NAIF Toolkit - Extended

NASA Technical Reports Server (NTRS)

Acton, Charles H., Jr.; Bachman, Nathaniel J.; Semenov, Boris V.; Wright, Edward D.

2010-01-01

The Navigation Ancillary Infor ma tion Facility (NAIF) at JPL, acting under the direction of NASA s Office of Space Science, has built a data system named SPICE (Spacecraft Planet Instrument Cmatrix Events) to assist scientists in planning and interpreting scientific observations (see figure). SPICE provides geometric and some other ancillary information needed to recover the full value of science instrument data, including correlation of individual instrument data sets with data from other instruments on the same or other spacecraft. This data system is used to produce space mission observation geometry data sets known as SPICE kernels. It is also used to read SPICE kernels and to compute derived quantities such as positions, orientations, lighting angles, etc. The SPICE toolkit consists of a subroutine/ function library, executable programs (both large applications and simple utilities that focus on kernel management), and simple examples of using SPICE toolkit subroutines. This software is very accurate, thoroughly tested, and portable to all computers. It is extremely stable and reusable on all missions. Since the previous version, three significant capabilities have been added: Interactive Data Language (IDL) interface, MATLAB interface, and a geometric event finder subsystem.

Estimation of Gravity Parameters Related to Simple Geometrical Structures by Developing an Approach Based on Deconvolution and Linear Optimization Techniques

NASA Astrophysics Data System (ADS)

Asfahani, J.; Tlas, M.

2015-10-01

An easy and practical method for interpreting residual gravity anomalies due to simple geometrically shaped models such as cylinders and spheres has been proposed in this paper. This proposed method is based on both the deconvolution technique and the simplex algorithm for linear optimization to most effectively estimate the model parameters, e.g., the depth from the surface to the center of a buried structure (sphere or horizontal cylinder) or the depth from the surface to the top of a buried object (vertical cylinder), and the amplitude coefficient from the residual gravity anomaly profile. The method was tested on synthetic data sets corrupted by different white Gaussian random noise levels to demonstrate the capability and reliability of the method. The results acquired show that the estimated parameter values derived by this proposed method are close to the assumed true parameter values. The validity of this method is also demonstrated using real field residual gravity anomalies from Cuba and Sweden. Comparable and acceptable agreement is shown between the results derived by this method and those derived from real field data.

Evaluation of methods for managing censored results when calculating the geometric mean.

PubMed

Mikkonen, Hannah G; Clarke, Bradley O; Dasika, Raghava; Wallis, Christian J; Reichman, Suzie M

2018-01-01

Currently, there are conflicting views on the best statistical methods for managing censored environmental data. The method commonly applied by environmental science researchers and professionals is to substitute half the limit of reporting for derivation of summary statistics. This approach has been criticised by some researchers, raising questions around the interpretation of historical scientific data. This study evaluated four complete soil datasets, at three levels of simulated censorship, to test the accuracy of a range of censored data management methods for calculation of the geometric mean. The methods assessed included removal of censored results, substitution of a fixed value (near zero, half the limit of reporting and the limit of reporting), substitution by nearest neighbour imputation, maximum likelihood estimation, regression on order substitution and Kaplan-Meier/survival analysis. This is the first time such a comprehensive range of censored data management methods have been applied to assess the accuracy of calculation of the geometric mean. The results of this study show that, for describing the geometric mean, the simple method of substitution of half the limit of reporting is comparable or more accurate than alternative censored data management methods, including nearest neighbour imputation methods. Copyright © 2017 Elsevier Ltd. All rights reserved.

Observations of the Geometry of Horizon-Based Optical Navigation

NASA Technical Reports Server (NTRS)

Christian, John; Robinson, Shane

2016-01-01

NASA's Orion Project has sparked a renewed interest in horizon-based optical navigation(OPNAV) techniques for spacecraft in the Earth-Moon system. Some approaches have begun to explore the geometry of horizon-based OPNAV and exploit the fact that it is a conic section problem. Therefore, the present paper focuses more deeply on understanding and leveraging the various geometric interpretations of horizon-based OPNAV. These results provide valuable insight into the fundamental workings of OPNAV solution methods, their convergence properties, and associated estimate covariance. Most importantly, the geometry and transformations uncovered in this paper lead to a simple and non-iterative solution to the generic horizon-based OPNAV problem. This represents a significant theoretical advancement over existing methods. Thus, we find that a clear understanding of geometric relationships is central to the prudent design, use, and operation of horizon-based OPNAV techniques.

