Geometric correlations and multifractals
International Nuclear Information System (INIS)
Amritkar, R.E.
1991-07-01
There are many situations where the usual statistical methods are not adequate to characterize correlations in the system. To characterize such situations we introduce mutual correlation dimensions which describe geometric correlations in the system. These dimensions allow us to distinguish between variables which are perfectly correlated with or without a phase lag, variables which are uncorrelated and variables which are partially correlated. We demonstrate the utility of our formalism by considering two examples from dynamical systems. The first example is about the loss of memory in chaotic signals and describes auto-correlations while the second example is about synchronization of chaotic signals and describes cross-correlations. (author). 19 refs, 6 figs
Exact Solutions for Einstein's Hyperbolic Geometric Flow
International Nuclear Information System (INIS)
He Chunlei
2008-01-01
In this paper we investigate the Einstein's hyperbolic geometric flow and obtain some interesting exact solutions for this kind of flow. Many interesting properties of these exact solutions have also been analyzed and we believe that these properties of Einstein's hyperbolic geometric flow are very helpful to understanding the Einstein equations and the hyperbolic geometric flow
Geometrical and Graphical Solutions of Quadratic Equations.
Hornsby, E. John, Jr.
1990-01-01
Presented are several geometrical and graphical methods of solving quadratic equations. Discussed are Greek origins, Carlyle's method, von Staudt's method, fixed graph methods and imaginary solutions. (CW)
Geometrical optics in correlated imaging systems
International Nuclear Information System (INIS)
Cao Dezhong; Xiong Jun; Wang Kaige
2005-01-01
We discuss the geometrical optics of correlated imaging for two kinds of spatial correlations corresponding, respectively, to a classical thermal light source and a quantum two-photon entangled source. Due to the different features in the second-order spatial correlation, the two sources obey different imaging equations. The quantum entangled source behaves as a mirror, whereas the classical thermal source looks like a phase-conjugate mirror in the correlated imaging
Mezzasalma, Stefano A
2007-12-04
A special theory of Brownian relativity was previously proposed to describe the universal picture arising in ideal polymer solutions. In brief, it redefines a Gaussian macromolecule in a 4-dimensional diffusive spacetime, establishing a (weak) Lorentz-Poincaré invariance between liquid and polymer Einstein's laws for Brownian movement. Here, aimed at inquiring into the effect of correlations, we deepen the extension of the special theory to a general formulation. The previous statistical equivalence, for dynamic trajectories of liquid molecules and static configurations of macromolecules, and rather obvious in uncorrelated systems, is enlarged by a more general principle of equivalence, for configurational statistics and geometrodynamics. Accordingly, the three geodesic motion, continuity, and field equations could be rewritten, and a number of scaling behaviors were recovered in a spacetime endowed with general static isotropic metric (i.e., for equilibrium polymer solutions). We also dealt with universality in the volume fraction and, unexpectedly, found that a hyperscaling relation of the form, (average size) x (diffusivity) x (viscosity)1/2 ~f(N0, phi0) is fulfilled in several regimes, both in the chain monomer number (N) and polymer volume fraction (phi). Entangled macromolecular dynamics was treated as a geodesic light deflection, entaglements acting in close analogy to the field generated by a spherically symmetric mass source, where length fluctuations of the chain primitive path behave as azimuth fluctuations of its shape. Finally, the general transformation rule for translational and diffusive frames gives a coordinate gauge invariance, suggesting a widened Lorentz-Poincaré symmetry for Brownian statistics. We expect this approach to find effective applications to solutions of arbitrarily large molecules displaying a variety of structures, where the effect of geometry is more explicit and significant in itself (e.g., surfactants, lipids, proteins).
New Geometric-distortion Solution for STIS FUV-MAMA
Sohn, S. Tony
2018-04-01
We derived a new geometric distortion solution for the STIS FUV-MAMA detector. To do this, positions of stars in 89 FUV-MAMA observations of NGC 6681 were compared to an astrometric standard catalog created using WFC3/UVIS imaging data to derive a fourth-order polynomial solution that transforms raw (x, y) positions to geometrically- corrected (x, y) positions. When compared to astrometric catalog positions, the FUV- MAMA position measurements based on the IDCTAB showed residuals with an RMS of â¼ 30 mas in each coordinate. Using the new IDCTAB, the RMS is reduced to â¼ 4 mas, or 0.16 FUV-MAMA pixels, in each coordinate. The updated IDCTAB is now being used in the HST STIS pipeline to process all STIS FUV-MAMA images.
Interferometric constraints on quantum geometrical shear noise correlations
Energy Technology Data Exchange (ETDEWEB)
Chou, Aaron; Glass, Henry; Richard Gustafson, H.; Hogan, Craig J.; Kamai, Brittany L.; Kwon, Ohkyung; Lanza, Robert; McCuller, Lee; Meyer, Stephan S.; Richardson, Jonathan W.; Stoughton, Chris; Tomlin, Ray; Weiss, Rainer
2017-07-20
Final measurements and analysis are reported from the first-generation Holometer, the first instrument capable of measuring correlated variations in space-time position at strain noise power spectral densities smaller than a Planck time. The apparatus consists of two co-located, but independent and isolated, 40 m power-recycled Michelson interferometers, whose outputs are cross-correlated to 25 MHz. The data are sensitive to correlations of differential position across the apparatus over a broad band of frequencies up to and exceeding the inverse light crossing time, 7.6 MHz. By measuring with Planck precision the correlation of position variations at spacelike separations, the Holometer searches for faint, irreducible correlated position noise backgrounds predicted by some models of quantum space-time geometry. The first-generation optical layout is sensitive to quantum geometrical noise correlations with shear symmetry---those that can be interpreted as a fundamental noncommutativity of space-time position in orthogonal directions. General experimental constraints are placed on parameters of a set of models of spatial shear noise correlations, with a sensitivity that exceeds the Planck-scale holographic information bound on position states by a large factor. This result significantly extends the upper limits placed on models of directional noncommutativity by currently operating gravitational wave observatories.
Geometric evolution of complex networks with degree correlations
Murphy, Charles; Allard, Antoine; Laurence, Edward; St-Onge, Guillaume; Dubé, Louis J.
2018-03-01
We present a general class of geometric network growth mechanisms by homogeneous attachment in which the links created at a given time t are distributed homogeneously between a new node and the existing nodes selected uniformly. This is achieved by creating links between nodes uniformly distributed in a homogeneous metric space according to a Fermi-Dirac connection probability with inverse temperature β and general time-dependent chemical potential μ (t ) . The chemical potential limits the spatial extent of newly created links. Using a hidden variable framework, we obtain an analytical expression for the degree sequence and show that μ (t ) can be fixed to yield any given degree distributions, including a scale-free degree distribution. Additionally, we find that depending on the order in which nodes appear in the network—its history—the degree-degree correlations can be tuned to be assortative or disassortative. The effect of the geometry on the structure is investigated through the average clustering coefficient 〈c 〉 . In the thermodynamic limit, we identify a phase transition between a random regime where 〈c 〉→0 when β 0 when β >βc .
Geometrical Solutions of Some Quadratic Equations with Non-Real Roots
Pathak, H. K.; Grewal, A. S.
2002-01-01
This note gives geometrical/graphical methods of finding solutions of the quadratic equation ax[squared] + bx + c = 0, a [not equal to] 0, with non-real roots. Three different cases which give rise to non-real roots of the quadratic equation have been discussed. In case I a geometrical construction and its proof for finding the solutions of the…
Geometric Series: A New Solution to the Dog Problem
Dion, Peter; Ho, Anthony
2013-01-01
This article describes what is often referred to as the dog, beetle, mice, ant, or turtle problem. Solutions to this problem exist, some being variations of each other, which involve mathematics of a wide range of complexity. Herein, the authors describe the intuitive solution and the calculus solution and then offer a completely new solution…
Refraction at a curved dielectric interface - Geometrical optics solution
Lee, S.-W.; Sheshadri, M. S.; Mittra, R.; Jamnejad, V.
1982-01-01
The transmission of a spherical or plane wave through an arbitrarily curved dielectric interface is solved by the geometrical optics theory. The transmitted field is proportional to the product of the conventional Fresnel's transmission coefficient and a divergence factor (DF), which describes the cross-sectional variation (convergence or divergence) of a ray pencil as the latter propagates in the transmitted region. The factor DF depends on the incident wavefront, the curvatures of the interface, and the relative indices of the two media. Explicit matrix formulas for calculating DF are given, and its physical significance is illustrated via examples.
Geometric projection filter: an efficient solution to the SLAM problem
Newman, Paul M.; Durrant-Whyte, Hugh F.
2001-10-01
This paper is concerned with the simultaneous localization and map building (SLAM) problem. The SLAM problem asks if it is possible for an autonomous vehicle to start in an unknown location in an unknown environment and then to incrementally build a map of this environment while simultaneously using this map to compute absolute vehicle location. Conventional approaches to this problem are plagued with a prohibitively large increase in computation with the size of the environment. This paper offers a new solution to the SLAM problem that is both consistent and computationally feasible. The proposed algorithm builds a map expressing the relationships between landmarks which is then transformed into landmark locations. Experimental results are presented employing the new algorithm on a subsea vehicle using a scanning sonar sensor.
Transverse correlations in triphoton entanglement: Geometrical and physical optics
International Nuclear Information System (INIS)
Wen Jianming; Rubin, Morton H.; Shih Yanhua; Xu, P.
2007-01-01
The transverse correlation of triphoton entanglement generated within a single crystal is analyzed. Among many interesting features of the transverse correlation, they arise from the spectral function F of the triphoton state produced in the parametric processes. One consequence of transverse effects of entangled states is quantum imaging, which is theoretically studied in photon counting measurements. Klyshko's two-photon advanced-wave picture is found to be applicable to the multiphoton entanglement with some modifications. We found that in the two-photon coincidence counting measurement by using triphoton entanglement, although the Gaussian thin lens equation (GTLE) holds, the imaging shown in coincidences is obscure and has a poor quality. This is because of tracing the remaining transverse modes in the untouched beam. In the triphoton imaging experiments, two kinds of cases have been examined. For the case that only one object with one thin lens is placed in the system, we found that the GTLE holds as expected in the triphoton coincidences and the effective distance between the lens and imaging plane is the parallel combination of two distances between the lens and two detectors weighted by wavelengths, which behaves as the parallel combination of resistors in the electromagnetism theory. Only in this case, a point-point correspondence for forming an image is well-accomplished. However, when two objects or two lenses are inserted in the system, though the GTLEs are well-satisfied, in general a point-point correspondence for imaging cannot be established. Under certain conditions, two blurred images may be observed in the coincidence counts. We have also studied the ghost interference-diffraction experiments by using double slits as apertures in triphoton entanglement. It was found that when two double slits are used in two optical beams, the interference-diffraction patterns show unusual features compared with the two-photon case. This unusual behavior is a
Geometric measure of quantum discord and total quantum correlations in an N-partite quantum state
International Nuclear Information System (INIS)
Hassan, Ali Saif M; Joag, Pramod S
2012-01-01
Quantum discord, as introduced by Ollivier and Zurek (2001 Phys. Rev. Lett. 88 017901), is a measure of the discrepancy between quantum versions of two classically equivalent expressions for mutual information and is found to be useful in quantification and application of quantum correlations in mixed states. It is viewed as a key resource present in certain quantum communication tasks and quantum computational models without containing much entanglement. An early step toward the quantification of quantum discord in a quantum state was by Dakic et al (2010 Phys. Rev. Lett. 105 190502) who introduced a geometric measure of quantum discord and derived an explicit formula for any two-qubit state. Recently, Luo and Fu (2010 Phys. Rev. A 82 034302) introduced a generic form of the geometric measure of quantum discord for a bipartite quantum state. We extend these results and find generic forms of the geometric measure of quantum discord and total quantum correlations in a general N-partite quantum state. Further, we obtain computable exact formulas for the geometric measure of quantum discord and total quantum correlations in an N-qubit quantum state. The exact formulas for the N-qubit quantum state can be used to get experimental estimates of the quantum discord and the total quantum correlation. (paper)
Directory of Open Access Journals (Sweden)
Huda E. Khalid
2016-08-01
Full Text Available This article sheds light on the possibility of finding the minimum solution set of neutrosophic relational geometric programming with (max, min composition. This work examines the privacy enjoyed by both neutrosophic logic and geometric programming, and how it affects the minimum solutions.
International Nuclear Information System (INIS)
Roga, W; Illuminati, F; Spehner, D
2016-01-01
We investigate and compare three distinguished geometric measures of bipartite quantum correlations that have been recently introduced in the literature: the geometric discord, the measurement-induced geometric discord, and the discord of response, each one defined according to three contractive distances on the set of quantum states, namely the trace, Bures, and Hellinger distances. We establish a set of exact algebraic relations and inequalities between the different measures. In particular, we show that the geometric discord and the discord of response based on the Hellinger distance are easy to compute analytically for all quantum states whenever the reference subsystem is a qubit. These two measures thus provide the first instance of discords that are simultaneously fully computable, reliable (since they satisfy all the basic Axioms that must be obeyed by a proper measure of quantum correlations), and operationally viable (in terms of state distinguishability). We apply the general mathematical structure to determine the closest classical-quantum state of a given state and the maximally quantum-correlated states at fixed global state purity according to the different distances, as well as a necessary condition for a channel to be quantumness breaking. (paper)
The Neumann Type Systems and Algebro-Geometric Solutions of a System of Coupled Integrable Equations
International Nuclear Information System (INIS)
Chen Jinbing; Qiao Zhijun
2011-01-01
A system of (1+1)-dimensional coupled integrable equations is decomposed into a pair of new Neumann type systems that separate the spatial and temporal variables for this system over a symplectic submanifold. Then, the Neumann type flows associated with the coupled integrable equations are integrated on the complex tour of a Riemann surface. Finally, the algebro-geometric solutions expressed by Riemann theta functions of the system of coupled integrable equations are obtained by means of the Jacobi inversion.
Fu, Zhongtao; Yang, Wenyu; Yang, Zhen
2013-08-01
In this paper, we present an efficient method based on geometric algebra for computing the solutions to the inverse kinematics problem (IKP) of the 6R robot manipulators with offset wrist. Due to the fact that there exist some difficulties to solve the inverse kinematics problem when the kinematics equations are complex, highly nonlinear, coupled and multiple solutions in terms of these robot manipulators stated mathematically, we apply the theory of Geometric Algebra to the kinematic modeling of 6R robot manipulators simply and generate closed-form kinematics equations, reformulate the problem as a generalized eigenvalue problem with symbolic elimination technique, and then yield 16 solutions. Finally, a spray painting robot, which conforms to the type of robot manipulators, is used as an example of implementation for the effectiveness and real-time of this method. The experimental results show that this method has a large advantage over the classical methods on geometric intuition, computation and real-time, and can be directly extended to all serial robot manipulators and completely automatized, which provides a new tool on the analysis and application of general robot manipulators.
Linear and support vector regressions based on geometrical correlation of data
Directory of Open Access Journals (Sweden)
Kaijun Wang
2007-10-01
Full Text Available Linear regression (LR and support vector regression (SVR are widely used in data analysis. Geometrical correlation learning (GcLearn was proposed recently to improve the predictive ability of LR and SVR through mining and using correlations between data of a variable (inner correlation. This paper theoretically analyzes prediction performance of the GcLearn method and proves that GcLearn LR and SVR will have better prediction performance than traditional LR and SVR for prediction tasks when good inner correlations are obtained and predictions by traditional LR and SVR are far away from their neighbor training data under inner correlation. This gives the applicable condition of GcLearn method.
International Nuclear Information System (INIS)
Xue, Liyuan; Yu, Yanxia; Cai, Xiaoya; Pan, Hui; Wang, Zisheng
2016-01-01
Highlights: • We find that the Pancharatnam phases include the information of quantum correlations. • We show that the sudden died and alive phenomena of quantum entanglement is original in the transition of Pancharatnam phase. • We find that the faster the Pancharatnam phases change, the slower the quantum correlations decay. • We find that a subspace of quantum entanglement can exist in the Y-state. • Our results provide a useful approach experimentally to implement the time-dependent geometric quantum computation. - Abstract: We investigate time-dependent Pancharatnam phases and the relations between such geometric phases and quantum correlations, i.e., quantum discord and concurrence, of superconducting two-qubit coupling system in dissipative environment with the mixture effects of four different eigenstates of density matrix. We find that the time-dependent Pancharatnam phases not only keep the motion memory of such a two-qubit system, but also include the information of quantum correlations. We show that the sudden died and alive phenomena of quantum entanglement are intrinsic in the transition of Pancharatnam phase in the X-state and the complex oscillations of Pancharatnam phase in the Y-state. The faster the Pancharatnam phases change, the slower the quantum correlations decay. In particular, we find that a subspace of quantum entanglement can exist in the Y-state by choosing suitable coupling parameters between two-qubit system and its environment, or initial conditions.
Demystifying the memory effect: A geometrical approach to understanding speckle correlations
Prunty, Aaron C.; Snieder, Roel K.
2017-05-01
The memory effect has seen a surge of research into its fundamental properties and applications since its discovery by Feng et al. [Phys. Rev. Lett. 61, 834 (1988)]. While the wave trajectories for which the memory effect holds are hidden implicitly in the diffusion probability function [Phys. Rev. B 40, 737 (1989)], the physical intuition of why these trajectories satisfy the memory effect has often been masked by the derivation of the memory correlation function itself. In this paper, we explicitly derive the specific trajectories through a random medium for which the memory effect holds. Our approach shows that the memory effect follows from a simple conservation argument, which imposes geometrical constraints on the random trajectories that contribute to the memory effect. We illustrate the time-domain effects of these geometrical constraints with numerical simulations of pulse transmission through a random medium. The results of our derivation and numerical simulations are consistent with established theory and experimentation.
International Nuclear Information System (INIS)
Choi, C. Y.; Park, C. T.; Kim, T. H.; Han, K. N.; Choe, S. H.
1995-01-01
A geometrical inverse heat conduction problem is solved for the development of Infrared Computerized-Axial-Tomography (IR CAT) Scan by using a boundary element method in conjunction with regularization procedure. In this problem, an overspecified temperature condition by infrared scanning is provided on the surface, and is used together with other conditions to solve the position of an unknown boundary (cavity). An auxiliary problem is introduced in the solution of this problem. By defining a hypothetical inner boundary for the auxiliary problem domain, the cavity is located interior to the domain and its position is determined by solving a potential problem. Boundary element method with regularization procedure is used to solve this problem, and the effects of regularization on the inverse solution method are investigated by means of numerical analysis
Closed-Form Solutions for Gradient Elastic Beams with Geometric Discontinuities by Laplace Transform
Directory of Open Access Journals (Sweden)
Mustafa Özgür Yayli
2013-01-01
Full Text Available The static bending solution of a gradient elastic beam with external discontinuities is presented by Laplace transform. Its utility lies in the ability to switch differential equations to algebraic forms that are more easily solved. A Laplace transformation is applied to the governing equation which is then solved for the static deflection of the microbeam. The exact static response of the gradient elastic beam with external discontinuities is obtained by applying known initial conditions when the others are derived from boundary conditions. The results are given in a series of figures and compared with their classical counterparts. The main contribution of this paper is to provide a closed-form solution for the static deflection of microbeams under geometric discontinuities.
Pairwise correlations via quantum discord and its geometric measure in a four-qubit spin chain
Directory of Open Access Journals (Sweden)
Abdel-Baset A. Mohamed
2013-04-01
Full Text Available The dynamic of pairwise correlations, including quantum entanglement (QE and discord (QD with geometric measure of quantum discord (GMQD, are shown in the four-qubit Heisenberg XX spin chain. The results show that the effect of the entanglement degree of the initial state on the pairwise correlations is stronger for alternate qubits than it is for nearest-neighbor qubits. This parameter results in sudden death for QE, but it cannot do so for QD and GMQD. With different values for this entanglement parameter of the initial state, QD and GMQD differ and are sensitive for any change in this parameter. It is found that GMQD is more robust than both QD and QE to describe correlations with nonzero values, which offers a valuable resource for quantum computation.
Energy Technology Data Exchange (ETDEWEB)
Shin, Dong Seok; Kim, Dong Su; Kim, Tae Ho; Kim, Kyeong Hyeon; Yoon, Do Kun; Suh, Tae Suk [The Catholic University of Korea, Seoul (Korea, Republic of); Kang, Seong Hee [Seoul National University Hospital, Seoul (Korea, Republic of); Cho, Min Seok [Asan Medical Center, Seoul (Korea, Republic of); Noh, Yu Yoon [Eulji University Hospital, Daejeon (Korea, Republic of)
2017-04-15
Three-dimensional dose (3D dose) can consider coverage of moving target, however it is difficult to provide dosimetric effect which occurs by respiratory motions. Four-dimensional dose (4D dose) which uses deformable image registration (DIR) algorithm from four-dimensional computed tomography (4DCT) images can consider dosimetric effect by respiratory motions. The dose difference between 3D dose and 4D dose can be varied according to the geometrical relationship between a planning target volume (PTV) and an organ at risk (OAR). The purpose of this study is to evaluate the correlation between the overlap volume histogram (OVH), which quantitatively shows the geometrical relationship between the PTV and OAR, and the dose differences. In conclusion, no significant statistical correlation was found between the OVH and dose differences. However, it was confirmed that a higher difference between the 3D and 4D doses could occur in cases that have smaller OVH value. No significant statistical correlation was found between the OVH and dose differences. However, it was confirmed that a higher difference between the 3D and 4D doses could occur in cases that have smaller OVH value.
Strongly correlated states of a small cold-atom cloud from geometric gauge fields
International Nuclear Information System (INIS)
Julia-Diaz, B.; Dagnino, D.; Barberan, N.; Guenter, K. J.; Dalibard, J.; Grass, T.; Lewenstein, M.
2011-01-01
Using exact diagonalization for a small system of cold bosonic atoms, we analyze the emergence of strongly correlated states in the presence of an artificial magnetic field. This gauge field is generated by a laser beam that couples two internal atomic states, and it is related to Berry's geometrical phase that emerges when an atom follows adiabatically one of the two eigenstates of the atom-laser coupling. Our approach allows us to go beyond the adiabatic approximation, and to characterize the generalized Laughlin wave functions that appear in the strong magnetic-field limit.
Strongly correlated states of a small cold-atom cloud from geometric gauge fields
Energy Technology Data Exchange (ETDEWEB)
Julia-Diaz, B. [Dept. ECM, Facultat de Fisica, U. Barcelona, E-08028 Barcelona (Spain); ICFO-Institut de Ciencies Fotoniques, Parc Mediterrani de la Tecnologia, E-08860 Barcelona (Spain); Dagnino, D.; Barberan, N. [Dept. ECM, Facultat de Fisica, U. Barcelona, E-08028 Barcelona (Spain); Guenter, K. J.; Dalibard, J. [Laboratoire Kastler Brossel, CNRS, UPMC, Ecole Normale Superieure, 24 rue Lhomond, F-75005 Paris (France); Grass, T. [ICFO-Institut de Ciencies Fotoniques, Parc Mediterrani de la Tecnologia, E-08860 Barcelona (Spain); Lewenstein, M. [ICFO-Institut de Ciencies Fotoniques, Parc Mediterrani de la Tecnologia, E-08860 Barcelona (Spain); ICREA-Institucio Catalana de Recerca i Estudis Avancats, E-08010 Barcelona (Spain)
2011-11-15
Using exact diagonalization for a small system of cold bosonic atoms, we analyze the emergence of strongly correlated states in the presence of an artificial magnetic field. This gauge field is generated by a laser beam that couples two internal atomic states, and it is related to Berry's geometrical phase that emerges when an atom follows adiabatically one of the two eigenstates of the atom-laser coupling. Our approach allows us to go beyond the adiabatic approximation, and to characterize the generalized Laughlin wave functions that appear in the strong magnetic-field limit.
Energy Technology Data Exchange (ETDEWEB)
Phillips, W.T. [Dept. of Radiology, Univ. of Texas Health Science Center, San Antonio, TX (United States); McMahan, C.A. [Dept. of Pathology, Univ. of Texas Health Science Center, San Antonio, TX (United States); Lasher, J.C. [Dept. of Radiology, Univ. of Texas Health Science Center, San Antonio, TX (United States); Blumhardt, M.R. [Dept. of Pathology, Univ. of Texas Health Science Center, San Antonio, TX (United States); Schwartz, J.G. [Dept. of Pathology, Univ. of Texas Health Science Center, San Antonio, TX (United States)
1995-02-01
Previous research has shown that the single anterior view of the stomach overestimates the gastric half-emptying time of a solid meal compared to the geometric mean of the anterior and posterior views. Little research has been performed comparing the various views of gastric emptying of a glucose solution. After an overnight fast, 49 nondiabetic subjects were given a 450 ml solution containing 50 g of glucose and 200 {mu}Ci of technetium-99m sulfur colloid. Sequential 1-min anterior, posterior, and left anterior oblique views were obtained every 15 min. The mean percent solution remaining in the stomach for all three views differed from the geometric mean by 1.9% or less at all time points. Average gastric half-emptying times were: geometric mean, 62.7{+-}3.3 min; anterior, 61.9{+-}3.2 min; posterior, 63.5{+-}3.5 min; and left anterior oblique, 61.6{+-}3.3 min. These half-emptying times were not statistically different. For individual patients, differences between all three views and the geometric mean were not clinically important. Approximately 95% of all patients are expected to have gastric half-emptying times measured by any of the three single views within 17 min of the gastric half-emptying time obtained using the geometric mean. The imaging of gastric emptying using glucose solutions can be performed using a convenient single view which allows continuous dynamic imaging. (orig.)
An online interactive geometric database including exact solutions of Einstein's field equations
International Nuclear Information System (INIS)
Ishak, Mustapha; Lake, Kayll
2002-01-01
We describe a new interactive database (GRDB) of geometric objects in the general area of differential geometry. Database objects include, but are not restricted to, exact solutions of Einstein's field equations. GRDB is designed for researchers (and teachers) in applied mathematics, physics and related fields. The flexible search environment allows the database to be useful over a wide spectrum of interests, for example, from practical considerations of neutron star models in astrophysics to abstract space-time classification schemes. The database is built using a modular and object-oriented design and uses several Java technologies (e.g. Applets, Servlets, JDBC). These are platform-independent and well adapted for applications developed for the World Wide Web. GRDB is accompanied by a virtual calculator (GRTensorJ), a graphical user interface to the computer algebra system GRTensorII, used to perform online coordinate, tetrad or basis calculations. The highly interactive nature of GRDB allows systematic internal self-checking and minimization of the required internal records. This new database is now available online at http://grdb.org
Existence of localizing solutions in plasticity via the geometric singular perturbation theory
Lee, Min-Gi
2017-01-31
Shear bands are narrow zones of intense shear observed during plastic deformations of metals at high strain rates. Because they often precede rupture, their study attracted attention as a mechanism of material failure. Here, we aim to reveal the onset of localization into shear bands using a simple model from viscoplasticity. We exploit the properties of scale invariance of the model to construct a family of self-similar focusing solutions that capture the nonlinear mechanism of shear band formation. The key step is to desingularize a reduced system of singular ordinary differential equations and reduce the problem into the construction of a heteroclinic orbit for an autonomous system of three first-order equations. The associated dynamical system has fast and slow time scales, forming a singularly perturbed problem. Geometric singular perturbation theory is applied to this problem to achieve an invariant surface. The flow on the invariant surface is analyzed via the Poincaré--Bendixson theorem to construct a heteroclinic orbit.
Directory of Open Access Journals (Sweden)
Pan Zhao
2018-01-01
Full Text Available In this paper we consider pricing problems of the geometric average Asian options under a non-Gaussian model, in which the underlying stock price is driven by a process based on non-extensive statistical mechanics. The model can describe the peak and fat tail characteristics of returns. Thus, the description of underlying asset price and the pricing of options are more accurate. Moreover, using the martingale method, we obtain closed form solutions for geometric average Asian options. Furthermore, the numerical analysis shows that the model can avoid underestimating risks relative to the Black-Scholes model.
Directory of Open Access Journals (Sweden)
Cai Ligang
2017-01-01
Full Text Available Instead improving the accuracy of machine tool by increasing the precision of key components level blindly in the production process, the method of combination of SNR quality loss function and machine tool geometric error correlation analysis to optimize five-axis machine tool geometric errors will be adopted. Firstly, the homogeneous transformation matrix method will be used to build five-axis machine tool geometric error modeling. Secondly, the SNR quality loss function will be used for cost modeling. And then, machine tool accuracy optimal objective function will be established based on the correlation analysis. Finally, ISIGHT combined with MATLAB will be applied to optimize each error. The results show that this method is reasonable and appropriate to relax the range of tolerance values, so as to reduce the manufacturing cost of machine tools.
Existence of localizing solutions in plasticity via the geometric singular perturbation theory
Lee, Min-Gi; Tzavaras, Athanasios
2017-01-01
system has fast and slow time scales, forming a singularly perturbed problem. Geometric singular perturbation theory is applied to this problem to achieve an invariant surface. The flow on the invariant surface is analyzed via the Poincaré
International Nuclear Information System (INIS)
Yamane, Hiroyuki
2013-01-01
The electronic structure of organic thin films and interfaces plays a crucial role in the performance of optoelectronic devices using organic semiconductors, and is seriously dominated by the geometric film/interface structure due to the anisotropic spatial distribution of molecular orbitals. This paper briefly reviews the recent progress of the examination of correlating electronic structure and geometric structure of archetypal organic semiconductor thin films and interfaces by using spectroscopic experiments with synchrotron radiation such as angle-resolved photoelectron spectroscopy, x-ray absorption spectroscopy, and x-ray standing wave. (author)
International Nuclear Information System (INIS)
Luo, Da-Wei; Xu, Jing-Bo
2014-01-01
We investigate the phenomenon of sudden transitions in geometric quantum correlation of two qubits in spin chain environments at finite temperature. It is shown that when only one qubit is coupled to the spin environment, the geometric discord exhibits a double sudden transition behavior, which is closely related to the quantum criticality of the spin chain environment. When two qubits are uniformly coupled to a common spin chain environment, the geometric discord is found to display a sudden transition behavior whereby the system transits from pure classical decoherence to pure quantum decoherence. Moreover, an interesting scaling behavior is revealed for the frozen time, and we also present a scheme to prolong the time during which the discord remains constant by applying bang–bang pulses. (paper)
Stricklin, J. A.; Haisler, W. E.; Von Riesemann, W. A.
1972-01-01
This paper presents an assessment of the solution procedures available for the analysis of inelastic and/or large deflection structural behavior. A literature survey is given which summarized the contribution of other researchers in the analysis of structural problems exhibiting material nonlinearities and combined geometric-material nonlinearities. Attention is focused at evaluating the available computation and solution techniques. Each of the solution techniques is developed from a common equation of equilibrium in terms of pseudo forces. The solution procedures are applied to circular plates and shells of revolution in an attempt to compare and evaluate each with respect to computational accuracy, economy, and efficiency. Based on the numerical studies, observations and comments are made with regard to the accuracy and economy of each solution technique.
Sela, Yaron; Eshed, Iris; Shapira, Shachar; Oran, Ariel; Vogel, Guy; Herman, Amir; Perry Pritsch, Moshe
2015-02-01
Magnetic resonance imaging (MRI) is considered to be the best non-invasive procedure for the evaluation of rotator cuff (RC) tendon tears. Burkhart's classification is a geometric classification of full-thickness RC tears on MRI. To correlate MRI and arthroscopic geometric full-thickness RC tears according to the Burkhart's classification with pre- and postoperative clinical findings. Patients who underwent arthroscopic RC repair between 2006 and 2010 were retrospectively evaluated. Preoperative MRI and arthroscopic surgical reports were reviewed for tear geometry (Burkhart's) by three (1 radiologist, 2 surgeons) and two (surgeons) readers. MRIs were also evaluated for tear size and change of tear size in successive sagittal sections and for muscle mass and fatty infiltration. Clinical examinations were performed preoperatively and at least 12 months afterwards. Postoperative function questionnaires were filled in by the patients. Forty-six patients (35 men, 11 women; mean age, 57 years; range, 41-72 years) were evaluated. Tears depicted on MRIs were classified as crescent in 11 patients (24%), longitudinal in three (6.5%), massive contracted in 29 (63%), and cuff arthropathy in three (6.5%). Muscle changes were noted almost exclusively in patients with massive tears and cuff arthropathy (16/32 patients, P = 0.013). MRIs and arthroscopic geometric classifications were in close agreement. Tear type did not correlate with pre- and postoperative physical examination or with postoperative clinical questionnaires scores. Geometric RC tear characterizations on preoperative MRIs were closely associated with arthroscopic findings. Postoperative results were not affected by the geometric pattern of the tears. © The Foundation Acta Radiologica 2014 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav.
Geometrical-optics solution to light scattering by droxtal ice crystals.
Zhang, Zhibo; Yang, Ping; Kattawar, George W; Tsay, Si-Chee; Baum, Bryan A; Hu, Yongxiang; Heymsfield, Andrew J; Reichardt, Jens
2004-04-20
We investigate the phase matrices of droxtals at wavelengths of 0.66 and 11 microm by using an improved geometrical-optics method. An efficient method is developed to specify the incident rays and the corresponding impinging points on the particle surface necessary to initialize the ray-tracing computations. At the 0.66-microm wavelength, the optical properties of droxtals are different from those of hexagonal ice crystals. At the 11-microm wavelength, the phase functions for droxtals are essentially featureless because of strong absorption within the particles, except for ripple structures that are caused by the phase interference of the diffracted wave.
Ray, S. Saha
2018-04-01
In this paper, the symmetry analysis and similarity reduction of the (2+1)-dimensional Bogoyavlensky-Konopelchenko (B-K) equation are investigated by means of the geometric approach of an invariance group, which is equivalent to the classical Lie symmetry method. Using the extended Harrison and Estabrook’s differential forms approach, the infinitesimal generators for (2+1)-dimensional B-K equation are obtained. Firstly, the vector field associated with the Lie group of transformation is derived. Then the symmetry reduction and the corresponding explicit exact solution of (2+1)-dimensional B-K equation is obtained.
Chung, Kun-Jen
2012-08-01
Cardenas-Barron [Cardenas-Barron, L.E. (2010) 'A Simple Method to Compute Economic order Quantities: Some Observations', Applied Mathematical Modelling, 34, 1684-1688] indicates that there are several functions in which the arithmetic-geometric mean method (AGM) does not give the minimum. This article presents another situation to reveal that the AGM inequality to locate the optimal solution may be invalid for Teng, Chen, and Goyal [Teng, J.T., Chen, J., and Goyal S.K. (2009), 'A Comprehensive Note on: An Inventory Model under Two Levels of Trade Credit and Limited Storage Space Derived without Derivatives', Applied Mathematical Modelling, 33, 4388-4396], Teng and Goyal [Teng, J.T., and Goyal S.K. (2009), 'Comment on 'Optimal Inventory Replenishment Policy for the EPQ Model under Trade Credit Derived without Derivatives', International Journal of Systems Science, 40, 1095-1098] and Hsieh, Chang, Weng, and Dye [Hsieh, T.P., Chang, H.J., Weng, M.W., and Dye, C.Y. (2008), 'A Simple Approach to an Integrated Single-vendor Single-buyer Inventory System with Shortage', Production Planning and Control, 19, 601-604]. So, the main purpose of this article is to adopt the calculus approach not only to overcome shortcomings of the arithmetic-geometric mean method of Teng et al. (2009), Teng and Goyal (2009) and Hsieh et al. (2008), but also to develop the complete solution procedures for them.
On the numerical evaluation of algebro-geometric solutions to integrable equations
International Nuclear Information System (INIS)
Kalla, C; Klein, C
2012-01-01
Physically meaningful periodic solutions to certain integrable partial differential equations are given in terms of multi-dimensional theta functions associated with real Riemann surfaces. Typical analytical problems in the numerical evaluation of these solutions are studied. In the case of hyperelliptic surfaces efficient algorithms exist even for almost degenerate surfaces. This allows the numerical study of solitonic limits. For general real Riemann surfaces, the choice of a homology basis adapted to the anti-holomorphic involution is important for a convenient formulation of the solutions and smoothness conditions. Since existing algorithms for algebraic curves produce a homology basis not related to automorphisms of the curve, we study symplectic transformations to an adapted basis and give explicit formulae for M-curves. As examples we discuss solutions of the Davey–Stewartson and the multi-component nonlinear Schrödinger equations
Solution of the equations for one-dimensional, two-phase, immiscible flow by geometric methods
Boronin, Ivan; Shevlyakov, Andrey
2018-03-01
Buckley-Leverett equations describe non viscous, immiscible, two-phase filtration, which is often of interest in modelling of oil production. For many parameters and initial conditions, the solutions of these equations exhibit non-smooth behaviour, namely discontinuities in form of shock waves. In this paper we obtain a novel method for the solution of Buckley-Leverett equations, which is based on geometry of differential equations. This method is fast, accurate, stable, and describes non-smooth phenomena. The main idea of the method is that classic discontinuous solutions correspond to the continuous surfaces in the space of jets - the so-called multi-valued solutions (Bocharov et al., Symmetries and conservation laws for differential equations of mathematical physics. American Mathematical Society, Providence, 1998). A mapping of multi-valued solutions from the jet space onto the plane of the independent variables is constructed. This mapping is not one-to-one, and its singular points form a curve on the plane of the independent variables, which is called the caustic. The real shock occurs at the points close to the caustic and is determined by the Rankine-Hugoniot conditions.
Geometric analysis of the solutions of two-phase flows: two-fluid model
International Nuclear Information System (INIS)
Kestin, J.; Zeng, D.L.
1984-01-01
This report contains a lightly edited draft of a study of the two-fluid model in two-phase flow. The motivation for the study stems from the authors' conviction that the construction of a computer code for any model should be preceded by a geometrical analysis of the pattern of trajectories in the phase space appropriate for the model. Such a study greatly facilitates the understanding of the phenomenon of choking and anticipates the computational difficulties which arise from the existence of singularities. The report contains a derivation of the six conservation equations of the model which includes a consideration of the simplifications imposed on a one-dimensional treatment by the presence of boundary layers at the wall and between the phases. The model is restricted to one-dimensional adiabatic flows of a single substance present in two phases, but thermodynamic equilibrium between the phases is not assumed. The role of closure conditions is defined but no specific closure conditions, or explicit equations of state, are introduced
Effects of solute--solvent attractive forces on hydrophobic correlations
International Nuclear Information System (INIS)
Pratt, L.R.; Chandler, D.
1980-01-01
A theory is presented for the effect of slowly varying attractive forces on correlations between nonpolar solutes in dilute aqueous solution. We find that hydrophobic correlations are sensitive to relatively long range slowly varying interactions. Thus, it is possible to make qualitative changes in these correlations by introducing small changes in the attractive forces. Several model calculations are presented to illustrate these facts. The contributions of the Lennard-Jones attractive forces to the computer simulation results of Pangali, Rao, and Berne are calculated. For this case it is found that the potential of mean force between spherical nonpolar solutes is hardly affected by inclusion of attractive forces. However, the osmotic second virial coefficient is dominated by the contributions of the attractive forces. For spherical solutes which provide a reasonable model for the methane molecule, inclusion of attractive forces produces a qualitative change in the methane--methane potential of mean force. The connection between these effects of slowly varying attractive forces and the enthalpic part of Ben-Naim's deltaA/sup H/I is discussed
Stochastic Geometric Models with Non-stationary Spatial Correlations in Lagrangian Fluid Flows
Gay-Balmaz, François; Holm, Darryl D.
2018-01-01
Inspired by spatiotemporal observations from satellites of the trajectories of objects drifting near the surface of the ocean in the National Oceanic and Atmospheric Administration's "Global Drifter Program", this paper develops data-driven stochastic models of geophysical fluid dynamics (GFD) with non-stationary spatial correlations representing the dynamical behaviour of oceanic currents. Three models are considered. Model 1 from Holm (Proc R Soc A 471:20140963, 2015) is reviewed, in which the spatial correlations are time independent. Two new models, called Model 2 and Model 3, introduce two different symmetry breaking mechanisms by which the spatial correlations may be advected by the flow. These models are derived using reduction by symmetry of stochastic variational principles, leading to stochastic Hamiltonian systems, whose momentum maps, conservation laws and Lie-Poisson bracket structures are used in developing the new stochastic Hamiltonian models of GFD.
Stochastic Geometric Models with Non-stationary Spatial Correlations in Lagrangian Fluid Flows
Gay-Balmaz, François; Holm, Darryl D.
2018-06-01
Inspired by spatiotemporal observations from satellites of the trajectories of objects drifting near the surface of the ocean in the National Oceanic and Atmospheric Administration's "Global Drifter Program", this paper develops data-driven stochastic models of geophysical fluid dynamics (GFD) with non-stationary spatial correlations representing the dynamical behaviour of oceanic currents. Three models are considered. Model 1 from Holm (Proc R Soc A 471:20140963, 2015) is reviewed, in which the spatial correlations are time independent. Two new models, called Model 2 and Model 3, introduce two different symmetry breaking mechanisms by which the spatial correlations may be advected by the flow. These models are derived using reduction by symmetry of stochastic variational principles, leading to stochastic Hamiltonian systems, whose momentum maps, conservation laws and Lie-Poisson bracket structures are used in developing the new stochastic Hamiltonian models of GFD.
A geometric analysis of hallux valgus: correlation with clinical assessment of severity
Piqué-Vidal, Carlos; Vila, Joan
2009-01-01
Background Application of plane geometry to the study of bunion deformity may represent an interesting and novel approach in the research field of hallux valgus. For the purpose of contributing to development of a different perspective in the assessment of hallux valgus, this study was conducted with three objectives: a) to determine the position on the intersection point of the perpendicular bisectors of the longitudinal axes of the first metatarsal and proximal phalanx (IP), b) to correlate the location of this point with hallux valgus deformity according to angular measurements and according to visual assessment of the severity carried out by three independent observers, and c) to assess whether this IP correlated with the radius of the first metatarsophalangeal arc circumference. Methods Measurements evaluated were intermetatarsal angle (IMA), hallux valgus angle (HVA), and proximal phalangeal articular angle (PPAA). The Autocad® program computed the location of the IP inside or outside of the foot. Three independent observers rated the severity of hallux valgus in photographs using a 100-mm visual analogue scale (VAS). Results Measurements of all angles except PPAA showed significantly lower values when the IP was located out of the foot more distantly and vice versa, significantly higher values for severe deformities in which the IP was found inside the foot (p < 0.001). The IP correlated significantly with VAS scores and with the length of the radius of the circle that included the first metatarsophalangeal arc circumference (p < 0.001) Conclusion The IP is a useful indicator of hallux valgus deformity because correlated significantly with IMA and HVA measurements, VAS scores obtained by visual inspection of the degree of deformity, and location of the center of the first metatarsophalangeal arc circumference. PMID:19442286
LISA time-delay interferometry zero-signal solution: Geometrical properties
International Nuclear Information System (INIS)
Tinto, Massimo; Larson, Shane L.
2004-01-01
Time-delay interferometry (TDI) is the data processing technique needed for generating interferometric combinations of data measured by the multiple Doppler readouts available onboard the three Laser Interferometer Space Antenna (LISA) spacecraft. Within the space of all possible interferometric combinations TDI can generate, we have derived a specific combination that has zero response to the gravitational wave signal, and called it the zero-signal solution (ZSS). This is a two-parameter family of linear combinations of the generators of the TDI space, and its response to a gravitational wave becomes null when these two parameters coincide with the values of the angles of the source location in the sky. Remarkably, the ZSS does not rely on any assumptions about the gravitational waveform, and in fact it works for waveforms of any kind. Our approach is analogous to the data analysis method introduced by Guersel and Tinto in the context of networks of Earth-based, wideband, interferometric gravitational wave detectors observing in coincidence a gravitational wave burst. The ZSS should be regarded as an application of the Guersel and Tinto method to the LISA data
Directory of Open Access Journals (Sweden)
Brieu M.
2010-06-01
Full Text Available Composite materials are today used for various industrial applications. However, delamination on free edges, where stress gradients are strong, still remain a problem. In the aim of a better understanding of such phenomenons, Digital Image Correlation (DIC measurements have been carried out on [(15n/-15n2]s laminates under uniaxial tensile strain. Three different composites with different mechanical properties and microstructure have been tested as well as two samples geometries: flat and with ply drop. Experimental results show high shear strain concentrations near 15°/-15° interlaminar interfaces on free edges which depend on material mechanical properties and microstructure and increase in the vicinity of a geometrical singularity.
A geometric analysis of hallux valgus: correlation with clinical assessment of severity
Directory of Open Access Journals (Sweden)
Vila Joan
2009-05-01
Full Text Available Abstract Background Application of plane geometry to the study of bunion deformity may represent an interesting and novel approach in the research field of hallux valgus. For the purpose of contributing to development of a different perspective in the assessment of hallux valgus, this study was conducted with three objectives: a to determine the position on the intersection point of the perpendicular bisectors of the longitudinal axes of the first metatarsal and proximal phalanx (IP, b to correlate the location of this point with hallux valgus deformity according to angular measurements and according to visual assessment of the severity carried out by three independent observers, and c to assess whether this IP correlated with the radius of the first metatarsophalangeal arc circumference. Methods Measurements evaluated were intermetatarsal angle (IMA, hallux valgus angle (HVA, and proximal phalangeal articular angle (PPAA. The Autocad® program computed the location of the IP inside or outside of the foot. Three independent observers rated the severity of hallux valgus in photographs using a 100-mm visual analogue scale (VAS. Results Measurements of all angles except PPAA showed significantly lower values when the IP was located out of the foot more distantly and vice versa, significantly higher values for severe deformities in which the IP was found inside the foot (p p Conclusion The IP is a useful indicator of hallux valgus deformity because correlated significantly with IMA and HVA measurements, VAS scores obtained by visual inspection of the degree of deformity, and location of the center of the first metatarsophalangeal arc circumference.
Novel correlations in two dimensions: Some exact solutions
International Nuclear Information System (INIS)
Murthy, M.V.; Bhaduri, R.K.; Sen, D.
1996-01-01
We construct a new many-body Hamiltonian with two- and three-body interactions in two space dimensions and obtain its exact many-body ground state for an arbitrary number of particles. This ground state has a novel pairwise correlation. A class of exact solutions for the excited states is also found. These excited states display an energy spectrum similar to the Calogero-Sutherland model in one dimension. The model reduces to an analog of the well-known trigonometric Sutherland model when projected on to a circular ring. copyright 1996 The American Physical Society
Energy Technology Data Exchange (ETDEWEB)
Jung, Jerome [Institut fuer Kernphysik, Goethe-Universitaet Frankfurt (Germany); Collaboration: ALICE-Collaboration
2015-07-01
The mean transverse momentum left angle p{sub T} right angle as a function of the charged-particle multiplicity N{sub ch} in pp, p-Pb and Pb-Pb collisions was recently published by ALICE. While in pp and in p-Pb collisions a strong increase of left angle p{sub T} right angle with N{sub ch} is observed, Pb-Pb collisions show a saturation at a much lower left angle p{sub T} right angle. Efforts of reproducing this behaviour in Pb-Pb with a superpositon of nucleon-nucleon interactions do not succeed. A superposition of p-Pb collisions seems to be more promising, since the p-Pb data shows characteristics of both pp and Pb-Pb collisions. The geometric distribution of the p-Pb impact parameters is based on the Woods-Saxon density distribution. Using the correlation of the impact parameter and the multiplicity N{sub ch} in p-Pb collisions a multiplicity-spectrum was generated. Combining this spectrum with experimental p-Pb data we present left angle p{sub T} right angle as a function of N{sub ch} in simulated Pb-Pb collisions and compare it to the correlation measured in Pb-Pb by ALICE.
Raut, Ashlesha S; Kalonia, Devendra S
2015-04-01
Opalescence indicates physical instability of a formulation because of the presence of aggregates or liquid-liquid phase separation in solution and has been reported for monoclonal antibody (mAb) formulations. Increased solution opalescence can be attributed to attractive protein-protein interactions (PPIs). Techniques including light scattering, AUC, or membrane osmometry are routinely employed to measure PPIs in dilute solutions, whereas opalescence is seen at relatively higher concentrations, where both long- and short-range forces contribute to overall PPIs. The mAb molecule studied here shows a unique property of high opalescence because of liquid-liquid phase separation. In this study, opalescence measurements are correlated to PPIs measured in diluted and concentrated solutions using light scattering (kD ) and high-frequency rheology (G'), respectively. Charges on the molecules were calculated using zeta potential measurements. Results indicate that high opalescence and phase separation are a result of the attractive interactions in solution; however, the presence of attractive interactions do not always imply phase separation. Temperature dependence of opalescence suggests that thermodynamic contribution to opalescence is significant and Tcloud can be utilized as a potential tool to assess attractive interactions in solution. © 2014 Wiley Periodicals, Inc. and the American Pharmacists Association.
Bera, Subrata; Bhattacharyya, S.
2018-04-01
A numerical investigation is performed on the electroosmotic flow (EOF) in a surface-modulated microchannel to induce enhanced solute mixing. The channel wall is modulated by placing surface-mounted obstacles of trigonometric shape along which the surface potential is considered to be different from the surface potential of the homogeneous part of the wall. The characteristics of the electrokinetic flow are governed by the Laplace equation for the distribution of external electric potential; the Poisson equation for the distribution of induced electric potential; the Nernst-Planck equations for the distribution of ions; and the Navier-Stokes equations for fluid flow simultaneously. These nonlinear coupled set of governing equations are solved numerically by a control volume method over the staggered system. The influence of the geometric modulation of the surface, surface potential heterogeneity and the bulk ionic concentration on the EOF is analyzed. Vortical flow develops near a surface modulation, and it becomes stronger when the surface potential of the modulated region is in opposite sign to the surface potential of the homogeneous part of the channel walls. Vortical flow also depends on the Debye length when the Debye length is in the order of the channel height. Pressure drop along the channel length is higher for a ribbed wall channel compared to the grooved wall case. The pressure drop decreases with the increase in the amplitude for a grooved channel, but increases for a ribbed channel. The mixing index is quantified through the standard deviation of the solute distribution. Our results show that mixing index is higher for the ribbed channel compared to the grooved channel with heterogeneous surface potential. The increase in potential heterogeneity in the modulated region also increases the mixing index in both grooved and ribbed channels. However, the mixing performance, which is the ratio of the mixing index to pressure drop, reduces with the rise in
Big Data Solution for CTBT Monitoring Using Global Cross Correlation
Gaillard, P.; Bobrov, D.; Dupont, A.; Grenouille, A.; Kitov, I. O.; Rozhkov, M.
