampling interval for moment determination. The need for fewer samples to determine moments agrees with intuition since less information should be required to determine a characteristic of a distribution compared with that required to construct the distribution. A formula for calculation of the moments from these samples is also derived. A numerical analysis is performed to quantify the accuracy of the calculated first moment for practical nonideal sampling conditions. The theory is applied to a high speed laser beam position detector, which uses the normalized first moment to measure raster line positional accuracy in a laser printer. The effects of the laser irradiance profile, sampling aperture, number of samples acquired, quantization, and noise are taken into account.
General exact harmonic analysis of in-plane timoshenko beam structures
Directory of Open Access Journals (Sweden)
C. A. N. Dias
Full Text Available The exact solution for the problem of damped, steady state response, of in-plane Timoshenko frames subjected to harmonically time varying external forces is here described. The solution is obtained by using the classical dynamic stiffness matrix (DSM, which is non-linear and transcendental in respect to the excitation frequency, and by performing the harmonic analysis using the Laplace transform. As an original contribution, the partial differential coupled governing equations, combining displacements and forces, are directly subjected to Laplace transforms, leading to the member DSM and to the equivalent load vector formulations. Additionally, the members may have rigid bodies attached at any of their ends where, optionally, internal forces can be released. The member matrices are then used to establish the global matrices that represent the dynamic equilibrium of the overall framed structure, preserving close similarity to the finite element method. Several application examples prove the certainty of the proposed method by comparing the model results with the ones available in the literature or with finite element analyses.
Li, Yi; Xu, Yanlong
2017-09-01
Considering uncertain geometrical and material parameters, the lower and upper bounds of the band gap of an undulated beam with periodically arched shape are studied by the Monte Carlo Simulation (MCS) and interval analysis based on the Taylor series. Given the random variations of the overall uncertain variables, scatter plots from the MCS are used to analyze the qualitative sensitivities of the band gap respect to these uncertainties. We find that the influence of uncertainty of the geometrical parameter on the band gap of the undulated beam is stronger than that of the material parameter. And this conclusion is also proved by the interval analysis based on the Taylor series. Our methodology can give a strategy to reduce the errors between the design and practical values of the band gaps by improving the accuracy of the specially selected uncertain design variables of the periodical structures.
Farr, J B; Dessy, F; De Wilde, O; Bietzer, O; Schönenberg, D
2013-07-01
The purpose of this investigation was to compare and contrast the measured fundamental properties of two new types of modulated proton scanning systems. This provides a basis for clinical expectations based on the scanned beam quality and a benchmark for computational models. Because the relatively small beam and fast scanning gave challenges to the characterization, a secondary purpose was to develop and apply new approaches where necessary to do so. The following performances of the proton scanning systems were investigated: beamlet alignment, static in-air beamlet size and shape, scanned in-air penumbra, scanned fluence map accuracy, geometric alignment of scanning system to isocenter, maximum field size, lateral and longitudinal field uniformity of a 1 l cubic uniform field, output stability over time, gantry angle invariance, monitoring system linearity, and reproducibility. A range of detectors was used: film, ionization chambers, lateral multielement and longitudinal multilayer ionization chambers, and a scintillation screen combined with a digital video camera. Characterization of the scanned fluence maps was performed with a software analysis tool. The resulting measurements and analysis indicated that the two types of delivery systems performed within specification for those aspects investigated. The significant differences were observed between the two types of scanning systems where one type exhibits a smaller spot size and associated penumbra than the other. The differential is minimum at maximum energy and increases inversely with decreasing energy. Additionally, the large spot system showed an increase in dose precision to a static target with layer rescanning whereas the small spot system did not. The measured results from the two types of modulated scanning types of system were consistent with their designs under the conditions tested. The most significant difference between the types of system was their proton spot size and associated resolution
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Farr, J. B.; Schoenenberg, D. [Westdeutsches Protonentherapiezentrum Essen, Universitaetsklinikum-Essen, Hufelandstrasse 55, 45147 Essen (Germany); Dessy, F.; De Wilde, O.; Bietzer, O. [Ion Beam Applications, Chemin du Cyclotron, 3, 1348 Louvain-la-Neuve (Belgium)
2013-07-15
Purpose: The purpose of this investigation was to compare and contrast the measured fundamental properties of two new types of modulated proton scanning systems. This provides a basis for clinical expectations based on the scanned beam quality and a benchmark for computational models. Because the relatively small beam and fast scanning gave challenges to the characterization, a secondary purpose was to develop and apply new approaches where necessary to do so.Methods: The following performances of the proton scanning systems were investigated: beamlet alignment, static in-air beamlet size and shape, scanned in-air penumbra, scanned fluence map accuracy, geometric alignment of scanning system to isocenter, maximum field size, lateral and longitudinal field uniformity of a 1 l cubic uniform field, output stability over time, gantry angle invariance, monitoring system linearity, and reproducibility. A range of detectors was used: film, ionization chambers, lateral multielement and longitudinal multilayer ionization chambers, and a scintillation screen combined with a digital video camera. Characterization of the scanned fluence maps was performed with a software analysis tool.Results: The resulting measurements and analysis indicated that the two types of delivery systems performed within specification for those aspects investigated. The significant differences were observed between the two types of scanning systems where one type exhibits a smaller spot size and associated penumbra than the other. The differential is minimum at maximum energy and increases inversely with decreasing energy. Additionally, the large spot system showed an increase in dose precision to a static target with layer rescanning whereas the small spot system did not.Conclusions: The measured results from the two types of modulated scanning types of system were consistent with their designs under the conditions tested. The most significant difference between the types of system was their proton
International Nuclear Information System (INIS)
Kim, Jeong Soo; Kim, Moon Kyum
2012-01-01
In this study, finite element analysis of beam on elastic foundation, which received great attention of researchers due to its wide applications in engineering, is performed for estimating dynamic responses of shallow foundation using exact stiffness matrix. First, element stiffness matrix based on the closed solution of beam on elastic foundation is derived. Then, we performed static finite element analysis included exact stiffness matrix numerically, comparing results from the analysis with some exact analysis solutions well known for verification. Finally, dynamic finite element analysis is performed for a shallow foundation structure under rectangular pulse loading using trapezoidal method. The dynamic analysis results exist in the reasonable range comparing solution of single degree of freedom problem under a similar condition. The results show that finite element analysis using exact stiffness matrix is evaluated as a good tool of estimating the dynamic response of structures on elastic foundation.
Directory of Open Access Journals (Sweden)
Vladimir P. Agapov
2017-01-01
Full Text Available Abstract. Objectives Modern building codes prescribe the calculation of building structures taking into account the nonlinearity of deformation. To achieve this goal, the task is to develop a methodology for calculating prestressed reinforced concrete beams, taking into account physical and geometric nonlinearity. Methods The methodology is based on nonlinear calculation algorithms implemented and tested in the computation complex PRINS (a program for calculating engineering constructions for other types of construction. As a tool for solving this problem, the finite element method is used. Non-linear calculation of constructions is carried out by the PRINS computational complex using the stepwise iterative method. In this case, an equation is constructed and solved at the loading step, using modified Lagrangian coordinates. Results The basic formulas necessary for both the formation and the solution of a system of nonlinear algebraic equations by the stepwise iteration method are given, taking into account the loading, unloading and possible additional loading. A method for simulating prestressing is described by setting the temperature action on the reinforcement and stressing steel rod. Different approaches to accounting for physical and geometric nonlinearity of reinforced concrete beam rods are considered. A calculation example of a flat beam is given, in which the behaviour of the beam is analysed at various stages of its loading up to destruction. Conclusion A program is developed for the calculation of flat and spatially reinforced concrete beams taking into account the nonlinearity of deformation. The program is adapted to the computational complex PRINS and as part of this complex is available to a wide range of engineering, scientific and technical specialists.
Geometrical Optics of Beams with Vortices: Berry Phase and Orbital Angular Momentum Hall Effect
International Nuclear Information System (INIS)
Bliokh, Konstantin Yu.
2006-01-01
We consider propagation of a paraxial beam carrying the spin angular momentum (polarization) and intrinsic orbital angular momentum (IOAM) in a smoothly inhomogeneous isotropic medium. It is shown that the presence of IOAM can dramatically enhance and rearrange the topological phenomena that previously were considered solely in connection to the polarization of transverse waves. In particular, the appearance of a new type of Berry phase that describes the parallel transport of the beam structure along a curved ray is predicted. We derive the ray equations demonstrating the splitting of beams with different values of IOAM. This is the orbital angular momentum Hall effect, which resembles the Magnus effect for optical vortices. Unlike the spin Hall effect of photons, it can be much larger in magnitude and is inherent to waves of any nature. Experimental means to detect the phenomena are discussed
Geometrical optics of beams with vortices: Berry phase and orbital angular momentum Hall effect.
Bliokh, Konstantin Yu
2006-07-28
We consider propagation of a paraxial beam carrying the spin angular momentum (polarization) and intrinsic orbital angular momentum (IOAM) in a smoothly inhomogeneous isotropic medium. It is shown that the presence of IOAM can dramatically enhance and rearrange the topological phenomena that previously were considered solely in connection to the polarization of transverse waves. In particular, the appearance of a new type of Berry phase that describes the parallel transport of the beam structure along a curved ray is predicted. We derive the ray equations demonstrating the splitting of beams with different values of IOAM. This is the orbital angular momentum Hall effect, which resembles the Magnus effect for optical vortices. Unlike the spin Hall effect of photons, it can be much larger in magnitude and is inherent to waves of any nature. Experimental means to detect the phenomena are discussed.
International Nuclear Information System (INIS)
Villeret, O.
1985-04-01
An algorithm is developed for the purpose of compter treatment planning of electron therapy. The method uses experimental absorbed dose distribution data in the irradiated medium for electron beams in the 8-20 MeV range delivered by the Sagittaire linear accelerator (study of central axis depth dose, beam profiles) in various geometrical conditions. Experimental verification of the computer program showed agreement with 2% between dose measurement and computer calculation [fr
Reaungamornrat, S.; Otake, Y.; Uneri, A.; Schafer, S.; Mirota, D. J.; Nithiananthan, S.; Stayman, J. W.; Khanna, A. J.; Reh, D. D.; Gallia, G. L.; Taylor, R. H.; Siewerdsen, J. H.
2012-02-01
Conventional surgical tracking configurations carry a variety of limitations in line-of-sight, geometric accuracy, and mismatch with the surgeon's perspective (for video augmentation). With increasing utilization of mobile C-arms, particularly those allowing cone-beam CT (CBCT), there is opportunity to better integrate surgical trackers at bedside to address such limitations. This paper describes a tracker configuration in which the tracker is mounted directly on the Carm. To maintain registration within a dynamic coordinate system, a reference marker visible across the full C-arm rotation is implemented, and the "Tracker-on-C" configuration is shown to provide improved target registration error (TRE) over a conventional in-room setup - (0.9+/-0.4) mm vs (1.9+/-0.7) mm, respectively. The system also can generate digitally reconstructed radiographs (DRRs) from the perspective of a tracked tool ("x-ray flashlight"), the tracker, or the C-arm ("virtual fluoroscopy"), with geometric accuracy in virtual fluoroscopy of (0.4+/-0.2) mm. Using a video-based tracker, planning data and DRRs can be superimposed on the video scene from a natural perspective over the surgical field, with geometric accuracy (0.8+/-0.3) pixels for planning data overlay and (0.6+/-0.4) pixels for DRR overlay across all C-arm angles. The field-of-view of fluoroscopy or CBCT can also be overlaid on real-time video ("Virtual Field Light") to assist C-arm positioning. The fixed transformation between the x-ray image and tracker facilitated quick, accurate intraoperative registration. The workflow and precision associated with a variety of realistic surgical tasks were significantly improved using the Tracker-on-C - for example, nearly a factor of 2 reduction in time required for C-arm positioning, reduction or elimination of dose in "hunting" for a specific fluoroscopic view, and confident placement of the x-ray FOV on the surgical target. The proposed configuration streamlines the integration of C
DEFF Research Database (Denmark)
Djernaes, Julie D.; Nielsen, Jon V.; Berg, Lise C.
2017-01-01
The widths of spaces between the thoracolumbar processi spinosi (interspinous spaces) are frequently assessed using radiography in sports horses; however effects of varying X-ray beam angles and geometric distortion have not been previously described. The aim of this prospective, observational...... study was to determine whether X-ray beam angle has an effect on apparent widths of interspinous spaces. Thoracolumbar spine specimens were collected from six equine cadavers and left-right lateral radiographs and sagittal and dorsal reconstructed computed tomographic (CT) images were acquired...... measurements. Effect of geometric distortion was evaluated by comparing the interspinous space in radiographs with sagittal and dorsal reconstructed CT images. A total of 49 interspinous spaces were sampled, yielding 274 measurements. X-ray beam angle significantly affected measured width of interspinous...
Berczynski, Pawel; Bliokh, Konstantin Yu; Kravtsov, Yuri A; Stateczny, Andrzej
2006-06-01
We present an ab initio account of the paraxial complex geometrical optics (CGO) in application to scalar Gaussian beam propagation and diffraction in a 3D smoothly inhomogeneous medium. The paraxial CGO deals with quadratic expansion of the complex eikonal and reduces the wave problem to the solution of ordinary differential equations of the Riccati type. This substantially simplifies the description of Gaussian beam diffraction as compared with full-wave or parabolic (quasi-optics) equations. For a Gaussian beam propagating in a homogeneous medium or along the symmetry axis in a lenslike medium, the CGO equations possess analytical solutions; otherwise, they can be readily solved numerically. As a nontrivial example we consider Gaussian beam propagation and diffraction along a helical ray in an axially symmetric waveguide medium. It is shown that the major axis of the beam's elliptical cross section grows unboundedly; it is oriented predominantly in the azimuthal (binormal) direction and does not obey the parallel-transport law.
Li, Zhaoyang; Kurita, Takashi; Miyanaga, Noriaki
2017-10-20
Zigzag and non-zigzag beam waist shifts in a multiple-pass zigzag slab amplifier are investigated based on the propagation of a Gaussian beam. Different incident angles in the zigzag and non-zigzag planes would introduce a direction-dependent waist-shift-difference, which distorts the beam quality in both the near- and far-fields. The theoretical model and analytical expressions of this phenomenon are presented, and intensity distributions in the two orthogonal planes are simulated and compared. A geometrical optics compensation method by a beam with 90° rotation is proposed, which not only could correct the direction-dependent waist-shift-difference but also possibly average the traditional thermally induced wavefront-distortion-difference between the horizontal and vertical beam directions.
Energy Technology Data Exchange (ETDEWEB)
Wang, Y. B. [Department of Mathematics, ShaoXing University, No.900, ChengNan Avenue 312000, ShaoXing, Zhejiang (China); Zhu, X. W., E-mail: xiaowuzhu1026@znufe.edu.cn [School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073 (China); Dai, H. H. [Department of Mathematics, City University of HongKong, 83 Tat Chee Avenue, Kowloon Tong, Hong Kong (China)
2016-08-15
Though widely used in modelling nano- and micro- structures, Eringen’s differential model shows some inconsistencies and recent study has demonstrated its differences between the integral model, which then implies the necessity of using the latter model. In this paper, an analytical study is taken to analyze static bending of nonlocal Euler-Bernoulli beams using Eringen’s two-phase local/nonlocal model. Firstly, a reduction method is proved rigorously, with which the integral equation in consideration can be reduced to a differential equation with mixed boundary value conditions. Then, the static bending problem is formulated and four types of boundary conditions with various loadings are considered. By solving the corresponding differential equations, exact solutions are obtained explicitly in all of the cases, especially for the paradoxical cantilever beam problem. Finally, asymptotic analysis of the exact solutions reveals clearly that, unlike the differential model, the integral model adopted herein has a consistent softening effect. Comparisons are also made with existing analytical and numerical results, which further shows the advantages of the analytical results obtained. Additionally, it seems that the once controversial nonlocal bar problem in the literature is well resolved by the reduction method.
International Nuclear Information System (INIS)
Wang, Y. B.; Zhu, X. W.; Dai, H. H.
2016-01-01
Though widely used in modelling nano- and micro- structures, Eringen’s differential model shows some inconsistencies and recent study has demonstrated its differences between the integral model, which then implies the necessity of using the latter model. In this paper, an analytical study is taken to analyze static bending of nonlocal Euler-Bernoulli beams using Eringen’s two-phase local/nonlocal model. Firstly, a reduction method is proved rigorously, with which the integral equation in consideration can be reduced to a differential equation with mixed boundary value conditions. Then, the static bending problem is formulated and four types of boundary conditions with various loadings are considered. By solving the corresponding differential equations, exact solutions are obtained explicitly in all of the cases, especially for the paradoxical cantilever beam problem. Finally, asymptotic analysis of the exact solutions reveals clearly that, unlike the differential model, the integral model adopted herein has a consistent softening effect. Comparisons are also made with existing analytical and numerical results, which further shows the advantages of the analytical results obtained. Additionally, it seems that the once controversial nonlocal bar problem in the literature is well resolved by the reduction method.
Vogelgesang, Jonas; Schorr, Christian
2016-12-01
We present a semi-discrete Landweber-Kaczmarz method for solving linear ill-posed problems and its application to Cone Beam tomography and laminography. Using a basis function-type discretization in the image domain, we derive a semi-discrete model of the underlying scanning system. Based on this model, the proposed method provides an approximate solution of the reconstruction problem, i.e. reconstructing the density function of a given object from its projections, in suitable subspaces equipped with basis function-dependent weights. This approach intuitively allows the incorporation of additional information about the inspected object leading to a more accurate model of the X-rays through the object. Also, physical conditions of the scanning geometry, like flat detectors in computerized tomography as used in non-destructive testing applications as well as non-regular scanning curves e.g. appearing in computed laminography (CL) applications, are directly taken into account during the modeling process. Finally, numerical experiments of a typical CL application in three dimensions are provided to verify the proposed method. The introduction of geometric prior information leads to a significantly increased image quality and superior reconstructions compared to standard iterative methods.
Korte, Dorota; Franko, Mladen
2015-01-01
In this work, complex geometrical optics is, for what we believe is the first time, applied instead of geometrical or wave optics to describe the probe beam interaction with the field of the thermal wave in photothermal beam deflection (photothermal deflection spectroscopy) experiments on thin films. On the basis of this approach the thermal (thermal diffusivity and conductivity), optical (energy band gap), and transport (carrier lifetime) parameters of the semiconductor thin films (pure TiO2, N- and C-doped TiO2, or TiO2/SiO2 composites deposited on a glass or aluminum support) were determined with better accuracy and simultaneously during one measurement. The results are in good agreement with results obtained by the use of other methods and reported in the literature.
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Battmann, A. [Marburg Univ. (Germany). Abt. fuer Strahlendiagnostik; Dieckmann, K.; Resch, A.; Poetter, R. [Allgemeines Krankenhaus, Wien (Austria). Universitaetsklinik Strahlentherapie und Strahlenbiologie; Battmann, A. [Giessen Univ. (Germany). Zentrum fuer Pathologie
2001-03-01
Background: The importance of the size of the primary tumor in lymphomas and its size after treatment is still uncertain. Assuming a prognostic relevance, an assessment of tumor volume before and after induction of chemotherapy has been performed in the pediatric Hodgkin's disease study (HD-90). Since an exact CT-scan-based volumetric tumor assessment is time-consuming and in some centers not possible, the tumor volume is often estimated based on simple geometric approximations. Aim of this study was the development of an easy to apply and nearly exact model of volume estimation compared to CT-scan-based tumor volume measurements. Material and Methods: thirty computed tomographies (CT) of mediastinal Hodgkin lymphomas of children aged 5 to 16 years have been examined. The CT scans were digitalized using a CCD camera combined with a frame grabber. Applying the Global Lab image software, the true tumor volume was determined excluding local organs, which did not belong to the lymphoma. Subsequently, volumes were assessed using simple geometric models (block, ellipsoid, octaeder) by using the maximum diameters of the tumor. The differences between the volume of the geometric models and the true volume, based on the CT scan evaluation, were compared. Results: the maximum diameters of a tumor can be used to calculate its volume based on simple geometric models. The model 'block' overestimates the volume by 89 to 268%. The model 'ellipsoid' overestimates the volume on average by 29%. The model 'octaeder' underestimates the volume on average by 18%. A division of the block volume by 2.3 approximated the geometric closest to the true volume: the average volume was overestimated by 2% in tumors with a volume larger than 20 ml. No model was sufficient to approximate tumors with a volume of less than 20 ml. Conclusions: for the estimation of tumor volumes in mediastinal Hodgkin lumphomas exceeding 20 ml, the formula 'block /2.3&apos
International Nuclear Information System (INIS)
Bello-Rivas, Juan M.; Elber, Ron
2015-01-01
A new theory and an exact computer algorithm for calculating kinetics and thermodynamic properties of a particle system are described. The algorithm avoids trapping in metastable states, which are typical challenges for Molecular Dynamics (MD) simulations on rough energy landscapes. It is based on the division of the full space into Voronoi cells. Prior knowledge or coarse sampling of space points provides the centers of the Voronoi cells. Short time trajectories are computed between the boundaries of the cells that we call milestones and are used to determine fluxes at the milestones. The flux function, an essential component of the new theory, provides a complete description of the statistical mechanics of the system at the resolution of the milestones. We illustrate the accuracy and efficiency of the exact Milestoning approach by comparing numerical results obtained on a model system using exact Milestoning with the results of long trajectories and with a solution of the corresponding Fokker-Planck equation. The theory uses an equation that resembles the approximate Milestoning method that was introduced in 2004 [A. K. Faradjian and R. Elber, J. Chem. Phys. 120(23), 10880-10889 (2004)]. However, the current formulation is exact and is still significantly more efficient than straightforward MD simulations on the system studied
Asymptotic and geometrical quantization
International Nuclear Information System (INIS)
Karasev, M.V.; Maslov, V.P.
1984-01-01
The main ideas of geometric-, deformation- and asymptotic quantizations are compared. It is shown that, on the one hand, the asymptotic approach is a direct generalization of exact geometric quantization, on the other hand, it generates deformation in multiplication of symbols and Poisson brackets. Besides investigating the general quantization diagram, its applications to the calculation of asymptotics of a series of eigenvalues of operators possessing symmetry groups are considered
Geometrical-optics approximation of forward scattering by coated particles.
Xu, Feng; Cai, Xiaoshu; Ren, Kuanfang
2004-03-20
By means of geometrical optics we present an approximation algorithm with which to accelerate the computation of scattering intensity distribution within a forward angular range (0 degrees-60 degrees) for coated particles illuminated by a collimated incident beam. Phases of emerging rays are exactly calculated to improve the approximation precision. This method proves effective for transparent and tiny absorbent particles with size parameters larger than 75 but fails to give good approximation results at scattering angles at which refractive rays are absent. When the absorption coefficient of a particle is greater than 0.01, the geometrical optics approximation is effective only for forward small angles, typically less than 10 degrees or so.
International Nuclear Information System (INIS)
Pili, Giorgio; Grimaldi, Luca; Fidanza, Christian; Florio, Elena T.; Petruzzelli, Maria F.; D'Errico, Maria P.; De Tommaso, Cristina; Tramacere, Francesco; Musaio, Francesca; Castagna, Roberta; Francavilla, Maria C.; Gianicolo, Emilio A.L.; Portaluri, Maurizio
2011-01-01
Purpose: To evaluate the probability of late cardiac mortality resulting from left breast irradiation planned with tangential fields and to compare this probability between the wedged beam and field-in-field (FIF) techniques and to investigate whether some geometric/dosimetric indicators can be determined to estimate the cardiac mortality probability before treatment begins. Methods and Materials: For 30 patients, differential dose-volume histograms were calculated for the wedged beam and FIF plans, and the corresponding cardiac mortality probabilities were determined using the relative seriality model. As a comparative index of the dose distribution uniformity, the planning target volume (PTV) percentages involved in 97-103% of prescribed dose were determined for the two techniques. Three geometric parameters were measured for each patient: the maximal length, indicates how much the heart contours were displaced toward the PTV, the angle subtended at the center of the computed tomography slice by the PTV contour, and the thorax width/thickness ratio. Results: Evaluating the differential dose-volume histograms showed that the gain in uniformity between the two techniques was about 1.5. With the FIF technique, the mean dose sparing for the heart, the left anterior descending coronary artery, and the lung was 15% (2.5 Gy vs. 2.2 Gy), 21% (11.3 Gy vs. 9.0 Gy), and 42% (8.0 Gy vs. 4.6 Gy) respectively, compared with the wedged beam technique. Also, the cardiac mortality probability decreased by 40% (from 0.9% to 0.5%). Three geometric parameters, the maximal length, angle subtended at the center of the computed tomography slice by the PTV contour, and thorax width/thickness ratio, were the determining factors (p = .06 for FIF, and p = .10 for wedged beam) for evaluating the cardiac mortality probability. Conclusion: The FIF technique seemed to yield a lower cardiac mortality probability than the conventional wedged beam technique. However, although our study
International Nuclear Information System (INIS)
Zeger, J.
1993-01-01
Organized criminals also tried to illegally transfer nuclear material through Austria. Two important questions have to be answered after the material is sized by police authorities: What is the composition of the material and where does it come from? By application of a broad range of analytical techniques, which were developed or refined by our experts, it is possible to measure the exact amount and isotopic composition of uranium and plutonium in any kind of samples. The criminalistic application is only a byproduct of the large scale work on controlling the peaceful application of nuclear energy, which is done in contract with the IAEA in the context of the 'Network of Analytical Laboratories'
Xu, Feng; Ren, Kuan Fang; Cai, Xiaoshu; Shen, Jianqi
2006-07-10
On the basis of our previous work on the extension of the geometrical-optics approximation to Gaussian beam scattering by a spherical particle, we present a further extension of the method to the scattering of a transparent or absorbing spheroidal particle with the same symmetric axis as the incident beam. As was done for the spherical particle, the phase shifts of the emerging rays due to focal lines, optical path, and total reflection are carefully considered. The angular position of the geometric rainbow of primary order is theoretically predicted. Compared with our results, the Möbius prediction of the rainbow angle has a discrepancy of less than 0.5 degrees for a spheroidal droplet of aspect radio kappa within 0.95 and 1.05 and less than 2 degrees for kappa within 0.89 and 1.11. The flux ratio index F, which qualitatively indicates the effect of a surface wave, is also studied and found to be dependent on the size, refractive index, and surface curvature of the particle.
International Nuclear Information System (INIS)
Woods, K; DiCostanzo, D; Gupta, N
2016-01-01
Purpose: To test the efficacy of a retrospective metal artifact reduction (MAR) reconstruction algorithm for a commercial computed tomography (CT) scanner for radiation therapy purposes. Methods: High Z geometric integrity and artifact reduction analysis was performed with three phantoms using General Electric’s (GE) Discovery CT. The three phantoms included: a Computerized Imaging Reference Systems (CIRS) electron density phantom (Model 062) with a 6.5 mm diameter titanium rod insert, a custom spine phantom using Synthes Spine hardware submerged in water, and a dental phantom with various high Z fillings submerged in water. Each phantom was reconstructed using MAR and compared against the original scan. Furthermore, each scenario was tested using standard and extended Hounsfield Unit (HU) ranges. High Z geometric integrity was performed using the CIRS phantom, while the artifact reduction was performed using all three phantoms. Results: Geometric integrity of the 6.5 mm diameter rod was slightly overestimated for non-MAR scans for both standard and extended HU. With MAR reconstruction, the rod was underestimated for both standard and extended HU. For artifact reduction, the mean and standard deviation was compared in a volume of interest (VOI) in the surrounding material (water and water equivalent material, ∼0HU). Overall, the mean value of the VOI was closer to 0 HU for the MAR reconstruction compared to the non-MAR scan for most phantoms. Additionally, the standard deviations for all phantoms were greatly reduced using MAR reconstruction. Conclusion: GE’s MAR reconstruction algorithm improves image quality with the presence of high Z material with minimal degradation of its geometric integrity. High Z delineation can be carried out with proper contouring techniques. The effects of beam hardening artifacts are greatly reduced with MAR reconstruction. Tissue corrections due to these artifacts can be eliminated for simple high Z geometries and greatly
Energy Technology Data Exchange (ETDEWEB)
Woods, K; DiCostanzo, D; Gupta, N [Ohio State University Columbus, OH (United States)
2016-06-15
Purpose: To test the efficacy of a retrospective metal artifact reduction (MAR) reconstruction algorithm for a commercial computed tomography (CT) scanner for radiation therapy purposes. Methods: High Z geometric integrity and artifact reduction analysis was performed with three phantoms using General Electric’s (GE) Discovery CT. The three phantoms included: a Computerized Imaging Reference Systems (CIRS) electron density phantom (Model 062) with a 6.5 mm diameter titanium rod insert, a custom spine phantom using Synthes Spine hardware submerged in water, and a dental phantom with various high Z fillings submerged in water. Each phantom was reconstructed using MAR and compared against the original scan. Furthermore, each scenario was tested using standard and extended Hounsfield Unit (HU) ranges. High Z geometric integrity was performed using the CIRS phantom, while the artifact reduction was performed using all three phantoms. Results: Geometric integrity of the 6.5 mm diameter rod was slightly overestimated for non-MAR scans for both standard and extended HU. With MAR reconstruction, the rod was underestimated for both standard and extended HU. For artifact reduction, the mean and standard deviation was compared in a volume of interest (VOI) in the surrounding material (water and water equivalent material, ∼0HU). Overall, the mean value of the VOI was closer to 0 HU for the MAR reconstruction compared to the non-MAR scan for most phantoms. Additionally, the standard deviations for all phantoms were greatly reduced using MAR reconstruction. Conclusion: GE’s MAR reconstruction algorithm improves image quality with the presence of high Z material with minimal degradation of its geometric integrity. High Z delineation can be carried out with proper contouring techniques. The effects of beam hardening artifacts are greatly reduced with MAR reconstruction. Tissue corrections due to these artifacts can be eliminated for simple high Z geometries and greatly
Geometric approximation algorithms
Har-Peled, Sariel
2011-01-01
Exact algorithms for dealing with geometric objects are complicated, hard to implement in practice, and slow. Over the last 20 years a theory of geometric approximation algorithms has emerged. These algorithms tend to be simple, fast, and more robust than their exact counterparts. This book is the first to cover geometric approximation algorithms in detail. In addition, more traditional computational geometry techniques that are widely used in developing such algorithms, like sampling, linear programming, etc., are also surveyed. Other topics covered include approximate nearest-neighbor search, shape approximation, coresets, dimension reduction, and embeddings. The topics covered are relatively independent and are supplemented by exercises. Close to 200 color figures are included in the text to illustrate proofs and ideas.
Directory of Open Access Journals (Sweden)
Hamid M. Sedighi
Full Text Available This paper investigates the dynamic pull-in instability of vibrating micro-beams undergoing large deflection under electrosatically actuation. The governing equation of motion is derived based on the modified couple stress theory. Homotopy Perturbation Method is employed to produce the high accuracy approximate solution as well as the second-order frequency- amplitude relationship. The nonlinear governing equation of micro beam vibrations predeformed by an electric field includes both even and odd nonlinearities. The influences of basic non-dimensional parameters on the pull-in instability as well as the natural frequency are studied. It is demonstrated that two terms in series expansions are sufficient to produce high accuracy solution of the micro-structure. The accuracy of proposed asymptotic approach is validated via numerical results. The phase portrait of the system exhibits periodic and homoclinic orbits.
International Nuclear Information System (INIS)
Bindoni, Luca
2005-01-01
A technique for geometric and dosimetric pretreatment verification of step-and-shoot intensity modulated radiotherapy treatments (IMRT) using a beam imaging system (BIS) made up of a charge-coupled device (CCD) digital camera optically coupled with a metal-plate/phosphor screen is described. Some physical properties of BIS were investigated in order to demonstrate its capability to perform measurements with a high spatial resolution and a high sampling rate. High-speed imaging, with a minimum charge integration time on the CCD of 120 ms, can be performed. The study of the signal-to-noise ratio as a function of sampling time is presented. In-plane and cross-line pixel size was measured to be 0.368±0.004 mm/pixel, which agrees within 0.5% of the manufacturer value of 0.366 mm. Spatial linearity results are very good and there are no detectable image distortions on whole 30x30 cm 2 detector area. A software routine was written to automatically extract positions of the collimator leaves from the images of the field shaped by the multileaf collimator (MLC) and also to compare them with the coordinates from the treatment planning system (TPS), thus directly testing both the MLC positioning and the treatment parameters transfer from TPS to the linear accelerator in a fast and precise way. The dosimetric capabilities (characteristics) of the imaging device for photon beams with energies of 6 and 15 MV were studied. Additional plexiglass buildup layers, depending on x-ray energy, were needed to reach maximum efficiency. The energy dependence of the BIS response versus dose and dose rate was found to be linear over a wide range. Relative output factors of BIS as a function of field size, compared with values measured with an ionization chamber, were in good accord for smaller field sizes ≤10x10 cm 2 but showed differences up to 4% for all the energies at the respective buildup depth for bigger fields. Square field profiles at water-equivalent buildup depths, extracted
Longitudinal impedance of a step-in for a round beam at arbitrary beam energy
Energy Technology Data Exchange (ETDEWEB)
Al-Khateeb, A.M., E-mail: a.alkhateeb@gsi.d [FAIR-Accelerator Theory Group, GSI Darmstadt, Planckstr. 1, D-64291 Darmstadt (Germany); Boine-Frankenheim, O.; Plotnikov, A. [FAIR-Accelerator Theory Group, GSI Darmstadt, Planckstr. 1, D-64291 Darmstadt (Germany); Shim, S.Y. [FAIR Division, Magnettechnik/Kryotechnik, GSI Darmstadt, Planckstr. 1, D-64291 Darmstadt (Germany); Haenichen, L. [Technische Universitaet Darmstadt, Institut fuer Theorie elektromagnetischer Felder, TEMF, Schlossgartenstr. 8, D-64289 Darmstadt (Germany)
2011-01-21
Contribution of step-in geometric discontinuity to the longitudinal coupling impedance has been obtained analytically using exact field matching. We assumed a perfectly conducting beam-pipe wall of two different radii connected coaxially at z=0 so that the contribution to the longitudinal coupling impedance is purely due to the beam-pipe geometric discontinuity. We also obtained the longitudinal loss factor for a Gaussian beam as a function of beam energy and bunch length. Results have been analyzed numerically for some representative parameters close to real machine parameters. Analytical results have also been compared with numerical simulation from CST at relativistic beam energies. We found a very good agreement between theory and simulation.
Energy Technology Data Exchange (ETDEWEB)
Ebata, T [Tohoku Univ., Sendai (Japan). Coll. of General Education
1976-06-01
The geometrical distribution inferred from the inelastic cross section is assumed to be proportional to the partial waves. The precocious scaling and the Q/sup 2/-dependence of various quantities are treated from the geometrical point of view. It is shown that the approximate conservation of the orbital angular momentum may be a very practical rule to understand the helicity structure of various hadronic and electromagnetic reactions. The rule can be applied to inclusive reactions as well. The model is also applied to large angle processes. Through the discussion, it is suggested that many peculiar properties of the quark-parton can be ascribed to the geometrical effects.
Bray, Hubert L; Mazzeo, Rafe; Sesum, Natasa
2015-01-01
This volume includes expanded versions of the lectures delivered in the Graduate Minicourse portion of the 2013 Park City Mathematics Institute session on Geometric Analysis. The papers give excellent high-level introductions, suitable for graduate students wishing to enter the field and experienced researchers alike, to a range of the most important areas of geometric analysis. These include: the general issue of geometric evolution, with more detailed lectures on Ricci flow and Kähler-Ricci flow, new progress on the analytic aspects of the Willmore equation as well as an introduction to the recent proof of the Willmore conjecture and new directions in min-max theory for geometric variational problems, the current state of the art regarding minimal surfaces in R^3, the role of critical metrics in Riemannian geometry, and the modern perspective on the study of eigenfunctions and eigenvalues for Laplace-Beltrami operators.
Niethammer, Marc; Hart, Gabriel L; Pace, Danielle F; Vespa, Paul M; Irimia, Andrei; Van Horn, John D; Aylward, Stephen R
2011-01-01
Standard image registration methods do not account for changes in image appearance. Hence, metamorphosis approaches have been developed which jointly estimate a space deformation and a change in image appearance to construct a spatio-temporal trajectory smoothly transforming a source to a target image. For standard metamorphosis, geometric changes are not explicitly modeled. We propose a geometric metamorphosis formulation, which explains changes in image appearance by a global deformation, a deformation of a geometric model, and an image composition model. This work is motivated by the clinical challenge of predicting the long-term effects of traumatic brain injuries based on time-series images. This work is also applicable to the quantification of tumor progression (e.g., estimating its infiltrating and displacing components) and predicting chronic blood perfusion changes after stroke. We demonstrate the utility of the method using simulated data as well as scans from a clinical traumatic brain injury patient.
Directory of Open Access Journals (Sweden)
Onur SAYMAN
2001-03-01
Full Text Available In the present study, an elastic-plastic stress analysis is carried out in a metal matrix composite cantilever beam loaded by a single force at its free end. A composite consisting of stainless-steel reinforced aluminium was produced for this work. The orientation angle of the fibers is chosen as 0°, 30°, 45°, 60° and 90°. The material is assumed to be perfectly plastic in the elasto-plastic solution. An analytical solution is performed for satisfying both the governing differential equation in the plane stress case and boundary conditions for small plastic deformations. The solution is carried out under the assumption of the Bernoulli-Navier hypotheses. The composite material is assumed as hardening linearly. The Tsai-Hill theory is used as a yield criterion.
Exact solutions in three-dimensional gravity
Garcia-Diaz, Alberto A
2017-01-01
A self-contained text, systematically presenting the determination and classification of exact solutions in three-dimensional Einstein gravity. This book explores the theoretical framework and general physical and geometrical characteristics of each class of solutions, and includes information on the researchers responsible for their discovery. Beginning with the physical character of the solutions, these are identified and ordered on the basis of their geometrical invariant properties, symmetries, and algebraic classifications, or from the standpoint of their physical nature, for example electrodynamic fields, fluid, scalar field, or dilaton. Consequently, this text serves as a thorough catalogue on 2+1 exact solutions to the Einstein equations coupled to matter and fields, and on vacuum solutions of topologically massive gravity with a cosmological constant. The solutions are also examined from different perspectives, enabling a conceptual bridge between exact solutions of three- and four-dimensional gravit...
International Nuclear Information System (INIS)
Ushveridze, A.G.
1992-01-01
This paper reports that quasi-exactly solvable (QES) models realize principally new type of exact solvability in quantum physics. These models are distinguished by the fact that the Schrodinger equations for them can be solved exactly only for certain limited parts of the spectrum, but not for the whole spectrum. They occupy an intermediate position between the exactly the authors solvable (ES) models and all the others. The number of energy levels for which the spectral problems can be solved exactly refer below to as the order of QES model. From the mathematical point of view the existence of QES models is not surprising. Indeed, if the term exact solvability expresses the possibility of total explicit diagonalization of infinite Hamiltonian matrix, then the term quasi-exact solvability implies the situation when the Hamiltonian matrix can be reduced explicitly to the block-diagonal form with one of the appearing blocks being finite
Exact Boundary Controllability of Electromagnetic Fields in a General Region
International Nuclear Information System (INIS)
Eller, M. M.; Masters, J. E.
2002-01-01
We prove exact controllability for Maxwell's system with variable coefficients in a bounded domain by a current flux in the boundary. The proof relies on a duality argument which reduces the proof of exact controllability to the proof of continuous observability for the homogeneous adjoint system. There is no geometric restriction imposed on the domain
Geometric scaling as traveling waves
International Nuclear Information System (INIS)
Munier, S.; Peschanski, R.
2003-01-01
We show the relevance of the nonlinear Fisher and Kolmogorov-Petrovsky-Piscounov (KPP) equation to the problem of high energy evolution of the QCD amplitudes. We explain how the traveling wave solutions of this equation are related to geometric scaling, a phenomenon observed in deep-inelastic scattering experiments. Geometric scaling is for the first time shown to result from an exact solution of nonlinear QCD evolution equations. Using general results on the KPP equation, we compute the velocity of the wave front, which gives the full high energy dependence of the saturation scale
Experimental validation of flexible multibody dynamics beam formulations
Energy Technology Data Exchange (ETDEWEB)
Bauchau, Olivier A., E-mail: olivier.bauchau@sjtu.edu.cn; Han, Shilei [University of Michigan-Shanghai Jiao Tong University Joint Institute (China); Mikkola, Aki; Matikainen, Marko K. [Lappeenranta University of Technology, Department of Mechanical Engineering (Finland); Gruber, Peter [Austrian Center of Competence in Mechatronics GmbH (Austria)
2015-08-15
In this paper, the accuracies of the geometrically exact beam and absolute nodal coordinate formulations are studied by comparing their predictions against an experimental data set referred to as the “Princeton beam experiment.” The experiment deals with a cantilevered beam experiencing coupled flap, lag, and twist deformations. In the absolute nodal coordinate formulation, two different beam elements are used. The first is based on a shear deformable approach in which the element kinematics is described using two nodes. The second is based on a recently proposed approach featuring three nodes. The numerical results for the geometrically exact beam formulation and the recently proposed three-node absolute nodal coordinate formulation agree well with the experimental data. The two-node beam element predictions are similar to those of linear beam theory. This study suggests that a careful and thorough evaluation of beam elements must be carried out to assess their ability to deal with the three-dimensional deformations typically found in flexible multibody systems.