Simple microfluidic stagnation point flow geometries

PubMed Central

Dockx, Greet; Verwijlen, Tom; Sempels, Wouter; Nagel, Mathias; Moldenaers, Paula; Hofkens, Johan; Vermant, Jan

2016-01-01

A geometrically simple flow cell is proposed to generate different types of stagnation flows, using a separation flow and small variations of the geometric parameters. Flows with high local deformation rates can be changed from purely rotational, over simple shear flow, to extensional flow in a region surrounding a stagnation point. Computational fluid dynamic calculations are used to analyse how variations of the geometrical parameters affect the flow field. These numerical calculations are compared to the experimentally obtained streamlines of different designs, which have been determined by high speed confocal microscopy. As the flow type is dictated predominantly by the geometrical parameters, such simple separating flow devices may alleviate the requirements for flow control, while offering good stability for a wide variety of flow types. PMID:27462382

Geometric Representations of Condition Queries on Three-Dimensional Vector Fields

NASA Technical Reports Server (NTRS)

Henze, Chris

1999-01-01

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

Absence of Vacuum Induced Berry Phases without the Rotating Wave Approximation in Cavity QED

NASA Astrophysics Data System (ADS)

Larson, Jonas

2012-01-01

We revisit earlier studies on Berry phases suggested to appear in certain cavity QED settings. It has been especially argued that a nontrivial geometric phase is achievable even in the situation of no cavity photons. We, however, show that such results hinge on imposing the rotating wave approximation (RWA), while without the RWA no Berry phases occur in these schemes. A geometrical interpretation of our results is obtained by introducing semiclassical energy surfaces which in a simple way brings out the phase-space dynamics. With the RWA, a conical intersection between the surfaces emerges and encircling it gives rise to the Berry phase. Without the RWA, the conical intersection is absent and therefore the Berry phase vanishes. It is believed that this is a first example showing how the application of the RWA in the Jaynes-Cummings model may lead to false conclusions, regardless of the mutual strengths between the system parameters.

Geometric and potential dynamics interpretation of the optic ring resonator bistability

NASA Astrophysics Data System (ADS)

Chiangga, S.; Chittha, T.; Frank, T. D.

2015-07-01

The optical bistability is a fundamental nonlinear feature of the ring resonator. A geometric and potential dynamics interpretation of the bistability is given. Accordingly, the bistability of the nonlinear system is shown to be a consequence of geometric laws of vector calculus describing the resonator ring. In contrast, the so-called transcendental relations that have been obtained in the literature in order to describe the optical wave are interpreted in terms of potential dynamical systems. The proposed novel interpretation provides new insights into the nature of the ring resonator optical bistability. The fundamental work by Rukhlenko, Premaratne and Agrawal (2010) as well as a more recent study by Chiangga, Pitakwongsaporn, Frank and Yupapin (2013) are considered.

Fisher metric, geometric entanglement, and spin networks

NASA Astrophysics Data System (ADS)

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.

Relative influence upon microwave emissivity of fine-scale stratigraphy, internal scattering, and dielectric properties

USGS Publications Warehouse

England, A.W.

1976-01-01

The microwave emissivity of relatively low-loss media such as snow, ice, frozen ground, and lunar soil is strongly influenced by fine-scale layering and by internal scattering. Radiometric data, however, are commonly interpreted using a model of emission from a homogeneous, dielectric halfspace whose emissivity derives exclusively from dielectric properties. Conclusions based upon these simple interpretations can be erroneous. Examples are presented showing that the emission from fresh or hardpacked snow over either frozen or moist soil is governed dominantly by the size distribution of ice grains in the snowpack. Similarly, the thickness of seasonally frozen soil and the concentration of rock clasts in lunar soil noticeably affect, respectively, the emissivities of northern latitude soils in winter and of the lunar regolith. Petrophysical data accumulated in support of the geophysical interpretation of microwave data must include measurements of not only dielectric properties, but also of geometric factors such as finescale layering and size distributions of grains, inclusions, and voids. ?? 1976 Birkha??user Verlag.

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

NASA Astrophysics Data System (ADS)

Horn, Martin Erik

2014-10-01

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

Atomic Dynamics in Simple Liquid: de Gennes Narrowing Revisited

NASA Astrophysics Data System (ADS)

Wu, Bin; Iwashita, Takuya; Egami, Takeshi

2018-03-01

The de Gennes narrowing phenomenon is frequently observed by neutron or x -ray scattering measurements of the dynamics of complex systems, such as liquids, proteins, colloids, and polymers. The characteristic slowing down of dynamics in the vicinity of the maximum of the total scattering intensity is commonly attributed to enhanced cooperativity. In this Letter, we present an alternative view on its origin through the examination of the time-dependent pair correlation function, the van Hove correlation function, for a model liquid in two, three, and four dimensions. We find that the relaxation time increases monotonically with distance and the dependence on distance varies with dimension. We propose a heuristic explanation of this dependence based on a simple geometrical model. This finding sheds new light on the interpretation of the de Gennes narrowing phenomenon and the α -relaxation time.

