Geometrical E-beam proximity correction for raster scan systems

Science.gov (United States)

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.

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.

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)

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...

Geometrical determinations of IMRT photon pencil-beam path in radiotherapy wedges and limit divergence angle with the Anisotropic Analytic Algorithm (AAA

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

Geometrically Nonlinear Static Analysis of Edge Cracked Timoshenko Beams Composed of Functionally Graded Material

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.

An improved exact inversion formula for solenoidal fields in cone beam vector tomography

Science.gov (United States)

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.

Stabilization of exact nonlinear Timoshenko beams in space by boundary feedback

Science.gov (United States)

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.

Exploring the relationship between structurally defined geometrical parameters of reinforced concrete beams and the thermal comfort on indoor environment

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...

Exact analytical solution of shear-induced flexural vibration of functionally graded piezoelectric beam

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.

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

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

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

Systematic error in the precision measurement of the mean wavelength of a nearly monochromatic neutron beam due to geometric errors

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.

Geometrical-optics approximation of forward scattering by coated particles.

Science.gov (United States)

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.

Geometric approximation algorithms

CERN Document Server

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.

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....

Quasistationary model of high-current relativistic electron beam. 1. Exact solution of Poisson equations

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

Geometric beam coupling impedance of LHC secondary collimators

Science.gov (United States)

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.

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.

Extension of geometrical-optics approximation to on-axis Gaussian beam scattering. I. By a spherical particle.

Science.gov (United States)

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.

A geometric method of constructing exact solutions in modified f(R,T)-gravity with Yang-Mills and Higgs interactions

CERN Document Server

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.

Influence of ion beam and geometrical parameters on properties of Si thin films grown by Ar ion beam sputtering

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.

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

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

Use of off-axis injection as an alternative to geometrically merging beams in an energy-recovering linac

Science.gov (United States)

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.

Lie symmetry analysis and reduction for exact solution of (2+1)-dimensional Bogoyavlensky-Konopelchenko equation by geometric approach

Science.gov (United States)

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.

Exact fan-beam image reconstruction algorithm for truncated projection data acquired from an asymmetric half-size detector

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

Geometric nonlinear effects on the planar dynamics of a pivoted flexible beam encountering a point-surface impact

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

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.

Laser Induced Breakdown Spectroscopy Based on Single Beam Splitting and Geometric Configuration for Effective Signal Enhancement

Science.gov (United States)

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

Geometrical correction of the e-beam proximity effect for raster scan systems

Science.gov (United States)

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.

HAWC2 and BeamDyn: Comparison Between Beam Structural Models for Aero-Servo-Elastic Frameworks: Preprint

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.

Exact solutions in three-dimensional gravity

CERN Document Server

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...

A theoretically exact reconstruction algorithm for helical cone-beam differential phase-contrast computed tomography

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)

Exact free vibration of multi-step Timoshenko beam system with several attachments

Science.gov (United States)

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.

A Timoshenko Piezoelectric Beam Finite Element with Consistent Performance Irrespective of Geometric and Material Configurations

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.

The Dynamic Response of an Euler-Bernoulli Beam on an Elastic Foundation by Finite Element Analysis using the Exact Stiffness Matrix

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.

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

Nonlinear focal shift beyond the geometrical focus in moderately focused acoustic beams.

Science.gov (United States)

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.

Nonlinear model of a rotating hub-beams structure: Equations of motion

Science.gov (United States)

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.

A geometrically exact formulation for three-dimensional numerical simulation of the umbilical cable in a deep-sea ROV system

Science.gov (United States)

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.

EFFECTS OF X-RAY BEAM ANGLE AND GEOMETRIC DISTORTION ON WIDTH OF EQUINE THORACOLUMBAR INTERSPINOUS SPACES USING RADIOGRAPHY AND COMPUTED TOMOGRAPHY

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...

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.

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

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

Research on the effects of geometrical and material uncertainties on the band gap of the undulated beam

Science.gov (United States)

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.

Beam heat load due to geometrical and resistive wall impedance in COLDDIAG

Science.gov (United States)

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.

Extension of non-linear beam models with deformable cross sections

Science.gov (United States)

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.

Asymptotically and exactly energy balanced augmented flux-ADER schemes with application to hyperbolic conservation laws with geometric source terms

Science.gov (United States)

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.

Modeling of the dynamics of GBB1005 Ball & Beam Educational Control System as a controlled mechanical system with a redundant coordinate

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.

Exact and variational calculations of eigenmodes for three-dimensional free electron laser interaction with a warm electron beam

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.

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.

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.

Antiferromagnetic geometric frustration under the influence of the next-nearest-neighbor interaction. An exactly solvable model

Science.gov (United States)

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.

Computational Contact Mechanics Geometrically Exact Theory for Arbitrary Shaped Bodies

CERN Document Server

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...

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.

Direction-dependent waist-shift-difference of Gaussian beam in a multiple-pass zigzag slab amplifier and geometrical optics compensation method.

Science.gov (United States)

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.

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

Exact solutions for the static bending of Euler-Bernoulli beams using Eringen’s two-phase local/nonlocal model

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.

Exact solutions for the static bending of Euler-Bernoulli beams using Eringen’s two-phase local/nonlocal model

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.

Variations of dose distribution in high energy electron beams as a function of geometrical parameters of irradiation. Application to computer calculation

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

Angularly symmetric splitting of a light beam upon reflection and refraction at an air-dielectric plane boundary.

Science.gov (United States)

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.

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

Application of complex geometrical optics to determination of thermal, transport, and optical parameters of thin films by the photothermal beam deflection technique.

Science.gov (United States)

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.

New vistas in refractive laser beam shaping with an analytic design approach

Science.gov (United States)

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.

Algebraic dynamics algorithm: Numerical comparison with Runge-Kutta algorithm and symplectic geometric algorithm

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.

Algebraic dynamics algorithm:Numerical comparison with Runge-Kutta algorithm and 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.

Diffraction of a Gaussian beam in a three-dimensional smoothly inhomogeneous medium: an eikonal-based complex geometrical-optics approach.

Science.gov (United States)

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.

APPLICATION OF FINITE ELEMENT METHOD TAKING INTO ACCOUNT PHYSICAL AND GEOMETRIC NONLINEARITY FOR THE CALCULATION OF PRESTRESSED REINFORCED CONCRETE BEAMS

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. 

Extension of geometrical-optics approximation to on-axis Gaussian beam scattering. II. By a spheroidal particle with end-on incidence.

Science.gov (United States)

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.

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....

Geometric Rationalization for Freeform Architecture

KAUST Repository

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

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 and wave optics of paraxial beams.

Science.gov (United States)

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.

Efficient 3D geometric and Zernike moments computation from unstructured surface meshes.

Science.gov (United States)

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.

Optical properties of polarization-dependent geometrical phase elements with partially polarized light

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

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

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

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

Geometric scalar theory of gravity beyond spherical symmetry

Science.gov (United States)

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.

A Differential Geometric Approach to Nonlinear Filtering: The Projection Filter

NARCIS (Netherlands)

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

Geometric and Dosimetric Approach to Determine Probability of Late Cardiac Mortality in Left Tangential Breast Irradiation: Comparison Between Wedged Beams and Field-in-Field Technique

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

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)

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.

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.

Design of mirror and monochromator crystals for a high-resolution multiwavelength anomalous diffraction beam line on a bending magnet at the ESRF

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

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

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.

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.

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

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.

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

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

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

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.

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 ...

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.

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

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 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

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.

Goos–Hänchen and Imbert–Fedorov beam shifts: an overview

International Nuclear Information System (INIS)

Bliokh, K Y; Aiello, A

2013-01-01

We consider reflection and transmission of polarized paraxial light beams at a plane dielectric interface. The field transformations taking into account a finite beam width are described based on the plane-wave representation and geometric rotations. Using geometrical-optics coordinate frames accompanying the beams, we construct an effective Jones matrix characterizing spatial-dispersion properties of the interface. This results in a unified self-consistent description of the Goos–Hänchen and Imbert–Fedorov shifts (the latter being also known as the spin Hall effect of light). Our description reveals the intimate relation of the transverse Imbert–Fedorov shift to the geometric phases between constituent waves in the beam spectrum and to the angular momentum conservation for the whole beam. Both spatial and angular shifts are considered as well as their analogues for higher-order vortex beams carrying intrinsic orbital angular momentum. We also give a brief overview of various extensions and generalizations of the basic beam-shift phenomena and related effects. (review article)

Bessel-like beams modulated by arbitrary radial functions

Science.gov (United States)

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.

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)

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.)

Geometric Topology and Shape Theory

CERN Document Server

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

Geometrical approach to tumor growth.

Science.gov (United States)

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.

TURTLE with MAD input (Trace Unlimited Rays Through Lumped Elements) -- A computer program for simulating charged particle beam transport systems and DECAY TURTLE including decay calculations

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.

TURTLE with MAD input (Trace Unlimited Rays Through Lumped Elements) -- A computer program for simulating charged particle beam transport systems and DECAY TURTLE including decay calculations

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

The Role of Geometrically Necessary Dislocations in Cantilever Beam Bending Experiments of Single Crystals

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.

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.

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)

Electric field distribution and current emission in a miniaturized geometrical diode

Science.gov (United States)

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.

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)

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

Geometrical aspects in optical wave-packet dynamics.

Science.gov (United States)

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.

Instrument-related geometrical factors affecting the intensity in XPS and ARXPS experiments

Energy Technology Data Exchange (ETDEWEB)

Herrera-Gomez, A., E-mail: aherrera@qro.cinvestav.mx [CINVESTAV-Unidad Queretaro, Queretaro 76230 (Mexico); Aguirre-Tostado, F.S. [Centro de Investigacion en Materiales Avanzados, Apodaca, Nuevo Leon 66600 (Mexico); Mani-Gonzalez, P.G.; Vazquez-Lepe, M.; Sanchez-Martinez, A.; Ceballos-Sanchez, O. [CINVESTAV-Unidad Queretaro, Queretaro 76230 (Mexico); Wallace, R.M. [Materials Science and Engineering, University of Texas at Dallas, Richardson, TX 75080 (United States); Conti, G.; Uritsky, Y. [Applied Materials, Santa Clara, CA 95054 (United States)

2011-11-15

Highlights: {yields} Instrument geometrical-factors affecting the XPS angular dependence are described. {yields} The geometrical factors in XPS instruments are transferable to other systems. {yields} Practical protocols are presented for assessing the size of analysis area and volume. {yields} Practical protocols are presented for assessing the size of the X-ray beam spot. {yields} Practical protocols are described for assessing the manipulator's axis of rotation. - Abstract: The angular dependence of the X-ray photoelectron spectroscopy (XPS) signal is influenced not only by the electron take-off angle, but also by instrument-related geometrical factors. The XPS signal is, in fact, integrated over the overlap between the X-ray beam, the spectrometer analysis volume, and the sample surface. This overlap depends on the size and shape of the spectrometer analysis volume and X-ray beam, as well as on their relative orientation. In this paper it is described the models and protocols for the characterization of the parameters defining the geometry of an XPS instrument. The protocols include practical methods for assessing the spectrometer analysis area and the X-ray beam spot dimension. Simple systems consisting of flat and 'thick' gold films on silicon wafers were employed. The parameters found with those samples are transferable to other more complex systems since they are geometrical in nature. The method allows for the prediction of the actual intensity of XPS peaks, hence removing the need of normalizing the peak areas to the area of a determined substrate peak. The associated reduction of the uncertainty in half is of special importance since the quantitative analysis of angle-resolved XPS data could be very sensitive to noise. Two rotating and one non-rotating XPS instruments are described. Some examples of the applications of the method are also provided.

Geometrical approach to tumor growth

OpenAIRE

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...

Sampling theorem for geometric moment determination and its application to a laser beam position detector.

Science.gov (United States)

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.

Scattering and absorption of light by ice particles: Solution by a new physical-geometric optics hybrid method

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.

Imprint reduction in rotating heavy ions beam energy deposition

Energy Technology Data Exchange (ETDEWEB)

Bret, A., E-mail: antoineclaude.bret@uclm.es [Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, MS-51, Cambridge, MA 02138 (United States); ETSI Industriales, Universidad Castilla-La Mancha, 13071 Ciudad Real (Spain); Instituto de Investigaciones Energéticas y Aplicaciones Industriales, Campus Universitario de Ciudad Real, 13071 Ciudad Real (Spain); Piriz, A.R., E-mail: Roberto.Piriz@uclm.es [ETSI Industriales, Universidad Castilla-La Mancha, 13071 Ciudad Real (Spain); Instituto de Investigaciones Energéticas y Aplicaciones Industriales, Campus Universitario de Ciudad Real, 13071 Ciudad Real (Spain); Tahir, N.A., E-mail: n.tahir@gsi.de [GSI Darmstadt, Plankstrasse 1, 64291 Darmstadt (Germany)

2014-01-01

The compression of a cylindrical target by a rotating heavy ions beam is contemplated in certain inertial fusion schemes or in heavy density matter experiments. Because the beam has its proper temporal profile, the energy deposition is asymmetric and leaves an imprint which can have important consequences for the rest of the process. In this paper, the Fourier components of the deposited ion density are computed exactly in terms of the beam temporal profile and its rotation frequency Ω. We show that for any beam profile of duration T, there exist an infinite number of values of ΩT canceling exactly any given harmonic. For the particular case of a parabolic profile, we find possible to cancel exactly the first harmonic and nearly cancel every other odd harmonics. In such case, the imprint amplitude is divided by 4 without any increase of Ω.

Imprint reduction in rotating heavy ions beam energy deposition

International Nuclear Information System (INIS)

Bret, A.; Piriz, A.R.; Tahir, N.A.

2014-01-01

The compression of a cylindrical target by a rotating heavy ions beam is contemplated in certain inertial fusion schemes or in heavy density matter experiments. Because the beam has its proper temporal profile, the energy deposition is asymmetric and leaves an imprint which can have important consequences for the rest of the process. In this paper, the Fourier components of the deposited ion density are computed exactly in terms of the beam temporal profile and its rotation frequency Ω. We show that for any beam profile of duration T, there exist an infinite number of values of ΩT canceling exactly any given harmonic. For the particular case of a parabolic profile, we find possible to cancel exactly the first harmonic and nearly cancel every other odd harmonics. In such case, the imprint amplitude is divided by 4 without any increase of Ω

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)

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

Fan-beam and cone-beam image reconstruction via filtering the backprojection image of differentiated projection data

International Nuclear Information System (INIS)

Zhuang Tingliang; Leng Shuai; Nett, Brian E; Chen Guanghong

2004-01-01

In this paper, a new image reconstruction scheme is presented based on Tuy's cone-beam inversion scheme and its fan-beam counterpart. It is demonstrated that Tuy's inversion scheme may be used to derive a new framework for fan-beam and cone-beam image reconstruction. In this new framework, images are reconstructed via filtering the backprojection image of differentiated projection data. The new framework is mathematically exact and is applicable to a general source trajectory provided the Tuy data sufficiency condition is satisfied. By choosing a piece-wise constant function for one of the components in the factorized weighting function, the filtering kernel is one dimensional, viz. the filtering process is along a straight line. Thus, the derived image reconstruction algorithm is mathematically exact and efficient. In the cone-beam case, the derived reconstruction algorithm is applicable to a large class of source trajectories where the pi-lines or the generalized pi-lines exist. In addition, the new reconstruction scheme survives the super-short scan mode in both the fan-beam and cone-beam cases provided the data are not transversely truncated. Numerical simulations were conducted to validate the new reconstruction scheme for the fan-beam case

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)

Tracker-on-C for cone-beam CT-guided surgery: evaluation of geometric accuracy and clinical applications

Science.gov (United States)

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

Growth rate of non-thermodynamic emittance of intense electron beams

International Nuclear Information System (INIS)

Carlsten, B.E.

1998-01-01

The nonlinear free-energy concept has been particularly useful in estimating the emittance growth resulting from any excess energy of electron beams in periodic and uniform channels. However, additional emittance growth, that is geometrical rather than thermodynamic in origin, is induced if the particles have different kinetic energies and axial velocities, which is common for mildly relativistic, very intense electron beams. This effect is especially strong if particles lose or gain significant kinetic energy due to the beam's potential depression, as the beam converges and diverges. In this paper we analyze these geometric emittance growth mechanisms for a uniform, continuous, intense electron beam in a focusing transport channel consisting of discrete solenoidal magnets, over distances short enough that the beam does not reach equilibrium. These emittance growth mechanisms are based on the effects of (1) energy variations leading to nonlinearities in the space-charge force even if the current density is uniform, (2) an axial velocity shear radially along the beam due to the beam's azimuthal motion in the solenoids, and (3) an energy redistribution of the beam as the beam compresses or expands. The geometric emittance growth is compared in magnitude with that resulting from the nonlinear free energy, for the case of a mismatched beam in a uniform channel, and is shown to dominate for certain experimental conditions. Rules for minimizing the emittance along a beamline are outlined. copyright 1998 The American Physical Society

Non-adiabatic quantum evolution: The S matrix as a geometrical phase factor

Energy Technology Data Exchange (ETDEWEB)

Saadi, Y., E-mail: S_yahiadz@yahoo.fr [Laboratoire de Physique Quantique et Systèmes Dynamiques, Faculté des Sciences, Université Ferhat Abbas de Sétif, Sétif 19000 (Algeria); Maamache, M. [Laboratoire de Physique Quantique et Systèmes Dynamiques, Faculté des Sciences, Université Ferhat Abbas de Sétif, Sétif 19000 (Algeria)

2012-03-19

We present a complete derivation of the exact evolution of quantum mechanics for the case when the underlying spectrum is continuous. We base our discussion on the use of the Weyl eigendifferentials. We show that a quantum system being in an eigenstate of an invariant will remain in the subspace generated by the eigenstates of the invariant, thereby acquiring a generalized non-adiabatic or Aharonov–Anandan geometric phase linked to the diagonal element of the S matrix. The modified Pöschl–Teller potential and the time-dependent linear potential are worked out as illustrations. -- Highlights: ► In this Letter we study the exact quantum evolution for continuous spectra problems. ► We base our discussion on the use of the Weyl eigendifferentials. ► We give a generalized Lewis and Riesenfeld phase for continuous spectra. ► This generalized phase or Aharonov–Anandan geometric phase is linked to the S matrix. ► The modified Pöschl–Teller and the linear potential are worked out as illustrations.

Vibrations and stability of complex beam systems

CERN Document Server

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...

Morphing of geometric composites via residual swelling.

Science.gov (United States)

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.

Wakefield effects in the SLC beam delivery system

International Nuclear Information System (INIS)

Napoly, O.

1996-06-01

Wakefield effects occurring in the SLC after the LI28 emittance measurement station could be responsible for part of all of the observed discrepancy between the expected vertical spot sizes at the IP and the measured ones. The strongest wakefields are generated by the parts of the beam chamber which are the closest to the beam, like collimators. In this note we review the effect of the following wakefield sources: geometric wakefields from final focus fixed and movable collimators, geometric and resistive wakefields from linac collimators jaws, resistive wakefields from the beam pipe at the sextupole and final transformer locations. We mostly concentrate on the transverse dipole and quadrupole wakefield effects, although the longitudinal wakefields are briefly studied at the end. We limit ourselves to the vertical beam dynamics and to the lowest (mainly linear) order of the wakefield expansion with respect to the beam offset, which excludes the near wall effect on the beam. (author)

Fractal supersymmetric QM, Geometric Probability and the Riemann Hypothesis

CERN Document Server

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...

SU-F-J-74: High Z Geometric Integrity and Beam Hardening Artifact Assessment Using a Retrospective Metal Artifact Reduction (MAR) Reconstruction Algorithm

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

SU-F-J-74: High Z Geometric Integrity and Beam Hardening Artifact Assessment Using a Retrospective Metal Artifact Reduction (MAR) Reconstruction Algorithm

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

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)

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

Coherent cancellation of geometric phase for the OH molecule in external fields

Science.gov (United States)

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.

Exact vibration analysis of a double-nanobeam-systems embedded in an elastic medium by a Hamiltonian-based method

Science.gov (United States)

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.

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.

A unified analysis of FBP-based algorithms in helical cone-beam and circular cone- and fan-beam scans

International Nuclear Information System (INIS)

Pan Xiaochuan; Xia Dan; Zou Yu; Yu Lifeng

2004-01-01

A circular scanning trajectory is and will likely remain a popular choice of trajectory in computed tomography (CT) imaging because it is easy to implement and control. Filtered-backprojection (FBP)-based algorithms have been developed previously for approximate and exact reconstruction of the entire image or a region of interest within the image in circular cone-beam and fan-beam cases. Recently, we have developed a 3D FBP-based algorithm for image reconstruction on PI-line segments in a helical cone-beam scan. In this work, we demonstrated that the 3D FBP-based algorithm indeed provided a rather general formulation for image reconstruction from divergent projections (such as cone-beam and fan-beam projections). On the basis of this formulation we derived new approximate or exact algorithms for image reconstruction in circular cone-beam or fan-beam scans, which can be interpreted as special cases of the helical scan. Existing algorithms corresponding to the derived algorithms were identified. We also performed a preliminary numerical study to verify our theoretical results in each of the cases. The results in the work can readily be generalized to other non-circular trajectories

Differential algebraic method for arbitrary order curvilinear-axis combined geometric-chromatic aberration analysis

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

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

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

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

Manifestations of geometric phases in a proton electric-dipole-moment experiment in an all-electric storage ring

Science.gov (United States)

Silenko, Alexander J.

2017-12-01

We consider a proton electric-dipole-moment experiment in an all-electric storage ring when the spin is frozen and local longitudinal and vertical electric fields alternate. In this experiment, the geometric (Berry) phases are very important. Due to the these phases, the spin rotates about the radial axis. The corresponding systematic error is rather important while it can be canceled with clockwise and counterclockwise beams. The geometric phases also lead to the spin rotation about the radial axis. This effect can be canceled with clockwise and counterclockwise beams as well. The sign of the azimuthal component of the angular velocity of the spin precession depends on the starting point where the spin orientation is perfect. The radial component of this quantity keeps its value and sign for each starting point. When the longitudinal and vertical electric fields are joined in the same sections without any alternation, the systematic error due to the geometric phases does not appear but another systematic effect of the spin rotation about the azimuthal axis takes place. It has opposite signs for clockwise and counterclockwise beams.

Exactly and quasi-exactly solvable 'discrete' quantum mechanics.

Science.gov (United States)

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.

Transmission of a Bessel beam through a circular aperture in an impedance screen

International Nuclear Information System (INIS)

Umul, Yusuf Ziya

2014-01-01

The scattering effect of a circular aperture, located in an impedance plane, on a Bessel beam is investigated by decomposing the scattered wave into two subcomponents, namely the geometrical optics and diffracted fields. The diffracted waves are investigated with the aid of the geometrical theory of diffraction. The detour parameter is evaluated and the existence zones of the geometrical optics fields are determined. The various aspects of the reflected and transmitted scattered waves, including the self healing of the beam, are studied numerically. (letter)

An algebraic geometric approach to separation of variables

CERN Document Server

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...

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.

Research on geometric rectification of the Large FOV Linear Array Whiskbroom Image

Science.gov (United States)

Liu, Dia; Liu, Hui-tong; Dong, Hao; Liu, Xiao-bo

2015-08-01

To solve the geometric distortion problem of large FOV linear array whiskbroom image, a model of multi center central projection collinearity equation was founded considering its whiskbroom and linear CCD imaging feature, and the principle of distortion was analyzed. Based on the rectification method with POS, we introduced the angular position sensor data of the servo system, and restored the geometric imaging process exactly. An indirect rectification scheme aiming at linear array imaging with best scanline searching method was adopted, matrixes for calculating the exterior orientation elements was redesigned. We improved two iterative algorithms for this device, and did comparison and analysis. The rectification for the images of airborne imaging experiment showed ideal effect.

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.

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.

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

Geometrical analysis of cytochrome c unfolding

Science.gov (United States)

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.

Exact ground-state correlation functions of one-dimenisonal strongly correlated electron models with resonating-valence-bond ground state

International Nuclear Information System (INIS)

Yamanaka, Masanori; Honjo, Shinsuke; Kohmoto, Mahito

1996-01-01

We investigate one-dimensional strongly correlated electron models which have the resonating-valence-bond state as the exact ground state. The correlation functions are evaluated exactly using the transfer matrix method for the geometric representations of the valence-bond states. In this method, we only treat matrices with small dimensions. This enables us to give analytical results. It is shown that the correlation functions decay exponentially with distance. The result suggests that there is a finite excitation gap, and that the ground state is insulating. Since the corresponding noninteracting systems may be insulating or metallic, we can say that the gap originates from strong correlation. The persistent currents of the present models are also investigated and found to be exactly vanishing

A fast and efficient method for sequential cone-beam tomography

International Nuclear Information System (INIS)

Koehler, Th.; Proksa, R.; Grass, M.

2001-01-01

Sequential cone-beam tomography is a method that uses data of two or more parallel circular trajectories of a cone-beam scanner to reconstruct the object function. We propose a condition for the data acquisition that ensures that all object points between two successive circles are irradiated over an angular span of the x-ray source position of exactly 360 deg. in total as seen along the rotation axis. A fast and efficient approximative reconstruction method for the proposed acquisition is presented which uses data from exactly 360 deg. for every object point. It is based on the Tent-FDK method which was recently developed for single circular cone-beam CT. The measurement geometry does not provide sufficient data for exact reconstruction but it is shown that the proposed reconstruction method provides satisfying image quality for small cone angles

A Semi-Discrete Landweber-Kaczmarz Method for Cone Beam Tomography and Laminography Exploiting Geometric Prior Information

Science.gov (United States)

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.

Gaussian beam diffraction in weakly anisotropic inhomogeneous media

Energy Technology Data Exchange (ETDEWEB)

Kravtsov, Yu.A., E-mail: kravtsov@am.szczecin.p [Institute of Physics, Maritime University of Szczecin, Szczecin 70-500 (Poland); Space Research Institute, Russian Academy of Science, Moscow 117 997 (Russian Federation); Berczynski, P., E-mail: pawel.berczynski@ps.p [Institute of Physics, West Pomeranian University of Technology, Szczecin 70-310 (Poland); Bieg, B., E-mail: b.bieg@am.szczecin.p [Institute of Physics, Maritime University of Szczecin, Szczecin 70-500 (Poland)

2009-08-10

Combination of quasi-isotropic approximation (QIA) of geometric optics with paraxial complex geometric optics (PCGO) is suggested, which allows describing both diffraction and polarization evolution of Gaussian electromagnetic beams in weakly anisotropic inhomogeneous media. Combination QIA/PCGO reduces Maxwell equations to the system of the ordinary differential equations of the first order and radically simplifies solution of various problems, related to microwave plasma diagnostics, including plasma polarimetry, interferometry and refractometry in thermonuclear reactors. Efficiency of the method is demonstrated by the example of electromagnetic beam diffraction in a linear layer of magnetized plasma with parameters, modeling tokamak plasma in the project ITER.