Energy Technology Data Exchange (ETDEWEB)
Singleton, Robert Jr. [Los Alamos National Laboratory; Israel, Daniel M. [Los Alamos National Laboratory; Doebling, Scott William [Los Alamos National Laboratory; Woods, Charles Nathan [Los Alamos National Laboratory; Kaul, Ann [Los Alamos National Laboratory; Walter, John William Jr [Los Alamos National Laboratory; Rogers, Michael Lloyd [Los Alamos National Laboratory
2016-05-09
For code verification, one compares the code output against known exact solutions. There are many standard test problems used in this capacity, such as the Noh and Sedov problems. ExactPack is a utility that integrates many of these exact solution codes into a common API (application program interface), and can be used as a stand-alone code or as a python package. ExactPack consists of python driver scripts that access a library of exact solutions written in Fortran or Python. The spatial profiles of the relevant physical quantities, such as the density, fluid velocity, sound speed, or internal energy, are returned at a time specified by the user. The solution profiles can be viewed and examined by a command line interface or a graphical user interface, and a number of analysis tools and unit tests are also provided. We have documented the physics of each problem in the solution library, and provided complete documentation on how to extend the library to include additional exact solutions. ExactPack’s code architecture makes it easy to extend the solution-code library to include additional exact solutions in a robust, reliable, and maintainable manner.
DEFF Research Database (Denmark)
Andersen, Jørgen Ellegaard; Borot, Gaëtan; Orantin, Nicolas
We propose a general theory whose main component are functorial assignments ∑→Ω∑ ∈ E (∑), for a large class of functors E from a certain category of bordered surfaces (∑'s) to a suitable a target category of topological vector spaces. The construction is done by summing appropriate compositions...... as Poisson structures on the moduli space of flat connections. The theory has a wider scope than that and one expects that many functorial objects in low-dimensional geometry and topology should have a GR construction. The geometric recursion has various projections to topological recursion (TR) and we...... in particular show it retrieves all previous variants and applications of TR. We also show that, for any initial data for topological recursion, one can construct initial data for GR with values in Frobenius algebra-valued continuous functions on Teichmueller space, such that the ωg,n of TR are obtained...
Geometric leaf placement strategies
International Nuclear Information System (INIS)
Fenwick, J D; Temple, S W P; Clements, R W; Lawrence, G P; Mayles, H M O; Mayles, W P M
2004-01-01
Geometric leaf placement strategies for multileaf collimators (MLCs) typically involve the expansion of the beam's-eye-view contour of a target by a uniform MLC margin, followed by movement of the leaves until some point on each leaf end touches the expanded contour. Film-based dose-distribution measurements have been made to determine appropriate MLC margins-characterized through an index d 90 -for multileaves set using one particular strategy to straight lines lying at various angles to the direction of leaf travel. Simple trigonometric relationships exist between different geometric leaf placement strategies and are used to generalize the results of the film work into d 90 values for several different strategies. Measured d 90 values vary both with angle and leaf placement strategy. A model has been derived that explains and describes quite well the observed variations of d 90 with angle. The d 90 angular variations of the strategies studied differ substantially, and geometric and dosimetric reasoning suggests that the best strategy is the one with the least angular variation. Using this criterion, the best straightforwardly implementable strategy studied is a 'touch circle' approach for which semicircles are imagined to be inscribed within leaf ends, the leaves being moved until the semicircles just touch the expanded target outline
AbouEisha, Hassan M.
2014-01-01
The problem of attribute reduction is an important problem related to feature selection and knowledge discovery. The problem of finding reducts with minimum cardinality is NP-hard. This paper suggests a new algorithm for finding exact reducts
Strongly correlated states of a small cold-atom cloud from geometric gauge fields
International Nuclear Information System (INIS)
Julia-Diaz, B.; Dagnino, D.; Barberan, N.; Guenter, K. J.; Dalibard, J.; Grass, T.; Lewenstein, M.
2011-01-01
Using exact diagonalization for a small system of cold bosonic atoms, we analyze the emergence of strongly correlated states in the presence of an artificial magnetic field. This gauge field is generated by a laser beam that couples two internal atomic states, and it is related to Berry's geometrical phase that emerges when an atom follows adiabatically one of the two eigenstates of the atom-laser coupling. Our approach allows us to go beyond the adiabatic approximation, and to characterize the generalized Laughlin wave functions that appear in the strong magnetic-field limit.
Strongly correlated states of a small cold-atom cloud from geometric gauge fields
Energy Technology Data Exchange (ETDEWEB)
Julia-Diaz, B. [Dept. ECM, Facultat de Fisica, U. Barcelona, E-08028 Barcelona (Spain); ICFO-Institut de Ciencies Fotoniques, Parc Mediterrani de la Tecnologia, E-08860 Barcelona (Spain); Dagnino, D.; Barberan, N. [Dept. ECM, Facultat de Fisica, U. Barcelona, E-08028 Barcelona (Spain); Guenter, K. J.; Dalibard, J. [Laboratoire Kastler Brossel, CNRS, UPMC, Ecole Normale Superieure, 24 rue Lhomond, F-75005 Paris (France); Grass, T. [ICFO-Institut de Ciencies Fotoniques, Parc Mediterrani de la Tecnologia, E-08860 Barcelona (Spain); Lewenstein, M. [ICFO-Institut de Ciencies Fotoniques, Parc Mediterrani de la Tecnologia, E-08860 Barcelona (Spain); ICREA-Institucio Catalana de Recerca i Estudis Avancats, E-08010 Barcelona (Spain)
2011-11-15
Using exact diagonalization for a small system of cold bosonic atoms, we analyze the emergence of strongly correlated states in the presence of an artificial magnetic field. This gauge field is generated by a laser beam that couples two internal atomic states, and it is related to Berry's geometrical phase that emerges when an atom follows adiabatically one of the two eigenstates of the atom-laser coupling. Our approach allows us to go beyond the adiabatic approximation, and to characterize the generalized Laughlin wave functions that appear in the strong magnetic-field limit.
A new geometrical gravitational theory
International Nuclear Information System (INIS)
Obata, T.; Chiba, J.; Oshima, H.
1981-01-01
A geometrical gravitational theory is developed. The field equations are uniquely determined apart from one unknown dimensionless parameter ω 2 . It is based on an extension of the Weyl geometry, and by the extension the gravitational coupling constant and the gravitational mass are made to be dynamical and geometrical. The fundamental geometrical objects in the theory are a metric gsub(μν) and two gauge scalars phi and psi. The theory satisfies the weak equivalence principle, but breaks the strong one generally. u(phi, psi) = phi is found out on the assumption that the strong one keeps holding good at least for bosons of low spins. Thus there is the simple correspondence between the geometrical objects and the gravitational objects. Since the theory satisfies the weak one, the inertial mass is also dynamical and geometrical in the same way as is the gravitational mass. Moreover, the cosmological term in the theory is a coscalar of power -4 algebraically made of psi and u(phi, psi), so it is dynamical, too. Finally spherically symmetric exact solutions are given. The permissible range of the unknown parameter ω 2 is experimentally determined by applying the solutions to the solar system. (author)
Geometrical approach to tumor growth
Escudero, Carlos
2006-01-01
Tumor growth has a number of features in common with a physical process known as molecular beam epitaxy. Both growth processes are characterized by the constraint of growth development to the body border, and surface diffusion of cells/particles at the growing edge. However, tumor growth implies an approximate spherical symmetry that makes necessary a geometrical treatment of the growth equations. The basic model was introduced in a former article [C. Escudero, Phys. Rev. E 73, 020902(R) (200...
The Geometric Nonlinear Generalized Brazier Effect
DEFF Research Database (Denmark)
Nikolajsen, Jan Ánike; Lauridsen, Peter Riddersholm; Damkilde, Lars
2016-01-01
that the generalized Brazier effect is a local effect not influencing the overall mechanical behavior of the structure significantly. The offset is a nonlinear geometric beam-type Finite Element calculation, which takes into account the large displacements and rotations. The beam-type model defines the stresses which...... mainly are in the direction of the beam axis. The generalized Brazier effect is calculated as a linear load case based on these stresses....
HAWC2 and BeamDyn: Comparison Between Beam Structural Models for Aero-Servo-Elastic Frameworks
DEFF Research Database (Denmark)
Pavese, Christian; Wang, Qi; Kim, Taeseong
2015-01-01
approaches to model the structural behaviour of modern wind turbine blades in operation. Through a series of benchmarking structural cases of increasing complexity, the capability of the two codes to simulate highly nonlinear effects is investigated and analyzed. Results show that even though...... the geometrically exact beam theory can better model effects such as very large deflections, rotations, and structural couplings, an approach based on a multi-body formulation assembled through linear elements is capable of computing accurate solutions for typical nonlinear beam theory benchmarking cases....
Energy Technology Data Exchange (ETDEWEB)
Pavese, Christian; Kim, Taeseong; Wang, Qi; Jonkman, Jason; Sprague, Michael A.
2016-08-01
This work presents a comparison of two beam codes for aero-servo-elastic frameworks: a new structural model for the aeroelastic code HAWC2 and a new nonlinear beam model, BeamDyn, for the aeroelastic modularization framework FAST v8. The main goal is to establish the suitability of the two approaches to model the structural behaviour of modern wind turbine blades in operation. Through a series of benchmarking structural cases of increasing complexity, the capability of the two codes to simulate highly nonlinear effects is investigated and analyzed. Results show that even though the geometrically exact beam theory can better model effects such as very large deflections, rotations, and structural couplings, an approach based on a multi-body formulation assembled through linear elements is capable of computing accurate solutions for typical nonlinear beam theory benchmarking cases.
A note on the geometric phase in adiabatic approximation
International Nuclear Information System (INIS)
Tong, D.M.; Singh, K.; Kwek, L.C.; Fan, X.J.; Oh, C.H.
2005-01-01
The adiabatic theorem shows that the instantaneous eigenstate is a good approximation of the exact solution for a quantum system in adiabatic evolution. One may therefore expect that the geometric phase calculated by using the eigenstate should be also a good approximation of exact geometric phase. However, we find that the former phase may differ appreciably from the latter if the evolution time is large enough
International Nuclear Information System (INIS)
Raju Viswanathan, R.
1991-09-01
We study examples of one dimensional matrix models whose potentials possess an energy spectrum that can be explicitly determined. This allows for an exact solution in the continuum limit. Specifically, step-like potentials and the Morse potential are considered. The step-like potentials show no scaling behaviour and the Morse potential (which corresponds to a γ = -1 model) has the interesting feature that there are no quantum corrections to the scaling behaviour in the continuum limit. (author). 5 refs
Exact Relativistic `Antigravity' Propulsion
Felber, Franklin S.
2006-01-01
The Schwarzschild solution is used to find the exact relativistic motion of a payload in the gravitational field of a mass moving with constant velocity. At radial approach or recession speeds faster than 3-1/2 times the speed of light, even a small mass gravitationally repels a payload. At relativistic speeds, a suitable mass can quickly propel a heavy payload from rest nearly to the speed of light with negligible stresses on the payload.
Exact approaches for scaffolding
Weller, Mathias; Chateau, Annie; Giroudeau, Rodolphe
2015-01-01
This paper presents new structural and algorithmic results around the scaffolding problem, which occurs prominently in next generation sequencing. The problem can be formalized as an optimization problem on a special graph, the "scaffold graph". We prove that the problem is polynomial if this graph is a tree by providing a dynamic programming algorithm for this case. This algorithm serves as a basis to deduce an exact algorithm for general graphs using a tree decomposition of the input. We ex...
On bivariate geometric distribution
Directory of Open Access Journals (Sweden)
K. Jayakumar
2013-05-01
Full Text Available Characterizations of bivariate geometric distribution using univariate and bivariate geometric compounding are obtained. Autoregressive models with marginals as bivariate geometric distribution are developed. Various bivariate geometric distributions analogous to important bivariate exponential distributions like, Marshall-Olkin’s bivariate exponential, Downton’s bivariate exponential and Hawkes’ bivariate exponential are presented.
Visualizing the Geometric Series.
Bennett, Albert B., Jr.
1989-01-01
Mathematical proofs often leave students unconvinced or without understanding of what has been proved, because they provide no visual-geometric representation. Presented are geometric models for the finite geometric series when r is a whole number, and the infinite geometric series when r is the reciprocal of a whole number. (MNS)
Geometric Topology and Shape Theory
Segal, Jack
1987-01-01
The aim of this international conference the third of its type was to survey recent developments in Geometric Topology and Shape Theory with an emphasis on their interaction. The volume contains original research papers and carefully selected survey of currently active areas. The main topics and themes represented by the papers of this volume include decomposition theory, cell-like mappings and CE-equivalent compacta, covering dimension versus cohomological dimension, ANR's and LCn-compacta, homology manifolds, embeddings of continua into manifolds, complement theorems in shape theory, approximate fibrations and shape fibrations, fibered shape, exact homologies and strong shape theory.
Prepotential approach to exact and quasi-exact solvabilities
International Nuclear Information System (INIS)
Ho, C.-L.
2008-01-01
Exact and quasi-exact solvabilities of the one-dimensional Schroedinger equation are discussed from a unified viewpoint based on the prepotential together with Bethe ansatz equations. This is a constructive approach which gives the potential as well as the eigenfunctions and eigenvalues simultaneously. The novel feature of the present work is the realization that both exact and quasi-exact solvabilities can be solely classified by two integers, the degrees of two polynomials which determine the change of variable and the zeroth order prepotential. Most of the well-known exactly and quasi-exactly solvable models, and many new quasi-exactly solvable ones, can be generated by appropriately choosing the two polynomials. This approach can be easily extended to the constructions of exactly and quasi-exactly solvable Dirac, Pauli, and Fokker-Planck equations
Liu, Yun-Fei; Liu, Shu-Fa; Duan, Jin-Zhuo
2018-01-01
The local electrochemical properties of galvanic corrosion for three coupled metals in a desalination plant were investigated with three wire-beam electrodes as wire sensors: aluminum brass (HAl77-2), titanium (TA2), and 316L stainless steel (316L SS). These electrodes were used with artificial seawater at different temperatures. The potential and current–density distributions of the three-metal coupled system are inhomogeneous. The HAl77-2 wire anodes were corroded in the three-metal coupled system. The TA2 wires acted as cathodes and were protected; the 316L SS wires acted as secondary cathodes. The temperature and electrode arrangement have important effects on the galvanic corrosion of the three-metal coupled system. The corrosion current of the HAl77-2 increased with temperature indicating enhanced anode corrosion at higher temperature. In addition, the corrosion of HAl77-2 was more significant when the HAl77-2 wires were located in the middle of the coupled system than with the other two metal arrangement styles. PMID:29495617
Ju, Hong; Yang, Yuan-Feng; Liu, Yun-Fei; Liu, Shu-Fa; Duan, Jin-Zhuo; Li, Yan
2018-02-28
The local electrochemical properties of galvanic corrosion for three coupled metals in a desalination plant were investigated with three wire-beam electrodes as wire sensors: aluminum brass (HAl77-2), titanium (TA2), and 316L stainless steel (316L SS). These electrodes were used with artificial seawater at different temperatures. The potential and current-density distributions of the three-metal coupled system are inhomogeneous. The HAl77-2 wire anodes were corroded in the three-metal coupled system. The TA2 wires acted as cathodes and were protected; the 316L SS wires acted as secondary cathodes. The temperature and electrode arrangement have important effects on the galvanic corrosion of the three-metal coupled system. The corrosion current of the HAl77-2 increased with temperature indicating enhanced anode corrosion at higher temperature. In addition, the corrosion of HAl77-2 was more significant when the HAl77-2 wires were located in the middle of the coupled system than with the other two metal arrangement styles.
Directory of Open Access Journals (Sweden)
Hong Ju
2018-02-01
Full Text Available The local electrochemical properties of galvanic corrosion for three coupled metals in a desalination plant were investigated with three wire-beam electrodes as wire sensors: aluminum brass (HAl77-2, titanium (TA2, and 316L stainless steel (316L SS. These electrodes were used with artificial seawater at different temperatures. The potential and current–density distributions of the three-metal coupled system are inhomogeneous. The HAl77-2 wire anodes were corroded in the three-metal coupled system. The TA2 wires acted as cathodes and were protected; the 316L SS wires acted as secondary cathodes. The temperature and electrode arrangement have important effects on the galvanic corrosion of the three-metal coupled system. The corrosion current of the HAl77-2 increased with temperature indicating enhanced anode corrosion at higher temperature. In addition, the corrosion of HAl77-2 was more significant when the HAl77-2 wires were located in the middle of the coupled system than with the other two metal arrangement styles.
Exactly marginal deformations from exceptional generalised geometry
Energy Technology Data Exchange (ETDEWEB)
Ashmore, Anthony [Merton College, University of Oxford,Merton Street, Oxford, OX1 4JD (United Kingdom); Mathematical Institute, University of Oxford,Andrew Wiles Building, Woodstock Road, Oxford, OX2 6GG (United Kingdom); Gabella, Maxime [Institute for Advanced Study,Einstein Drive, Princeton, NJ 08540 (United States); Graña, Mariana [Institut de Physique Théorique, CEA/Saclay,91191 Gif-sur-Yvette (France); Petrini, Michela [Sorbonne Université, UPMC Paris 05, UMR 7589, LPTHE,75005 Paris (France); Waldram, Daniel [Department of Physics, Imperial College London,Prince Consort Road, London, SW7 2AZ (United Kingdom)
2017-01-27
We apply exceptional generalised geometry to the study of exactly marginal deformations of N=1 SCFTs that are dual to generic AdS{sub 5} flux backgrounds in type IIB or eleven-dimensional supergravity. In the gauge theory, marginal deformations are parametrised by the space of chiral primary operators of conformal dimension three, while exactly marginal deformations correspond to quotienting this space by the complexified global symmetry group. We show how the supergravity analysis gives a geometric interpretation of the gauge theory results. The marginal deformations arise from deformations of generalised structures that solve moment maps for the generalised diffeomorphism group and have the correct charge under the generalised Reeb vector, generating the R-symmetry. If this is the only symmetry of the background, all marginal deformations are exactly marginal. If the background possesses extra isometries, there are obstructions that come from fixed points of the moment maps. The exactly marginal deformations are then given by a further quotient by these extra isometries. Our analysis holds for any N=2 AdS{sub 5} flux background. Focussing on the particular case of type IIB Sasaki-Einstein backgrounds we recover the result that marginal deformations correspond to perturbing the solution by three-form flux at first order. In various explicit examples, we show that our expression for the three-form flux matches those in the literature and the obstruction conditions match the one-loop beta functions of the dual SCFT.
Geometrically based optimization for extracranial radiosurgery
International Nuclear Information System (INIS)
Liu Ruiguo; Wagner, Thomas H; Buatti, John M; Modrick, Joseph; Dill, John; Meeks, Sanford L
2004-01-01
For static beam conformal intracranial radiosurgery, geometry of the beam arrangement dominates overall dose distribution. Maximizing beam separation in three dimensions decreases beam overlap, thus maximizing dose conformality and gradient outside of the target volume. Webb proposed arrangements of isotropically convergent beams that could be used as the starting point for a radiotherapy optimization process. We have developed an extracranial radiosurgery optimization method by extending Webb's isotropic beam arrangements to deliverable beam arrangements. This method uses an arrangement of N maximally separated converging vectors within the space available for beam delivery. Each bouquet of isotropic beam vectors is generated by a random sampling process that iteratively maximizes beam separation. Next, beam arrangement is optimized for critical structure avoidance while maintaining minimal overlap between beam entrance and exit pathways. This geometrically optimized beam set can then be used as a template for either conformal beam or intensity modulated extracranial radiosurgery. Preliminary results suggest that using this technique with conformal beam planning provides high plan conformality, a steep dose gradient outside of the tumour volume and acceptable critical structure avoidance in the majority of clinical cases
Energy Technology Data Exchange (ETDEWEB)
Jurkovic, I; Stathakis, S; Markovic, M; Papanikolaou, N [University of Texas Health Sciences Center San Antonio, San Antonio (United States); Mavroidis, P [University of Texas Health Sciences Center San Antonio, San Antonio (United States); University North Carolina, Chapel Hill, NC (United States)
2016-06-15
Purpose: To assess the value of cone beam CT (CBCT) combined with deformable image registration in estimating the accuracy of the delivered treatment and the suitability of the applied target margins. Methods: Two patients with lung tumor were selected. Using their CT images intensity modulated radiation therapy (IMRT) treatment plans were developed to deliver 66Gy to the 95% of the PTV in 2Gy fractions. Using the Velocity AI software, the planning CT of each patient was registered with the fractional CBCT images that were obtained through the course of the treatment. After a CT to CBCT deformable image registration (DIR), the same fractional deformation matrix was used for the deformation of the planned dose distributions, as well as of all the contoured volumes, to each CBCT dataset. The dosimetric differences between the planning target volume (PTV) and various organs at risk (OARs) were recorded and compared. Results: CBCT data such as CTV volume change and PTV coverage was analyzed. There was a moderate relationship between volume changes and contouring method (automatic contouring using the DIR transformation vs. manual contouring on each CBCT) for patient #1 (r = 0.49), and a strong relationship for patient #2 (r = 0.83). The average PTV volume coverage from all the CBCT datasets was 91.2% for patient #1 and 95.6% for patient #2. Conclusion: Daily setup variations, tumor volume motion and lung deformation due to breathing yield differences in the actual delivered dose distributions versus the planned ones. The results presented indicate that these differences are apparent even with the use of daily IGRT. In certain fractions, the margins used seem to be insufficient to ensure acceptable lung tumor coverage. The observed differences notably depend on the tumor volume size and location. A larger cohort of patient is under investigation to verify those findings.
International Nuclear Information System (INIS)
Jurkovic, I; Stathakis, S; Markovic, M; Papanikolaou, N; Mavroidis, P
2016-01-01
Purpose: To assess the value of cone beam CT (CBCT) combined with deformable image registration in estimating the accuracy of the delivered treatment and the suitability of the applied target margins. Methods: Two patients with lung tumor were selected. Using their CT images intensity modulated radiation therapy (IMRT) treatment plans were developed to deliver 66Gy to the 95% of the PTV in 2Gy fractions. Using the Velocity AI software, the planning CT of each patient was registered with the fractional CBCT images that were obtained through the course of the treatment. After a CT to CBCT deformable image registration (DIR), the same fractional deformation matrix was used for the deformation of the planned dose distributions, as well as of all the contoured volumes, to each CBCT dataset. The dosimetric differences between the planning target volume (PTV) and various organs at risk (OARs) were recorded and compared. Results: CBCT data such as CTV volume change and PTV coverage was analyzed. There was a moderate relationship between volume changes and contouring method (automatic contouring using the DIR transformation vs. manual contouring on each CBCT) for patient #1 (r = 0.49), and a strong relationship for patient #2 (r = 0.83). The average PTV volume coverage from all the CBCT datasets was 91.2% for patient #1 and 95.6% for patient #2. Conclusion: Daily setup variations, tumor volume motion and lung deformation due to breathing yield differences in the actual delivered dose distributions versus the planned ones. The results presented indicate that these differences are apparent even with the use of daily IGRT. In certain fractions, the margins used seem to be insufficient to ensure acceptable lung tumor coverage. The observed differences notably depend on the tumor volume size and location. A larger cohort of patient is under investigation to verify those findings.
Energy Technology Data Exchange (ETDEWEB)
Catterall, Simon; Kaplan, David B.; Unsal, Mithat
2009-03-31
We provide an introduction to recent lattice formulations of supersymmetric theories which are invariant under one or more real supersymmetries at nonzero lattice spacing. These include the especially interesting case of N = 4 SYM in four dimensions. We discuss approaches based both on twisted supersymmetry and orbifold-deconstruction techniques and show their equivalence in the case of gauge theories. The presence of an exact supersymmetry reduces and in some cases eliminates the need for fine tuning to achieve a continuum limit invariant under the full supersymmetry of the target theory. We discuss open problems.
AbouEisha, Hassan M.
2014-01-01
The problem of attribute reduction is an important problem related to feature selection and knowledge discovery. The problem of finding reducts with minimum cardinality is NP-hard. This paper suggests a new algorithm for finding exact reducts with minimum cardinality. This algorithm transforms the initial table to a decision table of a special kind, apply a set of simplification steps to this table, and use a dynamic programming algorithm to finish the construction of an optimal reduct. I present results of computer experiments for a collection of decision tables from UCIML Repository. For many of the experimented tables, the simplification steps solved the problem.
International Nuclear Information System (INIS)
Akimoto, Tetsuo; Katoh, Hiroyuki; Kitamoto, Yoshizumi; Shirai, Katsuyuki; Shioya, Mariko; Nakano, Takashi
2006-01-01
Purpose: To evaluate the advantages of anatomy-based inverse optimization (IO) in planning high-dose-rate (HDR) brachytherapy. Methods and Materials: A total of 114 patients who received HDR brachytherapy (9 Gy in two fractions) combined with hypofractionated external beam radiotherapy (EBRT) were analyzed. The dose distributions of HDR brachytherapy were optimized using geometric optimization (GO) in 70 patients and by anatomy-based IO in the remaining 44 patients. The correlation between the dose-volume histogram parameters, including the urethral dose and the incidence of acute genitourinary (GU) toxicity, was evaluated. Results: The averaged values of the percentage of volume receiving 80-150% of the prescribed minimal peripheral dose (V 8 -V 15 ) of the urethra generated by anatomy-based IO were significantly lower than the corresponding values generated by GO. Similarly, the averaged values of the minimal dose received by 5-50% of the target volume (D 5 -D 5 ) obtained using anatomy-based IO were significantly lower than those obtained using GO. Regarding acute toxicity, Grade 2 or worse acute GU toxicity developed in 23% of all patients, but was significantly lower in patients for whom anatomy-based IO (16%) was used than in those for whom GO was used (37%), consistent with the reduced urethral dose (p <0.01). Conclusion: The results of this study suggest that anatomy-based IO is superior to GO for dose optimization in HDR brachytherapy for prostate cancer
Extension of non-linear beam models with deformable cross sections
Sokolov, I.; Krylov, S.; Harari, I.
2015-12-01
Geometrically exact beam theory is extended to allow distortion of the cross section. We present an appropriate set of cross-section basis functions and provide physical insight to the cross-sectional distortion from linear elastostatics. The beam formulation in terms of material (back-rotated) beam internal force resultants and work-conjugate kinematic quantities emerges naturally from the material description of virtual work of constrained finite elasticity. The inclusion of cross-sectional deformation allows straightforward application of three-dimensional constitutive laws in the beam formulation. Beam counterparts of applied loads are expressed in terms of the original three-dimensional data. Special attention is paid to the treatment of the applied stress, keeping in mind applications such as hydrogel actuators under environmental stimuli or devices made of electroactive polymers. Numerical comparisons show the ability of the beam model to reproduce finite elasticity results with good efficiency.
Finite Element Formulation for Stability and Free Vibration Analysis of Timoshenko Beam
Directory of Open Access Journals (Sweden)
Abbas Moallemi-Oreh
2013-01-01
Full Text Available A two-node element is suggested for analyzing the stability and free vibration of Timoshenko beam. Cubic displacement polynomial and quadratic rotational fields are selected for this element. Moreover, it is assumed that shear strain of the element has the constant value. Interpolation functions for displacement field and beam rotation are exactly calculated by employing total beam energy and its stationing to shear strain. By exploiting these interpolation functions, beam elements' stiffness matrix is also examined. Furthermore, geometric stiffness matrix and mass matrix of the proposed element are calculated by writing governing equation on stability and beam free vibration. At last, accuracy and efficiency of proposed element are evaluated through numerical tests. These tests show high accuracy of the element in analyzing beam stability and finding its critical load and free vibration analysis.
Geometric phases and quantum computation
International Nuclear Information System (INIS)
Vedral, V.
2005-01-01
Full text: In my lectures I will talk about the notion of the geometric phase and explain its relevance for both fundamental quantum mechanics as well as quantum computation. The phase will be at first introduced via the idea of Pancharatnam which involves interference of three or more light beams. This notion will then be generalized to the evolving quantum systems. I will discuss both pure and mixed states as well as unitary and non-unitary evolutions. I will also show how the concept of the vacuum induced geometric phase arises in quantum optics. A simple measurement scheme involving a Mach Zehnder interferometer will be presented and will be used to illustrate all the concepts in the lecture. Finally, I will expose a simple generalization of the geometric phase to evolving degenerate states. This will be seen to lead to the possibility of universal quantum computation using geometric effects only. Moreover, this contains a promise of intrinsically fault tolerant quantum information processing, whose prospects will be outlined at the end of the lecture. (author)
Geometric Rationalization for Freeform Architecture
Jiang, Caigui
2016-06-20
The emergence of freeform architecture provides interesting geometric challenges with regards to the design and manufacturing of large-scale structures. To design these architectural structures, we have to consider two types of constraints. First, aesthetic constraints are important because the buildings have to be visually impressive. Sec- ond, functional constraints are important for the performance of a building and its e cient construction. This thesis contributes to the area of architectural geometry. Specifically, we are interested in the geometric rationalization of freeform architec- ture with the goal of combining aesthetic and functional constraints and construction requirements. Aesthetic requirements typically come from designers and architects. To obtain visually pleasing structures, they favor smoothness of the building shape, but also smoothness of the visible patterns on the surface. Functional requirements typically come from the engineers involved in the construction process. For exam- ple, covering freeform structures using planar panels is much cheaper than using non-planar ones. Further, constructed buildings have to be stable and should not collapse. In this thesis, we explore the geometric rationalization of freeform archi- tecture using four specific example problems inspired by real life applications. We achieve our results by developing optimization algorithms and a theoretical study of the underlying geometrical structure of the problems. The four example problems are the following: (1) The design of shading and lighting systems which are torsion-free structures with planar beams based on quad meshes. They satisfy the functionality requirements of preventing light from going inside a building as shad- ing systems or reflecting light into a building as lighting systems. (2) The Design of freeform honeycomb structures that are constructed based on hex-dominant meshes with a planar beam mounted along each edge. The beams intersect without
Federal Laboratory Consortium — Purpose: The mission of the Geometric Design Laboratory (GDL) is to support the Office of Safety Research and Development in research related to the geometric design...
International Nuclear Information System (INIS)
Golden, L.B.
1968-01-01
In atomic structure calculations, one has to evaluate the Slater integrals. In the present program, the authors evaluate exactly the Slater integral when hydrogenic wave functions are used for the bound-state orbitals. When hydrogenic wave functions are used, the Slater integrals involve integrands which can be written in the form of a product of an exponential, exp(ax) and a known analytic polynomial function, f(x). By repeated partial integration such an integral can be expressed in terms of a finite series involving the exponential, the polynomial function and its derivatives. PL/1-FORMAC has a built-in subroutine that will analytically find the derivatives of any multinomial. Thus, the finite series and hence the Slater integral can be evaluated analytically. (Auth.)
Geometrical approach to tumor growth.
Escudero, Carlos
2006-08-01
Tumor growth has a number of features in common with a physical process known as molecular beam epitaxy. Both growth processes are characterized by the constraint of growth development to the body border, and surface diffusion of cells and particles at the growing edge. However, tumor growth implies an approximate spherical symmetry that makes necessary a geometrical treatment of the growth equations. The basic model was introduced in a former paper [C. Escudero, Phys. Rev. E 73, 020902(R) (2006)], and in the present work we extend our analysis and try to shed light on the possible geometrical principles that drive tumor growth. We present two-dimensional models that reproduce the experimental observations, and analyze the unexplored three-dimensional case, for which interesting conclusions on tumor growth are derived.
BeamDyn: A High-Fidelity Wind Turbine Blade Solver in the FAST Modular Framework: Preprint
Energy Technology Data Exchange (ETDEWEB)
Wang, Q.; Sprague, M.; Jonkman, J.; Johnson, N.
2015-01-01
BeamDyn, a Legendre-spectral-finite-element implementation of geometrically exact beam theory (GEBT), was developed to meet the design challenges associated with highly flexible composite wind turbine blades. In this paper, the governing equations of GEBT are reformulated into a nonlinear state-space form to support its coupling within the modular framework of the FAST wind turbine computer-aided engineering (CAE) tool. Different time integration schemes (implicit and explicit) were implemented and examined for wind turbine analysis. Numerical examples are presented to demonstrate the capability of this new beam solver. An example analysis of a realistic wind turbine blade, the CX-100, is also presented as validation.
Analytically derived weighting factors for transmission tomography cone beam projections
International Nuclear Information System (INIS)
Yao Weiguang; Leszczynski, Konrad
2009-01-01
Weighting factors, which define the contributions of individual voxels of a 3D object to individual projection elements (pixels) on the detector, are the basic elements required in iterative tomographic reconstructions from transmission projections. Exact or as accurate as possible values for weighting factors are required in high-resolution reconstructions. Geometric complexity of the problem, however, makes it difficult to obtain exact weighting factor values. In this work, we derive an analytical expression for the weighting factors in cone beam projection geometry. The resulting formula is validated and applied to reconstruction from mega and kilovoltage x-ray cone beam projections. The reconstruction speed and accuracy are significantly improved by using the weighting factor values.
Geometric Transformations in Engineering Geometry
Directory of Open Access Journals (Sweden)
I. F. Borovikov
2015-01-01
Full Text Available Recently, for business purposes, in view of current trends and world experience in training engineers, research and faculty staff there has been a need to transform traditional courses of descriptive geometry into the course of engineering geometry in which the geometrical transformations have to become its main section. On the basis of critical analysis the paper gives suggestions to improve a presentation technique of this section both in the classroom and in academic literature, extend an application scope of geometrical transformations to solve the position and metric tasks and simulation of surfaces, as well as to design complex engineering configurations, which meet a number of pre-specified conditions.The article offers to make a number of considerable amendments to the terms and definitions used in the existing courses of descriptive geometry. It draws some conclusions and makes the appropriate proposals on feasibility of coordination in teaching the movement transformation in the courses of analytical and descriptive geometry. This will provide interdisciplinary team teaching and allow students to be convinced that a combination of analytical and graphic ways to solve geometric tasks is useful and reasonable.The traditional sections of learning courses need to be added with a theory of projective and bi-rational transformations. In terms of application simplicity and convenience it is enough to consider the central transformations when solving the applied tasks. These transformations contain a beam of sub-invariant (low-invariant straight lines on which the invariant curve induces non-involution and involution projectivities. The expediency of nonlinear transformations application is shown in the article by a specific example of geometric modeling of the interfacing surface "spar-blade".Implementation of these suggestions will contribute to a real transformation of a traditional course of descriptive geometry to the engineering geometry
Exactly and quasi-exactly solvable 'discrete' quantum mechanics.
Sasaki, Ryu
2011-03-28
A brief introduction to discrete quantum mechanics is given together with the main results on various exactly solvable systems. Namely, the intertwining relations, shape invariance, Heisenberg operator solutions, annihilation/creation operators and dynamical symmetry algebras, including the q-oscillator algebra and the Askey-Wilson algebra. A simple recipe to construct exactly and quasi-exactly solvable (QES) Hamiltonians in one-dimensional 'discrete' quantum mechanics is presented. It reproduces all the known Hamiltonians whose eigenfunctions consist of the Askey scheme of hypergeometric orthogonal polynomials of a continuous or a discrete variable. Several new exactly and QES Hamiltonians are constructed. The sinusoidal coordinate plays an essential role.
Calculation of the geometrical intensity on an image surface
International Nuclear Information System (INIS)
Seppala, L.G.
1975-01-01
Laser fusion experiments involve the focusing of high power laser beams onto fuel pellets. The geometrical intensity is of interest in the cases where the laser is focused to the center of the pellet. Analytic expressions and ray trace methods for evaluating the geometrical intensity are presented
Exact asymmetric Skyrmion in anisotropic ferromagnet and its helimagnetic application
Energy Technology Data Exchange (ETDEWEB)
Kundu, Anjan, E-mail: anjan.kundu@saha.ac.in
2016-08-15
Topological Skyrmions as intricate spin textures were observed experimentally in helimagnets on 2d plane. Theoretical foundation of such solitonic states to appear in pure ferromagnetic model, as exact solutions expressed through any analytic function, was made long ago by Belavin and Polyakov (BP). We propose an innovative generalization of the BP solution for an anisotropic ferromagnet, based on a physically motivated geometric (in-)equality, which takes the exact Skyrmion to a new class of functions beyond analyticity. The possibility of stabilizing such metastable states in helimagnets is discussed with the construction of individual Skyrmion, Skyrmion crystal and lattice with asymmetry, likely to be detected in precision experiments.
Exact piecewise flat gravitational waves
van de Meent, M.
2011-01-01
We generalize our previous linear result (van de Meent 2011 Class. Quantum Grav 28 075005) in obtaining gravitational waves from our piecewise flat model for gravity in 3+1 dimensions to exact piecewise flat configurations describing exact planar gravitational waves. We show explicitly how to
CONDITIONS FOR EXACT CAVALIERI ESTIMATION
Directory of Open Access Journals (Sweden)
Mónica Tinajero-Bravo
2014-03-01
Full Text Available Exact Cavalieri estimation amounts to zero variance estimation of an integral with systematic observations along a sampling axis. A sufficient condition is given, both in the continuous and the discrete cases, for exact Cavalieri sampling. The conclusions suggest improvements on the current stereological application of fractionator-type sampling.
Geometrical approach to fluid models
International Nuclear Information System (INIS)
Kuvshinov, B.N.; Schep, T.J.
1997-01-01
Differential geometry based upon the Cartan calculus of differential forms is applied to investigate invariant properties of equations that describe the motion of continuous media. The main feature of this approach is that physical quantities are treated as geometrical objects. The geometrical notion of invariance is introduced in terms of Lie derivatives and a general procedure for the construction of local and integral fluid invariants is presented. The solutions of the equations for invariant fields can be written in terms of Lagrange variables. A generalization of the Hamiltonian formalism for finite-dimensional systems to continuous media is proposed. Analogously to finite-dimensional systems, Hamiltonian fluids are introduced as systems that annihilate an exact two-form. It is shown that Euler and ideal, charged fluids satisfy this local definition of a Hamiltonian structure. A new class of scalar invariants of Hamiltonian fluids is constructed that generalizes the invariants that are related with gauge transformations and with symmetries (Noether). copyright 1997 American Institute of Physics
Validation of flexible multibody dynamics beam formulations using benchmark problems
Energy Technology Data Exchange (ETDEWEB)
Bauchau, Olivier A., E-mail: obauchau@umd.edu [University of Maryland (United States); Betsch, Peter [Karlsruhe Institute of Technology (Germany); Cardona, Alberto [CIMEC (UNL/Conicet) (Argentina); Gerstmayr, Johannes [Leopold-Franzens Universität Innsbruck (Austria); Jonker, Ben [University of Twente (Netherlands); Masarati, Pierangelo [Politecnico di Milano (Italy); Sonneville, Valentin [Université de Liège (Belgium)
2016-05-15
As the need to model flexibility arose in multibody dynamics, the floating frame of reference formulation was developed, but this approach can yield inaccurate results when elastic displacements becomes large. While the use of three-dimensional finite element formulations overcomes this problem, the associated computational cost is overwhelming. Consequently, beam models, which are one-dimensional approximations of three-dimensional elasticity, have become the workhorse of many flexible multibody dynamics codes. Numerous beam formulations have been proposed, such as the geometrically exact beam formulation or the absolute nodal coordinate formulation, to name just two. New solution strategies have been investigated as well, including the intrinsic beam formulation or the DAE approach. This paper provides a systematic comparison of these various approaches, which will be assessed by comparing their predictions for four benchmark problems. The first problem is the Princeton beam experiment, a study of the static large displacement and rotation behavior of a simple cantilevered beam under a gravity tip load. The second problem, the four-bar mechanism, focuses on a flexible mechanism involving beams and revolute joints. The third problem investigates the behavior of a beam bent in its plane of greatest flexural rigidity, resulting in lateral buckling when a critical value of the transverse load is reached. The last problem investigates the dynamic stability of a rotating shaft. The predictions of eight independent codes are compared for these four benchmark problems and are found to be in close agreement with each other and with experimental measurements, when available.
Geometrical method of decoupling
Directory of Open Access Journals (Sweden)
C. Baumgarten
2012-12-01
Full Text Available The computation of tunes and matched beam distributions are essential steps in the analysis of circular accelerators. If certain symmetries—like midplane symmetry—are present, then it is possible to treat the betatron motion in the horizontal, the vertical plane, and (under certain circumstances the longitudinal motion separately using the well-known Courant-Snyder theory, or to apply transformations that have been described previously as, for instance, the method of Teng and Edwards. In a preceding paper, it has been shown that this method requires a modification for the treatment of isochronous cyclotrons with non-negligible space charge forces. Unfortunately, the modification was numerically not as stable as desired and it was still unclear, if the extension would work for all conceivable cases. Hence, a systematic derivation of a more general treatment seemed advisable. In a second paper, the author suggested the use of real Dirac matrices as basic tools for coupled linear optics and gave a straightforward recipe to decouple positive definite Hamiltonians with imaginary eigenvalues. In this article this method is generalized and simplified in order to formulate a straightforward method to decouple Hamiltonian matrices with eigenvalues on the real and the imaginary axis. The decoupling of symplectic matrices which are exponentials of such Hamiltonian matrices can be deduced from this in a few steps. It is shown that this algebraic decoupling is closely related to a geometric “decoupling” by the orthogonalization of the vectors E[over →], B[over →], and P[over →], which were introduced with the so-called “electromechanical equivalence.” A mathematical analysis of the problem can be traced down to the task of finding a structure-preserving block diagonalization of symplectic or Hamiltonian matrices. Structure preservation means in this context that the (sequence of transformations must be symplectic and hence canonical. When
Exact cosmological solutions for MOG
International Nuclear Information System (INIS)
Roshan, Mahmood
2015-01-01
We find some new exact cosmological solutions for the covariant scalar-tensor-vector gravity theory, the so-called modified gravity (MOG). The exact solution of the vacuum field equations has been derived. Also, for non-vacuum cases we have found some exact solutions with the aid of the Noether symmetry approach. More specifically, the symmetry vector and also the Noether conserved quantity associated to the point-like Lagrangian of the theory have been found. Also we find the exact form of the generic vector field potential of this theory by considering the behavior of the relevant point-like Lagrangian under the infinitesimal generator of the Noether symmetry. Finally, we discuss the cosmological implications of the solutions. (orig.)