The Soil Foam Drainage Equation - an alternative model for unsaturated flow in porous media

NASA Astrophysics Data System (ADS)

Assouline, Shmuel; Lehmann, Peter; Hoogland, Frouke; Or, Dani

2017-04-01

The analogy between the geometry and dynamics of wet foam drainage and gravity drainage of unsaturated porous media expands modeling capabilities for capillary flows and supplements the standard Richards equation representation. The governing equation for draining foam (or a soil variant termed the soil foam drainage equation - SFDE) obviates the need for macroscopic unsaturated hydraulic conductivity function by an explicit account of diminishing flow pathway sizes as the medium gradually drains. Potential advantages of the proposed drainage foam formalism include direct description of transient flow without requiring constitutive functions; evolution of capillary cross sections that provides consistent description of self-regulating internal fluxes (e.g., towards field capacity); and a more intuitive geometrical picture of capillary flow across textural boundaries. We will present new and simple analytical expressions for drainage rates and volumes from unsaturated porous media subjected to different boundary conditions that are in good agreement with the numerical solution of the SFDE and experimental results. The foam drainage methodology expands the range of tools available for describing and quantifying unsaturated flows and provides geometrically tractable links between evolution of liquid configuration and flow dynamics in unsaturated porous media. The resulting geometrical representation of capillary drainage could improve understanding of colloid and pathogen transport. The explicit geometrical interpretation of flow pathways underlying the hydraulic functions used by the Richards equation offers new insights that benefit both approaches.

The influence of a high pressure gradient on unsteady velocity perturbations in the case of a turbulent supersonic flow

NASA Technical Reports Server (NTRS)

Dussauge, J. P.; Debieve, J. F.

1980-01-01

The amplification or reduction of unsteady velocity perturbations under the influence of strong flow acceleration or deceleration was studied. Supersonic flows with large velocity, pressure gradients, and the conditions in which the velocity fluctuations depend on the action of the average gradients of pressure and velocity rather than turbulence, are described. Results are analyzed statistically and interpreted as a return to laminar process. It is shown that this return to laminar implies negative values in the turbulence production terms for kinetic energy. A simple geometrical representation of the Reynolds stress production is given.

The Extensibility of an Interpreted Language Using Plugin Libraries

NASA Astrophysics Data System (ADS)

Herceg, Dorde; Radaković, Davorka

2011-09-01

Dynamic geometry software (DGS) are computer programs that allow one to create and manipulate geometrical drawings. They are mostly used in teaching and studying geometry. However, DGS can also be used to develop interactive drawings not directly related to geometry. Examples include teaching materials for numerical mathematics at secondary school and university levels, or interactive mathematical games for elementary school children. Such applications often surpass the intended purposes of the DGS and may require complicated programming on behalf of the user. In this paper we present a simple plug-in model which enables easy development and deployment of interactive GUI components for "Geometrijica", a DGS we are developing on Silverlight.

Generalized Stoner-Wohlfarth model accurately describing the switching processes in pseudo-single ferromagnetic particles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cimpoesu, Dorin, E-mail: cdorin@uaic.ro; Stoleriu, Laurentiu; Stancu, Alexandru

2013-12-14

We propose a generalized Stoner-Wohlfarth (SW) type model to describe various experimentally observed angular dependencies of the switching field in non-single-domain magnetic particles. Because the nonuniform magnetic states are generally characterized by complicated spin configurations with no simple analytical description, we maintain the macrospin hypothesis and we phenomenologically include the effects of nonuniformities only in the anisotropy energy, preserving as much as possible the elegance of SW model, the concept of critical curve and its geometric interpretation. We compare the results obtained with our model with full micromagnetic simulations in order to evaluate the performance and limits of our approach.

A Simple Pythagorean Interpretation of E2 = p2c2 + (mc2)2

NASA Astrophysics Data System (ADS)

Tobar, J. A.; Vargas, E. L.; Andrianarijaona, V. M.

2015-03-01

We are considering the relationship between the relativistic energy, the momentum, and the rest energy, E2 =p2c2 + (mc2)2 , and using geometrical means to analyze each individual portion in a spatial setting. The aforementioned equation suggests that pc and mc2 could be thought of as the two axis of a plane. According to de Broglie's hypothesis λ = h / p therefore suggesting that the pc-axis is connected to the wave properties of a moving object, and subsequently, the mc2-axis is connected to the particle properties. Consequently, these two axis could represent the particle and wave properties of the moving object. An overview of possible models and meaningful interpretations will be presented. Authors wish to give special thanks to Pacific Union College Student Senate in Angwin, California, for their financial support.

A scene-analysis approach to remote sensing. [San Francisco, California

NASA Technical Reports Server (NTRS)

Tenenbaum, J. M. (Principal Investigator); Fischler, M. A.; Wolf, H. C.