Gaussian beam diffraction in weakly anisotropic inhomogeneous media

International Nuclear Information System (INIS)

Kravtsov, Yu.A.; Berczynski, P.; Bieg, B.

2009-01-01

Combination of quasi-isotropic approximation (QIA) of geometric optics with paraxial complex geometric optics (PCGO) is suggested, which allows describing both diffraction and polarization evolution of Gaussian electromagnetic beams in weakly anisotropic inhomogeneous media. Combination QIA/PCGO reduces Maxwell equations to the system of the ordinary differential equations of the first order and radically simplifies solution of various problems, related to microwave plasma diagnostics, including plasma polarimetry, interferometry and refractometry in thermonuclear reactors. Efficiency of the method is demonstrated by the example of electromagnetic beam diffraction in a linear layer of magnetized plasma with parameters, modeling tokamak plasma in the project ITER.

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)

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.

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

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.

Improvement of Galilean refractive beam shaping system for accurately generating near-diffraction-limited flattop beam with arbitrary beam size.

Science.gov (United States)

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.

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

Geometrical modified nesbit corporoplasty to correct different types of penile curvature: description of the surgical procedure based on geometrical principles and long-term results.

Science.gov (United States)

Vicini, P; Di Nicola, S; Antonini, G; De Berardinis, E; Gentile, V; De Marco, F

2016-11-01

We present the use of a modified corporoplasty, based on geometrical principles, to determine the exact site for the incision in the tunica or plaque and the exact amount of albuginea for overlaying to correct with extreme precision the different types of congenital or acquired penile curvature due to Peyronie's disease. To describe our experience with a new surgical procedure for the enhancement of penile curvature avoiding any overcorrection or undercorrection. Between March 2004 and April 2013, a total of 74 patients underwent the geometrical modified corporoplasty. All patients had congenital curvature until 90° or acquired stable penile curvature 'less' than 60°, that made sexual intercourse very difficult or impossible, normal erectile function, absence of hourglass or hinge effect. Preoperative testing included a physical examination, 3 photographs (frontal, dorsal and lateral) of penis during erection, a 10 mcg PGE1-induced erection and Doppler ultrasound, administration of the International Index of Erectile Function (IIEF-15) questionnaire. A follow-up with postoperative evaluation at 12 weeks, 12 and 24 months, included the same preoperative testing. Satisfaction rates were better assessed with the use of validated questionnaire such as the International Erectile Dysfunction Inventory of the Treatment Satisfaction (EDITS). Statistical analysis with Student's t-test was performed using commercially available, personal computer software. A total of 25 patients had congenital penile curvature with a mean deviation of 46.8° (range 40-90), another 49 patients had Peyronie's disease with a mean deviation of 58.4 (range 45-60). No major complications were reported. Postoperative correction of the curvature was achieved in all patients (100%). Neither undercorrection nor overcorrection were recorded. No significant relapse (curvature>15°) occurred in our patients. Shortening of the penis was reported by 74% but did not influence the high overall

Quasi-exact solvability

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

Fundamental radiological and geometric performance of two types of proton beam modulated discrete scanning systems

Energy Technology Data Exchange (ETDEWEB)

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

Fundamental radiological and geometric performance of two types of proton beam modulated discrete scanning systems.

Science.gov (United States)

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

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)

ExactPack Documentation

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.

Tunable orbital angular momentum mode filter based on optical geometric transformation.

Science.gov (United States)

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.

Geometric calibration of a stationary digital breast tomosynthesis system based on distributed carbon nanotube X-ray source arrays.

Directory of Open Access Journals (Sweden)

Changhui Jiang

Full Text Available Stationary digital breast tomosynthesis (sDBT with distributed X-ray sources based on carbon nanotube (CNT field emission cathodes has been recently proposed as an approach that can prevent motion blur produced by traditional DBT systems. In this paper, we simulate a geometric calibration method based on a proposed multi-source CNT X-ray sDBT system. This method is a projection matrix-based approach with seven geometric parameters, all of which can be obtained from only one projection datum of the phantom. To our knowledge, this study reports the first application of this approach in a CNT-based multi-beam X-ray sDBT system. The simulation results showed that the extracted geometric parameters from the calculated projection matrix are extremely close to the input values and that the proposed method is effective and reliable for a square sDBT system. In addition, a traditional cone-beam computed tomography (CT system was also simulated, and the uncalibrated and calibrated geometric parameters were used in image reconstruction based on the filtered back-projection (FBP method. The results indicated that the images reconstructed with calibrated geometric parameters have fewer artifacts and are closer to the reference image. All the simulation tests showed that this geometric calibration method is optimized for sDBT systems but can also be applied to other application-specific CT imaging systems.

Geometric calibration of a stationary digital breast tomosynthesis system based on distributed carbon nanotube X-ray source arrays.

Science.gov (United States)

Jiang, Changhui; Zhang, Na; Gao, Juan; Hu, Zhanli

2017-01-01

Stationary digital breast tomosynthesis (sDBT) with distributed X-ray sources based on carbon nanotube (CNT) field emission cathodes has been recently proposed as an approach that can prevent motion blur produced by traditional DBT systems. In this paper, we simulate a geometric calibration method based on a proposed multi-source CNT X-ray sDBT system. This method is a projection matrix-based approach with seven geometric parameters, all of which can be obtained from only one projection datum of the phantom. To our knowledge, this study reports the first application of this approach in a CNT-based multi-beam X-ray sDBT system. The simulation results showed that the extracted geometric parameters from the calculated projection matrix are extremely close to the input values and that the proposed method is effective and reliable for a square sDBT system. In addition, a traditional cone-beam computed tomography (CT) system was also simulated, and the uncalibrated and calibrated geometric parameters were used in image reconstruction based on the filtered back-projection (FBP) method. The results indicated that the images reconstructed with calibrated geometric parameters have fewer artifacts and are closer to the reference image. All the simulation tests showed that this geometric calibration method is optimized for sDBT systems but can also be applied to other application-specific CT imaging systems.

Revealing the radial characteristics of Q-plate generated vortex beams

CSIR Research Space (South Africa)

Sephton, Bereneice

2016-07-01

Full Text Available Q-plates (QP) have become ubiquitous in experiments requiring the generation of vortex beams since its development in 2006. It consequently follows that it is important to characterize the vortex beams created by this geometric-phase optical element...

Geometrical basis for the Standard Model

Science.gov (United States)

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.

Exact analytical solutions of continuity equation for electron beams precipitating in Coulomb collisions

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.

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.

Blind Forensics of Successive Geometric Transformations in Digital Images Using Spectral Method: Theory and Applications.

Science.gov (United States)

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.

Geometric measures of quantum correlations: characterization, quantification, and comparison by distances and operations

International Nuclear Information System (INIS)

Roga, W; Illuminati, F; Spehner, D

2016-01-01

We investigate and compare three distinguished geometric measures of bipartite quantum correlations that have been recently introduced in the literature: the geometric discord, the measurement-induced geometric discord, and the discord of response, each one defined according to three contractive distances on the set of quantum states, namely the trace, Bures, and Hellinger distances. We establish a set of exact algebraic relations and inequalities between the different measures. In particular, we show that the geometric discord and the discord of response based on the Hellinger distance are easy to compute analytically for all quantum states whenever the reference subsystem is a qubit. These two measures thus provide the first instance of discords that are simultaneously fully computable, reliable (since they satisfy all the basic Axioms that must be obeyed by a proper measure of quantum correlations), and operationally viable (in terms of state distinguishability). We apply the general mathematical structure to determine the closest classical-quantum state of a given state and the maximally quantum-correlated states at fixed global state purity according to the different distances, as well as a necessary condition for a channel to be quantumness breaking. (paper)

A geometrical optics polarimetric bidirectional reflectance distribution function for dielectric and metallic surfaces.

Science.gov (United States)

Hyde, M W; Schmidt, J D; Havrilla, M J

2009-11-23

A polarimetric bidirectional reflectance distribution function (pBRDF), based on geometrical optics, is presented. The pBRDF incorporates a visibility (shadowing/masking) function and a Lambertian (diffuse) component which distinguishes it from other geometrical optics pBRDFs in literature. It is shown that these additions keep the pBRDF bounded (and thus a more realistic physical model) as the angle of incidence or observation approaches grazing and better able to model the behavior of light scattered from rough, reflective surfaces. In this paper, the theoretical development of the pBRDF is shown and discussed. Simulation results of a rough, perfect reflecting surface obtained using an exact, electromagnetic solution and experimental Mueller matrix results of two, rough metallic samples are presented to validate the pBRDF.

Exact solution of the relativistic Coulomb problem for two-particle bound states in the quasipotential approach

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

Experimental and Theoretical Investigations on the Validity of Geometrical Optics Model for Calculating the Stability of Optical Traps

NARCIS (Netherlands)

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

Squaring the Circle: Geometric Skewness and Symmetry Breaking for Passive Scalar Transport in Ducts and Pipes.

Science.gov (United States)

Aminian, Manuchehr; Bernardi, Francesca; Camassa, Roberto; McLaughlin, Richard M

2015-10-09

We study the role geometry plays in the emergence of asymmetries in diffusing passive scalars advected by pressure-driven flows in ducts and pipes of different aspect ratios. We uncover nonintuitive, multi-time-scale behavior gauged by a new statistic, which we term "geometric skewness" S^{G}, which measures instantaneously forming asymmetries at short times due to flow geometry. This signature distinguishes elliptical pipes of any aspect ratio, for which S^{G}=0, from rectangular ducts whose S^{G} is generically nonzero, and, interestingly, shows that a special duct of aspect ratio ≈0.53335 behaves like a circular pipe as its geometric skewness vanishes. Using a combination of exact solutions, novel short-time asymptotics, and Monte Carlo simulations, we establish the relevant time scales for plateaus and extrema in the evolution of the skewness and kurtosis for our class of geometries. For ducts limiting to channel geometries, we present new exact, single-series formulas for the first four moments on slices used to benchmark Monte Carlo simulations.

Plasmon Geometric Phase and Plasmon Hall Shift

Science.gov (United States)

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.

Exact solution of the mixed spin-1/2 and spin-S Ising-Heisenberg diamond chain

Directory of Open Access Journals (Sweden)

L. Čanová

2009-01-01

Full Text Available The geometric frustration in a class of the mixed spin-1/2 and spin-S Ising-Heisenberg diamond chains is investigated by combining three exact analytical techniques: Kambe projection method, decoration-iteration transformation and transfer-matrix method. The ground state, the magnetization process and the specific heat as a function of the external magnetic field are particularly examined for different strengths of the geometric frustration. It is shown that the increase of the Heisenberg spin value S raises the number of intermediate magnetization plateaux, which emerge in magnetization curves provided that the ground state is highly degenerate on behalf of a sufficiently strong geometric frustration. On the other hand, all intermediate magnetization plateaux merge into a linear magnetization versus magnetic field dependence in the limit of classical Heisenberg spin S → ∞. The enhanced magnetocaloric effect with cooling rate exceeding the one of paramagnetic salts is also detected when the disordered frustrated phase constitutes the ground state and the external magnetic field is small enough.

Geometry and Topology Optimization of Statically Determinate Beams under Fixed and Most Unfavorably Distributed Load

Directory of Open Access Journals (Sweden)

Agata Kozikowska

Full Text Available Abstract The paper concerns topology and geometry optimization of statically determinate beams with an arbitrary number of pin supports. The beams are simultaneously exposed to uniform dead load and arbitrarily distributed live load and optimized for the absolute maximum bending moment. First, all the beams with fixed topology are subjected to geometrical optimization by genetic algorithm. Strict mathematical formulas for calculation of optimal geometrical parameters are found for all topologies and any ratio of dead to live load. Then beams with the same minimal values of the objective function and different topologies are classified into groups called topological classes. The detailed characteristics of these classes are described.

A method for generating double-ring-shaped vector beams

Science.gov (United States)

Huan, Chen; Xiao-Hui, Ling; Zhi-Hong, Chen; Qian-Guang, Li; Hao, Lv; Hua-Qing, Yu; Xu-Nong, Yi

2016-07-01

We propose a method for generating double-ring-shaped vector beams. A step phase introduced by a spatial light modulator (SLM) first makes the incident laser beam have a nodal cycle. This phase is dynamic in nature because it depends on the optical length. Then a Pancharatnam-Berry phase (PBP) optical element is used to manipulate the local polarization of the optical field by modulating the geometric phase. The experimental results show that this scheme can effectively create double-ring-shaped vector beams. It provides much greater flexibility to manipulate the phase and polarization by simultaneously modulating the dynamic and the geometric phases. Project supported by the National Natural Science Foundation of China (Grant No. 11547017), the Hubei Engineering University Research Foundation, China (Grant No. z2014001), and the Natural Science Foundation of Hubei Province, China (Grant No. 2014CFB578).

Beam wandering statistics of twin thin laser beam propagation under generalized atmospheric conditions.

Science.gov (United States)

Pérez, Darío G; Funes, Gustavo

2012-12-03

Under the Geometrics Optics approximation is possible to estimate the covariance between the displacements of two thin beams after they have propagated through a turbulent medium. Previous works have concentrated in long propagation distances to provide models for the wandering statistics. These models are useful when the separation between beams is smaller than the propagation path-regardless of the characteristics scales of the turbulence. In this work we give a complete model for these covariances, behavior introducing absolute limits to the validity of former approximations. Moreover, these generalizations are established for non-Kolmogorov atmospheric models.

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

On geometric optics and surface waves for light scattering by spheres

International Nuclear Information System (INIS)

Liou, K.N.; Takano, Y.; Yang, P.

2010-01-01

A geometric optics approach including surface wave contributions has been developed for homogeneous and concentrically coated spheres. In this approach, a ray-by-ray tracing program was used for efficient computation of the extinction and absorption cross sections. The present geometric-optics surface-wave (GOS) theory for light scattering by spheres considers the surface wave contribution along the edge of a particle as a perturbation term to the geometric-optics core that includes Fresnel reflection-refraction and Fraunhofer diffraction. Accuracies of the GOS approach for spheres have been assessed through comparison with the results determined from the exact Lorenz-Mie (LM) theory in terms of the extinction efficiency, single-scattering albedo, and asymmetry factor in the size-wavelength ratio domain. In this quest, we have selected a range of real and imaginary refractive indices representative of water/ice and aerosol species and demonstrated close agreement between the results computed by GOS and LM. This provides the foundation to conduct physically reliable light absorption and scattering computations based on the GOS approach for aerosol aggregates associated with internal and external mixing states employing spheres as building blocks.

Geometric and Magnetic Axes of the LHC Dipole

CERN Document Server

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.

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.

Exotic Optical Beam Classes for Free-Space Communication

Science.gov (United States)

2016-03-24

wandering of an optical vortex is one of the significant problems with the application of vortex beams to FSO applications. From a geometrical optics ...AFRL-AFOSR-VA-TR-2016-0131 Exotic optical beam classes for free-space communication Greg Gbur UNIVERSITY OF NOTH CAROLINA AT CHARLOTTE Final Report...12-2015 4. TITLE AND SUBTITLE Exotic optical beam classes for free-space communication 5a. CONTRACT NUMBER 5b. GRANT NUMBER FA9550-13-1-0009 5c

Distortional Modes of Thin-Walled Beams

DEFF Research Database (Denmark)

Jönsson, Jeppe; Andreassen, Michael Joachim

2009-01-01

The classic thin-walled beam theory for open and closed cross-sections can be generalized by including distortional displacement modes. The introduction of additional displacement modes leads to coupled differential equations, which seems to have prohibited the use of exact shape functions...... in the modelling of coupled torsion and distortion. However, if the distortional displacement modes are chosen as those which decouple the differential equations as in non proportionally damped modal dynamic analysis then it may be possible to use exact shape functions and perform analysis on a reduced problem....... In the recently developed generalized beam theory (GBT) the natural distortional displacement modes are determined on the basis of a quadratic eigenvalue problem. However, as in linear modal dynamic analysis of proportionally damped structures this problem has been solved approximately using linear eigenvalue...

An Alternative High Luminosity LHC with Flat Optics and Long-Range Beam-Beam Compensation

CERN Document Server

AUTHOR|(CDS)2070952; Valishev, Aleksander; Shatilov, Dmitry

2015-01-01

In the baseline scenario of the High-Luminosity LHC (HL-LHC), the geometric loss of luminosity in the two high luminosity experiments due to collisions with a large crossing angle is recovered by tilting the bunches in the interaction region with the use of crab cavities. A possible backup scenario would rely on a reduced crossing angle together with flat optics (with different horizontal and vertical β∗ values) for the preservation of luminosity performance. However, the reduction of crossing angle coupled with the flat optics significantly enhances the strength of long-range beam-beam interactions. This paper discusses the possibility to mitigate the long-range beam-beam effects by current bearing wire compensators (or e-lens). We develop a new HL-LHC parameter list and analyze it in terms of integrated luminosity performance as compared to the baseline. Further, we evaluate the operational scenarios using numerical simulations of single-particle dynamics with beam-beam effects.

An Alternative High Luminosity LHC with Flat Optics and Long-Range Beam-Beam Compensation

Energy Technology Data Exchange (ETDEWEB)

Fartoukh, Stephane [CERN; Valishev, Alexander [Fermilab; Shatilov, Dmitry [BINP, Novosibirsk

2015-06-01

In the baseline scenario of the High-Luminosity LHC (HL-LHC), the geometric loss of luminosity in the two high luminosity experiments due to collisions with a large crossing angle is recovered by tilting the bunches in the interaction region with the use of crab cavities. A possible backup scenario would rely on a reduced crossing angle together with flat optics (with different horizontal and vertical $\\beta^{\\ast}$values) for the preservation of luminosity performance. However, the reduction of crossing angle coupled with the flat optics significantly enhances the strength of long-range beam-beam interactions. This paper discusses the possibility to mitigate the long-range beam-beam effects by current bearing wire compensators (or e-lens). We develop a new HL-LHC parameter list and analyze it in terms of integrated luminosity performance as compared to the baseline. Further, we evaluate the operational scenarios using numerical simulations of single-particle dynamics with beam-beam effects.

Dynamics modeling for a rigid-flexible coupling system with nonlinear deformation field

International Nuclear Information System (INIS)

Deng Fengyan; He Xingsuo; Li Liang; Zhang Juan

2007-01-01

In this paper, a moving flexible beam, which incorporates the effect of the geometrically nonlinear kinematics of deformation, is investigated. Considering the second-order coupling terms of deformation in the longitudinal and transverse deflections, the exact nonlinear strain-displacement relations for a beam element are described. The shear strains formulated by the present modeling method in this paper are zero, so it is reasonable to use geometrically nonlinear deformation fields to demonstrate and simplify a flexible beam undergoing large overall motions. Then, considering the coupling terms of deformation in two dimensions, finite element shape functions of a beam element and Lagrange's equations are employed for deriving the coupling dynamical formulations. The complete expression of the stiffness matrix and all coupling terms are included in the formulations. A model consisting of a rotating planar flexible beam is presented. Then the frequency and dynamical response are studied, and the differences among the zero-order model, first-order coupling model and the new present model are discussed. Numerical examples demonstrate that a 'stiffening beam' can be obtained, when more coupling terms of deformation are added to the longitudinal and transverse deformation field. It is shown that the traditional zero-order and first-order coupling models may not provide an exact dynamic model in some cases

Impact of geometric uncertainties on dose calculations for intensity modulated radiation therapy of prostate cancer

Science.gov (United States)

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

Theoretical and experimental nonlinear dynamics of a clamped-clamped beam MEMS resonator

NARCIS (Netherlands)

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

Beam-centric algorithm for pretreatment patient position correction in external beam radiation therapy

International Nuclear Information System (INIS)

Bose, Supratik; Shukla, Himanshu; Maltz, Jonathan

2010-01-01

Purpose: In current image guided pretreatment patient position adjustment methods, image registration is used to determine alignment parameters. Since most positioning hardware lacks the full six degrees of freedom (DOF), accuracy is compromised. The authors show that such compromises are often unnecessary when one models the planned treatment beams as part of the adjustment calculation process. The authors present a flexible algorithm for determining optimal realizable adjustments for both step-and-shoot and arc delivery methods. Methods: The beam shape model is based on the polygonal intersection of each beam segment with the plane in pretreatment image volume that passes through machine isocenter perpendicular to the central axis of the beam. Under a virtual six-DOF correction, ideal positions of these polygon vertices are computed. The proposed method determines the couch, gantry, and collimator adjustments that minimize the total mismatch of all vertices over all segments with respect to their ideal positions. Using this geometric error metric as a function of the number of available DOF, the user may select the most desirable correction regime. Results: For a simulated treatment plan consisting of three equally weighted coplanar fixed beams, the authors achieve a 7% residual geometric error (with respect to the ideal correction, considered 0% error) by applying gantry rotation as well as translation and isocentric rotation of the couch. For a clinical head-and-neck intensity modulated radiotherapy plan with seven beams and five segments per beam, the corresponding error is 6%. Correction involving only couch translation (typical clinical practice) leads to a much larger 18% mismatch. Clinically significant consequences of more accurate adjustment are apparent in the dose volume histograms of target and critical structures. Conclusions: The algorithm achieves improvements in delivery accuracy using standard delivery hardware without significantly increasing

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

Evaluation of the geometric accuracy of surrogate-based gated VMAT using intrafraction kilovoltage x-ray images

International Nuclear Information System (INIS)

Li Ruijiang; Mok, Edward; Han, Bin; Koong, Albert; Xing Lei

2012-01-01

Purpose: To evaluate the geometric accuracy of beam targeting in external surrogate-based gated volumetric modulated arc therapy (VMAT) using kilovoltage (kV) x-ray images acquired during dose delivery. Methods: Gated VMAT treatments were delivered using a Varian TrueBeam STx Linac for both physical phantoms and patients. Multiple gold fiducial markers were implanted near the target. The reference position was created for each implanted marker, representing its correct position at the gating threshold. The gating signal was generated from the RPM system. During the treatment, kV images were acquired immediately before MV beam-on at every breathing cycle, using the on-board imaging system. All implanted markers were detected and their 3D positions were estimated using in-house developed software. The positioning error of a marker is defined as the distance of the marker from its reference position for each frame of the images. The overall error of the system is defined as the average over all markers. For the phantom study, both sinusoidal motion (1D and 3D) and real human respiratory motion was simulated for the target and surrogate. In the baseline case, the two motions were synchronized for the first treatment fraction. To assess the effects of surrogate-target correlation on the geometric accuracy, a phase shift of 5% and 10% between the two motions was introduced. For the patient study, intrafraction kV images of five stereotactic body radiotherapy (SBRT) patients were acquired for one or two fractions. Results: For the phantom study, a high geometric accuracy was achieved in the baseline case (average error: 0.8 mm in the superior-inferior or SI direction). However, the treatment delivery is prone to geometric errors if changes in the target-surrogate relation occur during the treatment: the average error was increased to 2.3 and 4.7 mm for the phase shift of 5% and 10%, respectively. Results obtained with real human respiratory curves show a similar trend

Optimization of geometric parameters of heat exchange pipes pin finning

Science.gov (United States)

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.

Hydrogen ion species analysis and related neutral beam injection power assessment in the Heliotron E neutral beam injection system

International Nuclear Information System (INIS)

Sano, Fumimichi; Obiki, Tokuhiro; Sasaki, Akihiko; Iiyoshi, Atsuo; Uo, Koji

1982-01-01

The hydrogen ion species in a Heliotron E neutral beam injection system of maximum electric power 6.3 MW were analyzed in order to assess the neutral beam power injected into the torus. The masimum p roton ratio of the cylindrical bucket type ion source used was observed to be more than 90 percent assuming that the angular divergences for the respective species in the beam are the same. The experimental data are compared with calculations using a particle balance model. The analysis indicates that the net injection power reaches nearly 2.7 MW at the optimal conditions of the system considering the geometrical limitation of the neutral beam path. (author)

Semi-analytical solution to arbitrarily shaped beam scattering

Science.gov (United States)

Wang, Wenjie; Zhang, Huayong; Sun, Yufa

2017-07-01

Based on the field expansions in terms of appropriate spherical vector wave functions and the method of moments scheme, an exact semi-analytical solution to the scattering of an arbitrarily shaped beam is given. For incidence of a Gaussian beam, zero-order Bessel beam and Hertzian electric dipole radiation, numerical results of the normalized differential scattering cross section are presented to a spheroid and a circular cylinder of finite length, and the scattering properties are analyzed concisely.

Comparison of the accuracy of 3-dimensional cone-beam computed tomography and micro-computed tomography reconstructions by using different voxel sizes.

Science.gov (United States)

Maret, Delphine; Peters, Ove A; Galibourg, Antoine; Dumoncel, Jean; Esclassan, Rémi; Kahn, Jean-Luc; Sixou, Michel; Telmon, Norbert

2014-09-01

Cone-beam computed tomography (CBCT) data are, in principle, metrically exact. However, clinicians need to consider the precision of measurements of dental morphology as well as other hard tissue structures. CBCT spatial resolution, and thus image reconstruction quality, is restricted by the acquisition voxel size. The aim of this study was to assess geometric discrepancies among 3-dimensional CBCT reconstructions relative to the micro-CT reference. A total of 37 permanent teeth from 9 mandibles were scanned with CBCT 9500 and 9000 3D and micro-CT. After semiautomatic segmentation, reconstructions were obtained from CBCT acquisitions (voxel sizes 76, 200, and 300 μm) and from micro-CT (voxel size 41 μm). All reconstructions were positioned in the same plane by image registration. The topography of the geometric discrepancies was displayed by using a color map allowing the maximum differences to be located. The maximum differences were mainly found at the cervical margins and on the cusp tips or incisal edges. Geometric reconstruction discrepancies were significant at 300-μm resolution (P = .01, Wilcoxon test). To study hard tissue morphology, CBCT acquisitions require voxel sizes smaller than 300 μm. This experimental study will have to be complemented by studies in vivo that consider the conditions of clinical practice. Copyright © 2014 American Association of Endodontists. Published by Elsevier Inc. All rights reserved.

Structure-preserving integrators in nonlinear structural dynamics and flexible multibody dynamics

CERN Document Server

2016-01-01

This book focuses on structure-preserving numerical methods for flexible multibody dynamics, including nonlinear elastodynamics and geometrically exact models for beams and shells. It also deals with the newly emerging class of variational integrators as well as Lie-group integrators. It discusses two alternative approaches to the discretization in space of nonlinear beams and shells. Firstly, geometrically exact formulations, which are typically used in the finite element community and, secondly, the absolute nodal coordinate formulation, which is popular in the multibody dynamics community. Concerning the discretization in time, the energy-momentum method and its energy-decaying variants are discussed. It also addresses a number of issues that have arisen in the wake of the structure-preserving discretization in space. Among them are the parameterization of finite rotations, the incorporation of algebraic constraints and the computer implementation of the various numerical methods. The practical application...

Geometrical charged-particle optics

CERN Document Server

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...

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.)

