MODELING AND SIMULATION OF HIGH RESOLUTION OPTICAL REMOTE SENSING SATELLITE GEOMETRIC CHAIN

Directory of Open Access Journals (Sweden)

Z. Xia

2018-04-01

Full Text Available The high resolution satellite with the longer focal length and the larger aperture has been widely used in georeferencing of the observed scene in recent years. The consistent end to end model of high resolution remote sensing satellite geometric chain is presented, which consists of the scene, the three line array camera, the platform including attitude and position information, the time system and the processing algorithm. The integrated design of the camera and the star tracker is considered and the simulation method of the geolocation accuracy is put forward by introduce the new index of the angle between the camera and the star tracker. The model is validated by the geolocation accuracy simulation according to the test method of the ZY-3 satellite imagery rigorously. The simulation results show that the geolocation accuracy is within 25m, which is highly consistent with the test results. The geolocation accuracy can be improved about 7 m by the integrated design. The model combined with the simulation method is applicable to the geolocation accuracy estimate before the satellite launching.

Classical models for Regge trajectories

International Nuclear Information System (INIS)

Biedenharn, L.C.; Van Dam, H.; Marmo, G.; Morandi, G.; Mukunda, N.; Samuel, J.; Sudarshan, E.C.G.

1987-01-01

Two classical models for particles with internal structure and which describe Regge trajectories are developed. The remarkable geometric and other properties of the two internal spaces are highlighted. It is shown that the conditions of positive time-like four-velocity and energy momentum for the classical system imply strong and physically reasonable conditions on the Regge mass-spin relationship

From the geometric quantization to conformal field theory

International Nuclear Information System (INIS)

Alekseev, A.; Shatashvili, S.

1990-01-01

Investigation of 2d conformal field theory in terms of geometric quantization is given. We quantize the so-called model space of the compact Lie group, Virasoro group and Kac-Moody group. In particular, we give a geometrical interpretation of the Virasoro discrete series and explain that this type of geometric quantization reproduces the chiral part of CFT (minimal models, 2d-gravity, WZNW theory). In the appendix we discuss the relation between classical (constant) r-matrices and this geometrical approach. (orig.)

SOME PROPERTIES OF GEOMETRIC DEA MODELS

Directory of Open Access Journals (Sweden)

Ozren Despić

2013-02-01

Full Text Available Some specific geometric data envelopment analysis (DEA models are well known to the researchers in DEA through so-called multiplicative or log-linear efficiency models. Valuable properties of these models were noted by several authors but the models still remain somewhat obscure and rarely used in practice. The purpose of this paper is to show from a mathematical perspective where the geometric DEA fits in relation to the classical DEA, and to provide a brief overview of some benefits in using geometric DEA in practice of decision making and/or efficiency measurement.

Variation in the human ribs geometrical properties and mechanical response based on X-ray computed tomography images resolution.

Science.gov (United States)

Perz, Rafał; Toczyski, Jacek; Subit, Damien

2015-01-01

Computational models of the human body are commonly used for injury prediction in automobile safety research. To create these models, the geometry of the human body is typically obtained from segmentation of medical images such as computed tomography (CT) images that have a resolution between 0.2 and 1mm/pixel. While the accuracy of the geometrical and structural information obtained from these images depend greatly on their resolution, the effect of image resolution on the estimation of the ribs geometrical properties has yet to be established. To do so, each of the thirty-four sections of ribs obtained from a Post Mortem Human Surrogate (PMHS) was imaged using three different CT modalities: standard clinical CT (clinCT), high resolution clinical CT (HRclinCT), and microCT. The images were processed to estimate the rib cross-section geometry and mechanical properties, and the results were compared to those obtained from the microCT images by computing the 'deviation factor', a metric that quantifies the relative difference between results obtained from clinCT and HRclinCT to those obtained from microCT. Overall, clinCT images gave a deviation greater than 100%, and were therefore deemed inadequate for the purpose of this study. HRclinCT overestimated the rib cross-sectional area by 7.6%, the moments of inertia by about 50%, and the cortical shell area by 40.2%, while underestimating the trabecular area by 14.7%. Next, a parametric analysis was performed to quantify how the variations in the estimate of the geometrical properties affected the rib predicted mechanical response under antero-posterior loading. A variation of up to 45% for the predicted peak force and up to 50% for the predicted stiffness was observed. These results provide a quantitative estimate of the sensitivity of the response of the FE model to the resolution of the images used to generate it. They also suggest that a correction factor could be derived from the comparison between microCT and

Geometric Approaches to Quadratic Equations from Other Times and Places.

Science.gov (United States)

Allaire, Patricia R.; Bradley, Robert E.

2001-01-01

Focuses on geometric solutions of quadratic problems. Presents a collection of geometric techniques from ancient Babylonia, classical Greece, medieval Arabia, and early modern Europe to enhance the quadratic equation portion of an algebra course. (KHR)

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.

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)

A geometrical approach to free-field quantization

International Nuclear Information System (INIS)

Tabensky, R.; Valle, J.W.F.

1977-01-01

A geometrical approach to the quantization of free relativistic fields is given. Complex probability amplitudes are assigned to the solutions of the classical evolution equation. It is assumed that the evolution is stricly classical, according to the scalar unitary representation of the Poincare group in a functional space. The theory is equivalent to canonical quantization [pt

Controlling lightwave in Riemann space by merging geometrical optics with transformation optics.

Science.gov (United States)

Liu, Yichao; Sun, Fei; He, Sailing

2018-01-11

In geometrical optical design, we only need to choose a suitable combination of lenses, prims, and mirrors to design an optical path. It is a simple and classic method for engineers. However, people cannot design fantastical optical devices such as invisibility cloaks, optical wormholes, etc. by geometrical optics. Transformation optics has paved the way for these complicated designs. However, controlling the propagation of light by transformation optics is not a direct design process like geometrical optics. In this study, a novel mixed method for optical design is proposed which has both the simplicity of classic geometrical optics and the flexibility of transformation optics. This mixed method overcomes the limitations of classic optical design; at the same time, it gives intuitive guidance for optical design by transformation optics. Three novel optical devices with fantastic functions have been designed using this mixed method, including asymmetrical transmissions, bidirectional focusing, and bidirectional cloaking. These optical devices cannot be implemented by classic optics alone and are also too complicated to be designed by pure transformation optics. Numerical simulations based on both the ray tracing method and full-wave simulation method are carried out to verify the performance of these three optical devices.

Mass relations for two-dimensional classical configurations

International Nuclear Information System (INIS)

Tataru-Mihai, P.

1980-01-01

Using the two-dimensional sigma-nonlinear models as a framework mass relations for classical configurations of instanton/soliton type are derived. Our results suggest an interesting differential-geometric interpretation of the mass of a classical configuration in terms of the topological characteristics of an associated manifold. (orig.)

Geometrical optics in correlated imaging systems

International Nuclear Information System (INIS)

Cao Dezhong; Xiong Jun; Wang Kaige

2005-01-01

We discuss the geometrical optics of correlated imaging for two kinds of spatial correlations corresponding, respectively, to a classical thermal light source and a quantum two-photon entangled source. Due to the different features in the second-order spatial correlation, the two sources obey different imaging equations. The quantum entangled source behaves as a mirror, whereas the classical thermal source looks like a phase-conjugate mirror in the correlated imaging

High Resolution SAR Imaging Employing Geometric Features for Extracting Seismic Damage of Buildings

Science.gov (United States)

Cui, L. P.; Wang, X. P.; Dou, A. X.; Ding, X.

2018-04-01

Synthetic Aperture Radar (SAR) image is relatively easy to acquire but difficult for interpretation. This paper probes how to identify seismic damage of building using geometric features of SAR. The SAR imaging geometric features of buildings, such as the high intensity layover, bright line induced by double bounce backscattering and dark shadow is analysed, and show obvious differences texture features of homogeneity, similarity and entropy in combinatorial imaging geometric regions between the un-collapsed and collapsed buildings in airborne SAR images acquired in Yushu city damaged by 2010 Ms7.1 Yushu, Qinghai, China earthquake, which implicates a potential capability to discriminate collapsed and un-collapsed buildings from SAR image. Study also shows that the proportion of highlight (layover & bright line) area (HA) is related to the seismic damage degree, thus a SAR image damage index (SARDI), which related to the ratio of HA to the building occupation are of building in a street block (SA), is proposed. While HA is identified through feature extraction with high-pass and low-pass filtering of SAR image in frequency domain. A partial region with 58 natural street blocks in the Yushu City are selected as study area. Then according to the above method, HA is extracted, SARDI is then calculated and further classified into 3 classes. The results show effective through validation check with seismic damage classes interpreted artificially from post-earthquake airborne high resolution optical image, which shows total classification accuracy 89.3 %, Kappa coefficient 0.79 and identical to the practical seismic damage distribution. The results are also compared and discussed with the building damage identified from SAR image available by other authors.

Quantum no-singularity theorem from geometric flows

Science.gov (United States)

Alsaleh, Salwa; Alasfar, Lina; Faizal, Mir; Ali, Ahmed Farag

2018-04-01

In this paper, we analyze the classical geometric flow as a dynamical system. We obtain an action for this system, such that its equation of motion is the Raychaudhuri equation. This action will be used to quantize this system. As the Raychaudhuri equation is the basis for deriving the singularity theorems, we will be able to understand the effects and such a quantization will have on the classical singularity theorems. Thus, quantizing the geometric flow, we can demonstrate that a quantum space-time is complete (nonsingular). This is because the existence of a conjugate point is a necessary condition for the occurrence of singularities, and we will be able to demonstrate that such conjugate points cannot occur due to such quantum effects.

Constrained variational calculus for higher order classical field theories

Energy Technology Data Exchange (ETDEWEB)

Campos, Cedric M; De Leon, Manuel; De Diego, David MartIn, E-mail: cedricmc@icmat.e, E-mail: mdeleon@icmat.e, E-mail: david.martin@icmat.e [Instituto de Ciencias Matematicas, CSIC-UAM-UC3M-UCM, Serrano 123, 28006 Madrid (Spain)

2010-11-12

We develop an intrinsic geometrical setting for higher order constrained field theories. As a main tool we use an appropriate generalization of the classical Skinner-Rusk formalism. Some examples of applications are studied, in particular to the geometrical description of optimal control theory for partial differential equations.

Constrained variational calculus for higher order classical field theories

International Nuclear Information System (INIS)

Campos, Cedric M; De Leon, Manuel; De Diego, David MartIn

2010-01-01

We develop an intrinsic geometrical setting for higher order constrained field theories. As a main tool we use an appropriate generalization of the classical Skinner-Rusk formalism. Some examples of applications are studied, in particular to the geometrical description of optimal control theory for partial differential equations.

Dynamical systems in classical mechanics

CERN Document Server

Kozlov, V V

1995-01-01

This book shows that the phenomenon of integrability is related not only to Hamiltonian systems, but also to a wider variety of systems having invariant measures that often arise in nonholonomic mechanics. Each paper presents unique ideas and original approaches to various mathematical problems related to integrability, stability, and chaos in classical dynamics. Topics include… the inverse Lyapunov theorem on stability of equilibria geometrical aspects of Hamiltonian mechanics from a hydrodynamic perspective current unsolved problems in the dynamical systems approach to classical mechanics

A uniform geometrical optics and an extended uniform geometrical theory of diffraction for evaluating high frequency EM fields near smooth caustics and composite shadow boundaries

Science.gov (United States)

Constantinides, E. D.; Marhefka, R. J.

1994-01-01

A uniform geometrical optics (UGO) and an extended uniform geometrical theory of diffraction (EUTD) are developed for evaluating high frequency electromagnetic (EM) fields within transition regions associated with a two and three dimensional smooth caustic of reflected rays and a composite shadow boundary formed by the caustic termination or the confluence of the caustic with the reflection shadow boundary (RSB). The UGO is a uniform version of the classic geometrical optics (GO). It retains the simple ray optical expressions of classic GO and employs a new set of uniform reflection coefficients. The UGO also includes a uniform version of the complex GO ray field that exists on the dark side of the smooth caustic. The EUTD is an extension of the classic uniform geometrical theory of diffraction (UTD) and accounts for the non-ray optical behavior of the UGO reflected field near caustics by using a two-variable transition function in the expressions for the edge diffraction coefficients. It also uniformly recovers the classic UTD behavior of the edge diffracted field outside the composite shadow boundary transition region. The approach employed for constructing the UGO/EUTD solution is based on a spatial domain physical optics (PO) radiation integral representation for the fields which is then reduced using uniform asymptotic procedures. The UGO/EUTD analysis is also employed to investigate the far-zone RCS problem of plane wave scattering from two and three dimensional polynomial defined surfaces, and uniform reflection, zero-curvature, and edge diffraction coefficients are derived. Numerical results for the scattering and diffraction from cubic and fourth order polynomial strips are also shown and the UGO/EUTD solution is validated by comparison to an independent moment method (MM) solution. The UGO/EUTD solution is also compared with the classic GO/UTD solution. The failure of the classic techniques near caustics and composite shadow boundaries is clearly

Geometric group theory an introduction

CERN Document Server

Löh, Clara

2017-01-01

Inspired by classical geometry, geometric group theory has in turn provided a variety of applications to geometry, topology, group theory, number theory and graph theory. This carefully written textbook provides a rigorous introduction to this rapidly evolving field whose methods have proven to be powerful tools in neighbouring fields such as geometric topology. Geometric group theory is the study of finitely generated groups via the geometry of their associated Cayley graphs. It turns out that the essence of the geometry of such groups is captured in the key notion of quasi-isometry, a large-scale version of isometry whose invariants include growth types, curvature conditions, boundary constructions, and amenability. This book covers the foundations of quasi-geometry of groups at an advanced undergraduate level. The subject is illustrated by many elementary examples, outlooks on applications, as well as an extensive collection of exercises.

Geometric Theory of Reduction of Nonlinear Control Systems

Science.gov (United States)

Elkin, V. I.

2018-02-01

The foundations of a differential geometric theory of nonlinear control systems are described on the basis of categorical concepts (isomorphism, factorization, restrictions) by analogy with classical mathematical theories (of linear spaces, groups, etc.).

a Classical Isodual Theory of Antimatter and its Prediction of Antigravity

Science.gov (United States)

Santilli, Ruggero Maria

An inspection of the contemporary physics literature reveals that, while matter is treated at all levels of study, from Newtonian mechanics to quantum field theory, antimatter is solely treated at the level of second quantization. For the purpose of initiating the restoration of full equivalence in the treatment of matter and antimatter in due time, and as the classical foundations of an axiomatically consistent inclusion of gravitation in unified gauge theories recently appeared elsewhere, in this paper we present a classical representation of antimatter which begins at the primitive Newtonian level with corresponding formulations at all subsequent levels. By recalling that charge conjugation of particles into antiparticles is antiautomorphic, the proposed theory of antimatter is based on a new map, called isoduality, which is also antiautomorphic (and more generally, antiisomorphic), yet it is applicable beginning at the classical level and then persists at the quantum level where it becomes equivalent to charge conjugation. We therefore present, apparently for the first time, the classical isodual theory of antimatter, we identify the physical foundations of the theory as being the novel isodual Galilean, special and general relativities, and we show the compatibility of the theory with all available classical experimental data on antimatter. We identify the classical foundations of the prediction of antigravity for antimatter in the field of matter (or vice-versa) without any claim on its validity, and defer its resolution to specifically identified experiments. We identify the novel, classical, isodual electromagnetic waves which are predicted to be emitted by antimatter, the so-called space-time machine based on a novel non-Newtonian geometric propulsion, and other implications of the theory. We also introduce, apparently for the first time, the isodual space and time inversions and show that they are nontrivially different than the conventional ones, thus

Geometrical formulation of the conformal Ward identity

International Nuclear Information System (INIS)

Kachkachi, M.

2002-08-01

In this paper we use deep ideas in complex geometry that proved to be very powerful in unveiling the Polyakov measure on the moduli space of Riemann surfaces and lead to obtain the partition function of perturbative string theory for 2, 3, 4 loops. Indeed, a geometrical interpretation of the conformal Ward identity in two dimensional conformal field theory is proposed: the conformal anomaly is interpreted as a deformation of the complex structure of the basic Riemann surface. This point of view is in line with the modern trend of geometric quantizations that are based on deformations of classical structures. Then, we solve the conformal Ward identity by using this geometrical formalism. (author)

A classical approach to higher-derivative gravity

International Nuclear Information System (INIS)

Accioly, A.J.

1988-01-01

Two classical routes towards higher-derivative gravity theory are described. The first one is a geometrical route, starting from first principles. The second route is a formal one, and is based on a recent theorem by Castagnino et.al. [J. Math. Phys. 28 (1987) 1854]. A cosmological solution of the higher-derivative field equations is exhibited which in a classical framework singles out this gravitation theory. (author) [pt

Classical dynamics a modern perspective

CERN Document Server

Sudarshan, Ennackal Chandy George

2016-01-01

Classical dynamics is traditionally treated as an early stage in the development of physics, a stage that has long been superseded by more ambitious theories. Here, in this book, classical dynamics is treated as a subject on its own as well as a research frontier. Incorporating insights gained over the past several decades, the essential principles of classical dynamics are presented, while demonstrating that a number of key results originally considered only in the context of quantum theory and particle physics, have their foundations in classical dynamics.Graduate students in physics and practicing physicists will welcome the present approach to classical dynamics that encompasses systems of particles, free and interacting fields, and coupled systems. Lie groups and Lie algebras are incorporated at a basic level and are used in describing space-time symmetry groups. There is an extensive discussion on constrained systems, Dirac brackets and their geometrical interpretation. The Lie-algebraic description of ...

Geometric Phase of the Gyromotion for Charged Particles in a Time-dependent Magnetic Field

International Nuclear Information System (INIS)

Liu, Jian; Qin, Hong

2011-01-01

We study the dynamics of the gyrophase of a charged particle in a magnetic field which is uniform in space but changes slowly with time. As the magnetic field evolves slowly with time, the changing of the gyrophase is composed of two parts. The rst part is the dynamical phase, which is the time integral of the instantaneous gyrofrequency. The second part, called geometric gyrophase, is more interesting, and it is an example of the geometric phase which has found many important applications in different branches of physics. If the magnetic field returns to the initial value after a loop in the parameter space, then the geometric gyrophase equals the solid angle spanned by the loop in the parameter space. This classical geometric gyrophase is compared with the geometric phase (the Berry phase) of the spin wave function of an electron placed in the same adiabatically changing magnetic field. Even though gyromotion is not the classical counterpart of the quantum spin, the similarities between the geometric phases of the two cases nevertheless reveal the similar geometric nature of the different physics laws governing these two physics phenomena.

Understanding geometric algebra for electromagnetic theory

CERN Document Server

Arthur, John W

2011-01-01

"This book aims to disseminate geometric algebra as a straightforward mathematical tool set for working with and understanding classical electromagnetic theory. It's target readership is anyone who has some knowledge of electromagnetic theory, predominantly ordinary scientists and engineers who use it in the course of their work, or postgraduate students and senior undergraduates who are seeking to broaden their knowledge and increase their understanding of the subject. It is assumed that the reader is not a mathematical specialist and is neither familiar with geometric algebra or its application to electromagnetic theory. The modern approach, geometric algebra, is the mathematical tool set we should all have started out with and once the reader has a grasp of the subject, he or she cannot fail to realize that traditional vector analysis is really awkward and even misleading by comparison"--Provided by publisher.

Multiscale geometric modeling of macromolecules II: Lagrangian representation

Science.gov (United States)

Feng, Xin; Xia, Kelin; Chen, Zhan; Tong, Yiying; Wei, Guo-Wei

2013-01-01

Geometric modeling of biomolecules plays an essential role in the conceptualization of biolmolecular structure, function, dynamics and transport. Qualitatively, geometric modeling offers a basis for molecular visualization, which is crucial for the understanding of molecular structure and interactions. Quantitatively, geometric modeling bridges the gap between molecular information, such as that from X-ray, NMR and cryo-EM, and theoretical/mathematical models, such as molecular dynamics, the Poisson-Boltzmann equation and the Nernst-Planck equation. In this work, we present a family of variational multiscale geometric models for macromolecular systems. Our models are able to combine multiresolution geometric modeling with multiscale electrostatic modeling in a unified variational framework. We discuss a suite of techniques for molecular surface generation, molecular surface meshing, molecular volumetric meshing, and the estimation of Hadwiger’s functionals. Emphasis is given to the multiresolution representations of biomolecules and the associated multiscale electrostatic analyses as well as multiresolution curvature characterizations. The resulting fine resolution representations of a biomolecular system enable the detailed analysis of solvent-solute interaction, and ion channel dynamics, while our coarse resolution representations highlight the compatibility of protein-ligand bindings and possibility of protein-protein interactions. PMID:23813599

Classical geometry Euclidean, transformational, inversive, and projective

CERN Document Server

Leonard, I E; Liu, A C F; Tokarsky, G W

2014-01-01

Features the classical themes of geometry with plentiful applications in mathematics, education, engineering, and science Accessible and reader-friendly, Classical Geometry: Euclidean, Transformational, Inversive, and Projective introduces readers to a valuable discipline that is crucial to understanding bothspatial relationships and logical reasoning. Focusing on the development of geometric intuitionwhile avoiding the axiomatic method, a problem solving approach is encouraged throughout. The book is strategically divided into three sections: Part One focuses on Euclidean geometry, which p

Geometry from dynamics, classical and quantum

CERN Document Server

Cariñena, José F; Marmo, Giuseppe; Morandi, Giuseppe

2015-01-01

This book describes, by using elementary techniques, how some geometrical structures widely used today in many areas of physics, like symplectic, Poisson, Lagrangian, Hermitian, etc., emerge from dynamics. It is assumed that what can be accessed in actual experiences when studying a given system is just its dynamical behavior that is described by using a family of variables ("observables" of the system).   The book departs from the principle that ''dynamics is first'', and then tries to answer in what sense the sole dynamics determines the geometrical structures that have proved so useful to describe the dynamics in so many important instances. In this vein it is shown that most of the geometrical structures that are used in the standard presentations of classical dynamics (Jacobi, Poisson, symplectic, Hamiltonian, Lagrangian) are determined, though in general not uniquely, by the dynamics alone. The same program is accomplished for the geometrical structures relevant to describe quantum dynamics.  Finall...

High-resolution CT with histopathological correlates of the classic metaphyseal lesion of infant abuse

Energy Technology Data Exchange (ETDEWEB)

Tsai, Andy; Kleinman, Paul K. [Boston Children' s Hospital, Department of Radiology, Boston, MA (United States); McDonald, Anna G. [Office of the Chief Medical Examiner, Boston, MA (United States); Rosenberg, Andrew E. [University of Miami Hospital, Department of Pathology, Miami, FL (United States); Gupta, Rajiv [Massachusetts General Hospital, Department of Radiology, Boston, MA (United States)

2014-02-15

The classic metaphyseal lesion (CML) is a common high specificity indicator of infant abuse and its imaging features have been correlated histopathologically in infant fatalities. High-resolution CT imaging and histologic correlates were employed to (1) characterize the normal infant anatomy surrounding the chondro-osseous junction, and (2) confirm the 3-D model of the CML previously inferred from planar radiography and histopathology. Long bone specimens from 5 fatally abused infants, whose skeletal survey showed definite or suspected CMLs, were studied postmortem. After skeletal survey, selected specimens were resected and imaged with high-resolution digital radiography. They were then scanned with micro-CT (isotropic resolution of 45 μm{sup 3}) or with high-resolution flat-panel CT (isotropic resolutions of 200 μm{sup 3}). Visualization of the bony structures was carried out using image enhancement, segmentation and isosurface extraction, together with volume rendering and multiplanar reformatting. These findings were then correlated with histopathology. Study of normal infant bone clarifies the 3-D morphology of the subperiosteal bone collar (SPBC) and the radiographic zone of provisional calcification (ZPC). Studies on specimens with CML confirm that this lesion is a fracture extending in a planar fashion through the metaphysis, separating a mineralized fragment. This disk-like mineralized fragment has two components: (1) a thick peripheral component encompassing the SPBC; and (2) a thin central component comprised predominantly of the radiologic ZPC. By manipulating the 3-D model, the varying appearances of the CML are displayed. High-resolution CT coupled with histopathology provides elucidation of the morphology of the CML, a strong indicator of infant abuse. This new information may prove useful in assessing the biomechanical factors that produce this strong indicator of abusive assaults in infants. (orig.)

High-resolution CT with histopathological correlates of the classic metaphyseal lesion of infant abuse

International Nuclear Information System (INIS)

Tsai, Andy; Kleinman, Paul K.; McDonald, Anna G.; Rosenberg, Andrew E.; Gupta, Rajiv

2014-01-01

The classic metaphyseal lesion (CML) is a common high specificity indicator of infant abuse and its imaging features have been correlated histopathologically in infant fatalities. High-resolution CT imaging and histologic correlates were employed to (1) characterize the normal infant anatomy surrounding the chondro-osseous junction, and (2) confirm the 3-D model of the CML previously inferred from planar radiography and histopathology. Long bone specimens from 5 fatally abused infants, whose skeletal survey showed definite or suspected CMLs, were studied postmortem. After skeletal survey, selected specimens were resected and imaged with high-resolution digital radiography. They were then scanned with micro-CT (isotropic resolution of 45 μm 3 ) or with high-resolution flat-panel CT (isotropic resolutions of 200 μm 3 ). Visualization of the bony structures was carried out using image enhancement, segmentation and isosurface extraction, together with volume rendering and multiplanar reformatting. These findings were then correlated with histopathology. Study of normal infant bone clarifies the 3-D morphology of the subperiosteal bone collar (SPBC) and the radiographic zone of provisional calcification (ZPC). Studies on specimens with CML confirm that this lesion is a fracture extending in a planar fashion through the metaphysis, separating a mineralized fragment. This disk-like mineralized fragment has two components: (1) a thick peripheral component encompassing the SPBC; and (2) a thin central component comprised predominantly of the radiologic ZPC. By manipulating the 3-D model, the varying appearances of the CML are displayed. High-resolution CT coupled with histopathology provides elucidation of the morphology of the CML, a strong indicator of infant abuse. This new information may prove useful in assessing the biomechanical factors that produce this strong indicator of abusive assaults in infants. (orig.)

Generalized classical mechanics

International Nuclear Information System (INIS)

De Leon, M.; Rodrigues, P.R.

1985-01-01

The geometrical study of Classical Mechanics shows that the Hamiltonian (respectively, Lagrangian) formalism may be characterized by intrinsical structures canonically defined on the cotangent (respectively, tangent) bundle of a differentiable manifold. A generalized formalism for higher order Lagrangians is developed. Then the Hamiltonian form of the theory is developed. Finally, the Poisson brackets are defined and the conditions under which a mapping is a canonical transformation are studied. The Hamilton-Jacobi equation for this type of mechanics is established. (Auth.)

Quantum mechanics as a natural generalization of classical statistical mechanics

International Nuclear Information System (INIS)

Xu Laizi; Qian Shangwu

1994-01-01

By comparison between equations of motion of geometrical optics (GO) and that of classical statistical mechanics (CSM), it is found that there should be an analogy between GO and CSM instead of GO and classical mechanics (CM). Furthermore, by comparison between the classical limit (CL) of quantum mechanics (QM) and CSM, the authors find that CL of QM is CSM not CM, hence they demonstrated that QM is a natural generalization of CSM instead of CM

Principal bundles the classical case

CERN Document Server

Sontz, Stephen Bruce

2015-01-01

This introductory graduate level text provides a relatively quick path to a special topic in classical differential geometry: principal bundles.  While the topic of principal bundles in differential geometry has become classic, even standard, material in the modern graduate mathematics curriculum, the unique approach taken in this text presents the material in a way that is intuitive for both students of mathematics and of physics. The goal of this book is to present important, modern geometric ideas in a form readily accessible to students and researchers in both the physics and mathematics communities, providing each with an understanding and appreciation of the language and ideas of the other.

Geometrical methods in learning theory

International Nuclear Information System (INIS)

Burdet, G.; Combe, Ph.; Nencka, H.

2001-01-01

The methods of information theory provide natural approaches to learning algorithms in the case of stochastic formal neural networks. Most of the classical techniques are based on some extremization principle. A geometrical interpretation of the associated algorithms provides a powerful tool for understanding the learning process and its stability and offers a framework for discussing possible new learning rules. An illustration is given using sequential and parallel learning in the Boltzmann machine

Two particle entanglement and its geometric duals

International Nuclear Information System (INIS)

Wasay, Muhammad Abdul; Bashir, Asma

2017-01-01

We show that for a system of two entangled particles, there is a dual description to the particle equations in terms of classical theory of conformally stretched spacetime. We also connect these entangled particle equations with Finsler geometry. We show that this duality translates strongly coupled quantum equations in the pilot-wave limit to weakly coupled geometric equations. (orig.)

Two particle entanglement and its geometric duals

Energy Technology Data Exchange (ETDEWEB)

Wasay, Muhammad Abdul [University of Agriculture, Department of Physics, Faisalabad (Pakistan); Quaid-i-Azam University Campus, National Centre for Physics, Islamabad (Pakistan); Bashir, Asma [University of Agriculture, Department of Physics, Faisalabad (Pakistan)

2017-12-15

We show that for a system of two entangled particles, there is a dual description to the particle equations in terms of classical theory of conformally stretched spacetime. We also connect these entangled particle equations with Finsler geometry. We show that this duality translates strongly coupled quantum equations in the pilot-wave limit to weakly coupled geometric equations. (orig.)

Geometrical analysis of woven fabric microstructure based on micron-resolution computed tomography data

Science.gov (United States)

Krieger, Helga; Seide, Gunnar; Gries, Thomas; Stapleton, Scott E.

2018-04-01

The global mechanical properties of textiles such as elasticity and strength, as well as transport properties such as permeability depend strongly on the microstructure of the textile. Textiles are heterogeneous structures with highly anisotropic material properties, including local fiber orientation and local fiber volume fraction. In this paper, an algorithm is presented to generate a virtual 3D-model of a woven fabric architecture with information about the local fiber orientation and the local fiber volume fraction. The geometric data of the woven fabric impregnated with resin was obtained by micron-resolution computed tomography (μCT). The volumetric μCT-scan was discretized into cells and the microstructure of each cell was analyzed and homogenized. Furthermore, the discretized data was used to calculate the local permeability tensors of each cell. An example application of the analyzed data is the simulation of the resin flow through a woven fabric based on the determined local permeability tensors and on Darcy's law. The presented algorithm is an automated and robust method of going from μCT-scans to structural or flow models.

Lectures in geometric combinatorics

CERN Document Server

Thomas, Rekha R

2006-01-01

This book presents a course in the geometry of convex polytopes in arbitrary dimension, suitable for an advanced undergraduate or beginning graduate student. The book starts with the basics of polytope theory. Schlegel and Gale diagrams are introduced as geometric tools to visualize polytopes in high dimension and to unearth bizarre phenomena in polytopes. The heart of the book is a treatment of the secondary polytope of a point configuration and its connections to the state polytope of the toric ideal defined by the configuration. These polytopes are relatively recent constructs with numerous connections to discrete geometry, classical algebraic geometry, symplectic geometry, and combinatorics. The connections rely on Gr�bner bases of toric ideals and other methods from commutative algebra. The book is self-contained and does not require any background beyond basic linear algebra. With numerous figures and exercises, it can be used as a textbook for courses on geometric, combinatorial, and computational as...

A geometric Hamiltonian description of composite quantum systems and quantum entanglement

Science.gov (United States)

Pastorello, Davide

2015-05-01

Finite-dimensional Quantum Mechanics can be geometrically formulated as a proper classical-like Hamiltonian theory in a projective Hilbert space. The description of composite quantum systems within the geometric Hamiltonian framework is discussed in this paper. As summarized in the first part of this work, in the Hamiltonian formulation the phase space of a quantum system is the Kähler manifold given by the complex projective space P(H) of the Hilbert space H of the considered quantum theory. However the phase space of a bipartite system must be P(H1 ⊗ H2) and not simply P(H1) × P(H2) as suggested by the analogy with Classical Mechanics. A part of this paper is devoted to manage this problem. In the second part of the work, a definition of quantum entanglement and a proposal of entanglement measure are given in terms of a geometrical point of view (a rather studied topic in recent literature). Finally two known separability criteria are implemented in the Hamiltonian formalism.

Classical mathematics from Al-Khwarizmi to Descartes

CERN Document Server

Rashed, Roshdi

2014-01-01

This book follows the development of classical mathematics and the relation between work done in the Arab and Islamic worlds and that undertaken by the likes of Descartes and Fermat.'Early modern,' mathematics is a term widely used to refer to the mathematics which developed in the West during the sixteenth and seventeenth century. For many historians and philosophers this is the watershed which marks a radical departure from 'classical mathematics,' to more modern mathematics; heralding the arrival of algebra, geometrical algebra, and the mathematics of the continuous. In this book, Roshdi Ra

On chromatic and geometrical calibration

DEFF Research Database (Denmark)

Folm-Hansen, Jørgen

1999-01-01

The main subject of the present thesis is different methods for the geometrical and chromatic calibration of cameras in various environments. For the monochromatic issues of the calibration we present the acquisition of monochrome images, the classic monochrome aberrations and the various sources...... the correct interpolation method is described. For the chromatic issues of calibration we present the acquisition of colour and multi-spectral images, the chromatic aberrations and the various lens/camera based non-uniformities of the illumination of the image plane. It is described how the monochromatic...... to design calibration targets for both geometrical and chromatic calibration are described. We present some possible systematical errors on the detection of the objects in the calibration targets, if viewed in a non orthogonal angle, if the intensities are uneven or if the image blurring is uneven. Finally...

Quantum classical correspondence in nonrelativistic electrodynamics

International Nuclear Information System (INIS)

Ritchie, B.; Weatherford, C.A.

1999-01-01

A form of classical electrodynamic field exists which gives exact agreement with the operator field of quantum electrodynamics (QED) for the Lamb shift of a harmonically bound point electron. Here it is pointed out that this form of classical theory, with its physically acceptable interpretation, is the result of an unconventional resolution of a mathematically ambiguous term in classical field theory. Finally, a quantum classical correspondence principle is shown to exist in the sense that the classical field and expectation value of the QED operator field are identical, if retardation is neglected in the latter

Stochastic pump effect and geometric phases in dissipative and stochastic systems

Energy Technology Data Exchange (ETDEWEB)

Sinitsyn, Nikolai [Los Alamos National Laboratory

2008-01-01

The success of Berry phases in quantum mechanics stimulated the study of similar phenomena in other areas of physics, including the theory of living cell locomotion and motion of patterns in nonlinear media. More recently, geometric phases have been applied to systems operating in a strongly stochastic environment, such as molecular motors. We discuss such geometric effects in purely classical dissipative stochastic systems and their role in the theory of the stochastic pump effect (SPE).

Explicit integration of some integrable systems of classical mechanics

OpenAIRE

Basak Gancheva, Inna

2011-01-01

The main objective of the thesis is the analytical and geometrical study of several integrable finite-dimentional dynamical systems of classical mechanics, which are closely related, namely: - the classical generalization of the Euler top: the Zhukovski-Volterra (ZV) system describing the free motion of a gyrostat, i.e., a rigid body carrying a symmetric rotator whose axis is fixed in the body; - the Steklov-Lyapunov integrable case of the Kirchhoff equations describing the motio...

Workshop on Topology and Geometric Group Theory

CERN Document Server

Fowler, James; Lafont, Jean-Francois; Leary, Ian

2016-01-01

This book presents articles at the interface of two active areas of research: classical topology and the relatively new field of geometric group theory. It includes two long survey articles, one on proofs of the Farrell–Jones conjectures, and the other on ends of spaces and groups. In 2010–2011, Ohio State University (OSU) hosted a special year in topology and geometric group theory. Over the course of the year, there were seminars, workshops, short weekend conferences, and a major conference out of which this book resulted. Four other research articles complement these surveys, making this book ideal for graduate students and established mathematicians interested in entering this area of research.

Dynamics of unitarization by classicalization

International Nuclear Information System (INIS)

Dvali, Gia; Pirtskhalava, David

2011-01-01

We study dynamics of the classicalization phenomenon suggested in G. Dvali et al. , according to which a class of non-renormalizable theories self-unitarizes at very high-energies via creation of classical configurations (classicalons). We study this phenomenon in an explicit model of derivatively-self-coupled scalar that serves as a prototype for a Nambu-Goldstone-Stueckelberg field. We prepare the initial state in form of a collapsing wave-packet of a small occupation number but of very high energy, and observe that the classical configuration indeed develops. Our results confirm the previous estimates, showing that because of self-sourcing the wave-packet forms a classicalon configuration with radius that increases with center of mass energy. Thus, classicalization takes place before the waves get any chance of probing short-distances. The self-sourcing by energy is the crucial point, which makes classicalization phenomenon different from the ordinary dispersion of the wave-packets in other interacting theories. Thanks to this, unlike solitons or other non-perturbative objects, the production of classicalons is not only unsuppressed, but in fact dominates the high-energy scattering. In order to make the difference between classicalizing and non-classicalizing theories clear, we use a language in which the scattering cross section in a generic theory can be universally understood as a geometric cross section set by a classical radius down to which waves can propagate freely, before being scattered. We then show, that in non-classicalizing examples this radius shrinks with increasing energy and becomes microscopic, whereas in classicalizing theories expands and becomes macroscopic. We study analogous scattering in a Galileon system and discover that classicalization also takes place there, although somewhat differently. We thus observe, that classicalization is source-sensitive and that Goldstones pass the first test.

Concepts of classical optics

CERN Document Server

Strong, John

1958-01-01

An intermediate course in optics, this volume explores both experimental and theoretical concepts, offering practical knowledge of geometrical optics that will enhance students' comprehension of any relevant applied science. Its exposition of the concepts of classical optics is presented with a minimum of mathematical detail but presumes some knowledge of calculus, vectors, and complex numbers.Subjects include light as wave motion; superposition of wave motions; electromagnetic waves; interaction of light and matter; velocities and scattering of light; polarized light and dielectric boundarie

A Synthetic Approach to the Transfer Matrix Method in Classical and Quantum Physics

Science.gov (United States)

Pujol, O.; Perez, J. P.

2007-01-01

The aim of this paper is to propose a synthetic approach to the transfer matrix method in classical and quantum physics. This method is an efficient tool to deal with complicated physical systems of practical importance in geometrical light or charged particle optics, classical electronics, mechanics, electromagnetics and quantum physics. Teaching…

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.

Turning big bang into big bounce. I. Classical dynamics

Science.gov (United States)

Dzierżak, Piotr; Małkiewicz, Przemysław; Piechocki, Włodzimierz

2009-11-01

The big bounce (BB) transition within a flat Friedmann-Robertson-Walker model is analyzed in the setting of loop geometry underlying the loop cosmology. We solve the constraint of the theory at the classical level to identify physical phase space and find the Lie algebra of the Dirac observables. We express energy density of matter and geometrical functions in terms of the observables. It is the modification of classical theory by the loop geometry that is responsible for BB. The classical energy scale specific to BB depends on a parameter that should be fixed either by cosmological data or determined theoretically at quantum level, otherwise the energy scale stays unknown.

Graph Treewidth and Geometric Thickness Parameters

OpenAIRE

Dujmović, Vida; Wood, David R.

2005-01-01

Consider a drawing of a graph $G$ in the plane such that crossing edges are coloured differently. The minimum number of colours, taken over all drawings of $G$, is the classical graph parameter "thickness". By restricting the edges to be straight, we obtain the "geometric thickness". By further restricting the vertices to be in convex position, we obtain the "book thickness". This paper studies the relationship between these parameters and treewidth. Our first main result states that for grap...

Classical versus Computer Algebra Methods in Elementary Geometry

Science.gov (United States)

Pech, Pavel

2005-01-01

Computer algebra methods based on results of commutative algebra like Groebner bases of ideals and elimination of variables make it possible to solve complex, elementary and non elementary problems of geometry, which are difficult to solve using a classical approach. Computer algebra methods permit the proof of geometric theorems, automatic…

A projective constrained variational principle for a classical particle with spin

International Nuclear Information System (INIS)

Amorim, R.

1983-01-01

A geometric approach for variational principles with constraints is applied to obtain the equations of motion of a classical charged point particle with magnetic moment interacting with an external eletromagnetic field. (Author) [pt

Classical limit for quantum mechanical energy eigenfunctions

International Nuclear Information System (INIS)

Sen, D.; Sengupta, S.

2004-01-01

The classical limit problem is discussed for the quantum mechanical energy eigenfunctions using the Wentzel-Kramers-Brillouin approximation, free from the problem at the classical turning points. A proper perspective of the whole issue is sought to appreciate the significance of the discussion. It is observed that for bound states in arbitrary potential, appropriate limiting condition is definable in terms of a dimensionless classical limit parameter leading smoothly to all observable classical results. Most important results are the emergence of classical phase space, keeping the observable distribution functions non-zero only within the so-called classical region at the limit point and resolution of some well-known paradoxes. (author)

Hidden invariance of the free classical particle

International Nuclear Information System (INIS)

Garcia, S.

1994-01-01

A formalism describing the dynamics of classical and quantum systems from a group theoretical point of view is presented. We apply it to the simple example of the classical free particle. The Galileo group G is the symmetry group of the free equations of motion. Consideration of the free particle Lagrangian semi-invariance under G leads to a larger symmetry group, which is a central extension of the Galileo group by the real numbers. We study the dynamics associated with this group, and characterize quantities like Noether invariants and evolution equations in terms of group geometric objects. An extension of the Galileo group by U(1) leads to quantum mechanics

Non-stoquastic Hamiltonians in quantum annealing via geometric phases

Science.gov (United States)

Vinci, Walter; Lidar, Daniel A.

2017-09-01

We argue that a complete description of quantum annealing implemented with continuous variables must take into account the non-adiabatic Aharonov-Anandan geometric phase that arises when the system Hamiltonian changes during the anneal. We show that this geometric effect leads to the appearance of non-stoquasticity in the effective quantum Ising Hamiltonians that are typically used to describe quantum annealing with flux qubits. We explicitly demonstrate the effect of this geometric non-stoquasticity when quantum annealing is performed with a system of one and two coupled flux qubits. The realization of non-stoquastic Hamiltonians has important implications from a computational complexity perspective, since it is believed that in many cases quantum annealing with stoquastic Hamiltonians can be efficiently simulated via classical algorithms such as Quantum Monte Carlo. It is well known that the direct implementation of non-stoquastic Hamiltonians with flux qubits is particularly challenging. Our results suggest an alternative path for the implementation of non-stoquasticity via geometric phases that can be exploited for computational purposes.

Geometric quantization and general relativity

International Nuclear Information System (INIS)

Souriau, J.-M.

1977-01-01

The purpose of geometric quantization is to give a rigorous mathematical content to the 'correspondence principle' between classical and quantum mechanics. The main tools are borrowed on one hand from differential geometry and topology (differential manifolds, differential forms, fiber bundles, homology and cohomology, homotopy), on the other hand from analysis (functions of positive type, infinite dimensional group representations, pseudo-differential operators). Some satisfactory results have been obtained in the study of dynamical systems, but some fundamental questions are still waiting for an answer. The 'geometric quantization of fields', where some further well known difficulties arise, is still in a preliminary stage. In particular, the geometric quantization on the gravitational field is still a mere project. The situation is even more uncertain due to the fact that there is no experimental evidence of any quantum gravitational effect which could give us a hint towards what we are supposed to look for. The first level of both Quantum Theory, and General Relativity describes passive matter: influence by the field without being a source of it (first quantization and equivalence principle respectively). In both cases this is only an approximation (matter is always a source). But this approximation turns out to be the least uncertain part of the description, because on one hand the first quantization avoids the problems of renormalization and on the other hand the equivalence principle does not imply any choice of field equations (it is known that one can modify Einstein equations at short distances without changing their geometrical properties). (Auth.)

Geometrical dynamics of Born-Infeld objects

Energy Technology Data Exchange (ETDEWEB)

Cordero, Ruben [Departamento de Fisica, Escuela Superior de Fisica y Matematicas del I.P.N., Unidad Adolfo Lopez Mateos, Edificio 9, 07738 Mexico, D.F. (Mexico); Molgado, Alberto [Facultad de Ciencias, Universidad de Colima, Bernal DIaz del Castillo 340, Col. Villas San Sebastian, Colima (Mexico); Rojas, Efrain [Facultad de Fisica e Inteligencia Artificial, Universidad Veracruzana, 91000 Xalapa, Veracruz (Mexico)

2007-03-21

We present a geometrically inspired study of the dynamics of Dp-branes. We focus on the usual non-polynomial Dirac-Born-Infeld action for the worldvolume swept out by the brane in its evolution in general background spacetimes. We emphasize the form of the resulting equations of motion which are quite simple and resemble Newton's second law, complemented with a conservation law for a worldvolume bicurrent. We take a closer look at the classical Hamiltonian analysis which is supported by the ADM framework of general relativity. The constraints and their algebra are identified as well as the geometrical role they play in phase space. In order to illustrate our results, we review the dynamics of a D1-brane immersed in a AdS{sub 3} x S{sup 3} background spacetime. We exhibit the mechanical properties of Born-Infeld objects paving the way to a consistent quantum formulation.

Geometrical dynamics of Born-Infeld objects

International Nuclear Information System (INIS)

Cordero, Ruben; Molgado, Alberto; Rojas, Efrain

2007-01-01

We present a geometrically inspired study of the dynamics of Dp-branes. We focus on the usual non-polynomial Dirac-Born-Infeld action for the worldvolume swept out by the brane in its evolution in general background spacetimes. We emphasize the form of the resulting equations of motion which are quite simple and resemble Newton's second law, complemented with a conservation law for a worldvolume bicurrent. We take a closer look at the classical Hamiltonian analysis which is supported by the ADM framework of general relativity. The constraints and their algebra are identified as well as the geometrical role they play in phase space. In order to illustrate our results, we review the dynamics of a D1-brane immersed in a AdS 3 x S 3 background spacetime. We exhibit the mechanical properties of Born-Infeld objects paving the way to a consistent quantum formulation

Foucault's pendulum, a classical analog for the electron spin state

Science.gov (United States)

Linck, Rebecca A.

Spin has long been regarded as a fundamentally quantum phenomena that is incapable of being described classically. To bridge the gap and show that aspects of spin's quantum nature can be described classically, this work uses a classical Lagrangian based on the coupled oscillations of Foucault's pendulum as an analog for the electron spin state in an external magnetic field. With this analog it is possible to demonstrate that Foucault's pendulum not only serves as a basis for explaining geometric phase, but is also a basis for reproducing a broad range of behavior from Zeeman-like frequency splitting to precession of the spin state. By demonstrating that unmeasured electron spin states can be fully described in classical terms, this research opens the door to using the tools of classical physics to examine an inherently quantum phenomenon.

Geometrical superresolved imaging using nonperiodic spatial masking.

Science.gov (United States)

Borkowski, Amikam; Zalevsky, Zeev; Javidi, Bahram

2009-03-01

The resolution of every imaging system is limited either by the F-number of its optics or by the geometry of its detection array. The geometrical limitation is caused by lack of spatial sampling points as well as by the shape of every sampling pixel that generates spectral low-pass filtering. We present a novel approach to overcome the low-pass filtering that is due to the shape of the sampling pixels. The approach combines special algorithms together with spatial masking placed in the intermediate image plane and eventually allows geometrical superresolved imaging without relation to the actual shape of the pixels.

Blow-up Mechanism of Classical Solutions to Quasilinear Hyperbolic Systems in the Critical Case

Institute of Scientific and Technical Information of China (English)

无

2006-01-01

This paper deals with the blow-up phenomenon, particularly, the geometric blow-up mechanism, of classical solutions to the Cauchy problem for quasilinear hyperbolic systems in the critical case. We prove that it is still the envelope of the same family of characteristics which yields the blowup of classical solutions to the Cauchy problem in the critical case.

Geometrical explanation of the fractional complex transform and derivative chain rule for fractional calculus

International Nuclear Information System (INIS)

He, Ji-Huan; Elagan, S.K.; Li, Z.B.

2012-01-01

The fractional complex transform is suggested to convert a fractional differential equation with Jumarie's modification of Riemann–Liouville derivative into its classical differential partner. Understanding the fractional complex transform and the chain rule for fractional calculus are elucidated geometrically. -- Highlights: ► The chain rule for fractional calculus is invalid, a counter example is given. ► The fractional complex transform is explained geometrically. ► Fractional equations can be converted into differential equations.

Yang Mills instantons, geometrical aspects

International Nuclear Information System (INIS)

Stora, R.

1977-09-01

The word instanton has been coined by analogy with the word soliton. They both refer to solutions of elliptic non linear field equations with boundary conditions at infinity (of euclidean space time in the first case, euclidean space in the second case) lying on the set of classical vacua in such a way that stable topological properties emerge, susceptible to survive quantum effects, if those are small. Under this assumption, instantons are believed to be relevant to the description of tunnelling effects between classical vacua and signal some characteristics of the vacuum at the quantum level, whereas solitons should be associated with particles, i.e. discrete points in the mass spectrum. In one case the euclidean action is finite, in the other case, the energy is finite. From the mathematical point of view, the geometrical phenomena associated with the existence of solitons have forced physicists to learn rudiments of algebraic topology. The study of euclidean classical Yang Mills fields involves naturally mathematical items falling under the headings: differential geometry (fibre bundles, connections); differential topology (characteristic classes, index theory) and more recently algebraic geometry. These notes are divided as follows: a first section is devoted to a description of the physicist's views; a second section is devoted to the mathematician's vie

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.