2014-12-01
Due to the mismatch between data volume and the performance of the Information Technology infrastructure used in seismic data centers, it becomes more and more difficult to process all the data with traditional applications in a reasonable elapsed time. To fulfill their missions, the International Data Centre of the Comprehensive Nuclear-Test-Ban Treaty Organization (CTBTO/IDC) and the Département Analyse Surveillance Environnement of Commissariat à l'Energie atomique et aux énergies alternatives (CEA/DASE) collect, process and produce complex data sets whose volume is growing exponentially. In the medium term, computer architectures, data management systems and application algorithms will require fundamental changes to meet the needs. This problem is well known and identified as a "Big Data" challenge. To tackle this major task, the CEA/DASE takes part during two years to the "DataScale" project. Started in September 2013, DataScale gathers a large set of partners (research laboratories, SMEs and big companies). The common objective is to design efficient solutions using the synergy between Big Data solutions and the High Performance Computing (HPC). The project will evaluate the relevance of these technological solutions by implementing a demonstrator for seismic event detections thanks to massive waveform correlations. The IDC has developed an expertise on such techniques leading to an algorithm called "Master Event" and provides a high-quality dataset for an extensive cross correlation study. The objective of the project is to enhance the Master Event algorithm and to reanalyze 10 years of waveform data from the International Monitoring System (IMS) network thanks to a dedicated HPC infrastructure operated by the "Centre de Calcul Recherche et Technologie" at the CEA of Bruyères-le-Châtel. The dataset used for the demonstrator includes more than 300,000 seismic events, tens of millions of raw detections and more than 30 terabytes of continuous seismic data
Zhao, Peng; Fan, Engui
2015-04-01
In this paper, a new type of integrable differential-difference hierarchy, namely, the generalized relativistic Lotka-Volterra (GRLV) hierarchy, is introduced. This hierarchy is closely related to Lotka-Volterra lattice and relativistic Lotka-Volterra lattice, which allows us to provide a unified and effective way to obtain some exact solutions for both the Lotka-Volterra hierarchy and the relativistic Lotka-Volterra hierarchy. In particular, we shall construct algebro-geometric quasiperiodic solutions for the LV hierarchy and the RLV hierarchy in a unified manner on the basis of the finite gap integration theory.
International Nuclear Information System (INIS)
Shekhar, Raj; Lei, Peng; Castro-Pareja, Carlos R.; Plishker, William L.; D'Souza, Warren D.
2007-01-01
Conventional radiotherapy is planned using free-breathing computed tomography (CT), ignoring the motion and deformation of the anatomy from respiration. New breath-hold-synchronized, gated, and four-dimensional (4D) CT acquisition strategies are enabling radiotherapy planning utilizing a set of CT scans belonging to different phases of the breathing cycle. Such 4D treatment planning relies on the availability of tumor and organ contours in all phases. The current practice of manual segmentation is impractical for 4D CT, because it is time consuming and tedious. A viable solution is registration-based segmentation, through which contours provided by an expert for a particular phase are propagated to all other phases while accounting for phase-to-phase motion and anatomical deformation. Deformable image registration is central to this task, and a free-form deformation-based nonrigid image registration algorithm will be presented. Compared with the original algorithm, this version uses novel, computationally simpler geometric constraints to preserve the topology of the dense control-point grid used to represent free-form deformation and prevent tissue fold-over. Using mean squared difference as an image similarity criterion, the inhale phase is registered to the exhale phase of lung CT scans of five patients and of characteristically low-contrast abdominal CT scans of four patients. In addition, using expert contours for the inhale phase, the corresponding contours were automatically generated for the exhale phase. The accuracy of the segmentation (and hence deformable image registration) was judged by comparing automatically segmented contours with expert contours traced directly in the exhale phase scan using three metrics: volume overlap index, root mean square distance, and Hausdorff distance. The accuracy of the segmentation (in terms of radial distance mismatch) was approximately 2 mm in the thorax and 3 mm in the abdomen, which compares favorably to the
International Nuclear Information System (INIS)
Bi Lei; Yang Ping; Kattawar, George W.; Hu Yongxiang; Baum, Bryan A.
2011-01-01
A new physical-geometric optics hybrid (PGOH) method is developed to compute the scattering and absorption properties of ice particles. This method is suitable for studying the optical properties of ice particles with arbitrary orientations, complex refractive indices (i.e., particles with significant absorption), and size parameters (proportional to the ratio of particle size to incident wavelength) larger than ∼20, and includes consideration of the edge effects necessary for accurate determination of the extinction and absorption efficiencies. Light beams with polygon-shaped cross sections propagate within a particle and are traced by using a beam-splitting technique. The electric field associated with a beam is calculated using a beam-tracing process in which the amplitude and phase variations over the wavefront of the localized wave associated with the beam are considered analytically. The geometric-optics near field for each ray is obtained, and the single-scattering properties of particles are calculated from electromagnetic integral equations. The present method does not assume additional physical simplifications and approximations, except for geometric optics principles, and may be regarded as a 'benchmark' within the framework of the geometric optics approach. The computational time is on the order of seconds for a single-orientation simulation and is essentially independent of the size parameter. The single-scattering properties of oriented hexagonal ice particles (ice plates and hexagons) are presented. The numerical results are compared with those computed from the discrete-dipole-approximation (DDA) method.
Geometrical model of multiple production
International Nuclear Information System (INIS)
Chikovani, Z.E.; Jenkovszky, L.L.; Kvaratshelia, T.M.; Struminskij, B.V.
1988-01-01
The relation between geometrical and KNO-scaling and their violation is studied in a geometrical model of multiple production of hadrons. Predictions concerning the behaviour of correlation coefficients at future accelerators are given
Vacaru, Sergiu I.; Yazici, Enis
2014-01-01
We show that a geometric techniques can be elaborated and applied for constructing generic off-diagonal exact solutions in $f(R,T)$--modified gravity for systems of gravitational-Yang-Mills-Higgs equations. The corresponding classes of metrics and generalized connections are determined by generating and integration functions which depend, in general, on all space and time coordinates and may possess, or not, Killing symmetries. For nonholonomic constraints resulting in Levi-Civita configurations, we can extract solutions of the Einstein-Yang-Mills-Higgs equations. We show that the constructions simplify substantially for metrics with at least one Killing vector. There are provided and analyzed some examples of exact solutions describing generic off-diagonal modifications to black hole/ellipsoid and solitonic configurations.
cocor: a comprehensive solution for the statistical comparison of correlations.
Directory of Open Access Journals (Sweden)
Birk Diedenhofen
Full Text Available A valid comparison of the magnitude of two correlations requires researchers to directly contrast the correlations using an appropriate statistical test. In many popular statistics packages, however, tests for the significance of the difference between correlations are missing. To close this gap, we introduce cocor, a free software package for the R programming language. The cocor package covers a broad range of tests including the comparisons of independent and dependent correlations with either overlapping or nonoverlapping variables. The package also includes an implementation of Zou's confidence interval for all of these comparisons. The platform independent cocor package enhances the R statistical computing environment and is available for scripting. Two different graphical user interfaces-a plugin for RKWard and a web interface-make cocor a convenient and user-friendly tool.
Synchrotron radiation and atom pair correlation functions in electrolyte solutions
International Nuclear Information System (INIS)
Triolo, R.; D'Aprano, A.
1978-01-01
Despite the enormous effort invested in experimental determinations of the properties of water and aqueous solutions, understanding is still rudimentary. Many of the problems are consequences of a nonrigorous definition of interparticle interactions. It is now clear that after properly ion--water interactions in terms of probability functions of position and orientation it is possible to probe these interactions at molecular levels using diffraction experiments. The role of synchrotron x-ray radiation in this context is being examined. Emphasis is given to the possibility of performing different experiments analogous to those done using the isotopic substitution method in neutron diffraction
International Nuclear Information System (INIS)
Mendez, Derek; Watkins, Herschel; Qiao, Shenglan; Raines, Kevin S.; Lane, Thomas J.
2016-01-01
During X-ray exposure of a molecular solution, photons scattered from the same molecule are correlated. If molecular motion is insignificant during exposure, then differences in momentum transfer between correlated photons are direct measurements of the molecular structure. In conventional small- and wide-angle solution scattering, photon correlations are ignored. This report presents advances in a new biomolecular structural analysis technique, correlated X-ray scattering (CXS), which uses angular intensity correlations to recover hidden structural details from molecules in solution. Due to its intense rapid pulses, an X-ray free electron laser (XFEL) is an excellent tool for CXS experiments. A protocol is outlined for analysis of a CXS data set comprising a total of half a million X-ray exposures of solutions of small gold nanoparticles recorded at the Spring-8 Ångström Compact XFEL facility (SACLA). From the scattered intensities and their correlations, two populations of nanoparticle domains within the solution are distinguished: small twinned, and large probably non-twinned domains. Finally, it is shown analytically how, in a solution measurement, twinning information is only accessible via intensity correlations, demonstrating how CXS reveals atomic-level information from a disordered solution of like molecules.
Lee, Won-Joon; Wilkinson, Caroline M; Hwang, Hyeon-Shik; Lee, Sang-Mi
2015-05-01
Accuracy is the most important factor supporting the reliability of forensic facial reconstruction (FFR) comparing to the corresponding actual face. A number of methods have been employed to evaluate objective accuracy of FFR. Recently, it has been attempted that the degree of resemblance between computer-generated FFR and actual face is measured by geometric surface comparison method. In this study, three FFRs were produced employing live adult Korean subjects and three-dimensional computerized modeling software. The deviations of the facial surfaces between the FFR and the head scan CT of the corresponding subject were analyzed in reverse modeling software. The results were compared with those from a previous study which applied the same methodology as this study except average facial soft tissue depth dataset. Three FFRs of this study that applied updated dataset demonstrated lesser deviation errors between the facial surfaces of the FFR and corresponding subject than those from the previous study. The results proposed that appropriate average tissue depth data are important to increase quantitative accuracy of FFR. © 2015 American Academy of Forensic Sciences.
Energy Technology Data Exchange (ETDEWEB)
Ebata, T [Tohoku Univ., Sendai (Japan). Coll. of General Education
1976-06-01
The geometrical distribution inferred from the inelastic cross section is assumed to be proportional to the partial waves. The precocious scaling and the Q/sup 2/-dependence of various quantities are treated from the geometrical point of view. It is shown that the approximate conservation of the orbital angular momentum may be a very practical rule to understand the helicity structure of various hadronic and electromagnetic reactions. The rule can be applied to inclusive reactions as well. The model is also applied to large angle processes. Through the discussion, it is suggested that many peculiar properties of the quark-parton can be ascribed to the geometrical effects.
Galindo-Israel, V.; Imbriale, W.; Shogen, K.; Mittra, R.
1990-01-01
In obtaining solutions to the first-order nonlinear partial differential equations (PDEs) for synthesizing offset dual-shaped reflectors, it is found that previously observed computational problems can be avoided if the integration of the PDEs is started from an inner projected perimeter and integrated outward rather than starting from an outer projected perimeter and integrating inward. This procedure, however, introduces a new parameter, the main reflector inner perimeter radius p(o), when given a subreflector inner angle 0(o). Furthermore, a desired outer projected perimeter (e.g., a circle) is no longer guaranteed. Stability of the integration is maintained if some of the initial parameters are determined first from an approximate solution to the PDEs. A one-, two-, or three-parameter optimization algorithm can then be used to obtain a best set of parameters yielding a close fit to the desired projected outer rim. Good low cross-polarization mapping functions are also obtained. These methods are illustrated by synthesis of a high-gain offset-shaped Cassegrainian antenna and a low-noise offset-shaped Gregorian antenna.
Bray, Hubert L; Mazzeo, Rafe; Sesum, Natasa
2015-01-01
This volume includes expanded versions of the lectures delivered in the Graduate Minicourse portion of the 2013 Park City Mathematics Institute session on Geometric Analysis. The papers give excellent high-level introductions, suitable for graduate students wishing to enter the field and experienced researchers alike, to a range of the most important areas of geometric analysis. These include: the general issue of geometric evolution, with more detailed lectures on Ricci flow and Kähler-Ricci flow, new progress on the analytic aspects of the Willmore equation as well as an introduction to the recent proof of the Willmore conjecture and new directions in min-max theory for geometric variational problems, the current state of the art regarding minimal surfaces in R^3, the role of critical metrics in Riemannian geometry, and the modern perspective on the study of eigenfunctions and eigenvalues for Laplace-Beltrami operators.
Energy Technology Data Exchange (ETDEWEB)
Olivares Gomez, Edgardo; Cortez, Luis A. Barbosa [Universidade Estadual de Campinas (FEAGRI/UNICAMP), SP (Brazil). Fac. de Engenharia Agricola. Lab. de Termodinamica e Energia; Alarcon, Guillermo A. Rocca; Perez, Luis E. Brossard [Universidad de Oriente, Santiago de Cuba (Cuba)
2008-07-01
Two types of biomass solid particles, elephant grass (Pennisetum purpureum Schum. variety) and sugar cane trash, were studied in laboratory in order to obtain information about several physical and geometrical properties. In the both case, the length, breadth, and thickness of fifty particles selected randomly from each fraction of the size class, obtained by mechanical fractionation through sieves, were measured manually given their size. A geometric model of type rectangular base prism was adopted because based on observations it was demonstrated that the most of particles that were measured exhibited length which was significantly greater that width ( l >> a ). From these measurements average values for other properties were estimated, for example, characteristic dimension of particle, projected area of the rectangular prism, area of the prism rectangular section, volume of the rectangular prism, shape factors, sphericity, particles specific superficial area and equivalent diameter. A statistical analysis was done and proposed empirical and semi-empirical mathematical correlation models obtained by lineal regression, which show a goodness of fit of these equations to the reported experimental data. (author)
Georgescu, Dan I; Higham, Nicholas J; Peters, Gareth W
2018-03-01
We derive explicit solutions to the problem of completing a partially specified correlation matrix. Our results apply to several block structures for the unspecified entries that arise in insurance and risk management, where an insurance company with many lines of business is required to satisfy certain capital requirements but may have incomplete knowledge of the underlying correlation matrix. Among the many possible completions, we focus on the one with maximal determinant. This has attractive properties and we argue that it is suitable for use in the insurance application. Our explicit formulae enable easy solution of practical problems and are useful for testing more general algorithms for the maximal determinant correlation matrix completion problem.
Geometric statistical inference
International Nuclear Information System (INIS)
Periwal, Vipul
1999-01-01
A reparametrization-covariant formulation of the inverse problem of probability is explicitly solved for finite sample sizes. The inferred distribution is explicitly continuous for finite sample size. A geometric solution of the statistical inference problem in higher dimensions is outlined
Niethammer, Marc; Hart, Gabriel L; Pace, Danielle F; Vespa, Paul M; Irimia, Andrei; Van Horn, John D; Aylward, Stephen R
2011-01-01
Standard image registration methods do not account for changes in image appearance. Hence, metamorphosis approaches have been developed which jointly estimate a space deformation and a change in image appearance to construct a spatio-temporal trajectory smoothly transforming a source to a target image. For standard metamorphosis, geometric changes are not explicitly modeled. We propose a geometric metamorphosis formulation, which explains changes in image appearance by a global deformation, a deformation of a geometric model, and an image composition model. This work is motivated by the clinical challenge of predicting the long-term effects of traumatic brain injuries based on time-series images. This work is also applicable to the quantification of tumor progression (e.g., estimating its infiltrating and displacing components) and predicting chronic blood perfusion changes after stroke. We demonstrate the utility of the method using simulated data as well as scans from a clinical traumatic brain injury patient.
On geometrized gravitation theories
International Nuclear Information System (INIS)
Logunov, A.A.; Folomeshkin, V.N.
1977-01-01
General properties of the geometrized gravitation theories have been considered. Geometrization of the theory is realized only to the extent that by necessity follows from an experiment (geometrization of the density of the matter Lagrangian only). Aor a general case the gravitation field equations and the equations of motion for matter are formulated in the different Riemann spaces. A covariant formulation of the energy-momentum conservation laws is given in an arbitrary geometrized theory. The noncovariant notion of ''pseudotensor'' is not required in formulating the conservation laws. It is shown that in the general case (i.e., when there is an explicit dependence of the matter Lagrangian density on the covariant derivatives) a symmetric energy-momentum tensor of the matter is explicitly dependent on the curvature tensor. There are enlisted different geometrized theories that describe a known set of the experimental facts. The properties of one of the versions of the quasilinear geometrized theory that describes the experimental facts are considered. In such a theory the fundamental static spherically symmetrical solution has a singularity only in the coordinate origin. The theory permits to create a satisfactory model of the homogeneous nonstationary Universe
Directory of Open Access Journals (Sweden)
Alireza Rasekh
2016-11-01
Full Text Available In this paper, a set of correlations for the windage power losses in a 4 kW axial flux permanent magnet synchronous machine (AFPMSM is presented. In order to have an efficient machine, it is necessary to optimize the total electromagnetic and mechanical losses. Therefore, fast equations are needed to estimate the windage power losses of the machine. The geometry consists of an open rotor–stator with sixteen magnets at the periphery of the rotor with an annular opening in the entire disk. Air can flow in a channel being formed between the magnets and in a small gap region between the magnets and the stator surface. To construct the correlations, computational fluid dynamics (CFD simulations through the frozen rotor (FR method are performed at the practical ranges of the geometrical parameters, namely the gap size distance, the rotational speed of the rotor, the magnet thickness and the magnet angle. Thereafter, two categories of formulations are defined to make the windage losses dimensionless based on whether the losses are mainly due to the viscous forces or the pressure forces. At the end, the correlations can be achieved via curve fittings from the numerical data. The results reveal that the pressure forces are responsible for the windage losses for the side surfaces in the air-channel, whereas for the surfaces facing the stator surface in the gap, the viscous forces mainly contribute to the windage losses. Additionally, the results of the parametric study demonstrate that the overall windage losses in the machine escalate with an increase in either the rotational Reynolds number or the magnet thickness ratio. By contrast, the windage losses decrease once the magnet angle ratio enlarges. Moreover, it can be concluded that the proposed correlations are very useful tools in the design and optimizations of this type of electrical machine.
A solution of the Schrodinger equation with two-body correlations included
International Nuclear Information System (INIS)
Fabre de la Ripelle, M.
1984-01-01
A procedure for introducing the two-body correlations in the solution of the Schrodinger equation is described. The N-body Schrodinger equation for nucleons subject to two-(or many)-body N-N interaction has never been solved with accuracy except for few-body systems. Indeed it is difficult to take the two-body correlations generated by the interaction into account in the wave function
Exact solution of the one-dimensional fermionic model with correlated hopping
International Nuclear Information System (INIS)
Schadschneider, A.; Su Gang; Zittartz, J.
1997-01-01
We extend the Bethe Ansatz solution of a one-dimensional integrable fermionic model with correlated hopping to the parameter regime Δt > 1. It is found that the model is equivalent to one with interaction 2 - Δt, but with twisted boundary conditions. Apart from the ground state energy we investigate the low-lying excitations and the asymptotic behaviour of the correlation functions. As in the case of Δt < 1 we find dominating superconducting correlations for small doping. The behaviour in this regime therefore differs from that of the non-integrable model with symmetric bond-charge interaction (Hirsch model). (orig.)
Importance analysis for models with correlated variables and its sparse grid solution
International Nuclear Information System (INIS)
Li, Luyi; Lu, Zhenzhou
2013-01-01
For structural models involving correlated input variables, a novel interpretation for variance-based importance measures is proposed based on the contribution of the correlated input variables to the variance of the model output. After the novel interpretation of the variance-based importance measures is compared with the existing ones, two solutions of the variance-based importance measures of the correlated input variables are built on the sparse grid numerical integration (SGI): double-loop nested sparse grid integration (DSGI) method and single loop sparse grid integration (SSGI) method. The DSGI method solves the importance measure by decreasing the dimensionality of the input variables procedurally, while SSGI method performs importance analysis through extending the dimensionality of the inputs. Both of them can make full use of the advantages of the SGI, and are well tailored for different situations. By analyzing the results of several numerical and engineering examples, it is found that the novel proposed interpretation about the importance measures of the correlated input variables is reasonable, and the proposed methods for solving importance measures are efficient and accurate. -- Highlights: •The contribution of correlated variables to the variance of the output is analyzed. •A novel interpretation for variance-based indices of correlated variables is proposed. •Two solutions for variance-based importance measures of correlated variables are built
Shokeen, Namita; Issa, Christopher; Mukhopadhyay, Ashis
2017-12-01
We studied the diffusion of nanoparticles (NPs) within aqueous entangled solutions of polyethylene oxide (PEO) by using two different optical techniques. Fluorescence correlation spectroscopy, a method widely used to investigate nanoparticle dynamics in polymer solution, was used to measure the long-time diffusion coefficient (D) of 25 nm radius particles within high molecular weight, Mw = 600 kg/mol PEO in water solutions. Differential dynamic microscopy (DDM) was used to determine the wave-vector dependent dynamics of NPs within the same polymer solutions. Our results showed good agreement between the two methods, including demonstration of normal diffusion and almost identical diffusion coefficients obtained by both techniques. The research extends the scope of DDM to study the dynamics and rheological properties of soft matter at a nanoscale. The measured diffusion coefficients followed a scaling theory, which can be explained by the coupling between polymer dynamics and NP motion.
Mobile Watermarking against Geometrical Distortions
Directory of Open Access Journals (Sweden)
Jing Zhang
2015-08-01
Full Text Available Mobile watermarking robust to geometrical distortions is still a great challenge. In mobile watermarking, efficient computation is necessary because mobile devices have very limited resources due to power consumption. In this paper, we propose a low-complexity geometrically resilient watermarking approach based on the optimal tradeoff circular harmonic function (OTCHF correlation filter and the minimum average correlation energy Mellin radial harmonic (MACE-MRH correlation filter. By the rotation, translation and scale tolerance properties of the two kinds of filter, the proposed watermark detector can be robust to geometrical attacks. The embedded watermark is weighted by a perceptual mask which matches very well with the properties of the human visual system. Before correlation, a whitening process is utilized to improve watermark detection reliability. Experimental results demonstrate that the proposed watermarking approach is computationally efficient and robust to geometrical distortions.
Measurement and Correlation of the Ionic Conductivity of Ionic Liquid-Molecular Solvent Solutions
Institute of Scientific and Technical Information of China (English)
LI,Wen-Jing; HAN,Bu-Xing; TAO,Ran-Ting; ZHANG,Zhao-Fu; ZHANG,Jian-Ling
2007-01-01
The ionic conductivity of the solutions formed from 1-n-butyl-3-methylimidazolium tetrafluoroborate ([Bmim][BF4]) or 1-n-butyl-3-methylimidazolium hexafluorophosphate ([Bmim][PF6]) and different molecular solvents (MSs) were measured at 298.15 K. The molar conductivity of the ionic liquids (ILs) increased dramatically with increasing concentration of the MSs. It was found that the molar conductivity of the IL in the solutions studied in this work could be well correlated by the molar conductivity of the neat ILs and the dielectric constant and molar volume of the MSs.
DEFF Research Database (Denmark)
Andersen, Jørgen Ellegaard; Borot, Gaëtan; Orantin, Nicolas
We propose a general theory whose main component are functorial assignments ∑→Ω∑ ∈ E (∑), for a large class of functors E from a certain category of bordered surfaces (∑'s) to a suitable a target category of topological vector spaces. The construction is done by summing appropriate compositions...... as Poisson structures on the moduli space of flat connections. The theory has a wider scope than that and one expects that many functorial objects in low-dimensional geometry and topology should have a GR construction. The geometric recursion has various projections to topological recursion (TR) and we...... in particular show it retrieves all previous variants and applications of TR. We also show that, for any initial data for topological recursion, one can construct initial data for GR with values in Frobenius algebra-valued continuous functions on Teichmueller space, such that the ωg,n of TR are obtained...
International Nuclear Information System (INIS)
Hirano, Kazumi; Kinoshita, Takaaki; Uemura, Takeshi; Motohashi, Hozumi; Watanabe, Yohei; Ebihara, Tatsuhiko; Nishiyama, Hidetoshi; Sato, Mari; Suga, Mitsuo; Maruyama, Yuusuke; Tsuji, Noriko M.; Yamamoto, Masayuki; Nishihara, Shoko; Sato, Chikara
2014-01-01
Correlative light-electron microscopy of cells in a natural environment of aqueous liquid facilitates high-throughput observation of protein complex formation. ASEM allows the inverted SEM to observe the wet sample from below, while an optical microscope observes it from above quasi-simultaneously. The disposable ASEM dish with a silicon nitride (SiN) film window can be coated variously to realize the primary-culture of substrate-sensitive cells in a few milliliters of culture medium in a stable incubator environment. Neuron differentiation, neural networking, proplatelet-formation and phagocytosis were captured by optical or fluorescence microscopy, and imaged at high resolution by gold-labeled immuno-ASEM with/without metal staining. Fas expression on the cell surface was visualized, correlated to the spatial distribution of F-actin. Axonal partitioning was studied using primary-culture neurons, and presynaptic induction by GluRδ2-N-terminus-linked fluorescent magnetic beads was correlated to the presynaptic-marker Bassoon. Further, megakaryocytes secreting proplatelets were captured, and P-selectins with adherence activity were localized to some of the granules present by immuno-ASEM. The phagocytosis of lactic acid bacteria by dendritic cells was also imaged. Based on these studies, ASEM correlative microscopy promises to allow the study of various mesoscopic-scale dynamics in the near future. - Highlights: • In situ correlative light electron microscopy of samples in open solution by ASEM. • Primary cultures for in-solution CLEM by developing SiN-film coating methods • First visualization of fluorescent magnetic beads in aqueous solution by CLEM. • Presynaptic induction of neurons by GluRδ2-N-terminus-coated beads studied by CLEM. • Axonal partitioning, bacterial phagocytosis, platelet formation imaged by CLEM
Energy Technology Data Exchange (ETDEWEB)
Hirano, Kazumi; Kinoshita, Takaaki [Laboratory of Cell Biology, Department of Bioinformatics, Faculty of Engineering, Soka University, 1-236 Tangi-machi, Hachioji, Tokyo 192-8577 (Japan); Uemura, Takeshi [Department of Molecular Neurobiology and Pharmacology, Graduate School of Medicine, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033 (Japan); Department of Molecular and Cellular Physiology, Shinshu University School of Medicine, 3-1-1 Asahi, Matsumoto, Nagano 390-8621 (Japan); Motohashi, Hozumi [Department of Gene Expression Regulation, Institute of Development, Aging and Cancer, Tohoku University, 4-1 Seiryo-cho, Aoba-ku, Sendai 980-8575 (Japan); Watanabe, Yohei; Ebihara, Tatsuhiko [Biomedical Research Institute, National Institute of Industrial Science and Technology (AIST), 1-1-1 Higashi, Tsukuba 305-8566 (Japan); Nishiyama, Hidetoshi [JEOL Ltd., 1-2 Musashino 3-chome, Akishima, Tokyo 196-8558 (Japan); Sato, Mari [Biomedical Research Institute, National Institute of Industrial Science and Technology (AIST), 1-1-1 Higashi, Tsukuba 305-8566 (Japan); Suga, Mitsuo [JEOL Ltd., 1-2 Musashino 3-chome, Akishima, Tokyo 196-8558 (Japan); Maruyama, Yuusuke; Tsuji, Noriko M. [Biomedical Research Institute, National Institute of Industrial Science and Technology (AIST), 1-1-1 Higashi, Tsukuba 305-8566 (Japan); Yamamoto, Masayuki [Department of Medical Biochemistry, Tohoku University Graduate School of Medicine, 2-1 Seiryo-cho, Aoba-ku, Sendai 980-8575 (Japan); Nishihara, Shoko, E-mail: shoko@soka.ac.jp [Laboratory of Cell Biology, Department of Bioinformatics, Faculty of Engineering, Soka University, 1-236 Tangi-machi, Hachioji, Tokyo 192-8577 (Japan); Sato, Chikara, E-mail: ti-sato@aist.go.jp [Biomedical Research Institute, National Institute of Industrial Science and Technology (AIST), 1-1-1 Higashi, Tsukuba 305-8566 (Japan)
2014-08-01
Correlative light-electron microscopy of cells in a natural environment of aqueous liquid facilitates high-throughput observation of protein complex formation. ASEM allows the inverted SEM to observe the wet sample from below, while an optical microscope observes it from above quasi-simultaneously. The disposable ASEM dish with a silicon nitride (SiN) film window can be coated variously to realize the primary-culture of substrate-sensitive cells in a few milliliters of culture medium in a stable incubator environment. Neuron differentiation, neural networking, proplatelet-formation and phagocytosis were captured by optical or fluorescence microscopy, and imaged at high resolution by gold-labeled immuno-ASEM with/without metal staining. Fas expression on the cell surface was visualized, correlated to the spatial distribution of F-actin. Axonal partitioning was studied using primary-culture neurons, and presynaptic induction by GluRδ2-N-terminus-linked fluorescent magnetic beads was correlated to the presynaptic-marker Bassoon. Further, megakaryocytes secreting proplatelets were captured, and P-selectins with adherence activity were localized to some of the granules present by immuno-ASEM. The phagocytosis of lactic acid bacteria by dendritic cells was also imaged. Based on these studies, ASEM correlative microscopy promises to allow the study of various mesoscopic-scale dynamics in the near future. - Highlights: • In situ correlative light electron microscopy of samples in open solution by ASEM. • Primary cultures for in-solution CLEM by developing SiN-film coating methods • First visualization of fluorescent magnetic beads in aqueous solution by CLEM. • Presynaptic induction of neurons by GluRδ2-N-terminus-coated beads studied by CLEM. • Axonal partitioning, bacterial phagocytosis, platelet formation imaged by CLEM.
Directory of Open Access Journals (Sweden)
Samara de Azevedo Gomes Campos
Full Text Available Detection of occlusal caries with visual examination using ICDAS correlates strongly with histology under stereomicroscopy (SM, but dentin aspects under SM are ambiguous regarding mineral content. Thus, our aim was to test two null hypotheses: SM and microradiography result in similar correlations between ICDAS and histology; SM and microradiography result in similar positive (PPV and negative predictive values (NPV of ICDAS cut-off 1-2 (scores 0-2 as sound with histological threshold D3 (demineralization in the inner third of dentin. Occlusal surfaces of extracted permanent teeth (n = 115 were scored using ICDAS. Undemineralized ground sections were histologically scored using both SM without contrast solution and microradiography after immersion in Thoulet's solution 1.47 for 24 h (MRC. Correlation between ICDAS and histology differed from SM (0.782 to MRC (0.511 (p = 0.0002, with a large effect size "q" of 0.49 (95% CI: 0.638/0.338. For ICDAS cut-off 1-2 and D3, PPV from MRC (0.56 was higher than that from SM (0.28 (p< 0.00001; effect size h = 0.81, and NPV from MRC (0.72 was lower than that from SM (1,00 (p < 0.00001; effect size h = 1.58. In conclusion, SM overestimated the correlation between ICDAS and lesion depth, and underestimated the number of occlusal surfaces with ICDAS cut-off 1-2 and deep dentin demineralization.
Geometric inequalities methods of proving
Sedrakyan, Hayk
2017-01-01
This unique collection of new and classical problems provides full coverage of geometric inequalities. Many of the 1,000 exercises are presented with detailed author-prepared-solutions, developing creativity and an arsenal of new approaches for solving mathematical problems. This book can serve teachers, high-school students, and mathematical competitors. It may also be used as supplemental reading, providing readers with new and classical methods for proving geometric inequalities. .
International Nuclear Information System (INIS)
Sadeghi, Rahmat
2005-01-01
The polymer Wilson model and the polymer NRTL model have been extended for the representation of the excess enthalpy of multicomponent polymer solutions. Applicability of obtained equations in the correlation of the excess enthalpies of polymer solutions has been examined. It is found that the both models are suitable models in representing the published excess enthalpy data for the tested polymer solutions
Effect of simple solutes on the long range dipolar correlations in liquid water
Energy Technology Data Exchange (ETDEWEB)
Baul, Upayan, E-mail: upayanb@imsc.res.in; Anishetty, Ramesh, E-mail: ramesha@imsc.res.in; Vemparala, Satyavani, E-mail: vani@imsc.res.in [The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113 (India); Kanth, J. Maruthi Pradeep, E-mail: jmpkanth@gmail.com [Vectra LLC, Mount Road, Chennai 600006 (India)
2016-03-14
Intermolecular correlations in liquid water at ambient conditions have generally been characterized through short range density fluctuations described through the atomic pair distribution functions. Recent numerical and experimental results have suggested that such a description of order or structure in liquid water is incomplete and there exist considerably longer ranged orientational correlations in water that can be studied through dipolar correlations. In this study, using large scale classical, atomistic molecular dynamics simulations using TIP4P-Ew and TIP3P models of water, we show that salts such as sodium chloride (NaCl), potassium chloride (KCl), caesium chloride (CsCl), and magnesium chloride (MgCl{sub 2}) have a long range effect on the dipolar correlations, which cannot be explained by the notion of structure making and breaking by dissolved ions. Observed effects are explained through orientational stratification of water molecules around ions and their long range coupling to the global hydrogen bond network by virtue of the sum rule for water. The observations for single hydrophilic solutes are contrasted with the same for a single methane (CH{sub 4}) molecule. We observe that even a single small hydrophobe can result in enhancement of long range orientational correlations in liquid water, contrary to the case of dissolved ions, which have been observed to have a reducing effect. The observations from this study are discussed in the context of hydrophobic effect.
Energy Technology Data Exchange (ETDEWEB)
Meisel, D
1975-07-15
Recent experimental data concerning the rate constants for electron transfer reactions of organic systems in aqueous solutions and their equilibrium constants is examined for possible correlation. The data is correlated quite well by the Marcus theory, if a reorganization parameter, lambda, of 18 kcal/mole is used. Assuming that the only contribution to lambda is the free energy of rearrangement of the water molecules, an effective radius of 5 A for the reacting entities is estimated. For the zero free energy change reaction, i.e., electron exchange between a radical ion and its parent molecule, a rate constant of about 5 X 10/sup 7/ M/sup -1/ s/sup -1/ is predicted. (auth)
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
Evidence of three-body correlation functions in Rb+ and Sr2+ acetonitrile solutions
D'Angelo, P.; Pavel, N. V.
1999-09-01
The local structure of Sr2+ and Rb+ ions in acetonitrile has been investigated by x-ray absorption spectroscopy (XAS) and molecular dynamics simulations. The extended x-ray absorption fine structure above the Sr and Rb K edges has been interpreted in the framework of multiple scattering (MS) formalism and, for the first time, clear evidence of MS contributions has been found in noncomplexing ion solutions. Molecular dynamics has been used to generate the partial pair and triangular distribution functions from which model χ(k) signals have been constructed. The Sr2+ and Rb+ acetonitrile pair distribution functions show very sharp and well-defined first peaks indicating the presence of a well organized first solvation shell. Most of the linear acetonitrile molecules have been found to be distributed like hedgehog spines around the Sr2+ and Rb+ ions. The presence of three-body correlations has been singled out by the existence of well-defined peaks in the triangular configurations. Excellent agreement has been found between the theoretical and experimental data enforcing the reliability of the interatomic potentials used in the simulations. These results demonstrate the ability of the XAS technique in probing the higher-order correlation functions in solution.
Geometric scaling as traveling waves
International Nuclear Information System (INIS)
Munier, S.; Peschanski, R.
2003-01-01
We show the relevance of the nonlinear Fisher and Kolmogorov-Petrovsky-Piscounov (KPP) equation to the problem of high energy evolution of the QCD amplitudes. We explain how the traveling wave solutions of this equation are related to geometric scaling, a phenomenon observed in deep-inelastic scattering experiments. Geometric scaling is for the first time shown to result from an exact solution of nonlinear QCD evolution equations. Using general results on the KPP equation, we compute the velocity of the wave front, which gives the full high energy dependence of the saturation scale
Institute of Scientific and Technical Information of China (English)
杜殿楼; 杨潇
2012-01-01
A (2+1)-dimensional coupled modified Kadomtsev-Petviashvili (CMKP) equation is proposed, and its decomposition is derived by its Lax pair. Based on the theory of algebraic curve, an algebro-geometric solution of the CMKP equation is obtained.%提出一个(2+1)-维耦合的mKP(CMKP)方程,通过其Lax对,实现了该方程的分解.进一步借助代数曲线理论,给出其代数几何解.
Sample-averaged biexciton quantum yield measured by solution-phase photon correlation.
Beyler, Andrew P; Bischof, Thomas S; Cui, Jian; Coropceanu, Igor; Harris, Daniel K; Bawendi, Moungi G
2014-12-10
The brightness of nanoscale optical materials such as semiconductor nanocrystals is currently limited in high excitation flux applications by inefficient multiexciton fluorescence. We have devised a solution-phase photon correlation measurement that can conveniently and reliably measure the average biexciton-to-exciton quantum yield ratio of an entire sample without user selection bias. This technique can be used to investigate the multiexciton recombination dynamics of a broad scope of synthetically underdeveloped materials, including those with low exciton quantum yields and poor fluorescence stability. Here, we have applied this method to measure weak biexciton fluorescence in samples of visible-emitting InP/ZnS and InAs/ZnS core/shell nanocrystals, and to demonstrate that a rapid CdS shell growth procedure can markedly increase the biexciton fluorescence of CdSe nanocrystals.
Microrheology of polymeric solutions using x-ray photon correlation spectroscopy
International Nuclear Information System (INIS)
Papagiannopoulos, A; Waigh, T A; Fluerasu, A; Fernyhough, C; Madsen, A
2005-01-01
We demonstrate the technique of XPCS microrheology on opaque polymeric solutions (1-20% w/w) using colloidal silica probes. The short time decay of the intensity correlation function provides the mean square displacement (MSD) of the colloidal probes. The MSDs of the probes are subsequently transformed using the generalized Stokes-Einstein equation, allowing the linear viscoelastic spectra of a biopolymer (gellan) and a synthetic polyelectrolyte (polystyrene sulfonate, PSS) to be calculated over two decades of frequency. MSDs can be measured that are two orders of magnitude smaller than those possible with video particle tracking microrheology, with a sensitivity of ∼10 nm s -1 for displacements of ∼nms. The XPCS data for water, glycerol and PSS combs are in agreement with video particle tracking microrheology experiments performed at lower polymer concentrations. (letter to the editor)
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.
Numerical path integral solution to strong Coulomb correlation in one dimensional Hooke's atom
Ruokosenmäki, Ilkka; Gholizade, Hossein; Kylänpää, Ilkka; Rantala, Tapio T.
2017-01-01
We present a new approach based on real time domain Feynman path integrals (RTPI) for electronic structure calculations and quantum dynamics, which includes correlations between particles exactly but within the numerical accuracy. We demonstrate that incoherent propagation by keeping the wave function real is a novel method for finding and simulation of the ground state, similar to Diffusion Monte Carlo (DMC) method, but introducing new useful tools lacking in DMC. We use 1D Hooke's atom, a two-electron system with very strong correlation, as our test case, which we solve with incoherent RTPI (iRTPI) and compare against DMC. This system provides an excellent test case due to exact solutions for some confinements and because in 1D the Coulomb singularity is stronger than in two or three dimensional space. The use of Monte Carlo grid is shown to be efficient for which we determine useful numerical parameters. Furthermore, we discuss another novel approach achieved by combining the strengths of iRTPI and DMC. We also show usefulness of the perturbation theory for analytical approximates in case of strong confinements.
On bivariate geometric distribution
Directory of Open Access Journals (Sweden)
K. Jayakumar
2013-05-01
Full Text Available Characterizations of bivariate geometric distribution using univariate and bivariate geometric compounding are obtained. Autoregressive models with marginals as bivariate geometric distribution are developed. Various bivariate geometric distributions analogous to important bivariate exponential distributions like, Marshall-Olkin’s bivariate exponential, Downton’s bivariate exponential and Hawkes’ bivariate exponential are presented.
Visualizing the Geometric Series.
Bennett, Albert B., Jr.
1989-01-01
Mathematical proofs often leave students unconvinced or without understanding of what has been proved, because they provide no visual-geometric representation. Presented are geometric models for the finite geometric series when r is a whole number, and the infinite geometric series when r is the reciprocal of a whole number. (MNS)
A new geometrical gravitational theory
International Nuclear Information System (INIS)
Obata, T.; Chiba, J.; Oshima, H.
1981-01-01
A geometrical gravitational theory is developed. The field equations are uniquely determined apart from one unknown dimensionless parameter ω 2 . It is based on an extension of the Weyl geometry, and by the extension the gravitational coupling constant and the gravitational mass are made to be dynamical and geometrical. The fundamental geometrical objects in the theory are a metric gsub(μν) and two gauge scalars phi and psi. The theory satisfies the weak equivalence principle, but breaks the strong one generally. u(phi, psi) = phi is found out on the assumption that the strong one keeps holding good at least for bosons of low spins. Thus there is the simple correspondence between the geometrical objects and the gravitational objects. Since the theory satisfies the weak one, the inertial mass is also dynamical and geometrical in the same way as is the gravitational mass. Moreover, the cosmological term in the theory is a coscalar of power -4 algebraically made of psi and u(phi, psi), so it is dynamical, too. Finally spherically symmetric exact solutions are given. The permissible range of the unknown parameter ω 2 is experimentally determined by applying the solutions to the solar system. (author)
DEFF Research Database (Denmark)
Goncalves, Ana Saraiva; Kontogeorgis, Georgios; Harismiadis, Vassilis I.
1996-01-01
The van der Waals equation of state is used for the correlation and the prediction of the lower critical solution behavior or mixtures including a solvent and a polymer. The equation of state parameters for the polymer are estimated from experimental volumetric data at low pressures. The equation...
Geometric Approaches to Quadratic Equations from Other Times and Places.
Allaire, Patricia R.; Bradley, Robert E.
2001-01-01
Focuses on geometric solutions of quadratic problems. Presents a collection of geometric techniques from ancient Babylonia, classical Greece, medieval Arabia, and early modern Europe to enhance the quadratic equation portion of an algebra course. (KHR)
Geometric Mixing, Peristalsis, and the Geometric Phase of the Stomach.
Arrieta, Jorge; Cartwright, Julyan H E; Gouillart, Emmanuelle; Piro, Nicolas; Piro, Oreste; Tuval, Idan
2015-01-01
Mixing fluid in a container at low Reynolds number--in an inertialess environment--is not a trivial task. Reciprocating motions merely lead to cycles of mixing and unmixing, so continuous rotation, as used in many technological applications, would appear to be necessary. However, there is another solution: movement of the walls in a cyclical fashion to introduce a geometric phase. We show using journal-bearing flow as a model that such geometric mixing is a general tool for using deformable boundaries that return to the same position to mix fluid at low Reynolds number. We then simulate a biological example: we show that mixing in the stomach functions because of the "belly phase," peristaltic movement of the walls in a cyclical fashion introduces a geometric phase that avoids unmixing.
Geometric Mixing, Peristalsis, and the Geometric Phase of the Stomach.
Directory of Open Access Journals (Sweden)
Jorge Arrieta
Full Text Available Mixing fluid in a container at low Reynolds number--in an inertialess environment--is not a trivial task. Reciprocating motions merely lead to cycles of mixing and unmixing, so continuous rotation, as used in many technological applications, would appear to be necessary. However, there is another solution: movement of the walls in a cyclical fashion to introduce a geometric phase. We show using journal-bearing flow as a model that such geometric mixing is a general tool for using deformable boundaries that return to the same position to mix fluid at low Reynolds number. We then simulate a biological example: we show that mixing in the stomach functions because of the "belly phase," peristaltic movement of the walls in a cyclical fashion introduces a geometric phase that avoids unmixing.
Vahabzadeh Pasikhani, Javad; Gilani, Neda; Ebrahimian Pirbazari, Azadeh
2018-02-01
Freestanding TiO2 nanotubes (FSNTs) with various physical dimensions were fabricated by two-step anodization process with different voltages and anodization times. The detachment method employed in this study involved voltage reduction at the end of the second step and ultrasonic chemical treatment. The results demonstrated that this detachment method is a beneficial technique to create thin open-mouthed and closed-end FSNTs (with lengths of 6-14 μm). Moreover, the influences of anodization conditions on photocatalytic activity, structural properties and geometrical features of FSNTs in comparative degradation of two non-colored (2,4-dichlorophenol) and colored (methylene blue) pollutants were investigated. Findings revealed that the quantity of the photocatalyst utilized is an effective parameter and using the optimum weight (10 mg/100 ml of 2,4-dichlorophenol) could increase the efficiency of the process up to 21%. Further, the results demonstrated that if equal optimum weights of FSNTs are chosen, decreases in voltage and anodization time significantly influence the structural properties, geometrical features, and photodegradation efficiency. The enhancement achieved in the degradation of both 2,4-dichlorophenol and methylene blue using the nanotubes with the shortest diameter (54 nm) and length (6.5 μm), which possess the lowest porosity (0.5) and also the highest surface area (0.53 m2 g-1), nanotubes’ density (19 cm2 cm-2) and wall thickness to length ratio (2). In addition, the results obtained indicated that the degradation reactions follow first-order kinetics in the degradation of the both pollutants. The apparent degradation rate constant of methylene blue was approximately 1.2 times greater than of the 2,4-dichlorophenol due to the negative charge of the nanotubes’ surface and electrostatic adsorptions.
International Nuclear Information System (INIS)
Poels, Kenneth; Dhont, Jennifer; Verellen, Dirk; Blanck, Oliver; Ernst, Floris; Vandemeulebroucke, Jef; Depuydt, Tom; Storme, Guy; De Ridder, Mark
2015-01-01
Purpose: A head-to-head comparison of two clinical correlation models with a focus on geometrical accuracy for internal tumor motion estimation during real-time tumor tracking (RTTT). Methods and materials: Both the CyberKnife (CK) and the Vero systems perform RTTT with a correlation model that is able to describe hysteresis in the breathing motion. The CK dual-quadratic (DQ) model consists of two polynomial functions describing the trajectory of the tumor for inhale and exhale breathing motion, respectively. The Vero model is based on a two-dimensional (2D) function depending on position and speed of the external breathing signal to describe a closed-loop tumor trajectory. In this study, 20 s of internal motion data, using an 11 Hz (on average) full fluoroscopy (FF) sequence, was used for training of the CK and Vero models. Further, a subsampled set of 15 internal tumor positions (15p) equally spread over the different phases of the breathing motion was used for separate training of the CK DQ model. Also a linear model was trained using 15p and FF tumor motion data. Fifteen liver and lung cancer patients, treated on the Vero system with RTTT, were retrospectively evaluated comparing the CK FF, CK 15p and Vero FF models using an in-house developed simulator. The distance between estimated target position and the tumor position localized by X-ray imaging was measured in the beams-eye view (BEV) to calculate the 95th percentile BEV modeling errors (ME 95,BEV ). Additionally, the percentage of ME 95,BEV smaller than 5 mm (P 5mm ) was determined for all correlation models. Results: In general, no significant difference (p > 0.05, paired t-test) was found between the CK FF and Vero models. Based on patient-specific evaluation of the geometrical accuracy of the linear, CK DQ and Vero correlation models, no statistical necessity (p > 0.05, two-way ANOVA) of including hysteresis in correlation models was proven, although during inhale breathing motion, the linear model
Directory of Open Access Journals (Sweden)
Chifu E. N.
2009-07-01
Full Text Available Here, we present a profound and complete analytical solution to Einstein’s gravitational field equations exterior to astrophysically real or hypothetical time varying distribu- tions of mass or pressure within regions of spherical geometry. The single arbitrary function f in our proposed exterior metric tensor and constructed field equations makes our method unique, mathematically less combersome and astrophysically satisfactory. The obtained solution of Einstein’s gravitational field equations tends out to be a gen- eralization of Newton’s gravitational scalar potential exterior to the spherical mass or pressure distribution under consideration
Geometric procedures for civil engineers
Tonias, Elias C
2016-01-01
This book provides a multitude of geometric constructions usually encountered in civil engineering and surveying practice. A detailed geometric solution is provided to each construction as well as a step-by-step set of programming instructions for incorporation into a computing system. The volume is comprised of 12 chapters and appendices that may be grouped in three major parts: the first is intended for those who love geometry for its own sake and its evolution through the ages, in general, and, more specifically, with the introduction of the computer. The second section addresses geometric features used in the book and provides support procedures used by the constructions presented. The remaining chapters and the appendices contain the various constructions. The volume is ideal for engineering practitioners in civil and construction engineering and allied areas.
Transition curves for highway geometric design
Kobryń, Andrzej
2017-01-01
This book provides concise descriptions of the various solutions of transition curves, which can be used in geometric design of roads and highways. It presents mathematical methods and curvature functions for defining transition curves. .
Czech Academy of Sciences Publication Activity Database
Neustupa, Jiří
2014-01-01
Roč. 139, č. 4 (2014), s. 685-698 ISSN 0862-7959 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : Navier-Stokes equation * suitable weak solution * regularity Subject RIV: BA - General Mathematics http://hdl.handle.net/10338.dmlcz/144145
Geometrization of quantum physics
International Nuclear Information System (INIS)
Ol'khov, O.A.
2009-01-01
It is shown that the Dirac equation for a free particle can be considered as a description of specific distortion of the space Euclidean geometry (space topological defect). This approach is based on the possibility of interpretation of the wave function as vector realizing representation of the fundamental group of the closed topological space-time 4-manifold. Mass and spin appear to be topological invariants. Such a concept explains all so-called 'strange' properties of quantum formalism: probabilities, wave-particle duality, nonlocal instantaneous correlation between noninteracting particles (EPR-paradox) and so on. Acceptance of the suggested geometrical concept means rejection of atomistic concept where all matter is considered as consisting of more and more small elementary particles. There are no any particles a priory, before measurement: the notions of particles appear as a result of classical interpretation of the contact of the region of the curved space with a device
Geometrization of quantum physics
Ol'Khov, O. A.