Single beam collective effects in FCC-ee due to beam coupling impedance

CERN Document Server

Belli, Eleonora; Persichelli, Serena; Zobov, Mikhail

2016-01-01

The Future Circular Collider study, hosted by CERN to design post-LHC particle accelerator options in a worldwide context, is focused on proton-proton high-energy and electron-positron high-luminosity frontier machines. This new accelerator complex represents a great challenge under several aspects, which involve R&D on beam dynamics and new technologies. One very critical point in this context is represented by collective effects, generated by the interaction of the beam with self-induced electromagnetic fields, called wake fields, which could produce beam instabilities, thus reducing the machines performance and limiting the maximum stored current. It is therefore very important to be able to predict these effects and to study in detail potential solutions to counteract them. In this paper the resistive wall and some other important geometrical sources of impedance for the FCC electron-positron accelerator are identified and evaluated, and their impact on the beam dynamics, which in some cases could lea...

Single beam collective effects in FCC-ee due to beam coupling impedance

CERN Document Server

Belli, Eleonora

2016-01-01

The Future Circular Collider study, hosted by CERN to design post-LHC particle accelerator options in a worldwide context, is focused on proton-proton high-energy and electron-positron high-luminosity frontier machines. This new accelerator complex represents a great challenge under several aspects, which involve R&D on beam dynamics and new technologies. One very critical point in this context is represented by collective effects, generated by the interaction of the beam with self-induced electromagnetic fields, called wake fields, which could produce beam instabilities, thus reducing the machines performance and limiting the maximum stored current. It is therefore very important to be able to predict these effects and to study in detail potential solutions to counteract them. In this paper the resistive wall and some other important geometrical sources of impedance for the FCC electron-positron accelera- tor are identified and evaluated, and their impact on the beam dynamics, which in some cases could l...

Development of a simple system for simultaneously measuring 6DOF geometric motion errors of a linear guide.

Science.gov (United States)

Qibo, Feng; Bin, Zhang; Cunxing, Cui; Cuifang, Kuang; Yusheng, Zhai; Fenglin, You

2013-11-04

A simple method for simultaneously measuring the 6DOF geometric motion errors of the linear guide was proposed. The mechanisms for measuring straightness and angular errors and for enhancing their resolution are described in detail. A common-path method for measuring the laser beam drift was proposed and it was used to compensate the errors produced by the laser beam drift in the 6DOF geometric error measurements. A compact 6DOF system was built. Calibration experiments with certain standard measurement meters showed that our system has a standard deviation of 0.5 µm in a range of ± 100 µm for the straightness measurements, and standard deviations of 0.5", 0.5", and 1.0" in the range of ± 100" for pitch, yaw, and roll measurements, respectively.

Higher-order harmonics of limited diffraction Bessel beams

Science.gov (United States)

Ding; Lu

2000-03-01

We investigate theoretically the nonlinear propagation of the limited diffraction Bessel beam in nonlinear media, under the successive approximation of the KZK equation. The result shows that the nth-order harmonic of the Bessel beam, like its fundamental component, is radially limited diffracting, and that the main beamwidth of the nth-order harmonic is exactly 1/n times that of the fundamental.

A line beam electron gun for rapid thermal processing

Science.gov (United States)

Pauli, M.; Müller, J.; Hartkopf, K.; Barth, T.

1992-04-01

A line beam electron gun based on the Pierce gun type was developed. The line cathode was realized by a directly heated tungsten rod. The temperature distribution along the tungsten rod was simulated numerically. The simulation shows a flat temperature across 2/3 of the cathode length and it agrees with appropriate measurable parameters. The beam profiles of the electron gun perpendicular to the line direction were examined as a function of electrical and geometrical parameters: The space-charge distribution in front of the cathode was found to be responsible for the shape of the beam profile. The shape of the beam profile is weakly influenced by the acceleration to the anode. The heating current induced voltage drop along the cathode was found to be responsible for the nonuniform emission in line direction. A model for the emission behavior of the line beam electron gun was developed. The model is based on the results of the measurements and on a numerical simulation of the potential distribution in the area between Pierce reflectors and anode. The emission model shows a solution to homogenize the emission by a suitable variation of geometrical parameters in line direction. A linear variation was realized in experiment which enables a uniform emission across 2/3 of the cathode length. The beam profile is adjustable by a bias voltage between the cathode and the Pierce reflectors.

Many-beam electron extinction distances in zirconium

International Nuclear Information System (INIS)

Cann, C.D.

1977-05-01

Many-beam extinction distances have been calculated for twenty-two of the lowest order reflections in zirconium. Ten beams comprising the directly transmitted and the nine lowest order systematic reflections were included in each calculation. Extinction distances for each reflection were determined for electron accelerating voltages of 100 and 200 kV, both at the exact Bragg condition and at deviations up to two Bragg angles from this condition. (author)

The Brookhaven ATF low-emittance beam line

International Nuclear Information System (INIS)

Wang, X.J.; Kirk, H.G.

1991-01-01

One component of the experimental program at the Brookhaven Accelerator Test Facility (ATF) consists of a class of experiments which will study the acceleration of electrons through micron-size structures which are exposed in coincidence to a 100 GW CO 2 laser beam. These experiments require the development and control of an electron beam with geometric emittances on the order of 10 -10 m-rad and intensities on the order of 10 6 electrons. In this paper, the authors describe the strategies for producing such beams and the effects of higher-order aberrations. Particle tracking results are presented for the final-focus system

Compact electrostatic beam optics for multi-element focused ion beams: simulation and experiments.

Science.gov (United States)

Mathew, Jose V; Bhattacharjee, Sudeep

2011-01-01

Electrostatic beam optics for a multi-element focused ion beam (MEFIB) system comprising of a microwave multicusp plasma (ion) source is designed with the help of two widely known and commercially available beam simulation codes: AXCEL-INP and SIMION. The input parameters to the simulations are obtained from experiments carried out in the system. A single and a double Einzel lens system (ELS) with and without beam limiting apertures (S) have been investigated. For a 1 mm beam at the plasma electrode aperture, the rms emittance of the focused ion beam is found to reduce from ∼0.9 mm mrad for single ELS to ∼0.5 mm mrad for a double ELS, when S of 0.5 mm aperture size is employed. The emittance can be further improved to ∼0.1 mm mrad by maintaining S at ground potential, leading to reduction in beam spot size (∼10 μm). The double ELS design is optimized for different electrode geometrical parameters with tolerances of ±1 mm in electrode thickness, electrode aperture, inter electrode distance, and ±1° in electrode angle, providing a robust design. Experimental results obtained with the double ELS for the focused beam current and spot size, agree reasonably well with the simulations.

A general modeling method for I-V characteristics of geometrically and electrically configured photovoltaic arrays

International Nuclear Information System (INIS)

Liu Guangyu; Nguang, Sing Kiong; Partridge, Ashton

2011-01-01

Highlights: → A novel and general method is proposed for modeling PV arrays or modules. → A robust algorithm is used for the first time to improve the convergence to solution. → Auxiliary functions in other general methods are not compulsory in our method. → It is novel that geometric configuration is also incorporated. → A case study is performed to show the approach's advantages and unique features. - Abstract: A general method for modeling typical photovoltaic (PV) arrays and modules is proposed to find the exact current and voltage relationship of PV arrays or modules of geometrically and electrically different configurations. Nonlinear characteristic equations of electrical devices in solar array or module systems are numerically constructed without adding any virtual electrical components. Then, a robust damped Newton method is used to find exact I-V relationship of these general nonlinear equations, where the convergence is guaranteed. The model can deal with different mismatch effects such as different configurations of bypass diodes, and partial shading. Geometry coordinates of PV components are also considered to facilitate the modeling of the actual physical configuration. Simulation of a PV array with 48 modules, partially shaded by a concrete structure, is performed to verify the effectiveness and advantages of the proposed method.

Predicting the Onset of Cavitation in Automotive Torque Converters—Part I: Designs with Geometric Similitude

Directory of Open Access Journals (Sweden)

D. L. Robinette

2008-01-01

Full Text Available Dimensional analysis has been applied to automotive torque converters to understand the response of performance to changes in torque, size, working fluid, or operating temperature. The objective of this investigation was to develop a suitable dimensional analysis for estimating the effect of exact geometric scaling of a particular torque converter design on the onset of cavitation. Torque converter operating thresholds for cavitation were determined experimentally with a dynamometer test cell at the stall operating condition using nearfield acoustical measurements. Dimensionless quantities based upon either speed or torque at the onset of cavitation and flow properties (e.g., pressures and temperature dependent fluid properties were developed and compared. The proposed dimensionless stator torque quantity was found to be the most appropriate scaling law for extrapolating cavitation thresholds to multiple diameters. A power product model was fit on dimensionless stator torque data to create a model capable of predicting cavitation thresholds. Comparison of the model to test data taken over a range of operating points showed an error of 3.7%. This is the first paper of a two-part paper. In Part II, application of dimensional analysis will be expanded from torque converters with exact geometric similitude to those of more general design.

A research of possibility for negative muon production by a low energy electron beam accompanying ion beam

International Nuclear Information System (INIS)

Uramoto, Joshin.

1993-12-01

A low energy electron beam (≤ 2000 eV) is injected perpendicularly to a uniform magnetic field, together with a low energy positive ion beam. On this magnetic mass analysis (using the uniform magnetic field), a peak of secondary electron current to the beam collector (arranging as a mass analyzer of 90deg type), appears at an analyzing magnetic field which corresponds exactly to a relation of negative muon μ - (the mass m=207 m e and the charge q=e, where m e and e are mass and charge of electron). The ion beam is essential for the peak appearance, which is produced by decelerating electrically the electron beam in front of the entrance slit of the mass analyzer, and by introducing a neutral gas into the electron beam region and producing a plasma through the ionization. We consider that a very small amount of negative muons may be produced through local cyclotron motions of the injected beam electrons in the ion beam or by an interaction between the bunched beam electrons and beam ions. (author)

Geometric flows in Horava-Lifshitz gravity

CERN Document Server

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...

Exact milestoning

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

[Accurate 3D free-form registration between fan-beam CT and cone-beam CT].

Science.gov (United States)

Liang, Yueqiang; Xu, Hongbing; Li, Baosheng; Li, Hongsheng; Yang, Fujun

2012-06-01

Because the X-ray scatters, the CT numbers in cone-beam CT cannot exactly correspond to the electron densities. This, therefore, results in registration error when the intensity-based registration algorithm is used to register planning fan-beam CT and cone-beam CT. In order to reduce the registration error, we have developed an accurate gradient-based registration algorithm. The gradient-based deformable registration problem is described as a minimization of energy functional. Through the calculus of variations and Gauss-Seidel finite difference method, we derived the iterative formula of the deformable registration. The algorithm was implemented by GPU through OpenCL framework, with which the registration time was greatly reduced. Our experimental results showed that the proposed gradient-based registration algorithm could register more accurately the clinical cone-beam CT and fan-beam CT images compared with the intensity-based algorithm. The GPU-accelerated algorithm meets the real-time requirement in the online adaptive radiotherapy.

Free vibration of geometrically nonlinear micro-switches under electrostatic and Casimir forces

International Nuclear Information System (INIS)

Jia, X L; Kitipornchai, S; Lim, C W; Yang, J

2010-01-01

This paper investigates the free vibration characteristics of micro-switches under combined electrostatic, intermolecular forces and axial residual stress, with an emphasis on the effect of geometric nonlinear deformation due to mid-plane stretching and the influence of Casimir force. The micro-switch considered in this study is made of either homogeneous material or non-homogeneous functionally graded material with two material phases. The Euler–Bernoulli beam theory with von Karman type nonlinear kinematics is applied in the theoretical formulation. The principle of virtual work is used to derive the nonlinear governing differential equation. The eigenvalue problem which describes free vibration of the micro-beam at its statically deflected state is then solved using the differential quadrature method. The natural frequencies and mode shapes of micro-switches for four different boundary conditions (i.e. clamped–clamped, clamped–simply supported, simply supported and clamped–free) are obtained. The solutions are validated through direct comparisons with experimental and other existing results reported in previous studies. A parametric study is conducted to show the significant effects of geometric nonlinearity, Casimir force, axial residual stress and material composition for the natural frequencies

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.

Shear Strength of Concrete I-Beams - Contributions of Flanges

DEFF Research Database (Denmark)

Teoh, B. K.; Hoang, Cao Linh; Nielsen, Mogens Peter

1999-01-01

The contribution of flanges to the shear strength of reinforced concrete beams has up to now either been neglected or evaluated by very simple empirical formulas. However, the contribution may sometimes be large, up to 20-30%. In this paper the flange contribution for shear reinforced I-beams has...... range of geometrical parameters. The comparisons show that the method suggested does indeed lead to very accurate results....

Collimator for the SPS extracted beam

CERN Multimedia

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.

Stress and displacement analysis of a core plate, i.e. grid-perforated plate compound, modelled as an equivalent beam system

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.)

Mediastinal Hodgkin lymphomas in computertomography: exact CT-based volume assessment and approximations with simple geometric models; Mediastinale Hodgkin-Lymphone in der Computertomographie. Vergleich von exakter CT-gestuetzter Volumetrie und Volumenabschaetzung mit Hilfe einfacher geometrischer Modelle

Energy Technology Data Exchange (ETDEWEB)

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

Geometric and dosimetric verification of step-and-shoot modulated fields with a new fast and high resolution beam imaging system

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

Path Following in the Exact Penalty Method of Convex Programming.

Science.gov (United States)

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.

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

Geometrical optics analysis of the structural imperfection of retroreflection corner cubes with a nonlinear conjugate gradient method.

Science.gov (United States)

Kim, Hwi; Min, Sung-Wook; Lee, Byoungho

2008-12-01

Geometrical optics analysis of the structural imperfection of retroreflection corner cubes is described. In the analysis, a geometrical optics model of six-beam reflection patterns generated by an imperfect retroreflection corner cube is developed, and its structural error extraction is formulated as a nonlinear optimization problem. The nonlinear conjugate gradient method is employed for solving the nonlinear optimization problem, and its detailed implementation is described. The proposed method of analysis is a mathematical basis for the nondestructive optical inspection of imperfectly fabricated retroreflection corner cubes.

The Brookhaven ATF low-emittance beam line

International Nuclear Information System (INIS)

Wang, X.J.

1991-01-01

One component of the experimental program at the Brookhaven Accelerator Test Facility (ATF) consists of a class of experiments which will study the acceleration of electrons through micron-size structures which are exposed in coincidence to a 100 GW CO 2 laser beam. These experiments require the development and control of an electron beam with geometric emittances on the order of 10 -10 m-rad and intensities on the order of 10 6 electrons. In this paper, we describe the strategies for producing such beams and the effects of high-order aberrations. Particle tracking results are presented for the final-focus system. 9 refs., 6 figs., 2 tabs

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)

RELATIVISTIC DOPPLER BEAMING AND MISALIGNMENTS IN AGN JETS

International Nuclear Information System (INIS)

Singal, Ashok K.

2016-01-01

Radio maps of active galactic nuclei often show linear features, called jets, on both parsec and kiloparsec scales. These jets supposedly possess relativistic motion and are oriented close to the line of sight of the observer, and accordingly the relativistic Doppler beaming makes them look much brighter than they really are in their respective rest frames. The flux boosting due to the relativistic beaming is a very sensitive function of the jet orientation angle, as seen by the observer. Sometimes, large bends are seen in these jets, with misalignments being 90° or more, which might imply a change in the orientation angle that should cause a large change in the relativistic beaming factor. Hence, if relativistic beaming does play an important role in these jets such large bends should usually show high contrast in the brightness of the jets before and after the bend. It needs to be kept in mind that sometimes a small intrinsic change in the jet angle might appear as a much larger misalignment due to the effects of geometrical projection, especially when seen close to the line of sight. What really matters are the initial and final orientation angles of the jet with respect to the observer’s line of sight. Taking the geometrical projection effects properly into account, we calculate the consequences of the presumed relativistic beaming and demonstrate that there ought to be large brightness ratios in jets before and after the observed misalignments.

Relativistic Doppler Beaming and Misalignments in AGN Jets

Science.gov (United States)

Singal, Ashok K.

2016-08-01

Radio maps of active galactic nuclei often show linear features, called jets, on both parsec and kiloparsec scales. These jets supposedly possess relativistic motion and are oriented close to the line of sight of the observer, and accordingly the relativistic Doppler beaming makes them look much brighter than they really are in their respective rest frames. The flux boosting due to the relativistic beaming is a very sensitive function of the jet orientation angle, as seen by the observer. Sometimes, large bends are seen in these jets, with misalignments being 90° or more, which might imply a change in the orientation angle that should cause a large change in the relativistic beaming factor. Hence, if relativistic beaming does play an important role in these jets such large bends should usually show high contrast in the brightness of the jets before and after the bend. It needs to be kept in mind that sometimes a small intrinsic change in the jet angle might appear as a much larger misalignment due to the effects of geometrical projection, especially when seen close to the line of sight. What really matters are the initial and final orientation angles of the jet with respect to the observer’s line of sight. Taking the geometrical projection effects properly into account, we calculate the consequences of the presumed relativistic beaming and demonstrate that there ought to be large brightness ratios in jets before and after the observed misalignments.

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.

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

Measurement system and model for simultaneously measuring 6DOF geometric errors.

Science.gov (United States)

Zhao, Yuqiong; Zhang, Bin; Feng, Qibo

2017-09-04

A measurement system to simultaneously measure six degree-of-freedom (6DOF) geometric errors is proposed. The measurement method is based on a combination of mono-frequency laser interferometry and laser fiber collimation. A simpler and more integrated optical configuration is designed. To compensate for the measurement errors introduced by error crosstalk, element fabrication error, laser beam drift, and nonparallelism of two measurement beam, a unified measurement model, which can improve the measurement accuracy, is deduced and established using the ray-tracing method. A numerical simulation using the optical design software Zemax is conducted, and the results verify the correctness of the model. Several experiments are performed to demonstrate the feasibility and effectiveness of the proposed system and measurement model.

A Family of Exactly Solvable Radial Quantum Systems on Space of Non-Constant Curvature with Accidental Degeneracy in the Spectrum

Directory of Open Access Journals (Sweden)

Orlando Ragnisco

2010-12-01

Full Text Available A novel family of exactly solvable quantum systems on curved space is presented. The family is the quantum version of the classical Perlick family, which comprises all maximally superintegrable 3-dimensional Hamiltonian systems with spherical symmetry. The high number of symmetries (both geometrical and dynamical exhibited by the classical systems has a counterpart in the accidental degeneracy in the spectrum of the quantum systems. This family of quantum problem is completely solved with the techniques of the SUSYQM (supersymmetric quantum mechanics. We also analyze in detail the ordering problem arising in the quantization of the kinetic term of the classical Hamiltonian, stressing the link existing between two physically meaningful quantizations: the geometrical quantization and the position dependent mass quantization.

Visualizing the Geometric Series.

Science.gov (United States)

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)

Theory of third-harmonic generation using Bessel beams, and self-phase-matching

International Nuclear Information System (INIS)

Tewari, S.P.; Huang, H.; Boyd, R.W.

1996-01-01

Taking Bessel beams (J 0 beam) as a representation of a conical beam, and a slowly varying envelope approximation (SVEA) we obtain the results for the theory of third-harmonic generation from an atomic medium. We demonstrate how the phenomenon of self-phase-matching is contained in the transverse-phase-matching integral of the theory. A method to calculate the transverse-phase-matching integral containing four Bessel functions is described which avoids the computer calculations of the Bessel functions. In order to consolidate the SVEA result an alternate method is used to obtain the exact result for the third-harmonic generation. The conditions are identified in which the exact result goes over to the result of the SVEA. The theory for multiple Bessel beams is also discussed which has been shown to be the source of the wide width of the efficiency curve of the third-harmonic generation observed in experiments. copyright 1996 The American Physical Society

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

Geometric analysis

CERN Document Server

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.

An analytical model for shape memory alloy fiber-reinforced composite thin-walled beam undergoing large deflection

Directory of Open Access Journals (Sweden)

Yongsheng Ren

2015-03-01

Full Text Available The structural model of the thin-walled laminated beams with integral shape memory alloy active fibers and accounting for geometrically nonlinear is presented in this article. The structural modeling is split into two parts: a two-dimensional analysis over the cross section and a geometrically nonlinear analysis of a beam along the beam span. The variational asymptotic method is used to formulate the force–deformation relationship equations taking into account the presence of active shape memory alloy fibers distributed along the cross section of the beam. The geometrically nonlinear governing equations are derived using variational principle and based on the von Kármán-type nonlinear strain–displacement relations. The equations are then solved using Galerkin’s method and an incremental Newton–Raphson method. The validation for the proposed model has been carried out by comparison of the present results with those available in the literature. The results show that significant extension, bending, and twisting coupled nonlinear deflections occur during the phase transformation due to shape memory alloy actuation. The effects of the volume fraction of the shape memory alloy fiber and ply angle are also addressed.

Elastic analysis of beam support impact

International Nuclear Information System (INIS)

Salmon, M.A.; Verma, V.K.; Youtsos, T.G.

1982-01-01

The effect of gaps present in the seismic supports of nuclear piping systems has been studied with the use of such large general purpose analysis codes as ANSYS. Exact analytical solutions to two simple beam impact problems are obtained to serve as benchmarks for the evaluation of the ability of such codes to model impact between beam elements and their supports. Bernoulli-Euler beam theory and modal analysis are used to obtain analytical solutions for the motion of simply supported and fixed ended beams after impact with a spring support at midspan. The solutions are valid up to the time the beam loses contact with the spring support. Numerical results are obtained which show that convergence for both contact force and bending moment at the point of impact is slower as spring stiffness is increased. Finite element solutions obtained with ANSYS are compared to analytical results and good agreement is obtained

Spin-orbit beams for optical chirality measurement

Science.gov (United States)

Samlan, C. T.; Suna, Rashmi Ranjan; Naik, Dinesh N.; Viswanathan, Nirmal K.

2018-01-01

Accurate measurement of chirality is essential for the advancement of natural and pharmaceutical sciences. We report here a method to measure chirality using non-separable states of light with geometric phase-gradient in the circular polarization basis, which we refer to as spin-orbit beams. A modified polarization Sagnac interferometer is used to generate spin-orbit beams wherein the spin and orbital angular momentum of the input Gaussian beam are coupled. The out-of-phase interference between counter-propagating Gaussian beams with orthogonal spin states and lateral-shear or/and linear-phase difference between them results in spin-orbit beams with linear and azimuthal phase gradient. The spin-orbit beams interact efficiently with the chiral medium, inducing a measurable change in the center-of-mass of the beam, using the polarization rotation angle and hence the chirality of the medium are accurately calculated. Tunable dynamic range of measurement and flexibility to introduce large values of orbital angular momentum for the spin-orbit beam, to improve the measurement sensitivity, highlight the techniques' versatility.

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.

A Refined Zigzag Beam Theory for Composite and Sandwich Beams

Science.gov (United States)

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.

Beam Loss Simulation Studies for ALS Top-Off Operation

CERN Document Server

Nishimura, Hiroshi; Robin, David; Steier, Christoph

2005-01-01

The ALS is planning to operate with top-off injection at higher beam currents and smaller vertical beam size. As part of a radiation safety study for top-off, we carried out two kinds of tracking studies: (1) to confirm that the injected beam cannot go into users' photon beam lines, and (2) to control the location of beam dump when the storage ring RF is tripped. (1) is done by tracking electrons from a photon beam line to the injection sector inversely by including the magnetic field profiles, varying the field strength with geometric aperture limits to conclude that it is impossible. (2) is done by tracking an electron with radiation in the 6-dim space for different combinations of vertical scrapers for the realistic lattice with errors.

Torsion sensing based on patterned piezoelectric beams

Science.gov (United States)

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

CERN Document Server

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...

Auto calibration of a cone-beam-CT

International Nuclear Information System (INIS)

Gross, Daniel; Heil, Ulrich; Schulze, Ralf; Schoemer, Elmar; Schwanecke, Ulrich

2012-01-01

Purpose: This paper introduces a novel autocalibration method for cone-beam-CTs (CBCT) or flat-panel CTs, assuming a perfect rotation. The method is based on ellipse-fitting. Autocalibration refers to accurate recovery of the geometric alignment of a CBCT device from projection images alone, without any manual measurements. Methods: The authors use test objects containing small arbitrarily positioned radio-opaque markers. No information regarding the relative positions of the markers is used. In practice, the authors use three to eight metal ball bearings (diameter of 1 mm), e.g., positioned roughly in a vertical line such that their projection image curves on the detector preferably form large ellipses over the circular orbit. From this ellipse-to-curve mapping and also from its inversion the authors derive an explicit formula. Nonlinear optimization based on this mapping enables them to determine the six relevant parameters of the system up to the device rotation angle, which is sufficient to define the geometry of a CBCT-machine assuming a perfect rotational movement. These parameters also include out-of-plane rotations. The authors evaluate their method by simulation based on data used in two similar approaches [L. Smekal, M. Kachelriess, S. E, and K. Wa, “Geometric misalignment and calibration in cone-beam tomography,” Med. Phys. 31(12), 3242–3266 (2004); K. Yang, A. L. C. Kwan, D. F. Miller, and J. M. Boone, “A geometric calibration method for cone beam CT systems,” Med. Phys. 33(6), 1695–1706 (2006)]. This allows a direct comparison of accuracy. Furthermore, the authors present real-world 3D reconstructions of a dry human spine segment and an electronic device. The reconstructions were computed from projections taken with a commercial dental CBCT device having two different focus-to-detector distances that were both calibrated with their method. The authors compare their reconstruction with a reconstruction computed by the manufacturer of the

A cone-beam reconstruction algorithm using shift-variant filtering and cone-beam backprojection

International Nuclear Information System (INIS)

Defrise, M.; Clack, R.

1994-01-01

An exact inversion formula written in the form of shift-variant filtered-backprojection (FBP) is given for reconstruction from cone-beam data taken from any orbit satisfying Tuy's sufficiency conditions. The method is based on a result of Grangeat, involving the derivative of the three-dimensional (3-D) Radon transform, but unlike Grangeat's algorithm, no 3D rebinning step is required. Data redundancy, which occurs when several cone-beam projections supply the same values in the Radon domain, is handled using an elegant weighting function and without discarding data. The algorithm is expressed in a convenient cone-beam detector reference frame, and a specific example for the case of a dual orthogonal circular orbit is presented. When the method is applied to a single circular orbit, it is shown to be equivalent to the well-known algorithm of Feldkamp et al

Geometric and electronic structures of molecular ions from high energy collisions

International Nuclear Information System (INIS)

Groeneveld, K.O.

