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
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)
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.
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…
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.
Trigonal curves and algebro-geometric solutions to soliton hierarchies II.
Ma, Wen-Xiu
2017-07-01
This is a continuation of a study on Riemann theta function representations of algebro-geometric solutions to soliton hierarchies. In this part, we straighten out all flows in soliton hierarchies under the Abel-Jacobi coordinates associated with Lax pairs, upon determining the Riemann theta function representations of the Baker-Akhiezer functions, and generate algebro-geometric solutions to soliton hierarchies in terms of the Riemann theta functions, through observing asymptotic behaviours of the Baker-Akhiezer functions. We emphasize that we analyse the four-component AKNS soliton hierarchy in such a way that it leads to a general theory of trigonal curves applicable to construction of algebro-geometric solutions of an arbitrary soliton hierarchy.
Trigonal curves and algebro-geometric solutions to soliton hierarchies I.
Ma, Wen-Xiu
2017-07-01
This is the first part of a study, consisting of two parts, on Riemann theta function representations of algebro-geometric solutions to soliton hierarchies. In this part, using linear combinations of Lax matrices of soliton hierarchies, we introduce trigonal curves by their characteristic equations, explore general properties of meromorphic functions defined as ratios of the Baker-Akhiezer functions, and determine zeros and poles of the Baker-Akhiezer functions and their Dubrovin-type equations. We analyse the four-component AKNS soliton hierarchy in such a way that it leads to a general theory of trigonal curves applicable to construction of algebro-geometric solutions of an arbitrary soliton hierarchy.
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)
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.
Sasongko, Muhammad Bayu; Hodgson, Lauren A B; Wong, Tien Y; Kawasaki, Ryo; Cheung, Carol Y; Hsu, Wynne; Lee, Mong Li; Lau, Peter Q F; Mitchell, Paul; Wang, Jie Jin
2012-10-01
To assess the correlation and reproducibility of retinal vascular geometric measurements obtained from two stereo-paired fundus images. Thirty stereoscopic pairs of color optic disc-centered photographs from the Blue Mountains Eye Study were analyzed. Side-by-side grading was performed by a single grader, using semi-automated computer software to quantify the following retinal geometric parameters: (1) retinal arteriolar/venular caliber (CRAE/CRVE); (2) arteriole-to-venule ratio (AVR); (3) branching angle; and (4) tortuosity. We used Pearson correlation (r), intra-class correlation coefficient (ICC), and Bland-Altman plots to assess within-pair correlation and reproducibility for each parameter measured. Inter- and intra-grader r and ICC were high (all r > 0.90 and ICC > 0.90), except for branching angle (ICCs between 0.69-0.83). There was no significant difference between within-pair means of all retinal vascular geometric parameters, before and after excluding poor quality images. CRAE, CRVE, AVR, and arteriolar and venular tortuosity showed very high within-pair correlation and agreement (all r > 0.80 and all ICC > 0.90 respectively). Arteriolar and venular branching angles demonstrated moderate within-pair correlation (r = 0.65 and r = 0.62, respectively) and within-pair agreement (ICC = 0.76 and ICC = 0.77, respectively). Use of computer-assisted software to measure retinal vascular geometric parameters from paired fundus images was highly repeatable and is robust to differences in photographic angles of paired stereo images. Such measurements can be applied to evaluate temporal changes in longitudinal studies.
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.
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.
Pair correlations in crystalline solid solutions
Energy Technology Data Exchange (ETDEWEB)
Ice, G.E.; Sparks, C.J. [Oak Ridge National Lab., TN (United States); Shaffer, L. [Anderson Univ., IN (United States). Dept. of Physics; Zschack, P. [Oak Ridge Institute of Science and Education, TN (United States)
1994-06-01
Recent measurements of pair correlations in metallic solid solutions challenge simple models of atomic size in alloy structure. These measurements take advantage of intense and tunable synchrotron X radiation to control the x-ray scattering contrast between atoms in a solid solution. For binary alloys with elements nearby in the periodic table it is possible to tune the x-ray energy near the K edge so that the scattering contrast varies from near zero to {plus_minus}5 electron units. Even larger contrast variation is possible near L edges or with complementary x-ray and neutron diffraction data sets. With adjusted scattering contrast it is possible to measure short-range-order (SRO), even in alloys with elements nearby in the periodic table. It is also possible to detect chemically-specific static displacements of {plus_minus}0.001 {angstrom} or less and with fewer assumptions than with previous experimental methods. We compare the measured chemically-specific static displacements in Fe{sub 22.5}Ni{sub 77.5} and Cr{sub 47}Fe{sub 53} with previous models and with the results of other experiments.
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.
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
Islamova Anastasiya; Orlova Evgeniya; Zykov Ilya
2017-01-01
Change of geometrical characteristics of distilled water and aqueous ethanol solution droplets was studied under their evaporation on aluminum surface. According to change in the contact diameter three evaporation modes of distilled water droplet on polished aluminum surface were detected: increase in the contact area, pinning of a droplet (constant contact area), and droplet depinning (decrease in the contact diameter). During evaporation of aqueous ethanol solution droplets, two evaporation...
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.
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)
Geometric characteristics of the solitonic solution in the case of finite density
Zhunussova, Zhanat; Dosmagulova, Karlygash
2015-09-01
Some exact solutions of nonlinear partial differential equations are widely investigated both mathematical and physical points of view. Physically interesting solution as solitonic is well known. Also solitonic solution have simple behavior in bumping and are stable. There are various methods for searching of these exact solutions.
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
Angular correlation of annihilation photons in frozen aqueous solutions
DEFF Research Database (Denmark)
Milosevic-Kvajic, M.; Mogensen, O. E.; Kvajic, G.
1972-01-01
Linear‐slit angular correlation curves were obtained at about −140°C for frozen aqueous solutions of HF, HCl, HBr, HI, NH3, FeCl2, FeCl3, NaI, H2SO4, NHO3, MnSO4, KMnO4, K2Cr2O7, NaOH, and LiOH. We found no appreciable influence of a 4% concentration of the last seven impurities. Only halide‐cont...
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.
Rieger, Katrina A; Birch, Nathan P; Schiffman, Jessica D
2016-03-30
Electrospinning hydrophilic nanofiber mats that deliver hydrophobic agents would enable the development of new therapeutic wound dressings. However, the correlation between precursor solution properties and nanofiber morphology for polymer solutions electrospun with or without hydrophobic oils has not yet been demonstrated. Here, cinnamaldehyde (CIN) and hydrocinnamic alcohol (H-CIN) were electrospun in chitosan (CS)/poly(ethylene oxide) (PEO) nanofiber mats as a function of CS molecular weight and degree of acetylation (DA). Viscosity stress sweeps determined how the oils affected solution viscosity and chain entanglement (Ce) concentration. Experimentally, the maximum polymer:oil mass ratio electrospun was 1:3 and 1:6 for CS/PEO:CIN and:H-CIN, respectively; a higher chitosan DA increased the incorporation of H-CIN only. The correlations determined for electrospinning plant-derived oils could potentially be applied to other hydrophobic molecules, thus broadening the delivery of therapeutics from electrospun nanofiber mats. Copyright © 2015 Elsevier Ltd. All rights reserved.
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
Directory of Open Access Journals (Sweden)
Priyantha Wijayatunga
2016-06-01
Full Text Available Measuring strength or degree of statistical dependence between two random variables is a common problem in many domains. Pearson’s correlation coefficient ρ is an accurate measure of linear dependence. We show that ρ is a normalized, Euclidean type distance between joint probability distribution of the two random variables and that when their independence is assumed while keeping their marginal distributions. And the normalizing constant is the geometric mean of two maximal distances; each between the joint probability distribution when the full linear dependence is assumed while preserving respective marginal distribution and that when the independence is assumed. Usage of it is restricted to linear dependence because it is based on Euclidean type distances that are generally not metrics and considered full dependence is linear. Therefore, we argue that if a suitable distance metric is used while considering all possible maximal dependences then it can measure any non-linear dependence. But then, one must define all the full dependences. Hellinger distance that is a metric can be used as the distance measure between probability distributions and obtain a generalization of ρ for the discrete case.
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
Su, Lijuan; Wang, Fei; He, Peng; Dambon, Olaf; Klocke, Fritz; Yi, Allen Y.
2014-02-01
In precision glass molding, refractive index change and geometric deviation (or curve change as often referred to in industry) occurred during molding process can result in substantial amount of aberrations. Previously, refractive index change and geometric deviation were investigated in separate studies by the authors. However, optical performance of a molded glass lens depends on both refractive index and geometry. In order to mold lenses with optimal performance, both refractive index change and geometric deviation have to be taken into consideration simultaneously and compensated. This paper presented an integrated compensation procedure for modifying molds to compensate both refractive index change and geometric deviation. Group refractive index change predicted by the finite element method simulation was used to provide a modified geometry design for a desired lens. Geometric deviations of molded glass lenses with the modified design were analyzed with a previously developed numerical simulation approach, which is used to modify the mold shape. This procedure was validated by molding a generic aspherical glass lens. Both geometry and optical measurement results confirmed that the molded lens performed as specified by the original design. It also demonstrated that finite element method assisted compensation procedure can be used to predict the final optical performance of compression molded glass components. This research provided an opportunity for optics manufacturers to achieve better performance lens while maintaining lower cost and a shorter cycle time.
Shekhar, Raj; Lei, Peng; Castro-Pareja, Carlos R; Plishker, William L; D'Souza, Warren D
2007-07-01
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
de Rezende Barbosa, Marianne P da C; Vanderlei, Luiz C M; Neves, Lucas M; Takahashi, Carolina; Torquato, Paula R Dos S; Fortaleza, Ana Claúdia de S; Freitas Júnior, Ismael F; Sorpreso, Isabel C E; Abreu, Luiz C; Pérez Riera, Andrés R
2018-01-01
To evaluate the influence of functional training on the geometric indices of heart rate variability (HRV) and fractal correlation properties of the dynamics of heart rate in menopausal women. Of 39 women who were in the period of menopause for more than a year and who did not practice any regular physical activity were divided into: Functional training group (FTG = 50 ± 4.5 years; 67.64 ± 11.64 kg; 1.5 ± 0.05 m) that executed the functional training (FT) and all proposals by reviews and the Control group (58.45 ± 4.8 years; 66.91 ± 13.24 kg; 1.55 ± 0.05 m) who performed all assessments but not FT. The training consisted of 18 weeks (three times a week) and the volunteers performed three sets of 11 functional exercises followed by a walk in each of the sessions. The autonomic nervous system modulation was evaluated by analysis of HRV and the indices obtained were: RR intervals, RRTRI, TINN, SD1, SD2, SD1/SD2, qualitative analysis of Poincaré plot and DFA (alfa-1, alfa-2 and alfa-1/alfa-2). The Student's t-test for unpaired samples (normal data) or Mann-Whitney test nonnormal data) were used to compare the differences obtained between the final moment and the initial moment of the studied groups (p < .05). Were observed in the FTG: increased SD1 (CG 0.13 ± 4.00 vs. 3.60 ± 8.43), beat-to-beat global dispersion much greater as an increased in the dispersion of long-term RR intervals and increased fractal properties of short-term (α1) (CG -0.04 ± 0.13 vs. 0.07 ± 0.21). FT promoted a beneficial impact on cardiac autonomic modulation, characterized by increased parasympathetic activity and short-term fractal properties of the dynamics of the heart rate. © 2017 Wiley Periodicals, Inc.
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.
Vacaru, Sergiu I.; Veliev, Elşen Veli; Yazici, Enis
2014-09-01
We show that 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. Some examples of exact solutions describing generic off-diagonal modifications to black hole/ellipsoid and solitonic configurations are provided and analyzed.
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.
Ivey, James W; Lewis, David; Church, Tanya; Finlay, Warren H; Vehring, Reinhard
2014-04-25
A correlation equation for the mass median aerodynamic diameter (MMAD) of the aerosol emitted by solution metered dose inhalers (MDIs) is presented. A content equivalent diameter is defined and used to describe aerosols generated by evaporating metered dose inhaler sprays. A large set of cascade impaction data is analyzed, and the MMAD and geometric standard deviation is calculated for each datum. Using dimensional analysis, the mass median content equivalent diameter is correlated with formulation variables. Based on this correlation in combination with mass balance considerations and the definition of the aerodynamic diameter, an equation for prediction of the MMAD of an inhaler given the pressure of the propellant in the metering chamber of the MDI valve and the surface tension of the propellant is derived. The accuracy of the correlation equation is verified by comparison with literature results. The equation is applicable to both HFA (hydrofluoroalkane) propellants 134a and 227ea, with varying levels of co-solvent ethanol. Copyright © 2014 Elsevier B.V. All rights reserved.
Lieb, Wolfgang; Gona, Philimon; Larson, Martin G; Aragam, Jayashri; Zile, Michael R; Cheng, Susan; Benjamin, Emelia J; Vasan, Ramachandran S
2014-09-01
This study sought to evaluate pattern and clinical correlates of change in left ventricular (LV) geometry over a 4-year period in the community; it also assessed whether the pattern of change in LV geometry over 4 years predicts incident cardiovascular disease (CVD), including myocardial infarction, heart failure, and cardiovascular death, during an additional subsequent follow-up period. It is unclear how LV geometric patterns change over time and whether changes in LV geometry have prognostic significance. This study evaluated 4,492 observations (2,604 unique Framingham Heart Study participants attending consecutive examinations) to categorize LV geometry at baseline and after 4 years. Four groups were defined on the basis of the sex-specific distributions of left ventricular mass (LVM) and relative wall thickness (RWT) (normal: LVM and RWT geometry or concentric remodeling progressed infrequently (4% to 8%) to eccentric or concentric hypertrophy. Change from eccentric to concentric hypertrophy was uncommon (8%). Among participants with concentric hypertrophy, 19% developed eccentric hypertrophy within the 4-year period. Among participants with abnormal LV geometry at baseline, a significant proportion (29% to 53%) reverted to normal geometry within 4 years. Higher blood pressure, greater body mass index (BMI), advancing age, and male sex were key correlates of developing an abnormal geometry. Development of an abnormal LV geometric pattern over 4 years was associated with increased CVD risk (140 events) during a subsequent median follow-up of 12 years (adjusted-hazards ratio: 1.59; 95% confidence interval: 1.04 to 2.43). The longitudinal observations in the community suggest that dynamic changes in LV geometric pattern over time are common. Higher blood pressure and greater BMI are modifiable factors associated with the development of abnormal LV geometry, and such progression portends an adverse prognosis. Copyright © 2014 American College of Cardiology
International Nuclear Information System (INIS)
Mori, Toshifumi; Nakano, Katsuhiro; Kato, Shigeki
2010-01-01
The minimum energy conical intersection (MECI) optimization method with taking account of the dynamic electron correlation effect [T. Mori and S. Kato, Chem. Phys. Lett. 476, 97 (2009)] is extended to locate the MECI of nonequilibrium free energy surfaces in solution. A multistate electronic perturbation theory is introduced into the nonequilibrium free energy formula, which is defined as a function of solute and solvation coordinates. The analytical free energy gradient and interstate coupling vectors are derived, and are applied to locate MECIs in solution. The present method is applied to study the cis-trans photoisomerization reaction of a protonated Schiff base molecule (PSB3) in methanol (MeOH) solution. It is found that the effect of dynamic electron correlation largely lowers the energy of S 1 state. We also show that the solvation effect strongly stabilizes the MECI obtained by twisting the terminal C=N bond to become accessible in MeOH solution, whereas the conical intersection is found to be unstable in gas phase. The present study indicates that both electron correlation and solvation effects are important in the photoisomerization reaction of PSB3. The effect of counterion is also examined, and seems to be rather small in solution. The structures of free energy surfaces around MECIs are also discussed.
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.
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.
Sukhanova, L. A.; Khlestkov, Yu. A.
2017-11-01
On the basis of a new exact solution of the equations of GRT for centrally-symmetric charged dust, the internal structure of a nonstationary time-periodic wormhole with two static necks continued into two asymptoticallyflat vacuum parallel spaces is investigated, and it is shown that the reason for the appearance in some regions of the curved spacetime of a wormhole of negative energy densities of the dustlike matter, which arise when expansion gives way to compression, is a change in the sign of the scalar (Gaussian) curvature of 4-spacetime from positive to negative due to the appearance of two-dimensional coordinate surfaces with principal curvatures of different signs.
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)
An empirical method to correlate and predict solute distribution in ternary liquid-liquid systems
Directory of Open Access Journals (Sweden)
Zamaro J.M.
2002-01-01
Full Text Available This paper presents a method that combines activity coefficient models with Hand's equation for tie lines. The proposed method calculates solute distribution in liquid-liquid ternary systems. The combination improves the calculated solute distributions using activity coefficient models while Hand's equation gives a good correlation of the experimental tie lines. The method could be used to extrapolate experimental information.
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
International Nuclear Information System (INIS)
Zagrebnov, V.A.
1980-01-01
Using resolvents for Kirkwood-Zalburg, Kirkwood-Ruelle and Meier-Montroll operators, solutions of the finite-volume correlation equations for tempered boundary conditions are obtained explicity. The uniqueness theorem is proved. A connection of the correlation equations with the Dobrushin-Landford-Ruelle equations for the Gibbs probability measure is discussed
Muniz Oliva, Waldyr
2002-01-01
Geometric Mechanics here means mechanics on a pseudo-riemannian manifold and the main goal is the study of some mechanical models and concepts, with emphasis on the intrinsic and geometric aspects arising in classical problems. The first seven chapters are written in the spirit of Newtonian Mechanics while the last two ones as well as two of the four appendices describe the foundations and some aspects of Special and General Relativity. All the material has a coordinate free presentation but, for the sake of motivation, many examples and exercises are included in order to exhibit the desirable flavor of physical applications.
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.
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.
Geometrical Solutions of Quadratic Equations.
Grewal, A. S.; Godloza, L.
1999-01-01
Demonstrates that the equation of a circle (x-h)2 + (y-k)2 = r2 with center (h; k) and radius r reduces to a quadratic equation x2-2xh + (h2 + k2 -r2) = O at the intersection with the x-axis. Illustrates how to determine the center of a circle as well as a point on a circle. (Author/ASK)
Shoga, Janty S; Graham, Brian T; Wang, Liyun; Price, Christopher
2017-10-01
Articular cartilage is an avascular tissue; diffusive transport is critical for its homeostasis. While numerous techniques have been used to quantify diffusivity within porous, hydrated tissues and tissue engineered constructs, these techniques have suffered from issues regarding invasiveness and spatial resolution. In the present study, we implemented and compared two separate correlation spectroscopy techniques, fluorescence correlation spectroscopy (FCS) and raster image correlation spectroscopy (RICS), for the direct, and minimally-invasive quantification of fluorescent solute diffusion in agarose and articular cartilage. Specifically, we quantified the diffusional properties of fluorescein and Alexa Fluor 488-conjugated dextrans (3k and 10k) in aqueous solutions, agarose gels of varying concentration (i.e. 1, 3, 5%), and in different zones of juvenile bovine articular cartilage explants (i.e. superficial, middle, and deep). In agarose, properties of solute diffusion obtained via FCS and RICS were inversely related to molecule size, gel concentration, and applied strain. In cartilage, the diffusional properties of solutes were similarly dependent upon solute size, cartilage zone, and compressive strain; findings that agree with work utilizing other quantification techniques. In conclusion, this study established the utility of FCS and RICS as simple and minimally invasive techniques for quantifying microscale solute diffusivity within agarose constructs and articular cartilage explants.
Exact Solutions for Correlations in the Kagomé Ising Antiferromagnet
Barry, J. H.; Khatun, M.
The kagomé Ising antiferromagnet is highly frustrated with its pair correlation decaying exponentially at large distance for all temperatures including absolute zero. Hence, the spin system does not support long-range orderings and is devoid of any phase transition. One proves, via local star-triangle and decoration-decimation transformations, that correlations in the kagomé Ising antiferromagnet at arbitrary temperatures can be represented as linear combinations of correlations in the honeycomb Ising ferromagnet at high temperatures (disordered region). Existent knowledge of all honeycomb Ising correlations upon a select (spatially compact) 10-site cluster is thus sufficient to determine all present kagomé Ising correlations upon an associated 9-site cluster. Examples of resulting exact solutions for pair and multisite correlations in the kagomé Ising antiferromagnet are presented at all temperatures. Applications include joint configuration probabilities, thermodynamic response functions such as the specific heat and the initial perpendicular susceptibility, and the inelastic neutron scattering function.
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
Korotin, M. A.; Skorikov, N. A.
2015-06-01
A method for electronic structure calculations of strongly correlated materials based on the coherent potential approximation is formulated and implemented. Method is applied for investigation of the electronic structure and local magnetic moments of the strongly correlated systems with d- and f-electrons: NiO-ZnO solid solution, nonstoichiometric perovskite LaMnO3-x, doped compound TiO2:Fe, and rare-earth transition-metal intermetallic compound GdNi2:Mn.
Roerdink, J.B.T.M.
1982-01-01
It is shown that the cumulant expansion for linear stochastic differential equations, hitherto used to compute one-time averages of the solution process, is also capable of yielding the two-time correlation and probability density functions. The general case with a coefficient matrix, an
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
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.
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.
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...... of the initial data over all homotopy classes of successive excisions of embedded pair of pants. We provide sufficient conditions to guarantee these infinite sums converge and as a result, we can generate mapping class group invariant vectors Ω∑ which we call amplitudes. The initial data encode the amplitude...... for pair of pants and tori with one boundary, as well as the "recursion kernels" used for glueing. We give this construction the name of "geometric recursion", abbreviated GR. As an illustration, we show how to apply our formalism to various spaces of continuous functions over Teichmueller spaces, as well...
Geometric Mixing, Peristalsis, and the Geometric Phase of the Stomach
Arrieta, Jorge; Cartwright, Julian H.E.; Gouillart, Emmanuelle; Piro, Nicolas; Piro, Oreste; Tuval, Idan
2015-01-01
International audience; 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...
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.
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
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 interpretation of the geometric discord
International Nuclear Information System (INIS)
Yao, Yao; Li, Hong-Wei; Yin, Zhen-Qiang; Han, Zheng-Fu
2012-01-01
We investigate the level surfaces of geometric measure of quantum discord, and provide a pictorial interpretation of geometric discord for Bell-diagonal states. We have observed its nonanalytic behavior under decoherence employing this approach and interestingly found if we expect geometric discord to remain constant under phase-flip channel for a finite period, the initial state must be separable. Besides, this geometric understanding can be applied to verify the hierarchical relationships between geometric discord and the original one. The present work makes us conjecture that the incompatibility of these two definitions may originate from the discrepancy of the geometric structures of them. -- Highlights: ► We investigate geometry structure of geometric measure of quantum discord. ► If geometric discord is assumed to remain constant, the initial state must be separable. ► Geometry interpretation can be applied to verify hierarchical relationships between geometric discord and the original one.
CSIR Research Space (South Africa)
Makola, MM
2016-09-01
Full Text Available that all the geometrical isomers are potent radical scavengers. The lowest O H bond dissociation enthalpy value (70.599 kcal/mol) corresponds to the trans–trans isomer and is comparable to that of gallic acid, a commercially available antioxidant...
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.
Corrochano, Eduardo Bayro
2010-01-01
This book presents contributions from a global selection of experts in the field. This useful text offers new insights and solutions for the development of theorems, algorithms and advanced methods for real-time applications across a range of disciplines. Written in an accessible style, the discussion of all applications is enhanced by the inclusion of numerous examples, figures and experimental analysis. Features: provides a thorough discussion of several tasks for image processing, pattern recognition, computer vision, robotics and computer graphics using the geometric algebra framework; int
Geometric 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
Pegis, Michael L; McKeown, Bradley A; Kumar, Neeraj; Lang, Kai; Wasylenko, Derek J; Zhang, X Peter; Raugei, Simone; Mayer, James M
2016-11-23
Improved electrocatalysts for the oxygen reduction reaction (ORR) are critical for the advancement of fuel cell technologies. Herein, we report a series of 11 soluble iron porphyrin ORR electrocatalysts that possess turnover frequencies (TOFs) from 3 s -1 to an unprecedented value of 2.2 × 10 6 s -1 . These TOFs correlate with the ORR overpotential, which can be modulated by changing the E 1/2 of the catalyst using different ancillary ligands, by changing the solvent and solution acidity, and by changing the catalyst's protonation state. The overpotential is well-defined for these homogeneous electrocatalysts by the E 1/2 of the catalyst and the proton activity of the solution. This is the first such correlation for homogeneous ORR electrocatalysis, and it demonstrates that the remarkably fast TOFs are a consequence of high overpotential. The correlation with overpotential is surprising since the turnover limiting steps involve oxygen binding and protonation, as opposed to turnover limiting electron transfer commonly found in Tafel analysis of heterogeneous ORR materials. Computational studies show that the free energies for oxygen binding to the catalyst and for protonation of the superoxide complex are in general linearly related to the catalyst E 1/2 , and that this is the origin of the overpotential correlations. This analysis thus provides detailed understanding of the ORR barriers. The best catalysts involve partial decoupling of the influence of the second coordination sphere from the properties of the metal center, which is suggested as new molecular design strategy to avoid the limitations of the traditional scaling relationships for these catalysts.
Samanta, Soham; Kar, Chirantan; Das, Gopal
2015-09-01
Heterobis imine Schiff base probe L is able to discriminate geometrical isomers (maleic acid vs fumaric acid) through sharp colorimetric as well as fluorogenic responses even conspicuous with the naked eye. Colorimetric as well as fluorogenic sensing of maleic acid among various carboxylic acids was also demonstrated in ethanol-buffer medium. Sensing behavior of L was corroborated by (1)H NMR spectra, mass spectrometry, and theoretical calculations. Subsequently sensing behavior of L was used to probe maleic acid in starch rich food samples.
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.
Nieves, D J; Li, Y; Fernig, D G; Lévy, R
2015-06-01
Raster image correlation spectroscopy (RICS) measures the diffusion of fluorescently labelled molecules from stacks of confocal microscopy images by analysing correlations within the image. RICS enables the observation of a greater and, thus, more representative area of a biological system as compared to other single molecule approaches. Photothermal microscopy of gold nanoparticles allows long-term imaging of the same labelled molecules without photobleaching. Here, we implement RICS analysis on a photothermal microscope. The imaging of single gold nanoparticles at pixel dwell times short enough for RICS (60 μs) with a piezo-driven photothermal heterodyne microscope is demonstrated (photothermal raster image correlation spectroscopy, PhRICS). As a proof of principle, PhRICS is used to measure the diffusion coefficient of gold nanoparticles in glycerol : water solutions. The diffusion coefficients of the nanoparticles measured by PhRICS are consistent with their size, determined by transmission electron microscopy. PhRICS was then used to probe the diffusion speed of gold nanoparticle-labelled fibroblast growth factor 2 (FGF2) bound to heparan sulfate in the pericellular matrix of live fibroblast cells. The data are consistent with previous single nanoparticle tracking studies of the diffusion of FGF2 on these cells. Importantly, the data reveal faster FGF2 movement, previously inaccessible by photothermal tracking, and suggest that inhomogeneity in the distribution of bound FGF2 is dynamic.
Heidari, Peyman; Li, Li
2014-10-01
This work examines how heterogeneity structure, in particular correlation length, controls flow and solute transport. We used two-dimensional (2D) sandboxes (21.9 cm × 20.6 cm) and four modeling approaches, including 2D Advection-Dispersion Equation (ADE) with explicit heterogeneity structure, 1D ADE with average properties, and nonlocal Continuous Time Random Walk (CTRW) and fractional ADE (fADE). The goal is to answer two questions: (1) how and to what extent does correlation length control effective permeability and breakthrough curves (BTC)? (2) Which model can best reproduce data under what conditions? Sandboxes were packed with the same 20% (v/v) fine and 80% (v/v) coarse sands in three patterns that differ in correlation length. The Mixed cases contain uniformly distributed fine and coarse grains. The Four-zone and One-zone cases have four and one square fine zones, respectively. A total of seven experiments were carried out with permeability variance of 0.10 (LC), 0.22 (MC), and 0.43 (HC). Experimental data show that the BTC curves depend strongly on correlation length, especially in the HC cases. The HC One-zone (HCO) case shows distinct breakthrough steps arising from fast advection in the coarse zone, slow advection in the fine zone, and slow diffusion, while the LCO and MCO BTCs do not exhibit such behavior. With explicit representation of heterogeneity structure, 2D ADE reproduces BTCs well in all cases. CTRW reproduces temporal moments with smaller deviation from data than fADE in all cases except HCO, where fADE has the lowest deviation.
Geometric Mixing, Peristalsis, and the Geometric Phase of the Stomach
Arrieta, Jorge; Cartwright, Julyan H. E.; Gouillart, Emmanuelle; Piro, Nicolas; Piro, Oreste; Tuval, Idan
2012-01-01
© 2015 Arrieta et al. 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...
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 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)
DEFF Research Database (Denmark)
Goncalves, Ana Saraiva; Kontogeorgis, Georgios; Harismiadis, Vassilis I.
1996-01-01
and has been successfully used for the prediction of upper critical solution temperatures for various binary polymer solutions. In this work, we demonstrate and explain some of the problems which cubic equations of state exhibit in describing the lower critical solution behavior for polymer solutions......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...... of state parameters for the solvent are estimated via the classical Soave method, i.e. using the critical properties and a generalized equation for the energy parameter. When extended to mixtures, the van der Waals one-fluid mixing rules along with the Berthelot combining rule for the molecular cross...
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.
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.
PREFACE: Geometrically frustrated magnetism Geometrically frustrated magnetism
Gardner, Jason S.