2009-12-01
It is shown that the Dirac equation for free particle can be considered as a description of specific distortion of the space euclidean geometry (space topological defect). This approach is based on possibility of interpretation of the wave function as vector realizing representation of the fundamental group of the closed topological space-time 4-manifold. Mass and spin appear to be topological invariants. Such concept explains all so called “strange” properties of quantum formalism: probabilities, wave-particle duality, nonlocal instantaneous correlation between noninteracting particles (EPR-paradox) and so on. Acceptance of suggested geometrical concept means rejection of atomistic concept where all matter is considered as consisting of more and more small elementary particles. There is no any particles a priori, before measurement: the notions of particles appear as a result of classical interpretation of the contact of the region of the curved space with a device.
Federal Laboratory Consortium — Purpose: The mission of the Geometric Design Laboratory (GDL) is to support the Office of Safety Research and Development in research related to the geometric design...
Two-particle correlations in the one-dimensional Hubbard model: a ground-state analytical solution
Vallejo, E; Espinosa, J E
2003-01-01
A solution to the extended Hubbard Hamiltonian for the case of two-particles in an infinite one-dimensional lattice is presented, using a real-space mapping method and the Green function technique. This Hamiltonian considers the on-site (U) and the nearest-neighbor (V) interactions. The method is based on mapping the correlated many-body problem onto an equivalent site-impurity tight-binding one in a higher dimensional space. In this new space we obtained the analytical solution for the ground state binding energy. Results are in agreement with the numerical solution obtained previously [1], and with those obtained in the reciprocal space [2]. (Author)
Levitsky VYu; Panova, A A; Mozhaev, V V
1994-01-15
A correlation between the stability of alpha-chymotrypsin against irreversible thermal inactivation at high temperatures (long-term stability) and the coefficient of Setchenov equation as a measure of salting-in/out efficiency of solutes in the Hofmeister series has been found. An increase in the concentration of salting-in solutes (KSCN, urea, guanidinium chloride, formamide) leads to a many-fold decrease of the inactivation rate of the enzyme. In contrast, addition of salting-out solutes has a small effect on the long-term stability of alpha-chymotrypsin at high temperatures. The effects of solutes are additive with respect to their salting-in/out capacities; the stabilizing action of the solutes is determined by the calculated Setchenov coefficient of solution. The correlation is explained by a solute-driven shift of the conformational equilibrium between the 'low-temperature' native and the 'high-temperature' denatured forms of the enzyme within the range of the kinetic scheme put forward in the preceding paper in this journal: irreversible inactivation of the high-temperature form proceeds much more slowly compared with the low-temperature form.
A free-volume modification of GEM-QC to correlate VLE and LLE in polymer solutions
International Nuclear Information System (INIS)
Radfarnia, H.R.; Taghikhani, V.; Ghotbi, C.; Khoshkbarchi, M.K.
2004-01-01
The generalized quasi-chemical (GEM-QC) model proposed by Wang and Vera is modified to correlate better the phase equilibrium and to overcome the shortcoming of the original model to predict the lower critical solution temperature (LCST) of binary polymer solutions. This shortcoming is mainly because the GEM-QC model does not consider the effect of free-volume, which is important in systems containing molecules with large size differences. The proposed modification is based on replacing the combinatorial term of the GEM-QC model by a term proposed by Kontogerogis et al., which includes the effect of the free-volume. The main advantage of the free volume generalized quasi-chemical (GEM-QC-FV) model over the original GEM-QC is its ability to predict the phase behaviour of binary polymer solutions with LCST behaviour. In addition, the free volume UNIQUAC (UNIQUAC-FV) model is used to correlate VLE and LLE experimental data for binary polymer solutions. The comparison of the results obtained from the GEM-QC-FV model and the UNIQUAC-FV model shows the superiority of the GEM-QC-FV model in correlating the VLE and LLE experimental data for binary polymer solutions
International Nuclear Information System (INIS)
Almgren, M.; Grieser, F.; Powell, J.R.; Thomas, J.K.
1979-01-01
A linear correlation between the logarithm of the solubility in water of aromatic hydrocarbons and their normal boiling points is shown. Similarly, the logarithm of the distribution ratio of aromatic hydrocarbons in aqueous micellar solution is shown to be linearly related to the boiling points of the hydrocarbons. 2 figures, 2 tables
Random Sampling of Correlated Parameters – a Consistent Solution for Unfavourable Conditions
Energy Technology Data Exchange (ETDEWEB)
Žerovnik, G., E-mail: gasper.zerovnik@ijs.si [Jožef Stefan Institute, Jamova cesta 39, SI-1000 Ljubljana (Slovenia); Trkov, A. [Jožef Stefan Institute, Jamova cesta 39, SI-1000 Ljubljana (Slovenia); International Atomic Energy Agency, PO Box 100, A-1400 Vienna (Austria); Kodeli, I.A. [Jožef Stefan Institute, Jamova cesta 39, SI-1000 Ljubljana (Slovenia); Capote, R. [International Atomic Energy Agency, PO Box 100, A-1400 Vienna (Austria); Smith, D.L. [Argonne National Laboratory, 1710 Avenida del Mundo, Coronado, CA 92118-3073 (United States)
2015-01-15
Two methods for random sampling according to a multivariate lognormal distribution – the correlated sampling method and the method of transformation of correlation coefficients – are briefly presented. The methods are mathematically exact and enable consistent sampling of correlated inherently positive parameters with given information on the first two distribution moments. Furthermore, a weighted sampling method to accelerate the convergence of parameters with extremely large relative uncertainties is described. However, the method is efficient only for a limited number of correlated parameters.
Directory of Open Access Journals (Sweden)
Xun Yue
2012-01-01
Full Text Available Aquaporins are multifunctional membrane channels that facilitate the transmembrane transport of water and solutes. When transmembrane mineral nutrient transporters exhibit the same expression patterns as aquaporins under diverse temporal and physiological conditions, there is a greater probability that they interact. In this study, genome-wide temporal profiling of transcripts analysis and coexpression network-based approaches are used to examine the significant specificity correlation of aquaporins and transmembrane solute transporters in developing maize leaf. The results indicate that specific maize aquaporins are related to specific transmembrane solute transporters. The analysis demonstrates a systems-level correlation between aquaporins, nutrient transporters, and the homeostasis of mineral nutrients in developing maize leaf. Our results provide a resource for further studies into the physiological function of these aquaporins.
Isik, Dilek
This Ph.D. thesis is a result of multidisciplinary research bringing together fundamental concepts in thin film engineering, materials science, materials processing and characterization, electrochemistry, microfabrication, and device physics. Experiments were conducted by tackling scientific problems in the field of thin films and interfaces, with the aim to correlate the morphology, crystalline structure, electronic structure of thin films with the functional properties of the films and the performances of electronic devices based thereon. Furthermore, novel strategies based on interfacial phenomena at electrolyte/thin film interfaces were explored and exploited to control the electrical conductivity of the thin films. Three main chemical systems were the object of the studies performed during this Ph.D., two types of organic semiconductors (azomethine-based oligomers and polymers and soluble pentacene derivatives) and one metal oxide semiconductor (tungsten trioxide, WO3). To explore the morphological properties of the thin films, atomic force microscopy was employed. The morphological properties were further investigated by hyperspectral fluorescence microscopy and tentatively correlated to the charge transport properties of the films. X-ray diffraction (Grazing incidence XRD, GIXRD) was used to investigate the crystallinity of the film and the effect of the heat treatment on such crystallinity, as well as to understand the molecular arrangement of the organic molecules in the thin film. The charge transport properties of the films were evaluated in thin film transistor configuration. For electrolyte gated thin film transistors, time dependent transient measurements were conducted, in parallel to more conventional transistor characterizations, to explore the specific effects played on the gating by the anion and cation constituting the electrolyte. The capacitances of the electrical double layers at the electrolyte/WO3 interface were obtained from
Zhou, Zhenming; Liu, Qidi; Li, Shuwen; Li, Fei; Zou, Jing; Liao, Xiaobin; Yuan, Baoling; Sun, Wenjie
2018-04-26
This study focused on characterizing the correlation between the dephosphorization process of calcined water treatment plant sludge (C-WTPS) and the solution initial pH in batch experiments. The specific aim was to illustrate the effect of different initial pH on the adsorption and desorption of phosphorous in C-WTPS. In addition, the effects of solution initial pH on the release of ammonia nitrogen and total organic carbon (TOC) from C-WTPS and the change of pH after adsorption were also investigated. The results demonstrated that the initial pH significantly influenced the adsorption of phosphorus on C-WTPS. When initial pH was increased from 3 to 10, the phosphorous absorption capacity reduced by 76.5%. Especially, when the initial pH reached to 11, the phosphorus adsorption capacity became a negative value, indicating that C-WTPS released phosphorus into the solution. The addition of C-WTPS to the solution had little impact on the initial pH of the solution. The absorbed phosphorous on C-WTPS was relatively stable in the pH range of 3 to 10. Nevertheless, when the solution pH was higher than 11, it can be easily released into the solution. Furthermore, by comparison with WTPS, C-WTPS released less ammonia nitrogen and TOC into the solution and adsorbed more phosphorus from the solution in the experimental pH range. Therefore, C-WTPS is more suitable to serve as a cost-effective sorbent for phosphorus removal.
Geometric U-folds in four dimensions
Lazaroiu, C. I.; Shahbazi, C. S.
2018-01-01
We describe a general construction of geometric U-folds compatible with a non-trivial extension of the global formulation of four-dimensional extended supergravity on a differentiable spin manifold. The topology of geometric U-folds depends on certain flat fiber bundles which encode how supergravity fields are globally glued together. We show that smooth non-trivial U-folds of this type can exist only in theories where both the scalar and space-time manifolds have non-trivial fundamental group and in addition the scalar map of the solution is homotopically non-trivial. Consistency with string theory requires smooth geometric U-folds to be glued using subgroups of the effective discrete U-duality group, implying that the fundamental group of the scalar manifold of such solutions must be a subgroup of the latter. We construct simple examples of geometric U-folds in a generalization of the axion-dilaton model of \
Initial singularity and pure geometric field theories
Wanas, M. I.; Kamal, Mona M.; Dabash, Tahia F.
2018-01-01
In the present article we use a modified version of the geodesic equation, together with a modified version of the Raychaudhuri equation, to study initial singularities. These modified equations are used to account for the effect of the spin-torsion interaction on the existence of initial singularities in cosmological models. Such models are the results of solutions of the field equations of a class of field theories termed pure geometric. The geometric structure used in this study is an absolute parallelism structure satisfying the cosmological principle. It is shown that the existence of initial singularities is subject to some mathematical (geometric) conditions. The scheme suggested for this study can be easily generalized.
Energy Technology Data Exchange (ETDEWEB)
Varfolomeev, Mikhail A.; Rakipov, Ilnaz T. [Chemical Institute, Kazan Federal University, Kremlevskaya 18, Kazan 420008 (Russian Federation); Acree, William E., E-mail: acree@unt.edu [Department of Chemistry, 1155 Union Circle # 305070, University of North Texas, Denton, TX 76203-5017 (United States); Brumfield, Michela [Department of Chemistry, 1155 Union Circle # 305070, University of North Texas, Denton, TX 76203-5017 (United States); Abraham, Michael H. [Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ (United Kingdom)
2014-10-20
Highlights: • Enthalpies of solution measured for 48 solutes dissolved in mesitylene. • Enthalpies of solution measured for 81 solutes dissolved in p-xylene. • Abraham model correlations derived for enthalpies of solvation of solutes in mesitylene. • Abraham model correlations derived for enthalpies of solvation of solutes in p-xylene. • Hydrogen-bonding enthalpies reported for interactions of aromatic hydrocarbons with hydrogen-bond acidic solutes. - Abstract: Enthalpies of solution at infinite dilution of 48 organic solutes in mesitylene and 81 organic solutes in p-xylene were measured using isothermal solution calorimeter. Enthalpies of solvation for 92 organic vapors and gaseous solutes in mesitylene and for 130 gaseous compounds in p-xylene were determined from the experimental and literature data. Abraham model correlations are determined from the experimental enthalpy of solvation data. The derived correlations describe the experimental gas-to-mesitylene and gas-to-p-xylene solvation enthalpies to within average standard deviations of 1.87 kJ mol{sup −1} and 2.08 kJ mol{sup −1}, respectively. Enthalpies of X-H⋯π (X-O, N, and C) hydrogen bond formation of proton donor solutes (alcohols, amines, chlorinated hydrocarbons etc.) with mesitylene and p-xylene were calculated based on the Abraham solvation equation. Obtained values are in good agreement with the results determined using conventional methods.
ten Berge, Jos M.F.; Kiers, Henk A.L.
When r Principal Components are available for k variables, the correlation matrix is approximated in the least squares sense by the loading matrix times its transpose. The approximation is generally not perfect unless r = k. In the present paper it is shown that, when r is at or above the Ledermann
General solution of an exact correlation function factorization in conformal field theory
International Nuclear Information System (INIS)
Simmons, Jacob J H; Kleban, Peter
2009-01-01
The correlation function factorization with K a boundary operator product expansion coefficient, is known to hold for certain scaling operators at the two-dimensional percolation point and in a few other cases. Here the correlation functions are evaluated in the upper half-plane (or any conformally equivalent region) with x 1 and x 2 arbitrary points on the real axis, and z an arbitrary point in the interior. This type of result is of interest because it is both exact and universal, relates higher-order correlation functions to lower-order ones and has a simple interpretation in terms of cluster or loop probabilities in several statistical models. This motivated us to use the techniques of conformal field theory to determine the general conditions for its validity. Here, we discover that either (see display) factorizes in this way for any central charge c, generalizing previous results. In particular, the factorization holds for either FK (Fortuin–Kasteleyn) or spin clusters in the Q-state Potts models; it also applies to either the dense or dilute phases of the O(n) loop models. Further, only one other non-trivial set of highest-weight operators (in an irreducible Verma module) factorizes in this way. In this case the operators have negative dimension (for c<1) and do not seem to have a physical realization
DEFF Research Database (Denmark)
Boghosian, Soghomon; Berg, Rolf W.
1999-01-01
); (2) Nb2O5 + nS(2)O(7)(2-) (1) --> Y2n- (1); (3) MoO3 + nS(2)O(7)(2-) (1) --> Z(2n)- (1). It is shown that the solute complex species formed in the studied reactions have, respectively, the following stoichiometries: (1) n = 2, (VO)(2)O(SO4)(4)(4-); (2) n = 3, NbO(SO4)(3)(3-); (3) n = 1, MoO(SO4)(2)(2-)....
Newman, Michael J; Speller, Emily M; Barbé, Jérémy; Luke, Joel; Li, Meng; Li, Zhe; Wang, Zhao-Kui; Jain, Sagar M; Kim, Ji-Seon; Lee, Harrison Ka Hin; Tsoi, Wing Chung
2018-01-01
Solution-processed organic small molecule solar cells (SMSCs) have achieved efficiency over 11%. However, very few studies have focused on their stability under illumination and the origin of the degradation during the so-called burn-in period. Here, we studied the burn-in period of a solution-processed SMSC using benzodithiophene terthiophene rhodamine:[6,6]-phenyl C 71 butyric acid methyl ester (BTR:PC 71 BM) with increasing solvent vapour annealing time applied to the active layer, controlling the crystallisation of the BTR phase. We find that the burn-in behaviour is strongly correlated to the crystallinity of BTR. To look at the possible degradation mechanisms, we studied the fresh and photo-aged blend films with grazing incidence X-ray diffraction, UV-vis absorbance, Raman spectroscopy and photoluminescence (PL) spectroscopy. Although the crystallinity of BTR affects the performance drop during the burn-in period, the degradation is found not to originate from the crystallinity changes of the BTR phase, but correlates with changes in molecular conformation - rotation of the thiophene side chains, as resolved by Raman spectroscopy which could be correlated to slight photobleaching and changes in PL spectra.
Geometrical optics and optimal transport.
Rubinstein, Jacob; Wolansky, Gershon
2017-10-01
The Fermat principle is generalized to a system of rays. It is shown that all the ray mappings that are compatible with two given intensities of a monochromatic wave, measured at two planes, are stationary points of a canonical functional, which is the weighted average of the actions of all the rays. It is further shown that there exist at least two stationary points for this functional, implying that in the geometrical optics regime the phase from intensity problem has inherently more than one solution. The caustic structures of all the possible ray mappings are analyzed. A number of simulations illustrate the theoretical considerations.
International Nuclear Information System (INIS)
Bertsch, Floria; Bejarano, Jose Antonio; Corrales, Marco
2005-01-01
The correlation found, between the 2 most commonly used extraction solutions in soil laboratories of Costa Rica, is discussed for Ca, Mg, K, Zn and P determinations in soil analyses. Given the coexistence of extraction methodologies, it is of great relevance to provide users with information allowing an adequate interpretation of the analysis results. Using data exchanged among laboratories, at the national level, relationships between modified KCl-Olsen and Mehlich 3 solutions were established. For all elements determined, except for P, the association between both solutions is very clear and well-defined. Both solutions extract the same amounts of Ca and Mg; Mehlich 3 extracts 1.5 times more K than Modified Olsen. In the case of Zn, in Ca-rich soils (>10 cmol(+) 1 -1 ) Mehlich 3 extracts more Zn, so the critical level must be raised to 3.5 mg 1''- 1 ; whereas, in soils low in Ca ( -1 ), Mehlich 3 extracts less Zn than Modified Olsen, so the critical level must be lowered to 2.5 mg 1 -1 . As for P, the association is not clear at all. (author) [es
Big Data solution for CTBT monitoring: CEA-IDC joint global cross correlation project
Bobrov, Dmitry; Bell, Randy; Brachet, Nicolas; Gaillard, Pierre; Kitov, Ivan; Rozhkov, Mikhail
2014-05-01
Waveform cross-correlation when applied to historical datasets of seismic records provides dramatic improvements in detection, location, and magnitude estimation of natural and manmade seismic events. With correlation techniques, the amplitude threshold of signal detection can be reduced globally by a factor of 2 to 3 relative to currently standard beamforming and STA/LTA detector. The gain in sensitivity corresponds to a body wave magnitude reduction by 0.3 to 0.4 units and doubles the number of events meeting high quality requirements (e.g. detected by three and more seismic stations of the International Monitoring System (IMS). This gain is crucial for seismic monitoring under the Comprehensive Nuclear-Test-Ban Treaty. The International Data Centre (IDC) dataset includes more than 450,000 seismic events, tens of millions of raw detections and continuous seismic data from the primary IMS stations since 2000. This high-quality dataset is a natural candidate for an extensive cross correlation study and the basis of further enhancements in monitoring capabilities. Without this historical dataset recorded by the permanent IMS Seismic Network any improvements would not be feasible. However, due to the mismatch between the volume of data and the performance of the standard Information Technology infrastructure, it becomes impossible to process all the data within tolerable elapsed time. To tackle this problem known as "BigData", the CEA/DASE is part of the French project "DataScale". One objective is to reanalyze 10 years of waveform data from the IMS network with the cross-correlation technique thanks to a dedicated High Performance Computer (HPC) infrastructure operated by the Centre de Calcul Recherche et Technologie (CCRT) at the CEA of Bruyères-le-Châtel. Within 2 years we are planning to enhance detection and phase association algorithms (also using machine learning and automatic classification) and process about 30 terabytes of data provided by the IDC to
International Nuclear Information System (INIS)
D'Angelo, P.; Pavel, N.V.
1999-01-01
The solvation structure of Sr 2+ ions in acetonitrile has been studied by x-ray absorption spectroscopy (XAS) and molecular dynamics (MD) simulations. The extended x-ray absorption fine structure (EXAFS) above the Sr K-edge has been interpreted in the framework of the multiple scattering (MS) formalism and, for the first time, clear evidence of MS contributions has been found for non-complexing ions in solution. Molecular dynamics has been used to generate the partial pair g(r) and the three-body g(r 1 , r 2 , θ) distribution functions from which a model χ(k) has been constructed. An excellent agreement has been found between the theoretical and experimental data. This result demonstrates the ability of the XAS technique in probing three-body correlation functions in solutions. (au)
Druţu, Cornelia
2018-01-01
The key idea in geometric group theory is to study infinite groups by endowing them with a metric and treating them as geometric spaces. This applies to many groups naturally appearing in topology, geometry, and algebra, such as fundamental groups of manifolds, groups of matrices with integer coefficients, etc. The primary focus of this book is to cover the foundations of geometric group theory, including coarse topology, ultralimits and asymptotic cones, hyperbolic groups, isoperimetric inequalities, growth of groups, amenability, Kazhdan's Property (T) and the Haagerup property, as well as their characterizations in terms of group actions on median spaces and spaces with walls. The book contains proofs of several fundamental results of geometric group theory, such as Gromov's theorem on groups of polynomial growth, Tits's alternative, Stallings's theorem on ends of groups, Dunwoody's accessibility theorem, the Mostow Rigidity Theorem, and quasiisometric rigidity theorems of Tukia and Schwartz. This is the f...
Geometric and engineering drawing
Morling, K
2010-01-01
The new edition of this successful text describes all the geometric instructions and engineering drawing information that are likely to be needed by anyone preparing or interpreting drawings or designs with plenty of exercises to practice these principles.
Differential geometric structures
Poor, Walter A
2007-01-01
This introductory text defines geometric structure by specifying parallel transport in an appropriate fiber bundle and focusing on simplest cases of linear parallel transport in a vector bundle. 1981 edition.
Geometric ghosts and unitarity
International Nuclear Information System (INIS)
Ne'eman, Y.
1980-09-01
A review is given of the geometrical identification of the renormalization ghosts and the resulting derivation of Unitarity equations (BRST) for various gauges: Yang-Mills, Kalb-Ramond, and Soft-Group-Manifold
International Nuclear Information System (INIS)
Brown, R.; Alias, M.N.
1994-01-01
Ac impedance and dc polarization tests of 304 stainless steels coated by cathodic arc plasma deposition (CAPD) titanium nitride and zirconium nitride were conducted in aqueous chloride solution. Cyclic polarization data suggested passive films were formed over the nitride coatings which are most likely hydrated titanium oxide and zirconium oxides. ESCA analysis of fresh samples and samples exposed during impedance tests indicated a layer rich in oxygen over the ZrN coating after exposure but not over TiN coating. Chemical shifts in the Zr 3d 5/2 core electrons indicate transformation from ZrN to its oxide; the shifts in Ti 2P 3/2 did not support the change from TiN to its oxide. The influence of these shifts on corrosion protection is documented
Asymptotic and geometrical quantization
International Nuclear Information System (INIS)
Karasev, M.V.; Maslov, V.P.
1984-01-01
The main ideas of geometric-, deformation- and asymptotic quantizations are compared. It is shown that, on the one hand, the asymptotic approach is a direct generalization of exact geometric quantization, on the other hand, it generates deformation in multiplication of symbols and Poisson brackets. Besides investigating the general quantization diagram, its applications to the calculation of asymptotics of a series of eigenvalues of operators possessing symmetry groups are considered
Complete conformal field theory solution of a chiral six-point correlation function
International Nuclear Information System (INIS)
Simmons, Jacob J H; Kleban, Peter
2011-01-01
Using conformal field theory, we perform a complete analysis of the chiral six-point correlation function C(z)= 1,2 φ 1,2 Φ 1/2,0 (z, z-bar )φ 1,2 φ 1,2 >, with the four φ 1,2 operators at the corners of an arbitrary rectangle, and the point z = x + iy in the interior. We calculate this for arbitrary central charge (equivalently, SLE parameter κ > 0). C is of physical interest because for percolation (κ = 6) and many other two-dimensional critical points, it specifies the density at z of critical clusters conditioned to touch either or both vertical ends of the rectangle, with these ends 'wired', i.e. constrained to be in a single cluster, and the horizontal ends free. The correlation function may be written as the product of an algebraic prefactor f and a conformal block G, where f = f(x, y, m), with m a cross-ratio specified by the corners (m determines the aspect ratio of the rectangle). By appropriate choice of f and using coordinates that respect the symmetry of the problem, the conformal block G is found to be independent of either y or x, and given by an Appell function.
International Nuclear Information System (INIS)
Li, Kangli; Du, Shichao; Wu, Songgu; Cai, Dongchen; Wang, Jinxu; Zhang, Dejiang; Zhao, Kaifei; Yang, Peng; Yu, Bo; Guo, Baisong; Li, Daixi; Gong, Junbo
2016-01-01
Highlights: • The solubility of racemic oxiracetam in three binary solvents were determined. • The experimental solubility of racemic oxiracetam were correlated by four models. • The dissolution thermodynamic properties of racemic oxiracetam were calculated. - Abstract: In this paper, we proposed a static analysis method to experimentally determine the (solid + liquid) equilibrium of racemic oxiracetam in (methanol + water), (ethanol + water) and (isopropanol + water) binary solvents with alcohol mole fraction ranging from 0.30 to 0.90 at atmosphere pressure (p = 0.1 MPa). For the experiments, the temperatures range from (283.15 to 308.15) K. The results showed that the solubility of oxiracetam increased with the increasing temperature, while decreased with the increasing organic solvent fraction in all three tested binary solvent systems. The modified Apelblat model, the CNIBS/Redlich–Kister model, the combined version of Jouyban–Acree model and the NRTL model were employed to correlate the measured solubility values, respectively. Additionally, some of the thermodynamic properties which can help to evaluate its dissolution behavior were obtained based on the NRTL model.
Jiang, Shidong; Xu, Minzhong
2005-01-01
The analytical solutions for the general-four-wave-mixing hyperpolarizabilities $\\chi^{(3)}(-(w_1+w_2+w_3);w_1,w_2,w_3)$ on infinite chains under both Su-Shrieffer-Heeger and Takayama-Lin-Liu-Maki models of trans-polyacetylene are obtained through the scheme of dipole-dipole correlation. Analytical expressions of DC Kerr effect $\\chi^{(3)}(-w;0,0,w)$, DC-induced second harmonic generation $\\chi^{(3)}(-2w;0,w,w)$, optical Kerr effect $\\chi^{(3)}(-w;w,-w,w)$ and DC-electric-field-induced optica...
Bordello, Jorge; Novo, Mercedes; Al-Soufi, Wajih
2010-05-15
The dynamics of the exchange of the moderately hydrophobic neutral dye Coumarine 152 between the aqueous phase and the phase formed by neutral Triton X-100 micelles is studied by Fluorescence Correlation Spectroscopy. The changes in the photophysical properties of the dye in presence of the micelles are discussed. The low quantum yield, the low saturation threshold and the necessary high energetic excitation of this dye requires a careful selection of the experimental conditions in order to obtain dynamic and diffusional properties with reasonable precision. It is shown that the contrast between the brightness of free and bound dye has a strong influence on the sensitivity of the FCS experiment. The entry rate constant of the dye to the micelles, k(+)=(0.8±0.3)×10(10) M(-1) s(-1), is very near to the diffusion controlled limit. The high association equilibrium constant of K=(129±3)×10(3) M(-1) is mainly determined by the low exit rate constant, k(-)=(0.6±0.2)×10(5) s(-1). Copyright © 2010 Elsevier Inc. All rights reserved.
Tangram solved? Prefrontal cortex activation analysis during geometric problem solving.
Ayaz, Hasan; Shewokis, Patricia A; Izzetoğlu, Meltem; Çakır, Murat P; Onaral, Banu
2012-01-01
Recent neuroimaging studies have implicated prefrontal and parietal cortices for mathematical problem solving. Mental arithmetic tasks have been used extensively to study neural correlates of mathematical reasoning. In the present study we used geometric problem sets (tangram tasks) that require executive planning and visuospatial reasoning without any linguistic representation interference. We used portable optical brain imaging (functional near infrared spectroscopy--fNIR) to monitor hemodynamic changes within anterior prefrontal cortex during tangram tasks. Twelve healthy subjects were asked to solve a series of computerized tangram puzzles and control tasks that required same geometric shape manipulation without problem solving. Total hemoglobin (HbT) concentration changes indicated a significant increase during tangram problem solving in the right hemisphere. Moreover, HbT changes during failed trials (when no solution found) were significantly higher compared to successful trials. These preliminary results suggest that fNIR can be used to assess cortical activation changes induced by geometric problem solving. Since fNIR is safe, wearable and can be used in ecologically valid environments such as classrooms, this neuroimaging tool may help to improve and optimize learning in educational settings.
Geometric Models for Collaborative Search and Filtering
Bitton, Ephrat
2011-01-01
This dissertation explores the use of geometric and graphical models for a variety of information search and filtering applications. These models serve to provide an intuitive understanding of the problem domains and as well as computational efficiencies to our solution approaches. We begin by considering a search and rescue scenario where both…
Geometric Algorithms for Part Orienting and Probing
Panahi, F.
2015-01-01
In this thesis, detailed solutions are presented to several problems dealing with geometric shape and orientation of an object in the field of robotics and automation. We first have considered a general model for shape variations that allows variation along the entire boundary of an object, both in
Geometric approximation algorithms
Har-Peled, Sariel
2011-01-01
Exact algorithms for dealing with geometric objects are complicated, hard to implement in practice, and slow. Over the last 20 years a theory of geometric approximation algorithms has emerged. These algorithms tend to be simple, fast, and more robust than their exact counterparts. This book is the first to cover geometric approximation algorithms in detail. In addition, more traditional computational geometry techniques that are widely used in developing such algorithms, like sampling, linear programming, etc., are also surveyed. Other topics covered include approximate nearest-neighbor search, shape approximation, coresets, dimension reduction, and embeddings. The topics covered are relatively independent and are supplemented by exercises. Close to 200 color figures are included in the text to illustrate proofs and ideas.
Geometrical optical illusionists.
Wade, Nicholas J
2014-01-01
Geometrical optical illusions were given this title by Oppel in 1855. Variants on such small distortions of visual space were illustrated thereafter, many of which bear the names of those who first described them. Some original forms of the geometrical optical illusions are shown together with 'perceptual portraits' of those who described them. These include: Roget, Chevreul, Fick, Zöllner, Poggendorff, Hering, Kundt, Delboeuf Mach, Helmholtz, Hermann, von Bezold, Müller-Lyer, Lipps, Thiéry, Wundt, Münsterberg, Ebbinghaus, Titchener, Ponzo, Luckiesh, Sander, Ehrenstein, Gregory, Heard, White, Shepard, and. Lingelbach. The illusions are grouped under the headings of orientation, size, the combination of size and orientation, and contrast. Early theories of illusions, before geometrical optical illusions were so named, are mentioned briefly.
International Nuclear Information System (INIS)
La, H.
1992-01-01
A new geometric formulation of Liouville gravity based on the area preserving diffeo-morphism is given and a possible alternative to reinterpret Liouville gravity is suggested, namely, a scalar field coupled to two-dimensional gravity with a curvature constraint
A Geometric Dissection Problem
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 7; Issue 7. A Geometric Dissection Problem. M N Deshpande. Think It Over Volume 7 Issue 7 July 2002 pp 91-91. Fulltext. Click here to view fulltext PDF. Permanent link: https://www.ias.ac.in/article/fulltext/reso/007/07/0091-0091. Author Affiliations.
Geometric Series via Probability
Tesman, Barry
2012-01-01
Infinite series is a challenging topic in the undergraduate mathematics curriculum for many students. In fact, there is a vast literature in mathematics education research on convergence issues. One of the most important types of infinite series is the geometric series. Their beauty lies in the fact that they can be evaluated explicitly and that…
Pragmatic geometric model evaluation
Pamer, Robert
2015-04-01
Quantification of subsurface model reliability is mathematically and technically demanding as there are many different sources of uncertainty and some of the factors can be assessed merely in a subjective way. For many practical applications in industry or risk assessment (e. g. geothermal drilling) a quantitative estimation of possible geometric variations in depth unit is preferred over relative numbers because of cost calculations for different scenarios. The talk gives an overview of several factors that affect the geometry of structural subsurface models that are based upon typical geological survey organization (GSO) data like geological maps, borehole data and conceptually driven construction of subsurface elements (e. g. fault network). Within the context of the trans-European project "GeoMol" uncertainty analysis has to be very pragmatic also because of different data rights, data policies and modelling software between the project partners. In a case study a two-step evaluation methodology for geometric subsurface model uncertainty is being developed. In a first step several models of the same volume of interest have been calculated by omitting successively more and more input data types (seismic constraints, fault network, outcrop data). The positions of the various horizon surfaces are then compared. The procedure is equivalent to comparing data of various levels of detail and therefore structural complexity. This gives a measure of the structural significance of each data set in space and as a consequence areas of geometric complexity are identified. These areas are usually very data sensitive hence geometric variability in between individual data points in these areas is higher than in areas of low structural complexity. Instead of calculating a multitude of different models by varying some input data or parameters as it is done by Monte-Carlo-simulations, the aim of the second step of the evaluation procedure (which is part of the ongoing work) is to
Energy Technology Data Exchange (ETDEWEB)
Pelce, J; Malherbe, J; Pierre, B [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1965-07-01
Principal results are given of experimental research which has been carried out on the flow of a fluid along a surface fitted with herringbone fins. Aero-thermal tests have been effected on a large number of these surfaces whose geometrical parameters have been made to vary systematically. In particular, work on a large scale model has made it possible to analyse the mechanisms of heat transfer and of pressure drops. On this basis a theoretical study has led to the establishment of a correlation between the geometric configuration and the aero-thermal performances of these surfaces. Experimental results are in good agreement with the theoretical relationships. An expression has thus been derived applicable to this type of herring-boned surface in a wide zone. (authors) [French] L'ecoulement d'un fluide au voisinage d'une surface munie d'ailettes disposees en chevron a fait l'objet de recherches experimentales dont on a rappele les principaux resultats. Des essais aerothermiques ont ete effectues sur un grand nombre de ces surfaces dont a fait varier les parametres geometriques de facon systematique. En particulier, des etudes sur une maquette a grande echelle ont permis d'analyser les mecanismes de transfert de chaleur et de perte de charge. Sur ces bases, une etude theorique a conduit a des correlations entre la geometrie et les performances aerothermiques de ces surfaces. Les resultats experimentaux sont en bon accord avec les relations theoriques. On possede ainsi une formulation pour ce type de surface ailettee valable dans un domaine etendu. (auteurs)
Geometrical approach to fluid models
International Nuclear Information System (INIS)
Kuvshinov, B.N.; Schep, T.J.
1997-01-01
Differential geometry based upon the Cartan calculus of differential forms is applied to investigate invariant properties of equations that describe the motion of continuous media. The main feature of this approach is that physical quantities are treated as geometrical objects. The geometrical notion of invariance is introduced in terms of Lie derivatives and a general procedure for the construction of local and integral fluid invariants is presented. The solutions of the equations for invariant fields can be written in terms of Lagrange variables. A generalization of the Hamiltonian formalism for finite-dimensional systems to continuous media is proposed. Analogously to finite-dimensional systems, Hamiltonian fluids are introduced as systems that annihilate an exact two-form. It is shown that Euler and ideal, charged fluids satisfy this local definition of a Hamiltonian structure. A new class of scalar invariants of Hamiltonian fluids is constructed that generalizes the invariants that are related with gauge transformations and with symmetries (Noether). copyright 1997 American Institute of Physics
International Nuclear Information System (INIS)
Lin Peiyin; Soriano, Allan N.; Leron, Rhoda B.; Li Menghui
2010-01-01
As part of our systematic study on physicochemical characterization of ionic liquids, in this work, we report new measurements of electrolytic conductivity and molar heat capacity for aqueous solutions of two 1-ethyl-3-methylimidazolium-based ionic liquids, namely: 1-ethyl-3-methylimidazolium dicyanamide and 1-ethyl-3-methylimidazolium 2-(2-methoxyethoxy) ethylsulfate, at normal atmospheric condition and for temperatures up to 353.2 K. The electrolytic conductivity and molar heat capacity were measured by a commercial conductivity meter and a differential scanning calorimeter (DSC), respectively. The estimated experimental uncertainties for the electrolytic conductivity and molar heat capacity measurements were ±1% and ±2%, respectively. The property data are reported as functions of temperature and composition. A modified empirical equation from another researcher was used to correlate the temperature and composition dependence of the our electrolytic conductivity results. An excess molar heat capacity expression derived using a Redlich-Kister type equation was used to represent the temperature and composition dependence of the measured molar heat capacity and calculated excess molar heat capacity of the solvent systems considered. The correlations applied represent the our measurements satisfactorily as shown by an acceptable overall average deviation of 6.4% and 0.1%, respectively, for electrolytic conductivity and molar heat capacity.
Barry, J. H.; Muttalib, K. A.; Tanaka, T.
2008-01-01
We consider a two-dimensional (d=2) kagomé lattice gas model with attractive three-particle interactions around each triangular face of the kagomé lattice. Exact solutions are obtained for multiparticle correlations along the liquid and vapor branches of the coexistence curve and at criticality. The correlation solutions are also determined along the continuation of the curvilinear diameter of the coexistence region into the disordered fluid region. The method generates a linear algebraic system of correlation identities with coefficients dependent only upon the interaction parameter. Using a priori knowledge of pertinent solutions for the density and elementary triplet correlation, one finds a closed and linearly independent set of correlation identities defined upon a spatially compact nine-site cluster of the kagomé lattice. Resulting exact solution curves of the correlations are plotted and discussed as functions of the temperature and are compared with corresponding results in a traditional kagomé lattice gas having nearest-neighbor pair interactions. An example of application for the multiparticle correlations is demonstrated in cavitation theory.
Dynamics in geometrical confinement
Kremer, Friedrich
2014-01-01
This book describes the dynamics of low molecular weight and polymeric molecules when they are constrained under conditions of geometrical confinement. It covers geometrical confinement in different dimensionalities: (i) in nanometer thin layers or self supporting films (1-dimensional confinement) (ii) in pores or tubes with nanometric diameters (2-dimensional confinement) (iii) as micelles embedded in matrices (3-dimensional) or as nanodroplets.The dynamics under such conditions have been a much discussed and central topic in the focus of intense worldwide research activities within the last two decades. The present book discusses how the resulting molecular mobility is influenced by the subtle counterbalance between surface effects (typically slowing down molecular dynamics through attractive guest/host interactions) and confinement effects (typically increasing the mobility). It also explains how these influences can be modified and tuned, e.g. through appropriate surface coatings, film thicknesses or pore...
Bestvina, Mladen; Vogtmann, Karen
2014-01-01
Geometric group theory refers to the study of discrete groups using tools from topology, geometry, dynamics and analysis. The field is evolving very rapidly and the present volume provides an introduction to and overview of various topics which have played critical roles in this evolution. The book contains lecture notes from courses given at the Park City Math Institute on Geometric Group Theory. The institute consists of a set of intensive short courses offered by leaders in the field, designed to introduce students to exciting, current research in mathematics. These lectures do not duplicate standard courses available elsewhere. The courses begin at an introductory level suitable for graduate students and lead up to currently active topics of research. The articles in this volume include introductions to CAT(0) cube complexes and groups, to modern small cancellation theory, to isometry groups of general CAT(0) spaces, and a discussion of nilpotent genus in the context of mapping class groups and CAT(0) gro...
Lectures in geometric combinatorics
Thomas, Rekha R
2006-01-01
This book presents a course in the geometry of convex polytopes in arbitrary dimension, suitable for an advanced undergraduate or beginning graduate student. The book starts with the basics of polytope theory. Schlegel and Gale diagrams are introduced as geometric tools to visualize polytopes in high dimension and to unearth bizarre phenomena in polytopes. The heart of the book is a treatment of the secondary polytope of a point configuration and its connections to the state polytope of the toric ideal defined by the configuration. These polytopes are relatively recent constructs with numerous connections to discrete geometry, classical algebraic geometry, symplectic geometry, and combinatorics. The connections rely on Gr�bner bases of toric ideals and other methods from commutative algebra. The book is self-contained and does not require any background beyond basic linear algebra. With numerous figures and exercises, it can be used as a textbook for courses on geometric, combinatorial, and computational as...
Geometric information provider platform
Directory of Open Access Journals (Sweden)
Meisam Yousefzadeh
2015-07-01
Full Text Available Renovation of existing buildings is known as an essential stage in reduction of the energy loss. Considerable part of renovation process depends on geometric reconstruction of building based on semantic parameters. Following many research projects which were focused on parameterizing the energy usage, various energy modelling methods were developed during the last decade. On the other hand, by developing accurate measuring tools such as laser scanners, the interests of having accurate 3D building models are rapidly growing. But the automation of 3D building generation from laser point cloud or detection of specific objects in that is still a challenge. The goal is designing a platform through which required geometric information can be efficiently produced to support energy simulation software. Developing a reliable procedure which extracts required information from measured data and delivers them to a standard energy modelling system is the main purpose of the project.
Frè, Pietro Giuseppe
2013-01-01
‘Gravity, a Geometrical Course’ presents general relativity (GR) in a systematic and exhaustive way, covering three aspects that are homogenized into a single texture: i) the mathematical, geometrical foundations, exposed in a self consistent contemporary formalism, ii) the main physical, astrophysical and cosmological applications, updated to the issues of contemporary research and observations, with glimpses on supergravity and superstring theory, iii) the historical development of scientific ideas underlying both the birth of general relativity and its subsequent evolution. The book is divided in two volumes. Volume One is dedicated to the development of the theory and basic physical applications. It guides the reader from the foundation of special relativity to Einstein field equations, illustrating some basic applications in astrophysics. A detailed account of the historical and conceptual development of the theory is combined with the presentation of its mathematical foundations. Differe...
Ruffino, Fabio Ferrari
2013-01-01
Given a cohomology theory, there is a well-known abstract way to define the dual homology theory using the theory of spectra. In [4] the author provides a more geometric construction of the homology theory, using a generalization of the bordism groups. Such a generalization involves in its definition the vector bundle modification, which is a particular case of the Gysin map. In this paper we provide a more natural variant of that construction, which replaces the vector bundle modification wi...
Waerden, B
1996-01-01
From the reviews: "... Federer's timely and beautiful book indeed fills the need for a comprehensive treatise on geometric measure theory, and his detailed exposition leads from the foundations of the theory to the most recent discoveries. ... The author writes with a distinctive style which is both natural and powerfully economical in treating a complicated subject. This book is a major treatise in mathematics and is essential in the working library of the modern analyst." Bulletin of the London Mathematical Society.
Developing geometrical reasoning
Brown, Margaret; Jones, Keith; Taylor, Ron; Hirst, Ann
2004-01-01
This paper summarises a report (Brown, Jones & Taylor, 2003) to the UK Qualifications and Curriculum Authority of the work of one geometry group. The group was charged with developing and reporting on teaching ideas that focus on the development of geometrical reasoning at the secondary school level. The group was encouraged to explore what is possible both within and beyond the current requirements of the UK National Curriculum and the Key Stage 3 strategy, and to consider the whole atta...
Geometrically Consistent Mesh Modification
Bonito, A.
2010-01-01
A new paradigm of adaptivity is to execute refinement, coarsening, and smoothing of meshes on manifolds with incomplete information about their geometry and yet preserve position and curvature accuracy. We refer to this collectively as geometrically consistent (GC) mesh modification. We discuss the concept of discrete GC, show the failure of naive approaches, and propose and analyze a simple algorithm that is GC and accuracy preserving. © 2010 Society for Industrial and Applied Mathematics.
Geometric theory of information
2014-01-01
This book brings together geometric tools and their applications for Information analysis. It collects current and many uses of in the interdisciplinary fields of Information Geometry Manifolds in Advanced Signal, Image & Video Processing, Complex Data Modeling and Analysis, Information Ranking and Retrieval, Coding, Cognitive Systems, Optimal Control, Statistics on Manifolds, Machine Learning, Speech/sound recognition, and natural language treatment which are also substantially relevant for the industry.
Geometric leaf placement strategies
International Nuclear Information System (INIS)
Fenwick, J D; Temple, S W P; Clements, R W; Lawrence, G P; Mayles, H M O; Mayles, W P M
2004-01-01
Geometric leaf placement strategies for multileaf collimators (MLCs) typically involve the expansion of the beam's-eye-view contour of a target by a uniform MLC margin, followed by movement of the leaves until some point on each leaf end touches the expanded contour. Film-based dose-distribution measurements have been made to determine appropriate MLC margins-characterized through an index d 90 -for multileaves set using one particular strategy to straight lines lying at various angles to the direction of leaf travel. Simple trigonometric relationships exist between different geometric leaf placement strategies and are used to generalize the results of the film work into d 90 values for several different strategies. Measured d 90 values vary both with angle and leaf placement strategy. A model has been derived that explains and describes quite well the observed variations of d 90 with angle. The d 90 angular variations of the strategies studied differ substantially, and geometric and dosimetric reasoning suggests that the best strategy is the one with the least angular variation. Using this criterion, the best straightforwardly implementable strategy studied is a 'touch circle' approach for which semicircles are imagined to be inscribed within leaf ends, the leaves being moved until the semicircles just touch the expanded target outline
Studies in geometric quantization
International Nuclear Information System (INIS)
Tuynman, G.M.
1988-01-01
This thesis contains five chapters, of which the first, entitled 'What is prequantization, and what is geometric quantization?', is meant as an introduction to geometric quantization for the non-specialist. The second chapter, entitled 'Central extensions and physics' deals with the notion of central extensions of manifolds and elaborates and proves the statements made in the first chapter. Central extensions of manifolds occur in physics as the freedom of a phase factor in the quantum mechanical state vector, as the phase factor in the prequantization process of classical mechanics and it appears in mathematics when studying central extension of Lie groups. In this chapter the connection between these central extensions is investigated and a remarkable similarity between classical and quantum mechanics is shown. In chapter three a classical model is given for the hydrogen atom including spin-orbit and spin-spin interaction. The method of geometric quantization is applied to this model and the results are discussed. In the final chapters (4 and 5) an explicit method to calculate the operators corresponding to classical observables is given when the phase space is a Kaehler manifold. The obtained formula are then used to quantise symplectic manifolds which are irreducible hermitian symmetric spaces and the results are compared with other quantization procedures applied to these manifolds (in particular to Berezin's quantization). 91 refs.; 3 tabs
International Nuclear Information System (INIS)
Amaral, Antonio A.; Silva, Andreia dos S.; Carbonari, Arthur W.; Lapolli, Andre L.
2009-01-01
In this work, PAC spectroscopy has been used to obtain the hyperfine parameters in EDTA molecules in solutions with pH 4.3 and pH 10.5 both measured at 77 K and 295 K using 181 Hf( 181 Ta) as probe nuclei. Both dynamic and static interactions were measured in aqueous solution, crystallized and re-hydrated samples in order to examine the motion and structure of EDTA-molecules. The hyperfine parameters, quadrupole interaction frequency (ν Q ), asymmetry (η), and the dynamic interaction frequency (λ) were obtained. The outcomes show that the rotational correlation time (τ CR ) is larger than the half-life of the intermediate state of probe nuclei. For samples with pH 4.3 and pH 10.5, it was observed an increase in ν Q when the temperature decreases, as expected, and also a variation of η, which is an evidence of a change in the EDTA molecule structure. 181 Hf is bound only to a single molecule site when the pH was 4.3, differently from the results for pH 10.5 sample, which showed two fractions with different ν Q indicating the possibility of 181 Hf being bonded to two different sites of the molecule. Measurements of the dehydrated sample presented different results leading us to conclude that the preparation procedure can causes alterations in the chemical bounds. Concluding, these results showed a systematic behavior of the 181 Hf-EDTA, with the variation of pH from 4 to approximately 11, and they are important to the knowledge of the dynamic behavior of this molecule. (author)
Geometric Computing for Freeform Architecture
Wallner, J.; Pottmann, Helmut
2011-01-01
Geometric computing has recently found a new field of applications, namely the various geometric problems which lie at the heart of rationalization and construction-aware design processes of freeform architecture. We report on our work in this area
Progressive geometric algorithms
Alewijnse, S.P.A.; Bagautdinov, T.M.; de Berg, M.T.; Bouts, Q.W.; ten Brink, Alex P.; Buchin, K.A.; Westenberg, M.A.
2015-01-01
Progressive algorithms are algorithms that, on the way to computing a complete solution to the problem at hand, output intermediate solutions that approximate the complete solution increasingly well. We present a framework for analyzing such algorithms, and develop efficient progressive algorithms
Progressive geometric algorithms
Alewijnse, S.P.A.; Bagautdinov, T.M.; Berg, de M.T.; Bouts, Q.W.; Brink, ten A.P.; Buchin, K.; Westenberg, M.A.
2014-01-01
Progressive algorithms are algorithms that, on the way to computing a complete solution to the problem at hand, output intermediate solutions that approximate the complete solution increasingly well. We present a framework for analyzing such algorithms, and develop efficient progressive algorithms
A Color Image Watermarking Scheme Resistant against Geometrical Attacks
Directory of Open Access Journals (Sweden)
Y. Xing
2010-04-01
Full Text Available The geometrical attacks are still a problem for many digital watermarking algorithms at present. In this paper, we propose a watermarking algorithm for color images resistant to geometrical distortions (rotation and scaling. The singular value decomposition is used for watermark embedding and extraction. The log-polar map- ping (LPM and phase correlation method are used to register the position of geometrical distortion suffered by the watermarked image. Experiments with different kinds of color images and watermarks demonstrate that the watermarking algorithm is robust to common image processing attacks, especially geometrical attacks.
Geometric Constructions with the Computer.
Chuan, Jen-chung
The computer can be used as a tool to represent and communicate geometric knowledge. With the appropriate software, a geometric diagram can be manipulated through a series of animation that offers more than one particular snapshot as shown in a traditional mathematical text. Geometric constructions with the computer enable the learner to see and…
Is Geometric Frustration-Induced Disorder a Recipe for High Ionic Conductivity?
Düvel, Andre; Heitjans, Paul; Fedorov, Pavel; Scholz, Gudrun; Cibin, Giannantonio; Chadwick, Alan V; Pickup, David M; Ramos, Silvia; Sayle, Lewis W L; Sayle, Emma K L; Sayle, Thi X T; Sayle, Dean C
2017-04-26
Ionic conductivity is ubiquitous to many industrially important applications such as fuel cells, batteries, sensors, and catalysis. Tunable conductivity in these systems is therefore key to their commercial viability. Here, we show that geometric frustration can be exploited as a vehicle for conductivity tuning. In particular, we imposed geometric frustration upon a prototypical system, CaF 2 , by ball milling it with BaF 2 , to create nanostructured Ba 1-x Ca x F 2 solid solutions and increased its ionic conductivity by over 5 orders of magnitude. By mirroring each experiment with MD simulation, including "simulating synthesis", we reveal that geometric frustration confers, on a system at ambient temperature, structural and dynamical attributes that are typically associated with heating a material above its superionic transition temperature. These include structural disorder, excess volume, pseudovacancy arrays, and collective transport mechanisms; we show that the excess volume correlates with ionic conductivity for the Ba 1-x Ca x F 2 system. We also present evidence that geometric frustration-induced conductivity is a general phenomenon, which may help explain the high ionic conductivity in doped fluorite-structured oxides such as ceria and zirconia, with application for solid oxide fuel cells. A review on geometric frustration [ Nature 2015 , 521 , 303 ] remarks that classical crystallography is inadequate to describe systems with correlated disorder, but that correlated disorder has clear crystallographic signatures. Here, we identify two possible crystallographic signatures of geometric frustration: excess volume and correlated "snake-like" ionic transport; the latter infers correlated disorder. In particular, as one ion in the chain moves, all the other (correlated) ions in the chain move simultaneously. Critically, our simulations reveal snake-like chains, over 40 Å in length, which indicates long-range correlation in our disordered systems. Similarly
International Nuclear Information System (INIS)
Karnland, O.