1978-01-01

The author has identified the following significant results. Geometric correspondance between a sensed image and a symbolic map is established in an initial stage of processing by adjusting parameters of a sensed model so that the image features predicted from the map optimally match corresponding features extracted from the sensed image. Information in the map is then used to constrain where to look in an image, what to look for, and how to interpret what is seen. For simple monitoring tasks involving multispectral classification, these constraints significantly reduce computation, simplify interpretation, and improve the utility of the resulting information. Previously intractable tasks requiring spatial and textural analysis may become straightforward in the context established by the map knowledge. The use of map-guided image analysis in monitoring the volume of water in a reservoir, the number of boxcars in a railyard, and the number of ships in a harbor is demonstrated.

Efficient embedding of complex networks to hyperbolic space via their Laplacian

PubMed Central

Alanis-Lobato, Gregorio; Mier, Pablo; Andrade-Navarro, Miguel A.

2016-01-01

The different factors involved in the growth process of complex networks imprint valuable information in their observable topologies. How to exploit this information to accurately predict structural network changes is the subject of active research. A recent model of network growth sustains that the emergence of properties common to most complex systems is the result of certain trade-offs between node birth-time and similarity. This model has a geometric interpretation in hyperbolic space, where distances between nodes abstract this optimisation process. Current methods for network hyperbolic embedding search for node coordinates that maximise the likelihood that the network was produced by the afore-mentioned model. Here, a different strategy is followed in the form of the Laplacian-based Network Embedding, a simple yet accurate, efficient and data driven manifold learning approach, which allows for the quick geometric analysis of big networks. Comparisons against existing embedding and prediction techniques highlight its applicability to network evolution and link prediction. PMID:27445157

Efficient embedding of complex networks to hyperbolic space via their Laplacian

NASA Astrophysics Data System (ADS)

Alanis-Lobato, Gregorio; Mier, Pablo; Andrade-Navarro, Miguel A.

2016-07-01

The different factors involved in the growth process of complex networks imprint valuable information in their observable topologies. How to exploit this information to accurately predict structural network changes is the subject of active research. A recent model of network growth sustains that the emergence of properties common to most complex systems is the result of certain trade-offs between node birth-time and similarity. This model has a geometric interpretation in hyperbolic space, where distances between nodes abstract this optimisation process. Current methods for network hyperbolic embedding search for node coordinates that maximise the likelihood that the network was produced by the afore-mentioned model. Here, a different strategy is followed in the form of the Laplacian-based Network Embedding, a simple yet accurate, efficient and data driven manifold learning approach, which allows for the quick geometric analysis of big networks. Comparisons against existing embedding and prediction techniques highlight its applicability to network evolution and link prediction.

DECOMPOSITION OF THE PARTICLE AND CONNECTION OF PARTICLES IN THE TERMINI OF THE MOMENTUM SPACE

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chernikov, N.A.

1958-01-01

>Geometric and algebraic notions and ideas are used to obtain a geometric interpretation of the kinematics of nuclear reactions. Thus, extended analytic calculations combined with the transition from one reference system to another, are replaced by simple formulas of the hyperbolic trigonometry. Let a particle move with the velocity a in a reference system which moves with the velocity o. Then the modulus of the three-dimensional impulse of the particle is p/sub 0a/ = m c sh oa-bar/c, where m is the resting miss, c is the velocity of the light, oa-bar is the distance of the points o andmore » a in the momentum space. The kinetic energy epsilon /sub oa/ of the particle in the system o is epsilon / sub oa/=m c/sup 2/STAoa-bar/c-1!. Then the ratio epsilon /sub oa/m is the area divided by 2 pi of a circle of radius oa in the momentum space. (TCO)« less

Atomic Dynamics in Simple Liquid: de Gennes Narrowing Revisited

DOE PAGES

Wu, Bin; Iwashita, Takuya; Egami, Takeshi

2018-03-27

The de Gennes narrowing phenomenon is frequently observed by neutron or x-ray scattering measurements of the dynamics of complex systems, such as liquids, proteins, colloids, and polymers. The characteristic slowing down of dynamics in the vicinity of the maximum of the total scattering intensity is commonly attributed to enhanced cooperativity. In this Letter, we present an alternative view on its origin through the examination of the time-dependent pair correlation function, the van Hove correlation function, for a model liquid in two, three, and four dimensions. We find that the relaxation time increases monotonically with distance and the dependence on distancemore » varies with dimension. We propose a heuristic explanation of this dependence based on a simple geometrical model. Furthermore, this finding sheds new light on the interpretation of the de Gennes narrowing phenomenon and the α-relaxation time.« less

Atomic Dynamics in Simple Liquid: de Gennes Narrowing Revisited

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wu, Bin; Iwashita, Takuya; Egami, Takeshi