Druţu, Cornelia
2018-01-01
The key idea in geometric group theory is to study infinite groups by endowing them with a metric and treating them as geometric spaces. This applies to many groups naturally appearing in topology, geometry, and algebra, such as fundamental groups of manifolds, groups of matrices with integer coefficients, etc. The primary focus of this book is to cover the foundations of geometric group theory, including coarse topology, ultralimits and asymptotic cones, hyperbolic groups, isoperimetric inequalities, growth of groups, amenability, Kazhdan's Property (T) and the Haagerup property, as well as their characterizations in terms of group actions on median spaces and spaces with walls. The book contains proofs of several fundamental results of geometric group theory, such as Gromov's theorem on groups of polynomial growth, Tits's alternative, Stallings's theorem on ends of groups, Dunwoody's accessibility theorem, the Mostow Rigidity Theorem, and quasiisometric rigidity theorems of Tukia and Schwartz. This is the f...
Geometric and engineering drawing
Morling, K
2010-01-01
The new edition of this successful text describes all the geometric instructions and engineering drawing information that are likely to be needed by anyone preparing or interpreting drawings or designs with plenty of exercises to practice these principles.
Differential geometric structures
Poor, Walter A
2007-01-01
This introductory text defines geometric structure by specifying parallel transport in an appropriate fiber bundle and focusing on simplest cases of linear parallel transport in a vector bundle. 1981 edition.
Geometric ghosts and unitarity
International Nuclear Information System (INIS)
Ne'eman, Y.
1980-09-01
A review is given of the geometrical identification of the renormalization ghosts and the resulting derivation of Unitarity equations (BRST) for various gauges: Yang-Mills, Kalb-Ramond, and Soft-Group-Manifold
New vistas in refractive laser beam shaping with an analytic design approach
Duerr, Fabian; Thienpont, Hugo
2014-05-01
Many commercial, medical and scientific applications of the laser have been developed since its invention. Some of these applications require a specific beam irradiance distribution to ensure optimal performance. Often, it is possible to apply geometrical methods to design laser beam shapers. This common design approach is based on the ray mapping between the input plane and the output beam. Geometric ray mapping designs with two plano-aspheric lenses have been thoroughly studied in the past. Even though analytic expressions for various ray mapping functions do exist, the surface profiles of the lenses are still calculated numerically. In this work, we present an alternative novel design approach that allows direct calculation of the rotational symmetric lens profiles described by analytic functions. Starting from the example of a basic beam expander, a set of functional differential equations is derived from Fermat's principle. This formalism allows calculating the exact lens profiles described by Taylor series coefficients up to very high orders. To demonstrate the versatility of this new approach, two further cases are solved: a Gaussian to at-top irradiance beam shaping system, and a beam shaping system that generates a more complex dark-hollow Gaussian (donut-like) irradiance profile with zero intensity in the on-axis region. The presented ray tracing results confirm the high accuracy of all calculated solutions and indicate the potential of this design approach for refractive beam shaping applications.
On geometrized gravitation theories
International Nuclear Information System (INIS)
Logunov, A.A.; Folomeshkin, V.N.
1977-01-01
General properties of the geometrized gravitation theories have been considered. Geometrization of the theory is realized only to the extent that by necessity follows from an experiment (geometrization of the density of the matter Lagrangian only). Aor a general case the gravitation field equations and the equations of motion for matter are formulated in the different Riemann spaces. A covariant formulation of the energy-momentum conservation laws is given in an arbitrary geometrized theory. The noncovariant notion of ''pseudotensor'' is not required in formulating the conservation laws. It is shown that in the general case (i.e., when there is an explicit dependence of the matter Lagrangian density on the covariant derivatives) a symmetric energy-momentum tensor of the matter is explicitly dependent on the curvature tensor. There are enlisted different geometrized theories that describe a known set of the experimental facts. The properties of one of the versions of the quasilinear geometrized theory that describes the experimental facts are considered. In such a theory the fundamental static spherically symmetrical solution has a singularity only in the coordinate origin. The theory permits to create a satisfactory model of the homogeneous nonstationary Universe
Geometrical charged-particle optics
Rose, Harald
2012-01-01
This second edition is an extended version of the first edition of Geometrical Charged-Particle Optics. The updated reference monograph is intended as a guide for researchers and graduate students who are seeking a comprehensive treatment of the design of instruments and beam-guiding systems of charged particles and their propagation in electromagnetic fields. Wave aspects are included in this edition for explaining electron holography, the Aharanov-Bohm effect and the resolution of electron microscopes limited by diffraction. Several methods for calculating the electromagnetic field are presented and procedures are outlined for calculating the properties of systems with arbitrarily curved axis. Detailed methods are presented for designing and optimizing special components such as aberration correctors, spectrometers, energy filters monochromators, ion traps, electron mirrors and cathode lenses. In particular, the optics of rotationally symmetric lenses, quadrupoles, and systems composed of these elements are...
Directory of Open Access Journals (Sweden)
A. Ya. Krasinskii
2014-01-01
Full Text Available The method of research stability and stabilization of equilibrium of systems with geometrical constraints is elaborated and used for equilibrium for real mechatronic arrangement GBB1005 Ball & Beam. For mathematical model construction is used Shul'gin's equations with redundant coordinates. The through differentiation geometrical constraints obtained kinematic (holonomic constraints is necessary add for stability analysis. Asymptotic stability equilibrium for mechanical systems with redundant coordinates is possible , in spite of formal reduction to Lyapunov's especial case, if the number zero roots is equal the number constraints . More exact nonlinear mathematical model of the mechanical component Ball &Beam is considered in this paper. One nonlinear geometric constrain in this problem is allow find the new equilibrium position. The choice of linear control subsystem is depend from the choice of redundant coordinate.
Nonlinear model of a rotating hub-beams structure: Equations of motion
Warminski, Jerzy
2018-01-01
Dynamics of a rotating structure composed of a rigid hub and flexible beams is presented in the paper. A nonlinear model of a beam takes into account bending, extension and nonlinear curvature. The influence of geometric nonlinearity and nonconstant angular velocity on dynamics of the rotating structure is presented. The exact equations of motion and associated boundary conditions are derived on the basis of the Hamilton's principle. The simplification of the exact nonlinear mathematical model is proposed taking into account the second order approximation. The reduced partial differential equations of motion together with associated boundary conditions can be used to study natural or forced vibrations of a rotating structure considering constant or nonconstant angular speed of a rigid hub and an arbitrary number of flexible blades.
Exact analysis of discrete data
Hirji, Karim F
2005-01-01
Researchers in fields ranging from biology and medicine to the social sciences, law, and economics regularly encounter variables that are discrete or categorical in nature. While there is no dearth of books on the analysis and interpretation of such data, these generally focus on large sample methods. When sample sizes are not large or the data are otherwise sparse, exact methods--methods not based on asymptotic theory--are more accurate and therefore preferable.This book introduces the statistical theory, analysis methods, and computation techniques for exact analysis of discrete data. After reviewing the relevant discrete distributions, the author develops the exact methods from the ground up in a conceptually integrated manner. The topics covered range from univariate discrete data analysis, a single and several 2 x 2 tables, a single and several 2 x K tables, incidence density and inverse sampling designs, unmatched and matched case -control studies, paired binary and trinomial response models, and Markov...
Tuning piezoresistive transduction in nanomechanical resonators by geometrical asymmetries
Energy Technology Data Exchange (ETDEWEB)
Llobet, J.; Sansa, M.; Lorenzoni, M.; Pérez-Murano, F., E-mail: francesc.perez@csic.es [Institut de Microelectrònica de Barcelona (IMB-CNM CSIC), Campus UAB, 08193 Bellaterra (Spain); Borrisé, X. [Institut Català de Nanociència i Nanotecnologia (ICN2), Campus UAB, 08193 Bellaterra Spain (Spain); San Paulo, A. [Instituto de Microelectrónica de Madrid (IMM-CSIC), 28760 Tres Cantos, Madrid (Spain)
2015-08-17
The effect of geometrical asymmetries on the piezoresistive transduction in suspended double clamped beam nanomechanical resonators is investigated. Tapered silicon nano-beams, fabricated using a fast and flexible prototyping method, are employed to determine how the asymmetry affects the transduced piezoresistive signal for different mechanical resonant modes. This effect is attributed to the modulation of the strain in pre-strained double clamped beams, and it is confirmed by means of finite element simulations.
Luminosity geometric reduction factor from colliding bunches with different lengths
Energy Technology Data Exchange (ETDEWEB)
Verdu-Andres, S. [Brookhaven National Lab. (BNL), Upton, NY (United States)
2017-09-29
In the interaction point of the future electron-Ion collider eRHIC, the electron beam bunches are at least one order of magnitude shorter than the proton beam bunches. With the introduction of a crossing angle, the actual number of collisions resulting from the bunch collision gets reduced. Here we derive the expression for the luminosity geometric reduction factor when the bunches of the two incoming beams are not equal.
A Differential Geometric Approach to Nonlinear Filtering: The Projection Filter
Brigo, D.; Hanzon, B.; LeGland, F.
1998-01-01
This paper presents a new and systematic method of approximating exact nonlinear filters with finite dimensional filters, using the differential geometric approach to statistics. The projection filter is defined rigorously in the case of exponential families. A convenient exponential family is
Morphing of geometric composites via residual swelling.
Pezzulla, Matteo; Shillig, Steven A; Nardinocchi, Paola; Holmes, Douglas P
2015-08-07
Understanding and controlling the shape of thin, soft objects has been the focus of significant research efforts among physicists, biologists, and engineers in the last decade. These studies aim to utilize advanced materials in novel, adaptive ways such as fabricating smart actuators or mimicking living tissues. Here, we present the controlled growth-like morphing of 2D sheets into 3D shapes by preparing geometric composite structures that deform by residual swelling. The morphing of these geometric composites is dictated by both swelling and geometry, with diffusion controlling the swelling-induced actuation, and geometric confinement dictating the structure's deformed shape. Building on a simple mechanical analog, we present an analytical model that quantitatively describes how the Gaussian and mean curvatures of a thin disk are affected by the interplay among geometry, mechanics, and swelling. This model is in excellent agreement with our experiments and numerics. We show that the dynamics of residual swelling is dictated by a competition between two characteristic diffusive length scales governed by geometry. Our results provide the first 2D analog of Timoshenko's classical formula for the thermal bending of bimetallic beams - our generalization explains how the Gaussian curvature of a 2D geometric composite is affected by geometry and elasticity. The understanding conferred by these results suggests that the controlled shaping of geometric composites may provide a simple complement to traditional manufacturing techniques.
Geometrical optical illusionists.
Wade, Nicholas J
2014-01-01
Geometrical optical illusions were given this title by Oppel in 1855. Variants on such small distortions of visual space were illustrated thereafter, many of which bear the names of those who first described them. Some original forms of the geometrical optical illusions are shown together with 'perceptual portraits' of those who described them. These include: Roget, Chevreul, Fick, Zöllner, Poggendorff, Hering, Kundt, Delboeuf Mach, Helmholtz, Hermann, von Bezold, Müller-Lyer, Lipps, Thiéry, Wundt, Münsterberg, Ebbinghaus, Titchener, Ponzo, Luckiesh, Sander, Ehrenstein, Gregory, Heard, White, Shepard, and. Lingelbach. The illusions are grouped under the headings of orientation, size, the combination of size and orientation, and contrast. Early theories of illusions, before geometrical optical illusions were so named, are mentioned briefly.
Exact solitary waves of the Fisher equation
International Nuclear Information System (INIS)
Kudryashov, Nikolai A.
2005-01-01
New method is presented to search exact solutions of nonlinear differential equations. This approach is used to look for exact solutions of the Fisher equation. New exact solitary waves of the Fisher equation are given
International Nuclear Information System (INIS)
La, H.
1992-01-01
A new geometric formulation of Liouville gravity based on the area preserving diffeo-morphism is given and a possible alternative to reinterpret Liouville gravity is suggested, namely, a scalar field coupled to two-dimensional gravity with a curvature constraint
A Geometric Dissection Problem
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 7; Issue 7. A Geometric Dissection Problem. M N Deshpande. Think It Over Volume 7 Issue 7 July 2002 pp 91-91. Fulltext. Click here to view fulltext PDF. Permanent link: https://www.ias.ac.in/article/fulltext/reso/007/07/0091-0091. Author Affiliations.
Geometric statistical inference
International Nuclear Information System (INIS)
Periwal, Vipul
1999-01-01
A reparametrization-covariant formulation of the inverse problem of probability is explicitly solved for finite sample sizes. The inferred distribution is explicitly continuous for finite sample size. A geometric solution of the statistical inference problem in higher dimensions is outlined
Geometric Series via Probability
Tesman, Barry
2012-01-01
Infinite series is a challenging topic in the undergraduate mathematics curriculum for many students. In fact, there is a vast literature in mathematics education research on convergence issues. One of the most important types of infinite series is the geometric series. Their beauty lies in the fact that they can be evaluated explicitly and that…
Pragmatic geometric model evaluation
Pamer, Robert
2015-04-01
Quantification of subsurface model reliability is mathematically and technically demanding as there are many different sources of uncertainty and some of the factors can be assessed merely in a subjective way. For many practical applications in industry or risk assessment (e. g. geothermal drilling) a quantitative estimation of possible geometric variations in depth unit is preferred over relative numbers because of cost calculations for different scenarios. The talk gives an overview of several factors that affect the geometry of structural subsurface models that are based upon typical geological survey organization (GSO) data like geological maps, borehole data and conceptually driven construction of subsurface elements (e. g. fault network). Within the context of the trans-European project "GeoMol" uncertainty analysis has to be very pragmatic also because of different data rights, data policies and modelling software between the project partners. In a case study a two-step evaluation methodology for geometric subsurface model uncertainty is being developed. In a first step several models of the same volume of interest have been calculated by omitting successively more and more input data types (seismic constraints, fault network, outcrop data). The positions of the various horizon surfaces are then compared. The procedure is equivalent to comparing data of various levels of detail and therefore structural complexity. This gives a measure of the structural significance of each data set in space and as a consequence areas of geometric complexity are identified. These areas are usually very data sensitive hence geometric variability in between individual data points in these areas is higher than in areas of low structural complexity. Instead of calculating a multitude of different models by varying some input data or parameters as it is done by Monte-Carlo-simulations, the aim of the second step of the evaluation procedure (which is part of the ongoing work) is to
International Nuclear Information System (INIS)
Herr, W; Pieloni, T
2014-01-01
One of the most severe limitations in high-intensity particle colliders is the beam-beam interaction, i.e. the perturbation of the beams as they cross the opposing beams. This introduction to beam-beam effects concentrates on a description of the phenomena that are present in modern colliding beam facilities
Exact models for isotropic matter
Thirukkanesh, S.; Maharaj, S. D.
2006-04-01
We study the Einstein-Maxwell system of equations in spherically symmetric gravitational fields for static interior spacetimes. The condition for pressure isotropy is reduced to a recurrence equation with variable, rational coefficients. We demonstrate that this difference equation can be solved in general using mathematical induction. Consequently, we can find an explicit exact solution to the Einstein-Maxwell field equations. The metric functions, energy density, pressure and the electric field intensity can be found explicitly. Our result contains models found previously, including the neutron star model of Durgapal and Bannerji. By placing restrictions on parameters arising in the general series, we show that the series terminate and there exist two linearly independent solutions. Consequently, it is possible to find exact solutions in terms of elementary functions, namely polynomials and algebraic functions.
Exact solutions to quadratic gravity
Czech Academy of Sciences Publication Activity Database
Pravda, Vojtěch; Pravdová, Alena; Podolský, J.; Švarc, J.
2017-01-01
Roč. 95, č. 8 (2017), č. článku 084025. ISSN 2470-0010 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : quadratic gravity * exact solutions * Kundt spacetimes Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.568, year: 2016 https://journals.aps.org/prd/abstract/10.1103/PhysRevD.95.084025
Exact solutions to quadratic gravity
Czech Academy of Sciences Publication Activity Database
Pravda, Vojtěch; Pravdová, Alena; Podolský, J.; Švarc, J.
2017-01-01
Roč. 95, č. 8 (2017), č. článku 084025. ISSN 2470-0010 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : quadratic gravity * exact solutions * Kundt spacetimes Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.568, year: 2016 https://journals. aps .org/prd/abstract/10.1103/PhysRevD.95.084025
Criteria for exact qudit universality
International Nuclear Information System (INIS)
Brennen, Gavin K.; O'Leary, Dianne P.; Bullock, Stephen S.
2005-01-01
We describe criteria for implementation of quantum computation in qudits. A qudit is a d-dimensional system whose Hilbert space is spanned by states vertical bar 0>, vertical bar 1>, ..., vertical bar d-1>. An important earlier work [A. Muthukrishnan and C.R. Stroud, Jr., Phys. Rev. A 62, 052309 (2000)] describes how to exactly simulate an arbitrary unitary on multiple qudits using a 2d-1 parameter family of single qudit and two qudit gates. That technique is based on the spectral decomposition of unitaries. Here we generalize this argument to show that exact universality follows given a discrete set of single qudit Hamiltonians and one two-qudit Hamiltonian. The technique is related to the QR-matrix decomposition of numerical linear algebra. We consider a generic physical system in which the single qudit Hamiltonians are a small collection of H jk x =(ℎ/2π)Ω(vertical bar k> jk y =(ℎ/2π)Ω(i vertical bar k> jk x,y are allowed Hamiltonians. One qudit exact universality follows iff this graph is connected, and complete universality results if the two-qudit Hamiltonian H=(ℎ/2π)Ω vertical bar d-1,d-1> 87 Rb and construct an optimal gate sequence using Raman laser pulses
Azzam, R M A
2015-12-01
Conditions for achieving equal and opposite angular deflections of a light beam by reflection and refraction at an air-dielectric boundary are determined. Such angularly symmetric beam splitting (ASBS) is possible only if the angle of incidence is >60° by exactly one third of the angle of refraction. This simple law, plus Snell's law, leads to several analytical results that clarify all aspects of this phenomenon. In particular, it is shown that the intensities of the two symmetrically deflected beams can be equalized by proper choice of the prism refractive index and the azimuth of incident linearly polarized light. ASBS enables a geometrically attractive layout of optical systems that employ multiple prism beam splitters.
Discrete geometric structures for architecture
Pottmann, Helmut
2010-06-13
The emergence of freeform structures in contemporary architecture raises numerous challenging research problems, most of which are related to the actual fabrication and are a rich source of research topics in geometry and geometric computing. The talk will provide an overview of recent progress in this field, with a particular focus on discrete geometric structures. Most of these result from practical requirements on segmenting a freeform shape into planar panels and on the physical realization of supporting beams and nodes. A study of quadrilateral meshes with planar faces reveals beautiful relations to discrete differential geometry. In particular, we discuss meshes which discretize the network of principal curvature lines. Conical meshes are among these meshes; they possess conical offset meshes at a constant face/face distance, which in turn leads to a supporting beam layout with so-called torsion free nodes. This work can be generalized to a variety of multilayer structures and laid the ground for an adapted curvature theory for these meshes. There are also efforts on segmenting surfaces into planar hexagonal panels. Though these are less constrained than planar quadrilateral panels, this problem is still waiting for an elegant solution. Inspired by freeform designs in architecture which involve circles and spheres, we present a new kind of triangle mesh whose faces\\' in-circles form a packing, i.e., the in-circles of two triangles with a common edge have the same contact point on that edge. These "circle packing (CP) meshes" exhibit an aesthetic balance of shape and size of their faces. They are closely tied to sphere packings on surfaces and to various remarkable structures and patterns which are of interest in art, architecture, and design. CP meshes constitute a new link between architectural freeform design and computational conformal geometry. Recently, certain timber structures motivated us to study discrete patterns of geodesics on surfaces. This
Exact moduli space metrics for hyperbolic vortex polygons
International Nuclear Information System (INIS)
Krusch, S.; Speight, J. M.
2010-01-01
Exact metrics on some totally geodesic submanifolds of the moduli space of static hyperbolic N-vortices are derived. These submanifolds, denoted as Σ n,m , are spaces of C n -invariant vortex configurations with n single vortices at the vertices of a regular polygon and m=N-n coincident vortices at the polygon's center. The geometric properties of Σ n,m are investigated, and it is found that Σ n,n-1 is isometric to the hyperbolic plane of curvature -(3πn) -1 . The geodesic flow on Σ n,m and a geometrically natural variant of geodesic flow recently proposed by Collie and Tong ['The dynamics of Chern-Simons vortices', Phys. Rev. D Part. Fields Gravit. Cosmol. 78, 065013 (2008);e-print arXiv:hep-th/0805.0602] are analyzed in detail.
Dynamics in geometrical confinement
Kremer, Friedrich
2014-01-01
This book describes the dynamics of low molecular weight and polymeric molecules when they are constrained under conditions of geometrical confinement. It covers geometrical confinement in different dimensionalities: (i) in nanometer thin layers or self supporting films (1-dimensional confinement) (ii) in pores or tubes with nanometric diameters (2-dimensional confinement) (iii) as micelles embedded in matrices (3-dimensional) or as nanodroplets.The dynamics under such conditions have been a much discussed and central topic in the focus of intense worldwide research activities within the last two decades. The present book discusses how the resulting molecular mobility is influenced by the subtle counterbalance between surface effects (typically slowing down molecular dynamics through attractive guest/host interactions) and confinement effects (typically increasing the mobility). It also explains how these influences can be modified and tuned, e.g. through appropriate surface coatings, film thicknesses or pore...
Bestvina, Mladen; Vogtmann, Karen
2014-01-01
Geometric group theory refers to the study of discrete groups using tools from topology, geometry, dynamics and analysis. The field is evolving very rapidly and the present volume provides an introduction to and overview of various topics which have played critical roles in this evolution. The book contains lecture notes from courses given at the Park City Math Institute on Geometric Group Theory. The institute consists of a set of intensive short courses offered by leaders in the field, designed to introduce students to exciting, current research in mathematics. These lectures do not duplicate standard courses available elsewhere. The courses begin at an introductory level suitable for graduate students and lead up to currently active topics of research. The articles in this volume include introductions to CAT(0) cube complexes and groups, to modern small cancellation theory, to isometry groups of general CAT(0) spaces, and a discussion of nilpotent genus in the context of mapping class groups and CAT(0) gro...
Lectures in geometric combinatorics
Thomas, Rekha R
2006-01-01
This book presents a course in the geometry of convex polytopes in arbitrary dimension, suitable for an advanced undergraduate or beginning graduate student. The book starts with the basics of polytope theory. Schlegel and Gale diagrams are introduced as geometric tools to visualize polytopes in high dimension and to unearth bizarre phenomena in polytopes. The heart of the book is a treatment of the secondary polytope of a point configuration and its connections to the state polytope of the toric ideal defined by the configuration. These polytopes are relatively recent constructs with numerous connections to discrete geometry, classical algebraic geometry, symplectic geometry, and combinatorics. The connections rely on Gr�bner bases of toric ideals and other methods from commutative algebra. The book is self-contained and does not require any background beyond basic linear algebra. With numerous figures and exercises, it can be used as a textbook for courses on geometric, combinatorial, and computational as...
Geometric information provider platform
Directory of Open Access Journals (Sweden)
Meisam Yousefzadeh
2015-07-01
Full Text Available Renovation of existing buildings is known as an essential stage in reduction of the energy loss. Considerable part of renovation process depends on geometric reconstruction of building based on semantic parameters. Following many research projects which were focused on parameterizing the energy usage, various energy modelling methods were developed during the last decade. On the other hand, by developing accurate measuring tools such as laser scanners, the interests of having accurate 3D building models are rapidly growing. But the automation of 3D building generation from laser point cloud or detection of specific objects in that is still a challenge. The goal is designing a platform through which required geometric information can be efficiently produced to support energy simulation software. Developing a reliable procedure which extracts required information from measured data and delivers them to a standard energy modelling system is the main purpose of the project.
Frè, Pietro Giuseppe
2013-01-01
‘Gravity, a Geometrical Course’ presents general relativity (GR) in a systematic and exhaustive way, covering three aspects that are homogenized into a single texture: i) the mathematical, geometrical foundations, exposed in a self consistent contemporary formalism, ii) the main physical, astrophysical and cosmological applications, updated to the issues of contemporary research and observations, with glimpses on supergravity and superstring theory, iii) the historical development of scientific ideas underlying both the birth of general relativity and its subsequent evolution. The book is divided in two volumes. Volume One is dedicated to the development of the theory and basic physical applications. It guides the reader from the foundation of special relativity to Einstein field equations, illustrating some basic applications in astrophysics. A detailed account of the historical and conceptual development of the theory is combined with the presentation of its mathematical foundations. Differe...
Institute of Scientific and Technical Information of China (English)
WANG ShunJin; ZHANG Hua
2007-01-01
Based on the exact analytical solution of ordinary differential equations,a truncation of the Taylor series of the exact solution to the Nth order leads to the Nth order algebraic dynamics algorithm.A detailed numerical comparison is presented with Runge-Kutta algorithm and symplectic geometric algorithm for 12 test models.The results show that the algebraic dynamics algorithm can better preserve both geometrical and dynamical fidelity of a dynamical system at a controllable precision,and it can solve the problem of algorithm-induced dissipation for the Runge-Kutta algorithm and the problem of algorithm-induced phase shift for the symplectic geometric algorithm.
Institute of Scientific and Technical Information of China (English)
2007-01-01
Based on the exact analytical solution of ordinary differential equations, a truncation of the Taylor series of the exact solution to the Nth order leads to the Nth order algebraic dynamics algorithm. A detailed numerical comparison is presented with Runge-Kutta algorithm and symplectic geometric algorithm for 12 test models. The results show that the algebraic dynamics algorithm can better preserve both geometrical and dynamical fidelity of a dynamical system at a controllable precision, and it can solve the problem of algorithm-induced dissipation for the Runge-Kutta algorithm and the problem of algorithm-induced phase shift for the symplectic geometric algorithm.
Geometric phase modulation for stellar interferometry
International Nuclear Information System (INIS)
Roy, M.; Boschung, B.; Tango, W.J.; Davis, J.
2002-01-01
Full text: In a long baseline optical interferometer, the fringe visibility is normally measured by modulation of the optical path difference between the two arms of the instruments. To obtain accurate measurements, the spectral bandwidth must be narrow, limiting the sensitivity of the technique. The application of geometric phase modulation technique to stellar interferometry has been proposed by Tango and Davis. Modulation of the geometric phase has the potential for improving the sensitivity of optical interferometers, and specially the Sydney University Stellar Interferometer (SUSI), by allowing broad band modulation of the light signals. This is because a modulator that changes the geometric phase of the signal is, in principle, achromatic. Another advantage of using such a phase modulator is that it can be placed in the common path traversed by the two orthogonally polarized beams emerging from the beam combiner in a stellar interferometer. Thus the optical components of the modulator do not have to be interferometric quality and could be relatively easily introduced into SUSI. We have investigated the proposed application in a laboratory-based experiment using a Mach-Zehnder interferometer with white-light source. This can be seen as a small model of an amplitude stellar interferometer where the light source takes the place of the distant star and two corner mirrors replaces the entrance pupils of the stellar interferometer
Ruffino, Fabio Ferrari
2013-01-01
Given a cohomology theory, there is a well-known abstract way to define the dual homology theory using the theory of spectra. In [4] the author provides a more geometric construction of the homology theory, using a generalization of the bordism groups. Such a generalization involves in its definition the vector bundle modification, which is a particular case of the Gysin map. In this paper we provide a more natural variant of that construction, which replaces the vector bundle modification wi...
Waerden, B
1996-01-01
From the reviews: "... Federer's timely and beautiful book indeed fills the need for a comprehensive treatise on geometric measure theory, and his detailed exposition leads from the foundations of the theory to the most recent discoveries. ... The author writes with a distinctive style which is both natural and powerfully economical in treating a complicated subject. This book is a major treatise in mathematics and is essential in the working library of the modern analyst." Bulletin of the London Mathematical Society.
Developing geometrical reasoning
Brown, Margaret; Jones, Keith; Taylor, Ron; Hirst, Ann
2004-01-01
This paper summarises a report (Brown, Jones & Taylor, 2003) to the UK Qualifications and Curriculum Authority of the work of one geometry group. The group was charged with developing and reporting on teaching ideas that focus on the development of geometrical reasoning at the secondary school level. The group was encouraged to explore what is possible both within and beyond the current requirements of the UK National Curriculum and the Key Stage 3 strategy, and to consider the whole atta...
Geometrically Consistent Mesh Modification
Bonito, A.
2010-01-01
A new paradigm of adaptivity is to execute refinement, coarsening, and smoothing of meshes on manifolds with incomplete information about their geometry and yet preserve position and curvature accuracy. We refer to this collectively as geometrically consistent (GC) mesh modification. We discuss the concept of discrete GC, show the failure of naive approaches, and propose and analyze a simple algorithm that is GC and accuracy preserving. © 2010 Society for Industrial and Applied Mathematics.
Geometric theory of information
2014-01-01
This book brings together geometric tools and their applications for Information analysis. It collects current and many uses of in the interdisciplinary fields of Information Geometry Manifolds in Advanced Signal, Image & Video Processing, Complex Data Modeling and Analysis, Information Ranking and Retrieval, Coding, Cognitive Systems, Optimal Control, Statistics on Manifolds, Machine Learning, Speech/sound recognition, and natural language treatment which are also substantially relevant for the industry.
Implementation and efficiency of two geometric stiffening approaches
International Nuclear Information System (INIS)
Lugris, Urbano; Naya, Miguel A.; Perez, Jose A.; Cuadrado, Javier
2008-01-01
When the modeling of flexible bodies is required in multibody systems, the floating frame of reference formulations are probably the most efficient methods available. In the case of beams undergoing high speed rotations, the geometric stiffening effect can appear due to geometric nonlinearities, and it is often not captured by the aforementioned methods, since it is common to linearize the elastic forces assuming small deformations. The present work discusses the implementation of different existing methods developed to consider such geometric nonlinearities within a floating frame of reference formulation in natural coordinates, making emphasis on the relation between efficiency and accuracy of the resulting algorithms, seeking to provide practical criteria of use
Studies in geometric quantization
International Nuclear Information System (INIS)
Tuynman, G.M.
1988-01-01
This thesis contains five chapters, of which the first, entitled 'What is prequantization, and what is geometric quantization?', is meant as an introduction to geometric quantization for the non-specialist. The second chapter, entitled 'Central extensions and physics' deals with the notion of central extensions of manifolds and elaborates and proves the statements made in the first chapter. Central extensions of manifolds occur in physics as the freedom of a phase factor in the quantum mechanical state vector, as the phase factor in the prequantization process of classical mechanics and it appears in mathematics when studying central extension of Lie groups. In this chapter the connection between these central extensions is investigated and a remarkable similarity between classical and quantum mechanics is shown. In chapter three a classical model is given for the hydrogen atom including spin-orbit and spin-spin interaction. The method of geometric quantization is applied to this model and the results are discussed. In the final chapters (4 and 5) an explicit method to calculate the operators corresponding to classical observables is given when the phase space is a Kaehler manifold. The obtained formula are then used to quantise symplectic manifolds which are irreducible hermitian symmetric spaces and the results are compared with other quantization procedures applied to these manifolds (in particular to Berezin's quantization). 91 refs.; 3 tabs
Geometrical model of multiple production
International Nuclear Information System (INIS)
Chikovani, Z.E.; Jenkovszky, L.L.; Kvaratshelia, T.M.; Struminskij, B.V.
1988-01-01
The relation between geometrical and KNO-scaling and their violation is studied in a geometrical model of multiple production of hadrons. Predictions concerning the behaviour of correlation coefficients at future accelerators are given
Geometric Computing for Freeform Architecture
Wallner, J.; Pottmann, Helmut
2011-01-01
Geometric computing has recently found a new field of applications, namely the various geometric problems which lie at the heart of rationalization and construction-aware design processes of freeform architecture. We report on our work in this area
Exact constants in approximation theory
Korneichuk, N
1991-01-01
This book is intended as a self-contained introduction for non-specialists, or as a reference work for experts, to the particular area of approximation theory that is concerned with exact constants. The results apply mainly to extremal problems in approximation theory, which in turn are closely related to numerical analysis and optimization. The book encompasses a wide range of questions and problems: best approximation by polynomials and splines; linear approximation methods, such as spline-approximation; optimal reconstruction of functions and linear functionals. Many of the results are base
Geometric Constructions with the Computer.
Chuan, Jen-chung
The computer can be used as a tool to represent and communicate geometric knowledge. With the appropriate software, a geometric diagram can be manipulated through a series of animation that offers more than one particular snapshot as shown in a traditional mathematical text. Geometric constructions with the computer enable the learner to see and…
Plasmon Geometric Phase and Plasmon Hall Shift
Shi, Li-kun; Song, Justin C. W.
2018-04-01
The collective plasmonic modes of a metal comprise a simple pattern of oscillating charge density that yields enhanced light-matter interaction. Here we unveil that beneath this familiar facade plasmons possess a hidden internal structure that fundamentally alters its dynamics. In particular, we find that metals with nonzero Hall conductivity host plasmons with an intricate current density configuration that sharply departs from that of ordinary zero Hall conductivity metals. This nontrivial internal structure dramatically enriches the dynamics of plasmon propagation, enabling plasmon wave packets to acquire geometric phases as they scatter. At boundaries, these phases accumulate allowing plasmon waves that reflect off to experience a nonreciprocal parallel shift. This plasmon Hall shift, tunable by Hall conductivity as well as plasmon wavelength, displaces the incident and reflected plasmon trajectories and can be readily probed by near-field photonics techniques. Anomalous plasmon geometric phases dramatically enrich the nanophotonics toolbox, and yield radical new means for directing plasmonic beams.
Geometric Phase Generated Optical Illusion.
Yue, Fuyong; Zang, Xiaofei; Wen, Dandan; Li, Zile; Zhang, Chunmei; Liu, Huigang; Gerardot, Brian D; Wang, Wei; Zheng, Guoxing; Chen, Xianzhong
2017-09-12
An optical illusion, such as "Rubin's vase", is caused by the information gathered by the eye, which is processed in the brain to give a perception that does not tally with a physical measurement of the stimulus source. Metasurfaces are metamaterials of reduced dimensionality which have opened up new avenues for flat optics. The recent advancement in spin-controlled metasurface holograms has attracted considerate attention, providing a new method to realize optical illusions. We propose and experimentally demonstrate a metasurface device to generate an optical illusion. The metasurface device is designed to display two asymmetrically distributed off-axis images of "Rubin faces" with high fidelity, high efficiency and broadband operation that are interchangeable by controlling the helicity of the incident light. Upon the illumination of a linearly polarized light beam, the optical illusion of a 'vase' is perceived. Our result provides an intuitive demonstration of the figure-ground distinction that our brains make during the visual perception. The alliance between geometric metasurface and the optical illusion opens a pathway for new applications related to encryption, optical patterning, and information processing.
Exact axially symmetric galactic dynamos
Henriksen, R. N.; Woodfinden, A.; Irwin, J. A.
2018-05-01
We give a selection of exact dynamos in axial symmetry on a galactic scale. These include some steady examples, at least one of which is wholly analytic in terms of simple functions and has been discussed elsewhere. Most solutions are found in terms of special functions, such as associated Lagrange or hypergeometric functions. They may be considered exact in the sense that they are known to any desired accuracy in principle. The new aspect developed here is to present scale-invariant solutions with zero resistivity that are self-similar in time. The time dependence is either a power law or an exponential factor, but since the geometry of the solution is self-similar in time we do not need to fix a time to study it. Several examples are discussed. Our results demonstrate (without the need to invoke any other mechanisms) X-shaped magnetic fields and (axially symmetric) magnetic spiral arms (both of which are well observed and documented) and predict reversing rotation measures in galaxy haloes (now observed in the CHANG-ES sample) as well as the fact that planar magnetic spirals are lifted into the galactic halo.
Corrochano, Eduardo Bayro
2010-01-01
This book presents contributions from a global selection of experts in the field. This useful text offers new insights and solutions for the development of theorems, algorithms and advanced methods for real-time applications across a range of disciplines. Written in an accessible style, the discussion of all applications is enhanced by the inclusion of numerous examples, figures and experimental analysis. Features: provides a thorough discussion of several tasks for image processing, pattern recognition, computer vision, robotics and computer graphics using the geometric algebra framework; int
Geometric multipartite entanglement measures
International Nuclear Information System (INIS)
Paz-Silva, Gerardo A.; Reina, John H.
2007-01-01
Within the framework of constructions for quantifying entanglement, we build a natural scenario for the assembly of multipartite entanglement measures based on Hopf bundle-like mappings obtained through Clifford algebra representations. Then, given the non-factorizability of an arbitrary two-qubit density matrix, we give an alternate quantity that allows the construction of two types of entanglement measures based on their arithmetical and geometrical averages over all pairs of qubits in a register of size N, and thus fully characterize its degree and type of entanglement. We find that such an arithmetical average is both additive and strongly super additive
Geometric correlations and multifractals
International Nuclear Information System (INIS)
Amritkar, R.E.
1991-07-01
There are many situations where the usual statistical methods are not adequate to characterize correlations in the system. To characterize such situations we introduce mutual correlation dimensions which describe geometric correlations in the system. These dimensions allow us to distinguish between variables which are perfectly correlated with or without a phase lag, variables which are uncorrelated and variables which are partially correlated. We demonstrate the utility of our formalism by considering two examples from dynamical systems. The first example is about the loss of memory in chaotic signals and describes auto-correlations while the second example is about synchronization of chaotic signals and describes cross-correlations. (author). 19 refs, 6 figs
Geometric scalar theory of gravity beyond spherical symmetry
Moschella, U.; Novello, M.
2017-04-01
We construct several exact solutions for a recently proposed geometric scalar theory of gravity. We focus on a class of axisymmetric geometries and a big-bang-like geometry and discuss their Lorentzian character. The axisymmetric solutions are parametrized by an integer angular momentum l . The l =0 (spherical) case gives rise to the Schwarzschild geometry. The other solutions have naked singular surfaces. While not a priori obvious, all the solutions that we present here are globally Lorentzian. The Lorentzian signature appears to be a robust property of the disformal geometries solving the vacuum geometric scalar theory of gravity equations.
AESS: Accelerated Exact Stochastic Simulation
Jenkins, David D.; Peterson, Gregory D.
2011-12-01
The Stochastic Simulation Algorithm (SSA) developed by Gillespie provides a powerful mechanism for exploring the behavior of chemical systems with small species populations or with important noise contributions. Gene circuit simulations for systems biology commonly employ the SSA method, as do ecological applications. This algorithm tends to be computationally expensive, so researchers seek an efficient implementation of SSA. In this program package, the Accelerated Exact Stochastic Simulation Algorithm (AESS) contains optimized implementations of Gillespie's SSA that improve the performance of individual simulation runs or ensembles of simulations used for sweeping parameters or to provide statistically significant results. Program summaryProgram title: AESS Catalogue identifier: AEJW_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJW_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: University of Tennessee copyright agreement No. of lines in distributed program, including test data, etc.: 10 861 No. of bytes in distributed program, including test data, etc.: 394 631 Distribution format: tar.gz Programming language: C for processors, CUDA for NVIDIA GPUs Computer: Developed and tested on various x86 computers and NVIDIA C1060 Tesla and GTX 480 Fermi GPUs. The system targets x86 workstations, optionally with multicore processors or NVIDIA GPUs as accelerators. Operating system: Tested under Ubuntu Linux OS and CentOS 5.5 Linux OS Classification: 3, 16.12 Nature of problem: Simulation of chemical systems, particularly with low species populations, can be accurately performed using Gillespie's method of stochastic simulation. Numerous variations on the original stochastic simulation algorithm have been developed, including approaches that produce results with statistics that exactly match the chemical master equation (CME) as well as other approaches that approximate the CME. Solution
Perturbation of an exact strong gravity solution
International Nuclear Information System (INIS)
Baran, S.A.
1982-10-01
Perturbations of an exact strong gravity solution are investigated. It is shown, by using the new multipole expansions previously presented, that this exact and static spherically symmetric solution is stable under odd parity perturbations. (author)
Exact Bremsstrahlung and effective couplings
Energy Technology Data Exchange (ETDEWEB)
Mitev, Vladimir [Institut für Physik, WA THEP, Johannes Gutenberg-Universität Mainz,Staudingerweg 7, 55128 Mainz (Germany); Institut für Mathematik und Institut für Physik, Humboldt-Universität zu Berlin,IRIS Haus, Zum Großen Windkanal 6, 12489 Berlin (Germany); Pomoni, Elli [DESY Hamburg, Theory Group, Notkestrasse 85, D-22607 Hamburg (Germany); Physics Division, National Technical University of Athens,15780 Zografou Campus, Athens (Greece)
2016-06-13
We calculate supersymmetric Wilson loops on the ellipsoid for a large class of N=2 SCFT using the localization formula of Hama and Hosomichi. From them we extract the radiation emitted by an accelerating heavy probe quark as well as the entanglement entropy following the recent works of Lewkowycz-Maldacena and Fiol-Gerchkovitz-Komargodski. Comparing our results with the N=4 SYM ones, we obtain interpolating functions f(g{sup 2}) such that a given N=2 SCFT observable is obtained by replacing in the corresponding N=4 SYM result the coupling constant by f(g{sup 2}). These “exact effective couplings” encode the finite, relative renormalization between the N=2 and the N=4 gluon propagator and they interpolate between the weak and the strong coupling. We discuss the range of their applicability.
High Resolution Thermometry for EXACT
Panek, J. S.; Nash, A. E.; Larson, M.; Mulders, N.
2000-01-01
High Resolution Thermometers (HRTs) based on SQUID detection of the magnetization of a paramagnetic salt or a metal alloy has been commonly used for sub-nano Kelvin temperature resolution in low temperature physics experiments. The main applications to date have been for temperature ranges near the lambda point of He-4 (2.177 K). These thermometers made use of materials such as Cu(NH4)2Br4 *2H2O, GdCl3, or PdFe. None of these materials are suitable for EXACT, which will explore the region of the He-3/He-4 tricritical point at 0.87 K. The experiment requirements and properties of several candidate paramagnetic materials will be presented, as well as preliminary test results.