1998-01-01
A number of quite different quantitative models concerning swelling pressure in bentonite clay have been proposed. This report discusses a number of models which possibly can be used also for saline conditions. A discrepancy between calculated and measured values was noticed for all models at brine conditions. In general the models predicted a too low swelling pressure compared to what was experimentally found. An osmotic component in the clay/water system is proposed in order to improve the previous conservative use of the thermodynamic model. Calculations of this osmotic component is proposed to be made by use of the clay cation exchange capacity and Donnan equilibrium. Calculations made by this approach showed considerably better correlation to literature laboratory data, compared to calculations made by the previous conservative use of the thermodynamic model. A few verifying laboratory tests were made and are briefly described in the report. The improved model predicts a substantial bentonite swelling pressure also in a saturated sodium chloride solution if the density of the system is sufficiently high. This means in practice that the buffer in a KBS-3 repository will give rise to an acceptable swelling pressure, but that the positive effects of mixing bentonite into a backfill material will be lost if the system is exposed to brines. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Karnland, O. [Clay Technology, Lund (Sweden)
1997-12-01
A number of quite different quantitative models concerning swelling pressure in bentonite clay have been proposed by different researchers over the years. The present report examines some of the models which possibly may be used also for saline conditions. A discrepancy between calculated and measured values was noticed for all models at brine conditions. In general the models predicted a too low swelling pressure compared to what was experimentally found. An osmotic component in the clay/water system is proposed in order to improve the previous conservative use of the thermodynamic model. Calculations of this osmotic component is proposed to be made by use of the clay cation exchange capacity and Donnan equilibrium. Calculations made by this approach showed considerably better correlation to literature laboratory data, compared to calculations made by the previous conservative use of the thermodynamic model. A few verifying laboratory tests were made and are briefly described in the report. The improved thermodynamic model predicts substantial bentonite swelling pressures also in saturated sodium chloride solution if the density of the system is high enough. In practice, the model predicts a substantial swelling pressure for the buffer in a KBS-3 repository if the system is exposed to brines, but the positive effects of mixing bentonite into a backfill material will be lost, since the available compaction technique does not give a sufficiently high bentonite density 37 refs, 15 figs
Energy Technology Data Exchange (ETDEWEB)
Karnland, O. [Clay Technology, Lund (Sweden)
1998-01-01
A number of quite different quantitative models concerning swelling pressure in bentonite clay have been proposed. This report discusses a number of models which possibly can be used also for saline conditions. A discrepancy between calculated and measured values was noticed for all models at brine conditions. In general the models predicted a too low swelling pressure compared to what was experimentally found. An osmotic component in the clay/water system is proposed in order to improve the previous conservative use of the thermodynamic model. Calculations of this osmotic component is proposed to be made by use of the clay cation exchange capacity and Donnan equilibrium. Calculations made by this approach showed considerably better correlation to literature laboratory data, compared to calculations made by the previous conservative use of the thermodynamic model. A few verifying laboratory tests were made and are briefly described in the report. The improved model predicts a substantial bentonite swelling pressure also in a saturated sodium chloride solution if the density of the system is sufficiently high. This means in practice that the buffer in a KBS-3 repository will give rise to an acceptable swelling pressure, but that the positive effects of mixing bentonite into a backfill material will be lost if the system is exposed to brines. (orig.). 14 refs.
International Nuclear Information System (INIS)
Karnland, O.
1997-12-01
A number of quite different quantitative models concerning swelling pressure in bentonite clay have been proposed by different researchers over the years. The present report examines some of the models which possibly may be used also for saline conditions. A discrepancy between calculated and measured values was noticed for all models at brine conditions. In general the models predicted a too low swelling pressure compared to what was experimentally found. An osmotic component in the clay/water system is proposed in order to improve the previous conservative use of the thermodynamic model. Calculations of this osmotic component is proposed to be made by use of the clay cation exchange capacity and Donnan equilibrium. Calculations made by this approach showed considerably better correlation to literature laboratory data, compared to calculations made by the previous conservative use of the thermodynamic model. A few verifying laboratory tests were made and are briefly described in the report. The improved thermodynamic model predicts substantial bentonite swelling pressures also in saturated sodium chloride solution if the density of the system is high enough. In practice, the model predicts a substantial swelling pressure for the buffer in a KBS-3 repository if the system is exposed to brines, but the positive effects of mixing bentonite into a backfill material will be lost, since the available compaction technique does not give a sufficiently high bentonite density
Geometric multipartite entanglement measures
International Nuclear Information System (INIS)
Paz-Silva, Gerardo A.; Reina, John H.
2007-01-01
Within the framework of constructions for quantifying entanglement, we build a natural scenario for the assembly of multipartite entanglement measures based on Hopf bundle-like mappings obtained through Clifford algebra representations. Then, given the non-factorizability of an arbitrary two-qubit density matrix, we give an alternate quantity that allows the construction of two types of entanglement measures based on their arithmetical and geometrical averages over all pairs of qubits in a register of size N, and thus fully characterize its degree and type of entanglement. We find that such an arithmetical average is both additive and strongly super additive
Geometric scalar theory of gravity beyond spherical symmetry
Moschella, U.; Novello, M.
2017-04-01
We construct several exact solutions for a recently proposed geometric scalar theory of gravity. We focus on a class of axisymmetric geometries and a big-bang-like geometry and discuss their Lorentzian character. The axisymmetric solutions are parametrized by an integer angular momentum l . The l =0 (spherical) case gives rise to the Schwarzschild geometry. The other solutions have naked singular surfaces. While not a priori obvious, all the solutions that we present here are globally Lorentzian. The Lorentzian signature appears to be a robust property of the disformal geometries solving the vacuum geometric scalar theory of gravity equations.
Energy Technology Data Exchange (ETDEWEB)
Varfolomeev, Mikhail A.; Rakipov, Ilnaz T.; Khachatrian, Artashes A. [Department of Physical Chemistry, Kazan Federal University, Kremlevskaya 18, Kazan 420008 (Russian Federation); Acree, William E., E-mail: acree@unt.edu [Department of Chemistry, 1155 Union Circle # 305070, University of North Texas, Denton, TX 76203-5017 (United States); Brumfield, Michela [Department of Chemistry, 1155 Union Circle # 305070, University of North Texas, Denton, TX 76203-5017 (United States); Abraham, Michael H. [Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ (United Kingdom)
2015-10-10
Graphical abstract: - Highlights: • Enthalpies of solution measured for 43 solutes dissolved in chlorobenzene. • Enthalpies of solution measured for 72 solutes dissolved in 1,2-dichlorobenzene. • Mathematical expressions derived for predicting enthalpies of solvation of solutes in chlorobenzene. • Mathematical expressions derived for predicting enthalpies of solvation of solutes in 1,2-chlorobenzene. - Abstract: Enthalpies of solution at infinite dilution at 298 K, Δ{sub soln}H{sup A/Solvent}, have been measured by isothermal solution calorimetry for 43 and 72 organic solutes dissolved in chlorobenzene and 1,2-dichlorobenzene, respectively. The measured Δ{sub soln}H{sup A/Solvent} data, along with published Δ{sub soln}H{sup A/Solvent} values taken from the published literature for solutes dissolved in both chlorobenzene solvents, were converted to enthalpies of solvation, Δ{sub solv}H{sup A/Solvent}, using standard thermodynamic equations. Abraham model correlations were developed from the experimental Δ{sub solv}H{sup A/Solvent} data. The best derived correlations describe the experimental gas-to-chlorobenzene and gas-to-1,2-dichlorobenzene enthalpies of solvation to within standard deviations of 1.5 kJ mol{sup −1} and 1.9 kJ mol{sup −1}, respectively. Enthalpies of X−H…π (X – O, N, and C) hydrogen bond formation of proton donor solutes (alcohols, amines, chlorinated hydrocarbons, etc.) with chlorobenzene and 1,2-dichlorobenzene were calculated based on the Abraham solvation equation. Obtained values are in good agreement with the results determined using conventional methods.
Can EPR non-locality be geometrical?
International Nuclear Information System (INIS)
Ne'eman, Y.
1995-01-01
The presence in Quantum Mechanics of non-local correlations is one of the two fundamentally non-intuitive features of that theory. The non-local correlations themselves fall into two classes: EPR and Geometrical. The non-local characteristics of the geometrical type are well-understood and are not suspected of possibly generating acausal features, such as faster-than-light propagation of information. This has especially become true since the emergence of a geometrical treatment for the relevant gauge theories, i.e. Fiber Bundle geometry, in which the quantum non-localities are seen to correspond to pure homotopy considerations. This aspect is reviewed in section 2. Contrary-wise, from its very conception, the EPR situation was felt to be paradoxical. It has been suggested that the non-local features of EPR might also derive from geometrical considerations, like all other non-local characteristics of QM. In[7], one of the authors was able to point out several plausibility arguments for this thesis, emphasizing in particular similarities between the non-local correlations provided by any gauge field theory and those required by the preservation of the quantum numbers of the original EPR state-vector, throughout its spatially-extended mode. The derivation was, however, somewhat incomplete, especially because of the apparent difference between, on the one hand, the closed spatial loops arising in the analysis of the geometrical non-localities, from Aharonov-Bohm and Berry phases to magnetic monopoles and instantons, and on the other hand, in the EPR case, the open line drawn by the positions of the two moving decay products of the disintegrating particle. In what follows, the authors endeavor to remove this obstacle and show that as in all other QM non-localities, EPR is somehow related to closed loops, almost involving homotopy considerations. They develop this view in section 3
Geometrical framework for robust portfolio optimization
Bazovkin, Pavel
2014-01-01
We consider a vector-valued multivariate risk measure that depends on the user's profile given by the user's utility. It is constructed on the basis of weighted-mean trimmed regions and represents the solution of an optimization problem. The key feature of this measure is convexity. We apply the measure to the portfolio selection problem, employing different measures of performance as objective functions in a common geometrical framework.
ERC Workshop on Geometric Partial Differential Equations
Novaga, Matteo; Valdinoci, Enrico
2013-01-01
This book is the outcome of a conference held at the Centro De Giorgi of the Scuola Normale of Pisa in September 2012. The aim of the conference was to discuss recent results on nonlinear partial differential equations, and more specifically geometric evolutions and reaction-diffusion equations. Particular attention was paid to self-similar solutions, such as solitons and travelling waves, asymptotic behaviour, formation of singularities and qualitative properties of solutions. These problems arise in many models from Physics, Biology, Image Processing and Applied Mathematics in general, and have attracted a lot of attention in recent years.
International Nuclear Information System (INIS)
Noga, M.T.
1984-01-01
This thesis addresses a number of important problems that fall within the framework of the new discipline of Computational Geometry. The list of topics covered includes sorting and selection, convex hull algorithms, the L 1 hull, determination of the minimum encasing rectangle of a set of points, the Euclidean and L 1 diameter of a set of points, the metric traveling salesman problem, and finding the superrange of star-shaped and monotype polygons. The main theme of all the work was to develop a set of very fast state-of-the-art algorithms that supersede any rivals in terms of speed and ease of implementation. In some cases existing algorithms were refined; for others new techniques were developed that add to the present database of fast adaptive geometric algorithms. What emerges is a collection of techniques that is successful at merging modern tools developed in analysis of algorithms with those of classical geometry
Havelka, Jan
2008-01-01
Tato diplomová práce se zabývá akcelerací geometrických transformací obrazu s využitím GPU a architektury NVIDIA (R) CUDA TM. Časově kritické části kódu jsou přesunuty na GPU a vykonány paralelně. Jedním z výsledků je demonstrační aplikace pro porovnání výkonnosti obou architektur: CPU, a GPU v kombinaci s CPU. Pro referenční implementaci jsou použity vysoce optimalizované algoritmy z knihovny OpenCV, od firmy Intel. This master's thesis deals with acceleration of geometrical image transfo...
Geometric Programming Approach to an Interactive Fuzzy Inventory Problem
Directory of Open Access Journals (Sweden)
Nirmal Kumar Mandal
2011-01-01
Full Text Available An interactive multiobjective fuzzy inventory problem with two resource constraints is presented in this paper. The cost parameters and index parameters, the storage space, the budgetary cost, and the objective and constraint goals are imprecise in nature. These parameters and objective goals are quantified by linear/nonlinear membership functions. A compromise solution is obtained by geometric programming method. If the decision maker is not satisfied with this result, he/she may try to update the current solution to his/her satisfactory solution. In this way we implement man-machine interactive procedure to solve the problem through geometric programming method.
International Nuclear Information System (INIS)
Pazuki, G.R.
2005-01-01
In this study, osmotic coefficients and water activities in aqueous solutions have been modeled using a new approach based on the Pitzer model. This model contains two physically significant ionic parameters regarding ionic solvation and the closest distance of approach between ions in a solution. The proposed model was evaluated by estimating the osmotic coefficients of nine electrolytes in aqueous solutions. The obtained results showed that the model is suitable for predicting the osmotic coefficients in aqueous electrolyte solutions. Using adjustable parameters, which have been calculated from regression between the experimental osmotic coefficient and the results of this model, the water activity coefficients of aqueous solutions were calculated. The average absolute relative deviations of the osmotic coefficients between the experimental data and the calculated results were in agreement
Yang Mills instantons, geometrical aspects
International Nuclear Information System (INIS)
Stora, R.
1977-09-01
The word instanton has been coined by analogy with the word soliton. They both refer to solutions of elliptic non linear field equations with boundary conditions at infinity (of euclidean space time in the first case, euclidean space in the second case) lying on the set of classical vacua in such a way that stable topological properties emerge, susceptible to survive quantum effects, if those are small. Under this assumption, instantons are believed to be relevant to the description of tunnelling effects between classical vacua and signal some characteristics of the vacuum at the quantum level, whereas solitons should be associated with particles, i.e. discrete points in the mass spectrum. In one case the euclidean action is finite, in the other case, the energy is finite. From the mathematical point of view, the geometrical phenomena associated with the existence of solitons have forced physicists to learn rudiments of algebraic topology. The study of euclidean classical Yang Mills fields involves naturally mathematical items falling under the headings: differential geometry (fibre bundles, connections); differential topology (characteristic classes, index theory) and more recently algebraic geometry. These notes are divided as follows: a first section is devoted to a description of the physicist's views; a second section is devoted to the mathematician's vie
Noncritical String Liouville Theory and Geometric Bootstrap Hypothesis
Hadasz, Leszek; Jaskólski, Zbigniew
The applications of the existing Liouville theories for the description of the longitudinal dynamics of noncritical Nambu-Goto string are analyzed. We show that the recently developed DOZZ solution to the Liouville theory leads to the cut singularities in tree string amplitudes. We propose a new version of the Polyakov geometric approach to Liouville theory and formulate its basic consistency condition — the geometric bootstrap equation. Also in this approach the tree amplitudes develop cut singularities.
A note on the geometric phase in adiabatic approximation
International Nuclear Information System (INIS)
Tong, D.M.; Singh, K.; Kwek, L.C.; Fan, X.J.; Oh, C.H.
2005-01-01
The adiabatic theorem shows that the instantaneous eigenstate is a good approximation of the exact solution for a quantum system in adiabatic evolution. One may therefore expect that the geometric phase calculated by using the eigenstate should be also a good approximation of exact geometric phase. However, we find that the former phase may differ appreciably from the latter if the evolution time is large enough
Harmonic and geometric analysis
Citti, Giovanna; Pérez, Carlos; Sarti, Alessandro; Zhong, Xiao
2015-01-01
This book presents an expanded version of four series of lectures delivered by the authors at the CRM. Harmonic analysis, understood in a broad sense, has a very wide interplay with partial differential equations and in particular with the theory of quasiconformal mappings and its applications. Some areas in which real analysis has been extremely influential are PDE's and geometric analysis. Their foundations and subsequent developments made extensive use of the Calderón–Zygmund theory, especially the Lp inequalities for Calderón–Zygmund operators (Beurling transform and Riesz transform, among others) and the theory of Muckenhoupt weights. The first chapter is an application of harmonic analysis and the Heisenberg group to understanding human vision, while the second and third chapters cover some of the main topics on linear and multilinear harmonic analysis. The last serves as a comprehensive introduction to a deep result from De Giorgi, Moser and Nash on the regularity of elliptic partial differen...
Discrete geometric structures for architecture
Pottmann, Helmut
2010-06-13
The emergence of freeform structures in contemporary architecture raises numerous challenging research problems, most of which are related to the actual fabrication and are a rich source of research topics in geometry and geometric computing. The talk will provide an overview of recent progress in this field, with a particular focus on discrete geometric structures. Most of these result from practical requirements on segmenting a freeform shape into planar panels and on the physical realization of supporting beams and nodes. A study of quadrilateral meshes with planar faces reveals beautiful relations to discrete differential geometry. In particular, we discuss meshes which discretize the network of principal curvature lines. Conical meshes are among these meshes; they possess conical offset meshes at a constant face/face distance, which in turn leads to a supporting beam layout with so-called torsion free nodes. This work can be generalized to a variety of multilayer structures and laid the ground for an adapted curvature theory for these meshes. There are also efforts on segmenting surfaces into planar hexagonal panels. Though these are less constrained than planar quadrilateral panels, this problem is still waiting for an elegant solution. Inspired by freeform designs in architecture which involve circles and spheres, we present a new kind of triangle mesh whose faces\\' in-circles form a packing, i.e., the in-circles of two triangles with a common edge have the same contact point on that edge. These "circle packing (CP) meshes" exhibit an aesthetic balance of shape and size of their faces. They are closely tied to sphere packings on surfaces and to various remarkable structures and patterns which are of interest in art, architecture, and design. CP meshes constitute a new link between architectural freeform design and computational conformal geometry. Recently, certain timber structures motivated us to study discrete patterns of geodesics on surfaces. This
Regular Polygons and Geometric Series.
Jarrett, Joscelyn A.
1982-01-01
Examples of some geometric illustrations of limits are presented. It is believed the limit concept is among the most important topics in mathematics, yet many students do not have good intuitive feelings for the concept, since it is often taught very abstractly. Geometric examples are suggested as meaningful tools. (MP)
Geometric Invariants and Object Recognition.
1992-08-01
University of Chicago Press. Maybank , S.J. [1992], "The Projection of Two Non-coplanar Conics", in Geometric Invariance in Machine Vision, eds. J.L...J.L. Mundy and A. Zisserman, MIT Press, Cambridge, MA. Mundy, J.L., Kapur, .. , Maybank , S.J., and Quan, L. [1992a] "Geometric Inter- pretation of
Transmuted Complementary Weibull Geometric Distribution
Directory of Open Access Journals (Sweden)
Ahmed Z. A fify
2014-12-01
Full Text Available This paper provides a new generalization of the complementary Weibull geometric distribution that introduced by Tojeiro et al. (2014, using the quadratic rank transmutation map studied by Shaw and Buckley (2007. The new distribution is referred to as transmuted complementary Weibull geometric distribution (TCWGD. The TCWG distribution includes as special cases the complementary Weibull geometric distribution (CWGD, complementary exponential geometric distribution(CEGD,Weibull distribution (WD and exponential distribution (ED. Various structural properties of the new distribution including moments, quantiles, moment generating function and RØnyi entropy of the subject distribution are derived. We proposed the method of maximum likelihood for estimating the model parameters and obtain the observed information matrix. A real data set are used to compare the exibility of the transmuted version versus the complementary Weibull geometric distribution.
A GEOMETRICAL HEIGHT SCALE FOR SUNSPOT PENUMBRAE
International Nuclear Information System (INIS)
Puschmann, K. G.; Ruiz Cobo, B.; MartInez Pillet, V.
2010-01-01
Inversions of spectropolarimetric observations of penumbral filaments deliver the stratification of different physical quantities in an optical depth scale. However, without establishing a geometrical height scale, their three-dimensional geometrical structure cannot be derived. This is crucial in understanding the correct spatial variation of physical properties in the penumbral atmosphere and to provide insights into the mechanism capable of explaining the observed penumbral brightness. The aim of this work is to determine a global geometrical height scale in the penumbra by minimizing the divergence of the magnetic field vector and the deviations from static equilibrium as imposed by a force balance equation that includes pressure gradients, gravity, and the Lorentz force. Optical depth models are derived from the inversion of spectropolarimetric data of an active region observed with the Solar Optical Telescope on board the Hinode satellite. We use a genetic algorithm to determine the boundary condition for the inference of geometrical heights. The retrieved geometrical height scale permits the evaluation of the Wilson depression at each pixel and the correlation of physical quantities at each height. Our results fit into the uncombed penumbral scenario, i.e., a penumbra composed of flux tubes with channeled mass flow and with a weaker and more horizontal magnetic field as compared with the background field. The ascending material is hotter and denser than their surroundings. We do not find evidence of overturning convection or field-free regions in the inner penumbral area analyzed. The penumbral brightness can be explained by the energy transfer of the ascending mass carried by the Evershed flow, if the physical quantities below z = -75 km are extrapolated from the results of the inversion.
Geometrical Description of fractional quantum Hall quasiparticles
Park, Yeje; Yang, Bo; Haldane, F. D. M.
2012-02-01
We examine a description of fractional quantum Hall quasiparticles and quasiholes suggested by a recent geometrical approach (F. D. M. Haldane, Phys. Rev. Lett. 108, 116801 (2011)) to FQH systems, where the local excess electric charge density in the incompressible state is given by a topologically-quantized ``guiding-center spin'' times the Gaussian curvature of a ``guiding-center metric tensor'' that characterizes the local shape of the correlation hole around electrons in the fluid. We use a phenomenological energy function with two ingredients: the shear distortion energy of area-preserving distortions of the fluid, and a local (short-range) approximation to the Coulomb energy of the fluctuation of charge density associated with the Gaussian curvature. Quasiparticles and quasiholes of the 1/3 Laughlin state are modeled as ``punctures'' in the incompressible fluid which then relax by geometric distortion which generates Gaussian curvature, giving rise to the charge-density profile around the topological excitation.
Hydrodynamic Limit with Geometric Correction of Stationary Boltzmann Equation
Wu, Lei
2014-01-01
We consider the hydrodynamic limit of a stationary Boltzmann equation in a unit plate with in-flow boundary. We prove the solution can be approximated in $L^{\\infty}$ by the sum of interior solution which satisfies steady incompressible Navier-Stokes-Fourier system, and boundary layer with geometric correction. Also, we construct a counterexample to the classical theory which states the behavior of solution near boundary can be described by the Knudsen layer derived from the Milne problem.
Geometrical method of decoupling
Directory of Open Access Journals (Sweden)
C. Baumgarten
2012-12-01
Full Text Available The computation of tunes and matched beam distributions are essential steps in the analysis of circular accelerators. If certain symmetries—like midplane symmetry—are present, then it is possible to treat the betatron motion in the horizontal, the vertical plane, and (under certain circumstances the longitudinal motion separately using the well-known Courant-Snyder theory, or to apply transformations that have been described previously as, for instance, the method of Teng and Edwards. In a preceding paper, it has been shown that this method requires a modification for the treatment of isochronous cyclotrons with non-negligible space charge forces. Unfortunately, the modification was numerically not as stable as desired and it was still unclear, if the extension would work for all conceivable cases. Hence, a systematic derivation of a more general treatment seemed advisable. In a second paper, the author suggested the use of real Dirac matrices as basic tools for coupled linear optics and gave a straightforward recipe to decouple positive definite Hamiltonians with imaginary eigenvalues. In this article this method is generalized and simplified in order to formulate a straightforward method to decouple Hamiltonian matrices with eigenvalues on the real and the imaginary axis. The decoupling of symplectic matrices which are exponentials of such Hamiltonian matrices can be deduced from this in a few steps. It is shown that this algebraic decoupling is closely related to a geometric “decoupling” by the orthogonalization of the vectors E[over →], B[over →], and P[over →], which were introduced with the so-called “electromechanical equivalence.” A mathematical analysis of the problem can be traced down to the task of finding a structure-preserving block diagonalization of symplectic or Hamiltonian matrices. Structure preservation means in this context that the (sequence of transformations must be symplectic and hence canonical. When
DEFF Research Database (Denmark)
Hillyard, Stanley D; Baula, Victor; Tuttle, Wendy
2007-01-01
Dehydrated toads initiated water absorption response (WR) behavior and absorbed water from dilute NaCl solutions. With 200-250 mM NaCl, WR behavior and water absorption were both suppressed. With 200-250 mM Na-gluconate, WR initiation was significantly greater than with NaCl but water loss was gr...
Geometric inequalities for black holes
International Nuclear Information System (INIS)
Dain, Sergio
2013-01-01
Full text: A geometric inequality in General Relativity relates quantities that have both a physical interpretation and a geometrical definition. It is well known that the parameters that characterize the Kerr-Newman black hole satisfy several important geometric inequalities. Remarkably enough, some of these inequalities also hold for dynamical black holes. This kind of inequalities, which are valid in the dynamical and strong field regime, play an important role in the characterization of the gravitational collapse. They are closed related with the cosmic censorship conjecture. In this talk I will review recent results in this subject. (author)
Geometric Computing for Freeform Architecture
Wallner, J.
2011-06-03
Geometric computing has recently found a new field of applications, namely the various geometric problems which lie at the heart of rationalization and construction-aware design processes of freeform architecture. We report on our work in this area, dealing with meshes with planar faces and meshes which allow multilayer constructions (which is related to discrete surfaces and their curvatures), triangles meshes with circle-packing properties (which is related to conformal uniformization), and with the paneling problem. We emphasize the combination of numerical optimization and geometric knowledge.
Optical traps with geometric aberrations
International Nuclear Information System (INIS)
Roichman, Yael; Waldron, Alex; Gardel, Emily; Grier, David G.
2006-01-01
We assess the influence of geometric aberrations on the in-plane performance of optical traps by studying the dynamics of trapped colloidal spheres in deliberately distorted holographic optical tweezers. The lateral stiffness of the traps turns out to be insensitive to moderate amounts of coma, astigmatism, and spherical aberration. Moreover holographic aberration correction enables us to compensate inherent shortcomings in the optical train, thereby adaptively improving its performance. We also demonstrate the effects of geometric aberrations on the intensity profiles of optical vortices, whose readily measured deformations suggest a method for rapidly estimating and correcting geometric aberrations in holographic trapping systems
Geometric inequalities for black holes
Energy Technology Data Exchange (ETDEWEB)
Dain, Sergio [Universidad Nacional de Cordoba (Argentina)
2013-07-01
Full text: A geometric inequality in General Relativity relates quantities that have both a physical interpretation and a geometrical definition. It is well known that the parameters that characterize the Kerr-Newman black hole satisfy several important geometric inequalities. Remarkably enough, some of these inequalities also hold for dynamical black holes. This kind of inequalities, which are valid in the dynamical and strong field regime, play an important role in the characterization of the gravitational collapse. They are closed related with the cosmic censorship conjecture. In this talk I will review recent results in this subject. (author)
Geometric transitions on non-Kaehler manifolds
International Nuclear Information System (INIS)
Knauf, A.
2007-01-01
We study geometric transitions on the supergravity level using the basic idea of an earlier paper (M. Becker et al., 2004), where a pair of non-Kaehler backgrounds was constructed, which are related by a geometric transition. Here we embed this idea into an orientifold setup. The non-Kaehler backgrounds we obtain in type IIA are non-trivially fibered due to their construction from IIB via T-duality with Neveu-Schwarz flux. We demonstrate that these non-Kaehler manifolds are not half-flat and show that a symplectic structure exists on them at least locally. We also review the construction of new non-Kaehler backgrounds in type I and heterotic theory. They are found by a series of T- and S-duality and can be argued to be related by geometric transitions as well. A local toy model is provided that fulfills the flux equations of motion in IIB and the torsional relation in heterotic theory, and that is consistent with the U-duality relating both theories. For the heterotic theory we also propose a global solution that fulfills the torsional relation because it is similar to the Maldacena-Nunez background. (Abstract Copyright [2007], Wiley Periodicals, Inc.)
Nagata, Maika K C T; Brauchle, Paul S; Wang, Sen; Briggs, Sarah K; Hong, Young Soo; Laorenza, Daniel W; Lee, Andrea G; Westmoreland, T David
2016-08-16
Three new DOTAM (1,4,7,10-tetrakis(acetamido)-1,4,7,10-tetraazacyclododecane) complexes have been synthesized and characterized by X-ray crystallography: [Co(DOTAM)]Cl 2 •3H 2 O, [Ni(DOTAM)]Cl 2 •4H 2 O, and [Cu(DOTAM)](ClO 4 ) 2 •H 2 O. Solid state and solution IR spectroscopic features for a series of [M(DOTAM)] 2+ complexes (M=Mn, Co, Cu, Ni, Ca, Zn) correlate with solid state and solution coordination numbers. [Co(DOTAM)] 2+ , [Ni(DOTAM)] 2+ , and [Zn(DOTAM)] 2+ are demonstrated to be six-coordinate in both the solid state and in solution, while [Mn(DOTAM)] 2+ and [Ca(DOTAM)] 2+ are eight-coordinate in the solid state and remain so in solution. [Cu(DOTAM)] 2+ , which is five-coordinate by X-ray crystallography, is shown to increase its coordination number in solution to six-coordinate.
Discrete geometric structures for architecture
Pottmann, Helmut
2010-01-01
. The talk will provide an overview of recent progress in this field, with a particular focus on discrete geometric structures. Most of these result from practical requirements on segmenting a freeform shape into planar panels and on the physical realization
Geometric Rationalization for Freeform Architecture
Jiang, Caigui
2016-01-01
The emergence of freeform architecture provides interesting geometric challenges with regards to the design and manufacturing of large-scale structures. To design these architectural structures, we have to consider two types of constraints. First
Geometrical optics in general relativity
Loinger, A.
2006-01-01
General relativity includes geometrical optics. This basic fact has relevant consequences that concern the physical meaning of the discontinuity surfaces propagated in the gravitational field - as it was first emphasized by Levi-Civita.
Czech Academy of Sciences Publication Activity Database
Roth, Michal
2016-01-01
Roč. 50, č. 23 (2016), s. 12857-12863 ISSN 0013-936X R&D Projects: GA ČR(CZ) GA16-03749S Institutional support: RVO:68081715 Keywords : partitioning between water and supercritical CO2 * organic solutes * K-factor modeling * linear solvation energy relationship Subject RIV: CB - Analytical Chemistry, Separation Impact factor: 6.198, year: 2016
Geometric Correction of PHI Hyperspectral Image without Ground Control Points
International Nuclear Information System (INIS)
Luan, Kuifeng; Tong, Xiaohua; Liu, Xiangfeng; Ma, Yanhua; Shu, Rong; Xu, Weiming
2014-01-01
Geometric correction without ground control points (GCPs) is a very important topic. Conventional airborne photogrammetry is difficult to implement in areas where the installation of GCPs is not available. The technical of integrated GPS/INS systems providing the positioning and attitude of airborne systems is a potential solution in such areas. This paper first states the principle of geometric correction based on a combination of GPS and INS then the error of the geometric correction of Pushbroom Hyperspectral Imager (PHI) without GCP was analysed, then a flight test was carried out in an area of Damxung, Tibet. The experiment result showed that the error at straight track was small, generally less than 1 pixel, while the maximum error at cross track direction, was close to 2 pixels. The results show that geometric correction of PHI without GCP enables a variety of mapping products to be generated from airborne navigation and imagery data
Le, Tien Dung; Moyne, Christian; Murad, Marcio A.
2015-01-01
A new three-scale model is proposed to describe the movement of ionic species of different valences in swelling clays characterized by three separate length scales (nano, micro, and macro) and two levels of porosity (nano- and micropores). At the finest (nano) scale the medium is treated as charged clay particles saturated by aqueous electrolyte solution containing monovalent and divalent ions forming the electrical double layer. A new constitutive law is constructed for the disjoining pressure based on the numerical resolution of non-local problem at the nanoscale which, in contrast to the Poisson-Boltzmann theory for point charge ions, is capable of capturing the short-range interactions between the ions due to their finite size. At the intermediate scale (microscale), the two-phase homogenized particle/electrolyte solution system is represented by swollen clay clusters (or aggregates) with the nanoscale disjoining pressure incorporated in a modified form of Terzaghi's effective principle. At the macroscale, the electro-chemical-mechanical couplings within clay clusters is homogenized with the ion transport in the bulk fluid lying in the micro pores. The resultant macroscopic picture is governed by a three-scale model wherein ion transport takes place in the bulk solution strongly coupled with the mechanics of the clay clusters which play the role of sources/sinks of mass to the bulk fluid associated with ion adsorption/desorption in the electrical double layer at the nanoscale. Within the context of the quasi-steady version of the multiscale model, wherein the electrolyte solution in the nanopores is assumed at instantaneous thermodynamic equilibrium with the bulk fluid in the micropores, we build-up numerically the ion-adsorption isotherms along with the constitutive law of the retardation coefficients of monovalent and divalent ions. In addition, the constitutive law for the macroscopic swelling pressure is reconstructed numerically showing patterns of
Geometric flows in Horava-Lifshitz gravity
Bakas, Ioannis; Lust, Dieter; Petropoulos, Marios
2010-01-01
We consider instanton solutions of Euclidean Horava-Lifshitz gravity in four dimensions satisfying the detailed balance condition. They are described by geometric flows in three dimensions driven by certain combinations of the Cotton and Ricci tensors as well as the cosmological-constant term. The deformation curvature terms can have competing behavior leading to a variety of fixed points. The instantons interpolate between any two fixed points, which are vacua of topologically massive gravity with Lambda > 0, and their action is finite. Special emphasis is placed on configurations with SU(2) isometry associated with homogeneous but generally non-isotropic Bianchi IX model geometries. In this case, the combined Ricci-Cotton flow reduces to an autonomous system of ordinary differential equations whose properties are studied in detail for different couplings. The occurrence and stability of isotropic and anisotropic fixed points are investigated analytically and some exact solutions are obtained. The correspond...
A geometric viewpoint on generalized hydrodynamics
Directory of Open Access Journals (Sweden)
Benjamin Doyon
2018-01-01
Full Text Available Generalized hydrodynamics (GHD is a large-scale theory for the dynamics of many-body integrable systems. It consists of an infinite set of conservation laws for quasi-particles traveling with effective (“dressed” velocities that depend on the local state. We show that these equations can be recast into a geometric dynamical problem. They are conservation equations with state-independent quasi-particle velocities, in a space equipped with a family of metrics, parametrized by the quasi-particles' type and speed, that depend on the local state. In the classical hard rod or soliton gas picture, these metrics measure the free length of space as perceived by quasi-particles; in the quantum picture, they weigh space with the density of states available to them. Using this geometric construction, we find a general solution to the initial value problem of GHD, in terms of a set of integral equations where time appears explicitly. These integral equations are solvable by iteration and provide an extremely efficient solution algorithm for GHD.
Information Geometric Complexity of a Trivariate Gaussian Statistical Model
Directory of Open Access Journals (Sweden)
Domenico Felice
2014-05-01
Full Text Available We evaluate the information geometric complexity of entropic motion on low-dimensional Gaussian statistical manifolds in order to quantify how difficult it is to make macroscopic predictions about systems in the presence of limited information. Specifically, we observe that the complexity of such entropic inferences not only depends on the amount of available pieces of information but also on the manner in which such pieces are correlated. Finally, we uncover that, for certain correlational structures, the impossibility of reaching the most favorable configuration from an entropic inference viewpoint seems to lead to an information geometric analog of the well-known frustration effect that occurs in statistical physics.
The Riemannian geometry is not sufficient for the geometrization of the Maxwell's equations
Kulyabov, Dmitry S.; Korolkova, Anna V.; Velieva, Tatyana R.
2018-04-01
The transformation optics uses geometrized Maxwell's constitutive equations to solve the inverse problem of optics, namely to solve the problem of finding the parameters of the medium along the paths of propagation of the electromagnetic field. For the geometrization of Maxwell's constitutive equations, the quadratic Riemannian geometry is usually used. This is due to the use of the approaches of the general relativity. However, there arises the question of the insufficiency of the Riemannian structure for describing the constitutive tensor of the Maxwell's equations. The authors analyze the structure of the constitutive tensor and correlate it with the structure of the metric tensor of Riemannian geometry. It is concluded that the use of the quadratic metric for the geometrization of Maxwell's equations is insufficient, since the number of components of the metric tensor is less than the number of components of the constitutive tensor. A possible solution to this problem may be a transition to Finslerian geometry, in particular, the use of the Berwald-Moor metric to establish the structural correspondence between the field tensors of the electromagnetic field.
International Nuclear Information System (INIS)
Fuchs, M.
1998-01-01
The availability depends from a lot of factors, especially from design approaches. The way for the development of design approaches for attaining the safety requirements with more redundancy and without diversity of the systems, especially of safety systems, in NPPs in the past is not acceptable for the future because of cost reasons. It is necessary to find new technical ways to achieve a better availability, reliability and safety by lower costs. The simplification of safety systems by using passive systems may be a solution in the future. The development of a new boiling water reactor BWR 1000 in Germany by Siemens which is sponsored by German utilities and supported by various European partners can be named as such example. (author)
International Nuclear Information System (INIS)
Chaudhuri, N.K.; Sawant, R.M.
1997-09-01
Stability constants of the fluoride complexes of the actinides in different oxidation states measured by potentiometric method using fluoride ion selective electrode have been presented. Procedure and precautions required to overcome certain difficulties particular to actinide ions have been discussed. Literature data from various sources have been compiled. In order to have a reasonable comparison the stability constant (β 1 ) values obtained in diverse ionic strength media are converted to thermodynamic stability constant, β 1 0 , using Davies equation (a modification of Debye-Huckel equation). A correlation of the β 1 0 values with the fundamental properties of the actinide ions using various models available in the literature has been attempted. A semiempirical relation recently developed by Brown, Sylva and Ellis (BSE equation) appears to be most suitable. Using the values of ionic radii and best available values of the stability constants of a large number of metal ions from recent compilations a comparative study of the various models or relations available in the literature has been tried. For metal ions in general, the best correlation is obtained with the BSE equation. In an attempt to accommodate the unusual trend in the stability constants of the tetravalent actinides a modification in a parameter of the BSE equation has been proposed. Good agreement between the theoretically calculated and experimentally determined values for actinides in different oxidation states is then obtained in most of the cases. (author)
Directory of Open Access Journals (Sweden)
Nada Verdel
2016-02-01
Full Text Available The time-dependent role of cations was investigated by ageing four different aqueous solutions of cation chlorides. A linear correlation was found between the cations’ Setchenov coefficient for the salting-out of benzene and the increase in the conductivity with time. The conductivity of the structure-breaking cations or the chaotropes increased more significantly with time than the conductivity of the kosmotropes. Since larger water clusters accelerate the proton or hydroxyl hopping mechanism, we propose that the structuring of the hydration shells of the chaotropes might be spontaneously enhanced over time.
Space-time-matter analytic and geometric structures
Brüning, Jochen
2018-01-01
At the boundary of mathematics and mathematical physics, this monograph explores recent advances in the mathematical foundations of string theory and cosmology. The geometry of matter and the evolution of geometric structures as well as special solutions, singularities and stability properties of the underlying partial differential equations are discussed.
Inverse Kinematics for Industrial Robots using Conformal Geometric Algebra
Directory of Open Access Journals (Sweden)
Adam L. Kleppe
2016-01-01
Full Text Available This paper shows how the recently developed formulation of conformal geometric algebra can be used for analytic inverse kinematics of two six-link industrial manipulators with revolute joints. The paper demonstrates that the solution of the inverse kinematics in this framework relies on the intersection of geometric objects like lines, circles, planes and spheres, which provides the developer with valuable geometric intuition about the problem. It is believed that this will be very useful for new robot geometries and other mechanisms like cranes and topside drilling equipment. The paper extends previous results on inverse kinematics using conformal geometric algebra by providing consistent solutions for the joint angles for the different configurations depending on shoulder left or right, elbow up or down, and wrist flipped or not. Moreover, it is shown how to relate the solution to the Denavit-Hartenberg parameters of the robot. The solutions have been successfully implemented and tested extensively over the whole workspace of the manipulators.
A geometrical approach to free-field quantization
International Nuclear Information System (INIS)
Tabensky, R.; Valle, J.W.F.
1977-01-01
A geometrical approach to the quantization of free relativistic fields is given. Complex probability amplitudes are assigned to the solutions of the classical evolution equation. It is assumed that the evolution is stricly classical, according to the scalar unitary representation of the Poincare group in a functional space. The theory is equivalent to canonical quantization [pt
Geometric group theory an introduction
Löh, Clara
2017-01-01
Inspired by classical geometry, geometric group theory has in turn provided a variety of applications to geometry, topology, group theory, number theory and graph theory. This carefully written textbook provides a rigorous introduction to this rapidly evolving field whose methods have proven to be powerful tools in neighbouring fields such as geometric topology. Geometric group theory is the study of finitely generated groups via the geometry of their associated Cayley graphs. It turns out that the essence of the geometry of such groups is captured in the key notion of quasi-isometry, a large-scale version of isometry whose invariants include growth types, curvature conditions, boundary constructions, and amenability. This book covers the foundations of quasi-geometry of groups at an advanced undergraduate level. The subject is illustrated by many elementary examples, outlooks on applications, as well as an extensive collection of exercises.
International Nuclear Information System (INIS)
Endre, Z.H.; Kuchel, P.W.
1986-01-01
Metabolically active human erythrocytes were incubated with [α- 13 C]glycine which led to the specific enrichment of intracellular glutathione. The cells were then studied using 13 C-NMR in which the longitudinal relaxation times (T 1 ) and nuclear Overhauser enhancements of the free glycine and glutathione were measured. Bulk viscosities of the erythrocyte cytoplasm were measured using Ostwald capillary viscometry. Large differences existed between the latter viscosity estimates and those based upon NMR-T 1 measurements. The authors derived an equation from the theory of the viscosity of concentrated solutions which contains two phenomenological interaction parameters, a 'shape' factor and a 'volume' factor; it was fitted to data relating to the concentration dependence of viscosity measured by both methods. Under various conditions of extracellular osmotic pressure, erythrocytes change volume and thus the viscosity of the intracellular milieu is altered. The volume changes resulted in changes in the T 1 of [α- 13 C]glycine. Conversely, the authors showed that alterations in T 1 , when appropriately calibrated, could be used for monitoring changes in volume of metabolically active cells. (Auth.)
The relationship between the Wigner-Weyl kinetic formalism and the complex geometrical optics method
Maj, Omar
2004-01-01
The relationship between two different asymptotic techniques developed in order to describe the propagation of waves beyond the standard geometrical optics approximation, namely, the Wigner-Weyl kinetic formalism and the complex geometrical optics method, is addressed. More specifically, a solution of the wave kinetic equation, relevant to the Wigner-Weyl formalism, is obtained which yields the same wavefield intensity as the complex geometrical optics method. Such a relationship is also disc...
An introduction to geometrical physics
Aldrovandi, R
1995-01-01
This book stresses the unifying power of the geometrical framework in bringing together concepts from the different areas of physics. Common underpinnings of optics, elasticity, gravitation, relativistic fields, particle mechanics and other subjects are underlined. It attempts to extricate the notion of space currently in the physical literature from the metric connotation.The book's goal is to present mathematical ideas associated with geometrical physics in a rather introductory language. Included are many examples from elementary physics and also, for those wishing to reach a higher level o
Asymptotic geometric analysis, part I
Artstein-Avidan, Shiri
2015-01-01
The authors present the theory of asymptotic geometric analysis, a field which lies on the border between geometry and functional analysis. In this field, isometric problems that are typical for geometry in low dimensions are substituted by an "isomorphic" point of view, and an asymptotic approach (as dimension tends to infinity) is introduced. Geometry and analysis meet here in a non-trivial way. Basic examples of geometric inequalities in isomorphic form which are encountered in the book are the "isomorphic isoperimetric inequalities" which led to the discovery of the "concentration phenomen
Geometric integration for particle accelerators
International Nuclear Information System (INIS)
Forest, Etienne
2006-01-01
This paper is a very personal view of the field of geometric integration in accelerator physics-a field where often work of the highest quality is buried in lost technical notes or even not published; one has only to think of Simon van der Meer Nobel prize work on stochastic cooling-unpublished in any refereed journal. So I reconstructed the relevant history of geometrical integration in accelerator physics as much as I could by talking to collaborators and using my own understanding of the field. The reader should not be too surprised if this account is somewhere between history, science and perhaps even fiction
Geometrical spin symmetry and spin
International Nuclear Information System (INIS)
Pestov, I. B.
2011-01-01
Unification of General Theory of Relativity and Quantum Mechanics leads to General Quantum Mechanics which includes into itself spindynamics as a theory of spin phenomena. The key concepts of spindynamics are geometrical spin symmetry and the spin field (space of defining representation of spin symmetry). The essence of spin is the bipolar structure of geometrical spin symmetry induced by the gravitational potential. The bipolar structure provides a natural derivation of the equations of spindynamics. Spindynamics involves all phenomena connected with spin and provides new understanding of the strong interaction.
Geometric integration for particle accelerators
Forest, Étienne
2006-05-01
This paper is a very personal view of the field of geometric integration in accelerator physics—a field where often work of the highest quality is buried in lost technical notes or even not published; one has only to think of Simon van der Meer Nobel prize work on stochastic cooling—unpublished in any refereed journal. So I reconstructed the relevant history of geometrical integration in accelerator physics as much as I could by talking to collaborators and using my own understanding of the field. The reader should not be too surprised if this account is somewhere between history, science and perhaps even fiction.
Lattice degeneracies of geometric fermions
International Nuclear Information System (INIS)
Raszillier, H.
1983-05-01
We give the minimal numbers of degrees of freedom carried by geometric fermions on all lattices of maximal symmetries in d = 2, 3, and 4 dimensions. These numbers are lattice dependent, but in the (free) continuum limit, part of the degrees of freedom have to escape to infinity by a Wilson mechanism built in, and 2sup(d) survive for any lattice. On self-reciprocal lattices we compare the minimal numbers of degrees of freedom of geometric fermions with the minimal numbers of naive fermions on these lattices and argue that these numbers are equal. (orig.)
Time evolution in a geometric model of a particle
International Nuclear Information System (INIS)
Atiyah, M.F.; Franchetti, G.; Schroers, B.J.
2015-01-01
We analyse the properties of a (4+1)-dimensional Ricci-flat spacetime which may be viewed as an evolving Taub-NUT geometry, and give exact solutions of the Maxwell and gauged Dirac equation on this background. We interpret these solutions in terms of a geometric model of the electron and its spin, and discuss links between the resulting picture and Dirac’s Large Number Hypothesis.
Geometric Properties of Grassmannian Frames for and
Directory of Open Access Journals (Sweden)
Benedetto John J
2006-01-01
Full Text Available Grassmannian frames are frames satisfying a min-max correlation criterion. We translate a geometrically intuitive approach for two- and three-dimensional Euclidean space ( and into a new analytic method which is used to classify many Grassmannian frames in this setting. The method and associated algorithm decrease the maximum frame correlation, and hence give rise to the construction of specific examples of Grassmannian frames. Many of the results are known by other techniques, and even more generally, so that this paper can be viewed as tutorial. However, our analytic method is presented with the goal of developing it to address unresovled problems in -dimensional Hilbert spaces which serve as a setting for spherical codes, erasure channel modeling, and other aspects of communications theory.
Veeraraghavan, Srikant; Mazziotti, David A
2014-03-28
We present a density matrix approach for computing global solutions of restricted open-shell Hartree-Fock theory, based on semidefinite programming (SDP), that gives upper and lower bounds on the Hartree-Fock energy of quantum systems. While wave function approaches to Hartree-Fock theory yield an upper bound to the Hartree-Fock energy, we derive a semidefinite relaxation of Hartree-Fock theory that yields a rigorous lower bound on the Hartree-Fock energy. We also develop an upper-bound algorithm in which Hartree-Fock theory is cast as a SDP with a nonconvex constraint on the rank of the matrix variable. Equality of the upper- and lower-bound energies guarantees that the computed solution is the globally optimal solution of Hartree-Fock theory. The work extends a previously presented method for closed-shell systems [S. Veeraraghavan and D. A. Mazziotti, Phys. Rev. A 89, 010502-R (2014)]. For strongly correlated systems the SDP approach provides an alternative to the locally optimized Hartree-Fock energies and densities with a certificate of global optimality. Applications are made to the potential energy curves of C2, CN, Cr2, and NO2.
Height and Tilt Geometric Texture
DEFF Research Database (Denmark)
Andersen, Vedrana; Desbrun, Mathieu; Bærentzen, Jakob Andreas
2009-01-01
compromise between functionality and simplicity: it can efficiently handle and process geometric texture too complex to be represented as a height field, without having recourse to full blown mesh editing algorithms. The height-and-tilt representation proposed here is fully intrinsic to the mesh, making...
In Defence of Geometrical Algebra
Blasjo, V.N.E.
The geometrical algebra hypothesis was once the received interpretation of Greek mathematics. In recent decades, however, it has become anathema to many. I give a critical review of all arguments against it and offer a consistent rebuttal case against the modern consensus. Consequently, I find that
Geometrical interpretation of extended supergravity
International Nuclear Information System (INIS)
Townsend, P.K.; Nieuwenhuizen, P.van
1977-01-01
SO 2 extended supergravity is shown to be a geometrical theory, whose underlying gauge group is OSp(4,2). The couplings which gauge the SO 2 symmetry as well as the accompanying cosmological and masslike terms are directly obtained, and the usual SO 2 model is obtained after a Wigner-Inoenue group contraction. (Auth.)
Geometric scaling in exclusive processes
International Nuclear Information System (INIS)
Munier, S.; Wallon, S.