2011-04-01
Frustrated magnetism is an exciting and diverse field in condensed matter physics that has grown tremendously over the past 20 years. This special issue aims to capture some of that excitement in the field of geometrically frustrated magnets and is inspired by the 2010 Highly Frustrated Magnetism (HFM 2010) meeting in Baltimore, MD, USA. Geometric frustration is a broad phenomenon that results from an intrinsic incompatibility between some fundamental interactions and the underlying lattice geometry based on triangles and tetrahedra. Most studies have centred around the kagomé and pyrochlore based magnets but recent work has looked at other structures including the delafossite, langasites, hyper-kagomé, garnets and Laves phase materials to name a few. Personally, I hope this issue serves as a great reference to scientist both new and old to this field, and that we all continue to have fun in this very frustrated playground. Finally, I want to thank the HFM 2010 organizers and all the sponsors whose contributions were an essential part of the success of the meeting in Baltimore. Geometrically frustrated magnetism contents Spangolite: an s = 1/2 maple leaf lattice antiferromagnet? T Fennell, J O Piatek, R A Stephenson, G J Nilsen and H M Rønnow Two-dimensional magnetism and spin-size effect in the S = 1 triangular antiferromagnet NiGa2S4 Yusuke Nambu and Satoru Nakatsuji Short range ordering in the modified honeycomb lattice compound SrHo2O4 S Ghosh, H D Zhou, L Balicas, S Hill, J S Gardner, Y Qi and C R Wiebe Heavy fermion compounds on the geometrically frustrated Shastry-Sutherland lattice M S Kim and M C Aronson A neutron polarization analysis study of moment correlations in (Dy0.4Y0.6)T2 (T = Mn, Al) J R Stewart, J M Hillier, P Manuel and R Cywinski Elemental analysis and magnetism of hydronium jarosites—model kagome antiferromagnets and topological spin glasses A S Wills and W G Bisson The Herbertsmithite Hamiltonian: μSR measurements on single crystals
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.
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.
Inflationary perturbation theory is geometrical optics in phase space
Seery, David; Mulryne, David J.; Frazer, Jonathan; Ribeiro, Raquel H.
2012-09-01
A pressing problem in comparing inflationary models with observation is the accurate calculation of correlation functions. One approach is to evolve them using ordinary differential equations ("transport equations"), analogous to the Schwinger-Dyson hierarchy of in-out quantum field theory. We extend this approach to the complete set of momentum space correlation functions. A formal solution can be obtained using raytracing techniques adapted from geometrical optics. We reformulate inflationary perturbation theory in this language, and show that raytracing reproduces the familiar "δN" Taylor expansion. Our method produces ordinary differential equations which allow the Taylor coefficients to be computed efficiently. We use raytracing methods to express the gauge transformation between field fluctuations and the curvature perturbation, ζ, in geometrical terms. Using these results we give a compact expression for the nonlinear gauge-transform part of fNL in terms of the principal curvatures of uniform energy-density hypersurfaces in field space.
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. .
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 distributions 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 generalization of Newton's gravitational scalar potential exterior to the spherical mass or pressure distribution under consideration.
On Geometric Infinite Divisibility
Sandhya, E.; Pillai, R. N.
2014-01-01
The notion of geometric version of an infinitely divisible law is introduced. Concepts parallel to attraction and partial attraction are developed and studied in the setup of geometric summing of random variables.
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...
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
Huang, Ling C; Salvador-Silva, Mercedes; Leang, Ronika S
2016-10-24
To demonstrate correlations among in vitro assays used for assessing cytotoxicity of contact lens multipurpose solution (MPS) and propose the use of multiple assays as a part of preclinical evaluation for MPS biocompatibility assessment. The effect of four different MPS on cell cytotoxicity, metabolic activity, and membrane integrity was performed by evaluating toxicity, expression of tight junction protein zonula occludens-1, and transepithelial electrical resistance in human corneal epithelial cells and Chinese hamster fibroblast cells. Cytotoxicity of four MPS was assayed with five different experimental systems at various concentrations. In vitro MPS-induced cytotoxicity was dependent on assay choice, concentration of MPS used, and duration of treatment. Overall, MPS-1 and MPS-2 were comparable to MPS-4 and better than MPS-3 in maintaining corneal barrier integrity and cell viability. In vitro cytotoxicity testing with MPS exposure to monolayer of cells in culture could be used as a tool to understand the potential cytotoxicity profiles of MPS and possibly a predictor of clinical outcome. Furthermore, MPS effects on in vitro cytotoxicity are best demonstrated by performing multiple assays to evaluate cell viability, metabolic activity, and membrane integrity during development.
Geometric Results for Compressible Magnetohydrodynamics
Arter, Wayne
2013-01-01
Recently, compressible magnetohydrodynamics (MHD) has been elegantly formulated in terms of Lie derivatives. This paper exploits the geometrical properties of the Lie bracket to give new insights into the properties of compressible MHD behaviour, both with and without feedback of the magnetic field on the flow. These results are expected to be useful for the solution of MHD equations in both tokamak fusion experiments and space plasmas.
Geometric Error Analysis in Applied Calculus Problem Solving
Usman, Ahmed Ibrahim
2017-01-01
The paper investigates geometric errors students made as they tried to use their basic geometric knowledge in the solution of the Applied Calculus Optimization Problem (ACOP). Inaccuracies related to the drawing of geometric diagrams (visualization skills) and those associated with the application of basic differentiation concepts into ACOP…
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
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 \
Exact solutions for Ising-model correlations in the 3-12 (extended kagome´) lattice
Barry, J. H.; Khatun, M.
1995-03-01
The 3-12 (or extended kagomé) lattice is a three-coordinated irregular planar lattice having physical applications. Viewing its sites as the decoration sites of a doubly decorated honeycomb lattice, one proves via local star-triangle and double decoration-decimation transformations that 3-12 Ising correlations can be conveniently represented as linear combinations of honeycomb Ising correlations. Existent knowledge of all honeycomb Ising correlations upon a select (spatially compact) 10-site cluster is thus sufficient to determine all 3-12 Ising correlations upon an associated 18-site cluster. The total number of 3-12 Ising correlations defined upon this 18-site cluster is exceedingly large, but their actual count is less significant than the realization that each can now be found in a systematic and efficient fashion. Examples of resulting exact solutions for both even- and odd-number multisite correlations of the 3-12 Ising ferromagnet are presented at all temperatures. A simple scaling relationship is established between the asymptotic forms of the pair correlation in the 3-12 and honeycomb Ising models. Besides providing relatively direct derivations (no explicit magnetic fields or field derivatives) for the spontaneous magnetization and internal energy of the 3-12 Ising model, the mapping methods may be repeated recursively to secure Ising multisite correlations upon various other irregular planar lattices.
Geometric Dimensioning Sentence Structure.
McCuistion, Patrick J.
1991-01-01
Explanations of geometric dimensioning symbols are provided to assist in the comprehension of the implied basic sentence structure of modern geometric dimensioning and tolerance. The proper identification and interpretation of the substantive language within several exemplary engineering drawings, otherwise called feature control frames, is…
Water-water correlations in electrolyte solutions probed by hyper-Rayleigh scattering
Shelton, David P.
2017-12-01
Long-range ion-induced correlations between water molecules have been observed by second-harmonic or hyper-Rayleigh scattering experiments with conflicting results. The most recent work observed a large difference between the results for H2O and D2O, and large discrepancies with the previously proposed theory. However, the present observations are in quantitative agreement with the model where the ion electric field induces second harmonic generation by the water molecules, and ion-ion correlations given by the Debye-Huckel theory account for intensity saturation at high ion concentration. This work compares experimental results with theory and addresses the apparent discrepancies with previous experiments.
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.
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
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.
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
Directory of Open Access Journals (Sweden)
Maria de Hoyos Guajardo, Ph.D. Candidate, M.Sc., B.Eng.
2004-11-01
Full Text Available The theory that is presented below aims to conceptualise how a group of undergraduate students tackle non-routine mathematical problems during a problem-solving course. The aim of the course is to allow students to experience mathematics as a creative process and to reflect on their own experience. During the course, students are required to produce a written ‘rubric’ of their work, i.e., to document their thoughts as they occur as well as their emotionsduring the process. These ‘rubrics’ were used as the main source of data.Students’ problem-solving processes can be explained as a three-stage process that has been called ‘solutioning’. This process is presented in the six sections below. The first three refer to a common area of concern that can be called‘generating knowledge’. In this way, generating knowledge also includes issues related to ‘key ideas’ and ‘gaining understanding’. The third and the fourth sections refer to ‘generating’ and ‘validating a solution’, respectively. Finally, once solutions are generated and validated, students usually try to improve them further before presenting them as final results. Thus, the last section deals with‘improving a solution’. Although not all students go through all of the stages, it may be said that ‘solutioning’ considers students’ main concerns as they tackle non-routine mathematical problems.
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.
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
Directory of Open Access Journals (Sweden)
Nikolić Goran S.
2005-01-01
Full Text Available UV-VIS spectrophotometric investigations of Cu(II complexes with hydroge-nated dextran showed that the complexation of Cu(II-ions began at pH > 7. The formation of Cu(II complexes with dextran monomer units was observed at pH 7-12. With further increase in solution pH > 12, the Cu(II-dextran complex decomposed to Cu(OH42~-ions and dextran. With increasing solution pH the absorption maximum of complex solutions increased and shifted to shorter wavelength (hypsochromic shift compared with uncomplexed Cu(II. The UV spectra displayed bathochromic shifts. The changes of UV-VIS spectra with increasing in solution pH confirmed the formation of different kinds of complex species. The correlation between the results of UV-VIS spectrophotometry and the central metal ionligand coordination predicted that the copper binding within the complex depended on the pH and participation H2O molecules. Dextran complexes with Cu(II were formed by the displacement of water molecules from the coordination sphere of copper by OH groups. The analysis indicated that the Cu(II center was coordinated to two glucopyranose units of dextran. The spectrophotometric parameters of the investigated complexes were characteristic of a Cu(II-ion in a square-planar or tetragon ally distorted octahedral coordination.
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
Complete conformal field theory solution of a chiral six-point correlation function
Simmons, Jacob J. H.; Kleban, Peter
2011-08-01
Using conformal field theory, we perform a complete analysis of the chiral six-point correlation function C(z)=\\langle \\phi _{1,2}\\phi _{1,2} \\Phi _{1/2,0}(z, \\bar{z}) \\phi _{1,2}\\phi _{1,2} \\rangle, with the four phi1, 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.
Directory of Open Access Journals (Sweden)
Eva Anglada
2017-01-01
Full Text Available The correlation of the thermal mathematical models (TMMs of spacecrafts with the results of the thermal test is a demanding task in terms of time and effort. Theoretically, it can be automatized by means of optimization techniques, although this is a challenging task. Previous studies have shown the ability of genetic algorithms to perform this task in several cases, although some limitations have been detected. In addition, gradient-based methods, although also presenting some limitations, have provided good solutions in other technical fields. For this reason, the performance of genetic algorithms and gradient-based methods in the correlation of TMMs is discussed in this paper to compare the pros and cons of them. The case of study used in the comparison is a real space instrument flown aboard the International Space Station.
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.
Wooden Geometric Puzzles: Design and Hardness Proofs
Alt, H.; Bodlaender, H.L.; Kreveld, M.J. van; Rote, G.; Tel, G.
2008-01-01
We discuss some new geometric puzzles and the complexity of their extension to arbitrary sizes. For gate puzzles and two-layer puzzles we prove NP-completeness of solving them. Not only the solution of puzzles leads to interesting questions, but also puzzle design gives rise to interesting
Wooden Geometric Puzzles: Design and Hardness Proofs
Alt, H.; Bodlaender, H.L.; Kreveld, M.J. van; Rote, G.; Tel, G.
2007-01-01
We discuss some new geometric puzzles and the complexity of their extension to arbitrary sizes. For gate puzzles and two-layer puzzles we prove NP-completeness of solving them. Not only the solution of puzzles leads to interesting questions, but also puzzle design gives rise to interesting
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.
Pal, Nibedita; Dev Verma, Sachin; Singh, Moirangthem Kiran; Sen, Sobhan
2011-10-15
Fluorescence correlation spectroscopy (FCS) is an ideal tool for measuring molecular diffusion and size under extremely dilute conditions. However, the power of FCS has not been utilized to its best to measure diffusion and size parameters of complex chemical systems. Here, we apply FCS to measure the size, and, most importantly, the size distribution and polydispersity of a supramolecular nanostructure (i.e., microemulsion droplets, MEDs) in dilute solution. It is shown how the refractive index mismatch of a solution can be corrected in FCS to obtain accurate size parameters of particles, bypassing the optical matching problem of light scattering techniques that are used often for particle-size measurements. We studied the MEDs of 13 different W(0) values from 2 to 50 prepared in a ternary mixture of water, sodium bis(2-ethylhexyl) sulfosuccinate (AOT), and isooctane, with sulforhodamine-B as a fluorescent marker. We find that, near the optical matching point of MEDs, the dynamic light scattering (DLS) measurements underestimate the droplet sizes while FCS estimates the accurate ones. A Gaussian distribution model (GDM) and a maximum-entropy-based FCS data fitting model (MEMFCS) are used to analyze the fluorescence correlation curves that unfold Gaussian-type size distributions of MEDs in solution. We find the droplet size varies linearly with W(0) up to ~20, but beyond this W(0) value, the size variation deviates from this linearity. To explain nonlinear variation of droplet size for W(0) values beyond ~20, we invoke a model (the coated-droplet model) that incorporates the size polydispersity of the droplets. © 2011 American Chemical Society
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…
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.
Hamrang, Zahra; Pluen, Alain; Zindy, Egor; Clarke, David
2012-06-01
The application of raster image correlation spectroscopy (RICS) as a tool for the characterisation of protein diffusion was assessed using a model protein, bovine serum albumin (BSA), as a function of formulation and denaturing conditions. RICS results were also validated against dynamic light scattering and fluorescence correlation spectroscopy. Results from this study demonstrate correlation between outputs obtained from the three experimental techniques. Ionic strength independency was observed at pH 7, and a reduction in the corresponding diffusion coefficients was noted at pH 4.5 for 1 µM BSA-Alexa Fluor 488. Conversely, at pH 5.2, higher-concentration samples exhibited ionic strength dependency. Buffer composition, sample pretreatment, thermal denaturation and freeze-thaw cycling were also found to influence RICS output, with a reduction in the diffusion coefficient and the number of particles observed for both pH values. In conclusion, RICS analysis of images acquired using a commercial confocal microscope offers a potential scope for application to both quantitative and qualitative characterisation of macromolecular behaviour in solution. Copyright © 2012 Wiley Periodicals, Inc.
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)
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...
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...
Dong, Chaoqing; Liu, Heng; Ren, Jicun
2014-11-04
The current method for investigating the blinking behavior is to immobilize quantum dots (QDs) in the matrix and then apply a fluorescent technique to monitor the fluorescent trajectories of individual QDs. So far, no method can be used to directly assess the blinking state of ensemble QDs in free solution. In this study, a new method was described to characterize the blinking state of the QDs in free solution by combining single molecule fluorescence correlation spectroscopy (FCS) with ensemble spectroscopic methods. Its principle is based on the observation that the apparent concentration of bright QDs obtained by FCS is less than its actual concentration measured by ensemble spectroscopic method due to the QDs blinking. We proposed a blinking index (Kblink) for characterizing the blinking state of QDs, and Kblink is defined as the ratio of the actual concentration (Cb,actual) measured by the ensemble spectroscopic method to the apparent concentration (Cb,app) of QDs obtained by FCS. The effects of certain factors such as laser intensity, growth process, and ligands on blinking of QDs were investigated. The Kblink data of QDs obtained were successfully used to characterize the blinking state of QDs and explain certain experimental results.
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.
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.
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.
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
Perspective: Geometrically frustrated assemblies
Grason, Gregory M.
2016-09-01
This perspective will overview an emerging paradigm for self-organized soft materials, geometrically frustrated assemblies, where interactions between self-assembling elements (e.g., particles, macromolecules, proteins) favor local packing motifs that are incompatible with uniform global order in the assembly. This classification applies to a broad range of material assemblies including self-twisting protein filament bundles, amyloid fibers, chiral smectics and membranes, particle-coated droplets, curved protein shells, and phase-separated lipid vesicles. In assemblies, geometric frustration leads to a host of anomalous structural and thermodynamic properties, including heterogeneous and internally stressed equilibrium structures, self-limiting assembly, and topological defects in the equilibrium assembly structures. The purpose of this perspective is to (1) highlight the unifying principles and consequences of geometric frustration in soft matter assemblies; (2) classify the known distinct modes of frustration and review corresponding experimental examples; and (3) describe outstanding questions not yet addressed about the unique properties and behaviors of this broad class of systems.
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.
Geometric diffusion of quantum trajectories
Yang, Fan; Liu, Ren-Bao
2015-07-01
A quantum object can acquire a geometric phase (such as Berry phases and Aharonov-Bohm phases) when evolving along a path in a parameter space with non-trivial gauge structures. Inherent to quantum evolutions of wavepackets, quantum diffusion occurs along quantum trajectories. Here we show that quantum diffusion can also be geometric as characterized by the imaginary part of a geometric phase. The geometric quantum diffusion results from interference between different instantaneous eigenstate pathways which have different geometric phases during the adiabatic evolution. As a specific example, we study the quantum trajectories of optically excited electron-hole pairs in time-reversal symmetric insulators, driven by an elliptically polarized terahertz field. The imaginary geometric phase manifests itself as elliptical polarization in the terahertz sideband generation. The geometric quantum diffusion adds a new dimension to geometric phases and may have applications in many fields of physics, e.g., transport in topological insulators and novel electro-optical effects.
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.
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
Ambrosetti, Antonio; Malchiodi, Andrea
2009-01-01
This volume contains lecture notes on some topics in geometric analysis, a growing mathematical subject which uses analytical techniques, mostly of partial differential equations, to treat problems in differential geometry and mathematical physics. The presentation of the material should be rather accessible to non-experts in the field, since the presentation is didactic in nature. The reader will be provided with a survey containing some of the most exciting topics in the field, with a series of techniques used to treat such problems.
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 PROGRESSIONS ON ELLIPTIC CURVES.
Ciss, Abdoul Aziz; Moody, Dustin
2017-01-01
In this paper, we look at long geometric progressions on different model of elliptic curves, namely Weierstrass curves, Edwards and twisted Edwards curves, Huff curves and general quartics curves. By a geometric progression on an elliptic curve, we mean the existence of rational points on the curve whose x -coordinate (or y -coordinate) are in geometric progression. We find infinite families of twisted Edwards curves and Huff curves with geometric progressions of length 5, an infinite family of Weierstrass curves with 8 term progressions, as well as infinite families of quartic curves containing 10-term geometric progressions.
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.
Kitamura, Akira; Ishida, Yoshihito; Kubota, Hiroshi; Pack, Chan-Gi; Homma, Takayuki; Ito, Shinya; Araki, Kazutaka; Kinjo, Masataka; Nagata, Kazuhiro
2018-02-26
Heat shock protein 47 kDa (HSP47), an ER-resident and collagen-specific molecular chaperone, recognizes collagenous hydrophobic amino acid sequences (Gly-Pro-Hyp) and assists in secretion of correctly folded collagen. Elevated collagen production is correlated with HSP47 expression in various diseases, including fibrosis and keloid. HSP47 knockdown ameliorates liver fibrosis by inhibiting collagen secretion, and inhibition of the interaction of HSP47 with procollagen also prevents collagen secretion. Therefore, a high-throughput system for screening of drugs capable of inhibiting the interaction between HSP47 and collagen would aid the development of novel therapies for fibrotic diseases. In this study, we established a straightforward method for rapidly and quantitatively measuring the interaction between HSP47 and collagen in solution using fluorescence correlation spectroscopy (FCS). The diffusion rate of HSP47 labeled with Alexa Fluor 488 (HSP47-AF), a green fluorescent dye, decreased upon addition of type I or III collagen, whereas that of dye-labeled protein disulfide isomerase (PDI) or bovine serum albumin (BSA) did not, indicating that specific binding of HSP47 to collagen could be detected using FCS. Using this method, we calculated the dissociation constant of the interaction between HSP47 and collagen. The binding ratio between HSP47-AF and collagen did not change in the presence of sodium chloride, confirming that the interaction was hydrophobic in nature. In addition, we observed dissociation of collagen from HSP47 at low pH and re-association after recovery to neutral pH. These observations indicate that this system is appropriate for detecting the interaction between HSP47 and collagen, and could be applied to high-throughput screening for drugs capable of suppressing and/or curing fibrosis. Copyright © 2018 Elsevier Inc. All rights reserved.
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
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.
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
Directory of Open Access Journals (Sweden)
EMIL POPOVSKI
2006-10-01
Full Text Available The protonation of some meta and para substituted benzamides in sulfuric acid solutions was studied by UV spectroscopy in the 190–350 nm region. Principal component analysis was applied to separate the effect of protonation from the medium effect. The spectral region 200–350 nm was used for the calculation of the ionization ratio from coefficient of the first principal component, which explains about 95–98 % of the total variability. The dissociation constants as well as the solvation parameters m* and f were calculated using the excess acidity method and the Bunnett–Olsen method. The pKBH+ values obtained with the HA function (defined by the average m* -values are in satisfactory agreement with those calculated with the previously mentioned methods. The pKBH+ values were correlated with structure using the Hammett (r = – 0.91 and Taft approach. It was found that the inductive effect is more relevant than the resonance one for both substituted benzamides (meta and para.
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
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.)
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.
Energy Technology Data Exchange (ETDEWEB)
Goldberg, P.W.
1993-04-01
In this paper we consider the problem of learning the positions of spheres in metric spaces, given as data randomly drawn points classified according to whether they are internal or external to an unknown sphere. The particular metrics under consideration are geometrical shape metrics, and the results are intended to be applicable to the problem of learning to identify a shape from related shapes classified according to whether they resemble it visually. While it is typically NP-hard to locate a central point for a hypothesis sphere, we find that it is however often possible to obtain a non-spherical hypothesis which can accurately predict whether further random points lie within the unknown sphere. We exhibit algorithms which achieve this, and in the process indicate useful general techniques for computational learning. Finally we exhibit a natural shape metric and show that it defines a class of spheres not predictable in this sense, subject to standard cryptographic assumptions.
International Nuclear Information System (INIS)
Kobayashi, K.; Ohe, C.; Iguchi, K.
1996-01-01
The one-dimensional t-J model is investigated by the variational Monte Carlo method. A variational wave function based on the Bethe-ansatz solution is proposed, where the spin-charge separation is realized and a long-range correlation factor of Jastrow-type is included. In most regions of the phase diagram, this wave function provides an excellent description of the ground-state properties characterized as a Tomonaga-Luttinger liquid; both the amplitude and exponent of correlation functions are correctly reproduced. For the spin-gap phase, another trial state of correlated singlet pairs with a Jastrow factor is introduced. This wave function shows generalized Luther-Emery-liquid behavior, exhibiting enhanced superconducting correlations and exponential decay of the spin correlation function. Using these two variational wave functions, the whole phase diagram is determined. In addition, relations between the correlation exponent and variational parameters in the trial functions are derived. copyright 1996 The American Physical Society
Fukuda, Masakazu; Moriyama, Chifumi; Yamazaki, Tadao; Imaeda, Yoshimi; Koga, Akiko
2015-12-01
To investigate the relationship between viscosity of concentrated MAb solutions and particle size parameters obtained from small-angle X-ray scattering (SAXS). The viscosity of three MAb solutions (MAb1, MAb2, and MAb3; 40-200 mg/mL) was measured by electromagnetically spinning viscometer. The protein interactions of MAb solutions (at 60 mg/mL) was evaluated by SAXS. The phase behavior of 60 mg/mL MAb solutions in a low-salt buffer was observed after 1 week storage at 25°C. The MAb1 solutions exhibited the highest viscosity among the three MAbs in the buffer containing 50 mM NaCl. Viscosity of MAb1 solutions decreased with increasing temperature, increasing salt concentration, and addition of amino acids. Viscosity of MAb1 solutions was lowest in the buffer containing histidine, arginine, and aspartic acid. Particle size parameters obtained from SAXS measurements correlated very well with the viscosity of MAb solutions at 200 mg/mL. MAb1 exhibited liquid-liquid phase separation at a low salt concentration. Simultaneous addition of basic and acidic amino acids effectively suppressed intermolecular attractive interactions and decreased viscosity of MAb1 solutions. SAXS can be performed using a small volume of samples; therefore, the particle size parameters obtained from SAXS at intermediate protein concentration could be used to screen for low viscosity antibodies in the early development stage.
Non-geometric branes are DFT monopoles
Energy Technology Data Exchange (ETDEWEB)
Bakhmatov, Ilya [Kazan Federal University, Institute of Physics, General Relativity Department,Kremlevskaya 16a, 420111, Kazan (Russian Federation); Kleinschmidt, Axel [Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut),Am Mühlenberg 1, DE-14476 Potsdam (Germany); International Solvay Institutes,Campus Plaine C.P. 231, Boulevard du Triomphe, 1050 Bruxelles (Belgium); Musaev, Edvard T. [Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut),Am Mühlenberg 1, DE-14476 Potsdam (Germany); Kazan Federal University, Institute of Physics, General Relativity Department,Kremlevskaya 16a, 420111, Kazan (Russian Federation)
2016-10-14
The double field theory monopole solution by Berman and Rudolph is shown to reproduce non-geometric backgrounds with non-vanishing Q- and R-flux upon an appropriate choice of physical and dual coordinates. The obtained backgrounds depend non-trivially on dual coordinates and have only trivial monodromies. Upon smearing the solutions along the dual coordinates one reproduces the known 5{sub 2}{sup 2} solution for the Q-brane and co-dimension 1 solution for the R-brane. The T-duality invariant magnetic charge is explicitly calculated for all these backgrounds and is found to be equal to the magnetic charge of (unsmeared) NS5-brane.
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.
Stabilization of LCD devices via geometric alteration.
Jeon, Il; Yoon, MinSung; Lee, Je-Hoon
2013-02-20
Glass bending in LCD displays is an inherent problem that has challenged many engineers. As a solution to this problem, we propose a methodology that can tackle the root of the phenomenon in terms of linear elastic beam theory. Using this hypothesis, we devised a background theory and a solution. In this paper, we present a glass panel to which geometrical changes, such as furrow, groove, and curb have been applied. These geometrical changes are applied to the nonactive area of the glass panel. To confirm the validity of our approach, we conducted simulation tests as well as hands-on experiments to observe the thermo-mechanical behavior of the device under various conditions. The simulation results using the Ansys simulator show that the proposed technique can reduce the deformation level of panel bending by 40%. In the experiment using a bare cell with polarizer films attached and with performing the high temperature reliability test, the deformation level of panel bending is reduced by half compared to the reference glass panel without any geometric alteration.
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...
Chern-Simons term in the geometric theory of defects
Katanaev, M. O.
2017-10-01
The Chern-Simons term is used in the geometric theory of defects. The equilibrium equations with δ -function source are explicitly solved with respect to the S O (3 ) connection. This solution describes one straight linear disclination and corresponds to the singularity in the connection but not the metric which is the flat Euclidean metric. This is the first example of a disclination described within the geometric theory of defects. The corresponding angular rotation field is computed.
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
Fisher metric, geometric entanglement, and spin networks
Chirco, Goffredo; Mele, Fabio M.; Oriti, Daniele; Vitale, Patrizia
2018-02-01
Starting from recent results on the geometric formulation of quantum mechanics, we propose a new information geometric characterization of entanglement for spin network states in the context of quantum gravity. For the simple case of a single-link fixed graph (Wilson line), we detail the construction of a Riemannian Fisher metric tensor and a symplectic structure on the graph Hilbert space, showing how these encode the whole information about separability and entanglement. In particular, the Fisher metric defines an entanglement monotone which provides a notion of distance among states in the Hilbert space. In the maximally entangled gauge-invariant case, the entanglement monotone is proportional to a power of the area of the surface dual to the link thus supporting a connection between entanglement and the (simplicial) geometric properties of spin network states. We further extend such analysis to the study of nonlocal correlations between two nonadjacent regions of a generic spin network graph characterized by the bipartite unfolding of an intertwiner state. Our analysis confirms the interpretation of spin network bonds as a result of entanglement and to regard the same spin network graph as an information graph, whose connectivity encodes, both at the local and nonlocal level, the quantum correlations among its parts. This gives a further connection between entanglement and geometry.
Computer modeling of electromagnetic problems using the geometrical theory of diffraction
Burnside, W. D.
1976-01-01
Some applications of the geometrical theory of diffraction (GTD), a high frequency ray optical solution to electromagnetic problems, are presented. GTD extends geometric optics, which does not take into account the diffractions occurring at edges, vertices, and various other discontinuities. Diffraction solutions, analysis of basic structures, construction of more complex structures, and coupling using GTD are discussed.
Krebs, Derek; Budynas, Richard G.
A common procedure for performing a cross orthogonality check for the purpose of modal correlation between the test and the finite element analysis results incorporates the Guyan reduction method to obtain a reduced mass matrix. This paper describes a procedure which uses NASTRAN's Generalized Dynamic Reduction solution routine which is much more accurate than the standard Guyan reduction solution and which offers the advantage of not requiring the selection of mdof. Using NASTRAN's DMAP programming methods, a modal reduction of the full analytical mass matrix is performed based on the accelerometer locations and the analytical modal matrix results. The accuracy of the procedure is illustrated in two case studies.
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
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 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.
Antenna with Dielectric Having Geometric Patterns
Dudley, Kenneth L. (Inventor); Elliott, Holly A. (Inventor); Cravey, Robin L. (Inventor); Connell, John W. (Inventor); Ghose, Sayata (Inventor); Watson, Kent A. (Inventor); Smith, Jr., Joseph G. (Inventor)
2013-01-01
An antenna includes a ground plane, a dielectric disposed on the ground plane, and an electrically-conductive radiator disposed on the dielectric. The dielectric includes at least one layer of a first dielectric material and a second dielectric material that collectively define a dielectric geometric pattern, which may comprise a fractal geometry. The radiator defines a radiator geometric pattern, and the dielectric geometric pattern is geometrically identical, or substantially geometrically identical, to the radiator geometric pattern.
