WorldWideScience

Sample records for classical geometric resolution

  1. Classical geometric resolution of the Einstein—Podolsky—Rosen paradox

    OpenAIRE

    Ne'eman, Yuval

    1983-01-01

    I show that, in the geometry of a fiber bundle describing a gauge theory, curvature and parallel transport ensure and impose nonseparability. The “Einstein—Podolsky—Rosen paradox” is thus resolved “classically.” I conjecture that the ostentatiously “implausible” features of the quantum treatment are due to the fact that space—time separability, a basic assumption of single-particle nonrelativistic quantum mechanics, does not fit the bundle geometry of the complete physics.

  2. Geometric phase of a classical Aharonov–Bohm Hamiltonian

    International Nuclear Information System (INIS)

    We present a gauge-invariant approach for associating a geometric phase with the phase space trajectory of a classical dynamical system. As an application, we consider the classical analog of the quantum Aharonov–Bohm (AB) Hamiltonian for a charged particle orbiting around a current carrying long thin solenoid. We compute the classical geometric phase of a closed phase space trajectory, and also determine its dependence on the magnetic flux enclosed by the orbit. We study the similarities and differences between this classical geometric phase and the AB phase acquired by the wave function of the quantum AB Hamiltonian. We suggest an experiment to measure the geometric phase for the classical AB system, by using an appropriate optical fiber ring interferometer.

  3. Geometric phase of a classical Aharonov–Bohm Hamiltonian

    Energy Technology Data Exchange (ETDEWEB)

    Balakrishnan, Radha, E-mail: radha@imsc.res.in [The Institute of Mathematical Sciences, Chennai 600 113 (India); Satija, Indubala I. [Department of Physics, George Mason University, Fairfax, VA 22030 (United States)

    2013-06-17

    We present a gauge-invariant approach for associating a geometric phase with the phase space trajectory of a classical dynamical system. As an application, we consider the classical analog of the quantum Aharonov–Bohm (AB) Hamiltonian for a charged particle orbiting around a current carrying long thin solenoid. We compute the classical geometric phase of a closed phase space trajectory, and also determine its dependence on the magnetic flux enclosed by the orbit. We study the similarities and differences between this classical geometric phase and the AB phase acquired by the wave function of the quantum AB Hamiltonian. We suggest an experiment to measure the geometric phase for the classical AB system, by using an appropriate optical fiber ring interferometer.

  4. Effect of classical noise on the geometric quantum phase

    International Nuclear Information System (INIS)

    We consider the effect of classical noise applied to the geometric quantum phase of a spin 1/2 in a revolving magnetic field. The Berry phase shows some sensitivity to the noise because the Bloch vector cannot return to its original direction, and the variance caused by noise is proportional to the evolution time

  5. Background Independent Quantum Mechanics, Classical Geometric Forms and Geometric Quantum Mechanics-I

    OpenAIRE

    Pandya, Aalok

    2008-01-01

    The geometry of the symplectic structures and Fubini-Study metric is discussed. Discussion in the paper addresses geometry of Quantum Mechanics in the classical phase space. Also, geometry of Quantum Mechanics in the projective Hilbert space has been discussed for the chosen Quantum states. Since the theory of classical gravity is basically geometric in nature and Quantum Mechanics is in no way devoid of geometry, the explorations pertaining to more and more geometry in Quantum Mechanics coul...

  6. Geometric aspects in extended approach of equilibrium classical fluctuation theory

    Science.gov (United States)

    Velazquez, L.

    2011-11-01

    Previously, an extended approach of equilibrium classical fluctuation theory was developed compatible with the existence of anomalous response functions, e.g. states with negative heat capacities. Now, the geometric aspects associated with this new framework are analyzed. The analysis starts from the so-called reparametrization invariance: a special symmetry of distribution functions dp (I|θ) employed in classical equilibrium statistical mechanics that allows us to express the thermo-statistical relations in the same mathematical appearance in different coordinate representations. The existence of reparametrization invariance can be related to three different geometric frameworks: (1) a non-Riemannian formulation for classical fluctuation theory based on the concept of reparametrization dualities; (2) a Riemannian formulation defined on the manifold {P} of control parameters θ, where the main theorems of inference theory appear as dual counterparts of general fluctuation theorems, and Boltzmann-Gibbs distributions ωBG(I|θ) = exp(-θiIi)/Z(θ) admit a geometric generalization; and finally, (3) a Riemannian formulation defined on the manifold {M}_{\\theta } of macroscopic observables I, which appears as a counterpart approach of inference geometry.

  7. High resolution with RCBC using classical optics

    International Nuclear Information System (INIS)

    A brief assessment of the possibility of a classical optical system for RCBC to give a resolution of better than 50 microns is presented. Reference is made to the tests made in RCBC during August 1981 and to the system installed on the 40 inch SLAC chamber. (orig.)

  8. Fundamental Principles of Classical Mechanics: a Geometrical Perspectives

    Science.gov (United States)

    Lam, Kai S.

    2014-07-01

    Classical mechanics is the quantitative study of the laws of motion for oscopic physical systems with mass. The fundamental laws of this subject, known as Newton's Laws of Motion, are expressed in terms of second-order differential equations governing the time evolution of vectors in a so-called configuration space of a system (see Chapter 12). In an elementary setting, these are usually vectors in 3-dimensional Euclidean space, such as position vectors of point particles; but typically they can be vectors in higher dimensional and more abstract spaces. A general knowledge of the mathematical properties of vectors, not only in their most intuitive incarnations as directed arrows in physical space but as elements of abstract linear vector spaces, and those of linear operators (transformations) on vector spaces as well, is then indispensable in laying the groundwork for both the physical and the more advanced mathematical - more precisely topological and geometrical - concepts that will prove to be vital in our subject. In this beginning chapter we will review these properties, and introduce the all-important related notions of dual spaces and tensor products of vector spaces. The notational convention for vectorial and tensorial indices used for the rest of this book (except when otherwise specified) will also be established...

  9. Dynamics of mixed classical-quantum systems, geometric quantization and coherent states

    CERN Document Server

    Jauslin, H R

    2011-01-01

    We describe quantum and classical Hamiltonian dynamics in a common Hilbert space framework, that allows the treatment of mixed quantum-classical systems. The analysis of some examples illustrates the possibility of entanglement between classical and quantum systems. We give a summary of the main tools of Berezin-Toeplitz and geometric quantization, that provide a relation between the classical and the quantum models, based essentially on the selection of a subspace of the classical Hilbert space. Coherent states provide a systematic tool for the inverse process, called dequantization, that associates a classical Hamiltonian system to a given quantum dynamics through the choice of a complete set of coherent states.

  10. Joins via Geometric Resolutions: Worst-case and Beyond

    OpenAIRE

    Khamis, Mahmoud Abo; Ngo, Hung Q.; Ré, Christopher; Rudra, Atri

    2014-01-01

    We present a simple geometric framework for the relational join. Using this framework, we design an algorithm that achieves the fractional hypertree-width bound, which generalizes classical and recent worst-case algorithmic results on computing joins. In addition, we use our framework and the same algorithm to show a series of what are colloquially known as beyond worst-case results. The framework allows us to prove results for data stored in Btrees, multidimensional data structures, and even...

  11. Complete geometric computer simulation of a classical guitar

    Science.gov (United States)

    Bader, Rolf

    2005-04-01

    The aim of formulating a complete model of a classical guitar body as a transient-time geometry is to get detailed insight into the vibrating and coupling behavior of the time-dependent guitar system. Here, especially the evolution of the guitars initial transient can be looked at with great detail and the produced sounds from this computer implementation can be listened to. Therefore, a stand-alone software was developed to build, calculate, and visualize the guitar. The model splits the guitar body into top plate, back plate, ribs, neck, inclosed air, and strings and couples these parts together including the coupling of bending waves and in-plane waves of these plates to serve for a better understanding of the coupling between the guitar parts and between these two kinds of waves. The resulting waveforms are integrated over the geometry and the resulting sounds show up the different roles and contributions of the different guitar body parts to the guitar sound. Here cooperation with guitar makers is established, as changes on the guitars geometry on the resulting sound can be considered as computer simulation and promising new sound qualities can then be used again in real instrument production.

  12. Classical and quantum Fisher information in the geometrical formulation of quantum mechanics

    Energy Technology Data Exchange (ETDEWEB)

    Facchi, Paolo [Dipartimento di Matematica, Universita di Bari, I-70125 Bari (Italy); INFN, Sezione di Bari, I-70126 Bari (Italy); MECENAS, Universita Federico II di Napoli and Universita di Bari (Italy); Kulkarni, Ravi [Vivekananda Yoga Research Foundation, Bangalore 560 080 (India); Man' ko, V.I., E-mail: manko@na.infn.i [P.N. Lebedev Physical Institute, Leninskii Prospect 53, Moscow 119991 (Russian Federation); Marmo, Giuseppe [Dipartimento di Scienze Fisiche, Universita di Napoli ' Federico II' , I-80126 Napoli (Italy); INFN, Sezione di Napoli, I-80126 Napoli (Italy); MECENAS, Universita Federico II di Napoli and Universita di Bari (Italy); Sudarshan, E.C.G. [Department of Physics, University of Texas, Austin, TX 78712 (United States); Ventriglia, Franco [Dipartimento di Scienze Fisiche, Universita di Napoli ' Federico II' , I-80126 Napoli (Italy); INFN, Sezione di Napoli, I-80126 Napoli (Italy); MECENAS, Universita Federico II di Napoli and Universita di Bari (Italy)

    2010-11-01

    The tomographic picture of quantum mechanics has brought the description of quantum states closer to that of classical probability and statistics. On the other hand, the geometrical formulation of quantum mechanics introduces a metric tensor and a symplectic tensor (Hermitian tensor) on the space of pure states. By putting these two aspects together, we show that the Fisher information metric, both classical and quantum, can be described by means of the Hermitian tensor on the manifold of pure states.

  13. Classical and quantum Fisher information in the geometrical formulation of quantum mechanics

    International Nuclear Information System (INIS)

    The tomographic picture of quantum mechanics has brought the description of quantum states closer to that of classical probability and statistics. On the other hand, the geometrical formulation of quantum mechanics introduces a metric tensor and a symplectic tensor (Hermitian tensor) on the space of pure states. By putting these two aspects together, we show that the Fisher information metric, both classical and quantum, can be described by means of the Hermitian tensor on the manifold of pure states.

  14. Resolution and noise in ghost imaging with classical thermal light

    Institute of Scientific and Technical Information of China (English)

    Cheng Jing; Han Shen-Sheng; Yan Yi-Jing

    2006-01-01

    The resolution and classical noise in ghost imaging with a classical thermal light are investigated theoretically. For ghost imaging with a Gaussian Schell model source, the dependences of the resolution and noise on the spatial coherence of the source and the aperture in the imaging system are discussed and demonstrated by using numerical simulations.The results show that an incoherent source and a large aperture will lead to a good image quality and small noise.

  15. Spatially varying geometric phase in classically entangled vector beams of light

    Science.gov (United States)

    King-Smith, Andrew; Leary, Cody

    We present theoretical results describing a spatially varying geometric (Pancharatnam) phase present in vector modes of light, in which the polarization and transverse spatial mode degrees of freedom exhibit classical entanglement. We propose an experimental setup capable of characterizing this effect, in which a vector mode propagates through a Mach-Zehnder interferometer with a birefringent phase retarder present in one arm. Since the polarization state of a classically entangled light beam exhibits spatial variation across the transverse mode profile, the phase retarder gives rise to a spatially varying geometric phase in the beam propagating through it. When recombined with the reference beam from the other interferometer arm, the presence of the geometric phase is exhibited in the resulting interference pattern. We acknowledge funding from the Research Corporation for Science Advancement by means of a Cottrell College Science Award.

  16. Geometric multi-resolution analysis and data-driven convolutions

    Science.gov (United States)

    Strawn, Nate

    2015-09-01

    We introduce a procedure for learning discrete convolutional operators for generic datasets which recovers the standard block convolutional operators when applied to sets of natural images. They key observation is that the standard block convolutional operators on images are intuitive because humans naturally understand the grid structure of the self-evident functions over images spaces (pixels). This procedure first constructs a Geometric Multi-Resolution Analysis (GMRA) on the set of variables giving rise to a dataset, and then leverages the details of this data structure to identify subsets of variables upon which convolutional operators are supported, as well as a space of functions that can be shared coherently amongst these supports.

  17. Methods of geometric function theory in classical and modern problems for polynomials

    International Nuclear Information System (INIS)

    This paper gives a survey of classical and modern theorems on polynomials, proved using methods of geometric function theory. Most of the paper is devoted to results of the author and his students, established by applying majorization principles for holomorphic functions, the theory of univalent functions, the theory of capacities, and symmetrization. Auxiliary results and the proofs of some of the theorems are presented. Bibliography: 124 titles.

  18. Classical Tests of General Relativity: Brane-World Sun from Minimal Geometric Deformation

    OpenAIRE

    Casadio, Roberto; Ovalle, Jorge; da Rocha, Roldao

    2015-01-01

    We consider a solution of the effective four-dimensional brane-world equations, obtained from the General Relativistic Schwarzschild metric via the principle of Minimal Geometric Deformation, and investigate the corresponding signatures stemming from the possible existence of a warped extra dimension. In particular, we derive bounds on an extra-dimensional parameter, closely related with the fundamental gravitational length, from the experimental results of the classical tests of General Rela...

  19. Classical tests of general relativity: Brane-world Sun from minimal geometric deformation

    Science.gov (United States)

    Casadio, R.; Ovalle, J.; da Rocha, Roldão

    2015-05-01

    We consider a solution of the effective four-dimensional brane-world equations, obtained from the general relativistic Schwarzschild metric via the principle of minimal geometric deformation, and investigate the corresponding signatures stemming from the possible existence of a warped extra-dimension. In particular, we derive bounds on an extra-dimensional parameter, closely related with the fundamental gravitational length, from the experimental results of the classical tests of general relativity in the Solar system.

  20. Classical Tests of General Relativity: Brane-World Sun from Minimal Geometric Deformation

    CERN Document Server

    Casadio, Roberto; da Rocha, Roldao

    2015-01-01

    We consider a solution of the effective four-dimensional brane-world equations, obtained from the General Relativistic Schwarzschild metric via the principle of Minimal Geometric Deformation, and investigate the corresponding signatures stemming from the possible existence of a warped extra dimension. In particular, we derive bounds on an extra-dimensional parameter, closely related with the fundamental gravitational length, from the experimental results of the classical tests of General Relativity in the Solar system.

  1. Dye laser light for high-resolution classical photography

    International Nuclear Information System (INIS)

    The test run with the bubble chamber HOLEBC in October 1981 offered the opportunity of checking the usefulness of de-speckled dye laser light for illumination purposes in high-resolution classical dark field photography of small bubble chambers. (orig./HSI)

  2. Classical resolution of black hole singularities in arbitrary dimension

    CERN Document Server

    Bazeia, D; Olmo, Gonzalo J; Rubiera-Garcia, D; Sanchez-Puente, A

    2015-01-01

    A metric-affine approach is employed to study higher-dimensional modified gravity theories involving different powers and contractions of the Ricci tensor. It is shown that the field equations are \\emph{always} second-order, as opposed to the standard metric approach, where this is only achieved for Lagrangians of the Lovelock type. We point out that this property might have relevant implications for the AdS/CFT correspondence in black hole scenarios. We illustrate these aspects by considering the case of Born-Infeld gravity in $d$ dimensions, where we work out exact solutions for electrovacuum configurations. Our results put forward that black hole singularities in arbitrary dimensions can be cured in a purely classical geometric scenario governed by second-order field equations.

  3. Classical geometric phase of gyro-motion is a coherent quantum Berry phase

    CERN Document Server

    Zhu, Hongxuan

    2016-01-01

    We show that the geometric phase of the gyro-motion of a classical charged particle in a uniform time-dependent magnetic field described by Newton's equation is a coherent quantum Berry phase for the coherent states of the Schr\\"odinger equation or the Dirac equation. This equivalence is established by constructing coherent states for a particle using the energy eigenstates on the Landau levels and proving that the coherent states can maintain their status of coherent states during the slow varying of the magnetic field. It is discovered that orbital Berry phases of the eigenstates interfere coherently such that a coherent Berry phase for the coherent states can be naturally defined, which is exactly the geometric phase of the classical gyro-motion. This technique works for particles with and without spin. For particles with spin, on each of the eigenstates that makes up the coherent states, the Berry phase consists of two parts that can be identified as those due to the orbital and the spin motion. It is the...

  4. Investigation of geometrical and scoring grid resolution for Monte Carlo dose calculations for IMRT

    Science.gov (United States)

    DeSmedt, B.; Vanderstraeten, B.; Reynaert, N.; DeNeve, W.; Thierens, H.

    2005-09-01

    Monte Carlo based treatment planning of two different patient groups treated with step-and-shoot IMRT (head-and-neck and lung treatments) with different CT resolutions and scoring methods is performed to determine the effect of geometrical and scoring voxel sizes on DVHs and calculation times. Dose scoring is performed in two different ways: directly into geometrical voxels (or in a number of grouped geometrical voxels) or into scoring voxels defined by a separate scoring grid superimposed on the geometrical grid. For the head-and-neck cancer patients, more than 2% difference is noted in the right optical nerve when using voxel dimensions of 4 × 4 × 4 mm3 compared to the reference calculation with 1 × 1 × 2 mm3 voxel dimensions. For the lung cancer patients, 2% difference is noted in the spinal cord when using voxel dimensions of 4 × 4 × 10 mm3 compared to the 1 × 1 × 5 mm3 calculation. An independent scoring grid introduces several advantages. In cases where a relatively high geometrical resolution is required and where the scoring resolution is less important, the number of scoring voxels can be limited while maintaining a high geometrical resolution. This can be achieved either by grouping several geometrical voxels together into scoring voxels or by superimposing a separate scoring grid of spherical voxels with a user-defined radius on the geometrical grid. For the studied lung cancer cases, both methods produce accurate results and introduce a speed increase by a factor of 10-36. In cases where a low geometrical resolution is allowed, but where a high scoring resolution is required, superimposing a separate scoring grid on the geometrical grid allows a reduction in geometrical voxels while maintaining a high scoring resolution. For the studied head-and-neck cancer cases, calculations performed with a geometrical resolution of 2 × 2 × 2 mm3 and a separate scoring grid containing spherical scoring voxels with a radius of 2 mm produce accurate results

  5. Quantum-classical hybrids in a simplified model of QED and geometric phase induced by charged particle trajectory

    CERN Document Server

    Koide, T

    2016-01-01

    We derive a model of quantum-classical hybrids for a simplified model of quantum electrodynamics in the framework of the stochastic variational method. In this model, charged particle trajectories are affected by the interaction with quantized electromagnetic fields, and this quantum-classical interaction induces a displacement current. We further investigate a geometric phase in the wave functional of the gauge field configuration, which is induced by adiabatic motions of the charged particles. This phase contains the quantum-classical backreaction effect and usual Berry's phase is reproduced in the vanishing limit of the fluctuation of the charged particle trajectories.

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

    International Nuclear Information System (INIS)

    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

  7. Low Frequency Error Analysis and Calibration for High-Resolution Optical Satellite's Uncontrolled Geometric Positioning

    Science.gov (United States)

    Wang, Mi; Fang, Chengcheng; Yang, Bo; Cheng, Yufeng

    2016-06-01

    The low frequency error is a key factor which has affected uncontrolled geometry processing accuracy of the high-resolution optical image. To guarantee the geometric quality of imagery, this paper presents an on-orbit calibration method for the low frequency error based on geometric calibration field. Firstly, we introduce the overall flow of low frequency error on-orbit analysis and calibration, which includes optical axis angle variation detection of star sensor, relative calibration among star sensors, multi-star sensor information fusion, low frequency error model construction and verification. Secondly, we use optical axis angle change detection method to analyze the law of low frequency error variation. Thirdly, we respectively use the method of relative calibration and information fusion among star sensors to realize the datum unity and high precision attitude output. Finally, we realize the low frequency error model construction and optimal estimation of model parameters based on DEM/DOM of geometric calibration field. To evaluate the performance of the proposed calibration method, a certain type satellite's real data is used. Test results demonstrate that the calibration model in this paper can well describe the law of the low frequency error variation. The uncontrolled geometric positioning accuracy of the high-resolution optical image in the WGS-84 Coordinate Systems is obviously improved after the step-wise calibration.

  8. Resolution beyond classical limits with spatial frequency heterodyning

    Institute of Scientific and Technical Information of China (English)

    A. Mudassar; A. R. Harvey; A. H. Greenaway; J. D. C. Jones

    2006-01-01

    @@ A technique for coherent imaging based on spatial frequency heterodyning is described. Three images corresponding to three physical measurements are recorded. For the first measurement, a scene is simply illuminated with a coherent beam and for measurements 2 and 3, the scene is projected with cosine and sine fringes, respectively. Due to spatial frequency heterodyning, upper and lower side band information falls in the pass band of the imager. These bands are separated and correct phases and positions are assigned to these bands in the spatial frequency domain. An extension of bandwidth is achieved in the frequency domain and the inverse frequency domain data then give a high resolution coherent image.

  9. Pre-geometric structure of quantum and classical particles in terms of quaternion spinors

    CERN Document Server

    Yefremov, Alexander P

    2012-01-01

    It is shown that dyad vectors on a local domain of complex-number valued surface, when squared, form a set of four quaternion algebra units. A model of proto-particle is built by the dyad's rotation and stretching; this transformation violates metric properties of the surface, but the defect is cured by a stability condition for normalization functional over an abstract space. If the space is the physical one then the stability condition is precisely Schrodinger equation; separated real and imaginary parts of the condition are respectively equation of mass conservation and Hamilton-Jacoby equation. A 3D particle (composed of the proto-particle's parts) has to be conceived as a rotating massive point, its Lagrangian automatically becoming that of relativistic classical particle, energy and momentum proportional to Planck constant. In uence of a vector ?eld onto the particle's propagation causes automatic appearance of Pauli spin term in Schrodinger equation.

  10. The classical Generalized Constant Coupling method for Geometrically Frustrated Magnets revisited: Microscopic formulation and effect of perturbations beyond nearest neighbor interactions

    OpenAIRE

    Garcia-Adeva, A. J.; Huber, D. L.

    2001-01-01

    A microscopic derivation of the classical Generalized Constant Coupling (GCC) model for geometrically frustrated magnets is presented. Starting from the classical Heisenberg Hamiltonian, the partition function for clusters with p = 2, 3, 4 ,...spins in the presence of the inhomogeneous symmetry breaking fields (SBF) created by spins outside the unit is calculated. The effective fields characterizing the interaction between units naturally arise as averages over the SBF. These effective fields...

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

    Science.gov (United States)

    Wallis, David; Hansen, Lars N; Ben Britton, T; Wilkinson, Angus J

    2016-09-01

    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 (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. PMID:27337604

  12. Automatic Geometric Processing for Very High Resolution Optical Satellite Data Based on Vector Roads and Orthophotos

    Directory of Open Access Journals (Sweden)

    Peter Pehani

    2016-04-01

    Full Text Available In response to the increasing need for fast satellite image processing SPACE-SI developed STORM—a fully automatic image processing chain that performs all processing steps from the input optical images to web-delivered map-ready products for various sensors. This paper focuses on the automatic geometric corrections module and its adaptation to very high resolution (VHR multispectral images. In the automatic ground control points (GCPs extraction sub-module a two-step algorithm that utilizes vector roads as a reference layer and delivers GCPs for high resolution RapidEye images with near pixel accuracy was initially implemented. Super-fine positioning of individual GCPs onto an aerial orthophoto was introduced for VHR images. The enhanced algorithm is capable of achieving accuracy of approximately 1.5 pixels on WorldView-2 data. In the case of RapidEye images the accuracies of the physical sensor model reach sub-pixel values at independent check points. When compared to the reference national aerial orthophoto the accuracies of WorldView-2 orthoimages automatically produced with the rational function model reach near-pixel values. On a heterogeneous set of 41 RapidEye images the rate of automatic processing reached 97.6%. Image processing times remained under one hour for standard-size images of both sensor types.

  13. A Hamiltonian theory of adaptive resolution simulations of classical and quantum models of nuclei

    Science.gov (United States)

    Kreis, Karsten; Donadio, Davide; Kremer, Kurt; Potestio, Raffaello

    2015-03-01

    Quantum delocalization of atomic nuclei strongly affects the physical properties of low temperature systems, such as superfluid helium. However, also at room temperature nuclear quantum effects can play an important role for molecules composed by light atoms. An accurate modeling of these effects is possible making use of the Path Integral formulation of Quantum Mechanics. In simulations, this numerically expensive description can be restricted to a small region of space, while modeling the remaining atoms as classical particles. In this way the computational resources required can be significantly reduced. In the present talk we demonstrate the derivation of a Hamiltonian formulation for a bottom-up, theoretically solid coupling between a classical model and a Path Integral description of the same system. The coupling between the two models is established with the so-called Hamiltonian Adaptive Resolution Scheme, resulting in a fully adaptive setup in which molecules can freely diffuse across the classical and the Path Integral regions by smoothly switching their description on the fly. Finally, we show the validation of the approach by means of adaptive resolution simulations of low temperature parahydrogen. Graduate School Materials Science in Mainz, Staudinger Weg 9, 55128 Mainz, Germany.

  14. Genotyping of classical swine fever virus using high-resolution melt analysis.

    Science.gov (United States)

    Titov, Ilya; Tsybanov, Sodnom; Malogolovkin, Alexander

    2015-11-01

    Discrimination between different field and vaccine strains of classical swine fever virus (CSFV) is crucial for meaningful disease diagnosis and epidemiological investigation. In this study, a rapid method for differentiating vaccine strains and outbreak CSFV isolates by combined RT-PCR and high-resolution melt (HRM) analysis has been developed. The assay is based on PCR amplification of short fragments from the most variable region of CSFVgene E2, followed by HRM analysis of amplicons. Real-Time PCR/HRM for CSFV detection and differentiation analysis has sensitivity comparable to RT-qPCR and genotyping resolution comparable to E2 nucleotide sequencing. This assay in one step enables rapid and sensitive identification and genotype discrimination of CSFV in field samples, and thus will be valuable for CSF outbreak response and disease control. PMID:26300371

  15. On-Orbit Geometric Calibration Approach for High-Resolution Geostationary Optical Satellite GaoFen-4

    Science.gov (United States)

    Wang, Mi; Cheng, Yufeng; Long, Xiaoxiang; Yang, Bo

    2016-06-01

    The GaoFen-4 (GF-4) remote sensing satellite is China's first civilian high-resolution geostationary optical satellite, which has been launched at the end of December 2015. To guarantee the geometric quality of imagery, this paper presents an on-orbit geometric calibration method for the area-array camera of GF-4. Firstly, we introduce the imaging features of area-array camera of GF-4 and construct a rigorous imaging model based on the analysis of the major error sources from three aspects: attitude measurement error, orbit measurement error and camera distortion. Secondly, we construct an on-orbit geometric calibration model by selecting and optimizing parameters of the rigorous geometric imaging model. On this basis, the calibration parameters are divided into two groups: external and internal calibration parameters. The external parameters are installation angles between the area-array camera and the star tracker, and we propose a two-dimensional direction angle model as internal parameters to describe the distortion of the areaarray camera. Thirdly, we propose a stepwise parameters estimation method that external parameters are estimated firstly, then internal parameters are estimated based on the generalized camera frame determined by external parameters. Experiments based on the real data of GF-4 shows that after on-orbit geometric calibration, the geometric accuracy of the images without ground control points is significantly improved.

  16. 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.)

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

    International Nuclear Information System (INIS)

    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 μm3) or with high-resolution flat-panel CT (isotropic resolutions of 200 μm3). 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.)

  18. Possibility of using finite element method in the form of classical mixed method for geometrical nonlinear analysis of hinged-rod systems

    Directory of Open Access Journals (Sweden)

    Ignat’ev Aleksandr Vladimirovich

    2015-12-01

    Full Text Available At the present time a great number of works have been published, in which the problems of numerical solution of geometrical nonlinear tasks of calculating different types of structures are considered. Nevertheless the problem of the certainty of the numerical solution of geometrical nonlinear tasks of rod structures deformation (large displacements still provokes great interest. The quality of the solution for a certain task is proved only by the coincidence of the results obtained before using two different methods or with the experiment. The authors consider the numerical solution algorithm of geometrical nonlinear tasks of the deformation of hinged-rod systems (large displacements and turns both in case of high and gentle loading basing on the finite element method in the form of classical mixed method being developed by the authors. Solving the problem of static deformation of a flat mechanical hinged-rod system consisting of two linear-elastic rods the authors show the simplicity and efficiency of the algorithm when finding all the range equilibrium system states. The quality of the solution is proved by the coincidence of the results in case of gentle and heavy loading of the system and with the results of other investigations.

  19. Solving geometrically nonlinear tasks of the statics of hinged-rod systems basing on finite element method in the form of classical mixed method

    Directory of Open Access Journals (Sweden)

    Ignat’ev Aleksandr Vladimirovich

    2016-02-01

    Full Text Available The most widely used numerical method used in linear calculation of building structures is finite element method in traditional form of displacements. Different software is developed on its basis. Though it is only possible to check the certainty of these numerical solutions, especially of non-linear tasks of engineering structures’ deformation by the coincidence of the results obtained by two different methods. The authors solved geometrically nonlinear task of the static deformation of a flat hinged-rod system consisting of five linear elastic rods undergoing great tension-compression strains. The solution was obtained basing on the finite element method in the form of classical mixed method developed by the authors. The set of all equilibrium states of the system, both stable and unstable, and all the limit points were found. The certainty of the solution was approved by the coincidence of the results obtained by other authors basing on traditional finite element method in displacements.

  20. Why do mixed quantum-classical methods describe short-time dynamics through conical intersections so well? Analysis of geometric phase effects

    CERN Document Server

    Gherib, Rami; Izmaylov, Artur F

    2015-01-01

    Adequate simulation of non-adiabatic dynamics through conical intersection requires account for a non-trivial geometric phase (GP) emerging in electronic and nuclear wave-functions in the adiabatic representation. Popular mixed quantum-classical (MQC) methods, surface hopping and Ehrenfest, do not carry a nuclear wave-function to be able to incorporate the GP into nuclear dynamics. Surprisingly, the MQC methods reproduce ultra-fast interstate crossing dynamics generated with the exact quantum propagation so well as if they contained information about the GP. Using two-dimensional linear vibronic coupling models we unravel how the MQC methods can effectively mimic the most significant dynamical GP effects: 1) compensation for repulsive diagonal second order non-adiabatic couplings and 2) transfer enhancement for a fully cylindrically symmetric component of a nuclear distribution.

  1. Geometrically-based free-energy functional for confined hard-spheres and the density functional theory for simple classical systems

    International Nuclear Information System (INIS)

    Physics Department, Nuclear Research Center Negevu Some recent developments in classical density functional theory are reviewed briefly, concerning mainly dimensional cross-over, close packed configurations, symmetry breaking, and the freezing transition. The so called Fundamental Measure Functionals are based on the fundamental geometric measures of the individuals hard particles. They were originally derived by seeking an interpolation between the ideal gas and idea - liquid limits. Their general behavior depends crucially on their singularity at local packing fraction η(r) = ∫ dr'ρ(r')θ(R-(|r-r'|) equal one, η(r)=1 , where θ(x) is the Heaviside step function. Several very recent analyses revealed that the fundamental measure functionals, due to their singularity and their unique structure, have many of the basic physical properties expected from the exact (but unknowns) free-energy functional when applied to densely packed hard-spheres. These properties are important also for applications to continuous (''soft'') interactions

  2. HIGH-RESOLUTION IMAGING OF THE GEGENSCHEIN AND THE GEOMETRIC ALBEDO OF INTERPLANETARY DUST

    International Nuclear Information System (INIS)

    We performed optical observations of the Gegenschein using a liquid-nitrogen-cooled wide-field camera, the Wide-field Imager of Zodiacal light with ARray Detector (WIZARD), between 2003 March and 2006 November. We found a narrow brightness enhancement superimposed on the smooth gradient of the Gegenschein at the exact position of the antisolar point. Whereas the Gegenschein morphology changed according to the orbital motion of the Earth, the maximum brightness coincided with the antisolar direction throughout the year. We compared the observed morphology of the Gegenschein with those of models in which the spatial density of the interplanetary dust cloud was considered and found that the volume scattering phase function had a narrow backscattering enhancement. The morphology was reproducible with a spatial distribution model for infrared zodiacal emission. It is likely that the zero-phase peak (the so-called opposition effect) was caused by coherent backscattering and/or shadow-hiding effects on the rough surfaces of individual dust particles. These results suggest that big particles are responsible for both zodiacal light and zodiacal emission. Finally, we derived the geometric albedo of the smooth component of interplanetary dust, assuming big particles, and obtained a geometric albedo of 0.06 ± 0.01. The derived albedo is in accordance with collected dark micrometeorites and observed cometary dust particles. We concluded that chondritic particles are dominant near Earth space, supporting the recent theoretical study by dynamical simulation.

  3. The geometrization of matter proposal in the Barrett-Crane model and resolution of cosmological problems

    OpenAIRE

    Alexander, S.; Crane, L.; Sheppeard, M. D.

    2003-01-01

    We give an overview of the current issues in early universe cosmology and consider the potential resolution of these issues in an as yet nascent spin foam cosmology. The model is the Barrett-Crane Model for quantum gravity along with a generalization of manifold complexes to complexes including conical singularities.

  4. Detector, shielding and geometric design factors for a high-resolution PET system

    International Nuclear Information System (INIS)

    The authors have evaluated the resolution, efficiency and scatter rejection on a new high resolution PET system designed for animal studies which is based on a 2-D modular detector system. A digital positioning system was evaluated by testing different encoding methods. Tungsten inter-plane septa of different thicknesses and geometries were evaluated by Monte Carlo simulations and experiments. The detector system consists of a 6 x 8 array of BGO crystals coupled to 2 dual photomultiplier tubes (PMTs). The crystals are 3.5 mm wide with 4 mm spacing transaxially and are 6.25 mm long with 6.75 mm spacing axially. PMT outputs are digitized and Anger camera type logic is used to determine the X and Y location of the scintillation event

  5. Resolution to the quantum-classical dilemma in thermal ghost imaging

    OpenAIRE

    Chen, Lixiang

    2016-01-01

    There has been an intense debate on the quantum versus classical origin of ghost imaging with a thermal light source over the last two decades. A lot of distinguished work has contributed to this topic, both theoretically and experimentally, however, to this day this quantum-classical dilemma still persists. Here we formulate for the first time a density matrix in the photon orbital angular momentum (OAM) Hilbert space to fully characterize the two-arm ghost imaging system with the basic defi...

  6. Geometric mechanics

    CERN Document Server

    Muniz Oliva, Waldyr

    2002-01-01

    Geometric Mechanics here means mechanics on a pseudo-riemannian manifold and the main goal is the study of some mechanical models and concepts, with emphasis on the intrinsic and geometric aspects arising in classical problems. The first seven chapters are written in the spirit of Newtonian Mechanics while the last two ones as well as two of the four appendices describe the foundations and some aspects of Special and General Relativity. All the material has a coordinate free presentation but, for the sake of motivation, many examples and exercises are included in order to exhibit the desirable flavor of physical applications.

  7. Line-of-sight geometrical and instrumental resolution effects on intensity perturbations by sausage modes

    CERN Document Server

    Antolin, Patrick

    2013-01-01

    Diagnostics of MHD waves in the solar atmosphere is a topic which often encounters problems of interpretation, due partly to the high complexity of the solar atmospheric medium. Forward modeling can significantly guide interpretation, bridging the gap between numerical simulations and observations, and increasing the reliability of mode identification for application of MHD seismology. In this work we aim at determining the characteristics of the fast MHD sausage mode in the corona on the modulation of observable quantities such as line intensity and spectral line broadening. Effects of line-of-sight angle, and spatial, temporal and spectral resolutions are considered. We take a cylindrical tube simulating a loop in a low-{\\beta} coronal environment with an optically thin background, and let it oscillate with the fast sausage mode. A parametric study is performed. Among other results, we show that regardless of the ionisation state of the plasma, the variation of spectral line broadening can be significant, e...

  8. Geometric Algebra for Physicists

    Science.gov (United States)

    Doran, Chris; Lasenby, Anthony

    2007-11-01

    Preface; Notation; 1. Introduction; 2. Geometric algebra in two and three dimensions; 3. Classical mechanics; 4. Foundations of geometric algebra; 5. Relativity and spacetime; 6. Geometric calculus; 7. Classical electrodynamics; 8. Quantum theory and spinors; 9. Multiparticle states and quantum entanglement; 10. Geometry; 11. Further topics in calculus and group theory; 12. Lagrangian and Hamiltonian techniques; 13. Symmetry and gauge theory; 14. Gravitation; Bibliography; Index.

  9. Second-Order Systematicity of Associative Learning: A Paradox for Classical Compositionality and a Coalgebraic Resolution.

    Science.gov (United States)

    Phillips, Steven; Wilson, William H

    2016-01-01

    Systematicity is a property of cognitive architecture whereby having certain cognitive capacities implies having certain other "structurally related" cognitive capacities. The predominant classical explanation for systematicity appeals to a notion of common syntactic/symbolic structure among the systematically related capacities. Although learning is a (second-order) cognitive capacity of central interest to cognitive science, a systematic ability to learn certain cognitive capacities, i.e., second-order systematicity, has been given almost no attention in the literature. In this paper, we introduce learned associations as an instance of second-order systematicity that poses a paradox for classical theory, because this form of systematicity involves the kinds of associative constructions that were explicitly rejected by the classical explanation. Our category theoretic explanation of systematicity resolves this problem, because both first and second-order forms of systematicity are derived from the same categorical construction: universal morphisms, which generalize the notion of compositionality of constituent representations to (categorical) compositionality of constituent processes. We derive a model of systematic associative learning based on (co)recursion, which is an instance of a universal construction. These results provide further support for a category theory foundation for cognitive architecture. PMID:27505411

  10. 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.