Towards a theory of geometric graphs

CERN Document Server

Pach, Janos

2004-01-01

The early development of graph theory was heavily motivated and influenced by topological and geometric themes, such as the Konigsberg Bridge Problem, Euler's Polyhedral Formula, or Kuratowski's characterization of planar graphs. In 1936, when Denes Konig published his classical Theory of Finite and Infinite Graphs, the first book ever written on the subject, he stressed this connection by adding the subtitle Combinatorial Topology of Systems of Segments. He wanted to emphasize that the subject of his investigations was very concrete: planar figures consisting of points connected by straight-line segments. However, in the second half of the twentieth century, graph theoretical research took an interesting turn. In the most popular and most rapidly growing areas (the theory of random graphs, Ramsey theory, extremal graph theory, algebraic graph theory, etc.), graphs were considered as abstract binary relations rather than geometric objects. Many of the powerful techniques developed in these fields have been su...

Beyond the borders of classical optical measurements

International Nuclear Information System (INIS)

Eisenberg, H.; Khoury, G.; Fonseca, E.; Bouwmeester, D.

2006-01-01

Full Text: The limits of optical measurements are the subject to many recent works. It has been shown how by using non-classical photonic states, spatial resolution can exceed the diffraction limit [1]. The same states also improve interference measurements beyond the shot noise and up to the quantum Heisenberg limit [2]. On the other hand, a few methods have been suggested that improve the optical resolution by exploiting classical optical nonlinearities [3]. First, we will present a scheme that exploits the non-local quantum correlations of a second order entangled state produced by optical parametric down-conversion [4]. The scheme results with a non-classical state that can be used in quantum limited interferometry. It is also simply extendable to states of any photon number. Another method will be presented, where nonlinear measurements are induced by projecting the state of light onto the Fock space [5]. This process simulated optical nonlinearities up to the 7th order. We used those measurements to characterize the output of a standard polarization interferometer. Improved resolution was demonstrated, but a detailed analysis reveals the differences to the previous nonclassical approach

Performance improvement of ERP-based brain-computer interface via varied geometric patterns.

Science.gov (United States)

Ma, Zheng; Qiu, Tianshuang

2017-12-01

Recently, many studies have been focusing on optimizing the stimulus of an event-related potential (ERP)-based brain-computer interface (BCI). However, little is known about the effectiveness when increasing the stimulus unpredictability. We investigated a new stimulus type of varied geometric pattern where both complexity and unpredictability of the stimulus are increased. The proposed and classical paradigms were compared in within-subject experiments with 16 healthy participants. Results showed that the BCI performance was significantly improved for the proposed paradigm, with an average online written symbol rate increasing by 138% comparing with that of the classical paradigm. Amplitudes of primary ERP components, such as N1, P2a, P2b, N2, were also found to be significantly enhanced with the proposed paradigm. In this paper, a novel ERP BCI paradigm with a new stimulus type of varied geometric pattern is proposed. By jointly increasing the complexity and unpredictability of the stimulus, the performance of an ERP BCI could be considerably improved.

Using Priors to Compensate Geometrical Problems in Head-Mounted Eye Trackers

DEFF Research Database (Denmark)

Batista Narcizo, Fabricio; Ahmed, Zaheer; Hansen, Dan Witzner

The use of additional information (a.k.a. priors) to help the eye tracking process is presented as an alternative to compensate classical geometrical problems in head-mounted eye trackers. Priors can be obtained from several distinct sources, such as: sensors to collect information related...... estimation specially for uncalibrated head-mounted setups....

Determination of main geometric parameters of stereo-television equipment for radiation image representation

International Nuclear Information System (INIS)

Mamchev, G.V.

1985-01-01

Geometric distortions of the three-dimensional image of objects under testing are analyzed, quantitative values of stereovision zone depth, depth resolution are determined. It has been found that the potential depth of stereovision zone in a stereo-television unit should be established according to physiological peculiarities of perception of the observer. Dimensions of the stereovision zone in case of reproduction of orthoscopic images are larger than in case of pseudoscopic imaging at which the degree of geometric deformations of the three-dimensional image is considerably less. The most effective method of increasing the depth resolution of the stereo-X ray television unit consists in increasing the resolution of its separate elements, in the first turn, of the fluorescent screen or image converter

Assessing the geometric accuracy of UAV-based orthophotos ...

African Journals Online (AJOL)

In remote sensing and photogrammetric operations, the geometric quality of the imagery basically depends on the relation between pixel size and the map scale, contrast information, atmosphere and the sun elevation, the printing technology, screen resolution and the visual acuity. The Unmanned Aircraft System (UAS) ...

Projective geometry for polarization in geometric quantization

International Nuclear Information System (INIS)

Campbell, P.; Dodson, C.T.J.

1976-12-01

It is important to know the extent to which the procedure of geometric quantization depends on a choice of polarization of the symplectic manifold that is the classical phase space. Published results have so far been restricted to real and transversal polarizations. Here we also consider these cases by presenting a formulation in terms of projective geometry. It turns out that there is a natural characterization of real transversal polarizations and maps among them using projective concepts. We give explicit constructions for Rsup(2n)

Geometry of Lagrangian first-order classical field theories

International Nuclear Information System (INIS)

Echeverria-Enriquez, A.; Munoz-Lecanda, M.C.; Roman-Roy, N.

1996-01-01

We construct a lagrangian geometric formulation for first-order field theories using the canonical structures of first-order jet bundles, which are taken as the phase spaces of the systems in consideration. First of all, we construct all the geometric structures associated with a first-order jet bundle and, using them, we develop the lagrangian formalism, defining the canonical forms associated with a lagrangian density and the density of lagrangian energy, obtaining the Euler-Lagrange equations in two equivalent ways: as the result of a variational problem and developing the jet field formalism (which is a formulation more similar to the case of mechanical systems). A statement and proof of Noether's theorem is also given, using the latter formalism. Finally, some classical examples are briefly studied. (orig.)

A geometric renormalization group in discrete quantum space-time

International Nuclear Information System (INIS)

Requardt, Manfred

2003-01-01

We model quantum space-time on the Planck scale as dynamical networks of elementary relations or time dependent random graphs, the time dependence being an effect of the underlying dynamical network laws. We formulate a kind of geometric renormalization group on these (random) networks leading to a hierarchy of increasingly coarse-grained networks of overlapping lumps. We provide arguments that this process may generate a fixed limit phase, representing our continuous space-time on a mesoscopic or macroscopic scale, provided that the underlying discrete geometry is critical in a specific sense (geometric long range order). Our point of view is corroborated by a series of analytic and numerical results, which allow us to keep track of the geometric changes, taking place on the various scales of the resolution of space-time. Of particular conceptual importance are the notions of dimension of such random systems on the various scales and the notion of geometric criticality

Monomial geometric programming with an arbitrary fuzzy relational inequality

Directory of Open Access Journals (Sweden)

E. Shivanian

2015-11-01

Full Text Available In this paper, an optimization model with geometric objective function is presented. Geometric programming is widely used; many objective functions in optimization problems can be analyzed by geometric programming. We often encounter these in resource allocation and structure optimization and technology management, etc. On the other hand, fuzzy relation equalities and inequalities are also used in many areas. We here present a geometric programming model with a monomial objective function subject to the fuzzy relation inequality constraints with an arbitrary function. The feasible solution set is determined and compared with some common results in the literature. A necessary and sufficient condition and three other necessary conditions are presented to conceptualize the feasibility of the problem. In general a lower bound is always attainable for the optimal objective value by removing the components having no effect on the solution process. By separating problem to non-decreasing and non-increasing function to prove the optimal solution, we simplify operations to accelerate the resolution of the problem.

Classical Music Clustering Based on Acoustic Features

OpenAIRE

Wang, Xindi; Haque, Syed Arefinul

2017-01-01

In this paper we cluster 330 classical music pieces collected from MusicNet database based on their musical note sequence. We use shingling and chord trajectory matrices to create signature for each music piece and performed spectral clustering to find the clusters. Based on different resolution, the output clusters distinctively indicate composition from different classical music era and different composing style of the musicians.

Corrections to classical radiometry and the brightness of stars

International Nuclear Information System (INIS)

Siew, Ronian

2008-01-01

By combining Fourier optics with classical radiometry, a simple, compact formula is derived for computing the absolute irradiance of diffracted and aberrated images in optical systems. Within appropriate limits, the formula reduces to the familiar equations of classical radiometry and of physical optics. It is argued that the approach presented is pedagogically appealing as it combines the principal results of geometrical optics, physical optics and radiometry into a single equation, thus, providing a convenient and simple means of describing imaging phenomena at the level of an advanced undergraduate or introductory graduate course on radiometry. A practical example concerning the image irradiance of stars is discussed

Theoretical investigation of geometric structure and relative stability of classical and bridge structures in Hk-1ASiH2+, Hk-1ASiH2 system (A=Li, Na, Be, Mg, B, Al)

International Nuclear Information System (INIS)

Zyubin, A.S.; Zyubina, T.S.; Charkin, O.P.; Shlojfer, P.R.

1990-01-01

The influence of acceptor properties and structure of L + cation in the series L=Li, B, BeH, BH 2 and Na, Al, MgH, AlH 2 on relative stabilities of classical and bridge isomers in systems L + SiH 2 and LSiH 3 , in which L + cation interacts either with unshared pair Si(L + SiH 2 , LSiH 3 ) or with hydrogen atom (SiH 2 L + , SiH 3 L), have been investigated. Geometric parameters of alternative structures were determined at the level of SCF/3-211*, their relative stabilities were refined in the framework of MP3/6-311*. It is found that in LSiH 2 + ions bridge isomers are less stable than the classical ones, and when acceptor abilities of L + increase, the energy difference between them also increases. In systems LSiH 3 the regularities proved to be more complex and they are determined both by L + acceptor properties and its structure. Reasons for those regularities are discussed

The geometric Hopf invariant and surgery theory

CERN Document Server

Crabb, Michael

2017-01-01

Written by leading experts in the field, this monograph provides homotopy theoretic foundations for surgery theory on higher-dimensional manifolds. Presenting classical ideas in a modern framework, the authors carefully highlight how their results relate to (and generalize) existing results in the literature. The central result of the book expresses algebraic surgery theory in terms of the geometric Hopf invariant, a construction in stable homotopy theory which captures the double points of immersions. Many illustrative examples and applications of the abstract results are included in the book, making it of wide interest to topologists. Serving as a valuable reference, this work is aimed at graduate students and researchers interested in understanding how the algebraic and geometric topology fit together in the surgery theory of manifolds. It is the only book providing such a wide-ranging historical approach to the Hopf invariant, double points and surgery theory, with many results old and new. .

Ideal versus real: simulated annealing of experimentally derived and geometric platinum nanoparticles

Science.gov (United States)

Ellaby, Tom; Aarons, Jolyon; Varambhia, Aakash; Jones, Lewys; Nellist, Peter; Ozkaya, Dogan; Sarwar, Misbah; Thompsett, David; Skylaris, Chris-Kriton

2018-04-01

Platinum nanoparticles find significant use as catalysts in industrial applications such as fuel cells. Research into their design has focussed heavily on nanoparticle size and shape as they greatly influence activity. Using high throughput, high precision electron microscopy, the structures of commercially available Pt catalysts have been determined, and we have used classical and quantum atomistic simulations to examine and compare them with geometric cuboctahedral and truncated octahedral structures. A simulated annealing procedure was used both to explore the potential energy surface at different temperatures, and also to assess the effect on catalytic activity that annealing would have on nanoparticles with different geometries and sizes. The differences in response to annealing between the real and geometric nanoparticles are discussed in terms of thermal stability, coordination number and the proportion of optimal binding sites on the surface of the nanoparticles. We find that annealing both experimental and geometric nanoparticles results in structures that appear similar in shape and predicted activity, using oxygen adsorption as a measure. Annealing is predicted to increase the catalytic activity in all cases except the truncated octahedra, where it has the opposite effect. As our simulations have been performed with a classical force field, we also assess its suitability to describe the potential energy of such nanoparticles by comparing with large scale density functional theory calculations.

A geometric viewpoint on generalized hydrodynamics

Directory of Open Access Journals (Sweden)

Benjamin Doyon

2018-01-01

Full Text Available Generalized hydrodynamics (GHD is a large-scale theory for the dynamics of many-body integrable systems. It consists of an infinite set of conservation laws for quasi-particles traveling with effective (“dressed” velocities that depend on the local state. We show that these equations can be recast into a geometric dynamical problem. They are conservation equations with state-independent quasi-particle velocities, in a space equipped with a family of metrics, parametrized by the quasi-particles' type and speed, that depend on the local state. In the classical hard rod or soliton gas picture, these metrics measure the free length of space as perceived by quasi-particles; in the quantum picture, they weigh space with the density of states available to them. Using this geometric construction, we find a general solution to the initial value problem of GHD, in terms of a set of integral equations where time appears explicitly. These integral equations are solvable by iteration and provide an extremely efficient solution algorithm for GHD.

CLASSICAL AND NON-CLASSICAL PHILOSOPHICAL ANTHROPOLOGY: COMPARATIVE ANALYSIS

Directory of Open Access Journals (Sweden)

T. A. Kozlova

2018-01-01

Full Text Available Introduction: The goals and values of human life, the search for the meaning of human existence contain the potential for a meaningful, progressive development of philosophical and anthropological ideas at any time in history. One of the tasks of philosophical anthropology is the formation of the image of man, the choice of ways to achieve the ideal, the methods of comprehension and resolution of universal problems. The increasing processes of differentiation in science led to the formation of different views on the nature of man, to the distinction between classical and non-classical philosophical anthropology. А comparative analysis of these trends is given in this article.Materials and methods: The dialectical method is preferred in the question of research methodology, the hermeneutic and phenomenological approaches are used.Results: The development of philosophical anthropology correlates with the challenges of modernity. By tracking the trends of human change, philosophical anthropology changes the approach to the consideration of its main subject of research. The whole array of disciplines that study man comes to new discoveries, new theories, and philosophical anthropology changes its view of the vision, challenging the principles of classical philosophical anthropology.Classical philosophical anthropology elevates the biological nature of man to a pedestal, non-classical philosophical anthropology actualizes questions of language, culture, thinking, understanding, actualizes the hermeneutic and phenomenological approaches. The desire to understand a person in classical philosophical anthropology is based on the desire to fully reveal the biological mechanisms in a person. The perspective of treating a person in nonclassical philosophical anthropology is polyformen: man as a text, as a dreaming self, as an eternal transition. Non-classical philosophical anthropology, goes from the idea of identity to the idea of variability, from

Multiscale geometric modeling of macromolecules I: Cartesian representation

Science.gov (United States)

Xia, Kelin; Feng, Xin; Chen, Zhan; Tong, Yiying; Wei, Guo-Wei

2014-01-01

This paper focuses on the geometric modeling and computational algorithm development of biomolecular structures from two data sources: Protein Data Bank (PDB) and Electron Microscopy Data Bank (EMDB) in the Eulerian (or Cartesian) representation. Molecular surface (MS) contains non-smooth geometric singularities, such as cusps, tips and self-intersecting facets, which often lead to computational instabilities in molecular simulations, and violate the physical principle of surface free energy minimization. Variational multiscale surface definitions are proposed based on geometric flows and solvation analysis of biomolecular systems. Our approach leads to geometric and potential driven Laplace-Beltrami flows for biomolecular surface evolution and formation. The resulting surfaces are free of geometric singularities and minimize the total free energy of the biomolecular system. High order partial differential equation (PDE)-based nonlinear filters are employed for EMDB data processing. We show the efficacy of this approach in feature-preserving noise reduction. After the construction of protein multiresolution surfaces, we explore the analysis and characterization of surface morphology by using a variety of curvature definitions. Apart from the classical Gaussian curvature and mean curvature, maximum curvature, minimum curvature, shape index, and curvedness are also applied to macromolecular surface analysis for the first time. Our curvature analysis is uniquely coupled to the analysis of electrostatic surface potential, which is a by-product of our variational multiscale solvation models. As an expository investigation, we particularly emphasize the numerical algorithms and computational protocols for practical applications of the above multiscale geometric models. Such information may otherwise be scattered over the vast literature on this topic. Based on the curvature and electrostatic analysis from our multiresolution surfaces, we introduce a new concept, the

Multiscale geometric modeling of macromolecules I: Cartesian representation

Energy Technology Data Exchange (ETDEWEB)

Xia, Kelin [Department of Mathematics, Michigan State University, MI 48824 (United States); Feng, Xin [Department of Computer Science and Engineering, Michigan State University, MI 48824 (United States); Chen, Zhan [Department of Mathematics, Michigan State University, MI 48824 (United States); Tong, Yiying [Department of Computer Science and Engineering, Michigan State University, MI 48824 (United States); Wei, Guo-Wei, E-mail: wei@math.msu.edu [Department of Mathematics, Michigan State University, MI 48824 (United States); Department of Biochemistry and Molecular Biology, Michigan State University, MI 48824 (United States)

2014-01-15

This paper focuses on the geometric modeling and computational algorithm development of biomolecular structures from two data sources: Protein Data Bank (PDB) and Electron Microscopy Data Bank (EMDB) in the Eulerian (or Cartesian) representation. Molecular surface (MS) contains non-smooth geometric singularities, such as cusps, tips and self-intersecting facets, which often lead to computational instabilities in molecular simulations, and violate the physical principle of surface free energy minimization. Variational multiscale surface definitions are proposed based on geometric flows and solvation analysis of biomolecular systems. Our approach leads to geometric and potential driven Laplace–Beltrami flows for biomolecular surface evolution and formation. The resulting surfaces are free of geometric singularities and minimize the total free energy of the biomolecular system. High order partial differential equation (PDE)-based nonlinear filters are employed for EMDB data processing. We show the efficacy of this approach in feature-preserving noise reduction. After the construction of protein multiresolution surfaces, we explore the analysis and characterization of surface morphology by using a variety of curvature definitions. Apart from the classical Gaussian curvature and mean curvature, maximum curvature, minimum curvature, shape index, and curvedness are also applied to macromolecular surface analysis for the first time. Our curvature analysis is uniquely coupled to the analysis of electrostatic surface potential, which is a by-product of our variational multiscale solvation models. As an expository investigation, we particularly emphasize the numerical algorithms and computational protocols for practical applications of the above multiscale geometric models. Such information may otherwise be scattered over the vast literature on this topic. Based on the curvature and electrostatic analysis from our multiresolution surfaces, we introduce a new concept, the

Dynamics of classical and quantum fields an introduction

CERN Document Server

Setlur, Girish S

2014-01-01

Dynamics of Classical and Quantum Fields: An Introduction focuses on dynamical fields in non-relativistic physics. Written by a physicist for physicists, the book is designed to help readers develop analytical skills related to classical and quantum fields at the non-relativistic level, and think about the concepts and theory through numerous problems. In-depth yet accessible, the book presents new and conventional topics in a self-contained manner that beginners would find useful. A partial list of topics covered includes: Geometrical meaning of Legendre transformation in classical mechanics Dynamical symmetries in the context of Noether's theorem The derivation of the stress energy tensor of the electromagnetic field, the expression for strain energy in elastic bodies, and the Navier Stokes equation Concepts of right and left movers in case of a Fermi gas explained Functional integration is interpreted as a limit of a sequence of ordinary integrations Path integrals for one and two quantum particles and for...

Geometrically necessary dislocation densities in olivine obtained using high-angular resolution electron backscatter diffraction

Energy Technology Data Exchange (ETDEWEB)

Wallis, David, E-mail: davidwa@earth.ox.ac.uk [Department of Earth Sciences, University of Oxford, South Parks Road, Oxford, Oxfordshire, OX1 3AN (United Kingdom); Hansen, Lars N. [Department of Earth Sciences, University of Oxford, South Parks Road, Oxford, Oxfordshire, OX1 3AN (United Kingdom); Ben Britton, T. [Department of Materials, Imperial College London, Royal School of Mines, Exhibition Road, London SW7 2AZ (United Kingdom); Wilkinson, Angus J. [Department of Materials, University of Oxford, Parks Road, Oxford, Oxfordshire, OX1 3PH (United Kingdom)

2016-09-15

Dislocations in geological minerals are fundamental to the creep processes that control large-scale geodynamic phenomena. However, techniques to quantify their densities, distributions, and types over critical subgrain to polycrystal length scales are limited. The recent advent of high-angular resolution electron backscatter diffraction (HR-EBSD), based on diffraction pattern cross-correlation, offers a powerful new approach that has been utilised to analyse dislocation densities in the materials sciences. In particular, HR-EBSD yields significantly better angular resolution (<0.01°) than conventional EBSD (~0.5°), allowing very low dislocation densities to be analysed. We develop the application of HR-EBSD to olivine, the dominant mineral in Earth's upper mantle by testing (1) different inversion methods for estimating geometrically necessary dislocation (GND) densities, (2) the sensitivity of the method under a range of data acquisition settings, and (3) the ability of the technique to resolve a variety of olivine dislocation structures. The relatively low crystal symmetry (orthorhombic) and few slip systems in olivine result in well constrained GND density estimates. The GND density noise floor is inversely proportional to map step size, such that datasets can be optimised for analysing either short wavelength, high density structures (e.g. subgrain boundaries) or long wavelength, low amplitude orientation gradients. Comparison to conventional images of decorated dislocations demonstrates that HR-EBSD can characterise the dislocation distribution and reveal additional structure not captured by the decoration technique. HR-EBSD therefore provides a highly effective method for analysing dislocations in olivine and determining their role in accommodating macroscopic deformation. - Highlights: • Lattice orientation gradients in olivine were measured using HR-EBSD. • The limited number of olivine slip systems enable simple least squares inversion for GND

Geometry of Lagrangian first-order classical field theories

Energy Technology Data Exchange (ETDEWEB)

Echeverria-Enriquez, A. [Univ. Politecnica de Cataluna, Barcelona (Spain). Departamento de Matematica Aplicada y Telematica; Munoz-Lecanda, M.C. [Univ. Politecnica de Cataluna, Barcelona (Spain). Departamento de Matematica Aplicada y Telematica; Roman-Roy, N. [Univ. Politecnica de Cataluna, Barcelona (Spain). Departamento de Matematica Aplicada y Telematica

1996-10-01

We construct a lagrangian geometric formulation for first-order field theories using the canonical structures of first-order jet bundles, which are taken as the phase spaces of the systems in consideration. First of all, we construct all the geometric structures associated with a first-order jet bundle and, using them, we develop the lagrangian formalism, defining the canonical forms associated with a lagrangian density and the density of lagrangian energy, obtaining the Euler-Lagrange equations in two equivalent ways: as the result of a variational problem and developing the jet field formalism (which is a formulation more similar to the case of mechanical systems). A statement and proof of Noether`s theorem is also given, using the latter formalism. Finally, some classical examples are briefly studied. (orig.)

Optimal control for mathematical models of cancer therapies an application of geometric methods

CERN Document Server

Schättler, Heinz

2015-01-01

This book presents applications of geometric optimal control to real life biomedical problems with an emphasis on cancer treatments. A number of mathematical models for both classical and novel cancer treatments are presented as optimal control problems with the goal of constructing optimal protocols. The power of geometric methods is illustrated with fully worked out complete global solutions to these mathematically challenging problems. Elaborate constructions of optimal controls and corresponding system responses provide great examples of applications of the tools of geometric optimal control and the outcomes aid the design of simpler, practically realizable suboptimal protocols. The book blends mathematical rigor with practically important topics in an easily readable tutorial style. Graduate students and researchers in science and engineering, particularly biomathematics and more mathematical aspects of biomedical engineering, would find this book particularly useful.

Geometrically weighted semiconductor Frisch grid radiation spectrometers

Energy Technology Data Exchange (ETDEWEB)

McGregor, D.S. [Dept. of Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, MI 48109-2104 (United States); Rojeski, R.A. [Etec Systems, Inc., 26460 Corporate Ave., Hayward, CA 94545 (United States); He, Z. [Dept. of Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, MI 48109-2104 (United States); Wehe, D.K. [Dept. of Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, MI 48109-2104 (United States); Driver, M. [eV Products, 375 Saxonburg Blvd., Saxonburg, PA 16056 (United States); Blakely, M. [eV Products, 375 Saxonburg Blvd., Saxonburg, PA 16056 (United States)

1999-02-11

A new detector geometry is described with relatively high gamma ray energy resolution at room temperature. The device uses the geometric weighting effect, the small pixel effect and the Frisch grid effect to produce high gamma ray energy resolution. The design is simple and easy to construct. The device performs as a gamma ray spectrometer without the need for pulse shape rejection or correction, and it requires only one signal output to any commercially available charge sensitive preamplifier. The device operates very well with conventional NIM electronic systems. Presently, room temperature (23 deg. C) energy resolutions of 2.68% FWHM at 662 keV and 2.45% FWHM at 1.332 MeV have been measured with a 1 cm{sup 3} prism shaped CdZnTe device.

Hydrodynamic Limit with Geometric Correction of Stationary Boltzmann Equation

OpenAIRE

Wu, Lei

2014-01-01

We consider the hydrodynamic limit of a stationary Boltzmann equation in a unit plate with in-flow boundary. We prove the solution can be approximated in $L^{\\infty}$ by the sum of interior solution which satisfies steady incompressible Navier-Stokes-Fourier system, and boundary layer with geometric correction. Also, we construct a counterexample to the classical theory which states the behavior of solution near boundary can be described by the Knudsen layer derived from the Milne problem.

Influence from cavity decay on geometric quantum computation in the large-detuning cavity QED model

International Nuclear Information System (INIS)

Chen Changyong; Zhang Xiaolong; Deng Zhijiao; Gao Kelin; Feng Mang

2006-01-01

We introduce a general displacement operator to investigate the unconventional geometric quantum computation with dissipation under the model of many identical three-level atoms in a cavity, driven by a classical field. Our concrete calculation is made for the case of two atoms, based on a previous scheme [S.-B. Zheng, Phys. Rev. A 70, 052320 (2004)] for the large-detuning interaction of the atoms with the cavity mode. The analytical results we present will be helpful for experimental realization of geometric quantum computation in real cavities

Geometric Accuracy Investigations of SEVIRI High Resolution Visible (HRV Level 1.5 Imagery

Directory of Open Access Journals (Sweden)

Sultan Kocaman Aksakal

2013-05-01

Full Text Available GCOS (Global Climate Observing System is a long-term program for monitoring the climate, detecting the changes, and assessing their impacts. Remote sensing techniques are being increasingly used for climate-related measurements. Imagery of the SEVIRI instrument on board of the European geostationary satellites Meteosat-8 and Meteosat-9 are often used for the estimation of essential climate variables. In a joint project between the Swiss GCOS Office and ETH Zurich, geometric accuracy and temporal stability of 1-km resolution HRV channel imagery of SEVIRI have been evaluated over Switzerland. A set of tools and algorithms has been developed for the investigations. Statistical analysis and blunder detection have been integrated in the process for robust evaluation. The relative accuracy is evaluated by tracking large numbers of feature points in consecutive HRV images taken at 15-minute intervals. For the absolute accuracy evaluation, lakes in Switzerland and surroundings are used as reference. 20 lakes digitized from Landsat orthophotos are transformed into HRV images and matched via 2D translation terms at sub-pixel level. The algorithms are tested using HRV images taken on 24 days in 2008 (2 days per month. The results show that 2D shifts that are up to 8 pixels are present both in relative and absolute terms.

Performance Assessment and Geometric Calibration of RESOURCESAT-2

Science.gov (United States)

Radhadevi, P. V.; Solanki, S. S.; Akilan, A.; Jyothi, M. V.; Nagasubramanian, V.

2016-06-01

Resourcesat-2 (RS-2) has successfully completed five years of operations in its orbit. This satellite has multi-resolution and multi-spectral capabilities in a single platform. A continuous and autonomous co-registration, geo-location and radiometric calibration of image data from different sensors with widely varying view angles and resolution was one of the challenges of RS-2 data processing. On-orbit geometric performance of RS-2 sensors has been widely assessed and calibrated during the initial phase operations. Since then, as an ongoing activity, various geometric performance data are being generated periodically. This is performed with sites of dense ground control points (GCPs). These parameters are correlated to the direct geo-location accuracy of the RS-2 sensors and are monitored and validated to maintain the performance. This paper brings out the geometric accuracy assessment, calibration and validation done for about 500 datasets of RS-2. The objectives of this study are to ensure the best absolute and relative location accuracy of different cameras, location performance with payload steering and co-registration of multiple bands. This is done using a viewing geometry model, given ephemeris and attitude data, precise camera geometry and datum transformation. In the model, the forward and reverse transformations between the coordinate systems associated with the focal plane, payload, body, orbit and ground are rigorously and explicitly defined. System level tests using comparisons to ground check points have validated the operational geo-location accuracy performance and the stability of the calibration parameters.

The geometric phase analysis method based on the local high resolution discrete Fourier transform for deformation measurement

International Nuclear Information System (INIS)

Dai, Xianglu; Xie, Huimin; Wang, Huaixi; Li, Chuanwei; Wu, Lifu; Liu, Zhanwei

2014-01-01

The geometric phase analysis (GPA) method based on the local high resolution discrete Fourier transform (LHR-DFT) for deformation measurement, defined as LHR-DFT GPA, is proposed to improve the measurement accuracy. In the general GPA method, the fundamental frequency of the image plays a crucial role. However, the fast Fourier transform, which is generally employed in the general GPA method, could make it difficult to locate the fundamental frequency accurately when the fundamental frequency is not located at an integer pixel position in the Fourier spectrum. This study focuses on this issue and presents a LHR-DFT algorithm that can locate the fundamental frequency with sub-pixel precision in a specific frequency region for the GPA method. An error analysis is offered and simulation is conducted to verify the effectiveness of the proposed method; both results show that the LHR-DFT algorithm can accurately locate the fundamental frequency and improve the measurement accuracy of the GPA method. Furthermore, typical tensile and bending tests are carried out and the experimental results verify the effectiveness of the proposed method. (paper)

Classical Photogrammetry and Uav - Selected Ascpects

Science.gov (United States)

Mikrut, S.

2016-06-01

. Buildings and strips on the road were selected from whole data for the comparison of edges and details. The details on UAV images were not worse than those on classical photogrammetric ones. One might suppose that geometrically they also were correct. The results of aerotriangulation prove these facts, too. Final results from aerotriangulation were on the level of RMS = 1 pixel (about 3 cm). In general it can be said that photographs from UAVs are not worse than classic ones. In the author's opinion, geometric and radiometric qualities are at a similar level for this kind of area (a small village). This is a very significant result as regards mapping. It means that UAV data can be used in mapping production.

USGS High Resolution Orthoimagery Collection - Historical - National Geospatial Data Asset (NGDA) High Resolution Orthoimagery

Data.gov (United States)

U.S. Geological Survey, Department of the Interior — USGS high resolution orthorectified images from The National Map combine the image characteristics of an aerial photograph with the geometric qualities of a map. An...

Fast geometric algorithms

International Nuclear Information System (INIS)

Noga, M.T.

1984-01-01

This thesis addresses a number of important problems that fall within the framework of the new discipline of Computational Geometry. The list of topics covered includes sorting and selection, convex hull algorithms, the L 1 hull, determination of the minimum encasing rectangle of a set of points, the Euclidean and L 1 diameter of a set of points, the metric traveling salesman problem, and finding the superrange of star-shaped and monotype polygons. The main theme of all the work was to develop a set of very fast state-of-the-art algorithms that supersede any rivals in terms of speed and ease of implementation. In some cases existing algorithms were refined; for others new techniques were developed that add to the present database of fast adaptive geometric algorithms. What emerges is a collection of techniques that is successful at merging modern tools developed in analysis of algorithms with those of classical geometry

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...

Geometric calibration between PET scanner and structured light scanner

DEFF Research Database (Denmark)

Kjer, Hans Martin; Olesen, Oline Vinter; Paulsen, Rasmus Reinhold

2011-01-01

Head movements degrade the image quality of high resolution Positron Emission Tomography (PET) brain studies through blurring and artifacts. Manny image reconstruction methods allows for motion correction if the head position is tracked continuously during the study. Our method for motion tracking...... is a structured light scanner placed just above the patient tunnel on the High Resolution Research Tomograph (HRRT, Siemens). It continuously registers point clouds of a part of the patient's face. The relative motion is estimated as the rigid transformation between frames. A geometric calibration between...

The effects of geometric uncertainties on computational modelling of knee biomechanics

Science.gov (United States)

Meng, Qingen; Fisher, John; Wilcox, Ruth

2017-08-01

The geometry of the articular components of the knee is an important factor in predicting joint mechanics in computational models. There are a number of uncertainties in the definition of the geometry of cartilage and meniscus, and evaluating the effects of these uncertainties is fundamental to understanding the level of reliability of the models. In this study, the sensitivity of knee mechanics to geometric uncertainties was investigated by comparing polynomial-based and image-based knee models and varying the size of meniscus. The results suggested that the geometric uncertainties in cartilage and meniscus resulting from the resolution of MRI and the accuracy of segmentation caused considerable effects on the predicted knee mechanics. Moreover, even if the mathematical geometric descriptors can be very close to the imaged-based articular surfaces, the detailed contact pressure distribution produced by the mathematical geometric descriptors was not the same as that of the image-based model. However, the trends predicted by the models based on mathematical geometric descriptors were similar to those of the imaged-based models.

Hydrogen: Beyond the Classic Approximation

International Nuclear Information System (INIS)

Scivetti, Ivan

2003-01-01

The classical nucleus approximation is the most frequently used approach for the resolution of problems in condensed matter physics.However, there are systems in nature where it is necessary to introduce the nuclear degrees of freedom to obtain a correct description of the properties.Examples of this, are the systems with containing hydrogen.In this work, we have studied the resolution of the quantum nuclear problem for the particular case of the water molecule.The Hartree approximation has been used, i.e. we have considered that the nuclei are distinguishable particles.In addition, we have proposed a model to solve the tunneling process, which involves the resolution of the nuclear problem for configurations of the system away from its equilibrium position

The Higgs field and the resolution of the Cosmological Constant Paradox in the Weyl-geometrical Universe

Science.gov (United States)

De Martini, Francesco

2017-10-01

The nature of the scalar field responsible for the cosmological inflation is found to be rooted in the most fundamental concept of Weyl's differential geometry: the parallel displacement of vectors in curved space-time. Within this novel geometrical scenario, the standard electroweak theory of leptons based on the SU(2)L⊗U(1)Y as well as on the conformal groups of space-time Weyl's transformations is analysed within the framework of a general-relativistic, conformally covariant scalar-tensor theory that includes the electromagnetic and the Yang-Mills fields. A Higgs mechanism within a spontaneous symmetry breaking process is identified and this offers formal connections between some relevant properties of the elementary particles and the dark energy content of the Universe. An `effective cosmological potential': Veff is expressed in terms of the dark energy potential: via the `mass reduction parameter': , a general property of the Universe. The mass of the Higgs boson, which is considered a `free parameter' by the standard electroweak theory, by our theory is found to be proportional to the mass which accounts for the measured cosmological constant, i.e. the measured content of vacuum-energy in the Universe. The non-integrable application of Weyl's geometry leads to a Proca equation accounting for the dynamics of a φρ-particle, a vector-meson proposed as an an optimum candidate for dark matter. On the basis of previous cosmic microwave background results our theory leads, in the condition of cosmological `critical density', to the assessment of the average energy content of the φρ-excitation. The peculiar mathematical structure of Veff offers a clue towards a very general resolution of a most intriguing puzzle of modern quantum field theory, the `Cosmological Constant Paradox' (here referred to as the `Λ-Paradox'). Indeed, our `universal' theory offers a resolution of the Λ-Paradox for all exponential inflationary potentials: VΛ(T,φ)∝e-nφ, and for all

Effective state metamorphosis in semi-classical loop quantum cosmology

Energy Technology Data Exchange (ETDEWEB)

Singh, Parampreet [Institute for Gravitational Physics and Geometry, Pennsylvania State University, University Park, PA 16802 (United States)

2005-10-21

Modification to the behaviour of geometrical density at short scales is a key result of loop quantum cosmology, responsible for an interesting phenomenology in the very early universe. We demonstrate the way matter with arbitrary scale factor dependence in Hamiltonian incorporates this change in its effective dynamics in the loop-modified phase. For generic matter, the equation of state starts varying near a critical scale factor, becomes negative below it and violates the strong energy condition. This opens a new avenue to generalize various phenomenological applications in loop quantum cosmology. We show that different ways to define energy density may yield radically different results, especially for the case corresponding to classical dust. We also discuss implications for frequency dispersion induced by modification to geometric density at small scales.

PERFORMANCE ASSESSMENT AND GEOMETRIC CALIBRATION OF RESOURCESAT-2

Directory of Open Access Journals (Sweden)

P. V. Radhadevi

2016-06-01

Full Text Available Resourcesat-2 (RS-2 has successfully completed five years of operations in its orbit. This satellite has multi-resolution and multi-spectral capabilities in a single platform. A continuous and autonomous co-registration, geo-location and radiometric calibration of image data from different sensors with widely varying view angles and resolution was one of the challenges of RS-2 data processing. On-orbit geometric performance of RS-2 sensors has been widely assessed and calibrated during the initial phase operations. Since then, as an ongoing activity, various geometric performance data are being generated periodically. This is performed with sites of dense ground control points (GCPs. These parameters are correlated to the direct geo-location accuracy of the RS-2 sensors and are monitored and validated to maintain the performance. This paper brings out the geometric accuracy assessment, calibration and validation done for about 500 datasets of RS-2. The objectives of this study are to ensure the best absolute and relative location accuracy of different cameras, location performance with payload steering and co-registration of multiple bands. This is done using a viewing geometry model, given ephemeris and attitude data, precise camera geometry and datum transformation. In the model, the forward and reverse transformations between the coordinate systems associated with the focal plane, payload, body, orbit and ground are rigorously and explicitly defined. System level tests using comparisons to ground check points have validated the operational geo-location accuracy performance and the stability of the calibration parameters.

A classical optical approach to the ‘non-local Pancharatnam-like phases’ in Hanbury-Brown–Twiss correlations

Energy Technology Data Exchange (ETDEWEB)

Arvind, E-mail: arvind@iisermohali.ac.in [Department of Physical Sciences, Indian Institute of Science Education & Research (IISER) Mohali, Sector 81 SAS Nagar, Manauli PO 140306, Punjab (India); Chaturvedi, S., E-mail: subhash@iiserbhopal.ac.in [Department of Physics, Indian Institute of Science Education & Research (IISER) Bhopal, Bhopal Bypass Road, Bhauri, Bhopal 462066 (India); Mukunda, N., E-mail: nmukunda@gmail.com [Indian Academy of Sciences, C V Raman Avenue, Sadashivanagar, Bangalore 560080 (India)

2017-04-11

Highlights: • Pancharatnam-like phase in HBT correlations. • Mach–Zehnder type setup to clarify that the phases involved are not geometric phases. • No nonlocality involved since the treatment is classical. - Abstract: We examine a recent proposal to show the presence of nonlocal Pancharatnam type geometric phases in a quantum mechanical treatment of intensity interferometry measurements upon inclusion of polarizing elements in the setup. It is shown that a completely classical statistical treatment of such effects is adequate for practical purposes. Further we show that the phase angles that appear in the correlations, while at first sight appearing to resemble Pancharatnam phases in their mathematical structure, cannot actually be interpreted in that manner. We also describe a simpler Mach–Zehnder type setup where similar effects can be observed without use of the paraxial approximation.

A classical optical approach to the ‘non-local Pancharatnam-like phases’ in Hanbury-Brown–Twiss correlations

International Nuclear Information System (INIS)

Arvind; Chaturvedi, S.; Mukunda, N.

2017-01-01

Highlights: • Pancharatnam-like phase in HBT correlations. • Mach–Zehnder type setup to clarify that the phases involved are not geometric phases. • No nonlocality involved since the treatment is classical. - Abstract: We examine a recent proposal to show the presence of nonlocal Pancharatnam type geometric phases in a quantum mechanical treatment of intensity interferometry measurements upon inclusion of polarizing elements in the setup. It is shown that a completely classical statistical treatment of such effects is adequate for practical purposes. Further we show that the phase angles that appear in the correlations, while at first sight appearing to resemble Pancharatnam phases in their mathematical structure, cannot actually be interpreted in that manner. We also describe a simpler Mach–Zehnder type setup where similar effects can be observed without use of the paraxial approximation.

Landsat 8 Operational Land Imager On-Orbit Geometric Calibration and Performance

Directory of Open Access Journals (Sweden)

James Storey

2014-11-01

Full Text Available The Landsat 8 spacecraft was launched on 11 February 2013 carrying the Operational Land Imager (OLI payload for moderate resolution imaging in the visible, near infrared (NIR, and short-wave infrared (SWIR spectral bands. During the 90-day commissioning period following launch, several on-orbit geometric calibration activities were performed to refine the prelaunch calibration parameters. The results of these calibration activities were subsequently used to measure geometric performance characteristics in order to verify the OLI geometric requirements. Three types of geometric calibrations were performed including: (1 updating the OLI-to-spacecraft alignment knowledge; (2 refining the alignment of the sub-images from the multiple OLI sensor chips; and (3 refining the alignment of the OLI spectral bands. The aspects of geometric performance that were measured and verified included: (1 geolocation accuracy with terrain correction, but without ground control (L1Gt; (2 Level 1 product accuracy with terrain correction and ground control (L1T; (3 band-to-band registration accuracy; and (4 multi-temporal image-to-image registration accuracy. Using the results of the on-orbit calibration update, all aspects of geometric performance were shown to meet or exceed system requirements.

Geometrization of quantum physics

International Nuclear Information System (INIS)

Ol'khov, O.A.

2009-01-01

It is shown that the Dirac equation for a free particle can be considered as a description of specific distortion of the space Euclidean geometry (space topological defect). This approach is based on the possibility of interpretation of the wave function as vector realizing representation of the fundamental group of the closed topological space-time 4-manifold. Mass and spin appear to be topological invariants. Such a concept explains all so-called 'strange' properties of quantum formalism: probabilities, wave-particle duality, nonlocal instantaneous correlation between noninteracting particles (EPR-paradox) and so on. Acceptance of the suggested geometrical concept means rejection of atomistic concept where all matter is considered as consisting of more and more small elementary particles. There are no any particles a priory, before measurement: the notions of particles appear as a result of classical interpretation of the contact of the region of the curved space with a device

Geometrization of quantum physics

Science.gov (United States)

Ol'Khov, O. A.

2009-12-01

It is shown that the Dirac equation for free particle can be considered as a description of specific distortion of the space euclidean geometry (space topological defect). This approach is based on possibility of interpretation of the wave function as vector realizing representation of the fundamental group of the closed topological space-time 4-manifold. Mass and spin appear to be topological invariants. Such concept explains all so called “strange” properties of quantum formalism: probabilities, wave-particle duality, nonlocal instantaneous correlation between noninteracting particles (EPR-paradox) and so on. Acceptance of suggested geometrical concept means rejection of atomistic concept where all matter is considered as consisting of more and more small elementary particles. There is no any particles a priori, before measurement: the notions of particles appear as a result of classical interpretation of the contact of the region of the curved space with a device.

Chaos based on Riemannian geometric approach to Abelian-Higgs dynamical system

International Nuclear Information System (INIS)

Kawabe, Tetsuji

2003-01-01

Based on the Riemannian geometric approach, we study chaos of the Abelian-Higgs dynamical system derived from a classical field equation consisting of a spatially homogeneous Abelian gauge field and Higgs field. Using the global indicator of chaos formulated by the sectional curvature of the ambient manifold, we show that this approach brings the same qualitative and quantitative information about order and chaos as has been provided by the Lyapunov exponents in the conventional and phenomenological approach. We confirm that the mechanism of chaos is a parametric instability of the system. By analyzing a close relation between the sectional curvature and the Gaussian curvature, we point out that the Toda-Brumer criterion becomes a sufficient condition to the criterion based on this geometric approach as to the stability condition

Geometrical theory of ghost and Higgs fields and SU(2/1)

International Nuclear Information System (INIS)

Ne'eman, Y.; Thierry-Mieg, J.

1979-10-01

That a Principal Fiber Bundle provides a precise geometrical representation of Yang-Mills gauge theories has been known since 1963 and used since 1975. This work presents an entirely new domain of applications. The Feynman-DeWitt-Fadeev-Popov ghost-fields required in the renormalization procedure are identified with geometrical objects in the Principal Bundle. This procedure directly yields the BRS equations guaranteeing unitarity and Slavnov-Taylor invariance of the quantum effective Lagrangian. Except for one ghost field and its variation, this entire symmetry thus corresponds to classical notions, in that it is geometrical, and completely independent of the gauge-fixing procedure, which determines the quantized Lagrangian. These results may be used to fix the signs associated with the various ghost loops of quantum supergravity. The result is based upon the identification of a geometrical Z(2) x Z(2) double-gradation of the generalized fields in supergravity: [physical/ghost] fields and [integer/half integer] spins. Then the case of a supergroup as an internal symmetry gauge is considered. Ghosts geometrically associated to odd generators may be identified with the Goldstone-Nambu Higgs-Kibble scalar fields of conventional models with spontaneous symmetry breakdown. As an example, the chiral SU(3)/sub L/ x SU(3)/sub R/ flavor symmetry is realized by gauging the supergroup Q(3).Lastly, the main results concerning asthenodynamics (Weak-EM Unification) as given by the ghost-gauge SU(2/1) supergroup are recalled. 1 table

Classical geometrical interpretation of ghost fields and anomalies in Yang-Mills theory and quantum gravity

International Nuclear Information System (INIS)

Thierry-Mieg, J.

1985-01-01

The reinterpretation of the BRS equations of Quantum Field Theory as the Maurer Cartan equation of a classical principal fiber bundle leads to a simple gauge invariant classification of the anomalies in Yang Mills theory and gravity

Imaging resolution signal-to-noise ratio in transverse phase amplification from classical information theory

International Nuclear Information System (INIS)

French, Doug; Huang Zun; Pao, H.-Y.; Jovanovic, Igor

2009-01-01

A quantum phase amplifier operated in the spatial domain can improve the signal-to-noise ratio in imaging beyond the classical limit. The scaling of the signal-to-noise ratio with the gain of the quantum phase amplifier is derived from classical information theory

Wild, free-living rufous hummingbirds do not use geometric cues in a spatial task.

Science.gov (United States)

Hornsby, Mark A W; Hurly, T Andrew; Hamilton, Caitlin E; Pritchard, David J; Healy, Susan D

2014-10-01

In the laboratory, many species orient themselves using the geometric properties of an enclosure or array and geometric information is often preferred over visual cues. Whether animals use geometric cues when relocating rewarded locations in the wild, however, has rarely been investigated. We presented free-living rufous hummingbirds with a rectangular array of four artificial flowers to investigate learning of rewarded locations using geometric cues. In one treatment, we rewarded two of four flowers at diagonally opposite corners. In a second treatment, we provided a visual cue to the rewarded flower by connecting the flowers with "walls" consisting of four dowels (three white, one blue) laid on the ground connecting each of the flowers. Neither treatment elicited classical geometry results; instead, hummingbirds typically chose one particular flower over all others. When we exchanged that flower with another, hummingbirds tended to visit the original flower. These results suggest that (1) hummingbirds did not use geometric cues, but instead may have used a visually derived cue on the flowers themselves, and (2) using geometric cues may have been more difficult than using visual characteristics. Although hummingbirds typically prefer spatial over visual information, we hypothesize that they will not use geometric cues over stable visual features but that they make use of small, flower-specific visual cues. Such cues may play a more important role in foraging decisions than previously thought. Copyright © 2014 Elsevier B.V. All rights reserved.

Direct nuclear magnetic resonance identification and quantification of geometric isomers of conjugated linoleic acid in milk lipid fraction without derivatization steps: Overcoming sensitivity and resolution barriers

International Nuclear Information System (INIS)

Tsiafoulis, Constantinos G.; Skarlas, Theodore; Tzamaloukas, Ouranios; Miltiadou, Despoina; Gerothanassis, Ioannis P.

2014-01-01

Highlights: • The first NMR quantification of four geometric 18:2 CLA isomers has been achieved. • Sensitivity and resolution NMR barriers have been overcome. • Selective suppression and reduced 13 C spectral width have been utilized. • The method is applied in the milk lipid fraction without derivatization steps. • The method is selective, sensitive with very good analytical characteristics. - Abstract: We report the first successful direct and unequivocal identification and quantification of four minor geometric (9-cis, 11-trans) 18:2, (9-trans, 11-cis) 18:2, (9-cis, 11-cis) 18:2 and (9-trans, 11-trans) 18:2 conjugated linoleic acid (CLA) isomers in lipid fractions of lyophilized milk samples with the combined use of 1D 1 H-NMR, 2D 1 H- 1 H TOCSY and 2D 1 H- 13 C HSQC NMR. The significant sensitivity barrier has been successfully overcome under selective suppression of the major resonances, with over 10 4 greater equilibrium magnetization of the -(CH 2 ) n - 1 H spins compared to that of the 1 H spins of the conjugated bonds of the CLA isomers. The resolution barrier has been significantly increased using reduced 13 C spectral width in the 2D 1 H- 13 C HSQC experiment. The assignment was confirmed with spiking experiments with CLA standard compounds and the method does not require any derivatization steps for the lipid fraction. The proposed method is selective, sensitive and compares favorably with the GS-MS method of analysis

The Higgs field and the resolution of the Cosmological Constant Paradox in the Weyl-geometrical Universe.