1983-01-01

This chapter examines the characteristics of heavy ion collision and of beam foil spectroscopy. It discusses the kinematic consequences of the high energies and presents results from ''Coulomb explosion'' and structure determination of molecular ions. It demonstrates that studies of molecular ions with accelerators can provide electronic and geometric structure information of molecules or molecular ions and points out that the understanding of the microscopic processes at such high energies is incomplete and needs further experimental and theoretical efforts

Analytical fan-beam and cone-beam reconstruction algorithms with uniform attenuation correction for SPECT

International Nuclear Information System (INIS)

Tang Qiulin; Zeng, Gengsheng L; Gullberg, Grant T

2005-01-01

In this paper, we developed an analytical fan-beam reconstruction algorithm that compensates for uniform attenuation in SPECT. The new fan-beam algorithm is in the form of backprojection first, then filtering, and is mathematically exact. The algorithm is based on three components. The first one is the established generalized central-slice theorem, which relates the 1D Fourier transform of a set of arbitrary data and the 2D Fourier transform of the backprojected image. The second one is the fact that the backprojection of the fan-beam measurements is identical to the backprojection of the parallel measurements of the same object with the same attenuator. The third one is the stable analytical reconstruction algorithm for uniformly attenuated Radon data, developed by Metz and Pan. The fan-beam algorithm is then extended into a cone-beam reconstruction algorithm, where the orbit of the focal point of the cone-beam imaging geometry is a circle. This orbit geometry does not satisfy Tuy's condition and the obtained cone-beam algorithm is an approximation. In the cone-beam algorithm, the cone-beam data are first backprojected into the 3D image volume; then a slice-by-slice filtering is performed. This slice-by-slice filtering procedure is identical to that of the fan-beam algorithm. Both the fan-beam and cone-beam algorithms are efficient, and computer simulations are presented. The new cone-beam algorithm is compared with Bronnikov's cone-beam algorithm, and it is shown to have better performance with noisy projections

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.

Rayleigh's hypothesis and the geometrical optics limit.

Science.gov (United States)

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.

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.

Failure modes of composite sandwich beams

Directory of Open Access Journals (Sweden)

Gdoutos E.

2008-01-01

Full Text Available A thorough investigation of failure behavior of composite sandwich beams under three-and four-point bending was undertaken. The beams were made of unidirectional carbon/epoxy facings and a PVC closed-cell foam core. The constituent materials were fully characterized and in the case of the foam core, failure envelopes were developed for general two-dimensional states of stress. Various failure modes including facing wrinkling, indentation failure and core failure were observed and compared with analytical predictions. The initiation, propagation and interaction of failure modes depend on the type of loading, constituent material properties and geometrical dimensions.

Neutral-beam aiming and calorimetry for MFTF-B

International Nuclear Information System (INIS)

Goldner, A.I.; Margolies, D.

1981-01-01

The vessel for the Tandem Mirror Fusion Test Facility (MFTF-B) will have up to eleven 0.5-s-duration neutral-beam injectors for the initial heating of the MFTF-B plasma. Knowing the exact alignment of the beams and their total power is critical to the performance of the experiment. Using prototype aiming and calorimetry systems on the High Voltage Test Stand (HVTS) at Lawrence Livermore National Laboratory (LLNL), we hope to prove our ability to obtain an aiming accuracy of +-1 cm at the plasma and a calorimetric accuracy of +-5% of the actual total beam energy

Geometrical parton

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.

Discrete geometric structures for architecture

KAUST Repository

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

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

Collaborative spectrum sensing based on the ratio between largest eigenvalue and Geometric mean of eigenvalues

KAUST Repository

Shakir, Muhammad

2011-12-01

In this paper, we introduce a new detector referred to as Geometric mean detector (GEMD) which is based on the ratio of the largest eigenvalue to the Geometric mean of the eigenvalues for collaborative spectrum sensing. The decision threshold has been derived by employing Gaussian approximation approach. In this approach, the two random variables, i.e. The largest eigenvalue and the Geometric mean of the eigenvalues are considered as independent Gaussian random variables such that their cumulative distribution functions (CDFs) are approximated by a univariate Gaussian distribution function for any number of cooperating secondary users and received samples. The approximation approach is based on the calculation of exact analytical moments of the largest eigenvalue and the Geometric mean of the eigenvalues of the received covariance matrix. The decision threshold has been calculated by exploiting the CDF of the ratio of two Gaussian distributed random variables. In this context, we exchange the analytical moments of the two random variables with the moments of the Gaussian distribution function. The performance of the detector is compared with the performance of the energy detector and eigenvalue ratio detector. Analytical and simulation results show that our newly proposed detector yields considerable performance advantage in realistic spectrum sensing scenarios. Moreover, our results based on proposed approximation approach are in perfect agreement with the empirical results. © 2011 IEEE.

A rotating and warping projector/backprojector for fan-beam and cone-beam iterative algorithm

International Nuclear Information System (INIS)

Zeng, G.L.; Hsieh, Y.L.; Gullberg, G.T.

1994-01-01

A rotating-and-warping projector/backprojector is proposed for iterative algorithms used to reconstruct fan-beam and cone-beam single photon emission computed tomography (SPECT) data. The development of a new projector/backprojector for implementing attenuation, geometric point response, and scatter models is motivated by the need to reduce the computation time yet to preserve the fidelity of the corrected reconstruction. At each projection angle, the projector/backprojector first rotates the image volume so that the pixelized cube remains parallel to the detector, and then warps the image volume so that the fan-beam and cone-beam rays are converted into parallel rays. In the authors implementation, these two steps are combined so that the interpolation of voxel values are performed only once. The projection operation is achieved by a simple weighted summation, and the backprojection operation is achieved by copying weighted projection array values to the image volume. An advantage of this projector/backprojector is that the system point response function can be deconvolved via the Fast Fourier Transform using the shift-invariant property of the point response when the voxel-to-detector distance is constant. The fan-beam and cone-beam rotating-and-warping projector/backprojector is applied to SPECT data showing improved resolution

Diffraction, self-focusing, and the geometrical optics limit in laser produced plasmas

International Nuclear Information System (INIS)

Marchand, R.; Rankin, R.; Capjack, C.E.; Birnboim, A.

1987-01-01

The effect of diffraction on the self-modulation of an intense laser beam in an initially uniform hydrogen plasma is investigated. A formalism is used in which the diffraction term in the paraxial wave equation can be arbitrarily reduced by the use of a weight factor iota. In the limit where iota approaches zero, it is shown that the paraxial wave equation correctly reduces to the geometrical optics limit and that the problem then becomes formally equivalent to solving the ray-tracing equations. When iota = 1, the paraxial wave equation takes its usual form and diffraction is fully accounted for. This formalism is applied to the simulation of self-modulation of an intense laser beam in a hydrogen plasma, for which diffraction is shown to be significant

Analyser-based phase contrast image reconstruction using geometrical optics.

Science.gov (United States)

Kitchen, M J; Pavlov, K M; Siu, K K W; Menk, R H; Tromba, G; Lewis, R A

2007-07-21

Analyser-based phase contrast imaging can provide radiographs of exceptional contrast at high resolution (geometrical optics are satisfied. Analytical phase retrieval can be performed by fitting the analyser rocking curve with a symmetric Pearson type VII function. The Pearson VII function provided at least a 10% better fit to experimentally measured rocking curves than linear or Gaussian functions. A test phantom, a hollow nylon cylinder, was imaged at 20 keV using a Si(1 1 1) analyser at the ELETTRA synchrotron radiation facility. Our phase retrieval method yielded a more accurate object reconstruction than methods based on a linear fit to the rocking curve. Where reconstructions failed to map expected values, calculations of the Takagi number permitted distinction between the violation of the geometrical optics conditions and the failure of curve fitting procedures. The need for synchronized object/detector translation stages was removed by using a large, divergent beam and imaging the object in segments. Our image acquisition and reconstruction procedure enables quantitative phase retrieval for systems with a divergent source and accounts for imperfections in the analyser.

Fast and Exact Fiber Surfaces for Tetrahedral Meshes.

Science.gov (United States)

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.

Geometric Design Laboratory

Data.gov (United States)

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...

Effects of geometrical frustration on ferromagnetism in the Hubbard model on the generalised Shastry-Sutherland lattice

Science.gov (United States)

Farkašovský, Pavol

2018-05-01

The small-cluster exact-diagonalization calculations and the projector quantum Monte Carlo method are used to examine the competing effects of geometrical frustration and interaction on ferromagnetism in the Hubbard model on the generalised Shastry-Sutherland lattice. It is shown that the geometrical frustration stabilizes the ferromagnetic state at high electron concentrations ( n ≳ 7/4), where strong correlations between ferromagnetism and the shape of the noninteracting density of states are observed. In particular, it is found that ferromagnetism is stabilized for these values of frustration parameters, which lead to the single-peaked noninterating density of states at the band edge. Once, two or more peaks appear in the noninteracting density of states at the band edge the ferromagnetic state is suppressed. This opens a new route towards the understanding of ferromagnetism in strongly correlated systems.

Empirical modeling of high-intensity electron beam interaction with materials

Science.gov (United States)

Koleva, E.; Tsonevska, Ts; Mladenov, G.

2018-03-01

The paper proposes an empirical modeling approach to the prediction followed by optimization of the exact shape of the cross-section of a welded seam, as obtained by electron beam welding. The approach takes into account the electron beam welding process parameters, namely, electron beam power, welding speed, and distances from the magnetic lens of the electron gun to the focus position of the beam and to the surface of the samples treated. The results are verified by comparison with experimental results for type 1H18NT stainless steel samples. The ranges considered of the beam power and the welding speed are 4.2 – 8.4 kW and 3.333 – 13.333 mm/s, respectively.

Nonlinear wave-beam kinetic equilibrium in decelerating systems

International Nuclear Information System (INIS)

Grishin, V.K.; Shaposhnikova, E.N.

1981-01-01

The equilibrium state of the wave-beam system arising during the interaction of a particle beam and excited electromagnetic wave has been investigated on the basis of the analysis of the exact polution of a non-linear self-consistent linear equation using the complete system of conservation laws. A waveguide with a dielectric filler, into which a monoenergetic particle beam magnetized in a transverse plane is continuously injected, is used as a model of an decelerating system. A dispersion equation describing the system state and expression for the evaluation of efficiency of the beam energy conversion to the field energy have been obtained. It is concluded that larae fields and high efficiency of energy conversion are achieved during the marked beam reconstruction. States with different values of current and beam velocity but similar amplitudes of a longitudinal field are possible in the system considered [ru

Exact reconstruction in 2D dynamic CT: compensation of time-dependent affine deformations

International Nuclear Information System (INIS)

Roux, Sebastien; Desbat, Laurent; Koenig, Anne; Grangeat, Pierre

2004-01-01

This work is dedicated to the reduction of reconstruction artefacts due to motion occurring during the acquisition of computerized tomographic projections. This problem has to be solved when imaging moving organs such as the lungs or the heart. The proposed method belongs to the class of motion compensation algorithms, where the model of motion is included in the reconstruction formula. We address two fundamental questions. First what conditions on the deformation are required for the reconstruction of the object from projections acquired sequentially during the deformation, and second how do we reconstruct the object from those projections. Here we answer these questions in the particular case of 2D general time-dependent affine deformations, assuming the motion parameters are known. We treat the problem of admissibility conditions on the deformation in the parallel-beam and fan-beam cases. Then we propose exact reconstruction methods based on rebinning or sequential FBP formulae for each of these geometries and present reconstructed images obtained with the fan-beam algorithm on simulated data

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.

Science.gov (United States)

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.

Comparative study of beam losses and heat loads reduction methods in MITICA beam source

Energy Technology Data Exchange (ETDEWEB)

Sartori, E., E-mail: emanuele.sartori@igi.cnr.it; Agostinetti, P.; Dal Bello, S.; Marcuzzi, D.; Serianni, G.; Veltri, P. [Consorzio RFX, Euratom-ENEA association, C.so Stati Uniti 4, 35127 Padova (Italy); Sonato, P. [Consorzio RFX, Euratom-ENEA association, C.so Stati Uniti 4, 35127 Padova (Italy); Dipartimento di Ingegneria Elettrica, Padova University, Via Gradenigo 6/a, 35131 Padova (Italy)

2014-02-15

In negative ion electrostatic accelerators a considerable fraction of extracted ions is lost by collision processes causing efficiency loss and heat deposition over the components. Stripping is proportional to the local density of gas, which is steadily injected in the plasma source; its pumping from the extraction and acceleration stages is a key functionality for the prototype of the ITER Neutral Beam Injector, and it can be simulated with the 3D code AVOCADO. Different geometric solutions were tested aiming at the reduction of the gas density. The parameter space considered is limited by constraints given by optics, aiming, voltage holding, beam uniformity, and mechanical feasibility. The guidelines of the optimization process are presented together with the proposed solutions and the results of numerical simulations.

The effect of photometric and geometric context on photometric and geometric lightness effects.

Science.gov (United States)

Lee, Thomas Y; Brainard, David H

2014-01-24

We measured the lightness of probe tabs embedded at different orientations in various contextual images presented on a computer-controlled stereo display. Two background context planes met along a horizontal roof-like ridge. Each plane was a graphic rendering of a set of achromatic surfaces with the simulated illumination for each plane controlled independently. Photometric context was varied by changing the difference in simulated illumination intensity between the two background planes. Geometric context was varied by changing the angle between them. We parsed the data into separate photometric effects and geometric effects. For fixed geometry, varying photometric context led to linear changes in both the photometric and geometric effects. Varying geometric context did not produce a statistically reliable change in either the photometric or geometric effects.

RC T beams strengthened to shear with carbon fiber composites

Directory of Open Access Journals (Sweden)

L. A. Spagnolo JR

Full Text Available This paper presents the experimental data of the behavior of reinforced concrete beams strengthened to shear with carbon fiber composites. The tests were composed of eight T beams, b w=15 cm, h=40 cm, flange width 40 cm, flange height 8 cm, and length 300 cm, divided into two series with the same longitudinal steel reinforcement and a reference beam without strengthening in each series. The beams had two types of arrangement of internal steel stirrups. The test variables were the internal and external geometric ratio of the transverse reinforcement and the mechanical ratio of carbon fiber composites stirrups. All the beams were loaded at two points. The strengthened beams were submitted to a preloading and the strengthening was applied to the cracked beam. All the beams were designed in order to guarantee shear failure, and the ultimate load of the strengthened beams was 36% to 54% greater than the reference beams. The Cracking Sliding Model applied to the strengthened beams was evaluated and showed good agreement with the experimental results.

Electron and photon spread contributions to the radiological penumbra for small monoenergetic x-ray beam (<=2 MeV)

Science.gov (United States)

Pignol, Jean-Philippe; Keller, Brian M.

2009-05-01

Our team has previously published that submegavoltage photons could significantly improve the radiological penumbra for small size radiation fields. The present work uses Monte Carlo simulation to evaluate the contributions of secondary electrons and photon scatter to the penumbra region for various field sizes (5, 10, 20, and 40 mm in diameters) and for various monoenergetic photon beams (200, 400, 600, 800, 1000, and 2000 keV, and a standard 6 MV beam), minimizing geometrical and transmission penumbra. For field sizes less than 2 cm in diameter, photon scatter is negligible such that the secondary electrons are the main contributor to the radiological penumbra. Reducing the photon beam energy to the submegavoltage range reduces the range of secondary electrons and eventually improves the beam boundary sharpness. Provided that the geometrical penumbra and patient immobilization system are optimized, submegavoltage photon beams with effective photon energies in the 300 to 600 keV range, present significant advantages for multiple beam stereotactic irradiations of tumors less than 2 cm in diameter.

New target solution for a muon collider or a muon-decay neutrino beam facility: The granular waterfall target

Directory of Open Access Journals (Sweden)

Han-Jie Cai

2017-02-01

Full Text Available A new target solution, the granular waterfall target, is proposed here for a muon collider or a muon-decay neutrino beam facility, especially for the moment which adopts a 15 MW continuous-wave (cw superconducting linac. Compared to the mercury jet target, the granular waterfall target works by a much simpler mechanism which can operate with a much more powerful beam, which are indicated by the detailed investigations into the heat depositions and the evaluations of the temperature increases for different target concepts. By varying proton beam kinetic energy and the geometrical parameters of the waterfall target, an overall understanding of the figure of merit concerning muon production for this target concept as the target solutions of the long-baseline neutrino factory and the medium-baseline moment is obtained. With 8 GeV beam energy and the optimal geometrical parameters, the influence on muon yield by adopting different beam-target interaction parameters is explored. Studies and discussions of the design details concerning beam dumping are also presented.

Three-body problem in d-dimensional space: Ground state, (quasi)-exact-solvability

Science.gov (United States)

Turbiner, Alexander V.; Miller, Willard; Escobar-Ruiz, M. A.

2018-02-01

As a straightforward generalization and extension of our previous paper [A. V. Turbiner et al., "Three-body problem in 3D space: Ground state, (quasi)-exact-solvability," J. Phys. A: Math. Theor. 50, 215201 (2017)], we study the aspects of the quantum and classical dynamics of a 3-body system with equal masses, each body with d degrees of freedom, with interaction depending only on mutual (relative) distances. The study is restricted to solutions in the space of relative motion which are functions of mutual (relative) distances only. It is shown that the ground state (and some other states) in the quantum case and the planar trajectories (which are in the interaction plane) in the classical case are of this type. The quantum (and classical) Hamiltonian for which these states are eigenfunctions is derived. It corresponds to a three-dimensional quantum particle moving in a curved space with special d-dimension-independent metric in a certain d-dependent singular potential, while at d = 1, it elegantly degenerates to a two-dimensional particle moving in flat space. It admits a description in terms of pure geometrical characteristics of the interaction triangle which is defined by the three relative distances. The kinetic energy of the system is d-independent; it has a hidden sl(4, R) Lie (Poisson) algebra structure, alternatively, the hidden algebra h(3) typical for the H3 Calogero model as in the d = 3 case. We find an exactly solvable three-body S3-permutationally invariant, generalized harmonic oscillator-type potential as well as a quasi-exactly solvable three-body sextic polynomial type potential with singular terms. For both models, an extra first order integral exists. For d = 1, the whole family of 3-body (two-dimensional) Calogero-Moser-Sutherland systems as well as the Tremblay-Turbiner-Winternitz model is reproduced. It is shown that a straightforward generalization of the 3-body (rational) Calogero model to d > 1 leads to two primitive quasi-exactly

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.)

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.

Different roles of electron beam in two stream instability in an elliptical waveguide for generation and amplification of THz electromagnetic waves

Energy Technology Data Exchange (ETDEWEB)

Safari, S.; Jazi, B., E-mail: jaziada@kashanu.ac.ir [Department of Laser and Photonics, Faculty of Physics, University of Kashan, Kashan, Islamic Republic of Iran (Iran, Islamic Republic of); Jahanbakht, S. [Department of Communications Engineering, Faculty of Electrical And Computer Engineering, University of Kashan, Kashan, Islamic Republic of Iran (Iran, Islamic Republic of)

2016-08-15

In this work, two stream instability in a metallic waveguide with elliptical cross-section and with a hollow annular dielectric layer is studied for generation and amplification of THz electromagnetic waves. Dispersion relation of waves and their dependents to geometric dimensions and characteristics of the electron beam are analyzed. In continuation, the diagrams of growth rate for some operating frequencies are presented, so that effective factors on the growth rates, such as geometrical dimensions, dielectric constant of dielectric layer, accelerating voltage, and applied current intensity are analyzed. It is shown that while an electron beam is responsible for instability, another electron beam plays a stabilizing role.

Self-repeating properties of four-petal Gaussian vortex beams in quadratic index medium

Science.gov (United States)

Zou, Defeng; Li, Xiaohui; Chai, Tong; Zheng, Hairong

2018-05-01

In this paper, we investigate the propagation properties of four-petal Gaussian vortex (FPGV) beams propagating through the quadratic index medium, obtaining the analytical expression of FPGV beams. The effects of beam order n, topological charge m and beam waist ω0 are investigated. Results show that quadratic index medium support periodic distributions of FPGV beams. A hollow optical wall or an optical central principal maximum surrounded by symmetrical sidelobes will occur at the center of a period. At length, they will evolve into four petals structure, exactly same as the intensity distributions at source plane.

Geometric group theory

CERN Document Server

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...

Defining the crack pattern of RC beams through the golden section

International Nuclear Information System (INIS)

Fantilli, A P; Chiaia, B; Cennamo, C

2011-01-01

Both in architecture and arts, the golden section has been exclusively taken into consideration for its geometrical properties. Specifically, among all the proportions, the golden section can inspire beauty. Indeed, it has driven the construction of buildings for centuries. Nevertheless, as discussed for the first time in the present paper, static equilibrium of structures calls the golden section into play. This is the case of reinforced concrete beam in four point bending, whose average crack spacing in the constant moment zone increases of a factor equal to the irrational number 1.61803 when the geometrical dimensions of the beam are doubled. In other words, it can be argued that the centrality of golden section in the art of construction has profound physical meanings, as it can bring together the aesthetic of nature and architecture, and the equilibrium of stress flow in solid bodies.

Defining the crack pattern of RC beams through the golden section

Energy Technology Data Exchange (ETDEWEB)

Fantilli, A P; Chiaia, B [Department of Structural and Geotechnical Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino 10129 (Italy); Cennamo, C, E-mail: alessandro.fantilli@polito.it [Department of ' Cultura del Progetto' , Universita di Napoli SUN, via San Lorenzo, Aversa 81031 (Italy)

2011-07-19

Both in architecture and arts, the golden section has been exclusively taken into consideration for its geometrical properties. Specifically, among all the proportions, the golden section can inspire beauty. Indeed, it has driven the construction of buildings for centuries. Nevertheless, as discussed for the first time in the present paper, static equilibrium of structures calls the golden section into play. This is the case of reinforced concrete beam in four point bending, whose average crack spacing in the constant moment zone increases of a factor equal to the irrational number 1.61803 when the geometrical dimensions of the beam are doubled. In other words, it can be argued that the centrality of golden section in the art of construction has profound physical meanings, as it can bring together the aesthetic of nature and architecture, and the equilibrium of stress flow in solid bodies.

A new model for the collective beam-beam interaction

Energy Technology Data Exchange (ETDEWEB)

Ellison, J.A.; Sobol, A.V. [New Mexico Univ., Albuquerque, NM (United States); Vogt, M. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

2006-09-15

The Collective Beam-Beam interaction is studied in the framework of maps with a ''kick-lattice'' model in 4-D phase space. A novel approach to the classical method of averaging is used to derive an approximate map which is equivalent to a flow within the averaging approximation. The flow equation is a continuous-time Vlasov equation which we call the averaged Vlasov equation, the new model of this paper. The power of this approach is evidenced by the fact that the averaged Vlasov equation has exact equilibria and the associated lineralized equations have uncoupled azimuthal Fourier modes. The equation for the Fourier modes leads to a Fredholm integral equation of the third kind and the setting is ready-made for the development of a weakly nonlinear theory to study the coupling of the {pi} and {sigma} modes. The {pi} and {sigma} modes are calculated from the third kind integral equation and results are compared with the kick-lattice model. (orig.)

A new model for the collective beam-beam interaction

International Nuclear Information System (INIS)

Ellison, J.A.; Sobol, A.V.; Vogt, M.

2006-09-01

The Collective Beam-Beam interaction is studied in the framework of maps with a ''kick-lattice'' model in 4-D phase space. A novel approach to the classical method of averaging is used to derive an approximate map which is equivalent to a flow within the averaging approximation. The flow equation is a continuous-time Vlasov equation which we call the averaged Vlasov equation, the new model of this paper. The power of this approach is evidenced by the fact that the averaged Vlasov equation has exact equilibria and the associated lineralized equations have uncoupled azimuthal Fourier modes. The equation for the Fourier modes leads to a Fredholm integral equation of the third kind and the setting is ready-made for the development of a weakly nonlinear theory to study the coupling of the π and σ modes. The π and σ modes are calculated from the third kind integral equation and results are compared with the kick-lattice model. (orig.)

Quasi-exact solutions of nonlinear differential equations

OpenAIRE

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.

Geometric constraints in semiclassical initial value representation calculations in Cartesian coordinates: accurate reduction in zero-point energy.

Science.gov (United States)

Issack, Bilkiss B; Roy, Pierre-Nicholas

2005-08-22

An approach for the inclusion of geometric constraints in semiclassical initial value representation calculations is introduced. An important aspect of the approach is that Cartesian coordinates are used throughout. We devised an algorithm for the constrained sampling of initial conditions through the use of multivariate Gaussian distribution based on a projected Hessian. We also propose an approach for the constrained evaluation of the so-called Herman-Kluk prefactor in its exact log-derivative form. Sample calculations are performed for free and constrained rare-gas trimers. The results show that the proposed approach provides an accurate evaluation of the reduction in zero-point energy. Exact basis set calculations are used to assess the accuracy of the semiclassical results. Since Cartesian coordinates are used, the approach is general and applicable to a variety of molecular and atomic systems.

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

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

Concept selection of car bumper beam with developed hybrid bio-composite material

International Nuclear Information System (INIS)

Davoodi, M.M.; Sapuan, S.M.; Ahmad, D.; Aidy, A.; Khalina, A.; Jonoobi, Mehdi

2011-01-01

Highlights: → We simulate the low impact test by Abaqus Ver16R9 using the same material model. → Six different weighted criteria were discussed to nominate the best concept. → Double Hat Profile showed the best concept to fulfil the defined PDS. → Geometric parameters may overcome the weak inherent properties of bio composite. → Toughened bio-composite material may employ in structural automotive components. -- Abstract: Application of natural fibre composites is going to increase in different areas caused by environmental, technical and economic advantages. However, their low mechanical properties have limited their particular application in automotive structural components. Hybridizations with other reinforcements or matrices can improve mechanical properties of natural fibre composite. Moreover, geometric optimizations have a significant role in structural strength improvement. This study focused on selecting the best geometrical bumper beam concept to fulfill the safety parameters of the defined product design specification (PDS). The mechanical properties of developed hybrid composite material were considered in different bumper beam concepts with the same frontal curvature, thickness, and overall dimensions. The low-speed impact test was simulated under the same conditions in Abaqus V16R9 software. Six weighted criteria, which were deflection, strain energy, mass, cost, easy manufacturing, and the rib possibility were analyzed to form an evaluation matrix. Topsis method was employed to select the best concept. It is concluded that double hat profile (DHP) with defined material model can be used for bumper beam of a small car. In addition, selected concept can be strengthened by adding reinforced ribs or increasing the thickness of the bumper beam to comply with the defined PDS.

Efficiently computing exact geodesic loops within finite steps.

Science.gov (United States)

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.