  11. Accuracy of the geometric-mean method for determining spatial resolutions of tracking detectors in the presence of multiple Coulomb scattering

    CERN Document Server

    Zhang, Aiwu

    2016-01-01

    The geometric-mean method is often used to estimate the spatial resolution of a position-sensitive detector probed by tracks. It calculates the resolution solely from measured track data without using a detailed tracking simulation and without considering multiple Coulomb scattering effects. Two separate linear track fits are performed on the same data, one excluding and the other including the hit from the probed detector. The geometric mean of the widths of the corresponding exclusive and inclusive residual distributions for the probed detector is then taken as a measure of the intrinsic spatial resolution of the probed detector: $\\sigma=\\sqrt{\\sigma_{ex}\\cdot\\sigma_{in}}$. The validity of this method is examined for a range of resolutions with a stand-alone Geant4 Monte Carlo simulation that specifically takes multiple Coulomb scattering in the tracking detector materials into account. Using simulated as well as actual tracking data from a representative beam test scenario, we find that the geometric-mean ...

  12. Geometric Dequantization

    CERN Document Server

    Gozzi, E

    2004-01-01

    Dequantization is a set of rules which turn quantum mechanics (QM) into classical mechanics (CM). It is not the WKB limit of QM. In this paper we show that, by extending time to a 3-dimensional "supertime", we can dequantize the system in the sense of turning the Feynman path integral version of QM into the functional counterpart of the Koopman-von Neumann operatorial approach to CM. Somehow this procedure is the inverse of geometric quantization and we present it in three different polarizations: the Schroedinger, the momentum and the coherent states ones.

  13. ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS: Preparation of Macroscopic Quantum-Interference States for a Collection of Trapped Ions Via a Single Geometric Operation

    Science.gov (United States)

    Lin, Li-Hua

    2010-05-01

    We describe a scheme for the generation of macroscopic quantum-interference states for a collection of trapped ions by a single geometric phase operation. In the scheme the vibrational mode is displaced along a circle with the radius proportional to the number of ions in a certain ground electronic state. For a given interaction time, the vibrational mode returns to the original state, and the ionic system acquires a geometric phase proportional to the area of the circle, evolving from a coherent state to a superposition of two coherent states. The ions undergo no electronic transitions during the operation. Taking advantage of the inherent fault-tolerant feature of the geometric operation, our scheme is robust against decoherence.

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

    International Nuclear Information System (INIS)

    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.

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

    Energy Technology Data Exchange (ETDEWEB)

    Lorenzoni, Jose, E-mail: jls@med.puc.cl [Department of Neurosurgery, School of Medicine, Pontificia Universidad Catolica de Chile (Chile); David, Philippe, E-mail: pdavid@ulb.ac.be [Department of Radiology, Hopital Erasme, Universite Libre de Bruxelles, Brussels (Belgium); Levivier, Marc, E-mail: marc.levivier@chuv.ch [Department of Neurosurgery, Centre Hopitalier Universitaire Vaudois, Universite de Lausanne (Switzerland)

    2012-08-15

    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 Trade-Mark-Sign . 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.

  16. Resolution of sub-element length scales in Brownian dynamics simulations of biopolymer networks with geometrically exact beam finite elements

    Science.gov (United States)

    Müller, Kei W.; Meier, Christoph; Wall, Wolfgang A.

    2015-12-01

    Networks of crosslinked biopolymer filaments such as the cytoskeleton are the subject of intense research. Oftentimes, mechanics on the scale of single monomers (∼ 5 nm) govern the mechanics of the entire network (∼ 10 μm). Until now, one either resolved the small scales and lost the big (network) picture or focused on mechanics above the single-filament scale and neglected the molecular architecture. Therefore, the study of network mechanics influenced by the entire spectrum of relevant length scales has been infeasible so far. We propose a method that reconciles both small and large length scales without the otherwise inevitable loss in either numerical efficiency or geometrical (molecular) detail. Both explicitly modeled species, filaments and their crosslinkers, are discretized with geometrically exact beam finite elements of Simo-Reissner type. Through specific coupling conditions between the elements of the two species, mechanical joints can be established anywhere along a beam's centerline, enabling arbitrary densities of chemical binding sites. These binding sites can be oriented to model the monomeric architecture of polymers. First, we carefully discuss the method and then demonstrate its capabilities by means of a series of numerical examples.

  17. 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)

    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 13C 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 1H-NMR, 2D 1H-1H TOCSY and 2D 1H-13C HSQC NMR. The significant sensitivity barrier has been successfully overcome under selective suppression of the major resonances, with over 104 greater equilibrium magnetization of the -(CH2)n-1H spins compared to that of the 1H spins of the conjugated bonds of the CLA isomers. The resolution barrier has been significantly increased using reduced 13C spectral width in the 2D 1H-13C 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

  18. On the Bell-Plesset effects: The effects of uniform compression and geometrical convergence on the classical Rayleigh-Taylor instability

    International Nuclear Information System (INIS)

    The Rayleigh-Taylor (RT) instability of an accelerating fluid interface is examined considering the effects of compression and geometrical convergence on incompressible perturbations of an interface separating two homogeneous compressible fluid layers of different mass densities. These effects occur in the implosion of inertial confinement fusion capsules. A complete description of Bell-Plesset effects is presented in terms of a simple model formulated in terms of the mass amplitude of perturbations of planar, cylindrical, and spherical interfaces. This formulation makes a clear distinction between perturbation growth driven by buoyant force - the RT instability - and modifications of perturbation behavior by compression and geometrical convergence - the Bell-Plesset (BP) effects [G. I. Bell, Los Alamos National Laboratory, Report LA-1321 (1951); M. S. Plesset, J. Appl. Phys. 25, 96 (1954)]. BP effects modify RT growth rates and may affect RT stability criteria, but they are not a distinct instability. These effects vary widely in their nature and importance from application to application, depending on the relative rates of RT growth, radial convergence, and uniform compression. Limiting cases are compared and contrasted. BP effects are generally different for each component of the perturbation solution pair. BP effects on perturbation growth in cylindrical implosion experiments have been analyzed successfully [e.g., W. W. Hsing et al., Phys. Plasmas 4, 1832 (1997)], in terms of an incomplete single-component solution that is indistinguishable from unperturbed flow, indicating that the component exhibiting true ongoing perturbed motion is largely absent. This static mass perturbation solution is often treated as the one and only BP effect, even though it occurs as one of a pair of solutions and only in the limit of a vanishing RT effect

  19. 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

    Energy Technology Data Exchange (ETDEWEB)

    Tsiafoulis, Constantinos G. [NMR Center, University of Ioannina, Ioannina GR-45 110 (Greece); Skarlas, Theodore [Department of Chemistry, University of Ioannina, Ioannina GR-45 110 (Greece); Tzamaloukas, Ouranios; Miltiadou, Despoina [Department of Agricultural Sciences, Biotechnology and Food Sciences, Cyprus University of Technology, P.O Box 50329, Limassol 3603 (Cyprus); Gerothanassis, Ioannis P., E-mail: igeroth@uoi.gr [Department of Chemistry, University of Ioannina, Ioannina GR-45 110 (Greece)

    2014-04-01

    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 {sup 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 {sup 1}H-NMR, 2D {sup 1}H-{sup 1}H TOCSY and 2D {sup 1}H-{sup 13}C HSQC NMR. The significant sensitivity barrier has been successfully overcome under selective suppression of the major resonances, with over 10{sup 4} greater equilibrium magnetization of the -(CH{sub 2}){sub n}-{sup 1}H spins compared to that of the {sup 1}H spins of the conjugated bonds of the CLA isomers. The resolution barrier has been significantly increased using reduced {sup 13}C spectral width in the 2D {sup 1}H-{sup 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.

  20. Measurement of geometrically necessary dislocation density with high resolution electron backscatter diffraction: Effects of detector binning and step size

    International Nuclear Information System (INIS)

    Recent advances using cross-correlation analysis of full resolution high quality electron backscatter diffraction (EBSD) patterns have provided a method for quantitatively mapping the stored dislocation density at high spatial resolution. Larger areas could be mapped with image binning or coarser step sizes. We have studied the effects of image binning and step size on the recovery of GND density. Our results suggest that: (i) the measured lower bound GND density noise floor broadly agrees with Wilkinson and Randman’s 2009 prediction, where a decrease in step size or an increase in misorientation uncertainty increases the noise floor; (ii) increasing the step size results in a lower GND density being recovered as some dislocations are now considered as statistically stored dislocations (SSDs); (iii) in deformed samples the average GND density stays relatively constant as the degree of pattern binning is increased up to 8×8. Pattern binning thus provides a means of increasing the data acquisition and analysis rate without unduly degrading the data quality. - Highlights: ► Recovery of GND content using HR-EBSD was studied with differing CCD binning and sample step size. ► Increased binning results in poorer recovery of the stored GND density using Nye's analysis. ► High level of binning may be acceptable for severely deformed samples. ► Reduction in step size results in an increase in the measurement noise. ► Reduction in step size also leads to separation of dislocations into GNDs and SSDs

  1. Geometrical versus semiclassical quantization

    International Nuclear Information System (INIS)

    The dynamical variational approach based on geometrical quantization is demonstrated to be capable in describing the most important quantum mechanical quantities. In particular, the method appears to be much better under control than the traditional semiclassical methods in treating the systems whose classical counterparts are chaotic. The formal considerations are illustrated using an exactly solvable SU(3)-spin system. (orig.)

  2. Time and Geometric Quantization

    CERN Document Server

    Abrikosov, A A; Mauro, D

    2003-01-01

    In this paper we briefly review the functional version of the Koopman-von Neumann operatorial approach to classical mechanics. We then show that its quantization can be achieved by freezing to zero two Grassmannian partners of time. This method of quantization presents many similarities with the one known as Geometric Quantization.

  3. Gaussian geometric discord

    CERN Document Server

    Adesso, Gerardo

    2011-01-01

    We extend the geometric measure of quantum discord, introduced and computed for two-qubit states in [B. Dakic, C. Brukner, and V. Vedral, Phys. Rev. Lett. 105, 190502 (2010)], to quantify non-classical correlations in composite Gaussian states of continuous variable systems. We lay the formalism for the evaluation of a Gaussian geometric discord in two-mode Gaussian states, and present explicit formulas for the class of two-mode squeezed thermal states. In such a case, under physical constraints of bounded mean energy, geometric discord is shown to admit upper and lower bounds for a fixed value of the conventional (entropic) quantum discord. We finally discuss alternative geometric approaches to quantify Gaussian quadrature correlations.

  4. Studies in geometric quantization

    International Nuclear Information System (INIS)

    This thesis contains five chapters, of which the first, entitled 'What is prequantization, and what is geometric quantization?', is meant as an introduction to geometric quantization for the non-specialist. The second chapter, entitled 'Central extensions and physics' deals with the notion of central extensions of manifolds and elaborates and proves the statements made in the first chapter. Central extensions of manifolds occur in physics as the freedom of a phase factor in the quantum mechanical state vector, as the phase factor in the prequantization process of classical mechanics and it appears in mathematics when studying central extension of Lie groups. In this chapter the connection between these central extensions is investigated and a remarkable similarity between classical and quantum mechanics is shown. In chapter three a classical model is given for the hydrogen atom including spin-orbit and spin-spin interaction. The method of geometric quantization is applied to this model and the results are discussed. In the final chapters (4 and 5) an explicit method to calculate the operators corresponding to classical observables is given when the phase space is a Kaehler manifold. The obtained formula are then used to quantise symplectic manifolds which are irreducible hermitian symmetric spaces and the results are compared with other quantization procedures applied to these manifolds (in particular to Berezin's quantization). 91 refs.; 3 tabs

  5. Geometrical Bioelectrodynamics

    OpenAIRE

    Ivancevic, Vladimir G.; Ivancevic, Tijana T.

    2008-01-01

    This paper proposes rigorous geometrical treatment of bioelectrodynamics, underpinning two fast-growing biomedical research fields: bioelectromagnetism, which deals with the ability of life to produce its own electromagnetism, and bioelectromagnetics, which deals with the effect on life from external electromagnetism. Keywords: Bioelectrodynamics, exterior geometrical machinery, Dirac-Feynman quantum electrodynamics, functional electrical stimulation

  6. Path Integral Molecular Dynamics within the Grand Canonical-like Adaptive Resolution Technique: Quantum-Classical Simulation of Liquid Water

    CERN Document Server

    Agarwal, Animesh

    2015-01-01

    Quantum effects due to the spatial delocalization of light atoms are treated in molecular simulation via the path integral technique. Among several methods, Path Integral (PI) Molecular Dynamics (MD) is nowadays a powerful tool to investigate properties induced by spatial delocalization of atoms; however computationally this technique is very demanding. The abovementioned limitation implies the restriction of PIMD applications to relatively small systems and short time scales. One possible solution to overcome size and time limitation is to introduce PIMD algorithms into the Adaptive Resolution Simulation Scheme (AdResS). AdResS requires a relatively small region treated at path integral level and embeds it into a large molecular reservoir consisting of generic spherical coarse grained molecules. It was previously shown that the realization of the idea above, at a simple level, produced reasonable results for toy systems or simple/test systems like liquid parahydrogen. Encouraged by previous results, in this ...

  7. Geometrical Optics

    Science.gov (United States)

    Lindlein, Norbert; Leuchs, Gerd

    This chapter shall discuss the basics and the applications of geometrical optical methods in modern optics. Geometrical optics has a long tradition and some ideas are many centuries old. Nevertheless, the invention of modern personal computers which can perform several million floating-point operations in a second also revolutionized the methods of geometrical optics and so several analytical methods lost importance whereas numerical methods such as ray tracing became very important. Therefore, the emphasis in this chapter is also on modern numerical methods such as ray tracing and some other systematic methods such as the paraxial matrix theory.

  8. Magnetic field induced enlargement of the regime of critical fluctuations in the classical superconductor V3Si from high-resolution specific heat experiments.

    Science.gov (United States)

    Zheng, Y; Liu, Y; Toyota, N; Lortz, R

    2015-02-25

    We present high-resolution specific heat data from a high-purity single crystal of the classical superconductor V(3)Si, which reveal tiny lambda-shape anomalies at the superconducting transition superimposed onto the BCS specific heat jump in magnetic fields of 2 T and higher. The appearance of these anomalies is accompanied by a magnetic-field-induced broadening of the superconducting transition. We demonstrate, using scaling relations predicted by the fluctuation models of the 3d-XY and the 3d-lowest-Landau-level (3d-LLL) universality class that the effect of critical fluctuations becomes experimentally observable due to of a magnetic field-induced enlargement of the regime of critical fluctuations. The scaling indicates that a reduction of the effective dimensionality due to the confinement of quasiparticles into low Landau levels is responsible for this effect. PMID:25640214

  9. The Classical Cake Problem

    Science.gov (United States)

    Nelson, Norman N.; Fisch, Forest N.

    1973-01-01

    Discussed are techniques of presentation and solution of the Classical Cake Problem. A frosted cake with a square base is to be cut into n pieces with the volume of cake and frosting the same for each piece. Needed are minimal geometric concepts and the formula for the volume of a prism. (JP)

  10. GEOMETRIC TURBULENCE

    Directory of Open Access Journals (Sweden)

    Trunev A. P.

    2014-05-01

    Full Text Available In this article we have investigated the solutions of Maxwell's equations, Navier-Stokes equations and the Schrödinger associated with the solutions of Einstein's equations for empty space. It is shown that in some cases the geometric instability leading to turbulence on the mechanism of alternating viscosity, which offered by N.N. Yanenko. The mechanism of generation of matter from dark energy due to the geometric turbulence in the Big Bang has been discussed

  11. Grassmannians of classical buildings

    CERN Document Server

    Pankov, Mark

    2010-01-01

    Buildings are combinatorial constructions successfully exploited to study groups of various types. The vertex set of a building can be naturally decomposed into subsets called Grassmannians. The book contains both classical and more recent results on Grassmannians of buildings of classical types. It gives a modern interpretation of some classical results from the geometry of linear groups. The presented methods are applied to some geometric constructions non-related to buildings - Grassmannians of infinite-dimensional vector spaces and the sets of conjugate linear involutions. The book is self

  12. Spinors in Quantum Geometrical Theory

    OpenAIRE

    Galehouse, Daniel C.

    2002-01-01

    Spinors have played an essential but enigmatic role in modern physics since their discovery. Now that quantum-gravitational theories have started to become available, the inclusion of a description of spin in the development is natural and may bring about a profound understanding of the mathematical structure of fundamental physics. A program to attempt this is laid out here. Concepts from a known quantum-geometrical theory are reviewed: (1) Classical physics is replaced by a suitable geometr...

  13. Star products and geometric algebra

    International Nuclear Information System (INIS)

    The formalism of geometric algebra can be described as deformed super analysis. The deformation is done with a fermionic star product, that arises from deformation quantization of pseudoclassical mechanics. If one then extends the deformation to the bosonic coefficients of superanalysis one obtains quantum mechanics for systems with spin. This approach clarifies on the one hand the relation between Grassmann and Clifford structures in geometric algebra and on the other hand the relation between classical mechanics and quantum mechanics. Moreover it gives a formalism that allows to handle classical and quantum mechanics in a consistent manner

  14. Applying classical geometry intuition to quantum spin

    Science.gov (United States)

    Durfee, Dallin S.; Archibald, James L.

    2016-09-01

    Using concepts of geometric orthogonality and linear independence, we logically deduce the form of the Pauli spin matrices and the relationships between the three spatially orthogonal basis sets of the spin-1/2 system. Rather than a mathematically rigorous derivation, the relationships are found by forcing expectation values of the different basis states to have the properties we expect of a classical, geometric coordinate system. The process highlights the correspondence of quantum angular momentum with classical notions of geometric orthogonality, even for the inherently non-classical spin-1/2 system. In the process, differences in and connections between geometrical space and Hilbert space are illustrated.

  15. The geometric phase

    International Nuclear Information System (INIS)

    In 1983 the author found a geometric effect exists in the quantum waves that describe matter and its interactions on the smallest scales. In this case the anholonomy appears in a system's wave function (the mathematical description of a system's physical state) after the system has been transported around a cyclic circuit on an abstract surface in parameter space. He calls this anholonomy the geometric phase, because it manifests itself specifically as a shift in the wave function's phase: a quantity that describes where the wave function is in its oscillatory cycle at any given time and place. It so happens that the geometric phase provides an elegant explanation of various quantum-mechanical phenomena in systems whose environment undergoes a cyclic change: neutrons that pass through a helical magnetic field, polarized light in a coiled optic fiber and charged particles circling an isolated magnetic field. Perhaps more surprising is the fact that the geometric phase can also be generalized to applications in classical physics. Among other things, it offers a new way to describe the behavior of such textbook objects as pendulums

  16. Concepts of classical optics

    CERN Document Server

    Strong, John

    2004-01-01

    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

  17. Classical antiparticles

    Energy Technology Data Exchange (ETDEWEB)

    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). 13 refs., 1 tab.

  18. What is a Singularity in Geometrized Newtonian Gravitation?

    CERN Document Server

    Weatherall, James Owen

    2013-01-01

    I discuss singular spacetimes in the context of the geometrized formulation of Newtonian gravitation. I argue first that geodesic incompleteness is a natural criterion for when a model of geometrized Newtonian gravitation is singular, and then I show that singularities in this sense arise naturally in classical physics by stating and proving a classical version of the Raychaudhuri-Komar singularity theorem.

  19. Geometric Entropy

    CERN Document Server

    Das, Diptarka

    2010-01-01

    The laws of mechanics of stationary black holes bear a close resemblance with the laws of thermodynamics. This is not only a mathematical analogy but also a physical one that helps us answer deep questions related to the thermodynamic properties of the black holes. It turns out that we can define an entropy which is purely geometrical for black holes. In this thesis we explain Wald's formulation which identifies black hole entropy for an arbitrary covariant theory of gravity. We would like to know precisely what inputs go into arriving at Wald's formalism. This expression for the entropy clearly depends on the precise form of the action. The secondary theme of this thesis is to distinguish thermodynamic laws which are kinematic from those which are dynamical. We would like to see explicitly in the derivation of these laws, where exactly the form of action plays a role. In the beginning we motivate the definition of entropy using the Einstein-Hilbert Lagrangian. We encounter the Zeroth law, the Hawking radiati...

  20. Classical integrability

    Science.gov (United States)

    Torrielli, Alessandro

    2016-08-01

    We review some essential aspects of classically integrable systems. The detailed outline of the sections consists of: 1. Introduction and motivation, with historical remarks; 2. Liouville theorem and action-angle variables, with examples (harmonic oscillator, Kepler problem); 3. Algebraic tools: Lax pairs, monodromy and transfer matrices, classical r-matrices and exchange relations, non-ultralocal Poisson brackets, with examples (non-linear Schrödinger model, principal chiral field); 4. Features of classical r-matrices: Belavin–Drinfeld theorems, analyticity properties, and lift of the classical structures to quantum groups; 5. Classical inverse scattering method to solve integrable differential equations: soliton solutions, spectral properties and the Gel’fand–Levitan–Marchenko equation, with examples (KdV equation, Sine-Gordon model). Prepared for the Durham Young Researchers Integrability School, organised by the GATIS network. This is part of a collection of lecture notes.

  1. PREFACE: Geometrically frustrated magnetism Geometrically frustrated magnetism

    Science.gov (United States)

    Gardner, Jason S.

    2011-04-01

    Oren Ofer, Amit Keren, Jess H Brewer, Tianheng H Han and Young S Lee Classical topological order in kagome ice Andrew J Macdonald, Peter C W Holdsworth and Roger G Melko Magnetic phase diagrams of classical triangular and kagome antiferromagnets M V Gvozdikova, P-E Melchy and M E Zhitomirsky The ordering of XY spin glasses Hikaru Kawamura Dynamic and thermodynamic properties of the generalized diamond chain model for azurite Andreas Honecker, Shijie Hu, Robert Peters and Johannes Richter Classical height models with topological order Christopher L Henley A search for disorder in the spin glass double perovskites Sr2CaReO6 and Sr2MgReO6 using neutron diffraction and neutron pair distribution function analysis J E Greedan, Shahab Derakhshan, F Ramezanipour, J Siewenie and Th Proffen Order and disorder in the local and long-range structure of the spin-glass pyrochlore, Tb2Mo2O7 Yu Jiang, Ashfia Huq, Corwin H Booth, Georg Ehlers, John E Greedan and Jason S Gardner The magnetic phase diagram of Gd2Sn2O7 R S Freitas and J S Gardner Calculation of the expected zero-field muon relaxation rate in the geometrically frustrated rare earth pyrochlore Gd2Sn2O7 antiferromagnet P A McClarty, J N Cosman, A G Del Maestro and M J P Gingras Magnetic frustration in the disordered pyrochlore Yb2GaSbO7 J A Hodges, P Dalmas de Réotier, A Yaouanc, P C M Gubbens, P J C King and C Baines Titanium pyrochlore magnets: how much can be learned from magnetization measurements? O A Petrenko, M R Lees and G Balakrishnan Local susceptibility of the Yb2Ti2O7 rare earth pyrochlore computed from a Hamiltonian with anisotropic exchange J D Thompson, P A McClarty and M J P Gingras Slow and static spin correlations in Dy2 + xTi2 - xO7 - δ J S Gardner, G Ehlers, P Fouquet, B Farago and J R Stewart The spin ice Ho2Ti2O7 versus the spin liquid Tb2Ti2O7: field-induced magnetic structures A P Sazonov, A Gukasov and I Mirebeau Magnetic monopole dynamics in spin ice L D C Jaubert and P C W Holdsworth

  2. Geometrical methods in learning theory

    International Nuclear Information System (INIS)

    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

  3. High resolution telescope including an array of elemental telescopes aligned along a common axis and supported on a space frame with a pivot at its geometric center

    Science.gov (United States)

    Norbert, Massie A.; Yale, Oster

    1992-01-01

    A large effective-aperture, low-cost optical telescope with diffraction-limited resolution enables ground-based observation of near-earth space objects. The telescope has a non-redundant, thinned-aperture array in a center-mount, single-structure space frame. It employes speckle interferometric imaging to achieve diffraction-limited resolution. The signal-to-noise ratio problem is mitigated by moving the wavelength of operation to the near-IR, and the image is sensed by a Silicon CCD. The steerable, single-structure array presents a constant pupil. The center-mount, radar-like mount enables low-earth orbit space objects to be tracked as well as increases stiffness of the space frame. In the preferred embodiment, the array has elemental telescopes with subaperture of 2.1 m in a circle-of-nine configuration. The telescope array has an effective aperture of 12 m which provides a diffraction-limited resolution of 0.02 arc seconds. Pathlength matching of the telescope array is maintained by a electro-optical system employing laser metrology. Speckle imaging relaxes pathlength matching tolerance by one order of magnitude as compared to phased arrays. Many features of the telescope contribute to substantial reduction in costs. These include eliminating the conventional protective dome and reducing on-site construction activities. The cost of the telescope scales with the first power of the aperture rather than its third power as in conventional telescopes.

  4. Functional Techniques in Classical Mechanics

    CERN Document Server

    Gozzi, E

    2001-01-01

    In 1931 Koopman and von Neumann extended previous work of Liouville and provided an operatorial version of Classical Mechanics (CM). In this talk we will review a path-integral formulation of this operatorial version of CM. In particular we will study the geometrical nature of the many auxiliary variables present and of the unexpected universal symmetries generated by the functional technique.

  5. Classical Tunneling

    CERN Document Server

    Cohn, A G; Rabinowitz, Mario

    2003-01-01

    A classical representation of an extended body over barriers of height greater than the energy of the incident body is shown to have many features in common with quantum tunneling as the center-of-mass literally goes through the barrier. It is even classically possible to penetrate any finite barrier with a body of arbitrarily low energy if the body is sufficiently long. A distribution of body lengths around the de Broglie wavelength leads to reasonable agreement with the quantum transmission coefficient.

  6. Classical Tunneling

    OpenAIRE

    Cohn, Arthur; Rabinowitz, Mario

    2003-01-01

    A classical representation of an extended body over barriers of height greater than the energy of the incident body is shown to have many features in common with quantum tunneling as the center-of-mass literally goes through the barrier. It is even classically possible to penetrate any finite barrier with a body of arbitrarily low energy if the body is sufficiently long. A distribution of body lengths around the de Broglie wavelength leads to reasonable agreement with the quantum transmission...

  7. Classical Motion

    OpenAIRE

    Mould, Richard A

    2003-01-01

    Preciously given rules allow conscious systems to be included in quantum mechanical systems. There rules are derived from the empirical experience of an observer who witnesses a quantum mechanical interaction leading to the capture of a single particle. In the present paper it is shown that purely classical changes experienced by an observer are consistent with these rules. Three different interactions are considered, two of which combine classical and quantum mechanical changes. The previous...

  8. 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 ...

  9. High-resolution electron-energy-loss spectroscopy and photoelectron-diffraction studies of the geometric structure of adsorbates on single-crystal metal surfaces

    International Nuclear Information System (INIS)

    Two techniques which have made important contributions to the understanding of surface phenomena are high resolution electron energy loss spectroscopy (EELS) and photoelectron diffraction (PD). EELS is capable of directly measuring the vibrational modes of clean and adsorbate covered metal surfaces. In this work, the design, construction, and performance of a new EELS spectrometer are described. These results are discussed in terms of possible structures of the O-Cu(001) system. Recommendations for improvements in this EELS spectrometer and guidelines for future spectrometers are given. PD experiments provide accurate quantitative information about the geometry of atoms and molecules adsorbed on metal surfaces. The technique has advantages when used to study disordered overlayers, molecular overlayers, multiple site systems, and adsorbates which are weak electron scatterers. Four experiments were carried out which exploit these advantages

  10. Multivariate Statistical Analysis: A Geometric Perspective

    OpenAIRE

    Tyurin, Yuri N.

    2009-01-01

    A new, coordinate-free (geometric) approach to multivariate statistical analysis. General multivariate linear models and linear hypotheses are defined in geometric form. A method of constructing statistical criteria is defined for linear hypotheses. As a result, multivariate statistical analysis is developed in full analogy to classical statistical analysis. This approach is based on tensor products and modules over the ring of square matrices, supplied with an inner product.

  11. Classical Motion

    CERN Document Server

    Mould, R A

    2003-01-01

    Preciously given rules allow conscious systems to be included in quantum mechanical systems. There rules are derived from the empirical experience of an observer who witnesses a quantum mechanical interaction leading to the capture of a single particle. In the present paper it is shown that purely classical changes experienced by an observer are consistent with these rules. Three different interactions are considered, two of which combine classical and quantum mechanical changes. The previously given rules support all of these cases. Key Words: brain states, conscious observer, detector, measurement, probability current, state reduction, von Neumann, wave collapse.

  12. Geometric and Kinematic Structure of the Outflow/Envelope System of L1527 Revealed by Subarcsecond-resolution Observation of CS

    CERN Document Server

    Oya, Yoko; Lefloch, Bertrand; López-Sepulvre, Ana; Watanabe, Yoshimasa; Ceccarelli, Cecilia; Yamamoto, Satoshi

    2016-01-01

    Subarcsecond-resolution images of the rotational line emissions of CS and c-C$_3$H$_2$ obtained toward the low-mass protostar IRAS 04368$+$2557 in L1527 with the Atacama Large Millimeter/submillimeter Array are investigated to constrain the orientation of the outflow/envelope system. The distribution of CS consists of an envelope component extending from north to south and a faint butterfly-shaped outflow component. The kinematic structure of the envelope is well reproduced by a simple ballistic model of an infalling rotating envelope. Although the envelope has a nearly edge-on configuration, the inclination angle of the rotation axis from the plane of the sky is found to be 5$^\\circ$, where we find that the western side of the envelope faces the observer. This configuration is opposite to the direction of the large-scale ($\\sim$ 10$^4$ AU) outflow suggested previously from the $^{12}$CO ($J$=3$-$2) observation, and to the morphology of infrared reflection near the protostar ($\\sim$ 200 AU). The latter discre...

  13. Is classical flat Kasner spacetime flat in quantum gravity?

    Science.gov (United States)

    Singh, Parampreet

    2016-05-01

    Quantum nature of classical flat Kasner spacetime is studied using effective spacetime description in loop quantum cosmology (LQC). We find that even though the spacetime curvature vanishes at the classical level, nontrivial quantum gravitational effects can arise. For the standard loop quantization of Bianchi-I spacetime, which uniquely yields universal bounds on expansion and shear scalars and results in a generic resolution of strong singularities, we find that a flat Kasner metric is not a physical solution of the effective spacetime description, except in a limit. The lack of a flat Kasner metric at the quantum level results from a novel feature of the loop quantum Bianchi-I spacetime: quantum geometry induces nonvanishing spacetime curvature components, making it not Ricci flat even when no matter is present. The noncurvature singularity of the classical flat Kasner spacetime is avoided, and the effective spacetime transits from a flat Kasner spacetime in asymptotic future, to a Minkowski spacetime in asymptotic past. Interestingly, for an alternate loop quantization which does not share some of the fine features of the standard quantization, flat Kasner spacetime with expected classical features exists. In this case, even with nontrivial quantum geometric effects, the spacetime curvature vanishes. These examples show that the character of even a flat classical vacuum spacetime can alter in a fundamental way in quantum gravity and is sensitive to the quantization procedure.

  14. Classical entanglement

    OpenAIRE

    Danforth, Douglas G.

    2001-01-01

    Classical systems can be entangled. Entanglement is defined by coincidence correlations. Quantum entanglement experiments can be mimicked by a mechanical system with a single conserved variable and 77.8% conditional efficiency. Experiments are replicated for four particle entanglement swapping and GHZ entanglement.

  15. Classical Mechanics

    OpenAIRE

    Gallavotti, Giovanni

    1999-01-01

    This is the English version of a friendly graduate course on Classical Mechanics, containing about 80% of the material I covered during the January-June 1999 semester at IFUG in the Mexican city of Leon. For the Spanish version, see physics/9906066

  16. On bivariate geometric distribution

    OpenAIRE

    Jayakumar, K.; Davis Antony Mundassery

    2013-01-01

    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.

  17. Geometrical formulation of the conformal Ward identity

    International Nuclear Information System (INIS)

    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)

  18. Geometric Integration of Non-autonomous Systems with Application to Rotor Dynamics

    OpenAIRE

    Modin, Klas

    2011-01-01

    Geometric integration of non-autonomous classical engineering problems, such as rotor dynamics, is investigated. It is shown, both numerically and by backward error analysis, that geometric (structure preserving) integration algorithms are superior to conventional Runge-Kutta methods.

  19. 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.

  20. What is a singularity in geometrized Newtonian gravitation?

    OpenAIRE

    Weatherall, JO

    2013-01-01

    © 2014 by the Philosophy of Science Association. All rights reserved. I discuss singular space-times in the context of the geometrized formulation of Newtonian gravitation. I argue first that geodesic incompleteness is a natural criterion for when a model of geometrized Newtonian gravitation is singular, and then I show that singularities in this sense arise naturally in classical physics by stating and proving a classical version of the Raychaudhuri-Komar singularity theorem.

  1. What is a Singularity in Geometrized Newtonian Gravitation?

    OpenAIRE

    Weatherall, JO

    2013-01-01

    © 2014 by the Philosophy of Science Association. All rights reserved. I discuss singular space-times in the context of the geometrized formulation of Newtonian gravitation. I argue first that geodesic incompleteness is a natural criterion for when a model of geometrized Newtonian gravitation is singular, and then I show that singularities in this sense arise naturally in classical physics by stating and proving a classical version of the Raychaudhuri-Komar singularity theorem.

  2. High-resolution Kelvin probe microscopy in corrosion science: Scanning Kelvin probe force microscopy (SKPFM) versus classical scanning Kelvin probe (SKP)

    International Nuclear Information System (INIS)

    With the introduction of a Kelvin probe mode to atomic force microscopy, the so called scanning Kelvin probe force microscopy (SKPFM), the Kelvin probe technique finds application in a steadily increasing number of different fields, from corrosion science to microelectronics and biosciences. For many of these applications, high resolution is required as the relevant information lies in the sub-microscopic distribution of work functions or potentials, which explains the increasing interest in SKPFM. However, compared to the standard scanning Kelvin probe (SKP) technique SKPFM is prone to much more artefacts, which are often not taken into account in the interpretation of the results, as is also the case with the real physical nature of the measured data. A critical discussion of possible artefacts and on the interpretation of the data is presented in this paper, with the main focus on application in corrosion science

  3. Multipartite classical states and detecting quantum discord

    CERN Document Server

    Chen, Lin; Modi, Kavan; Vacanti, Giovanni

    2010-01-01

    We study various types of multipartite separable states in terms of their inherent classical features. For the two important classes of pseudo-classical, introduced here, and classical states, we provide necessary and sufficient conditions for deciding membership in both which can be checked in polynomial running time. Geometrically, the volume of these states in multipartite state space is found to be measure zero. We also provide a physical criterion for detecting non-classical states based on the commutivity of reduced states following local POVMs performed on individual subsystems.

  4. Geometric Computing Based on Computerized Descriptive Geometric

    Institute of Scientific and Technical Information of China (English)

    YU Hai-yan; HE Yuan-Jun

    2011-01-01

    Computer-aided Design (CAD), video games and other computer graphic related technology evolves substantial processing to geometric elements. A novel geometric computing method is proposed with the integration of descriptive geometry, math and computer algorithm. Firstly, geometric elements in general position are transformed to a special position in new coordinate system. Then a 3D problem is projected to new coordinate planes. Finally, according to 2D/3D correspondence principle in descriptive geometry, the solution is constructed computerized drawing process with ruler and compasses. In order to make this method a regular operation, a two-level pattern is established. Basic Layer is a set algebraic packaged function including about ten Primary Geometric Functions (PGF) and one projection transformation. In Application Layer, a proper coordinate is established and a sequence of PGFs is sought for to get the final results. Examples illustrate the advantages of our method on dimension reduction, regulatory and visual computing and robustness.

  5. Geometric formulation of Berezin deformation quantization

    Directory of Open Access Journals (Sweden)

    R. Roknizadeh

    2002-06-01

    Full Text Available   In this paper we try to formulate the Berezin quantization on projective Hilbert space P(H and use its geometric structure to construct a correspondence between a given classical theory and a given quantum theory. It wil be shown that the star product in berezin quantization is equivalent to the Posson bracket on coherent states manifold M, embodded in P(H, and the Berezin method is used to define a classical limit for geometric quantum mechnics. With this construction to all of the quantum observables are associated their covariant symbols, which form a poisson algebra on P(H and since the corresponding classical phase space has a natural Poisson structure, the Berezin quantization is then a systematic procedure to relate these tow piosson algebras.

  6. Classical tachyons

    International Nuclear Information System (INIS)

    A review of tachyons, with particular attention to their classical theory, is presented. The extension of Special Relativity to tachyons in two dimensional is first presented, an elegant model-theory which allows a better understanding also of ordinary physics. Then, the results are extended to the four-dimensional case (particular on tachyon mechanics) that can be derived without assuming the existence of Super-luminal reference-frames. Localizability and the unexpected apparent shape of tachyonic objects are discussed, and it is shown (on the basis of tachyon kinematics) how to solve the common causal paradoxes. In connection with General Relativity, particularly the problem of the apparent superluminal expansions in astrophysics is reviewed. The problem (still open) of the extension of relativitic theories to tachyons in four dimensions is tackled, and the electromagnetic theory of tachyons, a topic that can be relevant also for the experimental side, is reviewed. (Author)

  7. Geometric methods in classical field theory and continuous media

    OpenAIRE

    Campos, Cédric M.