An Exact Analytical Solution to Exponentially Tapered Piezoelectric Energy Harvester
Directory of Open Access Journals (Sweden)
H. Salmani
2015-01-01
Full Text Available It has been proven that tapering the piezoelectric beam through its length optimizes the power extracted from vibration based energy harvesting. This phenomenon has been investigated by some researchers using semianalytical, finite element and experimental methods. In this paper, an exact analytical solution is presented to calculate the power generated from vibration of exponentially tapered unimorph and bimorph with series and parallel connections. The mass normalized mode shapes of the exponentially tapered piezoelectric beam with tip mass are implemented to transfer the proposed electromechanical coupled equations into modal coordinates. The steady states harmonic solution results are verified both numerically and experimentally. Results show that there exist values for tapering parameter and electric resistance in a way that the output power per mass of the energy harvester will be maximized. Moreover it is concluded that the electric resistance must be higher than a specified value for gaining more power by tapering the beam.
International Nuclear Information System (INIS)
Noga, M.T.
1984-01-01
This thesis addresses a number of important problems that fall within the framework of the new discipline of Computational Geometry. The list of topics covered includes sorting and selection, convex hull algorithms, the L 1 hull, determination of the minimum encasing rectangle of a set of points, the Euclidean and L 1 diameter of a set of points, the metric traveling salesman problem, and finding the superrange of star-shaped and monotype polygons. The main theme of all the work was to develop a set of very fast state-of-the-art algorithms that supersede any rivals in terms of speed and ease of implementation. In some cases existing algorithms were refined; for others new techniques were developed that add to the present database of fast adaptive geometric algorithms. What emerges is a collection of techniques that is successful at merging modern tools developed in analysis of algorithms with those of classical geometry
Geometrization of quantum physics
International Nuclear Information System (INIS)
Ol'khov, O.A.
2009-01-01
It is shown that the Dirac equation for a free particle can be considered as a description of specific distortion of the space Euclidean geometry (space topological defect). This approach is based on the possibility of interpretation of the wave function as vector realizing representation of the fundamental group of the closed topological space-time 4-manifold. Mass and spin appear to be topological invariants. Such a concept explains all so-called 'strange' properties of quantum formalism: probabilities, wave-particle duality, nonlocal instantaneous correlation between noninteracting particles (EPR-paradox) and so on. Acceptance of the suggested geometrical concept means rejection of atomistic concept where all matter is considered as consisting of more and more small elementary particles. There are no any particles a priory, before measurement: the notions of particles appear as a result of classical interpretation of the contact of the region of the curved space with a device
Geometrization of quantum physics
Ol'Khov, O. A.
2009-12-01
It is shown that the Dirac equation for free particle can be considered as a description of specific distortion of the space euclidean geometry (space topological defect). This approach is based on possibility of interpretation of the wave function as vector realizing representation of the fundamental group of the closed topological space-time 4-manifold. Mass and spin appear to be topological invariants. Such concept explains all so called “strange” properties of quantum formalism: probabilities, wave-particle duality, nonlocal instantaneous correlation between noninteracting particles (EPR-paradox) and so on. Acceptance of suggested geometrical concept means rejection of atomistic concept where all matter is considered as consisting of more and more small elementary particles. There is no any particles a priori, before measurement: the notions of particles appear as a result of classical interpretation of the contact of the region of the curved space with a device.
Havelka, Jan
2008-01-01
Tato diplomová práce se zabývá akcelerací geometrických transformací obrazu s využitím GPU a architektury NVIDIA (R) CUDA TM. Časově kritické části kódu jsou přesunuty na GPU a vykonány paralelně. Jedním z výsledků je demonstrační aplikace pro porovnání výkonnosti obou architektur: CPU, a GPU v kombinaci s CPU. Pro referenční implementaci jsou použity vysoce optimalizované algoritmy z knihovny OpenCV, od firmy Intel. This master's thesis deals with acceleration of geometrical image transfo...
Time evolution in a geometric model of a particle
International Nuclear Information System (INIS)
Atiyah, M.F.; Franchetti, G.; Schroers, B.J.
2015-01-01
We analyse the properties of a (4+1)-dimensional Ricci-flat spacetime which may be viewed as an evolving Taub-NUT geometry, and give exact solutions of the Maxwell and gauged Dirac equation on this background. We interpret these solutions in terms of a geometric model of the electron and its spin, and discuss links between the resulting picture and Dirac’s Large Number Hypothesis.
Beam phase space and emittance
International Nuclear Information System (INIS)
Buon, J.
1990-12-01
The classical and elementary results for canonical phase space, the Liouville theorem and the beam emittance are reviewed. Then, the importance of phase portraits to obtain a geometrical description of motion is emphasized, with examples in accelerator physics. Finally, a statistical point of view is used to define beam emittance, to study its law of approximate conservation and to treat two particular examples
M.W. Kauw-A-Tjoe
2005-01-01
textabstractIn this thesis artificial intelligence ideas are applied to the domain of fine arts and especially modern art. First, we take a closer look at avant garde art movements of the late 19th and first half of the 20th century. After that, we make an analysis of the knowledge on which this art
Geometric flows in Horava-Lifshitz gravity
Bakas, Ioannis; Lust, Dieter; Petropoulos, Marios
2010-01-01
We consider instanton solutions of Euclidean Horava-Lifshitz gravity in four dimensions satisfying the detailed balance condition. They are described by geometric flows in three dimensions driven by certain combinations of the Cotton and Ricci tensors as well as the cosmological-constant term. The deformation curvature terms can have competing behavior leading to a variety of fixed points. The instantons interpolate between any two fixed points, which are vacua of topologically massive gravity with Lambda > 0, and their action is finite. Special emphasis is placed on configurations with SU(2) isometry associated with homogeneous but generally non-isotropic Bianchi IX model geometries. In this case, the combined Ricci-Cotton flow reduces to an autonomous system of ordinary differential equations whose properties are studied in detail for different couplings. The occurrence and stability of isotropic and anisotropic fixed points are investigated analytically and some exact solutions are obtained. The correspond...
Rayleigh's hypothesis and the geometrical optics limit.
Elfouhaily, Tanos; Hahn, Thomas
2006-09-22
The Rayleigh hypothesis (RH) is often invoked in the theoretical and numerical treatment of rough surface scattering in order to decouple the analytical form of the scattered field. The hypothesis stipulates that the scattered field away from the surface can be extended down onto the rough surface even though it is formed by solely up-going waves. Traditionally this hypothesis is systematically used to derive the Volterra series under the small perturbation method which is equivalent to the low-frequency limit. In this Letter we demonstrate that the RH also carries the high-frequency or the geometrical optics limit, at least to first order. This finding has never been explicitly derived in the literature. Our result comforts the idea that the RH might be an exact solution under some constraints in the general case of random rough surfaces and not only in the case of small-slope deterministic periodic gratings.
Harmonic and geometric analysis
Citti, Giovanna; Pérez, Carlos; Sarti, Alessandro; Zhong, Xiao
2015-01-01
This book presents an expanded version of four series of lectures delivered by the authors at the CRM. Harmonic analysis, understood in a broad sense, has a very wide interplay with partial differential equations and in particular with the theory of quasiconformal mappings and its applications. Some areas in which real analysis has been extremely influential are PDE's and geometric analysis. Their foundations and subsequent developments made extensive use of the Calderón–Zygmund theory, especially the Lp inequalities for Calderón–Zygmund operators (Beurling transform and Riesz transform, among others) and the theory of Muckenhoupt weights. The first chapter is an application of harmonic analysis and the Heisenberg group to understanding human vision, while the second and third chapters cover some of the main topics on linear and multilinear harmonic analysis. The last serves as a comprehensive introduction to a deep result from De Giorgi, Moser and Nash on the regularity of elliptic partial differen...
Geometrical analysis of cytochrome c unfolding
Urie, Kristopher G.; Pletneva, Ekaterina; Gray, Harry B.; Winkler, Jay R.; Kozak, John J.
2011-01-01
A geometrical model has been developed to study the unfolding of iso-1 cytochrome c. The model draws on the crystallographic data reported for this protein. These data were used to calculate the distance between specific residues in the folded state, and in a sequence of extended states defined by n = 3, 5, 7, 9, 11, 13, and 15 residue units. Exact calculations carried out for each of the 103 residues in the polypeptide chain demonstrate that different regions of the chain have different unfolding histories. Regions where there is a persistence of compact structures can be identified, and this geometrical characterization is fully consistent with analyses of time-resolved fluorescence energy-transfer (TrFET) data using dansyl-derivatized cysteine side-chain probes at positions 39, 50, 66, 85, and 99. The calculations were carried out assuming that different regions of the polypeptide chain unfold synchronously. To test this assumption, lattice Monte Carlo simulations were performed to study systematically the possible importance of asynchronicity. Calculations show that small departures from synchronous dynamics can arise if displacements of residues in the main body of the chain are much more sluggish than near-terminal residues.
Geometrical basis for the Standard Model
Potter, Franklin
1994-02-01
The robust character of the Standard Model is confirmed. Examination of its geometrical basis in three equivalent internal symmetry spaces-the unitary plane C 2, the quaternion space Q, and the real space R 4—as well as the real space R 3 uncovers mathematical properties that predict the physical properties of leptons and quarks. The finite rotational subgroups of the gauge group SU(2) L × U(1) Y generate exactly three lepton families and four quark families and reveal how quarks and leptons are related. Among the physical properties explained are the mass ratios of the six leptons and eight quarks, the origin of the left-handed preference by the weak interaction, the geometrical source of color symmetry, and the zero neutrino masses. The ( u, d) and ( c, s) quark families team together to satisfy the triangle anomaly cancellation with the electron family, while the other families pair one-to-one for cancellation. The spontaneously broken symmetry is discrete and needs no Higgs mechanism. Predictions include all massless neutrinos, the top quark at 160 GeV/ c 2, the b' quark at 80 GeV/ c 2, and the t' quark at 2600 GeV/ c 2.
Regular Polygons and Geometric Series.
Jarrett, Joscelyn A.
1982-01-01
Examples of some geometric illustrations of limits are presented. It is believed the limit concept is among the most important topics in mathematics, yet many students do not have good intuitive feelings for the concept, since it is often taught very abstractly. Geometric examples are suggested as meaningful tools. (MP)
Geometric Invariants and Object Recognition.
1992-08-01
University of Chicago Press. Maybank , S.J. [1992], "The Projection of Two Non-coplanar Conics", in Geometric Invariance in Machine Vision, eds. J.L...J.L. Mundy and A. Zisserman, MIT Press, Cambridge, MA. Mundy, J.L., Kapur, .. , Maybank , S.J., and Quan, L. [1992a] "Geometric Inter- pretation of
Quantum adiabatic approximation and the geometric phase
International Nuclear Information System (INIS)
Mostafazadeh, A.
1997-01-01
A precise definition of an adiabaticity parameter ν of a time-dependent Hamiltonian is proposed. A variation of the time-dependent perturbation theory is presented which yields a series expansion of the evolution operator U(τ)=summation scr(l) U (scr(l)) (τ) with U (scr(l)) (τ) being at least of the order ν scr(l) . In particular, U (0) (τ) corresponds to the adiabatic approximation and yields Berry close-quote s adiabatic phase. It is shown that this series expansion has nothing to do with the 1/τ expansion of U(τ). It is also shown that the nonadiabatic part of the evolution operator is generated by a transformed Hamiltonian which is off-diagonal in the eigenbasis of the initial Hamiltonian. This suggests the introduction of an adiabatic product expansion for U(τ) which turns out to yield exact expressions for U(τ) for a large number of quantum systems. In particular, a simple application of the adiabatic product expansion is used to show that for the Hamiltonian describing the dynamics of a magnetic dipole in an arbitrarily changing magnetic field, there exists another Hamiltonian with the same eigenvectors for which the Schroedinger equation is exactly solvable. Some related issues concerning geometric phases and their physical significance are also discussed. copyright 1997 The American Physical Society
Transmuted Complementary Weibull Geometric Distribution
Directory of Open Access Journals (Sweden)
Ahmed Z. A fify
2014-12-01
Full Text Available This paper provides a new generalization of the complementary Weibull geometric distribution that introduced by Tojeiro et al. (2014, using the quadratic rank transmutation map studied by Shaw and Buckley (2007. The new distribution is referred to as transmuted complementary Weibull geometric distribution (TCWGD. The TCWG distribution includes as special cases the complementary Weibull geometric distribution (CWGD, complementary exponential geometric distribution(CEGD,Weibull distribution (WD and exponential distribution (ED. Various structural properties of the new distribution including moments, quantiles, moment generating function and RØnyi entropy of the subject distribution are derived. We proposed the method of maximum likelihood for estimating the model parameters and obtain the observed information matrix. A real data set are used to compare the exibility of the transmuted version versus the complementary Weibull geometric distribution.
Ma, Haotong; Liu, Zejin; Jiang, Pengzhi; Xu, Xiaojun; Du, Shaojun
2011-07-04
We propose and demonstrate the improvement of conventional Galilean refractive beam shaping system for accurately generating near-diffraction-limited flattop beam with arbitrary beam size. Based on the detailed study of the refractive beam shaping system, we found that the conventional Galilean beam shaper can only work well for the magnifying beam shaping. Taking the transformation of input beam with Gaussian irradiance distribution into target beam with high order Fermi-Dirac flattop profile as an example, the shaper can only work well at the condition that the size of input and target beam meets R(0) ≥ 1.3 w(0). For the improvement, the shaper is regarded as the combination of magnifying and demagnifying beam shaping system. The surface and phase distributions of the improved Galilean beam shaping system are derived based on Geometric and Fourier Optics. By using the improved Galilean beam shaper, the accurate transformation of input beam with Gaussian irradiance distribution into target beam with flattop irradiance distribution is realized. The irradiance distribution of the output beam is coincident with that of the target beam and the corresponding phase distribution is maintained. The propagation performance of the output beam is greatly improved. Studies of the influences of beam size and beam order on the improved Galilean beam shaping system show that restriction of beam size has been greatly reduced. This improvement can also be used to redistribute the input beam with complicated irradiance distribution into output beam with complicated irradiance distribution.
Exact solutions for rotating charged dust
International Nuclear Information System (INIS)
Islam, J.N.
1984-01-01
Earlier work by the author on rotating charged dust is summarized. An incomplete class of exact solutions for differentially rotating charged dust in Newton-Maxwell theory for the equal mass and charge case that was found earlier is completed. A new global exact solution for cylindrically symmetric differentially rotating charged dust in Newton-Maxwell theory is presented. Lastly, a new exact solution for cylindrically symmetric rigidly rotating charged dust in general relativity is given. (author)
An exact linear dispersion relation for CRM instability
International Nuclear Information System (INIS)
Choyal, Y; Minami, K
2011-01-01
An exact self-consistent linear dispersion relation of a large orbit electron beam including two principles of cyclotron emission with oscillation frequencies above and below the relativistic electron frequency is derived and analyzed numerically for the first time in the literature. The two principles are cyclotron resonance maser (CRM) instability and Cherenkov instability in the azimuthal direction. Self-consistency in the formulation and inclusion of proper boundary conditions have removed the unphysical instability existing for infinitely large k z observed in conventional dispersion relations of CRM instability.
Renormgroup symmetries in problems of nonlinear geometrical optics
International Nuclear Information System (INIS)
Kovalev, V.F.
1996-01-01
Utilization and further development of the previously announced approach [1,2] enables one to construct renormgroup symmetries for a boundary value problem for the system of equations which describes propagation of a powerful radiation in a nonlinear medium in geometrical optics approximation. With the help of renormgroup symmetries new rigorous and approximate analytical solutions of nonlinear geometrical optics equations are obtained. Explicit analytical expressions are presented that characterize spatial evolution of laser beam which has an arbitrary intensity dependence at the boundary of the nonlinear medium. (author)
Geometric inequalities for black holes
International Nuclear Information System (INIS)
Dain, Sergio
2013-01-01
Full text: A geometric inequality in General Relativity relates quantities that have both a physical interpretation and a geometrical definition. It is well known that the parameters that characterize the Kerr-Newman black hole satisfy several important geometric inequalities. Remarkably enough, some of these inequalities also hold for dynamical black holes. This kind of inequalities, which are valid in the dynamical and strong field regime, play an important role in the characterization of the gravitational collapse. They are closed related with the cosmic censorship conjecture. In this talk I will review recent results in this subject. (author)
Geometric Computing for Freeform Architecture
Wallner, J.
2011-06-03
Geometric computing has recently found a new field of applications, namely the various geometric problems which lie at the heart of rationalization and construction-aware design processes of freeform architecture. We report on our work in this area, dealing with meshes with planar faces and meshes which allow multilayer constructions (which is related to discrete surfaces and their curvatures), triangles meshes with circle-packing properties (which is related to conformal uniformization), and with the paneling problem. We emphasize the combination of numerical optimization and geometric knowledge.
Optical traps with geometric aberrations
International Nuclear Information System (INIS)
Roichman, Yael; Waldron, Alex; Gardel, Emily; Grier, David G.
2006-01-01
We assess the influence of geometric aberrations on the in-plane performance of optical traps by studying the dynamics of trapped colloidal spheres in deliberately distorted holographic optical tweezers. The lateral stiffness of the traps turns out to be insensitive to moderate amounts of coma, astigmatism, and spherical aberration. Moreover holographic aberration correction enables us to compensate inherent shortcomings in the optical train, thereby adaptively improving its performance. We also demonstrate the effects of geometric aberrations on the intensity profiles of optical vortices, whose readily measured deformations suggest a method for rapidly estimating and correcting geometric aberrations in holographic trapping systems
Geometric inequalities for black holes
Energy Technology Data Exchange (ETDEWEB)
Dain, Sergio [Universidad Nacional de Cordoba (Argentina)
2013-07-01
Full text: A geometric inequality in General Relativity relates quantities that have both a physical interpretation and a geometrical definition. It is well known that the parameters that characterize the Kerr-Newman black hole satisfy several important geometric inequalities. Remarkably enough, some of these inequalities also hold for dynamical black holes. This kind of inequalities, which are valid in the dynamical and strong field regime, play an important role in the characterization of the gravitational collapse. They are closed related with the cosmic censorship conjecture. In this talk I will review recent results in this subject. (author)
Extremal black holes as exact string solutions
International Nuclear Information System (INIS)
Horowitz, G.T.; Tseytlin, A.A.
1994-01-01
We show that the leading order solution describing an extremal electrically charged black hole in string theory is, in fact, an exact solution to all orders in α' when interpreted in a Kaluza-Klein fashion. This follows from the observation that it can be obtained via dimensional reduction from a five-dimensional background which is proved to be an exact string solution
On exact solutions of scattering problems
International Nuclear Information System (INIS)
Nikishov, P.Yu.; Plekhanov, E.B.; Zakhariev, B.N.
1982-01-01
Examples illustrating the quality of the reconstruction of potentials from single-channel scattering data by using exactly solvable models are given. Simple exact solutions for multi-channel systems with non-degenerated resonance singularities of the scattering matrix are derived
Quasi exact solution of the Rabi Hamiltonian
Koç, R; Tuetuencueler, H
2002-01-01
A method is suggested to obtain the quasi exact solution of the Rabi Hamiltonian. It is conceptually simple and can be easily extended to other systems. The analytical expressions are obtained for eigenstates and eigenvalues in terms of orthogonal polynomials. It is also demonstrated that the Rabi system, in a particular case, coincides with the quasi exactly solvable Poeschl-Teller potential.
Exact, almost and delayed fault detection
DEFF Research Database (Denmark)
Niemann, Hans Henrik; Saberi, Ali; Stoorvogel, Anton A.
1999-01-01
Considers the problem of fault detection and isolation while using zero or almost zero threshold. A number of different fault detection and isolation problems using exact or almost exact disturbance decoupling are formulated. Solvability conditions are given for the formulated design problems....... The l-step delayed fault detection problem is also considered for discrete-time systems....
Topological order in an exactly solvable 3D spin model
International Nuclear Information System (INIS)
Bravyi, Sergey; Leemhuis, Bernhard; Terhal, Barbara M.
2011-01-01
Research highlights: RHtriangle We study exactly solvable spin model with six-qubit nearest neighbor interactions on a 3D face centered cubic lattice. RHtriangle The ground space of the model exhibits topological quantum order. RHtriangle Elementary excitations can be geometrically described as the corners of rectangular-shaped membranes. RHtriangle The ground space can encode 4g qubits where g is the greatest common divisor of the lattice dimensions. RHtriangle Logical operators acting on the encoded qubits are described in terms of closed strings and closed membranes. - Abstract: We study a 3D generalization of the toric code model introduced recently by Chamon. This is an exactly solvable spin model with six-qubit nearest-neighbor interactions on an FCC lattice whose ground space exhibits topological quantum order. The elementary excitations of this model which we call monopoles can be geometrically described as the corners of rectangular-shaped membranes. We prove that the creation of an isolated monopole separated from other monopoles by a distance R requires an operator acting on Ω(R 2 ) qubits. Composite particles that consist of two monopoles (dipoles) and four monopoles (quadrupoles) can be described as end-points of strings. The peculiar feature of the model is that dipole-type strings are rigid, that is, such strings must be aligned with face-diagonals of the lattice. For periodic boundary conditions the ground space can encode 4g qubits where g is the greatest common divisor of the lattice dimensions. We describe a complete set of logical operators acting on the encoded qubits in terms of closed strings and closed membranes.
Discrete geometric structures for architecture
Pottmann, Helmut
2010-01-01
. The talk will provide an overview of recent progress in this field, with a particular focus on discrete geometric structures. Most of these result from practical requirements on segmenting a freeform shape into planar panels and on the physical realization
Geometric Rationalization for Freeform Architecture
Jiang, Caigui
2016-01-01
The emergence of freeform architecture provides interesting geometric challenges with regards to the design and manufacturing of large-scale structures. To design these architectural structures, we have to consider two types of constraints. First
Geometrical optics in general relativity
Loinger, A.
2006-01-01
General relativity includes geometrical optics. This basic fact has relevant consequences that concern the physical meaning of the discontinuity surfaces propagated in the gravitational field - as it was first emphasized by Levi-Civita.
Mobile Watermarking against Geometrical Distortions
Directory of Open Access Journals (Sweden)
Jing Zhang
2015-08-01
Full Text Available Mobile watermarking robust to geometrical distortions is still a great challenge. In mobile watermarking, efficient computation is necessary because mobile devices have very limited resources due to power consumption. In this paper, we propose a low-complexity geometrically resilient watermarking approach based on the optimal tradeoff circular harmonic function (OTCHF correlation filter and the minimum average correlation energy Mellin radial harmonic (MACE-MRH correlation filter. By the rotation, translation and scale tolerance properties of the two kinds of filter, the proposed watermark detector can be robust to geometrical attacks. The embedded watermark is weighted by a perceptual mask which matches very well with the properties of the human visual system. Before correlation, a whitening process is utilized to improve watermark detection reliability. Experimental results demonstrate that the proposed watermarking approach is computationally efficient and robust to geometrical distortions.
Geometric inequalities methods of proving
Sedrakyan, Hayk
2017-01-01
This unique collection of new and classical problems provides full coverage of geometric inequalities. Many of the 1,000 exercises are presented with detailed author-prepared-solutions, developing creativity and an arsenal of new approaches for solving mathematical problems. This book can serve teachers, high-school students, and mathematical competitors. It may also be used as supplemental reading, providing readers with new and classical methods for proving geometric inequalities. .
Path Following in the Exact Penalty Method of Convex Programming.
Zhou, Hua; Lange, Kenneth
2015-07-01
Classical penalty methods solve a sequence of unconstrained problems that put greater and greater stress on meeting the constraints. In the limit as the penalty constant tends to ∞, one recovers the constrained solution. In the exact penalty method, squared penalties are replaced by absolute value penalties, and the solution is recovered for a finite value of the penalty constant. In practice, the kinks in the penalty and the unknown magnitude of the penalty constant prevent wide application of the exact penalty method in nonlinear programming. In this article, we examine a strategy of path following consistent with the exact penalty method. Instead of performing optimization at a single penalty constant, we trace the solution as a continuous function of the penalty constant. Thus, path following starts at the unconstrained solution and follows the solution path as the penalty constant increases. In the process, the solution path hits, slides along, and exits from the various constraints. For quadratic programming, the solution path is piecewise linear and takes large jumps from constraint to constraint. For a general convex program, the solution path is piecewise smooth, and path following operates by numerically solving an ordinary differential equation segment by segment. Our diverse applications to a) projection onto a convex set, b) nonnegative least squares, c) quadratically constrained quadratic programming, d) geometric programming, and e) semidefinite programming illustrate the mechanics and potential of path following. The final detour to image denoising demonstrates the relevance of path following to regularized estimation in inverse problems. In regularized estimation, one follows the solution path as the penalty constant decreases from a large value.
Exact optics - III. Schwarzschild's spectrograph camera revised
Willstrop, R. V.
2004-03-01
Karl Schwarzschild identified a system of two mirrors, each defined by conic sections, free of third-order spherical aberration, coma and astigmatism, and with a flat focal surface. He considered it impractical, because the field was too restricted. This system was rediscovered as a quadratic approximation to one of Lynden-Bell's `exact optics' designs which have wider fields. Thus the `exact optics' version has a moderate but useful field, with excellent definition, suitable for a spectrograph camera. The mirrors are strongly aspheric in both the Schwarzschild design and the exact optics version.
Quaternionic formulation of the exact parity model
Energy Technology Data Exchange (ETDEWEB)
Brumby, S.P.; Foot, R.; Volkas, R.R.
1996-02-28
The exact parity model (EPM) is a simple extension of the standard model which reinstates parity invariance as an unbroken symmetry of nature. The mirror matter sector of the model can interact with ordinary matter through gauge boson mixing, Higgs boson mixing and, if neutrinos are massive, through neutrino mixing. The last effect has experimental support through the observed solar and atmospheric neutrino anomalies. In the paper it is shown that the exact parity model can be formulated in a quaternionic framework. This suggests that the idea of mirror matter and exact parity may have profound implications for the mathematical formulation of quantum theory. 13 refs.
Quaternionic formulation of the exact parity model
International Nuclear Information System (INIS)
Brumby, S.P.; Foot, R.; Volkas, R.R.
1996-01-01
The exact parity model (EPM) is a simple extension of the standard model which reinstates parity invariance as an unbroken symmetry of nature. The mirror matter sector of the model can interact with ordinary matter through gauge boson mixing, Higgs boson mixing and, if neutrinos are massive, through neutrino mixing. The last effect has experimental support through the observed solar and atmospheric neutrino anomalies. In the paper it is shown that the exact parity model can be formulated in a quaternionic framework. This suggests that the idea of mirror matter and exact parity may have profound implications for the mathematical formulation of quantum theory. 13 refs
Geometric Mixing, Peristalsis, and the Geometric Phase of the Stomach.
Arrieta, Jorge; Cartwright, Julyan H E; Gouillart, Emmanuelle; Piro, Nicolas; Piro, Oreste; Tuval, Idan
2015-01-01
Mixing fluid in a container at low Reynolds number--in an inertialess environment--is not a trivial task. Reciprocating motions merely lead to cycles of mixing and unmixing, so continuous rotation, as used in many technological applications, would appear to be necessary. However, there is another solution: movement of the walls in a cyclical fashion to introduce a geometric phase. We show using journal-bearing flow as a model that such geometric mixing is a general tool for using deformable boundaries that return to the same position to mix fluid at low Reynolds number. We then simulate a biological example: we show that mixing in the stomach functions because of the "belly phase," peristaltic movement of the walls in a cyclical fashion introduces a geometric phase that avoids unmixing.
Geometric Mixing, Peristalsis, and the Geometric Phase of the Stomach.
Directory of Open Access Journals (Sweden)
Jorge Arrieta
Full Text Available Mixing fluid in a container at low Reynolds number--in an inertialess environment--is not a trivial task. Reciprocating motions merely lead to cycles of mixing and unmixing, so continuous rotation, as used in many technological applications, would appear to be necessary. However, there is another solution: movement of the walls in a cyclical fashion to introduce a geometric phase. We show using journal-bearing flow as a model that such geometric mixing is a general tool for using deformable boundaries that return to the same position to mix fluid at low Reynolds number. We then simulate a biological example: we show that mixing in the stomach functions because of the "belly phase," peristaltic movement of the walls in a cyclical fashion introduces a geometric phase that avoids unmixing.
An Exact Confidence Region in Multivariate Calibration
Mathew, Thomas; Kasala, Subramanyam
1994-01-01
In the multivariate calibration problem using a multivariate linear model, an exact confidence region is constructed. It is shown that the region is always nonempty and is invariant under nonsingular transformations.
Euclidean shortest paths exact or approximate algorithms
Li, Fajie
2014-01-01
This book reviews algorithms for the exact or approximate solution of shortest-path problems, with a specific focus on a class of algorithms called rubberband algorithms. The coverage includes mathematical proofs for many of the given statements.
Exact solutions, numerical relativity and gravitational radiation
International Nuclear Information System (INIS)
Winicour, J.
1986-01-01
In recent years, there has emerged a new use for exact solutions to Einstein's equation as checks on the accuracy of numerical relativity codes. Much has already been written about codes based upon the space-like Cauchy problem. In the case of two Killing vectors, a numerical characteristic initial value formulation based upon two intersecting families of null hypersurfaces has successfully evolved the Schwarzschild and the colliding plane wave vacuum solutions. Here the author discusses, in the context of exact solutions, numerical studies of gravitational radiation based upon the null cone initial value problem. Every stage of progress in the null cone approach has been associated with exact solutions in some sense. He begins by briefly recapping this history. Then he presents two new examples illustrating how exact solutions can be useful
Fast Exact Euclidean Distance (FEED) Transformation
Schouten, Theo; Kittler, J.; van den Broek, Egon; Petrou, M.; Nixon, M.
2004-01-01
Fast Exact Euclidean Distance (FEED) transformation is introduced, starting from the inverse of the distance transformation. The prohibitive computational cost of a naive implementation of traditional Euclidean Distance Transformation, is tackled by three operations: restriction of both the number
New exact wave solutions for Hirota equation
Indian Academy of Sciences (India)
2Department of Engineering Sciences, Faculty of Technology and Engineering,. University ... of nonlinear partial differential equations (NPDEs) in mathematical physics. Keywords. ... This method has been successfully applied to obtain exact.
Exact Algorithms for Solving Stochastic Games
DEFF Research Database (Denmark)
Hansen, Kristoffer Arnsfelt; Koucky, Michal; Lauritzen, Niels
2012-01-01
Shapley's discounted stochastic games, Everett's recursive games and Gillette's undiscounted stochastic games are classical models of game theory describing two-player zero-sum games of potentially infinite duration. We describe algorithms for exactly solving these games....
On exactly soluble model in quantum electrodynamics
International Nuclear Information System (INIS)
Bogolubov, N.N.; Shumovsky, A.S.; Fam Le Kien
1984-01-01
Equations of motion describing the dynamics of three-level atom of ladder type interacting with two modes of quantized radiation field are solved exactly. Evolution of level population and photon rumbers under different unitial conditions is irvestigated
Analytic progress on exact lattice chiral symmetry
International Nuclear Information System (INIS)
Kikukawa, Y.
2002-01-01
Theoretical issues of exact chiral symmetry on the lattice are discussed and related recent works are reviewed. For chiral theories, the construction with exact gauge invariance is reconsidered from the point of view of domain wall fermion. The issue in the construction of electroweak theory is also discussed. For vector-like theories, we discuss unitarity (positivity), Hamiltonian approach, and several generalizations of the Ginsparg-Wilson relation (algebraic and odd-dimensional)
Exact and approximate multiple diffraction calculations
International Nuclear Information System (INIS)
Alexander, Y.; Wallace, S.J.; Sparrow, D.A.
1976-08-01
A three-body potential scattering problem is solved in the fixed scatterer model exactly and approximately to test the validity of commonly used assumptions of multiple scattering calculations. The model problem involves two-body amplitudes that show diffraction-like differential scattering similar to high energy hadron-nucleon amplitudes. The exact fixed scatterer calculations are compared to Glauber approximation, eikonal-expansion results and a noneikonal approximation
Ion beam generation and focusing
International Nuclear Information System (INIS)
Miller, P.A.; Mendel, C.W.; Swain, D.W.; Goldstein, S.A.
1975-01-01
Calculations have shown that efficiently generated and focused ion beams could have significant advantages over electron beams in achieving ignition of inertially-confined thermonuclear fuel. Efficient ion beam generation implies use of a good ion source and suppression of net electron current. Net electron flow can be reduced by allowing electrons to reflex through a highly transparent anode or by use of transverse magnetic fields (either beam self-fields or externally applied fields). Geometric focusing can be achieved if the beam is generated by appropriately shaped electrodes. Experimental results are presented which demonstrate ion beam generation in both reflexing and pinched-flow diodes. Spherically shaped electrodes are used to concentrate a proton beam, and target response to proton deposition is studied
Exact bright and dark spatial soliton solutions in saturable nonlinear media
International Nuclear Information System (INIS)
Calvo, Gabriel F.; Belmonte-Beitia, Juan; Perez-Garcia, Victor M.
2009-01-01
We present exact analytical bright and dark (black and grey) solitary wave solutions of a nonlinear Schroedinger-type equation describing the propagation of spatial beams in media exhibiting a saturable nonlinearity (such as centrosymmetric photorefractive materials). A qualitative study of the stationary equation is carried out together with a discussion of the stability of the solutions.
Time-dependent field equations for paraxial relativistic electron beams: Beam Research Program
International Nuclear Information System (INIS)
Sharp, W.M.; Yu, S.S.; Lee, E.P.
1987-01-01
A simplified set of field equations for a paraxial relativistic electron beam is presented. These equations for the beam electrostatic potential phi and pinch potential Phi identical to A/sub z/ - phi retain previously neglected time-dependent terms and for axisymmetric beams reduce exactly to Maxwell's equations
An algebraic geometric approach to separation of variables
Schöbel, Konrad
2015-01-01
Konrad Schöbel aims to lay the foundations for a consequent algebraic geometric treatment of variable separation, which is one of the oldest and most powerful methods to construct exact solutions for the fundamental equations in classical and quantum physics. The present work reveals a surprising algebraic geometric structure behind the famous list of separation coordinates, bringing together a great range of mathematics and mathematical physics, from the late 19th century theory of separation of variables to modern moduli space theory, Stasheff polytopes and operads. "I am particularly impressed by his mastery of a variety of techniques and his ability to show clearly how they interact to produce his results.” (Jim Stasheff) Contents The Foundation: The Algebraic Integrability Conditions The Proof of Concept: A Complete Solution for the 3-Sphere The Generalisation: A Solution for Spheres of Arbitrary Dimension The Perspectives: Applications and Generalisations Target Groups Scientists in the fie...
Geometric phases in astigmatic optical modes of arbitrary order
International Nuclear Information System (INIS)
Habraken, Steven J. M.; Nienhuis, Gerard
2010-01-01
The transverse spatial structure of a paraxial beam of light is fully characterized by a set of parameters that vary only slowly under free propagation. They specify bosonic ladder operators that connect modes of different orders, in analogy to the ladder operators connecting harmonic-oscillator wave functions. The parameter spaces underlying sets of higher-order modes are isomorphic to the parameter space of the ladder operators. We study the geometry of this space and the geometric phase that arises from it. This phase constitutes the ultimate generalization of the Gouy phase in paraxial wave optics. It reduces to the ordinary Gouy phase and the geometric phase of nonastigmatic optical modes with orbital angular momentum in limiting cases. We briefly discuss the well-known analogy between geometric phases and the Aharonov-Bohm effect, which provides some complementary insights into the geometric nature and origin of the generalized Gouy phase shift. Our method also applies to the quantum-mechanical description of wave packets. It allows for obtaining complete sets of normalized solutions of the Schroedinger equation. Cyclic transformations of such wave packets give rise to a phase shift, which has a geometric interpretation in terms of the other degrees of freedom involved.
Geometric group theory an introduction
Löh, Clara
2017-01-01
Inspired by classical geometry, geometric group theory has in turn provided a variety of applications to geometry, topology, group theory, number theory and graph theory. This carefully written textbook provides a rigorous introduction to this rapidly evolving field whose methods have proven to be powerful tools in neighbouring fields such as geometric topology. Geometric group theory is the study of finitely generated groups via the geometry of their associated Cayley graphs. It turns out that the essence of the geometry of such groups is captured in the key notion of quasi-isometry, a large-scale version of isometry whose invariants include growth types, curvature conditions, boundary constructions, and amenability. This book covers the foundations of quasi-geometry of groups at an advanced undergraduate level. The subject is illustrated by many elementary examples, outlooks on applications, as well as an extensive collection of exercises.
Geometric procedures for civil engineers
Tonias, Elias C
2016-01-01
This book provides a multitude of geometric constructions usually encountered in civil engineering and surveying practice. A detailed geometric solution is provided to each construction as well as a step-by-step set of programming instructions for incorporation into a computing system. The volume is comprised of 12 chapters and appendices that may be grouped in three major parts: the first is intended for those who love geometry for its own sake and its evolution through the ages, in general, and, more specifically, with the introduction of the computer. The second section addresses geometric features used in the book and provides support procedures used by the constructions presented. The remaining chapters and the appendices contain the various constructions. The volume is ideal for engineering practitioners in civil and construction engineering and allied areas.
Geometric entanglement in topologically ordered states
International Nuclear Information System (INIS)
Orús, Román; Wei, Tzu-Chieh; Buerschaper, Oliver; Nest, Maarten Van den
2014-01-01
Here we investigate the connection between topological order and the geometric entanglement, as measured by the logarithm of the overlap between a given state and its closest product state of blocks. We do this for a variety of topologically ordered systems such as the toric code, double semion, colour code and quantum double models. As happens for the entanglement entropy, we find that for sufficiently large block sizes the geometric entanglement is, up to possible sub-leading corrections, the sum of two contributions: a bulk contribution obeying a boundary law times the number of blocks and a contribution quantifying the underlying pattern of long-range entanglement of the topologically ordered state. This topological contribution is also present in the case of single-spin blocks in most cases, and constitutes an alternative characterization of topological order for these quantum states based on a multipartite entanglement measure. In particular, we see that the topological term for the two-dimensional colour code is twice as much as the one for the toric code, in accordance with recent renormalization group arguments (Bombin et al 2012 New J. Phys. 14 073048). Motivated by these results, we also derive a general formalism to obtain upper- and lower-bounds to the geometric entanglement of states with a non-Abelian group symmetry, and which we explicitly use to analyse quantum double models. Furthermore, we also provide an analysis of the robustness of the topological contribution in terms of renormalization and perturbation theory arguments, as well as a numerical estimation for small systems. Some of the results in this paper rely on the ability to disentangle single sites from the quantum state, which is always possible for the systems that we consider. Additionally we relate our results to the behaviour of the relative entropy of entanglement in topologically ordered systems, and discuss a number of numerical approaches based on tensor networks that could be
An introduction to geometrical physics
Aldrovandi, R
1995-01-01
This book stresses the unifying power of the geometrical framework in bringing together concepts from the different areas of physics. Common underpinnings of optics, elasticity, gravitation, relativistic fields, particle mechanics and other subjects are underlined. It attempts to extricate the notion of space currently in the physical literature from the metric connotation.The book's goal is to present mathematical ideas associated with geometrical physics in a rather introductory language. Included are many examples from elementary physics and also, for those wishing to reach a higher level o
Asymptotic geometric analysis, part I
Artstein-Avidan, Shiri
2015-01-01
The authors present the theory of asymptotic geometric analysis, a field which lies on the border between geometry and functional analysis. In this field, isometric problems that are typical for geometry in low dimensions are substituted by an "isomorphic" point of view, and an asymptotic approach (as dimension tends to infinity) is introduced. Geometry and analysis meet here in a non-trivial way. Basic examples of geometric inequalities in isomorphic form which are encountered in the book are the "isomorphic isoperimetric inequalities" which led to the discovery of the "concentration phenomen
Geometric integration for particle accelerators
International Nuclear Information System (INIS)
Forest, Etienne
2006-01-01
This paper is a very personal view of the field of geometric integration in accelerator physics-a field where often work of the highest quality is buried in lost technical notes or even not published; one has only to think of Simon van der Meer Nobel prize work on stochastic cooling-unpublished in any refereed journal. So I reconstructed the relevant history of geometrical integration in accelerator physics as much as I could by talking to collaborators and using my own understanding of the field. The reader should not be too surprised if this account is somewhere between history, science and perhaps even fiction
Geometrical spin symmetry and spin
International Nuclear Information System (INIS)
Pestov, I. B.
2011-01-01
Unification of General Theory of Relativity and Quantum Mechanics leads to General Quantum Mechanics which includes into itself spindynamics as a theory of spin phenomena. The key concepts of spindynamics are geometrical spin symmetry and the spin field (space of defining representation of spin symmetry). The essence of spin is the bipolar structure of geometrical spin symmetry induced by the gravitational potential. The bipolar structure provides a natural derivation of the equations of spindynamics. Spindynamics involves all phenomena connected with spin and provides new understanding of the strong interaction.
Geometric integration for particle accelerators
Forest, Étienne
2006-05-01
This paper is a very personal view of the field of geometric integration in accelerator physics—a field where often work of the highest quality is buried in lost technical notes or even not published; one has only to think of Simon van der Meer Nobel prize work on stochastic cooling—unpublished in any refereed journal. So I reconstructed the relevant history of geometrical integration in accelerator physics as much as I could by talking to collaborators and using my own understanding of the field. The reader should not be too surprised if this account is somewhere between history, science and perhaps even fiction.
Lattice degeneracies of geometric fermions
International Nuclear Information System (INIS)
Raszillier, H.
1983-05-01
We give the minimal numbers of degrees of freedom carried by geometric fermions on all lattices of maximal symmetries in d = 2, 3, and 4 dimensions. These numbers are lattice dependent, but in the (free) continuum limit, part of the degrees of freedom have to escape to infinity by a Wilson mechanism built in, and 2sup(d) survive for any lattice. On self-reciprocal lattices we compare the minimal numbers of degrees of freedom of geometric fermions with the minimal numbers of naive fermions on these lattices and argue that these numbers are equal. (orig.)