Science.gov (United States)

De Martini, Francesco

2017-11-13

The nature of the scalar field responsible for the cosmological inflation is found to be rooted in the most fundamental concept of Weyl's differential geometry: the parallel displacement of vectors in curved space-time. Within this novel geometrical scenario, the standard electroweak theory of leptons based on the SU (2) L ⊗ U (1) Y as well as on the conformal groups of space-time Weyl's transformations is analysed within the framework of a general-relativistic, conformally covariant scalar-tensor theory that includes the electromagnetic and the Yang-Mills fields. A Higgs mechanism within a spontaneous symmetry breaking process is identified and this offers formal connections between some relevant properties of the elementary particles and the dark energy content of the Universe. An 'effective cosmological potential': V eff is expressed in terms of the dark energy potential: [Formula: see text] via the 'mass reduction parameter': [Formula: see text], a general property of the Universe. The mass of the Higgs boson, which is considered a 'free parameter' by the standard electroweak theory, by our theory is found to be proportional to the mass [Formula: see text] which accounts for the measured cosmological constant, i.e. the measured content of vacuum-energy in the Universe. The non-integrable application of Weyl's geometry leads to a Proca equation accounting for the dynamics of a ϕ ρ -particle, a vector-meson proposed as an an optimum candidate for dark matter. On the basis of previous cosmic microwave background results our theory leads, in the condition of cosmological 'critical density', to the assessment of the average energy content of the ϕ ρ -excitation. The peculiar mathematical structure of V eff offers a clue towards a very general resolution of a most intriguing puzzle of modern quantum field theory, the 'Cosmological Constant Paradox' (here referred to as the ' Λ -Paradox'). Indeed, our 'universal' theory offers a resolution of the Λ -Paradox

Classical geometrical interpretation of ghost fields and anomalies in Yang-Mills theory and quantum gravity

International Nuclear Information System (INIS)

Thierry-Mieg, J.

1985-01-01

This paper discusses the reinterpretation of the BRS equations of Quantum Field Theory as the Maurer Cartan equation of a classical principal fiber bundle leads to a simple gauge invariant classification of the anomalies in Yang Mills theory and gravity

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)

Canonical methods in classical and quantum gravity: An invitation to canonical LQG

Science.gov (United States)

Reyes, Juan D.

2018-04-01

Loop Quantum Gravity (LQG) is a candidate quantum theory of gravity still under construction. LQG was originally conceived as a background independent canonical quantization of Einstein’s general relativity theory. This contribution provides some physical motivations and an overview of some mathematical tools employed in canonical Loop Quantum Gravity. First, Hamiltonian classical methods are reviewed from a geometric perspective. Canonical Dirac quantization of general gauge systems is sketched next. The Hamiltonian formultation of gravity in geometric ADM and connection-triad variables is then presented to finally lay down the canonical loop quantization program. The presentation is geared toward advanced undergradute or graduate students in physics and/or non-specialists curious about LQG.

Geometric Methods in Physics XXXV

CERN Document Server

Odzijewicz, Anatol; Previato, Emma

2018-01-01

This book features a selection of articles based on the XXXV Białowieża Workshop on Geometric Methods in Physics, 2016. The series of Białowieża workshops, attended by a community of experts at the crossroads of mathematics and physics, is a major annual event in the field. The works in this book, based on presentations given at the workshop, are previously unpublished, at the cutting edge of current research, typically grounded in geometry and analysis, and with applications to classical and quantum physics. In 2016 the special session "Integrability and Geometry" in particular attracted pioneers and leading specialists in the field. Traditionally, the Białowieża Workshop is followed by a School on Geometry and Physics, for advanced graduate students and early-career researchers, and the book also includes extended abstracts of the lecture series.

Speed Geometric Quantum Logical Gate Based on Double-Hamiltonian Evolution under Large-Detuning Cavity QED Model

International Nuclear Information System (INIS)

Chen Changyong; Liu Zongliang; Kang Shuai; Li Shaohua

2010-01-01

We introduce the double-Hamiltonian evolution technique approach to investigate the unconventional geometric quantum logical gate with dissipation under the model of many identical three-level atoms in a cavity, driven by a classical field. Our concrete calculation is made for the case of two atoms for the large-detuning interaction of the atoms with the cavity mode. The main advantage of our scheme is of eliminating the photon flutuation in the cavity mode during the gating. The corresponding analytical results will be helpful for experimental realization of speed geometric quantum logical gate in real cavities. (general)

Bounding uncertainty in volumetric geometric models for terrestrial lidar observations of ecosystems.

Science.gov (United States)

Paynter, Ian; Genest, Daniel; Peri, Francesco; Schaaf, Crystal

2018-04-06

Volumetric models with known biases are shown to provide bounds for the uncertainty in estimations of volume for ecologically interesting objects, observed with a terrestrial laser scanner (TLS) instrument. Bounding cuboids, three-dimensional convex hull polygons, voxels, the Outer Hull Model and Square Based Columns (SBCs) are considered for their ability to estimate the volume of temperate and tropical trees, as well as geomorphological features such as bluffs and saltmarsh creeks. For temperate trees, supplementary geometric models are evaluated for their ability to bound the uncertainty in cylinder-based reconstructions, finding that coarser volumetric methods do not currently constrain volume meaningfully, but may be helpful with further refinement, or in hybridized models. Three-dimensional convex hull polygons consistently overestimate object volume, and SBCs consistently underestimate volume. Voxel estimations vary in their bias, due to the point density of the TLS data, and occlusion, particularly in trees. The response of the models to parametrization is analysed, observing unexpected trends in the SBC estimates for the drumlin dataset. Establishing that this result is due to the resolution of the TLS observations being insufficient to support the resolution of the geometric model, it is suggested that geometric models with predictable outcomes can also highlight data quality issues when they produce illogical results.

Multiscale unfolding of real networks by geometric renormalization

Science.gov (United States)

García-Pérez, Guillermo; Boguñá, Marián; Serrano, M. Ángeles

2018-06-01

Symmetries in physical theories denote invariance under some transformation, such as self-similarity under a change of scale. The renormalization group provides a powerful framework to study these symmetries, leading to a better understanding of the universal properties of phase transitions. However, the small-world property of complex networks complicates application of the renormalization group by introducing correlations between coexisting scales. Here, we provide a framework for the investigation of complex networks at different resolutions. The approach is based on geometric representations, which have been shown to sustain network navigability and to reveal the mechanisms that govern network structure and evolution. We define a geometric renormalization group for networks by embedding them into an underlying hidden metric space. We find that real scale-free networks show geometric scaling under this renormalization group transformation. We unfold the networks in a self-similar multilayer shell that distinguishes the coexisting scales and their interactions. This in turn offers a basis for exploring critical phenomena and universality in complex networks. It also affords us immediate practical applications, including high-fidelity smaller-scale replicas of large networks and a multiscale navigation protocol in hyperbolic space, which betters those on single layers.

A New Semi-Symmetric Unified Field Theory of the Classical Fields of Gravity and Electromagnetism

Directory of Open Access Journals (Sweden)

Suhendro I.

2007-10-01

Full Text Available We attempt to present a classical theoretical framework in which the gravitational and electromagnetic fields are unified as intrinsic geometric objects in the space-time manifold. For this purpose, we first present the preliminary geometric considerations dealing with the metric differential geometry of Cartan connections. The unified field theory is then developed as an extension of the general theory of relativity based on a semi- symmetric Cartan connection which is meant to be as close as possible structurally to the symmetric connection of the Einstein-Riemann space-time.

Random broadcast on random geometric graphs

Energy Technology Data Exchange (ETDEWEB)

Bradonjic, Milan [Los Alamos National Laboratory; Elsasser, Robert [UNIV OF PADERBORN; Friedrich, Tobias [ICSI/BERKELEY; Sauerwald, Tomas [ICSI/BERKELEY

2009-01-01

In this work, we consider the random broadcast time on random geometric graphs (RGGs). The classic random broadcast model, also known as push algorithm, is defined as: starting with one informed node, in each succeeding round every informed node chooses one of its neighbors uniformly at random and informs it. We consider the random broadcast time on RGGs, when with high probability: (i) RGG is connected, (ii) when there exists the giant component in RGG. We show that the random broadcast time is bounded by {Omicron}({radical} n + diam(component)), where diam(component) is a diameter of the entire graph, or the giant component, for the regimes (i), or (ii), respectively. In other words, for both regimes, we derive the broadcast time to be {Theta}(diam(G)), which is asymptotically optimal.

Classical field theory on electrodynamics, non-Abelian gauge theories and gravitation

CERN Document Server

Scheck, Florian

2012-01-01

The book describes Maxwell's equations first in their integral, directly testable form, then moves on to their local formulation. The first two chapters cover all essential properties of Maxwell's equations, including their symmetries and their covariance in a modern notation. Chapter 3 is devoted to Maxwell theory as a classical field theory and to solutions of the wave equation. Chapter 4 deals with important applications of Maxwell theory. It includes topical subjects such as metamaterials with negative refraction index and solutions of Helmholtz' equation in paraxial approximation relevant for the description of laser beams. Chapter 5 describes non-Abelian gauge theories from a classical, geometric point of view, in analogy to Maxwell theory as a prototype, and culminates in an application to the U(2) theory relevant for electroweak interactions. The last chapter 6 gives a concise summary of semi-Riemannian geometry as the framework for the classical field theory of gravitation. The chapter concludes wit...

Salt bridges: geometrically specific, designable interactions.

Science.gov (United States)

Donald, Jason E; Kulp, Daniel W; DeGrado, William F

2011-03-01

Salt bridges occur frequently in proteins, providing conformational specificity and contributing to molecular recognition and catalysis. We present a comprehensive analysis of these interactions in protein structures by surveying a large database of protein structures. Salt bridges between Asp or Glu and His, Arg, or Lys display extremely well-defined geometric preferences. Several previously observed preferences are confirmed, and others that were previously unrecognized are discovered. Salt bridges are explored for their preferences for different separations in sequence and in space, geometric preferences within proteins and at protein-protein interfaces, co-operativity in networked salt bridges, inclusion within metal-binding sites, preference for acidic electrons, apparent conformational side chain entropy reduction on formation, and degree of burial. Salt bridges occur far more frequently between residues at close than distant sequence separations, but, at close distances, there remain strong preferences for salt bridges at specific separations. Specific types of complex salt bridges, involving three or more members, are also discovered. As we observe a strong relationship between the propensity to form a salt bridge and the placement of salt-bridging residues in protein sequences, we discuss the role that salt bridges might play in kinetically influencing protein folding and thermodynamically stabilizing the native conformation. We also develop a quantitative method to select appropriate crystal structure resolution and B-factor cutoffs. Detailed knowledge of these geometric and sequence dependences should aid de novo design and prediction algorithms. Copyright © 2010 Wiley-Liss, Inc.

Accuracy of geometrical modelling of heat transfer from tissue to blood vessels

NARCIS (Netherlands)

Leeuwen, van G.M.J.; Kotte, A.N.T.J.; Bree, de J.; Koijk, van der J.F.; Crezee, J.; Lagendijk, J.J.W.

1997-01-01

We have developed a thermal model in which blood vessels are described as geometrical objects, 3D curves with associated diameters. Here the behaviour of the model is examined for low resolutions compared with the vessel diameter and for strongly curved vessels. The tests include a single straight

Unconventional geometric logic gate in a strong-driving-assisted multi-mode cavity

International Nuclear Information System (INIS)

Chang-Ning, Pan; Di-Wu, Yang; Xue-Hui, Zhao; Mao-Fa, Fang

2010-01-01

We propose a scheme to implement an unconventional geometric logic gate separately in a two-mode cavity and a multi-mode cavity assisted by a strong classical driving field. The effect of the cavity decay is included in the investigation. The numerical calculation is carried out, and the result shows that our scheme is more tolerant to cavity decay than the previous one because the time consumed for finishing the logic gate is doubly reduced. (general)

Artefacts in geometric phase analysis of compound materials.

Science.gov (United States)

Peters, Jonathan J P; Beanland, Richard; Alexe, Marin; Cockburn, John W; Revin, Dmitry G; Zhang, Shiyong Y; Sanchez, Ana M

2015-10-01

The geometric phase analysis (GPA) algorithm is known as a robust and straightforward technique that can be used to measure lattice strains in high resolution transmission electron microscope (TEM) images. It is also attractive for analysis of aberration-corrected scanning TEM (ac-STEM) images that resolve every atom column, since it uses Fourier transforms and does not require real-space peak detection and assignment to appropriate sublattices. Here it is demonstrated that, in ac-STEM images of compound materials with compositionally distinct atom columns, an additional geometric phase is present in the Fourier transform. If the structure changes from one area to another in the image (e.g. across an interface), the change in this additional phase will appear as a strain in conventional GPA, even if there is no lattice strain. Strategies to avoid this pitfall are outlined. Copyright © 2015 Elsevier B.V. All rights reserved.

Gauge field vacuum structure in geometrical aspect

International Nuclear Information System (INIS)

Konopleva, N.P.

2003-01-01

Vacuum conception is one of the main conceptions of quantum field theory. Its meaning in classical field theory is also very profound. In this case the vacuum conception is closely connected with ideas of the space-time geometry. The global and local geometrical space-time conceptions lead to different vacuum definitions and therefore to different ways of physical theory construction. Some aspects of the gauge field vacuum structure are analyzed. It is shown that in the gauge field theory the vacuum Einstein equation solutions describe the relativistic vacuum as common vacuum of all gauge fields and its sources. Instantons (both usual and hyperbolical) are regarded as nongravitating matter, because they have zero energy-momentum tensors and correspond to vacuum Einstein equations

Classical mechanics with Mathematica

CERN Document Server

Romano, Antonio

2018-01-01

This textbook takes a broad yet thorough approach to mechanics, aimed at bridging the gap between classical analytic and modern differential geometric approaches to the subject. Developed by the authors from over 30 years of teaching experience, the presentation is designed to give students an overview of the many different models used through the history of the field—from Newton to Hamilton—while also painting a clear picture of the most modern developments. The text is organized into two parts. The first focuses on developing the mathematical framework of linear algebra and differential geometry necessary for the remainder of the book. Topics covered include tensor algebra, Euclidean and symplectic vector spaces, differential manifolds, and absolute differential calculus. The second part of the book applies these topics to kinematics, rigid body dynamics, Lagrangian and Hamiltonian dynamics, Hamilton–Jacobi theory, completely integrable systems, statistical mechanics of equilibrium, and impulsive dyna...

A Spectral Geometrical Model for Compton Scatter Tomography Based on the SSS Approximation

DEFF Research Database (Denmark)

Kazantsev, Ivan G.; Olsen, Ulrik Lund; Poulsen, Henning Friis

2016-01-01

The forward model of single scatter in the Positron Emission Tomography for a detector system possessing an excellent spectral resolution under idealized geometrical assumptions is investigated. This model has the form of integral equations describing a flux of photons emanating from the same ann...

A new geometrical approach to Nash equilibria organization in Eisert's quantum games

International Nuclear Information System (INIS)

Schneider, David

2012-01-01

We extend the periodic point-based method for Eisert's quantum games (Schneider 2011 J. Phys. A: Math. Theor. 44 095301) to games not previously analyzed. From the comparison of different cases, we observe that games sharing the same classical features (as for instance the symmetrized Battle of the Sexes and the Chicken game) can have different characteristics after the quantization, and conversely, games with different classical behaviors (the Chicken game and the Prisoner's dilemma), are completely equivalent within Eisert's protocol. This fact is reflected in the structure of the map that the periodic point-procedure associates to the quantum game (from which the Nash equilibria are deduced). In order to understand how these unexpected outcomes are generated, we give a geometrical description of our observations in terms of bifurcation theory for maps. (paper)

Sudden transitions and scaling behavior of geometric quantum correlation for two qubits in quantum critical environments at finite temperature

International Nuclear Information System (INIS)

Luo, Da-Wei; Xu, Jing-Bo

2014-01-01

We investigate the phenomenon of sudden transitions in geometric quantum correlation of two qubits in spin chain environments at finite temperature. It is shown that when only one qubit is coupled to the spin environment, the geometric discord exhibits a double sudden transition behavior, which is closely related to the quantum criticality of the spin chain environment. When two qubits are uniformly coupled to a common spin chain environment, the geometric discord is found to display a sudden transition behavior whereby the system transits from pure classical decoherence to pure quantum decoherence. Moreover, an interesting scaling behavior is revealed for the frozen time, and we also present a scheme to prolong the time during which the discord remains constant by applying bang–bang pulses. (paper)

On covariant Poisson brackets in classical field theory

International Nuclear Information System (INIS)

Forger, Michael; Salles, Mário O.

2015-01-01

How to give a natural geometric definition of a covariant Poisson bracket in classical field theory has for a long time been an open problem—as testified by the extensive literature on “multisymplectic Poisson brackets,” together with the fact that all these proposals suffer from serious defects. On the other hand, the functional approach does provide a good candidate which has come to be known as the Peierls–De Witt bracket and whose construction in a geometrical setting is now well understood. Here, we show how the basic “multisymplectic Poisson bracket” already proposed in the 1970s can be derived from the Peierls–De Witt bracket, applied to a special class of functionals. This relation allows to trace back most (if not all) of the problems encountered in the past to ambiguities (the relation between differential forms on multiphase space and the functionals they define is not one-to-one) and also to the fact that this class of functionals does not form a Poisson subalgebra

On covariant Poisson brackets in classical field theory

Energy Technology Data Exchange (ETDEWEB)

Forger, Michael [Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, BR–05315-970 São Paulo, SP (Brazil); Salles, Mário O. [Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, BR–05315-970 São Paulo, SP (Brazil); Centro de Ciências Exatas e da Terra, Universidade Federal do Rio Grande do Norte, Campus Universitário – Lagoa Nova, BR–59078-970 Natal, RN (Brazil)

2015-10-15

How to give a natural geometric definition of a covariant Poisson bracket in classical field theory has for a long time been an open problem—as testified by the extensive literature on “multisymplectic Poisson brackets,” together with the fact that all these proposals suffer from serious defects. On the other hand, the functional approach does provide a good candidate which has come to be known as the Peierls–De Witt bracket and whose construction in a geometrical setting is now well understood. Here, we show how the basic “multisymplectic Poisson bracket” already proposed in the 1970s can be derived from the Peierls–De Witt bracket, applied to a special class of functionals. This relation allows to trace back most (if not all) of the problems encountered in the past to ambiguities (the relation between differential forms on multiphase space and the functionals they define is not one-to-one) and also to the fact that this class of functionals does not form a Poisson subalgebra.

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)

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.

Random Process Theory Approach to Geometric Heterogeneous Surfaces: Effective Fluid-Solid Interaction

Science.gov (United States)

Khlyupin, Aleksey; Aslyamov, Timur

2017-06-01

Realistic fluid-solid interaction potentials are essential in description of confined fluids especially in the case of geometric heterogeneous surfaces. Correlated random field is considered as a model of random surface with high geometric roughness. We provide the general theory of effective coarse-grained fluid-solid potential by proper averaging of the free energy of fluid molecules which interact with the solid media. This procedure is largely based on the theory of random processes. We apply first passage time probability problem and assume the local Markov properties of random surfaces. General expression of effective fluid-solid potential is obtained. In the case of small surface irregularities analytical approximation for effective potential is proposed. Both amorphous materials with large surface roughness and crystalline solids with several types of fcc lattices are considered. It is shown that the wider the lattice spacing in terms of molecular diameter of the fluid, the more obtained potentials differ from classical ones. A comparison with published Monte-Carlo simulations was discussed. The work provides a promising approach to explore how the random geometric heterogeneity affects on thermodynamic properties of the fluids.

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.

Geometric objects related to the potential of electric charges

International Nuclear Information System (INIS)

Mozrzymas, J.

1995-01-01

We derive explicit formulas for curvature and torsion of a line of the field of n electric charges. These formulas show that in general the torsion of a field line is not zero if n≥3. We also propose a geometric interpretation of the derived formulas. In the second part of the paper we present an outline of a new description of equipotential surfaces of two and three electric charges. In this description the golden section appears in a natural way when two electric charges are equal. This approach also relates an equipotential surface of three charges to the classic surface containing twenty seven straight lines. (author)

The geometrically averaged density of states calculated from the local Green's function as a measure of localization

International Nuclear Information System (INIS)

Wortis, R.; Song Yun; Atkinson, W.A.

2008-01-01

With the goal of measuring localization in disordered interacting systems, we examine the finite-size scaling of the geometrically averaged density of states calculated from the local Green's function with finite energy resolution. Our results show that, unlike in a simple energy binning procedure, there is no limit in which the finite energy resolution is irrelevant

High Resolution Optical Spectroscopy of the Classical Nova V5668 Sgr Showing the Presence of Lithium

Science.gov (United States)

Wagner, R. Mark; Woodward, Charles E.; Starrfield, Sumner; Ilyin, Ilya; Strassmeier, Klaus

2018-01-01

The classical nova (CN) V5668 Sgr was discovered on 2015 March 15.634 and initial optical spectra implied it was an Fe II-class CN. We obtained high resolution optical spectroscopy on 30 nights between 2015 April 3 and 2016 June 5 with the 2 x 8.4 m Large Binocular Telescope (LBT) and the 1.8 m Vatican Advanced Technology Telescope (VATT) using the Potsdam Echelle Polarimetric Spectroscopic Instrument (PEPSI). The spectra cover all or part of the 3830-9065 Å spectral region at a spectral resolution of up to 270,000 (1 km/s); the highest resolution currently available on any 8-10 m class telescope. The early spectra are dominated by emission lines of the Balmer and Paschen series of hydrogen, Fe II, Ca II, and Na I with P Cyg-type line profiles as well as emission lines of [O I]. Numerous interstellar lines and bands are readily apparent at high spectral resolution. The permitted line profiles show complex and dramatic variations in the multi-component P Cyg-type line profiles with time. We detect a weak blue-shifted absorption line at a velocity consistent with Li I 6708 Å when compared with the line profiles of Hβ, Fe II 5169 Å, and Na I D. This line is present in spectra obtained on 7 of 8 consecutive nights up to day 21 of the outburst; but absent on day 42 when it is evident that the ionization of the ejecta has significantly increased. The equivalent width of the line converted to a column density, and the resulting mass fraction, imply a significant enrichment of 7Li in the ejecta. 7Li is produced by the decay of unstable 7Be created during the thermonuclear runaway. The discovery of the resonance lines of 7Be II in the optical spectra of the recent CNe V339 Del, V2944 Oph, and V5668 Sgr by Tajitsu et al. (2016) and its subsequent decay to 7Li (half life of 53 days) suggests a significant enrichment of 7Li in the Galaxy from CNe is possible. Our observations of the Li I 6708 Å line in the early optical spectra of V5668 Sgr mark the second direct

Emergent Newtonian dynamics and the geometric origin of mass

International Nuclear Information System (INIS)

D’Alessio, Luca; Polkovnikov, Anatoli

2014-01-01

We consider a set of macroscopic (classical) degrees of freedom coupled to an arbitrary many-particle Hamiltonian system, quantum or classical. These degrees of freedom can represent positions of objects in space, their angles, shape distortions, magnetization, currents and so on. Expanding their dynamics near the adiabatic limit we find the emergent Newton’s second law (force is equal to the mass times acceleration) with an extra dissipative term. In systems with broken time reversal symmetry there is an additional Coriolis type force proportional to the Berry curvature. We give the microscopic definition of the mass tensor. The mass tensor is related to the non-equal time correlation functions in equilibrium and describes the dressing of the slow degree of freedom by virtual excitations in the system. In the classical (high-temperature) limit the mass tensor is given by the product of the inverse temperature and the Fubini–Study metric tensor determining the natural distance between the eigenstates of the Hamiltonian. For free particles this result reduces to the conventional definition of mass. This finding shows that any mass, at least in the classical limit, emerges from the distortions of the Hilbert space highlighting deep connections between any motion (not necessarily in space) and geometry. We illustrate our findings with four simple examples. -- Highlights: •Derive the macroscopic Newton’s equation from the microscopic many-particle Schrödinger’s equation. •Deep connection between geometry and dynamics. •Geometrical interpretation of the mass of macroscopic object as deformation of Hilbert space. •Microscopic expression for mass and friction tensors

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...

Integrated magnetic, geometric and discriminating sensor for instrumented Pigs; Sensor geometrico magnetico e discriminador integrado para pigs instrumentados

Energy Technology Data Exchange (ETDEWEB)

Lima, Vinicius de C. [Pontificia Univ. Catolica do Rio de Janeiro, RJ (Brazil); Von der Weid, Jean Pierre [Pontificia Univ. Catolica do Rio de Janeiro, RJ (Brazil). Centro de Estudos em Telecomunicacoes; Silva, Jose A.P. da [PipeWay Engenharia, Rio de Janeiro, RJ (Brazil); Camerini, Claudio Soligo; Oliveira, Carlos H.F. de [PETROBRAS S.A., Rio de Janeiro, RJ (Brazil). Centro de Pesquisas

2003-07-01

In this work it is presented a result of a research partnership between PUC-Rio, PETROBRAS, Pipeway. The development of an innovative sensor head for high resolution MFL Pigs, the GMD sensor, Geometric Magnetic and Discriminator. This head make the magnetic pipeline reading, in high resolution using the MFL - Magnetic Flux Leakage technique, adding to it the geometric reading as well as the discrimination of the defects, as being external or internal. This technique makes possible the inspection of geometry, magnetism and discrimination with only one crown of GMD sensors. In this paper technical aspects of the development, eg: the constructive details of the sensor, evaluation tests and laboratory results are presented. (author)

Generalized Faraday law derived from classical forces in a rotating frame

OpenAIRE

Choi, Taeseung

2009-01-01

We show the additional spin dependent classical force due to the rotation of an electron spin's rest frame is essential to derive a spin-Faraday law by using an analogy with the usual Faraday law. The contribution of the additional spin dependent force to the spin-Faraday law is the same as that of the spin geometric phase. With this observations, Faraday law is generalized to include both the usual Faraday and the spin-Faraday laws in a unified manner.

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.

Classical and multilinear harmonic analysis

CERN Document Server

Muscalu, Camil

2013-01-01

This two-volume text in harmonic analysis introduces a wealth of analytical results and techniques. It is largely self-contained and useful to graduates and researchers in pure and applied analysis. Numerous exercises and problems make the text suitable for self-study and the classroom alike. The first volume starts with classical one-dimensional topics: Fourier series; harmonic functions; Hilbert transform. Then the higher-dimensional Calderón-Zygmund and Littlewood-Paley theories are developed. Probabilistic methods and their applications are discussed, as are applications of harmonic analysis to partial differential equations. The volume concludes with an introduction to the Weyl calculus. The second volume goes beyond the classical to the highly contemporary and focuses on multilinear aspects of harmonic analysis: the bilinear Hilbert transform; Coifman-Meyer theory; Carleson's resolution of the Lusin conjecture; Calderón's commutators and the Cauchy integral on Lipschitz curves. The material in this vo...

A few insights into the nature of classical and quantum gravity via null-strut calculus

International Nuclear Information System (INIS)

Kheyfets, Arkady

1989-01-01

Null-strut calculus is a 3 + 1 formulation of standard Regge calculus, wherein the dynamics of 3-geometry is propagated in time along light rays, or 'null struts'. However, just as Regge calculus is a discrete and geometric tool for the description of Einstein's theory of gravitation, so too NSC offers itself as a discrete and geometric tool for the description of Einstein's spacetime as the dynamics of discrete spacelike 3-geometries in time, or discrete geometrodynamics. It has for its objectives to provide a discrete model of a 3 + 1 split of spacetime into space plus time, while in so doing to preserve and illuminate the geometric content of Einstein's theory of gravity. The feature of 'light-cone-produced duality' is central to null-strut calculus. This paper will capitalise on this feature, and will attempt to provide some insights into the nature of classical and quantum gravity. (Author)

Analysis of two-player quantum games in an EPR setting using Clifford's geometric algebra.

Science.gov (United States)

Chappell, James M; Iqbal, Azhar; Abbott, Derek

2012-01-01

The framework for playing quantum games in an Einstein-Podolsky-Rosen (EPR) type setting is investigated using the mathematical formalism of geometric algebra (GA). The main advantage of this framework is that the players' strategy sets remain identical to the ones in the classical mixed-strategy version of the game, and hence the quantum game becomes a proper extension of the classical game, avoiding a criticism of other quantum game frameworks. We produce a general solution for two-player games, and as examples, we analyze the games of Prisoners' Dilemma and Stag Hunt in the EPR setting. The use of GA allows a quantum-mechanical analysis without the use of complex numbers or the Dirac Bra-ket notation, and hence is more accessible to the non-physicist.

Investigation of spatial resolution characteristics of an in vivo microcomputed tomography system

Energy Technology Data Exchange (ETDEWEB)

Ghani, Muhammad U. [Center for Biomedical engineering and School of Electrical and Computer Engineering, University of Oklahoma, Norman, OK 73019 (United States); Zhou, Zhongxing [Center for Biomedical engineering and School of Electrical and Computer Engineering, University of Oklahoma, Norman, OK 73019 (United States); School of Precision and Optoelectronics Engineering, Tianjin University, Tianjin 300072 (China); Ren, Liqiang; Wong, Molly; Li, Yuhua; Zheng, Bin [Center for Biomedical engineering and School of Electrical and Computer Engineering, University of Oklahoma, Norman, OK 73019 (United States); Yang, Kai [Department of Radiology, Massachusetts General Hospital, 55 Fruit Street, Boston, MA 02114 (United States); Liu, Hong, E-mail: liu@ou.edu [Center for Biomedical engineering and School of Electrical and Computer Engineering, University of Oklahoma, Norman, OK 73019 (United States)

2016-01-21

The spatial resolution characteristics of an in vivo microcomputed tomography (CT) system was investigated in the in-plane (x–y), cross plane (z) and projection imaging modes. The microCT system utilized in this study employs a flat panel detector with a 127 µm pixel pitch, a microfocus x-ray tube with a focal spot size ranging from 5–30 µm, and accommodates three geometric magnifications (M) of 1.72, 2.54 and 5.10. The in-plane modulation transfer function (MTF) curves were measured as a function of the number of projections, geometric magnification (M), detector binning and reconstruction magnification (M{sub Recon}). The in plane cutoff frequency (10% MTF) ranged from 2.31 lp/mm (M=1.72, 2×2 binning) to 12.56 lp/mm (M=5.10, 1×1 binning) and a bar pattern phantom validated those measurements. A slight degradation in the spatial resolution was observed when comparing the image reconstruction with 511 and 918 projections, whose effect was visible at the lower frequencies. Small value of M{sub Recon} has little or no impact on the in-plane spatial resolution owning to a stable system. Large value of M{sub Recon} has implications on the spatial resolution and it was evident when comparing the bar pattern images reconstructed with M{sub Recon}=1.25 and 2.5. The cross plane MTF curves showed that the spatial resolution increased as the slice thickness decreased. The cutoff frequencies in the projection imaging mode yielded slightly higher values as compared to the in-plane and cross plane modes at all the geometric magnifications (M). At M=5.10, the cutoff resolution of the projection and cross plane on an ultra-high contrast resolution bar chip phantom were 14.9 lp/mm and 13–13.5 lp/mm. Due to the finite focal spot size of the x-ray tube, the detector blur and the reconstruction kernel functions, the system's spatial resolution does not reach the limiting spatial resolution as defined by the Nyquist's detector criteria with an ideal point source

Classical transport in field reversed mirrors: reactor implications

International Nuclear Information System (INIS)

Auerbach, S.P.; Condit, W.C.

1980-01-01

Assuming that the field-reversed mirror (or the closely related spheromak) turns out to be stable, the next crucial issue is transport of particles and heat. Of particular concern is the field null on axis (the X-point), which at first glance seems to allow particles to flow out unhindered. We have evaluated the classical diffusion coefficients for particles and heat in field-reversed mirrors, with particular reference to a class of Hill's vortex models. Two fairly surprising results emerge from this study. First, the diffusion-driven flow of particles and heat is finite at the X-points. This may be traced to the geometrical constraint that the current (and hence the ion-electron drag force, which causes cross-field transport) must vanish on axis. This conclusion holds for any transport model. Second, the classical diffusion coefficient D(psi), which governs both particle and heat flux, is finite on the separatrix. Indeed, in a wide class of Hill's vortex equilibria (spherical, oblate, or prolate) D(psi) is essentially independent of psi (except for the usual factor of n

Higher-order gravity and the classical equivalence principle

Science.gov (United States)

Accioly, Antonio; Herdy, Wallace

2017-11-01

As is well known, the deflection of any particle by a gravitational field within the context of Einstein’s general relativity — which is a geometrical theory — is, of course, nondispersive. Nevertheless, as we shall show in this paper, the mentioned result will change totally if the bending is analyzed — at the tree level — in the framework of higher-order gravity. Indeed, to first order, the deflection angle corresponding to the scattering of different quantum particles by the gravitational field mentioned above is not only spin dependent, it is also dispersive (energy-dependent). Consequently, it violates the classical equivalence principle (universality of free fall, or equality of inertial and gravitational masses) which is a nonlocal principle. However, contrary to popular belief, it is in agreement with the weak equivalence principle which is nothing but a statement about purely local effects. It is worthy of note that the weak equivalence principle encompasses the classical equivalence principle locally. We also show that the claim that there exists an incompatibility between quantum mechanics and the weak equivalence principle, is incorrect.

Rational top and its classical r-matrix

International Nuclear Information System (INIS)

Aminov, G; Arthamonov, S; Smirnov, A; Zotov, A

2014-01-01

We construct a rational integrable system (the rational top) on a co-adjoint orbit of SL N Lie group. It is described by the Lax operator with spectral parameter and classical non-dynamical skew-symmetric r-matrix. In the case of the orbit of minimal dimension the model is gauge equivalent to the rational Calogero–Moser (CM) system. To obtain the results we represent the Lax operator of the CM model in two different factorized forms—without spectral parameter (related to the spinless case) and another one with the spectral parameter. The latter gives rise to the rational top while the first one is related to generalized Cremmer–Gervais r-matrices. The gauge transformation relating the rational top and CM model provides the classical rational version of the IRF-Vertex correspondence. From the geometrical point of view it describes the modification of SL(N,C)-bundles over degenerated elliptic curve. In view of the Symplectic Hecke Correspondence the rational top is related to the rational spin CM model. Possible applications and generalizations of the suggested construction are discussed. In particular, the obtained r-matrix defines a class of KZB equations. (paper)

A geometric theory for semilinear almost-periodic parabolic partial differential equations on RN

International Nuclear Information System (INIS)

Vuillermot, P.A.

1991-01-01

In this short expository article we review various applications of some geometric methods which have been recently devised to investigate the long time behaviour of classical solutions to certain semilinear almost-periodic reaction-diffusion equations on R N . As a consequence, we also show how to construct almost-periodic attractors for such equations and how to investigate their stability properties. The class of problems which we analyse here contains in particular well known equations of population genetics. (author). 17 refs

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...

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)

The Eisenhart lift: a didactical introduction of modern geometrical concepts from Hamiltonian dynamics

International Nuclear Information System (INIS)

Cariglia, Marco; Alves, Filipe Kelmer

2015-01-01

This work originates from part of a final year undergraduate research project on the Eisenhart lift for Hamiltonian systems. The Eisenhart lift is a procedure to describe trajectories of a classical natural Hamiltonian system as geodesics in an enlarged space. We point out that it can be easily obtained from basic principles of Hamiltonian dynamics, and as such it represents a useful didactical way to introduce graduate students to several modern concepts of geometry applied to physics: curved spaces, both Riemannian and Lorentzian, conformal transformations, geometrization of interactions and extra dimensions, and geometrization of dynamical symmetries. For all these concepts the Eisenhart lift can be used as a theoretical tool that provides easily achievable examples, with the added benefit of also being a topic of current research with several applications, among which are included the study of dynamical systems and non-relativistic holography. (paper)

High resolution T{sub 2}{sup *}-weighted magnetic resonance imaging at 3 Tesla using PROPELLER-EPI

Energy Technology Data Exchange (ETDEWEB)

Kraemer, Martin; Reichenbach, Juergen R. [Jena University Hospital (Germany). Medical Physics Group

2014-09-01

We report the application of PROPELLER-EPI for high resolution T{sub 2}{sup *}-weighted imaging with sub-millimeter in-plane resolution on a clinical 3 Tesla scanner. Periodically rotated blades of a long-axis PROPELLER-EPI sequence were acquired with fast gradient echo readout and acquisition matrix of 320 x 50 per blade. Images were reconstructed by using 2D-gridding, phase and geometric distortion correction and compensation of resonance frequency drifts that occurred during extended measurements. To characterize these resonance frequency offsets, short FID calibration measurements were added to the PROPELLER-EPI sequence. Functional PROPELLER-EPI was performed with volunteers using a simple block design of right handed finger tapping. Results indicate that PROPELLER-EPI can be employed for fast, high resolution T{sub 2}{sup *}-weighted imaging provided geometric distortions and possible resonance frequency drifts are properly corrected. Even small resonance frequency drifts below 10 Hz as well as non-corrected geometric distortions degraded image quality substantially. In the initial fMRI experiment image quality and signal-to-noise ratio was sufficient for obtaining high resolution functional activation maps. (orig.)

Geometric properties of nucleic acids with potential for autobuilding

International Nuclear Information System (INIS)

Gruene, Tim; Sheldrick, George M.

2011-01-01

Algorithms and geometrical properties are described for the automated building of nucleic acids in experimental electron density. Medium- to high-resolution X-ray structures of DNA and RNA molecules were investigated to find geometric properties useful for automated model building in crystallographic electron-density maps. We describe a simple method, starting from a list of electron-density ‘blobs’, for identifying backbone phosphates and nucleic acid bases based on properties of the local electron-density distribution. This knowledge should be useful for the automated building of nucleic acid models into electron-density maps. We show that the distances and angles involving C1′ and the P atoms, using the pseudo-torsion angles η' and θ' that describe the …P—C1′—P—C1′… chain, provide a promising basis for building the nucleic acid polymer. These quantities show reasonably narrow distributions with asymmetry that should allow the direction of the phosphate backbone to be established

Analysis of two-player quantum games in an EPR setting using Clifford's geometric algebra.

Directory of Open Access Journals (Sweden)

James M Chappell

Full Text Available The framework for playing quantum games in an Einstein-Podolsky-Rosen (EPR type setting is investigated using the mathematical formalism of geometric algebra (GA. The main advantage of this framework is that the players' strategy sets remain identical to the ones in the classical mixed-strategy version of the game, and hence the quantum game becomes a proper extension of the classical game, avoiding a criticism of other quantum game frameworks. We produce a general solution for two-player games, and as examples, we analyze the games of Prisoners' Dilemma and Stag Hunt in the EPR setting. The use of GA allows a quantum-mechanical analysis without the use of complex numbers or the Dirac Bra-ket notation, and hence is more accessible to the non-physicist.

Classical impurity ion confinement in a toroidal magnetized fusion plasma.

Science.gov (United States)

Kumar, S T A; Den Hartog, D J; Caspary, K J; Magee, R M; Mirnov, V V; Chapman, B E; Craig, D; Fiksel, G; Sarff, J S

2012-03-23

High-resolution measurements of impurity ion dynamics provide first-time evidence of classical ion confinement in a toroidal, magnetically confined plasma. The density profile evolution of fully stripped carbon is measured in MST reversed-field pinch plasmas with reduced magnetic turbulence to assess Coulomb-collisional transport without the neoclassical enhancement from particle drift effects. The impurity density profile evolves to a hollow shape, consistent with the temperature screening mechanism of classical transport. Corroborating methane pellet injection experiments expose the sensitivity of the impurity particle confinement time to the residual magnetic fluctuation amplitude.

Using Geometrical Properties for Fast Indexation of Gaussian Vector Quantizers

Directory of Open Access Journals (Sweden)

Vassilieva EA

2007-01-01

Full Text Available Vector quantization is a classical method used in mobile communications. Each sequence of samples of the discretized vocal signal is associated to the closest -dimensional codevector of a given set called codebook. Only the binary indices of these codevectors (the codewords are transmitted over the channel. Since channels are generally noisy, the codewords received are often slightly different from the codewords sent. In order to minimize the distortion of the original signal due to this noisy transmission, codevectors indexed by one-bit different codewords should have a small mutual Euclidean distance. This paper is devoted to this problem of index assignment of binary codewords to the codevectors. When the vector quantizer has a Gaussian structure, we show that a fast index assignment algorithm based on simple geometrical and combinatorial considerations can improve the SNR at the receiver by 5dB with respect to a purely random assignment. We also show that in the Gaussian case this algorithm outperforms the classical combinatorial approach in the field.

Quantitative comparison between two geometrical layouts for diffraction enhanced imaging

International Nuclear Information System (INIS)

Huang Wanxia; Yuan Qingxi; Zhu Peiping; Wang Junyue; Shu Hang; Chen Bo; Hu Tiandou; Wu Ziyu

2007-01-01

Diffraction enhanced imaging (DEI) with two crystals has been performed at the 4W1A beamline at Beijing Synchrotron Radiation Facility (BSRF). Two different crystal geometrical layouts were used to collect images, in the first layout the rotation axis of the crystal has been set perpendicular to the orbital plane while in the second the axis is parallel to the orbital plane. Performance comparison between the two layouts is discussed in terms of thermal expansion of the crystal induced by the heat load, imaging homogeneity, spatial resolution and angular resolution. From both experimental and theoretical data we show that the best images may be obtained with the optical layout in which the rotation axis of the crystals is perpendicular to the orbital plane

Quantitative comparison between two geometrical layouts for diffraction enhanced imaging

Energy Technology Data Exchange (ETDEWEB)

Huang Wanxia; Yuan Qingxi [Beijing Synchrotron Radiation Facility, Institute of High Energy Physics, CAS, Beijing (China); Zhu Peiping [Beijing Synchrotron Radiation Facility, Institute of High Energy Physics, CAS, Beijing (China)], E-mail: zhupp@ihep.ac.cn; Wang Junyue; Shu Hang [Beijing Synchrotron Radiation Facility, Institute of High Energy Physics, CAS, Beijing (China); Chen Bo [Beijing Synchrotron Radiation Facility, Institute of High Energy Physics, CAS, Beijing (China); Department of Physics, University of Science and Technology of China, Hefei (China); Hu Tiandou [Beijing Synchrotron Radiation Facility, Institute of High Energy Physics, CAS, Beijing (China); Wu Ziyu [Beijing Synchrotron Radiation Facility, Institute of High Energy Physics, CAS, Beijing (China)], E-mail: wuzy@ihep.ac.cn

2007-07-15

Diffraction enhanced imaging (DEI) with two crystals has been performed at the 4W1A beamline at Beijing Synchrotron Radiation Facility (BSRF). Two different crystal geometrical layouts were used to collect images, in the first layout the rotation axis of the crystal has been set perpendicular to the orbital plane while in the second the axis is parallel to the orbital plane. Performance comparison between the two layouts is discussed in terms of thermal expansion of the crystal induced by the heat load, imaging homogeneity, spatial resolution and angular resolution. From both experimental and theoretical data we show that the best images may be obtained with the optical layout in which the rotation axis of the crystals is perpendicular to the orbital plane.

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.

Generalized Faraday law derived from classical forces in a rotating frame

International Nuclear Information System (INIS)

Choi, Taeseung

2010-01-01

We show that an additional spin-dependent classical force due to the rotation of an electron spin's rest frame is essential to derive a spin-Faraday law that has the same form as the usual Faraday law. We show that the contribution of the additional spin-dependent force to the spin-Faraday law is the same as the time derivative of the spin geometric phase. With this observations, the spin-Faraday law is generalized to include both an Aharonov-Casher (AC) effect and a scalar AC effect in a unified manner.

Geometric Potential Assessment for ZY3-02 Triple Linear Array Imagery

Directory of Open Access Journals (Sweden)

Kai Xu

2017-06-01

Full Text Available ZiYuan3-02 (ZY3-02 is the first remote sensing satellite for the development of China’s civil space infrastructure (CCSI and the second satellite in the ZiYuan3 series; it was launched successfully on 30 May 2016, aboard the CZ-4B rocket at the Taiyuan Satellite Launch Center (TSLC in China. Core payloads of ZY3-02 include a triple linear array camera (TLC and a multi-spectral camera, and this equipment will be used to acquire space geographic information with high-resolution and stereoscopic observations. Geometric quality is a key factor that affects the performance and potential of satellite imagery. For the purpose of evaluating comprehensively the geometric potential of ZY3-02, this paper introduces the method used for geometric calibration of the TLC onboard the satellite and a model for sensor corrected (SC products that serve as basic products delivered to users. Evaluation work was conducted by making a full assessment of the geometric performance. Furthermore, images of six regions and corresponding reference data were collected to implement the geometric calibration technique and evaluate the resulting geometric accuracy. Experimental results showed that the direct location performance and internal accuracy of SC products increased remarkably after calibration, and the planimetric and vertical accuracies with relatively few ground control points (GCPs were demonstrated to be better than 2.5 m and 2 m, respectively. Additionally, the derived digital surface model (DSM accuracy was better than 3 m (RMSE for flat terrain and 5 m (RMSE for mountainous terrain. However, given that several variations such as changes in the thermal environment can alter the camera’s installation angle, geometric performance will vary with the geographical location and imaging time changes. Generally, ZY3-02 can be used for 1:50,000 stereo mapping and can produce (and update larger-scale basic geographic information products.

Far-field super-resolution imaging of resonant multiples

KAUST Repository

Guo, Bowen

2016-05-20

We demonstrate for the first time that seismic resonant multiples, usually considered as noise, can be used for super-resolution imaging in the far-field region of sources and receivers. Tests with both synthetic data and field data show that resonant multiples can image reflector boundaries with resolutions more than twice the classical resolution limit. Resolution increases with the order of the resonant multiples. This procedure has important applications in earthquake and exploration seismology, radar, sonar, LIDAR (light detection and ranging), and ultrasound imaging, where the multiples can be used to make high-resolution images.

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...

Geometrical illusions are not always where you think they are

Directory of Open Access Journals (Sweden)

Jacques eNinio

2014-10-01

Full Text Available Geometrical illusions are known through a small core of classical illusions that were discovered in the second half of the 19th century. Most experimental studies and most theoretical discussions revolve around this core of illusions, as though all other illusions were obvious variants of these. Yet, many illusions, mostly described by German authors at the same time or at the beginning of the 20th century have been forgotten and are awaiting their rehabilitation. Recently, several new illusions were discovered, mainly by Italian authors, and they do not seem to take place into any current classification. Among the principles that are invoked to explain the illusions, there are principles relating to the metric aspects (contrast, assimilation, shrinkage, expansion, attraction of parallels principles relating to orientations (regression to right angles, orthogonal expansion or, more recently, to gestalt effects. It is possible to oppose, to many a classical stimulus, an illusion that apparently contradicts the lesson derived from this stimulus. Furthermore, some well-known illusory patterns may not be illusions at all, they capture legitimate paradoxes of shape perception.Here, metric effects are discussed within a measurement framework, in which the geometric illusions are the outcome of a measurement process. There would be a main convexity bias in the measures: the measured value m(x of an extant x would grow more than proportionally with x. This convexity principle, completed by a principle of compromise for conflicting measures can replace, for a large number of patterns, both the assimilation and the contrast effects. We know from evolutionary theory that the most pertinent classification criteria may not be the most salient ones (e.g., a dolphin is not a mammal. In order to obtain an objective classification of illusions, I initiated with Kevin O’Regan systematic work on orientation profiles (describing how the strength of an illusion

Is Geometric Frustration-Induced Disorder a Recipe for High Ionic Conductivity?

Science.gov (United States)

Düvel, Andre; Heitjans, Paul; Fedorov, Pavel; Scholz, Gudrun; Cibin, Giannantonio; Chadwick, Alan V; Pickup, David M; Ramos, Silvia; Sayle, Lewis W L; Sayle, Emma K L; Sayle, Thi X T; Sayle, Dean C

2017-04-26

Ionic conductivity is ubiquitous to many industrially important applications such as fuel cells, batteries, sensors, and catalysis. Tunable conductivity in these systems is therefore key to their commercial viability. Here, we show that geometric frustration can be exploited as a vehicle for conductivity tuning. In particular, we imposed geometric frustration upon a prototypical system, CaF 2 , by ball milling it with BaF 2 , to create nanostructured Ba 1-x Ca x F 2 solid solutions and increased its ionic conductivity by over 5 orders of magnitude. By mirroring each experiment with MD simulation, including "simulating synthesis", we reveal that geometric frustration confers, on a system at ambient temperature, structural and dynamical attributes that are typically associated with heating a material above its superionic transition temperature. These include structural disorder, excess volume, pseudovacancy arrays, and collective transport mechanisms; we show that the excess volume correlates with ionic conductivity for the Ba 1-x Ca x F 2 system. We also present evidence that geometric frustration-induced conductivity is a general phenomenon, which may help explain the high ionic conductivity in doped fluorite-structured oxides such as ceria and zirconia, with application for solid oxide fuel cells. A review on geometric frustration [ Nature 2015 , 521 , 303 ] remarks that classical crystallography is inadequate to describe systems with correlated disorder, but that correlated disorder has clear crystallographic signatures. Here, we identify two possible crystallographic signatures of geometric frustration: excess volume and correlated "snake-like" ionic transport; the latter infers correlated disorder. In particular, as one ion in the chain moves, all the other (correlated) ions in the chain move simultaneously. Critically, our simulations reveal snake-like chains, over 40 Å in length, which indicates long-range correlation in our disordered systems. Similarly

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

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.