    2010-01-01

    La monografía versa sobre teoría clásica de campos de orden superior. El lector podrá encontrar en sus capítulos iniciales una revisión de algunos de los hechos conocidos en mecánica clásica y teoría clásica de campos (de primer orden). En los capítulos nales, se expone la parte original de la memoria con la extensión de estas teorías a campos clásicos de orden superior, centrándose en la problemática de un formalismo canónico hamiltoniano. Algunos ejemplos son propuestos con ...

  8. 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

  9. Geometric Algebras and Extensors

    OpenAIRE

    Fernandez, V. V.; Moya, A. M.; Rodrigues Jr., W. A.

    2007-01-01

    This is the first paper in a series (of four) designed to show how to use geometric algebras of multivectors and extensors to a novel presentation of some topics of differential geometry which are important for a deeper understanding of geometrical theories of the gravitational field. In this first paper we introduce the key algebraic tools for the development of our program, namely the euclidean geometrical algebra of multivectors Cl(V,G_{E}) and the theory of its deformations leading to met...

  10. Geometrization of Trace Formulas

    CERN Document Server

    Frenkel, Edward

    2010-01-01

    Following our joint work arXiv:1003.4578 with Robert Langlands, we make the first steps toward developing geometric methods for analyzing trace formulas in the case of the function field of a curve defined over a finite field. We also suggest a conjectural framework of geometric trace formulas for curves defined over the complex field, which exploits the categorical version of the geometric Langlands correspondence.

  11. Lectures on Geometric Quantization

    OpenAIRE

    Śniatycki, Jędrzej

    2016-01-01

    These lectures notes are meant as an introduction to geometric quantization. In Section 1, I begin with presentation of the historical background of quantum mechanics. I continue with discoveries in the theory of representations of Lie groups, which lead to emergence of geometric quantization as a part of pure mathematics. This presentation is very subjective, flavored by my own understanding of the role of geometric quantization in quantum mechanics and representation theory. Sectio...

  12. Geometric gyrokinetic theory for edge plasmas

    International Nuclear Information System (INIS)

    It turns out that gyrokinetic theory can be geometrically formulated as a special case of a geometrically generalized Vlasov-Maxwell system. It is proposed that the phase space of the space-time is a seven-dimensional fiber bundle P over the four-dimensional space-time M, and that a Poincare-Cartan-Einstein 1-form γ on the seven-dimensional phase space determines a particle's worldline in the phase space. Through Liouville 6-form Ω and fiber integral, the 1-form γ also uniquely defines a geometrically generalized Vlasov-Maxwell system as a field theory for the collective electromagnetic field. The geometric gyrokinetic theory is then developed as a special case of the geometrically generalized Vlasov-Maxwell system. In its most general form, gyrokinetic theory is about a symmetry, called gyrosymmetry, for magnetized plasmas, and the 1-form γ again uniquely defines the gyrosymmetry. The objective is to decouple the gyrophase dynamics from the rest of the particle dynamics by finding the gyrosymmetry in γ. Compared to other methods of deriving the gyrokinetic equations, the advantage of the geometric approach is that it allows any approximation based on mathematical simplification or physical intuition to be made at the 1-form level, and yet the field theories still have the desirable exact conservation properties, such as phase space volume conservation and energy-momentum conservation if the 1-form does not depend on the space-time coordinate explicitly. A set of generalized gyrokinetic equations valid for the edge plasmas is then derived using this geometric method. This formalism allows large-amplitude, time-dependent background electromagnetic fields to be developed fully nonlinearly in addition to small-amplitude, short-wavelength electromagnetic perturbations. The fact that we adopted the geometric method in the present study does not necessarily imply that the major results reported here cannot be achieved using classical methods. What the geometric

  13. Geometric neural computing.

    Science.gov (United States)

    Bayro-Corrochano, E J

    2001-01-01

    This paper shows the analysis and design of feedforward neural networks using the coordinate-free system of Clifford or geometric algebra. It is shown that real-, complex-, and quaternion-valued neural networks are simply particular cases of the geometric algebra multidimensional neural networks and that some of them can also be generated using support multivector machines (SMVMs). Particularly, the generation of radial basis function for neurocomputing in geometric algebra is easier using the SMVM, which allows one to find automatically the optimal parameters. The use of support vector machines in the geometric algebra framework expands its sphere of applicability for multidimensional learning. Interesting examples of nonlinear problems show the effect of the use of an adequate Clifford geometric algebra which alleviate the training of neural networks and that of SMVMs. PMID:18249926

  14. Classical and stochastic Laplacian growth

    CERN Document Server

    Gustafsson, Björn; Vasil’ev, Alexander

    2014-01-01

    This monograph covers a multitude of concepts, results, and research topics originating from a classical moving-boundary problem in two dimensions (idealized Hele-Shaw flows, or classical Laplacian growth), which has strong connections to many exciting modern developments in mathematics and theoretical physics. Of particular interest are the relations between Laplacian growth and the infinite-size limit of ensembles of random matrices with complex eigenvalues; integrable hierarchies of differential equations and their spectral curves; classical and stochastic Löwner evolution and critical phenomena in two-dimensional statistical models; weak solutions of hyperbolic partial differential equations of singular-perturbation type; and resolution of singularities for compact Riemann surfaces with anti-holomorphic involution. The book also provides an abundance of exact classical solutions, many explicit examples of dynamics by conformal mapping as well as a solid foundation of potential theory. An extensive biblio...

  15. 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...... of non-uniformity of the illumination of the image plane. Only the image deforming aberrations and the non-uniformity of illumination are included in the calibration models. The topics of the pinhole camera model and the extension to the Direct Linear Transform (DLT) are described. It is shown how...... 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...

  16. Classical resolution of singularities in dilaton cosmologies

    CERN Document Server

    Bergshoeff, E A; Roest, D; Russo, J G; Townsend, P K

    2005-01-01

    For models of dilaton-gravity with a possible exponential potential, such as the tensor-scalar sector of IIA supergravity, we show how cosmological solutions correspond to trajectories in a 2D Milne space (parametrized by the dilaton and the scale factor). Cosmological singularities correspond to points at which a trajectory meets the Milne horizon, but the trajectories can be smoothly continued through the horizon to an instanton solution of the Euclidean theory. We find some exact cosmology/instanton solutions that lift to black holes in one higher dimension. For one such solution, the singularities of a big crunch to big bang transition mediated by an instanton phase lift to the black hole and cosmological horizons of de Sitter Schwarzschild spacetimes.

  17. Classical resolution of singularities in dilaton cosmologies

    NARCIS (Netherlands)

    Bergshoeff, EA; Collinucci, A; Roest, D; Russo, JG; Townsend, PK

    2005-01-01

    For models of dilaton gravity with a possible exponential potential, such as the tensor-scalar sector of ITA supergravity, we show how cosmological solutions correspond to trajectories in a 2D Milne space (parametrized by the dilaton and the scale factor). Cosmological singularities correspond to po

  18. 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.

  19. A Geometrical Approach to Iterative Isotone Regression

    OpenAIRE

    Guyader, Arnaud; Jégou, Nicolas; Németh, Alexander B.; Németh, Sándor Z.

    2012-01-01

    In the present paper, we propose and analyze a novel method for estimating a univariate regression function of bounded variation. The underpinning idea is to combine two classical tools in nonparametric statistics, namely isotonic regression and the estimation of additive models. A geometrical interpretation enables us to link this iterative method with Von Neumann's algorithm. Moreover, making a connection with the general property of isotonicity of projection onto convex cones, we derive an...

  20. Geometric Mechanics, Lagrangian Reduction, and Nonholonomic Systems

    OpenAIRE

    Cendra, Hernán; Marsden, Jerrold E.; Ratiu, Tudor S.

    2001-01-01

    This paper surveys selected recent progress in geometric mechanics, focussing on Lagrangian reduction and gives some new applications to nonholonomic systems, that is, mechanical systems with constraints typified by rolling without slipping. Reduction theory for mechanical systems with symmetry has its roots in the classical works in mechanics of Euler, Jacobi, Lagrange, Hamilton, Routh, Poincaré and others. The modern vision of mechanics includes, besides the traditional mechanics of part...

  1. Geometrical dynamics of Born-Infeld objects

    OpenAIRE

    Cordero, Ruben; Molgado, Alberto; Rojas, Efrain

    2007-01-01

    We present a geometrical inspired study of the dynamics of $Dp$-branes. We focus on the usual nonpolynomial 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 AD...

  2. Lectures on classical differential geometry

    CERN Document Server

    Struik, Dirk J

    1988-01-01

    Elementary, yet authoritative and scholarly, this book offers an excellent brief introduction to the classical theory of differential geometry. It is aimed at advanced undergraduate and graduate students who will find it not only highly readable but replete with illustrations carefully selected to help stimulate the student's visual understanding of geometry. The text features an abundance of problems, most of which are simple enough for class use, and often convey an interesting geometrical fact. A selection of more difficult problems has been included to challenge the ambitious student.Writ

  3. GEOMETRIC TURBULENCE IN GENERAL RELATIVITY

    Directory of Open Access Journals (Sweden)

    Trunev A. P.

    2015-03-01

    Full Text Available The article presents the simulation results of the metric of elementary particles, atoms, stars and galaxies in the general theory of relativity and Yang-Mills theory. We have shown metrics and field equations describing the transition to turbulence. The problems of a unified field theory with the turbulent fluctuations of the metric are considered. A transition from the Einstein equations to the diffusion equation and the Schrödinger equation in quantum mechanics is shown. Ther are examples of metrics in which the field equations are reduced to a single equation, it changes type depending on the equation of state. These examples can be seen as a transition to the geometric turbulence. It is shown that the field equations in general relativity can be reduced to a hyperbolic, elliptic or parabolic type. The equation of parabolic type describing the perturbations of the gravitational field on the scale of stars, galaxies and clusters of galaxies, which is a generalization of the theory of gravitation Newton-Poisson in case of Riemannian geometry, taking into account the curvature of space-time has been derived. It was found that the geometric turbulence leads to an exchange between regions of different scale. Under turbulent exchange material formed of two types of clusters, having positive and negative energy density that corresponds to the classical and quantum particle motion respectively. These results allow us to answer the question about the origin of the quantum theory

  4. Deforming Geometric Transitions

    OpenAIRE

    Rossi, Michele

    2013-01-01

    After a quick review of the wild structure of the complex moduli space of Calabi-Yau threefolds and the role of geometric transitions in this context (the Calabi-Yau web) the concept of "deformation equivalence" for geometric transitions is introduced to understand the arrows of the Gross-Reid Calabi-Yau web as deformation-equivalence classes of geometric transitions. Then the focus will be on some results and suitable examples to understand under which conditions it is possible to get "simpl...

  5. 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...

  6. A Protocol for the Creation of Useful Geometric Shape Metrics Illustrated with a Newly Derived Geometric Measure of Leaf Circularity

    Directory of Open Access Journals (Sweden)

    Jonathan D. Krieger

    2014-08-01

    Full Text Available Premise of the study: I present a protocol for creating geometric leaf shape metrics to facilitate widespread application of geometric morphometric methods to leaf shape measurement. Methods and Results: To quantify circularity, I created a novel shape metric in the form of the vector between a circle and a line, termed geometric circularity. Using leaves from 17 fern taxa, I performed a coordinate-point eigenshape analysis to empirically identify patterns of shape covariation. I then compared the geometric circularity metric to the empirically derived shape space and the standard metric, circularity shape factor. Conclusions: The geometric circularity metric was consistent with empirical patterns of shape covariation and appeared more biologically meaningful than the standard approach, the circularity shape factor. The protocol described here has the potential to make geometric morphometrics more accessible to plant biologists by generalizing the approach to developing synthetic shape metrics based on classic, qualitative shape descriptors.

  7. Nonuniform Markov Geometric Measures

    OpenAIRE

    Neunhäuserer, J.

    2015-01-01

    We generalize results of Fan and Zhang [6] on absolute continuity and singularity of the golden Markov geometric series to nonuniform stochastic series given by arbitrary Markov process. In addition we describe an application of these results in fractal geometry.

  8. 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.

  9. Geometrization of the physics with teleparallelism. II. Towards a fully geometric Dirac equation

    Science.gov (United States)

    Vargas, José G.; Torr, Douglas G.; Lecompte, Alvaro

    1992-04-01

    In an accompanying paper (I), it is shown that the basic equations of the theory of Lorentzian connections with teleparallelism (TP) acquire standard forms of physical field equations upon removal of the constraints represented by the Bianchi identities. A classical physical theory results that supersedes general relativity and Maxwell-Lorentz electrodynamics if the connection is viewed as Finslerian. The theory also encompasses a short-range, strong, classical interaction. It has, however, an open end, since the source side of the torsion field equation is not geometric. In this paper, Kaehler's partial geometrization of the Dirac equation is taken as a starting point for the development of fully geometric Dirac equations via the correspondence principle given in I. For this purpose, Kaehler's calculus (where the spinors are differential forms) is generalized so that it also applies when the torsion is not zero. The point is then made that the forms can take values in tangent Clifford algebras rather than in tensor algebras. The basic “Eigenschaft” of the Kaehler calculus also is examined from the physical perspective of dimensional analysis. Geometric Dirac equations of great structural simplicity are finally inferred from the standard Dirac equation by using the aforementioned correspondence principle. The realm of application of the Dirac theory is thus enriched in principle, though only at an abstract level at this point: the standard spinors, which are scalar-valued forms in the Kaehler version of that theory, become Clifford-valued. In addition, the geometrization of the Dirac equation implies a geometrization of the Dirac current. When this current is replaced in the field equations for the torsion, the theory of Paper I becomes fully geometric.

  10. An empirical model for pp scattering and geometrical scaling

    International Nuclear Information System (INIS)

    We present the result of an empirical model for elastic pp scattering at LHC which indicates that the asymptotic black disk limit R = σelastic/σtotal → 1/2 is not yet reached and discuss the implications on classical geometrical scaling behavior. We propose a geometrical scaling law for the position of the dip in elastic pp scattering which allows to make predictions valid both for intermediate and asymptotic energies.

  11. On sheets of orbit covers for classical semisimple Lie groups

    Institute of Scientific and Technical Information of China (English)

    梁科; 侯自新; 岳临渊

    2002-01-01

    David Vogan gave programmatic conjectures about the Dixmier's map and he made two conjectures that induction may be independent of the choice of parabolic group used and the sheets of orbit data are conjugated or disjointed[1]. In our previous paper, we gave a geometric version of the parabolic induction of the geometric orbit datum (i.e. orbit covers), and proved Vogan's first conjecture for geometric orbit datum:the parabolic induction of the geometric orbit datum is independent of the choice of parabolic group. In this paper, we will prove the other Vogan's conjecture, that is, the sheets are conjugated or disjointed for classical semisimple complex groups.``

  12. Geometric Realizations of Tricategories

    CERN Document Server

    Cegarra, Antonio M

    2012-01-01

    Any tricategory characteristically has associated various simplicial or pseudo-simplicial objects. This paper explores the relationship amongst three of them: the pseudo-simplicial bicategory so-called Grothendieck nerve of the tricategory, the simplicial bicategory termed its Segal nerve, and the simplicial set called its Street geometric nerve, and it proves the fact that the geometric realizations of all of these possible candidate 'nerves of the tricategory' are homotopy equivalent. Our results provide coherence for all reasonable extensions to tricategories of Quillen's definition of the 'classifying space' of a category as the geometric realization of the category's Grothendieck nerve. Many properties of the classifying space construction for tricategories may be easier to establish depending on the nerve used for realizations. For instance, by using Grothendieck nerves we state and prove the precise form in which the process of taking classifying spaces transports tricategorical coherence to homotopy c...

  13. 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

  14. 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...

  15. What classicality? Decoherence and Bohr's classical concepts

    CERN Document Server

    Schlosshauer, Maximilian

    2010-01-01

    Niels Bohr famously insisted on the indispensability of what he termed "classical concepts." In the context of the decoherence program, on the other hand, it has become fashionable to talk about the "dynamical emergence of classicality" from the quantum formalism alone. Does this mean that decoherence challenges Bohr's dictum and signifies a break with the Copenhagen interpretation-for example, that classical concepts do not need to be assumed but can be derived? In this paper we'll try to shine some light down the murky waters where formalism and philosophy cohabitate. To begin, we'll clarify the notion of classicality in the decoherence description. We'll then discuss Bohr's and Heisenberg's take on the quantum-classical problem and reflect on different meanings of the terms "classicality" and "classical concepts" in the writings of Bohr and his followers. This analysis will allow us to put forward some tentative suggestions for how we may better understand the relation between decoherence-induced classical...

  16. Geometric spin echo under zero field.

    Science.gov (United States)

    Sekiguchi, Yuhei; Komura, Yusuke; Mishima, Shota; Tanaka, Touta; Niikura, Naeko; Kosaka, Hideo

    2016-01-01

    Spin echo is a fundamental tool for quantum registers and biomedical imaging. It is believed that a strong magnetic field is needed for the spin echo to provide long memory and high resolution, since a degenerate spin cannot be controlled or addressed under a zero magnetic field. While a degenerate spin is never subject to dynamic control, it is still subject to geometric control. Here we show the spin echo of a degenerate spin subsystem, which is geometrically controlled via a mediating state split by the crystal field, in a nitrogen vacancy centre in diamond. The demonstration reveals that the degenerate spin is protected by inherent symmetry breaking called zero-field splitting. The geometric spin echo under zero field provides an ideal way to maintain the coherence without any dynamics, thus opening the way to pseudo-static quantum random access memory and non-invasive biosensors. PMID:27193936

  17. Nonadiabatic Geometric Angle in Nuclear Magnetic Resonance Connection

    OpenAIRE

    Cherbal, Omar; Maamache, Mustapha; Drir, Mahrez

    2005-01-01

    By using the Grassmannian invariant-angle coherents states approach, the classical analogue of the Aharonov-Anandan nonadiabatic geometrical phase is found for a spin one-half in Nuclear Magnetic Resonance (NMR). In the adiabatic limit, the semi-classical relation between the adiabatic Berry’s phase and Hannay’s angle gives exactly the experimental result observed by Suter et al[12].

  18. Mahavira's Geometrical Problems

    DEFF Research Database (Denmark)

    Høyrup, Jens

    Analysis of the geometrical chapters Mahavira's 9th-century Ganita-sara-sangraha reveals inspiration from several chronological levels of Near-Eastern and Mediterranean mathematics: (1)that known from Old Babylonian tablets, c. 1800-1600 BCE; (2)a Late Babylonian but pre-Seleucid Stratum, probabl...

  19. 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

  20. Hidden invariance of the free classical particle

    International Nuclear Information System (INIS)

    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

  1. 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.

  2. GEOMETRICALLY INVARIANT WATERMARKING BASED ON RADON TRANSFORMATION

    Institute of Scientific and Technical Information of China (English)

    Cai Lian; Du Sidan; Gao Duntang

    2005-01-01

    The weakness of classical watermarking methods is the vulnerability to geometrical distortions that widely occur during normal use of the media. In this letter, a new imagewatermarking method is presented to resist Rotation, Scale and Translation (RST) attacks. The watermark is embedded into a domain obtained by taking Radon transform of a circular area selected from the original image, and then extracting Two-Dimensional (2-D) Fourier magnitude of the Radon transformed image. Furthermore, to prevent the watermarked image from degrading due to inverse Radon transform, watermark signal is inversely Radon transformed individually.Experimental results demonstrate that the proposed scheme is able to withstand a variety of attacks including common geometric attacks.

  3. Geometrical dynamics of Born-Infeld objects

    International Nuclear Information System (INIS)

    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 AdS3 x S3 background spacetime. We exhibit the mechanical properties of Born-Infeld objects paving the way to a consistent quantum formulation

  4. Classical particle with spin and Clifford algebra

    International Nuclear Information System (INIS)

    Equations of motion of classical particle with spin in electromagnetic field are derived in terms of the Clifford algebra of the Minkowsky space. The use of the Clifford algebra simplifies the derivation of these equations as well as their form and process of their solving. The equations also get an evident geometric interpretation. The perturbation theory for these equations is formulated which allows to analyze the motion and the polarization of particles in various electromagnetic fields

  5. A geometric approach to tree shape statistics

    OpenAIRE

    Matsen, Frederick A.

    2005-01-01

    This article presents a new way to understand the descriptive ability of tree shape statistics. Where before tree shape statistics were chosen by their ability to distinguish between macroevolutionary models, the ``resolution'' presented in this paper quantifies the ability of a statistic to differentiate between similar and different trees. We term this a ``geometric'' approach to differentiate it from the model-based approach previously explored. A distinct advantage of this perspective is ...

  6. Generalized Geometric Quantum Speed Limits

    Science.gov (United States)

    Pires, Diego Paiva; Cianciaruso, Marco; Céleri, Lucas C.; Adesso, Gerardo; Soares-Pinto, Diogo O.

    2016-04-01

    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.

  7. Hydrogen: Beyond the Classic Approximation

    International Nuclear Information System (INIS)

    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

  8. 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...

  9. Geometric dynamics of optimization

    CERN Document Server

    Gay-Balmaz, F; Ratiu, T S

    2011-01-01

    This paper investigates a family of dynamical systems arising from an evolutionary re-interpretation of certain optimal control and optimization problems. We focus particularly on the application in image registration of the theory of \\emph{metamorphosis}. Metamorphosis is a means of tracking the optimal changes of shape that are necessary for registration of images with various types of data structures, without requiring that the transformations of shape be diffeomorphisms. This is a rich field whose possibilities are just beginning to be developed. In particular, metamorphosis and its related variants in the geometric approach to control and optimization can be expected to produce many exciting opportunities for new applications and analysis in geometric dynamics.

  10. Testing algebraic geometric codes

    Institute of Scientific and Technical Information of China (English)

    2009-01-01

    Property testing was initially studied from various motivations in 1990’s. A code C  GF (r)n is locally testable if there is a randomized algorithm which can distinguish with high possibility the codewords from a vector essentially far from the code by only accessing a very small (typically constant) number of the vector’s coordinates. The problem of testing codes was firstly studied by Blum, Luby and Rubinfeld and closely related to probabilistically checkable proofs (PCPs). How to characterize locally testable codes is a complex and challenge problem. The local tests have been studied for Reed-Solomon (RS), Reed-Muller (RM), cyclic, dual of BCH and the trace subcode of algebraicgeometric codes. In this paper we give testers for algebraic geometric codes with linear parameters (as functions of dimensions). We also give a moderate condition under which the family of algebraic geometric codes cannot be locally testable.

  11. A geometrical introduction to screw theory

    CERN Document Server

    Minguzzi, E

    2012-01-01

    Since the addition of applied forces must take into account the line of action, applied forces do not belong to a vector space. Screw theory removes this geometrical limitation and solves other mechanical problems by unifying, in a single concept, the translational and rotational degrees of freedom. Although venerable this theory is little known. By introducing some innovations, I show how screw theory can help us to rapidly develop several standard and less standard results in classical mechanics. The connection with the Lie algebra of the group of rigid maps is clarified.

  12. Computer Graphics & Geometric Modeling

    OpenAIRE

    Zsombor-Murray, Paul; O'Leary, Paul

    2006-01-01

    Least squares fitting of point sets to lines, planes, curves and surfaces is carried out using eigenvalues and eigenvectors to find the major principal moment of inertia axis of a point set taken as representing the mass distribution of a rigid body. This engineering geometric approach produces identical results when compared to methods of conventional minimization using partial derivatives with respect to linear equation coefficients. Extending the approach to the fitting of conics and quadr...

  13. Geometric measure theory

    CERN Document Server

    Waerden, B

    1996-01-01

    From the reviews: "... Federer's timely and beautiful book indeed fills the need for a comprehensive treatise on geometric measure theory, and his detailed exposition leads from the foundations of the theory to the most recent discoveries. ... The author writes with a distinctive style which is both natural and powerfully economical in treating a complicated subject. This book is a major treatise in mathematics and is essential in the working library of the modern analyst." Bulletin of the London Mathematical Society.

  14. Geometrically Consistent Mesh Modification

    KAUST Repository

    Bonito, A.

    2010-01-01

    A new paradigm of adaptivity is to execute refinement, coarsening, and smoothing of meshes on manifolds with incomplete information about their geometry and yet preserve position and curvature accuracy. We refer to this collectively as geometrically consistent (GC) mesh modification. We discuss the concept of discrete GC, show the failure of naive approaches, and propose and analyze a simple algorithm that is GC and accuracy preserving. © 2010 Society for Industrial and Applied Mathematics.

  15. Geometric unsharpness calculations

    Energy Technology Data Exchange (ETDEWEB)

    Anderson, D.J. [International Training and Education Group (INTEG), Oakville, Ontario (Canada)

    2008-07-15

    The majority of radiographers' geometric unsharpness calculations are normally performed with a mathematical formula. However, a majority of codes and standards refer to the use of a nomograph for this calculation. Upon first review, the use of a nomograph appears more complicated but with a few minutes of study and practice it can be just as effective. A review of this article should provide enlightenment. (author)

  16. Geometric theory of information

    CERN Document Server

    2014-01-01

    This book brings together geometric tools and their applications for Information analysis. It collects current and many uses of in the interdisciplinary fields of Information Geometry Manifolds in Advanced Signal, Image & Video Processing, Complex Data Modeling and Analysis, Information Ranking and Retrieval, Coding, Cognitive Systems, Optimal Control, Statistics on Manifolds, Machine Learning, Speech/sound recognition, and natural language treatment which are also substantially relevant for the industry.

  17. The quantum geometric limit

    CERN Document Server

    Lloyd, Seth

    2012-01-01

    This letter analyzes the limits that quantum mechanics imposes on the accuracy to which spacetime geometry can be measured. By applying the fundamental physical bounds to measurement accuracy to ensembles of clocks and signals moving in curved spacetime -- e.g., the global positioning system -- I derive a covariant version of the quantum geometric limit: the total number of ticks of clocks and clicks of detectors that can be contained in a four volume of spacetime of radius r and temporal extent t is less than or equal to rt/\\pi x_P t_P, where x_P, t_P are the Planck length and time. The quantum geometric limit bounds the number of events or `ops' that can take place in a four-volume of spacetime: each event is associated with a Planck-scale area. Conversely, I show that if each quantum event is associated with such an area, then Einstein's equations must hold. The quantum geometric limit is consistent with and complementary to the holographic bound which limits the number of bits that can exist within a spat...

  18. Geometric leaf placement strategies

    International Nuclear Information System (INIS)

    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 d90-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 d90 values for several different strategies. Measured d90 values vary both with angle and leaf placement strategy. A model has been derived that explains and describes quite well the observed variations of d90 with angle. The d90 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

  19. A new geometric description for Igusa's modular form $(azy)_5$

    CERN Document Server

    Fiorentino, Alessio

    2011-01-01

    The modular form $(azy)_5$ notably appears in one of Igusa's classic structure theorems as a generator of the ring of full modular forms in genus 2, being exhibited by means of a complicated algebraic expression. In this work a different description for this modular form is provided by resorting to a peculiar geometrical approach.

  20. Geometric formulations and variational integrators of discrete autonomous Birkhoff systems

    International Nuclear Information System (INIS)

    The variational integrators of autonomous Birkhoff systems are obtained by the discrete variational principle. The geometric structure of the discrete autonomous Birkhoff system is formulated. The discretization of mathematical pendulum shows that the discrete variational method is as effective as symplectic scheme for the autonomous Birkhoff systems. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

  1. Quantum computation using geometric algebra

    Science.gov (United States)

    Matzke, Douglas James

    This dissertation reports that arbitrary Boolean logic equations and operators can be represented in geometric algebra as linear equations composed entirely of orthonormal vectors using only addition and multiplication Geometric algebra is a topologically based algebraic system that naturally incorporates the inner and anticommutative outer products into a real valued geometric product, yet does not rely on complex numbers or matrices. A series of custom tools was designed and built to simplify geometric algebra expressions into a standard sum of products form, and automate the anticommutative geometric product and operations. Using this infrastructure, quantum bits (qubits), quantum registers and EPR-bits (ebits) are expressed symmetrically as geometric algebra expressions. Many known quantum computing gates, measurement operators, and especially the Bell/magic operators are also expressed as geometric products. These results demonstrate that geometric algebra can naturally and faithfully represent the central concepts, objects, and operators necessary for quantum computing, and can facilitate the design and construction of quantum computing tools.

  2. Geometric descriptions of entangled states by auxiliary varieties

    International Nuclear Information System (INIS)

    The aim of the paper is to propose geometric descriptions of multipartite entangled states using algebraic geometry. In the context of this paper, geometric means each stratum of the Hilbert space, corresponding to an entangled state, is an open subset of an algebraic variety built by classical geometric constructions (tangent lines, secant lines) from the set of separable states. In this setting, we describe well-known classifications of multipartite entanglement such as 2 × 2 × (n+ 1), for n⩾ 1, quantum systems and a new description with the 2 × 3 × 3 quantum system. Our results complete the approach of Miyake and make stronger connections with recent work of algebraic geometers. Moreover, for the quantum systems detailed in this paper, we propose an algorithm, based on the classical theory of invariants, to decide to which subvariety of the Hilbert space a given state belongs.

  3. Measurement of geometric phases by robust interferometric methods

    International Nuclear Information System (INIS)

    We present a novel interferometric arrangement that makes it possible to measure with great versatility geometric phases produced in polarization states of classical light. Our arrangement is robust against thermal and mechanical disturbances and can be set up in a Mach-Zehnder, a Michelson or a Sagnac configuration. We present results concerning the geometric phase as an extension of previous measurements of the Pancharatnam, or total phase. The geometric phase is obtained by compensating the dynamical contribution to the total phase, so as to extract out of it a purely geometric phase. This can be achieved over trajectories on the Poincare sphere that are not necessarily restricted to be great circles (geodesics). We thus demonstrate the feasibility of our method for dynamical extraction of the geometric contribution to the total phase, a prerequisite for building geometric quantum gates. Although our results correspond to polarization states of classical light, the same methodology could be applied in the case of polarization states of single photons.

  4. Algebraic geometric codes with applications

    Institute of Scientific and Technical Information of China (English)

    CHEN Hao

    2007-01-01

    The theory of linear error-correcting codes from algebraic geomet-ric curves (algebraic geometric (AG) codes or geometric Goppa codes) has been well-developed since the work of Goppa and Tsfasman, Vladut, and Zink in 1981-1982. In this paper we introduce to readers some recent progress in algebraic geometric codes and their applications in quantum error-correcting codes, secure multi-party computation and the construction of good binary codes.

  5. On Covariant Poisson Brackets in Classical Field Theory

    OpenAIRE

    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 unde...

  6. Geometrical theory of diffracted rays, orbiting and complex rays

    CERN Document Server

    De Micheli, Enrico

    2013-01-01

    In this article, the ray tracing method is studied beyond the classical geometrical theory. The trajectories are here regarded as geodesics in a Riemannian manifold, whose metric and topological properties are those induced by the refractive index (or, equivalently, by the potential). First, we derive the geometrical quantization rule, which is relevant to describe the orbiting bound-states observed in molecular physics. Next, we derive properties of the diffracted rays, regarded here as geodesics in a Riemannian manifold with boundary. A particular attention is devoted to the following problems: (i) modification of the classical stationary phase method suited to a neighborhood of a caustic; (ii) derivation of the connection formulae which enable one to obtain the uniformization of the classical eikonal approximation by patching up geodesic segments crossing the axial caustic; (iii) extension of the eikonal equation to mixed hyperbolic-elliptic systems, and generation of complex-valued rays in the shadow of t...

  7. GO++ : A modular Lagrangian/Eulerian software for Hamilton Jacobi equations of Geometric Optics type

    OpenAIRE

    Benamou, Jean-David; Hoch, Philippe

    2002-01-01

    We describe both the classical Lagrangian and the Eulerian methods for first order Hamilton-Jacobi equations of geometric optic type. We then explain the basic structure of the software and how new solvers/models can be added to it. A selection of numerical examples presented.Hamilton-Jacobi,Hamiltonian System, Ray Tracing, Viscosity Solution, Upwind Scheme, Geometric Optics, C++

  8. Schmidt number of pure states in bipartite quantum systems as an algebraic-geometric invariant

    CERN Document Server

    Chen, H

    2001-01-01

    Our previous work about algebraic-geometric invariants of the mixed states are extended and a stronger separability criterion is given. We also show that the Schmidt number of pure states in bipartite quantum systems, a classical concept, is actually an algebraic-geometric invariant.

  9. Geometric multipartite entanglement measures

    Energy Technology Data Exchange (ETDEWEB)

    Paz-Silva, Gerardo A. [Departamento de Fisica, Universidad del Valle, A.A. 25360, Cali (Colombia)]. E-mail: gerapaz@univalle.edu.co; Reina, John H. [Departamento de Fisica, Universidad del Valle, A.A. 25360, Cali (Colombia) and Institut fuer Theoretische Physik, Technische Universitaet Berlin, Hardenbergstr. 36, 10623 Berlin (Germany)]. E-mail: j.reina-estupinan@physics.ox.ac.uk

    2007-05-21

    Within the framework of constructions for quantifying entanglement, we build a natural scenario for the assembly of multipartite entanglement measures based on Hopf bundle-like mappings obtained through Clifford algebra representations. Then, given the non-factorizability of an arbitrary two-qubit density matrix, we give an alternate quantity that allows the construction of two types of entanglement measures based on their arithmetical and geometrical averages over all pairs of qubits in a register of size N, and thus fully characterize its degree and type of entanglement. We find that such an arithmetical average is both additive and strongly super additive.

  10. Geometric analysis and PDEs

    CERN Document Server

    Ambrosetti, Antonio; Malchiodi, Andrea

    2009-01-01

    This volume contains lecture notes on some topics in geometric analysis, a growing mathematical subject which uses analytical techniques, mostly of partial differential equations, to treat problems in differential geometry and mathematical physics. The presentation of the material should be rather accessible to non-experts in the field, since the presentation is didactic in nature. The reader will be provided with a survey containing some of the most exciting topics in the field, with a series of techniques used to treat such problems.

  11. Geometric correlations and multifractals

    International Nuclear Information System (INIS)

    There are many situations where the usual statistical methods are not adequate to characterize correlations in the system. To characterize such situations we introduce mutual correlation dimensions which describe geometric correlations in the system. These dimensions allow us to distinguish between variables which are perfectly correlated with or without a phase lag, variables which are uncorrelated and variables which are partially correlated. We demonstrate the utility of our formalism by considering two examples from dynamical systems. The first example is about the loss of memory in chaotic signals and describes auto-correlations while the second example is about synchronization of chaotic signals and describes cross-correlations. (author). 19 refs, 6 figs

  12. Geometric Algebra Computing

    CERN Document Server

    Corrochano, Eduardo Bayro

    2010-01-01

    This book presents contributions from a global selection of experts in the field. This useful text offers new insights and solutions for the development of theorems, algorithms and advanced methods for real-time applications across a range of disciplines. Written in an accessible style, the discussion of all applications is enhanced by the inclusion of numerous examples, figures and experimental analysis. Features: provides a thorough discussion of several tasks for image processing, pattern recognition, computer vision, robotics and computer graphics using the geometric algebra framework; int

  13. Robust Geometric Spanners

    CERN Document Server

    Bose, Prosenjit; Morin, Pat; Smid, Michiel

    2012-01-01

    Highly connected and yet sparse graphs (such as expanders or graphs of high treewidth) are fundamental, widely applicable and extensively studied combinatorial objects. We initiate the study of such highly connected graphs that are, in addition, geometric spanners. We define a property of spanners called robustness. Informally, when one removes a few vertices from a robust spanner, this harms only a small number of other vertices. We show that robust spanners must have a superlinear number of edges, even in one dimension. On the positive side, we give constructions, for any dimension, of robust spanners with a near-linear number of edges.

  14. 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

  15. Geometric Number Systems and Spinors

    CERN Document Server

    Sobczyk, Garret

    2015-01-01

    The real number system is geometrically extended to include three new anticommuting square roots of plus one, each such root representing the direction of a unit vector along the orthonormal coordinate axes of Euclidean 3-space. The resulting geometric (Clifford) algebra provides a geometric basis for the famous Pauli matrices which, in turn, proves the consistency of the rules of geometric algebra. The flexibility of the concept of geometric numbers opens the door to new understanding of the nature of space-time, and of Pauli and Dirac spinors as points on the Riemann sphere, including Lorentz boosts.

  16. Bidimensionality and Geometric Graphs

    CERN Document Server

    Fomin, Fedor V; Saurabh, Saket

    2011-01-01

    In this paper we use several of the key ideas from Bidimensionality to give a new generic approach to design EPTASs and subexponential time parameterized algorithms for problems on classes of graphs which are not minor closed, but instead exhibit a geometric structure. In particular we present EPTASs and subexponential time parameterized algorithms for Feedback Vertex Set, Vertex Cover, Connected Vertex Cover, Diamond Hitting Set, on map graphs and unit disk graphs, and for Cycle Packing and Minimum-Vertex Feedback Edge Set on unit disk graphs. Our results are based on the recent decomposition theorems proved by Fomin et al [SODA 2011], and our algorithms work directly on the input graph. Thus it is not necessary to compute the geometric representations of the input graph. To the best of our knowledge, these results are previously unknown, with the exception of the EPTAS and a subexponential time parameterized algorithm on unit disk graphs for Vertex Cover, which were obtained by Marx [ESA 2005] and Alber and...