The geometric role of symmetry breaking in gravity
International Nuclear Information System (INIS)
Wise, Derek K
2012-01-01
In gravity, breaking symmetry from a group G to a group H plays the role of describing geometry in relation to the geometry of the homogeneous space G/H. The deep reason for this is Cartan's 'method of equivalence,' giving, in particular, an exact correspondence between metrics and Cartan connections. I argue that broken symmetry is thus implicit in any gravity theory, for purely geometric reasons. As an application, I explain how this kind of thinking gives a new approach to Hamiltonian gravity in which an observer field spontaneously breaks Lorentz symmetry and gives a Cartan connection on space.
A simple numerical model of a geometrically nonlinear Timoshenko beam
Keijdener, C.; Metrikine, A.
2015-01-01
In the original problem for which this model was developed, onedimensional flexible objects interact through a non-linear contact model. Due to the non-linear nature of the contact model, a numerical time-domain approach was adopted. One of the goals was to see if the coupling between axial and
Height and Tilt Geometric Texture
DEFF Research Database (Denmark)
Andersen, Vedrana; Desbrun, Mathieu; Bærentzen, Jakob Andreas
2009-01-01
compromise between functionality and simplicity: it can efficiently handle and process geometric texture too complex to be represented as a height field, without having recourse to full blown mesh editing algorithms. The height-and-tilt representation proposed here is fully intrinsic to the mesh, making...
In Defence of Geometrical Algebra
Blasjo, V.N.E.
The geometrical algebra hypothesis was once the received interpretation of Greek mathematics. In recent decades, however, it has become anathema to many. I give a critical review of all arguments against it and offer a consistent rebuttal case against the modern consensus. Consequently, I find that
Geometrical interpretation of extended supergravity
International Nuclear Information System (INIS)
Townsend, P.K.; Nieuwenhuizen, P.van
1977-01-01
SO 2 extended supergravity is shown to be a geometrical theory, whose underlying gauge group is OSp(4,2). The couplings which gauge the SO 2 symmetry as well as the accompanying cosmological and masslike terms are directly obtained, and the usual SO 2 model is obtained after a Wigner-Inoenue group contraction. (Auth.)
Geometric scaling in exclusive processes
International Nuclear Information System (INIS)
Munier, S.; Wallon, S.
2003-01-01
We show that according to the present understanding of the energy evolution of the observables measured in deep-inelastic scattering, the photon-proton scattering amplitude has to exhibit geometric scaling at each impact parameter. We suggest a way to test this experimentally at HERA. A qualitative analysis based on published data is presented and discussed. (orig.)
Geometric quantization and general relativity
International Nuclear Information System (INIS)
Souriau, J.-M.
1977-01-01
The purpose of geometric quantization is to give a rigorous mathematical content to the 'correspondence principle' between classical and quantum mechanics. The main tools are borrowed on one hand from differential geometry and topology (differential manifolds, differential forms, fiber bundles, homology and cohomology, homotopy), on the other hand from analysis (functions of positive type, infinite dimensional group representations, pseudo-differential operators). Some satisfactory results have been obtained in the study of dynamical systems, but some fundamental questions are still waiting for an answer. The 'geometric quantization of fields', where some further well known difficulties arise, is still in a preliminary stage. In particular, the geometric quantization on the gravitational field is still a mere project. The situation is even more uncertain due to the fact that there is no experimental evidence of any quantum gravitational effect which could give us a hint towards what we are supposed to look for. The first level of both Quantum Theory, and General Relativity describes passive matter: influence by the field without being a source of it (first quantization and equivalence principle respectively). In both cases this is only an approximation (matter is always a source). But this approximation turns out to be the least uncertain part of the description, because on one hand the first quantization avoids the problems of renormalization and on the other hand the equivalence principle does not imply any choice of field equations (it is known that one can modify Einstein equations at short distances without changing their geometrical properties). (Auth.)
Geometric origin of central charges
International Nuclear Information System (INIS)
Lukierski, J.; Rytel, L.
1981-05-01
The complete set of N(N-1) central charge generators for D=4 N-extended super Poincare algebra is obtained by suitable contraction of OSp (2N; 4) superalgebra. The superspace realizations of the spinorial generators with central charges are derived. The conjugate set of N(N-1) additional bosonic superspace coordinates is introduced in an unique and geometric way. (author)
Vergence, Vision, and Geometric Optics
Keating, Michael P.
1975-01-01
Provides a definition of vergence in terms of the curvature of the wave fronts, and gives examples to illustrate the advantages of this approach. The vergence treatment of geometrical optics provides both conceptual and algebraic advantages, particularly for the life science student, over the traditional object distance-image distance-focal length…
Cartan's geometrical structure of supergravity
International Nuclear Information System (INIS)
Baaklini, N.S.
1977-06-01
The geometrical partnership of the vierbein and the spin-3/2 field in the structure of the supergravity Lagrangian is emphasized. Both fields are introduced as component of the same matrix differential form. The only local symmetry of the theory is SL(2,C)
International Nuclear Information System (INIS)
Teng, L.C.
1980-01-01
In colliding beam storage rings the beam collision regions are generally so short that the beam-beam interaction can be considered as a series of evenly spaced non-linear kicks superimposed on otherwise stable linear oscillations. Most of the numerical studies on computers were carried out in just this manner. But for some reason this model has not been extensively employed in analytical studies. This is perhaps because all analytical work has so far been done by mathematicians pursuing general transcendental features of non-linear mechanics for whom this specific model of the specific system of colliding beams is too parochial and too repugnantly physical. Be that as it may, this model is of direct interest to accelerator physicists and is amenable to (1) further simplification, (2) physical approximation, and (3) solution by analogy to known phenomena
A method to determine the detector locations of the cone-beam projection of the balls’ centers
International Nuclear Information System (INIS)
Deng, Lin; Xi, Xiaoqi; Li, Lei; Han, Yu; Yan, Bin
2015-01-01
In geometric calibration of cone-beam computed tomography (CBCT), sphere-like objects such as balls are widely imaged, the positioning information of which is obtained to determine the unknown geometric parameters. In this process, the accuracy of the detector location of CB projection of the center of the ball, which we call the center projection, is very important, since geometric calibration is sensitive to errors in the positioning information. Currently in almost all the geometric calibration using balls, the center projection is invariably estimated by the center of the support of the projection or the centroid of the intensity values inside the support approximately. Clackdoyle’s work indicates that the center projection is not always at the center of the support or the centroid of the intensity values inside, and has given a quantitative analysis of the maximum errors in evaluating the center projection by the centroid. In this paper, an exact method is proposed to calculate the center projection, utilizing both the detector location of the ellipse center and the two axis lengths of the ellipse. Numerical simulation results have demonstrated the precision and the robustness of the proposed method. Finally there are some comments on this work with non-uniform density balls, as well as the effect by the error occurred in the evaluation for the location of the orthogonal projection of the cone vertex onto the detector. (paper)
Exact solution of the hidden Markov processes
Saakian, David B.
2017-11-01
We write a master equation for the distributions related to hidden Markov processes (HMPs) and solve it using a functional equation. Thus the solution of HMPs is mapped exactly to the solution of the functional equation. For a general case the latter can be solved only numerically. We derive an exact expression for the entropy of HMPs. Our expression for the entropy is an alternative to the ones given before by the solution of integral equations. The exact solution is possible because actually the model can be considered as a generalized random walk on a one-dimensional strip. While we give the solution for the two second-order matrices, our solution can be easily generalized for the L values of the Markov process and M values of observables: We should be able to solve a system of L functional equations in the space of dimension M -1 .
Classes of exact Einstein Maxwell solutions
Komathiraj, K.; Maharaj, S. D.
2007-12-01
We find new classes of exact solutions to the Einstein Maxwell system of equations for a charged sphere with a particular choice of the electric field intensity and one of the gravitational potentials. The condition of pressure isotropy is reduced to a linear, second order differential equation which can be solved in general. Consequently we can find exact solutions to the Einstein Maxwell field equations corresponding to a static spherically symmetric gravitational potential in terms of hypergeometric functions. It is possible to find exact solutions which can be written explicitly in terms of elementary functions, namely polynomials and product of polynomials and algebraic functions. Uncharged solutions are regainable with our choice of electric field intensity; in particular we generate the Einstein universe for particular parameter values.
Energy Technology Data Exchange (ETDEWEB)
Carey, D.C.
1999-12-09
TURTLE is a computer program useful for determining many characteristics of a particle beam once an initial design has been achieved, Charged particle beams are usually designed by adjusting various beam line parameters to obtain desired values of certain elements of a transfer or beam matrix. Such beam line parameters may describe certain magnetic fields and their gradients, lengths and shapes of magnets, spacings between magnetic elements, or the initial beam accepted into the system. For such purposes one typically employs a matrix multiplication and fitting program such as TRANSPORT. TURTLE is designed to be used after TRANSPORT. For convenience of the user, the input formats of the two programs have been made compatible. The use of TURTLE should be restricted to beams with small phase space. The lumped element approximation, described below, precludes the inclusion of the effect of conventional local geometric aberrations (due to large phase space) or fourth and higher order. A reading of the discussion below will indicate clearly the exact uses and limitations of the approach taken in TURTLE.
International Nuclear Information System (INIS)
Carey, D.C.
1999-01-01
TURTLE is a computer program useful for determining many characteristics of a particle beam once an initial design has been achieved, Charged particle beams are usually designed by adjusting various beam line parameters to obtain desired values of certain elements of a transfer or beam matrix. Such beam line parameters may describe certain magnetic fields and their gradients, lengths and shapes of magnets, spacings between magnetic elements, or the initial beam accepted into the system. For such purposes one typically employs a matrix multiplication and fitting program such as TRANSPORT. TURTLE is designed to be used after TRANSPORT. For convenience of the user, the input formats of the two programs have been made compatible. The use of TURTLE should be restricted to beams with small phase space. The lumped element approximation, described below, precludes the inclusion of the effect of conventional local geometric aberrations (due to large phase space) or fourth and higher order. A reading of the discussion below will indicate clearly the exact uses and limitations of the approach taken in TURTLE
Exactly solvable birth and death processes
International Nuclear Information System (INIS)
Sasaki, Ryu
2009-01-01
Many examples of exactly solvable birth and death processes, a typical stationary Markov chain, are presented together with the explicit expressions of the transition probabilities. They are derived by similarity transforming exactly solvable 'matrix' quantum mechanics, which is recently proposed by Odake and the author [S. Odake and R. Sasaki, J. Math. Phys. 49, 053503 (2008)]. The (q-) Askey scheme of hypergeometric orthogonal polynomials of a discrete variable and their dual polynomials play a central role. The most generic solvable birth/death rates are rational functions of q x (with x being the population) corresponding to the q-Racah polynomial.
Assisted inflation from geometric tachyon
International Nuclear Information System (INIS)
Panigrahi, Kamal L.; Singh, Harvendra
2007-01-01
We study the effect of rolling of N D3-branes in the vicinity of NS5-branes. We find out that this system coupled with the four dimensional gravity gives the slow roll assisted inflation of the scalar field theory. Once again this expectation is exactly similar to that of N-tachyon assisted inflation on unstable D-branes
Beam limiter for thermonuclear fusion devices
International Nuclear Information System (INIS)
Kaminsky, M.S.
1977-01-01
The invention pertains to a beam limiter to prevent collisions between a plasma and the inner surface of a hollow body in which the plasma is confined. The patent claims pertain to suitable geometrical shapes of the beam limiter. (GG) [de
Fast and Exact Fiber Surfaces for Tetrahedral Meshes.
Klacansky, Pavol; Tierny, Julien; Carr, Hamish; Zhao Geng
2017-07-01
Isosurfaces are fundamental geometrical objects for the analysis and visualization of volumetric scalar fields. Recent work has generalized them to bivariate volumetric fields with fiber surfaces, the pre-image of polygons in range space. However, the existing algorithm for their computation is approximate, and is limited to closed polygons. Moreover, its runtime performance does not allow instantaneous updates of the fiber surfaces upon user edits of the polygons. Overall, these limitations prevent a reliable and interactive exploration of the space of fiber surfaces. This paper introduces the first algorithm for the exact computation of fiber surfaces in tetrahedral meshes. It assumes no restriction on the topology of the input polygon, handles degenerate cases and better captures sharp features induced by polygon bends. The algorithm also allows visualization of individual fibers on the output surface, better illustrating their relationship with data features in range space. To enable truly interactive exploration sessions, we further improve the runtime performance of this algorithm. In particular, we show that it is trivially parallelizable and that it scales nearly linearly with the number of cores. Further, we study acceleration data-structures both in geometrical domain and range space and we show how to generalize interval trees used in isosurface extraction to fiber surface extraction. Experiments demonstrate the superiority of our algorithm over previous work, both in terms of accuracy and running time, with up to two orders of magnitude speedups. This improvement enables interactive edits of range polygons with instantaneous updates of the fiber surface for exploration purpose. A VTK-based reference implementation is provided as additional material to reproduce our results.
Efficiently computing exact geodesic loops within finite steps.
Xin, Shi-Qing; He, Ying; Fu, Chi-Wing
2012-06-01
Closed geodesics, or geodesic loops, are crucial to the study of differential topology and differential geometry. Although the existence and properties of closed geodesics on smooth surfaces have been widely studied in mathematics community, relatively little progress has been made on how to compute them on polygonal surfaces. Most existing algorithms simply consider the mesh as a graph and so the resultant loops are restricted only on mesh edges, which are far from the actual geodesics. This paper is the first to prove the existence and uniqueness of geodesic loop restricted on a closed face sequence; it contributes also with an efficient algorithm to iteratively evolve an initial closed path on a given mesh into an exact geodesic loop within finite steps. Our proposed algorithm takes only an O(k) space complexity and an O(mk) time complexity (experimentally), where m is the number of vertices in the region bounded by the initial loop and the resultant geodesic loop, and k is the average number of edges in the edge sequences that the evolving loop passes through. In contrast to the existing geodesic curvature flow methods which compute an approximate geodesic loop within a predefined threshold, our method is exact and can apply directly to triangular meshes without needing to solve any differential equation with a numerical solver; it can run at interactive speed, e.g., in the order of milliseconds, for a mesh with around 50K vertices, and hence, significantly outperforms existing algorithms. Actually, our algorithm could run at interactive speed even for larger meshes. Besides the complexity of the input mesh, the geometric shape could also affect the number of evolving steps, i.e., the performance. We motivate our algorithm with an interactive shape segmentation example shown later in the paper.
Exactly solvable energy-dependent potentials
International Nuclear Information System (INIS)
Garcia-Martinez, J.; Garcia-Ravelo, J.; Pena, J.J.; Schulze-Halberg, A.
2009-01-01
We introduce a method for constructing exactly-solvable Schroedinger equations with energy-dependent potentials. Our method is based on converting a general linear differential equation of second order into a Schroedinger equation with energy-dependent potential. Particular examples presented here include harmonic oscillator, Coulomb and Morse potentials with various types of energy dependence.
Exact relativistic cylindrical solution of disordered radiation
International Nuclear Information System (INIS)
Fonseca Teixeira, A.F. da; Wolk, I.; Som, M.M.
1976-05-01
A source free disordered distribution of electromagnetic radiation is considered in Einstein' theory, and a time independent exact solution with cylindrical symmetry is obtained. The gravitation and pressure effects of the radiation alone are sufficient to give the distribution an equilibrium. A finite maximum concentration is found on the axis of symmetry, and decreases monotonically to zero outwards. Timelike and null geodesics are discussed
New exact solutions for two nonlinear equations
International Nuclear Information System (INIS)
Wang Quandi; Tang Minying
2008-01-01
In this Letter, we investigate two nonlinear equations given by u t -u xxt +3u 2 u x =2u x u xx +uu xxx and u t -u xxt +4u 2 u x =3u x u xx +uu xxx . Through some special phase orbits we obtain four new exact solutions for each equation above. Some previous results are extended
Exact Optimum Design of Segmented Thermoelectric Generators
Directory of Open Access Journals (Sweden)
M. Zare
2016-01-01
Full Text Available A considerable difference between experimental and theoretical results has been observed in the studies of segmented thermoelectric generators (STEGs. Because of simplicity, the approximate methods are widely used for design and optimization of the STEGs. This study is focused on employment of exact method for design and optimization of STEGs and comparison of exact and approximate results. Thus, using new highly efficient thermoelectric materials, four STEGs are proposed to operate in the temperature range of 300 to 1300 kelvins. The proposed STEGs are optimally designed to achieve maximum efficiency. Design and performance characteristics of the optimized generators including maximum conversion efficiency and length of elements are calculated through both exact and approximate methods. The comparison indicates that the approximate method can cause a difference up to 20% in calculation of some design characteristics despite its appropriate results in efficiency calculation. The results also show that the maximum theoretical efficiency of 23.08% is achievable using the new proposed STEGs. Compatibility factor of the selected materials for the proposed STEGs is also calculated using both exact and approximate methods. The comparison indicates a negligible difference in calculation of compatibility factor, despite the considerable difference in calculation of reduced efficiency (temperature independence efficiency.
Exactly solvable position dependent mass schroedinger equation
International Nuclear Information System (INIS)
Koc, R.; Tuetuencueler, H.; Koercuek, E.
2002-01-01
Exact solution of the Schrodinger equation with a variable mass is presented. We have derived general expressions for the eigenstates and eigenvalues of the position dependent mass systems. We provide supersymmetric and Lie algebraic methods to discuss the position dependent mass systems
Compiling Relational Bayesian Networks for Exact Inference
DEFF Research Database (Denmark)
Jaeger, Manfred; Darwiche, Adnan; Chavira, Mark
2006-01-01
We describe in this paper a system for exact inference with relational Bayesian networks as defined in the publicly available PRIMULA tool. The system is based on compiling propositional instances of relational Bayesian networks into arithmetic circuits and then performing online inference...
Compiling Relational Bayesian Networks for Exact Inference
DEFF Research Database (Denmark)
Jaeger, Manfred; Chavira, Mark; Darwiche, Adnan
2004-01-01
We describe a system for exact inference with relational Bayesian networks as defined in the publicly available \\primula\\ tool. The system is based on compiling propositional instances of relational Bayesian networks into arithmetic circuits and then performing online inference by evaluating...
International Nuclear Information System (INIS)
Roth, M.; Ferrer, J.; Simon, J.; Geissler, E.
1992-01-01
High intensity for diffraction experiments with high-energy resolution on an intense x-ray beam, like the bending magnet beam lines at the ESRF, requires a strict control of the curvature of the optical elements placed in the beam for geometrical focusing and for wavelength monochromatization. Unwanted curvatures can come from nonuniform and variable heating of the optical elements produced by the absorption of x rays. To design the CRG/D2AM beam line described in the accompanying paper, some new techniques were developed to control these effects based on geometrical, i.e., topological, considerations. (1) Cooling of the entrance mirror: longitudinal curvature can be strongly reduced by cooling the mirror from the sides (and not from the rear) and only near the reflecting surface (i.e., not over the whole lateral surface). The cooling can be achieved for instance with an isothermal liquid Ga eutectic bath. (2) Cooling of the first single-crystal Si monochromator: because of the size of the crystal, only cooling from the rear is conceivable in this case. It can be shown by calculation that the curvature due to the front-to-rear gradient can be exactly compensated by the thermal expansion of a metallic layer at the rear of the crystal, having a larger expansion coefficient than Si
A scheme of measurement of quantum-vacuum geometric phases in a noncoplanar fibre system
International Nuclear Information System (INIS)
Shen Jianqi
2004-01-01
We study the quantum-vacuum geometric phases resulting from the vacuum fluctuation of photon fields in a Tomita-Chiao-Wu noncoplanar curved fibre system, and suggest a scheme to test for the potential existence of such a vacuum effect. Since the signs of the quantum-vacuum geometric phases of left- and right-handed (LRH) circularly polarized light are opposite, the sum of the geometric phases at the vacuum level is necessarily zero in the fibre experiments performed previously by other authors. By using the present approach where a fibre made of gyroelectric media is employed, the quantum-vacuum geometric phases of LRH light cannot be exactly cancelled, and it may therefore be possible to test this experimentally. (letter to the editor)
On chromatic and geometrical calibration
DEFF Research Database (Denmark)
Folm-Hansen, Jørgen
1999-01-01
The main subject of the present thesis is different methods for the geometrical and chromatic calibration of cameras in various environments. For the monochromatic issues of the calibration we present the acquisition of monochrome images, the classic monochrome aberrations and the various sources...... the correct interpolation method is described. For the chromatic issues of calibration we present the acquisition of colour and multi-spectral images, the chromatic aberrations and the various lens/camera based non-uniformities of the illumination of the image plane. It is described how the monochromatic...... to design calibration targets for both geometrical and chromatic calibration are described. We present some possible systematical errors on the detection of the objects in the calibration targets, if viewed in a non orthogonal angle, if the intensities are uneven or if the image blurring is uneven. Finally...
What Makes a Beam Shaping Problem Difficult
International Nuclear Information System (INIS)
Romero, Louis; Dickey, Fred M.
2000-01-01
The authors have discussed the three factors that they believe are the most important in determining the difficulty of a beam shaping problem: scaling, smoothness, and coherence. The arguments have been almost completely based on considering how these factors influence beam shaping lenses that were designed using geometrical optics. However, they believe that these factors control the difficulty of beam shaping problems even if one does not base ones design strategy on geometrical optics. For example, they have shown that a lens designed using geometrical optics will not work well unless β is large. However, they have also shown that if β is small the uncertainty principle shows that it is impossible to do a good job of beam shaping no matter how one designs ones lens
Dissipative motion perturbation theory and exact solutions
International Nuclear Information System (INIS)
Lodder, J.J.
1976-06-01
Dissipative motion of classical and quantum systems is described. In particular, attention is paid to systems coupled to the radiation field. A dissipative equation of motion for a particle in an arbitrary potential coupled to the radiation field is derived by means of perturbation theory. The usual divrgencies associated with the radiation field are eliminated by the application of a theory of generalized functions. This theory is developed as a subject in its own right and is presented independently. The introduction of classical zero-point energy makes the classical equa tion of motion for the phase density formally the same as its quantum counterpart. In particular, it is shown that the classical zero-point energy prevents the collapse of a classical H-atom and gives rise to a classical ground state. For systems with a quadratic Hamiltoian, the equation of motion can be solved exactly, even in the continuum limit for the radiation field, by means of the new generalized functions. Classically, the Fokker-Planck equation is found without any approximations, and quantum mechanically, the only approximation is the neglect of the change in the ground state caused by the interaction. The derivation is valid even for strong damping and arbitrarily short times. There is no transient time. For harmonic oscillators complete equivalence is shown to exist between quantum mechanics and classical mechanics with zero-point energy. A discussion of the derivation of the Pauli equation is given and perturbation theory is compared with the exact derivation. The exactly solvable models are used to calculate the Langevin force of the radiation field. The result is that the classical Langevin force is exactly delta-correlated, while the quantum Langevin force is not delta-correlated at all. The fluctuation-dissipation theorem is shown to be an exact consequence of the solution to the equations of motion
Geometrical interpretation of optical absorption
Energy Technology Data Exchange (ETDEWEB)
Monzon, J. J.; Barriuso, A. G.; Sanchez-Soto, L. L. [Departamento de Optica, Facultad de Fisica, Universidad Complutense, E-28040 Madrid (Spain); Montesinos-Amilibia, J. M. [Departamento de Geometria y Topologia, Facultad de Matematicas, Universidad Complutense, E-28040 Madrid (Spain)
2011-08-15
We reinterpret the transfer matrix for an absorbing system in very simple geometrical terms. In appropriate variables, the system appears as performing a Lorentz transformation in a (1 + 3)-dimensional space. Using homogeneous coordinates, we map that action on the unit sphere, which is at the realm of the Klein model of hyperbolic geometry. The effects of absorption appear then as a loxodromic transformation, that is, a rhumb line crossing all the meridians at the same angle.
Parametric FEM for geometric biomembranes
Bonito, Andrea; Nochetto, Ricardo H.; Sebastian Pauletti, M.
2010-05-01
We consider geometric biomembranes governed by an L2-gradient flow for bending energy subject to area and volume constraints (Helfrich model). We give a concise derivation of a novel vector formulation, based on shape differential calculus, and corresponding discretization via parametric FEM using quadratic isoparametric elements and a semi-implicit Euler method. We document the performance of the new parametric FEM with a number of simulations leading to dumbbell, red blood cell and toroidal equilibrium shapes while exhibiting large deformations.
Geometrical methods in learning theory
International Nuclear Information System (INIS)
Burdet, G.; Combe, Ph.; Nencka, H.
2001-01-01
The methods of information theory provide natural approaches to learning algorithms in the case of stochastic formal neural networks. Most of the classical techniques are based on some extremization principle. A geometrical interpretation of the associated algorithms provides a powerful tool for understanding the learning process and its stability and offers a framework for discussing possible new learning rules. An illustration is given using sequential and parallel learning in the Boltzmann machine
International Nuclear Information System (INIS)
Cheng Min; Tang Tiantong; Lu Yilong; Yao Zhenhua
2003-01-01
The principle of differential algebra is applied to analyse and calculate arbitrary order curvilinear-axis combined geometric-chromatic aberrations of electron optical systems. Expressions of differential algebraic form of high order combined aberrations are obtained and arbitrary order combined aberrations can be calculated numerically. As an example, a typical wide electron beam focusing system with curved optical axes named magnetic immersion lens has been studied. All the second-order and third-order combined geometric-chromatic aberrations of the lens have been calculated, and the patterns of the corresponding geometric aberrations and combined aberrations have been given as well
Riemannian geometry and geometric analysis
Jost, Jürgen
2017-01-01
This established reference work continues to provide its readers with a gateway to some of the most interesting developments in contemporary geometry. It offers insight into a wide range of topics, including fundamental concepts of Riemannian geometry, such as geodesics, connections and curvature; the basic models and tools of geometric analysis, such as harmonic functions, forms, mappings, eigenvalues, the Dirac operator and the heat flow method; as well as the most important variational principles of theoretical physics, such as Yang-Mills, Ginzburg-Landau or the nonlinear sigma model of quantum field theory. The present volume connects all these topics in a systematic geometric framework. At the same time, it equips the reader with the working tools of the field and enables her or him to delve into geometric research. The 7th edition has been systematically reorganized and updated. Almost no page has been left unchanged. It also includes new material, for instance on symplectic geometry, as well as the B...
Geometric mean for subspace selection.
Tao, Dacheng; Li, Xuelong; Wu, Xindong; Maybank, Stephen J
2009-02-01
Subspace selection approaches are powerful tools in pattern classification and data visualization. One of the most important subspace approaches is the linear dimensionality reduction step in the Fisher's linear discriminant analysis (FLDA), which has been successfully employed in many fields such as biometrics, bioinformatics, and multimedia information management. However, the linear dimensionality reduction step in FLDA has a critical drawback: for a classification task with c classes, if the dimension of the projected subspace is strictly lower than c - 1, the projection to a subspace tends to merge those classes, which are close together in the original feature space. If separate classes are sampled from Gaussian distributions, all with identical covariance matrices, then the linear dimensionality reduction step in FLDA maximizes the mean value of the Kullback-Leibler (KL) divergences between different classes. Based on this viewpoint, the geometric mean for subspace selection is studied in this paper. Three criteria are analyzed: 1) maximization of the geometric mean of the KL divergences, 2) maximization of the geometric mean of the normalized KL divergences, and 3) the combination of 1 and 2. Preliminary experimental results based on synthetic data, UCI Machine Learning Repository, and handwriting digits show that the third criterion is a potential discriminative subspace selection method, which significantly reduces the class separation problem in comparing with the linear dimensionality reduction step in FLDA and its several representative extensions.
Beam phase space and emittance
International Nuclear Information System (INIS)
Buon, J.
1992-02-01
The classical and elementary results for canonical phase space, the Liouville theorem and the beam emittance are reviewed. Then, the importance of phase portraits to obtain a geometrical description of motion is emphasized, with examples in accelerator physics. Finally, a statistical point of view is used to define beam emittance, to study its law of approximate conservation, with three particular examples, and to introduce a beam envelope-ellipse and the β-function, emphasing the statistical features of its properties. (author) 14 refs.; 11 figs
Efficient 3D geometric and Zernike moments computation from unstructured surface meshes.
Pozo, José María; Villa-Uriol, Maria-Cruz; Frangi, Alejandro F
2011-03-01
This paper introduces and evaluates a fast exact algorithm and a series of faster approximate algorithms for the computation of 3D geometric moments from an unstructured surface mesh of triangles. Being based on the object surface reduces the computational complexity of these algorithms with respect to volumetric grid-based algorithms. In contrast, it can only be applied for the computation of geometric moments of homogeneous objects. This advantage and restriction is shared with other proposed algorithms based on the object boundary. The proposed exact algorithm reduces the computational complexity for computing geometric moments up to order N with respect to previously proposed exact algorithms, from N(9) to N(6). The approximate series algorithm appears as a power series on the rate between triangle size and object size, which can be truncated at any desired degree. The higher the number and quality of the triangles, the better the approximation. This approximate algorithm reduces the computational complexity to N(3). In addition, the paper introduces a fast algorithm for the computation of 3D Zernike moments from the computed geometric moments, with a computational complexity N(4), while the previously proposed algorithm is of order N(6). The error introduced by the proposed approximate algorithms is evaluated in different shapes and the cost-benefit ratio in terms of error, and computational time is analyzed for different moment orders.
Geometrical charged-particle optics. 2. ed.
International Nuclear Information System (INIS)
Rose, Harald
2013-01-01
Provides a unique theoretical treatment of charged-particle optics. Displays novel unpublished results on several topics. Provides insight into the properties of charged-particle devices. Treats wave optical properties of the electron. Presents the resolution limit of electron microscopes and novel theoretical treatment of the Stern-Gerlach effect. This second edition is an extended version of the first edition of Geometrical Charged-Particle Optics. The updated reference monograph is intended as a guide for researchers and graduate students who are seeking a comprehensive treatment of the design of instruments and beam-guiding systems of charged particles and their propagation in electromagnetic fields. Wave aspects are included in this edition for explaining electron holography, the Aharanov-Bohm effect and the resolution of electron microscopes limited by diffraction. Several methods for calculating the electromagnetic field are presented and procedures are outlined for calculating the properties of systems with arbitrarily curved axis. Detailed methods are presented for designing and optimizing special components such as aberration correctors, spectrometers, energy filters monochromators, ion traps, electron mirrors and cathode lenses. In particular, the optics of rotationally symmetric lenses, quadrupoles, and systems composed of these elements are discussed extensively. Beam properties such as emittance, brightness, transmissivity and the formation of caustics are outlined. Relativistic motion and spin precession of the electron are treated in a covariant way by introducing the Lorentz-invariant universal time and by extending Hamilton's principle from three to four spatial dimensions where the laboratory time is considered as the fourth pseudo-spatial coordinate. Using this procedure and introducing the self action of the electron, its accompanying electromagnetic field and its radiation field are calculated for arbitrary motion. In addition, the Stern
A directly heated electron beam line source
International Nuclear Information System (INIS)
Iqbal, M.; Masood, K.; Rafiq, M.; Chaudhry, M.A.
2002-05-01
A 140-mm cathode length, Electron Beam Line Source with a high degree of focusing of the beam is constructed. The design principles and basic characteristic considerations for electron beam line source consists of parallel plate electrode geometric array as well as a beam power of 35kW are worked out. The dimensions of the beam at the work site are 1.25xl00mm. The gun is designed basically for the study of evaporation and deposition characteristic of refractory metals for laboratory use. However, it may be equally used for melting and casting of these metals. (author)
Fractal supersymmetric QM, Geometric Probability and the Riemann Hypothesis
Castro, C
2004-01-01
The Riemann's hypothesis (RH) states that the nontrivial zeros of the Riemann zeta-function are of the form $ s_n =1/2+i\\lambda_n $. Earlier work on the RH based on supersymmetric QM, whose potential was related to the Gauss-Jacobi theta series, allows to provide the proper framework to construct the well defined algorithm to compute the probability to find a zero (an infinity of zeros) in the critical line. Geometric probability theory furnishes the answer to the very difficult question whether the probability that the RH is true is indeed equal to unity or not. To test the validity of this geometric probabilistic framework to compute the probability if the RH is true, we apply it directly to the the hyperbolic sine function $ \\sinh (s) $ case which obeys a trivial analog of the RH (the HSRH). Its zeros are equally spaced in the imaginary axis $ s_n = 0 + i n \\pi $. The geometric probability to find a zero (and an infinity of zeros) in the imaginary axis is exactly unity. We proceed with a fractal supersymme...
Theoretical and experimental nonlinear dynamics of a clamped-clamped beam MEMS resonator
Mestrom, R.M.C.; Fey, R.H.B.; Nijmeijer, H.
2008-01-01
Microelectromechanical resonators feature nonlineardynamic responses. A first-principles based modeling approach is proposed for a clamped-clamped beam resonator. Starting from the partial differential equation for the beam including geometric and electrostatic nonlinear effects, a reduced-order
International Nuclear Information System (INIS)
Gorodetski, Y.; Biener, G.; Niv, A.; Kleiner, V.; Hasman, E.
2005-01-01
Full Text:The behavior of geometrical phase elements illuminated with partially polarized monochromatic beams is being theoretically as well as experimentally investigated. The element discussed in this paper is composed of wave plates with retardation and space-variant orientation angle. We found that a beam emerging from such an element comprises two polarization orders of right and left-handed circularly polarized states with conjugate geometrical phase modification. This phase equals twice the orientation angle of the space-variant wave plate comprising the element. Apart from the two polarization orders, the emerging beam coherence polarization matrix comprises a matrix termed as the vectorial interference matrix. This matrix contains the information concerning the correlation between the two orthogonal circularly polarized portions of the incident beam. In this paper we measure this correlation by a simple interference experiment. Furthermore, we found that the equivalent mutual intensity of the emerging beam is being modulated according to the geometrical phase induced by the element. Other interesting phenomena along propagation will be discussed theoretically and experimentally demonstrated. We demonstrate experimentally our analysis by using a spherical geometrical phase element, which is realized by use of space-variant sub wavelength grating and illuminated with a CO 2 laser radiation of 10.6μm wavelength
One step geometrical calibration method for optical coherence tomography
International Nuclear Information System (INIS)
Díaz, Jesús Díaz; Ortmaier, Tobias; Stritzel, Jenny; Rahlves, Maik; Reithmeier, Eduard; Roth, Bernhard; Majdani, Omid
2016-01-01
We present a novel one-step calibration methodology for geometrical distortion correction for optical coherence tomography (OCT). A calibration standard especially designed for OCT is introduced, which consists of an array of inverse pyramidal structures. The use of multiple landmarks situated on four different height levels on the pyramids allow performing a 3D geometrical calibration. The calibration procedure itself is based on a parametric model of the OCT beam propagation. It is validated by experimental results and enables the reduction of systematic errors by more than one order of magnitude. In future, our results can improve OCT image reconstruction and interpretation for medical applications such as real time monitoring of surgery. (paper)
Chen, Chenglong; Ni, Jiangqun; Shen, Zhaoyi; Shi, Yun Qing
2017-06-01
Geometric transformations, such as resizing and rotation, are almost always needed when two or more images are spliced together to create convincing image forgeries. In recent years, researchers have developed many digital forensic techniques to identify these operations. Most previous works in this area focus on the analysis of images that have undergone single geometric transformations, e.g., resizing or rotation. In several recent works, researchers have addressed yet another practical and realistic situation: successive geometric transformations, e.g., repeated resizing, resizing-rotation, rotation-resizing, and repeated rotation. We will also concentrate on this topic in this paper. Specifically, we present an in-depth analysis in the frequency domain of the second-order statistics of the geometrically transformed images. We give an exact formulation of how the parameters of the first and second geometric transformations influence the appearance of periodic artifacts. The expected positions of characteristic resampling peaks are analytically derived. The theory developed here helps to address the gap left by previous works on this topic and is useful for image security and authentication, in particular, the forensics of geometric transformations in digital images. As an application of the developed theory, we present an effective method that allows one to distinguish between the aforementioned four different processing chains. The proposed method can further estimate all the geometric transformation parameters. This may provide useful clues for image forgery detection.
Geometrical aspects in optical wave-packet dynamics.
Onoda, Masaru; Murakami, Shuichi; Nagaosa, Naoto
2006-12-01
We construct a semiclassical theory for propagation of an optical wave packet in a nonconducting medium with a periodic structure of dielectric permittivity and magnetic permeability, i.e., a nonconducting photonic crystal. We employ a quantum-mechanical formalism in order to clarify its link to those of electronic systems. It involves the geometrical phase, i.e., Berry's phase, in a natural way, and describes an interplay between orbital motion and internal rotation. Based on the above theory, we discuss the geometrical aspects of the optical Hall effect. We also consider a reduction of the theory to a system without periodic structure and apply it to the transverse shift of an optical beam at an interface reflection or refraction. For a generic incident beam with an arbitrary polarization, an identical result for the transverse shift of each reflected or transmitted beam is given by the following different approaches: (i) analytic evaluation of wave-packet dynamics, (ii) total angular momentum (TAM) conservation for individual photons, and (iii) numerical simulation of wave-packet dynamics. It is consistent with a result by classical electrodynamics. This means that the TAM conservation for individual photons is already taken into account in wave optics, i.e., classical electrodynamics. Finally, we show an application of our theory to a two-dimensional photonic crystal, and propose an optimal design for the enhancement of the optical Hall effect in photonic crystals.
Exact WKB analysis and cluster algebras
International Nuclear Information System (INIS)
Iwaki, Kohei; Nakanishi, Tomoki
2014-01-01
We develop the mutation theory in the exact WKB analysis using the framework of cluster algebras. Under a continuous deformation of the potential of the Schrödinger equation on a compact Riemann surface, the Stokes graph may change the topology. We call this phenomenon the mutation of Stokes graphs. Along the mutation of Stokes graphs, the Voros symbols, which are monodromy data of the equation, also mutate due to the Stokes phenomenon. We show that the Voros symbols mutate as variables of a cluster algebra with surface realization. As an application, we obtain the identities of Stokes automorphisms associated with periods of cluster algebras. The paper also includes an extensive introduction of the exact WKB analysis and the surface realization of cluster algebras for nonexperts. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Cluster algebras in mathematical physics’. (paper)
Exact computation of the 9-j symbols
International Nuclear Information System (INIS)
Lai Shantao; Chiu Jingnan
1992-01-01
A useful algebraic formula for the 9-j symbol has been rewritten for convenient use on a computer. A simple FORTRAN program for the exact computation of 9-j symbols has been written for the VAX with VMS version V5,4-1 according to this formula. The results agree with the approximate values in existing literature. Some specific values of 9-j symbols needed for the intensity and alignments of three-photon nonresonant transitions are tabulated. Approximate 9-j symbol values beyond the limitation of the computer can also be computed by this program. The computer code of the exact computation of 3-j, 6-j and 9-j symbols are available through electronic mail upon request. (orig.)
Lattice sigma models with exact supersymmetry
International Nuclear Information System (INIS)
Simon Catterall; Sofiane Ghadab
2004-01-01
We show how to construct lattice sigma models in one, two and four dimensions which exhibit an exact fermionic symmetry. These models are discretized and twisted versions of conventional supersymmetric sigma models with N=2 supersymmetry. The fermionic symmetry corresponds to a scalar BRST charge built from the original supercharges. The lattice theories possess local actions and exhibit no fermion doubling. In the two and four dimensional theories we show that these lattice theories are invariant under additional discrete symmetries. We argue that the presence of these exact symmetries ensures that no fine tuning is required to achieve N=2 supersymmetry in the continuum limit. As a concrete example we show preliminary numerical results from a simulation of the O(3) supersymmetric sigma model in two dimensions. (author)
Model checking exact cost for attack scenarios
DEFF Research Database (Denmark)
Aslanyan, Zaruhi; Nielson, Flemming
2017-01-01
Attack trees constitute a powerful tool for modelling security threats. Many security analyses of attack trees can be seamlessly expressed as model checking of Markov Decision Processes obtained from the attack trees, thus reaping the benefits of a coherent framework and a mature tool support....... However, current model checking does not encompass the exact cost analysis of an attack, which is standard for attack trees. Our first contribution is the logic erPCTL with cost-related operators. The extended logic allows to analyse the probability of an event satisfying given cost bounds and to compute...... the exact cost of an event. Our second contribution is the model checking algorithm for erPCTL. Finally, we apply our framework to the analysis of attack trees....
Exact folded-band chaotic oscillator.
Corron, Ned J; Blakely, Jonathan N
2012-06-01
An exactly solvable chaotic oscillator with folded-band dynamics is shown. The oscillator is a hybrid dynamical system containing a linear ordinary differential equation and a nonlinear switching condition. Bounded oscillations are provably chaotic, and successive waveform maxima yield a one-dimensional piecewise-linear return map with segments of both positive and negative slopes. Continuous-time dynamics exhibit a folded-band topology similar to Rössler's oscillator. An exact solution is written as a linear convolution of a fixed basis pulse and a discrete binary sequence, from which an equivalent symbolic dynamics is obtained. The folded-band topology is shown to be dependent on the symbol grammar.
Exact geodesic distances in FLRW spacetimes
Cunningham, William J.; Rideout, David; Halverson, James; Krioukov, Dmitri
2017-11-01
Geodesics are used in a wide array of applications in cosmology and astrophysics. However, it is not a trivial task to efficiently calculate exact geodesic distances in an arbitrary spacetime. We show that in spatially flat (3 +1 )-dimensional Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes, it is possible to integrate the second-order geodesic differential equations, and derive a general method for finding both timelike and spacelike distances given initial-value or boundary-value constraints. In flat spacetimes with either dark energy or matter, whether dust, radiation, or a stiff fluid, we find an exact closed-form solution for geodesic distances. In spacetimes with a mixture of dark energy and matter, including spacetimes used to model our physical universe, there exists no closed-form solution, but we provide a fast numerical method to compute geodesics. A general method is also described for determining the geodesic connectedness of an FLRW manifold, provided only its scale factor.
New exact solutions of the Dirac equation
International Nuclear Information System (INIS)
Bagrov, V.G.; Gitman, D.M.; Zadorozhnyj, V.N.; Lavrov, P.M.; Shapovalov, V.N.