2003-01-01
We show that according to the present understanding of the energy evolution of the observables measured in deep-inelastic scattering, the photon-proton scattering amplitude has to exhibit geometric scaling at each impact parameter. We suggest a way to test this experimentally at HERA. A qualitative analysis based on published data is presented and discussed. (orig.)
Geometric quantization and general relativity
International Nuclear Information System (INIS)
Souriau, J.-M.
1977-01-01
The purpose of geometric quantization is to give a rigorous mathematical content to the 'correspondence principle' between classical and quantum mechanics. The main tools are borrowed on one hand from differential geometry and topology (differential manifolds, differential forms, fiber bundles, homology and cohomology, homotopy), on the other hand from analysis (functions of positive type, infinite dimensional group representations, pseudo-differential operators). Some satisfactory results have been obtained in the study of dynamical systems, but some fundamental questions are still waiting for an answer. The 'geometric quantization of fields', where some further well known difficulties arise, is still in a preliminary stage. In particular, the geometric quantization on the gravitational field is still a mere project. The situation is even more uncertain due to the fact that there is no experimental evidence of any quantum gravitational effect which could give us a hint towards what we are supposed to look for. The first level of both Quantum Theory, and General Relativity describes passive matter: influence by the field without being a source of it (first quantization and equivalence principle respectively). In both cases this is only an approximation (matter is always a source). But this approximation turns out to be the least uncertain part of the description, because on one hand the first quantization avoids the problems of renormalization and on the other hand the equivalence principle does not imply any choice of field equations (it is known that one can modify Einstein equations at short distances without changing their geometrical properties). (Auth.)
Geometric origin of central charges
International Nuclear Information System (INIS)
Lukierski, J.; Rytel, L.
1981-05-01
The complete set of N(N-1) central charge generators for D=4 N-extended super Poincare algebra is obtained by suitable contraction of OSp (2N; 4) superalgebra. The superspace realizations of the spinorial generators with central charges are derived. The conjugate set of N(N-1) additional bosonic superspace coordinates is introduced in an unique and geometric way. (author)
Vergence, Vision, and Geometric Optics
Keating, Michael P.
1975-01-01
Provides a definition of vergence in terms of the curvature of the wave fronts, and gives examples to illustrate the advantages of this approach. The vergence treatment of geometrical optics provides both conceptual and algebraic advantages, particularly for the life science student, over the traditional object distance-image distance-focal length…
Geometric phases and quantum computation
International Nuclear Information System (INIS)
Vedral, V.
2005-01-01
Full text: In my lectures I will talk about the notion of the geometric phase and explain its relevance for both fundamental quantum mechanics as well as quantum computation. The phase will be at first introduced via the idea of Pancharatnam which involves interference of three or more light beams. This notion will then be generalized to the evolving quantum systems. I will discuss both pure and mixed states as well as unitary and non-unitary evolutions. I will also show how the concept of the vacuum induced geometric phase arises in quantum optics. A simple measurement scheme involving a Mach Zehnder interferometer will be presented and will be used to illustrate all the concepts in the lecture. Finally, I will expose a simple generalization of the geometric phase to evolving degenerate states. This will be seen to lead to the possibility of universal quantum computation using geometric effects only. Moreover, this contains a promise of intrinsically fault tolerant quantum information processing, whose prospects will be outlined at the end of the lecture. (author)
Cartan's geometrical structure of supergravity
International Nuclear Information System (INIS)
Baaklini, N.S.
1977-06-01
The geometrical partnership of the vierbein and the spin-3/2 field in the structure of the supergravity Lagrangian is emphasized. Both fields are introduced as component of the same matrix differential form. The only local symmetry of the theory is SL(2,C)
Optimization of biotechnological systems through geometric programming
Directory of Open Access Journals (Sweden)
Torres Nestor V
2007-09-01
Full Text Available Abstract Background In the past, tasks of model based yield optimization in metabolic engineering were either approached with stoichiometric models or with structured nonlinear models such as S-systems or linear-logarithmic representations. These models stand out among most others, because they allow the optimization task to be converted into a linear program, for which efficient solution methods are widely available. For pathway models not in one of these formats, an Indirect Optimization Method (IOM was developed where the original model is sequentially represented as an S-system model, optimized in this format with linear programming methods, reinterpreted in the initial model form, and further optimized as necessary. Results A new method is proposed for this task. We show here that the model format of a Generalized Mass Action (GMA system may be optimized very efficiently with techniques of geometric programming. We briefly review the basics of GMA systems and of geometric programming, demonstrate how the latter may be applied to the former, and illustrate the combined method with a didactic problem and two examples based on models of real systems. The first is a relatively small yet representative model of the anaerobic fermentation pathway in S. cerevisiae, while the second describes the dynamics of the tryptophan operon in E. coli. Both models have previously been used for benchmarking purposes, thus facilitating comparisons with the proposed new method. In these comparisons, the geometric programming method was found to be equal or better than the earlier methods in terms of successful identification of optima and efficiency. Conclusion GMA systems are of importance, because they contain stoichiometric, mass action and S-systems as special cases, along with many other models. Furthermore, it was previously shown that algebraic equivalence transformations of variables are sufficient to convert virtually any types of dynamical models into
International Nuclear Information System (INIS)
Gautier, G; Ventura, L; Jerisian, R
2005-01-01
Deep single trenches can be produced at the edge of apertures of protective films masking the surface of silicon samples. This macropore formation, from polarized HF based solutions, is electrically activated depending on the mask geometrical and physical parameters whatever the silicon type or the electrolyte composition. The mask thickness increase is known to induce deeper trenches. In this paper, we show that we can predict and localize this phenomenon by simulating two dimensional hole current distributions below the mask. We demonstrate also the influence of the material permittivity on trench depth. These 2D simulation results are correlated with experimental results
Geometric Transformations in Engineering Geometry
Directory of Open Access Journals (Sweden)
I. F. Borovikov
2015-01-01
Full Text Available Recently, for business purposes, in view of current trends and world experience in training engineers, research and faculty staff there has been a need to transform traditional courses of descriptive geometry into the course of engineering geometry in which the geometrical transformations have to become its main section. On the basis of critical analysis the paper gives suggestions to improve a presentation technique of this section both in the classroom and in academic literature, extend an application scope of geometrical transformations to solve the position and metric tasks and simulation of surfaces, as well as to design complex engineering configurations, which meet a number of pre-specified conditions.The article offers to make a number of considerable amendments to the terms and definitions used in the existing courses of descriptive geometry. It draws some conclusions and makes the appropriate proposals on feasibility of coordination in teaching the movement transformation in the courses of analytical and descriptive geometry. This will provide interdisciplinary team teaching and allow students to be convinced that a combination of analytical and graphic ways to solve geometric tasks is useful and reasonable.The traditional sections of learning courses need to be added with a theory of projective and bi-rational transformations. In terms of application simplicity and convenience it is enough to consider the central transformations when solving the applied tasks. These transformations contain a beam of sub-invariant (low-invariant straight lines on which the invariant curve induces non-involution and involution projectivities. The expediency of nonlinear transformations application is shown in the article by a specific example of geometric modeling of the interfacing surface "spar-blade".Implementation of these suggestions will contribute to a real transformation of a traditional course of descriptive geometry to the engineering geometry
A differential-geometric approach to generalized linear models with grouped predictors
Augugliaro, Luigi; Mineo, Angelo M.; Wit, Ernst C.
We propose an extension of the differential-geometric least angle regression method to perform sparse group inference in a generalized linear model. An efficient algorithm is proposed to compute the solution curve. The proposed group differential-geometric least angle regression method has important
Geometrical optics of dense aerosols: forming dense plasma slabs.
Hay, Michael J; Valeo, Ernest J; Fisch, Nathaniel J
2013-11-01
Assembling a freestanding, sharp-edged slab of homogeneous material that is much denser than gas, but much more rarefied than a solid, is an outstanding technological challenge. The solution may lie in focusing a dense aerosol to assume this geometry. However, whereas the geometrical optics of dilute aerosols is a well-developed field, the dense aerosol limit is mostly unexplored. Yet controlling the geometrical optics of dense aerosols is necessary in preparing such a material slab. Focusing dense aerosols is shown here to be possible, but the finite particle density reduces the effective Stokes number of the flow, a critical result for controlled focusing.
Renormgroup symmetries in problems of nonlinear geometrical optics
International Nuclear Information System (INIS)
Kovalev, V.F.
1996-01-01
Utilization and further development of the previously announced approach [1,2] enables one to construct renormgroup symmetries for a boundary value problem for the system of equations which describes propagation of a powerful radiation in a nonlinear medium in geometrical optics approximation. With the help of renormgroup symmetries new rigorous and approximate analytical solutions of nonlinear geometrical optics equations are obtained. Explicit analytical expressions are presented that characterize spatial evolution of laser beam which has an arbitrary intensity dependence at the boundary of the nonlinear medium. (author)
Monomial geometric programming with an arbitrary fuzzy relational inequality
Directory of Open Access Journals (Sweden)
E. Shivanian
2015-11-01
Full Text Available In this paper, an optimization model with geometric objective function is presented. Geometric programming is widely used; many objective functions in optimization problems can be analyzed by geometric programming. We often encounter these in resource allocation and structure optimization and technology management, etc. On the other hand, fuzzy relation equalities and inequalities are also used in many areas. We here present a geometric programming model with a monomial objective function subject to the fuzzy relation inequality constraints with an arbitrary function. The feasible solution set is determined and compared with some common results in the literature. A necessary and sufficient condition and three other necessary conditions are presented to conceptualize the feasibility of the problem. In general a lower bound is always attainable for the optimal objective value by removing the components having no effect on the solution process. By separating problem to non-decreasing and non-increasing function to prove the optimal solution, we simplify operations to accelerate the resolution of the problem.
International Nuclear Information System (INIS)
Horn, Martin Erik
2014-01-01
It is still a great riddle to me why Wolfgang Pauli and P.A.M. Dirac had not fully grasped the meaning of their own mathematical constructions. They invented magnificent, fantastic and very important mathematical features of modern physics, but they only delivered half of the interpretations of their own inventions. Of course, Pauli matrices and Dirac matrices represent operators, which Pauli and Dirac discussed in length. But this is only part of the true meaning behind them, as the non-commutative ideas of Grassmann, Clifford, Hamilton and Cartan allow a second, very far reaching interpretation of Pauli and Dirac matrices. An introduction to this alternative interpretation will be discussed. Some applications of this view on Pauli and Dirac matrices are given, e.g. a geometric algebra picture of the plane wave solution of the Maxwell equation, a geometric algebra picture of special relativity, a toy model of SU(3) symmetry, and some only very preliminary thoughts about a possible geometric meaning of quantum mechanics
An algebraic geometric approach to separation of variables
Schöbel, Konrad
2015-01-01
Konrad Schöbel aims to lay the foundations for a consequent algebraic geometric treatment of variable separation, which is one of the oldest and most powerful methods to construct exact solutions for the fundamental equations in classical and quantum physics. The present work reveals a surprising algebraic geometric structure behind the famous list of separation coordinates, bringing together a great range of mathematics and mathematical physics, from the late 19th century theory of separation of variables to modern moduli space theory, Stasheff polytopes and operads. "I am particularly impressed by his mastery of a variety of techniques and his ability to show clearly how they interact to produce his results.” (Jim Stasheff) Contents The Foundation: The Algebraic Integrability Conditions The Proof of Concept: A Complete Solution for the 3-Sphere The Generalisation: A Solution for Spheres of Arbitrary Dimension The Perspectives: Applications and Generalisations Target Groups Scientists in the fie...
The Effect of Bulk Tachyon Field on the Dynamics of Geometrical Tachyon
International Nuclear Information System (INIS)
Papantonopoulos, Eleftherios; Pappa, Ioanna; Zamarias, Vassilios
2007-01-01
We study the dynamics of the geometrical tachyon field on an unstable D3-brane in the background of a bulk tachyon field of a D3-brane solution of Type-0 string theory. We find that the geometrical tachyon potential is modified by a function of the bulk tachyon and inflation occurs at weak string coupling, where the bulk tachyon condenses, near the top of the geometrical tachyon potential. We also find a late accelerating phase when the bulk tachyon asymptotes to zero and the geometrical tachyon field reaches the minimum of the potential
Gauge field vacuum structure in geometrical aspect
International Nuclear Information System (INIS)
Konopleva, N.P.
2003-01-01
Vacuum conception is one of the main conceptions of quantum field theory. Its meaning in classical field theory is also very profound. In this case the vacuum conception is closely connected with ideas of the space-time geometry. The global and local geometrical space-time conceptions lead to different vacuum definitions and therefore to different ways of physical theory construction. Some aspects of the gauge field vacuum structure are analyzed. It is shown that in the gauge field theory the vacuum Einstein equation solutions describe the relativistic vacuum as common vacuum of all gauge fields and its sources. Instantons (both usual and hyperbolical) are regarded as nongravitating matter, because they have zero energy-momentum tensors and correspond to vacuum Einstein equations
Fluid mechanics a geometrical point of view
Rajeev, S G
2018-01-01
Fluid Mechanics: A Geometrical Point of View emphasizes general principles of physics illustrated by simple examples in fluid mechanics. Advanced mathematics (e.g., Riemannian geometry and Lie groups) commonly used in other parts of theoretical physics (e.g. General Relativity or High Energy Physics) are explained and applied to fluid mechanics. This follows on from the author's book Advanced Mechanics (Oxford University Press, 2013). After introducing the fundamental equations (Euler and Navier-Stokes), the book provides particular cases: ideal and viscous flows, shocks, boundary layers, instabilities, and transients. A restrained look at integrable systems (KdV) leads into a formulation of an ideal fluid as a hamiltonian system. Arnold's deep idea, that the instability of a fluid can be understood using the curvature of the diffeomorphism group, will be explained. Leray's work on regularity of Navier-Stokes solutions, and the modern developments arising from it, will be explained in language for physicists...
Rayleigh's hypothesis and the geometrical optics limit.
Elfouhaily, Tanos; Hahn, Thomas
2006-09-22
The Rayleigh hypothesis (RH) is often invoked in the theoretical and numerical treatment of rough surface scattering in order to decouple the analytical form of the scattered field. The hypothesis stipulates that the scattered field away from the surface can be extended down onto the rough surface even though it is formed by solely up-going waves. Traditionally this hypothesis is systematically used to derive the Volterra series under the small perturbation method which is equivalent to the low-frequency limit. In this Letter we demonstrate that the RH also carries the high-frequency or the geometrical optics limit, at least to first order. This finding has never been explicitly derived in the literature. Our result comforts the idea that the RH might be an exact solution under some constraints in the general case of random rough surfaces and not only in the case of small-slope deterministic periodic gratings.
Geometric-optical illusions at isoluminance.
Hamburger, Kai; Hansen, Thorsten; Gegenfurtner, Karl R
2007-12-01
The idea of a largely segregated processing of color and form was initially supported by observations that geometric-optical illusions vanish under isoluminance. However, this finding is inconsistent with some psychophysical studies and also with physiological evidence showing that color and luminance are processed together by largely overlapping sets of neurons in the LGN, in V1, and in extrastriate areas. Here we examined the strength of nine geometric-optical illusions under isoluminance (Delboeuf, Ebbinghaus, Hering, Judd, Müller-Lyer, Poggendorff, Ponzo, Vertical, Zöllner). Subjects interactively manipulated computer-generated line drawings to counteract the illusory effect. In all cases, illusions presented under isoluminance (both for colors drawn from the cardinal L-M or S-(L+M) directions of DKL color space) were as effective as the luminance versions (both for high and low contrast). The magnitudes of the illusion effects were highly correlated across subjects for the different conditions. In two additional experiments we determined that the strong illusions observed under isoluminance were not due to individual deviations from the photometric point of isoluminance or due to chromatic aberrations. Our findings show that our conscious percept is affected similarly for both isoluminance and luminance conditions, suggesting that the joint processing for chromatic and luminance defined contours may extend well beyond early visual areas.
Auto-focusing accelerating hyper-geometric laser beams
International Nuclear Information System (INIS)
Kovalev, A A; Kotlyar, V V; Porfirev, A P
2016-01-01
We derive a new solution to the paraxial wave equation that defines a two-parameter family of three-dimensional structurally stable vortex annular auto-focusing hyper-geometric (AH) beams, with their complex amplitude expressed via a degenerate hyper-geometric function. The AH beams are found to carry an orbital angular momentum and be auto-focusing, propagating on an accelerating path toward a focus, where the annular intensity pattern is ‘sharply’ reduced in diameter. An explicit expression for the complex amplitude of vortex annular auto-focusing hyper-geometric-Gaussian beams is derived. The experiment has been shown to be in good agreement with theory. (paper)
On chromatic and geometrical calibration
DEFF Research Database (Denmark)
Folm-Hansen, Jørgen
1999-01-01
The main subject of the present thesis is different methods for the geometrical and chromatic calibration of cameras in various environments. For the monochromatic issues of the calibration we present the acquisition of monochrome images, the classic monochrome aberrations and the various sources...... the correct interpolation method is described. For the chromatic issues of calibration we present the acquisition of colour and multi-spectral images, the chromatic aberrations and the various lens/camera based non-uniformities of the illumination of the image plane. It is described how the monochromatic...... to design calibration targets for both geometrical and chromatic calibration are described. We present some possible systematical errors on the detection of the objects in the calibration targets, if viewed in a non orthogonal angle, if the intensities are uneven or if the image blurring is uneven. Finally...
Geometrical approach to tumor growth.
Escudero, Carlos
2006-08-01
Tumor growth has a number of features in common with a physical process known as molecular beam epitaxy. Both growth processes are characterized by the constraint of growth development to the body border, and surface diffusion of cells and particles at the growing edge. However, tumor growth implies an approximate spherical symmetry that makes necessary a geometrical treatment of the growth equations. The basic model was introduced in a former paper [C. Escudero, Phys. Rev. E 73, 020902(R) (2006)], and in the present work we extend our analysis and try to shed light on the possible geometrical principles that drive tumor growth. We present two-dimensional models that reproduce the experimental observations, and analyze the unexplored three-dimensional case, for which interesting conclusions on tumor growth are derived.
Geometrical interpretation of optical absorption
Energy Technology Data Exchange (ETDEWEB)
Monzon, J. J.; Barriuso, A. G.; Sanchez-Soto, L. L. [Departamento de Optica, Facultad de Fisica, Universidad Complutense, E-28040 Madrid (Spain); Montesinos-Amilibia, J. M. [Departamento de Geometria y Topologia, Facultad de Matematicas, Universidad Complutense, E-28040 Madrid (Spain)
2011-08-15
We reinterpret the transfer matrix for an absorbing system in very simple geometrical terms. In appropriate variables, the system appears as performing a Lorentz transformation in a (1 + 3)-dimensional space. Using homogeneous coordinates, we map that action on the unit sphere, which is at the realm of the Klein model of hyperbolic geometry. The effects of absorption appear then as a loxodromic transformation, that is, a rhumb line crossing all the meridians at the same angle.
Parametric FEM for geometric biomembranes
Bonito, Andrea; Nochetto, Ricardo H.; Sebastian Pauletti, M.
2010-05-01
We consider geometric biomembranes governed by an L2-gradient flow for bending energy subject to area and volume constraints (Helfrich model). We give a concise derivation of a novel vector formulation, based on shape differential calculus, and corresponding discretization via parametric FEM using quadratic isoparametric elements and a semi-implicit Euler method. We document the performance of the new parametric FEM with a number of simulations leading to dumbbell, red blood cell and toroidal equilibrium shapes while exhibiting large deformations.
Geometrical methods in learning theory
International Nuclear Information System (INIS)
Burdet, G.; Combe, Ph.; Nencka, H.
2001-01-01
The methods of information theory provide natural approaches to learning algorithms in the case of stochastic formal neural networks. Most of the classical techniques are based on some extremization principle. A geometrical interpretation of the associated algorithms provides a powerful tool for understanding the learning process and its stability and offers a framework for discussing possible new learning rules. An illustration is given using sequential and parallel learning in the Boltzmann machine
Geometrical approach to tumor growth
Escudero, Carlos
2006-01-01
Tumor growth has a number of features in common with a physical process known as molecular beam epitaxy. Both growth processes are characterized by the constraint of growth development to the body border, and surface diffusion of cells/particles at the growing edge. However, tumor growth implies an approximate spherical symmetry that makes necessary a geometrical treatment of the growth equations. The basic model was introduced in a former article [C. Escudero, Phys. Rev. E 73, 020902(R) (200...
Riemannian geometry and geometric analysis
Jost, Jürgen
2017-01-01
This established reference work continues to provide its readers with a gateway to some of the most interesting developments in contemporary geometry. It offers insight into a wide range of topics, including fundamental concepts of Riemannian geometry, such as geodesics, connections and curvature; the basic models and tools of geometric analysis, such as harmonic functions, forms, mappings, eigenvalues, the Dirac operator and the heat flow method; as well as the most important variational principles of theoretical physics, such as Yang-Mills, Ginzburg-Landau or the nonlinear sigma model of quantum field theory. The present volume connects all these topics in a systematic geometric framework. At the same time, it equips the reader with the working tools of the field and enables her or him to delve into geometric research. The 7th edition has been systematically reorganized and updated. Almost no page has been left unchanged. It also includes new material, for instance on symplectic geometry, as well as the B...
Geometric mean for subspace selection.
Tao, Dacheng; Li, Xuelong; Wu, Xindong; Maybank, Stephen J
2009-02-01
Subspace selection approaches are powerful tools in pattern classification and data visualization. One of the most important subspace approaches is the linear dimensionality reduction step in the Fisher's linear discriminant analysis (FLDA), which has been successfully employed in many fields such as biometrics, bioinformatics, and multimedia information management. However, the linear dimensionality reduction step in FLDA has a critical drawback: for a classification task with c classes, if the dimension of the projected subspace is strictly lower than c - 1, the projection to a subspace tends to merge those classes, which are close together in the original feature space. If separate classes are sampled from Gaussian distributions, all with identical covariance matrices, then the linear dimensionality reduction step in FLDA maximizes the mean value of the Kullback-Leibler (KL) divergences between different classes. Based on this viewpoint, the geometric mean for subspace selection is studied in this paper. Three criteria are analyzed: 1) maximization of the geometric mean of the KL divergences, 2) maximization of the geometric mean of the normalized KL divergences, and 3) the combination of 1 and 2. Preliminary experimental results based on synthetic data, UCI Machine Learning Repository, and handwriting digits show that the third criterion is a potential discriminative subspace selection method, which significantly reduces the class separation problem in comparing with the linear dimensionality reduction step in FLDA and its several representative extensions.
Chen, Yixing; Dupertuis, Nathan; Okur, Halil I.; Roke, Sylvie
2018-06-01
The temperature dependence of the femtosecond elastic second harmonic scattering (fs-ESHS) response of bulk light and heavy water and their electrolyte solutions is presented. We observe clear temperature dependent changes in the hydrogen (H)-bond network of water that show a decrease in the orientational order of water with increasing temperature. Although D2O has a more structured H-bond network (giving rise to more fs-ESHS intensity), the relative temperature dependence is larger in H2O. The changes are interpreted in terms of the symmetry of H-bonds and are indicators of nuclear quantum effects. Increasing the temperature in electrolyte solutions decreases the influence of the total electrostatic field from ions on the water-water correlations, as expected from Debye-Hückel theory, since the Debye length becomes longer. The effects are, however, 1.9 times (6.3 times) larger than those predicted for H2O (D2O). Since fs-ESHS responses can be computed from known molecular coordinates, our observations provide a unique opportunity to refine quantum mechanical models of water.
Multiscale geometric modeling of macromolecules II: Lagrangian representation
Feng, Xin; Xia, Kelin; Chen, Zhan; Tong, Yiying; Wei, Guo-Wei
2013-01-01
Geometric modeling of biomolecules plays an essential role in the conceptualization of biolmolecular structure, function, dynamics and transport. Qualitatively, geometric modeling offers a basis for molecular visualization, which is crucial for the understanding of molecular structure and interactions. Quantitatively, geometric modeling bridges the gap between molecular information, such as that from X-ray, NMR and cryo-EM, and theoretical/mathematical models, such as molecular dynamics, the Poisson-Boltzmann equation and the Nernst-Planck equation. In this work, we present a family of variational multiscale geometric models for macromolecular systems. Our models are able to combine multiresolution geometric modeling with multiscale electrostatic modeling in a unified variational framework. We discuss a suite of techniques for molecular surface generation, molecular surface meshing, molecular volumetric meshing, and the estimation of Hadwiger’s functionals. Emphasis is given to the multiresolution representations of biomolecules and the associated multiscale electrostatic analyses as well as multiresolution curvature characterizations. The resulting fine resolution representations of a biomolecular system enable the detailed analysis of solvent-solute interaction, and ion channel dynamics, while our coarse resolution representations highlight the compatibility of protein-ligand bindings and possibility of protein-protein interactions. PMID:23813599
Geometric phases in astigmatic optical modes of arbitrary order
International Nuclear Information System (INIS)
Habraken, Steven J. M.; Nienhuis, Gerard
2010-01-01
The transverse spatial structure of a paraxial beam of light is fully characterized by a set of parameters that vary only slowly under free propagation. They specify bosonic ladder operators that connect modes of different orders, in analogy to the ladder operators connecting harmonic-oscillator wave functions. The parameter spaces underlying sets of higher-order modes are isomorphic to the parameter space of the ladder operators. We study the geometry of this space and the geometric phase that arises from it. This phase constitutes the ultimate generalization of the Gouy phase in paraxial wave optics. It reduces to the ordinary Gouy phase and the geometric phase of nonastigmatic optical modes with orbital angular momentum in limiting cases. We briefly discuss the well-known analogy between geometric phases and the Aharonov-Bohm effect, which provides some complementary insights into the geometric nature and origin of the generalized Gouy phase shift. Our method also applies to the quantum-mechanical description of wave packets. It allows for obtaining complete sets of normalized solutions of the Schroedinger equation. Cyclic transformations of such wave packets give rise to a phase shift, which has a geometric interpretation in terms of the other degrees of freedom involved.
International Nuclear Information System (INIS)
Cabo, Alejandro; Claro, Francisco
2003-07-01
An analytic solution of the Hartree-Fock problem for a 2DEG at filling 1/3 and half an electron per unit cell is presented. The Coulomb interaction dynamically breaks the first Landau level in three narrow sub-bands, one of which is fully occupied and the other empty, as in the composite fermion model. The localized orbitals associated to the Bloch like single electron wavefunctions are nearly static, resembling the angular momentum eigenstates within a Landau level for non-interacting fermions. Strong correlations are expected owing to the large charge density overlap between neighboring plaquettes. A numerical evaluation brings the cohesive energy close to that of the best present day models. It is also found that correlations are long range, requiring over 50 particles spread over a finite sample to approach convergence. Since presently allowed exact calculations are far from this number, the question of how relevant the considered wave-function is for the description of the ground state of the 2DEG system remains open. (author)
Institute of Scientific and Technical Information of China (English)
WANG ShunJin; ZHANG Hua
2007-01-01
Based on the exact analytical solution of ordinary differential equations,a truncation of the Taylor series of the exact solution to the Nth order leads to the Nth order algebraic dynamics algorithm.A detailed numerical comparison is presented with Runge-Kutta algorithm and symplectic geometric algorithm for 12 test models.The results show that the algebraic dynamics algorithm can better preserve both geometrical and dynamical fidelity of a dynamical system at a controllable precision,and it can solve the problem of algorithm-induced dissipation for the Runge-Kutta algorithm and the problem of algorithm-induced phase shift for the symplectic geometric algorithm.
Institute of Scientific and Technical Information of China (English)
2007-01-01
Based on the exact analytical solution of ordinary differential equations, a truncation of the Taylor series of the exact solution to the Nth order leads to the Nth order algebraic dynamics algorithm. A detailed numerical comparison is presented with Runge-Kutta algorithm and symplectic geometric algorithm for 12 test models. The results show that the algebraic dynamics algorithm can better preserve both geometrical and dynamical fidelity of a dynamical system at a controllable precision, and it can solve the problem of algorithm-induced dissipation for the Runge-Kutta algorithm and the problem of algorithm-induced phase shift for the symplectic geometric algorithm.
Geometrically Induced Interactions and Bifurcations
Binder, Bernd
2010-01-01
In order to evaluate the proper boundary conditions in spin dynamics eventually leading to the emergence of natural and artificial solitons providing for strong interactions and potentials with monopole charges, the paper outlines a new concept referring to a curvature-invariant formalism, where superintegrability is given by a special isometric condition. Instead of referring to the spin operators and Casimir/Euler invariants as the generator of rotations, a curvature-invariant description is introduced utilizing a double Gudermann mapping function (generator of sine Gordon solitons and Mercator projection) cross-relating two angular variables, where geometric phases and rotations arise between surfaces of different curvature. Applying this stereographic projection to a superintegrable Hamiltonian can directly map linear oscillators to Kepler/Coulomb potentials and/or monopoles with Pöschl-Teller potentials and vice versa. In this sense a large scale Kepler/Coulomb (gravitational, electro-magnetic) wave dynamics with a hyperbolic metric could be mapped as a geodesic vertex flow to a local oscillator singularity (Dirac monopole) with spherical metrics and vice versa. Attracting fixed points and dynamic constraints are given by special isometries with magic precession angles. The nonlinear angular encoding directly provides for a Shannon mutual information entropy measure of the geodesic phase space flow. The emerging monopole patterns show relations to spiral Fresnel holography and Berry/Aharonov-Bohm geometric phases subject to bifurcation instabilities and singularities from phase ambiguities due to a local (entropy) overload. Neutral solitons and virtual patterns emerging and mediating in the overlap region between charged or twisted holographic patterns are visualized and directly assigned to the Berry geometric phase revealing the role of photons, neutrons, and neutrinos binding repulsive charges in Coulomb, strong and weak interaction.
Moving walls and geometric phases
Energy Technology Data Exchange (ETDEWEB)
Facchi, Paolo, E-mail: paolo.facchi@ba.infn.it [Dipartimento di Fisica and MECENAS, Università di Bari, I-70126 Bari (Italy); INFN, Sezione di Bari, I-70126 Bari (Italy); Garnero, Giancarlo, E-mail: giancarlo.garnero@uniba.it [Dipartimento di Fisica and MECENAS, Università di Bari, I-70126 Bari (Italy); INFN, Sezione di Bari, I-70126 Bari (Italy); Marmo, Giuseppe [Dipartimento di Scienze Fisiche and MECENAS, Università di Napoli “Federico II”, I-80126 Napoli (Italy); INFN, Sezione di Napoli, I-80126 Napoli (Italy); Samuel, Joseph [Raman Research Institute, 560080 Bangalore (India)
2016-09-15
We unveil the existence of a non-trivial Berry phase associated to the dynamics of a quantum particle in a one dimensional box with moving walls. It is shown that a suitable choice of boundary conditions has to be made in order to preserve unitarity. For these boundary conditions we compute explicitly the geometric phase two-form on the parameter space. The unboundedness of the Hamiltonian describing the system leads to a natural prescription of renormalization for divergent contributions arising from the boundary.
Geometric Topology and Shape Theory
Segal, Jack
1987-01-01
The aim of this international conference the third of its type was to survey recent developments in Geometric Topology and Shape Theory with an emphasis on their interaction. The volume contains original research papers and carefully selected survey of currently active areas. The main topics and themes represented by the papers of this volume include decomposition theory, cell-like mappings and CE-equivalent compacta, covering dimension versus cohomological dimension, ANR's and LCn-compacta, homology manifolds, embeddings of continua into manifolds, complement theorems in shape theory, approximate fibrations and shape fibrations, fibered shape, exact homologies and strong shape theory.
Geometric approach to soliton equations
International Nuclear Information System (INIS)
Sasaki, R.
1979-09-01
A class of nonlinear equations that can be solved in terms of nxn scattering problem is investigated. A systematic geometric method of exploiting conservation laws and related equations, the so-called prolongation structure, is worked out. The nxn problem is reduced to nsub(n-1)x(n-1) problems and finally to 2x2 problems, which have been comprehensively investigated recently by the author. A general method of deriving the infinite numbers of polynomial conservation laws for an nxn problem is presented. The cases of 3x3 and 2x2 problems are discussed explicitly. (Auth.)
Geometric Rationalization for Freeform Architecture
Jiang, Caigui
2016-06-20
The emergence of freeform architecture provides interesting geometric challenges with regards to the design and manufacturing of large-scale structures. To design these architectural structures, we have to consider two types of constraints. First, aesthetic constraints are important because the buildings have to be visually impressive. Sec- ond, functional constraints are important for the performance of a building and its e cient construction. This thesis contributes to the area of architectural geometry. Specifically, we are interested in the geometric rationalization of freeform architec- ture with the goal of combining aesthetic and functional constraints and construction requirements. Aesthetic requirements typically come from designers and architects. To obtain visually pleasing structures, they favor smoothness of the building shape, but also smoothness of the visible patterns on the surface. Functional requirements typically come from the engineers involved in the construction process. For exam- ple, covering freeform structures using planar panels is much cheaper than using non-planar ones. Further, constructed buildings have to be stable and should not collapse. In this thesis, we explore the geometric rationalization of freeform archi- tecture using four specific example problems inspired by real life applications. We achieve our results by developing optimization algorithms and a theoretical study of the underlying geometrical structure of the problems. The four example problems are the following: (1) The design of shading and lighting systems which are torsion-free structures with planar beams based on quad meshes. They satisfy the functionality requirements of preventing light from going inside a building as shad- ing systems or reflecting light into a building as lighting systems. (2) The Design of freeform honeycomb structures that are constructed based on hex-dominant meshes with a planar beam mounted along each edge. The beams intersect without
Field guide to geometrical optics
Greivenkamp, John E
2004-01-01
This Field Guide derives from the treatment of geometrical optics that has evolved from both the undergraduate and graduate programs at the Optical Sciences Center at the University of Arizona. The development is both rigorous and complete, and it features a consistent notation and sign convention. This volume covers Gaussian imagery, paraxial optics, first-order optical system design, system examples, illumination, chromatic effects, and an introduction to aberrations. The appendices provide supplemental material on radiometry and photometry, the human eye, and several other topics.
Geometric phase from dielectric matrix
International Nuclear Information System (INIS)
Banerjee, D.
2005-10-01
The dielectric property of the anisotropic optical medium is found by considering the polarized photon as two component spinor of spherical harmonics. The Geometric Phase of a polarized photon has been evaluated in two ways: the phase two-form of the dielectric matrix through a twist and the Pancharatnam phase (GP) by changing the angular momentum of the incident polarized photon over a closed triangular path on the extended Poincare sphere. The helicity in connection with the spin angular momentum of the chiral photon plays the key role in developing these phase holonomies. (author)
A history of geometrical methods
Coolidge, Julian Lowell
2013-01-01
Full and authoritative, this history of the techniques for dealing with geometric questions begins with synthetic geometry and its origins in Babylonian and Egyptian mathematics; reviews the contributions of China, Japan, India, and Greece; and discusses the non-Euclidean geometries. Subsequent sections cover algebraic geometry, starting with the precursors and advancing to the great awakening with Descartes; and differential geometry, from the early work of Huygens and Newton to projective and absolute differential geometry. The author's emphasis on proofs and notations, his comparisons betwe
Calculation of the geometric buckling for reactors of various shapes
Energy Technology Data Exchange (ETDEWEB)
Sjoestrand, N E
1958-05-15
A systematic investigation is made of the eleven coordinate systems in which the reactor equation {nabla}{sup 2}{phi} + B{sup 2}{phi} = 0 is separable. The fundamental solution and geometric buckling are given for those cases where the separated equations lead to known functions. It is especially shown that reactors of prolate and oblate spheroidal shape can be calculated in detail, and the results are given in extensive tables.
Image understanding using geometric context
Zhang, Xiaochun; Liu, Chuancai
2017-07-01
A Gibbs Sampler based topic model for image annotation, which takes into account the interaction between visual geometric context and related topic, is presented. Most of the existing topic models for scene annotation use segmentation-based algorithm. However, topic models using segmentation algorithm alone sometimes can produce erroneous results when used to annotate real-life scene pictures. Therefore, our algorithm makes use of peaks of image surface instead of segmentation regions. Existing approaches use SIFT algorithm and treat the peaks as round blob features. In this paper, the peaks are treated as anisotropic blob features, which models low level visual elements more precisely. In order to better utilize visual features, our model not only takes into consideration visual codeword, but also considers influence of visual properties to topic formation, such as orientation, width, length and color. The basic idea is based on the assumption that different topics will produce distinct visual appearance, and different visual appearance is helpful to distinguish topics. During the learning stage, each topic will be associated with a set of distributions of visual properties, which depicts appearance of the topic. This paper considers more geometric properties, which will reduce topic uncertainty and learn the images better. Tested with Corel5K, SAIAPR-TC12 and Espgame100k Datasets, our method performs moderately better than some state of the arts methods.
Exploring Eucladoceros ecomorphology using geometric morphometrics.
Curran, Sabrina C
2015-01-01
An increasingly common method for reconstructing paleoenvironmental parameters of hominin sites is ecological functional morphology (ecomorphology). This study provides a geometric morphometric study of cervid rearlimb morphology as it relates to phylogeny, size, and ecomorphology. These methods are then applied to an extinct Pleistocene cervid, Eucladoceros, which is found in some of the earliest hominin-occupied sites in Eurasia. Variation in cervid postcranial functional morphology associated with different habitats can be summarized as trade-offs between joint stability versus mobility and rapid movement versus power-generation. Cervids in open habitats emphasize limb stability to avoid joint dislocation during rapid flight from predators. Closed-adapted cervids require more joint mobility to rapidly switch directions in complex habitats. Two skeletal features (of the tibia and calcaneus) have significant phylogenetic signals, while two (the femur and third phalanx) do not. Additionally, morphology of two of these features (tibia and third phalanx) were correlated with body size. For the tibial analysis (but not the third phalanx) this correlation was ameliorated when phylogeny was taken into account. Eucladoceros specimens from France and Romania fall on the more open side of the habitat continuum, a result that is at odds with reconstructions of their diet as browsers, suggesting that they may have had a behavioral regime unlike any extant cervid. © 2014 Wiley Periodicals, Inc.
Design of Wideband MIMO Car-to-Car Channel Models Based on the Geometrical Street Scattering Model
Directory of Open Access Journals (Sweden)
Nurilla Avazov
2012-01-01
Full Text Available We propose a wideband multiple-input multiple-output (MIMO car-to-car (C2C channel model based on the geometrical street scattering model. Starting from the geometrical model, a MIMO reference channel model is derived under the assumption of single-bounce scattering in line-of-sight (LOS and non-LOS (NLOS propagation environments. The proposed channel model assumes an infinite number of scatterers, which are uniformly distributed in two rectangular areas located on both sides of the street. Analytical solutions are presented for the space-time-frequency cross-correlation function (STF-CCF, the two-dimensional (2D space CCF, the time-frequency CCF (TF-CCF, the temporal autocorrelation function (ACF, and the frequency correlation function (FCF. An efficient sum-of-cisoids (SOCs channel simulator is derived from the reference model. It is shown that the temporal ACF and the FCF of the SOC channel simulator fit very well to the corresponding correlation functions of the reference model. To validate the proposed channel model, the mean Doppler shift and the Doppler spread of the reference model have been matched to real-world measurement data. The comparison results demonstrate an excellent agreement between theory and measurements, which confirms the validity of the derived reference model. The proposed geometry-based channel simulator allows us to study the effect of nearby street scatterers on the performance of C2C communication systems.
Quasirandom geometric networks from low-discrepancy sequences
Estrada, Ernesto
2017-08-01
We define quasirandom geometric networks using low-discrepancy sequences, such as Halton, Sobol, and Niederreiter. The networks are built in d dimensions by considering the d -tuples of digits generated by these sequences as the coordinates of the vertices of the networks in a d -dimensional Id unit hypercube. Then, two vertices are connected by an edge if they are at a distance smaller than a connection radius. We investigate computationally 11 network-theoretic properties of two-dimensional quasirandom networks and compare them with analogous random geometric networks. We also study their degree distribution and their spectral density distributions. We conclude from this intensive computational study that in terms of the uniformity of the distribution of the vertices in the unit square, the quasirandom networks look more random than the random geometric networks. We include an analysis of potential strategies for generating higher-dimensional quasirandom networks, where it is know that some of the low-discrepancy sequences are highly correlated. In this respect, we conclude that up to dimension 20, the use of scrambling, skipping and leaping strategies generate quasirandom networks with the desired properties of uniformity. Finally, we consider a diffusive process taking place on the nodes and edges of the quasirandom and random geometric graphs. We show that the diffusion time is shorter in the quasirandom graphs as a consequence of their larger structural homogeneity. In the random geometric graphs the diffusion produces clusters of concentration that make the process more slow. Such clusters are a direct consequence of the heterogeneous and irregular distribution of the nodes in the unit square in which the generation of random geometric graphs is based on.
Record statistics of financial time series and geometric random walks.
Sabir, Behlool; Santhanam, M S
2014-09-01
The study of record statistics of correlated series in physics, such as random walks, is gaining momentum, and several analytical results have been obtained in the past few years. In this work, we study the record statistics of correlated empirical data for which random walk models have relevance. We obtain results for the records statistics of select stock market data and the geometric random walk, primarily through simulations. We show that the distribution of the age of records is a power law with the exponent α lying in the range 1.5≤α≤1.8. Further, the longest record ages follow the Fréchet distribution of extreme value theory. The records statistics of geometric random walk series is in good agreement with that obtained from empirical stock data.
Geometrical charged-particle optics
Rose, Harald
2012-01-01
This second edition is an extended version of the first edition of Geometrical Charged-Particle Optics. The updated reference monograph is intended as a guide for researchers and graduate students who are seeking a comprehensive treatment of the design of instruments and beam-guiding systems of charged particles and their propagation in electromagnetic fields. Wave aspects are included in this edition for explaining electron holography, the Aharanov-Bohm effect and the resolution of electron microscopes limited by diffraction. Several methods for calculating the electromagnetic field are presented and procedures are outlined for calculating the properties of systems with arbitrarily curved axis. Detailed methods are presented for designing and optimizing special components such as aberration correctors, spectrometers, energy filters monochromators, ion traps, electron mirrors and cathode lenses. In particular, the optics of rotationally symmetric lenses, quadrupoles, and systems composed of these elements are...
Geometrical setting of solid mechanics
International Nuclear Information System (INIS)
Fiala, Zdenek
2011-01-01
Highlights: → Solid mechanics within the Riemannian symmetric manifold GL (3, R)/O (3, R). → Generalized logarithmic strain. → Consistent linearization. → Incremental principle of virtual power. → Time-discrete approximation. - Abstract: The starting point in the geometrical setting of solid mechanics is to represent deformation process of a solid body as a trajectory in a convenient space with Riemannian geometry, and then to use the corresponding tools for its analysis. Based on virtual power of internal stresses, we show that such a configuration space is the (globally) symmetric space of symmetric positive-definite real matrices. From this unifying point of view, we shall analyse the logarithmic strain, the stress rate, as well as linearization and intrinsic integration of corresponding evolution equation.
Geometric Methods in Physics XXXV
Odzijewicz, Anatol; Previato, Emma
2018-01-01
This book features a selection of articles based on the XXXV Białowieża Workshop on Geometric Methods in Physics, 2016. The series of Białowieża workshops, attended by a community of experts at the crossroads of mathematics and physics, is a major annual event in the field. The works in this book, based on presentations given at the workshop, are previously unpublished, at the cutting edge of current research, typically grounded in geometry and analysis, and with applications to classical and quantum physics. In 2016 the special session "Integrability and Geometry" in particular attracted pioneers and leading specialists in the field. Traditionally, the Białowieża Workshop is followed by a School on Geometry and Physics, for advanced graduate students and early-career researchers, and the book also includes extended abstracts of the lecture series.
Geometric Operators on Boolean Functions
DEFF Research Database (Denmark)
Frisvad, Jeppe Revall; Falster, Peter
In truth-functional propositional logic, any propositional formula represents a Boolean function (according to some valuation of the formula). We describe operators based on Decartes' concept of constructing coordinate systems, for translation of a propositional formula to the image of a Boolean...... function. With this image of a Boolean function corresponding to a propositional formula, we prove that the orthogonal projection operator leads to a theorem describing all rules of inference in propositional reasoning. In other words, we can capture all kinds of inference in propositional logic by means...... of a few geometric operators working on the images of Boolean functions. The operators we describe, arise from the niche area of array-based logic and have previously been tightly bound to an array-based representation of Boolean functions. We redefine the operators in an abstract form to make them...
Geometric considerations in magnetron sputtering
International Nuclear Information System (INIS)
Thornton, J.A.
1982-01-01
The recent development of high performance magnetron type discharge sources has greatly enhaced the range of coating applications where sputtering is a viable deposition process. Magnetron sources can provide high current densities and sputtering rates, even at low pressures. They have much reduced substrate heating rates and can be scaled to large sizes. Magnetron sputter coating apparatuses can have a variety of geometric and plasma configurations. The target geometry affects the emission directions of both the sputtered atoms and the energetic ions which are neutralized and reflected at the cathode. This fact, coupled with the long mean free particle paths which are prevalent at low pressures, can make the coating properties very dependent on the apparatus geometry. This paper reviews the physics of magnetron operation and discusses the influences of apparatus geometry on the use of magnetrons for rf sputtering and reactive sputtering, as well as on the microstructure and internal stresses in sputtered metallic coatings. (author) [pt
Nano-scaling law: geometric foundation of thiolated gold nanomolecules.
Dass, Amala
2012-04-07
Thiolated gold nanomolecules show a power correlation between the number of gold atoms and the thiolate ligands with a 2/3 scaling similar to Platonic and Archimedean solids. Nanomolecule stability is influenced by a universal geometric factor that is foundational to its stability through the Euclidean surface rule, in addition to the electronic shell closing factor and staple motif requirements. This journal is © The Royal Society of Chemistry 2012
Operational geometric phase for mixed quantum states
International Nuclear Information System (INIS)
Andersson, O; Heydari, H
2013-01-01
The geometric phase has found a broad spectrum of applications in both classical and quantum physics, such as condensed matter and quantum computation. In this paper, we introduce an operational geometric phase for mixed quantum states, based on spectral weighted traces of holonomies, and we prove that it generalizes the standard definition of the geometric phase for mixed states, which is based on quantum interferometry. We also introduce higher order geometric phases, and prove that under a fairly weak, generically satisfied, requirement, there is always a well-defined geometric phase of some order. Our approach applies to general unitary evolutions of both non-degenerate and degenerate mixed states. Moreover, since we provide an explicit formula for the geometric phase that can be easily implemented, it is particularly well suited for computations in quantum physics. (paper)
Geometrical factors in the perception of sacredness
DEFF Research Database (Denmark)
Costa, Marco; Bonetti, Leonardo
2016-01-01
Geometrical and environmental factors in the perception of sacredness, dominance, and attractiveness were assessed by 137 participants in five tests. In the first test, a two-alternative forced-choice paradigm was used to test the perception of sacredness, dominance, and attractiveness in geometr......Geometrical and environmental factors in the perception of sacredness, dominance, and attractiveness were assessed by 137 participants in five tests. In the first test, a two-alternative forced-choice paradigm was used to test the perception of sacredness, dominance, and attractiveness...... in geometrical figures differing in shape, verticality, size, and symmetry. Verticality, symmetry, and convexity were found to be important factors in the perception of sacredness. In the second test, participants had to mark the point inside geometrical surfaces that was perceived as most sacred, dominant....... Geometrical factors in the perception of sacredness, dominance, and attractiveness were largely overlapping....
Guide to Geometric Algebra in Practice
Dorst, Leo
2011-01-01
This highly practical "Guide to Geometric Algebra in Practice" reviews algebraic techniques for geometrical problems in computer science and engineering, and the relationships between them. The topics covered range from powerful new theoretical developments, to successful applications, and the development of new software and hardware tools. This title: provides hands-on review exercises throughout the book, together with helpful chapter summaries; presents a concise introductory tutorial to conformal geometric algebra (CGA) in the appendices; examines the application of CGA for the d
Cartwright, Steven J
2018-02-01
The use of solvatochromic dyes to investigate homeopathic potencies holds out the promise of understanding the nature of serially succussed and diluted solutions at a fundamental physicochemical level. Recent studies have shown that a range of different dyes interact with potencies and, moreover, the nature of the interaction is beginning to allow certain specific characteristics of potencies to be delineated. The study reported in this article takes previous investigations further and aims to understand more about the nature of the interaction between potencies and solvatochromic dyes. To this end, the UV-visible spectra of a wide range of potential detectors of potencies have been examined using methodologies previously described. Results presented demonstrate that solvatochromic dyes are a sub-group of a larger class of compounds capable of demonstrating interactions with potencies. In particular, amino acids containing an aromatic bridge also show marked optical changes in the presence of potencies. Several specific features of molecular detectors can now be shown to be necessary for significant interactions with homeopathic potencies. These include systems with a large dipole moment, electron delocalisation, polarizability and molecular rigidity. Analysis of the optical changes occurring on interaction with potencies suggests that in all cases potencies increase the polarity of molecular detectors to a degree that correlates with the size of the compound's permanent or ground dipole moment. These results can be explained by inferring that potencies themselves have polarity. Possible candidates for the identity of potencies, based on these and previously reported results, are discussed. The Faculty of Homeopathy.
Geometrical shock dynamics for magnetohydrodynamic fast shocks
Mostert, W.; Pullin, D. I.; Samtaney, Ravi; Wheatley, V.
2016-01-01
We describe a formulation of two-dimensional geometrical shock dynamics (GSD) suitable for ideal magnetohydrodynamic (MHD) fast shocks under magnetic fields of general strength and orientation. The resulting area–Mach-number–shock-angle relation is then incorporated into a numerical method using pseudospectral differentiation. The MHD-GSD model is verified by comparison with results from nonlinear finite-volume solution of the complete ideal MHD equations applied to a shock implosion flow in the presence of an oblique and spatially varying magnetic field ahead of the shock. Results from application of the MHD-GSD equations to the stability of fast MHD shocks in two dimensions are presented. It is shown that the time to formation of triple points for both perturbed MHD and gas-dynamic shocks increases as (Formula presented.), where (Formula presented.) is a measure of the initial Mach-number perturbation. Symmetry breaking in the MHD case is demonstrated. In cylindrical converging geometry, in the presence of an azimuthal field produced by a line current, the MHD shock behaves in the mean as in Pullin et al. (Phys. Fluids, vol. 26, 2014, 097103), but suffers a greater relative pressure fluctuation along the shock than the gas-dynamic shock. © 2016 Cambridge University Press
Geometrical shock dynamics for magnetohydrodynamic fast shocks
Mostert, W.