Ling, Zongcheng; Cao, Fengke; Ni, Yuheng; Wu, Zhongchen; Zhang, Jiang; Li, Bo
2016-06-01
Detailed chemical, structural and spectroscopic properties of jarosite solid solution minerals are key information for their potential discoveries by future remote sensing and in-situ detections on Mars. We successfully synthesized seven homogeneous K-Na jarosite solid solutions under hydrothermal conditions at 140 °C, whose phase identifications and chemical compositions are confirmed by X-ray diffraction (XRD) and inductively coupled plasma mass spectrometry (ICP-MS). The chemical ratios of K/(K+Na) in jarosite solid solutions lead to systematic shifts of their characteristic Raman peaks ν1 (SO4)2- (from 1006 to 1011.3 cm-1), ν3 (SO4)2- (from 1100.6 to 1111.2 cm-1), ν2 (SO4)2- (from 434.2 to 444.8 cm-1) with the increase of Na content. While the OH stretching mode decreases with even larger peak position variations (e.g., ∼3410 cm-1 peak shifts from 3410.5 to 3385.7 cm-1) as the K-Na jarosite solid solutions are enriched in Na content. Raman spectroscopic measurements of the seven K-Na jarosite solid solutions enabled us to build a calibration that uses Raman peak positions to estimate K-Na variation in jarosite, which is the key step for their possible applications in the future Raman applications on Mars' missions (e.g., ExoMars and Mars 2020 missions). The band assignments and compositional related variations of their XRD, near-infrared (NIR) and mid-infrared (MIR) spectra also provide informative clues for identifying the jarosite minerals and inferring their composition during martian in-situ and remote sensing measurements.
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.
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...
Geometric actions for three-dimensional gravity
Barnich, G.; González, H. A.; Salgado-Rebolledo, P.
2018-01-01
The solution space of three-dimensional asymptotically anti-de Sitter or flat Einstein gravity is given by the coadjoint representation of two copies of the Virasoro group in the former and the centrally extended BMS3 group in the latter case. Dynamical actions that control these solution spaces are usually constructed by starting from the Chern–Simons formulation and imposing all boundary conditions. In this note, an alternative route is followed. We study in detail how to derive these actions from a group-theoretical viewpoint by constructing geometric actions for each of the coadjoint orbits, including the appropriate Hamiltonians. We briefly sketch relevant generalizations and potential applications beyond three-dimensional gravity.
A geometric viewpoint on generalized hydrodynamics
Doyon, Benjamin; Spohn, Herbert; Yoshimura, Takato
2018-01-01
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.
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
Czech Academy of Sciences Publication Activity Database
Bonné, T. B.; Lüdtke, K.; Jordan, R.; Štěpánek, Petr; Papadakis, C. M.
2004-01-01
Roč. 282, č. 12 (2004), s. 833-843 ISSN 0303-402X R&D Projects: GA AV ČR IAA4050403 Keywords : self-diffusion * fluorescence correlation spectroscopy * amphiphilic diblock copolymers Subject RIV: CD - Macromolecular Chemistry Impact factor: 1.110, year: 2004
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.
Kalmykov, Yu. P.; Coffey, W. T.; Waldron, J. T.
1996-08-01
The correlation time of the positional autocorrelation function is calculated exactly for one-dimensional translational Brownian motion of a particle in a 2-4 double-well potential in the noninertial limit. The calculations are carried out using the method of direct conversion (by averaging) of the Langevin equation for a nonlinear stochastic system to a set of differential-recurrence relations. These, in the present problem, reduce on taking the Laplace transform, to a three-term recurrence relation. Thus the correlation time Tc of the positional autocorrelation function may be formally expressed as a sum of products of infinite continued fractions which may be represented in series form as a sum of two term products of Whittaker's parabolic cylinder functions. The sum of this series may be expressed as an integral using the integral representation of the parabolic cylinder functions and subsequently the Taylor expansion of the error function, thus yielding the exact solution for Tc. This solution is in numerical agreement with that obtained by Perico et al. [J. Chem. Phys. 98, 564 (1993)] using the first passage time approach while previous asymptotic results obtained by solving the underlying Smoluchowski equation are recovered in the limit of high barrier heights. A simple empirical formula which provides a close approximation to the exact solution for all barrier heights is also given.
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 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.
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.
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.
Geometric identities in stereological particle analysis
DEFF Research Database (Denmark)
Kötzer, S.; Jensen, Eva Bjørn Vedel; Baddeley, A.
We review recent findings about geometric identities in integral geometry and geometric tomography, and their statistical application to stereological particle analysis. Open questions are discussed.......We review recent findings about geometric identities in integral geometry and geometric tomography, and their statistical application to stereological particle analysis. Open questions are discussed....
Geometric Langlands From Six Dimensions
Witten, Edward
2010-01-01
Geometric Langlands duality is usually formulated as a statement about Riemann surfaces, but it can be naturally understood as a consequence of electric-magnetic duality of four-dimensional gauge theory. This duality in turn is naturally understood as a consequence of the existence of a certain exotic supersymmetric conformal field theory in six dimensions. The same six-dimensional theory also gives a useful framework for understanding some recent mathematical results involving a counterpart of geometric Langlands duality for complex surfaces. (This article is based on a lecture at the Raoul Bott celebration, Montreal, June 2008.)
Catching homologies by geometric entropy
Felice, Domenico; Franzosi, Roberto; Mancini, Stefano; Pettini, Marco
2018-02-01
A geometric entropy is defined in terms of the Riemannian volume of the parameter space of a statistical manifold associated with a given network. As such it can be a good candidate for measuring networks complexity. Here we investigate its ability to single out topological features of networks proceeding in a bottom-up manner: first we consider small size networks by analytical methods and then large size networks by numerical techniques. Two different classes of networks, the random graphs and the scale-free networks, are investigated computing their Betti numbers and then showing the capability of geometric entropy of detecting homologies.
A Geometric Approach to the Problem of Unique Decomposition of Processes
Balabonski, Thibaut; Haucourt, Emmanuel
This paper proposes a geometric solution to the problem of prime decomposability of concurrent processes first explored by R. Milner and F. Moller in [MM93]. Concurrent programs are given a geometric semantics using cubical areas, for which a unique factorization theorem is proved. An effective factorization method which is correct and complete with respect to the geometric semantics is derived from the factorization theorem. This algorithm is implemented in the static analyzer ALCOOL.
Iso-geometric analysis for neutron diffusion problems
International Nuclear Information System (INIS)
Hall, S. K.; Eaton, M. D.; Williams, M. M. R.
2012-01-01
Iso-geometric analysis can be viewed as a generalisation of the finite element method. It permits the exact representation of a wider range of geometries including conic sections. This is possible due to the use of concepts employed in computer-aided design. The underlying mathematical representations from computer-aided design are used to capture both the geometry and approximate the solution. In this paper the neutron diffusion equation is solved using iso-geometric analysis. The practical advantages are highlighted by looking at the problem of a circular fuel pin in a square moderator. For this problem the finite element method requires the geometry to be approximated. This leads to errors in the shape and size of the interface between the fuel and the moderator. In contrast to this iso-geometric analysis allows the interface to be represented exactly. It is found that, due to a cancellation of errors, the finite element method converges more quickly than iso-geometric analysis for this problem. A fuel pin in a vacuum was then considered as this problem is highly sensitive to the leakage across the interface. In this case iso-geometric analysis greatly outperforms the finite element method. Due to the improvement in the representation of the geometry iso-geometric analysis can outperform traditional finite element methods. It is proposed that the use of iso-geometric analysis on neutron transport problems will allow deterministic solutions to be obtained for exact geometries. Something that is only currently possible with Monte Carlo techniques. (authors)
Sibi, N.; Subodh, G.
2017-12-01
Garnets are naturally occurring minerals with the general formula X3Y2Z3O12 having various applications. In the present study, the structural and physical properties of a garnet mineral obtained from Indian Rare Earth Ltd., Manavalakurichi, Tamil Nadu, India were comprehensively investigated. The compositional analysis using electron probe micro analysis (EPMA) revealed that the mineral belongs to almandine-pyrope solid solution (Al70Py29) with the chemical formula (Fe1.72Mg0.8Mn0.01Ca0.02) (Fe0.04Al2.36) Si2.93O12. Rietveld refinement of the x-ray diffraction pattern confirms that the space group is Ia{ - }\\overline{3} d with refined cubic lattice parameter a = 11.550(4) Å. The refined occupancy values of multiple cations in the dodecahedral and octahedral sites are in agreement with the EPMA data. Fourier transform infrared and FT Raman spectra show bands corresponding to almandine-pyrope solid solution. Peak splitting of IR and Raman bands confirms presence of multiple cations in the dodecahedral site. Thermogravimetric/differential thermal analysis shows that the mineral is stable up to 600°C in spite of the presence of Fe2+ ions. Low temperature magnetic susceptibility data is in agreement with the amount of Fe2+ ions present in the mineral. The dielectric constant of the mineral varied from 6 to 16.5 when sintered at temperatures ranging from 600°C to 1250°C.
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)
Gaussian geometric discord in terms of Hellinger distance
Suciu, Serban; Isar, Aurelian
2015-12-01
In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we address the quantification of general non-classical correlations in Gaussian states of continuous variable systems from a geometric perspective. We give a description of the Gaussian geometric discord by using the Hellinger distance as a measure for quantum correlations between two non-interacting non-resonant bosonic modes embedded in a thermal environment. We evaluate the Gaussian geometric discord by taking two-mode squeezed thermal states as initial states of the system and show that it has finite values between 0 and 1 and that it decays asymptotically to zero in time under the effect of the thermal bath.
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
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 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.)
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...
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)
Calculation of Weighted Geometric Dilution of Precision
Directory of Open Access Journals (Sweden)
Chien-Sheng Chen
2013-01-01
Full Text Available To achieve high accuracy in wireless positioning systems, both accurate measurements and good geometric relationship between the mobile device and the measurement units are required. Geometric dilution of precision (GDOP is widely used as a criterion for selecting measurement units, since it represents the geometric effect on the relationship between measurement error and positioning determination error. In the calculation of GDOP value, the maximum volume method does not necessarily guarantee the selection of the optimal four measurement units with minimum GDOP. The conventional matrix inversion method for GDOP calculation demands a large amount of operation and causes high power consumption. To select the subset of the most appropriate location measurement units which give the minimum positioning error, we need to consider not only the GDOP effect but also the error statistics property. In this paper, we employ the weighted GDOP (WGDOP, instead of GDOP, to select measurement units so as to improve the accuracy of location. The handheld global positioning system (GPS devices and mobile phones with GPS chips can merely provide limited calculation ability and power capacity. Therefore, it is very imperative to obtain WGDOP accurately and efficiently. This paper proposed two formations of WGDOP with less computation when four measurements are available for location purposes. The proposed formulae can reduce the computational complexity required for computing the matrix inversion. The simpler WGDOP formulae for both the 2D and the 3D location estimation, without inverting a matrix, can be applied not only to GPS but also to wireless sensor networks (WSN and cellular communication systems. Furthermore, the proposed formulae are able to provide precise solution of WGDOP calculation without incurring any approximation error.
Directory of Open Access Journals (Sweden)
Robert Hernández-Ortega
2012-12-01
Full Text Available Este trabajo tuvo como objetivo obtener un procedimiento, que al implementarse en un software para el diseño de transmisiones por engranajes cilíndricos con contacto exterior, correlacione automáticamente los parámetros geométricos mediante los contornos de bloqueo y así facilitar el trabajo del diseñador deengranajes. Para ello, se transformaron las expresiones matemáticas que definen las limitaciones geométricas para que puedan ser utilizadas en un programa que construya el contorno de bloqueo sin la intervención del diseñador. Se estableció además la secuencia en que estas deben ser calculadas. El procedimiento obtenido se implementó en un programa de computación obteniéndose una velocidad deejecución de 1 segundo aproximadamente. De esta forma se logró la correlación automática de los parámetros geométricos y un contorno de bloqueo que muestra el conjunto de valores de los coeficientes de corrección de las ruedas que pueden ser utilizados, construidos sin interacción con el diseñador.Palabras claves: contorno de bloqueo, engranajes, parámetros geométricos._______________________________________________________________________________AbstractThe aim of this work was to obtain a procedure, that when being implemented in the design software of spur and helical external gears, correlate the geometric parameters automatically by means of the blocking contours making easier the designer's work. The mathematical expressions that define the geometriclimitations were transformed so that they can be used in a program that it builds the blocking contour without the designer's intervention. Besides that it was settled down the sequence they should be calculated. The procedure was implemented in a calculation program obtaining an execution speed about 1 second. This way it was achieved the automatic correlation of the geometric parameters and a blockingcontour construction without the designer's intervention that it shows the
Chen, Y.; Boucherie, Richardus J.; Goseling, Jasper
2011-01-01
We consider the invariant measure of a homogeneous continuous-time Markov process in the quarter-plane. The basic solutions of the global balance equation are the geometric distributions. We first show that the invariant measure can not be a finite linear combination of basic geometric
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
Analytic results on the geometric entropy for free fields
International Nuclear Information System (INIS)
Casini, H; Huerta, M
2008-01-01
The trace of integer powers of the local density matrix ρ V corresponding to the vacuum state reduced to a region V can be formally expressed in terms of a functional integral on a manifold with conical singularities. Recently, some progress has been made in explicitly evaluating this type of integral for free fields. However, finding the associated geometric entropy remained, in general, a difficult task involving an analytic continuation in the conical angle. In this paper, we obtain this analytic continuation explicitly, exploiting a relation between the functional integral formulas and the Chung–Peschel expressions for ρ V in terms of correlators. The result is that the entropy is given in terms of a functional integral in flat Euclidean space with a cut on V where a specific boundary condition is imposed. As an example, we get the exact entanglement entropies for massive scalar and Dirac free fields in 1+1 dimensions in terms of the solutions of a nonlinear differential equation of the Painlevé V type
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.
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.
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...
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
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)
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
Geometric monodromy - Semisimplicity and maximality
Cadoret, Anna; Hui, Chun Yin; Tamagawa, Akio
2017-01-01
Let X be a connected scheme, smooth and separated over an alge- braically closed field k of characteristic p ≥ 0, let f: Y → X be a smooth proper morphism and x a geometric point on X. We prove that the tensor invariants of bounded length ≤ d of π1(X; x) acting on the étale cohomology groups H*(Yx;
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...
Polar metals by geometric design
Kim, T. H.; Puggioni, D.; Yuan, Y.; Xie, L.; Zhou, H.; Campbell, N.; Ryan, P. J.; Choi, Y.; Kim, J.-W.; Patzner, J. R.; Ryu, S.; Podkaminer, J. P.; Irwin, J.; Ma, Y.; Fennie, C. J.; Rzchowski, M. S.; Pan, X. Q.; Gopalan, V.; Rondinelli, J. M.; Eom, C. B.
2016-05-01
Gauss’s law dictates that the net electric field inside a conductor in electrostatic equilibrium is zero by effective charge screening; free carriers within a metal eliminate internal dipoles that may arise owing to asymmetric charge distributions. Quantum physics supports this view, demonstrating that delocalized electrons make a static macroscopic polarization, an ill-defined quantity in metals—it is exceedingly unusual to find a polar metal that exhibits long-range ordered dipoles owing to cooperative atomic displacements aligned from dipolar interactions as in insulating phases. Here we describe the quantum mechanical design and experimental realization of room-temperature polar metals in thin-film ANiO3 perovskite nickelates using a strategy based on atomic-scale control of inversion-preserving (centric) displacements. We predict with ab initio calculations that cooperative polar A cation displacements are geometrically stabilized with a non-equilibrium amplitude and tilt pattern of the corner-connected NiO6 octahedra—the structural signatures of perovskites—owing to geometric constraints imposed by the underlying substrate. Heteroepitaxial thin-films grown on LaAlO3 (111) substrates fulfil the design principles. We achieve both a conducting polar monoclinic oxide that is inaccessible in compositionally identical films grown on (001) substrates, and observe a hidden, previously unreported, non-equilibrium structure in thin-film geometries. We expect that the geometric stabilization approach will provide novel avenues for realizing new multifunctional materials with unusual coexisting properties.
An Information Geometric Analysis of Entangled Continuous Variable Quantum Systems
Energy Technology Data Exchange (ETDEWEB)
Kim, D-H [Institute for the Early Universe, Ewha Womans University, Seoul 120-750 (Korea, Republic of); Ali, S A [Department of Physics, State University of New York at Albany, 1400 Washington Avenue, Albany, NY 12222 (United States); Cafaro, C; Mancini, S [School of Science and Technology, Physics Division, University of Camerino, I-62032 Camerino (Italy)
2011-07-08
In this work, using information geometric (IG) techniques, we investigate the effects of micro-correlations on the evolution of maximal probability paths on statistical manifolds induced by systems whose microscopic degrees of freedom are Gaussian distributed. Analytical estimates of the information geometric entropy (IGE) as well as the IG analogue of the Lyapunov exponents are presented. It is shown that the entanglement duration is related to the scattering potential and incident particle energies. Finally, the degree of entanglement generated by an s-wave scattering event between minimum uncertainty wave-packets is computed in terms of the purity of the system.
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)
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 Computations On Indecisive Points
DEFF Research Database (Denmark)
Jørgensen, Allan Grønlund; Phillips, Jeff; Loffler, Maarten
2011-01-01
We study computing with indecisive point sets. Such points have spatial uncertainty where the true location is one of a finite number of possible locations. This data arises from probing distributions a few times or when the location is one of a few locations from a known database. In particular......, we study computing distributions of geometric functions such as the radius of the smallest enclosing ball and the diameter. Surprisingly, we can compute the distribution of the radius of the smallest enclosing ball exactly in polynomial time, but computing the same distribution for the diameter is #P...
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
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
Li, Shuoguo; Ji, Gang; Shi, Yang; Klausen, Lasse Hyldgaard; Niu, Tongxin; Wang, Shengliu; Huang, Xiaojun; Ding, Wei; Zhang, Xiang; Dong, Mingdong; Xu, Wei; Sun, Fei
2018-01-01
Cryo-correlative light and electron microscopy (cryo-CLEM) offers a unique way to analyze the high-resolution structural information of cryo-vitrified specimen by cryo-electron microscopy (cryo-EM) with the guide of the search for unique events by cryo-fluorescence microscopy (cryo-FM). To achieve cryo-FM, a trade-off must be made between the temperature and performance of objective lens. The temperature of specimen should be kept below devitrification while the distance between the objective lens and specimen should be short enough for high resolution imaging. Although special objective lens was designed in many current cryo-FM approaches, the unavoided frosting and ice contamination are still affecting the efficiency of cryo-CLEM. In addition, the correlation accuracy between cryo-FM and cryo-EM would be reduced during the current specimen transfer procedure. Here, we report an improved cryo-CLEM technique (high-vacuum optical platform for cryo-CLEM, HOPE) based on a high-vacuum optical stage and a commercial cryo-EM holder. The HOPE stage comprises of a special adapter to suit the cryo-EM holder and a high-vacuum chamber with an anti-contamination system. It provides a clean and enduring environment for cryo specimen, while the normal dry objective lens in room temperature can be used via the optical windows. The 'touch-free' specimen transfer via cryo-EM holder allows least specimen deformation and thus maximizes the correlation accuracy between cryo-FM and cryo-EM. Besides, we developed a software to perform semi-automatic cryo-EM acquisition of the target region localized by cryo-FM. Our work provides a new solution for cryo-CLEM and can be adapted for different commercial fluorescence microscope and electron microscope. Copyright © 2017 Elsevier Inc. All rights reserved.
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.
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...
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...
Geometrical charged-particle optics
Rose, Harald H
2009-01-01
This reference monograph covers all theoretical aspects of modern geometrical charged-particle optics. It is intended as a guide for researchers, who are involved in the design of electron optical instruments and beam-guiding systems for charged particles, and as a tutorial for graduate students seeking a comprehensive treatment. Procedures for calculating the properties of systems with arbitrarily curved axes are outlined in detail and methods are discussed for designing and optimizing special components such as aberration correctors, spectrometers, energy filters, monochromators, ion traps, electron mirrors and cathode lenses. Also addressed is the design of novel electron optical components enabling sub-Angstroem spatial resolution and sub-0.1eV energy resolution. Relativistic motion and spin precession of the electron is treated in a concise way by employing a covariant five-dimensional procedure.
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 algebra in plasma electrodynamics
Resendes, D. P.; Resendes
2013-10-01
Geometric algebra (GA) is a recent broad mathematical framework incorporating synthetic and coordinate geometry, complex variables, quarternions, vector analysis, matrix algebra, spinors, tensors, and differential forms. It has been claimed to be a unified language for physics. GA is presented in the context of the Maxwell-Plasma system. In this formalism the divergence and curl differential operators are united in a single vector derivative, which is invertible, in the form of a first-order Green function. The four Maxwell equations can be combined into a single equation (for homogeneous and constant media) or into two equations involving the invertible vector derivative for more complex media. GA is applied to simple examples to illustrate the compactness of the notation and coordinate-free computations.
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.
Geometric Analogue of Holographic Reduced Representation
Aerts, Diederik; Czachor, Marek; De Moor, Bart
2007-01-01
Holographic reduced representations (HRR) are based on superpositions of convolution-bound $n$-tuples, but the $n$-tuples cannot be regarded as vectors since the formalism is basis dependent. This is why HRR cannot be associated with geometric structures. Replacing convolutions by geometric products one arrives at reduced representations analogous to HRR but interpretable in terms of geometry. Variable bindings occurring in both HRR and its geometric analogue mathematically correspond to two ...
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
Geometric Aspects of Iterated Matrix Multiplication
DEFF Research Database (Denmark)
Gesmundo, Fulvio
2016-01-01
This paper studies geometric properties of the Iterated Matrix Multiplication polynomial and the hypersurface that it defines. We focus on geometric aspects that may be relevant for complexity theory such as the symmetry group of the polynomial, the dual variety and the Jacobian loci of the hyper......This paper studies geometric properties of the Iterated Matrix Multiplication polynomial and the hypersurface that it defines. We focus on geometric aspects that may be relevant for complexity theory such as the symmetry group of the polynomial, the dual variety and the Jacobian loci...
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. .
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)
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.
Generalized Geometric Quantum Speed Limits
Pires, Diego Paiva; Cianciaruso, Marco; Céleri, Lucas C.; Adesso, Gerardo; Soares-Pinto, Diogo O.
2016-04-01
The attempt to gain a theoretical understanding of the concept of time in quantum mechanics has triggered significant progress towards the search for faster and more efficient quantum technologies. One of such advances consists in the interpretation of the time-energy uncertainty relations as lower bounds for the minimal evolution time between two distinguishable states of a quantum system, also known as quantum speed limits. We investigate how the nonuniqueness of a bona fide measure of distinguishability defined on the quantum-state space affects the quantum speed limits and can be exploited in order to derive improved bounds. Specifically, we establish an infinite family of quantum speed limits valid for unitary and nonunitary evolutions, based on an elegant information geometric formalism. Our work unifies and generalizes existing results on quantum speed limits and provides instances of novel bounds that are tighter than any established one based on the conventional quantum Fisher information. We illustrate our findings with relevant examples, demonstrating the importance of choosing different information metrics for open system dynamics, as well as clarifying the roles of classical populations versus quantum coherences, in the determination and saturation of the speed limits. Our results can find applications in the optimization and control of quantum technologies such as quantum computation and metrology, and might provide new insights in fundamental investigations of quantum thermodynamics.
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 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.
Geometric aspects of ordering phenomena
Cugliandolo, Leticia F.
2017-01-01
A macroscopic system prepared in a disordered phase and quenched across a second-order phase transition into an ordered phase undergoes a coarsening process whereby it orders locally in one of the equilibrium states. The study of the evolution of the morphology of the ordered structures in two dimensions has recently unveiled two interesting and generic features. On the one hand, the dynamics first approach a critical percolating state via the growth of a new lengthscale and satisfying scaling properties with respect to it. The time needed to reach the critical percolating state diverges with the system size, though more weakly than the equilibration time. On the other hand, once the critical percolating structures established, the geometrical and statistical properties at larger scales than the one established by the usual dynamic growing length remain the ones of critical percolation. These observations are common to different microscopic dynamics (single spin flip, local and non-local spin exchange, voter) in pure or weakly disordered systems. We discuss these results and we refer to the relevant publications for details. xml:lang="fr"
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.
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 about assembly tools
Energy Technology Data Exchange (ETDEWEB)
Wilson, R.H.
1997-01-01
Planning for assembly requires reasoning about various tools used by humans, robots, or other automation to manipulate, attach, and test parts and subassemblies. This paper presents a general framework to represent and reason about geometric accessibility issues for a wide variety of such assembly tools. Central to the framework is a use volume encoding a minimum space that must be free in an assembly state to apply a given tool, and placement constraints on where that volume must be placed relative to the parts on which the tool acts. Determining whether a tool can be applied in a given assembly state is then reduced to an instance of the FINDPLACE problem. In addition, the author presents more efficient methods to integrate the framework into assembly planning. For tools that are applied either before or after their target parts are mated, one method pre-processes a single tool application for all possible states of assembly of a product in polynomial time, reducing all later state-tool queries to evaluations of a simple expression. For tools applied after their target parts are mated, a complementary method guarantees polynomial-time assembly planning. The author presents a wide variety of tools that can be described adequately using the approach, and surveys tool catalogs to determine coverage of standard tools. Finally, the author describes an implementation of the approach in an assembly planning system and experiments with a library of over one hundred manual and robotic tools and several complex assemblies.
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...
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
Geometric singular perturbation analysis of systems with friction
DEFF Research Database (Denmark)
Bossolini, Elena
This thesis is concerned with the application of geometric singular perturbation theory to mechanical systems with friction. The mathematical background on geometric singular perturbation theory, on the blow-up method, on non-smooth dynamical systems and on regularization is presented. Thereafter...... use a Poincaré compactiﬁcation to study the system near inﬁnity. At inﬁnity, the critical manifold loses hyperbolicity with an exponential rate. We use an adaptation of the blow-up method to recover the hyperbolicity. This enables the identiﬁcation of a new attracting manifold, that organises...... singular, in contrast to the regular stiction solutions that are forward unique. In order to further the understanding of the non-unique dynamics, we introduce a regularization of the model. This gives a singularly perturbed problem that captures the main features of the original discontinuous problem. We...
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 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.
A geometric characterization of arithmetic varieties
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
The main result is the characterization of arithmetically defined divisors in the plane as geometrically rigid divisors in the plane. Keywords. Equisingular; geometrically rigid. 1. Introduction. This paper is an attempt to generalize a result of Belyi (see [1]). Theorem (Belyi). Let C be a smooth projective curve over an algebraic ...
Early Sex Differences in Weighting Geometric Cues
Lourenco, Stella F.; Addy, Dede; Huttenlocher, Janellen; Fabian, Lydia
2011-01-01
When geometric and non-geometric information are both available for specifying location, men have been shown to rely more heavily on geometry compared to women. To shed insight on the nature and developmental origins of this sex difference, we examined how 18- to 24-month-olds represented the geometry of a surrounding (rectangular) space when…
Geometric Growing Patterns: What's the Rule?
Hourigan, Mairéad; Leavy, Aisling
2015-01-01
While within a geometric repeating pattern, there is an identifiable core which is made up of objects that repeat in a predictable manner, a geometric growing pattern (also called visual or pictorial growing patterns in other curricula) "is a pattern that is made from a sequence of figures [or objects] that change from one term to the next in…
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
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.
Li, Wei
2013-01-01
A linear scaling quantum chemistry method, generalized energy-based fragmentation (GEBF) approach has been extended to the explicitly correlated second-order Møller-Plesset perturbation theory F12 (MP2-F12) method and own N-layer integrated molecular orbital molecular mechanics (ONIOM) method, in which GEBF-MP2-F12, GEBF-MP2, and conventional density functional tight-binding methods could be used for different layers. Then the long-range interactions in dilute methanol aqueous solutions are studied by computing the binding energies between methanol molecule and water molecules in gas-phase and condensed phase methanol-water clusters with various sizes, which were taken from classic molecular dynamics (MD) snapshots. By comparing with the results of force field methods, including SPC, TIP3P, PCFF, and AMOEBA09, the GEBF-MP2-F12 and GEBF-ONIOM methods are shown to be powerful and efficient for studying the long-range interactions at a high level. With the GEBF-ONIOM(MP2-F12:MP2) and GEBF-ONIOM(MP2-F12:MP2:cDFTB) methods, the diameters of the largest nanoscale clusters under studies are about 2.4 nm (747 atoms and 10 209 basis functions with aug-cc-pVDZ basis set) and 4 nm (3351 atoms), respectively, which are almost impossible to be treated by conventional MP2 or MP2-F12 method. Thus, the GEBF-F12 and GEBF-ONIOM methods are expected to be a practical tool for studying the nanoscale clusters in condensed phase, providing an alternative benchmark for ab initio and density functional theory studies, and developing new force fields by combining with classic MD simulations.
Geometric Control of Patterned Linear Systems
Hamilton, Sarah C
2012-01-01
This monograph is aiming at researchers of systems control, especially those interested in multiagent systems, distributed and decentralized control, and structured systems. The book assumes no prior background in geometric control theory; however, a first year graduate course in linear control systems is desirable. Since not all control researchers today are exposed to geometric control theory, the book also adopts a tutorial style by way of examples that illustrate the geometric and abstract algebra concepts used in linear geometric control. In addition, the matrix calculations required for the studied control synthesis problems of linear multivariable control are illustrated via a set of running design examples. As such, some of the design examples are of higher dimension than one may typically see in a text; this is so that all the geometric features of the design problem are illuminated.