  17. Geometric time delay interferometry

    International Nuclear Information System (INIS)

    The space-based gravitational-wave observatory LISA, a NASA-ESA mission to be launched after 2012, will achieve its optimal sensitivity using time delay interferometry (TDI), a LISA-specific technique needed to cancel the otherwise overwhelming laser noise in the interspacecraft phase measurements. The TDI observables of the Michelson and Sagnac types have been interpreted physically as the virtual measurements of a synthesized interferometer. In this paper, I present Geometric TDI, a new and intuitive approach to extend this interpretation to all TDI observables. Unlike the standard algebraic formalism, Geometric TDI provides a combinatorial algorithm to explore exhaustively the space of second-generation TDI observables (i.e., those that cancel laser noise in LISA-like interferometers with time-dependent arm lengths). Using this algorithm, I survey the space of second-generation TDI observables of length (i.e., number of component phase measurements) up to 24, and I identify alternative, improved forms of the standard second-generation TDI observables. The alternative forms have improved high-frequency gravitational-wave sensitivity in realistic noise conditions (because they have fewer nulls in the gravitational-wave and noise response functions), and are less susceptible to instrumental gaps and glitches (because their component phase measurements span shorter time periods)

  18. Geometric Time Delay Interferometry

    CERN Document Server

    Vallisneri, M

    2005-01-01

    The space-based gravitational-wave observatory LISA, a NASA--ESA mission to be launched after 2012, will achieve its optimal sensitivity using Time Delay Interferometry (TDI), a LISA-specific technique needed to cancel the otherwise overwhelming laser noise in the inter-spacecraft phase measurements. In this paper I present_Geometric TDI_, a new, intuitive approach to derive the TDI observables and to understand them as the virtual measurements of a synthesized multi-beam interferometer. Unlike the standard algebraic formalism, Geometric TDI provides a combinatorial algorithm to explore exhaustively the space of _second-generation_ TDI observables (i.e., those that cancel laser noise in LISA-like interferometers with time-dependent armlengths). Using this algorithm, I survey the space of second-generation TDI observables of length (i.e., number of component phase measurements) up to 24, and I identify alternative, improved forms of the standard second-generation TDI observables. The alternative forms have imp...

  19. Bidirectional coherent classical communication

    OpenAIRE

    Harrow, Aram W.; Leung, Debbie W.

    2005-01-01

    A unitary interaction coupling two parties enables quantum or classical communication in both the forward and backward directions. Each communication capacity can be thought of as a tradeoff between the achievable rates of specific types of forward and backward communication. Our first result shows that for any bipartite unitary gate, bidirectional coherent classical communication is no more difficult than bidirectional classical communication — they have the same achievable rate regions. ...

  20. Entanglement in Classical Optics

    OpenAIRE

    Ghose, Partha; Mukherjee, Anirban

    2013-01-01

    The emerging field of entanglement or nonseparability in classical optics is reviewed, and its similarities with and differences from quantum entanglement clearly pointed out through a recapitulation of Hilbert spaces in general, the special restrictions on Hilbert spaces imposed in quantum mechanics and the role of Hilbert spaces in classical polarization optics. The production of Bell-like states in classical polarization optics is discussed, and new theorems are proved to discriminate betw...

  1. 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...

  2. The Quantum-Classical Transition: The Fate of the Complex Structure

    CERN Document Server

    Marmo, G; Simoni, A; Ventriglia, F

    2005-01-01

    According to Dirac, fundamental laws of Classical Mechanics should be recovered by means of an "appropriate limit" of Quantum Mechanics. In the same spirit it is reasonable to enquire about the fundamental geometric structures of Classical Mechanics which will survive the appropriate limit of Quantum Mechanics. This is the case for the symplectic structure. On the contrary, such geometric structures as the metric tensor and the complex structure, which are necessary for the formulation of the Quantum theory, may not survive the Classical limit, being not relevant in the Classical theory. Here we discuss the Classical limit of those geometric structures mainly in the Ehrenfest and Heisenberg pictures, i.e. at the level of observables rather than at the level of states. A brief discussion of the fate of the complex structure in the Quantum-Classical transition in the Schroedinger picture is also mentioned.

  3. Teleportation via classical entanglement

    CERN Document Server

    Rafsanjani, Seyed Mohammad Hashemi; Magaña-Loaiza, Omar S; Boyd, Robert W

    2015-01-01

    We present a classical counterpart to quantum teleportation that uses classical entanglement instead of quantum entanglement. In our implementation we take advantage of classical entanglement among three parties: orbital angular momentum (OAM), polarization, and the radial degrees of freedom of a beam of light. We demonstrate the teleportation of arbitrary OAM states, in the subspace spanned by any two OAM states, to the polarization of the same beam. Our letter presents the first classical demonstration of a commonly-perceived--quantum phenomenon that requires entanglement among more than two parties.

  4. 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

  5. A classical approach to higher-derivative gravity

    International Nuclear Information System (INIS)

    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)

  6. Geometrically weighted semiconductor Frisch grid radiation spectrometers

    International Nuclear Information System (INIS)

    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 cm3 prism shaped CdZnTe device

  7. Semi-classical expansion for a charged particle on a curved space background

    International Nuclear Information System (INIS)

    We give the semi-classical expansion, with remainder to any order in h, for the wave function of a nonrelativistic quantum particle in a classical external magnetic field on a curved space background. The basic assumption is of a ''no caustics condition'' on the underlying classical mechanics, at least up to the time in question. The gauge invariance of the result is emphasized together with a discussion of the geometric meaning of the classical mechanical quantities involved

  8. Non-Geometric F-Theory-Heterotic Duality

    CERN Document Server

    Gu, Jie

    2014-01-01

    In this work we study the duality between F-theory and the heterotic string beyond the stable degeneration limit in F-theory and large fiber limit in the heterotic theory. Building upon a recent proposal by Clingher-Doran and Malmendier-Morrison, which phrases the duality on the heterotic side for a particular class of models in terms of (fibered) genus two curves as non-geometric heterotic compactifications - we establish the precise limit to the semi-classical heterotic string in both eight and lower space-time dimensions. In particular for six dimensional theories, we argue that this class of non-geometric heterotic compactifications capture alpha'-quantum corrections to the semi-classical heterotic supergravity compactifications on elliptically fibered K3 surfaces. From the non-geometric heterotic theory, the semi-classical phase on the K3 surface is recovered from a remarkable limit of genus two Siegel modular forms combined with a geometric surgery operation. Finally, in four dimensions we analyze anoth...

  9. Systematics of geometric scaling

    International Nuclear Information System (INIS)

    Using all available data on the deep-inelastic cross-sections at HERA at x=-2, we look for geometric scaling of the form σγ*p(τ) where the scaling variable τ behaves alternatively like logQ2-λY, as in the original definition, or logQ2-λY, which is suggested by the asymptotic properties of the Balitsky-Kovchegov (BK) equation with running QCD coupling constant. A ''Quality Factor'' (QF) is defined, quantifying the phenomenological validity of the scaling and the uncertainty on the intercept λ. Both choices have a good QF, showing that the second choice is as valid as the first one, predicted for fixed coupling constant. A comparison between the QCD asymptotic predictions and data is made and the QF analysis shows that the agreement can be reached, provided going beyond leading logarithmic accuracy for the BK equation

  10. Lectures on Classical Integrability

    CERN Document Server

    Torrielli, Alessandro

    2016-01-01

    We review some essential aspects of classically integrable systems. The detailed outline of the lectures consists of: 1. Introduction and motivation, with historical remarks; 2. Liouville theorem and action-angle variables, with examples (harmonic oscillator, Kepler problem); 3. Algebraic tools: Lax pairs, monodromy and transfer matrices, classical r-matrices and exchange relations, non-ultralocal Poisson brackets, with examples (non-linear Schroedinger model, principal chiral field); 4. Features of classical r-matrices: Belavin-Drinfeld theorems, analyticity properties, and lift of the classical structures to quantum groups; 5. Classical inverse scattering method to solve integrable differential equations: soliton solutions, spectral properties and the Gel'fand-Levitan-Marchenko equation, with examples (KdV equation, Sine-Gordon model). Prepared for the Durham Young Researchers Integrability School, organised by the GATIS network. This is part of a collection of lecture notes.

  11. Current Concept of Geometrical Accuracy

    OpenAIRE

    Görög Augustín; Görögová Ingrid

    2014-01-01

    Within the solving VEGA 1/0615/12 research project "Influence of 5-axis grinding parameters on the shank cutter´s geometric accuracy", the research team will measure and evaluate geometrical accuracy of the produced parts. They will use the contemporary measurement technology (for example the optical 3D scanners). During the past few years, significant changes have occurred in the field of geometrical accuracy. The objective of this contribution is to analyse the current standards in the fiel...

  12. Geometric Return and Portfolio Analysis

    OpenAIRE

    Brian McCulloch

    2003-01-01

    Expected geometric return is routinely reported as a summary measure of the prospective performance of asset classes and investment portfolios. It has intuitive appeal because its historical counterpart, the geometric average, provides a useful annualised measure of the proportional change in wealth that actually occurred over a past time series, as if there had been no volatility in return. However, as a prospective measure, expected geometric return has limited value and often the expected ...

  13. Clifford (Geometric) Algebra Wavelet Transform

    OpenAIRE

    Hitzer, Eckhard

    2013-01-01

    While the Clifford (geometric) algebra Fourier Transform (CFT) is global, we introduce here the local Clifford (geometric) algebra (GA) wavelet concept. We show how for $n=2,3 (\\mod 4)$ continuous $Cl_n$-valued admissible wavelets can be constructed using the similitude group $SIM(n)$. We strictly aim for real geometric interpretation, and replace the imaginary unit $i \\in \\C$ therefore with a GA blade squaring to $-1$. Consequences due to non-commutativity arise. We express the admissibility...

  14. Introduction to Clifford's Geometric Algebra

    OpenAIRE

    Hitzer, Eckhard

    2013-01-01

    Geometric algebra was initiated by W.K. Clifford over 130 years ago. It unifies all branches of physics, and has found rich applications in robotics, signal processing, ray tracing, virtual reality, computer vision, vector field processing, tracking, geographic information systems and neural computing. This tutorial explains the basics of geometric algebra, with concrete examples of the plane, of 3D space, of spacetime, and the popular conformal model. Geometric algebras are ideal to represen...

  15. Geometric programming for communication systems

    CERN Document Server

    Chiang, Mung

    2014-01-01

    Recently Geometric Programming has been applied to study a variety of problems in the analysis and design of communication systems from information theory and queuing theory to signal processing and network protocols. ""Geometric Programming for Communication Systems"" begins its comprehensive treatment of the subject by providing an in-depth tutorial on the theory, algorithms, and modeling methods of Geometric Programming. It then gives a systematic survey of the applications of Geometric Programming to the study of communication systems. It collects in one place various published results in

  16. A projective constrained variational principle for a classical particle with spin

    International Nuclear Information System (INIS)

    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)

  17. Classical and quantum Kummer shape algebras

    Science.gov (United States)

    Odzijewicz, A.; Wawreniuk, E.

    2016-07-01

    We study a family of integrable systems of nonlinearly coupled harmonic oscillators on the classical and quantum levels. We show that the integrability of these systems follows from their symmetry characterized by algebras, here called Kummer shape algebras. The resolution of identity for a wide class of reproducing kernels is found. A number of examples, illustrating this theory, are also presented.

  18. Davidson and classical pragmatism

    Directory of Open Access Journals (Sweden)

    Paula Rossi

    2007-06-01

    Full Text Available In this paper I wish to trace some connections between Donald Davidson's work (1917-2003 and two major representatives of the classical pragmatist movement: Charles S. Peirce (1839-1914 and William James (1842-1910. I will start with a basic characterization of classical pragmatism; then, I shall examine certain conceptions in Peirce's and James' pragmatism, in order to establish affinities with Davidson´s thought. Finally, and bearing in mind the previous con-nections, I will reflect briefly on the relevance –often unrecognized- of classical pragmatist ideas in the context of contemporary philosophi-cal discussions.

  19. 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…

  20. Harmonic and geometric analysis

    CERN Document Server

    Citti, Giovanna; Pérez, Carlos; Sarti, Alessandro; Zhong, Xiao

    2015-01-01

    This book presents an expanded version of four series of lectures delivered by the authors at the CRM. Harmonic analysis, understood in a broad sense, has a very wide interplay with partial differential equations and in particular with the theory of quasiconformal mappings and its applications. Some areas in which real analysis has been extremely influential are PDE's and geometric analysis. Their foundations and subsequent developments made extensive use of the Calderón–Zygmund theory, especially the Lp inequalities for Calderón–Zygmund operators (Beurling transform and Riesz transform, among others) and the theory of Muckenhoupt weights.  The first chapter is an application of harmonic analysis and the Heisenberg group to understanding human vision, while the second and third chapters cover some of the main topics on linear and multilinear harmonic analysis. The last serves as a comprehensive introduction to a deep result from De Giorgi, Moser and Nash on the regularity of elliptic partial differen...

  1. Physics of classical electromagnetism

    CERN Document Server

    Fujimoto, Minoru

    2007-01-01

    The classical electromagnetism described by the Maxwell equations constitutes a fundamental law in contemporary physics. Even with the advent of sophisticated new materials, the principles of classical electromagnetism are still active in various applied areas in today’s advanced communication techniques. Physics of Classical Electromagnetism, by Minoru Fujimoto, is written with concise introductory arguments emphasizing the original field concept, with an aim at understanding objectives in modern information technology. Following basic discussions of electromagnetism with a modernized approach, this book will provide readers with an overview of current problems in high-frequency physics. To further the reader’s understanding of the concepts and applications discussed, each illustration within the book shows the location of all active charges, and the author has provided many worked-out examples throughout the book. Physics of Classical Electromagnetism is intended for students in physics and engineering ...

  2. Injuries in classical ballet.

    Science.gov (United States)

    Quirk, R

    1984-11-01

    The specialised medical knowledge about dancers' injuries is negligible compared with that which surrounds sports medicine. The author discusses his experience in the management of more than 2000 injuries sustained by dancers of classical ballet. PMID:6151832

  3. Classical and Quantum Intertwine

    OpenAIRE

    Blanchard, Ph.; Jadczyk, A.

    1993-01-01

    Model interactions between classical and quantum systems are briefly discussed. These include: general measurement-like couplings, Stern-Gerlach experiment, model of a counter, quantum Zeno effect, SQUID-tank model.

  4. A Primer on Geometric Mechanics

    OpenAIRE

    Lessig, Christian

    2012-01-01

    Geometric mechanics is usually studied in applied mathematics and most introductory texts are hence aimed at a mathematically minded audience. The present note tries to provide the intuition of geometric mechanics and to show the relevance of the subject for an understanding of "mechanics".

  5. Classical confined particles

    Science.gov (United States)

    Horzela, Andrzej; Kapuscik, Edward

    1993-01-01

    An alternative picture of classical many body mechanics is proposed. In this picture particles possess individual kinematics but are deprived from individual dynamics. Dynamics exists only for the many particle system as a whole. The theory is complete and allows to determine the trajectories of each particle. It is proposed to use our picture as a classical prototype for a realistic theory of confined particles.

  6. Davidson and classical pragmatism

    OpenAIRE

    Paula Rossi

    2007-01-01

    In this paper I wish to trace some connections between Donald Davidson's work (1917-2003) and two major representatives of the classical pragmatist movement: Charles S. Peirce (1839-1914) and William James (1842-1910). I will start with a basic characterization of classical pragmatism; then, I shall examine certain conceptions in Peirce's and James' pragmatism, in order to establish affinities with Davidson´s thought. Finally, and bearing in mind the previous con-nections, I will reflect brie...

  7. Non-Abelian geometric quantum memory with an atomic ensemble

    International Nuclear Information System (INIS)

    We study a quantum information storage scheme based on an atomic ensemble with near (also exact) three-photon resonance electromagnetically induced transparency (EIT). Each 4-level-atom is coupled to two classical control fields and a quantum probe field. Quantum information is adiabatically stored in the associated dark polariton manifold. An intrinsic nontrivial topological structure is discovered in our quantum memory implemented through the symmetric collective atomic excitations with a hidden SU(3) dynamical symmetry. By adiabatically changing the Rabi frequencies of two classical control fields, the quantum state can be retrieved up to a non-Abelian holonomy and thus decoded from the final state in a purely geometric way

  8. Lagrangian geometrical optics of nonadiabatic vector waves and spin particles

    CERN Document Server

    Ruiz, D E

    2015-01-01

    Linear vector waves, both quantum and classical, experience polarization-driven bending of ray trajectories and polarization dynamics that can be interpreted as the precession of the "wave spin". Both phenomena are governed by an effective gauge Hamiltonian, which vanishes in leading-order geometrical optics. This gauge Hamiltonian can be recognized as a generalization of the Stern-Gerlach Hamiltonian that is commonly known for spin-1/2 quantum particles. The corresponding reduced Lagrangians for continuous nondissipative waves and their geometrical-optics rays are derived from the fundamental wave Lagrangian. The resulting Euler-Lagrange equations can describe simultaneous interactions of $N$ resonant modes, where $N$ is arbitrary, and lead to equations for the wave spin, which happens to be a $(N^2-1)$-dimensional spin vector. As a special case, classical equations for a Dirac particle $(N=2)$ are deduced formally, without introducing additional postulates or interpretations, from the Dirac quantum Lagrangi...

  9. Geometric algebra, qubits, geometric evolution, and all that

    CERN Document Server

    Soiguine, Alexander M

    2015-01-01

    The earlier approach is used for description of qubits and geometric phase parameters, the things critical in the area of topological quantum computing. The used tool, Geometric (Clifford) Algebra is the most convenient formalism for that case. Generalization of formal complex plane to an an arbitrary plane in three dimensions and of usual Hopf fibration to the map generated by an arbitrary unit value element of even sub-algebra of the three-dimensional Geometric Algebra are resulting in more profound description of qubits compared to quantum mechanical Hilbert space formalism.

  10. 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.

  11. Geometric characterization of true quantum decoherence

    Science.gov (United States)

    Kayser, Julius; Luoma, Kimmo; Strunz, Walter T.

    2015-11-01

    Surprisingly often decoherence is due to classical fluctuations of ambient fields and may thus be described in terms of random unitary (RU) dynamics. However, there are decoherence channels where such a representation cannot exist. Based on a simple and intuitive geometric measure for the distance of an extremal channel to the convex set of RU channels we are able to characterize the set of true quantum phase-damping channels. Remarkably, using the Caley-Menger determinant, our measure may be assessed directly from the matrix representation of the channel. We find that the channel of maximum quantumness is closely related to a symmetric, informationally complete positive operator-valued measure on the environment. Our findings are in line with numerical results based on the entanglement of assistance.

  12. SQCD A Geometric Aperçu

    CERN Document Server

    Gray, James; He, Yang-Hui; Jejjala, Vishnu; Mekareeya, Noppadol

    2008-01-01

    We take new algebraic and geometric perspectives on the old subject of SQCD. We count chiral gauge invariant operators using generating functions, or Hilbert series, derived from the plethystic programme and the Molien-Weyl formula. Using the character expansion technique, we also see how the global symmetries are encoded in the generating functions. Equipped with these methods and techniques of algorithmic algebraic geometry, we obtain the character expansions for theories with arbitrary numbers of colours and flavours. Moreover, computational algebraic geometry allows us to systematically study the classical vacuum moduli space of SQCD and investigate such structures as its irreducible components, degree and syzygies. We find the vacuum manifolds of SQCD to be affine Calabi-Yau cones over weighted projective varieties.

  13. Geometric gauge fields, particle production, and time

    International Nuclear Information System (INIS)

    The geometric magnetic- and electric-type fields are shown to have nontrivial effects in the form of semiclassical back reactions from quantized matter fields on the adiabatically evolving classical background geometry. As a consequence of the gauge invariance of the induced reaction forces it then follows that the matter vacuum polarization in a space-time emerging out from a flat simply connected superspace does not have a gravitational effect. However, the vacuum instability and the associated particle production do have a nonzero back reaction which gets encoded in the electric scalar potential. The relationship between the standard semiclassical definition of time and the existence of a nontrivial Berry phase is also explored. This offers an interesting constraint on the initial quantum state of the Universe

  14. Exploring percolative landscapes: Infinite cascades of geometric phase transitions

    Science.gov (United States)

    Timonin, P. N.; Chitov, Gennady Y.

    2016-01-01

    The evolution of many kinetic processes in 1+1 (space-time) dimensions results in 2 D directed percolative landscapes. The active phases of these models possess numerous hidden geometric orders characterized by various types of large-scale and/or coarse-grained percolative backbones that we define. For the patterns originated in the classical directed percolation (DP) and contact process we show from the Monte Carlo simulation data that these percolative backbones emerge at specific critical points as a result of continuous phase transitions. These geometric transitions belong to the DP universality class and their nonlocal order parameters are the capacities of corresponding backbones. The multitude of conceivable percolative backbones implies the existence of infinite cascades of such geometric transitions in the kinetic processes considered. We present simple arguments to support the conjecture that such cascades of transitions are a generic feature of percolation as well as of many other transitions with nonlocal order parameters.

  15. Gaussian geometric discord in terms of Hellinger distance

    Energy Technology Data Exchange (ETDEWEB)

    Suciu, Serban, E-mail: serban.suciu@theory.nipne.ro; Isar, Aurelian [National Institute of Physics and Nuclear Engineering, P.O.Box MG-6, Bucharest-Magurele (Romania)

    2015-12-07

    In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we address the quantification of general non-classical correlations in Gaussian states of continuous variable systems from a geometric perspective. We give a description of the Gaussian geometric discord by using the Hellinger distance as a measure for quantum correlations between two non-interacting non-resonant bosonic modes embedded in a thermal environment. We evaluate the Gaussian geometric discord by taking two-mode squeezed thermal states as initial states of the system and show that it has finite values between 0 and 1 and that it decays asymptotically to zero in time under the effect of the thermal bath.

  16. Analysis of two-player quantum games using geometric algebra

    CERN Document Server

    Chappell, James M; Abbott, Derek

    2010-01-01

    The framework for playing quantum games in an Einstein-Podolsky-Rosen (EPR) type setting is investigated using the mathematical formalism of geometric algebra (GA). In this setting, the players' strategy sets remain identical to the ones in the classical mixed-strategy version of the game, which is then obtained as proper subset of the corresponding quantum game. As examples, using GA we analyze the games of Prisoners' Dilemma and Stag Hunt when played in the EPR type setting.

  17. From Newton's Universal Gravitation to Einstein's Geometric Theory of Gravity

    OpenAIRE

    Kobe, Donald H.; Srivastava, Ankit

    2013-01-01

    Starting with Newton's law of universal gravitation, we generalize it step-by-step to obtain Einstein's geometric theory of gravity. Newton's gravitational potential satisfies the Poisson equation. We relate the potential to a component of the metric tensor by equating the nonrelativistic result of the principle of stationary proper time to the Lagrangian for a classical gravitational field. In the Poisson equation the Laplacian of the component of the metric tensor is generalized to a cyclic...

  18. Entanglement in Quantum-Classical Hybrid

    Science.gov (United States)

    Zak, Michail

    2011-01-01

    It is noted that the phenomenon of entanglement is not a prerogative of quantum systems, but also occurs in other, non-classical systems such as quantum-classical hybrids, and covers the concept of entanglement as a special type of global constraint imposed upon a broad class of dynamical systems. Application of hybrid systems for physics of life, as well as for quantum-inspired computing, has been outlined. In representing the Schroedinger equation in the Madelung form, there is feedback from the Liouville equation to the Hamilton-Jacobi equation in the form of the quantum potential. Preserving the same topology, the innovators replaced the quantum potential with other types of feedback, and investigated the property of these hybrid systems. A function of probability density has been introduced. Non-locality associated with a global geometrical constraint that leads to an entanglement effect was demonstrated. Despite such a quantum like characteristic, the hybrid can be of classical scale and all the measurements can be performed classically. This new emergence of entanglement sheds light on the concept of non-locality in physics.

  19. Geometric phase mediated topological transport of sound vortices

    CERN Document Server

    Wang, Shubo; Chan, C T

    2016-01-01

    When a physical system undergoes a cyclic evolution, a non-integrable phase can arise in addition to the normal dynamical phase. This phase, depending only on the geometry of the path traversed in the parameter space and hence named geometric phase, has profound impact in both classical and quantum physics, leading to exotic phenomena such as electron weak anti-localization and light spin-Hall effect. Experimental observations of the geometric phase effect in classical system are typically realized using vector waves such as light characterized by a polarization. We show here that such an effect can also be realized in scalar wave systems such as sound wave. Using a helical hollow waveguide, we show that the geometric phase effect associated with the transportation of sound vortices, i.e. sound wave carrying intrinsic orbital angular momentum, can serve as a potential mechanism to control the flow of sound vortices with different topological charges, resulting in geometric phase-based sound vortex filters.

  20. 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

    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...

  1. Geometric algorithms for sensor networks.

    Science.gov (United States)

    Gao, Jie; Guibas, Leonidas

    2012-01-13

    This paper surveys the use of geometric methods for wireless sensor networks. The close relationship of sensor nodes with their embedded physical space imposes a unique geometric character on such systems. The physical locations of the sensor nodes greatly impact on system design in all aspects, from low-level networking and organization to high-level information processing and applications. This paper reviews work in the past 10 years on topics such as network localization, geometric routing, information discovery, data-centric routing and topology discovery. PMID:22124080

  2. 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)

  3. 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.

  4. Geometric picture of quantum discord for two-qubit quantum states

    CERN Document Server

    Shi, Mingjun; Sun, Chunxiao; Du, Jiangfeng

    2011-01-01

    Among various definitions of quantum correlations, quantum discord has attracted considerable attention. To find analytical expression of 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 about 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 analytica results about quantum discord have not been found yet. Based on the support of numerical computations, some conjectures are proposed to help us establish geometric picture. We find that the geometric picture for these states has intimate relationship wit...

  5. Classically-Controlled Quantum Computation

    OpenAIRE

    Perdrix, Simon; Jorrand, Philippe

    2004-01-01

    Quantum computations usually take place under the control of the classical world. We introduce a Classically-controlled Quantum Turing Machine (CQTM) which is a Turing Machine (TM) with a quantum tape for acting on quantum data, and a classical transition function for a formalized classical control. In CQTM, unitary transformations and measurements are allowed. We show that any classical TM is simulated by a CQTM without loss of efficiency. The gap between classical and quantum computations, ...

  6. 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…

  7. Learning Classical Music Club

    CERN Multimedia

    Learning Classical Music Club

    2010-01-01

    There is a new CERN Club called “Learning Classical Music at CERN”. We are aiming to give classical music lessons for different instruments (see link) for students from 5 to 100 years old. We are now ready to start our activities in the CERN barracks. We are now in the enrollment phase and hope to start lessons very soon ! Club info can be found in the list of CERN Club: http://user.web.cern.ch/user/Communication/SocialLifeActivities/Clubs/Clubs.html Salvatore Buontempo Club President

  8. A Single Classical Quark

    CERN Document Server

    Dzhunushaliev, V D

    1997-01-01

    The spherically symmetric solution in classical SU(3) Yang - Mills theory is found. It is supposed that such solution describes a classical quark. It is regular in origin and hence the interaction between two quarks is small on the small distance. The obtained solution has the singularity on infinity. It is possible that is the reason why the free quark cannot exist. Evidently, nonlocality of this object leads to the fact that in quantum chromodynamic the difficulties arise connected with investigation of quarks interaction on large distance.

  9. Classical Holographic Codes

    CERN Document Server

    Brehm, Enrico M

    2016-01-01

    In this work, we introduce classical holographic codes. These can be understood as concatenated probabilistic codes and can be represented as networks uniformly covering hyperbolic space. In particular, classical holographic codes can be interpreted as maps from bulk degrees of freedom to boundary degrees of freedom. Interestingly, they are shown to exhibit features similar to those expected from the AdS/CFT correspondence. Among these are a version of the Ryu-Takayanagi formula and intriguing properties regarding bulk reconstruction and boundary representations of bulk operations. We discuss the relation of our findings with expectations from AdS/CFT and, in particular, with recent results from quantum error correction.

  10. Classical mechanics with Maxima

    CERN Document Server

    Timberlake, Todd Keene

    2016-01-01

    This book guides undergraduate students in the use of Maxima—a computer algebra system—in solving problems in classical mechanics. It functions well as a supplement to a typical classical mechanics textbook. When it comes to problems that are too difficult to solve by hand, computer algebra systems that can perform symbolic mathematical manipulations are a valuable tool. Maxima is particularly attractive in that it is open-source, multiple-platform software that students can download and install free of charge. Lessons learned and capabilities developed using Maxima are easily transferred to other, proprietary software.

  11. Elementary classical hydrodynamics

    CERN Document Server

    Chirgwin, B H; Langford, W J; Maxwell, E A; Plumpton, C

    1967-01-01

    Elementary Classical Hydrodynamics deals with the fundamental principles of elementary classical hydrodynamics, with emphasis on the mechanics of inviscid fluids. Topics covered by this book include direct use of the equations of hydrodynamics, potential flows, two-dimensional fluid motion, waves in liquids, and compressible flows. Some general theorems such as Bernoulli's equation are also considered. This book is comprised of six chapters and begins by introducing the reader to the fundamental principles of fluid hydrodynamics, with emphasis on ways of studying the motion of a fluid. Basic c

  12. Classic Problems of Probability

    CERN Document Server

    Gorroochurn, Prakash

    2012-01-01

    "A great book, one that I will certainly add to my personal library."—Paul J. Nahin, Professor Emeritus of Electrical Engineering, University of New Hampshire Classic Problems of Probability presents a lively account of the most intriguing aspects of statistics. The book features a large collection of more than thirty classic probability problems which have been carefully selected for their interesting history, the way they have shaped the field, and their counterintuitive nature. From Cardano's 1564 Games of Chance to Jacob Bernoulli's 1713 Golden Theorem to Parrondo's 1996 Perplexin

  13. The classical nova outburst

    International Nuclear Information System (INIS)

    The classical nova outburst occurs on the white dwarf component in a close binary system. Nova systems are members of the general class of cataclysmic variables and other members of the class are the Dwarf Novae, AM Her variables, Intermediate Polars, Recurrent Novae, and some of the Symbiotic variables. Although multiwavelength observations have already provided important information about all of these systems, in this review I will concentrate on the outbursts of the classical and recurrent novae and refer to other members of the class only when necessary. 140 refs., 1 tab

  14. Current Concept of Geometrical Accuracy

    Science.gov (United States)

    Görög, Augustín; Görögová, Ingrid

    2014-06-01

    Within the solving VEGA 1/0615/12 research project "Influence of 5-axis grinding parameters on the shank cutteŕs geometric accuracy", the research team will measure and evaluate geometrical accuracy of the produced parts. They will use the contemporary measurement technology (for example the optical 3D scanners). During the past few years, significant changes have occurred in the field of geometrical accuracy. The objective of this contribution is to analyse the current standards in the field of geometric tolerance. It is necessary to bring an overview of the basic concepts and definitions in the field. It will prevent the use of outdated and invalidated terms and definitions in the field. The knowledge presented in the contribution will provide the new perspective of the measurement that will be evaluated according to the current standards.

  15. Current Concept of Geometrical Accuracy

    Directory of Open Access Journals (Sweden)

    Görög Augustín

    2014-06-01

    Full Text Available Within the solving VEGA 1/0615/12 research project "Influence of 5-axis grinding parameters on the shank cutter´s geometric accuracy", the research team will measure and evaluate geometrical accuracy of the produced parts. They will use the contemporary measurement technology (for example the optical 3D scanners. During the past few years, significant changes have occurred in the field of geometrical accuracy. The objective of this contribution is to analyse the current standards in the field of geometric tolerance. It is necessary to bring an overview of the basic concepts and definitions in the field. It will prevent the use of outdated and invalidated terms and definitions in the field. The knowledge presented in the contribution will provide the new perspective of the measurement that will be evaluated according to the current standards.

  16. Guitars, Violins, and Geometric Sequences

    Science.gov (United States)

    Barger, Rita; Haehl, Martha

    2007-01-01

    This article describes middle school mathematics activities that relate measurement, ratios, and geometric sequences to finger positions or the placement of frets on stringed musical instruments. (Contains 2 figures and 2 tables.)

  17. Geometric Analysis and General Relativity

    OpenAIRE

    Andersson, L.

    2005-01-01

    This article discusses methods of geometric analysis in general relativity, with special focus on the role of "critical surfaces" such as minimal surfaces, marginal surface, maximal surfaces and null surfaces.

  18. The Geometric Gravitational Internal Problem

    CERN Document Server

    González-Martin, G R

    2000-01-01

    In a geometric unified theory there is an energy momentum equation, apart from the field equations and equations of motion. The general relativity Einstein equation with cosmological constant follows from this energy momentum equation for empty space. For non empty space we obtain a generalized Einstein equation, relating the Einstein tensor to a geometric stress energy tensor. The matching exterior solution is in agreement with the standard relativity tests. Furthermore, there is a Newtonian limit where we obtain Poisson's equation.

  19. Exploring Geometric Shapes with Touch

    OpenAIRE

    Pietrzak, Thomas; Crossan, Andrew; Brewster, Stephen,; Martin, Benoît; Pecci, Isabelle

    2009-01-01

    We propose a new technique to help users to explore geometric shapes without vision. This technique is based on a guidance using directional cues with a pin array. This is an alternative to the usual technique that consists of raising the pins corresponding to dark pixels around the cursor. In this paper we compare the exploration of geometric shapes with our new technique in unimanual and bimanual conditions. The users made fewer errors in unimanual condition than in bimanual condition. Howe...

  20. Stochastic Geometric Partial Differential Equations

    Czech Academy of Sciences Publication Activity Database

    Brzezniak, Z.; Goldys, B.; Ondreját, Martin

    1. Singapore : World Scientific Publishing Company, 2011 - (Zhao, H.; Truman, A.), s. 1-32 ISBN 978-981-4360-91-3. - (Interdisciplinary Mathematical Sciences. 12) R&D Projects: GA ČR GAP201/10/0752 Institutional support: RVO:67985556 Keywords : stochastic geometric * partial differential equations Subject RIV: BA - General Mathematics http://library.utia.cas.cz/separaty/2012/SI/ondrejat-stochastic geometric partial differential equations. pdf

  1. The Geometric Gravitational Internal Problem

    OpenAIRE

    Gonzalez-Martin, Gustavo R.

    2000-01-01

    In a geometric unified theory there is an energy momentum equation, apart from the field equations and equations of motion. The general relativity Einstein equation with cosmological constant follows from this energy momentum equation for empty space. For non empty space we obtain a generalized Einstein equation, relating the Einstein tensor to a geometric stress energy tensor. The matching exterior solution is in agreement with the standard relativity tests. Furthermore, there is a Newtonian...

  2. Geometric symmetries in light nuclei

    CERN Document Server

    Bijker, Roelof

    2016-01-01

    The algebraic cluster model is is applied to study cluster states in the nuclei 12C and 16O. The observed level sequences can be understood in terms of the underlying discrete symmetry that characterizes the geometrical configuration of the alpha-particles, i.e. an equilateral triangle for 12C, and a regular tetrahedron for 16O. The structure of rotational bands provides a fingerprint of the underlying geometrical configuration of alpha-particles.

  3. 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.

  4. Antenna with Dielectric Having Geometric Patterns

    Science.gov (United States)

    Dudley, Kenneth L. (Inventor); Elliott, Holly A. (Inventor); Cravey, Robin L. (Inventor); Connell, John W. (Inventor); Ghose, Sayata (Inventor); Watson, Kent A. (Inventor); Smith, Jr., Joseph G. (Inventor)

    2013-01-01

    An antenna includes a ground plane, a dielectric disposed on the ground plane, and an electrically-conductive radiator disposed on the dielectric. The dielectric includes at least one layer of a first dielectric material and a second dielectric material that collectively define a dielectric geometric pattern, which may comprise a fractal geometry. The radiator defines a radiator geometric pattern, and the dielectric geometric pattern is geometrically identical, or substantially geometrically identical, to the radiator geometric pattern.

  5. Nuclear motion is classical

    CERN Document Server

    Frank, Irmgard

    2016-01-01

    The notion from ab-initio molecular dynamics simulations that nuclear motion is best described by classical Newton dynamics instead of the time-dependent Schr{\\"o}dinger equation is substantiated. In principle a single experiment should bring clarity. Caution is however necessary, as temperature dependent effects must be eliminated when trying to determine the existence of a zero-point energy.

  6. Strong Coupling and Classicalization

    CERN Document Server

    Dvali, Gia

    2016-01-01

    Classicalization is a phenomenon in which a theory prevents itself from entering into a strong-coupling regime, by redistributing the energy among many weakly-interacting soft quanta. In this way, the scattering process of some initial hard quanta splits into a large number of soft elementary processes. In short, the theory trades the strong coupling for a high-multiplicity of quanta. At very high energies, the outcome of such a scattering experiment is a production of soft states of high occupation number that are approximately classical. It is evident that black hole creation in particle collision at super-Planckian energies is a result of classicalization, but there is no a priory reason why this phenomenon must be limited to gravity. If the hierarchy problem is solved by classicalization, the LHC has a chance of detecting a tower of new resonances. The lowest-lying resonances must appear right at the strong coupling scale in form of short-lived elementary particles. The heavier members of the tower must b...

  7. Classical Iterative Methods

    Czech Academy of Sciences Publication Activity Database

    Axelsson, Owe

    1. Berlin, Heidelberg: Springer-Verlag, 2013 - (Björm, E.), s. 205-224 ISBN 978-3-540-70528-4 Institutional support: RVO:68145535 Keywords : classical iterative methods * applied computational mathematics * encyclopedia Subject RIV: BA - General Mathematics http://www.springerreference.com/docs/ navigation .do?m=Encyclopedia+of+Applied+and+Computational+Mathematics+%28Mathematics+and+Statistics%29-book224

  8. Classical and quantum satisfiability

    CERN Document Server

    de Araújo, Anderson; 10.4204/EPTCS.81.6

    2012-01-01

    We present the linear algebraic definition of QSAT and propose a direct logical characterization of such a definition. We then prove that this logical version of QSAT is not an extension of classical satisfiability problem (SAT). This shows that QSAT does not allow a direct comparison between the complexity classes NP and QMA, for which SAT and QSAT are respectively complete.