The de Gennes narrowing phenomenon is frequently observed by neutron or x-ray scattering measurements of the dynamics of complex systems, such as liquids, proteins, colloids, and polymers. The characteristic slowing down of dynamics in the vicinity of the maximum of the total scattering intensity is commonly attributed to enhanced cooperativity. In this Letter, we present an alternative view on its origin through the examination of the time-dependent pair correlation function, the van Hove correlation function, for a model liquid in two, three, and four dimensions. We find that the relaxation time increases monotonically with distance and the dependence on distancemore » varies with dimension. We propose a heuristic explanation of this dependence based on a simple geometrical model. Furthermore, this finding sheds new light on the interpretation of the de Gennes narrowing phenomenon and the α-relaxation time.« less

Texture Development and Material Flow Behavior During Refill Friction Stir Spot Welding of AlMgSc

NASA Astrophysics Data System (ADS)

Shen, Junjun; Lage, Sara B. M.; Suhuddin, Uceu F. H.; Bolfarini, Claudemiro; dos Santos, Jorge F.

2018-01-01

The microstructural evolution during refill friction stir spot welding of an AlMgSc alloy was studied. The primary texture that developed in all regions, with the exception of the weld center, was determined to be 〈110〉 fibers and interpreted as a simple shear texture with the 〈110〉 direction aligned with the shear direction. The material flow is mainly driven by two components: the simple shear acting on the horizontal plane causing an inward-directed spiral flow and the extrusion acting on the vertical plane causing an upward-directed or downward-directed flow. Under such a complex material flow, the weld center, which is subjected to minimal local strain, is the least recrystallized. In addition to the geometric effects of strain and grain subdivision, thermally activated high-angle grain boundary migration, particularly continuous dynamic recrystallization, drives the formation of refined grains in the stirred zone.

Immagini e Concetti in Geometria=The Figural and the Conceptual Components of Geometrical Concepts.

ERIC Educational Resources Information Center

Mariotti, Maria Alessandra

1992-01-01

Discusses geometrical reasoning in the framework of the theory of Figural Concepts to highlight the interaction between the figural and conceptual components of geometrical concepts. Examples of students' difficulties and errors in geometrical reasoning are interpreted according to the internal tension that appears in figural concepts resulting…

a Kml-Based Approach for Distributed Collaborative Interpretation of Remote Sensing Images in the Geo-Browser

NASA Astrophysics Data System (ADS)

Huang, L.; Zhu, X.; Guo, W.; Xiang, L.; Chen, X.; Mei, Y.

2012-07-01

Existing implementations of collaborative image interpretation have many limitations for very large satellite imageries, such as inefficient browsing, slow transmission, etc. This article presents a KML-based approach to support distributed, real-time, synchronous collaborative interpretation for remote sensing images in the geo-browser. As an OGC standard, KML (Keyhole Markup Language) has the advantage of organizing various types of geospatial data (including image, annotation, geometry, etc.) in the geo-browser. Existing KML elements can be used to describe simple interpretation results indicated by vector symbols. To enlarge its application, this article expands KML elements to describe some complex image processing operations, including band combination, grey transformation, geometric correction, etc. Improved KML is employed to describe and share interpretation operations and results among interpreters. Further, this article develops some collaboration related services that are collaboration launch service, perceiving service and communication service. The launch service creates a collaborative interpretation task and provides a unified interface for all participants. The perceiving service supports interpreters to share collaboration awareness. Communication service provides interpreters with written words communication. Finally, the GeoGlobe geo-browser (an extensible and flexible geospatial platform developed in LIESMARS) is selected to perform experiments of collaborative image interpretation. The geo-browser, which manage and visualize massive geospatial information, can provide distributed users with quick browsing and transmission. Meanwhile in the geo-browser, GIS data (for example DEM, DTM, thematic map and etc.) can be integrated to assist in improving accuracy of interpretation. Results show that the proposed method is available to support distributed collaborative interpretation of remote sensing image

Geometric interpretations of the Discrete Fourier Transform (DFT)

NASA Technical Reports Server (NTRS)

Campbell, C. W.

1984-01-01

One, two, and three dimensional Discrete Fourier Transforms (DFT) and geometric interpretations of their periodicities are presented. These operators are examined for their relationship with the two sided, continuous Fourier transform. Discrete or continuous transforms of real functions have certain symmetry properties. The symmetries are examined for the one, two, and three dimensional cases. Extension to higher dimension is straight forward.

The Effects of Formalism on Teacher Trainees' Algebraic and Geometric Interpretation of the Notions of Linear Dependency/Independency

ERIC Educational Resources Information Center

Ertekin, E.; Solak, S.; Yazici, E.