High-resolution CT findings of interstitial pneumonia in patients with dermatomyositis. Comparison between classic and amyopathic forms

International Nuclear Information System (INIS)

Watanabe, Wataru

2007-01-01

The objective of this study was to compare high-resolution CT (HRCT) findings of interstitial pneumonia associated with dermatomyositis (DM) based on disease form, classic (CDM) vs. amyopathic (ADM) form, and clinical presentation, acute or subacute vs. chronic presentation. HRCT findings of 18 patients (CDM 9, ADM 9) were reviewed retrospectively. HRCT was interpreted by two experienced, board-certified radiologists. Difference in the interpretation was settled by consensus. Frequency of the HRCT findings compared between CDM and ADM, and between acute or subacute and chronic presentation. The most frequent finding was bronchovascular bundle irregularity (77%), followed by ground-glass attenuation (72%), subpleural curvilinear shadow (72%) and parenchymal band (72%). Honeycombing was not noted in any case. Linear opacities were significantly more frequent, and bronchiectasis was significantly less frequent in ADM than in CDM (p<0.05). Bronchiectasis was more common in chronic than in acute/subacute presentation, but there was no statistically significant difference. HRCT findings of interstitial pneumonia associated with DM varied between CDM and ADM. Honeycombing was not noted in any case. Linear opacities were significantly more frequent, and bronchiectasis was significantly less frequent in ADM than in CDM. The findings on HRCT were not different between acute or subacute and chronic presentation. (author)

HIGH RESOLUTION AIRBORNE SHALLOW WATER MAPPING

Directory of Open Access Journals (Sweden)

F. Steinbacher

2012-07-01

Full Text Available In order to meet the requirements of the European Water Framework Directive (EU-WFD, authorities face the problem of repeatedly performing area-wide surveying of all kinds of inland waters. Especially for mid-sized or small rivers this is a considerable challenge imposing insurmountable logistical efforts and costs. It is therefore investigated if large-scale surveying of a river system on an operational basis is feasible by employing airborne hydrographic laser scanning. In cooperation with the Bavarian Water Authority (WWA Weilheim a pilot project was initiated by the Unit of Hydraulic Engineering at the University of Innsbruck and RIEGL Laser Measurement Systems exploiting the possibilities of a new LIDAR measurement system with high spatial resolution and high measurement rate to capture about 70 km of riverbed and foreland for the river Loisach in Bavaria/Germany and the estuary and parts of the shoreline (about 40km in length of lake Ammersee. The entire area surveyed was referenced to classic terrestrial cross-section surveys with the aim to derive products for the monitoring and managing needs of the inland water bodies forced by the EU-WFD. The survey was performed in July 2011 by helicopter and airplane and took 3 days in total. In addition, high resolution areal images were taken to provide an optical reference, offering a wide range of possibilities on further research, monitoring, and managing responsibilities. The operating altitude was about 500 m to maintain eye-safety, even for the aided eye, the airspeed was about 55 kts for the helicopter and 75 kts for the aircraft. The helicopter was used in the alpine regions while the fixed wing aircraft was used in the plains and the urban area, using appropriate scan rates to receive evenly distributed point clouds. The resulting point density ranged from 10 to 25 points per square meter. By carefully selecting days with optimum water quality, satisfactory penetration down to the river

High Resolution Airborne Shallow Water Mapping

Science.gov (United States)

Steinbacher, F.; Pfennigbauer, M.; Aufleger, M.; Ullrich, A.

2012-07-01

In order to meet the requirements of the European Water Framework Directive (EU-WFD), authorities face the problem of repeatedly performing area-wide surveying of all kinds of inland waters. Especially for mid-sized or small rivers this is a considerable challenge imposing insurmountable logistical efforts and costs. It is therefore investigated if large-scale surveying of a river system on an operational basis is feasible by employing airborne hydrographic laser scanning. In cooperation with the Bavarian Water Authority (WWA Weilheim) a pilot project was initiated by the Unit of Hydraulic Engineering at the University of Innsbruck and RIEGL Laser Measurement Systems exploiting the possibilities of a new LIDAR measurement system with high spatial resolution and high measurement rate to capture about 70 km of riverbed and foreland for the river Loisach in Bavaria/Germany and the estuary and parts of the shoreline (about 40km in length) of lake Ammersee. The entire area surveyed was referenced to classic terrestrial cross-section surveys with the aim to derive products for the monitoring and managing needs of the inland water bodies forced by the EU-WFD. The survey was performed in July 2011 by helicopter and airplane and took 3 days in total. In addition, high resolution areal images were taken to provide an optical reference, offering a wide range of possibilities on further research, monitoring, and managing responsibilities. The operating altitude was about 500 m to maintain eye-safety, even for the aided eye, the airspeed was about 55 kts for the helicopter and 75 kts for the aircraft. The helicopter was used in the alpine regions while the fixed wing aircraft was used in the plains and the urban area, using appropriate scan rates to receive evenly distributed point clouds. The resulting point density ranged from 10 to 25 points per square meter. By carefully selecting days with optimum water quality, satisfactory penetration down to the river bed was achieved

Classical field theory on electrodynamics, non-abelian gauge theories and gravitation

CERN Document Server

Scheck, Florian

2018-01-01

Scheck’s successful textbook presents a comprehensive treatment, ideally suited for a one-semester course. The textbook describes Maxwell's equations first in their integral, directly testable form, then moves on to their local formulation. The first two chapters cover all essential properties of Maxwell's equations, including their symmetries and their covariance in a modern notation. Chapter 3 is devoted to Maxwell's theory as a classical field theory and to solutions of the wave equation. Chapter 4 deals with important applications of Maxwell's theory. It includes topical subjects such as metamaterials with negative refraction index and solutions of Helmholtz' equation in paraxial approximation relevant for the description of laser beams. Chapter 5 describes non-Abelian gauge theories from a classical, geometric point of view, in analogy to Maxwell's theory as a prototype, and culminates in an application to the U(2) theory relevant for electroweak interactions. The last chapter 6 gives a concise summary...

Highway extraction from high resolution aerial photography using a geometric active contour model

Science.gov (United States)

Niu, Xutong

Highway extraction and vehicle detection are two of the most important steps in traffic-flow analysis from multi-frame aerial photographs. The traditional method of deriving traffic flow trajectories relies on manual vehicle counting from a sequence of aerial photographs, which is tedious and time-consuming. This research presents a new framework for semi-automatic highway extraction. The basis of the new framework is an improved geometric active contour (GAC) model. This novel model seeks to minimize an objective function that transforms a problem of propagation of regular curves into an optimization problem. The implementation of curve propagation is based on level set theory. By using an implicit representation of a two-dimensional curve, a level set approach can be used to deal with topological changes naturally, and the output is unaffected by different initial positions of the curve. However, the original GAC model, on which the new model is based, only incorporates boundary information into the curve propagation process. An error-producing phenomenon called leakage is inevitable wherever there is an uncertain weak edge. In this research, region-based information is added as a constraint into the original GAC model, thereby, giving this proposed method the ability of integrating both boundary and region-based information during the curve propagation. Adding the region-based constraint eliminates the leakage problem. This dissertation applies the proposed augmented GAC model to the problem of highway extraction from high-resolution aerial photography. First, an optimized stopping criterion is designed and used in the implementation of the GAC model. It effectively saves processing time and computations. Second, a seed point propagation framework is designed and implemented. This framework incorporates highway extraction, tracking, and linking into one procedure. A seed point is usually placed at an end node of highway segments close to the boundary of the

A Prefiltered Cuckoo Search Algorithm with Geometric Operators for Solving Sudoku Problems

Directory of Open Access Journals (Sweden)

Ricardo Soto

2014-01-01

Full Text Available The Sudoku is a famous logic-placement game, originally popularized in Japan and today widely employed as pastime and as testbed for search algorithms. The classic Sudoku consists in filling a 9×9 grid, divided into nine 3×3 regions, so that each column, row, and region contains different digits from 1 to 9. This game is known to be NP-complete, with existing various complete and incomplete search algorithms able to solve different instances of it. In this paper, we present a new cuckoo search algorithm for solving Sudoku puzzles combining prefiltering phases and geometric operations. The geometric operators allow one to correctly move toward promising regions of the combinatorial space, while the prefiltering phases are able to previously delete from domains the values that do not conduct to any feasible solution. This integration leads to a more efficient domain filtering and as a consequence to a faster solving process. We illustrate encouraging experimental results where our approach noticeably competes with the best approximate methods reported in the literature.

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.

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.

Artefacts in geometric phase analysis of compound materials

Energy Technology Data Exchange (ETDEWEB)

Peters, Jonathan J.P., E-mail: j.j.p.peters@warwick.ac.uk [Department of Physics, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL (United Kingdom); Beanland, Richard; Alexe, Marin [Department of Physics, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL (United Kingdom); Cockburn, John W.; Revin, Dmitry G.; Zhang, Shiyong Y. [Department of Physics and Astronomy, University of Sheffield, Hounsfield Road, Sheffield S3 7RH (United Kingdom); Sanchez, Ana M., E-mail: a.m.sanchez@warwick.ac.uk [Department of Physics, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL (United Kingdom)

2015-10-15

The geometric phase analysis (GPA) algorithm is known as a robust and straightforward technique that can be used to measure lattice strains in high resolution transmission electron microscope (TEM) images. It is also attractive for analysis of aberration-corrected scanning TEM (ac-STEM) images that resolve every atom column, since it uses Fourier transforms and does not require real-space peak detection and assignment to appropriate sublattices. Here it is demonstrated that, in ac-STEM images of compound materials with compositionally distinct atom columns, an additional geometric phase is present in the Fourier transform. If the structure changes from one area to another in the image (e.g. across an interface), the change in this additional phase will appear as a strain in conventional GPA, even if there is no lattice strain. Strategies to avoid this pitfall are outlined. - Highlights: • GPA is shown to produce incorrect strains when applied to images of compound materials. • A mathematical description is laid out for why GPA can produce artefacts. • The artefact is demonstrated using experimental and simulated data. • A ‘rule’ is set to avoid this artefact in GPA.

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 stochastic approach based on marked point processes for road mark detection from high resolution aerial images

Science.gov (United States)

Tournaire, O.; Paparoditis, N.

Road detection has been a topic of great interest in the photogrammetric and remote sensing communities since the end of the 70s. Many approaches dealing with various sensor resolutions, the nature of the scene or the wished accuracy of the extracted objects have been presented. This topic remains challenging today as the need for accurate and up-to-date data is becoming more and more important. Based on this context, we will study in this paper the road network from a particular point of view, focusing on road marks, and in particular dashed lines. Indeed, they are very useful clues, for evidence of a road, but also for tasks of a higher level. For instance, they can be used to enhance quality and to improve road databases. It is also possible to delineate the different circulation lanes, their width and functionality (speed limit, special lanes for buses or bicycles...). In this paper, we propose a new robust and accurate top-down approach for dashed line detection based on stochastic geometry. Our approach is automatic in the sense that no intervention from a human operator is necessary to initialise the algorithm or to track errors during the process. The core of our approach relies on defining geometric, radiometric and relational models for dashed lines objects. The model also has to deal with the interactions between the different objects making up a line, meaning that it introduces external knowledge taken from specifications. Our strategy is based on a stochastic method, and in particular marked point processes. Our goal is to find the objects configuration minimising an energy function made-up of a data attachment term measuring the consistency of the image with respect to the objects and a regularising term managing the relationship between neighbouring objects. To sample the energy function, we use Green algorithm's; coupled with a simulated annealing to find its minimum. Results from aerial images at various resolutions are presented showing that our

Evaluation of Geometrically Optimized Single- and Double-plane Interstitial High Dose Rate Implants with Respect to Conformality and Homogeneity

International Nuclear Information System (INIS)

Major, Tibor; Polgar, Csaba; Fodor, Janos; Takacsi-nagy, Zoltan; Mangel, Laszlo; Nemeth, Gyoergy

2003-01-01

The use of a stepping source in high dose rate brachytherapy supported with dwell-time optimization makes it possible to deviate from the classical dosimetry systems. Dose distributions of single- and double-plane implants were analysed for conformality and homogeneity at idealized target volumes. The Paris system was used for catheter positioning and target volume determination. Geometric optimization and individual dose prescription were applied. Volumetric indices and dose parameters were calculated at optimal active length, which was found to be equal to target volume length. The mean conformality, homogeneity, external volume and overdose volume indices were 0.78, 0.67, 0.22 and 0.13, respectively. The average minimum target and reference doses were 69% and 86%, respectively. Comparisons between the volumetric indices of geometrical optimized and non-optimized implants were also performed, and a significant difference was found regarding any index. The geometrical optimization resulted in superior conformality and slightly inferior homogeneity. At geometrically optimized implants, the active length can be reduced compared to non-optimized implants. Volumetric parameters and dose-volume histogram-based individual dose prescription are recommended for quantitative assessment of interstitial implants

A simulation study of high-resolution x-ray computed tomography imaging using irregular sampling with a photon-counting detector

International Nuclear Information System (INIS)

Lee, Seungwan; Choi, Yu-Na; Kim, Hee-Joung

2013-01-01

The purpose of this study was to improve the spatial resolution for the x-ray computed tomography (CT) imaging with a photon-counting detector using an irregular sampling method. The geometric shift-model of detector was proposed to produce the irregular sampling pattern and increase the number of samplings in the radial direction. The conventional micro-x-ray CT system and the novel system with the geometric shift-model of detector were simulated using analytic and Monte Carlo simulations. The projections were reconstructed using filtered back-projection (FBP), algebraic reconstruction technique (ART), and total variation (TV) minimization algorithms, and the reconstructed images were compared in terms of normalized root-mean-square error (NRMSE), full-width at half-maximum (FWHM), and coefficient-of-variation (COV). The results showed that the image quality improved in the novel system with the geometric shift-model of detector, and the NRMSE, FWHM, and COV were lower for the images reconstructed using the TV minimization technique in the novel system with the geometric shift-model of detector. The irregular sampling method produced by the geometric shift-model of detector can improve the spatial resolution and reduce artifacts and noise for reconstructed images obtained from an x-ray CT system with a photon-counting detector. -- Highlights: • We proposed a novel sampling method based on a spiral pattern to improve the spatial resolution. • The novel sampling method increased the number of samplings in the radial direction. • The spatial resolution was improved by the novel sampling method

Multiple-image hiding using super resolution reconstruction in high-frequency domains

Science.gov (United States)

Li, Xiao-Wei; Zhao, Wu-Xiang; Wang, Jun; Wang, Qiong-Hua

2017-12-01

In this paper, a robust multiple-image hiding method using the computer-generated integral imaging and the modified super-resolution reconstruction algorithm is proposed. In our work, the host image is first transformed into frequency domains by cellular automata (CA), to assure the quality of the stego-image, the secret images are embedded into the CA high-frequency domains. The proposed method has the following advantages: (1) robustness to geometric attacks because of the memory-distributed property of elemental images, (2) increasing quality of the reconstructed secret images as the scheme utilizes the modified super-resolution reconstruction algorithm. The simulation results show that the proposed multiple-image hiding method outperforms other similar hiding methods and is robust to some geometric attacks, e.g., Gaussian noise and JPEG compression attacks.

Resolution analysis in full waveform inversion

NARCIS (Netherlands)

Fichtner, A.; Trampert, J.

2011-01-01

We propose a new method for the quantitative resolution analysis in full seismic waveform inversion that overcomes the limitations of classical synthetic inversions while being computationally more efficient and applicable to any misfit measure. The method rests on (1) the local quadratic

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.

Geometric Methods in Physics : XXXIII Workshop

CERN Document Server

Bieliavsky, Pierre; Odzijewicz, Anatol; Schlichenmaier, Martin; Voronov, Theodore

2015-01-01

This book presents a selection of papers based on the XXXIII Białowieża Workshop on Geometric Methods in Physics, 2014. The Białowieża Workshops are among the most important meetings in the field and attract researchers from both mathematics and physics. The articles gathered here are mathematically rigorous and have important physical implications, addressing the application of geometry in classical and quantum physics. Despite their long tradition, the workshops remain at the cutting edge of ongoing research. For the last several years, each Białowieża Workshop has been followed by a School on Geometry and Physics, where advanced lectures for graduate students and young researchers are presented; some of the lectures are reproduced here. The unique atmosphere of the workshop and school is enhanced by its venue, framed by the natural beauty of the Białowieża forest in eastern Poland. The volume will be of interest to researchers and graduate students in mathematical physics, theoretical physics and m...

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…

Cepheids Geometrical Distances Using Space Interferometry

Science.gov (United States)

Marengo, M.; Karovska, M.; Sasselov, D. D.; Sanchez, M.

2004-05-01

A space based interferometer with a sub-milliarcsecond resolution in the UV-optical will provide a new avenue for the calibration of primary distance indicators with unprecedented accuracy, by allowing very accurate and stable measurements of Cepheids pulsation amplitudes at wavelengths not accessible from the ground. Sasselov & Karovska (1994) have shown that interferometers allow very accurate measurements of Cepheids distances by using a ``geometric'' variant of the Baade-Wesselink method. This method has been succesfully applied to derive distances and radii of nearby Cepheids using ground-based near-IR and optical interferometers, within a 15% accuracy level. Our study shows that the main source of error in these measurements is due to the perturbing effects of the Earth atmosphere, which is the limiting factor in the interferometer stability. A space interferometer will not suffer from this intrinsic limitations, and can potentially lead to improve astronomical distance measurements by an order of magnitude in precision. We discuss here the technical requirements that a space based facility will need to carry out this project, allowing distance measurements within a few percent accuracy level. We will finally discuss how a sub-milliarcsecond resolution will allow the direct distance determination for hundreds of galactic sources, and provide a substantial improvement in the zero-point of the Cepheid distance scale.

Solution of Inverse Kinematics for 6R Robot Manipulators With Offset Wrist Based on Geometric Algebra.

Science.gov (United States)

Fu, Zhongtao; Yang, Wenyu; Yang, Zhen

2013-08-01

In this paper, we present an efficient method based on geometric algebra for computing the solutions to the inverse kinematics problem (IKP) of the 6R robot manipulators with offset wrist. Due to the fact that there exist some difficulties to solve the inverse kinematics problem when the kinematics equations are complex, highly nonlinear, coupled and multiple solutions in terms of these robot manipulators stated mathematically, we apply the theory of Geometric Algebra to the kinematic modeling of 6R robot manipulators simply and generate closed-form kinematics equations, reformulate the problem as a generalized eigenvalue problem with symbolic elimination technique, and then yield 16 solutions. Finally, a spray painting robot, which conforms to the type of robot manipulators, is used as an example of implementation for the effectiveness and real-time of this method. The experimental results show that this method has a large advantage over the classical methods on geometric intuition, computation and real-time, and can be directly extended to all serial robot manipulators and completely automatized, which provides a new tool on the analysis and application of general robot manipulators.

Super-resolution from single photon emission: toward biological application

Science.gov (United States)

Moreva, E.; Traina, P.; Forneris, J.; Ditalia Tchernij, S.; Guarina, L.; Franchino, C.; Picollo, F.; Ruo Berchera, I.; Brida, G.; Degiovanni, I. P.; Carabelli, V.; Olivero, P.; Genovese, M.

2017-08-01

Properties of quantum light represent a tool for overcoming limits of classical optics. Several experiments have demonstrated this advantage ranging from quantum enhanced imaging to quantum illumination. In this work, experimental demonstration of quantum-enhanced resolution in confocal fluorescence microscopy will be presented. This is achieved by exploiting the non-classical photon statistics of fluorescence emission of single nitrogen-vacancy (NV) color centers in diamond. By developing a general model of super-resolution based on the direct sampling of the kth-order autocorrelation function of the photoluminescence signal, we show the possibility to resolve, in principle, arbitrarily close emitting centers. Finally, possible applications of NV-based fluorescent nanodiamonds in biosensing and future developments will be presented.

Classical confinement and outward convection of impurity ions in the MST RFP

Energy Technology Data Exchange (ETDEWEB)

Kumar, S. T. A.; Den Hartog, D. J.; Mirnov, V. V.; Eilerman, S.; Nornberg, M.; Reusch, J. A.; Sarff, J. S. [Department of Physics, University of Wisconsin-Madison, Madison, Wisconsin 53706 (United States); Center for Magnetic Self-Organization in Laboratory and Astrophysical Plasmas, University of Wisconsin-Madison, Madison, Wisconsin 53706 (United States); Caspary, K. J.; Chapman, B. E.; Parke, E. [Department of Physics, University of Wisconsin-Madison, Madison, Wisconsin 53706 (United States); Magee, R. M. [Department of Physics, West Virginia University, Morgantown, WV 26506 (United States); Brower, D. L.; Ding, W. X.; Lin, L. [Department of Physics and Astronomy, University of California, Los Angeles, California 90095 (United States); Craig, D. [Physics Department, Wheaton College, Wheaton, Illinois 60187 (United States); Fiksel, G. [Center for Magnetic Self-Organization in Laboratory and Astrophysical Plasmas, University of Wisconsin-Madison, Madison, Wisconsin 53706 (United States); Laboratory for Laser Energetics, University of Rochester, Rochester, New York (United States)

2012-05-15

Impurity ion dynamics measured with simultaneously high spatial and temporal resolution reveal classical ion transport in the reversed-field pinch. The boron, carbon, oxygen, and aluminum impurity ion density profiles are obtained in the Madison Symmetric Torus [R. N. Dexter et al., Fusion Technol. 19, 131 (1991)] using a fast, active charge-exchange-recombination-spectroscopy diagnostic. Measurements are made during improved-confinement plasmas obtained using inductive control of tearing instability to mitigate stochastic transport. At the onset of the transition to improved confinement, the impurity ion density profile becomes hollow, with a slow decay in the core region concurrent with an increase in the outer region, implying an outward convection of impurities. Impurity transport from Coulomb collisions in the reversed-field pinch is classical for all collisionality regimes, and analysis shows that the observed hollow profile and outward convection can be explained by the classical temperature screening mechanism. The profile agrees well with classical expectations. Experiments performed with impurity pellet injection provide further evidence for classical impurity ion confinement.

Construction of classical and non-classical coherent photon states

International Nuclear Information System (INIS)

Honegger, Reinhard; Rieckers, Alfred

2001-01-01

It is well known that the diagonal matrix elements of all-order coherent states for the quantized electromagnetic field have to constitute a Poisson distribution with respect to the photon number. The present work gives first the summary of a constructive scheme, developed previously, which determines in terms of an auxiliary Hilbert space all possible off-diagonal elements for the all-order coherent density operators in Fock space and which identifies all extremal coherent states. In terms of this formalism it is then demonstrated that each pure classical coherent state is a uniformly phase locked (quantum) coherent superposition of number states. In a mixed classical coherent state the exponential of the locked phase is shown to be replaced by a rather arbitrary unitary operator in the auxiliary Hilbert space. On the other hand classes for density operators--and for their normally ordered characteristic functions--of non-classical coherent states are obtained, especially by rather weak perturbations of classical coherent states. These illustrate various forms of breaking the classical uniform phase locking and exhibit rather peculiar properties, such as asymmetric fluctuations for the quadrature phase operators. Several criteria for non-classicality are put forward and applied to the elaborated non-classical coherent states, providing counterexamples against too simple arguments for classicality. It is concluded that classicality is only a stable concept for coherent states with macroscopic intensity

Classical, Semi-classical and Quantum Noise

CERN Document Server

Poor, H; Scully, Marlan

2012-01-01

David Middleton was a towering figure of 20th Century engineering and science and one of the founders of statistical communication theory. During the second World War, the young David Middleton, working with Van Fleck, devised the notion of the matched filter, which is the most basic method used for detecting signals in noise. Over the intervening six decades, the contributions of Middleton have become classics. This collection of essays by leading scientists, engineers and colleagues of David are in his honor and reflect the wide  influence that he has had on many fields. Also included is the introduction by Middleton to his forthcoming book, which gives a wonderful view of the field of communication, its history and his own views on the field that he developed over the past 60 years. Focusing on classical noise modeling and applications, Classical, Semi-Classical and Quantum Noise includes coverage of statistical communication theory, non-stationary noise, molecular footprints, noise suppression, Quantum e...

Classical properties and semiclassical quantization of a spherical nuclear potential

International Nuclear Information System (INIS)

Carbonell, J.; Brut, F.; Arvieu, R.; Touchard, J.

1984-03-01

The geometrical properties of the classical energy-action surface are studied for a nuclear Woods-Saxon-like spherical potential, in connection with the E.B.K. semiclassical method of quantization. Comparisons are made with other well known cases: the spherical harmonic oscillator and the spherical billiard. The shift of single particle energies from A = 208 to A = 16 is calculated by a simple method inspired by the Erhenfest adiabatic invariants. Semiclassical results are then compared with exact Schroedinger energies. It is seen that the most significant features of the single particle spectrum are explained by local properties of the energy action surface (curvature, slope) and by their evolution with the particle number

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.

Geometric Positioning Accuracy Improvement of ZY-3 Satellite Imagery Based on Statistical Learning Theory

Directory of Open Access Journals (Sweden)

Niangang Jiao

2018-05-01

Full Text Available With the increasing demand for high-resolution remote sensing images for mapping and monitoring the Earth’s environment, geometric positioning accuracy improvement plays a significant role in the image preprocessing step. Based on the statistical learning theory, we propose a new method to improve the geometric positioning accuracy without ground control points (GCPs. Multi-temporal images from the ZY-3 satellite are tested and the bias-compensated rational function model (RFM is applied as the block adjustment model in our experiment. An easy and stable weight strategy and the fast iterative shrinkage-thresholding (FIST algorithm which is widely used in the field of compressive sensing are improved and utilized to define the normal equation matrix and solve it. Then, the residual errors after traditional block adjustment are acquired and tested with the newly proposed inherent error compensation model based on statistical learning theory. The final results indicate that the geometric positioning accuracy of ZY-3 satellite imagery can be improved greatly with our proposed method.

Long-term stable time integration scheme for dynamic analysis of planar geometrically exact Timoshenko beams

Science.gov (United States)

Nguyen, Tien Long; Sansour, Carlo; Hjiaj, Mohammed

2017-05-01

In this paper, an energy-momentum method for geometrically exact Timoshenko-type beam is proposed. The classical time integration schemes in dynamics are known to exhibit instability in the non-linear regime. The so-called Timoshenko-type beam with the use of rotational degree of freedom leads to simpler strain relations and simpler expressions of the inertial terms as compared to the well known Bernoulli-type model. The treatment of the Bernoulli-model has been recently addressed by the authors. In this present work, we extend our approach of using the strain rates to define the strain fields to in-plane geometrically exact Timoshenko-type beams. The large rotational degrees of freedom are exactly computed. The well-known enhanced strain method is used to avoid locking phenomena. Conservation of energy, momentum and angular momentum is proved formally and numerically. The excellent performance of the formulation will be demonstrated through a range of examples.

Pulse radiolysis - new approaches to the classical technique

Energy Technology Data Exchange (ETDEWEB)

Zagorski, Z P [Institute of Nuclear Research, Warsaw (Poland)

1973-01-01

The present status of classical pulse radiolysis is described as well as trends in the further development of this technique (the investigation of radiolysis with nano- and picoseconds time resolution, new optica and electrochemical methods of intermediate species detection). The attention is concentrated on experimental difficulties of particular versions and the achievements are reviewed critically. This paper is the background for experiments being performed in the Institute of Nuclear Research on new techniques of pulse radiolysis.

Automatic cortical surface reconstruction of high-resolution T1 echo planar imaging data

OpenAIRE

Renvall, Ville; Witzel, Thomas; Wald, Lawrence L.; Polimeni, Jonathan R.

2016-01-01

Echo planar imaging (EPI) is the method of choice for the majority of functional magnetic resonance imaging (fMRI), yet EPI is prone to geometric distortions and thus misaligns with conventional anatomical reference data. The poor geometric correspondence between functional and anatomical data can lead to severe misplacements and corruption of detected activation patterns. However, recent advances in imaging technology have provided EPI data with increasing quality and resolution. Here we pre...

A comparison of classical histology to anatomy revealed by hard x-rays

Science.gov (United States)

Richter, Claus-Peter; Tan, Xiaodong; Young, Hunter; Stock, Stuart; Robinson, Alan; Byskosh, Orest; Zheng, Jing; Soriano, Carmen; Xiao, Xianghui; Whitlon, Donna

2016-10-01

Many diseases trigger morphological changes in affected tissue. Today, classical histology is still the "gold standard" used to study and describe those changes. Classical histology, however, is time consuming and requires chemical tissue manipulations that can result in significant tissue distortions. It is sometimes difficult to separate tissue-processing artifacts from changes caused by the disease process. We show that synchrotron X-ray phase-contrast micro-computed tomography (micro-CT) can be used to examine non-embedded, hydrated tissue at a resolution comparable to that obtained with classical histology. The data analysis from stacks of reconstructed micro-CT images is more flexible and faster than when using the classical, physically embedded sections that are by necessity fixed in a particular orientation. We show that in a three-dimensional (3D) structure with meticulous structural details such as the cochlea and the kidney, micro-CT is more flexible, faster and more convenient for morphological studies and disease diagnoses.

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.

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

Determination of scattering center of multipath signals using geometric optics and Fresnel zone concepts

Directory of Open Access Journals (Sweden)

Kamil Yavuz Kapusuz

2014-06-01

Full Text Available In this study, a method for determining scattering center (or center of scattering points of a multipath is proposed, provided that the direction of arrival of the multipath is known by the receiver. The method is based on classical electromagnetic wave principles in order to determine scattering center over irregular terrain. Geometrical optics (GO along with Fresnel zone concept is employed, as the receiver, the transmitter positions and irregular terrain data are assumed to be provided. The proposed method could be used at UHF bands, especially, operations of radars and electronic warfare applications.

MSCT versus CBCT: evaluation of high-resolution acquisition modes for dento-maxillary and skull-base imaging

Energy Technology Data Exchange (ETDEWEB)

Dillenseger, Jean-Philippe; Goetz, Christian [Hopitaux Universitaires de Strasbourg, Imagerie Preclinique-UF6237, Pole d' imagerie, Strasbourg (France); Universite de Strasbourg, Icube, equipe MMB, CNRS, Strasbourg (France); Universite de Strasbourg, Federation de Medecine Translationnelle de Strasbourg, Faculte de Medecine, Strasbourg (France); Matern, Jean-Francois [Hopitaux Universitaires de Strasbourg, Imagerie Preclinique-UF6237, Pole d' imagerie, Strasbourg (France); Universite de Strasbourg, Federation de Medecine Translationnelle de Strasbourg, Faculte de Medecine, Strasbourg (France); Gros, Catherine-Isabelle; Bornert, Fabien [Universite de Strasbourg, Federation de Medecine Translationnelle de Strasbourg, Faculte de Medecine, Strasbourg (France); Universite de Strasbourg, Faculte de Chirurgie Dentaire, Strasbourg (France); Le Minor, Jean-Marie [Universite de Strasbourg, Icube, equipe MMB, CNRS, Strasbourg (France); Universite de Strasbourg, Federation de Medecine Translationnelle de Strasbourg, Faculte de Medecine, Strasbourg (France); Universite de Strasbourg, Institut d' Anatomie Normale, Strasbourg (France); Constantinesco, Andre [Hopitaux Universitaires de Strasbourg, Imagerie Preclinique-UF6237, Pole d' imagerie, Strasbourg (France); Choquet, Philippe [Hopitaux Universitaires de Strasbourg, Imagerie Preclinique-UF6237, Pole d' imagerie, Strasbourg (France); Universite de Strasbourg, Icube, equipe MMB, CNRS, Strasbourg (France); Universite de Strasbourg, Federation de Medecine Translationnelle de Strasbourg, Faculte de Medecine, Strasbourg (France); Hopital de Hautepierre, Imagerie Preclinique, Biophysique et Medecine Nucleaire, Strasbourg Cedex (France)

2014-09-24

Our aim was to conduct a quantitative and qualitative evaluation of high-resolution skull-bone imaging for dentistry and otolaryngology using different architectures of recent X-ray computed tomography systems. Three multi-slice computed tomography (MSCT) systems and one Cone-beam computed tomography (CBCT) system were used in this study. All apparatuses were tested with installed acquisition modes and proprietary reconstruction software enabling high-resolution bone imaging. Quantitative analyses were performed with small fields of view with the preclinical vmCT phantom, which permits to measure spatial resolution, geometrical accuracy, linearity and homogeneity. Ten operators performed visual qualitative analyses on the vmCT phantom images, and on dry human skull images. Quantitative analysis showed no significant differences between protocols in terms of linearity and geometric accuracy. All MSCT systems present a better homogeneity than the CBCT. Both quantitative and visual analyses demonstrate that CBCT acquisitions are not better than the collimated helical MSCT mode. Our results demonstrate that current high-resolution MSCT protocols could exceed the performance of a previous generation CBCT system for spatial resolution and image homogeneity. (orig.)

MSCT versus CBCT: evaluation of high-resolution acquisition modes for dento-maxillary and skull-base imaging

International Nuclear Information System (INIS)

Dillenseger, Jean-Philippe; Goetz, Christian; Matern, Jean-Francois; Gros, Catherine-Isabelle; Bornert, Fabien; Le Minor, Jean-Marie; Constantinesco, Andre; Choquet, Philippe

2015-01-01

Our aim was to conduct a quantitative and qualitative evaluation of high-resolution skull-bone imaging for dentistry and otolaryngology using different architectures of recent X-ray computed tomography systems. Three multi-slice computed tomography (MSCT) systems and one Cone-beam computed tomography (CBCT) system were used in this study. All apparatuses were tested with installed acquisition modes and proprietary reconstruction software enabling high-resolution bone imaging. Quantitative analyses were performed with small fields of view with the preclinical vmCT phantom, which permits to measure spatial resolution, geometrical accuracy, linearity and homogeneity. Ten operators performed visual qualitative analyses on the vmCT phantom images, and on dry human skull images. Quantitative analysis showed no significant differences between protocols in terms of linearity and geometric accuracy. All MSCT systems present a better homogeneity than the CBCT. Both quantitative and visual analyses demonstrate that CBCT acquisitions are not better than the collimated helical MSCT mode. Our results demonstrate that current high-resolution MSCT protocols could exceed the performance of a previous generation CBCT system for spatial resolution and image homogeneity. (orig.)

DOA estimation for conformal vector-sensor array using geometric algebra

Science.gov (United States)

Meng, Tianzhen; Wu, Minjie; Yuan, Naichang

2017-12-01

In this paper, the problem of direction of arrival (DOA) estimation is considered in the case of multiple polarized signals impinging on the conformal electromagnetic vector-sensor array (CVA). We focus on modeling the manifold holistically by a new mathematical tool called geometric algebra. Compared with existing methods, the presented one has two main advantages. Firstly, it acquires higher resolution by preserving the orthogonality of the signal components. Secondly, it avoids the cumbersome matrix operations while performing the coordinate transformations, and therefore, has a much lower computational complexity. Simulation results are provided to demonstrate the effectiveness of the proposed algorithm.

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

The universal R-matrix and its associated quantum algebra as functionals of the classical r-matrix: the sl2 case

International Nuclear Information System (INIS)

Freidel, L.; Maillet, J.M.

1992-09-01

Using a geometrical approach to the quantum Yang-Baxter equation, the quantum algebra U h (sl 2 ) and its universal quantum R-matrix are explicitly constructed as functionals of the associated classical r-matrix. In this framework, the quantum algebra U h (sl 2 ) is naturally imbedded in the universal enveloping algebra of the sl 2 current algebra. (author) 13 refs

Geometric Model of Black Hole Quantum N-portrait, Extradimensions and Thermodynamics

Directory of Open Access Journals (Sweden)

Antonia M. Frassino

2016-05-01

Full Text Available Recently a short scale modified black hole metric, known as holographic metric, has been proposed in order to capture the self-complete character of gravity. In this paper we show that such a metric can reproduce some geometric features expected from the quantum N-portrait beyond the semi-classical limit. We show that for a generic N this corresponds to having an effective energy momentum tensor in Einstein equations or, equivalently, non-local terms in the gravity action. We also consider the higher dimensional extension of the metric and the case of an AdS cosmological term. We provide a detailed thermodynamic analysis of both cases, with particular reference to the repercussions on the Hawking-Page phase transition.

Physical principles, geometrical aspects, and locality properties of gauge field theories

International Nuclear Information System (INIS)

Mack, G.; Hamburg Univ.

1981-01-01

Gauge field theories, particularly Yang - Mills theories, are discussed at a classical level from a geometrical point of view. The introductory chapters are concentrated on physical principles and mathematical tools. The main part is devoted to locality problems in gauge field theories. Examples show that locality problems originate from two sources in pure Yang - Mills theories (without matter fields). One is topological and the other is related to the existence of degenerated field configurations of the infinitesimal holonomy groups on some extended region of space or space-time. Nondegenerate field configurations in theories with semisimple gauge groups can be analysed with the help of the concept of a local gauge. Such gauges play a central role in the discussion. (author)

Overcoming Registration Uncertainty in Image Super-Resolution: Maximize or Marginalize?

Directory of Open Access Journals (Sweden)

Andrew Zisserman

2007-01-01

Full Text Available In multiple-image super-resolution, a high-resolution image is estimated from a number of lower-resolution images. This usually involves computing the parameters of a generative imaging model (such as geometric and photometric registration, and blur and obtaining a MAP estimate by minimizing a cost function including an appropriate prior. Two alternative approaches are examined. First, both registrations and the super-resolution image are found simultaneously using a joint MAP optimization. Second, we perform Bayesian integration over the unknown image registration parameters, deriving a cost function whose only variables of interest are the pixel values of the super-resolution image. We also introduce a scheme to learn the parameters of the image prior as part of the super-resolution algorithm. We show examples on a number of real sequences including multiple stills, digital video, and DVDs of movies.

Geometric control theory for quantum back-action evasion

Energy Technology Data Exchange (ETDEWEB)

Yokotera, Yu; Yamamoto, Naoki [Keio University, Department of Applied Physics and Physico-Informatics, Yokohama (Japan)

2016-12-15

Engineering a sensor system for detecting an extremely tiny signal such as the gravitational-wave force is a very important subject in quantum physics. A major obstacle to this goal is that, in a simple detection setup, the measurement noise is lower bounded by the so-called standard quantum limit (SQL), which is originated from the intrinsic mechanical back-action noise. Hence, the sensor system has to be carefully engineered so that it evades the back-action noise and eventually beats the SQL. In this paper, based on the well-developed geometric control theory for classical disturbance decoupling problem, we provide a general method for designing an auxiliary (coherent feedback or direct interaction) controller for the sensor system to achieve the above-mentioned goal. This general theory is applied to a typical opto-mechanical sensor system. Also, we demonstrate a controller design for a practical situation where several experimental imperfections are present. (orig.)

Geometric control theory for quantum back-action evasion

International Nuclear Information System (INIS)

Yokotera, Yu; Yamamoto, Naoki

2016-01-01

Engineering a sensor system for detecting an extremely tiny signal such as the gravitational-wave force is a very important subject in quantum physics. A major obstacle to this goal is that, in a simple detection setup, the measurement noise is lower bounded by the so-called standard quantum limit (SQL), which is originated from the intrinsic mechanical back-action noise. Hence, the sensor system has to be carefully engineered so that it evades the back-action noise and eventually beats the SQL. In this paper, based on the well-developed geometric control theory for classical disturbance decoupling problem, we provide a general method for designing an auxiliary (coherent feedback or direct interaction) controller for the sensor system to achieve the above-mentioned goal. This general theory is applied to a typical opto-mechanical sensor system. Also, we demonstrate a controller design for a practical situation where several experimental imperfections are present. (orig.)

XXXIV Bialowieza Workshop on Geometric Methods in Physics

CERN Document Server

Ali, S; Bieliavsky, Pierre; Odzijewicz, Anatol; Schlichenmaier, Martin; Voronov, Theodore

2016-01-01

This book features a selection of articles based on the XXXIV Białowieża Workshop on Geometric Methods in Physics, 2015. The articles presented are mathematically rigorous, include important physical implications and address the application of geometry in classical and quantum physics. Special attention deserves the session devoted to discussions of Gerard Emch's most important and lasting achievements in mathematical physics. The Białowieża workshops are among the most important meetings in the field and gather participants from mathematics and physics alike. Despite their long tradition, the Workshops remain at the cutting edge of ongoing research. For the past several years, the Białowieża Workshop has been followed by a School on Geometry and Physics, where advanced lectures for graduate students and young researchers are presented. The unique atmosphere of the Workshop and School is enhanced by the venue, framed by the natural beauty of the Białowieża forest in eastern Poland.

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.

Reconstructed Image Spatial Resolution of Multiple Coincidences Compton Imager

Science.gov (United States)

Andreyev, Andriy; Sitek, Arkadiusz; Celler, Anna

2010-02-01

We study the multiple coincidences Compton imager (MCCI) which is based on a simultaneous acquisition of several photons emitted in cascade from a single nuclear decay. Theoretically, this technique should provide a major improvement in localization of a single radioactive source as compared to a standard Compton camera. In this work, we investigated the performance and limitations of MCCI using Monte Carlo computer simulations. Spatial resolutions of the reconstructed point source have been studied as a function of the MCCI parameters, including geometrical dimensions and detector characteristics such as materials, energy and spatial resolutions.

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

Discrete geometry: speculations on a new framework for classical electrodynamics

International Nuclear Information System (INIS)

Hemion, G.

1988-01-01

An attempt is made to describe the basic principles of physics in terms of discrete partially ordered sets. Geometric ideas are introduced by means of an action at a distance formulation of classical electrodynamics. The speculations are in two main directions: (i) Gravity, one of the four elementary forces of nature, seems to be fundamentally different from the other three forces. Could it be that gravity can be explained as a natural consequence of the discrete structure? (ii) The problem of the observer in quantum mechanics continues to cause conceptual problems. Can quantum statistics be explained in terms of finite ensembles of possible partially ordered sets? The development is guided at all stages by reference to the simplest, and most well-established principles of physics

Some studies on arithmetical chaos in classical and quantum mechanics

International Nuclear Information System (INIS)

Bolte, J.

1993-04-01

Several aspects of classical and quantum mechanics applied to a class of strongly chaotic systems are studied. The latter consists of single particles moving without external forces on surfaces of constant negative Gaussian curvature whose corresponding fundamental groups are supplied with an arithmetic structure. It is shown that the arithmetical features of the considered systems lead to exceptional properties of the corresponding spectra of lengths of closed geodesics (periodic orbits). The most significant one is an exponential growth of degeneracies in these geodesic length spectra. Furthermore, the arithmetical systems are distinguished by a structure that appears as a generalization of geometric symmetries. These pseudosymmetries occur in the quantization of the classical arithmetic systems as Hecke operators, which form an infinite algebra of self-adjoint operators commuting with the Hamiltonian. The statistical properties of quantum energies in the arithmetical systems have previously been identified as exceptional. They do not fit into the general scheme of random matrix theory. It is shown with the help of a simplified model for the spectral form factor how the spectral statistics in arithmetical quantum chaos can be understood by the properties of the corresponding classical geodesic length spectra. A decisive role is played by the exponentially increasing multiplicities of lengths. The model developed for the level spacings distribution and for the number variance is compared to the corresponding quantities obtained from quantum energies for a specific arithmetical system. Finally, the convergence properties of a representation for the Selberg zeta function as a Dirichlet series are studied. It turns out that the exceptional classical and quantum mechanical properties shared by the arithmetical systems prohibit a convergence of this important function in the physically interesting domain. (orig.)

Novel Geometrical Concept of a High Performance Brain PET Scanner Principle, Design and Performance Estimates

CERN Document Server

Séguinot, Jacques; Chesi, Enrico Guido; Joram, C; Mathot, S; Weilhammer, P; Chamizo-Llatas, M; Correia, J G; Ribeiro da Silva, M; Garibaldi, F; De Leo, R; Nappi, E; Corsi, F; Dragone, A; Schoenahl, F; Zaidi, H

2006-01-01

We present the principle, a possible implementation and performance estimates of a novel geometrical concept for a high resolution positron emission tomograph. The concept, which can for example be implemented in a brain PET device, promisses to lead to an essentially parallax free 3D image reconstruction with excellent spatial resolution and constrast, uniform over the complete field of view. The key components are matrices of long axially oriented scintillator crystals which are read out at both extremities by segmented Hybrid Photon Detectors. We discuss the relevant design considerations for a 3D axial PET camera module, motivate parameter and material choices, and estimate its performance in terms of spatial and energy resolution. We support these estimates by Monte Carlo simulations and in some cases by first experimental results. From the performance of a camera module, we extrapolate to the reconstruction resolution of a 3D axial PET scanner in a semi-analytical way and compare it to an existing state...

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)

Digital polarization holography advancing geometrical phase optics.

Science.gov (United States)

De Sio, Luciano; Roberts, David E; Liao, Zhi; Nersisyan, Sarik; Uskova, Olena; Wickboldt, Lloyd; Tabiryan, Nelson; Steeves, Diane M; Kimball, Brian R

2016-08-08

Geometrical phase or the fourth generation (4G) optics enables realization of optical components (lenses, prisms, gratings, spiral phase plates, etc.) by patterning the optical axis orientation in the plane of thin anisotropic films. Such components exhibit near 100% diffraction efficiency over a broadband of wavelengths. The films are obtained by coating liquid crystalline (LC) materials over substrates with patterned alignment conditions. Photo-anisotropic materials are used for producing desired alignment conditions at the substrate surface. We present and discuss here an opportunity of producing the widest variety of "free-form" 4G optical components with arbitrary spatial patterns of the optical anisotropy axis orientation with the aid of a digital spatial light polarization converter (DSLPC). The DSLPC is based on a reflective, high resolution spatial light modulator (SLM) combined with an "ad hoc" optical setup. The most attractive feature of the use of a DSLPC for photoalignment of nanometer thin photo-anisotropic coatings is that the orientation of the alignment layer, and therefore of the fabricated LC or LC polymer (LCP) components can be specified on a pixel-by-pixel basis with high spatial resolution. By varying the optical magnification or de-magnification the spatial resolution of the photoaligned layer can be adjusted to an optimum for each application. With a simple "click" it is possible to record different optical components as well as arbitrary patterns ranging from lenses to invisible labels and other transparent labels that reveal different images depending on the side from which they are viewed.

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.

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.

Classical emergence of intrinsic spin-orbit interaction of light at the nanoscale

Science.gov (United States)

Vázquez-Lozano, J. Enrique; Martínez, Alejandro

2018-03-01

Traditionally, in macroscopic geometrical optics intrinsic polarization and spatial degrees of freedom of light can be treated independently. However, at the subwavelength scale these properties appear to be coupled together, giving rise to the spin-orbit interaction (SOI) of light. In this work we address theoretically the classical emergence of the optical SOI at the nanoscale. By means of a full-vector analysis involving spherical vector waves we show that the spin-orbit factorizability condition, accounting for the mutual influence between the amplitude (spin) and phase (orbit), is fulfilled only in the far-field limit. On the other side, in the near-field region, an additional relative phase introduces an extra term that hinders the factorization and reveals an intricate dynamical behavior according to the SOI regime. As a result, we find a suitable theoretical framework able to capture analytically the main features of intrinsic SOI of light. Besides allowing for a better understanding into the mechanism leading to its classical emergence at the nanoscale, our approach may be useful to design experimental setups that enhance the response of SOI-based effects.

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

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)

Classical field theory. On electrodynamics, non-Abelian gauge theories and gravitation. 2. ed.

Energy Technology Data Exchange (ETDEWEB)

Scheck, Florian

2018-04-01

Scheck's successful textbook presents a comprehensive treatment, ideally suited for a one-semester course. The textbook describes Maxwell's equations first in their integral, directly testable form, then moves on to their local formulation. The first two chapters cover all essential properties of Maxwell's equations, including their symmetries and their covariance in a modern notation. Chapter 3 is devoted to Maxwell's theory as a classical field theory and to solutions of the wave equation. Chapter 4 deals with important applications of Maxwell's theory. It includes topical subjects such as metamaterials with negative refraction index and solutions of Helmholtz' equation in paraxial approximation relevant for the description of laser beams. Chapter 5 describes non-Abelian gauge theories from a classical, geometric point of view, in analogy to Maxwell's theory as a prototype, and culminates in an application to the U(2) theory relevant for electroweak interactions. The last chapter 6 gives a concise summary of semi-Riemannian geometry as the framework for the classical field theory of gravitation. The chapter concludes with a discussion of the Schwarzschild solution of Einstein's equations and the classical tests of general relativity. The new concept of this edition presents the content divided into two tracks: the fast track for master's students, providing the essentials, and the intensive track for all wanting to get in depth knowledge of the field. Cleary labeled material and sections guide students through the preferred level of treatment. Numerous problems and worked examples will provide successful access to Classical Field Theory.

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.

Recognition of Simple 3D Geometrical Objects under Partial Occlusion

Science.gov (United States)

Barchunova, Alexandra; Sommer, Gerald

In this paper we present a novel procedure for contour-based recognition of partially occluded three-dimensional objects. In our approach we use images of real and rendered objects whose contours have been deformed by a restricted change of the viewpoint. The preparatory part consists of contour extraction, preprocessing, local structure analysis and feature extraction. The main part deals with an extended construction and functionality of the classifier ensemble Adaptive Occlusion Classifier (AOC). It relies on a hierarchical fragmenting algorithm to perform a local structure analysis which is essential when dealing with occlusions. In the experimental part of this paper we present classification results for five classes of simple geometrical figures: prism, cylinder, half cylinder, a cube, and a bridge. We compare classification results for three classical feature extractors: Fourier descriptors, pseudo Zernike and Zernike moments.

The effects of spatial autoregressive dependencies on inference in ordinary least squares: a geometric approach

Science.gov (United States)

Smith, Tony E.; Lee, Ka Lok

2012-01-01

There is a common belief that the presence of residual spatial autocorrelation in ordinary least squares (OLS) regression leads to inflated significance levels in beta coefficients and, in particular, inflated levels relative to the more efficient spatial error model (SEM). However, our simulations show that this is not always the case. Hence, the purpose of this paper is to examine this question from a geometric viewpoint. The key idea is to characterize the OLS test statistic in terms of angle cosines and examine the geometric implications of this characterization. Our first result is to show that if the explanatory variables in the regression exhibit no spatial autocorrelation, then the distribution of test statistics for individual beta coefficients in OLS is independent of any spatial autocorrelation in the error term. Hence, inferences about betas exhibit all the optimality properties of the classic uncorrelated error case. However, a second more important series of results show that if spatial autocorrelation is present in both the dependent and explanatory variables, then the conventional wisdom is correct. In particular, even when an explanatory variable is statistically independent of the dependent variable, such joint spatial dependencies tend to produce "spurious correlation" that results in over-rejection of the null hypothesis. The underlying geometric nature of this problem is clarified by illustrative examples. The paper concludes with a brief discussion of some possible remedies for this problem.