  9. Why Study Classical Languages?

    Science.gov (United States)

    Lieberman, Samuel

    This speech emphasizes the significance of living literatures and living cultures which owe a direct debt to the Romans and the Greeks from whom they can trace their origins. After commenting on typical rejoinders to the question "Why study classical languages?" and poking fun at those who advance jaded, esoteric responses, the author dispels the…

  10. Classics in What Sense?

    Science.gov (United States)

    Camic, Charles

    2008-01-01

    They seem the perfect bookends for the social psychologist's collection of "classics" of the field. Two volumes, nearly identical in shape and weight and exactly a century old in 2008--each professing to usher "social psychology" into the world as they both place the hybrid expression square in their titles but then proceed to stake out the field…

  11. Mecanica Clasica (Classical Mechanics)

    OpenAIRE

    Rosu, H. C.

    1999-01-01

    First Internet graduate course on Classical Mechanics in Spanish (Castellano). This is about 80% of the material I covered during the January-June 1999 semester at IFUG in the Mexican city of Leon. English and Romanian versions are in (slow) progress and hopefully will be arXived. For a similar course on Quantum Mechanics, see physics/9808031

  12. Classical galactosaemia revisited

    NARCIS (Netherlands)

    A.M. Bosch

    2006-01-01

    Classical galactosaemia (McKusick 230400) is an: autosomal recessive disorder of galactose metabolism, caused by a deficiency of the enzyme galactose-1-phosphate uridyltransferase (GALT; EC 2.7.712). Most patients present in the neonatal period, after ingestion of galactose, with jaundice, hepatospl

  13. Classical Mythology. Fourth Edition.

    Science.gov (United States)

    Morford, Mark P. O.; Lenardon, Robert J.

    Designed for students with little or no background in classical literature, this book introduces the Greek and Roman myths of creation, myths of the gods, Greek sagas and local legends, and presents contemporary theories about the myths. Drawing on Homer, Hesiod, Pindar, Vergil, and others, the book provides many translations and paraphrases of…

  14. Classicism and Romanticism.

    Science.gov (United States)

    Huddleston, Gregory H.

    1993-01-01

    Describes one teacher's methods for introducing to secondary English students the concepts of Classicism and Romanticism in relation to pictures of gardens, architecture, music, and literary works. Outlines how the unit leads to a writing assignment based on collected responses over time. (HB)

  15. Mecanica Clasica (Classical Mechanics)

    CERN Document Server

    Rosu, H C

    1999-01-01

    First Internet undergraduate course on Classical Mechanics in Spanish (Castellano). This is about 80% of the material I covered during the January-June 1999 semester at IFUG in the Mexican city of Leon. English and Romanian versions are in (slow) progress and hopefully will be arXived. For a similar course on Quantum Mechanics, see physics/9808031

  16. Classical electromagnetic radiation

    CERN Document Server

    Heald, Mark A

    2012-01-01

    Newly corrected, this highly acclaimed text is suitable for advanced physics courses. The author presents a very accessible macroscopic view of classical electromagnetics that emphasizes integrating electromagnetic theory with physical optics. The survey follows the historical development of physics, culminating in the use of four-vector relativity to fully integrate electricity with magnetism.

  17. Multiscale geometric modeling of macromolecules II: Lagrangian representation.

    Science.gov (United States)

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

    2013-09-15

    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-electron microscopy, 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, whereas our coarse resolution representations highlight the compatibility of protein-ligand bindings and possibility of protein-protein interactions. PMID:23813599

  18. Dynamical fluctuations in classical adiabatic processes: General description and their implications

    OpenAIRE

    Zhang, Qi; Gong, Jiangbin; Oh, C. H.

    2010-01-01

    Dynamical fluctuations in classical adiabatic processes are not considered by the conventional classical adiabatic theorem. In this work a general result is derived to describe the intrinsic dynamical fluctuations in classical adiabatic processes. Interesting implications of our general result are discussed via two subtopics, namely, an intriguing adiabatic geometric phase in a dynamical model with an adiabatically moving fixed-point solution, and the possible "pollution" to Hannay's angle or...

  19. Geometric non-linear hexahedral elements with rotational DOFs

    Science.gov (United States)

    Meftah, Kamel; Zouari, Wajdi; Sedira, Lakhdar; Ayad, Rezak

    2016-01-01

    This paper presents an extension of two recently published conforming and non conforming eight-node hexahedral finite elements, presenting rotational degrees of freedom in addition to the classical displacement ones, to analyze geometric nonlinear problems. Their formulations are based on the so-called space fiber rotation concept that considers virtual rotations of a nodal fiber within the element which enhances the displacement vector approximation. To demonstrate the efficiency and accuracy of the proposed finite elements, several beam and shell nonlinear assessment tests are presented and the obtained results are principally compared with the classical first-order and second-order hexahedral elements responses as well as other advanced elements from the literature. In particular, it is shown that the proposed elements allow a correct prediction of the studied structures nonlinear behaviors including snap-through and snap-back instabilities and the accuracy of the non conforming element is close to the classical 20-node hexahedral element.

  20. A Mathematicians' View of Geometrical Unification of General Relativity and Quantum Physics

    CERN Document Server

    Vaugon, Michel

    2015-01-01

    This document contains a description of physics entirely based on a geometric presentation: all of the theory is described giving only a pseudo-riemannian manifold (M, g) of dimension n > 5 for which the g tensor is, in studied domains, almost everywhere of signature (-, -, +, ..., +). No object is added to this space-time, no general principle is supposed. The properties we impose to some domains of (M, g) are only simple geometric constraints, essentially based on the concept of "curvature". These geometric properties allow to define, depending on considered cases, some objects (frequently depicted by tensors) that are similar to the classical physics ones, they are however built here only from the g tensor. The links between these objects, coming from their natural definitions, give, applying standard theorems from the pseudo-riemannian geometry, all equations governing physical phenomena usually described by classical theories, including general relativity and quantum physics. The purely geometric approac...

  1. 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.

  2. Quantum emulation of classical dynamics

    OpenAIRE

    Margolus, Norman

    2011-01-01

    In statistical mechanics, it is well known that finite-state classical lattice models can be recast as quantum models, with distinct classical configurations identified with orthogonal basis states. This mapping makes classical statistical mechanics on a lattice a special case of quantum statistical mechanics, and classical combinatorial entropy a special case of quantum entropy. In a similar manner, finite-state classical dynamics can be recast as finite-energy quantum dynamics. This mapping...

  3. On the completeness of classical electromagnetism

    OpenAIRE

    Minotti, Fernando O.

    2006-01-01

    The possibility of an incompletness of the equations of electromagnetism is analyzed using a thought experiment that shows a non-physical behavior according to classical electromagnetism. Basically, from Maxwell equations it is shown that a particular passive, isolated circuit could present a transient growth of its currents. Resolution of this problem is sought within the context of the usual electromagnetism and also using the possibly simplest generalization of Maxwell equations, a reduced...

  4. 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).

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

    Energy Technology Data Exchange (ETDEWEB)

    He, Ji-Huan, E-mail: hejihuan@suda.edu.cn [National Engineering Laboratory for Modern Silk, College of Textile and Engineering, Soochow University, 199 Ren-ai Road, Suzhou 215123 (China); Elagan, S.K., E-mail: sayed_khalil2000@yahoo.com [Mathematics and Statistics Department, Faculty of Science, Taif University, P.O. 888 (Saudi Arabia); Department of Mathematics, Faculty of Science, Menofiya University, Shebin Elkom (Egypt); Li, Z.B., E-mail: zhengbiaoli@l26.com [College of Mathematics and Information Science, Qujing Normal University, Qujing, Yunnan 655011 (China)

    2012-01-09

    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.

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

    International Nuclear Information System (INIS)

    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.

  7. Randomness: quantum versus classical

    CERN Document Server

    Khrennikov, Andrei

    2015-01-01

    Recent tremendous development of quantum information theory led to a number of quantum technological projects, e.g., quantum random generators. This development stimulates a new wave of interest in quantum foundations. One of the most intriguing problems of quantum foundations is elaboration of a consistent and commonly accepted interpretation of quantum state. Closely related problem is clarification of the notion of quantum randomness and its interrelation with classical randomness. In this short review we shall discuss basics of classical theory of randomness (which by itself is very complex and characterized by diversity of approaches) and compare it with irreducible quantum randomness. The second part of this review is devoted to the information interpretation of quantum mechanics (QM) in the spirit of Zeilinger and Brukner (and QBism of Fuchs et al.) and physics in general (e.g., Wheeler's "it from bit") as well as digital philosophy of Chaitin (with historical coupling to ideas of Leibnitz). Finally, w...

  8. Classical and statistical thermodynamics

    CERN Document Server

    Rizk, Hanna A

    2016-01-01

    This is a text book of thermodynamics for the student who seeks thorough training in science or engineering. Systematic and thorough treatment of the fundamental principles rather than presenting the large mass of facts has been stressed. The book includes some of the historical and humanistic background of thermodynamics, but without affecting the continuity of the analytical treatment. For a clearer and more profound understanding of thermodynamics this book is highly recommended. In this respect, the author believes that a sound grounding in classical thermodynamics is an essential prerequisite for the understanding of statistical thermodynamics. Such a book comprising the two wide branches of thermodynamics is in fact unprecedented. Being a written work dealing systematically with the two main branches of thermodynamics, namely classical thermodynamics and statistical thermodynamics, together with some important indexes under only one cover, this treatise is so eminently useful.

  9. Computation in Classical Mechanics

    CERN Document Server

    Timberlake, Todd

    2007-01-01

    There is a growing consensus that physics majors need to learn computational skills, but many departments are still devoid of computation in their physics curriculum. Some departments may lack the resources or commitment to create a dedicated course or program in computational physics. One way around this difficulty is to include computation in a standard upper-level physics course. An intermediate classical mechanics course is particularly well suited for including computation. We discuss the ways we have used computation in our classical mechanics courses, focusing on how computational work can improve students' understanding of physics as well as their computational skills. We present examples of computational problems that serve these two purposes. In addition, we provide information about resources for instructors who would like to include computation in their courses.

  10. The classic project

    International Nuclear Information System (INIS)

    Exchange of data and algorithms among accelerator physics programs is difficult because of unnecessary differences in input formats and internal data structures. To alleviate these problems a C++ class library called CLASSIC (Class Library for Accelerator System Simulation and Control) is being developed with the goal to provide standard building blocks for computer programs used in accelerator design. It includes modules for building accelerator lattice structures in computer memory using a standard input language, a graphical user interface, or a programmed algorithm. It also provides simulation algorithms. These can easily be replaced by modules which communicate with the control system of the accelerator. Exchange of both data and algorithm between different programs using the CLASSIC library should present no difficulty

  11. Injuries in classical ballet

    Directory of Open Access Journals (Sweden)

    Adriana Coutinho de Azevedo Guimarães

    2008-06-01

    Full Text Available This study aimed to elucidate what injuries are most likely to occur due to classical ballet practice. The research used national and international bibliography. The bibliography analysis indicated that technical and esthetical demands lead to a practice of non-anatomical movements, causing the ballet dancer to suffer from a number of associated lesions. Most of the injuries are caused by technical mistakes and wrong training. Troubles in children are usually due to trying to force external rotation at hip level and to undue use of point ballet slippers. The commonest lesions are in feet and ankles, followed by knees and hips. The rarest ones are in the upper limbs. These injuries are caused by exercise excess, by repetitions always in the same side and by wrong and early use of point slippers. The study reached the conclusion that incorrect application of classical ballet technique predisposes the dancers to characteristic injuries.

  12. Classical Diophantine equations

    CERN Document Server

    1993-01-01

    The author had initiated a revision and translation of "Classical Diophantine Equations" prior to his death. Given the rapid advances in transcendence theory and diophantine approximation over recent years, one might fear that the present work, originally published in Russian in 1982, is mostly superseded. That is not so. A certain amount of updating had been prepared by the author himself before his untimely death. Some further revision was prepared by close colleagues. The first seven chapters provide a detailed, virtually exhaustive, discussion of the theory of lower bounds for linear forms in the logarithms of algebraic numbers and its applications to obtaining upper bounds for solutions to the eponymous classical diophantine equations. The detail may seem stark--- the author fears that the reader may react much as does the tourist on first seeing the centre Pompidou; notwithstanding that, Sprind zuk maintainsa pleasant and chatty approach, full of wise and interesting remarks. His emphases well warrant, ...

  13. Are superparamagnetic spins classical?

    OpenAIRE

    Garanin, D. A.

    2008-01-01

    Effective giant spins of magnetic nanoparticles are considered classically in the conventional theory of superparamagnetism based on the Landau-Lifshitz-Langevin equation. However, microscopic calculations for a large spin with uniaxial anisotropy, coupled to the lattice via the simplest generic mechanism, show that the results of the conventional theory are not reproduced in the limit S ->\\infty. In particular, the prefactor Gamma_0 in the Arrhenius escape rate over the barrier Gamma =Gamma_...

  14. Injuries in classical ballet

    OpenAIRE

    Adriana Coutinho de Azevedo Guimarães; Joseani Paulini Neves Simas

    2008-01-01

    This study aimed to elucidate what injuries are most likely to occur due to classical ballet practice. The research used national and international bibliography. The bibliography analysis indicated that technical and esthetical demands lead to a practice of non-anatomical movements, causing the ballet dancer to suffer from a number of associated lesions. Most of the injuries are caused by technical mistakes and wrong training. Troubles in children are usually due to trying to force external ...

  15. A Classic's New Charm

    Institute of Scientific and Technical Information of China (English)

    WANG HAIRONG

    2010-01-01

    @@ North Korea's Phibada Opera Troupe arrived in Beijing on May3,bringing with it a Korean opera adapted from China's classic novel A Dream of Red Mansions written by Cao Xueqin(around 1715-63),a great novelist of the Qing Dynasty(1644-1911).The troupe,invited by the Chinese Ministry of Culture,is one of the largest performing groups having visited China in recent years.

  16. Computation in Classical Mechanics

    OpenAIRE

    Timberlake, Todd; Hasbun, Javier E.

    2007-01-01

    There is a growing consensus that physics majors need to learn computational skills, but many departments are still devoid of computation in their physics curriculum. Some departments may lack the resources or commitment to create a dedicated course or program in computational physics. One way around this difficulty is to include computation in a standard upper-level physics course. An intermediate classical mechanics course is particularly well suited for including computation. We discuss th...

  17. Sociology and Classical Liberalism

    OpenAIRE

    KLEIN, Daniel; Stern, Lotta

    2005-01-01

    We advocate the development of a classical-liberal character within professional sociology. The American Sociological Association (ASA) is taken as representative of professional sociology in the United States. We review the ASA’s activities and organizational statements, to show the association’s leftist character. Internal criticism is often very uneasy about leftist domination of the field. We present survey results establishing that, in voting and in policy views, the ASA membership is mo...

  18. Revisiting a Classic

    Science.gov (United States)

    Rogers, Ibram

    2008-01-01

    As a 26-year-old English teacher in 1958, Chinua Achebe had no idea that the book he was writing would become a literary classic, not only in Africa but also throughout the world. He could only try to articulate the feelings he had for his countrymen and women. Achebe had a burning desire to tell the true story of Africa and African humanity. The…

  19. Diffusion of Classical Solitons

    OpenAIRE

    Dziarmaga, J.; Zakrzewski, W.

    1998-01-01

    We study the diffusion and deformation of classical solitons coupled to thermal noise. The diffusion coefficient for kinks in the $\\phi^4$ theory is predicted up to the second order in $kT$. The prediction is verified by numerical simulations. Multiskyrmions in the vector O(3) sigma model are studied within the same formalism. Thermal noise results in a diffusion on the multisoliton collective coordinate space (moduli space). There are entropic forces which tend, for example, to bind pairs of...

  20. Beyond the borders of classical optical measurements

    International Nuclear Information System (INIS)

    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

  1. What was classical genetics?

    Science.gov (United States)

    Waters, C Kenneth

    2004-12-01

    I present an account of classical genetics to challenge theory-biased approaches in the philosophy of science. Philosophers typically assume that scientific knowledge is ultimately structured by explanatory reasoning and that research programs in well-established sciences are organized around efforts to fill out a central theory and extend its explanatory range. In the case of classical genetics, philosophers assume that the knowledge was structured by T. H. Morgan's theory of transmission and that research throughout the later 1920s, 30s, and 40s was organized around efforts to further validate, develop, and extend this theory, I show that classical genetics was structured by an integration of explanatory reasoning (associated with the transmission theory) and investigative strategies (such as the 'genetic approach'). The investigative strategies, which have been overlooked in historical and philosophical accounts, were as important as the so-called laws of Mendelian genetics. By the later 1920s, geneticists of the Morgan school were no longer organizing research around the goal of explaining inheritance patterns; rather, they were using genetics to investigate a range of biological phenomena that extended well beyond the explanatory domain of transmission theories. Theory-biased approaches in history and philosophy of science fail to reveal the overall structure of scientific knowledge and obscure the way it functions. PMID:15682554

  2. Tomographic reconstruction with a priori geometrical information

    International Nuclear Information System (INIS)

    Computed tomography (CT) is critically important in medical diagnostics, but it is also the main source of human exposure to ionizing radiation. To reduce this risk factor, contemporary CT research strives to improve the trade-off between radiation dose and image quality, for instance by developing sensitive detectors (less radiation power), efficient irradiation geometries (less scattering and exposure) or optimized reconstruction algorithms (denoising, anti-aliasing, etc.). Examples of reconstruction strategies are direct algebraic inversion (ART), filtered Fourier back-projection (FBP) or orthogonal polynomial expansion on the disk (OPED). A new reconstruction algorithm for CT is proposed, integrating a priori geometrical information in order to reconstruct images from an under-sampled Radon data set, thereby directly reducing the required radiation exposure for a given image resolution. The integrated geometrical information could be partial and provided by a less invasive but possibly otherwise limited diagnostic tool, like magnetic resonance imaging. The proposed algorithm extends the algebraic inversion strategy (where x is the reconstructed image, b is the Radon spectrum and A is the projection matrix) by means of a penalization term, consisting of a gaussian smoothing kernel S truncated at some given edges (the a priori geometrical information): where β is a penalization parameter and I is the identity matrix. The numerical inversion is performed iteratively by the method of the conjugate gradient. An homogeneous and isotropic smoothing kernel penalization allows undersampling by imposing soft continuity conditions, generally blurring the image. By truncating the kernel on a given subset of known edges, these can remain sharp during the reconstruction. The available Radon data set information can therefore be more efficiently used to reconstruct the unknown areas. In algebraic terms, the global minimum of the penalized inversion is closer to the original

  3. Geometric phase and angle for noncyclic adiabatic change, revivals and measures of quantal instability

    International Nuclear Information System (INIS)

    Within the adiabatic theorem we must explicitly add to the instantaneous adiabatic vectors, parametrized by an external parameter following an open curve, a dynamical as well as a geometrical phase contribution to be able to predict the quantum observables. We give an alternative to Berry's proof for cyclic paths without use of Stokes's theorem that is then generalized to open paths. Recent analyses that argued, for an adiabatic open path case, that there is only dynamical phase change or that the situation is undefined are shown to be incorrect. The noncyclic geometric phase correction is discussed in detail for the spin in a magnetic field, an Aharonov-Bohm experiment and a resonator. Properties of the geometric phase contribution for open paths are studied. First, it is shown that degeneracies play an important role. Second, it is shown to be semiclassically related to a geometric angle shift on the final torus. The revival structure of wavepackets is shown to be affected by the noncyclic geometric phases of the, contributing instantaneous vectors that make the revived wavepacket to be shifted on the final torus by the classical geometric angle. We also propose two measures of quantum sensitivity to initial conditions. The first one is valid for quantum and classical Liouville states and it is given by the different distances of two close states to a third fixed state. The second measure is given by the divergence of the flow lines of suitable quantum phase space representations and reduces to the classical Lyapunov exponent. (author)

  4. 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.

  5. p/e Geometric Mass Ratio

    CERN Document Server

    González-Martin, G R

    2000-01-01

    A previously proposed geometric definition of mass in terms of energy, in a geometrical unified theory, is used to obtain a numerical expression for a ratio of masses of geometrical excitations. The resultant geometric ratio is approximately equal the ratio of the proton to electron physical masses.

  6. Geometric orbit datum and orbit covers

    Institute of Scientific and Technical Information of China (English)

    梁科; 侯自新

    2001-01-01

    Vogan conjectured that the parabolic induction of orbit data is independent of the choice of the parabolic subgroup. In this paper we first give the parabolic induction of orbit covers, whose relationship with geometric orbit datum is also induced. Hence we show a geometric interpretation of orbit data and finally prove the conjugation for geometric orbit datum using geometric method.

  7. Geometric integration for particle accelerators

    International Nuclear Information System (INIS)

    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

  8. Geometric formula for prism deflection

    Indian Academy of Sciences (India)

    Apoorva G Wagh; Veer Chand Rakhecha

    2004-08-01

    While studying neutron deflections produced by a magnetic prism, we have stumbled upon a simple `geometric' formula. For a prism of refractive index close to unity, the deflection simply equals the product of the refractive power − 1 and the base-to-height ratio of the prism, regardless of the apex angle. The base and height of the prism are measured respectively along and perpendicular to the direction of beam propagation within the prism. The geometric formula greatly simplifies the optimisation of prism parameters to suit any specific experiment.

  9. Exploring Geometric Shapes with Touch

    CERN Document Server

    Pietrzak, Thomas; Brewster, Stephen A; Martin, Benoît; Pecci, Isabelle; 10.1007/978-3-642-03655-2_18

    2012-01-01

    We propose a new technique to help users to explore geometric shapes without vision. This technique is based on a guidance using directional cues with a pin array. This is an alternative to the usual technique that consists of raising the pins corresponding to dark pixels around the cursor. In this paper we compare the exploration of geometric shapes with our new technique in unimanual and bimanual conditions. The users made fewer errors in unimanual condition than in bimanual condition. However they did not explore the shapes more quickly and there was no difference in confidence in their answer.

  10. Reverse geometric engineering of singularities

    International Nuclear Information System (INIS)

    One can geometrically engineer supersymmetric field theories theories by placing D-branes at or near singularities. The opposite process is described, where one can reconstruct the singularities from quiver theories. The description is in terms of a noncommutative quiver algebra which is constructed from the quiver diagram and the superpotential. The center of this noncommutative algebra is a commutative algebra, which is the ring of holomorphic functions on a variety V. If certain algebraic conditions are met, then the reverse geometric engineering produces V as the geometry that D-branes probe. It is also argued that the identification of V is invariant under Seiberg dualities. (author)

  11. Geometric pumping in autophoretic channels

    CERN Document Server

    Michelin, Sebastien; De Canio, Gabriele; Lobato-Dauzier, Nicolas; Lauga, Eric

    2015-01-01

    Many microfluidic devices use macroscopic pressure differentials to overcome viscous friction and generate flows in microchannels. In this work, we investigate how the chemical and geometric properties of the channel walls can drive a net flow by exploiting the autophoretic slip flows induced along active walls by local concentration gradients of a solute species. We show that chemical patterning of the wall is not required to generate and control a net flux within the channel, rather channel geometry alone is sufficient. Using numerical simulations, we determine how geometric characteristics of the wall influence channel flow rate, and confirm our results analytically in the asymptotic limit of lubrication theory.

  12. Geometric phase at graphene edge

    OpenAIRE

    Choi, Sang-Jun; Park, Sunghun; Sim, H. -S.

    2014-01-01

    We study the scattering phase shift of Dirac fermions at graphene edge. We find that when a plane wave of a Dirac fermion is reflected at an edge of graphene, its reflection phase is shifted by the geometric phase resulting from the change of the pseudospin of the Dirac fermion in the reflection. The geometric phase is the Pancharatnam-Berry phase that equals the half of the solid angle on Bloch sphere determined by the propagation direction of the incident wave and also by the orientation an...

  13. 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

  14. Some basic results on the sets of sequences with geometric calculus

    Science.gov (United States)

    Türkmen, Cengiz; Başar, Feyzi

    2012-08-01

    As an alternative to the classical calculus, Grossman and Katz [Non-Newtonian Calculus, Lee Press, Pigeon Cove, Massachusetts, 1972] introduced the non-Newtonian calculus consisting of the branches of geometric, anageometric and bigeometric calculus. Following Grossman and Katz, we construct the field C(G) of geometric complex numbers and the concept of geometric metric. Also we give the triangle and Minkowski's inequalities in the sense of geometric calculus. Later we respectively define the sets w(G), ℓ∞(G), c(G), c0(G) and ℓp(G) of all, bounded, convergent, null and p-absolutely summable sequences, in the sense of geometric calculus and show that each of the set forms a complete vector space on the field C(G).

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

    Energy Technology Data Exchange (ETDEWEB)

    Jian Liu and Hong Qin

    2011-07-18

    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.

  16. On Classical Ideal Gases

    Directory of Open Access Journals (Sweden)

    Laurent Chusseau

    2013-02-01

    Full Text Available We show that the thermodynamics of ideal gases may be derived solely from the Democritean concept of corpuscles moving in vacuum plus a principle of simplicity, namely that these laws are independent of the laws of motion, aside from the law of energy conservation. Only a single corpuscle in contact with a heat bath submitted to a z and t-invariant force is considered. Most of the end results are known but the method appears to be novel. The mathematics being elementary, the present paper should facilitate the understanding of the ideal gas law and of classical thermodynamics even though not-usually-taught concepts are being introduced.

  17. Mechanics classical and quantum

    CERN Document Server

    Taylor, T T

    2015-01-01

    Mechanics: Classical and Quantum explains the principles of quantum mechanics via the medium of analytical mechanics. The book describes Schrodinger's formulation, the Hamilton-Jacobi equation, and the Lagrangian formulation. The author discusses the Harmonic Oscillator, the generalized coordinates, velocities, as well as the application of the Lagrangian formulation to systems that are partially or entirely electromagnetic in character under certain conditions. The book examines waves on a string under tension, the isothermal cavity radiation, and the Rayleigh-Jeans result pertaining to the e

  18. A Classic Through Eternity

    Institute of Scientific and Technical Information of China (English)

    2002-01-01

    FIVE years ago, an ancient Chinese air was beamed to outer space as a PR exercise. To humankind, music is a universal language, so the tune seemed an ideal medium for communication with extraterrestrial intelligence. So far there has been no response, but it is believed that the tune will play for a billion years, and eventually be heard and understood. The melody is called High Mountain and Flowing Stream, and it is played on the guqin, a seven-stringed classical musical instrument similar to the zither.

  19. 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

  20. Multiscale geometric modeling of macromolecules I: Cartesian representation

    International Nuclear Information System (INIS)

    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

  1. Coordinate Geometric Approach to Spherometer

    CERN Document Server

    Khan, Sameen Ahmed

    2013-01-01

    The spherometer used for measuring radius of curvature of spherical surfaces is explicitly based on a geometric relation unique to circles and spheres. We present an alternate approach using coordinate geometry, which reproduces the well-known result for the spherometer and also leads to a scheme to study aspherical surfaces. We shall also briefly describe some of the modified spherometers.

  2. Celestial mechanics with geometric algebra

    Science.gov (United States)

    Hestenes, D.

    1983-01-01

    Geometric algebra is introduced as a general tool for Celestial Mechanics. A general method for handling finite rotations and rotational kinematics is presented. The constants of Kepler motion are derived and manipulated in a new way. A new spinor formulation of perturbation theory is developed.

  3. Geometric Operators on Boolean Functions

    DEFF Research Database (Denmark)

    Frisvad, Jeppe Revall; Falster, Peter

    of a few geometric operators working on the images of Boolean functions. The operators we describe, arise from the niche area of array-based logic and have previously been tightly bound to an array-based representation of Boolean functions. We redefine the operators in an abstract form to make them...

  4. Decoherence of geometric phase gates

    International Nuclear Information System (INIS)

    We consider the effects of certain forms of decoherence applied to both adiabatic and nonadiabatic geometric phase quantum gates. For a single qubit we illustrate path-dependent sensitivity to anisotropic noise and for two qubits we quantify the loss of entanglement as a function of decoherence

  5. Decoherence of geometric phase gates

    CERN Document Server

    Nazir, A; Munro, W J

    2002-01-01

    We consider the effects of certain forms of decoherence applied to both adiabatic and non-adiabatic geometric phase quantum gates. For a single qubit we illustrate path-dependent sensitivity to anisotropic noise and for two qubits we quantify the loss of entanglement as a function of decoherence.

  6. Prolongations of Geometric Overdetermined Systems

    OpenAIRE

    Branson, Thomas; Cap, Andreas; Eastwood, Michael; Gover, Rod

    2004-01-01

    We show that a wide class of geometrically defined overdetermined semilinear partial differential equations may be explicitly prolonged to obtain closed systems. As a consequence, in the case of linear equations we extract sharp bounds on the dimension of the solution space.

  7. Trace Anomaly in Geometric Discretization

    OpenAIRE

    Czech, Bartlomiej

    2007-01-01

    I develop the simplest geometric-discretized analogue of two dimensional scalar field theory, which qualitatively reproduces the trace anomaly of the continuous theory. The discrete analogue provides an interpretation of the trace anomaly in terms of a non-trivial transformation of electric-magnetic duality-invariant modes of resistor networks that accommodate both electric and magnetic charge currents.

  8. Improved Bounds for Geometric Permutations

    CERN Document Server

    Rubin, Natan; Sharir, Micha

    2010-01-01

    We show that the number of geometric permutations of an arbitrary collection of $n$ pairwise disjoint convex sets in $\\mathbb{R}^d$, for $d\\geq 3$, is $O(n^{2d-3}\\log n)$, improving Wenger's 20 years old bound of $O(n^{2d-2})$.

  9. Numerical calculation of classical and non-classical electrostatic potentials

    CERN Document Server

    Christensen, D; Neyenhuis, B; Christensen, Dan; Durfee, Dallin S.; Neyenhuis, Brian

    2006-01-01

    We present a numerical exercise in which classical and non-classical electrostatic potentials were calculated. The non-classical fields take into account effects due to a possible non-zero photon rest mass. We show that in the limit of small photon rest mass, both the classical and non-classical potential can be found by solving Poisson's equation twice, using the first calculation as a source term in the second calculation. Our results support the assumptions in a recent proposal to use ion interferometry to search for a non-zero photon rest mass.

  10. Fano Interference in Classical Oscillators

    Science.gov (United States)

    Satpathy, S.; Roy, A.; Mohapatra, A.

    2012-01-01

    We seek to illustrate Fano interference in a classical coupled oscillator by using classical analogues of the atom-laser interaction. We present an analogy between the dressed state picture of coherent atom-laser interaction and a classical coupled oscillator. The Autler-Townes splitting due to the atom-laser interaction is analogous to the…

  11. Recent developments in premetric classical electrodynamics

    CERN Document Server

    Hehl, F W; Obukhov, Yu N; Hehl, Friedrich W.; Itin, Yakov; Obukhov, Yuri N.

    2005-01-01

    Classical electrodynamics can be based on the conservation laws of electric charge and magnetic flux. Both laws are independent of the metric and the linear connection of spacetime. Within the framework of such a premetric electrodynamics -- provided a local and linear constitutive law of the vacuum is added -- the propagation of electromagnetic waves in the geometric-optics limit can be studied. The wave vectors of the wave fronts obey a quartic extended Fresnel equation. If one forbids birefringence in vacuum, the light cone emerges and Maxwell-Lorentz vacuum electrodynamics can be recovered. If minimal coupling of electrodynamics to gravity is assumed, then only the gravitational potential, i.e., the metric of spacetime, emerges in the constitutive law. We discuss recent results within this general framework.

  12. Relativistic like structure of classical thermodynamics

    Science.gov (United States)

    Quevedo, Hernando; Sánchez, Alberto; Vázquez, Alejandro

    2015-04-01

    We analyze in the context of geometrothermodynamics a Legendre invariant metric structure in the equilibrium space of an ideal gas. We introduce the concept of thermodynamic geodesic as a succession of points, each corresponding to a state of equilibrium, so that the resulting curve represents a quasi-static process. A rigorous geometric structure is derived in which the thermodynamic geodesics at a given point split the equilibrium space into two disconnected regions separated by adiabatic geodesics. This resembles the causal structure of special relativity, which we use to introduce the concept of adiabatic cone for thermodynamic systems. This result might be interpreted as an alternative indication of the inter-relationship between relativistic physics and classical thermodynamics.

  13. 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...

  14. A Dynamical model for non-geometric quantum black holes

    CERN Document Server

    Spallucci, Euro

    2016-01-01

    It has been recently proposed that quantum black holes can be described as N-graviton Bose-Einstein condensates. In this picture the quantum properties of BHs "... can be understood in terms of the single number N". However, so far, the dynamical origin of the occupational number N has not been specified. This description is alternative to the usual one, where black holes are believed to be well described geometrically even at the quantum level. In this paper we pursue the former point of view and develop a non-geometrical dynamical model of quantum black holes (BHs). In our model the occupational number N is proportional to the principal quantum number n of a Planckian harmonic oscillator. The so-called "classicalization" corresponds to the large-n limit, where the Schwarzschild horizon is recovered.

  15. Developments and retrospectives in Lie theory geometric and analytic methods

    CERN Document Server

    Penkov, Ivan; Wolf, Joseph

    2014-01-01

    This volume reviews and updates a prominent series of workshops in representation/Lie theory, and reflects the widespread influence of those  workshops in such areas as harmonic analysis, representation theory, differential geometry, algebraic geometry, and mathematical physics.  Many of the contributors have had leading roles in both the classical and modern developments of Lie theory and its applications. This Work, entitled Developments and Retrospectives in Lie Theory, and comprising 26 articles, is organized in two volumes: Algebraic Methods and Geometric and Analytic Methods. This is the Geometric and Analytic Methods volume. The Lie Theory Workshop series, founded by Joe Wolf and Ivan Penkov and joined shortly thereafter by Geoff Mason, has been running for over two decades. Travel to the workshops has usually been supported by the NSF, and local universities have provided hospitality. The workshop talks have been seminal in describing new perspectives in the field covering broad areas of current re...

  16. Geometric integrators for multiplicative viscoplasticity: analysis of error accumulation

    CERN Document Server

    Shutov, A V

    2009-01-01

    The inelastic incompressibility is a typical feature of metal plasticity/viscoplasticity. Over the last decade, there has been a great amount of research related to construction of numerical integration algorithms which exactly preserve this geometric property. In this paper we examine, both numerically and mathematically, the excellent accuracy and convergence characteristics of such geometric integrators. In terms of a classical model of finite viscoplasticity, we illustrate the notion of exponential stability of the exact solution. We show that this property enables the construction of effective and stable numerical algorithms, if incompressibility is exactly satisfied. On the other hand, if the incompressibility constraint is violated, spurious degrees of freedom are introduced. This results in the loss of the exponential stability and a dramatic deterioration of convergence behavior.

  17. Super-resolved imaging geometrical and diffraction approaches

    CERN Document Server

    2011-01-01

    In this brief we review several approaches that provide super resolved imaging, overcoming the geometrical limitation of the detector as well as the diffraction effects set by the F number of the imaging lens. In order to obtain the super resolved enhancement, we use spatially non-uniform and/or random transmission structures to encode the image or the aperture planes. The desired resolution enhanced images are obtained by post-processing decoding of the captured data.

  18. Mechanical Systems, Classical Models

    CERN Document Server

    Teodorescu, Petre P

    2009-01-01

    This third volume completes the Work Mechanical Systems, Classical Models. The first two volumes dealt with particle dynamics and with discrete and continuous mechanical systems. The present volume studies analytical mechanics. Topics like Lagrangian and Hamiltonian mechanics, the Hamilton-Jacobi method, and a study of systems with separate variables are thoroughly discussed. Also included are variational principles and canonical transformations, integral invariants and exterior differential calculus, and particular attention is given to non-holonomic mechanical systems. The author explains in detail all important aspects of the science of mechanics, regarded as a natural science, and shows how they are useful in understanding important natural phenomena and solving problems of interest in applied and engineering sciences. Professor Teodorescu has spent more than fifty years as a Professor of Mechanics at the University of Bucharest and this book relies on the extensive literature on the subject as well as th...

  19. Grassmannization of classical models

    CERN Document Server

    Pollet, Lode; Prokof'ev, Nikolay V; Svistunov, Boris V

    2016-01-01

    Applying Feynman diagrammatics to non-fermionic strongly correlated models with local constraints might seem generically impossible for two separate reasons: (i) the necessity to have a Gaussian (non-interacting) limit on top of which the perturbative diagrammatic expansion is generated by Wick's theorem, and (ii) the Dyson's collapse argument implying that the expansion in powers of coupling constant is divergent. We show that for arbitrary classical lattice models both problems can be solved/circumvented by reformulating the high-temperature expansion (more generally, any discrete representation of the model) in terms of Grassmann integrals. Discrete variables residing on either links, plaquettes, or sites of the lattice are associated with the Grassmann variables in such a way that the partition function (and correlations) of the original system and its Grassmann-field counterpart are identical. The expansion of the latter around its Gaussian point generates Feynman diagrams. A proof-of-principle implement...