2016-12-12
We describe a formulation of two-dimensional geometrical shock dynamics (GSD) suitable for ideal magnetohydrodynamic (MHD) fast shocks under magnetic fields of general strength and orientation. The resulting area–Mach-number–shock-angle relation is then incorporated into a numerical method using pseudospectral differentiation. The MHD-GSD model is verified by comparison with results from nonlinear finite-volume solution of the complete ideal MHD equations applied to a shock implosion flow in the presence of an oblique and spatially varying magnetic field ahead of the shock. Results from application of the MHD-GSD equations to the stability of fast MHD shocks in two dimensions are presented. It is shown that the time to formation of triple points for both perturbed MHD and gas-dynamic shocks increases as (Formula presented.), where (Formula presented.) is a measure of the initial Mach-number perturbation. Symmetry breaking in the MHD case is demonstrated. In cylindrical converging geometry, in the presence of an azimuthal field produced by a line current, the MHD shock behaves in the mean as in Pullin et al. (Phys. Fluids, vol. 26, 2014, 097103), but suffers a greater relative pressure fluctuation along the shock than the gas-dynamic shock. © 2016 Cambridge University Press
4th Italian-Japanese workshop on Geometric Properties for Parabolic and Elliptic PDE’s
Ishige, Kazuhiro; Nitsch, Carlo; Salani, Paolo
2016-01-01
This book collects recent research papers by respected specialists in the field. It presents advances in the field of geometric properties for parabolic and elliptic partial differential equations, an area that has always attracted great attention. It settles the basic issues (existence, uniqueness, stability and regularity of solutions of initial/boundary value problems) before focusing on the topological and/or geometric aspects. These topics interact with many other areas of research and rely on a wide range of mathematical tools and techniques, both analytic and geometric. The Italian and Japanese mathematical schools have a long history of research on PDEs and have numerous active groups collaborating in the study of the geometric properties of their solutions. .
Geometric asymmetry driven Janus micromotors
Zhao, Guanjia; Pumera, Martin
2014-09-01
The production and application of nano-/micromotors is of great importance. In order for the motors to work, asymmetry in their chemical composition or physical geometry must be present if no external asymmetric field is applied. In this paper, we present a ``coconut'' micromotor made of platinum through the partial or complete etching of the silica templates. It was shown that although both the inner and outer surfaces are made of the same material (Pt), motion of the structure can be observed as the convex surface is capable of generating oxygen bubbles. This finding shows that not only the chemical asymmetry of the micromotor, but also its geometric asymmetry can lead to fast propulsion of the motor. Moreover, a considerably higher velocity can be seen for partially etched coconut structures than the velocities of Janus or fully etched, shell-like motors. These findings will have great importance on the design of future micromotors.The production and application of nano-/micromotors is of great importance. In order for the motors to work, asymmetry in their chemical composition or physical geometry must be present if no external asymmetric field is applied. In this paper, we present a ``coconut'' micromotor made of platinum through the partial or complete etching of the silica templates. It was shown that although both the inner and outer surfaces are made of the same material (Pt), motion of the structure can be observed as the convex surface is capable of generating oxygen bubbles. This finding shows that not only the chemical asymmetry of the micromotor, but also its geometric asymmetry can lead to fast propulsion of the motor. Moreover, a considerably higher velocity can be seen for partially etched coconut structures than the velocities of Janus or fully etched, shell-like motors. These findings will have great importance on the design of future micromotors. Electronic supplementary information (ESI) available: Additional SEM images, data analysis, Videos S
An Analysis LANDSAT-4 Thematic Mapper Geometric Properties
Walker, R. E.; Zobrist, A. L.; Bryant, N. A.; Gokhman, B.; Friedman, S. Z.; Logan, T. L.
1984-01-01
LANDSAT Thematic Mapper P-data of Washington, D. C., Harrisburg, PA, and Salton Sea, CA are analyzed to determine magnitudes and causes of error in the geometric conformity of the data to known Earth surface geometry. Several tests of data geometry are performed. Intraband and interband correlation and registration are investigated, exclusive of map based ground truth. The magnitudes and statistical trends of pixel offsets between a single band's mirror scans (due to processing procedures) are computed, and the inter-band integrity of registration is analyzed. A line to line correlation analysis is included.
A sketch to the geometrical N=2-d=5 Yang-Mills theory over a supersymmetric group-manifold - I
International Nuclear Information System (INIS)
Borges, M.; Turin Univ.; Pio, G.
1983-03-01
This work concerns the search and the construction of a geometrical structure for a supersymmetric N=2-d=5 Yang-Mills theory on the group manifold. From criteria established throughout this paper, we build up an ansatz for the curvatures of our theory and then solve the Bianchi identities, whose solution is fundamental for the construction of the geometrical action. (author)
International Nuclear Information System (INIS)
Mori, N.; Kobayashi, K.
1996-01-01
A two-dimensional neutron diffusion equation is solved for regular polygonal regions by the finite Fourier transformation, and geometrical bucklings are calculated for regular 3-10 polygonal regions. In the case of the regular triangular region, it is found that a simple and rigorous analytic solution is obtained for the geometrical buckling and the distribution of the neutron current along the outer boundary. (author)
Institute of Scientific and Technical Information of China (English)
赵长伟; 马沛生
2003-01-01
Visosities and densities at ,several temperatures from 293.15 K to 313.15K are reported for L-ascorbic acid in aqueous glucose and sucrose solutions at different concentrations.The parameters of density,Viscosity coefficient B and partial molar volume are calculated by regression.The experimental results show that densities and viscositis decrease as temperature increases at the same solute and solvent (glucose and sucrose aueous solution)concentrations,and increase with concentration of glucose and sucrose at the same solute concentration and temperature,B increases with concentration of glucose and sucrose and temaperature,L-ascorbic acid is sturcture-breaker or structure-making for the glucose and sucrose aqueous solutions ,Furthermore,the solute-solvent interactions in ternary systems of water-glucose-electrolyte and water-sucrose-electrolyte are discussed.
Information geometric methods for complexity
Felice, Domenico; Cafaro, Carlo; Mancini, Stefano
2018-03-01
Research on the use of information geometry (IG) in modern physics has witnessed significant advances recently. In this review article, we report on the utilization of IG methods to define measures of complexity in both classical and, whenever available, quantum physical settings. A paradigmatic example of a dramatic change in complexity is given by phase transitions (PTs). Hence, we review both global and local aspects of PTs described in terms of the scalar curvature of the parameter manifold and the components of the metric tensor, respectively. We also report on the behavior of geodesic paths on the parameter manifold used to gain insight into the dynamics of PTs. Going further, we survey measures of complexity arising in the geometric framework. In particular, we quantify complexity of networks in terms of the Riemannian volume of the parameter space of a statistical manifold associated with a given network. We are also concerned with complexity measures that account for the interactions of a given number of parts of a system that cannot be described in terms of a smaller number of parts of the system. Finally, we investigate complexity measures of entropic motion on curved statistical manifolds that arise from a probabilistic description of physical systems in the presence of limited information. The Kullback-Leibler divergence, the distance to an exponential family and volumes of curved parameter manifolds, are examples of essential IG notions exploited in our discussion of complexity. We conclude by discussing strengths, limits, and possible future applications of IG methods to the physics of complexity.
Geometrical aspects of quantum spaces
International Nuclear Information System (INIS)
Ho, P.M.
1996-01-01
Various geometrical aspects of quantum spaces are presented showing the possibility of building physics on quantum spaces. In the first chapter the authors give the motivations for studying noncommutative geometry and also review the definition of a Hopf algebra and some general features of the differential geometry on quantum groups and quantum planes. In Chapter 2 and Chapter 3 the noncommutative version of differential calculus, integration and complex structure are established for the quantum sphere S 1 2 and the quantum complex projective space CP q (N), on which there are quantum group symmetries that are represented nonlinearly, and are respected by all the aforementioned structures. The braiding of S q 2 and CP q (N) is also described. In Chapter 4 the quantum projective geometry over the quantum projective space CP q (N) is developed. Collinearity conditions, coplanarity conditions, intersections and anharmonic ratios is described. In Chapter 5 an algebraic formulation of Reimannian geometry on quantum spaces is presented where Riemannian metric, distance, Laplacian, connection, and curvature have their quantum counterparts. This attempt is also extended to complex manifolds. Examples include the quantum sphere, the complex quantum projective space and the two-sheeted space. The quantum group of general coordinate transformations on some quantum spaces is also given
Geometric Reasoning for Automated Planning
Clement, Bradley J.; Knight, Russell L.; Broderick, Daniel
2012-01-01
An important aspect of mission planning for NASA s operation of the International Space Station is the allocation and management of space for supplies and equipment. The Stowage, Configuration Analysis, and Operations Planning teams collaborate to perform the bulk of that planning. A Geometric Reasoning Engine is developed in a way that can be shared by the teams to optimize item placement in the context of crew planning. The ISS crew spends (at the time of this writing) a third or more of their time moving supplies and equipment around. Better logistical support and optimized packing could make a significant impact on operational efficiency of the ISS. Currently, computational geometry and motion planning do not focus specifically on the optimized orientation and placement of 3D objects based on multiple distance and containment preferences and constraints. The software performs reasoning about the manipulation of 3D solid models in order to maximize an objective function based on distance. It optimizes for 3D orientation and placement. Spatial placement optimization is a general problem and can be applied to object packing or asset relocation.
Simulating geometrically complex blast scenarios
Directory of Open Access Journals (Sweden)
Ian G. Cullis
2016-04-01
Full Text Available The effects of blast waves generated by energetic and non-energetic sources are of continuing interest to the ballistics research community. Modern conflicts are increasingly characterised by asymmetric urban warfare, with improvised explosive devices (IEDs often playing a dominant role on the one hand and an armed forces requirement for minimal collateral effects from their weapons on the other. These problems are characterised by disparate length- and time-scales and may also be governed by complex physics. There is thus an increasing need to be able to rapidly assess and accurately predict the effects of energetic blast in topologically complex scenarios. To this end, this paper presents a new QinetiQ-developed advanced computational package called EAGLE-Blast, which is capable of accurately resolving the generation, propagation and interaction of blast waves around geometrically complex shapes such as vehicles and buildings. After a brief description of the numerical methodology, various blast scenario simulations are described and the results compared with experimental data to demonstrate the validation of the scheme and its ability to describe these complex scenarios accurately and efficiently. The paper concludes with a brief discussion on the use of the code in supporting the development of algorithms for fast running engineering models.
Generalized Geometric Quantum Speed Limits
Directory of Open Access Journals (Sweden)
Diego Paiva Pires
2016-06-01
Full Text Available The attempt to gain a theoretical understanding of the concept of time in quantum mechanics has triggered significant progress towards the search for faster and more efficient quantum technologies. One of such advances consists in the interpretation of the time-energy uncertainty relations as lower bounds for the minimal evolution time between two distinguishable states of a quantum system, also known as quantum speed limits. We investigate how the nonuniqueness of a bona fide measure of distinguishability defined on the quantum-state space affects the quantum speed limits and can be exploited in order to derive improved bounds. Specifically, we establish an infinite family of quantum speed limits valid for unitary and nonunitary evolutions, based on an elegant information geometric formalism. Our work unifies and generalizes existing results on quantum speed limits and provides instances of novel bounds that are tighter than any established one based on the conventional quantum Fisher information. We illustrate our findings with relevant examples, demonstrating the importance of choosing different information metrics for open system dynamics, as well as clarifying the roles of classical populations versus quantum coherences, in the determination and saturation of the speed limits. Our results can find applications in the optimization and control of quantum technologies such as quantum computation and metrology, and might provide new insights in fundamental investigations of quantum thermodynamics.
Geometric structure of percolation clusters.
Xu, Xiao; Wang, Junfeng; Zhou, Zongzheng; Garoni, Timothy M; Deng, Youjin
2014-01-01
We investigate the geometric properties of percolation clusters by studying square-lattice bond percolation on the torus. We show that the density of bridges and nonbridges both tend to 1/4 for large system sizes. Using Monte Carlo simulations, we study the probability that a given edge is not a bridge but has both its loop arcs in the same loop and find that it is governed by the two-arm exponent. We then classify bridges into two types: branches and junctions. A bridge is a branch iff at least one of the two clusters produced by its deletion is a tree. Starting from a percolation configuration and deleting the branches results in a leaf-free configuration, whereas, deleting all bridges produces a bridge-free configuration. Although branches account for ≈43% of all occupied bonds, we find that the fractal dimensions of the cluster size and hull length of leaf-free configurations are consistent with those for standard percolation configurations. By contrast, we find that the fractal dimensions of the cluster size and hull length of bridge-free configurations are given by the backbone and external perimeter dimensions, respectively. We estimate the backbone fractal dimension to be 1.643 36(10).
Geometric Phase Generated Optical Illusion.
Yue, Fuyong; Zang, Xiaofei; Wen, Dandan; Li, Zile; Zhang, Chunmei; Liu, Huigang; Gerardot, Brian D; Wang, Wei; Zheng, Guoxing; Chen, Xianzhong
2017-09-12
An optical illusion, such as "Rubin's vase", is caused by the information gathered by the eye, which is processed in the brain to give a perception that does not tally with a physical measurement of the stimulus source. Metasurfaces are metamaterials of reduced dimensionality which have opened up new avenues for flat optics. The recent advancement in spin-controlled metasurface holograms has attracted considerate attention, providing a new method to realize optical illusions. We propose and experimentally demonstrate a metasurface device to generate an optical illusion. The metasurface device is designed to display two asymmetrically distributed off-axis images of "Rubin faces" with high fidelity, high efficiency and broadband operation that are interchangeable by controlling the helicity of the incident light. Upon the illumination of a linearly polarized light beam, the optical illusion of a 'vase' is perceived. Our result provides an intuitive demonstration of the figure-ground distinction that our brains make during the visual perception. The alliance between geometric metasurface and the optical illusion opens a pathway for new applications related to encryption, optical patterning, and information processing.
Implementation of the geometrical problem in CNC metal cutting machine
Directory of Open Access Journals (Sweden)
Erokhin V.V.
2017-06-01
Full Text Available The article deals with the tasks of managing the production process (technological process and technological equip-ment, the most detailed analysis of the implementation of the geometric problem in CNC machines. The influence of the solution of the geometric CNC problem on the accuracy of workpiece machining is analyzed by implementing a certain interpolation algorithm and the values of the discreteness of the movements of the working bodies of the CNC machine. The technique of forming a given trajectory of motion of the machine's executive organ is given, by means of which it is required to ensure the coordinated movement of the shaping coordinates according to a certain law, depend-ing on the specified trajectory of the cutting edge of the tool. The advantages and disadvantages of the implementation of interpolation in CNC systems by various methods are considered, and particular attention is paid to combined meth-ods of realizing interpolation.
On the geometrical approach to the relativistic string theory
International Nuclear Information System (INIS)
Barbashov, B.M.; Nesterenko, V.V.
1978-01-01
In a geometrical approach to the string theory in the four-dimensional Minkowski space the relativistic invariant gauge proposed earlier for the string moving in three-dimensional space-time is used. In contrast to the results of previous paper the system of equations for the coefficients of the fundamental forms of the string model world sheet can be reduced now to one nonlinear Lionville equation again but for a complex valued function u. It is shown that in the case of space-time with arbitrary dimension there are such string motions which are described by one non-linear equation with a real function u. And as a consequence the soliton solutions investigated earlier take place in a geometrical approach to the string theory in any dimensional space-time
Geometrization of the electromagnetic field and dark matter
International Nuclear Information System (INIS)
Pestov, I.B.
2005-01-01
A general concept of potential field is introduced. The potential field that one puts in correspondence with dark matter, has fundamental geometrical interpretation (parallel transport) and has intrinsically inherent local symmetry. The equations of dark matter field are derived that are invariant with respect to the local transformations. It is shown how to reduce these equations to the Maxwell equations. Thus, the dark matter field may be considered as generalized electromagnetic field and a simple solution of the old problem is given to connect electromagnetic field with geometrical properties of the physical manifold itself. It is shown that gauge fixing renders generalized electromagnetic field effectively massive while the Maxwell electromagnetic field remains massless. To learn more about interactions between matter and dark matter on the microscopical level (and to recognize the fundamental role of internal symmetry) the general covariant Dirac equation is derived in the Minkowski space-time which describes the interactions of spinor field with dark matter field
Geometrization of the Electromagnetic Field and Dark Matter
Pestov, I B
2005-01-01
A general concept of potential field is introduced. The potential field that one puts in correspondence with dark matter, has fundamental geometrical interpretation (parallel transport) and has intrinsically inherent local symmetry. The equations of dark matter field are derived that are invariant with respect to the local transformations. It is shown how to reduce these equations to the Maxwell equations. Thus, the dark matter field may be considered as generalized lectromagnetic field and a simple solution of the old problem is given to connect electromagnetic field with geometrical properties of the physical manifold itself. It is shown that gauge fixing renders generalized electromagnetic field effectively massive while the Maxwell electromagnetic field remains massless. To learn more about interactions between matter and dark matter on the microscopical level (and to recognize the fundamental role of internal symmetry) the general covariant Dirac equation is derived in the Minkowski space--time which des...
Polarization ellipse and Stokes parameters in geometric algebra.
Santos, Adler G; Sugon, Quirino M; McNamara, Daniel J
2012-01-01
In this paper, we use geometric algebra to describe the polarization ellipse and Stokes parameters. We show that a solution to Maxwell's equation is a product of a complex basis vector in Jackson and a linear combination of plane wave functions. We convert both the amplitudes and the wave function arguments from complex scalars to complex vectors. This conversion allows us to separate the electric field vector and the imaginary magnetic field vector, because exponentials of imaginary scalars convert vectors to imaginary vectors and vice versa, while exponentials of imaginary vectors only rotate the vector or imaginary vector they are multiplied to. We convert this expression for polarized light into two other representations: the Cartesian representation and the rotated ellipse representation. We compute the conversion relations among the representation parameters and their corresponding Stokes parameters. And finally, we propose a set of geometric relations between the electric and magnetic fields that satisfy an equation similar to the Poincaré sphere equation.
Geometric effects of ICMEs on geomagnetic storms
Cho, KyungSuk; Lee, Jae-Ok
2017-04-01
It has been known that the geomagnetic storm is occurred by the interaction between the Interplanetary Coronal Mass Ejection (ICME) and the Earth's magnetosphere; especially, the southward Bz component of ICME is thought as the main trigger. In this study, we investigate the relationship between Dst index and solar wind conditions; which are the southward Bz, electric field (VBz), and time integral of electric field as well as ICME parameters derived from toroidal fitting model in order to find what is main factor to the geomagnetic storm. We also inspect locations of Earth in ICMEs to understand the geometric effects of the Interplanetary Flux Ropes (IFRs) on the geomagnetic storms. Among 59 CDAW ICME lists, we select 30 IFR events that are available by the toroidal fitting model and classify them into two sub-groups: geomagnetic storms associated with the Magnetic Clouds (MCs) and the compression regions ahead of the MCs (sheath). The main results are as follows: (1) The time integral of electric field has a higher correlation coefficient (cc) with Dst index than the other parameters: cc=0.85 for 25 MC events and cc=0.99 for 5 sheath events. (2) The sheath associated intense storms (Dst ≤-100nT) having usually occur at flank regions of ICMEs while the MC associated intense storms occur regardless of the locations of the Earth in ICMEs. The strength of a geomagnetic storm strongly depends on electric field of IFR and durations of the IFR passages through the Earth.
Donovan, Preston; Chehreghanianzabi, Yasaman; Rathinam, Muruhan; Zustiak, Silviya Petrova
2016-01-01
The study of diffusion in macromolecular solutions is important in many biomedical applications such as separations, drug delivery, and cell encapsulation, and key for many biological processes such as protein assembly and interstitial transport. Not surprisingly, multiple models for the a-priori prediction of diffusion in macromolecular environments have been proposed. However, most models include parameters that are not readily measurable, are specific to the polymer-solute-solvent system, or are fitted and do not have a physical meaning. Here, for the first time, we develop a homogenization theory framework for the prediction of effective solute diffusivity in macromolecular environments based on physical parameters that are easily measurable and not specific to the macromolecule-solute-solvent system. Homogenization theory is useful for situations where knowledge of fine-scale parameters is used to predict bulk system behavior. As a first approximation, we focus on a model where the solute is subjected to obstructed diffusion via stationary spherical obstacles. We find that the homogenization theory results agree well with computationally more expensive Monte Carlo simulations. Moreover, the homogenization theory agrees with effective diffusivities of a solute in dilute and semi-dilute polymer solutions measured using fluorescence correlation spectroscopy. Lastly, we provide a mathematical formula for the effective diffusivity in terms of a non-dimensional and easily measurable geometric system parameter.
Directory of Open Access Journals (Sweden)
Preston Donovan
Full Text Available The study of diffusion in macromolecular solutions is important in many biomedical applications such as separations, drug delivery, and cell encapsulation, and key for many biological processes such as protein assembly and interstitial transport. Not surprisingly, multiple models for the a-priori prediction of diffusion in macromolecular environments have been proposed. However, most models include parameters that are not readily measurable, are specific to the polymer-solute-solvent system, or are fitted and do not have a physical meaning. Here, for the first time, we develop a homogenization theory framework for the prediction of effective solute diffusivity in macromolecular environments based on physical parameters that are easily measurable and not specific to the macromolecule-solute-solvent system. Homogenization theory is useful for situations where knowledge of fine-scale parameters is used to predict bulk system behavior. As a first approximation, we focus on a model where the solute is subjected to obstructed diffusion via stationary spherical obstacles. We find that the homogenization theory results agree well with computationally more expensive Monte Carlo simulations. Moreover, the homogenization theory agrees with effective diffusivities of a solute in dilute and semi-dilute polymer solutions measured using fluorescence correlation spectroscopy. Lastly, we provide a mathematical formula for the effective diffusivity in terms of a non-dimensional and easily measurable geometric system parameter.
Geometrical scaling, furry branching and minijets
International Nuclear Information System (INIS)
Hwa, R.C.
1988-01-01
Scaling properties and their violations in hadronic collisions are discussed in the framework of the geometrical branching model. Geometrical scaling supplemented by Furry branching characterizes the soft component, while the production of jets specifies the hard component. Many features of multiparticle production processes are well described by this model. 21 refs
Geometric integrators for stochastic rigid body dynamics
Tretyakov, Mikhail
2016-01-05
Geometric integrators play an important role in simulating dynamical systems on long time intervals with high accuracy. We will illustrate geometric integration ideas within the stochastic context, mostly on examples of stochastic thermostats for rigid body dynamics. The talk will be mainly based on joint recent work with Rusland Davidchak and Tom Ouldridge.
Geometric integrators for stochastic rigid body dynamics
Tretyakov, Mikhail
2016-01-01
Geometric integrators play an important role in simulating dynamical systems on long time intervals with high accuracy. We will illustrate geometric integration ideas within the stochastic context, mostly on examples of stochastic thermostats for rigid body dynamics. The talk will be mainly based on joint recent work with Rusland Davidchak and Tom Ouldridge.
Geometric phases in discrete dynamical systems
Energy Technology Data Exchange (ETDEWEB)
Cartwright, Julyan H.E., E-mail: julyan.cartwright@csic.es [Instituto Andaluz de Ciencias de la Tierra, CSIC–Universidad de Granada, E-18100 Armilla, Granada (Spain); Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, E-18071 Granada (Spain); Piro, Nicolas, E-mail: nicolas.piro@epfl.ch [École Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne (Switzerland); Piro, Oreste, E-mail: piro@imedea.uib-csic.es [Departamento de Física, Universitat de les Illes Balears, E-07122 Palma de Mallorca (Spain); Tuval, Idan, E-mail: ituval@imedea.uib-csic.es [Mediterranean Institute for Advanced Studies, CSIC–Universitat de les Illes Balears, E-07190 Mallorca (Spain)
2016-10-14
In order to study the behaviour of discrete dynamical systems under adiabatic cyclic variations of their parameters, we consider discrete versions of adiabatically-rotated rotators. Parallelling the studies in continuous systems, we generalize the concept of geometric phase to discrete dynamics and investigate its presence in these rotators. For the rotated sine circle map, we demonstrate an analytical relationship between the geometric phase and the rotation number of the system. For the discrete version of the rotated rotator considered by Berry, the rotated standard map, we further explore this connection as well as the role of the geometric phase at the onset of chaos. Further into the chaotic regime, we show that the geometric phase is also related to the diffusive behaviour of the dynamical variables and the Lyapunov exponent. - Highlights: • We extend the concept of geometric phase to maps. • For the rotated sine circle map, we demonstrate an analytical relationship between the geometric phase and the rotation number. • For the rotated standard map, we explore the role of the geometric phase at the onset of chaos. • We show that the geometric phase is related to the diffusive behaviour of the dynamical variables and the Lyapunov exponent.
Geometrical optics and the diffraction phenomenon
International Nuclear Information System (INIS)
Timofeev, Aleksandr V
2005-01-01
This note outlines the principles of the geometrical optics of inhomogeneous waves whose description necessitates the use of complex values of the wave vector. Generalizing geometrical optics to inhomogeneous waves permits including in its scope the analysis of the diffraction phenomenon. (methodological notes)
Solving Absolute Value Equations Algebraically and Geometrically
Shiyuan, Wei
2005-01-01
The way in which students can improve their comprehension by understanding the geometrical meaning of algebraic equations or solving algebraic equation geometrically is described. Students can experiment with the conditions of the absolute value equation presented, for an interesting way to form an overall understanding of the concept.
Geometric design of part feeders
Berretty, R.-P.M.
2000-01-01
This thesis presents solutions for problems derived from industrial assembly and robotic manipulation. The basic tasks in a factory are manufacturing the parts, and combining them into the desired product. In automating these tasks, we want to use robot manipulators that require little or no
A geometrical model for DNA organization in bacteria.
Directory of Open Access Journals (Sweden)
Mathias Buenemann
Full Text Available Recent experimental studies have revealed that bacteria, such as C. crescentus, show a remarkable spatial ordering of their chromosome. A strong linear correlation has been found between the position of genes on the chromosomal map and their spatial position in the cellular volume. We show that this correlation can be explained by a purely geometrical model. Namely, self-avoidance of DNA, specific positioning of one or few DNA loci (such as origin or terminus together with the action of DNA compaction proteins (that organize the chromosome into topological domains are sufficient to get a linear arrangement of the chromosome along the cell axis. We develop a Monte-Carlo method that allows us to test our model numerically and to analyze the dependence of the spatial ordering on various physiologically relevant parameters. We show that the proposed geometrical ordering mechanism is robust and universal (i.e. does not depend on specific bacterial details. The geometrical mechanism should work in all bacteria that have compacted chromosomes with spatially fixed regions. We use our model to make specific and experimentally testable predictions about the spatial arrangement of the chromosome in mutants of C. crescentus and the growth-stage dependent ordering in E. coli.
An introduction to geometric computation
International Nuclear Information System (INIS)
Nievergelt, J.
1991-01-01
Computational geometry has some appealing features that make it ideal for learning about algorithms and data structures, namely the problem statements are easily understood, intuitively meaningful, and mathematically rigorous, problem statement, solution, and every step of the construction have natural visual representations that support abstract thinking and help in detecting errors of reasoning, and finally, these algorithms are practical because is easy to come up with examples where they can be applied. Figs
Non-geometric five-branes in heterotic supergravity
Energy Technology Data Exchange (ETDEWEB)
Sasaki, Shin; Yata, Masaya [Department of Physics, Kitasato University,Sagamihara 252-0373 (Japan); Department of Physics, National University of Singapore,2, Science Drive 3, Singapore 117542 (Singapore)
2016-11-10
We study T-duality chains of five-branes in heterotic supergravity where the first order α{sup ′}-corrections are present. By performing the α{sup ′}-corrected T-duality transformations of the heterotic NS5-brane solutions, we obtain the KK5-brane and the exotic 5{sub 2}{sup 2}-brane solutions associated with the symmetric, the neutral and the gauge NS5-branes. We find that the Yang-Mills gauge field in these solutions satisfies the self-duality condition in the three- and two-dimensional transverse spaces to the brane world-volumes. The O(2,2) monodromy structures of the 5{sub 2}{sup 2}-brane solutions are investigated by the α{sup ′}-corrected generalized metric. Our analysis shows that the symmetric 5{sub 2}{sup 2}-brane solution, which satisfies the standard embedding condition, is a T-fold and it exhibits the non-geometric nature. We also find that the neutral 5{sub 2}{sup 2}-brane solution is a T-fold at least at O(α{sup ′}). On the other hand, the gauge 5{sub 2}{sup 2}-brane solution is not a T-fold but show unusual structures of space-time.
Una primera lección de Geometría Algebraica Una primera lección de Geometría Algebraica
Directory of Open Access Journals (Sweden)
Carlos A. Cadavid
2005-12-01
Full Text Available En este articulo se explica cómo aparece la Geometría Algebraica, partiendo del estudio de los conjuntos de soluciones de sistemas algebraicos.This paper explains how Algebraic Geometry originated from the study of solution sets of algebraic systems.
Geometric picture of quantum discord for two-qubit quantum states
International Nuclear Information System (INIS)
Shi Mingjun; Jiang Fengjian; Sun Chunxiao; Du Jiangfeng
2011-01-01
Among various definitions of quantum correlations, quantum discord has attracted considerable attention. To find an analytical expression for quantum discord is an intractable task. Exact results are known only for very special states, namely two-qubit X-shaped states. We present in this paper a geometric viewpoint, from which two-qubit quantum discord can be described clearly. The known results on X state discord are restated in the directly perceivable geometric language. As a consequence, the dynamics of classical correlations and quantum discord for an X state in the presence of decoherence is endowed with geometric interpretation. More importantly, we extend the geometric method to the case of more general states, for which numerical as well as analytical results on quantum discord have not yet been obtained. Based on the support of numerical computations, some conjectures are proposed to help us establish the geometric picture. We find that the geometric picture for these states has an intimate relationship with that for X states. Thereby, in some cases, analytical expressions for classical correlations and quantum discord can be obtained.
Geometrical formulation of the conformal Ward identity
International Nuclear Information System (INIS)
Kachkachi, M.
2002-08-01
In this paper we use deep ideas in complex geometry that proved to be very powerful in unveiling the Polyakov measure on the moduli space of Riemann surfaces and lead to obtain the partition function of perturbative string theory for 2, 3, 4 loops. Indeed, a geometrical interpretation of the conformal Ward identity in two dimensional conformal field theory is proposed: the conformal anomaly is interpreted as a deformation of the complex structure of the basic Riemann surface. This point of view is in line with the modern trend of geometric quantizations that are based on deformations of classical structures. Then, we solve the conformal Ward identity by using this geometrical formalism. (author)
SOME PROPERTIES OF GEOMETRIC DEA MODELS
Directory of Open Access Journals (Sweden)
Ozren Despić
2013-02-01
Full Text Available Some specific geometric data envelopment analysis (DEA models are well known to the researchers in DEA through so-called multiplicative or log-linear efficiency models. Valuable properties of these models were noted by several authors but the models still remain somewhat obscure and rarely used in practice. The purpose of this paper is to show from a mathematical perspective where the geometric DEA fits in relation to the classical DEA, and to provide a brief overview of some benefits in using geometric DEA in practice of decision making and/or efficiency measurement.
Refined geometric transition and qq-characters
Kimura, Taro; Mori, Hironori; Sugimoto, Yuji
2018-01-01
We show the refinement of the prescription for the geometric transition in the refined topological string theory and, as its application, discuss a possibility to describe qq-characters from the string theory point of view. Though the suggested way to operate the refined geometric transition has passed through several checks, it is additionally found in this paper that the presence of the preferred direction brings a nontrivial effect. We provide the modified formula involving this point. We then apply our prescription of the refined geometric transition to proposing the stringy description of doubly quantized Seiberg-Witten curves called qq-characters in certain cases.
A Geometrical View of Higgs Effective Theory
CERN. Geneva
2016-01-01
A geometric formulation of Higgs Effective Field Theory (HEFT) is presented. Experimental observables are given in terms of geometric invariants of the scalar sigma model sector such as the curvature of the scalar field manifold M. We show how the curvature can be measured experimentally via Higgs cross-sections, W_L scattering, and the S parameter. The one-loop action of HEFT is given in terms of geometric invariants of M. The distinction between the Standard Model (SM) and HEFT is whether M is flat or curved, with the curvature a signal of the scale of new physics.
Geometrical analysis of the interacting boson model
International Nuclear Information System (INIS)
Dieperink, A.E.L.
1983-01-01
The Interacting Boson Model is considered, in relation with geometrical models and the application of mean field techniques to algebraic models, in three lectures. In the first, several methods are reviewed to establish a connection between the algebraic formulation of collective nuclear properties in terms of the group SU(6) and the geometric approach. In the second lecture the geometric interpretation of new degrees of freedom that arise in the neutron-proton IBA is discussed, and in the third one some further applications of algebraic techniques to the calculation of static and dynamic collective properties are presented. (U.K.)
Lectures on geometrical properties of nuclei
International Nuclear Information System (INIS)
Myers, W.D.
1975-11-01
Material concerning the geometrical properties of nuclei is drawn from a number of different sources. The leptodermous nature of nuclear density distributions and potential wells is used to draw together the various geometrical properties of these systems and to provide a unified means for their description. Extensive use is made of expansions of radial properties in terms of the surface diffuseness. A strong case is made for the use of convolution as a geometrical ansatz for generating diffuse surface distributions because of the number of simplifications that arise which are of practical importance. 7 figures
Stock price prediction using geometric Brownian motion
Farida Agustini, W.; Restu Affianti, Ika; Putri, Endah RM
2018-03-01
Geometric Brownian motion is a mathematical model for predicting the future price of stock. The phase that done before stock price prediction is determine stock expected price formulation and determine the confidence level of 95%. On stock price prediction using geometric Brownian Motion model, the algorithm starts from calculating the value of return, followed by estimating value of volatility and drift, obtain the stock price forecast, calculating the forecast MAPE, calculating the stock expected price and calculating the confidence level of 95%. Based on the research, the output analysis shows that geometric Brownian motion model is the prediction technique with high rate of accuracy. It is proven with forecast MAPE value ≤ 20%.
Geometrical E-beam proximity correction for raster scan systems
Belic, Nikola; Eisenmann, Hans; Hartmann, Hans; Waas, Thomas
1999-04-01
High pattern fidelity is a basic requirement for the generation of masks containing sub micro structures and for direct writing. Increasing needs mainly emerging from OPC at mask level and x-ray lithography require a correction of the e-beam proximity effect. The most part of e-beam writers are raster scan system. This paper describes a new method for geometrical pattern correction in order to provide a correction solution for e-beam system that are not able to apply variable doses.
Geometric theory of fundamental interactions. Foundations of unified physics
International Nuclear Information System (INIS)
Pestov, A.B.
2012-01-01
We put forward an idea that regularities of unified physics are in a simple relation: everything in the concept of space and the concept of space in everything. With this hypothesis as a ground, a conceptual structure of a unified geometrical theory of fundamental interactions is created and deductive derivation of its main equations is produced. The formulated theory gives solution of the actual problems, provides opportunity to understand the origin and nature of physical fields, local internal symmetry, time, energy, spin, charge, confinement, dark energy and dark matter, thus conforming the existence of new physics in its unity
Geometrical themes inspired by the n-body problem
Herrera, Haydeé; Herrera, Rafael
2018-01-01
Presenting a selection of recent developments in geometrical problems inspired by the N-body problem, these lecture notes offer a variety of approaches to study them, ranging from variational to dynamical, while developing new insights, making geometrical and topological detours, and providing historical references. A. Guillot’s notes aim to describe differential equations in the complex domain, motivated by the evolution of N particles moving on the plane subject to the influence of a magnetic field. Guillot studies such differential equations using different geometric structures on complex curves (in the sense of W. Thurston) in order to find isochronicity conditions. R. Montgomery’s notes deal with a version of the planar Newtonian three-body equation. Namely, he investigates the problem of whether every free homotopy class is realized by a periodic geodesic. The solution involves geometry, dynamical systems, and the McGehee blow-up. A novelty of the approach is the use of energy-balance in order t...
Numerical nonlinear complex geometrical optics algorithm for the 3D Calderón problem
DEFF Research Database (Denmark)
Delbary, Fabrice; Knudsen, Kim
2014-01-01
to the generalized Laplace equation. The 3D problem was solved in theory in late 1980s using complex geometrical optics solutions and a scattering transform. Several approximations to the reconstruction method have been suggested and implemented numerically in the literature, but here, for the first time, a complete...... computer implementation of the full nonlinear algorithm is given. First a boundary integral equation is solved by a Nystrom method for the traces of the complex geometrical optics solutions, second the scattering transform is computed and inverted using fast Fourier transform, and finally a boundary value...
Geometrical scaling of jet fragmentation photons
Energy Technology Data Exchange (ETDEWEB)
Hattori, Koichi, E-mail: koichi.hattori@riken.jp [RIKEN BNL Research Center, Brookhaven National Laboratory, Upton NY 11973 (United States); Theoretical Research Division, Nishina Center, RIKEN, Wako, Saitama 351-0198 (Japan); McLerran, Larry, E-mail: mclerran@bnl.gov [RIKEN BNL Research Center, Brookhaven National Laboratory, Upton NY 11973 (United States); Physics Dept., Bdg. 510A, Brookhaven National Laboratory, Upton, NY-11973 (United States); Physics Dept., China Central Normal University, Wuhan (China); Schenke, Björn, E-mail: bschenke@bnl.gov [Physics Dept., Bdg. 510A, Brookhaven National Laboratory, Upton, NY-11973 (United States)
2016-12-15
We discuss jet fragmentation photons in ultrarelativistic heavy-ion collisions. We argue that, if the jet distribution satisfies geometrical scaling and an anisotropic spectrum, these properties are transferred to photons during the jet fragmentation.
5th Dagstuhl Seminar on Geometric Modelling
Brunnett, Guido; Farin, Gerald; Goldman, Ron
2004-01-01
In 19 articles presented by leading experts in the field of geometric modelling the state-of-the-art on representing, modeling, and analyzing curves, surfaces as well as other 3-dimensional geometry is given. The range of applications include CAD/CAM-systems, computer graphics, scientific visualization, virtual reality, simulation and medical imaging. The content of this book is based on selected lectures given at a workshop held at IBFI Schloss Dagstuhl, Germany. Topics treated are: – curve and surface modelling – non-manifold modelling in CAD – multiresolution analysis of complex geometric models – surface reconstruction – variational design – computational geometry of curves and surfaces – 3D meshing – geometric modelling for scientific visualization – geometric models for biomedical applications
The perception of geometrical structure from congruence
Lappin, Joseph S.; Wason, Thomas D.
1989-01-01
The principle function of vision is to measure the environment. As demonstrated by the coordination of motor actions with the positions and trajectories of moving objects in cluttered environments and by rapid recognition of solid objects in varying contexts from changing perspectives, vision provides real-time information about the geometrical structure and location of environmental objects and events. The geometric information provided by 2-D spatial displays is examined. It is proposed that the geometry of this information is best understood not within the traditional framework of perspective trigonometry, but in terms of the structure of qualitative relations defined by congruences among intrinsic geometric relations in images of surfaces. The basic concepts of this geometrical theory are outlined.
Mechanisms of geometrical seismic attenuation
Directory of Open Access Journals (Sweden)
Igor B. Morozov
2011-07-01
Full Text Available In several recent reports, we have explained the frequency dependence of the apparent seismic quality-factor (Q observed in many studies according to the effects of geometrical attenuation, which was defined as the zero-frequency limit of the temporal attenuation coefficient. In particular, geometrical attenuation was found to be positive for most waves traveling within the lithosphere. Here, we present three theoretical models that illustrate the origin of this geometrical attenuation, and we investigate the causes of its preferential positive values. In addition, we discuss the physical basis and limitations of both the conventional and new attenuation models. For waves in media with slowly varying properties, geometrical attenuation is caused by variations in the wavefront curvature, which can be both positive (for defocusing and negative (for focusing. In media with velocity/density contrasts, incoherent reflectivity leads to geometrical-attenuation coefficients which are proportional to the mean squared reflectivity and are always positive. For «coherent» reflectivity, the geometrical attenuation is approximately zero, and the attenuation process can be described according to the concept of «scattering Q». However, the true meaning of this parameter is in describing the mean reflectivity within the medium, and not that of the traditional resonator quality factor known in mechanics. The general conclusion from these models is that non-zero and often positive levels of geometrical attenuation are common in realistic, heterogeneous media, both observationally and theoretically. When transformed into the conventional Q-factor form, this positive geometrical attenuation leads to Q values that quickly increase with frequency. These predictions show that the positive frequency-dependent Q observed in many datasets might represent artifacts of the transformations of the attenuation coefficients into Q.
Energy Technology Data Exchange (ETDEWEB)
Daoud, M., E-mail: m_daoud@hotmail.com [Department of Physics, Faculty of Sciences, University Ibnou Zohr, Agadir (Morocco); Ahl Laamara, R., E-mail: ahllaamara@gmail.com [LPHE-Modeling and Simulation, Faculty of Sciences, University Mohammed V, Rabat (Morocco); Centre of Physics and Mathematics, CPM, CNESTEN, Rabat (Morocco)
2012-07-16
We give the explicit expressions of the pairwise quantum correlations present in superpositions of multipartite coherent states. A special attention is devoted to the evaluation of the geometric quantum discord. The dynamics of quantum correlations under a dephasing channel is analyzed. A comparison of geometric measure of quantum discord with that of concurrence shows that quantum discord in multipartite coherent states is more resilient to dissipative environments than is quantum entanglement. To illustrate our results, we consider some special superpositions of Weyl–Heisenberg, SU(2) and SU(1,1) coherent states which interpolate between Werner and Greenberger–Horne–Zeilinger states. -- Highlights: ► Pairwise quantum correlations multipartite coherent states. ► Explicit expression of geometric quantum discord. ► Entanglement sudden death and quantum discord robustness. ► Generalized coherent states interpolating between Werner and Greenberger–Horne–Zeilinger states.
Geometric Implications of Maxwell's Equations
Smith, Felix T.
2015-03-01
Maxwell's synthesis of the varied results of the accumulated knowledge of electricity and magnetism, based largely on the searching insights of Faraday, still provide new issues to explore. A case in point is a well recognized anomaly in the Maxwell equations: The laws of electricity and magnetism require two 3-vector and two scalar equations, but only six dependent variables are available to be their solutions, the 3-vectors E and B. This leaves an apparent redundancy of two degrees of freedom (J. Rosen, AJP 48, 1071 (1980); Jiang, Wu, Povinelli, J. Comp. Phys. 125, 104 (1996)). The observed self-consistency of the eight equations suggests that they contain additional information. This can be sought as a previously unnoticed constraint connecting the space and time variables, r and t. This constraint can be identified. It distorts the otherwise Euclidean 3-space of r with the extremely slight, time dependent curvature k (t) =Rcurv-2 (t) of the 3-space of a hypersphere whose radius has the time dependence dRcurv / dt = +/- c nonrelativistically, or dRcurvLor / dt = +/- ic relativistically. The time dependence is exactly that of the Hubble expansion. Implications of this identification will be explored.
Geometrical properties of systems with spiral trajectories in R^3
Directory of Open Access Journals (Sweden)
Luka Korkut
2015-10-01
Full Text Available We study a class of second-order nonautonomous differential equations, and the corresponding planar and spatial systems, from the geometrical point of view. The oscillatory behavior of solutions at infinity is measured by oscillatory and phase dimensions, The oscillatory dimension is defined as the box dimension of the reflected solution near the origin, while the phase dimension is defined as the box dimension of a trajectory of the planar system in the phase plane. Using the phase dimension of the second-order equation we compute the box dimension of a spiral trajectory of the spatial system. This phase dimension of the second-order equation is connected to the asymptotic of the associated Poincare map. Also, the box dimension of a trajectory of the reduced normal form with one eigenvalue equals zero, and a pair of pure imaginary eigenvalues is computed when limit cycles bifurcate from the origin.
The problem 7 forming triangular geometric line field
Directory of Open Access Journals (Sweden)
Travush Vladimir Iljich
2016-01-01
Full Text Available Investigated a method of formation of triangular networks in the field. Delivered conditions the problem of locating a triangular network in the area. The criterion for assessing the effectiveness of the solution of the problem is the minimum number of sizes of the dome elements, the possibility of pre-assembly and pre-stressing. The solution of the problem of one embodiment of a triangular network of accommodation in a compatible spherical triangle and, accordingly, on the sphere. Optimization of triangular geometric network on a sphere on the criterion of minimum sizes of elements can be solved by placing the system in an irregular hexagon inscribed in a circle of minimal size, maximum regular hexagons.
The problem 4 of placement triangular geometric line field
Directory of Open Access Journals (Sweden)
Travush Vladimir Iljich
2016-01-01
Full Text Available One of the a method of formation of triangular networks in the field is investigated. Conditions the problem of locating a triangular network in the area are delivered. The criterion for assessing the effectiveness of the solution of the problem is the minimum number of sizes of the dome elements, the possibility of pre-assembly and pre-stressing. The solution of the problem of one embodiment of a triangular network of accommodation in a compatible spherical triangle and, accordingly, on the sphere. Optimization of triangular geometric network on a sphere on the criterion of minimum sizes of elements can be solved by placing the system in an irregular hexagon inscribed in a circle of minimal size, maximum regular hexagons.
Geometric properties of Banach spaces and nonlinear iterations
Chidume, Charles
2009-01-01
Nonlinear functional analysis and applications is an area of study that has provided fascination for many mathematicians across the world. This monograph delves specifically into the topic of the geometric properties of Banach spaces and nonlinear iterations, a subject of extensive research over the past thirty years. Chapters 1 to 5 develop materials on convexity and smoothness of Banach spaces, associated moduli and connections with duality maps. Key results obtained are summarized at the end of each chapter for easy reference. Chapters 6 to 23 deal with an in-depth, comprehensive and up-to-date coverage of the main ideas, concepts and results on iterative algorithms for the approximation of fixed points of nonlinear nonexpansive and pseudo-contractive-type mappings. This includes detailed workings on solutions of variational inequality problems, solutions of Hammerstein integral equations, and common fixed points (and common zeros) of families of nonlinear mappings. Carefully referenced and full of recent,...
Lie-Hamilton systems on curved spaces: a geometrical approach
Herranz, Francisco J.; de Lucas, Javier; Tobolski, Mariusz
2017-12-01
A Lie-Hamilton system is a nonautonomous system of first-order ordinary differential equations describing the integral curves of a t-dependent vector field taking values in a finite-dimensional Lie algebra, a Vessiot-Guldberg Lie algebra, of Hamiltonian vector fields relative to a Poisson structure. Its general solution can be written as an autonomous function, the superposition rule, of a generic finite family of particular solutions and a set of constants. We pioneer the study of Lie-Hamilton systems on Riemannian spaces (sphere, Euclidean and hyperbolic plane), pseudo-Riemannian spaces (anti-de Sitter, de Sitter, and Minkowski spacetimes) as well as on semi-Riemannian spaces (Newtonian spacetimes). Their corresponding constants of motion and superposition rules are obtained explicitly in a geometric way. This work extends the (graded) contraction of Lie algebras to a contraction procedure for Lie algebras of vector fields, Hamiltonian functions, and related symplectic structures, invariants, and superposition rules.
Triangular Geometrized Sampling Heuristics for Fast Optimal Motion Planning
Directory of Open Access Journals (Sweden)
Ahmed Hussain Qureshi
2015-02-01
Full Text Available Rapidly-exploring Random Tree (RRT-based algorithms have become increasingly popular due to their lower computational complexity as compared with other path planning algorithms. The recently presented RRT* motion planning algorithm improves upon the original RRT algorithm by providing optimal path solutions. While RRT determines an initial collision-free path fairly quickly, RRT* guarantees almost certain convergence to an optimal, obstacle-free path from the start to the goal points for any given geometrical environment. However, the main limitations of RRT* include its slow processing rate and high memory consumption, due to the large number of iterations required for calculating the optimal path. In order to overcome these limitations, we present another improvement, i.e, the Triangular Geometerized-RRT* (TG-RRT* algorithm, which utilizes triangular geometrical methods to improve the performance of the RRT* algorithm in terms of the processing time and a decreased number of iterations required for an optimal path solution. Simulations comparing the performance results of the improved TG-RRT* with RRT* are presented to demonstrate the overall improvement in performance and optimal path detection.
Czech Academy of Sciences Publication Activity Database
Planeta, Josef; Karásek, Pavel; Roth, Michal
2007-01-01
Roč. 111, č. 26 (2007), s. 7620-7625 ISSN 1520-6106 R&D Projects: GA AV ČR KJB400310504; GA ČR GA203/05/2106; GA ČR GA203/07/0886 Institutional research plan: CEZ:AV0Z40310501 Keywords : phosphonium ionic liquid * supercritical carbon dioxide * solute partition coefficient Subject RIV: CB - Analytical Chemistry, Separation Impact factor: 4.086, year: 2007
International Nuclear Information System (INIS)
Guo, X.Z.; Gao, K.W.; Chu, W.Y.; Qiao, L.J.
2003-01-01
The flow stress of a specimen of α-Ti before unloading is different with the yield stress of the same specimen after unloading and forming a passive film through immersing in a methanol solution at various constant potentials. The difference is the passive film-induced stress. The film-induced stress and susceptibility to stress corrosion cracking (SCC) in the methanol solution at various potentials were measured. At the stable open-circuit potential and under anodic polarization, both film-induced tensile stress σ p and susceptibility to SCC had a maximum value. The film-induced stress and SCC susceptibility, however, decreased steeply with a decrease in potential under cathodic polarization. When the potential V≤-280 mV SCE , the film-induced stress became compressive; correspondingly, susceptibility to SCC was zero. Therefore, the variation of film-induced stress with potential was consistent with that of susceptibility to SCC. A large film-induced tensile stress is the necessary condition for SCC of α-Ti in the methanol solution. The symbol and amount of the film-induced stress were related to the compositions of the passive film, which have been analyzed using the X-ray photoelectron spectrum (XPS)
Morphing of geometric composites via residual swelling.