Analyser-based phase contrast image reconstruction using geometrical optics

International Nuclear Information System (INIS)

Kitchen, M J; Pavlov, K M; Siu, K K W; Menk, R H; Tromba, G; Lewis, R A

2007-01-01

Analyser-based phase contrast imaging can provide radiographs of exceptional contrast at high resolution (<100 μm), whilst quantitative phase and attenuation information can be extracted using just two images when the approximations of geometrical optics are satisfied. Analytical phase retrieval can be performed by fitting the analyser rocking curve with a symmetric Pearson type VII function. The Pearson VII function provided at least a 10% better fit to experimentally measured rocking curves than linear or Gaussian functions. A test phantom, a hollow nylon cylinder, was imaged at 20 keV using a Si(1 1 1) analyser at the ELETTRA synchrotron radiation facility. Our phase retrieval method yielded a more accurate object reconstruction than methods based on a linear fit to the rocking curve. Where reconstructions failed to map expected values, calculations of the Takagi number permitted distinction between the violation of the geometrical optics conditions and the failure of curve fitting procedures. The need for synchronized object/detector translation stages was removed by using a large, divergent beam and imaging the object in segments. Our image acquisition and reconstruction procedure enables quantitative phase retrieval for systems with a divergent source and accounts for imperfections in the analyser

Enhancement of quasi-static strain energy harvesters using non-uniform cross-section post-buckled beams

Science.gov (United States)

Jiao, Pengcheng; Borchani, Wassim; Hasni, Hassene; Lajnef, Nizar

2017-08-01

Thanks to their efficiency enhancement systems based on post-buckled structural elements have been extensively used in many applications such as actuation, remote sensing and energy harvesting. The post-buckling snap-through behavior of bilaterally constrained beams has been exploited to create sensing or energy harvesting mechanisms for quasi-static applications. The conversion mechanism has been used to transform low-rate and low-frequency excitations into high-rate motions. Electric energy has been generated from such high-rate motions using piezoelectric transducers. However, lack of control over the post-buckling behavior severely limits the mechanism’s efficiency. This study aims to maximize the levels of harvestable power by controlling the location of snap-throughs along the beam at different buckling transitions. Since the snap-through location cannot be controlled by tuning the geometric properties of a uniform beam, non-uniform cross-sections are examined. An energy-based theoretical model is herein developed to predict the post-buckling response of non-prismatic beams. The total potential energy is minimized under constraints that represent the physical confinement of the beam between the lateral boundaries. The experimentally validated results show that changing the shape and geometric dimensions of non-uniform beams allows for the accurate controlling of the snap-through location at different buckling transitions. A 78.59% improvement in harvested energy levels has been achieved by optimization of beam shape.

Generalization of the geometric optical series approach for nonadiabatic scattering problems

International Nuclear Information System (INIS)

Herman, M.F.

1982-01-01

The geometric optical series approach of Bremmer is generalized for multisurface nonadiabatic scattering problems. This method yields the formal solution of the Schroedinger equation as an infinite series of multiple integrals. The zeroth order term corresponds to WKB propagation on a single adiabatic surface, while the general Nth order term involves N reflections and/or transitions between surfaces accompanied by ''free,'' single surface semiclassical propagation between the points of reflection and transition. Each term is integrated over all possible transition and reflection points. The adiabatic and diabatic limits of this expression are discussed. Numerical results, in which all reflections are ignored, are presented for curve crossing and noncrossing problems. These results are compared to exact quantum results and are shown to be highly accurate

Geometric metamorphosis.

Science.gov (United States)

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.

Wigner distribution function of circularly truncated light beams

NARCIS (Netherlands)

Bastiaans, M.J.; Nijhawan, O.P.; Gupta, A.K.; Musla, A.K.; Singh, Kehar

1998-01-01

Truncating a light beam is expressed as a convolution of its Wigner distribution function and the WDF of the truncating aperture. The WDF of a circular aperture is derived and an approximate expression - which is exact in the space and the spatial-frequency origin and whose integral over the spatial

Invisibility Cloaking Based on Geometrical Optics for Visible Light

Science.gov (United States)

Ichikawa, H.; Oura, M.; Taoda, T.

2013-06-01

Optical cloaking has been one of unattainable dreams and just a subject in fiction until recently. Several different approaches to cloaking have been proposed and demonstrated: stealth technology, active camouflage and transformation optics. The last one would be the most formal approach modifying electromagnetic field around an object to be cloaked with metamaterials. While cloaking based on transformation optics, though valid only at single frequency, is experimentally demonstrated in microwave region, its operation in visible spectrum is still distant from realisation mainly owing to difficulty in fabricating metamaterial structure whose elements are much smaller than wavelength of light. Here we show that achromatic optical cloaking in visible spectrum is possible with the mere principle based on geometrical optics. In combining a pair of polarising beam splitters and right-angled prisms, rays of light to be obstructed by an object can make a detour to an observer, while unobstructed rays go straight through two polarising beam splitters. What is observed eventually through the device is simply background image as if nothing exists in between.

Analysis of Dynamic Geometric Configuration of the Aortic Channel from the Perspective of Tornado-Like Flow Organization of Blood Flow.

Science.gov (United States)

Zhorzholiani, Sh T; Mironov, A A; Talygin, E A; Tsyganokov, Yu M; Agafonov, A M; Kiknadze, G I; Gorodkov, A Yu; Bokeriya, L A

2018-03-01

Analysis of the data of morphometry of aortic casts, aortography at different pressures, and multispiral computer tomography of the aorta with contrast and normal pulse pressure showed that geometric configuration of the flow channel of the aorta during the whole cardiac cycle corresponded to the conditions of self-organization of tornado-like quasipotential flow described by exact solutions of the Navier-Stokes equation and continuity of viscous fluid typical for this type of fluid flows. Increasing pressure in the aorta leads to a decrease in the degree of approximation of the channel geometry to the ratio of exact solution and increases the risk of distortions in the structure of the flow. A mechanism of evolution of tornado-like flow in the aorta was proposed.

Image-guided small animal radiation research platform: calibration of treatment beam alignment

International Nuclear Information System (INIS)

Matinfar, Mohammad; Iordachita, Iulian; Kazanzides, Peter; Ford, Eric; Wong, John

2009-01-01

Small animal research allows detailed study of biological processes, disease progression and response to therapy with the potential to provide a natural bridge to the clinical environment. The small animal radiation research platform (SARRP) is a portable system for precision irradiation with beam sizes down to approximately 0.5 mm and optimally planned radiation with on-board cone-beam CT (CBCT) guidance. This paper focuses on the geometric calibration of the system for high-precision irradiation. A novel technique for the calibration of the treatment beam is presented, which employs an x-ray camera whose precise positioning need not be known. Using the camera system we acquired a digitally reconstructed 3D 'star shot' for gantry calibration and then developed a technique to align each beam to a common isocenter with the robotic animal positioning stages. The calibration incorporates localization by cone-beam CT guidance. Uncorrected offsets of the beams with respect to the calibration origin ranged from 0.4 mm to 5.2 mm. With corrections, these alignment errors can be reduced to the sub-millimeter range. The calibration technique was used to deliver a stereotactic-like arc treatment to a phantom constructed with EBT Gafchromic films. All beams were shown to intersect at a common isocenter with a measured beam (FWHM) of approximately 1.07 mm using the 0.5 mm collimated beam. The desired positioning accuracy of the SARRP is 0.25 mm and the results indicate an accuracy of 0.2 mm. To fully realize the radiation localization capabilities of the SARRP, precise geometric calibration is required, as with any such system. The x-ray camera-based technique presented here provides a straightforward and semi-automatic method for system calibration.

Large amplitude forced vibration analysis of cross-beam system ...

African Journals Online (AJOL)

Large amplitude forced vibration behaviour of cross-beam system under harmonic excitation is studied, incorporating the effect of geometric non-linearity. The forced vibration analysis is carried out in an indirect way, in which the dynamic system is assumed to satisfy the force equilibrium condition at peak load value, thus ...

Perturbation treatment of the longitudinal coupling impedance of a toroidal beam tube

International Nuclear Information System (INIS)

Hahn, H.; Tepikian, S.

1991-01-01

A simple analytical expression for the longitudinal coupling impedance of a toroidal beam tube below the resonance region has been derived by expanding the electromagnetic fields of the toroidal beam tube in a power series in curvature and substituting directly into Maxwell's equations. The resulting expression consists of the impedance of the straight beam pipe plus a correction terms due to the curvature. It has been verified that this result gives excellent agreement to the exact solution below the first resonance. 5 refs., 2 figs., 3 tabs

Geometric Nonlinear Computation of Thin Rods and Shells

Science.gov (United States)

Grinspun, Eitan

2011-03-01

We develop simple, fast numerical codes for the dynamics of thin elastic rods and shells, by exploiting the connection between physics, geometry, and computation. By building a discrete mechanical picture from the ground up, mimicking the axioms, structures, and symmetries of the smooth setting, we produce numerical codes that not only are consistent in a classical sense, but also reproduce qualitative, characteristic behavior of a physical system----such as exact preservation of conservation laws----even for very coarse discretizations. As two recent examples, we present discrete computational models of elastic rods and shells, with straightforward extensions to the viscous setting. Even at coarse discretizations, the resulting simulations capture characteristic geometric instabilities. The numerical codes we describe are used in experimental mechanics, cinema, and consumer software products. This is joint work with Miklós Bergou, Basile Audoly, Max Wardetzky, and Etienne Vouga. This research is supported in part by the Sloan Foundation, the NSF, Adobe, Autodesk, Intel, the Walt Disney Company, and Weta Digital.

A geometric parameter study of piezoelectric coverage on a rectangular cantilever energy harvester

International Nuclear Information System (INIS)

Patel, R; McWilliam, S; Popov, A A

2011-01-01

This paper proposes a versatile model for optimizing the performance of a rectangular cantilever beam piezoelectric energy harvester used to convert ambient vibrations into electrical energy. The developed model accounts for geometric changes to the natural frequencies, mode shapes and damping in the structure. This is achieved through the combination of finite element modelling and a distributed parameter electromechanical model, including load resistor and charging capacitor models. The model has the potential for use in investigating the influence of numerous geometric changes on harvester performance, and incorporates a model for accounting for changes in damping as the geometry changes. The model is used to investigate the effects of substrate and piezoelectric layer length, and piezoelectric layer thickness on the performance of a microscale device. Findings from a parameter study indicate the existence of an optimum sample length due to increased mechanical damping for longer beams and improved power output using thicker piezoelectric layers. In practice, harvester design is normally based around a fixed operating frequency for a particular application, and improved performance is often achieved by operating at or near resonance. To achieve unbiased comparisons between different harvester designs, parameter studies are performed by changing multiple parameters simultaneously with the natural frequency held fixed. Performance enhancements were observed using shorter piezoelectric layers as compared to the conventional design, in which the piezoelectric layer and substrate are of equal length

Axial geometrical aberration correction up to 5th order with N-SYLC.

Science.gov (United States)

Hoque, Shahedul; Ito, Hiroyuki; Takaoka, Akio; Nishi, Ryuji

2017-11-01

We present N-SYLC (N-fold symmetric line currents) models to correct 5th order axial geometrical aberrations in electron microscopes. In our previous paper, we showed that 3rd order spherical aberration can be corrected by 3-SYLC doublet. After that, mainly the 5th order aberrations remain to limit the resolution. In this paper, we extend the doublet to quadruplet models also including octupole and dodecapole fields for correcting these higher order aberrations, without introducing any new unwanted ones. We prove the validity of our models by analytical calculations. Also by computer simulations, we show that for beam energy of 5keV and initial angle 10mrad at the corrector object plane, beam size of less than 0.5nm is achieved at the corrector image plane. Copyright © 2017 Elsevier B.V. All rights reserved.

Geometric Structure of 3D Spinal Curves: Plane Regions and Connecting Zones

Science.gov (United States)

Berthonnaud, E.; Hilmi, R.; Dimnet, J.

2012-01-01

This paper presents a new study of the geometric structure of 3D spinal curves. The spine is considered as an heterogeneous beam, compound of vertebrae and intervertebral discs. The spine is modeled as a deformable wire along which vertebrae are beads rotating about the wire. 3D spinal curves are compound of plane regions connected together by zones of transition. The 3D spinal curve is uniquely flexed along the plane regions. The angular offsets between adjacent regions are concentrated at level of the middle zones of transition, so illustrating the heterogeneity of the spinal geometric structure. The plane regions along the 3D spinal curve must satisfy two criteria: (i) a criterion of minimum distance between the curve and the regional plane and (ii) a criterion controlling that the curve is continuously plane at the level of the region. The geometric structure of each 3D spinal curve is characterized by the sizes and orientations of regional planes, by the parameters representing flexed regions and by the sizes and functions of zones of transition. Spinal curves of asymptomatic subjects show three plane regions corresponding to spinal curvatures: lumbar, thoracic and cervical curvatures. In some scoliotic spines, four plane regions may be detected. PMID:25031873

Flexural-torsional vibration of a tapered C-section beam

Science.gov (United States)

Dennis, Scott T.; Jones, Keith W.

2017-04-01

Previous studies have shown that numerical models of tapered thin-walled C-section beams based on a stepped or piecewise prismatic beam approximation are inaccurate regardless of the number of elements assumed in the discretization. Andrade recently addressed this problem by extending Vlasov beam theory to a tapered geometry resulting in new terms that vanish for the uniform beam. (See One-Dimensional Models for the Spatial Behaviour of Tapered Thin-Walled Bars with Open Cross-Sections: Static, Dynamic and Buckling Analyses, PhD Thesis, University of Coimbra, Portugal, 2012, https://estudogeral.sib.uc.pt) In this paper, we model the coupled bending-twisting vibration of a cantilevered tapered thin-walled C-section using a Galerkin approximation of Andrade's beam equations resulting in an 8-degree-of-freedom beam element. Experimental natural frequencies and mode shapes for 3 prismatic and 2 tapered channel beams are compared to model predictions. In addition, comparisons are made to detailed shell finite element models and exact solutions for the uniform beams to confirm the validity of the approach. Comparisons to the incorrect stepped model are also presented.

Non-material finite element modelling of large vibrations of axially moving strings and beams

Science.gov (United States)

Vetyukov, Yury

2018-02-01

We present a new mathematical model for the dynamics of a beam or a string, which moves in a given axial direction across a particular domain. Large in-plane vibrations are coupled with the gross axial motion, and a Lagrangian (material) form of the equations of structural mechanics becomes inefficient. The proposed mixed Eulerian-Lagrangian description features mechanical fields as functions of a spatial coordinate in the axial direction. The material travels across a finite element mesh, and the boundary conditions are applied in fixed nodes. Beginning with the variational equation of virtual work in its material form, we analytically derive the Lagrange's equations of motion of the second kind for the considered case of a discretized non-material control domain and for geometrically exact kinematics. The dynamic analysis is straightforward as soon as the strain and the kinetic energies of the control domain are available. In numerical simulations we demonstrate the rapid mesh convergence of the model, the effect of the bending stiffness and the dynamic instability when the axial velocity gets high. We also show correspondence to the results of fully Lagrangian benchmark solutions.

Dynamic modeling of geometrically nonlinear electrostatically actuated microbeams (Corotational Finite Element formulation and analysis)

Energy Technology Data Exchange (ETDEWEB)

Borhan, H; Ahmadian, M T [Sharif University of Technology, Center of Excellence for Design, Robotics and Automation, School of Mechanical Engineering, PO Box 11365-9567, Tehran (Iran, Islamic Republic of)

2006-04-01

In this paper, a complete nonlinear finite element model for coupled-domain MEMS devices with electrostatic actuation and squeeze film effect is developed. For this purpose, a corotational finite element formulation for the dynamic analysis of planer Euler beams is employed. In this method, the internal nodal forces due to deformation and intrinsic residual stresses, the inertial nodal forces, and the damping effect of squeezed air film are systematically derived by consistent linearization of the fully geometrically nonlinear beam theory using d'Alamber and virtual work principles. An incremental-iterative method based on the Newmark direct integration procedure and the Newton-Raphson algorithm is used to solve the nonlinear dynamic equilibrium equations. Numerical examples are presented and compared with experimental findings which indicate properly good agreement.

Effect of geometrical features various objects on the data quality obtained with measured by TLS

Science.gov (United States)

Pawłowicz, J. A.

2017-08-01

Collecting data on different building structures using Terrestrial Laser Scanning (TLS) has become in recent years a very popular due to minimize the time required to complete the task as compared to traditional methods. Technical parameters of 3D scanning devices (digitizers) are increasingly being improved, and the accuracy of the data collected allows you to play not only the geometry of an existing object in a digital image, but also enables the assessment of his condition. This is possible thanks to the digitalization of existing objects e.g., a 3D laser scanner, with which is obtained a digital data base is presented in the form of a cloud of points and by using reverse engineering. Measurements using laser scanners depends to a large extent, on the quality of the returning beam reflected from the target surface, towards the receiver. High impact on the strength and quality of the beam returning to the geometric features of the object. These properties may contribute to the emergence of some, sometimes even serious errors during scanning of various shapes. The study defined the effect of the laser beam distortion during the measurement objects with the same material but with different geometrical features on their three-dimensional imaging obtained from measurements made using TLS. We present the problem of data quality, dependent on the deflection of the beam intensity and shape of the object selected examples. The knowledge of these problems allows to obtain valuable data necessary for the implementation of digitization and the visualization of virtually any building structure made of any materials. The studies has been proven that the increase in the density of scanning does not affect the values of mean square error. The increase in the angle of incidence of the beam onto a flat surface, however, causes a decrease in the intensity of scattered radiation that reaches the receiver. The article presents an analysis of the laser beam reflected from broken at

Beam-smiling in bent-Laue monochromators

International Nuclear Information System (INIS)

Ren, B.; Dilmanian, F. A.; Wu, X. Y.; Huang, X.; Chapman, L. D.; Ivanov, I.; Zhong, Z.; Thomlinson, W. C.

1997-01-01

When a wide fan-shaped x-ray beam is diffracted by a bent crystal in the Laue geometry, the profile of the diffracted beam generally does not appear as a straight line, but as a line with its ends curved up or curved down. This effect, referred to as 'beam-smiling', has been a major obstacle in developing bent-Laue crystal monochromators for medical applications of synchrotron x-ray. We modeled a cylindrically bent crystal using the Finite Element Analysis (FEA) method, and we carried out experiments at the National Synchrotron Light Source and Cornell High Energy Synchrotron Source. Our studies show that, while beam-smiling exists in most of the crystal's area because of anticlastic bending effects, there is a region parallel to the bending axis of the crystal where the diffracted beam is 'smile-free'. By applying asymmetrical bending, this smile-free region can be shifted vertically away from the geometric center of the crystal, as desired. This leads to a novel method of compensating for beam-smiling. We will discuss the method of ''differential bending'' for smile removal, beam-smiling in the Cauchios and the polychromatic geometry, and the implications of the method on developing single- and double-bent Laue monochromators. The experimental results will be discussed, concentrating on specific beam-smiling observation and removal as applied to the new monochromator of the Multiple Energy Computed Tomography [MECT] project of the Medical Department, Brookhaven National Laboratory

Introduction to the polymorphic tracking code Fibre bundles, polymorphic Taylor types and "Exact tracking"

CERN Document Server

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...

Geometric Mixing, Peristalsis, and the Geometric Phase of the Stomach.

Science.gov (United States)

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.

A geometric formulation of the law of Aboav–Weaire in two and three dimensions

International Nuclear Information System (INIS)

Mason, J K; Ehrenborg, R; Lazar, E A

2012-01-01

The law of Aboav–Weaire is a simple mathematical expression deriving from empirical observations that the number of sides of a grain is related to the average number of sides of the neighboring grains, and is usually restricted to natural two-dimensional microstructures. Numerous attempts have been made to justify this relationship theoretically, or to derive an analogous relation in three dimensions. This paper provides several exact geometric results with expressions similar to that of the usual law of Aboav–Weaire, though with additional terms that may be used to establish when the law of Abaov–Weaire is a suitable approximation. Specifically, we derive several local relations that apply to individual grain clusters, and a corresponding global relation that is identical in two and three dimensions except for a single parameter ζ. The derivation requires the definition and investigation of the average excess curvature, a previously unconsidered physical quantity. An approximation to our exact result is compared to the results of extensive simulations in two and three dimensions, and we provide a compact expression that strikes a balance between complexity and accuracy. (paper)

Self-interference digital holography with a geometric-phase hologram lens.

Science.gov (United States)

Choi, KiHong; Yim, Junkyu; Yoo, Seunghwi; Min, Sung-Wook

2017-10-01

Self-interference digital holography (SIDH) is actively studied because the hologram acquisition under the incoherent illumination condition is available. The key component in this system is wavefront modulating optics, which modulates an incoming object wave into two different wavefront curvatures. In this Letter, the geometric-phase hologram lens is introduced in the SIDH system to perform as a polarization-sensitive wavefront modulator and a single-path beam splitter. This special optics has several features, such as high transparency, a modulation efficiency up to 99%, a thinness of a few millimeters, and a flat structure. The demonstration system is devised, and the numerical reconstruction results from an acquired complex hologram are presented.

Performance requirements of the MedAustron beam delivery system

CERN Document Server

AUTHOR|(CDS)2073034

The Austrian hadron therapy center MedAustron is currently under construction with patient treatment planned to commence in 2015. Tumors will be irradiated using proton and carbon ions, for which the steeply rising Bragg curve and finite range offer a better conformity of the dose to the geometrical shape of the tumor compared to conventional photon irradiation. The current trend is to move from passive scattering toward active scanning using a narrow pencil beam in order to reach an even better dose conformation and limit the need of patient specific hardware. The quality of the deposited dose will ultimately depend on the performance of the beam delivery chain: beam profile and extraction stability of the extracted beam, accuracy and ramp rate of the scanning magnet power supplies, and precision of the beam monitors used for verifying the delivered dose. With a sharp lateral penumbra, the transverse dose fall-off can be minimized. This is of particular importance in situations where the lesion is adjace...

Bifurcation and chaos of an axially accelerating viscoelastic beam

International Nuclear Information System (INIS)

Yang Xiaodong; Chen Liqun

2005-01-01

This paper investigates bifurcation and chaos of an axially accelerating viscoelastic beam. The Kelvin-Voigt model is adopted to constitute the material of the beam. Lagrangian strain is used to account for the beam's geometric nonlinearity. The nonlinear partial-differential equation governing transverse motion of the beam is derived from the Newton second law. The Galerkin method is applied to truncate the governing equation into a set of ordinary differential equations. By use of the Poincare map, the dynamical behavior is identified based on the numerical solutions of the ordinary differential equations. The bifurcation diagrams are presented in the case that the mean axial speed, the amplitude of speed fluctuation and the dynamic viscoelasticity is respectively varied while other parameters are fixed. The Lyapunov exponent is calculated to identify chaos. From numerical simulations, it is indicated that the periodic, quasi-periodic and chaotic motions occur in the transverse vibrations of the axially accelerating viscoelastic beam

Relativistic Beaming and Orientation Effects in BL Lacertae Objects ...

Indian Academy of Sciences (India)

tation paradigm for high peaked and low-peaked BL Lacs (X-ray and radio selected .... consequences of relativistic beaming and geometric projection were studied in high- ... model. If we assume α = 0 (for synchrotron self-absorbed sources) and β ∼ 1, it can .... for RBL and XBL subsamples at confidence level of ∼ 95.0%.

Exact piecewise flat gravitational waves

NARCIS (Netherlands)

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

Scattering and extinction of ion beams in a dusty plasma device

International Nuclear Information System (INIS)

Nakamura, Y.

2001-01-01

Collisions of ions with charged dust grains are important for the propagation of low frequency waves such as dust acoustic waves and dust ion-acoustic waves. The collision cross-sectional area of charged dust grains depends on the velocity of an ion beam. The collision cross-sectional area of charged dust grains with beam ions is measured. It is compared with the geometrical cross-sectional area of the grain. The experiment is performed in a dusty double-plasma device with glass beads of 8.9 μm in average diameter. The ion beam current and energy are measured with a directional retarding potential analyzer. It is observed that, when dust density inside the system is increased, the beam current ratio is reduced. From the reduction of the ion beam current, the effective cross-sectional area of the dust particle is estimated as a function of the beam energy

Geometric Phase Generated Optical Illusion.

Science.gov (United States)

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.

An exact solution of the extinction problem in supercritical multiplying systems

International Nuclear Information System (INIS)

Williams, M.M.R.

1979-01-01

Using the point model approximation and one-speed theory with no delayed neutrons a probability balance equation for neutrons by the backward method has been constructed. This probability gives the distribution of neutrons in a multiplying medium at a given time and also the distribution that a chain will have generated a specified number of neutrons before extinction. We consider the limit of this probability for super and subcritical systems for long times after the initial triggering neutron. This leads to the extinction probability and to the individual probabilities of neutron population. To obtain specific results we have used a variety of models for the neutron multiplicity in the fission process, ie Poisson, birth and death, geometric and binomial. Exact solutions for the extinction probability have been obtained and its sensitivity to various parameters examined. Finally, we use the 'quadratic approximation' and assess its accuracy; it is found to overestimate the extinction probability and to be useful only for multiplication factors near unity. (author)

The target volume concept at the recording of external beam radiotherapy

International Nuclear Information System (INIS)

Quast, U.; Glaeser, L.

1981-01-01

With the aim of complete, exact and reproducible manual recording and documentation of external beam radiotherapy a concept is proposed providing treatment planning and recording related to space and time for target volumes of different order corresponding to Ist, IInd or IIIrd part of treatment course, regarding all dose limiting organs at risk. The record consists of the dosage plan for medical treatment planning, the treatment plan for physical dose distribution planning and the treatment record of absorbed doses delivered as well as a checklist for patient and machine set-up, and labels for intended actions during treatment development. A clear arrangement of the record form in logical order was found, demanding exact specification of target(s) and beam(s) and their relation in space and time; asking for verbal and graphical description of target volumes, organs at risk, patient positioning, beam portals and dose reference points in terms of patients' anatomy; emphasizing the most important medical data by marked areas and leaving enough empty space for additional data, remarks or comments. During several years of clinical use these record forms proved to be suitable for all cases of external beam therapy, for complex situations of target volumes and treatment-scheduling, for all treatment techniques and radiation qualities and for all ways of physical treatment planning. They can be extended to automatic treatment verification, monitoring and recording as well as to the application of in-vivo-measurements of absorbed doses. (orig.) [de

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

Geometrical optical illusionists.

Science.gov (United States)

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.

A simple geometrical model describing shapes of soap films suspended on two rings

Science.gov (United States)

Herrmann, Felix J.; Kilvington, Charles D.; Wildenberg, Rebekah L.; Camacho, Franco E.; Walecki, Wojciech J.; Walecki, Peter S.; Walecki, Eve S.

2016-09-01

We measured and analysed the stability of two types of soap films suspended on two rings using the simple conical frusta-based model, where we use common definition of conical frustum as a portion of a cone that lies between two parallel planes cutting it. Using frusta-based we reproduced very well-known results for catenoid surfaces with and without a central disk. We present for the first time a simple conical frusta based spreadsheet model of the soap surface. This very simple, elementary, geometrical model produces results surprisingly well matching the experimental data and known exact analytical solutions. The experiment and the spreadsheet model can be used as a powerful teaching tool for pre-calculus and geometry students.