Geometric distortion correction for sinusoidally scanned images
International Nuclear Information System (INIS)
Xu, Lijun; Tian, Xiangrui; Li, Xiaolu; Shang, Guangyi; Yao, Junen
2011-01-01
A method for correcting the geometric distortion of sinusoidally scanned images was proposed. The generation mechanism of the geometric distortion in sinusoidally scanned images was analyzed. Based on the relationship between the coordinates of uniformly scanned points and those of sinusoidally scanned points, a transformation formula was obtained for correcting the geometric distortion when the sampling rate was a constant. By comparing the forward method with the inverse method, a hybrid method for correcting the geometric distortion of sinusoidally scanned images was proposed. This method takes advantage of both the forward and inverse methods and was proven to be better than either of them in terms of peak signal-to-noise ratio (PSNR). The time consumed by the hybrid method was between the other two. When a higher PSNR is desired, the hybrid method is recommended if time permits. In addition, it is a universal approach to the correction of geometric distortion of the images scanned in the sinusoidal mode
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.
Simple correlation equations for optimum design of annular fins with uniform thickness
International Nuclear Information System (INIS)
Arslanturk, Cihat
2005-01-01
Simple correlation equations for optimum design of annular fins with uniform cross section are obtained in the present work. The fin volume is fixed to obtain the dimensionless geometrical parameters of the fin with maximum heat transfer rates. The optimum radii ratio of an annular fin which maximizes the heat transfer rate has been found as a function of Biot number and the fin volume. The data from the present solutions is correlated for a suitable range of Biot number and the fin volume. The simple correlation equations presented in this work can assist for thermal design engineers for optimum design of annular fins of uniform thickness
Finsler-Geometric Continuum Mechanics
2016-05-01
general than classical approaches and can reproduce phase field solutions when certain simplifying assumptions are imposed. Upon invoking a conformal or...curvature, and so forth) may in turn depend on position and direction or in- ternal state. This generality is in contrast to classical Riemannian...general relativity,1 gravitation,2 quantum mechan- ics,3 electrodynamics ,4 heat conduction,5 and the mechanics of solids.6 The latter topic (i.e
Geometrical properties of gauge theories
International Nuclear Information System (INIS)
Grabiak, M.; Mueller, B.; Greiner, W.
1986-01-01
We calculate the metric of the orbit space in the free Yang--Mills theory and in scalar electrodynamics. From this metric we derive the curvature of the orbit space. We examine singular points where the curvature is ill defined. Finally we discuss the relation of the metric to the topological properties of the orbit space and the instanton solution. Copyright 1986 Academic Press, Inc
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.
Rational Geometrical Characters of Saddle Shape Cable Roof Supported by Tensioned Cables
Rocēns, K; Pakrastiņš, L; Serdjuks, D
1999-01-01
The saddle shape cable roof, which is supported by tension cables, is considered in the paper. The roof is kinematics invariable because of prestressing of rectangular (orthogonal) cable net The correlation between the main geometrical characters of the cable roof and weight of the cable net which is divided by the area covered by the cable roof, was ascertained by a numeral experiment. The main geometrical characters are the initial curvatures of stressing, suspension and tension cables and ...
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 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)
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 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...
Geometric continuum mechanics and induced beam theories
R Eugster, Simon
2015-01-01
This research monograph discusses novel approaches to geometric continuum mechanics and introduces beams as constraint continuous bodies. In the coordinate free and metric independent geometric formulation of continuum mechanics as well as for beam theories, the principle of virtual work serves as the fundamental principle of mechanics. Based on the perception of analytical mechanics that forces of a mechanical system are defined as dual quantities to the kinematical description, the virtual work approach is a systematic way to treat arbitrary mechanical systems. Whereas this methodology is very convenient to formulate induced beam theories, it is essential in geometric continuum mechanics when the assumptions on the physical space are relaxed and the space is modeled as a smooth manifold. The book addresses researcher and graduate students in engineering and mathematics interested in recent developments of a geometric formulation of continuum mechanics and a hierarchical development of induced beam theories.
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
Geometric symmetries in superfluid vortex dynamics
Kozik, Evgeny; Svistunov, Boris
2010-10-01
Dynamics of quantized vortex lines in a superfluid feature symmetries associated with the geometric character of the complex-valued field, w(z)=x(z)+iy(z) , describing the instant shape of the line. Along with a natural set of Noether’s constants of motion, which—apart from their rather specific expressions in terms of w(z) —are nothing but components of the total linear and angular momenta of the fluid, the geometric symmetry brings about crucial consequences for kinetics of distortion waves on the vortex lines, the Kelvin waves. It is the geometric symmetry that renders Kelvin-wave cascade local in the wave-number space. Similar considerations apply to other systems with purely geometric degrees of freedom.
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.
Nodal free geometric phases: Concept and application to geometric quantum computation
International Nuclear Information System (INIS)
Ericsson, Marie; Kult, David; Sjoeqvist, Erik; Aberg, Johan
2008-01-01
Nodal free geometric phases are the eigenvalues of the final member of a parallel transporting family of unitary operators. These phases are gauge invariant, always well defined, and can be measured interferometrically. Nodal free geometric phases can be used to construct various types of quantum phase gates
Estimating motors from a variety of geometric data in 3D conformal geometric algebra
Valkenburg, R.; Dorst, L.; Dorst, L.; Lasenby, J.
2011-01-01
The motion rotors, or motors, are used to model Euclidean motion in 3D conformal geometric algebra. In this chapter we present a technique for estimating the motor which best transforms one set of noisy geometric objects onto another. The technique reduces to an eigenrotator problem and has some
Numerical nonlinear complex geometrical optics algorithm for the 3D Calderón problem
DEFF Research Database (Denmark)
Delbary, Fabrice; Knudsen, Kim
2014-01-01
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...... 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...... to the simpler approximations. In addition, convergence of the numerical solution towards the exact solution of the boundary integral equation is proved....
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.
Geometrical factors in the perception of sacredness
DEFF Research Database (Denmark)
Costa, Marco; Bonetti, Leonardo
2016-01-01
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 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......, and attractive. The top and the center areas were associated with sacredness, dominance, and attractiveness. In the third test, peaks and elevated regions in landscapes were evaluated as more sacred, dominant, and attractive than valley regions. In the fourth test, three figures sharing the same area...
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.
Geometric inequalities for axially symmetric black holes
International Nuclear Information System (INIS)
Dain, Sergio
2012-01-01
A geometric inequality in general relativity relates quantities that have both a physical interpretation and a geometrical definition. It is well known that the parameters that characterize the Kerr-Newman black hole satisfy several important geometric inequalities. Remarkably enough, some of these inequalities also hold for dynamical black holes. This kind of inequalities play an important role in the characterization of the gravitational collapse; they are closely related with the cosmic censorship conjecture. Axially symmetric black holes are the natural candidates to study these inequalities because the quasi-local angular momentum is well defined for them. We review recent results in this subject and we also describe the main ideas behind the proofs. Finally, a list of relevant open problems is presented. (topical review)
EARLY HISTORY OF GEOMETRIC PROBABILITY AND STEREOLOGY
Directory of Open Access Journals (Sweden)
Magdalena Hykšová
2012-03-01
Full Text Available The paper provides an account of the history of geometric probability and stereology from the time of Newton to the early 20th century. It depicts the development of two parallel ways: on one hand, the theory of geometric probability was formed with minor attention paid to other applications than those concerning spatial chance games. On the other hand, practical rules of the estimation of area or volume fraction and other characteristics, easily deducible from geometric probability theory, were proposed without the knowledge of this branch. A special attention is paid to the paper of J.-É. Barbier published in 1860, which contained the fundamental stereological formulas, but remained almost unnoticed both by mathematicians and practicians.
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.
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.
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.
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.
Primary School Teacher Candidates' Geometric Habits of Mind
Köse, Nilu¨fer Y.; Tanisli, Dilek
2014-01-01
Geometric habits of mind are productive ways of thinking that support learning and using geometric concepts. Identifying primary school teacher candidates' geometric habits of mind is important as they affect the development of their future students' geometric thinking. Therefore, this study attempts to determine primary school teachers' geometric…
Alternate Derivation of Geometric Extended Kalman Filter by MEKF Approach
Chang, Lubin
2017-01-01
This note is devoted to deriving the measurement update of the geometric extended Kalman filter using the multiplicative extended Kalman filtering approach, resulting in the attitude estimator referred as geometric multiplicative extended Kalman filter. The equivalence of the derived geometric multiplicative extended Kalman filter and geometric extended Kalman filter is also demonstrated in this note.
Geometric Weil representation in characteristic two
Genestier, Alain; Lysenko, Sergey
2009-01-01
International audience; Let k be an algebraically closed field of characteristic two. Let R be the ring of Witt vectors of length two over k. We construct a group stack \\hat G over k, the metaplectic extension of the Greenberg realization of Sp_{2n}(R). We also construct a geometric analog of the Weil representation of \\hat G, this is a triangulated category on which \\hat G acts by functors. This triangulated category and the action are geometric in a suitable sense.
Robust topology optimization accounting for geometric imperfections
DEFF Research Database (Denmark)
Schevenels, M.; Jansen, M.; Lombaert, Geert
2013-01-01
performance. As a consequence, the actual structure may be far from optimal. In this paper, a robust approach to topology optimization is presented, taking into account two types of geometric imperfections: variations of (1) the crosssections and (2) the locations of structural elements. The first type......Topology optimization is a powerful method to optimize the performance of macro, micro, or nano structures. However, the geometry of the actual structure may differ from the optimized design due to manufacturing errors. Such geometric imperfections can have a significant impact on the structural...
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
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.
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 and calib......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...
Geometric nonlinear functional analysis volume 1
Benyamini, Yoav
1999-01-01
The book presents a systematic and unified study of geometric nonlinear functional analysis. This area has its classical roots in the beginning of the twentieth century and is now a very active research area, having close connections to geometric measure theory, probability, classical analysis, combinatorics, and Banach space theory. The main theme of the book is the study of uniformly continuous and Lipschitz functions between Banach spaces (e.g., differentiability, stability, approximation, existence of extensions, fixed points, etc.). This study leads naturally also to the classification of
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....
Towards geometrical calibration of x-ray computed tomography systems—a review
International Nuclear Information System (INIS)
Ferrucci, Massimiliano; Leach, Richard K; Giusca, Claudiu; Carmignato, Simone; Dewulf, Wim
2015-01-01
Industrial x-ray computed tomography (XCT) is seen as a potentially effective tool for the industrial inspection of complex parts. In particular, XCT is an attractive solution for the measurement of internal geometries, which are inaccessible by conventional coordinate measuring systems. While the technology is available and the benefits are recognized, methods to establish the measurement assurance of XCT systems are lacking. More specifically, the assessment of measurement uncertainty and the subsequent establishment of measurement traceability is a largely unknown process. This paper is a review of research that contributes to the development of a geometrical calibration procedure for XCT systems. A brief introduction to the geometry of cone-beam tomography systems is given, after which the geometrical influence factors are outlined. Mathematical measurement models play a significant role in understanding how geometrical offsets and misalignments contribute to error in measurements; therefore, the application of mathematical models in simulating geometrical errors is discussed and the corresponding literature is presented. Then, the various methods that have been developed to measure certain geometrical errors are reviewed. The findings from this review are discussed and suggestions are provided for future work towards the development of a comprehensive and practical geometrical calibration procedure. (topical review)
Geometrical and computer modeling of mechanical engineering surfaces products intersection line
Panchuk, K. L.; Kaygorodtseva, N. V.; Kaygorodtseva, T. N.; Yurkov, V. Yu
2017-06-01
In the design and manufacture of engineering products geometrical problem is known by shaping the surface of the product. An important element of general solution of this problem is to define the lines of surfaces intersection, forming the shape of designed product. Existing possibilities of modern CAD systems do not allow achieving fullness of the result in this direction. For example, control points and change point of visibility is difficult to identify in the product drawings. In addition, there are no possibilities of detecting imaginary points which are necessary for a complete analysis of intersection surfaces, and mapping these points in the drawing. The aim of the study is to develop a geometric algorithm of constructive determining the intersection line and is devoid of these shortcomings. The objectives of the study are testing the obtained algorithm by experimental verification with geometric modeling solutions to specific problems by tools CAD. This study adopted the method, which is based on quotient of geometric sets, which are regarded as intersecting surfaces in space E3 . One area of practical use of surface engineering products geometric algorithm - shaping is based on their intersection line.
Piretzidis, D.; Sra, G.; Sideris, M. G.
2016-12-01
This study explores new methods for identifying correlation errors in harmonic coefficients derived from monthly solutions of the Gravity Recovery and Climate Experiment (GRACE) satellite mission using pattern recognition and neural network algorithms. These correlation errors are evidenced in the differences between monthly solutions and can be suppressed using a de-correlation filter. In all studies so far, the implementation of the de-correlation filter starts from a specific minimum order (i.e., 11 for RL04 and 38 for RL05) until the maximum order of the monthly solution examined. This implementation method has two disadvantages, namely, the omission of filtering correlated coefficients of order less than the minimum order and the filtering of uncorrelated coefficients of order higher than the minimum order. In the first case, the filtered solution is not completely free of correlated errors, whereas the second case results in a monthly solution that suffers from loss of geophysical signal. In the present study, a new method of implementing the de-correlation filter is suggested, by identifying and filtering only the coefficients that show indications of high correlation. Several numerical and geometric properties of the harmonic coefficient series of all orders are examined. Extreme cases of both correlated and uncorrelated coefficients are selected, and their corresponding properties are used to train a two-layer feed-forward neural network. The objective of the neural network is to identify and quantify the correlation by providing the probability of an order of coefficients to be correlated. Results show good performance of the neural network, both in the validation stage of the training procedure and in the subsequent use of the trained network to classify independent coefficients. The neural network is also capable of identifying correlated coefficients even when a small number of training samples and neurons are used (e.g.,100 and 10, respectively).
Robust topology optimization accounting for geometric imperfections
DEFF Research Database (Denmark)
Schevenels, M.; Jansen, M.; Lombaert, Geert
2013-01-01
performance. As a consequence, the actual structure may be far from optimal. In this paper, a robust approach to topology optimization is presented, taking into account two types of geometric imperfections: variations of (1) the crosssections and (2) the locations of structural elements. The first type...
A graph spectrum based geometric biclustering algorithm.
Wang, Doris Z; Yan, Hong
2013-01-21
Biclustering is capable of performing simultaneous clustering on two dimensions of a data matrix and has many applications in pattern classification. For example, in microarray experiments, a subset of genes is co-expressed in a subset of conditions, and biclustering algorithms can be used to detect the coherent patterns in the data for further analysis of function. In this paper, we present a graph spectrum based geometric biclustering (GSGBC) algorithm. In the geometrical view, biclusters can be seen as different linear geometrical patterns in high dimensional spaces. Based on this, the modified Hough transform is used to find the Hough vector (HV) corresponding to sub-bicluster patterns in 2D spaces. A graph can be built regarding each HV as a node. The graph spectrum is utilized to identify the eigengroups in which the sub-biclusters are grouped naturally to produce larger biclusters. Through a comparative study, we find that the GSGBC achieves as good a result as GBC and outperforms other kinds of biclustering algorithms. Also, compared with the original geometrical biclustering algorithm, it reduces the computing time complexity significantly. We also show that biologically meaningful biclusters can be identified by our method from real microarray gene expression data. Copyright © 2012 Elsevier Ltd. All rights reserved.
An information theoretic approach to geometric clustering
Strouse, Dj; Schwab, David
Clustering is a basic task in data analysis for both understanding and pre-processing data. Classic clustering methods, such as k-means or EM fitting of a gaussian mixture model, are based on geometry. These geometric clustering methods group data points together based on their Euclidean distance from one another; roughly speaking, points within a cluster have smaller distances to one another than to points in other clusters. More recently, however, distributional clustering methods, such as the information bottleneck (IB) and deterministic information bottleneck (DIB), have been introduced that group data points based upon their conditional distributions over a target variable. Here, points within a cluster provide similar information about the target variable. Are distributional and geometric clustering related, and if so, how? Can we blend these two approaches? Here we first describe a method to incorporate geometric information into the (D)IB clustering algorithm, where the target variable our clustering should be informative about is the spatial location of the contained data points. This enables us to derive a novel set of geometric clustering algorithms, which we then compare to the classic methods mentioned above. Finally, we compare both approaches on data.
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.
Left ventricular hypertrophy, geometric patterns and clinical ...
African Journals Online (AJOL)
Background: Left ventricular hypertrophy can be due to various reasons including hypertension. It constitutes an increased cardiovascular risk. Various left ventricular geometric patterns occur in hypertension and may affect the cardiovascular risk profile of hypertensive subjects. Methods: One hundred and eighty eight ...
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.
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)
Online course Geometrical Optics for undergraduate students
Bakholdin, Alexey; Voznesenskaya, Anna; Romanova, Galina; Ivanova, Tatiana; Tolstoba, Nadezhda; Ezhova, Kseniia; Garshin, Aleksei; Trifonov, Oleg; Sazonenko, Dmitry; Ekimenkova, Alisa
2017-08-01
The paper is devoted to the description of the on-line course "Geometrical Optics" placed on the national open-education platform. The course is purposed mainly for undergraduate students in optics and related fields. We discuss key features of the on-line form of this course, the issues of its realization and learning outcomes' evaluation.
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.)
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
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....
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.)
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…
Reinforcing Geometric Properties with Shapedoku Puzzles
Wanko, Jeffrey J.; Nickell, Jennifer V.
2013-01-01
Shapedoku is a new type of puzzle that combines logic and spatial reasoning with understanding of basic geometric concepts such as slope, parallelism, perpendicularity, and properties of shapes. Shapedoku can be solved by individuals and, as demonstrated here, can form the basis of a review for geometry students as they create their own. In this…
GEOMETRIC MEASUREMENTS OF THE ACETABULUM IN ADULT ...
African Journals Online (AJOL)
hi-tech
2003-10-10
Oct 10, 2003 ... Objectives: To determine the acetabular depth as well as acetabular and centre edge angles; to assess the influence of sex, if any, in these geometric measurements; and to determine the prevalence of hip dysplasia in adult Malawians. Design: A retrospective study. Setting: Queen Elizabeth Central ...
Geometrical interpretation and architecture selection of MLP.
Xiang, Cheng; Ding, Shenqiang Q; Lee, Tong Heng
2005-01-01
A geometrical interpretation of the multilayer perceptron (MLP) is suggested in this paper. Some general guidelines for selecting the architecture of the MLP, i.e., the number of the hidden neurons and the hidden layers, are proposed based upon this interpretation and the controversial issue of whether four-layered MLP is superior to the three-layered MLP is also carefully examined.
On Arithmetic-Geometric-Mean Polynomials
Griffiths, Martin; MacHale, Des
2017-01-01
We study here an aspect of an infinite set "P" of multivariate polynomials, the elements of which are associated with the arithmetic-geometric-mean inequality. In particular, we show in this article that there exist infinite subsets of probability "P" for which every element may be expressed as a finite sum of squares of real…
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)
Geometric structures on loop and path spaces
Indian Academy of Sciences (India)
∗Departamento de Geometrıa y Topologıa, Facultad de Matemáticas,. Universidad Complutense de Madrid, 28040 Madrid, Spain. †Instituto de Ciencias ..... To finish, let us check that the familiar finite dimensional picture translates to this case. PROPOSITION 4.2. Let (M,g) be a Riemannian manifold which has a locally ...
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.
International Nuclear Information System (INIS)
Chaudhuri, N.K.; Sawant, R.M.; Sood, D.D.
1999-01-01
Literature data on the stability constants of the fluoride complexes of the actinides in different oxidation states have been compiled. In order to have a reasonable inter-comparison, the stability constant (β 1 ) values obtained in diverse ionic strength media are converted to so called thermodynamic stability constants, β 1 0 using the 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. 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 semi-empirical relation recently developed by BROWN, SYLVA and ELLIS (BSE equation) gives the best correlation. 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 obtained in most of the cases. Further improvements in theoretical relation as well as experimental data are required for better correlation. (author)
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.
Subjective surfaces: a geometric model for boundary completion
Energy Technology Data Exchange (ETDEWEB)
Sarti, Alessandro; Malladi, Ravi; Sethian, J.A.
2000-06-01
We present a geometric model and a computational method for segmentation of images with missing boundaries. In many situations, the human visual system fills in missing gaps in edges and boundaries, building and completing information that is not present. Boundary completion presents a considerable challenge in computer vision, since most algorithms attempt to exploit existing data. A large body of work concerns completion models, which postulate how to construct missing data; these models are often trained and specific to particular images. In this paper, we take the following, alternative perspective: we consider a reference point within an image as given, and then develop an algorithm which tries to build missing information on the basis of the given point of view and the available information as boundary data to the algorithm. Starting from this point of view, a surface is constructed. It is then evolved with the mean curvature flow in the metric induced by the image until a piecewise constant solution is reached. We test the computational model on modal completion, amodal completion, texture, photo and medical images. We extend the geometric model and the algorithm to 3D in order to extract shapes from low signal/noise ratio medical volumes. Results in 3D echocardiography and 3D fetal echography are presented.
The algebraic structure of geometric flows in two dimensions
Bakas, Ioannis
2005-01-01
There is a common description of different intrinsic geometric flows in two dimensions using Toda field equations associated to continual Lie algebras that incorporate the deformation variable t into their system. The Ricci flow admits zero curvature formulation in terms of an infinite dimensional algebra with Cartan operator d/dt. Likewise, the Calabi flow arises as Toda field equation associated to a supercontinual algebra with odd Cartan operator d/d \\theta - \\theta d/dt. Thus, taking the square root of the Cartan operator allows to connect the two distinct classes of geometric deformations of second and fourth order, respectively. The algebra is also used to construct formal solutions of the Calabi flow in terms of free fields by Backlund transformations, as for the Ricci flow. Some applications of the present framework to the general class of Robinson-Trautman metrics that describe spherical gravitational radiation in vacuum in four space-time dimensions are also discussed. Further iteration of the algor...
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.
Weighted geometric dilution of precision calculations with matrix multiplication.
Chen, Chien-Sheng
2015-01-05
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.
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.
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.
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.
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.
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
ABOUT ONE APPROACH OF TESTING GEOMETRICAL KNOWLEDGE SYSTEM BUILDING.
Directory of Open Access Journals (Sweden)
M. Lvov
2014-04-01
Full Text Available The paper presents an approach to testing system building of procedural geometric knowledge, i.e. knowledge of basic computational formulas and skills to use them. This approach consists in constructing the mathematical models for each academic module in Geometry. The main constructing objects are the templates of tests which represent mathematical models of tests set in general terms. Template of similar tests class is represented by a geometric drawing, formula-correlations system binding the elements of the drawing, by templates of test conditions and template of response. Each such template is used both in generating algorithms of similar specific tests’ plurality and algorithms of automatic validation of responses’ correctness. The proposed method makes it possible to describe a relatively simple class of specific tests. An important feature of the system is the ability to automatically check not only the final answer, but the intermediate answer formulas. For the implementation of the testing system is necessary to use methods of computer algebra and algebraic programming technology.
Maxwell-type behaviour from a geometrical structure
International Nuclear Information System (INIS)
Itin, Yakov
2006-01-01
We study which geometric structure can be constructed from the vierbein (frame/coframe) variables and which field models can be related to this geometry. The coframe field models, alternative to GR, are known as viable models for gravity, since they have the Schwarzschild solution. Since the local Lorentz invariance is violated, a physical interpretation of additional six degrees of freedom is required. The geometry of such models is usually given by two different connections-the Levi-Civita symmetric and metric-compatible connection and the Weitzenboeck flat connection. We construct a general family of linear connections of the same type, which includes two connections above as special limiting cases. We show that for dynamical propagation of six additional degrees of freedom it is necessary for the gauge field of infinitesimal transformations (antisymmetric tensor) to satisfy the system of two first-order differential equations. This system is similar to the vacuum Maxwell system and even coincides with it on a flat manifold. The corresponding 'Maxwell-compatible connections' are derived. Alternatively, we derive the same Maxwell-type system as a symmetry condition of the viable model Lagrangian. Consequently, we derive a nontrivial decomposition of the coframe field to the pure metric field plus a dynamical field of infinitesimal Lorentz rotations. An exact spherical-symmetric solution for our dynamical field is derived. It is bounded near the Schwarzschild radius. Further off, the solution is close to the Coulomb field
A geometric model of deviations from Vegard's rule
Urusov, Vadim S.
1992-06-01
There is much evidence that X-ray measurements of sufficient accuracy reveal deviations from the linear dependence of unit-cell parameters on composition, i.e., departures from Vegard's rule. The dependence of such deviations on composition for a random solid solution with one substitutional position ( A x1B x2C is usually of a parabolic form: δa=x 1x 2σ where σ is positive. Many attempts to explain these observations are based on elastic models. It is known that less than 50% of the predictions of these models are correct. An alternative model under consideration is a simple geometric one. It is concerned with secondary atomic displacements around substitutional defects, i.e., shifts of the second nearest neighbors. The result is structurally dependent and the analysis deals with binary solid solutions of B1 (CN=6), B3 (CN=4), and B2 (CN=8) structure types. For instance, in sodium chloride structure-type solid solutions, the following simple equation is valid, δ h=(3/2) x1x2( R) 2/ R, where R is the difference in interatomic distances of pure components and R is the average interatomic distance. Calculations for NaCl-KCl, NaCl-NaBr, KCl-KBr, and other systems are in good agreement with experimental data.
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)
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.
Hai, X.; Porcher, F.; Mayer, C.; Miraglia, S.
2018-02-01
Steady state and in-situ neutron powder diffraction on selected compositions of the magneto-caloric (La,Ce)(Fe,Si)13CxHy compounds has been used to locate the sites accommodated by the interstitial species and to reveal the structural modifications (breathing) that occur upon metal substitution and/or interstitial insertion. The latter type of measurement in which the sequential filling of interstitial sites is followed allows one to extract some useful hydrogenation kinetics data. This structural investigation has allowed to precise the deformations undergone by the complex metallic alloys La(Fe,Si)13 when subjected to light interstitial insertion or rare earth substitution at the cation site of the NaZn13-structure type. We attempt to correlate hydrogenation kinetics variations (depression or enhancement of the hydrogen absorption rate) with a particular inhomogeneous cell variation (breathing) and bonding of the NaZn13 structure-type.
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...
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. .
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
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...
Geometric modeling for computer aided design
Schwing, James L.
1993-01-01
Over the past several years, it has been the primary goal of this grant to design and implement software to be used in the conceptual design of aerospace vehicles. The work carried out under this grant was performed jointly with members of the Vehicle Analysis Branch (VAB) of NASA LaRC, Computer Sciences Corp., and Vigyan Corp. This has resulted in the development of several packages and design studies. Primary among these are the interactive geometric modeling tool, the Solid Modeling Aerospace Research Tool (smart), and the integration and execution tools provided by the Environment for Application Software Integration and Execution (EASIE). In addition, it is the purpose of the personnel of this grant to provide consultation in the areas of structural design, algorithm development, and software development and implementation, particularly in the areas of computer aided design, geometric surface representation, and parallel algorithms.
Universal geometrical scaling of the elliptic flow
Directory of Open Access Journals (Sweden)
Andrés C.
2015-01-01
Full Text Available The presence of scaling variables in experimental observables provide very valuable indications of the dynamics underlying a given physical process. In the last years, the search for geometric scaling, that is the presence of a scaling variable which encodes all geometrical information of the collision as well as other external quantities as the total energy, has been very active. This is motivated, in part, for being one of the genuine predictions of the Color Glass Condensate formalism for saturation of partonic densities. Here we extend these previous findings to the case of experimental data on elliptic flow. We find an excellent scaling for all centralities and energies, from RHIC to LHC, with a simple generalization of the scaling previously found for other observables and systems. Interestingly, the case of the photons, difficult to reconcile in most formalisms, nicely fit the scaling curve. We discuss on the possible interpretations of this finding in terms of initial or final state effects.
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 approach to gaussian beam propagation.
Laures, P
1967-04-01
The curvature of the wavefront and the spot size of a propagating Gaussian beam may be determined from simple geometrical transformations of the lateral foci. The analysis starts from the construction of the lateral foci in the case of a spherical Fabry-Perot. Then the cases of Gaussian beam propagation through media with different refractive indices, lenses, and simple optical systems are treated. Constructions show how propagation in the image space is readily determined in each case. This analysis is the generalization of the technique outlined by Deschamps and Mast. The geometrical constructions developed for simple cases are applied to the design of some special cases of interest in laser optics: cavities by a lens, laser zoom telescope, and ring cavity.
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.
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. .
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.
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.
GEOMETRICAL CHARACTERIZATION OF MICRO END MILLING TOOLS
DEFF Research Database (Denmark)
Borsetto, Francesca; Bariani, Paolo
/lubricants, milling strategies and controls. Moreover the accuracy of tool geometry directly affects the performance of the milling process influencing the dimensional tolerances of the machined part, the surface topography, the chip formation, the cutting forces and the tool-life. The dimensions of certain...... report is to develop procedures for the geometrical characterization of micro end milling tools in order to define a method suitable for the quality assurance in the micro cutting field....
Constellation design with geometric and probabilistic shaping
Zhang, Shaoliang; Yaman, Fatih
2018-02-01
A systematic study, including theory, simulation and experiments, is carried out to review the generalized pairwise optimization algorithm for designing optimized constellation. In order to verify its effectiveness, the algorithm is applied in three testing cases: 2-dimensional 8 quadrature amplitude modulation (QAM), 4-dimensional set-partitioning QAM, and probabilistic-shaped (PS) 32QAM. The results suggest that geometric shaping can work together with PS to further bridge the gap toward the Shannon limit.