Pezzulla, Matteo; Shillig, Steven A; Nardinocchi, Paola; Holmes, Douglas P
2015-08-07
Understanding and controlling the shape of thin, soft objects has been the focus of significant research efforts among physicists, biologists, and engineers in the last decade. These studies aim to utilize advanced materials in novel, adaptive ways such as fabricating smart actuators or mimicking living tissues. Here, we present the controlled growth-like morphing of 2D sheets into 3D shapes by preparing geometric composite structures that deform by residual swelling. The morphing of these geometric composites is dictated by both swelling and geometry, with diffusion controlling the swelling-induced actuation, and geometric confinement dictating the structure's deformed shape. Building on a simple mechanical analog, we present an analytical model that quantitatively describes how the Gaussian and mean curvatures of a thin disk are affected by the interplay among geometry, mechanics, and swelling. This model is in excellent agreement with our experiments and numerics. We show that the dynamics of residual swelling is dictated by a competition between two characteristic diffusive length scales governed by geometry. Our results provide the first 2D analog of Timoshenko's classical formula for the thermal bending of bimetallic beams - our generalization explains how the Gaussian curvature of a 2D geometric composite is affected by geometry and elasticity. The understanding conferred by these results suggests that the controlled shaping of geometric composites may provide a simple complement to traditional manufacturing techniques.
Geometric phases and hidden local gauge symmetry
International Nuclear Information System (INIS)
Fujikawa, Kazuo
2005-01-01
The analysis of geometric phases associated with level crossing is reduced to the familiar diagonalization of the Hamiltonian in the second quantized formulation. A hidden local gauge symmetry, which is associated with the arbitrariness of the phase choice of a complete orthonormal basis set, becomes explicit in this formulation (in particular, in the adiabatic approximation) and specifies physical observables. The choice of a basis set which specifies the coordinate in the functional space is arbitrary in the second quantization, and a subclass of coordinate transformations, which keeps the form of the action invariant, is recognized as the gauge symmetry. We discuss the implications of this hidden local gauge symmetry in detail by analyzing geometric phases for cyclic and noncyclic evolutions. It is shown that the hidden local symmetry provides a basic concept alternative to the notion of holonomy to analyze geometric phases and that the analysis based on the hidden local gauge symmetry leads to results consistent with the general prescription of Pancharatnam. We however note an important difference between the geometric phases for cyclic and noncyclic evolutions. We also explain a basic difference between our hidden local gauge symmetry and a gauge symmetry (or equivalence class) used by Aharonov and Anandan in their definition of generalized geometric phases
Directory of Open Access Journals (Sweden)
Delma Maria Cunha
2001-01-01
Full Text Available OBJECTIVE: To identiy left ventricular geometric patterns in hypertensive patients on echocardiography, and to correlate those patterns with casual blood pressure measurements and with the parameters obtained on a 24-hour ambulatory blood pressure monitoring. METHODS: We studied sixty hypertensive patients, grouped according to the Joint National Committee stages of hypertension.. Using the single- and two-dimensional Doppler Echocardiography, we analyzed the left ventricular mass and the geometric patterns through the correlation of left ventricular mass index and relative wall thickness. On ambulatory blood pressure monitoring we assessed the means and pressure loads in the different geometric patterns detected on echocardiography RESULTS: We identified three left ventricular geometric patterns: 1 concentric hypertrophy, in 25% of the patients; 2 concentric remodeling, in 25%; and 3 normal geometry, in 50%. Casual systolic blood pressure was higher in the group with concentric hypertrophy than in the other groups (p=0.001. Mean systolic pressure in the 24h, daytime and nighttime periods was also higher in patients with concentric hypertrophy, as compared to the other groups (p=0.003, p=0.004 and p=0.007. Daytime systolic load and nighttime diastolic load were higher in patients with concentric hypertrophy ( p=0.004 and p=0.01, respectively. CONCLUSIONS: Left ventricular geometric patterns show significant correlation with casual systolic blood pressure, and with means and pressure loads on ambulatory blood pressure monitoring.
Lith, van B.S.; Thije Boonkkamp, ten J.H.M.; IJzerman, W.L.; Tukker, T.W.
2015-01-01
We compute numerical solutions of Liouville's equation with a discontinuous Hamiltonian. We assume that the underlying Hamiltonian system has a well-defined behaviour even when the Hamiltonian is discontinuous. In the case of geometrical optics such a discontinuity yields the familiar Snell's law or
van Lith, B.S.; ten Thije Boonkkamp, J.H.M.; IJzerman, W.L.; Tukker, T.W.
A novel scheme is developed that computes numerical solutions of Liouville’s equation with a discontinuous Hamiltonian. It is assumed that the underlying Hamiltonian system has well-defined behaviour even when the Hamiltonian is discontinuous. In the case of geometrical optics such a discontinuity
Geometric inequalities for axially symmetric black holes
International Nuclear Information System (INIS)
Dain, Sergio
2012-01-01
A geometric inequality in general relativity relates quantities that have both a physical interpretation and a geometrical definition. It is well known that the parameters that characterize the Kerr-Newman black hole satisfy several important geometric inequalities. Remarkably enough, some of these inequalities also hold for dynamical black holes. This kind of inequalities play an important role in the characterization of the gravitational collapse; they are closely related with the cosmic censorship conjecture. Axially symmetric black holes are the natural candidates to study these inequalities because the quasi-local angular momentum is well defined for them. We review recent results in this subject and we also describe the main ideas behind the proofs. Finally, a list of relevant open problems is presented. (topical review)
MM Algorithms for Geometric and Signomial Programming.
Lange, Kenneth; Zhou, Hua
2014-02-01
This paper derives new algorithms for signomial programming, a generalization of geometric programming. The algorithms are based on a generic principle for optimization called the MM algorithm. In this setting, one can apply the geometric-arithmetic mean inequality and a supporting hyperplane inequality to create a surrogate function with parameters separated. Thus, unconstrained signomial programming reduces to a sequence of one-dimensional minimization problems. Simple examples demonstrate that the MM algorithm derived can converge to a boundary point or to one point of a continuum of minimum points. Conditions under which the minimum point is unique or occurs in the interior of parameter space are proved for geometric programming. Convergence to an interior point occurs at a linear rate. Finally, the MM framework easily accommodates equality and inequality constraints of signomial type. For the most important special case, constrained quadratic programming, the MM algorithm involves very simple updates.
The Geometric Phase of Stock Trading.
Altafini, Claudio
2016-01-01
Geometric phases describe how in a continuous-time dynamical system the displacement of a variable (called phase variable) can be related to other variables (shape variables) undergoing a cyclic motion, according to an area rule. The aim of this paper is to show that geometric phases can exist also for discrete-time systems, and even when the cycles in shape space have zero area. A context in which this principle can be applied is stock trading. A zero-area cycle in shape space represents the type of trading operations normally carried out by high-frequency traders (entering and exiting a position on a fast time-scale), while the phase variable represents the cash balance of a trader. Under the assumption that trading impacts stock prices, even zero-area cyclic trading operations can induce geometric phases, i.e., profits or losses, without affecting the stock quote.
Exponentiated Lomax Geometric Distribution: Properties and Applications
Directory of Open Access Journals (Sweden)
Amal Soliman Hassan
2017-09-01
Full Text Available In this paper, a new four-parameter lifetime distribution, called the exponentiated Lomax geometric (ELG is introduced. The new lifetime distribution contains the Lomax geometric and exponentiated Pareto geometric as new sub-models. Explicit algebraic formulas of probability density function, survival and hazard functions are derived. Various structural properties of the new model are derived including; quantile function, Re'nyi entropy, moments, probability weighted moments, order statistic, Lorenz and Bonferroni curves. The estimation of the model parameters is performed by maximum likelihood method and inference for a large sample is discussed. The flexibility and potentiality of the new model in comparison with some other distributions are shown via an application to a real data set. We hope that the new model will be an adequate model for applications in various studies.
Normed algebras and the geometric series test
Directory of Open Access Journals (Sweden)
Robert Kantrowitz
2017-11-01
Full Text Available The purpose of this article is to survey a class of normed algebras that share many central features of Banach algebras, save for completeness. The likeness of these algebras to Banach algebras derives from the fact that the geometric series test is valid, whereas the lack of completeness points to the failure of the absolute convergence test for series in the algebra. Our main result is a compendium of conditions that are all equivalent to the validity of the geometric series test for commutative unital normed algebras. Several examples in the final section showcase some incomplete normed algebras for which the geometric series test is valid, and still others for which it is not.
Geometric function theory in higher dimension
2017-01-01
The book collects the most relevant outcomes from the INdAM Workshop “Geometric Function Theory in Higher Dimension” held in Cortona on September 5-9, 2016. The Workshop was mainly devoted to discussions of basic open problems in the area, and this volume follows the same line. In particular, it offers a selection of original contributions on Loewner theory in one and higher dimensions, semigroups theory, iteration theory and related topics. Written by experts in geometric function theory in one and several complex variables, it focuses on new research frontiers in this area and on challenging open problems. The book is intended for graduate students and researchers working in complex analysis, several complex variables and geometric function theory.
EARLY HISTORY OF GEOMETRIC PROBABILITY AND STEREOLOGY
Directory of Open Access Journals (Sweden)
Magdalena Hykšová
2012-03-01
Full Text Available The paper provides an account of the history of geometric probability and stereology from the time of Newton to the early 20th century. It depicts the development of two parallel ways: on one hand, the theory of geometric probability was formed with minor attention paid to other applications than those concerning spatial chance games. On the other hand, practical rules of the estimation of area or volume fraction and other characteristics, easily deducible from geometric probability theory, were proposed without the knowledge of this branch. A special attention is paid to the paper of J.-É. Barbier published in 1860, which contained the fundamental stereological formulas, but remained almost unnoticed both by mathematicians and practicians.
Geometric optimization and sums of algebraic functions
Vigneron, Antoine E.
2014-01-01
We present a new optimization technique that yields the first FPTAS for several geometric problems. These problems reduce to optimizing a sum of nonnegative, constant description complexity algebraic functions. We first give an FPTAS for optimizing such a sum of algebraic functions, and then we apply it to several geometric optimization problems. We obtain the first FPTAS for two fundamental geometric shape-matching problems in fixed dimension: maximizing the volume of overlap of two polyhedra under rigid motions and minimizing their symmetric difference. We obtain the first FPTAS for other problems in fixed dimension, such as computing an optimal ray in a weighted subdivision, finding the largest axially symmetric subset of a polyhedron, and computing minimum-area hulls.
Understanding geometric algebra for electromagnetic theory
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.
Spherical projections and liftings in geometric tomography
DEFF Research Database (Denmark)
Goodey, Paul; Kiderlen, Markus; Weil, Wolfgang
2011-01-01
We consider a variety of integral transforms arising in Geometric Tomography. It will be shown that these can be put into a common framework using spherical projection and lifting operators. These operators will be applied to support functions and surface area measures of convex bodies and to rad......We consider a variety of integral transforms arising in Geometric Tomography. It will be shown that these can be put into a common framework using spherical projection and lifting operators. These operators will be applied to support functions and surface area measures of convex bodies...... and to radial functions of star bodies. We then investigate averages of lifted projections and show that they correspond to self-adjoint intertwining operators. We obtain formulas for the eigenvalues of these operators and use them to ascertain circumstances under which tomographic measurements determine...... the original bodies. This approach via mean lifted projections leads us to some unexpected relationships between seemingly disparate geometric constructions....
The effect of photometric and geometric context on photometric and geometric lightness effects.
Lee, Thomas Y; Brainard, David H
2014-01-24
We measured the lightness of probe tabs embedded at different orientations in various contextual images presented on a computer-controlled stereo display. Two background context planes met along a horizontal roof-like ridge. Each plane was a graphic rendering of a set of achromatic surfaces with the simulated illumination for each plane controlled independently. Photometric context was varied by changing the difference in simulated illumination intensity between the two background planes. Geometric context was varied by changing the angle between them. We parsed the data into separate photometric effects and geometric effects. For fixed geometry, varying photometric context led to linear changes in both the photometric and geometric effects. Varying geometric context did not produce a statistically reliable change in either the photometric or geometric effects.
Sudan-decoding generalized geometric Goppa codes
DEFF Research Database (Denmark)
Heydtmann, Agnes Eileen
2003-01-01
Generalized geometric Goppa codes are vector spaces of n-tuples with entries from different extension fields of a ground field. They are derived from evaluating functions similar to conventional geometric Goppa codes, but allowing evaluation in places of arbitrary degree. A decoding scheme...... for these codes based on Sudan's improved algorithm is presented and its error-correcting capacity is analyzed. For the implementation of the algorithm it is necessary that the so-called increasing zero bases of certain spaces of functions are available. A method to obtain such bases is developed....
The geometric phase in quantum physics
International Nuclear Information System (INIS)
Bohm, A.
1993-03-01
After an explanatory introduction, a quantum system in a classical time-dependent environment is discussed; an example is a magnetic moment in a classical magnetic field. At first, the general abelian case is discussed in the adiabatic approximation. Then the geometric phase for nonadiabatic change of the environment (Anandan--Aharonov phase) is introduced, and after that general cyclic (nonadiabatic) evolution is discussed. The mathematics of fiber bundles is introduced, and some of its results are used to describe the relation between the adiabatic Berry phase and the geometric phase for general cyclic evolution of a pure state. The discussion is restricted to the abelian, U(1) phase
Geometric modular action and transformation groups
International Nuclear Information System (INIS)
Summers, S.J.
1996-01-01
We study a weak form of geometric modular action, which is naturally associated with transformation groups of partially ordered sets and which provides these groups with projective representations. Under suitable conditions it is shown that these groups are implemented by point transformations of topological spaces serving as models for space-times, leading to groups which may be interpreted as symmetry groups of the space-times. As concrete examples, it is shown that the Poincare group and the de Sitter group can be derived from this condition of geometric modular action. Further consequences and examples are discussed. (orig.)
Geometrical methods for power network analysis
Energy Technology Data Exchange (ETDEWEB)
Bellucci, Stefano; Tiwari, Bhupendra Nath [Istituto Nazioneale di Fisica Nucleare, Frascati, Rome (Italy). Lab. Nazionali di Frascati; Gupta, Neeraj [Indian Institute of Technology, Kanpur (India). Dept. of Electrical Engineering
2013-02-01
Uses advanced geometrical methods to analyse power networks. Provides a self-contained and tutorial introduction. Includes a fully worked-out example for the IEEE 5 bus system. This book is a short introduction to power system planning and operation using advanced geometrical methods. The approach is based on well-known insights and techniques developed in theoretical physics in the context of Riemannian manifolds. The proof of principle and robustness of this approach is examined in the context of the IEEE 5 bus system. This work addresses applied mathematicians, theoretical physicists and power engineers interested in novel mathematical approaches to power network theory.
Aspects of the geometrical approach to supermanifolds
International Nuclear Information System (INIS)
Rogers, A.
1984-01-01
Various topics in the theory and application of the geometrical approach to supermanifolds are discussed. The construction of the superspace used in supergravity over an arbitrary spacetime manifold is described. Super Lie groups and their relation to graded Lie algebras (and more general structures referred to as 'graded Lie modules') are discussed, with examples. Certain supermanifolds, allowed in the geometric approach (using the fine topology), but having no analogue in the algebraic approach, are discussed. Finally lattice supersymmetry, and its relation to the differential geometry of supermanifolds, is discussed. (orig.)
Geometrical superresolved imaging using nonperiodic spatial masking.
Borkowski, Amikam; Zalevsky, Zeev; Javidi, Bahram
2009-03-01
The resolution of every imaging system is limited either by the F-number of its optics or by the geometry of its detection array. The geometrical limitation is caused by lack of spatial sampling points as well as by the shape of every sampling pixel that generates spectral low-pass filtering. We present a novel approach to overcome the low-pass filtering that is due to the shape of the sampling pixels. The approach combines special algorithms together with spatial masking placed in the intermediate image plane and eventually allows geometrical superresolved imaging without relation to the actual shape of the pixels.
Workshop on Topology and Geometric Group Theory
Fowler, James; Lafont, Jean-Francois; Leary, Ian
2016-01-01
This book presents articles at the interface of two active areas of research: classical topology and the relatively new field of geometric group theory. It includes two long survey articles, one on proofs of the Farrell–Jones conjectures, and the other on ends of spaces and groups. In 2010–2011, Ohio State University (OSU) hosted a special year in topology and geometric group theory. Over the course of the year, there were seminars, workshops, short weekend conferences, and a major conference out of which this book resulted. Four other research articles complement these surveys, making this book ideal for graduate students and established mathematicians interested in entering this area of research.
On the geometric nature of high energy nucleus-nucleus reaction cross sections
International Nuclear Information System (INIS)
Townsend, L.W.; Wilson, J.W.; Bidasaria, H.B.
1982-01-01
Within the context of a high energy double-folding optical potential approximation to the exact nucleus-nucleus multiple-scattering series, eikonal scattering theory is used to investigate the validity of geometric reaction cross sections in relativistic heavy ion collisions. The potential used includes a finite range interaction and nuclear single-particle densities extracted from nuclear charge distributions by unfolding the proton charge distribution. Pauli correlation effects are also included in an approximate way. The sensitivity of the predictions to be assumed interaction, Pauli correlation approximation, and nuclear density distributions is investigated. These results are in agreement with early predictions concerning the geometric nature of relativistic heavy ion collisions and in disagreement with a recent analysis, utilizing the zero range approximation, which suggested otherwise. Reasons for the lack of agreement between the analyses are also presented. Finally, approximate applicability for geometric reaction cross sections are determined
Theoretical frameworks for the learning of geometrical reasoning
Jones, Keith
1998-01-01
With the growth in interest in geometrical ideas it is important to be clear about the nature of geometrical reasoning and how it develops. This paper provides an overview of three theoretical frameworks for the learning of geometrical reasoning: the van Hiele model of thinking in geometry, Fischbein’s theory of figural concepts, and Duval’s cognitive model of geometrical reasoning. Each of these frameworks provides theoretical resources to support research into the development of geometrical...
Miao, Jian-Jian; Jin, Hui-Ke; Zhang, Fu-Chun; Zhou, Yi
2018-01-11
We study Kitaev model in one-dimension with open boundary condition by using exact analytic methods for non-interacting system at zero chemical potential as well as in the symmetric case of Δ = t, and by using density-matrix-renormalization-group method for interacting system with nearest neighbor repulsion interaction. We suggest and examine an edge correlation function of Majorana fermions to characterize the long range order in the topological superconducting states and study the phase diagram of the interating Kitaev chain.
Yang, Qing-Dan; Li, Ho-Wa; Cheng, Yuanhang; Guan, Zhiqiang; Liu, Taili; Ng, Tsz-Wai; Lee, Chun-Sing; Tsang, Sai-Wing
2016-03-23
Energy level alignment at the organic donor and acceptor interface is a key to determine the photovoltaic performance in organic solar cells, but direct probing of such energy alignment is still challenging especially for solution-processed bulk heterojunction (BHJ) thin films. Here we report a systematic investigation on probing the energy level alignment with different approaches in five commonly used polymer:[6,6]-phenyl-C71-butyric acid methyl ester (PCBM) BHJ systems. We find that by tuning the weight ratio of polymer to PCBM the electronic features from both polymer and PCBM can be obtained by photoemission spectroscopy. Using this approach, we find that some of the BHJ blends simply follow vacuum level alignment, but others show strong energy level shifting as a result of Fermi level pinning. Independently, by measuring the temperature-dependent open-circuit voltage (VOC), we find that the effective energy gap (Eeff), the energy difference between the highest occupied molecular orbital of the polymer donor (EHOMO-D) and lowest unoccupied molecular orbital of the PCBM acceptor (ELUMO-A), obtained by photoemission spectroscopy in all polymer:PCBM blends has an excellent agreement with the extrapolated VOC at 0 K. Consequently, the photovoltage loss of various organic BHJ photovoltaic devices at room temperature is in a range of 0.3-0.6 V. It is believed that the demonstrated direct measurement approach of the energy level alignment in solution-processed organic BHJ will bring deeper insight into the origin of the VOC and the corresponding photovoltage loss mechanism in organic photovoltaic cells.
Two particle entanglement and its geometric duals
Energy Technology Data Exchange (ETDEWEB)
Wasay, Muhammad Abdul [University of Agriculture, Department of Physics, Faisalabad (Pakistan); Quaid-i-Azam University Campus, National Centre for Physics, Islamabad (Pakistan); Bashir, Asma [University of Agriculture, Department of Physics, Faisalabad (Pakistan)
2017-12-15
We show that for a system of two entangled particles, there is a dual description to the particle equations in terms of classical theory of conformally stretched spacetime. We also connect these entangled particle equations with Finsler geometry. We show that this duality translates strongly coupled quantum equations in the pilot-wave limit to weakly coupled geometric equations. (orig.)
Impossible Geometric Constructions: A Calculus Writing Project
Awtrey, Chad
2013-01-01
This article discusses a writing project that offers students the opportunity to solve one of the most famous geometric problems of Greek antiquity; namely, the impossibility of trisecting the angle [pi]/3. Along the way, students study the history of Greek geometry problems as well as the life and achievements of Carl Friedrich Gauss. Included is…
Rejuvenating Allen's Arc with the Geometric Mean.
Phillips, William A.
1994-01-01
Contends that, despite ongoing criticism, Allen's arc elasticity formula remains entrenched in the microeconomics principles curriculum. Reviews the evolution and continuing scrutiny of the formula. Argues that the use of the geometric mean offers pedagogical advantages over the traditional arithmetic mean approach. (CFR)
Two particle entanglement and its geometric duals
International Nuclear Information System (INIS)
Wasay, Muhammad Abdul; Bashir, Asma
2017-01-01
We show that for a system of two entangled particles, there is a dual description to the particle equations in terms of classical theory of conformally stretched spacetime. We also connect these entangled particle equations with Finsler geometry. We show that this duality translates strongly coupled quantum equations in the pilot-wave limit to weakly coupled geometric equations. (orig.)
Geometric Abstract Art and Public Health Data
Centers for Disease Control (CDC) Podcasts
2016-10-18
Dr. Salaam Semaan, a CDC behavioral scientist, discusses the similarities between geometric abstract art and public health data analysis. Created: 10/18/2016 by National Center for Emerging and Zoonotic Infectious Diseases (NCEZID). Date Released: 10/18/2016.
Geometric phase topology in weak measurement
Samlan, C. T.; Viswanathan, Nirmal K.
2017-12-01
The geometric phase visualization proposed by Bhandari (R Bhandari 1997 Phys. Rep. 281 1-64) in the ellipticity-ellipse orientation basis of the polarization ellipse of light is implemented to understand the geometric aspects of weak measurement. The weak interaction of a pre-selected state, acheived via spin-Hall effect of light (SHEL), results in a spread in the polarization ellipticity (η) or ellipse orientation (χ) depending on the resulting spatial or angular shift, respectively. The post-selection leads to the projection of the η spread in the complementary χ basis results in the appearance of a geometric phase with helical phase topology in the η - χ parameter space. By representing the weak measurement on the Poincaré sphere and using Jones calculus, the complex weak value and the geometric phase topology are obtained. This deeper understanding of the weak measurement process enabled us to explore the techniques’ capabilities maximally, as demonstrated via SHEL in two examples—external reflection at glass-air interface and transmission through a tilted half-wave plate.
Geometrical tile design for complex neighborhoods.
Czeizler, Eugen; Kari, Lila
2009-01-01
Recent research has showed that tile systems are one of the most suitable theoretical frameworks for the spatial study and modeling of self-assembly processes, such as the formation of DNA and protein oligomeric structures. A Wang tile is a unit square, with glues on its edges, attaching to other tiles and forming larger and larger structures. Although quite intuitive, the idea of glues placed on the edges of a tile is not always natural for simulating the interactions occurring in some real systems. For example, when considering protein self-assembly, the shape of a protein is the main determinant of its functions and its interactions with other proteins. Our goal is to use geometric tiles, i.e., square tiles with geometrical protrusions on their edges, for simulating tiled paths (zippers) with complex neighborhoods, by ribbons of geometric tiles with simple, local neighborhoods. This paper is a step toward solving the general case of an arbitrary neighborhood, by proposing geometric tile designs that solve the case of a "tall" von Neumann neighborhood, the case of the f-shaped neighborhood, and the case of a 3 x 5 "filled" rectangular neighborhood. The techniques can be combined and generalized to solve the problem in the case of any neighborhood, centered at the tile of reference, and included in a 3 x (2k + 1) rectangle.
Geometric Representations for Discrete Fourier Transforms
Cambell, C. W.
1986-01-01
Simple geometric representations show symmetry and periodicity of discrete Fourier transforms (DFT's). Help in visualizing requirements for storing and manipulating transform value in computations. Representations useful in any number of dimensions, but particularly in one-, two-, and three-dimensional cases often encountered in practice.
Geometric Series and Computers--An Application.
McNerney, Charles R.
1983-01-01
This article considers the sum of a finite geometric series as applied to numeric data storage in the memory of an electronic digital computer. The presentation is viewed as relevant to programing in several languages and removes some of the mystique associated with syntax constraints that any language imposes. (MP)
Geometric Transformations in Middle School Mathematics Textbooks
Zorin, Barbara
2011-01-01
This study analyzed treatment of geometric transformations in presently available middle grades (6, 7, 8) student mathematics textbooks. Fourteen textbooks from four widely used textbook series were evaluated: two mainline publisher series, Pearson (Prentice Hall) and Glencoe (Math Connects); one National Science Foundation (NSF) funded curriculum…
Geometric calibration of ERS satellite SAR images
DEFF Research Database (Denmark)
Mohr, Johan Jacob; Madsen, Søren Nørvang
2001-01-01
Geometric calibration of the European Remote Sensing (ERS) Satellite synthetic aperture radar (SAR) slant range images is important in relation to mapping areas without ground reference points and also in relation to automated processing. The relevant SAR system parameters are discussed...
Non-crossing geometric steiner arborescences
Kostitsyna, I.; Speckmann, B.; Verbeek, K.A.B.; Okamoto, Yoshio; Tokuyama, Takeshi
2017-01-01
Motivated by the question of simultaneous embedding of several flow maps, we consider the problem of drawing multiple geometric Steiner arborescences with no crossings in the rectilinear and in the angle-restricted setting. When terminal-to-root paths are allowed to turn freely, we show that two
On Kaehler's geometric description of dirac fields
International Nuclear Information System (INIS)
Goeckeler, M.; Joos, H.
1983-12-01
A differential geometric generalization of the Dirac equation due to E. Kaehler seems to be an appropriate starting point for the lattice approximation of matter fields. It is the purpose of this lecture to illustrate several aspects of this approach. (orig./HSI)
Robust Geometric Control of a Distillation Column
DEFF Research Database (Denmark)
Kymmel, Mogens; Andersen, Henrik Weisberg
1987-01-01
A frequency domain method, which makes it possible to adjust multivariable controllers with respect to both nominal performance and robustness, is presented. The basic idea in the approach is that the designer assigns objectives such as steady-state tracking, maximum resonance peaks, bandwidth, m...... is used to examine and improve geometric control of a binary distillation column....
Non-equilibrium current via geometric scatterers
Czech Academy of Sciences Publication Activity Database
Exner, Pavel; Neidhardt, H.; Tater, Miloš; Zagrebnov, V. A.
2014-01-01
Roč. 47, č. 39 (2014), s. 395301 ISSN 1751-8113 R&D Projects: GA ČR(CZ) GA14-06818S Institutional support: RVO:61389005 Keywords : non-equilibrioum steady states * geometric scatterer * Landauer-Buttiker formula Subject RIV: BE - Theoretical Physics Impact factor: 1.583, year: 2014
Geometrical scaling in high energy hadron collisions
International Nuclear Information System (INIS)
Kundrat, V.; Lokajicek, M.V.
1984-06-01
The concept of geometrical scaling for high energy elastic hadron scattering is analyzed and its basic equations are solved in a consistent way. It is shown that they are applicable to a rather small interval of momentum transfers, e.g. maximally for |t| 2 for pp scattering at the ISR energies. (author)
Geometrical efficiency in computerized tomography: generalized model
International Nuclear Information System (INIS)
Costa, P.R.; Robilotta, C.C.
1992-01-01
A simplified model for producing sensitivity and exposure profiles in computerized tomographic system was recently developed allowing the forecast of profiles behaviour in the rotation center of the system. The generalization of this model for some point of the image plane was described, and the geometrical efficiency could be evaluated. (C.G.C.)
The Data Transfer Kit: A geometric rendezvous-based tool for multiphysics data transfer
International Nuclear Information System (INIS)
Slattery, S. R.; Wilson, P. P. H.; Pawlowski, R. P.
2013-01-01
The Data Transfer Kit (DTK) is a software library designed to provide parallel data transfer services for arbitrary physics components based on the concept of geometric rendezvous. The rendezvous algorithm provides a means to geometrically correlate two geometric domains that may be arbitrarily decomposed in a parallel simulation. By repartitioning both domains such that they have the same geometric domain on each parallel process, efficient and load balanced search operations and data transfer can be performed at a desirable algorithmic time complexity with low communication overhead relative to other types of mapping algorithms. With the increased development efforts in multiphysics simulation and other multiple mesh and geometry problems, generating parallel topology maps for transferring fields and other data between geometric domains is a common operation. The algorithms used to generate parallel topology maps based on the concept of geometric rendezvous as implemented in DTK are described with an example using a conjugate heat transfer calculation and thermal coupling with a neutronics code. In addition, we provide the results of initial scaling studies performed on the Jaguar Cray XK6 system at Oak Ridge National Laboratory for a worse-case-scenario problem in terms of algorithmic complexity that shows good scaling on 0(1 x 104) cores for topology map generation and excellent scaling on 0(1 x 105) cores for the data transfer operation with meshes of O(1 x 109) elements. (authors)
The Data Transfer Kit: A geometric rendezvous-based tool for multiphysics data transfer
Energy Technology Data Exchange (ETDEWEB)
Slattery, S. R.; Wilson, P. P. H. [Department of Engineering Physics, University of Wisconsin - Madison, 1500 Engineering Dr., Madison, WI 53706 (United States); Pawlowski, R. P. [Sandia National Laboratories, P.O. Box 5800, Albuquerque, NM 87185 (United States)
2013-07-01
The Data Transfer Kit (DTK) is a software library designed to provide parallel data transfer services for arbitrary physics components based on the concept of geometric rendezvous. The rendezvous algorithm provides a means to geometrically correlate two geometric domains that may be arbitrarily decomposed in a parallel simulation. By repartitioning both domains such that they have the same geometric domain on each parallel process, efficient and load balanced search operations and data transfer can be performed at a desirable algorithmic time complexity with low communication overhead relative to other types of mapping algorithms. With the increased development efforts in multiphysics simulation and other multiple mesh and geometry problems, generating parallel topology maps for transferring fields and other data between geometric domains is a common operation. The algorithms used to generate parallel topology maps based on the concept of geometric rendezvous as implemented in DTK are described with an example using a conjugate heat transfer calculation and thermal coupling with a neutronics code. In addition, we provide the results of initial scaling studies performed on the Jaguar Cray XK6 system at Oak Ridge National Laboratory for a worse-case-scenario problem in terms of algorithmic complexity that shows good scaling on 0(1 x 104) cores for topology map generation and excellent scaling on 0(1 x 105) cores for the data transfer operation with meshes of O(1 x 109) elements. (authors)
International Nuclear Information System (INIS)
Xie Chuan-Mei; Xing Hang; Zhang Zhan-Jun; Liu Yi-Min
2015-01-01
Quantum correlations in a family of states comprising any mixture of a pair of arbitrary bi-qubit product pure states are studied by employing geometric discord [Phys. Rev. Lett. 105 (2010) 190502] as the quantifier. First, the inherent symmetry in the family of states about local unitary transformations is revealed. Then, the analytic expression of geometric discords in the states is worked out. Some concrete discussions and analyses on the captured geometric discords are made so that their distinct features are exposed. It is found that, the more averagely the two bi-qubit product states are mixed, the bigger geometric discord the mixed state owns. Moreover, the monotonic relationships of geometric discord with different parameters are revealed. (paper)
Zhang, Wei-Guo; Li, Zhe; Liu, Yong-Jun
2018-01-01
In this paper, we study the pricing problem of the continuously monitored fixed and floating strike geometric Asian power options in a mixed fractional Brownian motion environment. First, we derive both closed-form solutions and mixed fractional partial differential equations for fixed and floating strike geometric Asian power options based on delta-hedging strategy and partial differential equation method. Second, we present the lower and upper bounds of the prices of fixed and floating strike geometric Asian power options under the assumption that both risk-free interest rate and volatility are interval numbers. Finally, numerical studies are performed to illustrate the performance of our proposed pricing model.
Analysis of thin plates with holes by using exact geometrical representation within XFEM.
Perumal, Logah; Tso, C P; Leng, Lim Thong
2016-05-01
This paper presents analysis of thin plates with holes within the context of XFEM. New integration techniques are developed for exact geometrical representation of the holes. Numerical and exact integration techniques are presented, with some limitations for the exact integration technique. Simulation results show that the proposed techniques help to reduce the solution error, due to the exact geometrical representation of the holes and utilization of appropriate quadrature rules. Discussion on minimum order of integration order needed to achieve good accuracy and convergence for the techniques presented in this work is also included.
On the motion of matter in the geometrical gauge field theory
International Nuclear Information System (INIS)
Konopleva, N.P.
2005-01-01
In the geometrical gauge field theory, the motion equations of matter (elementary particles) are connected with the field equations. The problems arising from this connection are discussed. For the first time, such problems arose in Einstein's General Relativity. Einstein hoped that solution of these problems will allow explanation of elementary particles nature without making use of quantum mechanics. But, as it turned out, the situation is more difficult. Here the corresponding problems are formulated for the connection of equations of particle motion and field equations in the geometrical gauge field theory. It is shown that appearance of the problems under discussion is an inevitable effect of passage to relativism and local symmetries
A Geometrical Framework for Covariance Matrices of Continuous and Categorical Variables
Vernizzi, Graziano; Nakai, Miki
2015-01-01
It is well known that a categorical random variable can be represented geometrically by a simplex. Accordingly, several measures of association between categorical variables have been proposed and discussed in the literature. Moreover, the standard definitions of covariance and correlation coefficient for continuous random variables have been…
Volume-based geometric modeling for radiation transport calculations
International Nuclear Information System (INIS)
Li, Z.; Williamson, J.F.
1992-01-01
Accurate theoretical characterization of radiation fields is a valuable tool in the design of complex systems, such as linac heads and intracavitary applicators, and for generation of basic dose calculation data that is inaccessible to experimental measurement. Both Monte Carlo and deterministic solutions to such problems require a system for accurately modeling complex 3-D geometries that supports ray tracing, point and segment classification, and 2-D graphical representation. Previous combinatorial approaches to solid modeling, which involve describing complex structures as set-theoretic combinations of simple objects, are limited in their ease of use and place unrealistic constraints on the geometric relations between objects such as excluding common boundaries. A new approach to volume-based solid modeling has been developed which is based upon topologically consistent definitions of boundary, interior, and exterior of a region. From these definitions, FORTRAN union, intersection, and difference routines have been developed that allow involuted and deeply nested structures to be described as set-theoretic combinations of ellipsoids, elliptic cylinders, prisms, cones, and planes that accommodate shared boundaries. Line segments between adjacent intersections on a trajectory are assigned to the appropriate region by a novel sorting algorithm that generalizes upon Siddon's approach. Two 2-D graphic display tools are developed to help the debugging of a given geometric model. In this paper, the mathematical basis of our system is described, it is contrasted to other approaches, and examples are discussed
Determination of Geometric Parameters of Space Steel Constructions
Directory of Open Access Journals (Sweden)
Jitka Suchá
2005-06-01
Full Text Available The paper contains conclusions of the PhD thesis „Accuracy of determination of geometric parameters of space steel construction using geodetic methods“. Generally it is a difficult task with high requirements for the accuracy and reliability of results, i.e. space coordinates of assessed points on a steel construction. A solution of this task is complicated by the effects of atmospheric influences to begin with the temperature, which strongly affects steel constructions. It is desirable to eliminate the influence of the temperature for the evaluation of the geometric parameters. A choice of an efficient geodetic method, which fulfils demanding requirements, is often affected with a constrained place in an immediate neighbourhood of the measured construction. These conditions disable the choice of efficient points configuration of a geodetic micro network, e.g. the for forward intersection. In addition, points of a construction are often hardly accessible and therefore marking is difficult. The space polar method appears efficient owing to the mentioned reasons and its advantages were increased with the implementation of self-adhesive reflex targets for the distance measurement which enable the ermanent marking of measured points already in the course of placing the construction.
Weighted Geometric Dilution of Precision Calculations with Matrix Multiplication
Directory of Open Access Journals (Sweden)
Chien-Sheng Chen
2015-01-01
Full Text Available To enhance the performance of location estimation in wireless positioning systems, the geometric dilution of precision (GDOP is widely used as a criterion for selecting measurement units. Since GDOP represents the geometric effect on the relationship between measurement error and positioning determination error, the smallest GDOP of the measurement unit subset is usually chosen for positioning. The conventional GDOP calculation using matrix inversion method requires many operations. Because more and more measurement units can be chosen nowadays, an efficient calculation should be designed to decrease the complexity. Since the performance of each measurement unit is different, the weighted GDOP (WGDOP, instead of GDOP, is used to select the measurement units to improve the accuracy of location. To calculate WGDOP effectively and efficiently, the closed-form solution for WGDOP calculation is proposed when more than four measurements are available. In this paper, an efficient WGDOP calculation method applying matrix multiplication that is easy for hardware implementation is proposed. In addition, the proposed method can be used when more than exactly four measurements are available. Even when using all-in-view method for positioning, the proposed method still can reduce the computational overhead. The proposed WGDOP methods with less computation are compatible with global positioning system (GPS, wireless sensor networks (WSN and cellular communication systems.
Geometric supergravity in D = 11 and its hidden supergroup
International Nuclear Information System (INIS)
D'Auria, R.; Fre, P.
1982-01-01
In this paper we address two questions: the geometrical formulation of D=11 supergravity and the derivation of the super Lie algebra it is based on. The solutions of the two problems are intimately related and are obtained via the introduction of the new concept of a Cartan integrable system described in this paper. The previously developed group manifold framework can be naturally extended to a Cartan integrable system manifold approach. Within this scheme we obtain a geometric action for D=11 supergravity based on a suitable Cartan system. This latter turns out to be compact description of a two-element class of supergroups containing besides Lorentz Jsub(ab), translation Psub(a) and ordinary supersymmetry Q, the following extra generators: two- and five-index skew-symmetric tensors Zsub(a1a2)Zsub(a1...a5) and a further spinorial charge Q'. Q' commutes with itself and everyhting else except Jsub(ab). It appears in the commutators of Q with Psub(a),Zsub(a1a2),Zsub(a1...a5). (orig.)
Polarimetry as a tool for the study of solutions of chiral solutes.
Orlova, Anna V; Andrade, Renato R; da Silva, Clarissa O; Zinin, Alexander I; Kononov, Leonid O
2014-01-13
Optical rotation of aqueous solutions of D-levoglucosan was studied experimentally in the 0.03-4.0 mol L(-1) concentration range and a nonlinear concentration dependence of specific optical rotation (SR) was revealed. Discontinuities observed in the concentration plot of SR (at 0.1, 0.3, 0.5, 1.0, and 2.0 mol L(-1)) are well correlated with those found by static and dynamic light scattering and identify concentration ranges in which different solution domains (supramers) may exist. The average SR experimental value for a D-levoglucosan aqueous solution ([α]D(28) -58.5±8.7 deg dm(-1) cm(-3) g(-1)) was found to be in good agreement with values obtained by theoretical calculation (TD-DFT/GIAO) of SR for 15 different conformers revealed by conformational sampling at the PCM/B3LYP/6-311++G(2d,2p)//B3LYP/6-31+G(d,p) level, which were shown to be strongly affected by the solvation microenvironment (0, 1, 2, and 3 explicit solvent molecules considered) due to local geometrical changes induced in the solute molecule. This exceptionally high sensitivity of SR makes polarimetry a unique method capable of sensing changes in the structure of supramers detected in this study. Copyright © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
PERFORMANCE ASSESSMENT AND GEOMETRIC CALIBRATION OF RESOURCESAT-2
Directory of Open Access Journals (Sweden)
P. V. Radhadevi
2016-06-01
Full Text Available Resourcesat-2 (RS-2 has successfully completed five years of operations in its orbit. This satellite has multi-resolution and multi-spectral capabilities in a single platform. A continuous and autonomous co-registration, geo-location and radiometric calibration of image data from different sensors with widely varying view angles and resolution was one of the challenges of RS-2 data processing. On-orbit geometric performance of RS-2 sensors has been widely assessed and calibrated during the initial phase operations. Since then, as an ongoing activity, various geometric performance data are being generated periodically. This is performed with sites of dense ground control points (GCPs. These parameters are correlated to the direct geo-location accuracy of the RS-2 sensors and are monitored and validated to maintain the performance. This paper brings out the geometric accuracy assessment, calibration and validation done for about 500 datasets of RS-2. The objectives of this study are to ensure the best absolute and relative location accuracy of different cameras, location performance with payload steering and co-registration of multiple bands. This is done using a viewing geometry model, given ephemeris and attitude data, precise camera geometry and datum transformation. In the model, the forward and reverse transformations between the coordinate systems associated with the focal plane, payload, body, orbit and ground are rigorously and explicitly defined. System level tests using comparisons to ground check points have validated the operational geo-location accuracy performance and the stability of the calibration parameters.
Power Series Solution to the Pendulum Equation
Benacka, Jan
2009-01-01
This note gives a power series solution to the pendulum equation that enables to investigate the system in an analytical way only, i.e. to avoid numeric methods. A method of determining the number of the terms for getting a required relative error is presented that uses bigger and lesser geometric series. The solution is suitable for modelling the…
Exact solutions in three-dimensional gravity
Garcia-Diaz, Alberto A
2017-01-01
A self-contained text, systematically presenting the determination and classification of exact solutions in three-dimensional Einstein gravity. This book explores the theoretical framework and general physical and geometrical characteristics of each class of solutions, and includes information on the researchers responsible for their discovery. Beginning with the physical character of the solutions, these are identified and ordered on the basis of their geometrical invariant properties, symmetries, and algebraic classifications, or from the standpoint of their physical nature, for example electrodynamic fields, fluid, scalar field, or dilaton. Consequently, this text serves as a thorough catalogue on 2+1 exact solutions to the Einstein equations coupled to matter and fields, and on vacuum solutions of topologically massive gravity with a cosmological constant. The solutions are also examined from different perspectives, enabling a conceptual bridge between exact solutions of three- and four-dimensional gravit...
Geometrical Effects on Nonlinear Electrodiffusion in Cell Physiology
Cartailler, J.; Schuss, Z.; Holcman, D.
2017-12-01
We report here new electrical laws, derived from nonlinear electrodiffusion theory, about the effect of the local geometrical structure, such as curvature, on the electrical properties of a cell. We adopt the Poisson-Nernst-Planck equations for charge concentration and electric potential as a model of electrodiffusion. In the case at hand, the entire boundary is impermeable to ions and the electric field satisfies the compatibility condition of Poisson's equation. We construct an asymptotic approximation for certain singular limits to the steady-state solution in a ball with an attached cusp-shaped funnel on its surface. As the number of charge increases, they concentrate at the end of cusp-shaped funnel. These results can be used in the design of nanopipettes and help to understand the local voltage changes inside dendrites and axons with heterogeneous local geometry.
A geometric feature of the Newton law of gravitation
Directory of Open Access Journals (Sweden)
Zhang Meirong
2017-06-01
Full Text Available In the Newton law of gravitation, the most miraculous fact is that the gravity is reciprocally proportional to the square of the distance between particles. In this paper, by assuming that the gravity is along with the line passing through particles and is proportional to the product of masses of particles, we will show that the above fact is equivalent to the geometric requirement that the gravity between two homogeneous balls is equal to that between two particles of the same masses located at the centers of balls. In fact, this will lead to a second-order Euler equation whose physical solution is reciprocally proportional to the square of the distance.
Accretion disc boundary layers - geometrically and optically thin case
International Nuclear Information System (INIS)
Regev, Oded; Hougerat, A.A.
1988-01-01
The method of matched asymptotic expansions is applied to an optically and geometrically thin boundary layer between an accretion disc and the accreting star. Analytical solutions are presented for a particular viscosity prescription in the boundary layer. For a typical example we find that the disc closely resembles standard steady-disc theory. It is identical to it everywhere save a narrow boundary layer, where the temperature increases rapidly inward (by an order of magnitude), the angular velocity achieves maximum and decreases to its surface value and other variables also undergo rapid changes. This and previous work can now be used to calculate the emission from accretion discs including the boundary layers for a wide range of parameters. (author)
Geometric and computer-aided spline hob modeling
Brailov, I. G.; Myasoedova, T. M.; Panchuk, K. L.; Krysova, I. V.; Rogoza, YU A.
2018-03-01
The paper considers acquiring the spline hob geometric model. The objective of the research is the development of a mathematical model of spline hob for spline shaft machining. The structure of the spline hob is described taking into consideration the motion in parameters of the machine tool system of cutting edge positioning and orientation. Computer-aided study is performed with the use of CAD and on the basis of 3D modeling methods. Vector representation of cutting edge geometry is accepted as the principal method of spline hob mathematical model development. The paper defines the correlations described by parametric vector functions representing helical cutting edges designed for spline shaft machining with consideration for helical movement in two dimensions. An application for acquiring the 3D model of spline hob is developed on the basis of AutoLISP for AutoCAD environment. The application presents the opportunity for the use of the acquired model for milling process imitation. An example of evaluation, analytical representation and computer modeling of the proposed geometrical model is reviewed. In the mentioned example, a calculation of key spline hob parameters assuring the capability of hobbing a spline shaft of standard design is performed. The polygonal and solid spline hob 3D models are acquired by the use of imitational computer modeling.
An analysis of Landsat-4 Thematic Mapper geometric properties
Walker, R. E.; Zobrist, A. L.; Bryant, N. A.; Gohkman, B.; Friedman, S. Z.; Logan, T. L.
1984-01-01
Landsat-4 Thematic Mapper data of Washington, DC, Harrisburg, PA, and Salton Sea, CA were analyzed to determine geometric integrity and conformity of the data to known earth surface geometry. Several tests were performed. Intraband correlation and interband registration were investigated. No problems were observed in the intraband analysis, and aside from indications of slight misregistration between bands of the primary versus bands of the secondary focal planes, interband registration was well within the specified tolerances. A substantial number of ground control points were found and used to check the images' conformity to the Space Oblique Mercator (SOM) projection of their respective areas. The means of the residual offsets, which included nonprocessing related measurement errors, were close to the one pixel level in the two scenes examined. The Harrisburg scene residual mean was 28.38 m (0.95 pixels) with a standard deviation of 19.82 m (0.66 pixels), while the mean and standard deviation for the Salton Sea scene were 40.46 (1.35 pixels) and 30.57 m (1.02 pixels), respectively. Overall, the data were judged to be a high geometric quality with errors close to those targeted by the TM sensor design specifications.
Geometric representation of fundamental particles' inertial mass
Energy Technology Data Exchange (ETDEWEB)
Schachter, L. [Technion-Israel Inst. of Tech., Haifa (Israel); Spencer, James [SLAC National Accelerator Lab., Menlo Park, CA (United States)
2015-07-22
A geometric representation of the (N = 279) masses of quarks, leptons, hadrons and gauge bosons was introduced by employing a Riemann Sphere facilitating the interpretation of the N masses in terms of a single particle, the Masson, which might be in one of the N eigen-states. Geometrically, its mass is the radius of the Riemann Sphere. Dynamically, its derived mass is near the mass of the nucleon regardless of whether it is determined from all N particles of only the hadrons, the mesons or the baryons separately. Ignoring all the other properties of these particles, it is shown that the eigen-values, the polar representation θ_{ν} of the masses on the Sphere, satisfy the symmetry θ_{ν} + θ_{N+1-ν} = π within less than 1% relative error. In addition, these pair correlations include the pairs θ_{γ} + θ_{top} ≃ π and θ_{gluon} + θ_{H} ≃ π as well as pairing the weak gauge bosons with the three neutrinos.
Multipartite entanglement in fermionic systems via a geometric measure
International Nuclear Information System (INIS)
Lari, Behzad; Durganandini, P.; Joag, Pramod S.
2010-01-01
We study multipartite entanglement in a system consisting of indistinguishable fermions. Specifically, we have proposed a geometric entanglement measure for N spin-(1/2) fermions distributed over 2L modes (single-particle states). The measure is defined on the 2L qubit space isomorphic to the Fock space for 2L single-particle states. This entanglement measure is defined for a given partition of 2L modes containing m≥2 subsets. Thus this measure applies to m≤2L partite fermionic systems where L is any finite number, giving the number of sites. The Hilbert spaces associated with these subsets may have different dimensions. Further, we have defined the local quantum operations with respect to a given partition of modes. This definition is generic and unifies different ways of dividing a fermionic system into subsystems. We have shown, using a representative case, that the geometric measure is invariant under local unitary operators corresponding to a given partition. We explicitly demonstrate the use of the measure to calculate multipartite entanglement in some correlated electron systems.
Geometrical and topological formulation of local gauge and supergauge theories
International Nuclear Information System (INIS)
Macrae, K.I.
1976-01-01
A geometrical and topological formulation of local gauge and supergauge invariance is presented. Analysis of experiments of the type described by Bohm and Aharanov and in the attempt to understand immersed submanifolds such as the string with internal symmetry, in a geometric setting, are led to the introduction of fiber bundles, superspaces. Many exact classical solutions to the equations of motion were considered for these gauge theories with specific choices of gauge group such as SU 4 . We describe some exact soliton solutions to these theories which have linear Regge trajectories, i.e., their angular momentum is a linear function of their mass squared. Next one discusses the actions and equations of motion for gauge theories whose base manifolds can have arbitrarily dimensioned submanifolds excised from them, manifolds with holes were discussed. These holes can have fractional quark charges when the structure group is, for example, SU 3 or SU 4 . By extending the concept of conservation of energy to include the excised submanifolds, their actions, and their equations of motion were derived showing that they can act as charged particles. Using the fractionality of the quark charges, are led to suggest a topological confinement mechanism for these particles. One also derives the actions and equations of motion for the string from this viewpoint. Some new Lie algebras which have anticommuting elements are introduced. Their gauge theories are described, and the possibility of fermionic actions for the anticommuting pieces is examined. Supersymmetric strings and their supergauge transformations were discussed and an extension was suggested of supersymmetry to immersed minimal submanifolds other than the string. Both quarklike and vectorlike fermions are included. Finally the invariance of both the equations of motion and the gauge conditions under supersymmetry transformations for these submanifolds were described
Optimal control for mathematical models of cancer therapies an application of geometric methods
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.