Ghost Spectroscopy with Classical Thermal Light Emitted by a Superluminescent Diode

Science.gov (United States)

Janassek, Patrick; Blumenstein, Sébastien; Elsäßer, Wolfgang

2018-02-01

We propose and realize the first classical ghost-imaging (GI) experiment in the frequency or wavelength domain, thus performing ghost spectroscopy using thermal light exhibiting photon bunching. The required wavelength correlations are provided by light emitted by spectrally broadband near-infrared amplified spontaneous emission of a semiconductor-based superluminescent diode. They are characterized by wavelength-resolved intensity cross-correlation measurements utilizing two-photon-absorption interferometry. Finally, a real-world spectroscopic application of this ghost spectroscopy with a classical light scheme is demonstrated in which an absorption band of trichloromethane (chloroform) at 1214 nm is reconstructed with a spectral resolution of 10 nm as a proof-of-principle experiment. This ghost-spectroscopy work fills the gap of a hitherto missing analogy between the spatial and the spectral domain in classical GI modalities, with the expectation of contributing towards a broader dissemination of correlated photon ghost modalities, hence paving the way towards more applications which exploit the favorable advantages.

Patterns of neurovascular compression in patients with classic trigeminal neuralgia: A high-resolution MRI-based study

International Nuclear Information System (INIS)

Lorenzoni, José; David, Philippe; Levivier, Marc

2012-01-01

Purpose: To describe the anatomical characteristics and patterns of neurovascular compression in patients suffering classic trigeminal neuralgia (CTN), using high-resolution magnetic resonance imaging (MRI). Materials and methods: The analysis of the anatomy of the trigeminal nerve, brain stem and the vascular structures related to this nerve was made in 100 consecutive patients treated with a Gamma Knife radiosurgery for CTN between December 1999 and September 2004. MRI studies (T1, T1 enhanced and T2-SPIR) with axial, coronal and sagital simultaneous visualization were dynamically assessed using the software GammaPlan™. Three-dimensional reconstructions were also developed in some representative cases. Results: In 93 patients (93%), there were one or several vascular structures in contact, either, with the trigeminal nerve, or close to its origin in the pons. The superior cerebellar artery was involved in 71 cases (76%). Other vessels identified were the antero-inferior cerebellar artery, the basilar artery, the vertebral artery, and some venous structures. Vascular compression was found anywhere along the trigeminal nerve. The mean distance between the nerve compression and the origin of the nerve in the brainstem was 3.76 ± 2.9 mm (range 0–9.8 mm). In 39 patients (42%), the vascular compression was located proximally and in 42 (45%) the compression was located distally. Nerve dislocation or distortion by the vessel was observed in 30 cases (32%). Conclusions: The findings of this study are similar to those reported in surgical and autopsy series. This non-invasive MRI-based approach could be useful for diagnostic and therapeutic decisions in CTN, and it could help to understand its pathogenesis.

A high resolution large dynamic range TDC circuit implementation

International Nuclear Information System (INIS)

Lei Wuhu; Liu Songqiu; Ye Weiguo; Han Hui; Li Pengyu

2003-01-01

Time measurement technology is usually used in nuclear experimentation. There are many methods of time measurement. The implementation method of Time to Digital Conversion (TDC) by means of electronic is a classical technology. The range and resolution of TDC is different according with different usage. A wide range and high resolution TDC circuit, including its theory and implementation way, is introduced in this paper. The test result is also given. (authors)

A high resolution large dynamic range TDC circuit implementation

International Nuclear Information System (INIS)

Lei Wuhu; Liu Songqiu; Li Pengyu; Han Hui; Ye Yanlin

2005-01-01

Time measurement technology is usually used in nuclear experimentation. There are many methods of time measurement. The implementation method of Time to Digital Conversion (TDC) by means of electronics is a classical technology. The range and resolution of TDC is different according with different usage. A wide range and high resolution TDC circuit, including its theory and implementation way, is introduced in this paper. The test result is also given. (authors)

Classic-Ada(TM)

Science.gov (United States)

Valley, Lois

1989-01-01

The SPS product, Classic-Ada, is a software tool that supports object-oriented Ada programming with powerful inheritance and dynamic binding. Object Oriented Design (OOD) is an easy, natural development paradigm, but it is not supported by Ada. Following the DOD Ada mandate, SPS developed Classic-Ada to provide a tool which supports OOD and implements code in Ada. It consists of a design language, a code generator and a toolset. As a design language, Classic-Ada supports the object-oriented principles of information hiding, data abstraction, dynamic binding, and inheritance. It also supports natural reuse and incremental development through inheritance, code factoring, and Ada, Classic-Ada, dynamic binding and static binding in the same program. Only nine new constructs were added to Ada to provide object-oriented design capabilities. The Classic-Ada code generator translates user application code into fully compliant, ready-to-run, standard Ada. The Classic-Ada toolset is fully supported by SPS and consists of an object generator, a builder, a dictionary manager, and a reporter. Demonstrations of Classic-Ada and the Classic-Ada Browser were given at the workshop.

On the self-interference in electron scattering: Copenhagen, Bohmian and geometrical interpretations of quantum mechanics

Science.gov (United States)

Tavernelli, Ivano

2018-06-01

Self-interference embodies the essence of the particle-wave formulation of quantum mechanics (QM). According to the Copenhagen interpretation of QM, self-interference by a double-slit requires a large transverse coherence of the incident wavepacket such that it covers the separation between the slits. Bohmian dynamics provides a first step in the separation of the particle-wave character of matter by introducing deterministic trajectories guided by a pilot wave that follows the time-dependent Schrödinger equation. In this work, I present a new description of the phenomenon of self-interference using the geometrical formulation of QM introduced in Tavernelli (2016). In particular, this formalism removes the need for the concept of wavefunction collapse in the interpretation of the act of measurement i.e., the emergence of the classical world. The three QM formulations (Schrödinger, Bohmian, and geometrical) are applied to the description of the scattering of a free electron by a hydrogen atom and a double-slit. The corresponding interpretations of self-interference are compared and discussed.

The Uniform geometrical Theory of Diffraction for elastodynamics: Plane wave scattering from a half-plane.

Science.gov (United States)

Djakou, Audrey Kamta; Darmon, Michel; Fradkin, Larissa; Potel, Catherine

2015-11-01

Diffraction phenomena studied in electromagnetism, acoustics, and elastodynamics are often modeled using integrals, such as the well-known Sommerfeld integral. The far field asymptotic evaluation of such integrals obtained using the method of steepest descent leads to the classical Geometrical Theory of Diffraction (GTD). It is well known that the method of steepest descent is inapplicable when the integrand's stationary phase point coalesces with its pole, explaining why GTD fails in zones where edge diffracted waves interfere with incident or reflected waves. To overcome this drawback, the Uniform geometrical Theory of Diffraction (UTD) has been developed previously in electromagnetism, based on a ray theory, which is particularly easy to implement. In this paper, UTD is developed for the canonical elastodynamic problem of the scattering of a plane wave by a half-plane. UTD is then compared to another uniform extension of GTD, the Uniform Asymptotic Theory (UAT) of diffraction, based on a more cumbersome ray theory. A good agreement between the two methods is obtained in the far field.

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....

Phase-Sensitive Coherence and the Classical-Quantum Boundary in Ghost Imaging

Science.gov (United States)

Erkmen, Baris I.; Hardy, Nicholas D.; Venkatraman, Dheera; Wong, Franco N. C.; Shapiro, Jeffrey H.

2011-01-01

The theory of partial coherence has a long and storied history in classical statistical optics. the vast majority of this work addresses fields that are statistically stationary in time, hence their complex envelopes only have phase-insensitive correlations. The quantum optics of squeezed-state generation, however, depends on nonlinear interactions producing baseband field operators with phase-insensitive and phase-sensitive correlations. Utilizing quantum light to enhance imaging has been a topic of considerable current interest, much of it involving biphotons, i.e., streams of entangled-photon pairs. Biphotons have been employed for quantum versions of optical coherence tomography, ghost imaging, holography, and lithography. However, their seemingly quantum features have been mimicked with classical-sate light, questioning wherein lies the classical-quantum boundary. We have shown, for the case of Gaussian-state light, that this boundary is intimately connected to the theory of phase-sensitive partial coherence. Here we present that theory, contrasting it with the familiar case of phase-insensitive partial coherence, and use it to elucidate the classical-quantum boundary of ghost imaging. We show, both theoretically and experimentally, that classical phase-sensitive light produces ghost imaging most closely mimicking those obtained in biphotons, and we derived the spatial resolution, image contrast, and signal-to-noise ratio of a standoff-sensing ghost imager, taking into account target-induced speckle.

The quantum Higgs field and the resolution of the cosmological constant paradox in the Weyl-geometrical Universe

Science.gov (United States)

de Martini, Francesco

The nature of the scalar field responsible for the cosmological inflation is found to be rooted in the most fundamental concept of the Weyl’s differential geometry: the parallel displacement of vectors in curved spacetime. Within this novel geometrical scenario, the standard electroweak theory of leptons based on the SU(2)L⊗U(1)Y as well as on the conformal groups of spacetime Weyl’s transformations is analyzed within the framework of a general-relativistic, conformally-covariant scalar-tensor theory that includes the electromagnetic and the Yang-Mills fields. A Higgs mechanism within a spontaneous symmetry breaking process is identified and this offers formal connections between some relevant properties of the elementary particles and the dark energy content of the Universe. An “effective cosmological potential”: Veff is expressed in terms of the dark energy potential: |VΛ| via the “mass reduction parameter”: |ζ|≡|Veff||VΛ|, a general property of the Universe. The mass of the Higgs boson, which is considered a “free parameter” by the standard electroweak theory, by our theory is found to be proportional to the mass MU≡|Veff| which contributes to the measured Cosmological Constant, i.e. the measured content of vacuum-energy in the Universe. The nonintegrable application of the Weyl’s geometry leads to a Proca equation accounting for the dynamics of a ϕρ-particle, a vector-meson proposed as an optimum candidate for Dark Matter. The peculiar mathematical structure of Veff offers a clue towards a very general resolution in 4-D of a most intriguing puzzle of modern quantum field theory, the “cosmological constant paradox”(here referred to as: “Λ-paradox”). Indeed, our “universal” theory offers a resolution of the “Λ-paradox” for all exponential inflationary potentials: VΛ(ϕ)∝e‑nϕ, and for all linear superpositions of these potentials, where n belongs to the mathematical set of the “real numbers”. An explicit

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

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)

Loire Classics: Reviving Classicism in some Loire Poets

Directory of Open Access Journals (Sweden)

Wim Verbaal

2017-06-01

Full Text Available The term 'Loire poets' has come to refer to a rather undefinable group of poets that in the second half of the eleventh century distinguishes itself through its refined poetics. They are often characterized as medieval humanists thanks to their renewed interest in the classics. Sometimes their movement is labelled a 'classicist' one. But what does this 'classicism' mean? Is it even permitted to speak of medieval 'classicisms'? This contribution approaches the question of whether we can apply this modern label to pre-modern phenomena. Moreover, it explores the changes in attitude towards the classics that sets the Loire poets off from their predecessors and contemporaries. The article focuses on poems by Hildebert of Lavardin, Baudri of Bourgueil, Marbod of Rennes, and Geoffrey of Reims. They are compared with some contemporary poets, such as Reginald of Canterbury and Sigebert of Gembloux.

Classical antiparticles

International Nuclear Information System (INIS)

Costella, J.P.; McKellar, B.H.J.; Rawlinson, A.A.

1997-03-01

We review how antiparticles may be introduced in classical relativistic mechanics, and emphasize that many of their paradoxical properties can be more transparently understood in the classical than in the quantum domain. (authors)

System for simultaneously measuring 6DOF geometric motion errors using a polarization maintaining fiber-coupled dual-frequency laser.

Science.gov (United States)

Cui, Cunxing; Feng, Qibo; Zhang, Bin; Zhao, Yuqiong

2016-03-21

A novel method for simultaneously measuring six degree-of-freedom (6DOF) geometric motion errors is proposed in this paper, and the corresponding measurement instrument is developed. Simultaneous measurement of 6DOF geometric motion errors using a polarization maintaining fiber-coupled dual-frequency laser is accomplished for the first time to the best of the authors' knowledge. Dual-frequency laser beams that are orthogonally linear polarized were adopted as the measuring datum. Positioning error measurement was achieved by heterodyne interferometry, and other 5DOF geometric motion errors were obtained by fiber collimation measurement. A series of experiments was performed to verify the effectiveness of the developed instrument. The experimental results showed that the stability and accuracy of the positioning error measurement are 31.1 nm and 0.5 μm, respectively. For the straightness error measurements, the stability and resolution are 60 and 40 nm, respectively, and the maximum deviation of repeatability is ± 0.15 μm in the x direction and ± 0.1 μm in the y direction. For pitch and yaw measurements, the stabilities are 0.03″ and 0.04″, the maximum deviations of repeatability are ± 0.18″ and ± 0.24″, and the accuracies are 0.4″ and 0.35″, respectively. The stability and resolution of roll measurement are 0.29″ and 0.2″, respectively, and the accuracy is 0.6″.

State-dependent classical potentials

International Nuclear Information System (INIS)

D'Amico, M.

2001-01-01

As alternative treatment to the potential operators of standard quantum mechanics is presented. The method is derived from Bohm's mechanics. The operator scalar (V) and vector (A) potential functions are replaced by a quantum potential. It is argued that the classical potential is a special limiting case of a more general quantum potential. The theory is illustrated by deriving an equivalent single-particle equation for the i-th particle of an n-body Bohmian system. The resulting effective state-dependent potential holds the interaction between the single-particle self-wave ψ s and the environment wave ψ e of the n - 1 remaining particles. The effective state-dependent potential is offered as a resolution to the Aharonov-Bohm effect where the phase difference is shown to result from the presence of ψ e . Finally, the interaction between ψ s and ψ e is illustrated graphically

Macroscopic polarization in crystalline dielectrics: the geometric phase approach

International Nuclear Information System (INIS)

Resta, R.

1994-01-01

The macroscopic electric polarization of a crystal is often defined as the dipole of a unit cell. In fact, such a dipole moment is ill defined, and the above definition is incorrect. Looking more closely, the quantity generally measured is differential polarization, defined with respect to a ''reference state'' of the same material. Such differential polarizations include either derivatives of the polarization (dielectric permittivity, Born effective charges, piezoelectricity, pyroelectricity) or finite differences (ferroelectricity). On the theoretical side, the differential concept is basic as well. Owing to continuity, a polarization difference is equivalent to a macroscopic current, which is directly accessible to the theory as a bulk property. Polarization is a quantum phenomenon and cannot be treated with a classical model, particularly whenever delocalized valence electrons are present in the dielectric. In a quantum picture, the current is basically a property of the phase of the wave functions, as opposed to the charge, which is a property of their modulus. An elegant and complete theory has recently been developed by King-Smith and Vanderbilt, in which the polarization difference between any two crystal states--in a null electric field--takes the form of a geometric quantum phase. This gives a comprehensive account of this theory, which is relevant for dealing with transverse-optic phonons, piezoelectricity, and ferroelectricity. Its relation to the established concepts of linear-response theory is also discussed. Within the geometric phase approach, the relevant polarization difference occurs as the circuit integral of a Berry connection (or ''vector potential''), while the corresponding curvature (or ''magnetic field'') provides the macroscopic linear response

Remote parallel rendering for high-resolution tiled display walls

KAUST Repository

Nachbaur, Daniel; Dumusc, Raphael; Bilgili, Ahmet; Hernando, Juan; Eilemann, Stefan

2014-01-01

© 2014 IEEE. We present a complete, robust and simple to use hardware and software stack delivering remote parallel rendering of complex geometrical and volumetric models to high resolution tiled display walls in a production environment. We describe the setup and configuration, present preliminary benchmarks showing interactive framerates, and describe our contributions for a seamless integration of all the software components.

Remote parallel rendering for high-resolution tiled display walls

KAUST Repository

Nachbaur, Daniel

2014-11-01

© 2014 IEEE. We present a complete, robust and simple to use hardware and software stack delivering remote parallel rendering of complex geometrical and volumetric models to high resolution tiled display walls in a production environment. We describe the setup and configuration, present preliminary benchmarks showing interactive framerates, and describe our contributions for a seamless integration of all the software components.

Generalized Geometric Quantum Speed Limits

Directory of Open Access Journals (Sweden)

Diego Paiva Pires

2016-06-01

Full Text Available The attempt to gain a theoretical understanding of the concept of time in quantum mechanics has triggered significant progress towards the search for faster and more efficient quantum technologies. One of such advances consists in the interpretation of the time-energy uncertainty relations as lower bounds for the minimal evolution time between two distinguishable states of a quantum system, also known as quantum speed limits. We investigate how the nonuniqueness of a bona fide measure of distinguishability defined on the quantum-state space affects the quantum speed limits and can be exploited in order to derive improved bounds. Specifically, we establish an infinite family of quantum speed limits valid for unitary and nonunitary evolutions, based on an elegant information geometric formalism. Our work unifies and generalizes existing results on quantum speed limits and provides instances of novel bounds that are tighter than any established one based on the conventional quantum Fisher information. We illustrate our findings with relevant examples, demonstrating the importance of choosing different information metrics for open system dynamics, as well as clarifying the roles of classical populations versus quantum coherences, in the determination and saturation of the speed limits. Our results can find applications in the optimization and control of quantum technologies such as quantum computation and metrology, and might provide new insights in fundamental investigations of quantum thermodynamics.

Geometric 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

OpenAIRE

Jones, Keith

1998-01-01

With the growth in interest in geometrical ideas it is important to be clear about the nature of geometrical reasoning and how it develops. This paper provides an overview of three theoretical frameworks for the learning of geometrical reasoning: the van Hiele model of thinking in geometry, Fischbein’s theory of figural concepts, and Duval’s cognitive model of geometrical reasoning. Each of these frameworks provides theoretical resources to support research into the development of geometrical...

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

Hyper-resolution urban flood modeling using high-resolution radar precipitation and LiDAR data

Science.gov (United States)

Noh, S. J.; Lee, S.; Lee, J.; Seo, D. J.

2016-12-01

Floods occur most frequently among all natural hazards, often causing widespread economic damage and loss of human lives. In particular, urban flooding is becoming increasingly costly and difficult to manage with a greater concentration of population and assets in urban centers. Despite of known benefits for accurate representation of small scale features and flow interaction among different flow domains, which have significant impact on flood propagation, high-resolution modeling has not been fully utilized due to expensive computation and various uncertainties from model structure, input and parameters. In this study, we assess the potential of hyper-resolution hydrologic-hydraulic modeling using high-resolution radar precipitation and LiDAR data for improved urban flood prediction and hazard mapping. We describe a hyper-resolution 1D-2D coupled urban flood model for pipe and surface flows and evaluate the accuracy of the street-level inundation information produced. For detailed geometric representation of urban areas and for computational efficiency, we use 1 m-resolution topographical data, processed from LiDAR measurements, in conjunction with adaptive mesh refinement. For street-level simulation in large urban areas at grid sizes of 1 to 10 m, a hybrid parallel computing scheme using MPI and openMP is also implemented in a high-performance computing system. The modeling approach developed is applied for the Johnson Creek Catchment ( 40 km2), which makes up the Arlington Urban Hydroinformatics Testbed. In addition, discussion will be given on availability of hyper-resolution simulation archive for improved real-time flood mapping.

Regular Polygons and Geometric Series.

Science.gov (United States)

Jarrett, Joscelyn A.

1982-01-01

Examples of some geometric illustrations of limits are presented. It is believed the limit concept is among the most important topics in mathematics, yet many students do not have good intuitive feelings for the concept, since it is often taught very abstractly. Geometric examples are suggested as meaningful tools. (MP)

Classical and modern power spectrum estimation for tune measurement in CSNS RCS

International Nuclear Information System (INIS)

Yang Xiaoyu; Xu Taoguang; Fu Shinian; Zeng Lei; Bian Xiaojuan

2013-01-01

Precise measurement of betatron tune is required for good operating condition of CSNS RCS. The fractional part of betatron tune is important and it can be measured by analyzing the signals of beam position from the appointed BPM. Usually these signals are contaminated during the acquisition process, therefore several power spectrum methods are used to improve the frequency resolution. In this article classical and modern power spectrum methods are used. In order to compare their performance, the results of simulation data and IQT data from J-PARC RCS are discussed. It is shown that modern power spectrum estimation has better performance than the classical ones, though the calculation is more complex. (authors)

Geometric Invariants and Object Recognition.

Science.gov (United States)

1992-08-01

University of Chicago Press. Maybank , S.J. [1992], "The Projection of Two Non-coplanar Conics", in Geometric Invariance in Machine Vision, eds. J.L...J.L. Mundy and A. Zisserman, MIT Press, Cambridge, MA. Mundy, J.L., Kapur, .. , Maybank , S.J., and Quan, L. [1992a] "Geometric Inter- pretation of

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.

Resolution enhancement in medical ultrasound imaging.

Science.gov (United States)

Ploquin, Marie; Basarab, Adrian; Kouamé, Denis

2015-01-01

Image resolution enhancement is a problem of considerable interest in all medical imaging modalities. Unlike general purpose imaging or video processing, for a very long time, medical image resolution enhancement has been based on optimization of the imaging devices. Although some recent works purport to deal with image postprocessing, much remains to be done regarding medical image enhancement via postprocessing, especially in ultrasound imaging. We face a resolution improvement issue in the case of medical ultrasound imaging. We propose to investigate this problem using multidimensional autoregressive (AR) models. Noting that the estimation of the envelope of an ultrasound radio frequency (RF) signal is very similar to the estimation of classical Fourier-based power spectrum estimation, we theoretically show that a domain change and a multidimensional AR model can be used to achieve super-resolution in ultrasound imaging provided the order is estimated correctly. Here, this is done by means of a technique that simultaneously estimates the order and the parameters of a multidimensional model using relevant regression matrix factorization. Doing so, the proposed method specifically fits ultrasound imaging and provides an estimated envelope. Moreover, an expression that links the theoretical image resolution to both the image acquisition features (such as the point spread function) and a postprocessing feature (the AR model) order is derived. The overall contribution of this work is threefold. First, it allows for automatic resolution improvement. Through a simple model and without any specific manual algorithmic parameter tuning, as is used in common methods, the proposed technique simply and exclusively uses the ultrasound RF signal as input and provides the improved B-mode as output. Second, it allows for the a priori prediction of the improvement in resolution via the knowledge of the parametric model order before actual processing. Finally, to achieve the

PLEIADES HR IN FLIGHT GEOMETRICAL CALIBRATION : LOCATION AND MAPPING OF THE FOCAL PLANE

Directory of Open Access Journals (Sweden)

F. de Lussy

2012-07-01

Full Text Available The Pleiades system, ORFEO system optical component (Optical and Radar Federated Earth Observation consists of a constellation of two satellites for very High Resolution panchromatic and multispectral optical observation of the Earth. Its mission is to cover all European civilian needs (mapping, tracking floods and fires and defence in the category of metric resolution: 0.7m Nadir. The first Pleiades satellite was launched at the end of last year. One of the key objectives of the Pleiades HR (PHR project is to achieve a location accuracy that will allow the use of images in GIS (Geographical Information System without geometrical model improvement by refining on ground control points. The image location without refined model was specified with the precision of the most commonly used tool ie the civil GPS. So the location accuracy has been specified at less than 12m for 90% of the images on a nominal satellite configuration. Very special care has been taken all along the PHR project realization to achieve this very good location accuracy. The final touch is given during the in-orbit commissioning phase which lasts until June 2012. The geometric quality implies to tune the parameters involved in the geolocation model (geometric calibration: besides attitude and orbit restitution tuning (not considered here, it consists in estimating the biases between the instrument orientation and the AOCS reference frame, and also the sight line of each detector in the focal plane. This is called static geometrical model. The analysis of dynamic perturbations outside of the model are the second most important image quality objective of in-flight commissioning, not described in this paper. Finally “image quality assessment” consists in evaluating the image quality obtained in the final products. For geolocation model, it is quantified by the absolute geolocation and the pointing accuracies, and it is a main contributor in length alteration and planimetric and

EVALUATION OF RATIONAL FUNCTION MODEL FOR GEOMETRIC MODELING OF CHANG'E-1 CCD IMAGES

Directory of Open Access Journals (Sweden)

Y. Liu

2012-08-01

Full Text Available Rational Function Model (RFM is a generic geometric model that has been widely used in geometric processing of high-resolution earth-observation satellite images, due to its generality and excellent capability of fitting complex rigorous sensor models. In this paper, the feasibility and precision of RFM for geometric modeling of China's Chang'E-1 (CE-1 lunar orbiter images is presented. The RFM parameters of forward-, nadir- and backward-looking CE-1 images are generated though least squares solution using virtual control points derived from the rigorous sensor model. The precision of the RFM is evaluated by comparing with the rigorous sensor model in both image space and object space. Experimental results using nine images from three orbits show that RFM can precisely fit the rigorous sensor model of CE-1 CCD images with a RMS residual error of 1/100 pixel level in image space and less than 5 meters in object space. This indicates that it is feasible to use RFM to describe the imaging geometry of CE-1 CCD images and spacecraft position and orientation. RFM will enable planetary data centers to have an option to supply RFM parameters of orbital images while keeping the original orbit trajectory data confidential.

Effect of track etch rate on geometric track characteristics for polymeric track detectors

International Nuclear Information System (INIS)

Abdel-Naby, A.A.; El-Akkad, F.A.

2001-01-01

Analysis of the variable track etch rate on geometric track characteristic for polymeric track detectors has been applied to the case of LR-155 II SSNTD. Spectrometric characteristics of low energy alpha particles response by the polymeric detector have been obtained. The track etching kinematics theory of development of minor diameter of the etched tracks has been applied. The calculations show that, for this type of detector, the energy dependence of the minor track diameter d is linear for small-etched removal layer h. The energy resolution gets better for higher etched removal layer

Bateman's dual system revisited: quantization, geometric phase and relation with the ground-state energy of the linear harmonic oscillator

International Nuclear Information System (INIS)

Blasone, Massimo; Jizba, Petr

2004-01-01

By using the Feynman-Hibbs prescription for the evolution amplitude, we quantize the system of a damped harmonic oscillator coupled to its time-reversed image, known as Bateman's dual system. The time-dependent quantum states of such a system are constructed and discussed entirely in the framework of the classical theory. The corresponding geometric (Pancharatnam) phase is calculated and found to be directly related to the ground-state energy of the 1D linear harmonic oscillator to which the 2D system reduces under appropriate constraint

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)

Guide to Geometric Algebra in Practice

CERN Document Server

Dorst, Leo

2011-01-01

This highly practical "Guide to Geometric Algebra in Practice" reviews algebraic techniques for geometrical problems in computer science and engineering, and the relationships between them. The topics covered range from powerful new theoretical developments, to successful applications, and the development of new software and hardware tools. This title: provides hands-on review exercises throughout the book, together with helpful chapter summaries; presents a concise introductory tutorial to conformal geometric algebra (CGA) in the appendices; examines the application of CGA for the d

Closed-Form Solutions for Gradient Elastic Beams with Geometric Discontinuities by Laplace Transform

Directory of Open Access Journals (Sweden)

Mustafa Özgür Yayli

2013-01-01

Full Text Available The static bending solution of a gradient elastic beam with external discontinuities is presented by Laplace transform. Its utility lies in the ability to switch differential equations to algebraic forms that are more easily solved. A Laplace transformation is applied to the governing equation which is then solved for the static deflection of the microbeam. The exact static response of the gradient elastic beam with external discontinuities is obtained by applying known initial conditions when the others are derived from boundary conditions. The results are given in a series of figures and compared with their classical counterparts. The main contribution of this paper is to provide a closed-form solution for the static deflection of microbeams under geometric discontinuities.

Application of up-sampling and resolution scaling to Fresnel reconstruction of digital holograms.

Science.gov (United States)

Williams, Logan A; Nehmetallah, Georges; Aylo, Rola; Banerjee, Partha P

2015-02-20

Fresnel transform implementation methods using numerical preprocessing techniques are investigated in this paper. First, it is shown that up-sampling dramatically reduces the minimum reconstruction distance requirements and allows maximal signal recovery by eliminating aliasing artifacts which typically occur at distances much less than the Rayleigh range of the object. Second, zero-padding is employed to arbitrarily scale numerical resolution for the purpose of resolution matching multiple holograms, where each hologram is recorded using dissimilar geometric or illumination parameters. Such preprocessing yields numerical resolution scaling at any distance. Both techniques are extensively illustrated using experimental results.

Geometric Phases for Mixed States in Trapped Ions

International Nuclear Information System (INIS)

Lu Hongxia

2006-01-01

The generalization of geometric phase from the pure states to the mixed states may have potential applications in constructing geometric quantum gates. We here investigate the mixed state geometric phases and visibilities of the trapped ion system in both non-degenerate and degenerate cases. In the proposed quantum system, the geometric phases are determined by the evolution time, the initial states of trapped ions, and the initial states of photons. Moreover, special periods are gained under which the geometric phases do not change with the initial states changing of photon parts in both non-degenerate and degenerate cases. The high detection efficiency in the ion trap system implies that the mixed state geometric phases proposed here can be easily tested.

Space-time evolution of a growth fold (Betic Cordillera, Spain). Evidences from 3D geometrical modelling

Science.gov (United States)

Martin-Rojas, Ivan; Alfaro, Pedro; Estévez, Antonio

2014-05-01

We present a study that encompasses several software tools (iGIS©, ArcGIS©, Autocad©, etc.) and data (geological mapping, high resolution digital topographic data, high resolution aerial photographs, etc.) to create a detailed 3D geometric model of an active fault propagation growth fold. This 3D model clearly shows structural features of the analysed fold, as well as growth relationships and sedimentary patterns. The results obtained permit us to discuss the kinematics and structural evolution of the fold and the fault in time and space. The study fault propagation fold is the Crevillente syncline. This fold represents the northern limit of the Bajo Segura Basin, an intermontane basin in the Eastern Betic Cordillera (SE Spain) developed from upper Miocene on. 3D features of the Crevillente syncline, including growth pattern, indicate that limb rotation and, consequently, fault activity was higher during Messinian than during Tortonian; consequently, fault activity was also higher. From Pliocene on our data point that limb rotation and fault activity steadies or probably decreases. This in time evolution of the Crevillente syncline is not the same all along the structure; actually the 3D geometric model indicates that observed lateral heterogeneity is related to along strike variation of fault displacement.

Energy flow in a bound electromagnetic field: resolution of apparent paradoxes

International Nuclear Information System (INIS)

Kholmetskii, A L; Yarman, T

2008-01-01

In this paper, we present a resolution of apparent paradoxes formulated in (Kholmetskii A L 2006 Apparent paradoxes in classical electrodynamics: the energy-momentum conservation law for a bound electromagnetic field Eur. J. Phys. 27 825-38; Kholmetskii A L and Yarman T 2008 Apparent paradoxes in classical electrodynamics: a fluid medium in an electromagnetic field Eur. J. Phys. 29 1127) and dealing with the energy flux in a bound electromagnetic field

Exact Solutions for Einstein's Hyperbolic Geometric Flow

International Nuclear Information System (INIS)

He Chunlei

2008-01-01

In this paper we investigate the Einstein's hyperbolic geometric flow and obtain some interesting exact solutions for this kind of flow. Many interesting properties of these exact solutions have also been analyzed and we believe that these properties of Einstein's hyperbolic geometric flow are very helpful to understanding the Einstein equations and the hyperbolic geometric flow

The Wigner representation of classical mechanics, quantization and classical limit

Energy Technology Data Exchange (ETDEWEB)

Bolivar, A.O. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)

2001-08-01

Starting from the Liouvillian formulation of classical physics it is possible by means of a Fourier transform to introduce the Wigner representation and to derive an operator structure to classical mechanisms. The importance of this new representation lies on the fact that it turns out to be suitable route to establish a general method of quantization directly from the equations of motion without alluding to the existence of Hamiltonian and Lagrangian functions. Following this approach we quantize only the motion of a Browian particle with non-linear friction in the Markovian approximation - the thermal bath may be quantum or classical -, thus when the bath is classically described we obtain a master equation which reduces to Caldeira-Legget equation for the linear friction case, and when the reservoir is quantum we get an equation reducing to the one found by Caldeira et al. By neglecting the environmental influence we show that the system can be approximately described by equations of motion in terms of wave function, such as the Schrodinger-Langevin equation and equations of the Caldirola-Kanai type. Finally to make the present study self-consistent we evaluate the classical limit of these dynamical equations employing a new classical limiting method h/2{pi} {yields} 0. (author)

The Wigner representation of classical mechanics, quantization and classical limit

International Nuclear Information System (INIS)

Bolivar, A.O.

2001-08-01

Starting from the Liouvillian formulation of classical physics it is possible by means of a Fourier transform to introduce the Wigner representation and to derive an operator structure to classical mechanisms. The importance of this new representation lies on the fact that it turns out to be suitable route to establish a general method of quantization directly from the equations of motion without alluding to the existence of Hamiltonian and Lagrangian functions. Following this approach we quantize only the motion of a Browian particle with non-linear friction in the Markovian approximation - the thermal bath may be quantum or classical -, thus when the bath is classically described we obtain a master equation which reduces to Caldeira-Legget equation for the linear friction case, and when the reservoir is quantum we get an equation reducing to the one found by Caldeira et al. By neglecting the environmental influence we show that the system can be approximately described by equations of motion in terms of wave function, such as the Schrodinger-Langevin equation and equations of the Caldirola-Kanai type. Finally to make the present study self-consistent we evaluate the classical limit of these dynamical equations employing a new classical limiting method h/2π → 0. (author)

Geometric control theory and sub-Riemannian geometry

CERN Document Server

Boscain, Ugo; Gauthier, Jean-Paul; Sarychev, Andrey; Sigalotti, Mario

2014-01-01

This volume presents recent advances in the interaction between Geometric Control Theory and sub-Riemannian geometry. On the one hand, Geometric Control Theory used the differential geometric and Lie algebraic language for studying controllability, motion planning, stabilizability and optimality for control systems. The geometric approach turned out to be fruitful in applications to robotics, vision modeling, mathematical physics etc. On the other hand, Riemannian geometry and its generalizations, such as  sub-Riemannian, Finslerian  geometry etc., have been actively adopting methods developed in the scope of geometric control. Application of these methods  has led to important results regarding geometry of sub-Riemannian spaces, regularity of sub-Riemannian distances, properties of the group  of diffeomorphisms of sub-Riemannian manifolds, local geometry and equivalence of distributions and sub-Riemannian structures, regularity of the Hausdorff volume.

Simultaneous correction of attenuation and geometric response in emission tomography applied to nuclear waste drums

International Nuclear Information System (INIS)

Thierry, Raphael

1999-01-01

Multi-photonic emission tomography is a non destructive technique applied to the control of radioactive waste drums. The emitted gamma rays are detected on the range [50 keV, 2 MeV] by a hyper pure germanium, of high resolution in energy, which enables to set up a detailed list of radionuclides contained within the drum. From different points of measurement located in a transaxial plane of the drum, the activity distribution is computed by a reconstruction algorithm. An algebraic modelling of the physical process has been developed in order to correct the different degrading phenomenon, in particular the attenuation and the detector geometric response. Attenuation through the materials constituting the barrel is the preponderant phenomena. Its ignorance prevents from accurate activity quantification. Its correction has been realised from an attenuation map obtained by a transmission tomograph. The detector geometric response, introducing a blurring within the detection, is compensated by an analytic model. An adequate modelling of those phenomenon is primordial: it highly contributes on a large scale the image quality and the quantification. The image reconstruction, requiring the resolution of sparse linear system, is realised by iterative algorithms. Due to the 'ill-posed' nature of tomographic reconstruction, it is necessary to use regularisation: by introducing an a priori information on the solution, the stabilisation of the methods is carried out. We chose to minimise the Maximum A Posteriori criterion. Its resolution is considered with a half-quadratic regularisation: it permits the preservation of natural discontinuities, and avoids global-over smoothing of the image. It is evaluated on real phantoms and waste drums. Efficient sampling of the data is considered. (author) [fr

Exit and Voice: Organizational Loyalty and Dispute Resolution Strategies

Science.gov (United States)

Hoffmann, Elizabeth A.

2006-01-01

This study compares workplace dispute resolution strategies (exit, voice and toleration) in matched pairs of conventional and worker-owned cooperative organizations operating in three industries--coal mining, taxicab driving and organic food distribution. Building on Hirschman's classic exit, voice and loyalty thesis, this research demonstrates…

A geometric morphometric analysis of hominin lower molars: Evolutionary implications and overview of postcanine dental variation.

Science.gov (United States)

Gómez-Robles, Aida; Bermúdez de Castro, José María; Martinón-Torres, María; Prado-Simón, Leyre; Arsuaga, Juan Luis

2015-05-01

Lower molars have been extensively studied in the context of hominin evolution using classic and geometric morphometric analyses, 2D and 3D approaches, evaluations of the external (outer enamel surface) and internal anatomy (dentine, pulp chamber, and radicular canals), and studies of the crown and root variation. In this study, we present a 2D geometric morphometric analysis of the crown anatomy of lower first, second, and third molars of a broad sample of hominins, including Pliocene and Lower, Middle, and Upper Pleistocene species coming from Africa, Asia, and Europe. We show that shape variability increases from first to second and third molars. While first molars tend to retain a relatively stable 5-cusped conformation throughout the hominin fossil record, second and third molars show marked distal reductions in later Homo species. This trend to distal reduction is similar to that observed in previous studies of premolars and upper second and third molars, and points to a correlated reduction of distal areas across the whole postcanine dentition. Results on lower molar variation, as well as on other postcanine teeth, show certain trends in European Pleistocene populations from the Atapuerca sites. Middle Pleistocene hominins from Sima de los Huesos show Neanderthal affinities and strong dental reduction, especially in the most distal molars. The degree of dental reduction in this population is stronger than that observed in classic Neanderthals. Homo antecessor hominins from Gran Dolina-TD6 have primitive lower teeth that contrast with their more derived upper teeth. The evolutionary implications of these dental affinities are discussed in light of recent paleogenetic studies. Copyright © 2015 Elsevier Ltd. All rights reserved.

Lectures on geometrical properties of nuclei

International Nuclear Information System (INIS)

Myers, W.D.

1975-11-01

Material concerning the geometrical properties of nuclei is drawn from a number of different sources. The leptodermous nature of nuclear density distributions and potential wells is used to draw together the various geometrical properties of these systems and to provide a unified means for their description. Extensive use is made of expansions of radial properties in terms of the surface diffuseness. A strong case is made for the use of convolution as a geometrical ansatz for generating diffuse surface distributions because of the number of simplifications that arise which are of practical importance. 7 figures

Why aortic elasticity differs among classical and non-classical mitral valve prolapsed?

Science.gov (United States)

Unlu, Murat; Demirkol, Sait; Aparci, Mustafa; Arslan, Zekeriya; Balta, Sevket; Dogan, Umuttan; Kilicarslan, Baris; Ozeke, Ozcan; Celik, Turgay; Iyisoy, Atila

2014-01-01

Mitral valve prolapse (MVP) is the most common valvular heart disease and characterized by the displacement of an abnormally thickened mitral valve leaflet into the left atrium during systole. There are two types of MVP, broadly classified as classic (thickness ≥5 mm) and non-classic (thickness elastic properties of the aorta in young male patients with classical and non-classical MVP. In the present study, 63 young adult males (mean age: 22.7 ± 4.2) were included. Patients were divided into classic MVP (n = 27) and non-classic MVP (n = 36) groups. Aortic strain, aortic distensibility and aortic stiffness index were calculated by using aortic diameters obtained by echocardiography and blood pressures measured by sphygmomanometer. There was no significant difference between the groups in terms of age, body mass index, left ventricular mass and ejection fraction. When comparing the MVP group it was found that aortic strain and aortic distensibility were increased (p = 0.0027, p = 0.016, respectively) whereas the aortic stiffness index was decreased (p = 0.06) in the classical MVP group. We concluded that the elastic properties of the aorta is increased in patients with classic MVP. Further large scale studies should be performed to understand of morphological and physiological properties of the aorta in patients with MVP.

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.

Classicality in quantum mechanics

Energy Technology Data Exchange (ETDEWEB)

Dreyer, Olaf [Theoretical Physics, Blackett Laboratory, Imperial College London, London, SW7 2AZ (United Kingdom)

2007-05-15

In this article we propose a solution to the measurement problem in quantum mechanics. We point out that the measurement problem can be traced to an a priori notion of classicality in the formulation of quantum mechanics. If this notion of classicality is dropped and instead classicality is defined in purely quantum mechanical terms the measurement problem can be avoided. We give such a definition of classicality. It identifies classicality as a property of large quantum system. We show how the probabilistic nature of quantum mechanics is a result of this notion of classicality. We also comment on what the implications of this view are for the search of a quantum theory of gravity.

Classicality in quantum mechanics

International Nuclear Information System (INIS)

Dreyer, Olaf

2007-01-01

In this article we propose a solution to the measurement problem in quantum mechanics. We point out that the measurement problem can be traced to an a priori notion of classicality in the formulation of quantum mechanics. If this notion of classicality is dropped and instead classicality is defined in purely quantum mechanical terms the measurement problem can be avoided. We give such a definition of classicality. It identifies classicality as a property of large quantum system. We show how the probabilistic nature of quantum mechanics is a result of this notion of classicality. We also comment on what the implications of this view are for the search of a quantum theory of gravity

DEM RECONSTRUCTION USING LIGHT FIELD AND BIDIRECTIONAL REFLECTANCE FUNCTION FROM MULTI-VIEW HIGH RESOLUTION SPATIAL IMAGES

Directory of Open Access Journals (Sweden)

F. de Vieilleville

2016-06-01

Full Text Available This paper presents a method for dense DSM reconstruction from high resolution, mono sensor, passive imagery, spatial panchromatic image sequence. The interest of our approach is four-fold. Firstly, we extend the core of light field approaches using an explicit BRDF model from the Image Synthesis community which is more realistic than the Lambertian model. The chosen model is the Cook-Torrance BRDF which enables us to model rough surfaces with specular effects using specific material parameters. Secondly, we extend light field approaches for non-pinhole sensors and non-rectilinear motion by using a proper geometric transformation on the image sequence. Thirdly, we produce a 3D volume cost embodying all the tested possible heights and filter it using simple methods such as Volume Cost Filtering or variational optimal methods. We have tested our method on a Pleiades image sequence on various locations with dense urban buildings and report encouraging results with respect to classic multi-label methods such as MIC-MAC, or more recent pipelines such as S2P. Last but not least, our method also produces maps of material parameters on the estimated points, allowing us to simplify building classification or road extraction.

Geometric phases for mixed states during cyclic evolutions

International Nuclear Information System (INIS)

Fu Libin; Chen Jingling

2004-01-01

The geometric phases of cyclic evolutions for mixed states are discussed in the framework of unitary evolution. A canonical 1-form is defined whose line integral gives the geometric phase, which is gauge invariant. It reduces to the Aharonov and Anandan phase in the pure state case. Our definition is consistent with the phase shift in the proposed experiment (Sjoeqvist et al 2000 Phys. Rev. Lett. 85 2845) for a cyclic evolution if the unitary transformation satisfies the parallel transport condition. A comprehensive geometric interpretation is also given. It shows that the geometric phases for mixed states share the same geometric sense with the pure states

Differential geometric structures

CERN Document Server

Poor, Walter A

2007-01-01

This introductory text defines geometric structure by specifying parallel transport in an appropriate fiber bundle and focusing on simplest cases of linear parallel transport in a vector bundle. 1981 edition.

Controlling the transport of an ion: classical and quantum mechanical solutions

International Nuclear Information System (INIS)

Fürst, H A; Poschinger, U G; Schmidt-Kaler, F; Singer, K; Goerz, M H; Koch, C P; Murphy, M; Montangero, S; Calarco, T

2014-01-01

The accurate transport of an ion over macroscopic distances represents a challenging control problem due to the different length and time scales that enter and the experimental limitations on the controls that need to be accounted for. Here, we investigate the performance of different control techniques for ion transport in state-of-the-art segmented miniaturized ion traps. We employ numerical optimization of classical trajectories and quantum wavepacket propagation as well as analytical solutions derived from invariant based inverse engineering and geometric optimal control. The applicability of each of the control methods depends on the length and time scales of the transport. Our comprehensive set of tools allows us make a number of observations. We find that accurate shuttling can be performed with operation times below the trap oscillation period. The maximum speed is limited by the maximum acceleration that can be exerted on the ion. When using controls obtained from classical dynamics for wavepacket propagation, wavepacket squeezing is the only quantum effect that comes into play for a large range of trapping parameters. We show that this can be corrected by a compensating force derived from invariant based inverse engineering, without a significant increase in the operation time. (paper)

Classical testing particles and (4 + N)-dimensional theories of space-time

International Nuclear Information System (INIS)

Nieto-Garcia, J.A.

1986-01-01

The Lagrangian theory of a classical relativistic spinning test particle (top) developed by Hanson and Regge and by Hojman is briefly reviewed. Special attention is devoted to the constraints imposed on the dynamical variables associated with the system of this theory. The equations for a relativistic top are formulated in a way suitable for use in the study of geometrical properties of the 4 + N-dimensional Kaluza-Klein background. It is shown that the equations of motion of a top in five dimensions reduce to the Hanson-Regge generalization of the Bargmann-Michel-Telegdi equations of motion in four dimensions when suitable conditions on the spin tensor are imposed. The classical bosonic relativistic string theory is discussed and the connection of this theory with the top theory is examined. It is found that the relation between the string and the top leads naturally to the consideration of a 3-dimensional extended system (called terron) which sweeps out a 4-dimensional surface as it evolves in a space-time. By using a square root procedure based on ideas by Teitelboim a theory of a supersymmetric top is developed. The quantization of the new supersymmetric system is discussed. Conclusions and suggestions for further research are given

J/sub z/-preserving propensities in molecular collisions. I. Quantal coupled states and classical impulsive approximations

International Nuclear Information System (INIS)

Khare, V.; Kouri, D.J.; Hoffman, D.K.

1981-01-01

The occurrence of j/sub z/-preserving propensities in atom--linear molecule collisions is considered within the contexts of the quantum mechanical CS approximation and of a classical model collision system. The latter involves an impulsive interaction which is the extreme limit of the class of potentials for which the CS approximation is expected to be valid. The classical model results in exact conservation of j/sub z/ along a ''kinematic apse.'' Quantum mechanically, the CS approximation is reformulated in a manner that clearly shows the relationship between the l choice and the degree and direction of j/sub z/ preservation. Away from the forward direction, the simplest choice obeying time reversal symmetry l=(l-script+l')/2, is shown to result in a propensity for preserving j/sub z/ along a ''geometric apse'' which coincides with the kinematic apse in the energy sudden limit, and for nonenergy sudden systems only differs significantly from it close to the forward direction

Random electrodynamics: the theory of classical electrodynamics with classical electromagnetic zero-point radiation

International Nuclear Information System (INIS)

Boyer, T.H.

1975-01-01

The theory of classical electrodynamics with classical electromagnetic zero-point radiation is outlined here under the title random electrodynamics. The work represents a reanalysis of the bounds of validity of classical electron theory which should sharpen the understanding of the connections and distinctions between classical and quantum theories. The new theory of random electrodynamics is a classical electron theory involving Newton's equations for particle motion due to the Lorentz force, and Maxwell's equations for the electromagnetic fields with point particles as sources. However, the theory departs from the classical electron theory of Lorentz in that it adopts a new boundary condition on Maxwell's equations. It is assumed that the homogeneous boundary condition involves random classical electromagnetic radiation with a Lorentz-invariant spectrum, classical electromagnetic zero-point radiation. The implications of random electrodynamics for atomic structure, atomic spectra, and particle-interference effects are discussed on an order-of-magnitude or heuristic level. Some detailed mathematical connections and some merely heuristic connections are noted between random electrodynamics and quantum theory. (U.S.)

Geometrical optics and the diffraction phenomenon

International Nuclear Information System (INIS)

Timofeev, Aleksandr V

2005-01-01

This note outlines the principles of the geometrical optics of inhomogeneous waves whose description necessitates the use of complex values of the wave vector. Generalizing geometrical optics to inhomogeneous waves permits including in its scope the analysis of the diffraction phenomenon. (methodological notes)

J. Genet. classic 101

Indian Academy of Sciences (India)

Journal of Genetics, Vol. 85, No. 2, August 2006. 101. Page 2. J. Genet. classic. 102. Journal of Genetics, Vol. 85, No. 2, August 2006. Page 3. J. Genet. classic. Journal of Genetics, Vol. 85, No. 2, August 2006. 103. Page 4. J. Genet. classic. 104. Journal of Genetics, Vol. 85, No. 2, August 2006. Page 5. J. Genet. classic.

J. Genet. classic 37

Indian Academy of Sciences (India)

Unknown

Journal of Genetics, Vol. 84, No. 1, April 2005. 37. Page 2. J. Genet. classic. Journal of Genetics, Vol. 84, No. 1, April 2005. 38. Page 3. J. Genet. classic. Journal of Genetics, Vol. 84, No. 1, April 2005. 39. Page 4. J. Genet. classic. Journal of Genetics, Vol. 84, No. 1, April 2005. 40. Page 5. J. Genet. classic. Journal of ...

Geometric U-folds in four dimensions

Science.gov (United States)

Lazaroiu, C. I.; Shahbazi, C. S.

2018-01-01

We describe a general construction of geometric U-folds compatible with a non-trivial extension of the global formulation of four-dimensional extended supergravity on a differentiable spin manifold. The topology of geometric U-folds depends on certain flat fiber bundles which encode how supergravity fields are globally glued together. We show that smooth non-trivial U-folds of this type can exist only in theories where both the scalar and space-time manifolds have non-trivial fundamental group and in addition the scalar map of the solution is homotopically non-trivial. Consistency with string theory requires smooth geometric U-folds to be glued using subgroups of the effective discrete U-duality group, implying that the fundamental group of the scalar manifold of such solutions must be a subgroup of the latter. We construct simple examples of geometric U-folds in a generalization of the axion-dilaton model of \

Towards high resolution polarisation analysis using double polarisation and ellipsoidal analysers

CERN Document Server

Martin-Y-Marero, D

2002-01-01

Classical polarisation analysis methods lack the combination of high resolution and high count rate necessary to cope with the demand of modern condensed-matter experiments. In this work, we present a method to achieve high resolution polarisation analysis based on a double polarisation system. Coupling this method with an ellipsoidal wavelength analyser, a high count rate can be achieved whilst delivering a resolution of around 10 mu eV. This method is ideally suited to pulsed sources, although it can be adapted to continuous sources as well. (orig.)