A CT simulator phantom for geometrical test
International Nuclear Information System (INIS)
Min, Chul Kee; Yi, Byong Yong; Ahn, Seung Do; Choi, Eun Kyung; Chang, Hye Sook
2000-01-01
To design and test the CT simulator phantom for geometrical test. The PMMA phantom was designed as a cylinder which is 20 cm in diameter and 24 cm in length, along with a 25x25x31 cm 3 rectangular parallelepiped. Radio-opaque wires of which diameter is 0.8 mm are attached on the other surface of the phantom as a spiral. The rectangular phantom was made of four 24x24xO.5 cm 3 square plates and each plate had a 24x24 cm 2 . 12x12 cm 2 , 6x6 cm 2 square line. The squares were placed to face the cylinder at angles 0 .deg., 15 .deg., 30 .deg., respectively. The rectangular phantom made it possible to measure the field size, couch angle, the collimator angle, the isocenter shift and the SSD, the measurements of the gantry angle from the cylindrical part. A virtual simulation Software, AcQSim TM , offered various conditions to perform virtual simulations and these results were used to perform the geometrical quality assurance of CT simulator. A 0.3-0.5 mm difference was found on the 24 cm field size which was created with the DRR measurements obtained by scanning of the rectangular phantom. The isocenter shift, the collimator rotation, the couch rotation, and the gantry rotation test showed 0.5-1 mm, 0.5-1 .deg. 0.5-1 .deg. , and 0.5-1 .deg. differences, respectively. We could not find any significant differences between the results from the two scanning methods. The geometrical test phantom developed in the study showed less than 1 mm (or 1 .deg. ) differences. The phantom could be used as a routine geometrical QC/OA tools, since the differences are within clinically acceptable ranges
Geometric Algebra Model of Distributed Representations
Patyk, Agnieszka
2010-01-01
Formalism based on GA is an alternative to distributed representation models developed so far --- Smolensky's tensor product, Holographic Reduced Representations (HRR) and Binary Spatter Code (BSC). Convolutions are replaced by geometric products, interpretable in terms of geometry which seems to be the most natural language for visualization of higher concepts. This paper recalls the main ideas behind the GA model and investigates recognition test results using both inner product and a clipp...
Geometrical Methods for Power Network Analysis
Bellucci, Stefano; Gupta, Neeraj
2013-01-01
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.
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.
An Information Geometric Framework for Dimensionality Reduction
Carter, Kevin M.; Raich, Raviv; Hero III, Alfred O.
2008-01-01
This report concerns the problem of dimensionality reduction through information geometric methods on statistical manifolds. While there has been considerable work recently presented regarding dimensionality reduction for the purposes of learning tasks such as classification, clustering, and visualization, these methods have focused primarily on Riemannian manifolds in Euclidean space. While sufficient for many applications, there are many high-dimensional signals which have no straightforwar...
Salt Bridges: Geometrically Specific, Designable Interactions
Donald, Jason E.; Kulp, Daniel W.; DeGrado, William F.
2011-01-01
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 ...
Protection from Unresponsive Flows with Geometric CHOKe
Eshete, Addisu Tadesse; Jiang, Yuming
2012-01-01
This paper proposes a simple and stateless active queue management (AQM) scheme, called geometric CHOKe (gCHOKe), to protect responsive flows from unresponsive ones. The proposed gCHOKe has its root on and is a generalization of the original CHOKe. It provides an extended power of flow protection, achieved by introducing an extra flow matching trial upon each successful matching of packets. Compared to the plain CHOKe, analysis and simulation show that gCHOKe can achieve over 20% improvement ...
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.
Geometric structures on loop and path spaces
Indian Academy of Sciences (India)
Geometric structures on loop and path spaces. VICENTE MU ˜NOZ ... Now consider the path space P(M) consisting of C∞. -maps γ: [0, 1] .... (7) which implies ω(U,V) = ∫ 1. 0 g. (. ∂U. ∂t. ,V. ) dt. (8). Now the kernel of this 2-form at a point γ is given by the parallel vector fields along γ. Therefore dim ker(ωγ ) ≤ n. There are ...
Inclusion of geometric uncertainties in treatment plan evaluation
International Nuclear Information System (INIS)
Herk, Marcel van; Remeijer, Peter; Lebesque, Joos V.
2002-01-01
Purpose: To correctly evaluate realistic treatment plans in terms of absorbed dose to the clinical target volume (CTV), equivalent uniform dose (EUD), and tumor control probability (TCP) in the presence of execution (random) and preparation (systematic) geometric errors. Materials and Methods: The dose matrix is blurred with all execution errors to estimate the total dose distribution of all fractions. To include preparation errors, the CTV is randomly displaced (and optionally rotated) many times with respect to its planned position while computing the dose, EUD, and TCP for the CTV using the blurred dose matrix. Probability distributions of these parameters are computed by combining the results with the probability of each particular preparation error. We verified the method by comparing it with an analytic solution. Next, idealized and realistic prostate plans were tested with varying margins and varying execution and preparation error levels. Results: Probability levels for the minimum dose, computed with the new method, are within 1% of the analytic solution. The impact of rotations depends strongly on the CTV shape. A margin of 10 mm between the CTV and planning target volume is adequate for three-field prostate treatments given the accuracy level in our department; i.e., the TCP in a population of patients, TCP pop , is reduced by less than 1% due to geometric errors. When reducing the margin to 6 mm, the dose must be increased from 80 to 87 Gy to maintain the same TCP pop . Only in regions with a high-dose gradient does such a margin reduction lead to a decrease in normal tissue dose for the same TCP pop . Based on a rough correspondence of 84% minimum dose with 98% EUD, a margin recipe was defined. To give 90% of patients at least 98% EUD, the planning target volume margin must be approximately 2.5 Σ + 0.7 σ - 3 mm, where Σ and σ are the combined standard deviations of the preparation and execution errors. This recipe corresponds accurately with 1% TCP
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.
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.
From map reading to geometric intuitions.
Dillon, Moira R; Spelke, Elizabeth S
2018-03-29
The origins and development of our geometric intuitions have been debated for millennia. The present study links children's developing intuitions about the properties of planar triangles to their developing abilities to read purely geometric maps. Six-year-old children are limited when navigating by maps that depict only the sides of a triangle in an environment composed of only the triangle's corners and vice versa. Six-year-old children also incorrectly judge how the angle size of the third corner of a triangle varies with changes to the other two corners. These limitations in map reading and in judgments about triangles are attenuated, respectively, by 10 and 12 years of age. Moreover, as children get older, their map reading predicts their geometric judgments on the triangle task. Map reading thus undergoes developmental changes that parallel an emerging capacity to reason explicitly about the distance and angle relations essential to euclidean geometry. (PsycINFO Database Record (c) 2018 APA, all rights reserved).
Matrix models, geometric engineering and elliptic genera
International Nuclear Information System (INIS)
Hollowood, Timothy; Iqbal, Amer; Vafa, Cumrun
2008-01-01
We compute the prepotential of N = 2 supersymmetric gauge theories in four dimensions obtained by toroidal compactifications of gauge theories from 6 dimensions, as a function of Kaehler and complex moduli of T 2 . We use three different methods to obtain this: matrix models, geometric engineering and instanton calculus. Matrix model approach involves summing up planar diagrams of an associated gauge theory on T 2 . Geometric engineering involves considering F-theory on elliptic threefolds, and using topological vertex to sum up worldsheet instantons. Instanton calculus involves computation of elliptic genera of instanton moduli spaces on R 4 . We study the compactifications of N = 2* theory in detail and establish equivalence of all these three approaches in this case. As a byproduct we geometrically engineer theories with massive adjoint fields. As one application, we show that the moduli space of mass deformed M5-branes wrapped on T 2 combines the Kaehler and complex moduli of T 2 and the mass parameter into the period matrix of a genus 2 curve
Time as a geometric property of space
Chappell, James; Hartnett, John; Iannella, Nicolangelo; Iqbal, Azhar; Abbott, Derek
2016-11-01
The proper description of time remains a key unsolved problem in science. Newton conceived of time as absolute and universal which `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.
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.
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.
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
On the Construction of a Geometric Invariant Measuring the Deviation from Kerr Data
Bäckdahl, Thomas; Valiente Kroon, Juan A.
2010-11-01
This article contains a detailed and rigorous proof of the construction of a geometric invariant for initial data sets for the Einstein vacuum field equations. This geometric invariant vanishes if and only if the initial data set corresponds to data for the Kerr spacetime, and thus, it characterises this type of data. The construction presented is valid for boosted and non-boosted initial data sets which are, in a sense, asymptotically Schwarzschildean. As a preliminary step to the construction of the geometric invariant, an analysis of a characterisation of the Kerr spacetime in terms of Killing spinors is carried out. A space spinor split of the (spacetime) Killing spinor equation is performed, to obtain a set of three conditions ensuring the existence of a Killing spinor of the development of the initial data set. In order to construct the geometric invariant, we introduce the notion of approximate Killing spinors. These spinors are symmetric valence 2 spinors intrinsic to the initial hypersurface and satisfy a certain second order elliptic equation ---the approximate Killing spinor equation. This equation arises as the Euler-Lagrange equation of a non-negative integral functional. This functional constitutes part of our geometric invariant ---however, the whole functional does not come from a variational principle. The asymptotic behaviour of solutions to the approximate Killing spinor equation is studied and an existence theorem is presented.
Logical and Geometrical Distance in Polyhedral Aristotelian Diagrams in Knowledge Representation
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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.
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.
Geometric quantum discord and non-Markovianity of structured reservoirs
Hu, Ming-Liang; Lian, Han-Li
2015-11-01
The reservoir memory effects can lead to information backflow and recurrence of the previously lost quantum correlations. We establish connections between the direction of information flow and variation of the geometric quantum discords (GQDs) measured respectively by the trace distance, the Hellinger distance, and the Bures distance for two qubits subjecting to the bosonic structured reservoirs, and unveil their dependence on a factor whose derivative signifies the (non-)Markovianity of the dynamics. By considering the reservoirs with Lorentzian and Ohmic-like spectra, we further demonstrated that the non-Markovianity induced by the backflow of information from the reservoirs to the system enhances the GQDs in most of the parameter regions. This highlights the potential of non-Markovianity as a resource for protecting the GQDs.
and Correlated Error-Regressor
African Journals Online (AJOL)
Nekky Umera
Abstract. In this study, we conduct several Monte-Carlo experiments to examine the sensitivity of the efficiency of FGLS estimators relative to OLS using the. Variance and RMSE criteria, in the presence of first order autocorrelated error terms which are also correlated with geometric regressor. We examine the sensitivity of ...
Body circumferences: clinical implications emerging from a new geometric model
Directory of Open Access Journals (Sweden)
Gallagher Dympna
2008-10-01
Full Text Available Abstract Background Body volume expands with the positive energy balance associated with the development of adult human obesity and this "growth" is captured by two widely used clinical metrics, waist circumference and body mass index (BMI. Empirical correlations between circumferences, BMI, and related body compartments are frequently reported but fail to provide an important common conceptual foundation that can be related to key clinical observations. A two-phase program was designed to fill this important gap: a geometric model linking body volume with circumferences and BMI was developed and validated in cross-sectional cohorts; and the model was applied to the evaluation of longitudinally monitored subjects during periods of voluntary weight loss. Concepts emerging from the developed model were then used to examine the relations between the evaluated clinical measures and body composition. Methods Two groups of healthy adults (n = 494 and 1499 were included in the cross-sectional model development/testing phase and subjects in two previous weight loss studies were included in the longitudinal model evaluation phase. Five circumferences (arm, waist, hip, thigh, and calf; average of sum, C, height (H, BMI, body volume (V; underwater weighing, and the volumes of major body compartments (whole-body magnetic resonance imaging were measured. Results The evaluation of a humanoid geometric model based a cylinder confirmed that V derived from C and H was highly correlated with measured V [R2 both males and females, 0.97; p 0.5. The scaling of individual circumferences to V/H varied, with waist the highest (V/H~0.6 and calf the lowest (V/H~0.3, indicating that the largest and smallest between-subject "growth" with greater body volume occurs in the abdominal area and lower extremities, respectively. A stepwise linear regression model including all five circumferences2 showed that each contributed independently to V/H. These cross
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…
Kang, Sung; Shan, Sicong; Kosmrlj, Andrej; Noorduin, Wim; Shian, Samuel; Weaver, James; Clarke, David; Bertoldi, Katia
2014-03-01
Geometrical frustration arises when a local order cannot propagate throughout the space due to geometrical constraints. It plays a major role in many natural and synthetic systems including water ice, spin ice, and metallic glasses. All of these geometrically frustrated systems are degenerate and tend to form disordered ground-state configurations. Here, we report a theoretical and experimental study on the behavior of buckling-induced geometrically frustrated triangular cellular structures. To our surprise, we find that mechanical instabilities induce complex ordered patterns with tunability. For structures with low porosity, an ordered symmetric pattern emerges, which shows striking correlations with the ideal spin solid. In contrast, for high porosity systems, an ordered chiral pattern forms with a new spin configuration. Our analysis using a spin-like model reveals that the connected geometry of the cellular structure plays a crucial role in the formation of ordered states in this system. Since in our study geometrical frustration is induced by a mechanical instability that is scale-independent, our findings can be extended to different materials, stimuli, and length scales, providing a general strategy to study and visualize the physics of frustration.
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
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 aspects of biological sequence comparison.
Stojmirović, Aleksandar; Yu, Yi-Kuo
2009-04-01
We introduce a geometric framework suitable for studying the relationships among biological sequences. In contrast to previous works, our formulation allows asymmetric distances (quasi-metrics), originating from uneven weighting of strings, which may induce non-trivial partial orders on sets of biosequences. The distances considered are more general than traditional generalized string edit distances. In particular, our framework enables non-trivial conversion between sequence similarities, both local and global, and distances. Our constructions apply to a wide class of scoring schemes and require much less restrictive gap penalties than the ones regularly used. Numerous examples are provided to illustrate the concepts introduced and their potential applications.
Conformal invariants topics in geometric function theory
Ahlfors, Lars V
2010-01-01
Most conformal invariants can be described in terms of extremal properties. Conformal invariants and extremal problems are therefore intimately linked and form together the central theme of this classic book which is primarily intended for students with approximately a year's background in complex variable theory. The book emphasizes the geometric approach as well as classical and semi-classical results which Lars Ahlfors felt every student of complex analysis should know before embarking on independent research. At the time of the book's original appearance, much of this material had never ap
Gradient vector flow fast geometric active contours.
Paragios, Nikos; Mellina-Gottardo, Olivier; Ramesh, Visvanathan
2004-03-01
In this paper, we propose an edge-driven bidirectional geometric flow for boundary extraction. To this end, we combine the geodesic active contour flow and the gradient vector flow external force for snakes. The resulting motion equation is considered within a level set formulation, can deal with topological changes and important shape deformations. An efficient numerical schema is used for the flow implementation that exhibits robust behavior and has fast convergence rate. Promising results on real and synthetic images demonstrate the potentials of the flow.
Geometric Algebra Model of Distributed Representations
Patyk, Agnieszka
Formalism based on GA is an alternative to distributed representation models developed so far: Smolensky's tensor product, Holographic Reduced Representations (HRR), and Binary Spatter Code (BSC). Convolutions are replaced by geometric products interpretable in terms of geometry, which seems to be the most natural language for visualization of higher concepts. This paper recalls the main ideas behind the GA model and investigates recognition test results using both inner product and a clipped version of matrix representation. The influence of accidental blade equality on recognition is also studied. Finally, the efficiency of the GA model is compared to that of previously developed models.
On the geometrization of electromagnetism by torsion
International Nuclear Information System (INIS)
Fonseca Neto, J.B. da.
1984-01-01
The possibility of electromagnetism geometrization using an four dimension Cartan geometry is investigated. The Lagrangian density which presents dual invariance for dyons electrodynamics formulated in term of two potentials is constructed. This theory by association of two potentials with track and with torsion pseudo-track and of the field with torsion covariant divergent is described. The minimum coupling of particle gravitational field of scalar and spinorial fields with dyon geometry theory by the minimum coupling of these fields with Cartan geometry was obtained. (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)
Geometric Sensitivity of a Pinhole Collimator.
Jacobowitz, Howard; Metzler, Scott D
2010-02-19
Geometric sensitivity for single photon emission computerized tomography (SPECT) is given by a double integral over the detection plane. It would be useful to be able to explicitly evaluate this quantity. This paper shows that the inner integral can be evaluated in the situation where there is no gamma ray penetration of the material surrounding the pinhole aperature. This is done by converting the integral to an integral in the complex plane and using Cauchy's theorem to replace it by one which can be evaluated in terms of elliptic functions.
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.
Geometric frustration of icosahedron in metallic glasses.
Hirata, A; Kang, L J; Fujita, T; Klumov, B; Matsue, K; Kotani, M; Yavari, A R; Chen, M W
2013-07-26
Icosahedral order has been suggested as the prevalent atomic motif of supercooled liquids and metallic glasses for more than half a century, because the icosahedron is highly close-packed but is difficult to grow, owing to structure frustration and the lack of translational periodicity. By means of angstrom-beam electron diffraction of single icosahedra, we report experimental observation of local icosahedral order in metallic glasses. All the detected icosahedra were found to be distorted with partially face-centered cubic symmetry, presenting compelling evidence on geometric frustration of local icosahedral order in metallic glasses.
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.
Geometric and Texture Inpainting by Gibbs Sampling
DEFF Research Database (Denmark)
Gustafsson, David Karl John; Pedersen, Kim Steenstrup; Nielsen, Mads
2007-01-01
. In this paper we use the well-known FRAME (Filters, Random Fields and Maximum Entropy) for inpainting. We introduce a temperature term in the learned FRAME Gibbs distribution. By sampling using different temperature in the FRAME Gibbs distribution, different contents of the image are reconstructed. We propose...... a two step method for inpainting using FRAME. First the geometric structure of the image is reconstructed by sampling from a cooled Gibbs distribution, then the stochastic component is reconstructed by sample froma heated Gibbs distribution. Both steps in the reconstruction process are necessary...
Toroidal Precession as a Geometric Phase
Energy Technology Data Exchange (ETDEWEB)
J.W. Burby and H. Qin
2012-09-26
Toroidal precession is commonly understood as the orbit-averaged toroidal drift of guiding centers in axisymmetric and quasisymmetric configurations. We give a new, more natural description of precession as a geometric phase effect. In particular, we show that the precession angle arises as the holonomy of a guiding center's poloidal trajectory relative to a principal connection. The fact that this description is physically appropriate is borne out with new, manifestly coordinate-independent expressions for the precession angle that apply to all types of orbits in tokamaks and quasisymmetric stellarators alike. We then describe how these expressions may be fruitfully employed in numerical calculations of precession.
Moduli stabilization in non-geometric backgrounds
International Nuclear Information System (INIS)
Becker, Katrin; Becker, Melanie; Vafa, Cumrun; Walcher, Johannes
2007-01-01
Type II orientifolds based on Landau-Ginzburg models are used to describe moduli stabilization for flux compactifications of type II theories from the world-sheet CFT point of view. We show that for certain types of type IIB orientifolds which have no Kaehler moduli and are therefore intrinsically non-geometric, all moduli can be explicitly stabilized in terms of fluxes. The resulting four-dimensional theories can describe Minkowski as well as anti-de Sitter vacua. This construction provides the first string vacuum with all moduli frozen and leading to a 4D Minkowski background
In the realm of the geometric transitions
International Nuclear Information System (INIS)
Alexander, Stephon; Becker, Katrin; Becker, Melanie; Dasgupta, Keshav; Knauf, Anke; Tatar, Radu
2005-01-01
We complete the duality cycle by constructing the geometric transition duals in the type IIB, type I and heterotic theories. We show that in the type IIB theory the background on the closed string side is a Kaehler deformed conifold, as expected, even though the mirror type IIA backgrounds are non-Kaehler (both before and after the transition). On the other hand, the type I and heterotic backgrounds are non-Kaehler. Therefore, on the heterotic side these backgrounds give rise to new torsional manifolds that have not been studied before. We show the consistency of these backgrounds by verifying the torsional equation
The Geometric-VaR Backtesting Method
DEFF Research Database (Denmark)
Wei, Wei; Pelletier, Denis
2014-01-01
This paper develops a new test to evaluate Value af Risk (VaR) forecasts. VaR is a standard risk measure widely utilized by financial institutions and regulators, yet estimating VaR is a challenging problem, and popular VaR forecast relies on unrealistic assumptions. Hence, assessing...... the performance of VaR is of great importance. We propose the geometric-VaR test which utilizes the duration between the violations of VaR as well as the value of VaR. We conduct a Monte Carlo study based on desk-level data and we find that our test has high power against various alternatives....
Application of geometric approximation to the CPMG experiment: Two- and three-site exchange
Chao, Fa-An; Byrd, R. Andrew
2017-04-01
The Carr-Purcell-Meiboom-Gill (CPMG) experiment is one of the most classical and well-known relaxation dispersion experiments in NMR spectroscopy, and it has been successfully applied to characterize biologically relevant conformational dynamics in many cases. Although the data analysis of the CPMG experiment for the 2-site exchange model can be facilitated by analytical solutions, the data analysis in a more complex exchange model generally requires computationally-intensive numerical analysis. Recently, a powerful computational strategy, geometric approximation, has been proposed to provide approximate numerical solutions for the adiabatic relaxation dispersion experiments where analytical solutions are neither available nor feasible. Here, we demonstrate the general potential of geometric approximation by providing a data analysis solution of the CPMG experiment for both the traditional 2-site model and a linear 3-site exchange model. The approximate numerical solution deviates less than 0.5% from the numerical solution on average, and the new approach is computationally 60,000-fold more efficient than the numerical approach. Moreover, we find that accurate dynamic parameters can be determined in most cases, and, for a range of experimental conditions, the relaxation can be assumed to follow mono-exponential decay. The method is general and applicable to any CPMG RD experiment (e.g. N, C‧, Cα, Hα, etc.) The approach forms a foundation of building solution surfaces to analyze the CPMG experiment for different models of 3-site exchange. Thus, the geometric approximation is a general strategy to analyze relaxation dispersion data in any system (biological or chemical) if the appropriate library can be built in a physically meaningful domain.
On the minimum of independent geometrically distributed random variables
Ciardo, Gianfranco; Leemis, Lawrence M.; Nicol, David
1994-01-01
The expectations E(X(sub 1)), E(Z(sub 1)), and E(Y(sub 1)) of the minimum of n independent geometric, modifies geometric, or exponential random variables with matching expectations differ. We show how this is accounted for by stochastic variability and how E(X(sub 1))/E(Y(sub 1)) equals the expected number of ties at the minimum for the geometric random variables. We then introduce the 'shifted geometric distribution' and show that there is a unique value of the shift for which the individual shifted geometric and exponential random variables match expectations both individually and in the minimums.
On unified field theories, dynamical torsion and geometrical models: II
International Nuclear Information System (INIS)
Cirilo-Lombardo, D.J.
2011-01-01
We analyze in this letter the same space-time structure as that presented in our previous reference (Part. Nucl, Lett. 2010. V.7, No.5. P.299-307), but relaxing now the condition a priori of the existence of a potential for the torsion. We show through exact cosmological solutions from this model, where the geometry is Euclidean RxO 3 ∼ RxSU(2), the relation between the space-time geometry and the structure of the gauge group. Precisely this relation is directly connected with the relation of the spin and torsion fields. The solution of this model is explicitly compared with our previous ones and we find that: i) the torsion is not identified directly with the Yang-Mills type strength field, ii) there exists a compatibility condition connected with the identification of the gauge group with the geometric structure of the space-time: this fact leads to the identification between derivatives of the scale factor a with the components of the torsion in order to allow the Hosoya-Ogura ansatz (namely, the alignment of the isospin with the frame geometry of the space-time), and iii) of two possible structures of the torsion the 'tratorial' form (the only one studied here) forbid wormhole configurations, leading only to cosmological instanton space-time in eternal expansion
Directory of Open Access Journals (Sweden)
Diana Marcela Perez Berrio
2014-07-01
Full Text Available Meniscus alloimplants have been used as a source of tissue for replacement in case of breakage or irreparable damage. To determine possible changes by conservation, the study proposed to geometrically evaluate fresh menisci and menisci preserved in 98% glycerin. 15 medial menisci from eight albino rabbits of New Zealand breed were used, divided into three groups: five fresh menisci (GI; five menisci preserved in 98% glycerin for eight months (GII, and five menisci preserved in 98% glycerin for eight months and then rehydrated in 0.9% saline solution for 24 hours (GIII. All menisci were measured with vernier caliper at seven points of their geometric structure. The study established that there were no statistical differences in the measurements of GII and GIII when compared to GI; there was no difference either in the measurements of GIII when compared to GII, thus rehydration in antibiotic saline solution for 24 hours can be considered unnecessary.
Fuzzy Decision-Making Approach in Geometric Programming for a Single Item EOQ Model
Directory of Open Access Journals (Sweden)
Monalisha Pattnaik
2015-06-01
Full Text Available Background and methods: Fuzzy decision-making approach is allowed in geometric programming for a single item EOQ model with dynamic ordering cost and demand-dependent unit cost. The setup cost varies with the quantity produced/purchased and the modification of objective function with storage area in the presence of imprecisely estimated parameters are investigated. It incorporates all concepts of a fuzzy arithmetic approach, the quantity ordered, and demand per unit compares both fuzzy geometric programming technique and other models for linear membership functions. Results and conclusions: Investigation of the properties of an optimal solution allows developing an algorithm whose validity is illustrated through an example problem and the results discu ssed. Sensitivity analysis of the optimal solution is also studied with respect to changes in different parameter values.
An Interpretation of Relativistic Spin Entanglement Using Geometric Algebra
McKenzie, Crystal-Ann
Entangled states are often given as one of the most bizarre examples of "weirdness" described as inherent to quantum mechanics. The present work reinterprets entanglement as not being a property of states at all, but rather as a relationship between the reference frames in which the states reside, which proposes to reduce "weirdness" of interpretation. Using the geometric Algebra of Physical Space, it has been shown that a classical form of the Dirac equation can be satisfied by any eigenspinor, which is a Lorentz transformation operator describing the relative velocity and relative orientation of the rest frame of a system as seen from a particular lab frame from which it is described. The real linear nature of the Dirac equation means any real linear superposition of such eigenspinors are also solutions. Thus, with entanglement modelled as an operator consisting of a linear superposition of rotation operators describing the possible relative orientations of a particular particle frame and the frame from which it is observed, it too can satisfy a bipartite form of the Dirac equation. To investigate this model, the present work applies relativistic boost transformations to the entangling operator in various ways, including as an identical boost of both parts in the same direction, and also as equal and oppositely-directed boosts. The resulting "entangling eigenspinors" are then analyzed in various ways, including the application to specific spin states --- only to discover that doing this results in a reduction of the information, which can be interpreted as a reduction in the amount of entanglement. By comparing this to the treatment of the Dirac equation in APS, it may be concluded that the application of the entangling eigenspinor to a state --- which models the typical approach of simply boosting an entangled state --- gives an incomplete account of what is happening. The full information is thus contained within the entangling eigenspinor, justifying the
DEFF Research Database (Denmark)
Lazarov, Boyan Stefanov; Schevenels, Mattias; Sigmund, Ole
2012-01-01
The aim of this paper is to introduce the stochastic collocation methods in topology optimization for mechanical systems with material and geometric uncertainties. The random variations are modeled by a memory-less transformation of spatially varying Gaussian random fields which ensures...... their physical admissibility. The stochastic collocation method combined with the proposed material and geometry uncertainty models provides robust designs by utilizing already developed deterministic solvers. The computational cost is discussed in details and solutions to decrease it, like sparse grids...
A geometric theory for semilinear almost-periodic parabolic partial differential equations on RN
International Nuclear Information System (INIS)
Vuillermot, P.A.
1991-01-01
In this short expository article we review various applications of some geometric methods which have been recently devised to investigate the long time behaviour of classical solutions to certain semilinear almost-periodic reaction-diffusion equations on R N . As a consequence, we also show how to construct almost-periodic attractors for such equations and how to investigate their stability properties. The class of problems which we analyse here contains in particular well known equations of population genetics. (author). 17 refs
Geometric Modelling of Octagonal Lamp Poles
Chan, T. O.; Lichti, D. D.
2014-06-01
Lamp poles are one of the most abundant highway and community components in modern cities. Their supporting parts are primarily tapered octagonal cones specifically designed for wind resistance. The geometry and the positions of the lamp poles are important information for various applications. For example, they are important to monitoring deformation of aged lamp poles, maintaining an efficient highway GIS system, and also facilitating possible feature-based calibration of mobile LiDAR systems. In this paper, we present a novel geometric model for octagonal lamp poles. The model consists of seven parameters in which a rotation about the z-axis is included, and points are constrained by the trigonometric property of 2D octagons after applying the rotations. For the geometric fitting of the lamp pole point cloud captured by a terrestrial LiDAR, accurate initial parameter values are essential. They can be estimated by first fitting the points to a circular cone model and this is followed by some basic point cloud processing techniques. The model was verified by fitting both simulated and real data. The real data includes several lamp pole point clouds captured by: (1) Faro Focus 3D and (2) Velodyne HDL-32E. The fitting results using the proposed model are promising, and up to 2.9 mm improvement in fitting accuracy was realized for the real lamp pole point clouds compared to using the conventional circular cone model. The overall result suggests that the proposed model is appropriate and rigorous.
Translating cosmological special relativity into geometric algebra
Horn, Martin Erik
2012-11-01
Geometric algebra and Clifford algebra are important tools to describe and analyze the physics of the world we live in. Although there is enormous empirical evidence that we are living in four dimensional spacetime, mathematical worlds of higher dimensions can be used to present the physical laws of our world in an aesthetical and didactical more appealing way. In physics and mathematics education we are therefore confronted with the question how these high dimensional spaces should be taught. But as an immediate confrontation of students with high dimensional compactified spacetimes would expect too much from them at the beginning of their university studies, it seems reasonable to approach the mathematics and physics of higher dimensions step by step. The first step naturally is the step from four dimensional spacetime of special relativity to a five dimensional spacetime world. As a toy model for this artificial world cosmological special relativity, invented by Moshe Carmeli, can be used. This five dimensional non-compactified approach describes a spacetime which consists not only of one time dimension and three space dimensions. In addition velocity is regarded as a fifth dimension. This model very probably will not represent physics correctly. But it can be used to discuss and analyze the consequences of an additional dimension in a clear and simple way. Unfortunately Carmeli has formulated cosmological special relativity in standard vector notation. Therefore a translation of cosmological special relativity into the mathematical language of Grassmann and Clifford (Geometric algebra) is given and the physics of cosmological special relativity is discussed.