2010-01-01

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…

Non-Abelian Geometric Phases Carried by the Quantum Noise Matrix

NASA Astrophysics Data System (ADS)

Bharath, H. M.; Boguslawski, Matthew; Barrios, Maryrose; Chapman, Michael

2017-04-01

Topological phases of matter are characterized by topological order parameters that are built using Berry's geometric phase. Berry's phase is the geometric information stored in the overall phase of a quantum state. We show that geometric information is also stored in the second and higher order spin moments of a quantum spin system, captured by a non-abelian geometric phase. The quantum state of a spin-S system is uniquely characterized by its spin moments up to order 2S. The first-order spin moment is the spin vector, and the second-order spin moment represents the spin fluctuation tensor, i.e., the quantum noise matrix. When the spin vector is transported along a loop in the Bloch ball, we show that the quantum noise matrix picks up a geometric phase. Considering spin-1 systems, we formulate this geometric phase as an SO(3) operator. Geometric phases are usually interpreted in terms of the solid angle subtended by the loop at the center. However, solid angles are not well defined for loops that pass through the center. Here, we introduce a generalized solid angle which is well defined for all loops inside the Bloch ball, in terms of which, we interpret the SO(3) geometric phase. This geometric phase can be used to characterize topological spin textures in cold atomic clouds.

Low-angle normal faulting and isostatic response in the Gulf of Suez: Evidence from seismic interpretation and geometric reconstruction

NASA Technical Reports Server (NTRS)

Perry, S. K.; Schamel, S.

1985-01-01

Tectonic extension within continental crust creates a variety of major features best classed as extensional orogens. These features have come under increasing attention in recent years, with the welding of field observation and theoretical concepts. Most recent advances have come from the Basin and Range Province of the southwestern United States and from the North Sea. Application of these geometric and isostatic concepts, in combination with seismic interpretation, to the southern Gulf of Suez, an active extensional orogen, allows generation of detailed structural maps and geometrically balanced sections which suggest a regional structural model. Geometric models which should prove to be a valuable adjunct to numerical and thermal models for the rifting process are discussed.

Higher-order gravity in higher dimensions: geometrical origins of four-dimensional cosmology?

NASA Astrophysics Data System (ADS)

Troisi, Antonio

2017-03-01

Determining the cosmological field equations is still very much debated and led to a wide discussion around different theoretical proposals. A suitable conceptual scheme could be represented by gravity models that naturally generalize Einstein theory like higher-order gravity theories and higher-dimensional ones. Both of these two different approaches allow one to define, at the effective level, Einstein field equations equipped with source-like energy-momentum tensors of geometrical origin. In this paper, the possibility is discussed to develop a five-dimensional fourth-order gravity model whose lower-dimensional reduction could provide an interpretation of cosmological four-dimensional matter-energy components. We describe the basic concepts of the model, the complete field equations formalism and the 5-D to 4-D reduction procedure. Five-dimensional f( R) field equations turn out to be equivalent, on the four-dimensional hypersurfaces orthogonal to the extra coordinate, to an Einstein-like cosmological model with three matter-energy tensors related with higher derivative and higher-dimensional counter-terms. By considering the gravity model with f(R)=f_0R^n the possibility is investigated to obtain five-dimensional power law solutions. The effective four-dimensional picture and the behaviour of the geometrically induced sources are finally outlined in correspondence to simple cases of such higher-dimensional solutions.

Nonlocal transformation optics.

PubMed

Castaldi, Giuseppe; Galdi, Vincenzo; Alù, Andrea; Engheta, Nader

2012-02-10

We show that the powerful framework of transformation optics may be exploited for engineering the nonlocal response of artificial electromagnetic materials. Relying on the form-invariant properties of coordinate-transformed Maxwell's equations in the spectral domain, we derive the general constitutive "blueprints" of transformation media yielding prescribed nonlocal field-manipulation effects and provide a physically incisive and powerful geometrical interpretation in terms of deformation of the equifrequency contours. In order to illustrate the potentials of our approach, we present an example of application to a wave-splitting refraction scenario, which may be implemented via a simple class of artificial materials. Our results provide a systematic and versatile framework which may open intriguing venues in dispersion engineering of artificial materials.

Expected Utility Illustrated: A Graphical Analysis of Gambles with More than Two Possible Outcomes

ERIC Educational Resources Information Center

Chen, Frederick H.

2010-01-01

The author presents a simple geometric method to graphically illustrate the expected utility from a gamble with more than two possible outcomes. This geometric result gives economics students a simple visual aid for studying expected utility theory and enables them to analyze a richer set of decision problems under uncertainty compared to what…

A Simple Geometric Method of Estimating the Error in Using Vieta's Product for [pi

ERIC Educational Resources Information Center

Osler, T. J.