Forward error correction based on algebraic-geometric theory

CERN Document Server

A Alzubi, Jafar; M Chen, Thomas

2014-01-01

This book covers the design, construction, and implementation of algebraic-geometric codes from Hermitian curves. Matlab simulations of algebraic-geometric codes and Reed-Solomon codes compare their bit error rate using different modulation schemes over additive white Gaussian noise channel model. Simulation results of Algebraic-geometric codes bit error rate performance using quadrature amplitude modulation (16QAM and 64QAM) are presented for the first time and shown to outperform Reed-Solomon codes at various code rates and channel models. The book proposes algebraic-geometric block turbo codes. It also presents simulation results that show an improved bit error rate performance at the cost of high system complexity due to using algebraic-geometric codes and Chase-Pyndiah’s algorithm simultaneously. The book proposes algebraic-geometric irregular block turbo codes (AG-IBTC) to reduce system complexity. Simulation results for AG-IBTCs are presented for the first time.

Efficient fully 3D list-mode TOF PET image reconstruction using a factorized system matrix with an image domain resolution model

International Nuclear Information System (INIS)

Zhou, Jian; Qi, Jinyi

2014-01-01

A factorized system matrix utilizing an image domain resolution model is attractive in fully 3D time-of-flight PET image reconstruction using list-mode data. In this paper, we study a factored model based on sparse matrix factorization that is comprised primarily of a simplified geometrical projection matrix and an image blurring matrix. Beside the commonly-used Siddon’s ray-tracer, we propose another more simplified geometrical projector based on the Bresenham’s ray-tracer which further reduces the computational cost. We discuss in general how to obtain an image blurring matrix associated with a geometrical projector, and provide theoretical analysis that can be used to inspect the efficiency in model factorization. In simulation studies, we investigate the performance of the proposed sparse factorization model in terms of spatial resolution, noise properties and computational cost. The quantitative results reveal that the factorization model can be as efficient as a non-factored model, while its computational cost can be much lower. In addition we conduct Monte Carlo simulations to identify the conditions under which the image resolution model can become more efficient in terms of image contrast recovery. We verify our observations using the provided theoretical analysis. The result offers a general guide to achieve the optimal reconstruction performance based on a sparse factorization model with an image domain resolution model. (paper)

Refined geometric transition and qq-characters

Science.gov (United States)

Kimura, Taro; Mori, Hironori; Sugimoto, Yuji

2018-01-01

We show the refinement of the prescription for the geometric transition in the refined topological string theory and, as its application, discuss a possibility to describe qq-characters from the string theory point of view. Though the suggested way to operate the refined geometric transition has passed through several checks, it is additionally found in this paper that the presence of the preferred direction brings a nontrivial effect. We provide the modified formula involving this point. We then apply our prescription of the refined geometric transition to proposing the stringy description of doubly quantized Seiberg-Witten curves called qq-characters in certain cases.

Design and construction of an Offner spectrometer based on geometrical analysis of ring fields.

Science.gov (United States)

Kim, Seo Hyun; Kong, Hong Jin; Lee, Jong Ung; Lee, Jun Ho; Lee, Jai Hoon

2014-08-01

A method to obtain an aberration-corrected Offner spectrometer without ray obstruction is proposed. A new, more efficient spectrometer optics design is suggested in order to increase its spectral resolution. The derivation of a new ring equation to eliminate ray obstruction is based on geometrical analysis of the ring fields for various numerical apertures. The analytical design applying this equation was demonstrated using the optical design software Code V in order to manufacture a spectrometer working in wavelengths of 900-1700 nm. The simulation results show that the new concept offers an analytical initial design taking the least time of calculation. The simulated spectrometer exhibited a modulation transfer function over 80% at Nyquist frequency, root-mean-square spot diameters under 8.6 μm, and a spectral resolution of 3.2 nm. The final design and its realization of a high resolution Offner spectrometer was demonstrated based on the simulation result. The equation and analytical design procedure shown here can be applied to most Offner systems regardless of the wavelength range.

The perception of geometrical structure from congruence

Science.gov (United States)

Lappin, Joseph S.; Wason, Thomas D.

1989-01-01

The principle function of vision is to measure the environment. As demonstrated by the coordination of motor actions with the positions and trajectories of moving objects in cluttered environments and by rapid recognition of solid objects in varying contexts from changing perspectives, vision provides real-time information about the geometrical structure and location of environmental objects and events. The geometric information provided by 2-D spatial displays is examined. It is proposed that the geometry of this information is best understood not within the traditional framework of perspective trigonometry, but in terms of the structure of qualitative relations defined by congruences among intrinsic geometric relations in images of surfaces. The basic concepts of this geometrical theory are outlined.

Muon reconstruction with a geometrical model in JUNO

Science.gov (United States)

Genster, C.; Schever, M.; Ludhova, L.; Soiron, M.; Stahl, A.; Wiebusch, C.

2018-03-01

The Jiangmen Neutrino Underground Observatory (JUNO) is a 20 kton liquid scintillator detector currently under construction near Kaiping in China. The physics program focuses on the determination of the neutrino mass hierarchy with reactor anti-neutrinos. For this purpose, JUNO is located 650 m underground with a distance of 53 km to two nuclear power plants. As a result, it is exposed to a muon flux that requires a precise muon reconstruction to make a veto of cosmogenic backgrounds viable. Established muon tracking algorithms use time residuals to a track hypothesis. We developed an alternative muon tracking algorithm that utilizes the geometrical shape of the fastest light. It models the full shape of the first, direct light produced along the muon track. From the intersection with the spherical PMT array, the track parameters are extracted with a likelihood fit. The algorithm finds a selection of PMTs based on their first hit times and charges. Subsequently, it fits on timing information only. On a sample of through-going muons with a full simulation of readout electronics, we report a spatial resolution of 20 cm of distance from the detector's center and an angular resolution of 1.6o over the whole detector. Additionally, a dead time estimation is performed to measure the impact of the muon veto. Including the step of waveform reconstruction on top of the track reconstruction, a loss in exposure of only 4% can be achieved compared to the case of a perfect tracking algorithm. When including only the PMT time resolution, but no further electronics simulation and waveform reconstruction, the exposure loss is only 1%.

Spontaneous coronary artery dissection: complete angiographic resolution without stenting

Directory of Open Access Journals (Sweden)

Alexandre Abizaid

2007-09-01

Full Text Available A case of spontaneous coronary artery dissection in a 49-year-oldwoman is presented. She did not present the classical cardiovascular riskfactors. Etiology and treatment are discussed. She underwent primarypercutaneous coronary intervention of the left anterior descendingartery with no stenting and had complete angiographic resolution.

Exploring classical Greek construction problems with interactive geometry software

CERN Document Server

Meskens, Ad

2017-01-01

In this book the classical Greek construction problems are explored in a didactical, enquiry based fashion using Interactive Geometry Software. The book traces the history of these problems, stating them in modern terminology. By focusing on constructions and the use of GeoGebra the reader is confronted with the same problems that ancient mathematicians once faced. The reader can step into the footsteps of Euclid, Viète and Cusanus amongst others and then by experimenting and discovering geometric relationships far exceed their accomplishments. Exploring these problems with the neusis-method lets him discover a class of interesting curves. By experimenting he will gain a deeper understanding of how mathematics is created. More than 100 exercises guide him through methods which were developed to try and solve the problems. The exercises are at the level of undergraduate students and only require knowledge of elementary Euclidean geometry and pre-calculus algebra. It is especially well-suited for those student...

Novel geometrical concept of a high-performance brain PET scanner. Principle, design and performance estimates

International Nuclear Information System (INIS)

Seguinot, J.; Braem, A.; Chesi, E.

2006-01-01

We present the principle, a possible implementation and performance estimates of a novel geometrical concept for a high-resolution positron emission tomograph. The concept, which can be for example implemented in a brain PET device, promises to lead to an essentially parallax-free 3D image reconstruction with excellent spatial resolution and contrast, uniform over the complete field of view. The key components are matrices of long axially oriented scintillator crystals which are read out at both extremities by segmented Hybrid Photon Detectors. We discuss the relevant design considerations for a 3D axial PET camera module, motivate parameter and material choices, and estimate its performance in terms of spatial and energy resolution. We support these estimates by Monte Carlo simulations and in some cases by first experimental results. From the performance of a camera module, we extrapolate to the reconstruction resolution of a 3D axial PET scanner in a semi-analytical way and compare it to an existing state-of-the art brain PET device. We finally describe a dedicated data acquisition system, capable to fully exploit the advantages of the proposed concept

A New, Adaptable, Optical High-Resolution 3-Axis Sensor

Directory of Open Access Journals (Sweden)

Niels Buchhold

2017-01-01

Full Text Available This article presents a new optical, multi-functional, high-resolution 3-axis sensor which serves to navigate and can, for example, replace standard joysticks in medical devices such as electric wheelchairs, surgical robots or medical diagnosis devices. A light source, e.g., a laser diode, is affixed to a movable axis and projects a random geometric shape on an image sensor (CMOS or CCD. The downstream microcontroller’s software identifies the geometric shape’s center, distortion and size, and then calculates x, y, and z coordinates, which can be processed in attached devices. Depending on the image sensor in use (e.g., 6.41 megapixels, the 3-axis sensor features a resolution of 1544 digits from right to left and 1038 digits up and down. Through interpolation, these values rise by a factor of 100. A unique feature is the exact reproducibility (deflection to coordinates and its precise ability to return to its neutral position. Moreover, optical signal processing provides a high level of protection against electromagnetic and radio frequency interference. The sensor is adaptive and adjustable to fit a user’s range of motion (stroke and force. This recommendation aims to optimize sensor systems such as joysticks in medical devices in terms of safety, ease of use, and adaptability.

An atomistic geometrical model of the B-DNA configuration for DNA-radiation interaction simulations

Science.gov (United States)

Bernal, M. A.; Sikansi, D.; Cavalcante, F.; Incerti, S.; Champion, C.; Ivanchenko, V.; Francis, Z.

2013-12-01

In this paper, an atomistic geometrical model for the B-DNA configuration is explained. This model accounts for five organization levels of the DNA, up to the 30 nm chromatin fiber. However, fragments of this fiber can be used to construct the whole genome. The algorithm developed in this work is capable to determine which is the closest atom with respect to an arbitrary point in space. It can be used in any application in which a DNA geometrical model is needed, for instance, in investigations related to the effects of ionizing radiations on the human genetic material. Successful consistency checks were carried out to test the proposed model. Catalogue identifier: AEPZ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEPZ_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 1245 No. of bytes in distributed program, including test data, etc.: 6574 Distribution format: tar.gz Programming language: FORTRAN. Computer: Any. Operating system: Multi-platform. RAM: 2 Gb Classification: 3. Nature of problem: The Monte Carlo method is used to simulate the interaction of ionizing radiation with the human genetic material in order to determine DNA damage yields per unit absorbed dose. To accomplish this task, an algorithm to determine if a given energy deposition lies within a given target is needed. This target can be an atom or any other structure of the genetic material. Solution method: This is a stand-alone subroutine describing an atomic-resolution geometrical model of the B-DNA configuration. It is able to determine the closest atom to an arbitrary point in space. This model accounts for five organization levels of the human genetic material, from the nucleotide pair up to the 30 nm chromatin fiber. This subroutine carries out a series of coordinate transformations

Quantum Computing's Classical Problem, Classical Computing's Quantum Problem

OpenAIRE

Van Meter, Rodney

2013-01-01

Tasked with the challenge to build better and better computers, quantum computing and classical computing face the same conundrum: the success of classical computing systems. Small quantum computing systems have been demonstrated, and intermediate-scale systems are on the horizon, capable of calculating numeric results or simulating physical systems far beyond what humans can do by hand. However, to be commercially viable, they must surpass what our wildly successful, highly advanced classica...

Geometric procedures for civil engineers

CERN Document Server

Tonias, Elias C

2016-01-01

This book provides a multitude of geometric constructions usually encountered in civil engineering and surveying practice.  A detailed geometric solution is provided to each construction as well as a step-by-step set of programming instructions for incorporation into a computing system. The volume is comprised of 12 chapters and appendices that may be grouped in three major parts: the first is intended for those who love geometry for its own sake and its evolution through the ages, in general, and, more specifically, with the introduction of the computer. The second section addresses geometric features used in the book and provides support procedures used by the constructions presented. The remaining chapters and the appendices contain the various constructions. The volume is ideal for engineering practitioners in civil and construction engineering and allied areas.

Effects of ray profile modeling on resolution recovery in clinical CT

International Nuclear Information System (INIS)

Hofmann, Christian; Knaup, Michael; Kachelrieß, Marc

2014-01-01

Purpose: Iterative image reconstruction gains more and more interest in clinical routine, as it promises to reduce image noise (and thereby patient dose), to reduce artifacts, or to improve spatial resolution. However, among vendors and researchers, there is no consensus of how to best achieve these goals. The authors are focusing on the aspect of geometric ray profile modeling, which is realized by some algorithms, while others model the ray as a straight line. The authors incorporate ray-modeling (RM) in nonregularized iterative reconstruction. That means, instead of using one simple single needle beam to represent the x-ray, the authors evaluate the double integral of attenuation path length over the finite source distribution and the finite detector element size in the numerical forward projection. Our investigations aim at analyzing the resolution recovery (RR) effects of RM. Resolution recovery means that frequencies can be recovered beyond the resolution limit of the imaging system. In order to evaluate, whether clinical CT images can benefit from modeling the geometrical properties of each x-ray, the authors performed a 2D simulation study of a clinical CT fan-beam geometry that includes the precise modeling of these geometrical properties. Methods: All simulations and reconstructions are performed in native fan-beam geometry. A water phantom with resolution bar patterns and a Forbild thorax phantom with circular resolution patterns representing calcifications in the heart region are simulated. An FBP reconstruction with a Ram–Lak kernel is used as a reference reconstruction. The FBP is compared to iterative reconstruction techniques with and without RM: An ordered subsets convex (OSC) algorithm without any RM (OSC), an OSC where the forward projection is modeled concerning the finite focal spot and detector size (OSC-RM) and an OSC with RM and with a matched forward and backprojection pair (OSC-T-RM, T for transpose). In all cases, noise was matched to

Geometrical relaxation of excitations in one-dimensional conjugated polymers; Giichijigen kyoeki kobunshi reiki jotai no shusa kozo kanwa

Energy Technology Data Exchange (ETDEWEB)

Yoshizawa, M. [Tohoku University, Sendai (Japan). Faculty of Engineering

1995-12-15

Large ultrafast optical nonlinearities in conjugated polymers have attracted much attention because of possible applications to nonlinear optical devices. One-dimensional systems such as conjugated polymers have localized excited states with geometrical relaxation. In this study, photoexcited states in polydiacetylene has been investigated by femtosecond Raman gain spectroscopy with 300-fs resolution. A new photoinduced Raman peak with lifetime of 1.5 ps has been observed at 1200cm{sup -1} for the first time. This peak indicates acetylene-like structure of the main chain relaxes to butatriene-like structure due to the formation of self-trapped exciting with the geometrical relaxation. The formation and decay kinetics of the Raman signals is consistent with the relaxation processes of exciting observed by femtosecond absorption spectroscopy. 8 refs., 5 figs.

5th Dagstuhl Seminar on Geometric Modelling

CERN Document Server

Brunnett, Guido; Farin, Gerald; Goldman, Ron

2004-01-01

In 19 articles presented by leading experts in the field of geometric modelling the state-of-the-art on representing, modeling, and analyzing curves, surfaces as well as other 3-dimensional geometry is given. The range of applications include CAD/CAM-systems, computer graphics, scientific visualization, virtual reality, simulation and medical imaging. The content of this book is based on selected lectures given at a workshop held at IBFI Schloss Dagstuhl, Germany. Topics treated are: – curve and surface modelling – non-manifold modelling in CAD – multiresolution analysis of complex geometric models – surface reconstruction – variational design – computational geometry of curves and surfaces – 3D meshing – geometric modelling for scientific visualization – geometric models for biomedical applications

Geometrical scaling, furry branching and minijets

International Nuclear Information System (INIS)

Hwa, R.C.

1988-01-01

Scaling properties and their violations in hadronic collisions are discussed in the framework of the geometrical branching model. Geometrical scaling supplemented by Furry branching characterizes the soft component, while the production of jets specifies the hard component. Many features of multiparticle production processes are well described by this model. 21 refs

Accuracy of hiatal hernia detection with esophageal high-resolution manometry

NARCIS (Netherlands)

Weijenborg, P. W.; van Hoeij, F. B.; Smout, A. J. P. M.; Bredenoord, A. J.

2015-01-01

The diagnosis of a sliding hiatal hernia is classically made with endoscopy or barium esophagogram. Spatial separation of the lower esophageal sphincter (LES) and diaphragm, the hallmark of hiatal hernia, can also be observed on high-resolution manometry (HRM), but the diagnostic accuracy of this

Automatic cortical surface reconstruction of high-resolution T1 echo planar imaging data.

Science.gov (United States)

Renvall, Ville; Witzel, Thomas; Wald, Lawrence L; Polimeni, Jonathan R

2016-07-01

Echo planar imaging (EPI) is the method of choice for the majority of functional magnetic resonance imaging (fMRI), yet EPI is prone to geometric distortions and thus misaligns with conventional anatomical reference data. The poor geometric correspondence between functional and anatomical data can lead to severe misplacements and corruption of detected activation patterns. However, recent advances in imaging technology have provided EPI data with increasing quality and resolution. Here we present a framework for deriving cortical surface reconstructions directly from high-resolution EPI-based reference images that provide anatomical models exactly geometric distortion-matched to the functional data. Anatomical EPI data with 1mm isotropic voxel size were acquired using a fast multiple inversion recovery time EPI sequence (MI-EPI) at 7T, from which quantitative T1 maps were calculated. Using these T1 maps, volumetric data mimicking the tissue contrast of standard anatomical data were synthesized using the Bloch equations, and these T1-weighted data were automatically processed using FreeSurfer. The spatial alignment between T2(⁎)-weighted EPI data and the synthetic T1-weighted anatomical MI-EPI-based images was improved compared to the conventional anatomical reference. In particular, the alignment near the regions vulnerable to distortion due to magnetic susceptibility differences was improved, and sampling of the adjacent tissue classes outside of the cortex was reduced when using cortical surface reconstructions derived directly from the MI-EPI reference. The MI-EPI method therefore produces high-quality anatomical data that can be automatically segmented with standard software, providing cortical surface reconstructions that are geometrically matched to the BOLD fMRI data. Copyright © 2016 Elsevier Inc. All rights reserved.

Methods for studying the focal spot size and resolution of diagnostic X-ray tubes

International Nuclear Information System (INIS)

Fairbanks, R.; Doust, C.

1979-01-01

Attention is given to techniques appropriate for use in the clinical situation. The focal spot size is critical to geometric unsharpness and hence the quality of the finished radiograph, but pinhole imaging of the focal spot is extremely difficult in clinical practice. The resolution of an X-ray tube, although a function of focal spot size, is of more importance in radiography. A comparison is made of various resolution grids suitable for quality control use in X-ray departments. (U.K.)

Geometric integrator for simulations in the canonical ensemble

Energy Technology Data Exchange (ETDEWEB)

Tapias, Diego, E-mail: diego.tapias@nucleares.unam.mx [Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, Ciudad de México 04510 (Mexico); Sanders, David P., E-mail: dpsanders@ciencias.unam.mx [Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, Ciudad de México 04510 (Mexico); Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139 (United States); Bravetti, Alessandro, E-mail: alessandro.bravetti@iimas.unam.mx [Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Ciudad Universitaria, Ciudad de México 04510 (Mexico)

2016-08-28

We introduce a geometric integrator for molecular dynamics simulations of physical systems in the canonical ensemble that preserves the invariant distribution in equations arising from the density dynamics algorithm, with any possible type of thermostat. Our integrator thus constitutes a unified framework that allows the study and comparison of different thermostats and of their influence on the equilibrium and non-equilibrium (thermo-)dynamic properties of a system. To show the validity and the generality of the integrator, we implement it with a second-order, time-reversible method and apply it to the simulation of a Lennard-Jones system with three different thermostats, obtaining good conservation of the geometrical properties and recovering the expected thermodynamic results. Moreover, to show the advantage of our geometric integrator over a non-geometric one, we compare the results with those obtained by using the non-geometric Gear integrator, which is frequently used to perform simulations in the canonical ensemble. The non-geometric integrator induces a drift in the invariant quantity, while our integrator has no such drift, thus ensuring that the system is effectively sampling the correct ensemble.

Geometric integrator for simulations in the canonical ensemble

International Nuclear Information System (INIS)

Tapias, Diego; Sanders, David P.; Bravetti, Alessandro

2016-01-01

We introduce a geometric integrator for molecular dynamics simulations of physical systems in the canonical ensemble that preserves the invariant distribution in equations arising from the density dynamics algorithm, with any possible type of thermostat. Our integrator thus constitutes a unified framework that allows the study and comparison of different thermostats and of their influence on the equilibrium and non-equilibrium (thermo-)dynamic properties of a system. To show the validity and the generality of the integrator, we implement it with a second-order, time-reversible method and apply it to the simulation of a Lennard-Jones system with three different thermostats, obtaining good conservation of the geometrical properties and recovering the expected thermodynamic results. Moreover, to show the advantage of our geometric integrator over a non-geometric one, we compare the results with those obtained by using the non-geometric Gear integrator, which is frequently used to perform simulations in the canonical ensemble. The non-geometric integrator induces a drift in the invariant quantity, while our integrator has no such drift, thus ensuring that the system is effectively sampling the correct ensemble.

Introduction to the virtual special issue on super-resolution imaging techniques

Science.gov (United States)

Cao, Liangcai; Liu, Zhengjun

2017-12-01

Until quite recently, the resolution of optical imaging instruments, including telescopes, cameras and microscopes, was considered to be limited by the diffraction of light and by image sensors. In the past few years, many exciting super-resolution approaches have emerged that demonstrate intriguing ways to bypass the classical limit in optics and detectors. More and more research groups are engaged in the study of advanced super-resolution schemes, devices, algorithms, systems, and applications [1-6]. Super-resolution techniques involve new methods in science and engineering of optics [7,8], measurements [9,10], chemistry [11,12] and information [13,14]. Promising applications, particularly in biomedical research and semiconductor industry, have been successfully demonstrated.

Boundary conditions, energies and gravitational heat in general relativity (a classical analysis)

International Nuclear Information System (INIS)

Francaviglia, M; Raiteri, M

2004-01-01

The variation of the energy for a gravitational system is directly defined from the Hamiltonian field equations of general relativity. When the variation of the energy is written in a covariant form, it splits into two (covariant) contributions: one of them is the Komar energy, while the other is the so-called covariant ADM correction term. When specific boundary conditions are analysed one sees that the Komar energy is related to the gravitational heat while the ADM correction term plays the role of the Helmholtz free energy. These properties allow one to establish, inside a classical geometric framework, a formal analogy between gravitation and the laws governing the evolution of a thermodynamical system. The analogy applies to stationary spacetimes admitting multiple causal horizons as well as to AdS Taub-bolt solutions

Geometric Liouville gravity

International Nuclear Information System (INIS)

La, H.

1992-01-01

A new geometric formulation of Liouville gravity based on the area preserving diffeo-morphism is given and a possible alternative to reinterpret Liouville gravity is suggested, namely, a scalar field coupled to two-dimensional gravity with a curvature constraint

Geometric phase topology in weak measurement

Science.gov (United States)

Samlan, C. T.; Viswanathan, Nirmal K.

2017-12-01

The geometric phase visualization proposed by Bhandari (R Bhandari 1997 Phys. Rep. 281 1-64) in the ellipticity-ellipse orientation basis of the polarization ellipse of light is implemented to understand the geometric aspects of weak measurement. The weak interaction of a pre-selected state, acheived via spin-Hall effect of light (SHEL), results in a spread in the polarization ellipticity (η) or ellipse orientation (χ) depending on the resulting spatial or angular shift, respectively. The post-selection leads to the projection of the η spread in the complementary χ basis results in the appearance of a geometric phase with helical phase topology in the η - χ parameter space. By representing the weak measurement on the Poincaré sphere and using Jones calculus, the complex weak value and the geometric phase topology are obtained. This deeper understanding of the weak measurement process enabled us to explore the techniques’ capabilities maximally, as demonstrated via SHEL in two examples—external reflection at glass-air interface and transmission through a tilted half-wave plate.

Fermions from classical statistics

International Nuclear Information System (INIS)

Wetterich, C.

2010-01-01

We describe fermions in terms of a classical statistical ensemble. The states τ of this ensemble are characterized by a sequence of values one or zero or a corresponding set of two-level observables. Every classical probability distribution can be associated to a quantum state for fermions. If the time evolution of the classical probabilities p τ amounts to a rotation of the wave function q τ (t)=±√(p τ (t)), we infer the unitary time evolution of a quantum system of fermions according to a Schroedinger equation. We establish how such classical statistical ensembles can be mapped to Grassmann functional integrals. Quantum field theories for fermions arise for a suitable time evolution of classical probabilities for generalized Ising models.

Classical mechanics

CERN Document Server

Benacquista, Matthew J

2018-01-01

This textbook provides an introduction to classical mechanics at a level intermediate between the typical undergraduate and advanced graduate level. This text describes the background and tools for use in the fields of modern physics, such as quantum mechanics, astrophysics, particle physics, and relativity. Students who have had basic undergraduate classical mechanics or who have a good understanding of the mathematical methods of physics will benefit from this book.

Geometric statistical inference

International Nuclear Information System (INIS)

Periwal, Vipul

1999-01-01

A reparametrization-covariant formulation of the inverse problem of probability is explicitly solved for finite sample sizes. The inferred distribution is explicitly continuous for finite sample size. A geometric solution of the statistical inference problem in higher dimensions is outlined

Geometrical Method for Thermal Instability of Nonlinearly Charged BTZ Black Holes

International Nuclear Information System (INIS)

Panahiyan, Shahram; Hendi, Seyed Hossein; Eslam Panah, Behzad

2015-01-01

We consider three-dimensional BTZ black holes with three models of nonlinear electrodynamics as source. Calculating heat capacity, we study the stability and phase transitions of these black holes. We show that Maxwell, logarithmic, and exponential theories yield only type one phase transition which is related to the root(s) of heat capacity, whereas, for correction form of nonlinear electrodynamics, heat capacity contains two roots and one divergence point. Next, we use geometrical approach for studying classical thermodynamical behavior of the system. We show that Weinhold and Ruppeiner metrics fail to provide fruitful results and the consequences of the Quevedo approach are not completely matched to the heat capacity results. Then, we employ a new metric for solving this problem. We show that this approach is successful and all divergencies of its Ricci scalar and phase transition points coincide. We also show that there is no phase transition for uncharged BTZ black holes.

Mixing geometric and radiometric features for change classification

Science.gov (United States)

Fournier, Alexandre; Descombes, Xavier; Zerubia, Josiane

2008-02-01

Most basic change detection algorithms use a pixel-based approach. Whereas such approach is quite well defined for monitoring important area changes (such as urban growth monitoring) in low resolution images, an object based approach seems more relevant when the change detection is specifically aimed toward targets (such as small buildings and vehicles). In this paper, we present an approach that mixes radiometric and geometric features to qualify the changed zones. The goal is to establish bounds (appearance, disappearance, substitution ...) between the detected changes and the underlying objects. We proceed by first clustering the change map (containing each pixel bitemporal radiosity) in different classes using the entropy-kmeans algorithm. Assuming that most man-made objects have a polygonal shape, a polygonal approximation algorithm is then used in order to characterize the resulting zone shapes. Hence allowing us to refine the primary rough classification, by integrating the polygon orientations in the state space. Tests are currently conducted on Quickbird data.

Geometrical modelling of scanning probe microscopes and characterization of errors

International Nuclear Information System (INIS)

Marinello, F; Savio, E; Bariani, P; Carmignato, S

2009-01-01

Scanning probe microscopes (SPMs) allow quantitative evaluation of surface topography with ultra-high resolution, as a result of accurate actuation combined with the sharpness of tips. SPMs measure sequentially, by scanning surfaces in a raster fashion: topography maps commonly consist of data sets ideally reported in an orthonormal rectilinear Cartesian coordinate system. However, due to scanning errors and measurement distortions, the measurement process is far from the ideal Cartesian condition. The paper addresses geometrical modelling of the scanning system dynamics, presenting a mathematical model which describes the surface metric x-, y- and z- coordinates as a function of the measured x'-, y'- and z'-coordinates respectively. The complete mathematical model provides a relevant contribution to characterization and calibration, and ultimately to traceability, of SPMs, when applied for quantitative characterization

The representations of Lie groups and geometric quantizations

International Nuclear Information System (INIS)

Zhao Qiang

1998-01-01

In this paper we discuss the relation between representations of Lie groups and geometric quantizations. A series of representations of Lie groups are constructed by geometric quantization of coadjoint orbits. Particularly, all representations of compact Lie groups, holomorphic discrete series of representations and spherical representations of reductive Lie groups are constructed by geometric quantizations of elliptic and hyperbolic coadjoint orbits. (orig.)

Nonadiabatic geometrical quantum gates in semiconductor quantum dots

International Nuclear Information System (INIS)

Solinas, Paolo; Zanghi, Nino; Zanardi, Paolo; Rossi, Fausto

2003-01-01

In this paper, we study the implementation of nonadiabatic geometrical quantum gates with in semiconductor quantum dots. Different quantum information enconding (manipulation) schemes exploiting excitonic degrees of freedom are discussed. By means of the Aharanov-Anandan geometrical phase, one can avoid the limitations of adiabatic schemes relying on adiabatic Berry phase; fast geometrical quantum gates can be, in principle, implemented

Identifying and Fostering Higher Levels of Geometric Thinking

Science.gov (United States)

Škrbec, Maja; Cadež, Tatjana Hodnik

2015-01-01

Pierre M. Van Hiele created five levels of geometric thinking. We decided to identify the level of geometric thinking in the students in Slovenia, aged 9 to 11 years. The majority of students (60.7%) are at the transition between the zero (visual) level and the first (descriptive) level of geometric thinking. Nearly a third (31.7%) of students is…

Thermal fluctuations in the classical superconductor Nb3Sn from high-resolution specific-heat measurements

International Nuclear Information System (INIS)

Lortz, Rolf; Wang Yuxing; Junod, Alain; Toyota, Naoki

2007-01-01

The range of thermal fluctuations in 'classical' bulk superconductors is extremely small and especially in low-fields hardly experimentally accessible. With a new type of calorimeter we were able to detect a tiny lambda anomaly in the specific-heat of the superconductor Nb 3 Sn within a narrow temperature range around the H c2 line. We show that the evolution of the anomaly as a function of magnetic field follows scaling laws expected in the presence of critical thermal fluctuations

Geometric constructions for repulsive gravity and quantization

International Nuclear Information System (INIS)

Hohmann, Manuel

2010-11-01

In this thesis we present two geometric theories designed to extend general relativity. It can be seen as one of the aims of such theories to model the observed accelerating expansion of the universe as a gravitational phenomenon, or to provide a mathematical structure for the formulation of quantum field theories on curved spacetimes and quantum gravity. This thesis splits into two parts: In the first part we consider multimetric gravity theories containing N>1 standard model copies which interact only gravitationally and repel each other in the Newtonian limit. The dynamics of each of the standard model copies is governed by its own metric tensor. We show that the antisymmetric case, in which the mutual repulsion between the different matter sectors is of equal strength compared to the attractive gravitational force within each sector, is prohibited by a no-go theorem for N=2. We further show that this theorem does not hold for N>2 by explicitly constructing an antisymmetric multimetric repulsive gravity theory. We then examine several properties of this theory. Most notably, we derive a simple cosmological model and show that the accelerating expansion of the late universe can indeed be explained by the mutual repulsion between the different matter sectors. We further present a simple model for structure formation and show that our model leads to the formation of filament-like structures and voids. Finally, we show that multimetric repulsive gravity is compatible with high-precision solar system data using the parametrized post-Newtonian formalism. In the second part of the thesis we propose a mathematical model of quantum spacetime as an infinite-dimensional manifold locally homeomorphic to an appropriate Schwartz space. This extends and unifies both the standard function space construction of quantum mechanics and the differentiable manifold structure of classical spacetime. In this picture we demonstrate that classical spacetime emerges as a finite

Geometric constructions for repulsive gravity and quantization

Energy Technology Data Exchange (ETDEWEB)

Hohmann, Manuel

2010-11-15

In this thesis we present two geometric theories designed to extend general relativity. It can be seen as one of the aims of such theories to model the observed accelerating expansion of the universe as a gravitational phenomenon, or to provide a mathematical structure for the formulation of quantum field theories on curved spacetimes and quantum gravity. This thesis splits into two parts: In the first part we consider multimetric gravity theories containing N>1 standard model copies which interact only gravitationally and repel each other in the Newtonian limit. The dynamics of each of the standard model copies is governed by its own metric tensor. We show that the antisymmetric case, in which the mutual repulsion between the different matter sectors is of equal strength compared to the attractive gravitational force within each sector, is prohibited by a no-go theorem for N=2. We further show that this theorem does not hold for N>2 by explicitly constructing an antisymmetric multimetric repulsive gravity theory. We then examine several properties of this theory. Most notably, we derive a simple cosmological model and show that the accelerating expansion of the late universe can indeed be explained by the mutual repulsion between the different matter sectors. We further present a simple model for structure formation and show that our model leads to the formation of filament-like structures and voids. Finally, we show that multimetric repulsive gravity is compatible with high-precision solar system data using the parametrized post-Newtonian formalism. In the second part of the thesis we propose a mathematical model of quantum spacetime as an infinite-dimensional manifold locally homeomorphic to an appropriate Schwartz space. This extends and unifies both the standard function space construction of quantum mechanics and the differentiable manifold structure of classical spacetime. In this picture we demonstrate that classical spacetime emerges as a finite

Information geometric methods for complexity

Science.gov (United States)

Felice, Domenico; Cafaro, Carlo; Mancini, Stefano

2018-03-01

Research on the use of information geometry (IG) in modern physics has witnessed significant advances recently. In this review article, we report on the utilization of IG methods to define measures of complexity in both classical and, whenever available, quantum physical settings. A paradigmatic example of a dramatic change in complexity is given by phase transitions (PTs). Hence, we review both global and local aspects of PTs described in terms of the scalar curvature of the parameter manifold and the components of the metric tensor, respectively. We also report on the behavior of geodesic paths on the parameter manifold used to gain insight into the dynamics of PTs. Going further, we survey measures of complexity arising in the geometric framework. In particular, we quantify complexity of networks in terms of the Riemannian volume of the parameter space of a statistical manifold associated with a given network. We are also concerned with complexity measures that account for the interactions of a given number of parts of a system that cannot be described in terms of a smaller number of parts of the system. Finally, we investigate complexity measures of entropic motion on curved statistical manifolds that arise from a probabilistic description of physical systems in the presence of limited information. The Kullback-Leibler divergence, the distance to an exponential family and volumes of curved parameter manifolds, are examples of essential IG notions exploited in our discussion of complexity. We conclude by discussing strengths, limits, and possible future applications of IG methods to the physics of complexity.

Riemannian geometry and geometric analysis

CERN Document Server

Jost, Jürgen

2017-01-01

This established reference work continues to provide its readers with a gateway to some of the most interesting developments in contemporary geometry. It offers insight into a wide range of topics, including fundamental concepts of Riemannian geometry, such as geodesics, connections and curvature; the basic models and tools of geometric analysis, such as harmonic functions, forms, mappings, eigenvalues, the Dirac operator and the heat flow method; as well as the most important variational principles of theoretical physics, such as Yang-Mills, Ginzburg-Landau or the nonlinear sigma model of quantum field theory. The present volume connects all these topics in a systematic geometric framework. At the same time, it equips the reader with the working tools of the field and enables her or him to delve into geometric research.  The 7th edition has been systematically reorganized and updated. Almost no page has been left unchanged. It also includes new material, for instance on symplectic geometry, as well as the B...

Adaptive resolution simulation of salt solutions

International Nuclear Information System (INIS)

Bevc, Staš; Praprotnik, Matej; Junghans, Christoph; Kremer, Kurt

2013-01-01

We present an adaptive resolution simulation of aqueous salt (NaCl) solutions at ambient conditions using the adaptive resolution scheme. Our multiscale approach concurrently couples the atomistic and coarse-grained models of the aqueous NaCl, where water molecules and ions change their resolution while moving from one resolution domain to the other. We employ standard extended simple point charge (SPC/E) and simple point charge (SPC) water models in combination with AMBER and GROMOS force fields for ion interactions in the atomistic domain. Electrostatics in our model are described by the generalized reaction field method. The effective interactions for water–water and water–ion interactions in the coarse-grained model are derived using structure-based coarse-graining approach while the Coulomb interactions between ions are appropriately screened. To ensure an even distribution of water molecules and ions across the simulation box we employ thermodynamic forces. We demonstrate that the equilibrium structural, e.g. radial distribution functions and density distributions of all the species, and dynamical properties are correctly reproduced by our adaptive resolution method. Our multiscale approach, which is general and can be used for any classical non-polarizable force-field and/or types of ions, will significantly speed up biomolecular simulation involving aqueous salt. (paper)

Mathematical and information-geometrical entropy for phenomenological Fourier and non-Fourier heat conduction

Science.gov (United States)

Li, Shu-Nan; Cao, Bing-Yang

2017-09-01

The second law of thermodynamics governs the direction of heat transport, which provides the foundational definition of thermodynamic Clausius entropy. The definitions of entropy are further generalized for the phenomenological heat transport models in the frameworks of classical irreversible thermodynamics and extended irreversible thermodynamics (EIT). In this work, entropic functions from mathematics are combined with phenomenological heat conduction models and connected to several information-geometrical conceptions. The long-time behaviors of these mathematical entropies exhibit a wide diversity and physical pictures in phenomenological heat conductions, including the tendency to thermal equilibrium, and exponential decay of nonequilibrium and asymptotics, which build a bridge between the macroscopic and microscopic modelings. In contrast with the EIT entropies, the mathematical entropies expressed in terms of the internal energy function can avoid singularity paired with nonpositive local absolute temperature caused by non-Fourier heat conduction models.

ACQUISION OF GEOMETRICAL DATA OF SMALL RIVERS WITH AN UNMANNED WATER VEHICLE

Directory of Open Access Journals (Sweden)

H. Sardemann

2018-05-01

Full Text Available Rivers with small- and medium-scaled catchments have been increasingly affected by extreme events, i.e. flash floods, in the last years. New methods to describe and predict these events are developed in the interdisciplinary research project EXTRUSO. Flash flood events happen on small temporal and spatial scales, stressing the necessity of high-resolution input data for hydrological and hydrodynamic modelling. Among others, the benefit of high-resolution digital terrain models (DTMs will be evaluated in the project. This article introduces a boat-based approach for the acquisition of geometrical and morphological data of small rivers and their banks. An unmanned water vehicle (UWV is used as a multi-sensor platform to collect 3D-point clouds of the riverbanks, as well as bathymetric measurements of water depth and river morphology. The UWV is equipped with a mobile Lidar, a panorama camera, an echo sounder and a positioning unit. Whole (sub- catchments of small rivers can be digitalized and provided for hydrological modelling when UWV-based and UAV (unmanned aerial vehicle based point clouds are fused.

J. Genet. classic 235

Indian Academy of Sciences (India)

Unknown

Journal of Genetics, Vol. 83, No. 3, December 2004. 235. Page 2. J. Genet. classic. Journal of Genetics, Vol. 83, No. 3, December 2004. 236. Page 3. J. Genet. classic. Journal of Genetics, Vol. 83, No. 3, December 2004. 237. Page 4. J. Genet. classic. Journal of Genetics, Vol. 83, No. 3, December 2004. 238. Page 5 ...

Geometric function theory in higher dimension

CERN Document Server

2017-01-01

The book collects the most relevant outcomes from the INdAM Workshop “Geometric Function Theory in Higher Dimension” held in Cortona on September 5-9, 2016. The Workshop was mainly devoted to discussions of basic open problems in the area, and this volume follows the same line. In particular, it offers a selection of original contributions on Loewner theory in one and higher dimensions, semigroups theory, iteration theory and related topics. Written by experts in geometric function theory in one and several complex variables, it focuses on new research frontiers in this area and on challenging open problems. The book is intended for graduate students and researchers working in complex analysis, several complex variables and geometric function theory.

An introduction to geometrical physics

CERN Document Server

Aldrovandi, R

1995-01-01

This book stresses the unifying power of the geometrical framework in bringing together concepts from the different areas of physics. Common underpinnings of optics, elasticity, gravitation, relativistic fields, particle mechanics and other subjects are underlined. It attempts to extricate the notion of space currently in the physical literature from the metric connotation.The book's goal is to present mathematical ideas associated with geometrical physics in a rather introductory language. Included are many examples from elementary physics and also, for those wishing to reach a higher level o

Quantum mechanics from classical statistics

International Nuclear Information System (INIS)

Wetterich, C.

2010-01-01

Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by only a few probabilistic observables. Their expectation values define a density matrix if they obey a 'purity constraint'. Then all the usual laws of quantum mechanics follow, including Heisenberg's uncertainty relation, entanglement and a violation of Bell's inequalities. No concepts beyond classical statistics are needed for quantum physics - the differences are only apparent and result from the particularities of those classical statistical systems which admit a quantum mechanical description. Born's rule for quantum mechanical probabilities follows from the probability concept for a classical statistical ensemble. In particular, we show how the non-commuting properties of quantum operators are associated to the use of conditional probabilities within the classical system, and how a unitary time evolution reflects the isolation of the subsystem. As an illustration, we discuss a classical statistical implementation of a quantum computer.

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

Classical and semi-classical solutions of the Yang--Mills theory

International Nuclear Information System (INIS)

Jackiw, R.; Nohl, C.; Rebbi, C.

1977-12-01

This review summarizes what is known at present about classical solutions to Yang-Mills theory both in Euclidean and Minkowski space. The quantal meaning of these solutions is also discussed. Solutions in Euclidean space expose multiple vacua and tunnelling of the quantum theory. Those in Minkowski space-time provide a semi-classical spectrum for a conformal generator

Geometric treatment of electromagnetic phenomena in conducting materials: variational principles

Energy Technology Data Exchange (ETDEWEB)

BadIa-Majos, A [Departamento de Fisica de la Materia Condensada-ICMA, Universidad de Zaragoza (Spain); Carinena, J F [Departamento de Fisica Teorica, Universidad de Zaragoza (Spain); Lopez, C [Departamento de Matematicas, Universidad de Alcala de Henares (Spain)

2006-11-24

The dynamical equations of an electromagnetic field coupled with a conducting material are studied. The properties of the interaction are described by a classical field theory with tensorial material laws in spacetime geometry. We show that the main features of superconducting response emerge in a natural way within the covariance, gauge invariance and variational formulation requirements. In particular, the Ginzburg-Landau theory follows straightforwardly from the London equations when fundamental symmetry properties are considered. Unconventional properties, such as the interaction of superconductors with electrostatic fields are naturally introduced in the geometric theory, at a phenomenological level. The BCS background is also suggested by macroscopic fingerprints of the internal symmetries. It is also shown that dissipative conducting behaviour may be approximately treated in a variational framework after breaking covariance for adiabatic processes. Thus, nonconservative laws of interaction are formulated by a purely spatial variational principle, in a quasi-stationary time discretized evolution. This theory justifies a class of nonfunctional phenomenological principles, introduced for dealing with exotic conduction properties of matter (BadIa and Lopez 2001 Phys. Rev. Lett. 87 127004)

SALT high-resolution spectroscopy of nova PNV J15384000-4744500

Science.gov (United States)

Aydi, E.; Buckley, D. A. H.; Mohamed, S.; Whitelock, P. A.

2018-06-01

We report on high-resolution spectroscopy of PNV J15384000-4744500 which was reported as a possible nova by Rob Kaufman (Bright, Victoria, Australia; CBAT follow-up: http://www.cbat.eps.harvard.edu/unconf/followups/J15384000-4744500.html) and confirmed as a classical nova by F. Walter (ATel #11681).

High voltage/high resolution studies of metal and semiconductor interfaces

International Nuclear Information System (INIS)

Westmacott, K.H.; Dahmen, U.

1989-11-01

The application of high resolution transmission electron microscopy to the study of homo- or hetero-phase interface structures requires specimens that meet stringent criteria. In some systems the necessary geometric imaging conditions are established naturally, thus greatly simplifying the analysis. This is illustrated for a diamond-hexagonal/diamond-cubic interface in deformed silicon, a Σ99 tilt boundary in a pure aluminum bicrystal, and a germanium precipitate in an aluminum matrix. 13 refs., 5 figs

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

Geometrical spin symmetry and spin

International Nuclear Information System (INIS)

Pestov, I. B.

2011-01-01

Unification of General Theory of Relativity and Quantum Mechanics leads to General Quantum Mechanics which includes into itself spindynamics as a theory of spin phenomena. The key concepts of spindynamics are geometrical spin symmetry and the spin field (space of defining representation of spin symmetry). The essence of spin is the bipolar structure of geometrical spin symmetry induced by the gravitational potential. The bipolar structure provides a natural derivation of the equations of spindynamics. Spindynamics involves all phenomena connected with spin and provides new understanding of the strong interaction.

Asymptotic geometric analysis, part I

CERN Document Server

Artstein-Avidan, Shiri

2015-01-01

The authors present the theory of asymptotic geometric analysis, a field which lies on the border between geometry and functional analysis. In this field, isometric problems that are typical for geometry in low dimensions are substituted by an "isomorphic" point of view, and an asymptotic approach (as dimension tends to infinity) is introduced. Geometry and analysis meet here in a non-trivial way. Basic examples of geometric inequalities in isomorphic form which are encountered in the book are the "isomorphic isoperimetric inequalities" which led to the discovery of the "concentration phenomen

Quantum flesh on classical bones: Semiclassical bridges across the quantum-classical divide

Energy Technology Data Exchange (ETDEWEB)

Bokulich, Alisa [Center for Philosophy and History of Science, Boston University, Boston, MA (United States)

2014-07-01

Traditionally quantum mechanics is viewed as having made a sharp break from classical mechanics, and the concepts and methods of these two theories are viewed as incommensurable with one another. A closer examination of the history of quantum mechanics, however, reveals that there is a strong sense in which quantum mechanics was built on the backbone of classical mechanics. As a result, there is a considerable structural continuity between these two theories, despite their important differences. These structural continuities provide a ground for semiclassical methods in which classical structures, such as trajectories, are used to investigate and model quantum phenomena. After briefly tracing the history of semiclassical approaches, I show how current research in semiclassical mechanics is revealing new bridges across the quantum-classical divide.

Greek classicism in living structure? Some deductive pathways in animal morphology.

Science.gov (United States)

Zweers, G A

1985-01-01

Classical temples in ancient Greece show two deterministic illusionistic principles of architecture, which govern their functional design: geometric proportionalism and a set of illusion-strengthening rules in the proportionalism's "stochastic margin". Animal morphology, in its mechanistic-deductive revival, applies just one architectural principle, which is not always satisfactory. Whether a "Greek Classical" situation occurs in the architecture of living structure is to be investigated by extreme testing with deductive methods. Three deductive methods for explanation of living structure in animal morphology are proposed: the parts, the compromise, and the transformation deduction. The methods are based upon the systems concept for an organism, the flow chart for a functionalistic picture, and the network chart for a structuralistic picture, whereas the "optimal design" serves as the architectural principle for living structure. These methods show clearly the high explanatory power of deductive methods in morphology, but they also make one open end most explicit: neutral issues do exist. Full explanation of living structure asks for three entries: functional design within architectural and transformational constraints. The transformational constraint brings necessarily in a stochastic component: an at random variation being a sort of "free management space". This variation must be a variation from the deterministic principle of the optimal design, since any transformation requires space for plasticity in structure and action, and flexibility in role fulfilling. Nevertheless, finally the question comes up whether for animal structure a similar situation exists as in Greek Classical temples. This means that the at random variation, that is found when the optimal design is used to explain structure, comprises apart from a stochastic part also real deviations being yet another deterministic part. This deterministic part could be a set of rules that governs

Geometrical analysis of the interacting boson model

International Nuclear Information System (INIS)

Dieperink, A.E.L.

1983-01-01

The Interacting Boson Model is considered, in relation with geometrical models and the application of mean field techniques to algebraic models, in three lectures. In the first, several methods are reviewed to establish a connection between the algebraic formulation of collective nuclear properties in terms of the group SU(6) and the geometric approach. In the second lecture the geometric interpretation of new degrees of freedom that arise in the neutron-proton IBA is discussed, and in the third one some further applications of algebraic techniques to the calculation of static and dynamic collective properties are presented. (U.K.)

A Geometrical View of Higgs Effective Theory

CERN Multimedia

CERN. Geneva

2016-01-01

A geometric formulation of Higgs Effective Field Theory (HEFT) is presented. Experimental observables are given in terms of geometric invariants of the scalar sigma model sector such as the curvature of the scalar field manifold M. We show how the curvature can be measured experimentally via Higgs cross-sections, W_L scattering, and the S parameter. The one-loop action of HEFT is given in terms of geometric invariants of M. The distinction between the Standard Model (SM) and HEFT is whether M is flat or curved, with the curvature a signal of the scale of new physics.