1980-01-01
Search for new exact solutions of the Dirac and Klein-Gordon equations are in progress. Considered are general properties of the Dirac equation solutions for an electron in a purely magnetic field, in combination with a longitudinal magnetic and transverse electric fields. New solutions for the equations of charge motion in an electromagnetic field of axial symmetry and in a nonstationary field of a special form have been found for potentials selected concretely
Exact BPS bound for noncommutative baby Skyrmions
International Nuclear Information System (INIS)
Domrin, Andrei; Lechtenfeld, Olaf; Linares, Román; Maceda, Marco
2013-01-01
The noncommutative baby Skyrme model is a Moyal deformation of the two-dimensional sigma model plus a Skyrme term, with a group-valued or Grassmannian target. Exact abelian solitonic solutions have been identified analytically in this model, with a singular commutative limit. Inside any given Grassmannian, we establish a BPS bound for the energy functional, which is saturated by these baby Skyrmions. This asserts their stability for unit charge, as we also test in second-order perturbation theory
Exact solutions and singularities in string theory
International Nuclear Information System (INIS)
Horowitz, G.T.; Tseytlin, A.A.
1994-01-01
We construct two new classes of exact solutions to string theory which are not of the standard plane wave of gauged WZW type. Many of these solutions have curvature singularities. The first class includes the fundamental string solution, for which the string coupling vanishes near the singularity. This suggests that the singularity may not be removed by quantum corrections. The second class consists of hybrids of plane wave and gauged WZW solutions. We discuss a four-dimensional example in detail
Exact diagonalization library for quantum electron models
Iskakov, Sergei; Danilov, Michael
2018-04-01
We present an exact diagonalization C++ template library (EDLib) for solving quantum electron models, including the single-band finite Hubbard cluster and the multi-orbital impurity Anderson model. The observables that can be computed using EDLib are single particle Green's functions and spin-spin correlation functions. This code provides three different types of Hamiltonian matrix storage that can be chosen based on the model.
Exactly and completely integrable nonlinear dynamical systems
International Nuclear Information System (INIS)
Leznov, A.N.; Savel'ev, M.V.
1987-01-01
The survey is devoted to a consitent exposition of the group-algebraic methods for the integration of systems of nonlinear partial differential equations possessing a nontrivial internal symmetry algebra. Samples of exactly and completely integrable wave and evolution equations are considered in detail, including generalized (periodic and finite nonperiodic Toda lattice, nonlinear Schroedinger, Korteweg-de Vries, Lotka-Volterra equations, etc.) For exactly integrable systems the general solutions of the Cauchy and Goursat problems are given in an explicit form, while for completely integrable systems an effective method for the construction of their soliton solutions is developed. Application of the developed methods to a differential geometry problem of classification of the integrable manifolds embeddings is discussed. For exactly integrable systems the supersymmetric extensions are constructed. By the example of the generalized Toda lattice a quantization scheme is developed. It includes an explicit derivation of the corresponding Heisenberg operators and their desription in terms of the quantum algebras of the Hopf type. Among multidimensional systems the four-dimensional self-dual Yang-Mills equations are investigated most attentively with a goal of constructing their general solutions
International Nuclear Information System (INIS)
Cannoni, Mirco
2015-01-01
We show that the standard theory of thermal production and chemical decoupling of WIMPs is incomplete. The hypothesis that WIMPs are produced and decouple from a thermal bath implies that the rate equation the bath particles interacting with the WIMPs is an algebraic equation that constraints the actual WIMPs abundance to have a precise analytical form down to the temperature x * = m χ /T * . The point x., which coincides with the stationary point of the equation for the quantity Δ = Y-Y 0 , is where the maximum departure of the WIMPs abundance Y from the thermal value Y 0 is reached. For each mass m χ and total annihilation cross section left angle σ ann υ r right angle, the temperature x * and the actual WIMPs abundance Y(x * ) are exactly known. This value provides the true initial condition for the usual differential equation that have to be integrated in the interval x ≥ x * . The matching of the two abundances at x * is continuous and differentiable. The dependence of the present relic abundance on the abundance at an intermediate temperature is an exact result. The exact theory suggests a new analytical approximation that furnishes the relic abundance accurate at the level of 1.2 % in the case of S-wave and P-wave scattering cross sections. We conclude the paper studying the evolution of the WIMPs chemical potential and the entropy production using methods of non-equilibrium thermodynamics. (orig.)
Cannoni, Mirco
2015-03-01
We show that the standard theory of thermal production and chemical decoupling of WIMPs is incomplete. The hypothesis that WIMPs are produced and decouple from a thermal bath implies that the rate equation the bath particles interacting with the WIMPs is an algebraic equation that constraints the actual WIMPs abundance to have a precise analytical form down to the temperature . The point , which coincides with the stationary point of the equation for the quantity , is where the maximum departure of the WIMPs abundance from the thermal value is reached. For each mass and total annihilation cross section , the temperature and the actual WIMPs abundance are exactly known. This value provides the true initial condition for the usual differential equation that have to be integrated in the interval . The matching of the two abundances at is continuous and differentiable. The dependence of the present relic abundance on the abundance at an intermediate temperature is an exact result. The exact theory suggests a new analytical approximation that furnishes the relic abundance accurate at the level of 1-2 % in the case of -wave and -wave scattering cross sections. We conclude the paper studying the evolution of the WIMPs chemical potential and the entropy production using methods of non-equilibrium thermodynamics.
Exact Theory of Compressible Fluid Turbulence
Drivas, Theodore; Eyink, Gregory
2017-11-01
We obtain exact results for compressible turbulence with any equation of state, using coarse-graining/filtering. We find two mechanisms of turbulent kinetic energy dissipation: scale-local energy cascade and ``pressure-work defect'', or pressure-work at viscous scales exceeding that in the inertial-range. Planar shocks in an ideal gas dissipate all kinetic energy by pressure-work defect, but the effect is omitted by standard LES modeling of pressure-dilatation. We also obtain a novel inverse cascade of thermodynamic entropy, injected by microscopic entropy production, cascaded upscale, and removed by large-scale cooling. This nonlinear process is missed by the Kovasznay linear mode decomposition, treating entropy as a passive scalar. For small Mach number we recover the incompressible ``negentropy cascade'' predicted by Obukhov. We derive exact Kolmogorov 4/5th-type laws for energy and entropy cascades, constraining scaling exponents of velocity, density, and internal energy to sub-Kolmogorov values. Although precise exponents and detailed physics are Mach-dependent, our exact results hold at all Mach numbers. Flow realizations at infinite Reynolds are ``dissipative weak solutions'' of compressible Euler equations, similarly as Onsager proposed for incompressible turbulence.
Bakker schut, T.C.; Bakker Schut, Tom C.; Hesselink, Gerlo; Hesselink, Gerlo; de Grooth, B.G.; Greve, Jan
1991-01-01
We have developed a computer program based on the geometrical optics approach proposed by Roosen to calculate the forces on dielectric spheres in focused laser beams. We have explicitly taken into account the polarization of the laser light and thd divergence of the laser beam. The model can be used
Geometrically Induced Interactions and Bifurcations
Binder, Bernd
2010-01-01
In order to evaluate the proper boundary conditions in spin dynamics eventually leading to the emergence of natural and artificial solitons providing for strong interactions and potentials with monopole charges, the paper outlines a new concept referring to a curvature-invariant formalism, where superintegrability is given by a special isometric condition. Instead of referring to the spin operators and Casimir/Euler invariants as the generator of rotations, a curvature-invariant description is introduced utilizing a double Gudermann mapping function (generator of sine Gordon solitons and Mercator projection) cross-relating two angular variables, where geometric phases and rotations arise between surfaces of different curvature. Applying this stereographic projection to a superintegrable Hamiltonian can directly map linear oscillators to Kepler/Coulomb potentials and/or monopoles with Pöschl-Teller potentials and vice versa. In this sense a large scale Kepler/Coulomb (gravitational, electro-magnetic) wave dynamics with a hyperbolic metric could be mapped as a geodesic vertex flow to a local oscillator singularity (Dirac monopole) with spherical metrics and vice versa. Attracting fixed points and dynamic constraints are given by special isometries with magic precession angles. The nonlinear angular encoding directly provides for a Shannon mutual information entropy measure of the geodesic phase space flow. The emerging monopole patterns show relations to spiral Fresnel holography and Berry/Aharonov-Bohm geometric phases subject to bifurcation instabilities and singularities from phase ambiguities due to a local (entropy) overload. Neutral solitons and virtual patterns emerging and mediating in the overlap region between charged or twisted holographic patterns are visualized and directly assigned to the Berry geometric phase revealing the role of photons, neutrons, and neutrinos binding repulsive charges in Coulomb, strong and weak interaction.
Moving walls and geometric phases
Energy Technology Data Exchange (ETDEWEB)
Facchi, Paolo, E-mail: paolo.facchi@ba.infn.it [Dipartimento di Fisica and MECENAS, Università di Bari, I-70126 Bari (Italy); INFN, Sezione di Bari, I-70126 Bari (Italy); Garnero, Giancarlo, E-mail: giancarlo.garnero@uniba.it [Dipartimento di Fisica and MECENAS, Università di Bari, I-70126 Bari (Italy); INFN, Sezione di Bari, I-70126 Bari (Italy); Marmo, Giuseppe [Dipartimento di Scienze Fisiche and MECENAS, Università di Napoli “Federico II”, I-80126 Napoli (Italy); INFN, Sezione di Napoli, I-80126 Napoli (Italy); Samuel, Joseph [Raman Research Institute, 560080 Bangalore (India)
2016-09-15
We unveil the existence of a non-trivial Berry phase associated to the dynamics of a quantum particle in a one dimensional box with moving walls. It is shown that a suitable choice of boundary conditions has to be made in order to preserve unitarity. For these boundary conditions we compute explicitly the geometric phase two-form on the parameter space. The unboundedness of the Hamiltonian describing the system leads to a natural prescription of renormalization for divergent contributions arising from the boundary.
Geometric approach to soliton equations
International Nuclear Information System (INIS)
Sasaki, R.
1979-09-01
A class of nonlinear equations that can be solved in terms of nxn scattering problem is investigated. A systematic geometric method of exploiting conservation laws and related equations, the so-called prolongation structure, is worked out. The nxn problem is reduced to nsub(n-1)x(n-1) problems and finally to 2x2 problems, which have been comprehensively investigated recently by the author. A general method of deriving the infinite numbers of polynomial conservation laws for an nxn problem is presented. The cases of 3x3 and 2x2 problems are discussed explicitly. (Auth.)
Field guide to geometrical optics
Greivenkamp, John E
2004-01-01
This Field Guide derives from the treatment of geometrical optics that has evolved from both the undergraduate and graduate programs at the Optical Sciences Center at the University of Arizona. The development is both rigorous and complete, and it features a consistent notation and sign convention. This volume covers Gaussian imagery, paraxial optics, first-order optical system design, system examples, illumination, chromatic effects, and an introduction to aberrations. The appendices provide supplemental material on radiometry and photometry, the human eye, and several other topics.
Geometric phase from dielectric matrix
International Nuclear Information System (INIS)
Banerjee, D.
2005-10-01
The dielectric property of the anisotropic optical medium is found by considering the polarized photon as two component spinor of spherical harmonics. The Geometric Phase of a polarized photon has been evaluated in two ways: the phase two-form of the dielectric matrix through a twist and the Pancharatnam phase (GP) by changing the angular momentum of the incident polarized photon over a closed triangular path on the extended Poincare sphere. The helicity in connection with the spin angular momentum of the chiral photon plays the key role in developing these phase holonomies. (author)
A history of geometrical methods
Coolidge, Julian Lowell
2013-01-01
Full and authoritative, this history of the techniques for dealing with geometric questions begins with synthetic geometry and its origins in Babylonian and Egyptian mathematics; reviews the contributions of China, Japan, India, and Greece; and discusses the non-Euclidean geometries. Subsequent sections cover algebraic geometry, starting with the precursors and advancing to the great awakening with Descartes; and differential geometry, from the early work of Huygens and Newton to projective and absolute differential geometry. The author's emphasis on proofs and notations, his comparisons betwe
Geometrical optics and optimal transport.
Rubinstein, Jacob; Wolansky, Gershon
2017-10-01
The Fermat principle is generalized to a system of rays. It is shown that all the ray mappings that are compatible with two given intensities of a monochromatic wave, measured at two planes, are stationary points of a canonical functional, which is the weighted average of the actions of all the rays. It is further shown that there exist at least two stationary points for this functional, implying that in the geometrical optics regime the phase from intensity problem has inherently more than one solution. The caustic structures of all the possible ray mappings are analyzed. A number of simulations illustrate the theoretical considerations.
The geometric content of the interacting boson model for molecular spectra
International Nuclear Information System (INIS)
Levit, S.; Smilansky, U.
1981-12-01
The recently proposed algebraic model for collective spectra of diatomic molecules is analysed in terms of conventional geometrical degrees of freedom. We present a mapping of the algebraic Hamiltonian onto an exactly solvable geometrical Hamiltonian with the Morse potential. This mapping explains the success of the algebraic model in reproducing the low lying part of molecular spectra. At the same time the mapping shows that the expression for the dipole transition operator in terms of boson operators differs from the simplest IBM expression and in general must include many-body boson terms. The study also provides an insight into the problem of possible interpretations of the bosons in the nuclear IBM. (author)
Quasi-exact solutions of nonlinear differential equations
Kudryashov, Nikolay A.; Kochanov, Mark B.
2014-01-01
The concept of quasi-exact solutions of nonlinear differential equations is introduced. Quasi-exact solution expands the idea of exact solution for additional values of parameters of differential equation. These solutions are approximate solutions of nonlinear differential equations but they are close to exact solutions. Quasi-exact solutions of the the Kuramoto--Sivashinsky, the Korteweg--de Vries--Burgers and the Kawahara equations are founded.
Stress Measurement by Geometrical Optics
Robinson, R. S.; Rossnagel, S. M.
1986-01-01
Fast, simple technique measures stresses in thin films. Sample disk bowed by stress into approximately spherical shape. Reflected image of disk magnified by amount related to curvature and, therefore, stress. Method requires sample substrate, such as cheap microscope cover slide, two mirrors, laser light beam, and screen.
Geometrically induced metastability and holography
Energy Technology Data Exchange (ETDEWEB)
Aganagic, Mina; Aganagic, Mina; Beem, Christopher; Seo, Jihye; Vafa, Cumrun
2006-10-23
We construct metastable configurations of branes and anti-branes wrapping 2-spheres inside local Calabi-Yau manifolds and study their large N duals. These duals are Calabi-Yau manifolds in which the wrapped 2-spheres have been replaced by 3-spheres with flux through them, and supersymmetry is spontaneously broken. The geometry of the non-supersymmetric vacuum is exactly calculable to all orders of the't Hooft parameter, and to the leading order in 1/N. The computation utilizes the same matrix model techniques that were used in the supersymmetric context. This provides a novel mechanism for breaking supersymmetry in the context of flux compactifications.
Exact solution to the 'auxiliary extra-dimension' model of massive gravity
International Nuclear Information System (INIS)
Hassan, S.F.; Rosen, Rachel A.
2011-01-01
The 'auxiliary extra-dimension' model was proposed in order to provide a geometrical interpretation to modifications of general relativity, in particular to non-linear massive gravity. In this context, the theory was shown to be ghost free to third order in perturbations, in the decoupling limit. In this work, we exactly solve the equation of motion in the extra dimension, to obtain a purely 4-dimensional theory. Using this solution, it is shown that the ghost appears at the fourth order and beyond. We explore potential modifications to address the ghost issue and find that their consistent implementation requires going beyond the present framework.
Exact Gell-Mann-Low function of supersymmetric Yang-Mills theories from instanton calculus
International Nuclear Information System (INIS)
Novikov, V.A.; Shifman, M.A.; Vainshtein, A.I.; Zakharov, V.I.
1983-01-01
The instanton contribution to the vacuum energy is supersymmetric Yang-Mills theories is considered. Using renormalizability of the theory the exact beta function for n-extended supersymmetry (n=1, 2, 4) is found. The coefficients of the beta function have a geometrical meaning - they are associated with the number of boson and fermion zero modes in the instanton field. If extra matter superfields are added the method allows one to fix the first two coefficients. A non-renormalization theorem which extends cancellation of vacuum loops to the case of the external instanton field is proved
Exact Gell-Mann-Low function of supersymmetric Yang-Mills theories from instanton calculus
International Nuclear Information System (INIS)
Novikov, V.A.; Shifman, M.A.; Vainshtein, A.I.; Zakharov, V.I.
1983-01-01
The instanton contribution to the vacuum energy in supersymmetric Yang-Mills theories is considered. Using the renormalizability of the theory we find the exact beta function for n-extended supersymmetry (n=1, 2, 4). The coefficients of the beta function have a geometrical meaning: they are associated with the number of boson and fermion zero modes in the instanton field. If extra matter superfields are added our method allows one to fix the first two coefficients. We prove a non-renormalization theorem which extends the cancellation of vacuum loops to the case of the external instanton field. (orig.)
Image understanding using geometric context
Zhang, Xiaochun; Liu, Chuancai
2017-07-01
A Gibbs Sampler based topic model for image annotation, which takes into account the interaction between visual geometric context and related topic, is presented. Most of the existing topic models for scene annotation use segmentation-based algorithm. However, topic models using segmentation algorithm alone sometimes can produce erroneous results when used to annotate real-life scene pictures. Therefore, our algorithm makes use of peaks of image surface instead of segmentation regions. Existing approaches use SIFT algorithm and treat the peaks as round blob features. In this paper, the peaks are treated as anisotropic blob features, which models low level visual elements more precisely. In order to better utilize visual features, our model not only takes into consideration visual codeword, but also considers influence of visual properties to topic formation, such as orientation, width, length and color. The basic idea is based on the assumption that different topics will produce distinct visual appearance, and different visual appearance is helpful to distinguish topics. During the learning stage, each topic will be associated with a set of distributions of visual properties, which depicts appearance of the topic. This paper considers more geometric properties, which will reduce topic uncertainty and learn the images better. Tested with Corel5K, SAIAPR-TC12 and Espgame100k Datasets, our method performs moderately better than some state of the arts methods.
Vibrations and stability of complex beam systems
Stojanović, Vladimir
2015-01-01
This book reports on solved problems concerning vibrations and stability of complex beam systems. The complexity of a system is considered from two points of view: the complexity originating from the nature of the structure, in the case of two or more elastically connected beams; and the complexity derived from the dynamic behavior of the system, in the case of a damaged single beam, resulting from the harm done to its simple structure. Furthermore, the book describes the analytical derivation of equations of two or more elastically connected beams, using four different theories (Euler, Rayleigh, Timoshenko and Reddy-Bickford). It also reports on a new, improved p-version of the finite element method for geometrically nonlinear vibrations. The new method provides more accurate approximations of solutions, while also allowing us to analyze geometrically nonlinear vibrations. The book describes the appearance of longitudinal vibrations of damaged clamped-clamped beams as a result of discontinuity (damage). It...
International Nuclear Information System (INIS)
Chao, A.W.
1992-01-01
There are two physical pictures that describe the beam-beam interaction in a storage ring collider: The weak-strong and the strong-strong pictures. Both pictures play a role in determining the beam-beam behavior. This review addresses only the strong-strong picture. The corresponding beam dynamical effects are referred to as the coherent beam-beam effects. Some basic knowledge of the weak-strong picture is assumed. To be specific, two beams of opposite charges are considered. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Cannoni, Mirco [Universidad de Huelva, Departamento de Fisica Aplicada, Facultad de Ciencias Experimentales, Huelva (Spain)
2015-03-01
We show that the standard theory of thermal production and chemical decoupling of WIMPs is incomplete. The hypothesis that WIMPs are produced and decouple from a thermal bath implies that the rate equation the bath particles interacting with the WIMPs is an algebraic equation that constraints the actual WIMPs abundance to have a precise analytical form down to the temperature x{sub *} = m{sub χ}/T{sub *}. The point x., which coincides with the stationary point of the equation for the quantity Δ = Y-Y{sub 0}, is where the maximum departure of the WIMPs abundance Y from the thermal value Y{sub 0} is reached. For each mass m{sub χ} and total annihilation cross section left angle σ{sub ann}υ{sub r} right angle, the temperature x{sub *} and the actual WIMPs abundance Y(x{sub *}) are exactly known. This value provides the true initial condition for the usual differential equation that have to be integrated in the interval x ≥ x{sub *}. The matching of the two abundances at x{sub *} is continuous and differentiable. The dependence of the present relic abundance on the abundance at an intermediate temperature is an exact result. The exact theory suggests a new analytical approximation that furnishes the relic abundance accurate at the level of 1.2 % in the case of S-wave and P-wave scattering cross sections. We conclude the paper studying the evolution of the WIMPs chemical potential and the entropy production using methods of non-equilibrium thermodynamics. (orig.)
An exact solution in Einstein-Cartan
International Nuclear Information System (INIS)
Roque, W.L.
1982-01-01
The exact solution of the field equations of the Einstein-Cartan theory is obtained for an artificial dust of radially polarized spins, with spherical symmetry and static. For a best estimation of the effect due the spin, the energy-momentum metric tensor is considered null. The gravitational field dynamics is studied for several torsion strengths, through the massive and spinless test-particle moviment, in particular for null torsion Schwarzschild solutions is again obtained. It is observed that the gravitational effects related to the torsin (spin) sometimes are attractives sometimes are repulsives, depending of the torsion values and of the test-particle position and velocity. (L.C.) [pt
Exact renormalization group equations: an introductory review
Bagnuls, C.; Bervillier, C.
2001-07-01
We critically review the use of the exact renormalization group equations (ERGE) in the framework of the scalar theory. We lay emphasis on the existence of different versions of the ERGE and on an approximation method to solve it: the derivative expansion. The leading order of this expansion appears as an excellent textbook example to underline the nonperturbative features of the Wilson renormalization group theory. We limit ourselves to the consideration of the scalar field (this is why it is an introductory review) but the reader will find (at the end of the review) a set of references to existing studies on more complex systems.
Exactly soluble problems in statistical mechanics
International Nuclear Information System (INIS)
Yang, C.N.
1983-01-01
In the last few years, a number of two-dimensional classical and one-dimensional quantum mechanical problems in statistical mechanics have been exactly solved. Although these problems range over models of diverse physical interest, their solutions were obtained using very similar mathematical methods. In these lectures, the main points of the methods are discussed. In this introductory lecture, an overall survey of all these problems without going into the detailed method of solution is given. In later lectures, they shall concentrate on one particular problem: the delta function interaction in one dimension, and go into the details of that problem
An exact approach for aggregated formulations
DEFF Research Database (Denmark)
Gamst, Mette; Spoorendonk, Simon; Røpke, Stefan
Aggregating formulations is a powerful approach for problems to take on tractable forms. Aggregation may lead to loss of information, i.e. the aggregated formulation may be an approximation of the original problem. In branch-and-bound context, aggregation can also complicate branching, e.g. when...... optimality cannot be guaranteed by branching on aggregated variables. We present a generic exact solution method to remedy the drawbacks of aggregation. It combines the original and aggregated formulations and applies Benders' decomposition. We apply the method to the Split Delivery Vehicle Routing Problem....
International Nuclear Information System (INIS)
Kapshay, V.N.; Skachkov, N.B.
1979-01-01
A composite system of two relativistic particles is studied on the basis of the Kadyshevsky quasipotential equation, in which the ''Coulomb'' potential is taken in the form of a propagator of the massless-scalar-particle exchange. The obtained exact solutions to this equation are shown to be a geometrical generalization of nonrelativistic Coulomb wave functions in the sense of change of the Euclidean geometry of momentum space to the Lobachevsky geometry
Geometric and Magnetic Axes of the LHC Dipole
Bajko, M; Buzio, M; Deferne, G; Ferracin, P; García-Pérez, J; Scandale, Walter; Todesco, Ezio
2001-01-01
The 15-m long superconducting dipoles of the Large Hadron Collider (LHC) with two-in-one design are curved by about 5 mrad to follow the beam trajectory. They are supported on three cold feet to minimise the vertical sagitta induced by their 35 tonnes weight. The cold masses contain at both ends local multipolar correctors to compensate for the detrimental effect of persistent current during injection. We discuss how we measure and control the geometrical shape of the cold mass and the alignment of the associated correctors and how we identify the magnetic axis of the field-shape harmonics with respect to the expected beam reference orbit. We present results relative to prototype dipoles obtained both at room temperature and in operational conditions at 1.9 K.
Electric/magnetic deformations of S3 and AdS3, and geometric cosets
International Nuclear Information System (INIS)
Israel, D.; Kounnas, C.; Marios Petropoulos, P.; Orlando, D.
2005-01-01
We analyze asymmetric marginal deformations of SU(2) k and SL(2,R) k WZW models. These appear in heterotic string backgrounds with non-vanishing Neveu-Schwarz three-forms plus electric or magnetic fields, depending on whether the deformation is elliptic, hyperbolic or parabolic. Asymmetric deformations create new families of exact string vacua. The geometries which are generated in this way, deformed S 3 or AdS 3 , include in particular geometric cosets such as S 2 , AdS 2 or H 2 . Hence, the latter are consistent, exact conformal sigma models, with electric or magnetic backgrounds. We discuss various geometric and symmetry properties of the deformations at hand as well as their spectra and partition functions, with special attention to the supersymmetric AdS 2 x S 2 background. We also comment on potential holographic applications. (Abstract Copyright [2005], Wiley Periodicals, Inc.)
Geometrical setting of solid mechanics
International Nuclear Information System (INIS)
Fiala, Zdenek
2011-01-01
Highlights: → Solid mechanics within the Riemannian symmetric manifold GL (3, R)/O (3, R). → Generalized logarithmic strain. → Consistent linearization. → Incremental principle of virtual power. → Time-discrete approximation. - Abstract: The starting point in the geometrical setting of solid mechanics is to represent deformation process of a solid body as a trajectory in a convenient space with Riemannian geometry, and then to use the corresponding tools for its analysis. Based on virtual power of internal stresses, we show that such a configuration space is the (globally) symmetric space of symmetric positive-definite real matrices. From this unifying point of view, we shall analyse the logarithmic strain, the stress rate, as well as linearization and intrinsic integration of corresponding evolution equation.
Geometric Methods in Physics XXXV
Odzijewicz, Anatol; Previato, Emma
2018-01-01
This book features a selection of articles based on the XXXV Białowieża Workshop on Geometric Methods in Physics, 2016. The series of Białowieża workshops, attended by a community of experts at the crossroads of mathematics and physics, is a major annual event in the field. The works in this book, based on presentations given at the workshop, are previously unpublished, at the cutting edge of current research, typically grounded in geometry and analysis, and with applications to classical and quantum physics. In 2016 the special session "Integrability and Geometry" in particular attracted pioneers and leading specialists in the field. Traditionally, the Białowieża Workshop is followed by a School on Geometry and Physics, for advanced graduate students and early-career researchers, and the book also includes extended abstracts of the lecture series.
Geometric Operators on Boolean Functions
DEFF Research Database (Denmark)
Frisvad, Jeppe Revall; Falster, Peter
In truth-functional propositional logic, any propositional formula represents a Boolean function (according to some valuation of the formula). We describe operators based on Decartes' concept of constructing coordinate systems, for translation of a propositional formula to the image of a Boolean...... function. With this image of a Boolean function corresponding to a propositional formula, we prove that the orthogonal projection operator leads to a theorem describing all rules of inference in propositional reasoning. In other words, we can capture all kinds of inference in propositional logic by means...... of a few geometric operators working on the images of Boolean functions. The operators we describe, arise from the niche area of array-based logic and have previously been tightly bound to an array-based representation of Boolean functions. We redefine the operators in an abstract form to make them...
Geometric considerations in magnetron sputtering
International Nuclear Information System (INIS)
Thornton, J.A.
1982-01-01
The recent development of high performance magnetron type discharge sources has greatly enhaced the range of coating applications where sputtering is a viable deposition process. Magnetron sources can provide high current densities and sputtering rates, even at low pressures. They have much reduced substrate heating rates and can be scaled to large sizes. Magnetron sputter coating apparatuses can have a variety of geometric and plasma configurations. The target geometry affects the emission directions of both the sputtered atoms and the energetic ions which are neutralized and reflected at the cathode. This fact, coupled with the long mean free particle paths which are prevalent at low pressures, can make the coating properties very dependent on the apparatus geometry. This paper reviews the physics of magnetron operation and discusses the influences of apparatus geometry on the use of magnetrons for rf sputtering and reactive sputtering, as well as on the microstructure and internal stresses in sputtered metallic coatings. (author) [pt
Exact and Heuristic Algorithms for Runway Scheduling
Malik, Waqar A.; Jung, Yoon C.
2016-01-01
This paper explores the Single Runway Scheduling (SRS) problem with arrivals, departures, and crossing aircraft on the airport surface. Constraints for wake vortex separations, departure area navigation separations and departure time window restrictions are explicitly considered. The main objective of this research is to develop exact and heuristic based algorithms that can be used in real-time decision support tools for Air Traffic Control Tower (ATCT) controllers. The paper provides a multi-objective dynamic programming (DP) based algorithm that finds the exact solution to the SRS problem, but may prove unusable for application in real-time environment due to large computation times for moderate sized problems. We next propose a second algorithm that uses heuristics to restrict the search space for the DP based algorithm. A third algorithm based on a combination of insertion and local search (ILS) heuristics is then presented. Simulation conducted for the east side of Dallas/Fort Worth International Airport allows comparison of the three proposed algorithms and indicates that the ILS algorithm performs favorably in its ability to find efficient solutions and its computation times.
Exact model reduction of combinatorial reaction networks
Directory of Open Access Journals (Sweden)
Fey Dirk
2008-08-01
Full Text Available Abstract Background Receptors and scaffold proteins usually possess a high number of distinct binding domains inducing the formation of large multiprotein signaling complexes. Due to combinatorial reasons the number of distinguishable species grows exponentially with the number of binding domains and can easily reach several millions. Even by including only a limited number of components and binding domains the resulting models are very large and hardly manageable. A novel model reduction technique allows the significant reduction and modularization of these models. Results We introduce methods that extend and complete the already introduced approach. For instance, we provide techniques to handle the formation of multi-scaffold complexes as well as receptor dimerization. Furthermore, we discuss a new modeling approach that allows the direct generation of exactly reduced model structures. The developed methods are used to reduce a model of EGF and insulin receptor crosstalk comprising 5,182 ordinary differential equations (ODEs to a model with 87 ODEs. Conclusion The methods, presented in this contribution, significantly enhance the available methods to exactly reduce models of combinatorial reaction networks.
Exact combinatorial approach to finite coagulating systems
Fronczak, Agata; Chmiel, Anna; Fronczak, Piotr
2018-02-01
This paper outlines an exact combinatorial approach to finite coagulating systems. In this approach, cluster sizes and time are discrete and the binary aggregation alone governs the time evolution of the systems. By considering the growth histories of all possible clusters, an exact expression is derived for the probability of a coagulating system with an arbitrary kernel being found in a given cluster configuration when monodisperse initial conditions are applied. Then this probability is used to calculate the time-dependent distribution for the number of clusters of a given size, the average number of such clusters, and that average's standard deviation. The correctness of our general expressions is proved based on the (analytical and numerical) results obtained for systems with the constant kernel. In addition, the results obtained are compared with the results arising from the solutions to the mean-field Smoluchowski coagulation equation, indicating its weak points. The paper closes with a brief discussion on the extensibility to other systems of the approach presented herein, emphasizing the issue of arbitrary initial conditions.
Exact simulation of max-stable processes.
Dombry, Clément; Engelke, Sebastian; Oesting, Marco
2016-06-01
Max-stable processes play an important role as models for spatial extreme events. Their complex structure as the pointwise maximum over an infinite number of random functions makes their simulation difficult. Algorithms based on finite approximations are often inexact and computationally inefficient. We present a new algorithm for exact simulation of a max-stable process at a finite number of locations. It relies on the idea of simulating only the extremal functions, that is, those functions in the construction of a max-stable process that effectively contribute to the pointwise maximum. We further generalize the algorithm by Dieker & Mikosch (2015) for Brown-Resnick processes and use it for exact simulation via the spectral measure. We study the complexity of both algorithms, prove that our new approach via extremal functions is always more efficient, and provide closed-form expressions for their implementation that cover most popular models for max-stable processes and multivariate extreme value distributions. For simulation on dense grids, an adaptive design of the extremal function algorithm is proposed.
Exact collisional moments for plasma fluid theories
Pfefferle, David; Hirvijoki, Eero; Lingam, Manasvi
2017-10-01
The velocity-space moments of the often troublesome nonlinear Landau collision operator are expressed exactly in terms of multi-index Hermite-polynomial moments of the distribution functions. The collisional moments are shown to be generated by derivatives of two well-known functions, namely the Rosenbluth-MacDonald-Judd-Trubnikov potentials for a Gaussian distribution. The resulting formula has a nonlinear dependency on the relative mean flow of the colliding species normalised to the root-mean-square of the corresponding thermal velocities, and a bilinear dependency on densities and higher-order velocity moments of the distribution functions, with no restriction on temperature, flow or mass ratio of the species. The result can be applied to both the classic transport theory of plasmas, that relies on the Chapman-Enskog method, as well as to deriving collisional fluid equations that follow Grad's moment approach. As an illustrative example, we provide the collisional ten-moment equations with exact conservation laws for momentum- and energy-transfer rate.
Explicitly broken supersymmetry with exactly massless moduli
Energy Technology Data Exchange (ETDEWEB)
Dong, Xi [Stanford Institute for Theoretical Physics, Department of Physics, Stanford University,Stanford, CA 94305 (United States); Freedman, Daniel Z. [Stanford Institute for Theoretical Physics, Department of Physics, Stanford University,Stanford, CA 94305 (United States); Center for Theoretical Physics and Department of Mathematics,Massachusetts Institute of Technology,Cambridge, MA 02139 (United States); Zhao, Yue [Stanford Institute for Theoretical Physics, Department of Physics, Stanford University,Stanford, CA 94305 (United States)
2016-06-16
The AdS/CFT correspondence is applied to an analogue of the little hierarchy problem in three-dimensional supersymmetric theories. The bulk is governed by a supergravity theory in which a U(1) × U(1) R-symmetry is gauged by Chern-Simons fields. The bulk theory is deformed by a boundary term quadratic in the gauge fields. It breaks SUSY completely and sources an exactly marginal operator in the dual CFT. SUSY breaking is communicated by gauge interactions to bulk scalar fields and their spinor superpartners. The bulk-to-boundary propagator of the Chern-Simons fields is a total derivative with respect to the bulk coordinates. Integration by parts and the Ward identity permit evaluation of SUSY breaking effects to all orders in the strength of the deformation. The R-charges of scalars and spinors differ so large SUSY breaking mass shifts are generated. Masses of R-neutral particles such as scalar moduli are not shifted to any order in the deformation strength, despite the fact that they may couple to R-charged fields running in loops. We also obtain a universal deformation formula for correlation functions under an exactly marginal deformation by a product of holomorphic and anti-holomorphic U(1) currents.
Geometric picture of quantum discord for two-qubit quantum states
International Nuclear Information System (INIS)
Shi Mingjun; Jiang Fengjian; Sun Chunxiao; Du Jiangfeng
2011-01-01
Among various definitions of quantum correlations, quantum discord has attracted considerable attention. To find an analytical expression for quantum discord is an intractable task. Exact results are known only for very special states, namely two-qubit X-shaped states. We present in this paper a geometric viewpoint, from which two-qubit quantum discord can be described clearly. The known results on X state discord are restated in the directly perceivable geometric language. As a consequence, the dynamics of classical correlations and quantum discord for an X state in the presence of decoherence is endowed with geometric interpretation. More importantly, we extend the geometric method to the case of more general states, for which numerical as well as analytical results on quantum discord have not yet been obtained. Based on the support of numerical computations, some conjectures are proposed to help us establish the geometric picture. We find that the geometric picture for these states has an intimate relationship with that for X states. Thereby, in some cases, analytical expressions for classical correlations and quantum discord can be obtained.
Geometric solitons of Hamiltonian flows on manifolds
Energy Technology Data Exchange (ETDEWEB)
Song, Chong, E-mail: songchong@xmu.edu.cn [School of Mathematical Sciences, Xiamen University, Xiamen 361005 (China); Sun, Xiaowei, E-mail: sunxw@cufe.edu.cn [School of Applied Mathematics, Central University of Finance and Economics, Beijing 100081 (China); Wang, Youde, E-mail: wyd@math.ac.cn [Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190 (China)
2013-12-15
It is well-known that the LIE (Locally Induction Equation) admit soliton-type solutions and same soliton solutions arise from different and apparently irrelevant physical models. By comparing the solitons of LIE and Killing magnetic geodesics, we observe that these solitons are essentially decided by two families of isometries of the domain and the target space, respectively. With this insight, we propose the new concept of geometric solitons of Hamiltonian flows on manifolds, such as geometric Schrödinger flows and KdV flows for maps. Moreover, we give several examples of geometric solitons of the Schrödinger flow and geometric KdV flow, including magnetic curves as geometric Schrödinger solitons and explicit geometric KdV solitons on surfaces of revolution.
Operational geometric phase for mixed quantum states
International Nuclear Information System (INIS)
Andersson, O; Heydari, H
2013-01-01
The geometric phase has found a broad spectrum of applications in both classical and quantum physics, such as condensed matter and quantum computation. In this paper, we introduce an operational geometric phase for mixed quantum states, based on spectral weighted traces of holonomies, and we prove that it generalizes the standard definition of the geometric phase for mixed states, which is based on quantum interferometry. We also introduce higher order geometric phases, and prove that under a fairly weak, generically satisfied, requirement, there is always a well-defined geometric phase of some order. Our approach applies to general unitary evolutions of both non-degenerate and degenerate mixed states. Moreover, since we provide an explicit formula for the geometric phase that can be easily implemented, it is particularly well suited for computations in quantum physics. (paper)
Geometrical factors in the perception of sacredness
DEFF Research Database (Denmark)
Costa, Marco; Bonetti, Leonardo
2016-01-01
Geometrical and environmental factors in the perception of sacredness, dominance, and attractiveness were assessed by 137 participants in five tests. In the first test, a two-alternative forced-choice paradigm was used to test the perception of sacredness, dominance, and attractiveness in geometr......Geometrical and environmental factors in the perception of sacredness, dominance, and attractiveness were assessed by 137 participants in five tests. In the first test, a two-alternative forced-choice paradigm was used to test the perception of sacredness, dominance, and attractiveness...... in geometrical figures differing in shape, verticality, size, and symmetry. Verticality, symmetry, and convexity were found to be important factors in the perception of sacredness. In the second test, participants had to mark the point inside geometrical surfaces that was perceived as most sacred, dominant....... Geometrical factors in the perception of sacredness, dominance, and attractiveness were largely overlapping....
Linearization: Geometric, Complex, and Conditional
Directory of Open Access Journals (Sweden)
Asghar Qadir
2012-01-01
Full Text Available Lie symmetry analysis provides a systematic method of obtaining exact solutions of nonlinear (systems of differential equations, whether partial or ordinary. Of special interest is the procedure that Lie developed to transform scalar nonlinear second-order ordinary differential equations to linear form. Not much work was done in this direction to start with, but recently there have been various developments. Here, first the original work of Lie (and the early developments on it, and then more recent developments based on geometry and complex analysis, apart from Lie’s own method of algebra (namely, Lie group theory, are reviewed. It is relevant to mention that much of the work is not linearization but uses the base of linearization.
Influence of geometrical unsharpness on detection of tight defects by radiographic examination
International Nuclear Information System (INIS)
Bodson, F.; Crescenzo, E.; Thomas, A.
1983-01-01
A study was undertaken to evaluate the influence of geometric unsharpness on defects' visibility for radiographic examinations carried out with Iridium 192 and Cobalt 60 sources. This study enabled the authors to demonstrate that, even in the case of highly detrimental implementation conditions (increase in geometric unsharpness obtained via a reduction in the source-to-film distance, when the defect is not in the beam axis), the worsening in defects' visibility was dependent on defect type, nature of material, thickness radiographed, source energy, and geometric exposure conditions (dimension of the source, enlargement of the defect). Without establishing maximum admissible values, they nevertheless assert that these should be determined by taking these parameters into account. In particular it seems possible to accept greater geometric unsharpness values for small thicknesses than for large ones, in the examination of welded joints using Iridium 192 and Cobalt 60
Dark-field electron holography for the measurement of geometric phase
International Nuclear Information System (INIS)
Hytch, M.J.; Houdellier, F.; Huee, F.; Snoeck, E.
2011-01-01
The genesis, theoretical basis and practical application of the new electron holographic dark-field technique for mapping strain in nanostructures are presented. The development places geometric phase within a unified theoretical framework for phase measurements by electron holography. The total phase of the transmitted and diffracted beams is described as a sum of four contributions: crystalline, electrostatic, magnetic and geometric. Each contribution is outlined briefly and leads to the proposal to measure geometric phase by dark-field electron holography (DFEH). The experimental conditions, phase reconstruction and analysis are detailed for off-axis electron holography using examples from the field of semiconductors. A method for correcting for thickness variations will be proposed and demonstrated using the phase from the corresponding bright-field electron hologram. -- Highlights: → Unified description of phase measurements in electron holography. → Detailed description of dark-field electron holography for geometric phase measurements. → Correction procedure for systematic errors due to thickness variations.
Production of ion beam by conical pinched electron beam diode
International Nuclear Information System (INIS)
Matsukawa, Y.; Nakagawa, Y.
1982-01-01
Some properties of the ion beam produced by pinched electron beam diode having conical shape electrodes and organic insulator anode was studied. Ion energy is about 200keV and the peak diode current is about 30 kA. At 11cm from the diode apex, not the geometrical focus point, concentrated ion beam was obtained. Its density is more than 500A/cm 2 . The mean ion current density within the radius of 1.6cm around the axis from conical diode is two or three times that from an usual pinched electron beam diode with flat parallel electrodes of same dimension and impedance under the same conditions. (author)
Guide to Geometric Algebra in Practice
Dorst, Leo
2011-01-01
This highly practical "Guide to Geometric Algebra in Practice" reviews algebraic techniques for geometrical problems in computer science and engineering, and the relationships between them. The topics covered range from powerful new theoretical developments, to successful applications, and the development of new software and hardware tools. This title: provides hands-on review exercises throughout the book, together with helpful chapter summaries; presents a concise introductory tutorial to conformal geometric algebra (CGA) in the appendices; examines the application of CGA for the d
Optimization of geometric parameters of heat exchange pipes pin finning
Akulov, K. A.; Golik, V. V.; Voronin, K. S.; Zakirzakov, A. G.