  20. Geometric methods for the design of mechanisms

    Science.gov (United States)

    Stokes, Ann Westagard

    1993-01-01

    Challenges posed by the process of designing robotic mechanisms have provided a new impetus to research in the classical subjects of kinematics, elastic analysis, and multibody dynamics. Historically, mechanism designers have considered these areas of analysis to be generally separate and distinct sciences. However, there are significant classes of problems which require a combination of these methods to arrive at a satisfactory solution. For example, both the compliance and the inertia distribution strongly influence the performance of a robotic manipulator. In this thesis, geometric methods are applied to the analysis of mechanisms where kinematics, elasticity, and dynamics play fundamental and interactive roles. Tools for the mathematical analysis, design, and optimization of a class of holonomic and nonholonomic mechanisms are developed. Specific contributions of this thesis include a network theory for elasto-kinematic systems. The applicability of the network theory is demonstrated by employing it to calculate the optimal distribution of joint compliance in a serial manipulator. In addition, the advantage of applying Lie group theoretic approaches to mechanisms requiring specific dynamic properties is demonstrated by extending Brockett's product of exponentials formula to the domain of dynamics. Conditions for the design of manipulators having inertia matrices which are constant in joint angle coordinates are developed. Finally, analysis and design techniques are developed for a class of mechanisms which rectify oscillations into secular motions. These techniques are applied to the analysis of free-floating chains that can reorient themselves in zero angular momentum processes and to the analysis of rattleback tops.

  1. 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...

  2. Citation classics in epilepsy

    Directory of Open Access Journals (Sweden)

    Maryann Wilson

    2013-01-01

    Full Text Available BACKGROUND: The impact of a scientific article is proportional to the citations it has received. In this study, we set out to identify the most cited works in epileptology in order to evaluate research trends in this field. METHODS: According to the Web of Science database, articles with more than 400 citations qualify as "citation classics". We conducted a literature search on the ISI Web of Science bibliometric database for scientific articles relevant to epilepsy. RESULTS: We retrieved 67 highly cited articles (400 or more citations, which were published in 31 journals: 17 clinical studies, 42 laboratory studies, 5 reviews and 3 classification articles. Clinical studies consisted of epidemiological analyses (n=3, studies on the clinical phenomenology of epilepsy (n=5 – including behavioral and prognostic aspects – and articles focusing on pharmacological (n=6 and non-pharmacological (n=3 treatment. The laboratory studies dealt with genetics (n=6, animal models (n=27, and neurobiology (n=9 – including both neurophysiology and neuropathology studies. The majority (61% of citation classics on epilepsy were published after 1986, possibly reflecting the expansion of research interest in laboratory studies driven by the development of new methodologies, specifically in the fields of genetics and animal models. Consequently, clinical studies were highly cited both before and after the mid 80s, whilst laboratory researches became widely cited after 1990. CONCLUSIONS: Our study indicates that the main drivers of scientific impact in the field of epileptology have increasingly become genetic and neurobiological studies, along with research on animal models of epilepsy. These articles are able to gain the highest numbers of citations in the time span of a few years and suggest potential directions for future research.

  3. The verdict geometric quality library.

    Energy Technology Data Exchange (ETDEWEB)

    Knupp, Patrick Michael; Ernst, C.D. (Elemental Technologies, Inc., American Fork, UT); Thompson, David C. (Sandia National Laboratories, Livermore, CA); Stimpson, C.J. (Elemental Technologies, Inc., American Fork, UT); Pebay, Philippe Pierre

    2006-03-01

    Verdict is a collection of subroutines for evaluating the geometric qualities of triangles, quadrilaterals, tetrahedra, and hexahedra using a variety of metrics. A metric is a real number assigned to one of these shapes depending on its particular vertex coordinates. These metrics are used to evaluate the input to finite element, finite volume, boundary element, and other types of solvers that approximate the solution to partial differential equations defined over regions of space. The geometric qualities of these regions is usually strongly tied to the accuracy these solvers are able to obtain in their approximations. The subroutines are written in C++ and have a simple C interface. Each metric may be evaluated individually or in combination. When multiple metrics are evaluated at once, they share common calculations to lower the cost of the evaluation.

  4. Guiding light via geometric phases

    CERN Document Server

    Slussarenko, Sergei; Jisha, Chandroth P; Piccirillo, Bruno; Santamato, Enrico; Assanto, Gaetano; Marrucci, Lorenzo

    2015-01-01

    Known methods for transverse confinement and guidance of light can be grouped into a few basic mechanisms, the most common being metallic reflection, total internal reflection and photonic-bandgap (or Bragg) reflection. All of them essentially rely on changes of the refractive index, that is on scalar properties of light. Recently, processes based on "geometric Berry phases", such as manipulation of polarization states or deflection of spinning-light rays, have attracted considerable interest in the contexts of singular optics and structured light. Here, we disclose a new approach to light waveguiding, using geometric Berry phases and exploiting polarization states and their handling. This can be realized in structured three-dimensional anisotropic media, in which the optic axis lies orthogonal to the propagation direction and is modulated along it and across the transverse plane, so that the refractive index remains constant but a phase distortion can be imposed on a beam. In addition to a complete theoretic...

  5. Height and Tilt Geometric Texture

    DEFF Research Database (Denmark)

    Andersen, Vedrana; Desbrun, Mathieu; Bærentzen, Jakob Andreas; Aanæs, Henrik

    We propose a new intrinsic representation of geometric texture over triangle meshes. Our approach extends the conventional height field texture representation by incorporating displacements in the tangential plane in the form of a normal tilt. This texture representation offers a good practical...... compromise between functionality and simplicity: it can efficiently handle and process geometric texture too complex to be represented as a height field, without having recourse to full blown mesh editing algorithms. The height-and-tilt representation proposed here is fully intrinsic to the mesh, making...... texture editing and animation (such as bending or waving) intuitively controllable over arbitrary base mesh. We also provide simple methods for texture extraction and transfer using our height-and-field representation....

  6. A non-geometrical approach to quantum gravity

    CERN Document Server

    Ivanov, Michael A

    2009-01-01

    Some results of author's work in a non-geometrical approach to quantum gravity are reviewed here, among them: a quantum mechanism of classical gravity giving a possibility to compute the Newton constant; asymptotic freedom at short distances; interaction of photons with the graviton background leading to the important cosmological consequences; the time delay of photons due to interactions with gravitons; deceleration of massive bodies in the graviton background which may be connected with the Pioneer anomaly and with the problem of dark matter.

  7. Hydrodynamic limit with geometric correction of stationary Boltzmann equation

    Science.gov (United States)

    Wu, Lei

    2016-05-01

    We consider the hydrodynamic limit of a stationary Boltzmann equation in a unit plate with in-flow boundary. The classical theory claims that the solution can be approximated by the sum of interior solution which satisfies steady incompressible Navier-Stokes-Fourier system, and boundary layer derived from Milne problem. In this paper, we construct counterexamples to disprove such formulation in L∞ both for its proof and result. Also, we show the hydrodynamic limit with a different boundary layer expansion with geometric correction.

  8. GEOMETRIC TURBULENCE AND QUANTUM THEORY

    Directory of Open Access Journals (Sweden)

    Trunev A. P.

    2014-06-01

    Full Text Available The parabolic equation describing the evolution of the gravitational field is derived from Einstein equation. The instability of metric leads to a geometric pattern of turbulence. Microscopic turbulent pulsations generate two kinds of matter with positive and negative energy density, respectively. It is shown that in the case of negative energy density parabolic equation leads to an equation of Schrödinger type

  9. Geometrical formalism in gauge theories

    OpenAIRE

    Kubyshin, Yuri A.

    2003-01-01

    We review the basic elements of the geometrical formalism for description of gauge fields and the theory of invariant connections, and their applications to the coset space dimensional reduction of Yang-Mills theories. We also discuss the problem of classification of principal fibre bundles, which is important for the quantization of gauge theories. Some results for bundles over two-dimensional spaces are presented.

  10. Science, Art and Geometrical Imagination

    OpenAIRE

    Luminet, J. -P.

    2009-01-01

    From the geocentric, closed world model of Antiquity to the wraparound universe models of relativistic cosmology, the parallel history of space representations in science and art illustrates the fundamental role of geometric imagination in innovative findings. Through the analysis of works of various artists and scientists like Plato, Durer, Kepler, Escher, Grisey or the present author, it is shown how the process of creation in science and in the arts rests on aesthetical principles such as ...

  11. Constrained ballistics and geometrical optics

    OpenAIRE

    Epstein, Marcelo

    2014-01-01

    The problem of constant-speed ballistics is studied under the umbrella of non-linear non-holonomic constrained systems. The Newtonian approach is shown to be equivalent to the use of Chetaev's rule to incorporate the constraint within the initially unconstrained formulation. Although the resulting equations are not, in principle, obtained from a variational statement, it is shown that the trajectories coincide with those of geometrical optics in a medium with a suitably chosen refractive inde...

  12. Geometrical structure of Laplacian eigenfunctions

    OpenAIRE

    Grebenkov, Denis S.; Nguyen, Binh-Thanh

    2012-01-01

    We summarize the properties of eigenvalues and eigenfunctions of the Laplace operator in bounded Euclidean domains with Dirichlet, Neumann or Robin boundary condition. We keep the presentation at a level accessible to scientists from various disciplines ranging from mathematics to physics and computer sciences. The main focus is put onto multiple intricate relations between the shape of a domain and the geometrical structure of eigenfunctions.

  13. Geometric Results for Compressible Magnetohydrodynamics

    OpenAIRE

    Arter, Wayne

    2013-01-01

    Recently, compressible magnetohydrodynamics (MHD) has been elegantly formulated in terms of Lie derivatives. This paper exploits the geometrical properties of the Lie bracket to give new insights into the properties of compressible MHD behaviour, both with and without feedback of the magnetic field on the flow. These results are expected to be useful for the solution of MHD equations in both tokamak fusion experiments and space plasmas.

  14. Geometric Representations of Language Taxonomies

    OpenAIRE

    Blanchard, Ph.; Petroni, F.; Serva, M.; Volchenkov, D.

    2011-01-01

    Abstract A Markov chain analysis of a network generated by the matrix of lexical distances allows for representing complex relationships between different languages in a language family geometrically, in terms of distances and angles. The fully automated method for construction of language taxonomy is tested on a sample of fifty languages of the IndoEuropean language group and applied to a sample of fifty languages of the Austronesian language group. The Anatolian and Kurgan hypoth...

  15. Polar metals by geometric design

    Science.gov (United States)

    Kim, T. H.; Puggioni, D.; Yuan, Y.; Xie, L.; Zhou, H.; Campbell, N.; Ryan, P. J.; Choi, Y.; Kim, J.-W.; Patzner, J. R.; Ryu, S.; Podkaminer, J. P.; Irwin, J.; Ma, Y.; Fennie, C. J.; Rzchowski, M. S.; Pan, X. Q.; Gopalan, V.; Rondinelli, J. M.; Eom, C. B.

    2016-05-01

    Gauss’s law dictates that the net electric field inside a conductor in electrostatic equilibrium is zero by effective charge screening; free carriers within a metal eliminate internal dipoles that may arise owing to asymmetric charge distributions. Quantum physics supports this view, demonstrating that delocalized electrons make a static macroscopic polarization, an ill-defined quantity in metals—it is exceedingly unusual to find a polar metal that exhibits long-range ordered dipoles owing to cooperative atomic displacements aligned from dipolar interactions as in insulating phases. Here we describe the quantum mechanical design and experimental realization of room-temperature polar metals in thin-film ANiO3 perovskite nickelates using a strategy based on atomic-scale control of inversion-preserving (centric) displacements. We predict with ab initio calculations that cooperative polar A cation displacements are geometrically stabilized with a non-equilibrium amplitude and tilt pattern of the corner-connected NiO6 octahedra—the structural signatures of perovskites—owing to geometric constraints imposed by the underlying substrate. Heteroepitaxial thin-films grown on LaAlO3 (111) substrates fulfil the design principles. We achieve both a conducting polar monoclinic oxide that is inaccessible in compositionally identical films grown on (001) substrates, and observe a hidden, previously unreported, non-equilibrium structure in thin-film geometries. We expect that the geometric stabilization approach will provide novel avenues for realizing new multifunctional materials with unusual coexisting properties.

  16. Is classical flat Kasner spacetime flat in quantum gravity?

    OpenAIRE

    Singh, Parampreet

    2016-01-01

    Quantum nature of classical flat Kasner spacetime is studied using effective spacetime description in loop quantum cosmology. We find that even though the spacetime curvature vanishes at the classical level, non-trivial quantum gravitational effects can arise. For the standard loop quantization of Bianchi-I spacetime, which uniquely yields universal bounds on expansion and shear scalars and results in a generic resolution of strong singularities, we find that a flat Kasner metric is not a phy...

  17. Minimal resolution

    OpenAIRE

    Weidenbach, C.

    1994-01-01

    Minimal resolution restricts the applicability of resolution and factorization to minimal literals. Minimality is an abstract criterion. It is shown that if the minimality criterion satisfies certain properties minimal resolution is sound and complete. Hyper resolution, ordered resolution and lock resolution are known instances of minimal resolution. We also introduce new instances of the general completeness result, correct some mistakes in existing literature and give some general redundanc...

  18. Study of non-classical light imaging technology

    International Nuclear Information System (INIS)

    Non-classical light that generates through the optical parametric down-conversion process by using an optical parametric oscillator is introduced, and the imaging system based on the light is built. The characteristics of the light and the spatial resolution of the image are studied. The light irradiates directly on the object plate, producing a mass of signal photons, then the signal photons are collected by the charge-coupled device. The output electrical signal is collected by a high-speed data collection card and processed with software. Finally, the object image is acquired, and its revised image is obtained by image processing. The results indicate that the resolution of the image based on the non-classical infrared light is 1.43 times that of infrared coherent light. The non-classical light can be widely used for high-resolution imaging, spectrum analysis, and micro-biological sample detection.

  19. Time Monitoring Variability of Classical Be Stars

    Science.gov (United States)

    Kuhn, Benjamin; Eisner, Joshua A.; Stone, Jordan

    2016-01-01

    Classical Be stars are B type stars that show hydrogen emission in their spectra, and exhibit variability across the electromagnetic spectrum, including visible and infrared wavelengths. While spectroscopic variability in the optical range has been studied previously, the near infrared region has not been investigated as thoroughly. We present multiple epochs of near infrared spectroscopy for a sample of eight Classical Be stars. Our observations were taken using the FSPEC instrument on the 90-inch Bok reflector telescope at Kitt Peak during the months of May and June of 2010 and 2011. We targeted the Brackett Gamma emission line of hydrogen with a resolution of ≈3500. Using Python we developed tools to analyze the reduced and calibrated spectra, as well as compute equivalent widths. Time-series spectra indicate that a majority of the systems exhibit spectroscopic variability. By monitoring the strengths of the emission feature over time we aim to constrain the physical properties of these systems.

  20. Quantum ring in the eyes of geometric (Clifford) algebra

    Science.gov (United States)

    Dargys, A.

    2013-01-01

    The quantum ring with spin-orbit interaction included is analyzed in a nonstandard way using Clifford or geometric algebra (GA). The solution of the Schrödinger-Pauli equation is presented in terms of rotors having clear classical mechanics interpretation, i.e., in GA the rotors act in 3D Euclidean space rather than as operators in an abstract Hilbert space. This classical-like property of spin control in GA provides a more transparent approach in designing and understanding spintronic devices. The aim of the paper is to attract readers attention to new possibilities in spin physics and to demonstrate how the quantum ring problem can be solved by GA methods.

  1. Classicalization of quantum variables and quantum–classical hybrids

    International Nuclear Information System (INIS)

    The extraction of classical degrees of freedom in quantum mechanics is studied in the stochastic variational method. By using this classicalization, a hybrid model constructed from quantum and classical variables (quantum–classical hybrids) is derived. In this procedure, conservation laws such as energy are maintained, and Ehrenfest's theorem is still satisfied with modification. The criterion for the applicability of quantum–classical hybrids is also discussed. - Highlights: • The new derivation of a quantum–classical hybrid (QCH) model is discussed based on a variational principle. • Any conserved quantities are automatically defined as the invariant transforms of a stochastic action. • The quantitative criterion to determine the validity of QCH is proposed. • Ehrenfest's theorem is satisfied in a modified way

  2. 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...

  3. 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

    2016-08-01

    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. PMID:27505793

  4. Rotational dynamics with geometric algebra

    Science.gov (United States)

    Hestenes, D.

    1983-01-01

    A new spinor formulation of rotational dynamics is developed. A general theorem is established reducing the theory of the symmetric top to that of the spherical top. The classical problems of Lagrange and Poinsot are treated in detail, along with a modern application to the theory of magnetic resonance.

  5. Classical resolution of black hole singularities via wormholes

    International Nuclear Information System (INIS)

    In certain extensions of General Relativity, wormholes generated by spherically symmetric electric fields can resolve black hole singularities without necessarily removing curvature divergences. This is shown by studying geodesic completeness, the behavior of time-like congruences going through the divergent region, and by means of scattering of waves off the wormhole. This provides an example of the logical independence between curvature divergences and space-time singularities, concepts very often identified with each other in the literature. (orig.)

  6. Classical resolution of black hole singularities via wormholes

    Science.gov (United States)

    Olmo, Gonzalo J.; Rubiera-Garcia, D.; Sanchez-Puente, A.

    2016-03-01

    In certain extensions of General Relativity, wormholes generated by spherically symmetric electric fields can resolve black hole singularities without necessarily removing curvature divergences. This is shown by studying geodesic completeness, the behavior of time-like congruences going through the divergent region, and by means of scattering of waves off the wormhole. This provides an example of the logical independence between curvature divergences and space-time singularities, concepts very often identified with each other in the literature.

  7. Classical resolution of black hole singularities via wormholes

    Energy Technology Data Exchange (ETDEWEB)

    Olmo, Gonzalo J. [Universidad de Valencia, Departamento de Fisica Teorica and IFIC, Centro Mixto Universidad de Valencia-CSIC, Valencia (Spain); Universidade Federal da Paraiba, Departamento de Fisica, Joao Pessoa, Paraiba (Brazil); Rubiera-Garcia, D. [Universidade de Lisboa, Faculdade de Ciencias, Instituto de Astrofisica e Ciencias do Espaco, Lisbon (Portugal); Fudan University, Department of Physics, Center for Field Theory and Particle Physics, Shanghai (China); Sanchez-Puente, A. [Universidad de Valencia, Departamento de Fisica Teorica and IFIC, Centro Mixto Universidad de Valencia-CSIC, Valencia (Spain)

    2016-03-15

    In certain extensions of General Relativity, wormholes generated by spherically symmetric electric fields can resolve black hole singularities without necessarily removing curvature divergences. This is shown by studying geodesic completeness, the behavior of time-like congruences going through the divergent region, and by means of scattering of waves off the wormhole. This provides an example of the logical independence between curvature divergences and space-time singularities, concepts very often identified with each other in the literature. (orig.)

  8. Exact Solutions for Einstein's Hyperbolic Geometric Flow

    Institute of Scientific and Technical Information of China (English)

    HE Chun-Lei

    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.

  9. Classical competing risks

    CERN Document Server

    Crowder, Martin J

    2001-01-01

    If something can fail, it can often fail in one of several ways and sometimes in more than one way at a time. There is always some cause of failure, and almost always, more than one possible cause. In one sense, then, survival analysis is a lost cause. The methods of Competing Risks have often been neglected in the survival analysis literature. Written by a leading statistician, Classical Competing Risks thoroughly examines the probability framework and statistical analysis of data of Competing Risks. The author explores both the theory of the subject and the practicalities of fitting the models to data. In a coherent, self-contained, and sequential account, the treatment moves from the bare bones of the Competing Risks setup and the associated likelihood functions through survival analysis using hazard functions. It examines discrete failure times and the difficulties of identifiability, and concludes with an introduction to the counting-process approach and the associated martingale theory.With a dearth of ...

  10. Classical Fourier analysis

    CERN Document Server

    Grafakos, Loukas

    2014-01-01

    The main goal of this text is to present the theoretical foundation of the field of Fourier analysis on Euclidean spaces. It covers classical topics such as interpolation, Fourier series, the Fourier transform, maximal functions, singular integrals, and Littlewood–Paley theory. The primary readership is intended to be graduate students in mathematics with the prerequisite including satisfactory completion of courses in real and complex variables. The coverage of topics and exposition style are designed to leave no gaps in understanding and stimulate further study. This third edition includes new Sections 3.5, 4.4, 4.5 as well as a new chapter on “Weighted Inequalities,” which has been moved from GTM 250, 2nd Edition. Appendices I and B.9 are also new to this edition.  Countless corrections and improvements have been made to the material from the second edition. Additions and improvements include: more examples and applications, new and more relevant hints for the existing exercises, new exercises, and...

  11. Classics in radio astronomy

    CERN Document Server

    Sullivan, Woodruff Turner

    1982-01-01

    Radio techniques were the nrst to lead astronomy away from the quiescent and limited Universe revealed by traditional observations at optical wave­ lengths. In the earliest days of radio astronomy, a handful of radio physicists and engineers made one startling discovery after another as they opened up the radio sky. With this collection of classic papers and the extensive intro­ ductory material, the reader can experience these exciting discoveries, as well as understand the developing techniques and follow the motivations which prompted the various lines of inquiry. For instance he or she will follow in detail the several attempts to detect radio waves from the sun at the turn of the century; the unravelling by Jansky of a "steady hiss type static"; the incredible story of Reber who built a 9 meter dish in his backyard in 1937 and then mapped the Milky Way; the vital discoveries by Hey and colleagues of radio bursts from the Sun and of a discrete source in the constellation of Cygnus; the development of re...

  12. GONG ClassicMerge: Pipeline and Product

    CERN Document Server

    Hughes, Anna L H; Kholikov, Shukur

    2016-01-01

    A recent processing effort has been undertaken in order to extend the range-of-coverage of the GONG merged dopplergrams. The GONG-Classic-era observations have now been merged to provide, albeit at lower resolution, mrvzi data as far back as May of 1995. The contents of this document provide an overview of what these data look like, the processing steps used to generate them from the original site observations, and the outcomes of a few initial quality-assurance tests designed to validate the final merged images. Based on these tests, the GONG project is releasing this data product to the user community (http://nisp.nso.edu/data).

  13. Classical and quantum effective theories

    CERN Document Server

    Polonyi, Janos

    2014-01-01

    A generalization of the action principle of classical mechanics, motivated by the Closed Time Path (CTP) scheme of quantum field theory, is presented to deal with initial condition problems and dissipative forces. The similarities of the classical and the quantum cases are underlined. In particular, effective interactions which describe classical dissipative forces represent the system-environment entanglement. The relation between the traditional effective theories and their CTP extension is briefly discussed and few qualitative examples are mentioned.

  14. Population in the classic economics

    OpenAIRE

    Adnan Doğruyol

    2013-01-01

    Growth subject in economics is an important factor of development. Classic economics ecole indicates the population as main variable which tender of growth. On the other hand T. R. Malthus is known as economist who regards population as a problem and brings up it among the classical economists. However, Adam Smith is an intellectual who discussed population problem earlier on the classic economics theory. According to Adam Smith one of the main factors that realise the growth is labour. In ad...

  15. Coherent Communication of Classical Messages

    OpenAIRE

    Harrow, Aram W.

    2003-01-01

    We define "coherent communication" in terms of a simple primitive, show it is equivalent to the ability to send a classical message with a unitary or isometric operation, and use it to relate other resources in quantum information theory. Using coherent communication, we are able to generalize super-dense coding to prepare arbitrary quantum states instead of only classical messages. We also derive single-letter formulae for the classical and quantum capacities of a bipartite unitary gate assi...

  16. 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. PMID:19727989

  17. Polar Metals by Geometric Design

    Energy Technology Data Exchange (ETDEWEB)

    Kim, T. H.; Puggioni, D.; Yuan, Y.; Xie, L.; Zhou, H.; Campbell, N.; Ryan, P.J.; Choi, Y.; Kim, J.-W.; Patzner, J. R.; Ryu, S.; Podkaminer, J. P.; Irwin, J.; Ma, Y.; Fennie, C. J.; Rzchowski, M. S.; Pan, X. Q.; Gopalan, V.; Rondinelli, J. M.; Eom, C. B.

    2016-05-05

    Gauss's law dictates that the net electric field inside a conductor in electrostatic equilibrium is zero by effective charge screening; free carriers within a metal eliminate internal dipoles that may arise owing to asymmetric charge distributions(1). Quantum physics supports this view(2), demonstrating that delocalized electrons make a static macroscopic polarization, an ill-defined quantity in metals(3)-it is exceedingly unusual to find a polar metal that exhibits long-range ordered dipoles owing to cooperative atomic displacements aligned from dipolar interactions as in insulating phases(4). Here we describe the quantum mechanical design and experimental realization of room-temperature polar metals in thin-film ANiO(3) perovskite nickelates using a strategy based on atomic-scale control of inversion-preserving (centric) displacements(5). We predict with ab initio calculations that cooperative polar A cation displacements are geometrically stabilized with a non-equilibrium amplitude and tilt pattern of the corner-connected NiO6 octahedra-the structural signatures of perovskites-owing to geometric constraints imposed by the underlying substrate. Heteroepitaxial thin-films grown on LaAlO3 (111) substrates fulfil the design principles. We achieve both a conducting polar monoclinic oxide that is inaccessible in compositionally identical films grown on (001) substrates, and observe a hidden, previously unreported(6-10), non-equilibrium structure in thin-film geometries. We expect that the geometric stabilization approach will provide novel avenues for realizing new multifunctional materials with unusual coexisting properties.

  18. Geometrical Applications of Split Octonions

    CERN Document Server

    Gogberashvili, Merab

    2015-01-01

    Physical signals and space-time intervals are described in terms of split octonions. Geometrical symmetries are represented by the automorphism group of the algebra - the real non-compact form of Cartan's smallest exceptional group G2. This group generates specific rotations of (3+4)-vector parts of split octonions with three extra time-like coordinates and in certain limits reduces to standard Lorentz group. In this picture several physical characteristics of ordinary (3+1)-dimensional theory (such as: number of spatial dimensions, existence of maximal velocities, the uncertainty principle, some quantum numbers) are naturally emerge from the properties of the algebra.

  19. Symmetries of Islamic geometrical patterns

    CERN Document Server

    Abas, Jan; Salman, Amer Shaker

    1994-01-01

    This book on symmetric geometric patterns of Islamic art has educational, aesthetic, cultural and practical purposes. Its central purpose is to bring to the attention of the world in general, and the people of Islamic culture in particular, the potential of the art for providing a unified experience of science and art in the context of mathematical education. Unlike other books on Islamic patterns, this book emphasizes the educational potential in the context of modern physics, chemistry, crystallography and computer graphics. The symmetric structure of about 250 Islamic patterns is presented.

  20. Geometric Topology and Shape Theory

    CERN Document Server

    Segal, Jack

    1987-01-01

    The aim of this international conference the third of its type was to survey recent developments in Geometric Topology and Shape Theory with an emphasis on their interaction. The volume contains original research papers and carefully selected survey of currently active areas. The main topics and themes represented by the papers of this volume include decomposition theory, cell-like mappings and CE-equivalent compacta, covering dimension versus cohomological dimension, ANR's and LCn-compacta, homology manifolds, embeddings of continua into manifolds, complement theorems in shape theory, approximate fibrations and shape fibrations, fibered shape, exact homologies and strong shape theory.

  1. Science, art and geometrical imagination

    Science.gov (United States)

    Luminet, Jean-Pierre

    2011-06-01

    From the geocentric, closed world model of Antiquity to the wraparound universe models of relativistic cosmology, the parallel history of space representations in science and art illustrates the fundamental rôle of geometric imagination in innovative findings. Through the analysis of works of various artists and scientists like Plato, Dürer, Kepler, Escher, Grisey or the author, it is shown how the process of creation in science and in the arts rests on aesthetical principles such as symmetry, regular polyhedra, laws of harmonic proportion, tessellations, group theory, etc., as well as on beauty, conciseness and an emotional approach of the world.

  2. Science, Art and Geometrical Imagination

    CERN Document Server

    Luminet, J -P

    2009-01-01

    From the geocentric, closed world model of Antiquity to the wraparound universe models of relativistic cosmology, the parallel history of space representations in science and art illustrates the fundamental role of geometric imagination in innovative findings. Through the analysis of works of various artists and scientists like Plato, Durer, Kepler, Escher, Grisey or the present author, it is shown how the process of creation in science and in the arts rests on aesthetical principles such as symmetry, regular polyhedra, laws of harmonic proportion, tessellations, group theory, etc., as well as beauty, conciseness and emotional approach of the world.

  3. A history of geometrical methods

    CERN Document Server

    Coolidge, Julian Lowell

    2013-01-01

    Full and authoritative, this history of the techniques for dealing with geometric questions begins with synthetic geometry and its origins in Babylonian and Egyptian mathematics; reviews the contributions of China, Japan, India, and Greece; and discusses the non-Euclidean geometries. Subsequent sections cover algebraic geometry, starting with the precursors and advancing to the great awakening with Descartes; and differential geometry, from the early work of Huygens and Newton to projective and absolute differential geometry. The author's emphasis on proofs and notations, his comparisons betwe

  4. Geometric approach to soliton equations

    International Nuclear Information System (INIS)

    A class of nonlinear equations that can be solved in terms of nxn scattering problem is investigated. A systematic geometric method of exploiting conservation laws and related equations, the so-called prolongation structure, is worked out. The nxn problem is reduced to nsub(n-1)x(n-1) problems and finally to 2x2 problems, which have been comprehensively investigated recently by the author. A general method of deriving the infinite numbers of polynomial conservation laws for an nxn problem is presented. The cases of 3x3 and 2x2 problems are discussed explicitly. (Auth.)

  5. Geometric Rationalization for Freeform Architecture

    KAUST Repository

    jiang, caigui

    2016-06-20

    The emergence of freeform architecture provides interesting geometric challenges with regards to the design and manufacturing of large-scale structures. To design these architectural structures, we have to consider two types of constraints. First, aesthetic constraints are important because the buildings have to be visually impressive. Sec- ond, functional constraints are important for the performance of a building and its e cient construction. This thesis contributes to the area of architectural geometry. Specifically, we are interested in the geometric rationalization of freeform architec- ture with the goal of combining aesthetic and functional constraints and construction requirements. Aesthetic requirements typically come from designers and architects. To obtain visually pleasing structures, they favor smoothness of the building shape, but also smoothness of the visible patterns on the surface. Functional requirements typically come from the engineers involved in the construction process. For exam- ple, covering freeform structures using planar panels is much cheaper than using non-planar ones. Further, constructed buildings have to be stable and should not collapse. In this thesis, we explore the geometric rationalization of freeform archi- tecture using four specific example problems inspired by real life applications. We achieve our results by developing optimization algorithms and a theoretical study of the underlying geometrical structure of the problems. The four example problems are the following: (1) The design of shading and lighting systems which are torsion-free structures with planar beams based on quad meshes. They satisfy the functionality requirements of preventing light from going inside a building as shad- ing systems or reflecting light into a building as lighting systems. (2) The Design of freeform honeycomb structures that are constructed based on hex-dominant meshes with a planar beam mounted along each edge. The beams intersect without

  6. A Classic Beauty

    Science.gov (United States)

    2007-01-01

    M51, whose name comes from being the 51st entry in Charles Messier's catalog, is considered to be one of the classic examples of a spiral galaxy. At a distance of about 30 million light-years from Earth, it is also one of the brightest spirals in the night sky. A composite image of M51, also known as the Whirlpool Galaxy, shows the majesty of its structure in a dramatic new way through several of NASA's orbiting observatories. X-ray data from NASA's Chandra X-ray Observatory reveals point-like sources (purple) that are black holes and neutron stars in binary star systems. Chandra also detects a diffuse glow of hot gas that permeates the space between the stars. Optical data from the Hubble Space Telescope (green) and infrared emission from the Spitzer Space Telescope (red) both highlight long lanes in the spiral arms that consist of stars and gas laced with dust. A view of M51 with the Galaxy Evolution Explorer telescope shows hot, young stars that produce lots of ultraviolet energy (blue). The textbook spiral structure is thought be the result of an interaction M51 is experiencing with its close galactic neighbor, NGC 5195, which is seen just above. Some simulations suggest M51's sharp spiral shape was partially caused when NGC 5195 passed through its main disk about 500 million years ago. This gravitational tug of war may also have triggered an increased level of star formation in M51. The companion galaxy's pull would be inducing extra starbirth by compressing gas, jump-starting the process by which stars form.

  7. A synthetic approach to the transfer matrix method in classical and quantum physics

    International Nuclear Information System (INIS)

    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 would benefit by using the abcd-matrix which in addition is easy to implement on a personal computer

  8. A synthetic approach to the transfer matrix method in classical and quantum physics

    Science.gov (United States)

    Pujol, O.; Pérez, J. P.

    2007-07-01

    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 would benefit by using the abcd-matrix which in addition is easy to implement on a personal computer.

  9. Lagrangian geometrical optics of nonadiabatic vector waves and spin particles

    Science.gov (United States)

    Ruiz, D. E.; Dodin, I. Y.

    2015-10-01

    Linear vector waves, both quantum and classical, experience polarization-driven bending of ray trajectories and polarization dynamics that can be interpreted as the precession of the "wave spin". Both phenomena are governed by an effective gauge Hamiltonian vanishing in leading-order geometrical optics. This gauge Hamiltonian can be recognized as a generalization of the Stern-Gerlach Hamiltonian that is commonly known for spin-1/2 quantum particles. The corresponding reduced Lagrangians for continuous nondissipative waves and their geometrical-optics rays are derived from the fundamental wave Lagrangian. The resulting Euler-Lagrange equations can describe simultaneous interactions of N resonant modes, where N is arbitrary, and lead to equations for the wave spin, which happens to be an (N2 - 1)-dimensional spin vector. As a special case, classical equations for a Dirac particle (N = 2) are deduced formally, without introducing additional postulates or interpretations, from the Dirac quantum Lagrangian with the Pauli term. The model reproduces the Bargmann-Michel-Telegdi equations with added Stern-Gerlach force.

  10. Lagrangian geometrical optics of nonadiabatic vector waves and spin particles

    Energy Technology Data Exchange (ETDEWEB)

    Ruiz, D. E. [Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences; Dodin, I. Y. [Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences

    2015-10-01

    Linear vector waves, both quantum and classical, experience polarization-driven bending of ray trajectories and polarization dynamics that can be interpreted as the precession of the "wave spin". Both phenomena are governed by an effective gauge Hamiltonian vanishing in leading-order geometrical optics. This gauge Hamiltonian can be recognized as a generalization of the Stern-Gerlach Hamiltonian that is commonly known for spin-1/2 quantum particles. The corresponding reduced Lagrangians for continuous nondissipative waves and their geometrical-optics rays are derived from the fundamental wave Lagrangian. The resulting Euler-Lagrange equations can describe simultaneous interactions of N resonant modes, where N is arbitrary, and lead to equations for the wave spin, which happens to be an (N-2 - 1)-dimensional spin vector. As a special case, classical equations for a Dirac particle (N = 2) are deduced formally, without introducing additional postulates or interpretations, from the Dirac quantum Lagrangian with the Pauli term. The model reproduces the Bargmann-Michel-Telegdi equations with added Stern-Gerlach force. (C) 2015 Elsevier B.V. All rights reserved.

  11. Geometric pumping in autophoretic channels

    Science.gov (United States)

    Michelin, Sebastien; Montenegro Johnson, Thomas; de Canio, Gabriele; Lobatto-Dauzier, Nicolas; Lauga, Eric

    2015-11-01

    Pumping at the microscale has important applications from biological fluid handling to lab-on-a-chip systems. It can be achieved either from a global (e.g. imposed pressure gradient) or local forcing (e.g. ciliary pumping). Phoretic slip flows generated from concentration or temperature gradients are examples of such local flow forcing. Autophoresis is currently receiving much attention for the design of self-propelled particles achieving force- and torque-free locomotion by combining two essential surface properties: (i) an activity that modifies the solute content of the particle's environment (e.g. catalytic reaction or solute release), and (ii) a mobility that generates a slip flow from the resulting local concentration gradients. Recent work showed that geometric asymmetry is sufficient for a chemically-homogeneous particle to self-propel. Here we extend this idea to micro-pumping in active channels whose walls possess both chemical activity and phoretic mobility. Using a combination of theoretical analysis and numerical simulations, we show that geometrically-asymmetric but chemically-homogeneous channels can generate pumping and analyze the resulting flow patterns.

  12. Geometrically focused neutral beam accelerators

    International Nuclear Information System (INIS)

    A more reliable 40 kV, 65 A power supply drain at 0.4 A/cm2, neutral-beam accelerator was developed for the Tandem Mirror Experiment (TMX). Multiple slotted aperture grids of 60% transparency are fabricated from refractory metal wires mounted to form a spherical surface. This geometrically focuses the beam by aiming individual beamlets at the center of curvature of the spherical grid (r = 3.2 m). We attain greater reliability and faster conditioning with geometrical focusing than with the previous technique of electrostatically steering beamlets to a common point. Electrostatic steering, accomplished by offsetting grid wires, is satisfactory if the offset of a beamlet is much less than the distance from the beamlet to the grids. It was found that Pierce Angle entrance grids performed better if sharper edged. A redesigned accelerator grid support structure reduced the number of ceramic-to-metal vacuum joints, and eliminated O rings between precisely aligned parts. The suppressor grid feedthrough is required to withstand a maximum voltage of 15 kV occurring during breakdown, greatly exceeding the operating voltage of 1.5 kV. Convenient fabrication and assembly techniques have been developed. Assembly of accelerators and plasma sources in a clean room appears to reduce the conditioning time. Following the successful testing of the prototype, eight 40 kV accelerators were built for TMX. Furthermore, ten 20 kV versions were built that are modifiable to 40 kV by exchanging the entrance grid

  13. Geometric realization for substitution tilings

    CERN Document Server

    Barge, Marcy

    2011-01-01

    Given an n-dimensional substitution whose associated linear expansion is unimodular and hyperbolic, we use elements of the one-dimensional integer \\v{C}ech cohomology of the associated tiling space to construct a finite-to-one semi-conjugacy, called geometric realization, between the substitution induced dynamics and an invariant set of a hyperbolic toral automorphism. If the linear expansion satisfies a Pisot family condition and the rank of the module of generalized return vectors equals the generalized degree of the linear expansion, the image of geometric realization is the entire torus and coincides with the map onto the maximal equicontinuous factor of the translation action on the tiling space. We are led to formulate a higher-dimensional generalization of the Pisot Substitution Conjecture: If the linear expansion satisfies the Pisot family condition and the rank of the one-dimensional cohomology of the tiling space equals the generalized degree of the linear expansion, then the translation action on t...