2007-01-01

Vieta's famous product using factors that are nested radicals is the oldest infinite product as well as the first non-iterative method for finding [pi]. In this paper a simple geometric construction intimately related to this product is described. The construction provides the same approximations to [pi] as are given by partial products from…

Relation between the chord length distribution of an infinitely long cylinder and that of its base

NASA Astrophysics Data System (ADS)

Sukiasian, H. S.; Gille, Wilfried

2007-05-01

Chord length distributions are defined for planar and spatial geometric figures. There exist connections between the planar and the spatial cases: The chord length distribution densities (CLDs) of a cylinder B and its base S (the cylinder's orthogonal cross section) are interrelated by a simple, surveyable integral transformation. From this transformation, it was concluded that the odd moments of the CLD f(x ) of S define the leading asymptotic terms of the CLD Aμ(r) of B. The power series of Aμ(r) at r =0 can be traced back to the derivatives of f(x ) in the origin. As a general conclusion, there exist different geometric bodies B in R3 with the same CLD Aμ(r). An exact recognition of B via its CLD is not possible. CLDs do not characterize spatial sets. This result is of importance in materials science in order to avoid wrong interpretations in structure research. The new CLD integral transformation has been illustrated in connection with the transitions triangle→triangular rod and rectangle→rectangular rod.

Non-compact Groups, Coherent States, Relativistic Wave Equations and the Harmonic Oscillator II: Physical and Geometrical Considerations

NASA Astrophysics Data System (ADS)

Cirilo-Lombardo, Diego Julio

2009-04-01

The physical meaning of the particularly simple non-degenerate supermetric, introduced in the previous part by the authors, is elucidated and the possible connection with processes of topological origin in high energy physics is analyzed and discussed. New possible mechanism of the localization of the fields in a particular sector of the supermanifold is proposed and the similarity and differences with a 5-dimensional warped model are shown. The relation with gauge theories of supergravity based in the OSP(1/4) group is explicitly given and the possible original action is presented. We also show that in this non-degenerate super-model the physic states, in contrast with the basic states, are observables and can be interpreted as tomographic projections or generalized representations of operators belonging to the metaplectic group Mp(2). The advantage of geometrical formulations based on non-degenerate super-manifolds over degenerate ones is pointed out and the description and the analysis of some interesting aspects of the simplest Riemannian superspaces are presented from the point of view of the possible vacuum solutions.

A Simple Pythagorean Interpretation of E2 = p2 c2 + (mc2)2

NASA Astrophysics Data System (ADS)

Tobar, J. A.; Guillen, C. I.; Vargas, E. L.; Andrianarijaona, V. M.

2015-04-01

We are considering the relationship between the relativistic energy, the momentum, and the rest energy, E2 =p2c2 + (mc2)2 , and using geometrical means to analyze each individual portion in a spatial setting. The aforementioned equation suggests that pc and mc2 could be thought of as the two axis of a plane. According to de Broglie's hypothesis λ = h / p therefore suggesting that the pc-axis is connected to the wave properties of a moving object, and subsequently, the mc2-axis is connected to the particle properties such as its moment of inertia. Consequently, these two axes could represent the particle (matter) and wave properties of the moving object. An overview of possible models and meaningful interpretations, which agree with Dirac's prediction of the electron's magnetic moment, will be presented. Authors wish to give special thanks to Pacific Union College Student Senate in Angwin, California, for their financial support.

Isotope effects in aqueous solvation of simple halides

NASA Astrophysics Data System (ADS)

Videla, Pablo E.; Rossky, Peter J.; Laria, D.

2018-03-01

We present a path-integral-molecular-dynamics study of the thermodynamic stabilities of DOH⋯ X- and HOD⋯ X- (X = F, Cl, Br, I) coordination in aqueous solutions at ambient conditions. In agreement with experimental evidence, our results for the F- case reveal a clear stabilization of the latter motif, whereas, in the rest of the halogen series, the former articulation prevails. The DOH⋯ X- preference becomes more marked the larger the size of the ionic solute. A physical interpretation of these tendencies is provided in terms of an analysis of the global quantum kinetic energies of the light atoms and their geometrical decomposition. The stabilization of the alternative ionic coordination geometries is the result of a delicate balance arising from quantum spatial dispersions along parallel and perpendicular directions with respect to the relevant O-H⋯X- axis, as the strength of the water-halide H-bond varies. This interpretation is corroborated by a complementary analysis performed on the different spectroscopic signals of the corresponding IR spectra.

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

NASA Astrophysics Data System (ADS)

Tavernelli, Ivano

2018-06-01

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

The Geometry of Resonant Signatures in Debris Disks with Planets

NASA Astrophysics Data System (ADS)

Kuchner, M. J.; Holman, M. J.