2018-05-01
The work is devoted to optimization of geometric parameters of the pin finning of heat-exchanging pipes. Pin fins were considered from the point of view of mechanics of a deformed solid body as overhang beams with a uniformly distributed load. It was found out under what geometric parameters of the nib (diameter and length); the stresses in it from the influence of the washer fluid will not exceed the yield strength of the material (aluminum). Optimal values of the geometric parameters of nibs were obtained for different velocities of the medium washed by them. As a flow medium, water and air were chosen, and the cross section of the nibs was round and square. Pin finning turned out to be more than 3 times more compact than circumferential finning, so its use makes it possible to increase the number of fins per meter of the heat-exchanging pipe. And it is well-known that this is the main method for increasing the heat transfer of a convective surface, giving them an indisputable advantage.
Flexural Free Vibrations of Multistep Nonuniform Beams
Directory of Open Access Journals (Sweden)
Guojin Tan
2016-01-01
Full Text Available This paper presents an exact approach to investigate the flexural free vibrations of multistep nonuniform beams. Firstly, one-step beam with moment of inertia and mass per unit length varying as I(x=α11+βxr+4 and m(x=α21+βxr was studied. By using appropriate transformations, the differential equation for flexural free vibration of one-step beam with variable cross section is reduced to a four-order differential equation with constant coefficients. According to different types of roots for the characteristic equation of four-order differential equation with constant coefficients, two kinds of modal shape functions are obtained, and the general solutions for flexural free vibration of one-step beam with variable cross section are presented. An exact approach to solve the natural frequencies and modal shapes of multistep beam with variable cross section is presented by using transfer matrix method, the exact general solutions of one-step beam, and iterative method. Numerical examples reveal that the calculated frequencies and modal shapes are in good agreement with the finite element method (FEM, which demonstrates the solutions of present method are exact ones.
Geometrical and Graphical Solutions of Quadratic Equations.
Hornsby, E. John, Jr.
1990-01-01
Presented are several geometrical and graphical methods of solving quadratic equations. Discussed are Greek origins, Carlyle's method, von Staudt's method, fixed graph methods and imaginary solutions. (CW)
Electric field distribution and current emission in a miniaturized geometrical diode
Lin, Jinpu; Wong, Patrick Y.; Yang, Penglu; Lau, Y. Y.; Tang, W.; Zhang, Peng
2017-06-01
We study the electric field distribution and current emission in a miniaturized geometrical diode. Using Schwarz-Christoffel transformation, we calculate exactly the electric field inside a finite vacuum cathode-anode (A-K) gap with a single trapezoid protrusion on one of the electrode surfaces. It is found that there is a strong field enhancement on both electrodes near the protrusion, when the ratio of the A-K gap distance to the protrusion height d /h spot checked against COMSOL simulations. We calculate the effective field enhancement factor for the field emission current, by integrating the local Fowler-Nordheim current density along the electrode surfaces. We systematically examine the electric field enhancement and the current rectification of the miniaturized geometrical diode for various geometric dimensions and applied electric fields.
On the geometric nature of high energy nucleus-nucleus reaction cross sections
International Nuclear Information System (INIS)
Townsend, L.W.; Wilson, J.W.; Bidasaria, H.B.
1982-01-01
Within the context of a high energy double-folding optical potential approximation to the exact nucleus-nucleus multiple-scattering series, eikonal scattering theory is used to investigate the validity of geometric reaction cross sections in relativistic heavy ion collisions. The potential used includes a finite range interaction and nuclear single-particle densities extracted from nuclear charge distributions by unfolding the proton charge distribution. Pauli correlation effects are also included in an approximate way. The sensitivity of the predictions to be assumed interaction, Pauli correlation approximation, and nuclear density distributions is investigated. These results are in agreement with early predictions concerning the geometric nature of relativistic heavy ion collisions and in disagreement with a recent analysis, utilizing the zero range approximation, which suggested otherwise. Reasons for the lack of agreement between the analyses are also presented. Finally, approximate applicability for geometric reaction cross sections are determined
Geometrical and topological formulation of local gauge and supergauge theories
International Nuclear Information System (INIS)
Macrae, K.I.
1976-01-01
A geometrical and topological formulation of local gauge and supergauge invariance is presented. Analysis of experiments of the type described by Bohm and Aharanov and in the attempt to understand immersed submanifolds such as the string with internal symmetry, in a geometric setting, are led to the introduction of fiber bundles, superspaces. Many exact classical solutions to the equations of motion were considered for these gauge theories with specific choices of gauge group such as SU 4 . We describe some exact soliton solutions to these theories which have linear Regge trajectories, i.e., their angular momentum is a linear function of their mass squared. Next one discusses the actions and equations of motion for gauge theories whose base manifolds can have arbitrarily dimensioned submanifolds excised from them, manifolds with holes were discussed. These holes can have fractional quark charges when the structure group is, for example, SU 3 or SU 4 . By extending the concept of conservation of energy to include the excised submanifolds, their actions, and their equations of motion were derived showing that they can act as charged particles. Using the fractionality of the quark charges, are led to suggest a topological confinement mechanism for these particles. One also derives the actions and equations of motion for the string from this viewpoint. Some new Lie algebras which have anticommuting elements are introduced. Their gauge theories are described, and the possibility of fermionic actions for the anticommuting pieces is examined. Supersymmetric strings and their supergauge transformations were discussed and an extension was suggested of supersymmetry to immersed minimal submanifolds other than the string. Both quarklike and vectorlike fermions are included. Finally the invariance of both the equations of motion and the gauge conditions under supersymmetry transformations for these submanifolds were described
Exact solutions for some discrete models of the Boltzmann equation
International Nuclear Information System (INIS)
Cabannes, H.; Hong Tiem, D.
1987-01-01
For the simplest of the discrete models of the Boltzmann equation: the Broadwell model, exact solutions have been obtained by Cornille in the form of bisolitons. In the present Note, we build exact solutions for more complex models [fr
Geometric measure of quantum discord and total quantum correlations in an N-partite quantum state
International Nuclear Information System (INIS)
Hassan, Ali Saif M; Joag, Pramod S
2012-01-01
Quantum discord, as introduced by Ollivier and Zurek (2001 Phys. Rev. Lett. 88 017901), is a measure of the discrepancy between quantum versions of two classically equivalent expressions for mutual information and is found to be useful in quantification and application of quantum correlations in mixed states. It is viewed as a key resource present in certain quantum communication tasks and quantum computational models without containing much entanglement. An early step toward the quantification of quantum discord in a quantum state was by Dakic et al (2010 Phys. Rev. Lett. 105 190502) who introduced a geometric measure of quantum discord and derived an explicit formula for any two-qubit state. Recently, Luo and Fu (2010 Phys. Rev. A 82 034302) introduced a generic form of the geometric measure of quantum discord for a bipartite quantum state. We extend these results and find generic forms of the geometric measure of quantum discord and total quantum correlations in a general N-partite quantum state. Further, we obtain computable exact formulas for the geometric measure of quantum discord and total quantum correlations in an N-qubit quantum state. The exact formulas for the N-qubit quantum state can be used to get experimental estimates of the quantum discord and the total quantum correlation. (paper)
Exact Solution and Exotic Fluid in Cosmology
Directory of Open Access Journals (Sweden)
Phillial Oh
2012-09-01
Full Text Available We investigate cosmological consequences of nonlinear sigma model coupled with a cosmological fluid which satisfies the continuity equation. The target space action is of the de Sitter type and is composed of four scalar fields. The potential which is a function of only one of the scalar fields is also introduced. We perform a general analysis of the ensuing cosmological equations and give various critical points and their properties. Then, we show that the model exhibits an exact cosmological solution which yields a transition from matter domination into dark energy epoch and compare it with the Λ-CDM behavior. Especially, we calculate the age of the Universe and show that it is consistent with the observational value if the equation of the state ωf of the cosmological fluid is within the range of 0.13 < ωf < 0.22. Some implication of this result is also discussed.
A search for exact superstring vacua
Peterman, Andreas; Zichichi, Antonino
1994-01-01
We investigate $2d$ sigma-models with a $2+N$ dimensional Minkowski signature target space metric and Killing symmetry, specifically supersymmetrized, and see under which conditions they might lead to corresponding exact string vacua. It appears that the issue relies heavily on the properties of the vector $M_{\\mu}$, a reparametrization term, which needs to possess a definite form for the Weyl invariance to be satisfied. We give, in the $n = 1$ supersymmetric case, two non-renormalization theorems from which we can relate the $u$ component of $M_{\\mu}$ to the $\\beta^G_{uu}$ function. We work out this $(u,u)$ component of the $\\beta^G$ function and find a non-vanishing contribution at four loops. Therefore, it turns out that at order $\\alpha^{\\prime 4}$, there are in general non-vanishing contributions to $M_u$ that prevent us from deducing superstring vacua in closed form.
Interference-exact radiative transfer equation
DEFF Research Database (Denmark)
Partanen, Mikko; Haÿrynen, Teppo; Oksanen, Jani
2017-01-01
Maxwell's equations with stochastic or quantum optical source terms accounting for the quantum nature of light. We show that both the nonlocal wave and local particle features associated with interference and emission of propagating fields in stratified geometries can be fully captured by local damping...... and scattering coefficients derived from the recently introduced quantized fluctuational electrodynamics (QFED) framework. In addition to describing the nonlocal optical interference processes as local directionally resolved effects, this allows reformulating the well known and widely used radiative transfer...... equation (RTE) as a physically transparent interference-exact model that extends the useful range of computationally efficient and quantum optically accurate interference-aware optical models from simple structures to full optical devices....
Exact iterative reconstruction for the interior problem
International Nuclear Information System (INIS)
Zeng, Gengsheng L; Gullberg, Grant T
2009-01-01
There is a trend in single photon emission computed tomography (SPECT) that small and dedicated imaging systems are becoming popular. For example, many companies are developing small dedicated cardiac SPECT systems with different designs. These dedicated systems have a smaller field of view (FOV) than a full-size clinical system. Thus data truncation has become the norm rather than the exception in these systems. Therefore, it is important to develop region of interest (ROI) reconstruction algorithms using truncated data. This paper is a stepping stone toward this direction. This paper shows that the common generic iterative image reconstruction algorithms are able to exactly reconstruct the ROI under the conditions that the convex ROI is fully sampled and the image value in a sub-region within the ROI is known. If the ROI includes a sub-region that is outside the patient body, then the conditions can be easily satisfied.
On truncations of the exact renormalization group
Morris, T R
1994-01-01
We investigate the Exact Renormalization Group (ERG) description of (Z_2 invariant) one-component scalar field theory, in the approximation in which all momentum dependence is discarded in the effective vertices. In this context we show how one can perform a systematic search for non-perturbative continuum limits without making any assumption about the form of the lagrangian. Concentrating on the non-perturbative three dimensional Wilson fixed point, we then show that the sequence of truncations n=2,3,\\dots, obtained by expanding about the field \\varphi=0 and discarding all powers \\varphi^{2n+2} and higher, yields solutions that at first converge to the answer obtained without truncation, but then cease to further converge beyond a certain point. No completely reliable method exists to reject the many spurious solutions that are also found. These properties are explained in terms of the analytic behaviour of the untruncated solutions -- which we describe in some detail.
Exact solutions to operator differential equations
International Nuclear Information System (INIS)
Bender, C.M.
1992-01-01
In this talk we consider the Heisenberg equations of motion q = -i(q, H), p = -i(p, H), for the quantum-mechanical Hamiltonian H(p, q) having one degree of freedom. It is a commonly held belief that such operator differential equations are intractable. However, a technique is presented here that allows one to obtain exact, closed-form solutions for huge classes of Hamiltonians. This technique, which is a generalization of the classical action-angle variable methods, allows us to solve, albeit formally and implicitly, the operator differential equations of two anharmonic oscillators whose Hamiltonians are H = p 2 /2 + q 4 /4 and H = p 4 /4 + q 4 /4
Exact solutions to chaotic and stochastic systems
González, J. A.; Reyes, L. I.; Guerrero, L. E.
2001-03-01
We investigate functions that are exact solutions to chaotic dynamical systems. A generalization of these functions can produce truly random numbers. For the first time, we present solutions to random maps. This allows us to check, analytically, some recent results about the complexity of random dynamical systems. We confirm the result that a negative Lyapunov exponent does not imply predictability in random systems. We test the effectiveness of forecasting methods in distinguishing between chaotic and random time series. Using the explicit random functions, we can give explicit analytical formulas for the output signal in some systems with stochastic resonance. We study the influence of chaos on the stochastic resonance. We show, theoretically, the existence of a new type of solitonic stochastic resonance, where the shape of the kink is crucial. Using our models we can predict specific patterns in the output signal of stochastic resonance systems.
Exactly soluble QCD and confinement of quarks
International Nuclear Information System (INIS)
Rusakov, B.
1997-01-01
An exactly soluble non-perturbative model of the pure gauge QCD is derived as a weak coupling limit of the lattice theory in plaquette formulation [B. Rusakov, Phys. Lett. B 398 (1997) 331]. The model represents QCD as a theory of the weakly interacting field strength fluxes. The area law behavior of the Wilson loop average is a direct result of this representation: the total flux through macroscopic loop is the additive (due to the weakness of the interaction) function of the elementary fluxes. The compactness of the gauge group is shown to be the factor which prevents the elementary fluxes contributions from cancellation. There is no area law in the non-compact theory. (orig.)
Exact classical scaling formalism for nonreactive processes
International Nuclear Information System (INIS)
DePristo, A.E.
1981-01-01
A general nonreactive collision system is considered with internal molecular variables (p, r) and/or (I, theta) of arbitrary dimensions and relative translational variables (P, R) of three or less dimensions. We derive an exact classical scaling formalism which relates the collisional change in any function of molecular variables directly to the initial values of these variables. The collision dynamics is then described by an explicit function of the initial point in the internal molecular phase space, for a fixed point in the relative translational phase space. In other words, the systematic variation of the internal molecular properties (e.g., actions and average internal kinetic energies) is given as a function of the initial internal action-angle variables. A simple three term approximation to the exact formalism is derived, the natural variables of which are the internal action I and internal linear momenta p. For the final average internal kinetic energies T, the result is T-T/sup( 0 ) = α+βp/sup( 0 )+γI/sup( 0 ), where the superscripted ''0'' indicates the initial value. The parameters α, β, and γ in this scaling theory are directly related to the moments of the change in average internal kinetic energy. Utilizing a very limited number of input moments generated from classical trajectory calculations, the scaling can be used to predict the entire distribution of final internal variables as a function of initial internal actions and linear momenta. Initial examples for atom--collinear harmonic oscillator collision systems are presented in detail, with the scaling predictions (e.g., moments and quasiclassical histogram transition probabilities) being generally very good to excellent quantitatively
Dynamics of an Imperfect Microbeam Considering its Exact Shape
Bataineh, Ahmad M.
2014-08-17
We study the static and dynamic behavior of electrically actuated micromachined arches. First, we conduct experiments on micromachined polysilicon beams by driving them electrically and varying their amplitude and frequency of voltage loads. The results reveal several interesting nonlinear phenomena of jumps, hysteresis, and softening behaviors. Next, we conduct analytical and theoretical investigation to understand the experiments. First, we solve the Eigen value problem analytically. We study the effect of the initial rise on the natural frequency and mode shapes, and use a Galerkin-based procedure to derive a reduced order model, which is then used to solve both the static and dynamic responses. We use two symmetric modes in the reduced order model to have accurate and converged results. We use long time integration to solve the nonlinear ordinary differential equations, and then modify our model using effective length to match experimental results. To further improve the matching with the experimental data, we curve-fit the exact profile of the microbeam to match the experimentally measured profile and use it in the reduced-order model to generate frequency-response curves. Finally, we use another numerical technique, the shooting technique, to solve the nonlinear ordinary differential equations. By using shooting and the curve fitted function, we found that we get good agreement with the experimental data.
Construction of exact solutions for the Stern-Gerlach effect
International Nuclear Information System (INIS)
Diaz Bulnes, J.; Oliveira, I.S.
2001-01-01
We obtain exact solutions for the Schroedinger-Pauli matrix equation for a neutral particle of spin 1/2 in a magnetic field with a field gradient. The analytical wave functions are written on the symmetry plane Y = 0, which contains the incident and splitted beams, in terms of the Airy functions. The time-evolution of the probability, |Ψ+| 2 and |Ψ-| 2 , and the eigenenergies are calculated. The include a small contribution from the field gradient, α, proportional to (α ℎ) 2/3 , which amount to equal energy displacements on both magnetic levels. The results are generalized for spin S = 3/2, and in this case we found that the m = ±1/2 and m = ±3/2 magnetic sublevels are unequally splitted by the field gradient, being the difference in energy of the order 0.4 MHz. Replacing real experimental parameters we obtained a spatial splitting of the spin up and spin down states of the order Δz ≅4 mm, in accordance to a real Stern-Gerlach experiment. (author)
Geometric asymmetry driven Janus micromotors
Zhao, Guanjia; Pumera, Martin
2014-09-01
The production and application of nano-/micromotors is of great importance. In order for the motors to work, asymmetry in their chemical composition or physical geometry must be present if no external asymmetric field is applied. In this paper, we present a ``coconut'' micromotor made of platinum through the partial or complete etching of the silica templates. It was shown that although both the inner and outer surfaces are made of the same material (Pt), motion of the structure can be observed as the convex surface is capable of generating oxygen bubbles. This finding shows that not only the chemical asymmetry of the micromotor, but also its geometric asymmetry can lead to fast propulsion of the motor. Moreover, a considerably higher velocity can be seen for partially etched coconut structures than the velocities of Janus or fully etched, shell-like motors. These findings will have great importance on the design of future micromotors.The production and application of nano-/micromotors is of great importance. In order for the motors to work, asymmetry in their chemical composition or physical geometry must be present if no external asymmetric field is applied. In this paper, we present a ``coconut'' micromotor made of platinum through the partial or complete etching of the silica templates. It was shown that although both the inner and outer surfaces are made of the same material (Pt), motion of the structure can be observed as the convex surface is capable of generating oxygen bubbles. This finding shows that not only the chemical asymmetry of the micromotor, but also its geometric asymmetry can lead to fast propulsion of the motor. Moreover, a considerably higher velocity can be seen for partially etched coconut structures than the velocities of Janus or fully etched, shell-like motors. These findings will have great importance on the design of future micromotors. Electronic supplementary information (ESI) available: Additional SEM images, data analysis, Videos S
New exact solutions of the mBBM equation
International Nuclear Information System (INIS)
Zhang Zhe; Li Desheng
2013-01-01
The enhanced modified simple equation method presented in this article is applied to construct the exact solutions of modified Benjamin-Bona-Mahoney equation. Some new exact solutions are derived by using this method. When some parameters are taken as special values, the solitary wave solutions can be got from the exact solutions. It is shown that the method introduced in this paper has general significance in searching for exact solutions to the nonlinear evolution equations. (authors)
Jargalsaikhan, Bolor
Checking copositivity of a matrix is a co-NP-complete problem. This paper studies copositive matrices with certain spectral properties. It shows that an indefinite matrix with exactly one positive eigenvalue is copositive if and only if the matrix is nonnegative. Moreover, it shows that finding out
International Nuclear Information System (INIS)
Frank, R.; Engel, R.
1979-01-01
The core support plate is a very important component of the reactor pressure vessel internals. Therefore, an exact stress analysis is desired. This analysis will cause high computer costs with a detailed FEM-model because of the complexity of this compound system. In this paper, a method is suggested to solve the problem with a much cheaper beam element model. The main problem is to establish an equivalent beam system with nearly the same stiffness property as the perforated circular plate stiffened by a grid. Furthermore, the system must allow to determine the maximum stresses with sufficient accuracy. The calculation of the equivalent beam stiffness is based on the analysis of perforated plates by T. SLOT and W.J. O'DONNELL. This analysis method utilizes the concept of the equivalent solid plate. In this method, the perforated plate is replaced by a solid one which is geometrically similar to the perforated plate but has modified values of the elastic constants. The simple equivalent beam system of one half of the core support plate (symmetry) was loaded with a pressure difference and stresses and displacements were analysed. After that, these results were compared with the stress and displacement analysis of a part of the real structure. This substructure was discretized by three-dimensional 20-node brick-elements. The comparison of the results of the two models shows that the stresses and displacements, calculated with the simple beam model, are in good agreement with those of the real structure. (orig.)
Modeling space charge in beams for heavy-ion fusion
International Nuclear Information System (INIS)
Sharp, W.M.
1995-01-01
A new analytic model is presented which accurately estimates the radially averaged axial component of the space-charge field of an axisymmetric heavy-ion beam in a cylindrical beam pipe. The model recovers details of the field near the beam ends that are overlooked by simpler models, and the results compare well to exact solutions of Poisson's equation. Field values are shown for several simple beam profiles and are compared with values obtained from simpler models
A summary of some beam-beam models
International Nuclear Information System (INIS)
Chao, A.W.
1989-01-01
Two categories of theoretical models for the beam-beam interaction are reviewed: the linear-lens models and the single-resonance models. In a linear-lens model, the beam-beam force is linearized and represented by a localized linear lens. Analyses of incoherent single particle effects can be performed exactly in these models by using matrix techniques. Although the results do not agree with the experimental observations in many respects, the linear-lens models constitute a starting point of our understanding of the beam-beam interaction. In the single-resonance models, one is concerned with the possible incoherent instabilities as the betatron tune of some of the particles is close to a certain rational number. It is assumed in these models that one and only one such rational number dominates the single-particle beam-beam effects. It is found that static single resonances cannot explain many of the experimental results. Some attempts have been made to modify the static single-resonance theory by including some mechanisms for diffusive tune fluctuations or periodic tune modulations. These modified single-resonance models have met only with some limited qualitative success. 21 refs., 13 figs
Bessel-like beams modulated by arbitrary radial functions
Herman; Wiggins
2000-06-01
An approximate method for determining the radial and axial intensity of a Bessel-like beam is presented for the general case in which a radial Bessel distribution of any order is modulated by an arbitrary function. For Bessel-Gauss, generalized Bessel-Gauss, and Bessel-super-Gauss beams, this simple approximation yields results that are very close to the exact values, while they are exact for Bessel beams. A practical beam that can be generated with a combination of simple lenses is also analyzed and illustrated.
Exact solitary waves of the Korteveg - de Vries - Burgers equation
Kudryashov, N. A.
2004-01-01
New approach is presented to search exact solutions of nonlinear differential equations. This method is used to look for exact solutions of the Korteveg -- de Vries -- Burgers equation. New exact solitary waves of the Korteveg -- de Vries -- Burgers equation are found.
Information geometric methods for complexity
Felice, Domenico; Cafaro, Carlo; Mancini, Stefano
2018-03-01
Research on the use of information geometry (IG) in modern physics has witnessed significant advances recently. In this review article, we report on the utilization of IG methods to define measures of complexity in both classical and, whenever available, quantum physical settings. A paradigmatic example of a dramatic change in complexity is given by phase transitions (PTs). Hence, we review both global and local aspects of PTs described in terms of the scalar curvature of the parameter manifold and the components of the metric tensor, respectively. We also report on the behavior of geodesic paths on the parameter manifold used to gain insight into the dynamics of PTs. Going further, we survey measures of complexity arising in the geometric framework. In particular, we quantify complexity of networks in terms of the Riemannian volume of the parameter space of a statistical manifold associated with a given network. We are also concerned with complexity measures that account for the interactions of a given number of parts of a system that cannot be described in terms of a smaller number of parts of the system. Finally, we investigate complexity measures of entropic motion on curved statistical manifolds that arise from a probabilistic description of physical systems in the presence of limited information. The Kullback-Leibler divergence, the distance to an exponential family and volumes of curved parameter manifolds, are examples of essential IG notions exploited in our discussion of complexity. We conclude by discussing strengths, limits, and possible future applications of IG methods to the physics of complexity.
Geometrical aspects of quantum spaces
International Nuclear Information System (INIS)
Ho, P.M.
1996-01-01
Various geometrical aspects of quantum spaces are presented showing the possibility of building physics on quantum spaces. In the first chapter the authors give the motivations for studying noncommutative geometry and also review the definition of a Hopf algebra and some general features of the differential geometry on quantum groups and quantum planes. In Chapter 2 and Chapter 3 the noncommutative version of differential calculus, integration and complex structure are established for the quantum sphere S 1 2 and the quantum complex projective space CP q (N), on which there are quantum group symmetries that are represented nonlinearly, and are respected by all the aforementioned structures. The braiding of S q 2 and CP q (N) is also described. In Chapter 4 the quantum projective geometry over the quantum projective space CP q (N) is developed. Collinearity conditions, coplanarity conditions, intersections and anharmonic ratios is described. In Chapter 5 an algebraic formulation of Reimannian geometry on quantum spaces is presented where Riemannian metric, distance, Laplacian, connection, and curvature have their quantum counterparts. This attempt is also extended to complex manifolds. Examples include the quantum sphere, the complex quantum projective space and the two-sheeted space. The quantum group of general coordinate transformations on some quantum spaces is also given
Yang Mills instantons, geometrical aspects
International Nuclear Information System (INIS)
Stora, R.
1977-09-01
The word instanton has been coined by analogy with the word soliton. They both refer to solutions of elliptic non linear field equations with boundary conditions at infinity (of euclidean space time in the first case, euclidean space in the second case) lying on the set of classical vacua in such a way that stable topological properties emerge, susceptible to survive quantum effects, if those are small. Under this assumption, instantons are believed to be relevant to the description of tunnelling effects between classical vacua and signal some characteristics of the vacuum at the quantum level, whereas solitons should be associated with particles, i.e. discrete points in the mass spectrum. In one case the euclidean action is finite, in the other case, the energy is finite. From the mathematical point of view, the geometrical phenomena associated with the existence of solitons have forced physicists to learn rudiments of algebraic topology. The study of euclidean classical Yang Mills fields involves naturally mathematical items falling under the headings: differential geometry (fibre bundles, connections); differential topology (characteristic classes, index theory) and more recently algebraic geometry. These notes are divided as follows: a first section is devoted to a description of the physicist's views; a second section is devoted to the mathematician's vie
Geometric Reasoning for Automated Planning
Clement, Bradley J.; Knight, Russell L.; Broderick, Daniel
2012-01-01
An important aspect of mission planning for NASA s operation of the International Space Station is the allocation and management of space for supplies and equipment. The Stowage, Configuration Analysis, and Operations Planning teams collaborate to perform the bulk of that planning. A Geometric Reasoning Engine is developed in a way that can be shared by the teams to optimize item placement in the context of crew planning. The ISS crew spends (at the time of this writing) a third or more of their time moving supplies and equipment around. Better logistical support and optimized packing could make a significant impact on operational efficiency of the ISS. Currently, computational geometry and motion planning do not focus specifically on the optimized orientation and placement of 3D objects based on multiple distance and containment preferences and constraints. The software performs reasoning about the manipulation of 3D solid models in order to maximize an objective function based on distance. It optimizes for 3D orientation and placement. Spatial placement optimization is a general problem and can be applied to object packing or asset relocation.
Simulating geometrically complex blast scenarios
Directory of Open Access Journals (Sweden)
Ian G. Cullis
2016-04-01
Full Text Available The effects of blast waves generated by energetic and non-energetic sources are of continuing interest to the ballistics research community. Modern conflicts are increasingly characterised by asymmetric urban warfare, with improvised explosive devices (IEDs often playing a dominant role on the one hand and an armed forces requirement for minimal collateral effects from their weapons on the other. These problems are characterised by disparate length- and time-scales and may also be governed by complex physics. There is thus an increasing need to be able to rapidly assess and accurately predict the effects of energetic blast in topologically complex scenarios. To this end, this paper presents a new QinetiQ-developed advanced computational package called EAGLE-Blast, which is capable of accurately resolving the generation, propagation and interaction of blast waves around geometrically complex shapes such as vehicles and buildings. After a brief description of the numerical methodology, various blast scenario simulations are described and the results compared with experimental data to demonstrate the validation of the scheme and its ability to describe these complex scenarios accurately and efficiently. The paper concludes with a brief discussion on the use of the code in supporting the development of algorithms for fast running engineering models.
Generalized Geometric Quantum Speed Limits
Directory of Open Access Journals (Sweden)
Diego Paiva Pires
2016-06-01
Full Text Available The attempt to gain a theoretical understanding of the concept of time in quantum mechanics has triggered significant progress towards the search for faster and more efficient quantum technologies. One of such advances consists in the interpretation of the time-energy uncertainty relations as lower bounds for the minimal evolution time between two distinguishable states of a quantum system, also known as quantum speed limits. We investigate how the nonuniqueness of a bona fide measure of distinguishability defined on the quantum-state space affects the quantum speed limits and can be exploited in order to derive improved bounds. Specifically, we establish an infinite family of quantum speed limits valid for unitary and nonunitary evolutions, based on an elegant information geometric formalism. Our work unifies and generalizes existing results on quantum speed limits and provides instances of novel bounds that are tighter than any established one based on the conventional quantum Fisher information. We illustrate our findings with relevant examples, demonstrating the importance of choosing different information metrics for open system dynamics, as well as clarifying the roles of classical populations versus quantum coherences, in the determination and saturation of the speed limits. Our results can find applications in the optimization and control of quantum technologies such as quantum computation and metrology, and might provide new insights in fundamental investigations of quantum thermodynamics.
Geometric structure of percolation clusters.
Xu, Xiao; Wang, Junfeng; Zhou, Zongzheng; Garoni, Timothy M; Deng, Youjin
2014-01-01
We investigate the geometric properties of percolation clusters by studying square-lattice bond percolation on the torus. We show that the density of bridges and nonbridges both tend to 1/4 for large system sizes. Using Monte Carlo simulations, we study the probability that a given edge is not a bridge but has both its loop arcs in the same loop and find that it is governed by the two-arm exponent. We then classify bridges into two types: branches and junctions. A bridge is a branch iff at least one of the two clusters produced by its deletion is a tree. Starting from a percolation configuration and deleting the branches results in a leaf-free configuration, whereas, deleting all bridges produces a bridge-free configuration. Although branches account for ≈43% of all occupied bonds, we find that the fractal dimensions of the cluster size and hull length of leaf-free configurations are consistent with those for standard percolation configurations. By contrast, we find that the fractal dimensions of the cluster size and hull length of bridge-free configurations are given by the backbone and external perimeter dimensions, respectively. We estimate the backbone fractal dimension to be 1.643 36(10).
Weighted Geometric Dilution of Precision Calculations with Matrix Multiplication
Directory of Open Access Journals (Sweden)
Chien-Sheng Chen
2015-01-01
Full Text Available To enhance the performance of location estimation in wireless positioning systems, the geometric dilution of precision (GDOP is widely used as a criterion for selecting measurement units. Since GDOP represents the geometric effect on the relationship between measurement error and positioning determination error, the smallest GDOP of the measurement unit subset is usually chosen for positioning. The conventional GDOP calculation using matrix inversion method requires many operations. Because more and more measurement units can be chosen nowadays, an efficient calculation should be designed to decrease the complexity. Since the performance of each measurement unit is different, the weighted GDOP (WGDOP, instead of GDOP, is used to select the measurement units to improve the accuracy of location. To calculate WGDOP effectively and efficiently, the closed-form solution for WGDOP calculation is proposed when more than four measurements are available. In this paper, an efficient WGDOP calculation method applying matrix multiplication that is easy for hardware implementation is proposed. In addition, the proposed method can be used when more than exactly four measurements are available. Even when using all-in-view method for positioning, the proposed method still can reduce the computational overhead. The proposed WGDOP methods with less computation are compatible with global positioning system (GPS, wireless sensor networks (WSN and cellular communication systems.
Boussard, Daniel
1987-01-01
We begin by giving a description of the radio-frequency generator-cavity-beam coupled system in terms of basic quantities. Taking beam loading and cavity detuning into account, expressions for the cavity impedance as seen by the generator and as seen by the beam are derived. Subsequently methods of beam-loading compensation by cavity detuning, radio-frequency feedback and feedforward are described. Examples of digital radio-frequency phase and amplitude control for the special case of superco...
International Nuclear Information System (INIS)
Pendelbury, J.M.; Smith, K.F.
1987-01-01
Studies with directed collision-free beams of particles continue to play an important role in the development of modern physics and chemistry. The deflections suffered by such beams as they pass through electric and magnetic fields or laser radiation provide some of the most direct information about the individual constituents of the beam; the scattering observed when two beams intersect yields important data about the intermolecular forces responsible for the scattering. (author)
Geometrical scaling, furry branching and minijets
International Nuclear Information System (INIS)
Hwa, R.C.
1988-01-01
Scaling properties and their violations in hadronic collisions are discussed in the framework of the geometrical branching model. Geometrical scaling supplemented by Furry branching characterizes the soft component, while the production of jets specifies the hard component. Many features of multiparticle production processes are well described by this model. 21 refs
Geometric integrators for stochastic rigid body dynamics
Tretyakov, Mikhail
2016-01-05
Geometric integrators play an important role in simulating dynamical systems on long time intervals with high accuracy. We will illustrate geometric integration ideas within the stochastic context, mostly on examples of stochastic thermostats for rigid body dynamics. The talk will be mainly based on joint recent work with Rusland Davidchak and Tom Ouldridge.
Geometric integrators for stochastic rigid body dynamics
Tretyakov, Mikhail
2016-01-01
Geometric integrators play an important role in simulating dynamical systems on long time intervals with high accuracy. We will illustrate geometric integration ideas within the stochastic context, mostly on examples of stochastic thermostats for rigid body dynamics. The talk will be mainly based on joint recent work with Rusland Davidchak and Tom Ouldridge.
Geometric phases in discrete dynamical systems
Energy Technology Data Exchange (ETDEWEB)
Cartwright, Julyan H.E., E-mail: julyan.cartwright@csic.es [Instituto Andaluz de Ciencias de la Tierra, CSIC–Universidad de Granada, E-18100 Armilla, Granada (Spain); Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, E-18071 Granada (Spain); Piro, Nicolas, E-mail: nicolas.piro@epfl.ch [École Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne (Switzerland); Piro, Oreste, E-mail: piro@imedea.uib-csic.es [Departamento de Física, Universitat de les Illes Balears, E-07122 Palma de Mallorca (Spain); Tuval, Idan, E-mail: ituval@imedea.uib-csic.es [Mediterranean Institute for Advanced Studies, CSIC–Universitat de les Illes Balears, E-07190 Mallorca (Spain)
2016-10-14
In order to study the behaviour of discrete dynamical systems under adiabatic cyclic variations of their parameters, we consider discrete versions of adiabatically-rotated rotators. Parallelling the studies in continuous systems, we generalize the concept of geometric phase to discrete dynamics and investigate its presence in these rotators. For the rotated sine circle map, we demonstrate an analytical relationship between the geometric phase and the rotation number of the system. For the discrete version of the rotated rotator considered by Berry, the rotated standard map, we further explore this connection as well as the role of the geometric phase at the onset of chaos. Further into the chaotic regime, we show that the geometric phase is also related to the diffusive behaviour of the dynamical variables and the Lyapunov exponent. - Highlights: • We extend the concept of geometric phase to maps. • For the rotated sine circle map, we demonstrate an analytical relationship between the geometric phase and the rotation number. • For the rotated standard map, we explore the role of the geometric phase at the onset of chaos. • We show that the geometric phase is related to the diffusive behaviour of the dynamical variables and the Lyapunov exponent.
Geometrical optics and the diffraction phenomenon
International Nuclear Information System (INIS)
Timofeev, Aleksandr V
2005-01-01
This note outlines the principles of the geometrical optics of inhomogeneous waves whose description necessitates the use of complex values of the wave vector. Generalizing geometrical optics to inhomogeneous waves permits including in its scope the analysis of the diffraction phenomenon. (methodological notes)
Solving Absolute Value Equations Algebraically and Geometrically
Shiyuan, Wei
2005-01-01
The way in which students can improve their comprehension by understanding the geometrical meaning of algebraic equations or solving algebraic equation geometrically is described. Students can experiment with the conditions of the absolute value equation presented, for an interesting way to form an overall understanding of the concept.
Zhou, Zhenhuan; Li, Yuejie; Fan, Junhai; Rong, Dalun; Sui, Guohao; Xu, Chenghui
2018-05-01
A new Hamiltonian-based approach is presented for finding exact solutions for transverse vibrations of double-nanobeam-systems embedded in an elastic medium. The continuum model is established within the frameworks of the symplectic methodology and the nonlocal Euler-Bernoulli and Timoshenko beam beams. The symplectic eigenfunctions are obtained after expressing the governing equations in a Hamiltonian form. Exact frequency equations, vibration modes and displacement amplitudes are obtained by using symplectic eigenfunctions and end conditions. Comparisons with previously published work are presented to illustrate the accuracy and reliability of the proposed method. The comprehensive results for arbitrary boundary conditions could serve as benchmark results for verifying numerically obtained solutions. In addition, a study on the difference between the nonlocal beam and the nonlocal plate is also included.
Geometric Implications of Maxwell's Equations
Smith, Felix T.
2015-03-01
Maxwell's synthesis of the varied results of the accumulated knowledge of electricity and magnetism, based largely on the searching insights of Faraday, still provide new issues to explore. A case in point is a well recognized anomaly in the Maxwell equations: The laws of electricity and magnetism require two 3-vector and two scalar equations, but only six dependent variables are available to be their solutions, the 3-vectors E and B. This leaves an apparent redundancy of two degrees of freedom (J. Rosen, AJP 48, 1071 (1980); Jiang, Wu, Povinelli, J. Comp. Phys. 125, 104 (1996)). The observed self-consistency of the eight equations suggests that they contain additional information. This can be sought as a previously unnoticed constraint connecting the space and time variables, r and t. This constraint can be identified. It distorts the otherwise Euclidean 3-space of r with the extremely slight, time dependent curvature k (t) =Rcurv-2 (t) of the 3-space of a hypersphere whose radius has the time dependence dRcurv / dt = +/- c nonrelativistically, or dRcurvLor / dt = +/- ic relativistically. The time dependence is exactly that of the Hubble expansion. Implications of this identification will be explored.
Duality invariant class of exact string backgrounds
Klimcík, C
1994-01-01
We consider a class of $2+D$ - dimensional string backgrounds with a target space metric having a covariantly constant null Killing vector and flat `transverse' part. The corresponding sigma models are invariant under $D$ abelian isometries and are transformed by $O(D,D)$ duality into models belonging to the same class. The leading-order solutions of the conformal invariance equations (metric, antisymmetric tensor and dilaton), as well as the action of $O(D,D)$ duality transformations on them, are exact, i.e. are not modified by $\\a'$-corrections. This makes a discussion of different space-time representations of the same string solution (related by $O(D,D|Z)$ duality subgroup) rather explicit. We show that the $O(D,D)$ duality may connect curved $2+D$-dimensional backgrounds with solutions having flat metric but, in general, non-trivial antisymmetric tensor and dilaton. We discuss several particular examples including the $2+D=4$ - dimensional background that was recently interpreted in terms of a WZW model.
Exact-exchange-based quasiparticle calculations
International Nuclear Information System (INIS)
Aulbur, Wilfried G.; Staedele, Martin; Goerling, Andreas
2000-01-01
One-particle wave functions and energies from Kohn-Sham calculations with the exact local Kohn-Sham exchange and the local density approximation (LDA) correlation potential [EXX(c)] are used as input for quasiparticle calculations in the GW approximation (GWA) for eight semiconductors. Quasiparticle corrections to EXX(c) band gaps are small when EXX(c) band gaps are close to experiment. In the case of diamond, quasiparticle calculations are essential to remedy a 0.7 eV underestimate of the experimental band gap within EXX(c). The accuracy of EXX(c)-based GWA calculations for the determination of band gaps is as good as the accuracy of LDA-based GWA calculations. For the lowest valence band width a qualitatively different behavior is observed for medium- and wide-gap materials. The valence band width of medium- (wide-) gap materials is reduced (increased) in EXX(c) compared to the LDA. Quasiparticle corrections lead to a further reduction (increase). As a consequence, EXX(c)-based quasiparticle calculations give valence band widths that are generally 1-2 eV smaller (larger) than experiment for medium- (wide-) gap materials. (c) 2000 The American Physical Society
Generalized exact holographic mapping with wavelets
Lee, Ching Hua
2017-12-01
The idea of renormalization and scale invariance is pervasive across disciplines. It has not only drawn numerous surprising connections between physical systems under the guise of holographic duality, but has also inspired the development of wavelet theory now widely used in signal processing. Synergizing on these two developments, we describe in this paper a generalized exact holographic mapping that maps a generic N -dimensional lattice system to a (N +1 )-dimensional holographic dual, with the emergent dimension representing scale. In previous works, this was achieved via the iterations of the simplest of all unitary mappings, the Haar mapping, which fails to preserve the form of most Hamiltonians. By taking advantage of the full generality of biorthogonal wavelets, our new generalized holographic mapping framework is able to preserve the form of a large class of lattice Hamiltonians. By explicitly separating features that are fundamentally associated with the physical system from those that are basis specific, we also obtain a clearer understanding of how the resultant bulk geometry arises. For instance, the number of nonvanishing moments of the high-pass wavelet filter is revealed to be proportional to the radius of the dual anti-de Sitter space geometry. We conclude by proposing modifications to the mapping for systems with generic Fermi pockets.