  14. Geometrical deployment for braided stent.

    Science.gov (United States)

    Bouillot, Pierre; Brina, Olivier; Ouared, Rafik; Yilmaz, Hasan; Farhat, Mohamed; Erceg, Gorislav; Lovblad, Karl-Olof; Vargas, Maria Isabel; Kulcsar, Zsolt; Pereira, Vitor Mendes

    2016-05-01

    The prediction of flow diverter stent (FDS) implantation for the treatment of intracranial aneurysms (IAs) is being increasingly required for hemodynamic simulations and procedural planning. In this paper, a deployment model was developed based on geometrical properties of braided stents. The proposed mathematical description is first applied on idealized toroidal vessels demonstrating the stent shortening in curved vessels. It is subsequently generalized to patient specific vasculature predicting the position of the filaments along with the length and local porosity of the stent. In parallel, in-vitro and in-vivo FDS deployments were measured by contrast-enhanced cone beam CT (CBCT) in idealized and patient-specific geometries. These measurements showed a very good qualitative and quantitative agreement with the virtual deployments and provided experimental validations of the underlying geometrical assumptions. In particular, they highlighted the importance of the stent radius assessment in the accuracy of the deployment prediction. Thanks to its low computational cost, the proposed model is potentially implementable in clinical practice providing critical information for patient safety and treatment outcome assessment. PMID:26891065

  15. Measurement error in geometric morphometrics.

    Science.gov (United States)

    Fruciano, Carmelo

    2016-06-01

    Geometric morphometrics-a set of methods for the statistical analysis of shape once saluted as a revolutionary advancement in the analysis of morphology -is now mature and routinely used in ecology and evolution. However, a factor often disregarded in empirical studies is the presence and the extent of measurement error. This is potentially a very serious issue because random measurement error can inflate the amount of variance and, since many statistical analyses are based on the amount of "explained" relative to "residual" variance, can result in loss of statistical power. On the other hand, systematic bias can affect statistical analyses by biasing the results (i.e. variation due to bias is incorporated in the analysis and treated as biologically-meaningful variation). Here, I briefly review common sources of error in geometric morphometrics. I then review the most commonly used methods to measure and account for both random and non-random measurement error, providing a worked example using a real dataset. PMID:27038025

  16. 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

  17. Geometric constructions for repulsive gravity and quantization

    International Nuclear Information System (INIS)

    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

  18. Geometric effects of fuel regression rate in hybrid rocket motors

    Institute of Scientific and Technical Information of China (English)

    CAI GuoBiao; ZHANG YuanJun; WANG PengFei; HUI Tian; ZHAO Sheng; YU NanJia

    2016-01-01

    The geometric configuration of the solid fuel is a key parameter affecting the fuel regression rate in hybrid rocket motors.In this paper,a semi-empirical regression rate model is developed to investigate the geometric effect on the fuel regression rate by incorporating the hydraulic diameter into the classical model.The semi-empirical model indicates that the fuel regression rate decreases with increasing hydraulic diameter and is proportional to dh-0.2 when convective heat transfer is dominant.Then a numerical model considering turbulence,combustion,solid fuel pyrolysis,and a solid-gas coupling model is established to further investigate the geometric effect.Eight motors with different solid fuel grains are simulated,and four methods of scaling the regression rate between different solid fuel grains are compared.The results indicate that the solid fuel regression rates are approximate the same when the hydraulic diameters are equal.The numerical results verify the accuracy of the semi-empirical model.

  19. Radiometric and Geometric Accuracy Analysis of Rasat Pan Imagery

    Science.gov (United States)

    Kocaman, S.; Yalcin, I.; Guler, M.

    2016-06-01

    RASAT is the second Turkish Earth Observation satellite which was launched in 2011. It operates with pushbroom principle and acquires panchromatic and MS images with 7.5 m and 15 m resolutions, respectively. The swath width of the sensor is 30 km. The main aim of this study is to analyse the radiometric and geometric quality of RASAT images. A systematic validation approach for the RASAT imagery and its products is being applied. RASAT image pair acquired over Kesan city in Edirne province of Turkey are used for the investigations. The raw RASAT data (L0) are processed by Turkish Space Agency (TUBITAK-UZAY) to produce higher level image products. The image products include radiometrically processed (L1), georeferenced (L2) and orthorectified (L3) data, as well as pansharpened images. The image quality assessments include visual inspections, noise, MTF and histogram analyses. The geometric accuracy assessment results are only preliminary and the assessment is performed using the raw images. The geometric accuracy potential is investigated using 3D ground control points extracted from road intersections, which were measured manually in stereo from aerial images with 20 cm resolution and accuracy. The initial results of the study, which were performed using one RASAT panchromatic image pair, are presented in this paper.

  20. Classical Music Fan Chen Li

    Institute of Scientific and Technical Information of China (English)

    2002-01-01

    The heyday of Beijing’s classical music beganin 1993, when top-quality sound equipment andrecords were imported. Also in that year, BeijingMusic Radio presented a classical music programtitled "Fan’s Club" and founded the "Music and

  1. Dynamical Symmetries in Classical Mechanics

    Science.gov (United States)

    Boozer, A. D.

    2012-01-01

    We show how symmetries of a classical dynamical system can be described in terms of operators that act on the state space for the system. We illustrate our results by considering a number of possible symmetries that a classical dynamical system might have, and for each symmetry we give examples of dynamical systems that do and do not possess that…

  2. Geometrical charged-particle optics. 2. ed.

    Energy Technology Data Exchange (ETDEWEB)

    Rose, Harald [Technische Univ. Darmstadt (Germany). Inst. fuer Angewandte Physik

    2013-03-01

    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

  3. Geometric Langevin equations on submanifolds and applications to the stochastic melt-spinning process of nonwovens and biology

    OpenAIRE

    Grothaus, Martin; Stilgenbauer, Patrik

    2012-01-01

    In this article we develop geometric versions of the classical Langevin equation on regular submanifolds in euclidean space in an easy, natural way and combine them with a bunch of applications. The equations are formulated as Stratonovich stochastic differential equations on manifolds. The first version of the geometric Langevin equation has already been detected before by Leli\\`evre, Rousset and Stoltz with a different derivation. We propose an additional extension of the models, the geomet...

  4. LUNGEOMETRY- GEOMETRICAL INVESTIGATION OF LUNGE

    Directory of Open Access Journals (Sweden)

    R.Vinodh Rajkumar

    2015-02-01

    Full Text Available Physiotherapists must learn the biomechanics of lunge in detail to clearly understand its significance in human life and implement effective training measures to overcome the limiting factors of proper lunge of their clientele. To understand the biomechanical value of every movement, interesting experimental learning methods must be employed to kindle the Physiotherapists to actively take part in research activities from the under-graduate level onwards. Lungeometry is a novel, simple and inexpensive experimental investigation of lunge, applying basic geometrical methods taking near normal lower limb length dimensions and rationale approaches into consideration. Lungeometry can give a foundation to learn other forms of lunges like forward lunge, weighted lunges, lateral lunges. This model of learning biomechanics of movements using fundamental geometry techniques is expected to strongly connect with any futuristic Physiotherapy curricular structure.

  5. Geometric interpretation of phyllotaxis transition

    CERN Document Server

    Okabe, Takuya

    2012-01-01

    The original problem of phyllotaxis was focused on the regular arrangements of leaves on mature stems represented by common fractions such as 1/2, 1/3, 2/5, 3/8, 5/13, etc. The phyllotaxis fraction is not fixed for each plant but it may undergo stepwise transitions during ontogeny, despite contrasting observation that the arrangement of leaf primordia at shoot apical meristems changes continuously. No explanation has been given so far for the mechanism of the phyllotaxis transition, excepting suggestion resorting to genetic programs operating at some specific stages. Here it is pointed out that varying length of the leaf trace acts as an important factor to control the transition by analyzing Larson's diagram of the procambial system of young cottonwood plants. The transition is interpreted as a necessary consequence of geometric constraints that the leaf traces cannot be fitted into a fractional pattern unless their length is shorter than the denominator times the internode.

  6. Geometric Mean Neutrino Mass Relation

    Science.gov (United States)

    He, Xiao-Gang; Zee, A.

    Present experimental data from neutrino oscillations have provided much information about the neutrino mixing angles. Since neutrino oscillations only determine the mass squared differences Δ m2ij = m2i - m2j, the absolute values for neutrino masses mi, can not be determined using data just from oscillations. In this work we study implications on neutrino masses from a geometric mean mass relation m2 = √ {m1m_3} which enables one to determined the absolute masses of the neutrinos. We find that the central values of the three neutrino masses and their 2σ errors to be m1 = (1.58 ± 0.18)meV, m2 = (9.04 ± 0.42)meV, and m3 = (51.8 ± 3.5)meV. Implications for cosmological observation, beta decay and neutrinoless double beta decays are discussed.

  7. Autophoretic locomotion from geometric asymmetry

    CERN Document Server

    Michelin, Sebastien

    2015-01-01

    Among the few methods which have been proposed to create small-scale swimmers, those relying on self-phoretic mechanisms present an interesting design challenge in that chemical gradients are required to generate net propulsion. Building on recent work, we propose that asymmetries in geometry are sufficient to induce chemical gradients and swimming. We illustrate this idea using two different calculations. We first calculate exactly the self-propulsion speed of a system composed of two spheres of unequal sizes but identically chemically homogeneous. We then consider arbitrary, small-amplitude, shape deformations of a chemically-homogeneous sphere, and calculate asymptotically the self-propulsion velocity induced by the shape asymmetries. Our results demonstrate how geometric asymmetries can be tuned to induce large locomotion speeds without the need of chemical patterning.

  8. Phenomenological modeling of Geometric Metasurfaces

    CERN Document Server

    Ye, Weimin; Xiang, Yuanjiang; Fan, Dianyuan; Zhang, Shuang

    2015-01-01

    Metasurfaces, with their superior capability in manipulating the optical wavefront at the subwavelength scale and low manufacturing complexity, have shown great potential for planar photonics and novel optical devices. However, vector field simulation of metasurfaces is so far limited to periodic-structured metasurfaces containing a small number of meta-atoms in the unit cell by using full-wave numerical methods. Here, we propose a general phenomenological method to analytically model metasurfaces made up of arbitrarily distributed meta-atoms based on the assumption that the meta-atoms possess localized resonances with Lorentz-Drude forms, whose exact form can be retrieved from the full wave simulation of a single element. Applied to phase modulated geometric metasurfaces, our analytical results show good agreement with full-wave numerical simulations. The proposed theory provides an efficient method to model and design optical devices based on metasurfaces.

  9. Entanglement assisted classical communication simulates "classical communication" without causal order

    OpenAIRE

    Akibue, Seiseki; Owari, Masaki; Kato, Go; Murao, Mio

    2016-01-01

    Phenomena induced by the existence of entanglement, such as nonlocal correlations, exhibit characteristic properties of quantum mechanics distinguishing from classical theories. When entanglement is accompanied by classical communication, it enhances the power of quantum operations jointly performed by two spatially separated parties. Such a power has been analyzed by the gap between the performances of joint quantum operations implementable by local operations at each party connected by clas...

  10. Geometric solitons of Hamiltonian flows on manifolds

    International Nuclear Information System (INIS)

    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

  11. 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.

  12. Optimizing the geometrical accuracy of curvilinear meshes

    CERN Document Server

    Toulorge, Thomas; Remacle, Jean-François

    2015-01-01

    This paper presents a method to generate valid high order meshes with optimized geometrical accuracy. The high order meshing procedure starts with a linear mesh, that is subsequently curved without taking care of the validity of the high order elements. An optimization procedure is then used to both untangle invalid elements and optimize the geometrical accuracy of the mesh. Standard measures of the distance between curves are considered to evaluate the geometrical accuracy in planar two-dimensional meshes, but they prove computationally too costly for optimization purposes. A fast estimate of the geometrical accuracy, based on Taylor expansions of the curves, is introduced. An unconstrained optimization procedure based on this estimate is shown to yield significant improvements in the geometrical accuracy of high order meshes, as measured by the standard Haudorff distance between the geometrical model and the mesh. Several examples illustrate the beneficial impact of this method on CFD solutions, with a part...

  13. Quantum localization of Classical Mechanics

    CERN Document Server

    Batalin, Igor A

    2016-01-01

    Quantum localization of classical mechanics within the BRST-BFV and BV (or field-antifield) quantization methods are studied. It is shown that a special choice of gauge fixing functions (or BRST-BFV charge) together with the unitary limit leads to Hamiltonian localization in the path integral of the BRST-BFV formalism. In turn, we find that a special choice of gauge fixing functions being proportional to extremals of an initial non-degenerate classical action together with a very special solution of the classical master equation result in Lagrangian localization in the partition function of the BV formalism.

  14. Quantum localization of classical mechanics

    Science.gov (United States)

    Batalin, Igor A.; Lavrov, Peter M.

    2016-07-01

    Quantum localization of classical mechanics within the BRST-BFV and BV (or field-antifield) quantization methods are studied. It is shown that a special choice of gauge fixing functions (or BRST-BFV charge) together with the unitary limit leads to Hamiltonian localization in the path integral of the BRST-BFV formalism. In turn, we find that a special choice of gauge fixing functions being proportional to extremals of an initial non-degenerate classical action together with a very special solution of the classical master equation result in Lagrangian localization in the partition function of the BV formalism.

  15. The Wigner representation of classical mechanics, quantization and classical limit

    International Nuclear Information System (INIS)

    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)

  16. Effective state metamorphosis in semi-classical loop quantum cosmology

    International Nuclear Information System (INIS)

    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

  17. Geometry of Lagrangian first-order classical field theories

    International Nuclear Information System (INIS)

    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.)

  18. 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.)

  19. Analysis of Geometrical Specification Model Based on the New GeometricalProduct Specification Language

    Institute of Scientific and Technical Information of China (English)

    马利民; 王金星; 蒋向前; 李柱; 徐振高

    2004-01-01

    Geometrical Product Specification and verification (GPS) is an ISO standard system coveting standards of size, dimension,geometrical tolerance and surface texture of geometrical product. ISO/TC213 on the GPS has been working towards coordination of the previous standards in tolerance and related metrology in order to publish the next generation of the GPS language. This paper introduces the geometrical product specification model for design, manufacturing and verification based on the improved GPS and its new concepts,i.e., surface models, geometrical features and operations. An application example for the geometrical product specification model is then given.

  20. Geometric Scene Parsing with Hierarchical LSTM

    OpenAIRE

    Peng, Zhanglin; Zhang, Ruimao; Liang, Xiaodan; Liu, Xiaobai; Lin, Liang

    2016-01-01

    This paper addresses the problem of geometric scene parsing, i.e. simultaneously labeling geometric surfaces (e.g. sky, ground and vertical plane) and determining the interaction relations (e.g. layering, supporting, siding and affinity) between main regions. This problem is more challenging than the traditional semantic scene labeling, as recovering geometric structures necessarily requires the rich and diverse contextual information. To achieve these goals, we propose a novel recurrent neur...

  1. 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

  2. A Geometric Approach to Noncommutative Principal Bundles

    CERN Document Server

    Wagner, Stefan

    2011-01-01

    From a geometrical point of view it is, so far, not sufficiently well understood what should be a "noncommutative principal bundle". Still, there is a well-developed abstract algebraic approach using the theory of Hopf algebras. An important handicap of this approach is the ignorance of topological and geometrical aspects. The aim of this thesis is to develop a geometrically oriented approach to the noncommutative geometry of principal bundles based on dynamical systems and the representation theory of the corresponding transformation group.

  3. Report on Workshop on Geometric Scattering

    DEFF Research Database (Denmark)

    As part of the activities of MaPhySto a workshop on geometric scattering was organized at University of Aarhus, November 5-7, 1998. The workshop was narrowly focused on geometric scattering, and in particular the use of geometric scattering in understanding the structure of the scattering operator...... for the quantum mechanical many-body problem. A number of other questions were also discussed in detail, including the resonances and various geometric questions. This report includes the program of the workshop, a collection of previews, abstracts, and reports on the lectures, with extensive...

  4. Geometrical and Graphical Solutions of Quadratic Equations.

    Science.gov (United States)

    Hornsby, E. John, Jr.

    1990-01-01

    Presented are several geometrical and graphical methods of solving quadratic equations. Discussed are Greek origins, Carlyle's method, von Staudt's method, fixed graph methods and imaginary solutions. (CW)

  5. Geometric Langevin equations on submanifolds and applications to the stochastic melt-spinning process of nonwovens and biology

    CERN Document Server

    Grothaus, Martin

    2012-01-01

    In this article we develop geometric versions of the classical Langevin equation on regular submanifolds in euclidean space in an easy, natural way and combine them with a bunch of applications. The equations are formulated as Stratonovich stochastic differential equations on manifolds. The first version of the geometric Langevin equation has already been detected before by Leli\\`evre, Rousset and Stoltz with a different derivation. We propose an additional extension of the models, the geometric Langevin equations with velocity of constant absolute value. The latters are seemingly new and provide a galaxy of new, beautiful and powerful mathematical models. Up to the authors best knowledge there are not many mathematical papers available dealing with geometric Langevin processes. We connect the first version of the geometric Langevin equation via proving that its generator coincides with the generalized Langevin operator proposed by Soloveitchik, Jorgensen and Kolokoltsov. All our studies are strongly motivate...

  6. Geometric Representation of Interacting Non-Relativistic Open Strings using Extended Objects

    CERN Document Server

    Arias, P J; Fuenmayor, E; Leal, L

    2013-01-01

    Non-relativistic charged open strings coupled with Abelian gauge fields are quantized in a geometric representation that generalizes the Loop Representation. The model consists of open-strings interacting through a Kalb-Ramond field in four dimensions. The geometric representation proposed uses lines and surfaces that can be interpreted as an extension of the picture of Faraday's lines of classical electromagnetism. This representation results to be consistent, provided the coupling constant (the "charge" of the string) is quantized. The Schr\\"odinger equation in this representation is also presented.

  7. Probabilistic and Geometric Languages in the Context of the Principle of Least Action

    CERN Document Server

    Terekhovich, Vladislav

    2012-01-01

    This paper explores the question of the unification of the three basic languages of physics, the geometric language of forces, the geometric language of fields or 4-dimensional space-time, and the probabilistic language of quantum mechanics. I will show that on the one hand, equations in each of these languages may be derived from any form of the Principle of Least Action (PLA). On the other hand, Feynman's `path integral' method could explain the physical sense of these particular forms of PLA. In conclusion, I will show that the axioms of classical and relativistic mechanics become consequences of Feynman's formulation of quantum mechanics.

  8. Seismic imaging: From classical to adjoint tomography

    Science.gov (United States)

    Liu, Q.; Gu, Y. J.

    2012-09-01

    Seismic tomography has been a vital tool in probing the Earth's internal structure and enhancing our knowledge of dynamical processes in the Earth's crust and mantle. While various tomographic techniques differ in data types utilized (e.g., body vs. surface waves), data sensitivity (ray vs. finite-frequency approximations), and choices of model parameterization and regularization, most global mantle tomographic models agree well at long wavelengths, owing to the presence and typical dimensions of cold subducted oceanic lithospheres and hot, ascending mantle plumes (e.g., in central Pacific and Africa). Structures at relatively small length scales remain controversial, though, as will be discussed in this paper, they are becoming increasingly resolvable with the fast expanding global and regional seismic networks and improved forward modeling and inversion techniques. This review paper aims to provide an overview of classical tomography methods, key debates pertaining to the resolution of mantle tomographic models, as well as to highlight recent theoretical and computational advances in forward-modeling methods that spearheaded the developments in accurate computation of sensitivity kernels and adjoint tomography. The first part of the paper is devoted to traditional traveltime and waveform tomography. While these approaches established a firm foundation for global and regional seismic tomography, data coverage and the use of approximate sensitivity kernels remained as key limiting factors in the resolution of the targeted structures. In comparison to classical tomography, adjoint tomography takes advantage of full 3D numerical simulations in forward modeling and, in many ways, revolutionizes the seismic imaging of heterogeneous structures with strong velocity contrasts. For this reason, this review provides details of the implementation, resolution and potential challenges of adjoint tomography. Further discussions of techniques that are presently popular in

  9. New perspectives on classical electromagnetism

    OpenAIRE

    Cote, Paul J.

    2009-01-01

    The fallacies associated with the gauge concept in electromagnetism are illustrated. A clearer and more valid formulation of the basics of classical electromagnetism is provided by recognizing existing physical constraints as well as the physical reality of the vector potential.

  10. Classical Mechanics and Symplectic Integration

    DEFF Research Database (Denmark)

    Nordkvist, Nikolaj; Hjorth, Poul G.

    2005-01-01

    Content: Classical mechanics: Calculus of variations, Lagrange’s equations, Symmetries and Noether’s theorem, Hamilton’s equations, cannonical transformations, integrable systems, pertubation theory. Symplectic integration: Numerical integrators, symplectic integrators, main theorem on symplectic...

  11. Fano interference in classical oscillators

    International Nuclear Information System (INIS)

    We seek to illustrate Fano interference in a classical coupled oscillator by using classical analogues of the atom-laser interaction. We present an analogy between the dressed state picture of coherent atom-laser interaction and a classical coupled oscillator. The Autler-Townes splitting due to the atom-laser interaction is analogous to the splitting of normal-mode frequencies of a coupled oscillator. Using this analogy, we simulate and experimentally demonstrate Fano interference and the associated phenomena in three-level atoms in a coupled electrical resonator circuit. This work aims to highlight analogies between classical and quantum systems for students at the postgraduate and graduate levels. Also, the reported technique can be easily realized in undergraduate laboratories. (paper)

  12. Elementary charges in classical electrodynamics

    OpenAIRE

    KAPU'{S}CIK, Edward

    1999-01-01

    In the framework of classical electrodynamics elementary particles are treated as capacitors. The electrostatic potentials satisfy equations of the Schrödinger type. An interesting "quantization condition" for elementary charges is derived.

  13. Probabilities for classically forbidden transitions using classical and classical path methods

    International Nuclear Information System (INIS)

    Limits are established for the applicability of purely classical methods for calculating nonreactive, inelastic transition probabilities in collinear collisions of a structureless atom and a harmonic oscillator. These limits, obtained by comparison with previous exact quantum mechanical results, indicate that such methods are inappropriate not only for ''classically forbidden'' but for many ''classically allowed'' transitions (in spite of the fact that they are widely used to calculate probabilities for such processes). A classical path method in the context of infinite-order time-dependent perturbation theory is described which yields extremely accurate transition probabilities even for the most classically forbidden transitions in the collinear atom--harmonic oscillator system. The essential features of this method are: (1) the use of the expectation value of the total interaction potential in determining the atom--oscillator (central force) trajectory, and (2) the use of the arithmetic mean of the initial and final velocities of relative motion in the (elastic) central force trajectory. This choice of interaction potential allows the relative motion to be coupled to changes in the internal state of the oscillator. The present classical method is further applied to three-dimensional atom-breathing sphere collisions, and exact quantum mechanical calculations are also carried out. Comparison of the classical path and exact quantum results shows excellent agreement both in the specific inelastic cross section and in the individual partial-wave contributions

  14. Anderson localization from classical trajectories

    OpenAIRE

    Brouwer, Piet W.; Altland, Alexander

    2008-01-01

    We show that Anderson localization in quasi-one dimensional conductors with ballistic electron dynamics, such as an array of ballistic chaotic cavities connected via ballistic contacts, can be understood in terms of classical electron trajectories only. At large length scales, an exponential proliferation of trajectories of nearly identical classical action generates an abundance of interference terms, which eventually leads to a suppression of transport coefficients. We quantitatively descri...

  15. Gaussian Dynamics is Classical Dynamics

    OpenAIRE

    Habib, Salman

    2004-01-01

    A direct comparison of quantum and classical dynamical systems can be accomplished through the use of distribution functions. This is useful for both fundamental investigations such as the nature of the quantum-classical transition as well as for applications such as quantum feedback control. By affording a clear separation between kinematical and dynamical quantum effects, the Wigner distribution is particularly valuable in this regard. Here we discuss some consequences of the fact that when...

  16. Quantum systems as classical systems

    OpenAIRE

    Cassa, Antonio

    2001-01-01

    A characteristical property of a classical physical theory is that the observables are real functions taking an exact outcome on every (pure) state; in a quantum theory, at the contrary, a given observable on a given state can take several values with only a predictable probability. However, even in the classical case, when an observer is intrinsically unable to distinguish between some distinct states he can convince himself that the measure of its ''observables'' can have several values in ...

  17. Quantum money with classical verification

    International Nuclear Information System (INIS)

    We propose and construct a quantum money scheme that allows verification through classical communication with a bank. This is the first demonstration that a secure quantum money scheme exists that does not require quantum communication for coin verification. Our scheme is secure against adaptive adversaries - this property is not directly related to the possibility of classical verification, nevertheless none of the earlier quantum money constructions is known to possess it

  18. Classical theory of radiating strings

    Science.gov (United States)

    Copeland, Edmund J.; Haws, D.; Hindmarsh, M.

    1990-01-01

    The divergent part of the self force of a radiating string coupled to gravity, an antisymmetric tensor and a dilaton in four dimensions are calculated to first order in classical perturbation theory. While this divergence can be absorbed into a renormalization of the string tension, demanding that both it and the divergence in the energy momentum tensor vanish forces the string to have the couplings of compactified N = 1 D = 10 supergravity. In effect, supersymmetry cures the classical infinities.

  19. Quantum money with classical verification

    Energy Technology Data Exchange (ETDEWEB)

    Gavinsky, Dmitry [NEC Laboratories America, Princeton, NJ (United States)

    2014-12-04

    We propose and construct a quantum money scheme that allows verification through classical communication with a bank. This is the first demonstration that a secure quantum money scheme exists that does not require quantum communication for coin verification. Our scheme is secure against adaptive adversaries - this property is not directly related to the possibility of classical verification, nevertheless none of the earlier quantum money constructions is known to possess it.

  20. Effective State Metamorphosis in Semi-Classical Loop Quantum Cosmology

    CERN Document Server

    Singh, P

    2005-01-01

    Modification to the behavior 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 a perfect fluid with arbitrary equation of state incorporates this change in its effective dynamics in the loop modified phase. We show that irrespective of the choice of matter component, stress-energy conservation law generically implies that classical equation of state metamorphoses itself to an effective negative equation of state below a critical scale determined by the theory.

  1. Isynchronous motion in classical mechanics

    International Nuclear Information System (INIS)

    Those oscillatory motions for which the period is independent of the total energy are investigated. There is only one corresponding symmetric potential, the quadratic potential of the simple harmonic motion but infinite classes of asymmetric potentials must be considered. Geometric and analytic requirements of isochronism are discussed and several specific examples are given

  2. Constellations and projective classical groups

    International Nuclear Information System (INIS)

    The constellation concept is recalled (geometrical description of a ray in a vector space). The groups PO(n + 1, C) or PSp(n + 1, C) are shown to preserve 'harmonic conjugation' between two constellations. The action of the Lorentz subgroup and its rotation subgroup is described. Finally, a theorem concerning Clebsch-Gordan product of constellations is proved. (orig.)

  3. Geometric reasoning about assembly tools

    Energy Technology Data Exchange (ETDEWEB)

    Wilson, R.H.

    1997-01-01

    Planning for assembly requires reasoning about various tools used by humans, robots, or other automation to manipulate, attach, and test parts and subassemblies. This paper presents a general framework to represent and reason about geometric accessibility issues for a wide variety of such assembly tools. Central to the framework is a use volume encoding a minimum space that must be free in an assembly state to apply a given tool, and placement constraints on where that volume must be placed relative to the parts on which the tool acts. Determining whether a tool can be applied in a given assembly state is then reduced to an instance of the FINDPLACE problem. In addition, the author presents more efficient methods to integrate the framework into assembly planning. For tools that are applied either before or after their target parts are mated, one method pre-processes a single tool application for all possible states of assembly of a product in polynomial time, reducing all later state-tool queries to evaluations of a simple expression. For tools applied after their target parts are mated, a complementary method guarantees polynomial-time assembly planning. The author presents a wide variety of tools that can be described adequately using the approach, and surveys tool catalogs to determine coverage of standard tools. Finally, the author describes an implementation of the approach in an assembly planning system and experiments with a library of over one hundred manual and robotic tools and several complex assemblies.

  4. Geometric aspects of dibaryon operators

    CERN Document Server

    Beil, Charlie

    2008-01-01

    The AdS/CFT correspondence for N=1 Super conformal field theories suggests that dibaryon operators are dual to D-brane states that are point like in AdS and that wrap various cycles in a Sasaki-Einstein manifold. It also suggests that the volume of the D-brane gives the R-charge of the corresponding operator. We elucidate various aspects of this correspondence, paying particular care to study the case of branes at the tip of three different Calabi Yau cones. We show that the arrows in the quiver diagram describing the conformal field theory can be thought of as global sections of a non-trivial holomorphic vector bundle over the Calabi-Yau geometry. We suggest that the zero locus of these sections gives the geometric map that lets us tie a particular dibaryon to a holomorphic cycle, by intersecting the corresponding cycle with the Sasaki-Einstein locus at fixed distance from the origin. We show that this can be compared with the corresponding volumes of the Sasaki-Einstein space and that one gets exact agreeme...

  5. Geometric Reasoning for Automated Planning

    Science.gov (United States)

    Clement, Bradley J.; Knight, Russell L.; Broderick, Daniel

    2012-01-01

    An important aspect of mission planning for NASA s operation of the International Space Station is the allocation and management of space for supplies and equipment. The Stowage, Configuration Analysis, and Operations Planning teams collaborate to perform the bulk of that planning. A Geometric Reasoning Engine is developed in a way that can be shared by the teams to optimize item placement in the context of crew planning. The ISS crew spends (at the time of this writing) a third or more of their time moving supplies and equipment around. Better logistical support and optimized packing could make a significant impact on operational efficiency of the ISS. Currently, computational geometry and motion planning do not focus specifically on the optimized orientation and placement of 3D objects based on multiple distance and containment preferences and constraints. The software performs reasoning about the manipulation of 3D solid models in order to maximize an objective function based on distance. It optimizes for 3D orientation and placement. Spatial placement optimization is a general problem and can be applied to object packing or asset relocation.

  6. Simulating geometrically complex blast scenarios

    Directory of Open Access Journals (Sweden)

    Ian G. Cullis

    2016-04-01

    Full Text Available The effects of blast waves generated by energetic and non-energetic sources are of continuing interest to the ballistics research community. Modern conflicts are increasingly characterised by asymmetric urban warfare, with improvised explosive devices (IEDs often playing a dominant role on the one hand and an armed forces requirement for minimal collateral effects from their weapons on the other. These problems are characterised by disparate length- and time-scales and may also be governed by complex physics. There is thus an increasing need to be able to rapidly assess and accurately predict the effects of energetic blast in topologically complex scenarios. To this end, this paper presents a new QinetiQ-developed advanced computational package called EAGLE-Blast, which is capable of accurately resolving the generation, propagation and interaction of blast waves around geometrically complex shapes such as vehicles and buildings. After a brief description of the numerical methodology, various blast scenario simulations are described and the results compared with experimental data to demonstrate the validation of the scheme and its ability to describe these complex scenarios accurately and efficiently. The paper concludes with a brief discussion on the use of the code in supporting the development of algorithms for fast running engineering models.

  7. Geometrical aspects of quantum spaces

    International Nuclear Information System (INIS)

    Various geometrical aspects of quantum spaces are presented showing the possibility of building physics on quantum spaces. In the first chapter the authors give the motivations for studying noncommutative geometry and also review the definition of a Hopf algebra and some general features of the differential geometry on quantum groups and quantum planes. In Chapter 2 and Chapter 3 the noncommutative version of differential calculus, integration and complex structure are established for the quantum sphere S12 and the quantum complex projective space CPq(N), on which there are quantum group symmetries that are represented nonlinearly, and are respected by all the aforementioned structures. The braiding of Sq2 and CPq(N) is also described. In Chapter 4 the quantum projective geometry over the quantum projective space CPq(N) is developed. Collinearity conditions, coplanarity conditions, intersections and anharmonic ratios is described. In Chapter 5 an algebraic formulation of Reimannian geometry on quantum spaces is presented where Riemannian metric, distance, Laplacian, connection, and curvature have their quantum counterparts. This attempt is also extended to complex manifolds. Examples include the quantum sphere, the complex quantum projective space and the two-sheeted space. The quantum group of general coordinate transformations on some quantum spaces is also given

  8. Geometrical aspects of quantum spaces

    Energy Technology Data Exchange (ETDEWEB)

    Ho, P.M. [Lawrence Berkeley Lab., CA (United States). Theoretical Physics Group

    1996-05-11

    Various geometrical aspects of quantum spaces are presented showing the possibility of building physics on quantum spaces. In the first chapter the authors give the motivations for studying noncommutative geometry and also review the definition of a Hopf algebra and some general features of the differential geometry on quantum groups and quantum planes. In Chapter 2 and Chapter 3 the noncommutative version of differential calculus, integration and complex structure are established for the quantum sphere S{sub 1}{sup 2} and the quantum complex projective space CP{sub q}(N), on which there are quantum group symmetries that are represented nonlinearly, and are respected by all the aforementioned structures. The braiding of S{sub q}{sup 2} and CP{sub q}(N) is also described. In Chapter 4 the quantum projective geometry over the quantum projective space CP{sub q}(N) is developed. Collinearity conditions, coplanarity conditions, intersections and anharmonic ratios is described. In Chapter 5 an algebraic formulation of Reimannian geometry on quantum spaces is presented where Riemannian metric, distance, Laplacian, connection, and curvature have their quantum counterparts. This attempt is also extended to complex manifolds. Examples include the quantum sphere, the complex quantum projective space and the two-sheeted space. The quantum group of general coordinate transformations on some quantum spaces is also given.

  9. Simulating geometrically complex blast scenarios

    Institute of Scientific and Technical Information of China (English)

    Ian G. CULLIS; Nikos NIKIFORAKIS; Peter FRANKL; Philip BLAKELY; Paul BENNETT; Paul GREENWOOD

    2016-01-01

    The effects of blast waves generated by energetic and non-energetic sources are of continuing interest to the ballistics research community. Modern conflicts are increasingly characterised by asymmetric urban warfare, with improvised explosive devices (IEDs) often playing a dominant role on the one hand and an armed forces requirement for minimal collateral effects from their weapons on the other. These problems are characterised by disparate length-and time-scales and may also be governed by complex physics. There is thus an increasing need to be able to rapidly assess and accurately predict the effects of energetic blast in topologically complex scenarios. To this end, this paper presents a new QinetiQ-developed advanced computational package called EAGLE-Blast, which is capable of accurately resolving the generation, propagation and interaction of blast waves around geometrically complex shapes such as vehicles and buildings. After a brief description of the numerical methodology, various blast scenario simulations are described and the results compared with experimental data to demonstrate the validation of the scheme and its ability to describe these complex scenarios accurately and efficiently. The paper concludes with a brief discussion on the use of the code in supporting the development of algorithms for fast running engineering models.

  10. The geometric semantics of algebraic quantum mechanics.

    Science.gov (United States)

    Cruz Morales, John Alexander; Zilber, Boris

    2015-08-01

    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. PMID:26124252

  11. 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...

  12. On the Geometric Transformations and Auxetic Materials

    Directory of Open Access Journals (Sweden)

    Veturia Chiroiu

    2011-09-01

    Full Text Available A new approach to obtain various architectures for auxetic foams by using the property of Helmholtz equation to be invariant under geometric transformations is described in this paper. The versatility of the geometric transformations is illustrated in order to obtain the auxetic version from the conventional foam.

  13. On children's images and geometrical literacy

    Czech Academy of Sciences Publication Activity Database

    Kuřina, F.; Tichá, Marie; Hošpesová, A.

    Rzeszow : Wydawnictwo Universytetu Rzieszowkiego, 2009, s. 53-64. ISBN 978-83-7338-473-6 R&D Projects: GA ČR(CZ) GA406/08/0710 Institutional research plan: CEZ:AV0Z10190503 Keywords : mathematical education * 6-years old children * geometrical images * geometrical literacy Subject RIV: AM - Education

  14. 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.

  15. On geometric Langlands theory and stacks

    NARCIS (Netherlands)

    Poirier, Cécile Florence Christine

    2008-01-01

    R.Langlands conjectured the existence of a bridge between two parts of number theory. This correspondence, called 'Langlands conjecture' was proved by L. Lafforgue who obtained a Fields medal for his work. G. Laumon gave a geometric translation of a part of the theorem, called 'geometric Langlands c

  16. Geometrical splitting and reduction of Feynman diagrams

    CERN Document Server

    Davydychev, Andrei I

    2016-01-01

    A geometrical approach to the calculation of N-point Feynman diagrams is reviewed. It is shown that the geometrical splitting yields useful connections between Feynman integrals with different momenta and masses. It is demonstrated how these results can be used to reduce the number of variables in the occurring functions.

  17. Geometric configuration in robot kinematic design

    OpenAIRE

    Rooney, Joe

    2006-01-01

    A lattice of geometries is presented and compared for representing some geometrical aspects of the kinematic design of robot systems and subsystems. Three geometries (set theory, topology and projective geometry) are briefly explored in more detail in the context of three geometric configurations in robotics (robot groupings, robot connectivities and robot motion sensor patterns).

  18. Gaining Insights into Children's Geometric Knowledge

    Science.gov (United States)

    Mack, Nancy K.