Transverse acceptance calculation for continuous ion beam injection into the electron beam ion trap charge breeder of the ReA post-accelerator

Energy Technology Data Exchange (ETDEWEB)

Kittimanapun, K., E-mail: kritsadak@slri.or.th [National Superconducting Cyclotron Laboratory (NSCL), Michigan State University (MSU), 640 S. Shaw Lane, East Lansing, Michigan 48824 (United States); Synchrotron Light Research Institute (SLRI), 111 University Avenue, Muang District, Nakhon Ratchasima, 30000 (Thailand); Baumann, T.M.; Lapierre, A.; Schwarz, S. [National Superconducting Cyclotron Laboratory (NSCL), Michigan State University (MSU), 640 S. Shaw Lane, East Lansing, Michigan 48824 (United States); Bollen, G. [National Superconducting Cyclotron Laboratory (NSCL), Michigan State University (MSU), 640 S. Shaw Lane, East Lansing, Michigan 48824 (United States); Facility for Rare Isotope Beams (FRIB), Michigan State University, 640 S. Shaw Lane, East Lansing, Michigan 48824 (United States)

2015-11-11

The ReA post-accelerator at the National Superconducting Cyclotron Laboratory (NSCL) employs an electron beam ion trap (EBIT) as a charge breeder. A Monte-Carlo simulation code was developed to calculate the transverse acceptance phase space of the EBIT for continuously injected ion beams and to determine the capture efficiency in dependence of the transverse beam emittance. For this purpose, the code records the position and time of changes in charge state of injected ions, leading either to capture or loss of ions. To benchmark and validate the code, calculated capture efficiencies were compared with results from a geometrical model and measurements. The results of the code agree with the experimental findings within a few 10%. The code predicts a maximum total capture efficiency of 50% for EBIT parameters readily achievable and an efficiency of up to 80% for an electron beam current density of 1900 A/cm{sup 2}.

Enhancing neutron beam production with a convoluted moderator

Energy Technology Data Exchange (ETDEWEB)

Iverson, E.B., E-mail: iversoneb@ornl.gov [Spallation Neutron Source, Oak Ridge National Laboratory, Oak Ridge, TN 37831 (United States); Baxter, D.V. [Center for the Exploration of Energy and Matter, Indiana University, Bloomington, IN 47408 (United States); Muhrer, G. [Lujan Neutron Scattering Center, Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, NM 87545 (United States); Ansell, S.; Dalgliesh, R. [ISIS Facility, Rutherford Appleton Laboratory, Chilton (United Kingdom); Gallmeier, F.X. [Spallation Neutron Source, Oak Ridge National Laboratory, Oak Ridge, TN 37831 (United States); Kaiser, H. [Center for the Exploration of Energy and Matter, Indiana University, Bloomington, IN 47408 (United States); Lu, W. [Spallation Neutron Source, Oak Ridge National Laboratory, Oak Ridge, TN 37831 (United States)

2014-10-21

We describe a new concept for a neutron moderating assembly resulting in the more efficient production of slow neutron beams. The Convoluted Moderator, a heterogeneous stack of interleaved moderating material and nearly transparent single-crystal spacers, is a directionally enhanced neutron beam source, improving beam emission over an angular range comparable to the range accepted by neutron beam lines and guides. We have demonstrated gains of 50% in slow neutron intensity for a given fast neutron production rate while simultaneously reducing the wavelength-dependent emission time dispersion by 25%, both coming from a geometric effect in which the neutron beam lines view a large surface area of moderating material in a relatively small volume. Additionally, we have confirmed a Bragg-enhancement effect arising from coherent scattering within the single-crystal spacers. We have not observed hypothesized refractive effects leading to additional gains at long wavelength. In addition to confirmation of the validity of the Convoluted Moderator concept, our measurements provide a series of benchmark experiments suitable for developing simulation and analysis techniques for practical optimization and eventual implementation at slow neutron source facilities.

Final focus test beam alignment: A draft proposal

International Nuclear Information System (INIS)

Fischer, G.E.; Ruland, R.E.

1989-03-01

The Final Focus Test Beam is a transport line designed to transmit 50 GeV electron beams of SLC emittance (3 x 10 -10 radian-meters) straight through the central arm of the Beam Switchyard (BSY C line) with a final focus point out in the Research Yard but relatively near the end of the switchyard tunnel. The hardware, methods and procedures outlined in this proposal are dedicated to measuring the placement of mechanical objects with respect to certain defined geometric axes. We wish to emphasize that the very difficult problems of locating the effective magnetic axes of focusing elements, the effective electrical center of beam position monitors and even the effective axis of the incident beam relative to mechanical reference surfaces is outside the scope of this work. Further, this proposal is restricted to the act of measurement and does not consider the vital task of on-line mechanical repositioning of elements that will, in likelihood, be called upon during operation of the system. 16 refs., 16 figs., 4 tabs

Annular beam shaping and optical trepanning

Science.gov (United States)

Zeng, Danyong

Percussion drilling and trepanning are two laser drilling methods. Percussion drilling is accomplished by focusing the laser beam to approximately the required diameter of the hole, exposing the material to one or a series of laser pulses at the same spot to melt and vaporize the material. Drilling by trepanning involves cutting a hole by rotating a laser beam with an optical element or an x-y galvo-scanner. Optical trepanning is a new laser drilling method using an annular beam. The annular beams allow numerous irradiance profiles to supply laser energy to the workpiece and thus provide more flexibility in affecting the hole quality than a traditional circular laser beam. Heating depth is important for drilling application. Since there are no good ways to measure the temperature inside substrate during the drilling process, an analytical model for optical trepanning has been developed by considering an axisymmetric, transient heat conduction equation, and the evolutions of the melting temperature isotherm, which is referred to as the melt boundary in this study, are calculated to investigate the influences of the laser pulse shapes and intensity profiles on the hole geometry. This mathematical model provides a means of understanding the thermal effect of laser irradiation with different annular beam shapes. To take account of conduction in the solid, vaporization and convection due to the melt flow caused by an assist gas, an analytical two-dimensional model is developed for optical trepanning. The influences of pulse duration, laser pulse length, pulse repetition rate, intensity profiles and beam radius are investigated to examine their effects on the recast layer thickness, hole depth and taper. The ray tracing technique of geometrical optics is employed to design the necessary optics to transform a Gaussian laser beam into an annular beam of different intensity profiles. Such profiles include half Gaussian with maximum intensities at the inner and outer

Geometric Constructions with the Computer.

Science.gov (United States)

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…

Behavior of obliquely incident vector Bessel beams at planar interfaces

KAUST Repository

Salem, Mohamed; Bagci, Hakan

2013-01-01

We investigate the behavior of full-vector electromagnetic Bessel beams obliquely incident at an interface between two electrically different media. We employ a Fourier transform domain representation of Bessel beams to determine their behavior upon reflection and transmission. This transform, which is geometric in nature, consists of elliptical support curves with complex weighting associated with them. The behavior of the scattered field at an interface is highly complex, owing to its full-vector nature; nevertheless, this behavior has a straightforward representation in the transform domain geometry. The analysis shows that the reflected field forms a different vector Bessel beam, but in general, the transmitted field cannot be represented as a Bessel beam. Nevertheless, using this approach, we demonstrate a method to propagate a Bessel beam in the refractive medium by launching a non- Bessel beam at the interface. Several interesting phenomena related to the behavior of Bessel beams are illustrated, such as polarized reflection at Brewster's angle incidence, and the Goos-Hänchen and Imbert-Federov shifts in the case of total reflection. © 2013 Optical Society of America.

Behavior of obliquely incident vector Bessel beams at planar interfaces

KAUST Repository

Salem, Mohamed

2013-01-01

We investigate the behavior of full-vector electromagnetic Bessel beams obliquely incident at an interface between two electrically different media. We employ a Fourier transform domain representation of Bessel beams to determine their behavior upon reflection and transmission. This transform, which is geometric in nature, consists of elliptical support curves with complex weighting associated with them. The behavior of the scattered field at an interface is highly complex, owing to its full-vector nature; nevertheless, this behavior has a straightforward representation in the transform domain geometry. The analysis shows that the reflected field forms a different vector Bessel beam, but in general, the transmitted field cannot be represented as a Bessel beam. Nevertheless, using this approach, we demonstrate a method to propagate a Bessel beam in the refractive medium by launching a non- Bessel beam at the interface. Several interesting phenomena related to the behavior of Bessel beams are illustrated, such as polarized reflection at Brewster\\'s angle incidence, and the Goos-Hänchen and Imbert-Federov shifts in the case of total reflection. © 2013 Optical Society of America.

DESIGN OF BEAM-EXTRACTION SEPTUM MAGNET FOR THE SNS

International Nuclear Information System (INIS)

TSOUPAS, N.; LEE, Y.Y.; RANK, J.; TUOZZOLO, J.

2001-01-01

The beam-extraction process from the SNS accumulator ring [1,2] requires a Lambertson septum magnet. In this paper we discuss the geometrical and magnetic field requirements of the magnet and present results obtained from two and three dimensional magnetic field calculations that shows the field quality in the regions of interest of the septum magnet

Maps on statistical manifolds exactly reduced from the Perron-Frobenius equations for solvable chaotic maps

Science.gov (United States)

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.

Wakefield and the diffraction model due to a flat beam moving past a conducting wedge

International Nuclear Information System (INIS)

Chao, A.W.; Henke, H.

1995-07-01

A collimator is often used to clean a beam of its excessive tail particles. If the beam intensity is high enough or if the beam is brought too close to the collimator, however, the wakefields generated by the beam-collimator interaction can cause additional beam tails to grow, thus defeating, or even worsening, the beam-tail cleaning process. The wakefield generated by a sheet beam moving past a conducting wedge has been obtained in closed form by Henke using the method of conformal mapping. This result is applied in the present work to obtain the wake force and the transverse kick received by a test charge moving with the beam. For the beam to be approximated as sheet beams, it is assumed to be flat and the collimator is assumed to have an infinite extent in the flat dimention. We derive an exact expression for the transverse wake force delivered to particles in the beam bunch. Implication of emittance growth as a beam passes closely by a collimator is discussed. We consider two idealized wedge geometries: In Section 2, when the wedge has the geometry as a disrupted beam pipe, and in Section 3, when it is like a semi-infinite screen. Unfortunately, we do not have solutions for more realistic collimator geometries such as when it is tapered to minimize the wakefield effects. However, our results should still serve as pessimistic limiting cases. An interesting opportunity is offered by our exact calculation of the wakefields: it can be used to confront the diffraction model used to estimate the high-frequency impedance of a cavity structure. It is shown that the field pattern, as well as the impedance, agrees with those obtained by the diffraction model in appropriate limits

Optical tractor Bessel polarized beams

Science.gov (United States)

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.

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.

Numerical simulation of the processes of small-diameter high-current electron beam shaping and injection

CERN Document Server

Gordeev, V S; Myskov, G A

2001-01-01

With the aid of BEAM 25 program there was carried out the numerical simulation of the non-stationary process of shaping a small-diameter (<= 20mm) high-current hollow electron beam in a diode with magnetic insulation,as well as of the process of beam injection into the accelerating LIA track. The diode configuration for the purpose of eliminating the leakage of electron flux to the anode surface was update. Presented are the results of calculation of the injected beam characteristics (amplitude-time parameters of a current pulse, space-angle distributions of electrons etc.) depending on diode geometric parameters.

Effects of coating on the optical trapping efficiency of microspheres via geometrical optics approximation.

Science.gov (United States)

Park, Bum Jun; Furst, Eric M

2014-09-23

We present the optical trapping forces that are generated when a single laser beam strongly focuses on a coated dielectric microsphere. On the basis of geometrical optics approximation (GOA), in which a particle intercepts all of the rays that make up a single laser beam, we calculate the trapping forces with varying coating thickness and refractive index values. To increase the optical trapping efficiency, the refractive index (n(b)) of the coating is selected such that n(a) < n(b) < n(c), where na and nc are the refractive indices of the medium and the core material, respectively. The thickness of the coating also increases trapping efficiency. Importantly, we find that trapping forces for the coated particles are predominantly determined by two rays: the incident ray and the first refracted ray to the medium.

Neutral particle beam alternative concept for ITER

International Nuclear Information System (INIS)

Sedgley, D.; Brook, J.; Luzzi, T.; Deutsch, L.

1989-01-01

An analysis of an ITER neutral particle beam system is presented. The analysis covers the neutralizer, ion dumps, pumping, and geometric aspects. The US beam concept for ITER consists of three or four clusters of beamlines delivering approximately 80 MW total of 1.6-MeV deuterium to three or four reactor ports. Each cluster has three self-contained beamlines featuring plasma neutralizers and electrostatic ion dumps. In this study, each of the beamlines has two source assemblies with separate gas neutralizers and magnetic ion dumps. Deuterium is injected into the gas neutralizers by a separate system. Saddle-shaped copper coils augment the tokamak poloidal field to turn the charged particles into the ion dumps. The gas flow from the source, neutralizer, and ion dump is pumped by regenerable cryopanels. The effect of the port between the TF coils and the beam injection angle on the plasma footprint was studied

Partial volume and aliasing artefacts in helical cone-beam CT

International Nuclear Information System (INIS)

Zou Yu; Sidky, Emil Y; Pan, Xiaochuan

2004-01-01

A generalization of the quasi-exact algorithms of Kudo et al (2000 IEEE Trans. Med. Imaging 19 902-21) is developed that allows for data acquisition in a 'practical' frame for clinical diagnostic helical, cone-beam computed tomography (CT). The algorithm is investigated using data that model nonlinear partial volume averaging. This investigation leads to an understanding of aliasing artefacts in helical, cone-beam CT image reconstruction. An ad hoc scheme is proposed to mitigate artefacts due to the nonlinear partial volume and aliasing artefacts

Thermo-mechanical analysis of FG nanobeam with attached tip mass: an exact solution

Science.gov (United States)

Ghadiri, Majid; Jafari, Ali

2016-12-01

Present disquisition proposes an analytical solution method for exploring the vibration characteristics of a cantilever functionally graded nanobeam with a concentrated mass exposed to thermal loading for the first time. Thermo-mechanical properties of FGM nanobeam are supposed to change through the thickness direction of beam based on the rule of power-law (P-FGM). The small-scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. Linear temperature rise (LTR) through thickness direction is studied. Existence of centralized mass in the free end of nanobeam influences the mechanical and physical properties. Timoshenko beam theory is employed to derive the nonlocal governing equations and boundary conditions of FGM beam attached with a tip mass under temperature field via Hamilton's principle. An exact solution procedure is exploited to achieve the non-dimensional frequency of FG nanobeam exposed to temperature field with a tip mass. A parametric study is led to assess the efficacy of temperature changes, tip mass, small scale, beam thickness, power-law exponent, slenderness and thermal loading on the natural frequencies of FG cantilever nanobeam with a point mass at the free end. It is concluded that these parameters play remarkable roles on the dynamic behavior of FG nanobeam subjected to LTR with a tip mass. The results for simpler states are confirmed with known data in the literature. Presented numerical results can serve as benchmarks for future thermo-mechanical analyses of FG nanobeam with tip mass.

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)

Simulation of the Beam-Beam Effects in e+e- Storage Rings with a Method of Reducing the Region of Mesh

Energy Technology Data Exchange (ETDEWEB)

Cai, Yunhai

2000-08-31

A highly accurate self-consistent particle code to simulate the beam-beam collision in e{sup +}e{sup -} storage rings has been developed. It adopts a method of solving the Poisson equation with an open boundary. The method consists of two steps: assigning the potential on a finite boundary using the Green's function, and then solving the potential inside the boundary with a fast Poisson solver. Since the solution of the Poisson's equation is unique, the authors solution is exactly the same as the one obtained by simply using the Green's function. The method allows us to select much smaller region of mesh and therefore increase the resolution of the solver. The better resolution makes more accurate the calculation of the dynamics in the core of the beams. The luminosity simulated with this method agrees quantitatively with the measurement for the PEP-II B-factory ring in the linear and nonlinear beam current regimes, demonstrating its predictive capability in detail.

Beam-smiling in bent-Laue monochromators

International Nuclear Information System (INIS)

Ren, B.; Dilmanian, F.A.; Wu, X.Y.; Huang, X.; Ivanov, I.; Thomlinson, W.C.

1997-01-01

When a wide fan-shaped x-ray beam is diffracted by a bent crystal in the Laue geometry, the profile of the diffracted beam generally does not appear as a straight line, but as a line with its ends curved up or curved down. This effect, referred to as ' beam-smiling', has been a major obstacle in developing bent-Laue crystal monochromators for medical applications of synchrotron x-ray. We modeled a cylindrically bent crystal using the Finite Element Analysis (FEA) method, and we carried out experiments at the National Synchrotron Light Source and Cornell High Energy Synchrotron Source. Our studies show that, while beam-smiling exists in most of the crystal close-quote s area because of anticlastic bending effects, there is a region parallel to the bending axis of the crystal where the diffracted beam is ' smile-free'. By applying asymmetrical bending, this smile-free region can be shifted vertically away from the geometric center of the crystal, as desired. This leads to a novel method of compensating for beam-smiling. We will discuss the method of ' differential bending' for smile removal, beam-smiling in the Cauchios and the polychromatic geometry, and the implications of the method on developing single- and double-bent Laue monochromators. The experimental results will be discussed, concentrating on specific beam-smiling observation and removal as applied to the new monochromator of the Multiple Energy Computed Tomography [MECT] project of the Medical Department, Brookhaven National Laboratory. copyright 1997 American Institute of Physics

Multistable wireless micro-actuator based on antagonistic pre-shaped double beams

International Nuclear Information System (INIS)

Liu, X; Lamarque, F; Doré, E; Pouille, P

2015-01-01

This paper presents a monolithic multistable micro-actuator based on antagonistic pre-shaped double beams. The designed micro-actuator is formed by two rows of bistable micro-actuators providing four stable positions. The bistable mechanism for each row is a pair of antagonistic pre-shaped beams. This bistable mechanism has an easier pre-load operation compared to the pre-compressed bistable beams method. Furthermore, it solves the asymmetrical force output problem of parallel pre-shaped bistable double beams. At the same time, the geometrical limit is lower than parallel pre-shaped bistable double beams, which ensures a smaller stroke of the micro-actuator with the same dimensions. The designed micro-actuator is fabricated using laser cutting machine on medium density fiberboard (MDF). The bistability and merits of antagonistic pre-shaped double beams are experimentally validated. Finally, a contactless actuation test is performed using 660 nm wavelength laser heating shape memory alloy (SMA) active elements. (paper)

Multistable wireless micro-actuator based on antagonistic pre-shaped double beams

Science.gov (United States)

Liu, X.; Lamarque, F.; Doré, E.; Pouille, P.

2015-07-01

This paper presents a monolithic multistable micro-actuator based on antagonistic pre-shaped double beams. The designed micro-actuator is formed by two rows of bistable micro-actuators providing four stable positions. The bistable mechanism for each row is a pair of antagonistic pre-shaped beams. This bistable mechanism has an easier pre-load operation compared to the pre-compressed bistable beams method. Furthermore, it solves the asymmetrical force output problem of parallel pre-shaped bistable double beams. At the same time, the geometrical limit is lower than parallel pre-shaped bistable double beams, which ensures a smaller stroke of the micro-actuator with the same dimensions. The designed micro-actuator is fabricated using laser cutting machine on medium density fiberboard (MDF). The bistability and merits of antagonistic pre-shaped double beams are experimentally validated. Finally, a contactless actuation test is performed using 660 nm wavelength laser heating shape memory alloy (SMA) active elements.

Laser-induced stimulated Raman scattering in the forward direction of a droplet - Comparison of Mie theory with geometrical optics

Science.gov (United States)

Srivastava, Vandana; Jarzembski, Maurice A.

1991-01-01

This paper uses Mie theory to treat electromagnetic scattering and to evaluate field enhancement in the forward direction of a small droplet irradiated by a high-energy beam and compares the results of calculations with the field-enhancement evaluation obtained via geometrical optics treatment. Results of this comparison suggest that the field enhancement located at the critical ring region encircling the axis in the forward direction of the droplet can support laser-induced Raman scattering. The results are supported by experimental observations of the interaction of a 120-micron-diam water droplet with a high-energy Nd:YAG laser beam.

Pulse propagation in a two-pass optical amplifier with arbitrary laser beams overlap

Directory of Open Access Journals (Sweden)

AH Farahbod

2011-09-01

Full Text Available An analytical model for two-pass optical amplifier with arbitrary beams overlap has been developed which generalized the classical theory of Frantz-Nodvik for single pass amplifier. The effect of counterpropagating beams on gain and output energy fluence included in the model. Moreover, the appropriate limiting relations for two special cases of weak input signal and saturation state of the amplifier gain have been derived. The results indicate that for complete beams overlap, the gain and output energy have the least values. The model predictions are consistent with experimental observations and exact analytical model for two-pass amplifier when beam propagation paths are coincided.

Beam optics simulation of rare-RI ring at RI beam factory in RIKEN

International Nuclear Information System (INIS)

Arai, I.; Ozawa, A.; Yasuda, Y.

2009-01-01

The cyclotron-like storage ring dedicated to Rare-RI Ring project consists of 6 magnetic sectors and 6 straight sections, having a circumference of 56.13 m. The magnetic sector works for both bending and focusing. The total circulation is assumed to be 1,000 turns. Over the momentum range from -1% to +1% in ∆p/p, the required isochronicity is 10 -6 while the beam emittance is several tens of π mm-mrad. To examine the design of cyclotron-like storage ring and fix its parameters, we have developed a high precision beam optics simulation. To achieve the precision as high as possible within a feasible computational time, we have adopted a geometrical tracking assuming a circular orbit for a small spatial segment. For that purpose, it is enough that the magnetic sector is divided into 150 sub-sectors in calculation. In each sub-sector, the magnetic field is given as a function of radial position but uniform around the vicinity of beam trajectory. The beam trajectory is evaluated in 4th order Runge-Kutta algorithm. Finally, we have achieved a precision of 10 -9 in ∆T/T and a computational time of 1.8 sec on a typical PC server for ray tracing of single particle undergoing a circulation of 1,000 turns. (author)

Performance evaluation of the whole-body PET scanner ECAT EXACT HR+

International Nuclear Information System (INIS)

Adam, L.E.; Zaers, J.; Ostertag, H.; Trojan, H.

1996-01-01

The performance parameters of the whole-body PET scanner ECAT EXACT HR + were determined following the standard proposed by the International Electrotechnical Commission (IEC). The tests were expanded by some measurements concerning the accuracy of the correction algorithms and the geometric fidelity of the reconstructed images. The scanner consists of 32 rings, each with 576 BGO detectors (4.05 x 4.39 x 30 mm 3 ) covering an axial field-of-view of 15.5 cm and a patient port of 56.2 cm. The transaxial resolution in the 2D (3D) mode is 4.5 (4.3) mm at the center. It increases to 8.9 (8.3) mm radially and to 5.8 (5.2) mm tangentially at a radial distance of r = 20 cm. The average axial resolution varies between 4.9 (4.1) mm FWHM at the center and 8.8 (8.1) mm at r = 20 cm. The system sensitivity for true events is 5.85 (26.4) cps/Bq/ml (measured with a 20 cm cylinder phantom). The 50% dead-time losses where reached for a true event count rate of 286 (500) kcps at an activity concentration of 74 (25) kBq/ml. The system scatter fraction is 0.24 (0.35). The correction algorithms work reliable, except for the 3D attenuation correction. The ECAT EXACT HR + has a good and nearly isotropic spatial resolution. Due to the small detector elements, however, it has a low slice sensitivity which is a limiting factor for image quality

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.

A multiwire secondary emission profile monitor for small emittance beams

International Nuclear Information System (INIS)

Chehab, R.; Bonnard, J.; Humbert, G.; Leblond, B.; Saury, J.L.

1985-01-01

A secondary emission monitor using two multiwire grids separated by a positively biased collector has been constructed and tested with a 1 GeV electron beam at the Orsay Linac. The monitor installed just before the electron-positron converter has 8 gold-plated-tungsten wires of 0.1 mm diameter equally spaced 0.2 mm apart in each plane. Each wire is connected with an integrator using a low-bias current operational amplifier. The wire planes and the collector are moved into the beam by a stepping motor : that allows beam-position verification. We measured narrow profiles for 1 Amp peak current pulses of 30 nanoseconds width. Profiles are displayed on a scope and allow emittance determination by the three gradient method. Such a monitor is very useful to control the electron beam position and dimensions on the converter, because the positron source dimensions are rather bigger than those of the incident beam and the geometrical acceptance of the positron Linac is limited

A unified construction for the algebro-geometric quasiperiodic solutions of the Lotka-Volterra and relativistic Lotka-Volterra hierarchy

Science.gov (United States)

Zhao, Peng; Fan, Engui

2015-04-01

In this paper, a new type of integrable differential-difference hierarchy, namely, the generalized relativistic Lotka-Volterra (GRLV) hierarchy, is introduced. This hierarchy is closely related to Lotka-Volterra lattice and relativistic Lotka-Volterra lattice, which allows us to provide a unified and effective way to obtain some exact solutions for both the Lotka-Volterra hierarchy and the relativistic Lotka-Volterra hierarchy. In particular, we shall construct algebro-geometric quasiperiodic solutions for the LV hierarchy and the RLV hierarchy in a unified manner on the basis of the finite gap integration theory.

Optical tractor Bessel polarized beams

International Nuclear Information System (INIS)

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 α_0. 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. - Highlights: • Optical tractor Bessel polarized beams are

Finite element formulation for dynamics of planar flexible multi-beam system

International Nuclear Information System (INIS)

Liu Zhuyong; Hong Jiazhen; Liu Jinyang

2009-01-01

In some previous geometric nonlinear finite element formulations, due to the use of axial displacement, the contribution of all the elements lying between the reference node of zero axial displacement and the element to the foreshortening effect should be taken into account. In this paper, a finite element formulation is proposed based on geometric nonlinear elastic theory and finite element technique. The coupling deformation terms of an arbitrary point only relate to the nodal coordinates of the element at which the point is located. Based on Hamilton principle, dynamic equations of elastic beams undergoing large overall motions are derived. To investigate the effect of coupling deformation terms on system dynamic characters and reduce the dynamic equations, a complete dynamic model and three reduced models of hub-beam are prospected. When the Cartesian deformation coordinates are adopted, the results indicate that the terms related to the coupling deformation in the inertia forces of dynamic equations have small effect on system dynamic behavior and may be neglected, whereas the terms related to coupling deformation in the elastic forces are important for system dynamic behavior and should be considered in dynamic equation. Numerical examples of the rotating beam and flexible beam system are carried out to demonstrate the accuracy and validity of this dynamic model. Furthermore, it is shown that a small number of finite elements are needed to obtain a stable solution using the present coupling finite element formulation

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.

Fluctuating twistor-beam solutions and Pre-Quantum Kerr-Schild geometry

Energy Technology Data Exchange (ETDEWEB)

Burinskii, Alexander, E-mail: bur@ibrae.ac.r [Laboratory of Theoretical Physics, NSI Russian Academy of Sciences, B.Tulskaya 52, Moscow, 115191 (Russian Federation)

2010-04-01

Kerr-Schild (KS) geometry is based on a congruence of twistors which is determined by the Kerr theorem. We describe time-dependent KS solutions for electromagnetic excitations of black-holes taking into account the consistent back-reaction to metric. The exact solutions have the form of singular beam-like pulses supported on twistor null lines of the Kerr congruence. The twistor-beams have very strong back reaction to metric and BH horizon and produce a fluctuating KS geometry which takes an intermediate position between the Classical and Quantum gravity.