Geometric correction of APEX hyperspectral data
Directory of Open Access Journals (Sweden)
Vreys Kristin
2016-03-01
Full Text Available Hyperspectral imagery originating from airborne sensors is nowadays widely used for the detailed characterization of land surface. The correct mapping of the pixel positions to ground locations largely contributes to the success of the applications. Accurate geometric correction, also referred to as “orthorectification”, is thus an important prerequisite which must be performed prior to using airborne imagery for evaluations like change detection, or mapping or overlaying the imagery with existing data sets or maps. A so-called “ortho-image” provides an accurate representation of the earth’s surface, having been adjusted for lens distortions, camera tilt and topographic relief. In this paper, we describe the different steps in the geometric correction process of APEX hyperspectral data, as applied in the Central Data Processing Center (CDPC at the Flemish Institute for Technological Research (VITO, Mol, Belgium. APEX ortho-images are generated through direct georeferencing of the raw images, thereby making use of sensor interior and exterior orientation data, boresight calibration data and elevation data. They can be referenced to any userspecified output projection system and can be resampled to any output pixel size.
Implicit face prototype learning from geometric information.
Or, Charles C-F; Wilson, Hugh R
2013-04-19
There is evidence that humans implicitly learn an average or prototype of previously studied faces, as the unseen face prototype is falsely recognized as having been learned (Solso & McCarthy, 1981). Here we investigated the extent and nature of face prototype formation where observers' memory was tested after they studied synthetic faces defined purely in geometric terms in a multidimensional face space. We found a strong prototype effect: The basic results showed that the unseen prototype averaged from the studied faces was falsely identified as learned at a rate of 86.3%, whereas individual studied faces were identified correctly 66.3% of the time and the distractors were incorrectly identified as having been learned only 32.4% of the time. This prototype learning lasted at least 1 week. Face prototype learning occurred even when the studied faces were further from the unseen prototype than the median variation in the population. Prototype memory formation was evident in addition to memory formation of studied face exemplars as demonstrated in our models. Additional studies showed that the prototype effect can be generalized across viewpoints, and head shape and internal features separately contribute to prototype formation. Thus, implicit face prototype extraction in a multidimensional space is a very general aspect of geometric face learning. Copyright © 2013 Elsevier Ltd. All rights reserved.
Dropwise Condensation Enhancement on Geometric Features
Zhao, Yajing; Preston, Daniel J.; Lu, Zhengmao; Wang, Evelyn N.
Dropwise condensation, which has been demonstrated to exhibit a 5-7X higher heat transfer coefficient compared with state-of-the-art filmwise condensation, contributes to energy savings in a wide range of applications such as desalination systems, steam cycles and dew harvesting. In order to enhance dropwise condensation performance, previous studies have investigated the effects of surface geometric features on droplet growth rates and found that bumps protruding from surfaces can effectively promote dropwise condensation. In this work, we show that while bumps on surfaces enable droplets to grow faster in some cases, there are also cases where bumps on surfaces actually degrade dropwise condensation. We numerically simulated and experimentally demonstrated that even the same surface geometric feature can exert completely opposite effects on dropwise condensation of water under two different working conditions (pure vapor vs. air vapor mixture). This phenomenon is explained by comparing the heat and mass transfer resistance of the surface structure to that of the vapor transport during dropwise condensation. We expect that the fundamental understanding developed in this study will provide useful guidelines for relevant condensation applications.
Geometric rectification for nanoscale vibrational energy harvesting
Bustos-Marún, Raúl A.
2018-02-01
In this work, we present a mechanism that, based on quantum-mechanical principles, allows one to recover kinetic energy at the nanoscale. Our premise is that very small mechanical excitations, such as those arising from sound waves propagating through a nanoscale system or similar phenomena, can be quite generally converted into useful electrical work by applying the same principles behind conventional adiabatic quantum pumping. The proposal is potentially useful for nanoscale vibrational energy harvesting where it can have several advantages. The most important one is that it avoids the use of classical rectification mechanisms as it is based on what we call geometric rectification. We show that this geometric rectification results from applying appropriate but quite general initial conditions to damped harmonic systems coupled to electronic reservoirs. We analyze an analytically solvable example consisting of a wire suspended over permanent charges where we find the condition for maximizing the pumped charge. We also studied the effects of coupling the system to a capacitor including the effect of current-induced forces and analyzing the steady-state voltage of operation. Finally, we show how quantum effects can be used to boost the performance of the proposed device.
Geometric reconstruction methods for electron tomography
International Nuclear Information System (INIS)
Alpers, Andreas; Gardner, Richard J.; König, Stefan; Pennington, Robert S.; Boothroyd, Chris B.; Houben, Lothar; Dunin-Borkowski, Rafal E.; Joost Batenburg, Kees
2013-01-01
Electron tomography is becoming an increasingly important tool in materials science for studying the three-dimensional morphologies and chemical compositions of nanostructures. The image quality obtained by many current algorithms is seriously affected by the problems of missing wedge artefacts and non-linear projection intensities due to diffraction effects. The former refers to the fact that data cannot be acquired over the full 180° tilt range; the latter implies that for some orientations, crystalline structures can show strong contrast changes. To overcome these problems we introduce and discuss several algorithms from the mathematical fields of geometric and discrete tomography. The algorithms incorporate geometric prior knowledge (mainly convexity and homogeneity), which also in principle considerably reduces the number of tilt angles required. Results are discussed for the reconstruction of an InAs nanowire. - Highlights: ► Four algorithms for electron tomography are introduced that utilize prior knowledge. ► Objects are assumed to be homogeneous; convexity and regularity is also discussed. ► We are able to reconstruct slices of a nanowire from as few as four projections. ► Algorithms should be selected based on the specific reconstruction task at hand
Ertekin, E.; Solak, S.; Yazici, E.
2010-12-01
The aim of this study is to identify the effects of formalism in teaching on primary and secondary school mathematics teacher trainees' algebraic and geometric interpretations of the notions of linear dependency/independency. Quantitative research methods are drawn in order to determine differences in success levels between algebraic and geometric interpretations of the linear dependency/independency of vectors presented in two- and three-dimensional space. On the other hand, qualitative research methods were utilized in order to investigate thinking modes involved in the geometric interpretation of the same notion. The participants were a total of 144 teacher trainees registered at the Selçuk University, Education Faculty in 2007-2008 academic year. 33 participants were first year students at Secondary Mathematics Education Department, while 111 were second year students at Primary Mathematics Education Department. The results indicated that correlations between the formal definition of the notions of linear dependency/independency and the items of the test which required algebraic and geometric interpretation were both low. Yet, the correlation for the algebraic dimension of the test was higher than the geometric dimension. Likewise, algebraic mean success score was significantly higher than the geometric mean score.
A white–cyan-red LED system for low correlated colour temperature lighting
DEFF Research Database (Denmark)
Chakrabarti, Maumita; Thorseth, Anders; Corell, Dennis Dan
2015-01-01
A white LED complemented by cyan and red LEDs is a good candidate for achieving high colour rendering at low correlated colour temperatures. This is usually very difficult with commercially available white LEDs. In addition, the system is able to replace incandescent lighting in many applications......; for example, the lighting for museum display cases. To investigate and optimize the colour and light distribution properties, both spectral and geometrical modelling are used. Mapping of the possible combinations of LEDs is used to locate the optimal solutions within the colour gamut, with emphasis...
Characterizing Floral Symmetry in the Core Goodeniaceae with Geometric Morphometrics.
Gardner, Andrew G; Fitz Gerald, Jonathan N; Menz, John; Shepherd, Kelly A; Howarth, Dianella G; Jabaily, Rachel S
2016-01-01
Core Goodeniaceae is a clade of ~330 species primarily distributed in Australia. Considerable variation in flower morphology exists within this group and we aim to use geometric morphometrics to characterize this variation across the two major subclades: Scaevola sensu lato (s.l.) and Goodenia s.l., the latter of which was hypothesized to exhibit greater variability in floral symmetry form. We test the hypothesis that floral morphological variation can be adequately characterized by our morphometric approach, and that discrete groups of floral symmetry morphologies exist, which broadly correlate with subjectively determined groups. From 335 images of 44 species in the Core Goodeniaceae, two principal components were computed that describe >98% of variation in all datasets. Increasing values of PC1 ventralize the dorsal petals (increasing the angle between them), whereas increasing values of PC2 primarily ventralize the lateral petals (decreasing the angle between them). Manipulation of these two morphological "axes" alone was sufficient to recreate any of the general floral symmetry patterns in the Core Goodeniaceae. Goodenia s.l. exhibits greater variance than Scaevola s.l. in PC1 and PC2, and has a significantly lower mean value for PC1. Clustering clearly separates fan-flowers (with dorsal petals at least 120° separated) from the others, whereas the distinction between pseudo-radial and bilabiate clusters is less clear and may form a continuum rather than two distinct groups. Transitioning from the average fan-flower to the average non-fan-flower is described almost exclusively by PC1, whereas PC2 partially describes the transition between bilabiate and pseudo-radial morphologies. Our geometric morphometric method accurately models Core Goodeniaceae floral symmetry diversity.
Constantinides, E. D.; Marhefka, R. J.
1994-01-01
A uniform geometrical optics (UGO) and an extended uniform geometrical theory of diffraction (EUTD) are developed for evaluating high frequency electromagnetic (EM) fields within transition regions associated with a two and three dimensional smooth caustic of reflected rays and a composite shadow boundary formed by the caustic termination or the confluence of the caustic with the reflection shadow boundary (RSB). The UGO is a uniform version of the classic geometrical optics (GO). It retains the simple ray optical expressions of classic GO and employs a new set of uniform reflection coefficients. The UGO also includes a uniform version of the complex GO ray field that exists on the dark side of the smooth caustic. The EUTD is an extension of the classic uniform geometrical theory of diffraction (UTD) and accounts for the non-ray optical behavior of the UGO reflected field near caustics by using a two-variable transition function in the expressions for the edge diffraction coefficients. It also uniformly recovers the classic UTD behavior of the edge diffracted field outside the composite shadow boundary transition region. The approach employed for constructing the UGO/EUTD solution is based on a spatial domain physical optics (PO) radiation integral representation for the fields which is then reduced using uniform asymptotic procedures. The UGO/EUTD analysis is also employed to investigate the far-zone RCS problem of plane wave scattering from two and three dimensional polynomial defined surfaces, and uniform reflection, zero-curvature, and edge diffraction coefficients are derived. Numerical results for the scattering and diffraction from cubic and fourth order polynomial strips are also shown and the UGO/EUTD solution is validated by comparison to an independent moment method (MM) solution. The UGO/EUTD solution is also compared with the classic GO/UTD solution. The failure of the classic techniques near caustics and composite shadow boundaries is clearly
Modern Geometric Methods of Distance Determination
Thévenin, Frédéric; Falanga, Maurizio; Kuo, Cheng Yu; Pietrzyński, Grzegorz; Yamaguchi, Masaki
2017-11-01
Building a 3D picture of the Universe at any distance is one of the major challenges in astronomy, from the nearby Solar System to distant Quasars and galaxies. This goal has forced astronomers to develop techniques to estimate or to measure the distance of point sources on the sky. While most distance estimates used since the beginning of the 20th century are based on our understanding of the physics of objects of the Universe: stars, galaxies, QSOs, the direct measures of distances are based on the geometric methods as developed in ancient Greece: the parallax, which has been applied to stars for the first time in the mid-19th century. In this review, different techniques of geometrical astrometry applied to various stellar and cosmological (Megamaser) objects are presented. They consist in parallax measurements from ground based equipment or from space missions, but also in the study of binary stars or, as we shall see, of binary systems in distant extragalactic sources using radio telescopes. The Gaia mission will be presented in the context of stellar physics and galactic structure, because this key space mission in astronomy will bring a breakthrough in our understanding of stars, galaxies and the Universe in their nature and evolution with time. Measuring the distance to a star is the starting point for an unbiased description of its physics and the estimate of its fundamental parameters like its age. Applying these studies to candles such as the Cepheids will impact our large distance studies and calibration of other candles. The text is constructed as follows: introducing the parallax concept and measurement, we shall present briefly the Gaia satellite which will be the future base catalogue of stellar astronomy in the near future. Cepheids will be discussed just after to demonstrate the state of the art in distance measurements in the Universe with these variable stars, with the objective of 1% of error in distances that could be applied to our closest
Geometric Aspects and Some Uses of Deformed Models of Thermostatistics
Directory of Open Access Journals (Sweden)
Alexandre Gavrilik
2018-02-01
Full Text Available We consider diverse deformed Bose gas models (DBGMs focusing on distributions and correlations of any order, and also on deformed thermodynamics. For so-called μ -deformed Bose gas model ( μ -DBGM, main thermodynamic aspects are treated: total number of particles, deformed partition function, etc. Using a geometric approach, we confirm the existence of critical behavior—Bose-like condensation; we find the critical temperature T c ( μ depending on μ so that T c ( μ > T c ( Bose for μ > 0 . This fact and other advantages of μ -DBGM relative to the usual Bose gas, e.g., stronger effective inter-particle attraction (controlled by the parameter μ , allow us to consider the condensate in μ -DBGM as a candidate for modeling dark matter. As another, quite successful application we discuss the usage of the two-parameter ( μ ˜ , q -deformed BGM for effective description of the peculiar (non-Bose like behavior of two-pion correlations observed in the STAR experiment at RHIC (Brookhaven. Herein, we point out the transparent role of the two deformation parameters μ ˜ and q as being responsible for compositeness and (effective account of interactions of pions, respectively.
Hepson, Ozlem Ersoy; Daǧ, Idris
2018-01-01
In this paper, a subdomain Galerkin method is set up to find solutions of singularly perturbed boundary value problems which are used widely in many areas such as chemical reactor theory, aerodynamics, quantum mechanics, reaction-diffusion process, optimal control, etc. A combination of the cubic B-spline base functions as an approximation function is used to build up the presented method over the geometrically graded mesh. Thus finer mesh can be established through the end parts of the problem domain where steep solutions exist.
Geometric methods for discrete dynamical systems
Easton, Robert W
1998-01-01
This book looks at dynamics as an iteration process where the output of a function is fed back as an input to determine the evolution of an initial state over time. The theory examines errors which arise from round-off in numerical simulations, from the inexactness of mathematical models used to describe physical processes, and from the effects of external controls. The author provides an introduction accessible to beginning graduate students and emphasizing geometric aspects of the theory. Conley''s ideas about rough orbits and chain-recurrence play a central role in the treatment. The book will be a useful reference for mathematicians, scientists, and engineers studying this field, and an ideal text for graduate courses in dynamical systems.
Noncyclic geometric changes of quantum states
International Nuclear Information System (INIS)
Kult, David; Sjoeqvist, Erik; Aaberg, Johan
2006-01-01
Non-Abelian quantum holonomies, i.e., unitary state changes solely induced by geometric properties of a quantum system, have been much under focus in the physics community as generalizations of the Abelian Berry phase. Apart from being a general phenomenon displayed in various subfields of quantum physics, the use of holonomies has lately been suggested as a robust technique to obtain quantum gates; the building blocks of quantum computers. Non-Abelian holonomies are usually associated with cyclic changes of quantum systems, but here we consider a generalization to noncyclic evolutions. We argue that this open-path holonomy can be used to construct quantum gates. We also show that a structure of partially defined holonomies emerges from the open-path holonomy. This structure has no counterpart in the Abelian setting. We illustrate the general ideas using an example that may be accessible to tests in various physical systems
Geometric extension through Schwarzschild r = 0
International Nuclear Information System (INIS)
Lynden-Bell, D.; Katz, J.; Hebrew Univ., Jerusalem
1990-01-01
Singularities in space-time are not necessarily cancers in the manifold but can herald interesting topological change in the space-time at places where there are several different tangent Minkowski spaces. Most discussions of gravitational collapse cease when space-time becomes singular. In the 'hour-glass' universe we have an example where the singularity develops in empty space; here we give a geometrical extension through the singularity in which geodesics that enter it emerge into a new space. The result extends Schwarzschild space and is periodic in 'extended' Penrose coordinates. There is a topological singularity but no mass at r = 0. The extension is mildly nonanalytic but unique. It is based on the concept that time does not stop and that empty space-times which develop singularities must still have zero Ricci tensors even where the Riemann tensor becomes infinite. (author)
Geometrical model of the Baltic artesian basin
Sennikovs, J.; Virbulis, J.; Bethers, U.
2012-04-01
Baltic artesian basin (BAB) is a multi-layer sedimentary basin spanning around 480'000 km2. BAB is located in the territory of Latvia, Lithuania and Estonia, parts of Poland, Russia, Belarus and large area of the Baltic Sea, including island of Gotland. The thickness of sedimentary cover is about 5000 m in the south-western part. Crystalline bedding reaches the surface in the northern and north-western parts. The aim of the present work is development of the model of geometric structure and three dimensional finite element mesh for the hydrogeological model of the whole BAB. The information that is used to build the geometrical structure includes: (1) Stratigraphic information from boreholes in Latvia and Estonia (2) Maps of height isolines of geological layers for Latvia and Lithuania (3) Maps of sub-quaternary deposits in Latvia and Lithuania (4) Maps of fault lines on the crystalline basement surface in Latvia, Lithuania and Estonia (5) Buried valley data from Latvia and Estonia (6) Earth topography data (7) Baltic sea depth data (8) Data from published geological cross-sections, information from books and other sources. Unification of the heterogeneous information from different sources, which are employed for building of the geometrical structure of the model are performed. Special algorithms are developed for this purpose considering the priority, importance and plausibility of each of the data sources. Pre-processing of the borehole information to screen out the outlying borehole data has been performed. Model of geological structure contains 42 layers. It includes aquifers and aquitards from Cambrian up to the Quaternary deposits. Fault displacements are incorporated into the model taking into account data from the published structural maps. Four reconstructed regional erosion surfaces (upper Ordovician, Devonian, Permian and Quaternary) are included into the model Three dimensional mesh of the geological structure is constructed layer-wise. The triangular
Geometrically unfitted finite element methods and applications
Burman, Erik; Larson, Mats; Olshanskii, Maxim
2017-01-01
This book provides a snapshot of the state of the art of the rapidly evolving field of integration of geometric data in finite element computations. The contributions to this volume, based on research presented at the UCL workshop on the topic in January 2016, include three review papers on core topics such as fictitious domain methods for elasticity, trace finite element methods for partial differential equations defined on surfaces, and Nitsche’s method for contact problems. Five chapters present original research articles on related theoretical topics, including Lagrange multiplier methods, interface problems, bulk-surface coupling, and approximation of partial differential equations on moving domains. Finally, two chapters discuss advanced applications such as crack propagation or flow in fractured poroelastic media. This is the first volume that provides a comprehensive overview of the field of unfitted finite element methods, including recent techniques such as cutFEM, traceFEM, ghost penalty, and aug...
Random broadcast on random geometric graphs
Energy Technology Data Exchange (ETDEWEB)
Bradonjic, Milan [Los Alamos National Laboratory; Elsasser, Robert [UNIV OF PADERBORN; Friedrich, Tobias [ICSI/BERKELEY; Sauerwald, Tomas [ICSI/BERKELEY
2009-01-01
In this work, we consider the random broadcast time on random geometric graphs (RGGs). The classic random broadcast model, also known as push algorithm, is defined as: starting with one informed node, in each succeeding round every informed node chooses one of its neighbors uniformly at random and informs it. We consider the random broadcast time on RGGs, when with high probability: (i) RGG is connected, (ii) when there exists the giant component in RGG. We show that the random broadcast time is bounded by {Omicron}({radical} n + diam(component)), where diam(component) is a diameter of the entire graph, or the giant component, for the regimes (i), or (ii), respectively. In other words, for both regimes, we derive the broadcast time to be {Theta}(diam(G)), which is asymptotically optimal.
Analytic and geometric study of stratified spaces
Pflaum, Markus J
2001-01-01
The book provides an introduction to stratification theory leading the reader up to modern research topics in the field. The first part presents the basics of stratification theory, in particular the Whitney conditions and Mather's control theory, and introduces the notion of a smooth structure. Moreover, it explains how one can use smooth structures to transfer differential geometric and analytic methods from the arena of manifolds to stratified spaces. In the second part the methods established in the first part are applied to particular classes of stratified spaces like for example orbit spaces. Then a new de Rham theory for stratified spaces is established and finally the Hochschild (co)homology theory of smooth functions on certain classes of stratified spaces is studied. The book should be accessible to readers acquainted with the basics of topology, analysis and differential geometry.
Geometric theory of discrete nonautonomous dynamical systems
Pötzsche, Christian
2010-01-01
Nonautonomous dynamical systems provide a mathematical framework for temporally changing phenomena, where the law of evolution varies in time due to seasonal, modulation, controlling or even random effects. Our goal is to provide an approach to the corresponding geometric theory of nonautonomous discrete dynamical systems in infinite-dimensional spaces by virtue of 2-parameter semigroups (processes). These dynamical systems are generated by implicit difference equations, which explicitly depend on time. Compactness and dissipativity conditions are provided for such problems in order to have attractors using the natural concept of pullback convergence. Concerning a necessary linear theory, our hyperbolicity concept is based on exponential dichotomies and splittings. This concept is in turn used to construct nonautonomous invariant manifolds, so-called fiber bundles, and deduce linearization theorems. The results are illustrated using temporal and full discretizations of evolutionary differential equations.
Random geometric graphs with general connection functions
Dettmann, Carl P.; Georgiou, Orestis
2016-03-01
In the original (1961) Gilbert model of random geometric graphs, nodes are placed according to a Poisson point process, and links formed between those within a fixed range. Motivated by wireless ad hoc networks "soft" or "probabilistic" connection models have recently been introduced, involving a "connection function" H (r ) that gives the probability that two nodes at distance r are linked (directly connect). In many applications (not only wireless networks), it is desirable that the graph is connected; that is, every node is linked to every other node in a multihop fashion. Here the connection probability of a dense network in a convex domain in two or three dimensions is expressed in terms of contributions from boundary components for a very general class of connection functions. It turns out that only a few quantities such as moments of the connection function appear. Good agreement is found with special cases from previous studies and with numerical simulations.
Point- and curve-based geometric conflation
López-Vázquez, C.
2013-01-01
Geometric conflation is the process undertaken to modify the coordinates of features in dataset A in order to match corresponding ones in dataset B. The overwhelming majority of the literature considers the use of points as features to define the transformation. In this article we present a procedure to consider one-dimensional curves also, which are commonly available as Global Navigation Satellite System (GNSS) tracks, routes, coastlines, and so on, in order to define the estimate of the displacements to be applied to each object in A. The procedure involves three steps, including the partial matching of corresponding curves, the computation of some analytical expression, and the addition of a correction term in order to satisfy basic cartographic rules. A numerical example is presented. © 2013 Copyright Taylor and Francis Group, LLC.
Geometrical evaluation of the Maslov index
International Nuclear Information System (INIS)
Takahashi, Satoshi; Takatsuka, Kazuo
2004-01-01
A geometrical method to calculate the Maslov index, which is an important part of the quantum phase, is proposed. This method is particularly useful for the recently proposed amplitude-free quasicorrelation function approach for the quantization of chaos [K. Hotta and K. Takatsuka, J. Phys. A 36, 4785 (2003)]. In this theory the Maslov index is involved with no need to calculate the amplitude factor, which is usually obtained through integration of the stability matrix. Since this matrix constitutes the major origin of difficulty in semiclassical quantization of chaos and since its integration is time consuming, the present method, which avoids the stability matrix, should assist in opening a gate for practical semiclassical quantization of chaos in a large molecular system
Geometric regularizations and dual conifold transitions
International Nuclear Information System (INIS)
Landsteiner, Karl; Lazaroiu, Calin I.
2003-01-01
We consider a geometric regularization for the class of conifold transitions relating D-brane systems on noncompact Calabi-Yau spaces to certain flux backgrounds. This regularization respects the SL(2,Z) invariance of the flux superpotential, and allows for computation of the relevant periods through the method of Picard-Fuchs equations. The regularized geometry is a noncompact Calabi-Yau which can be viewed as a monodromic fibration, with the nontrivial monodromy being induced by the regulator. It reduces to the original, non-monodromic background when the regulator is removed. Using this regularization, we discuss the simple case of the local conifold, and show how the relevant field-theoretic information can be extracted in this approach. (author)
The Geometric Nonlinear Generalized Brazier Effect
DEFF Research Database (Denmark)
Nikolajsen, Jan Ánike; Lauridsen, Peter Riddersholm; Damkilde, Lars
2016-01-01
denoted the generalized Brazier effect. The original work of Brazier dealt with very large deformations that changed the cross section significantly and hereby also the bending moment of inertia and the bending moment capacity. In this paper the aim is to describe the Brazier effect for smaller...... deformation not taking into account the change in moment of inertia. However, the generalized Brazier effect gives additional stresses directed perpendicular to the beam axis. In composite structures these extra stresses may influence the fatigue life significantly. The paper demonstrates a linearized method...... 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...
COMPARISON OF METHODS FOR GEOMETRIC CAMERA CALIBRATION
Directory of Open Access Journals (Sweden)
J. Hieronymus
2012-09-01
Full Text Available Methods for geometric calibration of cameras in close-range photogrammetry are established and well investigated. The most common one is based on test-fields with well-known pattern, which are observed from different directions. The parameters of a distortion model are calculated using bundle-block-adjustment-algorithms. This methods works well for short focal lengths, but is essentially more problematic to use with large focal lengths. Those would require very large test-fields and surrounding space. To overcome this problem, there is another common method for calibration used in remote sensing. It employs measurements using collimator and a goniometer. A third calibration method uses diffractive optical elements (DOE to project holograms of well known pattern. In this paper these three calibration methods are compared empirically, especially in terms of accuracy. A camera has been calibrated with those methods mentioned above. All methods provide a set of distortion correction parameters as used by the photogrammetric software Australis. The resulting parameter values are very similar for all investigated methods. The three sets of distortion parameters are crosscompared against all three calibration methods. This is achieved by inserting the gained distortion parameters as fixed input into the calibration algorithms and only adjusting the exterior orientation. The RMS (root mean square of the remaining image coordinate residuals are taken as a measure of distortion correction quality. There are differences resulting from the different calibration methods. Nevertheless the measure is small for every comparison, which means that all three calibration methods can be used for accurate geometric calibration.
A Geometric Representation of Collective Attention Flows.
Directory of Open Access Journals (Sweden)
Peiteng Shi
Full Text Available With the fast development of Internet and WWW, "information overload" has become an overwhelming problem, and collective attention of users will play a more important role nowadays. As a result, knowing how collective attention distributes and flows among different websites is the first step to understand the underlying dynamics of attention on WWW. In this paper, we propose a method to embed a large number of web sites into a high dimensional Euclidean space according to the novel concept of flow distance, which both considers connection topology between sites and collective click behaviors of users. With this geometric representation, we visualize the attention flow in the data set of Indiana university clickstream over one day. It turns out that all the websites can be embedded into a 20 dimensional ball, in which, close sites are always visited by users sequentially. The distributions of websites, attention flows, and dissipations can be divided into three spherical crowns (core, interim, and periphery. 20% popular sites (Google.com, Myspace.com, Facebook.com, etc. attracting 75% attention flows with only 55% dissipations (log off users locate in the central layer with the radius 4.1. While 60% sites attracting only about 22% traffics with almost 38% dissipations locate in the middle area with radius between 4.1 and 6.3. Other 20% sites are far from the central area. All the cumulative distributions of variables can be well fitted by "S"-shaped curves. And the patterns are stable across different periods. Thus, the overall distribution and the dynamics of collective attention on websites can be well exhibited by this geometric representation.
A Geometric Representation of Collective Attention Flows.
Shi, Peiteng; Huang, Xiaohan; Wang, Jun; Zhang, Jiang; Deng, Su; Wu, Yahui
2015-01-01
With the fast development of Internet and WWW, "information overload" has become an overwhelming problem, and collective attention of users will play a more important role nowadays. As a result, knowing how collective attention distributes and flows among different websites is the first step to understand the underlying dynamics of attention on WWW. In this paper, we propose a method to embed a large number of web sites into a high dimensional Euclidean space according to the novel concept of flow distance, which both considers connection topology between sites and collective click behaviors of users. With this geometric representation, we visualize the attention flow in the data set of Indiana university clickstream over one day. It turns out that all the websites can be embedded into a 20 dimensional ball, in which, close sites are always visited by users sequentially. The distributions of websites, attention flows, and dissipations can be divided into three spherical crowns (core, interim, and periphery). 20% popular sites (Google.com, Myspace.com, Facebook.com, etc.) attracting 75% attention flows with only 55% dissipations (log off users) locate in the central layer with the radius 4.1. While 60% sites attracting only about 22% traffics with almost 38% dissipations locate in the middle area with radius between 4.1 and 6.3. Other 20% sites are far from the central area. All the cumulative distributions of variables can be well fitted by "S"-shaped curves. And the patterns are stable across different periods. Thus, the overall distribution and the dynamics of collective attention on websites can be well exhibited by this geometric representation.
Mol, H.G.J.; Janssen, H.G.; Cramers, C.A.; Brinkman, U.A.T.
1996-01-01
The effect of geometrical deformation of open‐tubular extraction columns on peak dispersion of retained solutes is evaluated. By coiling or stitching of the columns peak dispersion is decreased, with a factor of two and more than five, respectively, due to secondary flow enhanced radial dispersion.