    2007-01-01

    This article describes how research on children's geometric thinking was used in conjunction with the picture book "The Greedy Triangle" to gain valuable insights into children's prior geometric knowledge of polygons. Exercises focused on the names, visual appearance, and properties of polygons, as well as real-world connections for each, are…

  19. 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

  20. Emergent Newtonian dynamics and the geometric origin of mass

    International Nuclear Information System (INIS)

    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

  1. Emergent Newtonian dynamics and the geometric origin of mass

    Energy Technology Data Exchange (ETDEWEB)

    D’Alessio, Luca, E-mail: dalessio@bu.edu [Department of Physics, The Pennsylvania State University, University Park, PA 16802 (United States); Physics Department, Boston University, Boston, MA 02215 (United States); Polkovnikov, Anatoli, E-mail: asp@bu.edu [Physics Department, Boston University, Boston, MA 02215 (United States)

    2014-06-15

    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.

  2. High Resolution Orthoimagery = Orthorectified Metro Areas: 2000 - Present

    Data.gov (United States)

    U.S. Geological Survey, Department of the Interior — High resolution orthorectified images combine the image characteristics of an aerial photograph with the geometric qualities of a map. An orthoimage is a...

  3. Does classical liberalism imply democracy?

    Directory of Open Access Journals (Sweden)

    David Ellerman

    2015-12-01

    Full Text Available There is a fault line running through classical liberalism as to whether or not democratic self-governance is a necessary part of a liberal social order. The democratic and non-democratic strains of classical liberalism are both present today—particularly in the United States. Many contemporary libertarians and neo-Austrian economists represent the non-democratic strain in their promotion of non-democratic sovereign city-states (start-up cities or charter cities. We will take the late James M. Buchanan as a representative of the democratic strain of classical liberalism. Since the fundamental norm of classical liberalism is consent, we must start with the intellectual history of the voluntary slavery contract, the coverture marriage contract, and the voluntary non-democratic constitution (or pactum subjectionis. Next we recover the theory of inalienable rights that descends from the Reformation doctrine of the inalienability of conscience through the Enlightenment (e.g. Spinoza and Hutcheson in the abolitionist and democratic movements. Consent-based governments divide into those based on the subjects’ alienation of power to a sovereign and those based on the citizens’ delegation of power to representatives. Inalienable rights theory rules out that alienation in favor of delegation, so the citizens remain the ultimate principals and the form of government is democratic. Thus the argument concludes in agreement with Buchanan that the classical liberal endorsement of sovereign individuals acting in the marketplace generalizes to the joint action of individuals as the principals in their own organizations.

  4. No Return to Classical Reality

    CERN Document Server

    Jennings, David

    2015-01-01

    At a fundamental level, the classical picture of the world is dead, and has been dead now for almost a century. Pinning down exactly which quantum phenomena are responsible for this has proved to be a tricky and controversial question, but a lot of progress has been made in the past few decades. We now have a range of precise statements showing that whatever the ultimate laws of Nature are, they cannot be classical. In this article, we review results on the fundamental phenomena of quantum theory that cannot be understood in classical terms. We proceed by first granting quite a broad notion of classicality, describe a range of quantum phenomena (such as randomness, discreteness, the indistinguishability of states, measurement-uncertainty, measurement-disturbance, complementarity, noncommutativity, interference, the no-cloning theorem, and the collapse of the wave-packet) that do fall under its liberal scope, and then finally describe some aspects of quantum physics that can never admit a classical understandi...

  5. A note on geometric method-based procedures to calculate the Hurst exponent

    Science.gov (United States)

    Trinidad Segovia, J. E.; Fernández-Martínez, M.; Sánchez-Granero, M. A.

    2012-03-01

    Geometric method-based procedures, which we will call GM algorithms hereafter, were introduced in M.A. Sánchez-Granero, J.E. Trinidad Segovia, J. García Pérez, Some comments on Hurst exponent and the long memory processes on capital markets, Phys. A 387 (2008) 5543-5551, to calculate the Hurst exponent of a time series. The authors proved that GM algorithms, based on a geometrical approach, are more accurate than classical algorithms, especially with short length time series. The main contribution of this paper is to provide a mathematical background for the validity of these two algorithms to calculate the Hurst exponent H of random processes with stationary and self-affine increments. In particular, we show that these procedures are valid not only for exploring long memory in classical processes such as (fractional) Brownian motions, but also for estimating the Hurst exponent of (fractional) Lévy stable motions.

  6. Lensless Fourier-Transform Ghost Imaging with Classical Incoherent Light

    CERN Document Server

    Zhang, M; Shen, X; Liu, Y; Liu, H; Cheng, J; Han, S; Zhang, Minghui; Wei, Qing; Shen, Xia; Liu, Yongfeng; Liu, Honglin; Cheng, Jing; Han, Shensheng

    2006-01-01

    The Fourier-Transform ghost imaging of both amplitude-only and pure-phase objects was experimentally observed with classical incoherent light at Fresnel distance by a new lensless scheme. The experimental results are in good agreement with the standard Fourier-transform of the corresponding objects. This scheme provides a new route towards aberration-free diffraction-limited 3D images with classically incoherent thermal light, which have no resolution and depth-of-field limitations of lens-based tomographic systems.

  7. Lensless Fourier-transform ghost imaging with classical incoherent light

    International Nuclear Information System (INIS)

    The Fourier-transform ghost imaging of both amplitude-only and pure-phase objects was experimentally observed with classical incoherent light at Fresnel distance by a lensless scheme. The experimental results are in good agreement with the standard Fourier transform of the corresponding objects. This scheme provides a route toward aberration-free diffraction-limited three-dimensional images with classically incoherent thermal light (or neutrons), which have no resolution and depth-of-field limitations of lens-based tomographic systems

  8. Elastic interactions between two-dimensional geometric defects.

    Science.gov (United States)

    Moshe, Michael; Sharon, Eran; Kupferman, Raz

    2015-12-01

    In this paper, we introduce a methodology applicable to a wide range of localized two-dimensional sources of stress. This methodology is based on a geometric formulation of elasticity. Localized sources of stress are viewed as singular defects-point charges of the curvature associated with a reference metric. The stress field in the presence of defects can be solved using a scalar stress function that generalizes the classical Airy stress function to the case of materials with nontrivial geometry. This approach allows the calculation of interaction energies between various types of defects. We apply our methodology to two physical systems: shear-induced failure of amorphous materials and the mechanical interaction between contracting cells. PMID:26764699

  9. The Grassmannian variety geometric and representation-theoretic aspects

    CERN Document Server

    Lakshmibai, V

    2015-01-01

    This book gives a comprehensive treatment of the Grassmannian varieties and their Schubert subvarieties, focusing on the geometric and representation-theoretic aspects of Grassmannian varieties. Research of Grassmannian varieties is centered at the crossroads of commutative algebra, algebraic geometry, representation theory, and combinatorics. Therefore, this  text uniquely presents an exciting playing field  for graduate students and researchers in mathematics, physics, and computer science, to expand their knowledge in the field of algebraic geometry. The standard monomial theory (SMT) for the Grassmannian varieties and their Schubert subvarieties are introduced and the text presents some important applications of SMT including the Cohen–Macaulay property, normality, unique factoriality, Gorenstein property, singular loci of Schubert varieties, toric degenerations of Schubert varieties, and the relationship between Schubert varieties and classical invariant theory. This text would serve well as a refere...

  10. Complex geometrical optics of Kerr type nonlinear media

    Science.gov (United States)

    Berczynski, P.; Kravtsov, Yu. A.; Sukhorukov, A. P.

    2010-03-01

    The paper generalizes paraxial complex geometrical optics (PCGO) for Gaussian beam (GB) propagation in nonlinear media of Kerr type. Ordinary differential equations for the beam amplitude and for complex curvature of the wave front are derived, which describe the evolution of axially symmetric GB in a Kerr type nonlinear medium. It is shown that PCGO readily provides the solutions of NLS equation obtained earlier from diffraction theory on the basis of the aberration-free approach. Besides reproducing classical results of self-focusing PCGO readily describes an influence of the initial curvature of the wave front on the beam evolution in a medium of Kerr type including a nonlinear graded-index fiber. The range of applicability of the PCGO theory is discussed as well which is helpful for avoiding nonphysical solutions.

  11. Remarks on the geometrical properties of semiclassically quantized strings

    CERN Document Server

    Forini, V; Griguolo, L; Seminara, D; Vescovi, E

    2015-01-01

    We discuss some geometrical aspects of the semiclassical quantization of string solutions in Type IIB Green-Schwarz action on $\\ads_5\\times \\sphere^5$. We concentrate on quadratic fluctuations around classical configurations, expressing the relevant differential operators in terms of (intrinsic and extrinsic) invariants of the background geometry. The aim of our exercises is to present some compact expressions encoding the spectral properties of bosonic and fermionic fluctuations. The appearing of non-trivial structures on the relevant bundles and their role in concrete computations are also considered. We corroborate the presentation of general formulas by working out explicitly a couple of relevant examples, namely the spinning string and the latitude BPS Wilson loop.

  12. Remarks on the geometrical properties of semiclassically quantized strings

    Science.gov (United States)

    Forini, V.; Puletti, V. Giangreco M.; Griguolo, L.; Seminara, D.; Vescovi, E.

    2015-11-01

    We discuss some geometrical aspects of the semiclassical quantization of string solutions in type IIB Green-Schwarz action on {{{AdS}}}5× {{{S}}}5. We concentrate on quadratic fluctuations around classical configurations, expressing the relevant differential operators in terms of (intrinsic and extrinsic) invariants of the background geometry. The aim of our exercise is to present some compact expressions encoding the spectral properties of bosonic and fermionic fluctuations. The appearing of non-trivial structures on the relevant bundles and their role in concrete computations are also considered. We corroborate the presentation of general formulas by working out explicitly a couple of relevant examples, namely the spinning string and the latitude BPS Wilson loop.

  13. From Newton's Universal Gravitation to Einstein's Geometric Theory of Gravity

    CERN Document Server

    Kobe, Donald H

    2013-01-01

    Starting with Newton's law of universal gravitation, we generalize it step-by-step to obtain Einstein's geometric theory of gravity. Newton's gravitational potential satisfies the Poisson equation. We relate the potential to a component of the metric tensor by equating the nonrelativistic result of the principle of stationary proper time to the Lagrangian for a classical gravitational field. In the Poisson equation the Laplacian of the component of the metric tensor is generalized to a cyclic linear combination of the second derivatives of the metric tensor. In local coordinates it is a single component of the Ricci tensor. This component of the Ricci tensor is proportional to the mass density that is related to a single component of the energy-momentum stress tensor and its trace. We thus obtain a single component of Einstein's gravitational field equation in local coordinates. From the principle of general covariance applied to a single component, we obtain all tensor components of Einstein's gravitational ...

  14. Geometric Backreaction of Modified Quantum Vacua and Diffeomorphrisim Covarience

    CERN Document Server

    Asfar, L A Al; Mahroussah, A

    2015-01-01

    In this paper we have shown that squeezed modified quantum vacua have an effect on the background geometry by solving the semi-classical Einstein Field Equations in modified vacuum. The resultant geometry is similar to (anti) de Sitter spacetime. This geometry could explain the change of causal structure - speed of light- in such vacua without violating diffeomorphism covariance or causality.The superluminal propagation of photons in Casimir vacuum is deduced from the effective electromagnetic action in the resultant curved geometry. Singling between different vacua is shown not to violate causality as well when the geometric effect on the null rays is considered, causing a refraction of those rays when travelling between unbounded and modified vacua.

  15. Differential Geometrically Consistent Artificial Viscosity in Comoving Curvilinear Coordinates

    CERN Document Server

    Höller, Harald; Dorfi, Ernst; Benger, Werner

    2013-01-01

    Context. High-resolution numerical methods have been developed for nonlinear, discontinuous problems as they appear in simulations of astrophysical objects. One of the strategies applied is the concept of artificial viscosity. Aims. Grid-based numerical simulations ideally utilize problem-oriented grids in order to minimize the necessary number of cells at a given (desired) spatial resolution. We want to propose a modified tensor of artificial viscosity which is employable for generally comoving, curvilinear grids. Methods. We study a differential geometrically consistent artificial viscosity analytically and visualize a comparison of our result to previous implementations by applying it to a simple self-similar velocity field. We give a general introduction to artificial viscosity first and motivate its application in numerical analysis. Then we present how a tensor of artificial viscosity has to be designed when going beyond common static Eulerian or Lagrangian comoving rectangular grids. Results. We find t...

  16. Classical isodual theory of antimatter

    CERN Document Server

    Santilli, R M

    1997-01-01

    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 treatments of matter and antimatter in due time, in this paper we present a classical representation of antimatter which begins at the primitive Newtonian level with expected images at all subsequent levels. By recalling that charge conjugation of particles into antiparticles is anti-automorphic, the proposed theory of antimatter is based on a new map, called isoduality, which is also anti-automorphic, yet it is applicable beginning at the classical level and then persists at the quantum level. As part of our study, we present novel anti-isomorphic isodual images of the Galilean, special and general relativities and show the compatibility of their representation of antimatter with all available classical experi...

  17. Casimir Effect The Classical Limit

    CERN Document Server

    Feinberg, J; Revzen, M

    2001-01-01

    We analyze the high temperature limit of the Casimir effect. A simple physical argument suggests that the Casimir energy (as opposed to the Casimir free energy) should vanish in the classical limit. We check the validity of this argument for massless scalar field confined in a cavity with boundaries of arbitrary shape, using path integral formalism. We are able to verify this suggestion only when the boundaries consist of disjoint pieces. Moreover, we find in these cases that the contribution to the Casimir entropy by field modes that depend on that separation, tends, in the classical limit, to a finite asymptotic value which depends only on the geometry of the cavity. Thus the Casimir force between disjoint pieces of the boundary in the classical limit is entropy driven and is governed by a dimensionless number characterizing the arbitrary geometry of the cavity. Contributions to the Casimir thermodynamical quantities due to each individual connected component of the boundary exhibit logarithmic deviations i...

  18. Population in the classic economics

    Directory of Open Access Journals (Sweden)

    Adnan Doğruyol

    2013-02-01

    Full Text Available Growth subject in economics is an important factor of development. Classic economics ecole indicates the population as main variable which tender of growth. On the other hand T. R. Malthus is known as economist who regards population as a problem and brings up it among the classical economists. However, Adam Smith is an intellectual who discussed population problem earlier on the classic economics theory. According to Adam Smith one of the main factors that realise the growth is labour. In addition to population made it established. The aim of this study is analyzing the mental relationship between Malthus whose name has been identified with relation between population-growth and Smith who discussed this subject first time but put it off on process of theorisation.

  19. A wave-optics approach to paraxial geometrical laws based on continuity at boundaries

    Science.gov (United States)

    Liñares, J.; Nistal, M. C.

    2011-09-01

    We present a derivation of the paraxial geometrical laws starting from a wave-optics approach, in particular by using simple continuity conditions of paraxial spherical waves at boundaries (discontinuities) between optical media. Paraxial geometrical imaging and magnification laws, under refraction and reflection at boundaries, are derived for several instructive cases and without using Fresnel diffraction theory. The primary aim is to provide a complementary insight into the standard axiomatic approach of paraxial geometrical optics and likewise to allow the introduction of some wave imaging concepts, such as the transmittance function, with a notable didactic interest for advanced subjects such as Fourier optics. This approach provides a more homogeneous vision of classical optics in which the use of the optical field continuity conditions at a boundary is a usual requirement as is clearly seen, for example, in the case of the derivation of Fresnel formulas. The work is particularly intended for university physics teachers and pregraduate and first year postgraduate students.

  20. Geometric optics of Bloch waves in a chiral and dissipative medium

    International Nuclear Information System (INIS)

    We present a geometric optics theory for the transport of quantum particles (or classical waves) in a chiral and dissipative periodic crystal subject to slowly varying perturbations in space and time. Taking account of some properties of particles and media neglected in previous theory, we find important additional terms in the equations of motion of particles. The (energy) current density field, which traces the geometric optics rays, is not only governed by the Bloch band energy dispersion but also involves there additional fields. These are the angular momentum of the particle, the dissipation dipole density, and various geometric gauge fields in the extended phase space spanned by space time and its reciprocal, momentum, and frequency. For simplicity, the theory is presented using light propagation in photonic crystals.

  1. Correspondence between geometrical and differential definitions of the sine and cosine functions and connection with kinematics

    CERN Document Server

    Petrache, Horia I

    2011-01-01

    In classical physics, the familiar sine and cosine functions appear in two forms: (1) geometrical, in the treatment of vectors such as forces and velocities, and (2) differential, as solutions of oscillation and wave equations. These two forms correspond to two different definitions of trigonometric functions, one geometrical using right triangles and unit circles, and the other employing differential equations. Although the two definitions must be equivalent, this equivalence is not demonstrated in textbooks. In this manuscript, the equivalence between the geometrical and the differential definition is presented assuming no a priori knowledge of the properties of sine and cosine functions. We start with the usual length projections on the unit circle and use elementary geometry and elementary calculus to arrive to harmonic differential equations. This more general and abstract treatment not only reveals the equivalence of the two definitions but also provides an instructive perspective on circular and harmon...

  2. 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.

  3. Information Geometry in Time Dependent Quantum Systems and the Geometric Phase

    OpenAIRE

    Dey, Anshuman; Paul, Suvankar; Roy, Pratim; Sarkar, Tapobrata(Department of Physics, Indian Institute of Technology, Kanpur, 208016, India)

    2016-01-01

    We study information theoretic geometry in time dependent quantum mechanical systems. First, we discuss global properties of the parameter manifold for two level systems exemplified by i) Rabi oscillations and ii) quenching dynamics of the XY spin chain in a transverse magnetic field, when driven across anisotropic criticality. Next, we comment upon the nature of the geometric phase from classical holonomy analyses of such parameter manifolds. In the context of the transverse XY model in the ...

  4. A New Training Method for Feedforward Neural Networks Based on Geometric Contraction Property of Activation Functions

    OpenAIRE

    Birtea, Petre; Cernazanu-Glavan, Cosmin; Sisu, Alexandru

    2016-01-01

    We propose a new training method for a feedforward neural network having the activation functions with the geometric contraction property. The method consists of constructing a new functional that is less nonlinear in comparison with the classical functional by removing the nonlinearity of the activation functions from the output layer. We validate this new method by a series of experiments that show an improved learning speed and also a better classification error.

  5. Geometric descriptors of road surface texture in relation to tire/road noise

    OpenAIRE

    ANFOSSO, Fabienne; Do, Minh Tan

    2002-01-01

    The paper deals with the determination of geometric parameters in order to study the relationship between the tire/road noise and the texture of road surfaces. The approach was found to be an alternative to the classical spectral analyses and the numerical simulations of the tire/road contact. Texture parameters were derived from previous works in LCPC related to the influence of the microtexture of road surfaces on the skid resistance. Use of these parameters was justified by the considerati...

  6. Seismic noise filters, vertical resonance frequency reduction with geometric anti-springs: a feasibility study

    International Nuclear Information System (INIS)

    The achievement of low resonance frequency in vertical action oscillators is the most difficult of the basic ingredients for seismic noise attenuation filters. These oscillations are achieved by means of 'anti-springs' systems coupled with more classical suspension springs. Magnetic anti-springs have been used so far. Geometric anti-springs have been studied and the concept tested in this work, opening the way to a simpler and better performance seismic attenuation filters. (author)

  7. Assessing the morphological variability of Unio Delphinus spengler, 1783 (bivalvia : unionidae) using geometric morphometry

    OpenAIRE

    Morais, Pedro; Rufino, Marta M.; Reis, Joaquim; Dias, Ester; Sousa, Ronaldo Gomes

    2014-01-01

    The morphological variability of freshwater bivalve species, observed between and within river basins, may hamper their correct identification, even by experienced researchers. Classic morphometric measurements, i.e. shell length, height and thickness, or their ratios, are generally insufficient to distinguish populations and/or species. These issues may be overcome using a geometric morphometric method, which allows analysis of the overall shape of the individual, independently o...

  8. Comparing classical and quantum equilibration

    CERN Document Server

    Malabarba, Artur S L; Short, Anthony J

    2016-01-01

    By using a physically-relevant and theory independent definition of measurement-based equilibration, we show quantitatively that equilibration is easier for quantum systems than for classical systems, in the situation where the initial state of the system is completely known (pure state). This shows that quantum equilibration is a fundamental, nigh unavoidable, aspect of physical systems, while classical equilibration relies on experimental ignorance. When the state is not completely known, a mixed state, this framework also shows quantum equilibration requires weaker conditions.

  9. Classical planning and causal implicatures

    DEFF Research Database (Denmark)

    Blackburn, Patrick Rowan; Benotti, Luciana

    In this paper we motivate and describe a dialogue manager (called Frolog) which uses classical planning to infer causal implicatures. A causal implicature is a type of Gricean relation implicature, a highly context dependent form of inference. As we shall see, causal implicatures are important for...... generate clarification requests"; as a result we can model task-oriented dialogue as an interactive process locally structured by negotiation of the underlying task. We give several examples of Frolog-human dialog, discuss the limitations imposed by the classical planning paradigm, and indicate the...

  10. Classical analogy of Fano resonances

    International Nuclear Information System (INIS)

    We present an analogy of Fano resonances in quantum interference to classical resonances in the harmonic oscillator system. It has a manifestation as a coupled behaviour of two effective oscillators associated with propagating and evanescent waves. We illustrate this point by considering a classical system of two coupled oscillators and interfering electron waves in a quasi-one-dimensional narrow constriction with a quantum dot. Our approach provides a novel insight into Fano resonance physics and provides a helpful view in teaching Fano resonances

  11. Conceptual aspects of geometric quantum computation

    Science.gov (United States)

    Sjöqvist, Erik; Azimi Mousolou, Vahid; Canali, Carlo M.

    2016-07-01

    Geometric quantum computation is the idea that geometric phases can be used to implement quantum gates, i.e., the basic elements of the Boolean network that forms a quantum computer. Although originally thought to be limited to adiabatic evolution, controlled by slowly changing parameters, this form of quantum computation can as well be realized at high speed by using nonadiabatic schemes. Recent advances in quantum gate technology have allowed for experimental demonstrations of different types of geometric gates in adiabatic and nonadiabatic evolution. Here, we address some conceptual issues that arise in the realizations of geometric gates. We examine the appearance of dynamical phases in quantum evolution and point out that not all dynamical phases need to be compensated for in geometric quantum computation. We delineate the relation between Abelian and non-Abelian geometric gates and find an explicit physical example where the two types of gates coincide. We identify differences and similarities between adiabatic and nonadiabatic realizations of quantum computation based on non-Abelian geometric phases.

  12. Geometric quantum discord under noisy environment

    Science.gov (United States)

    Huang, Zhiming; Qiu, Daowen

    2016-05-01

    In this work, we mainly analyze the dynamics of geometric quantum discord under a common dissipating environment. Our results indicate that geometric quantum discord is generated when the initial state is a product state. The geometric quantum discord increases from zero to a stable value with the increasing time, and the variations of stable values depend on the system size. For different initial product states, geometric quantum discord has some different behaviors in contrast with entanglement. For initial maximally entangled state, it is shown that geometric quantum discord decays with the increasing dissipated time. It is found that for EPR state, entanglement is more robust than geometric quantum discord, which is a sharp contrast to the existing result that quantum discord is more robust than entanglement in noisy environments. However, for GHZ state and W state, geometric quantum discord is more stable than entanglement. By the comparison of quantum discord and entanglement, we find that a common dissipating environment brings complicated effects on quantum correlation, which may deepen our understanding of physical impacts of decohering environment on quantum correlation. In the end, we analyze the effects of collective dephasing noise and rotating noise to a class of two-qubit X states, and we find that quantum correlation is not altered by the collective noises.

  13. Geometric programming, chemical equilibrium, and the anti-entropy function.

    Science.gov (United States)

    Duffin, R J; Zener, C

    1969-07-01

    THE CULMINATION OF THIS PAPER IS THE FOLLOWING DUALITY PRINCIPLE OF THERMODYNAMICS: maximum S = minimum S(*). (1) The left side of relation (1) is the classical characterization of equilibrium. It says to maximize the entropy function S with respect to extensive variables which are subject to certain constraints. The right side of (1) is a new characterization of equilibrium and concerns minimization of an anti-entropy function S(*) with respect to intensive variables. Relation (1) is applied to the chemical equilibrium of a mixture of gases at constant temperature and volume. Then (1) specializes to minimum F = maximum F(*), (2) where F is the Helmholtz function for free energy and F(*) is an anti-Helmholtz function. The right-side of (2) is an unconstrained maximization problem and gives a simplified practical procedure for calculating equilibrium concentrations. We also give a direct proof of (2) by the duality theorem of geometric programming. The duality theorem of geometric programming states that minimum cost = maximum anti-cost. (30). PMID:16591769

  14. A Geometric Characterization of Arithmetic Varieties

    Indian Academy of Sciences (India)

    Kapil Hari Paranjape

    2002-08-01

    A result of Belyi can be stated as follows. Every curve defined over a number field can be expressed as a cover of the projective line with branch locus contained in a rigid divisor. We define the notion of geometrically rigid divisors in surfaces and then show that every surface defined over a number field can be expressed as a cover of the projective plane with branch locus contained in a geometrically rigid divisor in the plane. The main result is the characterization of arithmetically defined divisors in the plane as geometrically rigid divisors in the plane.

  15. Variance optimal stopping for geometric Levy processes

    DEFF Research Database (Denmark)

    Gad, Kamille Sofie Tågholt; Pedersen, Jesper Lund

    2015-01-01

    The main result of this paper is the solution to the optimal stopping problem of maximizing the variance of a geometric Lévy process. We call this problem the variance problem. We show that, for some geometric Lévy processes, we achieve higher variances by allowing randomized stopping. Furthermore......, for some geometric Lévy processes, the problem has a solution only if randomized stopping is allowed. When randomized stopping is allowed, we give a solution to the variance problem. We identify the Lévy processes for which the allowance of randomized stopping times increases the maximum variance....... When it does, we also solve the variance problem without randomized stopping....

  16. Noncyclic geometric phase for neutrino oscillation

    CERN Document Server

    Wang, X B; Liu, Y; Oh, C H; Wang, Xiang-Bin; Liu, Yong

    2001-01-01

    We provide explicit formulae for the noncyclic geometric phases or Pancharatnam phases of neutrino oscillations. Since Pancharatnam phase is a generalization of the Berry phase, our results generalize the previous findings for Berry phase in a recent paper [Phys. Lett. B, 466 (1999) 262]. Unlike the Berry phase, the noncyclic geometric phase offers distinctive advantage in terms of measurement and prediction. In particular, for three-flavor mixing, our explicit formula offers an alternative means of determining the CP-violating phase. Our results can also be extended easily to explore geometric phase associated with neutron-antineutron oscillations.

  17. A Geometrical View of Higgs Effective Theory

    CERN Document Server

    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.

  18. CLASSIC APPROACH TO BUSINESS COACHING

    OpenAIRE

    Żukowska, Joanna

    2011-01-01

    The purpose of this paper is to present business coaching in a classical way. An overview of coaching definitions will be provided. Attention will be drawn to coaching components and varieties. Moreover, a brief description of coach competences and tools supporting their work will be offered. Joanna Żukowska

  19. Identity from classical invariant theory

    International Nuclear Information System (INIS)

    A simple derivation is given of a well-known relation involving the so-called Cayley Operator of classical invariant theory. The proof is induction-free and independent of Capelli's identity; it makes use only of a known-theorem in the theory of determinants and some elementary combinatorics

  20. On classical and quantum liftings

    OpenAIRE

    Accardi, L.; Chruściński, Dariusz; Kossakowski, Andrzej; Matsuoka, T.; Ohya, Masanori

    2011-01-01

    We analyze the procedure of lifting in classical stochastic and quantum systems. It enables one to `lift' a state of a system into a state of `system+reservoir'. This procedure is important both in quantum information theory and the theory of open systems. We illustrate the general theory of liftings by a particular class related to so called circulant states.

  1. Classical Virasoro irregular conformal block

    CERN Document Server

    Rim, Chaiho

    2015-01-01

    Virasoro irregular conformal block with arbitrary rank is obtained for the classical limit or equivalently Nekrasov-Shatashvili limit using the beta-deformed irregular matrix model (Penner-type matrix model for the irregular conformal block). The same result is derived using the generalized Mathieu equation which is equivalent to the loop equation of the irregular matrix model.

  2. Teaching Classical Mechanics Using Smartphones

    Science.gov (United States)

    Chevrier, Joel; Madani, Laya; Ledenmat, Simon; Bsiesy, Ahmad

    2013-01-01

    A number of articles published in this column have dealt with topics in classical mechanics. This note describes some additional examples employing a smartphone and the new software iMecaProf. Steve Jobs presented the iPhone as "perfect for gaming." Thanks to its microsensors connected in real time to the numerical world, physics…

  3. Classical Music as Enforced Utopia

    Science.gov (United States)

    Leech-Wilkinson, Daniel

    2016-01-01

    In classical music composition, whatever thematic or harmonic conflicts may be engineered along the way, everything always turns out for the best. Similar utopian thinking underlies performance: performers see their job as faithfully carrying out their master's (the composer's) wishes. The more perfectly they represent them, the happier the…

  4. Measurement-Based Classical Computation

    Science.gov (United States)

    Hoban, Matty J.; Wallman, Joel J.; Anwar, Hussain; Usher, Naïri; Raussendorf, Robert; Browne, Dan E.

    2014-04-01

    Measurement-based quantum computation (MBQC) is a model of quantum computation, in which computation proceeds via adaptive single qubit measurements on a multiqubit quantum state. It is computationally equivalent to the circuit model. Unlike the circuit model, however, its classical analog is little studied. Here we present a classical analog of MBQC whose computational complexity presents a rich structure. To do so, we identify uniform families of quantum computations [refining the circuits introduced by Bremner et al. Proc. R. Soc. A 467, 459 (2010)] whose output is likely hard to exactly simulate (sample) classically. We demonstrate that these circuit families can be efficiently implemented in the MBQC model without adaptive measurement and, thus, can be achieved in a classical analog of MBQC whose resource state is a probability distribution which has been created quantum mechanically. Such states (by definition) violate no Bell inequality, but, if widely held beliefs about computational complexity are true, they, nevertheless, exhibit nonclassicality when used as a computational resource—an imprint of their quantum origin.

  5. Invariants in Supersymmetric Classical Mechanics

    OpenAIRE

    Alonso Izquierdo, Alberto; González León, Miguel Ángel; Mateos Guilarte, Juan

    2000-01-01

    [EN] The bosonic second invariant of SuperLiouville models in supersymmetric classical mechanics is described. [ES] El segundo campo cuántico de bosones invariante del modelo SuperLiouville es descrito en la mecanica clasica supersimétrica.

  6. Quantum Proofs for Classical Theorems

    OpenAIRE

    Drucker, A.; Wolf,

    2009-01-01

    Alongside the development of quantum algorithms and quantum complexity theory in recent years, quantum techniques have also proved instrumental in obtaining results in classical (non-quantum) areas. In this paper we survey these results and the quantum toolbox they use.

  7. Agglomeration Economies in Classical Music

    DEFF Research Database (Denmark)

    Borowiecki, Karol Jan

    2015-01-01

    This study investigates agglomeration effects for classical music production in a wide range of cities for a global sample of composers born between 1750 and 1899. Theory suggests a trade-off between agglomeration economies (peer effects) and diseconomies (peer crowding). I test this hypothesis...

  8. Neo-classical impurity transport

    International Nuclear Information System (INIS)

    The neo-classical theory for impurity transport in a toroidal plasma is outlined, and the results discussed. A general account is given of the impurity behaviour and its dependence on collisionality. The underlying physics is described with special attention to the role of the poloidal rotation

  9. On Classical and Quantum Cryptography

    OpenAIRE

    I. V. Volovich; Volovich, Ya. I.

    2001-01-01

    Lectures on classical and quantum cryptography. Contents: Private key cryptosystems. Elements of number theory. Public key cryptography and RSA cryptosystem. Shannon`s entropy and mutual information. Entropic uncertainty relations. The no cloning theorem. The BB84 quantum cryptographic protocol. Security proofs. Bell`s theorem. The EPRBE quantum cryptographic protocol.

  10. Supersymmetric classical mechanics: free case

    International Nuclear Information System (INIS)

    We present a review work on Supersymmetric Classical Mechanics in the context of a Lagrangian formalism, with N = 1-supersymmetry. We show that the N = 1 supersymmetry does not allow the introduction of a potencial energy term depending on a single commuting supercoordinate, φ(t;Θ). (author)

  11. Study on the Grey Polynomial Geometric Programming

    Institute of Scientific and Technical Information of China (English)

    LUODang

    2005-01-01

    In the model of geometric programming, values of parameters cannot be gotten owing to data fluctuation and incompletion. But reasonable bounds of these parameters can be attained. This is to say, parameters of this model can be regarded as interval grey numbers. When the model contains grey numbers, it is hard for common programming method to solve them. By combining the common programming model with the grey system theory,and using some analysis strategies, a model of grey polynomial geometric programming, a model of 8 positioned geometric programming and their quasi-optimum solution or optimum solution are put forward. At the same time, we also developed an algorithm for the problem.This approach brings a new way for the application research of geometric programming. An example at the end of this paper shows the rationality and feasibility of the algorithm.

  12. The geometric genus of hypersurface singularities

    OpenAIRE

    Andras Nemethi; Baldur Sigurdsson

    2014-01-01

    Using the path lattice cohomology we provide a conceptual topological characterization of the geometric genus for certain complex normal surface singularities with rational homology sphere links, which is uniformly valid for all superisolated and Newton non--degenerate hypersurface singularities.

  13. Surgical correction of gynecomastia: a geometric approach.

    Science.gov (United States)

    Martin, Antony E; Olinger, Thomas A; Yu, Jack C

    2015-05-01

    Many techniques are available for surgical correction of gynecomastia. In this article, we describe a technique based on geometrical principles that is simple to execute, effective, highly reproducible, and relies less on intuition of the surgeon. PMID:25919255

  14. 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

  15. Quantum nonlocality, and the end of classical space-time

    CERN Document Server

    Banerjee, Shreya; Singh, T P

    2016-01-01

    Quantum non-local correlations and the acausal, spooky action at a distance suggest a discord between quantum theory and special relativity. We propose a resolution for this discord by first observing that there is a problem of time in quantum theory. There should exist a reformulation of quantum theory which does not refer to classical time. Such a reformulation is obtained by suggesting that space-time is fundamentally non-commutative. Quantum theory without classical time is the equilibrium statistical thermodynamics of the underlying non-commutative relativity. Stochastic fluctuations about equilibrium give rise to the classical limit and ordinary space-time geometry. However, measurement on an entangled state can be correctly described only in the underlying non-commutative space-time, where there is no causality violation, nor a spooky action at a distance.

  16. Geodesic active fields--a geometric framework for image registration.

    Science.gov (United States)

    Zosso, Dominique; Bresson, Xavier; Thiran, Jean-Philippe

    2011-05-01

    In this paper we present a novel geometric framework called geodesic active fields for general image registration. In image registration, one looks for the underlying deformation field that best maps one image onto another. This is a classic ill-posed inverse problem, which is usually solved by adding a regularization term. Here, we propose a multiplicative coupling between the registration term and the regularization term, which turns out to be equivalent to embed the deformation field in a weighted minimal surface problem. Then, the deformation field is driven by a minimization flow toward a harmonic map corresponding to the solution of the registration problem. This proposed approach for registration shares close similarities with the well-known geodesic active contours model in image segmentation, where the segmentation term (the edge detector function) is coupled with the regularization term (the length functional) via multiplication as well. As a matter of fact, our proposed geometric model is actually the exact mathematical generalization to vector fields of the weighted length problem for curves and surfaces introduced by Caselles-Kimmel-Sapiro. The energy of the deformation field is measured with the Polyakov energy weighted by a suitable image distance, borrowed from standard registration models. We investigate three different weighting functions, the squared error and the approximated absolute error for monomodal images, and the local joint entropy for multimodal images. As compared to specialized state-of-the-art methods tailored for specific applications, our geometric framework involves important contributions. Firstly, our general formulation for registration works on any parametrizable, smooth and differentiable surface, including nonflat and multiscale images. In the latter case, multiscale images are registered at all scales simultaneously, and the relations between space and scale are intrinsically being accounted for. Second, this method is, to

  17. Mechanisms of geometrical seismic attenuation

    Directory of Open Access Journals (Sweden)

    Igor B. Morozov

    2011-07-01

    Full Text Available In several recent reports, we have explained the frequency dependence of the apparent seismic quality-factor (Q observed in many studies according to the effects of geometrical attenuation, which was defined as the zero-frequency limit of the temporal attenuation coefficient. In particular, geometrical attenuation was found to be positive for most waves traveling within the lithosphere. Here, we present three theoretical models that illustrate the origin of this geometrical attenuation, and we investigate the causes of its preferential positive values. In addition, we discuss the physical basis and limitations of both the conventional and new attenuation models. For waves in media with slowly varying properties, geometrical attenuation is caused by variations in the wavefront curvature, which can be both positive (for defocusing and negative (for focusing. In media with velocity/density contrasts, incoherent reflectivity leads to geometrical-attenuation coefficients which are proportional to the mean squared reflectivity and are always positive. For «coherent» reflectivity, the geometrical attenuation is approximately zero, and the attenuation process can be described according to the concept of «scattering Q». However, the true meaning of this parameter is in describing the mean reflectivity within the medium, and not that of the traditional resonator quality factor known in mechanics. The general conclusion from these models is that non-zero and often positive levels of geometrical attenuation are common in realistic, heterogeneous media, both observationally and theoretically. When transformed into the conventional Q-factor form, this positive geometrical attenuation leads to Q values that quickly increase with frequency. These predictions show that the positive frequency-dependent Q observed in many datasets might represent artifacts of the transformations of the attenuation coefficients into Q.