Geometric phases and hidden local gauge symmetry

International Nuclear Information System (INIS)

Fujikawa, Kazuo

2005-01-01

The analysis of geometric phases associated with level crossing is reduced to the familiar diagonalization of the Hamiltonian in the second quantized formulation. A hidden local gauge symmetry, which is associated with the arbitrariness of the phase choice of a complete orthonormal basis set, becomes explicit in this formulation (in particular, in the adiabatic approximation) and specifies physical observables. The choice of a basis set which specifies the coordinate in the functional space is arbitrary in the second quantization, and a subclass of coordinate transformations, which keeps the form of the action invariant, is recognized as the gauge symmetry. We discuss the implications of this hidden local gauge symmetry in detail by analyzing geometric phases for cyclic and noncyclic evolutions. It is shown that the hidden local symmetry provides a basic concept alternative to the notion of holonomy to analyze geometric phases and that the analysis based on the hidden local gauge symmetry leads to results consistent with the general prescription of Pancharatnam. We however note an important difference between the geometric phases for cyclic and noncyclic evolutions. We also explain a basic difference between our hidden local gauge symmetry and a gauge symmetry (or equivalence class) used by Aharonov and Anandan in their definition of generalized geometric phases

Geometric group theory

CERN Document Server

Bestvina, Mladen; Vogtmann, Karen

2014-01-01

Geometric group theory refers to the study of discrete groups using tools from topology, geometry, dynamics and analysis. The field is evolving very rapidly and the present volume provides an introduction to and overview of various topics which have played critical roles in this evolution. The book contains lecture notes from courses given at the Park City Math Institute on Geometric Group Theory. The institute consists of a set of intensive short courses offered by leaders in the field, designed to introduce students to exciting, current research in mathematics. These lectures do not duplicate standard courses available elsewhere. The courses begin at an introductory level suitable for graduate students and lead up to currently active topics of research. The articles in this volume include introductions to CAT(0) cube complexes and groups, to modern small cancellation theory, to isometry groups of general CAT(0) spaces, and a discussion of nilpotent genus in the context of mapping class groups and CAT(0) gro...

Direct gauging of the Poincare group V. Group scaling, classical gauge theory, and gravitational corrections

International Nuclear Information System (INIS)

Edelen, D.G.B.

1986-01-01

Homogeneous scaling of the group space of the Poincare group, P 10 , is shown to induce scalings of all geometric quantities associated with the local action of P 10 . The field equations for both the translation and the Lorentz rotation compensating fields reduce to O(1) equations if the scaling parameter is set equal to the general relativistic gravitational coupling constant 8πGc -4 . Standard expansions of all field variables in power series in the scaling parameter give the following results. The zeroth-order field equations are exactly the classical field equations for matter fields on Minkowski space subject to local action of an internal symmetry group (classical gauge theory). The expansion process is shown to break P 10 -gauge covariance of the theory, and hence solving the zeroth-order field equations imposes an implicit system of P 10 -gauge conditions. Explicit systems of field equations are obtained for the first- and higher-order approximations. The first-order translation field equations are driven by the momentum-energy tensor of the matter and internal compensating fields in the zeroth order (classical gauge theory), while the first-order Lorentz rotation field equations are driven by the spin currents of the same classical gauge theory. Field equations for the first-order gravitational corrections to the matter fields and the gauge fields for the internal symmetry group are obtained. Direct Poincare gauge theory is thus shown to satisfy the first two of the three-part acid test of any unified field theory. Satisfaction of the third part of the test, at least for finite neighborhoods, seems probable

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

Quantum remnants in the classical limit

International Nuclear Information System (INIS)

Kowalski, A.M.; Plastino, A.

2016-01-01

We analyze here the common features of two dynamical regimes: a quantum and a classical one. We deal with a well known semi-classic system in its route towards the classical limit, together with its purely classic counterpart. We wish to ascertain i) whether some quantum remnants can be found in the classical limit and ii) the details of the quantum-classic transition. The so-called mutual information is the appropriate quantifier for this task. Additionally, we study the Bandt–Pompe's symbolic patterns that characterize dynamical time series (representative of the semi-classical system under scrutiny) in their evolution towards the classical limit. - Highlights: • We investigate the classical limit (CL) of a well known semi classical model. • The study is made by reference to the Bandt Pompe symbolic approach. • The number and type of associated symbols changes as one proceeds towards the CL. • We ascertain which symbols pertaining to the quantum zone remain in the CL.

Quantum remnants in the classical limit

Energy Technology Data Exchange (ETDEWEB)

Kowalski, A.M., E-mail: kowalski@fisica.unlp.edu.ar [Instituto de Física (IFLP-CCT-Conicet), Universidad Nacional de La Plata, C.C. 727, 1900 La Plata (Argentina); Comision de Investigaciones Científicas (CIC) (Argentina); Plastino, A., E-mail: plastino@fisica.unlp.edu.ar [Instituto de Física (IFLP-CCT-Conicet), Universidad Nacional de La Plata, C.C. 727, 1900 La Plata (Argentina); Argentina' s National Research Council (CONICET) (Argentina); SThAR, EPFL Innovation Park, Lausanne (Switzerland)

2016-09-16

We analyze here the common features of two dynamical regimes: a quantum and a classical one. We deal with a well known semi-classic system in its route towards the classical limit, together with its purely classic counterpart. We wish to ascertain i) whether some quantum remnants can be found in the classical limit and ii) the details of the quantum-classic transition. The so-called mutual information is the appropriate quantifier for this task. Additionally, we study the Bandt–Pompe's symbolic patterns that characterize dynamical time series (representative of the semi-classical system under scrutiny) in their evolution towards the classical limit. - Highlights: • We investigate the classical limit (CL) of a well known semi classical model. • The study is made by reference to the Bandt Pompe symbolic approach. • The number and type of associated symbols changes as one proceeds towards the CL. • We ascertain which symbols pertaining to the quantum zone remain in the CL.

Ultrafast time-resolved absorption spectroscopy of geometric isomers of carotenoids

International Nuclear Information System (INIS)

Niedzwiedzki, Dariusz M.; Sandberg, Daniel J.; Cong, Hong; Sandberg, Megan N.; Gibson, George N.; Birge, Robert R.; Frank, Harry A.

2009-01-01

The structures of a number of stereoisomers of carotenoids have been revealed in three-dimensional X-ray crystallographic investigations of pigment-protein complexes from photosynthetic organisms. Despite these structural elucidations, the reason for the presence of stereoisomers in these systems is not well understood. An important unresolved issue is whether the natural selection of geometric isomers of carotenoids in photosynthetic pigment-protein complexes is determined by the structure of the protein binding site or by the need for the organism to accomplish a specific physiological task. The association of cis isomers of a carotenoid with reaction centers and trans isomers of the same carotenoid with light-harvesting pigment-protein complexes has led to the hypothesis that the stereoisomers play distinctly different physiological roles. A systematic investigation of the photophysics and photochemistry of purified, stable geometric isomers of carotenoids is needed to understand if a relationship between stereochemistry and biological function exists. In this work we present a comparative study of the spectroscopy and excited state dynamics of cis and trans isomers of three different open-chain carotenoids in solution. The molecules are neurosporene (n = 9), spheroidene (n = 10), and spirilloxanthin (n = 13), where n is the number of conjugated π-electron double bonds. The spectroscopic experiments were carried out on geometric isomers of the carotenoids purified by high performance liquid chromatography (HPLC) and then frozen to 77 K to inhibit isomerization. The spectral data taken at 77 K provide a high resolution view of the spectroscopic differences between geometric isomers. The kinetic data reveal that the lifetime of the lowest excited singlet state of a cis-isomer is consistently shorter than that of its corresponding all-trans counterpart despite the fact that the excited state energy of the cis molecule is typically higher than that of the trans

Reversal permanent charge and reversal potential: case studies via classical Poisson–Nernst–Planck models

International Nuclear Information System (INIS)

Eisenberg, Bob; Liu, Weishi; Xu, Hongguo

2015-01-01

In this work, we are interested in effects of a simple profile of permanent charges on ionic flows. We determine when a permanent charge produces current reversal. We adopt the classical Poisson–Nernst–Planck (PNP) models of ionic flows for this study. The starting point of our analysis is the recently developed geometric singular perturbation approach for PNP models. Under the setting in the paper for case studies, we are able to identify a single governing equation for the existence and the value of the permanent charge for a current reversal. A number of interesting features are established. The related topic on reversal potential can be viewed as a dual problem and is briefly examined in this work too. (paper)

Geometrical charged-particle optics. 2. ed.

International Nuclear Information System (INIS)

Rose, Harald

2013-01-01

Provides a unique theoretical treatment of charged-particle optics. Displays novel unpublished results on several topics. Provides insight into the properties of charged-particle devices. Treats wave optical properties of the electron. Presents the resolution limit of electron microscopes and novel theoretical treatment of the Stern-Gerlach effect. This second edition is an extended version of the first edition of Geometrical Charged-Particle Optics. The updated reference monograph is intended as a guide for researchers and graduate students who are seeking a comprehensive treatment of the design of instruments and beam-guiding systems of charged particles and their propagation in electromagnetic fields. Wave aspects are included in this edition for explaining electron holography, the Aharanov-Bohm effect and the resolution of electron microscopes limited by diffraction. Several methods for calculating the electromagnetic field are presented and procedures are outlined for calculating the properties of systems with arbitrarily curved axis. Detailed methods are presented for designing and optimizing special components such as aberration correctors, spectrometers, energy filters monochromators, ion traps, electron mirrors and cathode lenses. In particular, the optics of rotationally symmetric lenses, quadrupoles, and systems composed of these elements are discussed extensively. Beam properties such as emittance, brightness, transmissivity and the formation of caustics are outlined. Relativistic motion and spin precession of the electron are treated in a covariant way by introducing the Lorentz-invariant universal time and by extending Hamilton's principle from three to four spatial dimensions where the laboratory time is considered as the fourth pseudo-spatial coordinate. Using this procedure and introducing the self action of the electron, its accompanying electromagnetic field and its radiation field are calculated for arbitrary motion. In addition, the Stern

Non-Markovian effect on the geometric phase of a dissipative qubit

International Nuclear Information System (INIS)

Chen Juanjuan; Tong Qingjun; An Junhong; Luo Honggang; Oh, C. H.

2010-01-01

We studied the geometric phase of a two-level atom coupled to an environment with Lorentzian spectral density. The non-Markovian effect on the geometric phase is explored analytically and numerically. In the weak coupling limit, the lowest order correction to the geometric phase is derived analytically and the general case is calculated numerically. It was found that the correction to the geometric phase is significantly large if the spectral width is small, and in this case the non-Markovian dynamics has a significant impact on the geometric phase. When the spectral width increases, the correction to the geometric phase becomes negligible, which shows the robustness of the geometric phase to the environmental white noises. The result is significant to the quantum information processing based on the geometric phase.

Integrability and soliton in a classical one dimensional site dependent biquadratic Heisenberg spin chain and the effect of nonlinear inhomogeneity

International Nuclear Information System (INIS)

Kavitha, L.; Daniel, M.

2002-07-01

The integrability of one dimensional classical continuum inhomogeneous biquadratic Heisenberg spin chain and the effect of nonlinear inhomogeneity on the soliton of an underlying completely integrable spin model are studied. The dynamics of the spin system is expressed in terms of a higher order generalized nonlinear Schroedinger equation through a differential geometric approach which becomes integrable for a particular choice of the biquadratic exchange interaction and for linear inhomogeneity. The effect of nonlinear inhomogeneity on the spin soliton is studied by carrying out a multiple scale perturbation analysis. (author)

Geometry-based approach to studying the semi-classical limit in quantum dynamics by the coherent states and quantum mechanics on the torus

International Nuclear Information System (INIS)

Faure, F.

1993-01-01

This thesis deals with problems linked to the study of the semi-classical limit in quantum dynamics. The first part presents a geometrical formulation which is tantamount to the time dependent variational principle. The classical dynamics is considered as an orthogonal projection of the quantum dynamics on the family of coherent states. The angle of projection provides an information on the validity of the approximation. This angle is studied in an illustrating example. In the second part, we study quantum mechanics on the torus as a phase space, and particularly degeneracies in the spectrum of Harper like models or kicked Harper like models which manifest chaotic dynamics. These models find direct applications in solid state physics, especially with the quantum Hall effect. In this study, we use the Chern index, which is a topological characterization of the localization of the eigenfunctions as some periodicity conditions are changed. The use of the Husimi distribution provides a phase space representation of the quantum states. We discuss the role played by separatrix-states, by the effects of quantum tunneling, and by a classically chaotic dynamics. (orig.)

Some Hermite–Hadamard Type Inequalities for Geometrically Quasi ...

Indian Academy of Sciences (India)

Abstract. In the paper, we introduce a new concept 'geometrically quasi-convex function' and establish some Hermite–Hadamard type inequalities for functions whose derivatives are of geometric quasi-convexity.

The high resolution spaghetti hadron calorimeter

International Nuclear Information System (INIS)

Jenni, P.; Sonderegger, P.; Paar, H.P.; Wigmans, R.

1987-01-01

It is proposed to build a prototype for a hadron calorimeter with scintillating plastic fibres as active material. The absorber material is lead. Provided that these components are used in the appropriate volume ratio, excellent performance may be expected, e.g. an energy resolution of 30%/√E for jet detection. The proposed design offers additional advantages compared to the classical sandwich calorimeter structures in terms of granularity, hermiticity, uniformity, compactness, readout, radiation resistivity, stability and calibration. 22 refs.; 7 figs

Quantum models of classical systems

International Nuclear Information System (INIS)

Hájíček, P

2015-01-01

Quantum statistical methods that are commonly used for the derivation of classical thermodynamic properties are extended to classical mechanical properties. The usual assumption that every real motion of a classical mechanical system is represented by a sharp trajectory is not testable and is replaced by a class of fuzzy models, the so-called maximum entropy (ME) packets. The fuzzier are the compared classical and quantum ME packets, the better seems to be the match between their dynamical trajectories. Classical and quantum models of a stiff rod will be constructed to illustrate the resulting unified quantum theory of thermodynamic and mechanical properties. (paper)

Improving spatial resolution in quantum imaging beyond the Rayleigh diffraction limit using multiphoton W entangled states

Energy Technology Data Exchange (ETDEWEB)

Wen Jianming, E-mail: jianming.wen@gmail.co [National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093 (China); Department of Physics, University of Arkansas, Fayetteville, AR 72701 (United States); Du, Shengwang [Department of Physics, Hong Kong University of Science and Technology, Clear Bay (Hong Kong); Xiao Min [National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093 (China); Department of Physics, University of Arkansas, Fayetteville, AR 72701 (United States); School of Modern Engineering and Applied Science, Nanjing University, Nanjing 210093 (China)

2010-08-23

Using multiphoton entangled states, we demonstrate improving spatial imaging resolution beyond the Rayleigh diffraction limit in the quantum imaging process. In particular, we examine resolution enhancement using triphoton W state and a factor of 2 is achievable as with the use of the Greenberger-Horne-Zeilinger state, compared to using a classical-light source.

Geometric Hypergraph Learning for Visual Tracking

OpenAIRE

Du, Dawei; Qi, Honggang; Wen, Longyin; Tian, Qi; Huang, Qingming; Lyu, Siwei

2016-01-01

Graph based representation is widely used in visual tracking field by finding correct correspondences between target parts in consecutive frames. However, most graph based trackers consider pairwise geometric relations between local parts. They do not make full use of the target's intrinsic structure, thereby making the representation easily disturbed by errors in pairwise affinities when large deformation and occlusion occur. In this paper, we propose a geometric hypergraph learning based tr...

Sparse geometric graphs with small dilation

NARCIS (Netherlands)

Aronov, B.; Berg, de M.; Cheong, O.; Gudmundsson, J.; Haverkort, H.J.; Vigneron, A.; Deng, X.; Du, D.

2005-01-01

Given a set S of n points in the plane, and an integer k such that 0 = k geometric graph with vertex set S, at most n – 1 + k edges, and dilation O(n / (k + 1)) can be computed in time O(n log n). We also construct n–point sets for which any geometric graph with n – 1 + k edges

Geometric ghosts and unitarity

International Nuclear Information System (INIS)

Ne'eman, Y.

1980-09-01

A review is given of the geometrical identification of the renormalization ghosts and the resulting derivation of Unitarity equations (BRST) for various gauges: Yang-Mills, Kalb-Ramond, and Soft-Group-Manifold

A Color Image Watermarking Scheme Resistant against Geometrical Attacks

Directory of Open Access Journals (Sweden)

Y. Xing

2010-04-01

Full Text Available The geometrical attacks are still a problem for many digital watermarking algorithms at present. In this paper, we propose a watermarking algorithm for color images resistant to geometrical distortions (rotation and scaling. The singular value decomposition is used for watermark embedding and extraction. The log-polar map- ping (LPM and phase correlation method are used to register the position of geometrical distortion suffered by the watermarked image. Experiments with different kinds of color images and watermarks demonstrate that the watermarking algorithm is robust to common image processing attacks, especially geometrical attacks.

Wave Mechanics or Wave Statistical Mechanics

International Nuclear Information System (INIS)

Qian Shangwu; Xu Laizi

2007-01-01

By comparison between equations of motion of geometrical optics and that of classical statistical mechanics, this paper finds that there should be an analogy between geometrical optics and classical statistical mechanics instead of geometrical mechanics and classical mechanics. Furthermore, by comparison between the classical limit of quantum mechanics and classical statistical mechanics, it finds that classical limit of quantum mechanics is classical statistical mechanics not classical mechanics, hence it demonstrates that quantum mechanics is a natural generalization of classical statistical mechanics instead of classical mechanics. Thence quantum mechanics in its true appearance is a wave statistical mechanics instead of a wave mechanics.

Solving Absolute Value Equations Algebraically and Geometrically

Science.gov (United States)

Shiyuan, Wei

2005-01-01

The way in which students can improve their comprehension by understanding the geometrical meaning of algebraic equations or solving algebraic equation geometrically is described. Students can experiment with the conditions of the absolute value equation presented, for an interesting way to form an overall understanding of the concept.

Quasirandom geometric networks from low-discrepancy sequences

Science.gov (United States)

Estrada, Ernesto

2017-08-01

We define quasirandom geometric networks using low-discrepancy sequences, such as Halton, Sobol, and Niederreiter. The networks are built in d dimensions by considering the d -tuples of digits generated by these sequences as the coordinates of the vertices of the networks in a d -dimensional Id unit hypercube. Then, two vertices are connected by an edge if they are at a distance smaller than a connection radius. We investigate computationally 11 network-theoretic properties of two-dimensional quasirandom networks and compare them with analogous random geometric networks. We also study their degree distribution and their spectral density distributions. We conclude from this intensive computational study that in terms of the uniformity of the distribution of the vertices in the unit square, the quasirandom networks look more random than the random geometric networks. We include an analysis of potential strategies for generating higher-dimensional quasirandom networks, where it is know that some of the low-discrepancy sequences are highly correlated. In this respect, we conclude that up to dimension 20, the use of scrambling, skipping and leaping strategies generate quasirandom networks with the desired properties of uniformity. Finally, we consider a diffusive process taking place on the nodes and edges of the quasirandom and random geometric graphs. We show that the diffusion time is shorter in the quasirandom graphs as a consequence of their larger structural homogeneity. In the random geometric graphs the diffusion produces clusters of concentration that make the process more slow. Such clusters are a direct consequence of the heterogeneous and irregular distribution of the nodes in the unit square in which the generation of random geometric graphs is based on.

Geometric convergence of some two-point Pade approximations

International Nuclear Information System (INIS)

Nemeth, G.

1983-01-01

The geometric convergences of some two-point Pade approximations are investigated on the real positive axis and on certain infinite sets of the complex plane. Some theorems concerning the geometric convergence of Pade approximations are proved, and bounds on geometric convergence rates are given. The results may be interesting considering the applications both in numerical computations and in approximation theory. As a specific case, the numerical calculations connected with the plasma dispersion function may be performed. (D.Gy.)

TESTFIELD TRENTO: GEOMETRIC EVALUATION OF VERY HIGH RESOLUTION SATELLITE IMAGERY

Directory of Open Access Journals (Sweden)

G. Agugiaro

2012-07-01

Full Text Available Today the use of spaceborne Very High Spatial Resolution (VHSR optical sensors for automatic 3D information extraction is increasing in the scientific and civil communities. The 3D Optical Metrology (3DOM Unit of the Bruno Kessler Foundation (FBK in Trento (Italy has collected stereo VHSR satellite imagery, as well as aerial and terrestrial data over Trento, with the aim to create a complete data collection with state-of-the-art datasets for investigations on image analysis, automatic digital surface model (DSM generation, 2D/3D feature extraction, city modelling and data fusion. The testfield region covers the city of Trento, characterised by very dense urban (historical centre, residential and industrial areas, and the surrounding hills and steep mountains (approximate height range 200-2100 m with cultivations, forests and bare soil. This paper reports the analysis conducted in FBK on the VHSR spaceborne imagery of Trento testfield for 3D information extraction. The data include two stereo-pairs acquired by WorldView-2 in August 2010 and by GeoEye-1 in September 2011 in panchromatic and multispectral mode, together with their original Rational Polynomial Coefficients (RPC, and the position and description of well distributed ground points. For reference and validation, a DSM from airborne LiDAR acquisition is used. The paper gives details on the project and the dataset characteristics. The results achieved by 3DOM on DSM extraction from WorldView-2 and GeoEye-1 stereo-pairs are shown and commented.

Auto-focusing accelerating hyper-geometric laser beams

International Nuclear Information System (INIS)

Kovalev, A A; Kotlyar, V V; Porfirev, A P

2016-01-01

We derive a new solution to the paraxial wave equation that defines a two-parameter family of three-dimensional structurally stable vortex annular auto-focusing hyper-geometric (AH) beams, with their complex amplitude expressed via a degenerate hyper-geometric function. The AH beams are found to carry an orbital angular momentum and be auto-focusing, propagating on an accelerating path toward a focus, where the annular intensity pattern is ‘sharply’ reduced in diameter. An explicit expression for the complex amplitude of vortex annular auto-focusing hyper-geometric-Gaussian beams is derived. The experiment has been shown to be in good agreement with theory. (paper)

Sum rules in classical scattering

International Nuclear Information System (INIS)

Bolle, D.; Osborn, T.A.

1981-01-01

This paper derives sum rules associated with the classical scattering of two particles. These sum rules are the analogs of Levinson's theorem in quantum mechanics which provides a relationship between the number of bound-state wavefunctions and the energy integral of the time delay of the scattering process. The associated classical relation is an identity involving classical time delay and an integral over the classical bound-state density. We show that equalities between the Nth-order energy moment of the classical time delay and the Nth-order energy moment of the classical bound-state density hold in both a local and a global form. Local sum rules involve the time delay defined on a finite but otherwise arbitrary coordinate space volume S and the bound-state density associated with this same region. Global sum rules are those that obtain when S is the whole coordinate space. Both the local and global sum rules are derived for potentials of arbitrary shape and for scattering in any space dimension. Finally the set of classical sum rules, together with the known quantum mechanical analogs, are shown to provide a unified method of obtaining the high-temperature expansion of the classical, respectively the quantum-mechanical, virial coefficients

Jordan-Schwinger map, 3D harmonic oscillator constants of motion, and classical and quantum parameters characterizing electromagnetic wave polarization

International Nuclear Information System (INIS)

Mota, R D; Xicotencatl, M A; Granados, V D

2004-01-01

In this work we introduce a generalization of the Jauch and Rohrlich quantum Stokes operators when the arrival direction from the source is unknown a priori. We define the generalized Stokes operators as the Jordan-Schwinger map of a triplet of harmonic oscillators with the Gell-Mann and Ne'eman matrices of the SU(3) symmetry group. We show that the elements of the Jordan-Schwinger map are the constants of motion of the three-dimensional isotropic harmonic oscillator. Also, we show that the generalized Stokes operators together with the Gell-Mann and Ne'eman matrices may be used to expand the polarization matrix. By taking the expectation value of the Stokes operators in a three-mode coherent state of the electromagnetic field, we obtain the corresponding generalized classical Stokes parameters. Finally, by means of the constants of motion of the classical 3D isotropic harmonic oscillator we describe the geometrical properties of the polarization ellipse

Jordan Schwinger map, 3D harmonic oscillator constants of motion, and classical and quantum parameters characterizing electromagnetic wave polarization

Science.gov (United States)

Mota, R. D.; Xicoténcatl, M. A.; Granados, V. D.

2004-02-01

In this work we introduce a generalization of the Jauch and Rohrlich quantum Stokes operators when the arrival direction from the source is unknown a priori. We define the generalized Stokes operators as the Jordan-Schwinger map of a triplet of harmonic oscillators with the Gell-Mann and Ne'eman matrices of the SU(3) symmetry group. We show that the elements of the Jordan-Schwinger map are the constants of motion of the three-dimensional isotropic harmonic oscillator. Also, we show that the generalized Stokes operators together with the Gell-Mann and Ne'eman matrices may be used to expand the polarization matrix. By taking the expectation value of the Stokes operators in a three-mode coherent state of the electromagnetic field, we obtain the corresponding generalized classical Stokes parameters. Finally, by means of the constants of motion of the classical 3D isotropic harmonic oscillator we describe the geometrical properties of the polarization ellipse.

Jordan-Schwinger map, 3D harmonic oscillator constants of motion, and classical and quantum parameters characterizing electromagnetic wave polarization

Energy Technology Data Exchange (ETDEWEB)

Mota, R D [Unidad Profesional Interdisciplinaria de IngenierIa y TecnologIas Avanzadas, IPN. Av. Instituto Politecnico Nacional 2580, Col. La Laguna Ticoman, 07340 Mexico DF (Mexico); Xicotencatl, M A [Departamento de Matematicas del Centro de Investigacion y Estudios Avanzados del IPN, Mexico DF, 07000 (Mexico); Granados, V D [Escuela Superior de FIsica y Matematicas, Instituto Politecnico Nacional, Ed. 9, Unidad Profesional Adolfo Lopez Mateos, 07738 Mexico DF (Mexico)

2004-02-20

In this work we introduce a generalization of the Jauch and Rohrlich quantum Stokes operators when the arrival direction from the source is unknown a priori. We define the generalized Stokes operators as the Jordan-Schwinger map of a triplet of harmonic oscillators with the Gell-Mann and Ne'eman matrices of the SU(3) symmetry group. We show that the elements of the Jordan-Schwinger map are the constants of motion of the three-dimensional isotropic harmonic oscillator. Also, we show that the generalized Stokes operators together with the Gell-Mann and Ne'eman matrices may be used to expand the polarization matrix. By taking the expectation value of the Stokes operators in a three-mode coherent state of the electromagnetic field, we obtain the corresponding generalized classical Stokes parameters. Finally, by means of the constants of motion of the classical 3D isotropic harmonic oscillator we describe the geometrical properties of the polarization ellipse.

Lattice degeneracies of geometric fermions

International Nuclear Information System (INIS)

Raszillier, H.

1983-05-01

We give the minimal numbers of degrees of freedom carried by geometric fermions on all lattices of maximal symmetries in d = 2, 3, and 4 dimensions. These numbers are lattice dependent, but in the (free) continuum limit, part of the degrees of freedom have to escape to infinity by a Wilson mechanism built in, and 2sup(d) survive for any lattice. On self-reciprocal lattices we compare the minimal numbers of degrees of freedom of geometric fermions with the minimal numbers of naive fermions on these lattices and argue that these numbers are equal. (orig.)

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

The Inappropriate Symmetries of Multivariate Statistical Analysis in Geometric Morphometrics.

Science.gov (United States)

Bookstein, Fred L

In today's geometric morphometrics the commonest multivariate statistical procedures, such as principal component analysis or regressions of Procrustes shape coordinates on Centroid Size, embody a tacit roster of symmetries -axioms concerning the homogeneity of the multiple spatial domains or descriptor vectors involved-that do not correspond to actual biological fact. These techniques are hence inappropriate for any application regarding which we have a-priori biological knowledge to the contrary (e.g., genetic/morphogenetic processes common to multiple landmarks, the range of normal in anatomy atlases, the consequences of growth or function for form). But nearly every morphometric investigation is motivated by prior insights of this sort. We therefore need new tools that explicitly incorporate these elements of knowledge, should they be quantitative, to break the symmetries of the classic morphometric approaches. Some of these are already available in our literature but deserve to be known more widely: deflated (spatially adaptive) reference distributions of Procrustes coordinates, Sewall Wright's century-old variant of factor analysis, the geometric algebra of importing explicit biomechanical formulas into Procrustes space. Other methods, not yet fully formulated, might involve parameterized models for strain in idealized forms under load, principled approaches to the separation of functional from Brownian aspects of shape variation over time, and, in general, a better understanding of how the formalism of landmarks interacts with the many other approaches to quantification of anatomy. To more powerfully organize inferences from the high-dimensional measurements that characterize so much of today's organismal biology, tomorrow's toolkit must rely neither on principal component analysis nor on the Procrustes distance formula, but instead on sound prior biological knowledge as expressed in formulas whose coefficients are not all the same. I describe the problems

Unified field theory from the classical wave equation: Preliminary application to atomic and nuclear structure

Energy Technology Data Exchange (ETDEWEB)

Múnera, Héctor A., E-mail: hmunera@hotmail.com [Centro Internacional de Física (CIF), Apartado Aéreo 4948, Bogotá, Colombia, South America (Colombia); Retired professor, Department of Physics, Universidad Nacional de Colombia, Bogotá, Colombia, South America (Colombia)

2016-07-07

It is postulated that there exists a fundamental energy-like fluid, which occupies the flat three-dimensional Euclidean space that contains our universe, and obeys the two basic laws of classical physics: conservation of linear momentum, and conservation of total energy; the fluid is described by the classical wave equation (CWE), which was Schrödinger’s first candidate to develop his quantum theory. Novel solutions for the CWE discovered twenty years ago are nonharmonic, inherently quantized, and universal in the sense of scale invariance, thus leading to quantization at all scales of the universe, from galactic clusters to the sub-quark world, and yielding a unified Lorentz-invariant quantum theory ab initio. Quingal solutions are isomorphic under both neo-Galilean and Lorentz transformations, and exhibit nother remarkable property: intrinsic unstability for large values of ℓ (a quantum number), thus limiting the size of each system at a given scale. Unstability and scale-invariance together lead to nested structures observed in our solar system; unstability may explain the small number of rows in the chemical periodic table, and nuclear unstability of nuclides beyond lead and bismuth. Quingal functions lend mathematical basis for Boscovich’s unified force (which is compatible with many pieces of evidence collected over the past century), and also yield a simple geometrical solution for the classical three-body problem, which is a useful model for electronic orbits in simple diatomic molecules. A testable prediction for the helicoidal-type force is suggested.

Thomas Young's contributions to geometrical optics.

Science.gov (United States)

Atchison, David A; Charman, W Neil

2011-07-01

In addition to his work on physical optics, Thomas Young (1773-1829) made several contributions to geometrical optics, most of which received little recognition in his time or since. We describe and assess some of these contributions: Young's construction (the basis for much of his geometric work), paraxial refraction equations, oblique astigmatism and field curvature, and gradient-index optics. © 2011 The Authors. Clinical and Experimental Optometry © 2011 Optometrists Association Australia.

An Introduction to Geometric Algebra with some Preliminary Thoughts on the Geometric Meaning of Quantum Mechanics

International Nuclear Information System (INIS)

Horn, Martin Erik

2014-01-01

It is still a great riddle to me why Wolfgang Pauli and P.A.M. Dirac had not fully grasped the meaning of their own mathematical constructions. They invented magnificent, fantastic and very important mathematical features of modern physics, but they only delivered half of the interpretations of their own inventions. Of course, Pauli matrices and Dirac matrices represent operators, which Pauli and Dirac discussed in length. But this is only part of the true meaning behind them, as the non-commutative ideas of Grassmann, Clifford, Hamilton and Cartan allow a second, very far reaching interpretation of Pauli and Dirac matrices. An introduction to this alternative interpretation will be discussed. Some applications of this view on Pauli and Dirac matrices are given, e.g. a geometric algebra picture of the plane wave solution of the Maxwell equation, a geometric algebra picture of special relativity, a toy model of SU(3) symmetry, and some only very preliminary thoughts about a possible geometric meaning of quantum mechanics

Geometric integrators for stochastic rigid body dynamics

KAUST Repository

Tretyakov, Mikhail

2016-01-05

Geometric integrators play an important role in simulating dynamical systems on long time intervals with high accuracy. We will illustrate geometric integration ideas within the stochastic context, mostly on examples of stochastic thermostats for rigid body dynamics. The talk will be mainly based on joint recent work with Rusland Davidchak and Tom Ouldridge.

Geometric integrators for stochastic rigid body dynamics

KAUST Repository

Tretyakov, Mikhail

2016-01-01

Geometric integrators play an important role in simulating dynamical systems on long time intervals with high accuracy. We will illustrate geometric integration ideas within the stochastic context, mostly on examples of stochastic thermostats for rigid body dynamics. The talk will be mainly based on joint recent work with Rusland Davidchak and Tom Ouldridge.

Mathematical physics classical mechanics

CERN Document Server

Knauf, Andreas

2018-01-01

As a limit theory of quantum mechanics, classical dynamics comprises a large variety of phenomena, from computable (integrable) to chaotic (mixing) behavior. This book presents the KAM (Kolmogorov-Arnold-Moser) theory and asymptotic completeness in classical scattering. Including a wealth of fascinating examples in physics, it offers not only an excellent selection of basic topics, but also an introduction to a number of current areas of research in the field of classical mechanics. Thanks to the didactic structure and concise appendices, the presentation is self-contained and requires only knowledge of the basic courses in mathematics. The book addresses the needs of graduate and senior undergraduate students in mathematics and physics, and of researchers interested in approaching classical mechanics from a modern point of view.

Lung segmentation from HRCT using united geometric active contours

Science.gov (United States)

Liu, Junwei; Li, Chuanfu; Xiong, Jin; Feng, Huanqing

2007-12-01

Accurate lung segmentation from high resolution CT images is a challenging task due to various detail tracheal structures, missing boundary segments and complex lung anatomy. One popular method is based on gray-level threshold, however its results are usually rough. A united geometric active contours model based on level set is proposed for lung segmentation in this paper. Particularly, this method combines local boundary information and region statistical-based model synchronously: 1) Boundary term ensures the integrality of lung tissue.2) Region term makes the level set function evolve with global characteristic and independent on initial settings. A penalizing energy term is introduced into the model, which forces the level set function evolving without re-initialization. The method is found to be much more efficient in lung segmentation than other methods that are only based on boundary or region. Results are shown by 3D lung surface reconstruction, which indicates that the method will play an important role in the design of computer-aided diagnostic (CAD) system.

Length-scale effect due to periodic variation of geometrically necessary dislocation densities

DEFF Research Database (Denmark)

Oztop, M. S.; Niordson, Christian Frithiof; Kysar, J. W.

2013-01-01

Strain gradient plasticity theories have been successful in predicting qualitative aspects of the length scale effect, most notably the increase in yield strength and hardness as the size of the deforming volume decreases. However new experimental methodologies enabled by recent developments...... of high spatial resolution diffraction methods in a scanning electron microscope give a much more quantitative understanding of plastic deformation at small length scales. Specifically, geometrically necessary dislocation densities (GND) can now be measured and provide detailed information about...... the microstructure of deformed metals in addition to the size effect. Recent GND measurements have revealed a distribution of length scales that evolves within a metal undergoing plastic deformation. Furthermore, these experiments have shown an accumulation of GND densities in cell walls as well as a variation...

Estimating reaction rate constants: comparison between traditional curve fitting and curve resolution

NARCIS (Netherlands)

Bijlsma, S.; Boelens, H. F. M.; Hoefsloot, H. C. J.; Smilde, A. K.

2000-01-01

A traditional curve fitting (TCF) algorithm is compared with a classical curve resolution (CCR) approach for estimating reaction rate constants from spectral data obtained in time of a chemical reaction. In the TCF algorithm, reaction rate constants an estimated from the absorbance versus time data

Classical and quantum dynamics from classical paths to path integrals

CERN Document Server

Dittrich, Walter

2017-01-01

Graduate students who wish to become familiar with advanced computational strategies in classical and quantum dynamics will find in this book both the fundamentals of a standard course and a detailed treatment of the time-dependent oscillator, Chern-Simons mechanics, the Maslov anomaly and the Berry phase, to name just a few topics. Well-chosen and detailed examples illustrate perturbation theory, canonical transformations and the action principle, and demonstrate the usage of path integrals. The fifth edition has been revised and enlarged to include chapters on quantum electrodynamics, in particular, Schwinger’s proper time method and the treatment of classical and quantum mechanics with Lie brackets and pseudocanonical transformations. It is shown that operator quantum electrodynamics can be equivalently described with c-numbers, as demonstrated by calculating the propagation function for an electron in a prescribed classical electromagnetic field.

Geometric reconstruction methods for electron tomography

DEFF Research Database (Denmark)

Alpers, Andreas; Gardner, Richard J.; König, Stefan

2013-01-01

Electron tomography is becoming an increasingly important tool in materials science for studying the three-dimensional morphologies and chemical compositions of nanostructures. The image quality obtained by many current algorithms is seriously affected by the problems of missing wedge artefacts...... and discuss several algorithms from the mathematical fields of geometric and discrete tomography. The algorithms incorporate geometric prior knowledge (mainly convexity and homogeneity), which also in principle considerably reduces the number of tilt angles required. Results are discussed...

Normed algebras and the geometric series test

Directory of Open Access Journals (Sweden)

Robert Kantrowitz

2017-11-01

Full Text Available The purpose of this article is to survey a class of normed algebras that share many central features of Banach algebras, save for completeness. The likeness of these algebras to Banach algebras derives from the fact that the geometric series test is valid, whereas the lack of completeness points to the failure of the absolute convergence test for series in the algebra. Our main result is a compendium of conditions that are all equivalent to the validity of the geometric series test for commutative unital normed algebras. Several examples in the final section showcase some incomplete normed algebras for which the geometric series test is valid, and still others for which it is not.

Initial singularity and pure geometric field theories

Science.gov (United States)

Wanas, M. I.; Kamal, Mona M.; Dabash, Tahia F.

2018-01-01

In the present article we use a modified version of the geodesic equation, together with a modified version of the Raychaudhuri equation, to study initial singularities. These modified equations are used to account for the effect of the spin-torsion interaction on the existence of initial singularities in cosmological models. Such models are the results of solutions of the field equations of a class of field theories termed pure geometric. The geometric structure used in this study is an absolute parallelism structure satisfying the cosmological principle. It is shown that the existence of initial singularities is subject to some mathematical (geometric) conditions. The scheme suggested for this study can be easily generalized.

Stock price prediction using geometric Brownian motion

Science.gov (United States)

Farida Agustini, W.; Restu Affianti, Ika; Putri, Endah RM

2018-03-01

Geometric Brownian motion is a mathematical model for predicting the future price of stock. The phase that done before stock price prediction is determine stock expected price formulation and determine the confidence level of 95%. On stock price prediction using geometric Brownian Motion model, the algorithm starts from calculating the value of return, followed by estimating value of volatility and drift, obtain the stock price forecast, calculating the forecast MAPE, calculating the stock expected price and calculating the confidence level of 95%. Based on the research, the output analysis shows that geometric Brownian motion model is the prediction technique with high rate of accuracy. It is proven with forecast MAPE value ≤ 20%.

Geometric optimization and sums of algebraic functions

KAUST Repository

Vigneron, Antoine E.

2014-01-01

We present a new optimization technique that yields the first FPTAS for several geometric problems. These problems reduce to optimizing a sum of nonnegative, constant description complexity algebraic functions. We first give an FPTAS for optimizing such a sum of algebraic functions, and then we apply it to several geometric optimization problems. We obtain the first FPTAS for two fundamental geometric shape-matching problems in fixed dimension: maximizing the volume of overlap of two polyhedra under rigid motions and minimizing their symmetric difference. We obtain the first FPTAS for other problems in fixed dimension, such as computing an optimal ray in a weighted subdivision, finding the largest axially symmetric subset of a polyhedron, and computing minimum-area hulls.

The Geometric Phase of Stock Trading.

Science.gov (United States)

Altafini, Claudio

2016-01-01

Geometric phases describe how in a continuous-time dynamical system the displacement of a variable (called phase variable) can be related to other variables (shape variables) undergoing a cyclic motion, according to an area rule. The aim of this paper is to show that geometric phases can exist also for discrete-time systems, and even when the cycles in shape space have zero area. A context in which this principle can be applied is stock trading. A zero-area cycle in shape space represents the type of trading operations normally carried out by high-frequency traders (entering and exiting a position on a fast time-scale), while the phase variable represents the cash balance of a trader. Under the assumption that trading impacts stock prices, even zero-area cyclic trading operations can induce geometric phases, i.e., profits or losses, without affecting the stock quote.

Can EPR non-locality be geometrical?

International Nuclear Information System (INIS)

Ne'eman, Y.

1995-01-01

The presence in Quantum Mechanics of non-local correlations is one of the two fundamentally non-intuitive features of that theory. The non-local correlations themselves fall into two classes: EPR and Geometrical. The non-local characteristics of the geometrical type are well-understood and are not suspected of possibly generating acausal features, such as faster-than-light propagation of information. This has especially become true since the emergence of a geometrical treatment for the relevant gauge theories, i.e. Fiber Bundle geometry, in which the quantum non-localities are seen to correspond to pure homotopy considerations. This aspect is reviewed in section 2. Contrary-wise, from its very conception, the EPR situation was felt to be paradoxical. It has been suggested that the non-local features of EPR might also derive from geometrical considerations, like all other non-local characteristics of QM. In[7], one of the authors was able to point out several plausibility arguments for this thesis, emphasizing in particular similarities between the non-local correlations provided by any gauge field theory and those required by the preservation of the quantum numbers of the original EPR state-vector, throughout its spatially-extended mode. The derivation was, however, somewhat incomplete, especially because of the apparent difference between, on the one hand, the closed spatial loops arising in the analysis of the geometrical non-localities, from Aharonov-Bohm and Berry phases to magnetic monopoles and instantons, and on the other hand, in the EPR case, the open line drawn by the positions of the two moving decay products of the disintegrating particle. In what follows, the authors endeavor to remove this obstacle and show that as in all other QM non-localities, EPR is somehow related to closed loops, almost involving homotopy considerations. They develop this view in section 3

Geometrical treatment of Clifford algebras and spinors with applications to the dynamics of spin particles

International Nuclear Information System (INIS)

Dimakis, A.

1983-01-01

The algebraic structure of the real Clifford algebras (CA) of vector spaces with non-degenerated scalar product of arbitrary signature is studied, and a classification formula for this is obtained. The latter is based on three sequences of integer numbers from which one is the Radon-Harwitz sequence. A new representation method of real CA is constructed. This leads to a geometrical representation of real Clifford algebras in which the representation spaces are subspaces of the CA itself (''spinor spaces''). One of these spinor spaces is a subalgebra of the original CA. The relation between CA and external algebras is studied. Each external algebra with a scalar product possesses the structure of a CA. From the geometric representation developed here then follows that spinors are inhomogeneous external forms. The transformation behaviour of spinors under the orthogonal, as well as under the general linear group is studied. By means of these algebraic results the spinor connexion and the covariant Dirac operator on a differential manifold are introduced. In the geometrical representation a further in ternal SL(2,R) symmetry of the Dirac equation (DE) is shown. Furthermore other equivalent formulations of the DE can be obtained. Of special interest is the tetrade formulation of the DE. A generalization of the DE is introduced. The equations of motion of the classical relativistic spin particle are derived by means of spinors and CA from a variational principle. From this interesting formal analogies with the supersymmetric theories of the spin particle result. Finally the DE in the curved space-time is established and studied in the tetrade formulation. Using the methods developed here a new exact solution of the coupled Einstein-Curtan-Dirac theory was found (massice ''Ghost-Dirac fields''). (orig.) [de

Classical An-W-geometry

International Nuclear Information System (INIS)

Gervais, J.L.

1993-01-01

By analyzing the extrinsic geometry of two dimensional surfaces chirally embedded in C P n (the C P n W-surface), we give exact treatments in various aspects of the classical W-geometry in the conformal gauge: First, the basis of tangent and normal vectors are defined at regular points of the surface, such that their infinitesimal displacements are given by connections which coincide with the vector potentials of the (conformal) A n -Toda Lax pair. Since the latter is known to be intrinsically related with the W symmetries, this gives the geometrical meaning of the A n W-Algebra. Second, W-surfaces are put in one-to-one correspondence with solutions of the conformally-reduced WZNW model, which is such that the Toda fields give the Cartan part in the Gauss decomposition of its solutions. Third, the additional variables of the Toda hierarchy are used as coordinates of C P n . This allows us to show that W-transformations may be extended as particular diffeomorphisms of this target-space. Higher-dimensional generalizations of the WZNW equations are derived and related with the Zakharov-Shabat equations of the Toda hierarchy. Fourth, singular points are studied from a global viewpoint, using our earlier observation that W-surfaces may be regarded as instantons. The global indices of the W-geometry, which are written in terms of the Toda fields, are shown to be the instanton numbers for associated mappings of W-surfaces into the Grassmannians. The relation with the singularities of W-surface is derived by combining the Toda equations with the Gauss-Bonnet theorem. (orig.)

Geometrical tile design for complex neighborhoods.

Science.gov (United States)

Czeizler, Eugen; Kari, Lila

2009-01-01

Recent research has showed that tile systems are one of the most suitable theoretical frameworks for the spatial study and modeling of self-assembly processes, such as the formation of DNA and protein oligomeric structures. A Wang tile is a unit square, with glues on its edges, attaching to other tiles and forming larger and larger structures. Although quite intuitive, the idea of glues placed on the edges of a tile is not always natural for simulating the interactions occurring in some real systems. For example, when considering protein self-assembly, the shape of a protein is the main determinant of its functions and its interactions with other proteins. Our goal is to use geometric tiles, i.e., square tiles with geometrical protrusions on their edges, for simulating tiled paths (zippers) with complex neighborhoods, by ribbons of geometric tiles with simple, local neighborhoods. This paper is a step toward solving the general case of an arbitrary neighborhood, by proposing geometric tile designs that solve the case of a "tall" von Neumann neighborhood, the case of the f-shaped neighborhood, and the case of a 3 x 5 "filled" rectangular neighborhood. The techniques can be combined and generalized to solve the problem in the case of any neighborhood, centered at the tile of reference, and included in a 3 x (2k + 1) rectangle.

Geometric integration for particle accelerators

Science.gov (United States)

Forest, Étienne

2006-05-01

This paper is a very personal view of the field of geometric integration in accelerator physics—a field where often work of the highest quality is buried in lost technical notes or even not published; one has only to think of Simon van der Meer Nobel prize work on stochastic cooling—unpublished in any refereed journal. So I reconstructed the relevant history of geometrical integration in accelerator physics as much as I could by talking to collaborators and using my own understanding of the field. The reader should not be too surprised if this account is somewhere between history, science and perhaps even fiction.

Geometric integration for particle accelerators

International Nuclear Information System (INIS)

Forest, Etienne

2006-01-01

This paper is a very personal view of the field of geometric integration in accelerator physics-a field where often work of the highest quality is buried in lost technical notes or even not published; one has only to think of Simon van der Meer Nobel prize work on stochastic cooling-unpublished in any refereed journal. So I reconstructed the relevant history of geometrical integration in accelerator physics as much as I could by talking to collaborators and using my own understanding of the field. The reader should not be too surprised if this account is somewhere between history, science and perhaps even fiction

Observation of the geometric phase using photon echoes

International Nuclear Information System (INIS)

Tian, Mingzhen; Reibel, Randy R.; Barber, Zeb W.; Fischer, Joe A.; Babbitt, Wm. Randall

2003-01-01

The geometric phase of an atomic system has been observed in V-type three-level barium atoms using photon echoes. The geometric phase results from a cyclic evolution of a two-level subsystem driven by a laser pulse. The phase change is observed on the echo field produced on a different subsystem that is coupled via the ground state to the driven subsystem. The measured geometric phase was half of the solid angle subtended by the Bloch vector along the driven evolution circuit. This evolution has the potential to form universal operations of quantum bits

Variational data assimilation system with nesting model for high resolution ocean circulation

Energy Technology Data Exchange (ETDEWEB)

Ishikawa, Yoichi; Igarashi, Hiromichi; Hiyoshi, Yoshimasa; Sasaki, Yuji; Wakamatsu, Tsuyoshi; Awaji, Toshiyuki [Center for Earth Information Science and Technology, Japan Agency for Marine-Earth Science and Technology, 3173-25 Showa-machi, Kanazawa-Ku, Yokohama 236-0001 (Japan); In, Teiji [Japan Marine Science Foundation, 4-24, Minato-cho, Mutsu, Aomori, 035-0064 (Japan); Nakada, Satoshi [Graduate School of Maritime Science, Kobe University, 5-1-1, Fukae-minamimachi, Higashinada-Ku, Kobe, 658-0022 (Japan); Nishina, Kei, E-mail: ishikaway@jamstec.go.jp [Graduate School of Science, Kyoto University, Kitashirakawaoiwake-cho, Sakyo-Ku, Kyoto, 606-8502 (Japan)

2015-10-15

To obtain the high-resolution analysis fields for ocean circulation, a new incremental approach is developed using a four-dimensional variational data assimilation system with nesting models. The results show that there are substantial biases when using a classical method combined with data assimilation and downscaling, caused by different dynamics resulting from the different resolutions of the models used within the nesting models. However, a remarkable reduction in biases of the low-resolution model relative to the high-resolution model was observed using our new approach in narrow strait regions, such as the Tsushima and Tsugaru straits, where the difference in the dynamics represented by the high- and low-resolution models is substantial. In addition, error reductions are demonstrated in the downstream region of these narrow channels associated with the propagation of information through the model dynamics. (paper)

Geometric and engineering drawing

CERN Document Server

Morling, K

2010-01-01

The new edition of this successful text describes all the geometric instructions and engineering drawing information that are likely to be needed by anyone preparing or interpreting drawings or designs with plenty of exercises to practice these principles.

Classical trajectory methods in molecular collisions

International Nuclear Information System (INIS)

Porter, R.N.; Raff, L.M.