Fluctuating twistor-beam solutions and Pre-Quantum Kerr-Schild geometry

International Nuclear Information System (INIS)

Burinskii, Alexander

2010-01-01

Kerr-Schild (KS) geometry is based on a congruence of twistors which is determined by the Kerr theorem. We describe time-dependent KS solutions for electromagnetic excitations of black-holes taking into account the consistent back-reaction to metric. The exact solutions have the form of singular beam-like pulses supported on twistor null lines of the Kerr congruence. The twistor-beams have very strong back reaction to metric and BH horizon and produce a fluctuating KS geometry which takes an intermediate position between the Classical and Quantum gravity.

Measuring the self-healing of the spatially inhomogeneous states of polarization of vector Bessel beams

CSIR Research Space (South Africa)

Milione, G

2015-02-01

Full Text Available be simply understood via geometric optics [3]. When a portion of a Bessel beam is obstructed in one plane, the unobstructed conical rays interfere in its shadow region in another plane, as shown in Fig. 1(e). Due to this property, Bessel beams have been... extensively studied and have been used for a number of applications; for comprehensive reviews see [4–7]. For example, when using a Bessel beam for optical trapping, it is possible to simultaneously trap multiple particles in well separated planes [8...

Finite Element Model for Nonlinear Analysis of Reinforced Concrete Beams and Plane Frames

Directory of Open Access Journals (Sweden)

R.S.B. STRAMANDINOLI

Full Text Available Abstract In this work, a two-dimensional finite element (FE model for physical and geometric nonlinear analysis of reinforced concrete beams and plane frames, developed by the authors, is presented. The FE model is based on the Euler-Bernoulli Beam Theory, in which shear deformations are neglected. The bar elements have three nodes with a total of seven degrees of freedom. Three Gauss-points are utilized for the element integration, with the element section discretized into layers at each Gauss point (Fiber Model. It is assumed that concrete and reinforcing bars are perfectly bonded, and each section layer is assumed to be under a uniaxial stress-state. Nonlinear constitutive laws are utilized for both concrete and reinforcing steel layers, and a refined tension-stiffening model, developed by the authors, is included. The Total Lagrangean Formulation is adopted for geometric nonlinear consideration and several methods can be utilized to achieve equilibrium convergence of the nonlinear equations. The developed model is implemented into a computer program named ANEST/CA, which is validated by comparison with some tests on RC beams and plane frames, showing an excellent correlation between numerical and experimental results.

Laser radiation in active amplifying media treated as a transport problem - Transfer equation derived and exactly solved

Science.gov (United States)

Gupta, S. R. D.; Gupta, Santanu D.

1991-10-01

The flow of laser radiation in a plane-parallel cylindrical slab of active amplifying medium with axial symmetry is treated as a problem in radiative transfer. The appropriate one-dimensional transfer equation describing the transfer of laser radiation has been derived by an appeal to Einstein's A, B coefficients (describing the processes of stimulated line absorption, spontaneous line emission, and stimulated line emission sustained by population inversion in the medium) and considering the 'rate equations' to completely establish the rational of the transfer equation obtained. The equation is then exactly solved and the angular distribution of the emergent laser beam intensity is obtained; its numerically computed values are given in tables and plotted in graphs showing the nature of peaks of the emerging laser beam intensity about the axis of the laser cylinder.

Recent observations of beam plasma interactions in the ionosphere and a comparison with laboratory studies of the beam plasma discharge

International Nuclear Information System (INIS)

Bernstein, W.; Holzworth, R.H.; Kellogg, P.J.; Monson, S.J.; Whalen, B.A.

1982-01-01

This chapter summarizes the experimental results which relate to collective beam-plasma interactions from a recent electron beam injection rocket flight launched into an active aurora. NASA rocket 27:010 AE carried a modest accelerator which injected programmed electron beams of <100 ma at 2 and 4 kV into the ionosphere plasma over the altitude range 120-240 km. Topics considered include a description of the payloads, accelerator operation, diagnostics (aft section, aft payload geometric configuration, wave diagnostics, TAD instrumentation), experimental results (161 eV-20 KeV electrons, thermal ions, TAD data, wave measurements), and laboratory results (energetic particles, photometric observations). A major objective of this experiment was the possible identification of the ignition of the Beam-Plasma Discharge (BPD) which has been intensively studied in laboratory configurations. The results indicate that BPD ignition occurred for Im current pulses at 2 and 4 kV and during the 3 kHz modulation period. It is concluded that many of the observed characteristics are similar to the BPD characteristics observed in the laboratory

Cold-fluid theory of equilibrium and stability of a high-intensity periodically twisted ellipse-shaped charged-particle beam

Directory of Open Access Journals (Sweden)

Jing Zhou

2006-03-01

Full Text Available It is shown that there exists an exact paraxial cold-fluid equilibrium of a high-intensity, space-charge-dominated charged-particle beam with a periodically twisted elliptic cross section in a nonaxisymmetric periodic magnetic field. Generalized envelope equations, which determine the beam envelopes, ellipse orientation, density, and internal flow velocity profiles, are derived. Nonrelativistic and relativistic examples of such beam equilibria are presented. The equilibrium and stability of such beams are demonstrated by self-consistent particle-in-cell (PIC simulations.

Beam shaping of light sources using circular photonic crystal funnel

Science.gov (United States)

Kumar, Mrityunjay; Kumar, Mithun; Dinesh Kumar, V.

2012-10-01

A novel two-dimensional circular photonic crystal (CPC) structure with a sectorial opening for shaping the beam of light sources was designed and investigated. When combined with light sources, the structure acts like an antenna emitting a directional beam which could be advantageously used in several nanophotonic applications. Using the two-dimensional finite-difference time-domain (2D FDTD) method, we examined the effects of geometrical parameters of the structure on the directional and transmission properties of emitted radiation. Further, we examined the transmitting and receiving properties of a pair of identical structures as a function of distance between them.

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

Laser focusing of high-energy charged-particle beams

International Nuclear Information System (INIS)

Channell, P.J.

1986-01-01

It is shown that laser focusing of high-energy charged-particle beams using the inverse Cherenkov effect is well suited for applications with large linear colliders. Very high gradient (>0.5 MG/cm) lenses result that can be added sequentially without AG cancellation. These lenses are swell understood, have small geometric aberrations, and offer the possibility of correlating phase and energy aberrations to produce an achromatic final focus

Free and Forced Vibrations of an Axially-Loaded Timoshenko Multi-Span Beam Carrying a Number of Various Concentrated Elements

Directory of Open Access Journals (Sweden)

Yusuf Yesilce

2012-01-01

Full Text Available In the existing reports regarding free and forced vibrations of the beams, most of them studied a uniform beam carrying various concentrated elements using Bernoulli-Euler Beam Theory (BET but without axial force. The purpose of this paper is to utilize the numerical assembly technique to determine the exact frequency-response amplitudes of the axially-loaded Timoshenko multi-span beam carrying a number of various concentrated elements (including point masses, rotary inertias, linear springs and rotational springs and subjected to a harmonic concentrated force and the exact natural frequencies and mode shapes of the beam for the free vibration analysis. The model allows analyzing the influence of the shear and axial force and harmonic concentrated force effects and intermediate concentrated elements on the dynamic behavior of the beams by using Timoshenko Beam Theory (TBT. At first, the coefficient matrices for the intermediate concentrated elements, an intermediate pinned support, applied harmonic force, left-end support and right-end support of Timoshenko beam are derived. After the derivation of the coefficient matrices, the numerical assembly technique is used to establish the overall coefficient matrix for the whole vibrating system. Finally, solving the equations associated with the last overall coefficient matrix one determines the exact dynamic response amplitudes of the forced vibrating system corresponding to each specified exciting frequency of the harmonic force. Equating the determinant of the overall coefficient matrix to zero one determines the natural frequencies of the free vibrating system (the case of zero harmonic force and substituting the corresponding values of integration constants into the related eigenfunctions one determines the associated mode shapes. The calculated vibration amplitudes of the forced vibrating systems and the natural frequencies of the free vibrating systems are given in tables for different values of

Achromatic beam transport of High Current Injector

International Nuclear Information System (INIS)

Kumar, Sarvesh; Mandal, A.

2016-01-01

The high current injector (HCI) provides intense ion beams of high charge state using a high temperature superconducting ECR ion source. The ion beam is accelerated upto a final energy of 1.8 MeV/u due to an electrostatic potential, a radio frequency quadrupole (RFQ) and a drift tube linac (DTL). The ion beam has to be transported to superconducting LINAC which is around 50 m away from DTL. This section is termed as high energy beam transport section (HEBT) and is used to match the beam both in transverse and longitudinal phase space to the entrance of LINAC. The HEBT section is made up of four 90 deg. achromatic bends and interconnecting magnetic quadrupole triplets. Two RF bunchers have been used for longitudinal phase matching to the LINAC. The ion optical design of HEBT section has been simulated using different beam dynamics codes like TRACEWIN, GICOSY and TRACE 3D. The field computation code OPERA 3D has been utilized for hardware design of all the magnets. All the dipole and quadrupole magnets have been field mapped and their test results such as edge angles measurements, homogeneity and harmonic analysis etc. are reported. The whole design of HEBT section has been performed such that the most of the beam optical components share same hardware design and there is ample space for beam diagnostics as per geometry of the building. Many combination of achromatic bends have been simulated to transport the beam in HEBT section but finally the four 90 deg. achromatic bend configuration is found to be the best satisfying all the geometrical constraints with simplified beam tuning process in real time

Composite Beam Theory with Material Nonlinearities and Progressive Damage

Science.gov (United States)

Jiang, Fang

Beam has historically found its broad applications. Nowadays, many engineering constructions still rely on this type of structure which could be made of anisotropic and heterogeneous materials. These applications motivate the development of beam theory in which the impact of material nonlinearities and damage on the global constitutive behavior has been a focus in recent years. Reliable predictions of these nonlinear beam responses depend on not only the quality of the material description but also a comprehensively generalized multiscale methodology which fills the theoretical gaps between the scales in an efficient yet high-fidelity manner. The conventional beam modeling methodologies which are built upon ad hoc assumptions are in lack of such reliability in need. Therefore, the focus of this dissertation is to create a reliable yet efficient method and the corresponding tool for composite beam modeling. A nonlinear beam theory is developed based on the Mechanics of Structure Genome (MSG) using the variational asymptotic method (VAM). The three-dimensional (3D) nonlinear continuum problem is rigorously reduced to a one-dimensional (1D) beam model and a two-dimensional (2D) cross-sectional analysis featuring both geometric and material nonlinearities by exploiting the small geometric parameter which is an inherent geometric characteristic of the beam. The 2D nonlinear cross-sectional analysis utilizes the 3D material models to homogenize the beam cross-sectional constitutive responses considering the nonlinear elasticity and progressive damage. The results from such a homogenization are inputs as constitutive laws into the global nonlinear 1D beam analysis. The theoretical foundation is formulated without unnecessary kinematic assumptions. Curvilinear coordinates and vector calculus are utilized to build the 3D deformation gradient tensor, of which the components are formulated in terms of cross-sectional coordinates, generalized beam strains, unknown warping

Calibration of Monte Carlo simulation code to low voltage electron beams through radiachromic dosimetry

International Nuclear Information System (INIS)

Weiss, D.E.; Kalweit, H.W.; Kensek, R.P.

1994-01-01

A simple multilayer slab model of an electron beam using the ITS/TIGER code can consistently account for about 80% of the actual dose delivered by a low voltage electron beam. The difference in calculated values is principally due to the 3D hibachi structure which blocks 22% of the beam. A 3D model was constructed using the ITS/ACCEPT code to improve upon the TIGER simulations. A rectangular source description update to the code and reproduction of all key geometric elements involved, including the hibachi, accounted for 90-95% of the dose received by routine dosimetry

Beam profiles for fast neutrons; and reply

International Nuclear Information System (INIS)

Bewley, D.K.; Parnell, C.J.; Bloch, P.

1976-01-01

The authors express surprise that Bloch et al. (Bloch, P.H., Hendry, G.O., Hilton, J.L., Quam, W.M., Reinhard, D.K., and Wilson, C., 1976, Phys. Med. Biol., Vol. 21, 450) justified a target size of 5.5 x 5.5 cm in a neutron generator by comparison with the profile given by a 2.5 MV X-ray generator. The penumbral width of this new neutron generator is more than twice that of a modern megavoltage X-ray machine, and larger than those of beams from standard 60 Co units, or of the Hammersmith Hospital cyclotron beam. The large target size of the neutron generator may have to be accepted as a necessary evil, but should not be considered satisfactory. In reply, one of the authors of the original note presents the results of calculations of beam profiles for 14 MeV neutron beams in a tissue-equivalent phantom, and suggests that the broader profiles are principally caused by the larger probability of side scatter, not by source size. The most fruitful approach to sharpening the neutron beam profile would seem to be to design a field flattening filter to increase relative dose near the edge inside the geometrically defined field. Calculations indicating that Bewley and Parnell have underestimated the penumbral widths of 60 Co beams are also presented. (U.K.)

Development of high current density neutral beam injector with a low energy for interaction of plasma facing materials

International Nuclear Information System (INIS)

Nishikawa, Masahiro; Ueda, Yoshio; Goto, Seiichi

1991-01-01

A high current density neutral beam injector with a low energy has been developed to investigate interactions with plasma facing materials and propagation processes of damages. The high current density neutral beam has been produced by geometrical focusing method employing a spherical electrode system. The hydrogen beam with the current density of 140 mA/cm 2 has been obtained on the focal point in the case of the acceleration energy of 8 keV. (orig.)

'Diffraction-free' optical beams in inverse free electron laser accelerators

International Nuclear Information System (INIS)

Cai, S.Y.; Bhattacharjee, A.; Marshall, T.C.

1988-01-01

'Diffraction-free' optical beams correspond to exact solutions of the wave equation in free space with the remarkable property that they propagate with negligible transverse spreading for distances much larger than the Rayleigh range. The requirement for this to occur is a large aperture. Using a 2D computer code, we find that these optical beams will also propagate with negligible diffraction even when perturbed by the electron beam in an IFEL; indeed they match well the FEL requirement for the accelerator. The numerical simulations are performed for the proposed facility at Brookhaven in which λ s =10 μm, B=1.5 T (linearly tapered l w =1.31-6.28 cm) and the optical beam power is either 8x10 11 W or 2.3x10 10 W. Approximately 70% of the electrons constituting a beam of current 5 mA or 15 A, radius 0.14 mm and initial energy of 50 MeV is accelerated at 50 MeV/m. (orig.)

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

Pragmatic geometric model evaluation

Science.gov (United States)

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

Size effects on free vibration of heterogeneous beams

Directory of Open Access Journals (Sweden)

Hassanati Bahman

2018-01-01

Full Text Available In this paper the influence of microstructure on the free vibration of geometrically similar heterogeneous beams with free-free boundary conditions was numerically investigated by detailed finite element analysis (FEA to identify and quantify any effect of beam size on transverse modal frequencies when the microstructural scale is comparable to the overall size. ANSYS Mechanical APDL was used to generate specific unit cells at the microstructural scale comprised of two isotropic materials with different material properties. Unit cell variants containing voids and inclusions were considered. At the macroscopic scale, four beam sizes consisting of one, two, three or four layers of defined unit cells were represented by repeatedly regenerating the unit cell as necessary. In all four beam sizes the aspect ratio was kept constant. Changes to the volume fractions of each material were introduced while keeping the homogenized properties of the beam fixed. The influence of the beam surface morphology on the results was also investigated. The ANSYS results were compared with the analytical results from solution to Timoshenko beam and nonlocal Timoshenko beam as well as numerical results for a Micropolar beam. In nonlocal Timoshenko beams the Eringen’s small length scale coefficients were estimated for some of the studied models. Numerical analyses based on Micropolar theory were carried out to study the modal frequencies and a method was suggested to estimate characteristic length in bending and coupling number via transverse vibration which verifies the use of Micropolar elasticity theory in dynamic analysis.

Dosimetric evaluations and comparisons between different techniques (Fan beam, Cone beam, OPT) in the dental industry and not

International Nuclear Information System (INIS)

Rampado, O.

2014-01-01

In recent years there has been an impressive evolution and spread of cone beam tomographic equipment, in particular in the dental and maxillofacial surgery. These devices exhibit unique characteristics both from the point of view of the geometric parameters of exposure than the quality of the beams radiating employed. In parallel to this technological development it was dealt with the quantification of the dose to the patient, with a discussion between experts to define what are the variables most appropriate to use and the appropriate ways of measuring. And it is of interest also the discussion on the comparison of the risks associated with the use of this method as an alternative to traditional techniques or other tomographic techniques, both on the criteria of optimization in the realization of the tests.

Photon beam polarization and non-dipolar angular distributions

International Nuclear Information System (INIS)

Peshkin, M.

1996-01-01

Angular distributions of ejecta from unoriented atoms and molecules depend upon the polarization state of the incident x-rays as well as upon the dynamics of the physical systems being studied. I recommend a simple geometrical way of looking at the polarization and its effects upon angular distributions. The polarization is represented as a vector in a parameter space that faithfully represents the polarization of the beam. The simple dependence of the angular dependence of the angular distributions on the polarization vector enables easy extraction of the dynamical information contained in those angular distributions. No new physical results emerge from this geometrical approach, but known consequences of the symmetries appear in an easily visualized form that I find pleasing and that has proved to be useful for planning experiments and for analyzing data

Exact phase boundaries and topological phase transitions of the X Y Z spin chain

Science.gov (United States)

Jafari, S. A.

2017-07-01

Within the block spin renormalization group, we give a very simple derivation of the exact phase boundaries of the X Y Z spin chain. First, we identify the Ising order along x ̂ or y ̂ as attractive renormalization group fixed points of the Kitaev chain. Then, in a global phase space composed of the anisotropy λ of the X Y interaction and the coupling Δ of the Δ σzσz interaction, we find that the above fixed points remain attractive in the two-dimesional parameter space. We therefore classify the gapped phases of the X Y Z spin chain as: (1) either attracted to the Ising limit of the Kitaev-chain, which in turn is characterized by winding number ±1 , depending on whether the Ising order parameter is along x ̂ or y ̂ directions; or (2) attracted to the charge density wave (CDW) phases of the underlying Jordan-Wigner fermions, which is characterized by zero winding number. We therefore establish that the exact phase boundaries of the X Y Z model in Baxter's solution indeed correspond to topological phase transitions. The topological nature of the phase transitions of the X Y Z model justifies why our analytical solution of the three-site problem that is at the core of the present renormalization group treatment is able to produce the exact phase boundaries of Baxter's solution. We argue that the distribution of the winding numbers between the three Ising phases is a matter of choice of the coordinate system, and therefore the CDW-Ising phase is entitled to host appropriate form of zero modes. We further observe that in the Kitaev-chain the renormalization group flow can be cast into a geometric progression of a properly identified parameter. We show that this new parameter is actually the size of the (Majorana) zero modes.

Using geometric algebra to understand pattern rotations in multiple mirror optical systems

International Nuclear Information System (INIS)

Hanlon, J.; Ziock, H.

1997-01-01

Geometric Algebra (GA) is a new formulation of Clifford Algebra that includes vector analysis without notation changes. Most applications of Ga have been in theoretical physics, but GA is also a very good analysis tool for engineering. As an example, the authors use GA to study pattern rotation in optical systems with multiple mirror reflections. The common ways to analyze pattern rotations are to use rotation matrices or optical ray trace codes, but these are often inconvenient. The authors use GA to develop a simple expression for pattern rotation that is useful for designing or tolerancing pattern rotations in a multiple mirror optical system by inspection. Pattern rotation is used in many optical engineering systems, but it is not normally covered in optical system engineering texts. Pattern rotation is important in optical systems such as: (1) the 192 beam National ignition Facility (NIF), which uses square laser beams in close packed arrays to cut costs; (2) visual optical systems, which use pattern rotation to present the image to the observer in the appropriate orientation, and (3) the UR90 unstable ring resonator, which uses pattern rotation to fill a rectangular laser gain region and provide a filled-in laser output beam

Theory of longitudinal atomic beam spin echo and parity violating Berry-phases in atoms; Theorie des longitudinalen Atomstrahl-Spinechos und paritaetsverletzende Berry-Phasen in Atomen

Energy Technology Data Exchange (ETDEWEB)

Bergmann, T.F.

2006-07-19

We present a nonrelativistic theory for the quantum mechanical description of longitudinal atomic beam spin echo experiments, where a beam of neutral atoms is subjected to static electric and magnetic fields. The atomic wave function is the solution of a matrix-valued Schroedinger equation and can be written as superposition of local (atomic) eigenstates of the potential matrix. The position- and time-dependent amplitude function of each eigenstate represents an atomic wave packet and can be calculated in a series expansion with a master formula that we derive. The zeroth order of this series expansion describes the adiabatic limit, whereas the higher order contributions contain the mixing of the eigenstates and the corresponding amplitude functions. We give a tutorial for the theoretical description of longitudinal atomic beam spin echo experiments and for the so-called Fahrplan model, which is a visualisation tool for the propagation of wave packets of different atomic eigenstates. As an example for the application of our theory, we study parity violating geometric (Berry-)phases. In this context, we define geometric flux densities, which for certain field configurations can be used to illustrate geometric phases in a vector diagram. Considering an example with a specific field configuration, we prove the existence of a parity violating geometric phase. (orig.)

Computer generation of cobalt-60 single beam dose distribution using an analytical beam model

International Nuclear Information System (INIS)

Jayaraman, S.

1981-01-01

A beam dose calculation model based on evaluation of tissue air ratios (TAR) and scatter air ratios (SAR) for cobalt-60 beams of rectangular cross section has been developed. Off-central axis fall-off of primary radiation intensity is derived by an empirical formulation involving an arctangent function with the slope of the geometrical penumbra acting as an essential constant. Central axis TAR and SAR values are assessed by semi-empirical polynomial expressions employing the two sides of the rectangular field as the bariables. The model utilises a minimum number of parametric constants and is useful for computer generation of isodose curves. The model is capable of accounting for situations where wedge filters or split field shielding blocks, are encountered. Further it could be widely applied with minor modifications to several makes of the currently available cobalt-60 units. The paper explains the model and shows examples of the results obtained in comparison with the corresponding experimentally determined dose distributions. (orig.) [de

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

Graphene geometric diodes for terahertz rectennas

International Nuclear Information System (INIS)

Zhu Zixu; Joshi, Saumil; Grover, Sachit; Moddel, Garret

2013-01-01

We demonstrate a new thin-film graphene diode called a geometric diode that relies on geometric asymmetry to provide rectification at 28 THz. The geometric diode is coupled to an optical antenna to form a rectenna that rectifies incoming radiation. This is the first reported graphene-based antenna-coupled diode working at 28 THz, and potentially at optical frequencies. The planar structure of the geometric diode provides a low RC time constant, on the order of 10 −15 s, required for operation at optical frequencies, and a low impedance for efficient power transfer from the antenna. Fabricated geometric diodes show asymmetric current–voltage characteristics consistent with Monte Carlo simulations for the devices. Rectennas employing the geometric diode coupled to metal and graphene antennas rectify 10.6 µm radiation, corresponding to an operating frequency of 28 THz. The graphene bowtie antenna is the first demonstrated functional antenna made using graphene. Its response indicates that graphene is a suitable terahertz resonator material. Applications for this terahertz diode include terahertz-wave and optical detection, ultra-high-speed electronics and optical power conversion. (paper)

Geometric Computing for Freeform Architecture

KAUST Repository

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.

Image-projection ion-beam lithography

International Nuclear Information System (INIS)

Miller, P.A.

1989-01-01

Image-projection ion-beam lithography is an attractive alternative for submicron patterning because it may provide high throughput; it uses demagnification to gain advantages in reticle fabrication, inspection, and lifetime; and it enjoys the precise deposition characteristics of ions which cause essentially no collateral damage. This lithographic option involves extracting low-mass ions (e.g., He + ) from a plasma source, transmitting the ions at low voltage through a stencil reticle, and then accelerating and focusing the ions electrostatically onto a resist-coated wafer. While the advantages of this technology have been demonstrated experimentally by the work of IMS (Austria), many difficulties still impede extension of the technology to the high-volume production of microelectronic devices. We report a computational study of a lithography system designed to address problem areas in field size, telecentricity, and chromatic and geometric aberration. We present a novel ion-column-design approach and conceptual ion-source and column designs which address these issues. We find that image-projection ion-beam technology should in principle meet high-volume-production requirements. The technical success of our present relatively compact-column design requires that a glow-discharge-based ion source (or equivalent cold source) be developed and that moderate further improvement in geometric aberration levels be obtained. Our system requires that image predistortion be employed during reticle fabrication to overcome distortion due to residual image nonlinearity and space-charge forces. This constitutes a software data preparation step, as do correcting for distortions in electron lithography columns and performing proximity-effect corrections. Areas needing further fundamental work are identified

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.

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)

Beam-induced depolarisation at the HERMES transversely polarised hydrogen target

International Nuclear Information System (INIS)

Tait, P.

2006-01-01

This thesis describes the polarised hydrogen target of the HERMES experiment at DESY in Hamburg. The HERMES target is based on hyperfine-splitting of hydrogen in an external magnetic field and provides nuclear-polarised hydrogen for the HERMES experiment. Particular emphasis is placed on the phenomenon of beam-induced depolarisation. The HERA electron beam consists of short bunches which produce a high-frequency magnetic field. A Fourier analysis of these bunches leads to a series of harmonics, based on the fundamental frequency of roughly 10.4 MHz, which can cause a transition between hyperfine states of the target atoms. Only through careful setting of the external magnetic field is it possible to avoid these transitions and the resulting depolarisation of the target gas. Measurements of these resonances were made during the first HERMES run 1995-2000. The target region was modified in 2001 to allow HERMES to use hydrogen polarised perpendicularly to the direction of the electron beam. This modification gave HERMES access to the so-called 'Transversity' distribution for the first time, but also allows additional resonances in the target, which were previously forbidden by selection rules. The measurement and minimisation of these 'Sigma resonances' are presented. A distinctive feature of the HERMES experiment is its novel storage cell which allows target atoms to make multiple passes of the HERA beam. An exact description of beam-induced depolarisation must therefore consider the geometry of the storage cell and the distribution of the magnetic field throughout the cell. Calculations of the depolarisation can be made by solving the time-dependent Schroedinger equation using first-order perturbation theory. A simple analytical model and a molecular-flow Monte-Carlo are used to predict the exact shape of the resonances. The first measurements of the resonances with a transverse magnetic holding field are presented and compared with the simulations. (orig.)