Optical rectification using geometrical field enhancement in gold nano-arrays
Piltan, S.; Sievenpiper, D.
2017-11-01
Conversion of photons to electrical energy has a wide variety of applications including imaging, solar energy harvesting, and IR detection. A rectenna device consists of an antenna in addition to a rectifying element to absorb the incident radiation within a certain frequency range. We designed, fabricated, and measured an optical rectifier taking advantage of asymmetrical field enhancement for forward and reverse currents due to geometrical constraints. The gold nano-structures as well as the geometrical parameters offer enhanced light-matter interaction at 382 THz. Using the Taylor expansion of the time-dependent current as a function of the external bias and oscillating optical excitation, we obtained responsivities close to quantum limit of operation. This geometrical approach can offer an efficient, broadband, and scalable solution for energy conversion and detection in the future.
The study on the import of the geometric body by GDML in GEANT4
International Nuclear Information System (INIS)
Sun Baodong; Liu Huilan; Sun Dawang; Xie Zhaoyang; Song Yushou
2014-01-01
Geometry Description Markup Language (GDML) can be used as an application interface program to import the geometric body into GEANT4. It greatly simplifies the detector construction work with high reliability. With this mechanism the geometric data of a detector is described in an XML file and read by the XML parser embedded in GEANT4. The geometric structure of a detector is designed in CAD toolkit Solidworks and saved as a standard STEP file. Then, by FastRad the STEP file is transformed into XML script, which is readable for GEANT4. In comparison with the detectors constructed by Constructed Solid Geometry (CSG) provided by GEANT4, those imported by GDML also satisfies the requests of general simulation application. At the same time, some solutions and tips for several common problems during the progress constructing the detectors by GDML are given. (authors)
Geometric description of images as topographic maps
Caselles, Vicent
2010-01-01
This volume discusses the basic geometric contents of an image and presents a tree data structure to handle those contents efficiently. The nodes of the tree are derived from connected components of level sets of the intensity, while the edges represent inclusion information. Grain filters, morphological operators simplifying these geometric contents, are analyzed and several applications to image comparison and registration, and to edge and corner detection, are presented. The mathematically inclined reader may be most interested in Chapters 2 to 6, which generalize the topological Morse description to continuous or semicontinuous functions, while mathematical morphologists may more closely consider grain filters in Chapter 3. Computer scientists will find algorithmic considerations in Chapters 6 and 7, the full justification of which may be found in Chapters 2 and 4 respectively. Lastly, all readers can learn more about the motivation for this work in the image processing applications presented in Chapter 8...
Towards a theory of geometric graphs
Pach, Janos
2004-01-01
The early development of graph theory was heavily motivated and influenced by topological and geometric themes, such as the Konigsberg Bridge Problem, Euler's Polyhedral Formula, or Kuratowski's characterization of planar graphs. In 1936, when Denes Konig published his classical Theory of Finite and Infinite Graphs, the first book ever written on the subject, he stressed this connection by adding the subtitle Combinatorial Topology of Systems of Segments. He wanted to emphasize that the subject of his investigations was very concrete: planar figures consisting of points connected by straight-line segments. However, in the second half of the twentieth century, graph theoretical research took an interesting turn. In the most popular and most rapidly growing areas (the theory of random graphs, Ramsey theory, extremal graph theory, algebraic graph theory, etc.), graphs were considered as abstract binary relations rather than geometric objects. Many of the powerful techniques developed in these fields have been su...
Plasmon Geometric Phase and Plasmon Hall Shift
Shi, Li-kun; Song, Justin C. W.
2018-04-01
The collective plasmonic modes of a metal comprise a simple pattern of oscillating charge density that yields enhanced light-matter interaction. Here we unveil that beneath this familiar facade plasmons possess a hidden internal structure that fundamentally alters its dynamics. In particular, we find that metals with nonzero Hall conductivity host plasmons with an intricate current density configuration that sharply departs from that of ordinary zero Hall conductivity metals. This nontrivial internal structure dramatically enriches the dynamics of plasmon propagation, enabling plasmon wave packets to acquire geometric phases as they scatter. At boundaries, these phases accumulate allowing plasmon waves that reflect off to experience a nonreciprocal parallel shift. This plasmon Hall shift, tunable by Hall conductivity as well as plasmon wavelength, displaces the incident and reflected plasmon trajectories and can be readily probed by near-field photonics techniques. Anomalous plasmon geometric phases dramatically enrich the nanophotonics toolbox, and yield radical new means for directing plasmonic beams.
Geometric mechanics of periodic pleated origami.
Wei, Z Y; Guo, Z V; Dudte, L; Liang, H Y; Mahadevan, L
2013-05-24
Origami structures are mechanical metamaterials with properties that arise almost exclusively from the geometry of the constituent folds and the constraint of piecewise isometric deformations. Here we characterize the geometry and planar and nonplanar effective elastic response of a simple periodically folded Miura-ori structure, which is composed of identical unit cells of mountain and valley folds with four-coordinated ridges, defined completely by two angles and two lengths. We show that the in-plane and out-of-plane Poisson's ratios are equal in magnitude, but opposite in sign, independent of material properties. Furthermore, we show that effective bending stiffness of the unit cell is singular, allowing us to characterize the two-dimensional deformation of a plate in terms of a one-dimensional theory. Finally, we solve the inverse design problem of determining the geometric parameters for the optimal geometric and mechanical response of these extreme structures.
Manfredini, Maria; Morbidelli, Daniele; Polidoro, Sergio; Uguzzoni, Francesco
2015-01-01
The analysis of PDEs is a prominent discipline in mathematics research, both in terms of its theoretical aspects and its relevance in applications. In recent years, the geometric properties of linear and nonlinear second order PDEs of elliptic and parabolic type have been extensively studied by many outstanding researchers. This book collects contributions from a selected group of leading experts who took part in the INdAM meeting "Geometric methods in PDEs", on the occasion of the 70th birthday of Ermanno Lanconelli. They describe a number of new achievements and/or the state of the art in their discipline of research, providing readers an overview of recent progress and future research trends in PDEs. In particular, the volume collects significant results for sub-elliptic equations, potential theory and diffusion equations, with an emphasis on comparing different methodologies and on their implications for theory and applications. .
A Practical Guide to Experimental Geometrical Optics
Garbovskiy, Yuriy A.; Glushchenko, Anatoliy V.
2017-12-01
Preface; 1. Markets of optical materials, components, accessories, light sources and detectors; 2. Introduction to optical experiments: light producing, light managing, light detection and measuring; 3. Light detectors based on semiconductors: photoresistors, photodiodes in a photo-galvanic regime. Principles of operation and measurements; 4. Linear light detectors based on photodiodes; 5. Basic laws of geometrical optics: experimental verification; 6. Converging and diverging thin lenses; 7. Thick lenses; 8. Lens systems; 9. Simple optical instruments I: the eye and the magnifier, eyepieces and telescopes; 10. Simple optical instruments II: light illuminators and microscope; 11. Spherical mirrors; 12. Introduction to optical aberrations; 13. Elements of optical radiometry; 14. Cylindrical lenses and vials; 15. Methods of geometrical optics to measure refractive index; 16. Dispersion of light and prism spectroscope; 17. Elements of computer aided optical design; Index.
Coated sphere scattering by geometric optics approximation.
Mengran, Zhai; Qieni, Lü; Hongxia, Zhang; Yinxin, Zhang
2014-10-01
A new geometric optics model has been developed for the calculation of light scattering by a coated sphere, and the analytic expression for scattering is presented according to whether rays hit the core or not. The ray of various geometric optics approximation (GOA) terms is parameterized by the number of reflections in the coating/core interface, the coating/medium interface, and the number of chords in the core, with the degeneracy path and repeated path terms considered for the rays striking the core, which simplifies the calculation. For the ray missing the core, the various GOA terms are dealt with by a homogeneous sphere. The scattering intensity of coated particles are calculated and then compared with those of Debye series and Aden-Kerker theory. The consistency of the results proves the validity of the method proposed in this work.
The geometric Hopf invariant and surgery theory
Crabb, Michael
2017-01-01
Written by leading experts in the field, this monograph provides homotopy theoretic foundations for surgery theory on higher-dimensional manifolds. Presenting classical ideas in a modern framework, the authors carefully highlight how their results relate to (and generalize) existing results in the literature. The central result of the book expresses algebraic surgery theory in terms of the geometric Hopf invariant, a construction in stable homotopy theory which captures the double points of immersions. Many illustrative examples and applications of the abstract results are included in the book, making it of wide interest to topologists. Serving as a valuable reference, this work is aimed at graduate students and researchers interested in understanding how the algebraic and geometric topology fit together in the surgery theory of manifolds. It is the only book providing such a wide-ranging historical approach to the Hopf invariant, double points and surgery theory, with many results old and new. .
Geometric modeling in probability and statistics
Calin, Ovidiu
2014-01-01
This book covers topics of Informational Geometry, a field which deals with the differential geometric study of the manifold probability density functions. This is a field that is increasingly attracting the interest of researchers from many different areas of science, including mathematics, statistics, geometry, computer science, signal processing, physics and neuroscience. It is the authors’ hope that the present book will be a valuable reference for researchers and graduate students in one of the aforementioned fields. This textbook is a unified presentation of differential geometry and probability theory, and constitutes a text for a course directed at graduate or advanced undergraduate students interested in applications of differential geometry in probability and statistics. The book contains over 100 proposed exercises meant to help students deepen their understanding, and it is accompanied by software that is able to provide numerical computations of several information geometric objects. The reader...
Geometrical dynamics of Born-Infeld objects
Energy Technology Data Exchange (ETDEWEB)
Cordero, Ruben [Departamento de Fisica, Escuela Superior de Fisica y Matematicas del I.P.N., Unidad Adolfo Lopez Mateos, Edificio 9, 07738 Mexico, D.F. (Mexico); Molgado, Alberto [Facultad de Ciencias, Universidad de Colima, Bernal DIaz del Castillo 340, Col. Villas San Sebastian, Colima (Mexico); Rojas, Efrain [Facultad de Fisica e Inteligencia Artificial, Universidad Veracruzana, 91000 Xalapa, Veracruz (Mexico)
2007-03-21
We present a geometrically inspired study of the dynamics of Dp-branes. We focus on the usual non-polynomial Dirac-Born-Infeld action for the worldvolume swept out by the brane in its evolution in general background spacetimes. We emphasize the form of the resulting equations of motion which are quite simple and resemble Newton's second law, complemented with a conservation law for a worldvolume bicurrent. We take a closer look at the classical Hamiltonian analysis which is supported by the ADM framework of general relativity. The constraints and their algebra are identified as well as the geometrical role they play in phase space. In order to illustrate our results, we review the dynamics of a D1-brane immersed in a AdS{sub 3} x S{sup 3} background spacetime. We exhibit the mechanical properties of Born-Infeld objects paving the way to a consistent quantum formulation.
Geometrical dynamics of Born-Infeld objects
International Nuclear Information System (INIS)
Cordero, Ruben; Molgado, Alberto; Rojas, Efrain
2007-01-01
We present a geometrically inspired study of the dynamics of Dp-branes. We focus on the usual non-polynomial Dirac-Born-Infeld action for the worldvolume swept out by the brane in its evolution in general background spacetimes. We emphasize the form of the resulting equations of motion which are quite simple and resemble Newton's second law, complemented with a conservation law for a worldvolume bicurrent. We take a closer look at the classical Hamiltonian analysis which is supported by the ADM framework of general relativity. The constraints and their algebra are identified as well as the geometrical role they play in phase space. In order to illustrate our results, we review the dynamics of a D1-brane immersed in a AdS 3 x S 3 background spacetime. We exhibit the mechanical properties of Born-Infeld objects paving the way to a consistent quantum formulation
A practical guide to experimental geometrical optics
Garbovskiy, Yuriy A
2017-01-01
A concise, yet deep introduction to experimental, geometrical optics, this book begins with fundamental concepts and then develops the practical skills and research techniques routinely used in modern laboratories. Suitable for students, researchers and optical engineers, this accessible text teaches readers how to build their own optical laboratory and to design and perform optical experiments. It uses a hands-on approach which fills a gap between theory-based textbooks and laboratory manuals, allowing the reader to develop their practical skills in this interdisciplinary field, and also explores the ways in which this knowledge can be applied to the design and production of commercial optical devices. Including supplementary online resources to help readers track and evaluate their experimental results, this text is the ideal companion for anyone with a practical interest in experimental geometrical optics.
A simple geometrical approach to particle production in collisions with nuclei
International Nuclear Information System (INIS)
Dias de Deus, J.
1975-11-01
It is argued that hadron collisions with nuclei are similar to hadron-hadron collisions, having similar properties for the impact parameter distributions and the leading particle spectra. The relevant existing high energy data, including the universality of multiplicity distributions and the possibility of geometrical scaling in reactions with nuclei, are easily understood in the framework of geometrical models by extending to p-nucleus collisions what was learnt about impact parameter and leading particles in p-p collisions. The question of forward-backward correlations and photo and electroproduction are briefly discussed. (author)
Fast decoding algorithms for geometric coded apertures
International Nuclear Information System (INIS)
Byard, Kevin
2015-01-01
Fast decoding algorithms are described for the class of coded aperture designs known as geometric coded apertures which were introduced by Gourlay and Stephen. When compared to the direct decoding method, the algorithms significantly reduce the number of calculations required when performing the decoding for these apertures and hence speed up the decoding process. Experimental tests confirm the efficacy of these fast algorithms, demonstrating a speed up of approximately two to three orders of magnitude over direct decoding.
Geometric measure theory a beginner's guide
Morgan, Frank
1995-01-01
Geometric measure theory is the mathematical framework for the study of crystal growth, clusters of soap bubbles, and similar structures involving minimization of energy. Morgan emphasizes geometry over proofs and technicalities, and includes a bibliography and abundant illustrations and examples. This Second Edition features a new chapter on soap bubbles as well as updated sections addressing volume constraints, surfaces in manifolds, free boundaries, and Besicovitch constant results. The text will introduce newcomers to the field and appeal to mathematicians working in the field.
Geometrical Aspects of non-gravitational interactions
Roldan, Omar; Barros Jr, C. C.
2016-01-01
In this work we look for a geometric description of non-gravitational forces. The basic ideas are proposed studying the interaction between a punctual particle and an electromagnetic external field. For this purpose, we introduce the concept of proper space-time, that allow us to describe this interaction in a way analogous to the one that the general relativity theory does for gravitation. The field equations that define this geometry are similar to the Einstein's equations, where in general...
Chirality: a relational geometric-physical property.
Gerlach, Hans
2013-11-01
The definition of the term chirality by Lord Kelvin in 1893 and 1904 is analyzed by taking crystallography at that time into account. This shows clearly that chirality is a relational geometric-physical property, i.e., two relations between isometric objects are possible: homochiral or heterochiral. In scientific articles the relational term chirality is often mistaken for the two valued measure for the individual (absolute) sense of chirality, an arbitrary attributive term. © 2013 Wiley Periodicals, Inc.
Geometric (Berry) phases in neutron molecular spectroscopy
International Nuclear Information System (INIS)
Lovesey, S.W.
1992-02-01
A theory of neutron scattering by nuclei in a molecule, accompanied by an electronic transition, is formulated with attention to gauge potentials and geometric phases in the Born-Oppenheimer scheme. Non-degenerate and nearly degenerate electronic levels are considered. For nearly degenerate levels it is shown that, the cross-section is free of the singular structure which characterizes the corresponding gauge potential for the phase, and much larger than for well separated electronic states. (author)
Geometric continuum regularization of quantum field theory
International Nuclear Information System (INIS)
Halpern, M.B.
1989-01-01
An overview of the continuum regularization program is given. The program is traced from its roots in stochastic quantization, with emphasis on the examples of regularized gauge theory, the regularized general nonlinear sigma model and regularized quantum gravity. In its coordinate-invariant form, the regularization is seen as entirely geometric: only the supermetric on field deformations is regularized, and the prescription provides universal nonperturbative invariant continuum regularization across all quantum field theory. 54 refs
Graph Treewidth and Geometric Thickness Parameters
Dujmović, Vida; Wood, David R.
2005-01-01
Consider a drawing of a graph $G$ in the plane such that crossing edges are coloured differently. The minimum number of colours, taken over all drawings of $G$, is the classical graph parameter "thickness". By restricting the edges to be straight, we obtain the "geometric thickness". By further restricting the vertices to be in convex position, we obtain the "book thickness". This paper studies the relationship between these parameters and treewidth. Our first main result states that for grap...
Geometric morphometric footprint analysis of young women
Domjanic, Jacqueline; Fieder, Martin; Seidler, Horst; Mitteroecker, Philipp
2013-01-01
Background Most published attempts to quantify footprint shape are based on a small number of measurements. We applied geometric morphometric methods to study shape variation of the complete footprint outline in a sample of 83 adult women. Methods The outline of the footprint, including the toes, was represented by a comprehensive set of 85 landmarks and semilandmarks. Shape coordinates were computed by Generalized Procrustes Analysis. Results The first four principal components represented t...
Geometrical characterization of micro end milling tools
DEFF Research Database (Denmark)
Borsetto, Francesca; Bariani, Paolo; Bissacco, Giuliano
2005-01-01
Performance of the milling process is directly affected by the accuracy of tool geometry. Development of methods suitable for dimensional characterization of such tools, with low measurement uncertainties is therefore of relevance. The present article focuses on the geometrical characterization...... of a flat micro end milling tool with a nominal mill diameter of 200 microns. An experimental investigation was carried out involving two different non-contact systems...
Geometric Measure Theory and Minimal Surfaces
Bombieri, Enrico
2011-01-01
W.K. ALLARD: On the first variation of area and generalized mean curvature.- F.J. ALMGREN Jr.: Geometric measure theory and elliptic variational problems.- E. GIUSTI: Minimal surfaces with obstacles.- J. GUCKENHEIMER: Singularities in soap-bubble-like and soap-film-like surfaces.- D. KINDERLEHRER: The analyticity of the coincidence set in variational inequalities.- M. MIRANDA: Boundaries of Caciopoli sets in the calculus of variations.- L. PICCININI: De Giorgi's measure and thin obstacles.
Nociones de geometría vectorial
Ospina Arteaga, Omar Evelio
1990-01-01
Las presentes notas de geometría vectorial pretenden ser una ayuda para los estudiantes que se inician en el tema de vectores y deberá ser complementado con ejercicios sobre el tema. Este texto contiene temas de interés tales como: Espacios euclidianos, Distancian entre dos puntos, Concepto de vector, Igualdad de vectores, entre otros relacionados con el estudio de vectores.
Geometrical Determinants of Neuronal Actin Waves
Tomba, Caterina; Bra?ni, C?line; Bugnicourt, Ghislain; Cohen, Floriane; Friedrich, Benjamin M.; Gov, Nir S.; Villard, Catherine
2017-01-01
Hippocampal neurons produce in their early stages of growth propagative, actin-rich dynamical structures called actin waves. The directional motion of actin waves from the soma to the tip of neuronal extensions has been associated with net forward growth, and ultimately with the specification of neurites into axon and dendrites. Here, geometrical cues are used to control actin wave dynamics by constraining neurons on adhesive stripes of various widths. A key observable, the average time betwe...
Multiphase flow in geometrically simple fracture intersections
Basagaoglu, H.; Meakin, P.; Green, C.T.; Mathew, M.; ,
2006-01-01
A two-dimensional lattice Boltzmann (LB) model with fluid-fluid and solid-fluid interaction potentials was used to study gravity-driven flow in geometrically simple fracture intersections. Simulated scenarios included fluid dripping from a fracture aperture, two-phase flow through intersecting fractures and thin-film flow on smooth and undulating solid surfaces. Qualitative comparisons with recently published experimental findings indicate that for these scenarios the LB model captured the underlying physics reasonably well.
The Geometric Nonlinear Generalized Brazier Effect
DEFF Research Database (Denmark)
Nikolajsen, Jan Ánike; Lauridsen, Peter Riddersholm; Damkilde, Lars
2016-01-01
that the generalized Brazier effect is a local effect not influencing the overall mechanical behavior of the structure significantly. The offset is a nonlinear geometric beam-type Finite Element calculation, which takes into account the large displacements and rotations. The beam-type model defines the stresses which...... mainly are in the direction of the beam axis. The generalized Brazier effect is calculated as a linear load case based on these stresses....
Time as a geometric property of space
Directory of Open Access Journals (Sweden)
James Michael Chappell
2016-11-01
Full Text Available The proper description of time remains a key unsolved problem in science. Newton conceived of time as absolute and universal which it `flows equably without relation to anything external'}. In the nineteenth century, the four-dimensional algebraic structure of the quaternions developed by Hamilton, inspired him to suggest that they could provide a unified representation of space and time. With the publishing of Einstein's theory of special relativity these ideas then lead to the generally accepted Minkowski spacetime formulation in 1908. Minkowski, though, rejected the formalism of quaternions suggested by Hamilton and adopted rather an approach using four-vectors. The Minkowski framework is indeed found to provide a versatile formalism for describing the relationship between space and time in accordance with Einstein's relativistic principles, but nevertheless fails to provide more fundamental insights into the nature of time itself. In order to answer this question we begin by exploring the geometric properties of three-dimensional space that we model using Clifford geometric algebra, which is found to contain sufficient complexity to provide a natural description of spacetime. This description using Clifford algebra is found to provide a natural alternative to the Minkowski formulation as well as providing new insights into the nature of time. Our main result is that time is the scalar component of a Clifford space and can be viewed as an intrinsic geometric property of three-dimensional space without the need for the specific addition of a fourth dimension.
Ricci flow and geometrization of 3-manifolds
Morgan, John W
2010-01-01
This book is based on lectures given at Stanford University in 2009. The purpose of the lectures and of the book is to give an introductory overview of how to use Ricci flow and Ricci flow with surgery to establish the Poincar� Conjecture and the more general Geometrization Conjecture for 3-dimensional manifolds. Most of the material is geometric and analytic in nature; a crucial ingredient is understanding singularity development for 3-dimensional Ricci flows and for 3-dimensional Ricci flows with surgery. This understanding is crucial for extending Ricci flows with surgery so that they are defined for all positive time. Once this result is in place, one must study the nature of the time-slices as the time goes to infinity in order to deduce the topological consequences. The goal of the authors is to present the major geometric and analytic results and themes of the subject without weighing down the presentation with too many details. This book can be read as an introduction to more complete treatments of ...
Salt bridges: geometrically specific, designable interactions.
Donald, Jason E; Kulp, Daniel W; DeGrado, William F
2011-03-01
Salt bridges occur frequently in proteins, providing conformational specificity and contributing to molecular recognition and catalysis. We present a comprehensive analysis of these interactions in protein structures by surveying a large database of protein structures. Salt bridges between Asp or Glu and His, Arg, or Lys display extremely well-defined geometric preferences. Several previously observed preferences are confirmed, and others that were previously unrecognized are discovered. Salt bridges are explored for their preferences for different separations in sequence and in space, geometric preferences within proteins and at protein-protein interfaces, co-operativity in networked salt bridges, inclusion within metal-binding sites, preference for acidic electrons, apparent conformational side chain entropy reduction on formation, and degree of burial. Salt bridges occur far more frequently between residues at close than distant sequence separations, but, at close distances, there remain strong preferences for salt bridges at specific separations. Specific types of complex salt bridges, involving three or more members, are also discovered. As we observe a strong relationship between the propensity to form a salt bridge and the placement of salt-bridging residues in protein sequences, we discuss the role that salt bridges might play in kinetically influencing protein folding and thermodynamically stabilizing the native conformation. We also develop a quantitative method to select appropriate crystal structure resolution and B-factor cutoffs. Detailed knowledge of these geometric and sequence dependences should aid de novo design and prediction algorithms. Copyright © 2010 Wiley-Liss, Inc.
Geometric phase effects in ultracold chemistry
Hazra, Jisha; Naduvalath, Balakrishnan; Kendrick, Brian K.
2016-05-01
In molecules, the geometric phase, also known as Berry's phase, originates from the adiabatic transport of the electronic wavefunction when the nuclei follow a closed path encircling a conical intersection between two electronic potential energy surfaces. It is demonstrated that the inclusion of the geometric phase has an important effect on ultracold chemical reaction rates. The effect appears in rotationally and vibrationally resolved integral cross sections as well as cross sections summed over all product quantum states. It arises from interference between scattering amplitudes of two reaction pathways: a direct path and a looping path that encircle the conical intersection between the two lowest adiabatic electronic potential energy surfaces. Illustrative results are presented for the O+ OH --> H+ O2 reaction and for hydrogen exchange in H+ H2 and D+HD reactions. It is also qualitatively demonstrated that the geometric phase effect can be modulated by applying an external electric field allowing the possibility of quantum control of chemical reactions in the ultracold regime. This work was supported in part by NSF Grant PHY-1505557 (N.B.) and ARO MURI Grant No. W911NF-12-1-0476 (N.B.).
Edit propagation using geometric relationship functions
Guerrero, Paul; Jeschke, Stefan; Wimmer, Michael; Wonka, Peter
2014-01-01
We propose a method for propagating edit operations in 2D vector graphics, based on geometric relationship functions. These functions quantify the geometric relationship of a point to a polygon, such as the distance to the boundary or the direction to the closest corner vertex. The level sets of the relationship functions describe points with the same relationship to a polygon. For a given query point, we first determine a set of relationships to local features, construct all level sets for these relationships, and accumulate them. The maxima of the resulting distribution are points with similar geometric relationships. We show extensions to handle mirror symmetries, and discuss the use of relationship functions as local coordinate systems. Our method can be applied, for example, to interactive floorplan editing, and it is especially useful for large layouts, where individual edits would be cumbersome. We demonstrate populating 2D layouts with tens to hundreds of objects by propagating relatively few edit operations. © 2014 ACM 0730-0301/2014/03- ART15 $15.00.
Edit propagation using geometric relationship functions
Guerrero, Paul
2014-04-15
We propose a method for propagating edit operations in 2D vector graphics, based on geometric relationship functions. These functions quantify the geometric relationship of a point to a polygon, such as the distance to the boundary or the direction to the closest corner vertex. The level sets of the relationship functions describe points with the same relationship to a polygon. For a given query point, we first determine a set of relationships to local features, construct all level sets for these relationships, and accumulate them. The maxima of the resulting distribution are points with similar geometric relationships. We show extensions to handle mirror symmetries, and discuss the use of relationship functions as local coordinate systems. Our method can be applied, for example, to interactive floorplan editing, and it is especially useful for large layouts, where individual edits would be cumbersome. We demonstrate populating 2D layouts with tens to hundreds of objects by propagating relatively few edit operations. © 2014 ACM 0730-0301/2014/03- ART15 $15.00.
Geometric phase modulation for stellar interferometry
International Nuclear Information System (INIS)
Roy, M.; Boschung, B.; Tango, W.J.; Davis, J.
2002-01-01
Full text: In a long baseline optical interferometer, the fringe visibility is normally measured by modulation of the optical path difference between the two arms of the instruments. To obtain accurate measurements, the spectral bandwidth must be narrow, limiting the sensitivity of the technique. The application of geometric phase modulation technique to stellar interferometry has been proposed by Tango and Davis. Modulation of the geometric phase has the potential for improving the sensitivity of optical interferometers, and specially the Sydney University Stellar Interferometer (SUSI), by allowing broad band modulation of the light signals. This is because a modulator that changes the geometric phase of the signal is, in principle, achromatic. Another advantage of using such a phase modulator is that it can be placed in the common path traversed by the two orthogonally polarized beams emerging from the beam combiner in a stellar interferometer. Thus the optical components of the modulator do not have to be interferometric quality and could be relatively easily introduced into SUSI. We have investigated the proposed application in a laboratory-based experiment using a Mach-Zehnder interferometer with white-light source. This can be seen as a small model of an amplitude stellar interferometer where the light source takes the place of the distant star and two corner mirrors replaces the entrance pupils of the stellar interferometer
Plasma geometric optics analysis and computation
International Nuclear Information System (INIS)
Smith, T.M.
1983-01-01
Important practical applications in the generation, manipulation, and diagnosis of laboratory thermonuclear plasmas have created a need for elaborate computational capabilities in the study of high frequency wave propagation in plasmas. A reduced description of such waves suitable for digital computation is provided by the theory of plasma geometric optics. The existing theory is beset by a variety of special cases in which the straightforward analytical approach fails, and has been formulated with little attention to problems of numerical implementation of that analysis. The standard field equations are derived for the first time from kinetic theory. A discussion of certain terms previously, and erroneously, omitted from the expansion of the plasma constitutive relation is given. A powerful but little known computational prescription for determining the geometric optics field in the neighborhood of caustic singularities is rigorously developed, and a boundary layer analysis for the asymptotic matching of the plasma geometric optics field across caustic singularities is performed for the first time with considerable generality. A proper treatment of birefringence is detailed, wherein a breakdown of the fundamental perturbation theory is identified and circumvented. A general ray tracing computer code suitable for applications to radiation heating and diagnostic problems is presented and described
Approximate joint diagonalization and geometric mean of symmetric positive definite matrices.
Directory of Open Access Journals (Sweden)
Marco Congedo
Full Text Available We explore the connection between two problems that have arisen independently in the signal processing and related fields: the estimation of the geometric mean of a set of symmetric positive definite (SPD matrices and their approximate joint diagonalization (AJD. Today there is a considerable interest in estimating the geometric mean of a SPD matrix set in the manifold of SPD matrices endowed with the Fisher information metric. The resulting mean has several important invariance properties and has proven very useful in diverse engineering applications such as biomedical and image data processing. While for two SPD matrices the mean has an algebraic closed form solution, for a set of more than two SPD matrices it can only be estimated by iterative algorithms. However, none of the existing iterative algorithms feature at the same time fast convergence, low computational complexity per iteration and guarantee of convergence. For this reason, recently other definitions of geometric mean based on symmetric divergence measures, such as the Bhattacharyya divergence, have been considered. The resulting means, although possibly useful in practice, do not satisfy all desirable invariance properties. In this paper we consider geometric means of covariance matrices estimated on high-dimensional time-series, assuming that the data is generated according to an instantaneous mixing model, which is very common in signal processing. We show that in these circumstances we can approximate the Fisher information geometric mean by employing an efficient AJD algorithm. Our approximation is in general much closer to the Fisher information geometric mean as compared to its competitors and verifies many invariance properties. Furthermore, convergence is guaranteed, the computational complexity is low and the convergence rate is quadratic. The accuracy of this new geometric mean approximation is demonstrated by means of simulations.
Approximate joint diagonalization and geometric mean of symmetric positive definite matrices.
Congedo, Marco; Afsari, Bijan; Barachant, Alexandre; Moakher, Maher
2014-01-01
We explore the connection between two problems that have arisen independently in the signal processing and related fields: the estimation of the geometric mean of a set of symmetric positive definite (SPD) matrices and their approximate joint diagonalization (AJD). Today there is a considerable interest in estimating the geometric mean of a SPD matrix set in the manifold of SPD matrices endowed with the Fisher information metric. The resulting mean has several important invariance properties and has proven very useful in diverse engineering applications such as biomedical and image data processing. While for two SPD matrices the mean has an algebraic closed form solution, for a set of more than two SPD matrices it can only be estimated by iterative algorithms. However, none of the existing iterative algorithms feature at the same time fast convergence, low computational complexity per iteration and guarantee of convergence. For this reason, recently other definitions of geometric mean based on symmetric divergence measures, such as the Bhattacharyya divergence, have been considered. The resulting means, although possibly useful in practice, do not satisfy all desirable invariance properties. In this paper we consider geometric means of covariance matrices estimated on high-dimensional time-series, assuming that the data is generated according to an instantaneous mixing model, which is very common in signal processing. We show that in these circumstances we can approximate the Fisher information geometric mean by employing an efficient AJD algorithm. Our approximation is in general much closer to the Fisher information geometric mean as compared to its competitors and verifies many invariance properties. Furthermore, convergence is guaranteed, the computational complexity is low and the convergence rate is quadratic. The accuracy of this new geometric mean approximation is demonstrated by means of simulations.
Anisotropic solutions by gravitational decoupling
Ovalle, J.; Casadio, R.; da Rocha, R.; Sotomayor, A.
2018-02-01
We investigate the extension of isotropic interior solutions for static self-gravitating systems to include the effects of anisotropic spherically symmetric gravitational sources by means of the gravitational decoupling realised via the minimal geometric deformation approach. In particular, the matching conditions at the surface of the star with the outer Schwarzschild space-time are studied in great detail, and we describe how to generate, from a single physically acceptable isotropic solution, new families of anisotropic solutions whose physical acceptability is also inherited from their isotropic parent.
Anisotropic solutions by gravitational decoupling
Energy Technology Data Exchange (ETDEWEB)
Ovalle, J. [Silesian University in Opava, Institute of Physics and Research Centre of Theoretical Physics and Astrophysics, Faculty of Philosophy and Science, Opava (Czech Republic); Universidad Simon Bolivar, Departamento de Fisica, Caracas (Venezuela, Bolivarian Republic of); Casadio, R. [Alma Mater Universita di Bologna, Dipartimento di Fisica e Astronomia, Bologna (Italy); Istituto Nazionale di Fisica Nucleare, Bologna (Italy); Rocha, R. da [Universidade Federal do ABC (UFABC), Centro de Matematica, Computacao e Cognicao, Santo Andre, SP (Brazil); Sotomayor, A. [Universidad de Antofagasta, Departamento de Matematicas, Antofagasta (Chile)
2018-02-15
We investigate the extension of isotropic interior solutions for static self-gravitating systems to include the effects of anisotropic spherically symmetric gravitational sources by means of the gravitational decoupling realised via the minimal geometric deformation approach. In particular, the matching conditions at the surface of the star with the outer Schwarzschild space-time are studied in great detail, and we describe how to generate, from a single physically acceptable isotropic solution, new families of anisotropic solutions whose physical acceptability is also inherited from their isotropic parent. (orig.)
Logical and Geometrical Distance in Polyhedral Aristotelian Diagrams in Knowledge Representation
Directory of Open Access Journals (Sweden)
Lorenz Demey
2017-09-01
Full Text Available Aristotelian diagrams visualize the logical relations among a finite set of objects. These diagrams originated in philosophy, but recently, they have also been used extensively in artificial intelligence, in order to study (connections between various knowledge representation formalisms. In this paper, we develop the idea that Aristotelian diagrams can be fruitfully studied as geometrical entities. In particular, we focus on four polyhedral Aristotelian diagrams for the Boolean algebra B 4 , viz. the rhombic dodecahedron, the tetrakis hexahedron, the tetraicosahedron and the nested tetrahedron. After an in-depth investigation of the geometrical properties and interrelationships of these polyhedral diagrams, we analyze the correlation (or lack thereof between logical (Hamming and geometrical (Euclidean distance in each of these diagrams. The outcome of this analysis is that the Aristotelian rhombic dodecahedron and tetrakis hexahedron exhibit the strongest degree of correlation between logical and geometrical distance; the tetraicosahedron performs worse; and the nested tetrahedron has the lowest degree of correlation. Finally, these results are used to shed new light on the relative strengths and weaknesses of these polyhedral Aristotelian diagrams, by appealing to the congruence principle from cognitive research on diagram design.
Coherent cancellation of geometric phase for the OH molecule in external fields
Bhattacharya, M.; Marin, S.; Kleinert, M.
2014-05-01
The OH molecule in its ground state presents a versatile platform for precision measurement and quantum information processing. These applications vitally depend on the accurate measurement of transition energies between the OH levels. Significant sources of systematic errors in these measurements are shifts based on the geometric phase arising from the magnetic and electric fields used for manipulating OH. In this article, we present these geometric phases for fields that vary harmonically in time, as in the Ramsey technique. Our calculation of the phases is exact within the description provided by our recent analytic solution of an effective Stark-Zeeman Hamiltonian for the OH ground state. This Hamiltonian has been shown to model experimental data accurately. We find that the OH geometric phases exhibit rich structure as a function of the field rotation rate. Remarkably, we find rotation rates where the geometric phase accumulated by a specific state is zero, or where the relative geometric phase between two states vanishes. We expect these findings to be of importance to precision experiments on OH involving time-varying fields. More specifically, our analysis quantitatively characterizes an important item in the error budget for precision spectroscopy of ground-state OH.
The Geometric Phase in Quantum Systems
International Nuclear Information System (INIS)
Pascazio, S
2003-01-01
The discovery of the geometric phase is one of the most interesting and intriguing findings of the last few decades. It led to a deeper understanding of the concept of phase in quantum mechanics and motivated a surge of interest in fundamental quantum mechanical issues, disclosing unexpected applications in very diverse fields of physics. Although the key ideas underlying the existence of a purely geometrical phase had already been proposed in 1956 by Pancharatnam, it was Michael Berry who revived this issue 30 years later. The clarity of Berry's seminal paper, in 1984, was extraordinary. Research on the topic flourished at such a pace that it became difficult for non-experts to follow the many different theoretical ideas and experimental proposals which ensued. Diverse concepts in independent areas of mathematics, physics and chemistry were being applied, for what was (and can still be considered) a nascent arena for theory, experiments and technology. Although collections of papers by different authors appeared in the literature, sometimes with ample introductions, surprisingly, to the best of my knowledge, no specific and exhaustive book has ever been written on this subject. The Geometric Phase in Quantum Systems is the first thorough book on geometric phases and fills an important gap in the physical literature. Other books on the subject will undoubtedly follow. But it will take a fairly long time before other authors can cover that same variety of concepts in such a comprehensive manner. The book is enjoyable. The choice of topics presented is well balanced and appropriate. The appendices are well written, understandable and exhaustive - three rare qualities. I also find it praiseworthy that the authors decided to explicitly carry out most of the calculations, avoiding, as much as possible, the use of the joke 'after a straightforward calculation, one finds...' This was one of the sentences I used to dislike most during my undergraduate studies. A student is
Shaping up: a geometric morphometric approach to assemblage ecomorphology.
Bower, L M; Piller, K R
2015-09-01
This study adopts an ecomorphological approach to test the utility of body shape as a predictor of niche relationships among a stream fish assemblage of the Tickfaw River (Lake Pontchartrain Basin) in southeastern Louisiana, U.S.A. To examine the potential influence of evolutionary constraints, analyses were performed with and without the influence of phylogeny. Fish assemblages were sampled throughout the year, and ecological data (habitat and tropic guild) and body shape (geometric morphometric) data were collected for each fish specimen. Multivariate analyses were performed to examine relationships and differences between body shape and ecological data. Results indicate that a relationship exists between body shape and trophic guild as well as flow regime, but no significant correlation between body shape and substratum was found. Body shape was a reliable indicator of position within assemblage niche space. © 2015 The Fisheries Society of the British Isles.
Some Hermite–Hadamard Type Inequalities for Geometrically Quasi ...
Indian Academy of Sciences (India)
Abstract. In the paper, we introduce a new concept 'geometrically quasi-convex function' and establish some Hermite–Hadamard type inequalities for functions whose derivatives are of geometric quasi-convexity.
A Divergence Median-based Geometric Detector with A Weighted Averaging Filter
Hua, Xiaoqiang; Cheng, Yongqiang; Li, Yubo; Wang, Hongqiang; Qin, Yuliang
2018-01-01
To overcome the performance degradation of the classical fast Fourier transform (FFT)-based constant false alarm rate detector with the limited sample data, a divergence median-based geometric detector on the Riemannian manifold of Heimitian positive definite matrices is proposed in this paper. In particular, an autocorrelation matrix is used to model the correlation of sample data. This method of the modeling can avoid the poor Doppler resolution as well as the energy spread of the Doppler filter banks result from the FFT. Moreover, a weighted averaging filter, conceived from the philosophy of the bilateral filtering in image denoising, is proposed and combined within the geometric detection framework. As the weighted averaging filter acts as the clutter suppression, the performance of the geometric detector is improved. Numerical experiments are given to validate the effectiveness of our proposed method.
Monte Carlo methods for flux expansion solutions of transport problems
International Nuclear Information System (INIS)
Spanier, J.
1999-01-01
Adaptive Monte Carlo methods, based on the use of either correlated sampling or importance sampling, to obtain global solutions to certain transport problems have recently been described. The resulting learning algorithms are capable of achieving geometric convergence when applied to the estimation of a finite number of coefficients in a flux expansion representation of the global solution. However, because of the nonphysical nature of the random walk simulations needed to perform importance sampling, conventional transport estimators and source sampling techniques require modification to be used successfully in conjunction with such flux expansion methods. It is shown how these problems can be overcome. First, the traditional path length estimators in wide use in particle transport simulations are generalized to include rather general detector functions (which, in this application, are the individual basis functions chosen for the flus expansion). Second, it is shown how to sample from the signed probabilities that arise as source density functions in these applications, without destroying the zero variance property needed to ensure geometric convergence to zero error
Nonadiabatic geometrical quantum gates in semiconductor quantum dots
International Nuclear Information System (INIS)
Solinas, Paolo; Zanghi, Nino; Zanardi, Paolo; Rossi, Fausto
2003-01-01
In this paper, we study the implementation of nonadiabatic geometrical quantum gates with in semiconductor quantum dots. Different quantum information enconding (manipulation) schemes exploiting excitonic degrees of freedom are discussed. By means of the Aharanov-Anandan geometrical phase, one can avoid the limitations of adiabatic schemes relying on adiabatic Berry phase; fast geometrical quantum gates can be, in principle, implemented
The representations of Lie groups and geometric quantizations
International Nuclear Information System (INIS)
Zhao Qiang
1998-01-01
In this paper we discuss the relation between representations of Lie groups and geometric quantizations. A series of representations of Lie groups are constructed by geometric quantization of coadjoint orbits. Particularly, all representations of compact Lie groups, holomorphic discrete series of representations and spherical representations of reductive Lie groups are constructed by geometric quantizations of elliptic and hyperbolic coadjoint orbits. (orig.)
Identifying and Fostering Higher Levels of Geometric Thinking
Škrbec, Maja; Cadež, Tatjana Hodnik
2015-01-01
Pierre M. Van Hiele created five levels of geometric thinking. We decided to identify the level of geometric thinking in the students in Slovenia, aged 9 to 11 years. The majority of students (60.7%) are at the transition between the zero (visual) level and the first (descriptive) level of geometric thinking. Nearly a third (31.7%) of students is…
Entropic noises-induced resonance in a geometrically confined system
International Nuclear Information System (INIS)
Zeng, Chunhua; Gong, Ailing; Wang, Hua
2012-01-01
We consider the motion of Brownian particles through a narrow tube of varying cross-section in a geometrically confined system subjected to a sinusoidal oscillating force. The varying cross-section of the confinement results in an effective purely entropic potential in reduced dimension. Besides an additive Langevin force, one external additive and another multiplicative noise are acting along the x-direction. We demonstrate that the presence of a periodic input may give rise to a maximum and a minimum of the spectral amplification at corresponding optimal values of the noise strength, and therefore to the appearance of the purely entropic stochastic resonance and reverse-resonance phenomena. Furthermore, we show that the cross-correlation between two noises leads to a decrease of the spectral amplification, i.e., we observe the cross-correlation between two noises weakening the resonance. Mechanisms for the cross-correlation weakening the resonance are explained from the point of view of the effective purely entropic potential. (paper)
Geometric component of charge pumping current in nMOSFETs due to low-temperature irradiation
Witczak, S. C.; King, E. E.; Saks, N. S.; Lacoe, R. C.; Shaneyfelt, M. R.; Hash, G. L.; Hjalmarson, H. P.; Mayer, D. C.
2002-12-01
The geometric component of charge pumping current was examined in n-channel metal-oxide-silicon field effect transistors (MOSFETs) following low-temperature irradiation. In addition to the usual dependencies on channel length and gate bias transition time, the geometric component was found to increase with radiation-induced oxide-trapped charge density and decreasing temperature. A postirradiation injection of electrons into the gate oxide reduces the geometric component along with the density of oxide-trapped charge, which clearly demonstrates that the two are correlated. A fit of the injection data to a first-order model for trapping kinetics indicates that the electron trapping occurs predominantly at a single type of Coulomb-attractive trap site. The geometric component results primarily from the bulk recombination of channel electrons that fail to transport to the source or drain during the transition from inversion to accumulation. The radiation response of these transistors suggests that Coulomb scattering by oxide-trapped charge increases the bulk recombination at low temperatures by impeding electron transport. These results imply that the geometric component must be properly accounted for when charge pumping irradiated n-channel MOSFETs at low temperatures.
Austin, Jonathan P; Sundararajan, Mahesh; Vincent, Mark A; Hillier, Ian H
2009-08-14
The geometric and electronic structures of the aqua, chloro, acetato, hydroxo and carbonato complexes of U, Np and Pu in both their (VI) and (V) oxidation states, and in an aqueous environment, have been studied using density functional theory methods. We have obtained micro-solvated structures derived from molecular dynamics simulations and included the bulk solvent using a continuum model. We find that two different hydrogen bonding patterns involving the axial actinyl oxygen atoms are sometimes possible, and may give rise to different An-O bond lengths and vibrational frequencies. These alternative structures are reflected in the experimental An-O bond lengths of the aqua and carbonato complexes. The variation of the redox potential of the uranyl complexes with the different ligands has been studied using both BP86 and B3LYP functionals. The relative values for the four uranium complexes having anionic ligands are in surprisingly good agreement with experiment, although the absolute values are in error by approximately 1 eV. The absolute error for the aqua species is much less, leading to an incorrect order of the redox potentials of the aqua and chloro species.
Geometric derivation of the quantum speed limit
International Nuclear Information System (INIS)
Jones, Philip J.; Kok, Pieter
2010-01-01
The Mandelstam-Tamm and Margolus-Levitin inequalities play an important role in the study of quantum-mechanical processes in nature since they provide general limits on the speed of dynamical evolution. However, to date there has been only one derivation of the Margolus-Levitin inequality. In this paper, alternative geometric derivations for both inequalities are obtained from the statistical distance between quantum states. The inequalities are shown to hold for unitary evolution of pure and mixed states, and a counterexample to the inequalities is given for evolution described by completely positive trace-preserving maps. The counterexample shows that there is no quantum speed limit for nonunitary evolution.
A geometric form of the canonical commutation
International Nuclear Information System (INIS)
Guz, W.
1987-01-01
Some aspects of a geometric approach to quantum theory, in which the quantum-mechanical position and momentum operators are represented by covariant derivatives, are here developed. Here, the previously estabilished formalism of Caianiello and his co-workers is extended to the case of an integrable almost complex Hermitian manifold. The general theory is then applied to the two-dimensional case, where the structure of the 'quantum geometry' induced in the manifold by the quantum-mechanical CCR can be explicitly determined
Geometrical scaling vs factorizable eikonal models
Kiang, D
1975-01-01
Among various theoretical explanations or interpretations for the experimental data on the differential cross-sections of elastic proton-proton scattering at CERN ISR, the following two seem to be most remarkable: A) the excellent agreement of the Chou-Yang model prediction of d sigma /dt with data at square root s=53 GeV, B) the general manifestation of geometrical scaling (GS). The paper confronts GS with eikonal models with factorizable opaqueness, with special emphasis on the Chou-Yang model. (12 refs).
On geometrical splitting in nonanalog Monte Carlo
International Nuclear Information System (INIS)
Lux, I.
1985-01-01
A very general geometrical procedure is considered, and it is shown how the free flights, the statistical weights and the contribution of particles participating in splitting are to be chosen in order to reach unbiased estimates in games where the transition kernels are nonanalog. Equations governing the second moment of the score and the number of flights to be stimulated are derived. It is shown that the post-splitting weights of the fragments are to be chosen equal to reach maximum gain in variance. Conditions are derived under which the expected number of flights remains finite. Simplified example illustrate the optimization of the procedure (author)
Projective geometry for polarization in geometric quantization
International Nuclear Information System (INIS)
Campbell, P.; Dodson, C.T.J.
1976-12-01
It is important to know the extent to which the procedure of geometric quantization depends on a choice of polarization of the symplectic manifold that is the classical phase space. Published results have so far been restricted to real and transversal polarizations. Here we also consider these cases by presenting a formulation in terms of projective geometry. It turns out that there is a natural characterization of real transversal polarizations and maps among them using projective concepts. We give explicit constructions for Rsup(2n)
Irreducible geometric subgroups of classical algebraic groups
Burness, Timothy C; Testerman, Donna M
2016-01-01
Let G be a simple classical algebraic group over an algebraically closed field K of characteristic p \\ge 0 with natural module W. Let H be a closed subgroup of G and let V be a non-trivial irreducible tensor-indecomposable p-restricted rational KG-module such that the restriction of V to H is irreducible. In this paper the authors classify the triples (G,H,V) of this form, where H is a disconnected maximal positive-dimensional closed subgroup of G preserving a natural geometric structure on W.
Geometric and numerical foundations of movements
Mansard, Nicolas; Lasserre, Jean-Bernard
2017-01-01
This book aims at gathering roboticists, control theorists, neuroscientists, and mathematicians, in order to promote a multidisciplinary research on movement analysis. It follows the workshop “ Geometric and Numerical Foundations of Movements ” held at LAAS-CNRS in Toulouse in November 2015[1]. Its objective is to lay the foundations for a mutual understanding that is essential for synergetic development in motion research. In particular, the book promotes applications to robotics --and control in general-- of new optimization techniques based on recent results from real algebraic geometry.
Geometric Algebra Techniques in Flux Compactifications
International Nuclear Information System (INIS)
Coman, Ioana Alexandra; Lazaroiu, Calin Iuliu; Babalic, Elena Mirela
2016-01-01
We study “constrained generalized Killing (s)pinors,” which characterize supersymmetric flux compactifications of supergravity theories. Using geometric algebra techniques, we give conceptually clear and computationally effective methods for translating supersymmetry conditions into differential and algebraic constraints on collections of differential forms. In particular, we give a synthetic description of Fierz identities, which are an important ingredient of such problems. As an application, we show how our approach can be used to efficiently treat N=1 compactification of M-theory on eight manifolds and prove that we recover results previously obtained in the literature.