1976-01-01

The discussion of classical trajectory methods in molecular collisions includes classical dynamics, Hamiltonian mechanics, classical scattering cross sections and rate coefficients, statistical averaging, the selection of initial states, integration of equations of motion, analysis of final states, consecutive collisions, and the prognosis for classical molecular scattering calculations. 61 references

Study into Point Cloud Geometric Rigidity and Accuracy of TLS-Based Identification of Geometric Bodies

Science.gov (United States)

Klapa, Przemyslaw; Mitka, Bartosz; Zygmunt, Mariusz

2017-12-01

Capability of obtaining a multimillion point cloud in a very short time has made the Terrestrial Laser Scanning (TLS) a widely used tool in many fields of science and technology. The TLS accuracy matches traditional devices used in land surveying (tacheometry, GNSS - RTK), but like any measurement it is burdened with error which affects the precise identification of objects based on their image in the form of a point cloud. The point’s coordinates are determined indirectly by means of measuring the angles and calculating the time of travel of the electromagnetic wave. Each such component has a measurement error which is translated into the final result. The XYZ coordinates of a measuring point are determined with some uncertainty and the very accuracy of determining these coordinates is reduced as the distance to the instrument increases. The paper presents the results of examination of geometrical stability of a point cloud obtained by means terrestrial laser scanner and accuracy evaluation of solids determined using the cloud. Leica P40 scanner and two different settings of measuring points were used in the tests. The first concept involved placing a few balls in the field and then scanning them from various sides at similar distances. The second part of measurement involved placing balls and scanning them a few times from one side but at varying distances from the instrument to the object. Each measurement encompassed a scan of the object with automatic determination of its position and geometry. The desk studies involved a semiautomatic fitting of solids and measurement of their geometrical elements, and comparison of parameters that determine their geometry and location in space. The differences of measures of geometrical elements of balls and translations vectors of the solids centres indicate the geometrical changes of the point cloud depending on the scanning distance and parameters. The results indicate the changes in the geometry of scanned objects

Microsphere-based super-resolution scanning optical microscope.

Science.gov (United States)

Huszka, Gergely; Yang, Hui; Gijs, Martin A M

2017-06-26

High-refractive index dielectric microspheres positioned within the field of view of a microscope objective in a dielectric medium can focus the light into a so-called photonic nanojet. A sample placed in such nanojet can be imaged by the objective with super-resolution, i.e. with a resolution beyond the classical diffraction limit. However, when imaging nanostructures on a substrate, the propagation distance of a light wave in the dielectric medium in between the substrate and the microsphere must be small enough to reveal the sample's nanometric features. Therefore, only the central part of an image obtained through a microsphere shows super-resolution details, which are typically ∼100 nm using white light (peak at λ = 600 nm). We have performed finite element simulations of the role of this critical distance in the super-resolution effect. Super-resolution imaging of a sample placed beneath the microsphere is only possible within a very restricted central area of ∼10 μm 2 , where the separation distance between the substrate and the microsphere surface is very small (∼1 μm). To generate super-resolution images over larger areas of the sample, we have fixed a microsphere on a frame attached to the microscope objective, which is automatically scanned over the sample in a step-by-step fashion. This generates a set of image tiles, which are subsequently stitched into a single super-resolution image (with resolution of λ/4-λ/5) of a sample area of up to ∼10 4 μm 2 . Scanning a standard optical microscope objective with microsphere therefore enables super-resolution microscopy over the complete field-of-view of the objective.

Fast collision resolution for real time services in SDMA based wireless ATM networks

DEFF Research Database (Denmark)

Vornefeld, U.; Schieimer, D.; Walke, B.

1999-01-01

protocol, the influence of SDMA on a contention based access protocol is investigated under collision resolution schemes derived from classical splitting algorithms. Although this work is embedded in the framework of wireless ATM and HIPERLAN/2 systems, the ideas are generally applicable....

Geometric inequalities for axially symmetric black holes

International Nuclear Information System (INIS)

Dain, Sergio

2012-01-01

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 play an important role in the characterization of the gravitational collapse; they are closely related with the cosmic censorship conjecture. Axially symmetric black holes are the natural candidates to study these inequalities because the quasi-local angular momentum is well defined for them. We review recent results in this subject and we also describe the main ideas behind the proofs. Finally, a list of relevant open problems is presented. (topical review)

EARLY HISTORY OF GEOMETRIC PROBABILITY AND STEREOLOGY

Directory of Open Access Journals (Sweden)

Magdalena Hykšová

2012-03-01

Full Text Available The paper provides an account of the history of geometric probability and stereology from the time of Newton to the early 20th century. It depicts the development of two parallel ways: on one hand, the theory of geometric probability was formed with minor attention paid to other applications than those concerning spatial chance games. On the other hand, practical rules of the estimation of area or volume fraction and other characteristics, easily deducible from geometric probability theory, were proposed without the knowledge of this branch. A special attention is paid to the paper of J.-É. Barbier published in 1860, which contained the fundamental stereological formulas, but remained almost unnoticed both by mathematicians and practicians.

Zwitters: Particles between quantum and classical

International Nuclear Information System (INIS)

Wetterich, C.

2012-01-01

We describe both quantum particles and classical particles in terms of a classical statistical ensemble, with a probability distribution in phase space. By use of a wave function in phase space both can be treated in the same quantum formalism. Quantum particles are characterized by a specific choice of observables and time evolution of the probability density. Then interference and tunneling are found within classical statistics. Zwitters are (effective) one-particle states for which the time evolution interpolates between quantum and classical particles. Experimental bounds on a small parameter can test quantum mechanics. -- Highlights: ► Quantum particles can be described within classical statistics. ► Classical particles are formulated in quantum formalism. ► Zwitters interpolate between classical and quantum particles. ► Zwitters allow for quantitative tests of quantum mechanics. ► Zwitters could be effective one-particle descriptions of droplets.

Geometric Analysis of Vein Fracture Networks From the Awibengkok Core, Indonesia

Science.gov (United States)

Khatwa, A.; Bruhn, R. L.; Brown, S. R.

2003-12-01

Fracture network systems within rocks are important features for the transportation and remediation of hazardous waste, oil and gas production, geothermal energy extraction and the formation of vein fillings and ore deposits. A variety of methods, including computational and laboratory modeling have been employed to further understand the dynamic nature of fractures and fracture systems (e.g. Ebel and Brown, this session). To substantiate these studies, it is also necessary to analyze the characteristics and morphology of naturally occurring vein systems. The Awibengkok core from a geothermal system in West Java, Indonesia provided an excellent opportunity to study geometric and petrologic characteristics of vein systems in volcanic rock. Vein minerals included chlorite, calcite, quartz, zeolites and sulphides. To obtain geometric data on the veins, we employed a neural net image processing technique to analyze high-resolution digital photography of the veins. We trained a neural net processor to map the extent of the vein using RGB pixel training classes. The resulting classification image was then converted to a binary image file and processed through a MatLab program that we designed to calculate vein geometric statistics, including aperture and roughness. We also performed detailed petrographic and microscopic geometric analysis on the veins to determine the history of mineralization and fracturing. We found that multi-phase mineralization due to chemical dissolution and re-precipitation as well as mechanical fracturing was a common feature in many of the veins and that it had a significant role for interpreting vein tortuosity and history of permeability. We used our micro- and macro-scale observations to construct four hypothetical permeability models that compliment the numerical and laboratory modeled data reported by Ebel and Brown. In each model, permeability changes, and in most cases fluctuates, differently over time as the tortuosity and aperture of

Geometric factors in the magnetoresistance of n-doped InAs epilayers

KAUST Repository

Sun, Jian

2013-11-27

We investigate the magnetoresistance (MR) effect in n-doped InAs and InAs/metal hybrid devices with geometries tailored to elucidate the physical mechanism and the role of geometry in the MR. Despite the isotropic Fermi surface in InAs, we observe a strong intrinsic MR in the InAs epilayer due to the existence of a surface conducting layer. Experimental comparison confirms that the extraordinary MR in the InAs/metal hybrids outperforms the orbital MR in the Corbino disk in terms of both the MR ratio and the magnetic field resolution. The results also indicate the advantage of a two-contact configuration in the hybrid devices over a four-contact one with respect to the magnetic field resolution. This is in contrast to previously reported results, where performance was evaluated in terms of the MR ratio and a four-contact configuration was found to be optimal. By applying Kohler\\'s rule, we find that at temperatures above 75 K the extraordinary MR violates Kohler\\'s rule, due to multiple relaxation rates, whereas the orbital MR obeys it. This finding can be used to distinguish the two geometric effects, the extraordinary MR and the orbital MR, from each other.

Thermal fluctuations in the classical superconductor Nb{sub 3}Sn from high-resolution specific-heat measurements

Energy Technology Data Exchange (ETDEWEB)

Lortz, Rolf [Department of Condensed Matter Physics, University of Geneva, 24 Quai Ernest-Ansermet, CH-1211 Geneva 4 (Switzerland)], E-mail: Rolf.Lortz@physics.unige.ch; Wang Yuxing; Junod, Alain [Department of Condensed Matter Physics, University of Geneva, 24 Quai Ernest-Ansermet, CH-1211 Geneva 4 (Switzerland); Toyota, Naoki [Physics Department, Graduate School of Science, Tohoku University, 980-8571 Sendai (Japan)

2007-09-01

The range of thermal fluctuations in 'classical' bulk superconductors is extremely small and especially in low-fields hardly experimentally accessible. With a new type of calorimeter we were able to detect a tiny lambda anomaly in the specific-heat of the superconductor Nb{sub 3}Sn within a narrow temperature range around the H{sub c2} line. We show that the evolution of the anomaly as a function of magnetic field follows scaling laws expected in the presence of critical thermal fluctuations.

Classical Trajectories and Quantum Spectra

Science.gov (United States)

Mielnik, Bogdan; Reyes, Marco A.

1996-01-01

A classical model of the Schrodinger's wave packet is considered. The problem of finding the energy levels corresponds to a classical manipulation game. It leads to an approximate but non-perturbative method of finding the eigenvalues, exploring the bifurcations of classical trajectories. The role of squeezing turns out decisive in the generation of the discrete spectra.

The classic: Bone morphogenetic protein.

Science.gov (United States)

Urist, Marshall R; Strates, Basil S

2009-12-01

This Classic Article is a reprint of the original work by Marshall R. Urist and Basil S. Strates, Bone Morphogenetic Protein. An accompanying biographical sketch of Marshall R. Urist, MD is available at DOI 10.1007/s11999-009-1067-4; a second Classic Article is available at DOI 10.1007/s11999-009-1069-2; and a third Classic Article is available at DOI 10.1007/s11999-009-1070-9. The Classic Article is copyright 1971 by Sage Publications Inc. Journals and is reprinted with permission from Urist MR, Strates BS. Bone morphogenetic protein. J Dent Res. 1971;50:1392-1406.

The Spacetime Memory of Geometric Phases and Quantum Computing

CERN Document Server

Binder, B

2002-01-01

Spacetime memory is defined with a holonomic approach to information processing, where multi-state stability is introduced by a non-linear phase-locked loop. Geometric phases serve as the carrier of physical information and geometric memory (of orientation) given by a path integral measure of curvature that is periodically refreshed. Regarding the resulting spin-orbit coupling and gauge field, the geometric nature of spacetime memory suggests to assign intrinsic computational properties to the electromagnetic field.

The Need for Accurate Geometric and Radiometric Corrections of Drone-Borne Hyperspectral Data for Mineral Exploration: MEPHySTo—A Toolbox for Pre-Processing Drone-Borne Hyperspectral Data

Directory of Open Access Journals (Sweden)

Sandra Jakob

2017-01-01

Full Text Available Drone-borne hyperspectral imaging is a new and promising technique for fast and precise acquisition, as well as delivery of high-resolution hyperspectral data to a large variety of end-users. Drones can overcome the scale gap between field and air-borne remote sensing, thus providing high-resolution and multi-temporal data. They are easy to use, flexible and deliver data within cm-scale resolution. So far, however, drone-borne imagery has prominently and successfully been almost solely used in precision agriculture and photogrammetry. Drone technology currently mainly relies on structure-from-motion photogrammetry, aerial photography and agricultural monitoring. Recently, a few hyperspectral sensors became available for drones, but complex geometric and radiometric effects complicate their use for geology-related studies. Using two examples, we first show that precise corrections are required for any geological mapping. We then present a processing toolbox for frame-based hyperspectral imaging systems adapted for the complex correction of drone-borne hyperspectral imagery. The toolbox performs sensor- and platform-specific geometric distortion corrections. Furthermore, a topographic correction step is implemented to correct for rough terrain surfaces. We recommend the c-factor-algorithm for geological applications. To our knowledge, we demonstrate for the first time the applicability of the corrected dataset for lithological mapping and mineral exploration.

The geometric semantics of algebraic quantum mechanics.

Science.gov (United States)

Cruz Morales, John Alexander; Zilber, Boris

2015-08-06

In this paper, we will present an ongoing project that aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We argue that this approach provides a geometric semantics for such a formalism by means of establishing a (non-commutative) duality between certain algebraic and geometric objects. © 2015 The Author(s) Published by the Royal Society. All rights reserved.

Dynamics in geometrical confinement

CERN Document Server

Kremer, Friedrich

2014-01-01

This book describes the dynamics of low molecular weight and polymeric molecules when they are constrained under conditions of geometrical confinement. It covers geometrical confinement in different dimensionalities: (i) in nanometer thin layers or self supporting films (1-dimensional confinement) (ii) in pores or tubes with nanometric diameters (2-dimensional confinement) (iii) as micelles embedded in matrices (3-dimensional) or as nanodroplets.The dynamics under such conditions have been a much discussed and central topic in the focus of intense worldwide research activities within the last two decades. The present book discusses how the resulting molecular mobility is influenced by the subtle counterbalance between surface effects (typically slowing down molecular dynamics through attractive guest/host interactions) and confinement effects (typically increasing the mobility). It also explains how these influences can be modified and tuned, e.g. through appropriate surface coatings, film thicknesses or pore...

Gravity, a geometrical course

CERN Document Server

Frè, Pietro Giuseppe

2013-01-01

‘Gravity, a Geometrical Course’ presents general relativity (GR) in a systematic and exhaustive way, covering three aspects that are homogenized into a single texture: i) the mathematical, geometrical foundations, exposed in a self consistent contemporary formalism, ii) the main physical, astrophysical and cosmological applications,  updated to the issues of contemporary research and observations, with glimpses on supergravity and superstring theory, iii) the historical development of scientific ideas underlying both the birth of general relativity and its subsequent evolution. The book is divided in two volumes.   Volume One is dedicated to the development of the theory and basic physical applications. It guides the reader from the foundation of special relativity to Einstein field equations, illustrating some basic applications in astrophysics. A detailed  account  of the historical and conceptual development of the theory is combined with the presentation of its mathematical foundations.  Differe...

Observational study of differences in head position for high notes in famous classical and non-classical male singers.

Science.gov (United States)

Amarante Andrade, Pedro; Švec, Jan G

2016-07-01

Differences in classical and non-classical singing are due primarily to aesthetic style requirements. The head position can affect the sound quality. This study aimed at comparing the head position for famous classical and non-classical male singers performing high notes. Images of 39 Western classical and 34 non-classical male singers during live performances were obtained from YouTube. Ten raters evaluated the frontal rotational head position (depression versus elevation) and transverse head position (retraction versus protraction) visually using a visual analogue scale. The results showed a significant difference for frontal rotational head position. Most non-classical singers in the sample elevated their heads for high notes while the classical singers were observed to keep it around the neutral position. This difference may be attributed to different singing techniques and phonatory system adjustments utilized by each group.

Improvement of optical imaging resolution by a negative refraction photonic crystal with a solid immersion lens

International Nuclear Information System (INIS)

Tseng, M.-C.; Chen, L.-W.; Liu, C.-Y.

2008-01-01

Photonic crystals (PCs) have many potential applications because of their ability to control light-wave propagation. We have investigated the solid immersion lens (SIL) technology in imaging system based on negative refraction PCs and analyzed the influence of refractive index and geometric parameters of SIL on imaging resolution. In the finite element method calculation, the resolution of our optical system has improved greatly. The high performance of imaging resolution was achieved with shorter radius and larger refractive index of SIL. Furthermore, the effects of the three kinds of SILs at the same radius were analyzed. Such a mechanism of negative refraction PCs and SILs should open up a new application for designing components in optical imaging systems

Exponentiated Lomax Geometric Distribution: Properties and Applications

Directory of Open Access Journals (Sweden)

Amal Soliman Hassan

2017-09-01

Full Text Available In this paper, a new four-parameter lifetime distribution, called the exponentiated Lomax geometric (ELG is introduced. The new lifetime distribution contains the Lomax geometric and exponentiated Pareto geometric as new sub-models. Explicit algebraic formulas of probability density function, survival and hazard functions are derived. Various structural properties of the new model are derived including; quantile function, Re'nyi entropy, moments, probability weighted moments, order statistic, Lorenz and Bonferroni curves. The estimation of the model parameters is performed by maximum likelihood method and inference for a large sample is discussed. The flexibility and potentiality of the new model in comparison with some other distributions are shown via an application to a real data set. We hope that the new model will be an adequate model for applications in various studies.

Sudan-decoding generalized geometric Goppa codes

DEFF Research Database (Denmark)

Heydtmann, Agnes Eileen

2003-01-01

Generalized geometric Goppa codes are vector spaces of n-tuples with entries from different extension fields of a ground field. They are derived from evaluating functions similar to conventional geometric Goppa codes, but allowing evaluation in places of arbitrary degree. A decoding scheme...... for these codes based on Sudan's improved algorithm is presented and its error-correcting capacity is analyzed. For the implementation of the algorithm it is necessary that the so-called increasing zero bases of certain spaces of functions are available. A method to obtain such bases is developed....

Geometric approach to the design of an imaging probe to evaluate the iridocorneal angle structures

Science.gov (United States)

Hong, Xun Jie Jeesmond; V. K., Shinoj; Murukeshan, V. M.; Baskaran, M.; Aung, Tin

2017-06-01

Photographic imaging methods allow the tracking of anatomical changes in the iridocorneal angle structures and the monitoring of treatment responses overtime. In this work, we aim to design an imaging probe to evaluate the iridocorneal angle structures using geometrical optics. We first perform an analytical analysis on light propagation from the anterior chamber of the eye to the exterior medium using Snell's law. This is followed by adopting a strategy to achieve uniform near field irradiance, by simplifying the complex non-rotational symmetric irradiance distribution of LEDs tilted at an angle. The optimization is based on the geometric design considerations of an angled circular ring array of 4 LEDs (or a 2 × 2 square LED array). The design equation give insights on variable parameters such as the illumination angle of the LEDs, ring array radius, viewing angle of the LEDs, and the working distance. A micro color CCD video camera that has sufficient resolution to resolve the iridocorneal angle structures at the required working distance is then chosen. The proposed design aspects fulfil the safety requirements recommended by the International Commission on Non-ionizing Radiation Protection.

Geometrical intuition and the learning and teaching of geometry

OpenAIRE

Fujita, Taro; Jones, Keith; Yamamoto, Shinya

2004-01-01

Intuition is often regarded as essential in the learning of geometry, but how such skills might be effectively developed in students remains an open question. This paper reviews the role and importance of geometrical intuition and suggests it involves the skills to create and manipulate geometrical figures in the mind, to see geometrical properties, to relate images to concepts and theorems in geometry, and decide where and how to start when solving problems in geometry. Based on these theore...

Bi-photon spectral correlation measurements from a silicon nanowire in the quantum and classical regimes

Science.gov (United States)

Jizan, Iman; Helt, L. G.; Xiong, Chunle; Collins, Matthew J.; Choi, Duk-Yong; Joon Chae, Chang; Liscidini, Marco; Steel, M. J.; Eggleton, Benjamin J.; Clark, Alex S.

2015-01-01

The growing requirement for photon pairs with specific spectral correlations in quantum optics experiments has created a demand for fast, high resolution and accurate source characterisation. A promising tool for such characterisation uses classical stimulated processes, in which an additional seed laser stimulates photon generation yielding much higher count rates, as recently demonstrated for a χ(2) integrated source in A. Eckstein et al. Laser Photon. Rev. 8, L76 (2014). In this work we extend these results to χ(3) integrated sources, directly measuring for the first time the relation between spectral correlation measurements via stimulated and spontaneous four wave mixing in an integrated optical waveguide, a silicon nanowire. We directly confirm the speed-up due to higher count rates and demonstrate that this allows additional resolution to be gained when compared to traditional coincidence measurements without any increase in measurement time. As the pump pulse duration can influence the degree of spectral correlation, all of our measurements are taken for two different pump pulse widths. This allows us to confirm that the classical stimulated process correctly captures the degree of spectral correlation regardless of pump pulse duration, and cements its place as an essential characterisation method for the development of future quantum integrated devices. PMID:26218609

Classic and Golli Myelin Basic Protein have distinct developmental trajectories in human visual cortex.

Science.gov (United States)

Siu, Caitlin R; Balsor, Justin L; Jones, David G; Murphy, Kathryn M

2015-01-01

Traditionally, myelin is viewed as insulation around axons, however, more recent studies have shown it also plays an important role in plasticity, axonal metabolism, and neuroimmune signaling. Myelin is a complex multi-protein structure composed of hundreds of proteins, with Myelin Basic Protein (MBP) being the most studied. MBP has two families: Classic-MBP that is necessary for activity driven compaction of myelin around axons, and Golli-MBP that is found in neurons, oligodendrocytes, and T-cells. Furthermore, Golli-MBP has been called a "molecular link" between the nervous and immune systems. In visual cortex specifically, myelin proteins interact with immune processes to affect experience-dependent plasticity. We studied myelin in human visual cortex using Western blotting to quantify Classic- and Golli-MBP expression in post-mortem tissue samples ranging in age from 20 days to 80 years. We found that Classic- and Golli-MBP have different patterns of change across the lifespan. Classic-MBP gradually increases to 42 years and then declines into aging. Golli-MBP has early developmental changes that are coincident with milestones in visual system sensitive period, and gradually increases into aging. There are three stages in the balance between Classic- and Golli-MBP expression, with Golli-MBP dominating early, then shifting to Classic-MBP, and back to Golli-MBP in aging. Also Golli-MBP has a wave of high inter-individual variability during childhood. These results about cortical MBP expression are timely because they compliment recent advances in MRI techniques that produce high resolution maps of cortical myelin in normal and diseased brain. In addition, the unique pattern of Golli-MBP expression across the lifespan suggests that it supports high levels of neuroimmune interaction in cortical development and in aging.

Markkinointiviestintäsuunnitelma : Classic Coffee Oy

OpenAIRE

Eerola, Laura

2015-01-01

Opinnäytetyön aiheena oli laatia markkinointiviestintäsuunnitelma kalenterivuodelle 2016 vuosikellon muodossa, toimintansa jo vakiinnuttaneelle Classic Coffee Oy:lle. Classic Coffee Oy on vuonna 2011 perustettu, Tampereella toimiva kahvila-alan yritys joka tarjoaa lounaskahvilatoiminnan lisäksi laadukkaita konditoria-palveluita, yritys- ja kokoustarjoiluja sekä tilavuokrausta. Classic Coffee Oy:llä on yksi kahvila, Classic Coffee Tampella. Kahvila sijaitsee Tampellassa, Tampereen keskustan vä...

Classical higher-order processes

DEFF Research Database (Denmark)

Montesi, Fabrizio

2017-01-01

Classical Processes (CP) is a calculus where the proof theory of classical linear logic types processes à la Π-calculus, building on a Curry-Howard correspondence between session types and linear propositions. We contribute to this research line by extending CP with process mobility, inspired by ...

Ingredients of the Eddy Soup: A Geometric Decomposition of Eddy-Mean Flow Interactions

Science.gov (United States)

Waterman, S.; Lilly, J. M.

2014-12-01

Understanding eddy-mean flow interactions is a long-standing problem in geophysical fluid dynamics with modern relevance to the task of representing eddy effects in coarse resolution models while preserving their dependence on the underlying dynamics of the flow field. Exploiting the recognition that the velocity covariance matrix/eddy stress tensor that describes eddy fluxes, also encodes information about eddy size, shape and orientation through its geometric representation in the form of the so-called variance ellipse, suggests a potentially fruitful way forward. Here we present a new framework that describes eddy-mean flow interactions in terms of a geometric description of the eddy motion, and illustrate it with an application to an unstable jet. Specifically we show that the eddy vorticity flux divergence F, a key dynamical quantity describing the average effect of fluctuations on the time-mean flow, may be decomposed into two components with distinct geometric interpretations: 1. variations in variance ellipse orientation; and 2. variations in the anisotropic part of the eddy kinetic energy, a function of the variance ellipse size and shape. Application of the divergence theorem shows that F integrated over a region is explained entirely by variations in these two quantities around the region's periphery. This framework has the potential to offer new insights into eddy-mean flow interactions in a number of ways. It identifies the ingredients of the eddy motion that have a mean flow forcing effect, it links eddy effects to spatial patterns of variance ellipse geometry that can suggest the mechanisms underpinning these effects, and finally it illustrates the importance of resolving eddy shape and orientation, and not just eddy size/energy, to accurately represent eddy feedback effects. These concepts will be both discussed and illustrated.

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

Geometric transitions, flops and non-Kahler manifolds: I

International Nuclear Information System (INIS)

Becker, Melanie; Dasgupta, Keshav; Knauf, Anke; Tatar, Radu

2004-01-01

We construct a duality cycle which provides a complete supergravity description of geometric transitions in type II theories via a flop in M-theory. This cycle connects the different supergravity descriptions before and after the geometric transitions. Our construction reproduces many of the known phenomena studied earlier in the literature and allows us to describe some new and interesting aspects in a simple and elegant fashion. A precise supergravity description of new torsional manifolds that appear on the type IIA side with branes and fluxes and the corresponding geometric transition are obtained. A local description of new G2 manifolds that are circle fibrations over non-Kahler manifolds is presented

Active Learning Environment with Lenses in Geometric Optics

Science.gov (United States)

Tural, Güner

2015-01-01

Geometric optics is one of the difficult topics for students within physics discipline. Students learn better via student-centered active learning environments than the teacher-centered learning environments. So this study aimed to present a guide for middle school teachers to teach lenses in geometric optics via active learning environment…

Geometric Representations of Condition Queries on Three-Dimensional Vector Fields

Science.gov (United States)

Henze, Chris

1999-01-01

Condition queries on distributed data ask where particular conditions are satisfied. It is possible to represent condition queries as geometric objects by plotting field data in various spaces derived from the data, and by selecting loci within these derived spaces which signify the desired conditions. Rather simple geometric partitions of derived spaces can represent complex condition queries because much complexity can be encapsulated in the derived space mapping itself A geometric view of condition queries provides a useful conceptual unification, allowing one to intuitively understand many existing vector field feature detection algorithms -- and to design new ones -- as variations on a common theme. A geometric representation of condition queries also provides a simple and coherent basis for computer implementation, reducing a wide variety of existing and potential vector field feature detection techniques to a few simple geometric operations.

Edit propagation using geometric relationship functions

KAUST Repository

Guerrero, Paul; Jeschke, Stefan; Wimmer, Michael; Wonka, Peter

2014-01-01

We propose a method for propagating edit operations in 2D vector graphics, based on geometric relationship functions. These functions quantify the geometric relationship of a point to a polygon, such as the distance to the boundary or the direction to the closest corner vertex. The level sets of the relationship functions describe points with the same relationship to a polygon. For a given query point, we first determine a set of relationships to local features, construct all level sets for these relationships, and accumulate them. The maxima of the resulting distribution are points with similar geometric relationships. We show extensions to handle mirror symmetries, and discuss the use of relationship functions as local coordinate systems. Our method can be applied, for example, to interactive floorplan editing, and it is especially useful for large layouts, where individual edits would be cumbersome. We demonstrate populating 2D layouts with tens to hundreds of objects by propagating relatively few edit operations. © 2014 ACM 0730-0301/2014/03- ART15 $15.00.

Edit propagation using geometric relationship functions

KAUST Repository

Guerrero, Paul

2014-04-15

We propose a method for propagating edit operations in 2D vector graphics, based on geometric relationship functions. These functions quantify the geometric relationship of a point to a polygon, such as the distance to the boundary or the direction to the closest corner vertex. The level sets of the relationship functions describe points with the same relationship to a polygon. For a given query point, we first determine a set of relationships to local features, construct all level sets for these relationships, and accumulate them. The maxima of the resulting distribution are points with similar geometric relationships. We show extensions to handle mirror symmetries, and discuss the use of relationship functions as local coordinate systems. Our method can be applied, for example, to interactive floorplan editing, and it is especially useful for large layouts, where individual edits would be cumbersome. We demonstrate populating 2D layouts with tens to hundreds of objects by propagating relatively few edit operations. © 2014 ACM 0730-0301/2014/03- ART15 $15.00.

Local quantum channels preserving classical correlations

International Nuclear Information System (INIS)

Guo Zhihua; Cao Huaixin

2013-01-01

The aim of this paper is to discuss local quantum channels that preserve classical correlations. First, we give two equivalent characterizations of classical correlated states. Then we obtain the relationships among classical correlation-preserving local quantum channels, commutativity-preserving local quantum channels and commutativity-preserving quantum channels on each subsystem. Furthermore, for a two-qubit system, we show the general form of classical correlation-preserving local quantum channels. (paper)

A GEOMETRICAL HEIGHT SCALE FOR SUNSPOT PENUMBRAE

International Nuclear Information System (INIS)

Puschmann, K. G.; Ruiz Cobo, B.; MartInez Pillet, V.

2010-01-01

Inversions of spectropolarimetric observations of penumbral filaments deliver the stratification of different physical quantities in an optical depth scale. However, without establishing a geometrical height scale, their three-dimensional geometrical structure cannot be derived. This is crucial in understanding the correct spatial variation of physical properties in the penumbral atmosphere and to provide insights into the mechanism capable of explaining the observed penumbral brightness. The aim of this work is to determine a global geometrical height scale in the penumbra by minimizing the divergence of the magnetic field vector and the deviations from static equilibrium as imposed by a force balance equation that includes pressure gradients, gravity, and the Lorentz force. Optical depth models are derived from the inversion of spectropolarimetric data of an active region observed with the Solar Optical Telescope on board the Hinode satellite. We use a genetic algorithm to determine the boundary condition for the inference of geometrical heights. The retrieved geometrical height scale permits the evaluation of the Wilson depression at each pixel and the correlation of physical quantities at each height. Our results fit into the uncombed penumbral scenario, i.e., a penumbra composed of flux tubes with channeled mass flow and with a weaker and more horizontal magnetic field as compared with the background field. The ascending material is hotter and denser than their surroundings. We do not find evidence of overturning convection or field-free regions in the inner penumbral area analyzed. The penumbral brightness can be explained by the energy transfer of the ascending mass carried by the Evershed flow, if the physical quantities below z = -75 km are extrapolated from the results of the inversion.

Ultrafast time-resolved absorption spectroscopy of geometric isomers of xanthophylls

Science.gov (United States)

Niedzwiedzki, Dariusz M.; Enriquez, Miriam M.; LaFountain, Amy M.; Frank, Harry A.

2010-07-01

This paper presents an ultrafast optical spectroscopic investigation of the excited state energies, lifetimes and spectra of specific geometric isomers of neoxanthin, violaxanthin, lutein, and zeaxanthin. All- trans- and 15,15'- cis-β-carotene were also examined. The spectroscopy was done on molecules purified by HPLC frozen immediately to inhibit isomerization. The spectra were taken at 77 K to maintain the configurations and to provide better spectral resolution than seen at room temperature. The kinetics reveal that for all of the molecules except neoxanthin, the S 1 state lifetime of the cis isomers is shorter than that of the all- trans isomers. The S 1 excited state energies of all the isomers were determined by recording S 1 → S 2 transient absorption spectra. The results obtained in this manner at cryogenic temperatures provide an unprecedented level of precision in the measurement of the S 1 energies of these xanthophylls, which are critical components in light-harvesting pigment-protein complexes of green plants.

Multiple reflection Michelson interferometer with picometer resolution.

Science.gov (United States)

Pisani, Marco

2008-12-22

A Michelson interferometer based on an optical set-up allowing multiple reflection between two plane mirrors performs the multiplication of the optical path by a factor N, proportionally increasing the resolution of the measurement. A multiplication factor of almost two orders of magnitude has been demonstrated with a simple set-up. The technique can be applied to any interferometric measurement where the classical interferometer limits due to fringe nonlinearities and quantum noise are an issue. Applications in precision engineering, vibration analysis, nanometrology, and spectroscopy are foreseen.

Classicalization of Gravitons and Goldstones

CERN Document Server

Dvali, Gia; Kehagias, Alex

2011-01-01

We establish a close parallel between classicalization of gravitons and derivatively-coupled Nambu-Goldstone-type scalars. We show, that black hole formation in high energy scattering process represents classicalization with the classicalization radius given by Schwarzschild radius of center of mass energy, and with the precursor of black hole entropy being given by number of soft quanta composing this classical configuration. Such an entropy-equivalent is defined for scalar classicalons also and is responsible for exponential suppression of their decay into small number of final particles. This parallel works in both ways. For optimists that are willing to hypothesize that gravity may indeed self-unitarize at high energies via black hole formation, it illustrates that the Goldstones may not be much different in this respect, and they classicalize essentially by similar dynamics as gravitons. In the other direction, it may serve as an useful de-mystifier of via-black-hole-unitarization process and of the role...

Geometric information provider platform

Directory of Open Access Journals (Sweden)

Meisam Yousefzadeh

2015-07-01

Full Text Available Renovation of existing buildings is known as an essential stage in reduction of the energy loss. Considerable part of renovation process depends on geometric reconstruction of building based on semantic parameters. Following many research projects which were focused on parameterizing the energy usage, various energy modelling methods were developed during the last decade. On the other hand, by developing accurate measuring tools such as laser scanners, the interests of having accurate 3D building models are rapidly growing. But the automation of 3D building generation from laser point cloud or detection of specific objects in that is still a challenge.  The goal is designing a platform through which required geometric information can be efficiently produced to support energy simulation software. Developing a reliable procedure which extracts required information from measured data and delivers them to a standard energy modelling system is the main purpose of the project.

Classical mechanics with calculus of variations and optimal control an intuitive introduction

CERN Document Server

Levi, Mark

2014-01-01

This is an intuitively motivated presentation of many topics in classical mechanics and related areas of control theory and calculus of variations. All topics throughout the book are treated with zero tolerance for unrevealing definitions and for proofs which leave the reader in the dark. Some areas of particular interest are: an extremely short derivation of the ellipticity of planetary orbits; a statement and an explanation of the "tennis racket paradox"; a heuristic explanation (and a rigorous treatment) of the gyroscopic effect; a revealing equivalence between the dynamics of a particle and statics of a spring; a short geometrical explanation of Pontryagin's Maximum Principle, and more. In the last chapter, aimed at more advanced readers, the Hamiltonian and the momentum are compared to forces in a certain static problem. This gives a palpable physical meaning to some seemingly abstract concepts and theorems. With minimal prerequisites consisting of basic calculus and basic undergraduate physics, this boo...

Classical spins in superconductors

Energy Technology Data Exchange (ETDEWEB)

Shiba, H [Tokyo Univ.; Maki, K

1968-08-01

It is shown that there exists a localized excited state in the energy gap in a superconductor with a classical spin. At finite concentration localized excited states around classical spins form an impurity band. The process of growth of the impurity band and its effects on observable quantities are investigated.

Multiwire proportional chambers with a high spatial resolution for X radiation detection and localization

International Nuclear Information System (INIS)

Algre, J.-L.

1975-01-01

A multiwire proportional counter, with a high spatial resolution has been developed, and some basic characteristics of this type of detector specified. A method of calculating the potential and consequently the field at each point of the volume limited by the counter was defined. The method allows the problems of the outer wires to be solved, and the consequences of a wire displacement predicted. The analysis of the pulses observed on both cathode and anode showed that they were hardly formed from the only ion migration from the cathode to the anode. An estimation of the formation time duration established that in argon mixtures with a low percentage of methane, Ar + ions are in majority. Then it can be predicted that anode wires are not to be spaced by less than 1mm when a conventional electronics is used. The study of the multiplication factor as a function of the main geometric parameters of the counter gave a relation between the multiplication coefficient and the geometric parameters of the chamber; consequently the optimal operation conditions can be predicted. Especially, the diameter of the multiplying wires must be as weak as possible to improve the energy resolution of the detector. A localization method showed that an interpolation may be done between two wires so that, with 1mm spaced wires, the two-dimensional position of an event can be determined with a resolution better than 0.5mm for both directions [fr

Adaptive multi-resolution Modularity for detecting communities in networks

Science.gov (United States)

Chen, Shi; Wang, Zhi-Zhong; Bao, Mei-Hua; Tang, Liang; Zhou, Ji; Xiang, Ju; Li, Jian-Ming; Yi, Chen-He

2018-02-01

Community structure is a common topological property of complex networks, which attracted much attention from various fields. Optimizing quality functions for community structures is a kind of popular strategy for community detection, such as Modularity optimization. Here, we introduce a general definition of Modularity, by which several classical (multi-resolution) Modularity can be derived, and then propose a kind of adaptive (multi-resolution) Modularity that can combine the advantages of different Modularity. By applying the Modularity to various synthetic and real-world networks, we study the behaviors of the methods, showing the validity and advantages of the multi-resolution Modularity in community detection. The adaptive Modularity, as a kind of multi-resolution method, can naturally solve the first-type limit of Modularity and detect communities at different scales; it can quicken the disconnecting of communities and delay the breakup of communities in heterogeneous networks; and thus it is expected to generate the stable community structures in networks more effectively and have stronger tolerance against the second-type limit of Modularity.

CLASSICS

Indian Academy of Sciences (India)

2013-11-11

Nov 11, 2013 ... Polanyi's classic paper, co-authored by Henry Eyring, reproduced in this ... spatial conf guration of the atoms in terms of the energy function of the diatomic .... The present communication deals with the construction of such .... These three contributions are complemented by a fourth term if one takes into.

DMSA-scintigraphy in paediatrics: is the evaluation of the geometric mean necessary for the calculation of the differential renal function?

International Nuclear Information System (INIS)

Porn, U.; Alalp, S.; Fischer, S.; Dresel, S.; Rossmueller, B.; Hahn, K.

2001-01-01

For assessment of differential renal function (PF) by means of static renal scintigraphy with Tc-99m-dimercaptosuccinic acid (DMSA) the calculation of the geometric mean of counts from the anterior and posterior view is recommended. Aim of this retrospective study was to find out, if the anterior view is necessary to receive an accurate differential renal function by calculating the geometric mean compared to calculating PF using the counts of the posterior view only. Methods: 164 DMSA-scans of 151 children (86 f, 65 m) aged 16 d to 16 a (4.7 ± 3.9 a) were reviewed. The scans were performed using a dual head gamma camera (Picker Prism 2000 XP, low energy ultra high resolution collimator, matrix 256 x 256, 300 kcts/view, Zoom: 1.6-2.0). Background corrected values from both kidneys anterior and posterior were obtained. Using region of interest technique PF was calculated using the counts of the dorsal view and compared with the calculated geometric mean [SQR(Cts dors x Cts ventr )]. Results: The differential function of the right kidney was significantly less when compared to the calculation of the geometric mean (p geom and the PF dors was 1.5 ± 1.4%. A difference ≥5% (5.0-9.5%) was obtained in only 6/164 scans (3.7%). Three of 6 patients presented with an underestimated PF dors due to dystopic kidneys on the left side in 2 patients and on the right side in one patient. The other 3 patients with a difference >5% did not show any renal abnormality. Conclusion: The calculation of the PF from the posterior view only will give an underestimated value of the right kidney compared to the calculation of the geometric mean. This effect is not relevant for the calculation of the differential renal function in orthotopic kidneys, so that in these cases the anterior view is not necessary. However, geometric mean calculation to obtain reliable values for differential renal function should be applied in cases with an obvious anatomical abnormality. (orig.) [de

[Calculation of the partial function of the kidney with DMSA in pediatrics: is the evaluation of the geometric mean necessary?].

Science.gov (United States)

Porn, U; Rossmüller, B; Alalp, S; Fischer, S; Dresel, S; Hahn, K

2001-08-01

For assessment of differential renal function (PF) by means of static renal scintigraphy with Tc-99m-dimercaptosuccinic acid (DMSA) the calculation of the geometric mean of counts from the anterior and posterior view is recommended. Of this retrospective study was to find out, if the anterior view is necessary to receive an accurate differential renal function by calculating the geometric mean compared to calculating PF using the counts of the posterior view only. 164 DMSA-scans of 151 children (86 f, 65 m) aged 16 d to 16 a (4.7 +/- 3.9 a) were reviewed. The scans were performed using a dual head gamma camera (Picker Prism 2000 XP, low energy ultra high resolution collimator, matrix 256 x 256, 300 kcts/view, Zoom: 1.6-2.0). Background corrected values from both kidneys anterior and posterior were obtained. Using region of interest technique PF was calculated using the counts of the dorsal view and compared with the calculated geometric mean [SQR(Ctsdors x Ctsventr)]. The differential function of the right kidney was significantly less when compared to the calculation of the geometric mean (p or = 5% (5.0-9.5%) was obtained in only 6/164 scans (3.7%). Three of 6 patients presented with an underestimated PFdors due to dystopic kidneys on the left side in 2 patients and on the right side in one patient. The other 3 patients with a difference > 5% did not show any renal abnormality. The calculation of the PF from the posterior view only will give an underestimated value of the right kidney compared to the calculation of the geometric mean. This effect is not relevant for the calculation of the differential renal function in orthotopic kidneys, so that in these cases the anterior view is not necessary. However, geometric mean calculation to obtain reliable values for differential renal function should be applied in cases with an obvious anatomical abnormality.

Geometrical methods for power network analysis

Energy Technology Data Exchange (ETDEWEB)

Bellucci, Stefano; Tiwari, Bhupendra Nath [Istituto Nazioneale di Fisica Nucleare, Frascati, Rome (Italy). Lab. Nazionali di Frascati; Gupta, Neeraj [Indian Institute of Technology, Kanpur (India). Dept. of Electrical Engineering

2013-02-01

Uses advanced geometrical methods to analyse power networks. Provides a self-contained and tutorial introduction. Includes a fully worked-out example for the IEEE 5 bus system. This book is a short introduction to power system planning and operation using advanced geometrical methods. The approach is based on well-known insights and techniques developed in theoretical physics in the context of Riemannian manifolds. The proof of principle and robustness of this approach is examined in the context of the IEEE 5 bus system. This work addresses applied mathematicians, theoretical physicists and power engineers interested in novel mathematical approaches to power network theory.

Geometric modular action and transformation groups

International Nuclear Information System (INIS)

Summers, S.J.

1996-01-01

We study a weak form of geometric modular action, which is naturally associated with transformation groups of partially ordered sets and which provides these groups with projective representations. Under suitable conditions it is shown that these groups are implemented by point transformations of topological spaces serving as models for space-times, leading to groups which may be interpreted as symmetry groups of the space-times. As concrete examples, it is shown that the Poincare group and the de Sitter group can be derived from this condition of geometric modular action. Further consequences and examples are discussed. (orig.)

Effect analysis of geometric parameters of floating raft on isolation performance

Directory of Open Access Journals (Sweden)

LI Shangda

2017-12-01

Full Text Available [Objectives] This paper focuses on the effects of the geometric parameters of a floating raft on isolation performance.[Methods] Based on the idea that the weight of a floating raft remains constant, a parametric finite element model is established using geometric parameters, and the effects of the geometric parameters when isolation performance is measured by vibration level difference are discussed.[Results] The effects of the geometric parameters of a floating raft on isolation performance are mainly reflected in the middle and high frequency areas. The most important geometric parameters which have an impact on isolation performance are the raft's height, length to width ratio and number of ribs. Adjusting the geometric parameters of the raft is one effective way to avoid the vibration frequency of mechanical equipment.[Conclusions] This paper has some practical value for the engineering design of floating raft isolation systems.

The resolution of inflammation: Principles and challenges.

Science.gov (United States)

Headland, Sarah E; Norling, Lucy V

2015-05-01

The concept that chemokines, cytokines and pro-inflammatory mediators act in a co-ordinated fashion to drive the initiation of the inflammatory reaction is well understood. The significance of such networks acting during the resolution of inflammation however is poorly appreciated. In recent years, specific pro-resolving mediators were discovered which activate resolution pathways to return tissues to homeostasis. These mediators are diverse in nature, and include specialized lipid mediators (lipoxins, resolvins, protectins and maresins) proteins (annexin A1, galectins) and peptides, gaseous mediators including hydrogen sulphide, a purine (adenosine), as well as neuromodulator release under the control of the vagus nerve. Functionally, they can act to limit further leukocyte recruitment, induce neutrophil apoptosis and enhance efferocytosis by macrophages. They can also switch macrophages from classical to alternatively activated cells, promote the return of non-apoptotic cells to the lymphatics and help initiate tissue repair mechanisms and healing. Within this review we highlight the essential cellular aspects required for successful tissue resolution, briefly discuss the pro-resolution mediators that drive these processes and consider potential challenges faced by researchers in the quest to discover how inflammation resolves and why chronic inflammation persists. Copyright © 2015 Elsevier Ltd. All rights reserved.

Geometric Aspects of Quantum Mechanics and Quantum Entanglement

International Nuclear Information System (INIS)

Chruscinski, Dariusz

2006-01-01

It is shown that the standard non-relativistic Quantum Mechanics gives rise to elegant and rich geometrical structures. The space of quantum states is endowed with nontrivial Fubini-Study metric which is responsible for the 'peculiarities' of the quantum world. We show that there is also intricate connection between geometrical structures and quantum entanglement

Geometric mean for subspace selection.

Science.gov (United States)

Tao, Dacheng; Li, Xuelong; Wu, Xindong; Maybank, Stephen J

2009-02-01

Subspace selection approaches are powerful tools in pattern classification and data visualization. One of the most important subspace approaches is the linear dimensionality reduction step in the Fisher's linear discriminant analysis (FLDA), which has been successfully employed in many fields such as biometrics, bioinformatics, and multimedia information management. However, the linear dimensionality reduction step in FLDA has a critical drawback: for a classification task with c classes, if the dimension of the projected subspace is strictly lower than c - 1, the projection to a subspace tends to merge those classes, which are close together in the original feature space. If separate classes are sampled from Gaussian distributions, all with identical covariance matrices, then the linear dimensionality reduction step in FLDA maximizes the mean value of the Kullback-Leibler (KL) divergences between different classes. Based on this viewpoint, the geometric mean for subspace selection is studied in this paper. Three criteria are analyzed: 1) maximization of the geometric mean of the KL divergences, 2) maximization of the geometric mean of the normalized KL divergences, and 3) the combination of 1 and 2. Preliminary experimental results based on synthetic data, UCI Machine Learning Repository, and handwriting digits show that the third criterion is a potential discriminative subspace selection method, which significantly reduces the class separation problem in comparing with the linear dimensionality reduction step in FLDA and its several representative extensions.

Experimental realization of universal geometric quantum gates with solid-state spins.

Science.gov (United States)

Zu, C; Wang, W-B; He, L; Zhang, W-G; Dai, C-Y; Wang, F; Duan, L-M

2014-10-02

Experimental realization of a universal set of quantum logic gates is the central requirement for the implementation of a quantum computer. In an 'all-geometric' approach to quantum computation, the quantum gates are implemented using Berry phases and their non-Abelian extensions, holonomies, from geometric transformation of quantum states in the Hilbert space. Apart from its fundamental interest and rich mathematical structure, the geometric approach has some built-in noise-resilience features. On the experimental side, geometric phases and holonomies have been observed in thermal ensembles of liquid molecules using nuclear magnetic resonance; however, such systems are known to be non-scalable for the purposes of quantum computing. There are proposals to implement geometric quantum computation in scalable experimental platforms such as trapped ions, superconducting quantum bits and quantum dots, and a recent experiment has realized geometric single-bit gates in a superconducting system. Here we report the experimental realization of a universal set of geometric quantum gates using the solid-state spins of diamond nitrogen-vacancy centres. These diamond defects provide a scalable experimental platform with the potential for room-temperature quantum computing, which has attracted strong interest in recent years. Our experiment shows that all-geometric and potentially robust quantum computation can be realized with solid-state spin quantum bits, making use of recent advances in the coherent control of this system.

An information geometric approach to least squares minimization

Science.gov (United States)

Transtrum, Mark; Machta, Benjamin; Sethna, James

2009-03-01

Parameter estimation by nonlinear least squares minimization is a ubiquitous problem that has an elegant geometric interpretation: all possible parameter values induce a manifold embedded within the space of data. The minimization problem is then to find the point on the manifold closest to the origin. The standard algorithm for minimizing sums of squares, the Levenberg-Marquardt algorithm, also has geometric meaning. When the standard algorithm fails to efficiently find accurate fits to the data, geometric considerations suggest improvements. Problems involving large numbers of parameters, such as often arise in biological contexts, are notoriously difficult. We suggest an algorithm based on geodesic motion that may offer improvements over the standard algorithm for a certain class of problems.

Uhlmann's geometric phase in presence of isotropic decoherence

International Nuclear Information System (INIS)

Tidstroem, Jonas; Sjoeqvist, Erik

2003-01-01

Uhlmann's mixed state geometric phase [Rep. Math. Phys. 24, 229 (1986)] is analyzed in the case of a qubit affected by isotropic decoherence treated in the Markovian approximation. It is demonstrated that this phase decreases rapidly with increasing decoherence rate and that it is most fragile to weak decoherence for pure or nearly pure initial states. In the unitary case, we compare Uhlmann's geometric phase for mixed states with that occurring in standard Mach-Zehnder interferometry [Phys. Rev. Lett. 85, 2845 (2000)] and show that the latter is more robust to reduction in the length of the Bloch vector. We also describe how Uhlmann's geometric phase in the present case could in principle be realized experimentally