The metric geometric mean transference and the problem of the average eye
Directory of Open Access Journals (Sweden)
W. F. Harris
2008-12-01
Full Text Available An average refractive error is readily obtained as an arithmetic average of refractive errors. But how does one characterize the first-order optical character of an average eye? Solutions have been offered including via the exponential-mean-log transference. The exponential-mean-log transference ap-pears to work well in practice but there is the niggling problem that the method does not work with all optical systems. Ideally one would like to be able to calculate an average for eyes in exactly the same way for all optical systems. This paper examines the potential of a relatively newly described mean, the metric geometric mean of positive definite (and, therefore, symmetric matrices. We extend the definition of the metric geometric mean to matrices that are not symmetric and then apply it to ray transferences of optical systems. The metric geometric mean of two transferences is shown to satisfy the requirement that symplecticity be pre-served. Numerical examples show that the mean seems to give a reasonable average for two eyes. Unfortunately, however, what seem reasonable generalizations to the mean of more than two eyes turn out not to be satisfactory in general. These generalizations do work well for thin systems. One concludes that, unless other generalizations can be found, the metric geometric mean suffers from more disadvantages than the exponential-mean-logarithm and has no advantages over it.
Computational fluid dynamics simulation and geometric design of hydraulic turbine draft tube
Directory of Open Access Journals (Sweden)
JB Sosa
2015-10-01
Full Text Available Any hydraulic reaction turbine is installed with a draft tube that impacts widely the entire turbine performance, on which its functions are as follows: drive the flux in appropriate manner after it releases its energy to the runner; recover the suction head by a suction effect; and improve the dynamic energy in the runner outlet. All these functions are strongly linked to the geometric definition of the draft tube. This article proposes a geometric parametrization and analysis of a Francis turbine draft tube. Based on the parametric definition, geometric changes in the draft tube are proposed and the turbine performance is modeled by computational fluid dynamics; the boundary conditions are set by measurements performed in a hydroelectric power plant. This modeling allows us to see the influence of the draft tube shape on the entire turbine performance. The numerical analysis is based on the steady-state solution of the turbine component flows for different guide vanes opening and multiple modified draft tubes. The computational fluid dynamics predictions are validated using hydroelectric plant measurements. The prediction of the turbine performance is successful and it is linked to the draft tube geometric features; therefore, it is possible to obtain a draft tube parameter value that results in a desired turbine performance.
Geometrically Nonlinear Static Analysis of 3D Trusses Using the Arc-Length Method
Hrinda, Glenn A.
2006-01-01
Rigorous analysis of geometrically nonlinear structures demands creating mathematical models that accurately include loading and support conditions and, more importantly, model the stiffness and response of the structure. Nonlinear geometric structures often contain critical points with snap-through behavior during the response to large loads. Studying the post buckling behavior during a portion of a structure's unstable load history may be necessary. Primary structures made from ductile materials will stretch enough prior to failure for loads to redistribute producing sudden and often catastrophic collapses that are difficult to predict. The responses and redistribution of the internal loads during collapses and possible sharp snap-back of structures have frequently caused numerical difficulties in analysis procedures. The presence of critical stability points and unstable equilibrium paths are major difficulties that numerical solutions must pass to fully capture the nonlinear response. Some hurdles still exist in finding nonlinear responses of structures under large geometric changes. Predicting snap-through and snap-back of certain structures has been difficult and time consuming. Also difficult is finding how much load a structure may still carry safely. Highly geometrically nonlinear responses of structures exhibiting complex snap-back behavior are presented and analyzed with a finite element approach. The arc-length method will be reviewed and shown to predict the proper response and follow the nonlinear equilibrium path through limit points.
Forward error correction based on algebraic-geometric theory
A Alzubi, Jafar; M Chen, Thomas
2014-01-01
This book covers the design, construction, and implementation of algebraic-geometric codes from Hermitian curves. Matlab simulations of algebraic-geometric codes and Reed-Solomon codes compare their bit error rate using different modulation schemes over additive white Gaussian noise channel model. Simulation results of Algebraic-geometric codes bit error rate performance using quadrature amplitude modulation (16QAM and 64QAM) are presented for the first time and shown to outperform Reed-Solomon codes at various code rates and channel models. The book proposes algebraic-geometric block turbo codes. It also presents simulation results that show an improved bit error rate performance at the cost of high system complexity due to using algebraic-geometric codes and Chase-Pyndiah’s algorithm simultaneously. The book proposes algebraic-geometric irregular block turbo codes (AG-IBTC) to reduce system complexity. Simulation results for AG-IBTCs are presented for the first time.
DEFF Research Database (Denmark)
Hirst, Andrew G.; Glazier, Douglas S.; Atkinson, David
2014-01-01
Metabolism fuels all of life’s activities, from biochemical reactions to ecological interactions. According to two intensely debated theories, body size affects metabolism via geometrical influences on the transport of resources and wastes. However, these theories differ crucially in whether...... theory, but contradicting the negative correlations predicted by resource-transport network models. This finding explains strong deviations from predictions of widely adopted theory, and underpins a new explanation for mass-invariant metabolic scaling during ontogeny in animals and plants...
Intercorporate Security Event Correlation
Directory of Open Access Journals (Sweden)
D. O. Kovalev
2010-03-01
Full Text Available Security controls are prone to false positives and false negatives which can lead to unwanted reputation losses for the bank. The reputational database within the security operations center (SOC and intercorporate correlation of security events are offered as a solution to increase attack detection fidelity. The theses introduce the definition and structure of the reputation, architectures of reputational exchange and the place of intercorporate correlation in overall SOC correlation analysis.
Three dimensional magnetic solutions in massive gravity with (nonlinear field
Directory of Open Access Journals (Sweden)
S.H. Hendi
2017-12-01
Full Text Available The Noble Prize in physics 2016 motivates one to study different aspects of topological properties and topological defects as their related objects. Considering the significant role of the topological defects (especially magnetic strings in cosmology, here, we will investigate three dimensional horizonless magnetic solutions in the presence of two generalizations: massive gravity and nonlinear electromagnetic field. The effects of these two generalizations on properties of the solutions and their geometrical structure are investigated. The differences between de Sitter and anti de Sitter solutions are highlighted and conditions regarding the existence of phase transition in geometrical structure of the solutions are studied.
Pandya, Aalok
2008-01-01
The geometry of the symplectic structures and Fubini-Study metric is discussed. Discussion in the paper addresses geometry of Quantum Mechanics in the classical phase space. Also, geometry of Quantum Mechanics in the projective Hilbert space has been discussed for the chosen Quantum states. Since the theory of classical gravity is basically geometric in nature and Quantum Mechanics is in no way devoid of geometry, the explorations pertaining to more and more geometry in Quantum Mechanics coul...
Entropy Measures as Geometrical Tools in the Study of Cosmology
Directory of Open Access Journals (Sweden)
Gilbert Weinstein
2017-12-01
Full Text Available Classical chaos is often characterized as exponential divergence of nearby trajectories. In many interesting cases these trajectories can be identified with geodesic curves. We define here the entropy by S = ln χ ( x with χ ( x being the distance between two nearby geodesics. We derive an equation for the entropy, which by transformation to a Riccati-type equation becomes similar to the Jacobi equation. We further show that the geodesic equation for a null geodesic in a double-warped spacetime leads to the same entropy equation. By applying a Robertson–Walker metric for a flat three-dimensional Euclidean space expanding as a function of time, we again reach the entropy equation stressing the connection between the chosen entropy measure and time. We finally turn to the Raychaudhuri equation for expansion, which also is a Riccati equation similar to the transformed entropy equation. Those Riccati-type equations have solutions of the same form as the Jacobi equation. The Raychaudhuri equation can be transformed to a harmonic oscillator equation, and it has been shown that the geodesic deviation equation of Jacobi is essentially equivalent to that of a harmonic oscillator. The Raychaudhuri equations are strong geometrical tools in the study of general relativity and cosmology. We suggest a refined entropy measure applicable in cosmology and defined by the average deviation of the geodesics in a congruence.
Efficient Geometric Sound Propagation Using Visibility Culling
Chandak, Anish
2011-07-01
Simulating propagation of sound can improve the sense of realism in interactive applications such as video games and can lead to better designs in engineering applications such as architectural acoustics. In this thesis, we present geometric sound propagation techniques which are faster than prior methods and map well to upcoming parallel multi-core CPUs. We model specular reflections by using the image-source method and model finite-edge diffraction by using the well-known Biot-Tolstoy-Medwin (BTM) model. We accelerate the computation of specular reflections by applying novel visibility algorithms, FastV and AD-Frustum, which compute visibility from a point. We accelerate finite-edge diffraction modeling by applying a novel visibility algorithm which computes visibility from a region. Our visibility algorithms are based on frustum tracing and exploit recent advances in fast ray-hierarchy intersections, data-parallel computations, and scalable, multi-core algorithms. The AD-Frustum algorithm adapts its computation to the scene complexity and allows small errors in computing specular reflection paths for higher computational efficiency. FastV and our visibility algorithm from a region are general, object-space, conservative visibility algorithms that together significantly reduce the number of image sources compared to other techniques while preserving the same accuracy. Our geometric propagation algorithms are an order of magnitude faster than prior approaches for modeling specular reflections and two to ten times faster for modeling finite-edge diffraction. Our algorithms are interactive, scale almost linearly on multi-core CPUs, and can handle large, complex, and dynamic scenes. We also compare the accuracy of our sound propagation algorithms with other methods. Once sound propagation is performed, it is desirable to listen to the propagated sound in interactive and engineering applications. We can generate smooth, artifact-free output audio signals by applying
Geometric changes of parotid glands caused by hydration during chemoradiotherapy
International Nuclear Information System (INIS)
Kager, Petronella M.; Weerdenburg, Sanne C. C. van; Kranen, Simon R. van; Beek, Suzanne van; Lamers-Kuijper, Elisabeth A.; Heemsbergen, Wilma D.; Hamming-Vrieze, Olga; Remeijer, Peter
2015-01-01
Plan adaptation during the course of (chemo)radiotherapy of H&N cancer requires repeat CT scanning to capture anatomy changes such as parotid gland shrinkage. Hydration, applied to prevent nephrotoxicity from cisplatin, could temporarily alter the hydrogen balance and hence the captured anatomy. The aim of this study was to determine geometric changes of parotid glands as function of hydration during chemoradiotherapy compared to a control group treated with radiotherapy only. This study included an experimental group (n = 19) receiving chemoradiotherapy, and a control group (n = 19) receiving radiotherapy only. Chemoradiotherapy patients received cisplatin with 9 l of saline solution during hydration in the first, fourth and seventh week. The delineations of the parotid glands on the planning CT scan were automatically propagated to Cone Beam CT scans using deformable image registration. Relative volume and position of the parotid glands were determined at the second chemotherapy cycle (week four) and at fraction 35. When saline solution was administrated, the volume temporarily increased on the first day (7.2 %, p < 0.001), second day (10.8 %, p < 0.001) and third day (7.0 %, p = 0.016). The gland positions shifted lateral, the distance between glands increased on the first day with 1.5 mm (p < 0.001), on the second day 2.2 mm (p < 0.001). At fraction 35, with both groups the mean shrinkage was 24 % ± 11 % (1SD) and the mean medial distance between the parotid glands decreased by 0.47 cm ± 0.27 cm. Hydration significantly modulates parotid gland geometry. Unless, in the context of adaptive RT, a repeat CT scan is timed during a chemotherapy cycle, these effects are of minor clinical relevance
A geometric multigrid Poisson solver for domains containing solid inclusions
Botto, Lorenzo
2013-03-01
A Cartesian grid method for the fast solution of the Poisson equation in three-dimensional domains with embedded solid inclusions is presented and its performance analyzed. The efficiency of the method, which assume Neumann conditions at the immersed boundaries, is comparable to that of a multigrid method for regular domains. The method is light in terms of memory usage, and easily adaptable to parallel architectures. Tests with random and ordered arrays of solid inclusions, including spheres and ellipsoids, demonstrate smooth convergence of the residual for small separation between the inclusion surfaces. This feature is important, for instance, in simulations of nearly-touching finite-size particles. The implementation of the method, “MG-Inc”, is available online. Catalogue identifier: AEOE_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEOE_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 19068 No. of bytes in distributed program, including test data, etc.: 215118 Distribution format: tar.gz Programming language: C++ (fully tested with GNU GCC compiler). Computer: Any machine supporting standard C++ compiler. Operating system: Any OS supporting standard C++ compiler. RAM: About 150MB for 1283 resolution Classification: 4.3. Nature of problem: Poisson equation in domains containing inclusions; Neumann boundary conditions at immersed boundaries. Solution method: Geometric multigrid with finite-volume discretization. Restrictions: Stair-case representation of the immersed boundaries. Running time: Typically a fraction of a minute for 1283 resolution.
Klapa, Przemyslaw; Mitka, Bartosz; Zygmunt, Mariusz
2017-12-01
Capability of obtaining a multimillion point cloud in a very short time has made the Terrestrial Laser Scanning (TLS) a widely used tool in many fields of science and technology. The TLS accuracy matches traditional devices used in land surveying (tacheometry, GNSS – RTK), but like any measurement it is burdened with error which affects the precise identification of objects based on their image in the form of a point cloud. The point’s coordinates are determined indirectly by means of measuring the angles and calculating the time of travel of the electromagnetic wave. Each such component has a measurement error which is translated into the final result. The XYZ coordinates of a measuring point are determined with some uncertainty and the very accuracy of determining these coordinates is reduced as the distance to the instrument increases. The paper presents the results of examination of geometrical stability of a point cloud obtained by means terrestrial laser scanner and accuracy evaluation of solids determined using the cloud. Leica P40 scanner and two different settings of measuring points were used in the tests. The first concept involved placing a few balls in the field and then scanning them from various sides at similar distances. The second part of measurement involved placing balls and scanning them a few times from one side but at varying distances from the instrument to the object. Each measurement encompassed a scan of the object with automatic determination of its position and geometry. The desk studies involved a semiautomatic fitting of solids and measurement of their geometrical elements, and comparison of parameters that determine their geometry and location in space. The differences of measures of geometrical elements of balls and translations vectors of the solids centres indicate the geometrical changes of the point cloud depending on the scanning distance and parameters. The results indicate the changes in the geometry of scanned objects
Hydrophobic solvation of nonspherical solutes
International Nuclear Information System (INIS)
Pratt, L.R.; Chandler, D.
1980-01-01
The theory of hydrophobic effects presented by Pratt and Chandler is generalized to include nonpolar solutes which are distinctly aspherical. The theory is used to study the solvation of simple aspherical hydrocarbon solutes in liquid water. The radial solvation of each component of diatomiclike solutes is studied as a function of their separation, or bond length. From these results it is found that when the bond length is large enough that one water molecule can fit between the apolar pair, the radial solvation of each is the same as that when the bond length approaches infinity. The solvation of the various sites of the homologous series methane, ethane, propane, and n-butane is also studied, and effects of the geometrical structure of the solutes on their solvation is discussed
Geometric perturbation theory and plasma physics
International Nuclear Information System (INIS)
Omohundro, S.M.
1985-01-01
Modern differential geometric techniques are used to unify the physical asymptotics underlying mechanics, wave theory, and statistical mechanics. The approach gives new insights into the structure of physical theories and is suited to the needs of modern large-scale computer simulation and symbol manipulation systems. A coordinate-free formulation of non-singular perturbation theory is given, from which a new Hamiltonian perturbation structure is derived and related to the unperturbed structure in five different ways. The theory of perturbations in the presence of symmetry is developed, and the method of averaging is related to reduction by a circle-group action. The pseudo-forces and magnetic Poisson bracket terms due to reduction are given a natural asymptotic interpretation. Similar terms due to changing reference frames are related to the method of variation of parameters, which is also given a Hamiltonian formulation. These methods are used to answer a long-standing question posed by Kruskal about nearly periodic systems. The answer leads to a new secular perturbation theory that contains no adhoc elements, which is then applied to gyromotion. Eikonal wave theory is given a Hamiltonian formulation that generalizes Whitham's Lagrangian approach. The evolution of wave action density on ray phase space is given a Hamiltonian structure using a Lie-Poisson bracket. The relationship between dissipative and Hamiltonian systems is discussed. A theory motivated by free electron lasers gives new restrictions on the change of area of projected parallelepipeds under canonical transformations
Mathematical methods in geometrization of coal field
Shurygin, D. N.; Kalinchenko, V. M.; Tkachev, V. A.; Tretyak, A. Ya
2017-10-01
In the work, the approach to increase overall performance of collieries on the basis of an increase in accuracy of geometrization of coal thicknesses is considered. The sequence of stages of mathematical modelling of spatial placing of indicators of a deposit taking into account allocation of homogeneous sites of thickness and an establishment of quantitative interrelations between mountain-geological indicators of coal layers is offered. As a uniform mathematical method for modelling of various interrelations, it is offered to use a method of the group accounting of arguments (MGUA), one of versions of the regressive analysis. This approach can find application during delimitation between geological homogeneous sites of coal thicknesses in the form of a linear discriminant function. By an example of division into districts of a mine field in the conditions of mine “Sadkinsky” (East Donbass), the use of the complex approach for forecasting of zones of the small amplitude of disturbance of a coal layer on the basis of the discriminant analysis and MGUA is shown.
Quasiparticle vanishing driven by geometrical frustration
Trumper, A. E.; Gazza, C. J.; Manuel, L. O.
2004-05-01
We investigate the single hole dynamics in the triangular t-J model. We study the structure of the hole spectral function, assuming the existence of a 120° magnetic Néel order. Within the self-consistent Born approximation (SCBA) there is a strong momentum and t sign dependence of the spectra, related to the underlying magnetic structure and the particle-hole asymmetry of the model. For positive t, and in the strong coupling regime, we find that the low-energy quasiparticle excitations vanish outside the neighborhood of the magnetic Goldstone modes; while for negative t the quasiparticle excitations are always well defined. In the latter, we also find resonances of magnetic origin whose energies scale as (J/t)2/3 and can be identified with string excitations. We argue that this complex structure of the spectra is due to the subtle interplay between magnon-assisted and free-hopping mechanisms. Our predictions are supported by an excellent agreement between the SCBA and the exact results on finite-size clusters. We conclude that the conventional quasiparticle picture can be broken by the effect of geometrical magnetic frustration.
Geometrical properties of a 'snowflake' divertor
International Nuclear Information System (INIS)
Ryutov, D. D.
2007-01-01
Using a simple set of poloidal field coils, one can reach the situation in which the null of the poloidal magnetic field in the divertor region is of second order, not of first order as in the usual X-point divertor. Then, the separatrix in the vicinity of the null point splits the poloidal plane not into four sectors, but into six sectors, making the whole structure look like a snowflake (hence the name). This arrangement allows one to spread the heat load over a much broader area than in the case of a standard divertor. A disadvantage of this configuration is that it is topologically unstable, and, with the current in the plasma varying with time, it would switch either to the standard X-point mode, or to the mode with two X-points close to each other. To avoid this problem, it is suggested to have a current in the divertor coils that is roughly 5% higher than in an ''optimum'' regime (the one in which a snowflake separatrix is formed). In this mode, the configuration becomes stable and can be controlled by varying the current in the divertor coils in concert with the plasma current; on the other hand, a strong flaring of the scrape-off layer still remains in force. Geometrical properties of this configuration are analyzed. Potential advantages and disadvantages of this scheme are discussed
UAV CAMERAS: OVERVIEW AND GEOMETRIC CALIBRATION BENCHMARK
Directory of Open Access Journals (Sweden)
M. Cramer
2017-08-01
Full Text Available Different UAV platforms and sensors are used in mapping already, many of them equipped with (sometimes modified cameras as known from the consumer market. Even though these systems normally fulfil their requested mapping accuracy, the question arises, which system performs best? This asks for a benchmark, to check selected UAV based camera systems in well-defined, reproducible environments. Such benchmark is tried within this work here. Nine different cameras used on UAV platforms, representing typical camera classes, are considered. The focus is laid on the geometry here, which is tightly linked to the process of geometrical calibration of the system. In most applications the calibration is performed in-situ, i.e. calibration parameters are obtained as part of the project data itself. This is often motivated because consumer cameras do not keep constant geometry, thus, cannot be seen as metric cameras. Still, some of the commercial systems are quite stable over time, as it was proven from repeated (terrestrial calibrations runs. Already (pre-calibrated systems may offer advantages, especially when the block geometry of the project does not allow for a stable and sufficient in-situ calibration. Especially for such scenario close to metric UAV cameras may have advantages. Empirical airborne test flights in a calibration field have shown how block geometry influences the estimated calibration parameters and how consistent the parameters from lab calibration can be reproduced.
Uav Cameras: Overview and Geometric Calibration Benchmark
Cramer, M.; Przybilla, H.-J.; Zurhorst, A.
2017-08-01
Different UAV platforms and sensors are used in mapping already, many of them equipped with (sometimes) modified cameras as known from the consumer market. Even though these systems normally fulfil their requested mapping accuracy, the question arises, which system performs best? This asks for a benchmark, to check selected UAV based camera systems in well-defined, reproducible environments. Such benchmark is tried within this work here. Nine different cameras used on UAV platforms, representing typical camera classes, are considered. The focus is laid on the geometry here, which is tightly linked to the process of geometrical calibration of the system. In most applications the calibration is performed in-situ, i.e. calibration parameters are obtained as part of the project data itself. This is often motivated because consumer cameras do not keep constant geometry, thus, cannot be seen as metric cameras. Still, some of the commercial systems are quite stable over time, as it was proven from repeated (terrestrial) calibrations runs. Already (pre-)calibrated systems may offer advantages, especially when the block geometry of the project does not allow for a stable and sufficient in-situ calibration. Especially for such scenario close to metric UAV cameras may have advantages. Empirical airborne test flights in a calibration field have shown how block geometry influences the estimated calibration parameters and how consistent the parameters from lab calibration can be reproduced.
Geometrically based optimization for extracranial radiosurgery
International Nuclear Information System (INIS)
Liu Ruiguo; Wagner, Thomas H; Buatti, John M; Modrick, Joseph; Dill, John; Meeks, Sanford L
2004-01-01
For static beam conformal intracranial radiosurgery, geometry of the beam arrangement dominates overall dose distribution. Maximizing beam separation in three dimensions decreases beam overlap, thus maximizing dose conformality and gradient outside of the target volume. Webb proposed arrangements of isotropically convergent beams that could be used as the starting point for a radiotherapy optimization process. We have developed an extracranial radiosurgery optimization method by extending Webb's isotropic beam arrangements to deliverable beam arrangements. This method uses an arrangement of N maximally separated converging vectors within the space available for beam delivery. Each bouquet of isotropic beam vectors is generated by a random sampling process that iteratively maximizes beam separation. Next, beam arrangement is optimized for critical structure avoidance while maintaining minimal overlap between beam entrance and exit pathways. This geometrically optimized beam set can then be used as a template for either conformal beam or intensity modulated extracranial radiosurgery. Preliminary results suggest that using this technique with conformal beam planning provides high plan conformality, a steep dose gradient outside of the tumour volume and acceptable critical structure avoidance in the majority of clinical cases
Geometric Methods in Physics : XXXIII Workshop
Bieliavsky, Pierre; Odzijewicz, Anatol; Schlichenmaier, Martin; Voronov, Theodore
2015-01-01
This book presents a selection of papers based on the XXXIII Białowieża Workshop on Geometric Methods in Physics, 2014. The Białowieża Workshops are among the most important meetings in the field and attract researchers from both mathematics and physics. The articles gathered here are mathematically rigorous and have important physical implications, addressing the application of geometry in classical and quantum physics. Despite their long tradition, the workshops remain at the cutting edge of ongoing research. For the last several years, each Białowieża Workshop has been followed by a School on Geometry and Physics, where advanced lectures for graduate students and young researchers are presented; some of the lectures are reproduced here. The unique atmosphere of the workshop and school is enhanced by its venue, framed by the natural beauty of the Białowieża forest in eastern Poland. The volume will be of interest to researchers and graduate students in mathematical physics, theoretical physics and m...
Optimization of Gad Pattern with Geometrical Weight
International Nuclear Information System (INIS)
Chang, Do Ik; Woo, Hae Seuk; Choi, Seong Min
2009-01-01
The prevailing burnable absorber for domestic nuclear power plants is a gad fuel rod which is used for the partial control of excess reactivity and power peaking. The radial peaking factor, which is one of the critical constraints for the plant safety depends largely on the number of gad bearing rods and the location of gad rods within fuel assembly. Also the concentration of gad, UO 2 enrichment in the gad fuel rod, and fuel lattice type play important roles for the resultant radial power peaking. Since fuel is upgraded periodically and longer fuel cycle management requires more burnable absorbers or higher gad weight percent, it is required frequently to search for the optimized gad patterns, i.e., the distribution of gad fuel rods within assembly, for the various fuel environment and fuel management changes. In this study, the gad pattern optimization algorithm with respect to radial power peaking factor using geometrical weight is proposed for a single gad weight percent, in which the candidates of the optimized gad pattern are determined based on the weighting of the gad rod location and the guide tube. Also the pattern evaluation is performed systematically to determine the optimal gad pattern for the various situation
Association among geometric configurations of palatal rugae.
Saadeh, M; Ghafari, J G; Haddad, R V; Ayoub, F
2017-07-01
The associations between the length and morphological shape-related characteristics of palatal rugae have not been fully explored. We aimed to assess the possible association among various geometric configurations of the palatal rugae in an adult population. The maxillary dental casts of 217 non-growing subjects (95 males, 122 females, mean age 25.5±7.6 years) were scanned (laser scanning system Perceptron ScanWorks® V5) and digitized for linear measurements. The casts were also surveyed for visual categorization into curved, wavy, straight and other topographical forms, along with spatial direction of the rugae and the presence of unification. The rugae were categorized as primary, secondary, and fragmentary based on their lengths (> 5mm, 2-3mm, rugae groupings. Primary and backward-directed rugae prevailed in the total sample (84.7% and 49.3%, respectively). Wavy form was dominant among primary lengths, while straight form was associated with the shorter secondary and fragmentary groups (p=0.0042). Absence of unification was the norm (88.8%). Associations of length and shape characteristics among palatal rugae combine wavy patterns with increased length, and straight forms with shorter folds. These features contribute to the definition of ruga individuality in combination rather than separately.
Geometric Model of a Coronal Cavity
Kucera, Therese A.; Gibson, S. E.; Ratawicki, D.; Dove, J.; deToma, G.; Hao, J.; Hudson, H. S.; Marque, C.; McIntosh, P. S.; Reeves, K. K.;
2010-01-01
We observed a coronal cavity from August 8-18 2007 during a multi-instrument observing campaign organized under the auspices of the International Heliophysical Year (IHY). Here we present initial efforts to model the cavity with a geometrical streamer-cavity model. The model is based the white-light streamer mode] of Gibson et a]. (2003 ), which has been enhanced by the addition of a cavity and the capability to model EUV and X-ray emission. The cavity is modeled with an elliptical cross-section and Gaussian fall-off in length and width inside the streamer. Density and temperature can be varied in the streamer and cavity and constrained via comparison with data. Although this model is purely morphological, it allows for three-dimensional, multi-temperature analysis and characterization of the data, which can then provide constraints for future physical modeling. Initial comparisons to STEREO/EUVI images of the cavity and streamer show that the model can provide a good fit to the data. This work is part of the effort of the International Space Science Institute International Team on Prominence Cavities
Austerity and geometric structure of field theories
International Nuclear Information System (INIS)
Kheyfets, A.
1986-01-01
The relation between the austerity idea and the geometric structure of the three basic field theories - electrodynamics, Yang-Mills theory, and general relativity - is studied. One of the most significant manifestations of the austerity idea in field theories is thought to be expressed by the boundary of a boundary principle (BBP). The BBP says that almost all content of the field theories can be deduced from the topological identity of delta dot produced with delta = 0 used twice, at the 1-2-3-dimensional level (providing the homogeneous field equations), and at the 2-3-4-dimensional level (providing the conservation laws for the source currents). There are some difficulties in this line of thought due to the apparent lack of universality in application of the BBP to the three basic modern field theories above. This dissertation: (a) analyzes the difficulties by means of algebraic topology, integration theory, and modern differential geometry based on the concepts of principal bundles and Ehresmann connections: (b) extends the BBP to the unified Kaluza-Klein theory; (c) reformulates the inhomogeneous field equations and the BBP in terms of E. Cartan moment of rotation, in the way universal for the three theories and compatible with the original austerity idea; and (d) underlines the important role of the soldering structure on spacetime, and indicates that the future development of the austerity idea would involve the generalized theories
Exact solutions of holonomic quantum computation
International Nuclear Information System (INIS)
Tanimura, Shogo; Hayashi, Daisuke; Nakahara, Mikio
2004-01-01
Holonomic quantum computation is analyzed from geometrical viewpoint. We develop an optimization scheme in which an arbitrary unitary gate is implemented with a small circle in a complex projective space. Exact solutions for the Hadamard, CNOT and 2-qubit discrete Fourier transformation gates are explicitly constructed
Black hole acoustics in the minimal geometric deformation of a de Laval nozzle
Energy Technology Data Exchange (ETDEWEB)
Rocha, Roldao da [Universidade Federal do ABC-UFABC, Centro de Matematica, Computacao e Cognicao, Santo Andre (Brazil)
2017-05-15
The correspondence between sound waves, in a de Laval propelling nozzle, and quasinormal modes emitted by brane-world black holes deformed by a 5D bulk Weyl fluid are here explored and scrutinized. The analysis of sound waves patterns in a de Laval nozzle in the laboratory, reciprocally, is here shown to provide relevant data about the 5D bulk Weyl fluid and its on-brane projection, comprised by the minimal geometrically deformed compact stellar distribution on the brane. Acoustic perturbations of the gas fluid flow in the de Laval nozzle are proved to coincide with the quasinormal modes of black holes solutions deformed by the 5D Weyl fluid, in the geometric deformation procedure. Hence, in a phenomenological Eoetvoes-Friedmann fluid brane-world model, the realistic shape of a de Laval nozzle is derived and its consequences studied. (orig.)
Stupishin, L. U.; Nikitin, K. E.; Kolesnikov, A. G.