STELLAR: fast and exact local alignments
Directory of Open Access Journals (Sweden)
Weese David
2011-10-01
Full Text Available Abstract Background Large-scale comparison of genomic sequences requires reliable tools for the search of local alignments. Practical local aligners are in general fast, but heuristic, and hence sometimes miss significant matches. Results We present here the local pairwise aligner STELLAR that has full sensitivity for ε-alignments, i.e. guarantees to report all local alignments of a given minimal length and maximal error rate. The aligner is composed of two steps, filtering and verification. We apply the SWIFT algorithm for lossless filtering, and have developed a new verification strategy that we prove to be exact. Our results on simulated and real genomic data confirm and quantify the conjecture that heuristic tools like BLAST or BLAT miss a large percentage of significant local alignments. Conclusions STELLAR is very practical and fast on very long sequences which makes it a suitable new tool for finding local alignments between genomic sequences under the edit distance model. Binaries are freely available for Linux, Windows, and Mac OS X at http://www.seqan.de/projects/stellar. The source code is freely distributed with the SeqAn C++ library version 1.3 and later at http://www.seqan.de.
Exact renormalization group for gauge theories
International Nuclear Information System (INIS)
Balaban, T.; Imbrie, J.; Jaffe, A.
1984-01-01
Renormalization group ideas have been extremely important to progress in our understanding of gauge field theory. Particularly the idea of asymptotic freedom leads us to hope that nonabelian gauge theories exist in four dimensions and yet are capable of producing the physics we observe-quarks confined in meson and baryon states. For a thorough understanding of the ultraviolet behavior of gauge theories, we need to go beyond the approximation of the theory at some momentum scale by theories with one or a small number of coupling constants. In other words, we need a method of performing exact renormalization group transformations, keeping control of higher order effects, nonlocal effects, and large field effects that are usually ignored. Rigorous renormalization group methods have been described or proposed in the lectures of Gawedzki, Kupiainen, Mack, and Mitter. Earlier work of Glimm and Jaffe and Gallavotti et al. on the /phi/ model in three dimensions were quite important to later developments in this area. We present here a block spin procedure which works for gauge theories, at least in the superrenormalizable case. It should be enlightening for the reader to compare the various methods described in these proceedings-especially from the point of view of how each method is suited to the physics of the problem it is used to study
International Nuclear Information System (INIS)
Bogaty, J.; Clifft, B.E.; Zinkann, G.P.; Pardo, R.C.
1995-01-01
The ECR-PII injector beam line is operated at a fixed ion velocity. The platform high voltage is chosen so that all ions have a velocity of 0.0085c at the PII entrance. If a previous tune configuration for the linac is to be used, the beam arrival time must be matched to the previous tune as well. A nondestructive beam-phase pickup detector was developed and installed at the entrance to the PII linac. This device provides continuous phase and beam current information and allows quick optimization of the beam injected into PII. Bunches traverse a short tubular electrode thereby inducing displacement currents. These currents are brought outside the vacuum interface where a lumped inductance resonates electrode capacitance at one of the bunching harmonic frequencies. This configuration yields a basic sensitivity of a few hundred millivolts signal per microampere of beam current. Beam-induced radiofrequency signals are summed against an offset frequency generated by our master oscillator. The resulting kilohertz difference frequency conveys beam intensity and bunch phase information which is sent to separate processing channels. One channel utilizes a phase locked loop which stabilizes phase readings if beam is unstable. The other channel uses a linear full wave active rectifier circuit which converts kilohertz sine wave signal amplitude to a D.C. voltage representing beam current. A prototype set of electronics is now in use with the detector and we began to use the system in operation to set the arrival beam phase. A permanent version of the electronics system for the phase detector is now under construction. Additional nondestructive beam intensity and phase monitors at the open-quotes Boosterclose quotes and open-quotes ATLASclose quotes linac sections are planned as well as on some of the high-energy beam lines. Such a monitor will be particularly useful for FMA experiments where the primary beam hits one of the electric deflector plates
Coherent cancellation of geometric phase for the OH molecule in external fields
Bhattacharya, M.; Marin, S.; Kleinert, M.
2014-05-01
The OH molecule in its ground state presents a versatile platform for precision measurement and quantum information processing. These applications vitally depend on the accurate measurement of transition energies between the OH levels. Significant sources of systematic errors in these measurements are shifts based on the geometric phase arising from the magnetic and electric fields used for manipulating OH. In this article, we present these geometric phases for fields that vary harmonically in time, as in the Ramsey technique. Our calculation of the phases is exact within the description provided by our recent analytic solution of an effective Stark-Zeeman Hamiltonian for the OH ground state. This Hamiltonian has been shown to model experimental data accurately. We find that the OH geometric phases exhibit rich structure as a function of the field rotation rate. Remarkably, we find rotation rates where the geometric phase accumulated by a specific state is zero, or where the relative geometric phase between two states vanishes. We expect these findings to be of importance to precision experiments on OH involving time-varying fields. More specifically, our analysis quantitatively characterizes an important item in the error budget for precision spectroscopy of ground-state OH.
Research of z-axis geometric dose efficiency in multi-detector computed tomography
International Nuclear Information System (INIS)
Kim, You Hyun; Kim, Moon Chan
2006-01-01
With the recent prevalence of helical CT and multi-slice CT, which deliver higher radiation dose than conventional CT due to overbeaming effect in X-ray exposure and interpolation technique in image reconstruction. Although multi-detector and helical CT scanner provide a variety of opportunities for patient dose reduction, the potential risk for high radiation levels in CT examination can't be overemphasized in spite of acquiring more diagnostic information. So much more concerns is necessary about dose characteristics of CT scanner, especially dose efficient design as well as dose modulation software, because dose efficiency built into the scanner's design is probably the most important aspect of successful low dose clinical performance. This study was conducted to evaluate z-axis geometric dose efficiency in single detector CT and each level multi-detector CT, as well as to compare z-axis dose efficiency with change of technical scan parameters such as focal spot size of tube, beam collimation, detector combination, scan mode, pitch size, slice width and interval. The results obtained were as follows; 1. SDCT was most highest and 4 MDCT was most lowest in z-axis geometric dose efficiency among SDCT, 4, 8, 16, 64 slice MDCT made by GE manufacture. 2. Small focal spot was 0.67-13.62% higher than large focal spot in z-axis geometric dose efficiency at MDCT. 3. Large beam collimation was 3.13-51.52% higher than small beam collimation in z-axis geometric dose efficiency at MDCT. Z-axis geometric dose efficiency was same at 4 slice MDCT in all condition and 8 slice MDCT of large beam collimation with change of detector combination, but was changed irregularly at 8 slice MDCT of small beam collimation and 16 slice MDCT in all condition with change of detector combination. 5. There was no significant difference for z-axis geometric dose efficiency between conventional scan and helical scan, and with change of pitch factor, as well as change of slice width or interval for
High-performance geometric phase elements in silica glass
Directory of Open Access Journals (Sweden)
Rokas Drevinskas
2017-06-01
Full Text Available High-precision three-dimensional ultrafast laser direct nanostructuring of silica glass resulting in multi-layered space-variant dielectric metasurfaces embedded in volume is demonstrated. Continuous phase profiles of nearly any optical component are achieved solely by the means of geometric phase. Complex designs of half-wave retarders with 90% transmission at 532 nm and >95% transmission at >1 μm, including polarization gratings with efficiency nearing 90% and computer generated holograms with a phase gradient of ∼0.8π rad/μm, were fabricated. A vortex half-wave retarder generating a single beam optical vortex with a tunable orbital angular momentum of up to ±100ℏ is shown. The high damage threshold of silica elements enables the simultaneous optical manipulation of a large number of micro-objects using high-power laser beams. Thus, the continuous control of torque without altering the intensity distribution was implemented in optical trapping demonstration with a total of 5 W average power, which is otherwise impossible with alternate beam shaping devices. In principle, the direct-write technique can be extended to any transparent material that supports laser assisted nanostructuring and can be effectively exploited for the integration of printed optics into multi-functional optoelectronic systems.
Torsion sensing based on patterned piezoelectric beams
Cha, Youngsu; You, Hangil
2018-03-01
In this study, we investigated the sensing characteristics of piezoelectric beams under torsional loads. We used partially patterned piezoelectric beams to sense torsion. In particular, the piezoelectric patches are located symmetrically with respect to the line of the shear center of the beam. The patterned piezoelectric beam is modeled as a slender beam, and its electrical responses are obtained by piezoelectric electromechanical equations. To validate the modeling framework, experiments are performed using a setup that forces pure torsional deformation. Three different geometric configurations of the patterned piezoelectric layer are used for the experiments. The frequency and amplitude of the forced torsional load are systematically varied in order to study the behavior of the piezoelectric sensor. Experimental results demonstrate that two voltage outputs of the piezoelectric beam are approximately out of phase with identical amplitude. Moreover, the length of the piezoelectric layers has a significant influence on the sensing properties. Our theoretical predictions using the model support the experimental findings.
Laser Diode Beam Basics, Manipulations and Characterizations
Sun, Haiyin
2012-01-01
Many optical design technical books are available for many years which mainly deal with image optics design based on geometric optics and using sequential raytracing technique. Some books slightly touched laser beam manipulation optics design. On the other hand many books on laser diodes have been published that extensively deal with laser diode physics with little touching on laser diode beam manipulations and characterizations. There are some internet resources dealing with laser diode beams. However, these internet resources have not covered enough materials with enough details on laser diode beam manipulations and characterizations. A technical book concentrated on laser diode beam manipulations and characterizations can fit in to the open and provide useful information to laser diode users. Laser Diode Beam Basics, Manipulations and Characterizations is concentrated on the very practical side of the subject, it only discusses the basic physics and mathematics that are necessary for the readers in order...
Geometrical formulation of the conformal Ward identity
International Nuclear Information System (INIS)
Kachkachi, M.
2002-08-01
In this paper we use deep ideas in complex geometry that proved to be very powerful in unveiling the Polyakov measure on the moduli space of Riemann surfaces and lead to obtain the partition function of perturbative string theory for 2, 3, 4 loops. Indeed, a geometrical interpretation of the conformal Ward identity in two dimensional conformal field theory is proposed: the conformal anomaly is interpreted as a deformation of the complex structure of the basic Riemann surface. This point of view is in line with the modern trend of geometric quantizations that are based on deformations of classical structures. Then, we solve the conformal Ward identity by using this geometrical formalism. (author)
Initial singularity and pure geometric field theories
Wanas, M. I.; Kamal, Mona M.; Dabash, Tahia F.
2018-01-01
In the present article we use a modified version of the geodesic equation, together with a modified version of the Raychaudhuri equation, to study initial singularities. These modified equations are used to account for the effect of the spin-torsion interaction on the existence of initial singularities in cosmological models. Such models are the results of solutions of the field equations of a class of field theories termed pure geometric. The geometric structure used in this study is an absolute parallelism structure satisfying the cosmological principle. It is shown that the existence of initial singularities is subject to some mathematical (geometric) conditions. The scheme suggested for this study can be easily generalized.
SOME PROPERTIES OF GEOMETRIC DEA MODELS
Directory of Open Access Journals (Sweden)
Ozren Despić
2013-02-01
Full Text Available Some specific geometric data envelopment analysis (DEA models are well known to the researchers in DEA through so-called multiplicative or log-linear efficiency models. Valuable properties of these models were noted by several authors but the models still remain somewhat obscure and rarely used in practice. The purpose of this paper is to show from a mathematical perspective where the geometric DEA fits in relation to the classical DEA, and to provide a brief overview of some benefits in using geometric DEA in practice of decision making and/or efficiency measurement.
Refined geometric transition and qq-characters
Kimura, Taro; Mori, Hironori; Sugimoto, Yuji
2018-01-01
We show the refinement of the prescription for the geometric transition in the refined topological string theory and, as its application, discuss a possibility to describe qq-characters from the string theory point of view. Though the suggested way to operate the refined geometric transition has passed through several checks, it is additionally found in this paper that the presence of the preferred direction brings a nontrivial effect. We provide the modified formula involving this point. We then apply our prescription of the refined geometric transition to proposing the stringy description of doubly quantized Seiberg-Witten curves called qq-characters in certain cases.
A Geometrical View of Higgs Effective Theory
CERN. Geneva
2016-01-01
A geometric formulation of Higgs Effective Field Theory (HEFT) is presented. Experimental observables are given in terms of geometric invariants of the scalar sigma model sector such as the curvature of the scalar field manifold M. We show how the curvature can be measured experimentally via Higgs cross-sections, W_L scattering, and the S parameter. The one-loop action of HEFT is given in terms of geometric invariants of M. The distinction between the Standard Model (SM) and HEFT is whether M is flat or curved, with the curvature a signal of the scale of new physics.
Geometrical analysis of the interacting boson model
International Nuclear Information System (INIS)
Dieperink, A.E.L.
1983-01-01
The Interacting Boson Model is considered, in relation with geometrical models and the application of mean field techniques to algebraic models, in three lectures. In the first, several methods are reviewed to establish a connection between the algebraic formulation of collective nuclear properties in terms of the group SU(6) and the geometric approach. In the second lecture the geometric interpretation of new degrees of freedom that arise in the neutron-proton IBA is discussed, and in the third one some further applications of algebraic techniques to the calculation of static and dynamic collective properties are presented. (U.K.)
Lectures on geometrical properties of nuclei
International Nuclear Information System (INIS)
Myers, W.D.
1975-11-01
Material concerning the geometrical properties of nuclei is drawn from a number of different sources. The leptodermous nature of nuclear density distributions and potential wells is used to draw together the various geometrical properties of these systems and to provide a unified means for their description. Extensive use is made of expansions of radial properties in terms of the surface diffuseness. A strong case is made for the use of convolution as a geometrical ansatz for generating diffuse surface distributions because of the number of simplifications that arise which are of practical importance. 7 figures
Stock price prediction using geometric Brownian motion
Farida Agustini, W.; Restu Affianti, Ika; Putri, Endah RM
2018-03-01
Geometric Brownian motion is a mathematical model for predicting the future price of stock. The phase that done before stock price prediction is determine stock expected price formulation and determine the confidence level of 95%. On stock price prediction using geometric Brownian Motion model, the algorithm starts from calculating the value of return, followed by estimating value of volatility and drift, obtain the stock price forecast, calculating the forecast MAPE, calculating the stock expected price and calculating the confidence level of 95%. Based on the research, the output analysis shows that geometric Brownian motion model is the prediction technique with high rate of accuracy. It is proven with forecast MAPE value ≤ 20%.
Exact sampling hardness of Ising spin models
Fefferman, B.; Foss-Feig, M.; Gorshkov, A. V.
2017-09-01
We study the complexity of classically sampling from the output distribution of an Ising spin model, which can be implemented naturally in a variety of atomic, molecular, and optical systems. In particular, we construct a specific example of an Ising Hamiltonian that, after time evolution starting from a trivial initial state, produces a particular output configuration with probability very nearly proportional to the square of the permanent of a matrix with arbitrary integer entries. In a similar spirit to boson sampling, the ability to sample classically from the probability distribution induced by time evolution under this Hamiltonian would imply unlikely complexity theoretic consequences, suggesting that the dynamics of such a spin model cannot be efficiently simulated with a classical computer. Physical Ising spin systems capable of achieving problem-size instances (i.e., qubit numbers) large enough so that classical sampling of the output distribution is classically difficult in practice may be achievable in the near future. Unlike boson sampling, our current results only imply hardness of exact classical sampling, leaving open the important question of whether a much stronger approximate-sampling hardness result holds in this context. The latter is most likely necessary to enable a convincing experimental demonstration of quantum supremacy. As referenced in a recent paper [A. Bouland, L. Mancinska, and X. Zhang, in Proceedings of the 31st Conference on Computational Complexity (CCC 2016), Leibniz International Proceedings in Informatics (Schloss Dagstuhl-Leibniz-Zentrum für Informatik, Dagstuhl, 2016)], our result completes the sampling hardness classification of two-qubit commuting Hamiltonians.
Schmidt, F; McIntosh, E
2002-01-01
This is a description of the basic ideas behind the ``Polymorphic Tracking Code'' or PTC. PTC is truly a ``kick code'' or symplectic integrator in the tradition of TRACYII, SixTrack, and TEAPOT. However it separates correctly the mathematical atlas of charts and the magnets at a structural level by implementing a ``restricted fibre bundle.'' The resulting structures allow backward propagation and recirculation, something not possible in standard tracking codes. Also PTC is polymorphic in handling real (single, double and even quadruple precision) and Taylor series. Therefore it has all the tools associated to the TPSA packages: Lie methods, Normal Forms, Cosy-Infinity capabilities, beam envelopes for radiation, etc., as well as parameter dependence on-the-fly. However PTC is an integrator, and as such, one must, generally, adhere to the Talman ``exactness'' view of modelling. Incidentally, it supports exact sector and rectangular bends as well. Of course, one can certainly bypass its integrator and the user i...
Boundary controllability for a nonlinear beam equation
Directory of Open Access Journals (Sweden)
Xiao-Min Cao
2015-09-01
Full Text Available This article concerns a nonlinear system modeling the bending vibrations of a nonlinear beam of length $L>0$. First, we derive the existence of long time solutions near an equilibrium. Then we prove that the nonlinear beam is locally exact controllable around the equilibrium in $H^4(0,L$ and with control functions in $H^2(0,T$. The approach we used are open mapping theorem, local controllability established by linearization, and the induction.
Effect of geometric imperfections on the ultimate moment capacity of cold-formed sigma-shape se
Directory of Open Access Journals (Sweden)
Bassem L. Gendy
2017-08-01
Full Text Available In recent years, cold formed steel sections are used more and more as primary framing components and as a secondary structural system. They are used as purlins and side rails or floor joist, and after that in the building envelops. Beams are not perfectly straight and are usually associated with geometric imperfections. Initial geometric imperfections can significantly influence the stability response of cold-formed steel members. This paper reports a numerical investigation concerning the effect of these imperfections on the behavior of the simply supported beams subjected to a uniform bending moment. The beam profile is cold formed sigma sections. Group of beams with different overall member slenderness ratios were studied. Several approaches have been utilized to model the geometric imperfections. First, the elastic buckling modes were considered as the imperfect beam shape. In this approach, the elastic buckling analysis was done first to get the elastic buckling modes. In the second approach, the imperfections were considered by assuming the beam bent in a half sine wave along its length. Finally, combination of these two approaches was considered. Results reveal that, the ultimate bending moments of beams with short and intermediate overall slenderness ratios are sensitive to the imperfect shape that comprise compression flange local buckling.
Electron beams, lenses, and optics. Volume 2
International Nuclear Information System (INIS)
El-Kareh, A.B.; El-Kareh, J.C.J.
1970-01-01
This volume presents a systematic coverage of aberrations. It analyzes the geometrical aberrations and treats the spherical and chromatic aberrations in great detail. The coefficients of spherical and chromatic aberration have been computed for a series of electrostatic and magnetic lenses and are listed in table form. The book also covers space charge and its effect on highly focused electron beams
MIRKO - An interactive program for beam lines and synchrotrons
International Nuclear Information System (INIS)
Franczak, B.
1984-01-01
The ion-optical design of beam lines and synchrotrons is usually not done by a single run of one program. It takes many iterations of calculation, examination of results, and modification of input data. In most cases the first order design has to be followed by the investigation of higher order effects, i.e. chromatic and geometrical aberrations or resonance phenomena. The interactive computer program MIRKO is operated from a terminal and has a command structure, which enables the user to edit data, perform calculations, and to obtain alpha or graphics output on the terminal in any desired sequence. With graphics one can recognize the properties of an optical system much faster than with numbers only. Thus modifications of input data depending on the results of calculations can be made easily without stopping and restarting the program. Higher order effects can sometimes influence the first order design. Therefore, particle tracking capability was included in MIRKO as well as the calculation of stop band widths for synchrotrons. Consequently a large variety of phenomena can be studied with one program in one session based upon exactly the same data for the optical system and the possibility of fast switching between the different features
International Nuclear Information System (INIS)
Bi Lei; Yang Ping; Kattawar, George W.; Hu Yongxiang; Baum, Bryan A.
2011-01-01
A new physical-geometric optics hybrid (PGOH) method is developed to compute the scattering and absorption properties of ice particles. This method is suitable for studying the optical properties of ice particles with arbitrary orientations, complex refractive indices (i.e., particles with significant absorption), and size parameters (proportional to the ratio of particle size to incident wavelength) larger than ∼20, and includes consideration of the edge effects necessary for accurate determination of the extinction and absorption efficiencies. Light beams with polygon-shaped cross sections propagate within a particle and are traced by using a beam-splitting technique. The electric field associated with a beam is calculated using a beam-tracing process in which the amplitude and phase variations over the wavefront of the localized wave associated with the beam are considered analytically. The geometric-optics near field for each ray is obtained, and the single-scattering properties of particles are calculated from electromagnetic integral equations. The present method does not assume additional physical simplifications and approximations, except for geometric optics principles, and may be regarded as a 'benchmark' within the framework of the geometric optics approach. The computational time is on the order of seconds for a single-orientation simulation and is essentially independent of the size parameter. The single-scattering properties of oriented hexagonal ice particles (ice plates and hexagons) are presented. The numerical results are compared with those computed from the discrete-dipole-approximation (DDA) method.
Time measurement - technical importance of most exact clocks
International Nuclear Information System (INIS)
Goebel, E.O.; Riehle, F.
2004-01-01
The exactness of the best atomic clocks currently shows a temporal variation of 1 second in 30 million years. This means that we have reached the point of the most exact frequency and time measurement ever. In the past, there was a trend towards increasing the exactness in an increasingly fast sequence. Will this trend continue? And who will profit from it? This article is meant to give answers to these questions. This is done by presenting first the level reached currently with the best atomic clocks and describing the research activities running worldwide with the aim of achieving even more exact clocks. In the second part, we present examples of various areas of technical subjects and research in which the most exact clocks are being applied presently and even more exact ones will be needed in the future [de
Transition curves for highway geometric design
Kobryń, Andrzej
2017-01-01
This book provides concise descriptions of the various solutions of transition curves, which can be used in geometric design of roads and highways. It presents mathematical methods and curvature functions for defining transition curves. .
Geometrical scaling of jet fragmentation photons
Energy Technology Data Exchange (ETDEWEB)
Hattori, Koichi, E-mail: koichi.hattori@riken.jp [RIKEN BNL Research Center, Brookhaven National Laboratory, Upton NY 11973 (United States); Theoretical Research Division, Nishina Center, RIKEN, Wako, Saitama 351-0198 (Japan); McLerran, Larry, E-mail: mclerran@bnl.gov [RIKEN BNL Research Center, Brookhaven National Laboratory, Upton NY 11973 (United States); Physics Dept., Bdg. 510A, Brookhaven National Laboratory, Upton, NY-11973 (United States); Physics Dept., China Central Normal University, Wuhan (China); Schenke, Björn, E-mail: bschenke@bnl.gov [Physics Dept., Bdg. 510A, Brookhaven National Laboratory, Upton, NY-11973 (United States)
2016-12-15
We discuss jet fragmentation photons in ultrarelativistic heavy-ion collisions. We argue that, if the jet distribution satisfies geometrical scaling and an anisotropic spectrum, these properties are transferred to photons during the jet fragmentation.
Geometric U-folds in four dimensions
Lazaroiu, C. I.; Shahbazi, C. S.
2018-01-01
We describe a general construction of geometric U-folds compatible with a non-trivial extension of the global formulation of four-dimensional extended supergravity on a differentiable spin manifold. The topology of geometric U-folds depends on certain flat fiber bundles which encode how supergravity fields are globally glued together. We show that smooth non-trivial U-folds of this type can exist only in theories where both the scalar and space-time manifolds have non-trivial fundamental group and in addition the scalar map of the solution is homotopically non-trivial. Consistency with string theory requires smooth geometric U-folds to be glued using subgroups of the effective discrete U-duality group, implying that the fundamental group of the scalar manifold of such solutions must be a subgroup of the latter. We construct simple examples of geometric U-folds in a generalization of the axion-dilaton model of \
5th Dagstuhl Seminar on Geometric Modelling
Brunnett, Guido; Farin, Gerald; Goldman, Ron
2004-01-01
In 19 articles presented by leading experts in the field of geometric modelling the state-of-the-art on representing, modeling, and analyzing curves, surfaces as well as other 3-dimensional geometry is given. The range of applications include CAD/CAM-systems, computer graphics, scientific visualization, virtual reality, simulation and medical imaging. The content of this book is based on selected lectures given at a workshop held at IBFI Schloss Dagstuhl, Germany. Topics treated are: – curve and surface modelling – non-manifold modelling in CAD – multiresolution analysis of complex geometric models – surface reconstruction – variational design – computational geometry of curves and surfaces – 3D meshing – geometric modelling for scientific visualization – geometric models for biomedical applications
The perception of geometrical structure from congruence
Lappin, Joseph S.; Wason, Thomas D.
1989-01-01
The principle function of vision is to measure the environment. As demonstrated by the coordination of motor actions with the positions and trajectories of moving objects in cluttered environments and by rapid recognition of solid objects in varying contexts from changing perspectives, vision provides real-time information about the geometrical structure and location of environmental objects and events. The geometric information provided by 2-D spatial displays is examined. It is proposed that the geometry of this information is best understood not within the traditional framework of perspective trigonometry, but in terms of the structure of qualitative relations defined by congruences among intrinsic geometric relations in images of surfaces. The basic concepts of this geometrical theory are outlined.
Mechanisms of geometrical seismic attenuation
Directory of Open Access Journals (Sweden)
Igor B. Morozov
2011-07-01
Full Text Available In several recent reports, we have explained the frequency dependence of the apparent seismic quality-factor (Q observed in many studies according to the effects of geometrical attenuation, which was defined as the zero-frequency limit of the temporal attenuation coefficient. In particular, geometrical attenuation was found to be positive for most waves traveling within the lithosphere. Here, we present three theoretical models that illustrate the origin of this geometrical attenuation, and we investigate the causes of its preferential positive values. In addition, we discuss the physical basis and limitations of both the conventional and new attenuation models. For waves in media with slowly varying properties, geometrical attenuation is caused by variations in the wavefront curvature, which can be both positive (for defocusing and negative (for focusing. In media with velocity/density contrasts, incoherent reflectivity leads to geometrical-attenuation coefficients which are proportional to the mean squared reflectivity and are always positive. For «coherent» reflectivity, the geometrical attenuation is approximately zero, and the attenuation process can be described according to the concept of «scattering Q». However, the true meaning of this parameter is in describing the mean reflectivity within the medium, and not that of the traditional resonator quality factor known in mechanics. The general conclusion from these models is that non-zero and often positive levels of geometrical attenuation are common in realistic, heterogeneous media, both observationally and theoretically. When transformed into the conventional Q-factor form, this positive geometrical attenuation leads to Q values that quickly increase with frequency. These predictions show that the positive frequency-dependent Q observed in many datasets might represent artifacts of the transformations of the attenuation coefficients into Q.
Optimization of the geometrical stability in square ring laser gyroscopes
International Nuclear Information System (INIS)
Santagata, R; Beghi, A; Cuccato, D; Belfi, J; Beverini, N; Virgilio, A Di; Ortolan, A; Porzio, A; Solimeno, S
2015-01-01
Ultra-sensitive ring laser gyroscopes are regarded as potential detectors of the general relativistic frame-dragging effect due to the rotation of the Earth. Our project for this goal is called GINGER (gyroscopes in general relativity), and consists of a ground-based triaxial array of ring lasers aimed at measuring the rotation rate of the Earth with an accuracy of 10 −14 rad s −1 . Such an ambitious goal is now within reach, as large-area ring lasers are very close to the required sensitivity and stability. However, demanding constraints on the geometrical stability of the optical path of the laser inside the ring cavity are required. Thus, we have begun a detailed study of the geometry of an optical cavity in order to find a control strategy for its geometry that could meet the specifications of the GINGER project. As the cavity perimeter has a stationary point for the square configuration, we identify a set of transformations on the mirror positions that allows us to adjust the laser beam steering to the shape of a square. We show that the geometrical stability of a square cavity strongly increases by implementing a suitable system to measure the mirror distances, and that the geometry stabilization can be achieved by measuring the absolute lengths of the two diagonals and the perimeter of the ring. (paper)
Optical tractor Bessel polarized beams
Mitri, F. G.; Li, R. X.; Guo, L. X.; Ding, C. Y.
2017-01-01
Axial and transverse radiation force cross-sections of optical tractor Bessel polarized beams are theoretically investigated for a dielectric sphere with particular emphasis on the beam topological charge (or order), half-cone angle and polarization. The angular spectrum decomposition method (ASDM) is used to derive the non-paraxial electromagnetic (EM) field components of the Bessel beams. The multipole expansion method using vector spherical harmonics is utilized and appropriate beam-shape coefficients are derived in order to compute the radiation force cross-sections. The analysis has no limitation to a particular range of frequencies such that the Rayleigh, Mie or geometrical optics regimes can all be considered effectively using the present rigorous formalism. The focus of this investigation is to identify some of the tractor beam conditions so as to achieve retrograde motion of a dielectric sphere located arbitrarily in space. Numerical computations for the axial and transverse radiation force cross-sections are presented for linear, right-circular, radial, azimuthal and mixed polarizations of the individual plane waves forming the Bessel beams of zeroth- and first-order (with positive or negative helicity), respectively. As the sphere shifts off the beam's axis, the axial pulling (tractor) force is weakened. Moreover, the transverse radiation force cross-section field changes with the sphere's size factor ka (where k is the wavenumber and a is the sphere radius). Both stable and unstable equilibrium regions around the beam's axis are found, depending on the choice of ka and the half-cone angle α0. These results are particularly important in the development of emergent technologies for the photophoretic assembly of optically-engineered (meta)materials with designed properties using optical tractor (vortex) beams, particle manipulation, levitation and positioning, and other applications.
A Refined Zigzag Beam Theory for Composite and Sandwich Beams
Tessler, Alexander; Sciuva, Marco Di; Gherlone, Marco
2009-01-01
A new refined theory for laminated composite and sandwich beams that contains the kinematics of the Timoshenko Beam Theory as a proper baseline subset is presented. This variationally consistent theory is derived from the virtual work principle and employs a novel piecewise linear zigzag function that provides a more realistic representation of the deformation states of transverse-shear flexible beams than other similar theories. This new zigzag function is unique in that it vanishes at the top and bottom bounding surfaces of a beam. The formulation does not enforce continuity of the transverse shear stress across the beam s cross-section, yet is robust. Two major shortcomings that are inherent in the previous zigzag theories, shear-force inconsistency and difficulties in simulating clamped boundary conditions, and that have greatly limited the utility of these previous theories are discussed in detail. An approach that has successfully resolved these shortcomings is presented herein. Exact solutions for simply supported and cantilevered beams subjected to static loads are derived and the improved modelling capability of the new zigzag beam theory is demonstrated. In particular, extensive results for thick beams with highly heterogeneous material lay-ups are discussed and compared with corresponding results obtained from elasticity solutions, two other zigzag theories, and high-fidelity finite element analyses. Comparisons with the baseline Timoshenko Beam Theory are also presented. The comparisons clearly show the improved accuracy of the new, refined zigzag theory presented herein over similar existing theories. This new theory can be readily extended to plate and shell structures, and should be useful for obtaining relatively low-cost, accurate estimates of structural response needed to design an important class of high-performance aerospace structures.
CSIR Research Space (South Africa)
Ngcobo, S
2011-11-01
Full Text Available The transformation of a Gaussian beam (GB) into a symmetrical higher order TEMp0 Laguerre Gaussian beam (LGB) intensity distribution of which is further rectified and transformed into a Gaussian intensity distribution in the plane of a converging...
Jiang, Runqing
Intensity-modulated radiation therapy (IMRT) uses non-uniform beam intensities within a radiation field to provide patient-specific dose shaping, resulting in a dose distribution that conforms tightly to the planning target volume (PTV). Unavoidable geometric uncertainty arising from patient repositioning and internal organ motion can lead to lower conformality index (CI) during treatment delivery, a decrease in tumor control probability (TCP) and an increase in normal tissue complication probability (NTCP). The CI of the IMRT plan depends heavily on steep dose gradients between the PTV and organ at risk (OAR). Geometric uncertainties reduce the planned dose gradients and result in a less steep or "blurred" dose gradient. The blurred dose gradients can be maximized by constraining the dose objective function in the static IMRT plan or by reducing geometric uncertainty during treatment with corrective verification imaging. Internal organ motion and setup error were evaluated simultaneously for 118 individual patients with implanted fiducials and MV electronic portal imaging (EPI). A Gaussian probability density function (PDF) is reasonable for modeling geometric uncertainties as indicated by the 118 patients group. The Gaussian PDF is patient specific and group standard deviation (SD) should not be used for accurate treatment planning for individual patients. In addition, individual SD should not be determined or predicted from small imaging samples because of random nature of the fluctuations. Frequent verification imaging should be employed in situations where geometric uncertainties are expected. Cumulative PDF data can be used for re-planning to assess accuracy of delivered dose. Group data is useful for determining worst case discrepancy between planned and delivered dose. The margins for the PTV should ideally represent true geometric uncertainties. The measured geometric uncertainties were used in this thesis to assess PTV coverage, dose to OAR, equivalent
Towards an exact relativistic theory of Earth's geoid undulation
International Nuclear Information System (INIS)
Kopeikin, Sergei M.; Mazurova, Elena M.; Karpik, Alexander P.
2015-01-01
The present paper extends the Newtonian concept of the geoid in classic geodesy towards the realm of general relativity by utilizing the covariant geometric methods of the perturbation theory of curved manifolds. It yields a covariant definition of the anomalous (disturbing) gravity potential and formulates differential equation for it in the form of a covariant Laplace equation. The paper also derives the Bruns equation for calculation of geoid's height with full account for relativistic effects beyond the Newtonian approximation. A brief discussion of the relativistic Bruns formula is provided. - Highlights: • We apply general relativity to define the exact concept of relativistic geoid. • We derive relativistic equation of geoid and the reference level surface. • We employ the manifold perturbation theory to discuss geoid's undulation
Towards an exact relativistic theory of Earth's geoid undulation
Energy Technology Data Exchange (ETDEWEB)
Kopeikin, Sergei M., E-mail: kopeikins@missouri.edu [Department of Physics & Astronomy, University of Missouri, Columbia, MO 65211 (United States); Siberian State Geodetic Academy, 10 Plakhotny St., Novosibirsk 630108 (Russian Federation); Mazurova, Elena M., E-mail: e_mazurova@mail.ru [Moscow State University of Geodesy and Cartography, 4 Gorokhovsky Alley, Moscow 105064 (Russian Federation); Siberian State Geodetic Academy, 10 Plakhotny St., Novosibirsk 630108 (Russian Federation); Karpik, Alexander P., E-mail: rector@ssga.ru [Siberian State Geodetic Academy, 10 Plakhotny St., Novosibirsk 630108 (Russian Federation)
2015-08-14
The present paper extends the Newtonian concept of the geoid in classic geodesy towards the realm of general relativity by utilizing the covariant geometric methods of the perturbation theory of curved manifolds. It yields a covariant definition of the anomalous (disturbing) gravity potential and formulates differential equation for it in the form of a covariant Laplace equation. The paper also derives the Bruns equation for calculation of geoid's height with full account for relativistic effects beyond the Newtonian approximation. A brief discussion of the relativistic Bruns formula is provided. - Highlights: • We apply general relativity to define the exact concept of relativistic geoid. • We derive relativistic equation of geoid and the reference level surface. • We employ the manifold perturbation theory to discuss geoid's undulation.
Goto, Shin-itiro; Umeno, Ken
2018-03-01
Maps on a parameter space for expressing distribution functions are exactly derived from the Perron-Frobenius equations for a generalized Boole transform family. Here the generalized Boole transform family is a one-parameter family of maps, where it is defined on a subset of the real line and its probability distribution function is the Cauchy distribution with some parameters. With this reduction, some relations between the statistical picture and the orbital one are shown. From the viewpoint of information geometry, the parameter space can be identified with a statistical manifold, and then it is shown that the derived maps can be characterized. Also, with an induced symplectic structure from a statistical structure, symplectic and information geometric aspects of the derived maps are discussed.
Neutron beam tomography software
International Nuclear Information System (INIS)
Newbery, A.C.R.
1988-05-01
When a sample is traversed by a neutron beam, inhomogeneities in the sample will cause deflections, and the deflections will permit conclusions to be drawn concerning the location and size of the inhomogeneities. The associated computation is similar to problems in tomography, analogous to X-ray tomography though significantly different in detail. We do not have any point-sample information, but only mean values over short line segments. Since each mean value is derived from a separate neutron counter, the quantity of available data has to be modest; also, since each datum is an integral, its geometric precision is inferior to that of X-ray data. Our software is designed to cope with these difficulties. (orig.) [de
Tunable orbital angular momentum mode filter based on optical geometric transformation.
Huang, Hao; Ren, Yongxiong; Xie, Guodong; Yan, Yan; Yue, Yang; Ahmed, Nisar; Lavery, Martin P J; Padgett, Miles J; Dolinar, Sam; Tur, Moshe; Willner, Alan E
2014-03-15
We present a tunable mode filter for spatially multiplexed laser beams carrying orbital angular momentum (OAM). The filter comprises an optical geometric transformation-based OAM mode sorter and a spatial light modulator (SLM). The programmable SLM can selectively control the passing/blocking of each input OAM beam. We experimentally demonstrate tunable filtering of one or multiple OAM modes from four multiplexed input OAM modes with vortex charge of ℓ=-9, -4, +4, and +9. The measured output power suppression ratio of the propagated modes to the blocked modes exceeds 14.5 dB.
Characteristics of possible beam losses in superconducting cyclotron
International Nuclear Information System (INIS)
Pradhan, J.; Paul, Santanu; Debnath, Jayanta; Dutta, Atanu; Bhunia, Uttam; Naser, Md. Zamal Abdul; Singh, Vinay; Agrawal, Ankur; Dey, Malay Kanti
2015-01-01
In a compact superconducting cyclotron large coherent oscillation and off-centering of the beam may cause large amount of beam loss. The off-centered beam may hit the beam chamber wall prohibiting extraction of the beam. Or it may hit the RF liner surfaces due to vertical blow-up across various resonances during acceleration. The vertical shift of beam caused by the mis-alignment gradually moves the beam out of geometrical median plane eventually leading to internal beam losses. The loss of isochronisms results the reduction of beam intensity depending on the particle phase history. Small field perturbations generated by trim coils have been used to identify the beam loss mechanisms in the superconducting cyclotron at out centre. Besides, the beam loss due to interaction of accelerating ions with residual gases is also discussed. The beam profile obtained from differential and three finger probes gives a clear insight of the loss-mechanism. The paper describes different beam losses observed in the cyclotron with corresponding beam profiles under different field perturbations, Special emphasis is given on characteristics features of beam-current profile to identify the cause of beam loss. (author)
Collimator for the SPS extracted beam
CERN PhotoLab
1976-01-01
This is a water cooled copper collimator (TCSA) which has exactly the shape of the cross section of the downstream magnetic beam splitter. Parts of the blown up primary proton beam pass above/below and left through this collimator. A small part of the protons is absorbed in the thin copper wedges. In this way the downstream magnetic splitter of the same cross section receives already a beam where its magnetic wedges are no longer hit by protons. The upstream, water cooled collimator, more resistant to protons, has cast a 'shadow' onto the downstream magnetic splitter, less resistant to protons. Gualtero Del Torre stands on the left.
Linear orbit parameters for the exact equations of motion
International Nuclear Information System (INIS)
Parzen, G.
1995-01-01
This paper defines the beta function and other linear orbit parameters using the exact equations of motion. The β, α and ψ functions are redefined using the exact equations. Expressions are found for the transfer matrix and the emittance. The differential equations for η = x/β 1/2 is found. New relationships between α, β, ψ and ν are derived
Exact solution for the generalized Telegraph Fisher's equation
International Nuclear Information System (INIS)
Abdusalam, H.A.; Fahmy, E.S.
2009-01-01
In this paper, we applied the factorization scheme for the generalized Telegraph Fisher's equation and an exact particular solution has been found. The exact particular solution for the generalized Fisher's equation was obtained as a particular case of the generalized Telegraph Fisher's equation and the two-parameter solution can be obtained when n=2.
Exact solutions of some nonlinear partial differential equations using ...
Indian Academy of Sciences (India)
The functional variable method is a powerful solution method for obtaining exact solutions of some nonlinear partial differential equations. In this paper, the functional variable method is used to establish exact solutions of the generalized forms of Klein–Gordon equation, the (2 + 1)-dimensional Camassa–Holm ...
Exact Finite Differences. The Derivative on Non Uniformly Spaced Partitions
Directory of Open Access Journals (Sweden)
Armando Martínez-Pérez
2017-10-01
Full Text Available We define a finite-differences derivative operation, on a non uniformly spaced partition, which has the exponential function as an exact eigenvector. We discuss some properties of this operator and we propose a definition for the components of a finite-differences momentum operator. This allows us to perform exact discrete calculations.
Exact Cover Problem in Milton Babbitt's All-partition Array
DEFF Research Database (Denmark)
Bemman, Brian; Meredith, David
2015-01-01
One aspect of analyzing Milton Babbitt’s (1916–2011) all- partition arrays requires finding a sequence of distinct, non-overlapping aggregate regions that completely and exactly covers an irregular matrix of pitch class integers. This is an example of the so-called exact cover problem. Given a set...
New exact solutions of the Dirac equation. 11
International Nuclear Information System (INIS)
Bagrov, V.G.; Noskov, M.D.
1984-01-01
Investigations into determining new exact solutions of relativistic wave equations started in another paper were continued. Exact solutions of the Dirac, Klein-Gordon equations and classical relativistic equations of motion in four new types of external electromagnetic fields were found
New exact travelling wave solutions for the Ostrovsky equation
International Nuclear Information System (INIS)
Kangalgil, Figen; Ayaz, Fatma
2008-01-01
In this Letter, auxiliary equation method is proposed for constructing more general exact solutions of nonlinear partial differential equation with the aid of symbolic computation. In order to illustrate the validity and the advantages of the method we choose the Ostrovsky equation. As a result, many new and more general exact solutions have been obtained for the equation
Energy vs. density on paths toward exact density functionals
DEFF Research Database (Denmark)
Kepp, Kasper Planeta
2018-01-01
Recently, the progression toward more exact density functional theory has been questioned, implying a need for more formal ways to systematically measure progress, i.e. a “path”. Here I use the Hohenberg-Kohn theorems and the definition of normality by Burke et al. to define a path toward exactness...