Geometric Computing for Freeform Architecture

KAUST Repository

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 discretization of Schrödinger equation

Energy Technology Data Exchange (ETDEWEB)

Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru

2016-01-08

There are different approaches to discretization of the Schrödinger equation with some approximations. In this paper we derive a discrete equation that can be considered as exact discretization of the continuous Schrödinger equation. The proposed discrete equation is an equation with difference of integer order that is represented by infinite series. We suggest differences, which are characterized by power-law Fourier transforms. These differences can be considered as exact discrete analogs of derivatives of integer orders. Physically the suggested discrete equation describes a chain (or lattice) model with long-range interaction of power-law form. Mathematically it is a uniquely highlighted difference equation that exactly corresponds to the continuous Schrödinger equation. Using the Young's inequality for convolution, we prove that suggested differences are operators on the Hilbert space of square-summable sequences. We prove that the wave functions, which are exact discrete analogs of the free particle and harmonic oscillator solutions of the continuous Schrödinger equations, are solutions of the suggested discrete Schrödinger equations. - Highlights: • Exact discretization of the continuous Schrödinger equation is suggested. • New long-range interactions of power-law form are suggested. • Solutions of discrete Schrödinger equation are exact discrete analogs of continuous solutions.

Exact discretization of Schrödinger equation

International Nuclear Information System (INIS)

Tarasov, Vasily E.

2016-01-01

There are different approaches to discretization of the Schrödinger equation with some approximations. In this paper we derive a discrete equation that can be considered as exact discretization of the continuous Schrödinger equation. The proposed discrete equation is an equation with difference of integer order that is represented by infinite series. We suggest differences, which are characterized by power-law Fourier transforms. These differences can be considered as exact discrete analogs of derivatives of integer orders. Physically the suggested discrete equation describes a chain (or lattice) model with long-range interaction of power-law form. Mathematically it is a uniquely highlighted difference equation that exactly corresponds to the continuous Schrödinger equation. Using the Young's inequality for convolution, we prove that suggested differences are operators on the Hilbert space of square-summable sequences. We prove that the wave functions, which are exact discrete analogs of the free particle and harmonic oscillator solutions of the continuous Schrödinger equations, are solutions of the suggested discrete Schrödinger equations. - Highlights: • Exact discretization of the continuous Schrödinger equation is suggested. • New long-range interactions of power-law form are suggested. • Solutions of discrete Schrödinger equation are exact discrete analogs of continuous solutions.

Superconducting resonators as beam splitters for linear-optics quantum computation.

Science.gov (United States)

Chirolli, Luca; Burkard, Guido; Kumar, Shwetank; Divincenzo, David P

2010-06-11

We propose and analyze a technique for producing a beam-splitting quantum gate between two modes of a ring-resonator superconducting cavity. The cavity has two integrated superconducting quantum interference devices (SQUIDs) that are modulated by applying an external magnetic field. The gate is accomplished by applying a radio frequency pulse to one of the SQUIDs at the difference of the two mode frequencies. Departures from perfect beam splitting only arise from corrections to the rotating wave approximation; an exact calculation gives a fidelity of >0.9992. Our construction completes the toolkit for linear-optics quantum computing in circuit quantum electrodynamics.

A combined dynamic analysis method for geometrically nonlinear vibration isolators with elastic rings

Science.gov (United States)

Hu, Zhan; Zheng, Gangtie

2016-08-01

A combined analysis method is developed in the present paper for studying the dynamic properties of a type of geometrically nonlinear vibration isolator, which is composed of push-pull configuration rings. This method combines the geometrically nonlinear theory of curved beams and the Harmonic Balance Method to overcome the difficulty in calculating the vibration and vibration transmissibility under large deformations of the ring structure. Using the proposed method, nonlinear dynamic behaviors of this isolator, such as the lock situation due to the coulomb damping and the usual jump resulting from the nonlinear stiffness, can be investigated. Numerical solutions based on the primary harmonic balance are first verified by direct integration results. Then, the whole procedure of this combined analysis method is demonstrated and validated by slowly sinusoidal sweeping experiments with different amplitudes of the base excitation. Both numerical and experimental results indicate that this type of isolator behaves as a hardening spring with increasing amplitude of the base excitation, which makes it suitable for isolating both steady-state vibrations and transient shocks.

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.

Entanglement of two-qubit photon beam by magnetic field

Energy Technology Data Exchange (ETDEWEB)

Levin, A.D.; Castro, R.A. [University of Sao Paulo, Institute of Physics, CP 66318, Sao Paulo (Brazil); Gitman, D.M. [University of Sao Paulo, Institute of Physics, CP 66318, Sao Paulo (Brazil); P.N. Lebedev Physical Institute, Moscow (Russian Federation); Tomsk State University, Tomsk (Russian Federation)

2014-09-15

We study the possibility of affecting the entanglement in a two-qubit system consisting of two photons with different fixed frequencies but with two arbitrary linear polarizations, moving in the same direction, with the help of an applied external magnetic field. The interaction between the magnetic field and the photons in our model is achieved through intermediate electrons that interact both with the photons and the magnetic field. The possibility of an exact theoretical analysis of this scheme is based on well-known exact solutions that describe the interaction of an electron subjected to an external magnetic field (or a medium of electrons not interacting with each other) with a quantized field of two photons. We adapt these exact solutions to the case under consideration. Using explicit wave functions for the resulting electromagnetic field, we calculate the entanglement measures (the information and the Schmidt ones) of the photon beam as functions of the applied magnetic field and the parameters of the electron medium. (orig.)

Harmonic oscillator in heat bath: Exact simulation of time-lapse-recorded data and exact analytical benchmark statistics

DEFF Research Database (Denmark)

Nørrelykke, Simon F; Flyvbjerg, Henrik

2011-01-01

The stochastic dynamics of the damped harmonic oscillator in a heat bath is simulated with an algorithm that is exact for time steps of arbitrary size. Exact analytical results are given for correlation functions and power spectra in the form they acquire when computed from experimental time...

Vibration suppression of composite laminated beams using distributed piezoelectric patches

International Nuclear Information System (INIS)

Foda, M A; Almajed, A A; ElMadany, M M

2010-01-01

The focus of this paper is to develop an analytical and straightforward approach to suppress the steady state transverse vibration of a symmetric cross-ply laminated composite beam that is excited by an external harmonic force. This is achieved by bonding patches of piezoelectric material at selected locations along the beam. The governing equations for the system are formulated and the dynamic Green's functions are used to obtain an exact solution for the problem. A scheme is proposed for determining the values of the driving voltages, the dimensions of the PZT patches and their locations along the beam, in order to confine the vibration in a certain chosen region where the vibration is not harmful and leave the other chosen region stationary or vibrating with very small amplitudes. Beams with different boundary conditions are considered. Numerical case studies are presented to verify the utility of the proposed scheme

Natural Vibration of a Beam with a Breathing Oblique Crack

Directory of Open Access Journals (Sweden)

Yijiang Ma

2017-01-01

Full Text Available An analytical method is proposed to calculate the natural frequency of a cantilever beam with a breathing oblique crack. A double-linear-springs-model is developed in the modal analysis process to describe the breathing oblique crack, and the breathing behaviour of the oblique crack is objectively simulated. The finite element method (FEM analysis software ABAQUS is used to calculate the geometric correction factors when the cracked plate is subjected to a pure bending moment at different oblique crack angles and relative depths. The Galerkin method is applied to simplify the cracked beam to a single degree of freedom system, allowing the natural frequency of the beam with the breathing oblique crack to be calculated. Compared with the natural frequencies of the breathing oblique cracked beam obtained using the ABAQUS FEM method, the proposed analytical method exhibits a high computational accuracy, with a maximum error of only 4.65%.

Reggeon effects in a geometrical model of elastic scattering. [Crossover curves, dip depth, scattering amplitude, 10 to 10,000 GeV

Energy Technology Data Exchange (ETDEWEB)

Dias de Deus, J [Instituto de Fisica e Matematica, Lisboa (Portugal); Kroll, P [Wuppertal Univ. (Gesamthochschule) (Germany, F.R.)

1976-08-21

The inclusion of secondary contributions Reggeons and real parts by changing the radial scale but exactly preserving geometrical scaling (GS) alloys an exclusion of GS to lower energies. The crossover curves in proton proton, Kp, and *pp are in this way correctly described. A GS formula relating two measurable quantities, the depth of the dip in proton proton scattering and the ratio of the real to immaginary part of the amplitude at t=0, is shown to be valid in the 10-1000 GeV region.

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)

Initial application of a geometric QA tool for integrated MV and kV imaging systems on three image guided radiotherapy systems.

Science.gov (United States)

Mao, Weihua; Speiser, Michael; Medin, Paul; Papiez, Lech; Solberg, Timothy; Xing, Lei

2011-05-01

Several linacs with integrated kilovoltage (kV) imaging have been developed for delivery of image guided radiation therapy (IGRT). High geometric accuracy and coincidence of kV imaging systems and megavoltage (MV) beam delivery are essential for successful image guidance. A geometric QA tool has been adapted for routine QA for evaluating and characterizing the geometric accuracy of kV and MV cone-beam imaging systems. The purpose of this work is to demonstrate the application of methodology to routine QA across three IGRT-dedicated linac platforms. It has been applied to a Varian Trilogy (Varian Medical Systems, Palo Alto, CA), an Elekta SynergyS (Elekta, Stockholm, Sweden), and a Brainlab Vero (Brainlab AG, Feldkirchen, Germany). Both the Trilogy and SynergyS linacs are equipped with a retractable kV x-ray tube and a flat panel detector. The Vero utilizes a rotating, rigid ring structure integrating a MV x-ray head mounted on orthogonal gimbals, an electronic portal imaging device (EPID), two kV x-ray tubes, and two fixed flat panel detectors. This dual kV imaging system provides orthogonal radiographs, CBCT images, and real-time fluoroscopic monitoring. Two QA phantoms were built to suit different field sizes. Projection images of a QA phantom were acquired using MV and kV imaging systems at a series of gantry angles. Software developed for this study was used to analyze the projection images and calculate nine geometric parameters for each projection. The Trilogy was characterized five times over one year, while the SynergyS was characterized four times and the Vero once. Over 6500 individual projections were acquired and analyzed. Quantitative geometric parameters of both MV and kV imaging systems, as well as the isocenter consistency of the imaging systems, were successfully evaluated. A geometric tool has been successfully implemented for calibration and QA of integrated kV and MV across a variety of radiotherapy platforms. X-ray source angle deviations up to

Errors in dual x-ray beam differential absorptiometry

International Nuclear Information System (INIS)

Bolin, F.; Preuss, L.; Gilbert, K.; Bugenis, C.

1977-01-01

Errors pertinent to the dual beam absorptiometry system have been studied and five areas are given in detail: (1) scattering, in which a computer analysis of multiple scattering shows little error due to this effect; (2) geometrical configuration effects, in which the slope of the sample is shown to influence the accuracy of the measurement; (3) Poisson variations, wherein it is shown that a simultaneous reduction can be obtained in both dosage and statistical error; (4) absorption coefficients, in which the effect of variation in absorption coefficient compilations is shown to have a critical effect on the interpretations of experimental data; and (5) filtering, wherein is shown the need for filters on dual beam systems using a characteristic x-ray output. A zero filter system is outlined

Triplasmatron sources for broad and reactive ion beams

International Nuclear Information System (INIS)

Lejeune, C.; Grandchamp, J.P.; Kessi, O.; Gilles, J.P.

1986-01-01

Two alternative discharge structures, which are both convenient for the extraction of broad and reactive ion beams, are described. They have been designed in order to overcome both lifetime and beam contamination problems while preserving a high ionization efficiency and a smooth plasma uniformity. They both use a hot cathode duoplasmatron discharge to inject ionizing electrons into the main ionization chamber, according to the triplasmatron concept. The triplasmatron multipolar ion source (TMIS) uses the magnetic multipolar containment of both electrons and ions, whereas the triplasmatron reflex ion source (TRIS) uses the electrostatic and geometric containment of the ionizing electrons. The behaviour and performance of both structures are reported and discussed with a special emphasis to the operation with either oxygen or fluorocarbon gases. (author)

Wave-optics description of self-healing mechanism in Bessel beams.

Science.gov (United States)

Aiello, Andrea; Agarwal, Girish S

2014-12-15

Bessel beams' great importance in optics lies in that these propagate without spreading and can reconstruct themselves behind an obstruction placed across their path. However, a rigorous wave-optics explanation of the latter property is missing. In this work, we study the reconstruction mechanism by means of a wave-optics description. We obtain expressions for the minimum distance beyond the obstruction at which the beam reconstructs itself, which are in close agreement with the traditional one determined from geometrical optics. Our results show that the physics underlying the self-healing mechanism can be entirely explained in terms of the propagation of plane waves with radial wave vectors lying on a ring.

Investigations on KONUS beam dynamics using the pre-stripper drift tube linac at GSI

Science.gov (United States)

Xiao, C.; Du, X. N.; Groening, L.

2018-04-01

Interdigital H-mode (IH) drift tube linacs (DTLs) based on KONUS beam dynamics are very sensitive to the rf-phases and voltages at the gaps between tubes. In order to design these DTLs, a deep understanding of the underlying longitudinal beam dynamics is mandatory. The report presents tracking simulations along an IH-DTL using the PARTRAN and BEAMPATH codes together with MATHCAD and CST. Simulation results illustrate that the beam dynamics design of the pre-stripper IH-DTL at GSI is sensitive to slight deviations of rf-phase and gap voltages with impact to the mean beam energy at the DTL exit. Applying the existing geometrical design, rf-voltages, and rf-phases of the DTL were re-adjusted. In simulations this re-optimized design can provide for more than 90% of transmission of an intense 15 emA beam keeping the reduction of beam brilliance below 25%.

The physics of crystalline beams

International Nuclear Information System (INIS)

Schiffer, J.P.

1995-01-01

It seems that the time has come in the pursuit of lower and lower beam temperatures to start focusing more detailed attention to the reality of storage rings--conventional cooling techniques and measures of temperature are generally not the appropriate ones at the lowest temperatures. Finding solutions to these serious problems does not appear to be impossible, but these considerations must be kept in mind in designing new storage rings with the aim to approach the regime of ordered three-dimensional beams. In particular, such rings will have to: Use calculations of the lattice with the full effects of space charge included. (N.B. averaged over time, space charge exactly cancels the focusing fields for a cold beam and therefore must be explicitly included.) Find technical solutions and incorporate several of; cooling to introduce a longitudinal velocity gradient and favor constant angular velocity; high multiplicity in bending and focusing elements; stronger focusing (high betatron tune); and high symmetry in the ring design. Finally, simulations should try to incorporate as much realism as possible, with larger repeating cells and more detailed descriptions of the lattice

Study of radiation-thermal effect of electron beam on steel and cast iron

International Nuclear Information System (INIS)

Machurin, E.S.; Lonchin, G.M.

1980-01-01

Studied is the influence of radiation-heat treatment by high energy (3-4.5 MeV) electron beam on the structure and properties of carbon steels (65G, 90KhF) and cast iron. Metallography and electron microscopy methods are used to study microstructure. It is shown that after the treatment by the electron beam there is observed noticeable structure grinding, sample fracture viscosity (even in a quenched state), increase of hardness and impact strength. The mechanism of metal heating process by electron beam is calculated and temperature field is defined in a heating region accounting for electron beam characteristics, medium and geometric factor. Theoretical data are close to experimental ones obtained in a course of determining the microhardness of irradiated samples for the cases of electron treatment duration up to 10 s

Three-dimensional single-photon emission computed tomography using cone beam collimation (CB-SPECT)

International Nuclear Information System (INIS)

Jaszczak, R.J.; Floyd, C.E. Jr.; Manglos, S.H.; Greer, K.L.; Coleman, R.E.

1986-01-01

A simple and economically practical method of improving the sensitivity of camera-based SPECT was developed using converging (cone-beam) collimation. This geometry is particularly advantageous for SPECT devices using large field-of-view cameras in imaging smaller, centrally located activity distributions. Geometric sensitivities, spatial resolutions, and fields-of-view of a cone-beam collimator having a focal length of 48 cm and a similarly designed parallel hole collimator were compared analytically. At 15 cm from the collimator surface the point-source sensitivity of the cone-beam collimator was 2.4 times the sensitivity of the parallel-hole collimator. SPECT projection data (simulated using Monte Carlo methodology) were reconstructed using a 3-D filtered backprojection algorithm. Cone-beam emission CT (CB-SPECT) seems potentially useful for animal investigations, pediatric studies, and for brain imaging

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....

Characteristics of steady vibration in a rotating hub-beam system

Science.gov (United States)

Zhao, Zhen; Liu, Caishan; Ma, Wei

2016-02-01

A rotating beam features a puzzling character in which its frequencies and modal shapes may vary with the hub's inertia and its rotating speed. To highlight the essential nature behind the vibration phenomena, we analyze the steady vibration of a rotating Euler-Bernoulli beam with a quasi-steady-state stretch. Newton's law is used to derive the equations governing the beam's elastic motion and the hub's rotation. A combination of these equations results in a nonlinear partial differential equation (PDE) that fully reflects the mutual interaction between the two kinds of motion. Via the Fourier series expansion within a finite interval of time, we reduce the PDE into an infinite system of a nonlinear ordinary differential equation (ODE) in spatial domain. We further nondimensionalize the ODE and discretize it via a difference method. The frequencies and modal shapes of a general rotating beam are then determined numerically. For a low-speed beam where the ignorance of geometric stiffening is feasible, the beam's vibration characteristics are solved analytically. We validate our numerical method and the analytical solutions by comparing with either the past experiments or the past numerical findings reported in existing literature. Finally, systematic simulations are performed to demonstrate how the beam's eigenfrequencies vary with the hub's inertia and rotating speed.

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)

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)

Experimental Results and Numerical Simulation of the Target RCS using Gaussian Beam Summation Method

Directory of Open Access Journals (Sweden)

Ghanmi Helmi

2018-05-01

Full Text Available This paper presents a numerical and experimental study of Radar Cross Section (RCS of radar targets using Gaussian Beam Summation (GBS method. The purpose GBS method has several advantages over ray method, mainly on the caustic problem. To evaluate the performance of the chosen method, we started the analysis of the RCS using Gaussian Beam Summation (GBS and Gaussian Beam Launching (GBL, the asymptotic models Physical Optic (PO, Geometrical Theory of Diffraction (GTD and the rigorous Method of Moment (MoM. Then, we showed the experimental validation of the numerical results using experimental measurements which have been executed in the anechoic chamber of Lab-STICC at ENSTA Bretagne. The numerical and experimental results of the RCS are studied and given as a function of various parameters: polarization type, target size, Gaussian beams number and Gaussian beams width.

Exact analysis of discrete data

CERN Document Server

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...

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....

An isodose shift technique for obliquely incident electron beams

International Nuclear Information System (INIS)

Ulin, K.; Sternick, E.S.

1989-01-01

It is well known that when an electron beam is incident obliquely on the surface of a phantom, the depth dose curve measured normal to the surface is shifted toward the surface. Based on geometrical arguments alone, the depth of the nth isodose line for an electron beam incident at an angle θ should be equal to the product of cos θ and the depth of the nth isodose line at normal incidence. This method, however, ignores the effects of scatter and can lead to significant errors in isodose placement for beams at large angles of incidence. A semi-empirical functional relationship and a table of isodose shift factors have been developed with which one may easily calculate the depth of any isodose line for beams at incident angles of 0 degree to 60 degree. The isodose shift factors are tabulated in terms of beam energy (6--22 MeV) and isodose line (10%--90%) and are shown to be relatively independent of beam size and incident angle for angles <60 degree. Extensive measurements have been made on a Varian Clinac 2500 linear accelerator with a parallel-plate chamber and polystyrene phantom. The dependence of the chamber response on beam angulation has been checked, and the scaling factor of the polystyrene phantom has been determined to be equal to 1.00

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

Selection of coplanar or noncoplanar beams using three-dimensional optimization based on maximum beam separation and minimized nontarget irradiation

International Nuclear Information System (INIS)

Das, Shiva K.; Marks, Lawrence B.

1997-01-01

Purpose: The design of an appropriate set of multiple fixed fields to achieve a steep dose gradient at the tumor edge, with minimal normal tissue exposure, is a very difficult problem, since a virtually infinite number of possible beam orientations exists. In practice we have selected beams in an iterative and often time-consuming process. This work proposes an optimization method, based on geometric and dose elements, to effectively arrive at a set of beam orientations. Methods and Materials: Beams are selected by minimizing a goal function including an angle function (beam separation for steep dose gradient at target edge) and a length function (related to normal tissue dose volume histogram). The relative importance of these two factors may be adjusted depending on the clinic situation. The model is flexible and can include case specific practical anatomic and physical considerations. Results: In extremely simple situations, the goal function yields results consistent with well-known analytical solutions. When applied to more complex clinical situations, it provides clinically reasonable solutions similar to those empirically developed by the clinician. The optimization process takes approximately 25 min on a UNIX workstation. Conclusion: The optimization scheme provides a practical means for rapidly designing multiple field coplanar or noncoplanar treatments. It overcomes limitations in human three-dimensional visualization such as trying to visualize beam directions and keeping track of the hinge angle between beams while accounting for anatomic/machine constraints. In practice, it has been used as a starting point for physicians to make modifications, based on their clinical judgment

The optics of the Final Focus Test Beam

International Nuclear Information System (INIS)

Irwin, J.; Brown, K.; Bulos, F.; Burke, D.; Helm, R.; Roy, G.; Ruth, R.; Yamamoto, N.; Oide, K.

1991-01-01

The Final Focus Test Beam (FFTB), currently under construction at the end of the SLAC Linac, is being built by an international collaboration as a test bed for ideas and methods required in the design and construction of final focus systems for next generation e + e - linear colliders. The FFTB lattice shown is based on the previously developed principle of using sextupole pairs in a dispersive region to compensate chromaticity. The linear lattice was optimized for length, and implementation of diagnostic procedures. The transformations between sextupole pairs (CCX and CCY) are exactly -I, the matrix for the intermediate transformer (BX) is exactly diagonal, and the dispersion function has zero slope at the sextupoles and is thus zero at the minimum of the β x function in the intermediate transformer

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)

CALCULATION ALGORITHM TRUSS UNDER CRANE BEAMS

Directory of Open Access Journals (Sweden)

N. K. Akaev1

2016-01-01

Full Text Available Aim.The task of reducing the deflection and increase the rigidity of single-span beams are made. In the article the calculation algorithm for truss crane girders is determined.Methods. To identify the internal effort required for the selection of cross section elements the design uses the Green's function.Results. It was found that the simplest truss system reduces deflection and increases the strength of design. The upper crossbar is subjected not only to bending and shear and compression work due to tightening tension. Preliminary determination of the geometrical characteristics of the crane farms elements are offered to make a comparison with previous similar configuration of his farms, using a simple approximate calculation methods.Conclusion.The method of sequential movements (incrementally the two bridge cranes along the length of the upper crossbar truss beams is suggested. We give the corresponding formulas and conditions of safety.

A beam-profile monitor for the BNL Accelerator Test Facility (ATF)

International Nuclear Information System (INIS)

Russell, D.P.; McDonald, K.T.

1989-01-01

A beam-profile monitor has been designed to diagnose the 5-MeV high-brightness electron beam from the rf gun of the BNL Accelerator Test Facility (ATF). The monitor consists of a phosphor screen viewed by a CCD camera. The video images are digitized and stored by a framegrabber and analyzed by an IBM PC-AT to extract the emittance. Details of the hardware configuration are presented, along with the spatial resolution of the system measured as a function of phosphor-screen thickness. The strategies which will be used to measure the transverse and longitudinal emittances are briefly mentioned. The system should be capable of measuring a transverse geometric emittance of around 1 mm-mrad, as will be typical of the ATF beam. 6 refs., 2 figs

Generalized Kapchinskij-Vladimirskij Distribution and Envelope Equation for High-intensity Beams in a Coupled Transverse Focusing Lattice

International Nuclear Information System (INIS)

Qin, Hong; Chung, Moses; Davidson, Ronald C.

2009-01-01

In an uncoupled lattice, the Kapchinskij-Vladimirskij (KV) distribution function first analyzed in 1959 is the only known exact solution of the nonlinear Vlasov-Maxwell equations for high- intensity beams including self-fields in a self-consistent manner. The KV solution is generalized here to high-intensity beams in a coupled transverse lattice using the recently developed generalized Courant-Snyder invariant for coupled transverse dynamics. This solution projects to a rotating, pulsating elliptical beam in transverse configuration space, determined by the generalized matrix envelope equation.

Bench calibration of INDUS-2 beam position indicators

International Nuclear Information System (INIS)

Tyagi, Y.; Banerji, Anil; Kotaiah, S.

2005-01-01

A third generation synchrotron radiation source of energy 2.5 GeV named INDUS-2 at Centre for Advanced Technology (C.A.T), Indore (M.P) is in the advanced stage of construction. Accurate determination and correction of beam closed orbit in INDUS-2 machine within 100 of microns is a very desirable goal. Bench based calibration of Beam Position Indicators (BPI) play a very important and useful role during initial commissioning of electron machines. To precisely measure transverse position of electron beam in the Indus-2 storage ring, 56 Beam Position Indicators (BPI) will be installed in INDUS-2 machine. Out of 56 Beam Position Indicators 40 are of individual type whereas 16 are integrated with dipole vacuum chamber. The Beam Position Indicators are required to be calibrated before they can be installed. The calibration is done to determine electrical offset with respect to defined mechanical centre, to determine displacement sensitivities as well as non linearity's of BPI. Ideally when beam passes through the geometrical center of BPI's, all electrodes should have same signal strength. However due to different capacitance of electrodes and offset and drift in electronics, the electrical centre (mechanical x, y where all electrodes shows same signal strength) differs from mechanical centre of BPI. A fully automatic calibration system has been developed to carry out the calibration of Beam Position Indicators. A calibration software has been developed which has necessary utilities to process and display calibration data and results. This paper describes the calibration results of Indus-2 BPM. (author)

Geometric phases for nonlinear coherent and squeezed states

International Nuclear Information System (INIS)

Yang Dabao; Chen Ying; Chen Jingling; Zhang Fulin

2011-01-01

The geometric phases for standard coherent states which are widely used in quantum optics have attracted considerable attention. Nevertheless, few physicists consider the counterparts of nonlinear coherent states, which are useful in the description of the motion of a trapped ion. In this paper, the non-unitary and non-cyclic geometric phases for two nonlinear coherent and one squeezed states are formulated, respectively. Moreover, some of their common properties are discussed, such as gauge invariance, non-locality and nonlinear effects. The nonlinear functions have dramatic impacts on the evolution of the corresponding geometric phases. They speed the evolution up or down. So this property may have an application in controlling or measuring geometric phase. For the squeezed case, when the squeezed parameter r → ∞, the limiting value of the geometric phase is also determined by a nonlinear function at a given time and angular velocity. In addition, the geometric phases for standard coherent and squeezed states are obtained under a particular condition. When the time evolution undergoes a period, their corresponding cyclic geometric phases are achieved as well. And the distinction between the geometric phases of the two coherent states may be regarded as a geometric criterion.

Theoretical frameworks for the learning of geometrical reasoning