2018-02-01
The article is concerned with a methodology of optimal design of geometrically nonlinear (flexible) shells of revolution of minimum weight with strength, stability and strain constraints. The problem of optimal design with constraints is reduced to the problem of unconstrained minimization using the penalty functions method. Stress-strain state of shell is determined within the geometrically nonlinear deformation theory. A special feature of the methodology is the use of a mixed finite-element formulation based on the Galerkin method. Test problems for determining the optimal form and thickness distribution of a shell of minimum weight are considered. The validity of the results obtained using the developed methodology is analyzed, and the efficiency of various optimization algorithms is compared to solve the set problem. The developed methodology has demonstrated the possibility and accuracy of finding the optimal solution.
Biologic and physical fractionation effects of random geometric errors
van Herk, Marcel; Witte, Marnix; van der Geer, Joris; Schneider, Christoph; Lebesque, Joos V.
2003-01-01
PURPOSE: We are developing a system to model the effect of random and systematic geometric errors on radiotherapy delivery. The purpose of this study was to investigate biologic and physical fractionation effects of random geometric errors and respiration motion and compare the resulting dose
Creativity and Motivation for Geometric Tasks Designing in Education
Rumanová, Lucia; Smiešková, Edita
2015-01-01
In this paper we focus on creativity needed for geometric tasks designing, visualization of geometric problems and use of ICT. We present some examples of various problems related to tessellations. Altogether 21 students--pre-service teachers participated in our activity within a geometry course at CPU in Nitra, Slovakia. Our attempt was to…
Active Learning Environment with Lenses in Geometric Optics
Tural, Güner
2015-01-01
Geometric optics is one of the difficult topics for students within physics discipline. Students learn better via student-centered active learning environments than the teacher-centered learning environments. So this study aimed to present a guide for middle school teachers to teach lenses in geometric optics via active learning environment…
Covering an arithmetic progression with geometric progressions and vice versa
Sanna, Carlo
2013-01-01
We show that there exists a positive constant C such that the following holds: Given an infinite arithmetic progression A of real numbers and a sufficiently large integer n (depending on A), there needs at least Cn geometric progressions to cover the first n terms of A. A similar result is presented, with the role of arithmetic and geometric progressions reversed.
Geometric calculus: a new computational tool for Riemannian geometry
International Nuclear Information System (INIS)
Moussiaux, A.; Tombal, P.
1988-01-01
We compare geometric calculus applied to Riemannian geometry with Cartan's exterior calculus method. The correspondence between the two methods is clearly established. The results obtained by a package written in an algebraic language and doing general manipulations on multivectors are compared. We see that the geometric calculus is as powerful as exterior calculus
Aspects of random geometric graphs : Pursuit-evasion and treewidth
Li, A.
2015-01-01
In this thesis, we studied two aspects of random geometric graphs: pursuit-evasion and treewidth. We first studied one pursuit-evasion game: Cops and Robbers. This game, which dates back to 1970s, are studied extensively in recent years. We investigate this game on random geometric graphs, and get
Geometric deviation modeling by kinematic matrix based on Lagrangian coordinate
Liu, Weidong; Hu, Yueming; Liu, Yu; Dai, Wanyi
2015-09-01
Typical representation of dimension and geometric accuracy is limited to the self-representation of dimension and geometric deviation based on geometry variation thinking, yet the interactivity affection of geometric variation and gesture variation of multi-rigid body is not included. In this paper, a kinematic matrix model based on Lagrangian coordinate is introduced, with the purpose of unified model for geometric variation and gesture variation and their interactive and integrated analysis. Kinematic model with joint, local base and movable base is built. The ideal feature of functional geometry is treated as the base body; the fitting feature of functional geometry is treated as the adjacent movable body; the local base of the kinematic model is fixed onto the ideal geometry, and the movable base of the kinematic model is fixed onto the fitting geometry. Furthermore, the geometric deviation is treated as relative location or rotation variation between the movable base and the local base, and it's expressed by the Lagrangian coordinate. Moreover, kinematic matrix based on Lagrangian coordinate for different types of geometry tolerance zones is constructed, and total freedom for each kinematic model is discussed. Finally, the Lagrangian coordinate library, kinematic matrix library for geometric deviation modeling is illustrated, and an example of block and piston fits is introduced. Dimension and geometric tolerances of the shaft and hole fitting feature are constructed by kinematic matrix and Lagrangian coordinate, and the results indicate that the proposed kinematic matrix is capable and robust in dimension and geometric tolerances modeling.
Homothetic Transformations and Geometric Loci: Properties of Triangles and Quadrilaterals
Mammana, Maria Flavia
2016-01-01
In this paper, we use geometric transformations to find some interesting properties related with geometric loci. In particular, given a triangle or a cyclic quadrilateral, the locus generated by the centroid or by the orthocentre (for triangles) or by the anticentre (for cyclic quadrilaterals) when one vertex moves on the circumcircle of the…
3D facial geometric features for constrained local model
Cheng, Shiyang; Zafeiriou, Stefanos; Asthana, Ashish; Asthana, Akshay; Pantic, Maja
2014-01-01
We propose a 3D Constrained Local Model framework for deformable face alignment in depth image. Our framework exploits the intrinsic 3D geometric information in depth data by utilizing robust histogram-based 3D geometric features that are based on normal vectors. In addition, we demonstrate the
A Framework for Assessing Reading Comprehension of Geometric Construction Texts
Yang, Kai-Lin; Li, Jian-Lin
2018-01-01
This study investigates one issue related to reading mathematical texts by presenting a two-dimensional framework for assessing reading comprehension of geometric construction texts. The two dimensions of the framework were formulated by modifying categories of reading literacy and drawing on key elements of geometric construction texts. Three…
On quantizing gravity and geometrizing quantum mechanics
Directory of Open Access Journals (Sweden)
Ali Mostafazadeh
2005-09-01
Full Text Available We elaborate on some recent results on a solution of the Hilbert-space problem in minisuperspace quantum cosmology and discuss the consequences of making the (geometry of the Hilbert space of ordinary nonrelativistic quantum systems time-dependent. The latter reveals a remarkable similarity between Quantum Mechanics and General Relativity.
Geometric Models for Isotropic Random Porous Media: A Review
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Helmut Hermann
2014-01-01
Full Text Available Models for random porous media are considered. The models are isotropic both from the local and the macroscopic point of view; that is, the pores have spherical shape or their surface shows piecewise spherical curvature, and there is no macroscopic gradient of any geometrical feature. Both closed-pore and open-pore systems are discussed. The Poisson grain model, the model of hard spheres packing, and the penetrable sphere model are used; variable size distribution of the pores is included. A parameter is introduced which controls the degree of open-porosity. Besides systems built up by a single solid phase, models for porous media with the internal surface coated by a second phase are treated. Volume fraction, surface area, and correlation functions are given explicitly where applicable; otherwise numerical methods for determination are described. Effective medium theory is applied to calculate physical properties for the models such as isotropic elastic moduli, thermal and electrical conductivity, and static dielectric constant. The methods presented are exemplified by applications: small-angle scattering of systems showing fractal-like behavior in limited ranges of linear dimension, optimization of nanoporous insulating materials, and improvement of properties of open-pore systems by atomic layer deposition of a second phase on the internal surface.
Geometric Studies of Shunt and Lead Orientation in EEC Devices
Werner, F. M.; Solin, S. A.
2014-03-01
Electric field sensors are ubiquitous in modern technology, from field effect transistors (FETs) in circuit boards to point-of-care testing (POCT) devices used in detecting the presence of specific protein markers in blood. The transport properties of these devices are limited by two general categories: intrinsic material properties and extrinsic geometric effects. Devices with a maximum electric field resolution of 3.05V/cm were previously reported. The metal semiconductor hybrid (MSH) devices are constructed by forming a Schottky interface between a mesa of nGaAs and Ti, while four ohmic leads surround the perimeter of the mesa and are used for four point resistance measurements. These devices exhibit extraordinary electroconductance (EEC) and make it possible to correlate measured four point resistance to changes in the local electric field. While maximizing the EEC response by optimizing the intrinsic material properties has been theoretically investigated, we present a phenomenological study of the impact of lead orientation and shunt geometry in the sensing capabilities of these devices. S.A.S. is a co-founder of and has a financial interest in PixelEXX, a start-up company whose mission is to market imaging arrays.
Generating solutions to the Einstein field equations
Contopoulos, I. G.; Esposito, F. P.; Kleidis, K.; Papadopoulos, D. B.; Witten, L.
2016-11-01
Exact solutions to the Einstein field equations may be generated from already existing ones (seed solutions), that admit at least one Killing vector. In this framework, a space of potentials is introduced. By the use of symmetries in this space, the set of potentials associated to a known solution is transformed into a new set, either by continuous transformations or by discrete transformations. In view of this method, and upon consideration of continuous transformations, we arrive at some exact, stationary axisymmetric solutions to the Einstein field equations in vacuum, that may be of geometrical or/and physical interest.
Geometric control theory and sub-Riemannian geometry
Boscain, Ugo; Gauthier, Jean-Paul; Sarychev, Andrey; Sigalotti, Mario
2014-01-01
This volume presents recent advances in the interaction between Geometric Control Theory and sub-Riemannian geometry. On the one hand, Geometric Control Theory used the differential geometric and Lie algebraic language for studying controllability, motion planning, stabilizability and optimality for control systems. The geometric approach turned out to be fruitful in applications to robotics, vision modeling, mathematical physics etc. On the other hand, Riemannian geometry and its generalizations, such as sub-Riemannian, Finslerian geometry etc., have been actively adopting methods developed in the scope of geometric control. Application of these methods has led to important results regarding geometry of sub-Riemannian spaces, regularity of sub-Riemannian distances, properties of the group of diffeomorphisms of sub-Riemannian manifolds, local geometry and equivalence of distributions and sub-Riemannian structures, regularity of the Hausdorff volume.
Cronin, V. S.; Lindsay, R. D.
2011-12-01
Geomorphic analysis of hillshade images produced from aerial LiDAR data has been successful in identifying youthful fault traces. For example, the recently discovered Polaris fault just northwest of Lake Tahoe, California/Nevada, was recognized using LiDAR data that had been acquired by local government to assist land-use planning. Subsequent trenching by consultants under contract to the US Army Corps of Engineers has demonstrated Holocene displacement. The Polaris fault is inferred to be capable of generating a magnitude 6.4-6.9 earthquake, based on its apparent length and offset characteristics (Hunter and others, 2011, BSSA 101[3], 1162-1181). Dingler and others (2009, GSA Bull 121[7/8], 1089-1107) describe paleoseismic or geomorphic evidence for late Neogene displacement along other faults in the area, including the West Tahoe-Dollar Point, Stateline-North Tahoe, and Incline Village faults. We have used the seismo-lineament analysis method (SLAM; Cronin and others, 2008, Env Eng Geol 14[3], 199-219) to establish a tentative spatial correlation between each of the previously mentioned faults, as well as with segments of the Dog Valley fault system, and one or more earthquake(s). The ~18 earthquakes we have tentatively correlated with faults in the Tahoe-Truckee area occurred between 1966 and 2008, with magnitudes between 3 and ~6. Given the focal mechanism solution for a well-located shallow-focus earthquake, the nodal planes can be projected to Earth's surface as represented by a DEM, plus-or-minus the vertical and horizontal uncertainty in the focal location, to yield two seismo-lineament swaths. The trace of the fault that generated the earthquake is likely to be found within one of the two swaths [1] if the fault surface is emergent, and [2] if the fault surface is approximately planar in the vicinity of the focus. Seismo-lineaments from several of the earthquakes studied overlap in a manner that suggests they are associated with the same fault. The surface
Dong, Weihua; Lan, Jianhang; Liang, Shunlin; Yao, Wei; Zhan, Zhicheng
2017-08-01
LiDAR has been an effective technology for acquiring urban land cover data in recent decades. Previous studies indicate that geometric features have a strong impact on land cover classification. Here, we analyzed an urban LiDAR dataset to explore the optimal feature subset from 25 geometric features incorporating 25 scales under 6 definitions for urban land cover classification. We performed a feature selection strategy to remove irrelevant or redundant features based on the correlation coefficient between features and classification accuracy of each features. The neighborhood scales were divided into small (0.5-1.5 m), medium (1.5-6 m) and large (>6 m) scale. Combining features with lower correlation coefficient and better classification performance would improve classification accuracy. The feature depicting homogeneity or heterogeneity of points would be calculated at a small scale, and the features to smooth points at a medium scale and the features of height different at large scale. As to the neighborhood definition, cuboid and cylinder were recommended. This study can guide the selection of optimal geometric features with adaptive neighborhood scale for urban land cover classification.
GEOMETRICAL PARAMETERS OF EGGS IN BIRD SYSTEMATICS
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I. S. Mityay
2014-12-01
Full Text Available Our ideas are based on the following assumptions. Egg as a standalone system is formed within another system, which is the body of the female. Both systems are implemented on the basis of a common genetic code. In this regard, for example, the dendrogram constructed by morphological criteria eggs should be approximately equal to those constructed by other molecular or morphological criteria adult birds. It should be noted that the dendrogram show only the degree of genetic similarity of taxa, therefore, the identity of materials depends on the number of analyzed criteria and their quality, ie, they should be the backbone. The greater the number of system-features will be included in the analysis and in one other case, the like are dendrogram. In other cases, we will have a fragmentary similarity, which is also very important when dealing with controversial issues. The main message of our research was to figure out the eligibility of usage the morphological characteristics of eggs as additional information in taxonomy and phylogeny of birds. Our studies show that the shape parameters of bird eggs show a stable attachment to certain types of birds and complex traits are species-specific. Dendrogram and diagrams built by the quantitative value of these signs, exhibit significant similarity with the dendrogram constructed by morphological, comparative anatomy, paleontology and molecular criteria for adult birds. This suggests the possibility of using morphological parameters eggs as additional information in dealing with taxonomy and phylogeny of birds. Keywords: oology, geometrical parameters of eggs, bird systematics
Geometrical Conditions Indispensable for Muscle Contraction
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Ludmila Skubiszak
2011-03-01
Full Text Available Computer simulation has uncovered the geometrical conditions under which the vertebrate striated muscle sarcomere can contract. First, all thick filaments should have identical structure, namely: three myosin cross-bridges, building a crown, should be aligned at angles of 0°, 120°, 180°, and the successive crowns and the two filament halves should be turned around 120°. Second, all thick filaments should act simultaneously. Third, coordination in action of the myosin cross-bridges should exist, namely: the three cross-bridges of a crown should act simultaneously and the cross-bridge crowns axially 43 and 14.333 nm apart should act, respectively, simultaneously and with a phase shift. Fifth, six thin filaments surrounding the thick filament should be turned around 180° to each other in each sarcomere half. Sixth, thin filaments should be oppositely oriented in relation to the sarcomere middle. Finally, the structure of each of the thin filaments should change in consequence of strong interaction with myosin heads, namely: the axial distance and the angular alignment between neighboring actin monomers should be, respectively, 2.867 nm and 168° instead of 2.75 nm and 166.15°. These conditions ensure the stereo-specific interaction between actin and myosin and good agreement with the data gathered by electron microscopy and X-ray diffraction methods. The results suggest that the force is generated not only by the myosin cross-bridges but also by the thin filaments; the former acts by cyclical unwrapping and wrapping the thick filament backbone, and the latter byelongation.
Geometric perturbation theory and plasma physics
Energy Technology Data Exchange (ETDEWEB)
Omohundro, S.M.
1985-04-04
Modern differential geometric techniques are used to unify the physical asymptotics underlying mechanics, wave theory and statistical mechanics. The approach gives new insights into the structure of physical theories and is suited to the needs of modern large-scale computer simulation and symbol manipulation systems. A coordinate-free formulation of non-singular perturbation theory is given, from which a new Hamiltonian perturbation structure is derived and related to the unperturbed structure. The theory of perturbations in the presence of symmetry is developed, and the method of averaging is related to reduction by a circle group action. The pseudo-forces and magnetic Poisson bracket terms due to reduction are given a natural asymptotic interpretation. Similar terms due to changing reference frames are related to the method of variation of parameters, which is also given a Hamiltonian formulation. These methods are used to answer a question about nearly periodic systems. The answer leads to a new secular perturbation theory that contains no ad hoc elements. Eikonal wave theory is given a Hamiltonian formulation that generalizes Whitham's Lagrangian approach. The evolution of wave action density on ray phase space is given a Hamiltonian structure using a Lie-Poisson bracket. The relationship between dissipative and Hamiltonian systems is discussed. A new type of attractor is defined which attracts both forward and backward in time and is shown to occur in infinite-dimensional Hamiltonian systems with dissipative behavior. The theory of Smale horseshoes is applied to gyromotion in the neighborhood of a magnetic field reversal and the phenomenon of reinsertion in area-preserving horseshoes is introduced. The central limit theorem is proved by renormalization group techniques. A natural symplectic structure for thermodynamics is shown to arise asymptotically from the maximum entropy formalism.
Geometric perturbation theory and plasma physics
International Nuclear Information System (INIS)
Omohundro, S.M.
1985-01-01
Modern differential geometric techniques are used to unify the physical asymptotics underlying mechanics, wave theory and statistical mechanics. The approach gives new insights into the structure of physical theories and is suited to the needs of modern large-scale computer simulation and symbol manipulation systems. A coordinate-free formulation of non-singular perturbation theory is given, from which a new Hamiltonian perturbation structure is derived and related to the unperturbed structure. The theory of perturbations in the presence of symmetry is developed, and the method of averaging is related to reduction by a circle group action. The pseudo-forces and magnetic Poisson bracket terms due to reduction are given a natural asymptotic interpretation. Similar terms due to changing reference frames are related to the method of variation of parameters, which is also given a Hamiltonian formulation. These methods are used to answer a question about nearly periodic systems. The answer leads to a new secular perturbation theory that contains no ad hoc elements. Eikonal wave theory is given a Hamiltonian formulation that generalizes Whitham's Lagrangian approach. The evolution of wave action density on ray phase space is given a Hamiltonian structure using a Lie-Poisson bracket. The relationship between dissipative and Hamiltonian systems is discussed. A new type of attractor is defined which attracts both forward and backward in time and is shown to occur in infinite-dimensional Hamiltonian systems with dissipative behavior. The theory of Smale horseshoes is applied to gyromotion in the neighborhood of a magnetic field reversal and the phenomenon of reinsertion in area-preserving horseshoes is introduced. The central limit theorem is proved by renormalization group techniques. A natural symplectic structure for thermodynamics is shown to arise asymptotically from the maximum entropy formalism
Geometrization and Generalization of the Kowalevski Top
Dragović, Vladimir
2010-08-01
A new view on the Kowalevski top and the Kowalevski integration procedure is presented. For more than a century, the Kowalevski 1889 case, has attracted full attention of a wide community as the highlight of the classical theory of integrable systems. Despite hundreds of papers on the subject, the Kowalevski integration is still understood as a magic recipe, an unbelievable sequence of skillful tricks, unexpected identities and smart changes of variables. The novelty of our present approach is based on our four observations. The first one is that the so-called fundamental Kowalevski equation is an instance of a pencil equation of the theory of conics which leads us to a new geometric interpretation of the Kowalevski variables w, x 1, x 2 as the pencil parameter and the Darboux coordinates, respectively. The second is observation of the key algebraic property of the pencil equation which is followed by introduction and study of a new class of discriminantly separable polynomials. All steps of the Kowalevski integration procedure are now derived as easy and transparent logical consequences of our theory of discriminantly separable polynomials. The third observation connects the Kowalevski integration and the pencil equation with the theory of multi-valued groups. The Kowalevski change of variables is now recognized as an example of a two-valued group operation and its action. The final observation is surprising equivalence of the associativity of the two-valued group operation and its action to the n = 3 case of the Great Poncelet Theorem for pencils of conics.
Geometric Monte Carlo and black Janus geometries
Energy Technology Data Exchange (ETDEWEB)
Bak, Dongsu, E-mail: dsbak@uos.ac.kr [Physics Department, University of Seoul, Seoul 02504 (Korea, Republic of); B.W. Lee Center for Fields, Gravity & Strings, Institute for Basic Sciences, Daejeon 34047 (Korea, Republic of); Kim, Chanju, E-mail: cjkim@ewha.ac.kr [Department of Physics, Ewha Womans University, Seoul 03760 (Korea, Republic of); Kim, Kyung Kiu, E-mail: kimkyungkiu@gmail.com [Department of Physics, Sejong University, Seoul 05006 (Korea, Republic of); Department of Physics, College of Science, Yonsei University, Seoul 03722 (Korea, Republic of); Min, Hyunsoo, E-mail: hsmin@uos.ac.kr [Physics Department, University of Seoul, Seoul 02504 (Korea, Republic of); Song, Jeong-Pil, E-mail: jeong_pil_song@brown.edu [Department of Chemistry, Brown University, Providence, RI 02912 (United States)
2017-04-10
We describe an application of the Monte Carlo method to the Janus deformation of the black brane background. We present numerical results for three and five dimensional black Janus geometries with planar and spherical interfaces. In particular, we argue that the 5D geometry with a spherical interface has an application in understanding the finite temperature bag-like QCD model via the AdS/CFT correspondence. The accuracy and convergence of the algorithm are evaluated with respect to the grid spacing. The systematic errors of the method are determined using an exact solution of 3D black Janus. This numerical approach for solving linear problems is unaffected initial guess of a trial solution and can handle an arbitrary geometry under various boundary conditions in the presence of source fields.
Geometric Singularities of the Stokes Problem
Directory of Open Access Journals (Sweden)
Nejmeddine Chorfi
2014-01-01
Full Text Available When the domain is a polygon of ℝ2, the solution of a partial differential equation is written as a sum of a regular part and a linear combination of singular functions. The purpose of this paper is to present explicitly the singular functions of Stokes problem. We prove the Kondratiev method in the case of the crack. We finish by giving some regularity results.
Pitfalls of using the geometric-mean combining rule in the density gradient theory
DEFF Research Database (Denmark)
Liang, Xiaodong; Michelsen, Michael Locht; Kontogeorgis, Georgios
2016-01-01
. It has been found that the solution profile passes a saddle point of the tangent plane distance, which is independent of the influence parameters. It has been shown that the numerical pitfalls could occur for both vapor liquid and liquid liquid equilibrium systems. Shape density change inside......It is popular and attractive to model the interfacial tension using the density gradient theory with the geometric-mean combining rule, in which the same equation of state is used for the interface and bulk phases. The computational efficiency is the most important advantage of this theory....... In this work, it has been mathematically shown that the theory fails if the solution profile is not monotonic in the path function, which is defined as the summation of the density multiplied by the square root of the influence parameter over all components. A computational solution procedure is then presented...
Geometric Generalisation of Surrogate Model-Based Optimisation to Combinatorial and Program Spaces
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Yong-Hyuk Kim
2014-01-01
Full Text Available Surrogate models (SMs can profitably be employed, often in conjunction with evolutionary algorithms, in optimisation in which it is expensive to test candidate solutions. The spatial intuition behind SMs makes them naturally suited to continuous problems, and the only combinatorial problems that have been previously addressed are those with solutions that can be encoded as integer vectors. We show how radial basis functions can provide a generalised SM for combinatorial problems which have a geometric solution representation, through the conversion of that representation to a different metric space. This approach allows an SM to be cast in a natural way for the problem at hand, without ad hoc adaptation to a specific representation. We test this adaptation process on problems involving binary strings, permutations, and tree-based genetic programs.
Capability of geometric features to classify ships in SAR imagery
Lang, Haitao; Wu, Siwen; Lai, Quan; Ma, Li
2016-10-01
Ship classification in synthetic aperture radar (SAR) imagery has become a new hotspot in remote sensing community for its valuable potential in many maritime applications. Several kinds of ship features, such as geometric features, polarimetric features, and scattering features have been widely applied on ship classification tasks. Compared with polarimetric features and scattering features, which are subject to SAR parameters (e.g., sensor type, incidence angle, polarization, etc.) and environment factors (e.g., sea state, wind, wave, current, etc.), geometric features are relatively independent of SAR and environment factors, and easy to be extracted stably from SAR imagery. In this paper, the capability of geometric features to classify ships in SAR imagery with various resolution has been investigated. Firstly, the relationship between the geometric feature extraction accuracy and the SAR imagery resolution is analyzed. It shows that the minimum bounding rectangle (MBR) of ship can be extracted exactly in terms of absolute precision by the proposed automatic ship-sea segmentation method. Next, six simple but effective geometric features are extracted to build a ship representation for the subsequent classification task. These six geometric features are composed of length (f1), width (f2), area (f3), perimeter (f4), elongatedness (f5) and compactness (f6). Among them, two basic features, length (f1) and width (f2), are directly extracted based on the MBR of ship, the other four are derived from those two basic features. The capability of the utilized geometric features to classify ships are validated on two data set with different image resolutions. The results show that the performance of ship classification solely by geometric features is close to that obtained by the state-of-the-art methods, which obtained by a combination of multiple kinds of features, including scattering features and geometric features after a complex feature selection process.
Geometrical optimization for strictly localized structures
Mo, Yirong
2003-07-01
Recently we proposed the block localized wavefunction (BLW) approach which takes the advantages of valence bond theory and molecular orbital theory and defines the wavefunctions for resonance structures based on the assumption that all electrons and orbitals are partitioned into a few subgroups. In this work, we implement the geometrical optimization of the BLW method based on the algorithm proposed by Gianinetti and coworkers. Thus, we can study the conjugation effect on not only the molecular stability, but also the molecular geometry. With this capability, the π conjugation effect in trans-polyenes C2nH2n+2 (n=2-5) as well as in formamide and its analogs are studied by optimizing their delocalized and strictly localized forms with the 6-31G(d) and 6-311+G(d,p) basis sets. Although it has been well presumed that the π resonance shortens the single bonds and lengthens the double bonds with the delocalization of π electrons across the whole line in polyenes, our optimization of the strictly localized structures quantitatively shows that when the conjugation effect is "turned off," the double bond lengths will be identical to the CC bond length in ethylene and the single Csp2-Csp2 bond length will be about 1.513-1.517 Å. In agreement with the classical Hückel theory, the resonance energies in polyenes are approximately in proportion to the number of double bonds. Similarly, resonance is responsible not only for the planarity of formamide, thioformamide, and selenoformamide, but also for the lengthening of the CX (X=O,S,Se) double bond and the shortening of the CN bonds. Although it is assumed that the CX bond polarization decreases in the order of O>S>Se, the π electronic delocalization increases in the opposite order, i.e., formamide
Geometric constructions for repulsive gravity and quantization
Energy Technology Data Exchange (ETDEWEB)
Hohmann, Manuel
2010-11-15
In this thesis we present two geometric theories designed to extend general relativity. It can be seen as one of the aims of such theories to model the observed accelerating expansion of the universe as a gravitational phenomenon, or to provide a mathematical structure for the formulation of quantum field theories on curved spacetimes and quantum gravity. This thesis splits into two parts: In the first part we consider multimetric gravity theories containing N>1 standard model copies which interact only gravitationally and repel each other in the Newtonian limit. The dynamics of each of the standard model copies is governed by its own metric tensor. We show that the antisymmetric case, in which the mutual repulsion between the different matter sectors is of equal strength compared to the attractive gravitational force within each sector, is prohibited by a no-go theorem for N=2. We further show that this theorem does not hold for N>2 by explicitly constructing an antisymmetric multimetric repulsive gravity theory. We then examine several properties of this theory. Most notably, we derive a simple cosmological model and show that the accelerating expansion of the late universe can indeed be explained by the mutual repulsion between the different matter sectors. We further present a simple model for structure formation and show that our model leads to the formation of filament-like structures and voids. Finally, we show that multimetric repulsive gravity is compatible with high-precision solar system data using the parametrized post-Newtonian formalism. In the second part of the thesis we propose a mathematical model of quantum spacetime as an infinite-dimensional manifold locally homeomorphic to an appropriate Schwartz space. This extends and unifies both the standard function space construction of quantum mechanics and the differentiable manifold structure of classical spacetime. In this picture we demonstrate that classical spacetime emerges as a finite
Spanners for geometric intersection graphs with applications
Directory of Open Access Journals (Sweden)
Martin Fürer
2012-05-01
Full Text Available A ball graph is an intersection graph of a set of balls with arbitrary radii. Given a real numbert>1, we say that a subgraph G' of a graph G is a t-spanner of G, if for every pair of verticesu,v in G, there exists a path in G' of length at most t times the distance between u and v inG. In this paper, we consider the problem of efficiently constructing sparse spanners of ball graphs which supports fast shortest path distance queries.We present the first algorithm for constructing spanners of ball graphs. For a ball graph in Rk, we construct a (1+ε-spanner for any ε>0 with O(nε-k+1 edges in O(n2ℓ+δε-k logℓ S time, using an efficient partitioning of space into hypercubes and solving intersection problems. Here ℓ=1-1/(⌊k/2⌋+2, δ is any positive constant, and S is the ratio between the largest and smallest radius. For the special case when the balls all have unit size, we show that the complexity of constructing a (1+ε-spanner is almost equal to the complexity of constructing a Euclidean minimum spanning tree. The algorithm extends naturally to other disk-likeobjects, also in higher dimensions.The algorithm uses an efficient subdivision of space to construct a sparse graph having many of the same distance properties as the input ball graph. Additionally, the constructed spanners have a small vertex separator decomposition (hereditary. In dimension k=2, the disk graph spanner has an O(n1/2ε-3/2+ε-3log S separator. The presence of a small separator is then exploited to obtain very efficient data structures for approximate distance queries. The results on geometric graph separators might be of independent interest. For example, since complete Euclidean graphs are just a special case of (unit ball graphs, our results also provide a new approach for constructing spanners with small separators in these graphs.
Camilli, Fabio; Prados, Emmanuel
2011-01-01
International audience; Viscosity solution is a notion of weak solution for a class of partial differential equations of Hamilton-Jacobi type. The range of applications of the notions of viscosity solution and Hamilton-Jacobi equations is enormous, including common class of partial differential equations such as evolutive problems and problems with boundary conditions, equations arising in optimal control theory, differential games, second-order equations arising in stochastic optimal control...