2002-09-01

Using simple geometrical arguments, we paint an overview of the variety of resonant structures a single planet with moderate eccentricity (e < 0.6) can create in a dynamically cold, optically thin dust disk. This overview may serve as a key for interpreting images of perturbed debris disks and inferring the dynamical properties of the planets responsible for the perturbations. We compare the resonant structures found in the solar system with observations of planetary systems around Vega and other stars and we offer a new model for the asymmetries in the Epsilon Eridani disk. This work was performed in part under contract with the Jet Propulsion Laboratory (JPL) through the Michelson Fellowship program funded by NASA as an element of the Planet Finder Program.

Reading Angles in Maps

ERIC Educational Resources Information Center

Izard, Véronique; O'Donnell, Evan; Spelke, Elizabeth S.

2014-01-01

Preschool children can navigate by simple geometric maps of the environment, but the nature of the geometric relations they use in map reading remains unclear. Here, children were tested specifically on their sensitivity to angle. Forty-eight children (age 47:15-53:30 months) were presented with fragments of geometric maps, in which angle sections…

A Wave-Optics Approach to Paraxial Geometrical Laws Based on Continuity at Boundaries

ERIC Educational Resources Information Center

Linares, J.; Nistal, M. C.

2011-01-01

We present a derivation of the paraxial geometrical laws starting from a wave-optics approach, in particular by using simple continuity conditions of paraxial spherical waves at boundaries (discontinuities) between optical media. Paraxial geometrical imaging and magnification laws, under refraction and reflection at boundaries, are derived for…

Nonadiabatic conditional geometric phase shift with NMR.

PubMed

Xiang-Bin, W; Keiji, M

2001-08-27

A conditional geometric phase shift gate, which is fault tolerant to certain types of errors due to its geometric nature, was realized recently via nuclear magnetic resonance (NMR) under adiabatic conditions. However, in quantum computation, everything must be completed within the decoherence time. The adiabatic condition makes any fast conditional Berry phase (cyclic adiabatic geometric phase) shift gate impossible. Here we show that by using a newly designed sequence of simple operations with an additional vertical magnetic field, the conditional geometric phase shift gate can be run nonadiabatically. Therefore geometric quantum computation can be done at the same rate as usual quantum computation.

Multiphase flow in geometrically simple fracture intersections

USGS Publications Warehouse

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.

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

NASA Astrophysics Data System (ADS)

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

2016-09-01

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

Approximate method for calculating convective heat flux on the surface of bodies of simple geometric shapes

NASA Astrophysics Data System (ADS)

Kuzenov, V. V.; Ryzhkov, S. V.

2017-02-01

The paper formulated engineering and physical mathematical model for aerothermodynamics hypersonic flight vehicle (HFV) in laminar and turbulent boundary layers (model designed for an approximate estimate of the convective heat flow in the range of speeds M = 6-28, and height H = 20-80 km). 2D versions of calculations of convective heat flows for bodies of simple geometric forms (individual elements of the design HFV) are presented.

Differential Kinematics Of Contemporary Industrial Robots

NASA Astrophysics Data System (ADS)

Szkodny, T.

2014-08-01

The paper presents a simple method of avoiding singular configurations of contemporary industrial robot manipulators of such renowned companies as ABB, Fanuc, Mitsubishi, Adept, Kawasaki, COMAU and KUKA. To determine the singular configurations of these manipulators a global form of description of the end-effector kinematics was prepared, relative to the other links. On the basis of this description , the formula for the Jacobian was defined in the end-effector coordinates. Next, a closed form of the determinant of the Jacobian was derived. From the formula, singular configurations, where the determinant's value equals zero, were determined. Additionally, geometric interpretations of these configurations were given and they were illustrated. For the exemplary manipulator, small corrections of joint variables preventing the reduction of the Jacobian order were suggested. An analysis of positional errors, caused by these corrections, was presented

Shocks and finite-time singularities in Hele-Shaw flow

DOE Office of Scientific and Technical Information (OSTI.GOV)

Teodorescu, Razvan; Wiegmann, P; Lee, S-y

Hele-Shaw flow at vanishing surface tension is ill-defined. In finite time, the flow develops cusplike singularities. We show that the ill-defined problem admits a weak dispersive solution when singularities give rise to a graph of shock waves propagating in the viscous fluid. The graph of shocks grows and branches. Velocity and pressure jump across the shock. We formulate a few simple physical principles which single out the dispersive solution and interpret shocks as lines of decompressed fluid. We also formulate the dispersive solution in algebro-geometrical terms as an evolution of Krichever-Boutroux complex curve. We study in details the most genericmore » (2,3) cusp singularity which gives rise to an elementary branching event. This solution is self-similar and expressed in terms of elliptic functions.« less

Covariant Derivatives and the Renormalization Group Equation

NASA Astrophysics Data System (ADS)

Dolan, Brian P.

The renormalization group equation for N-point correlation functions can be interpreted in a geometrical manner as an equation for Lie transport of amplitudes in the space of couplings. The vector field generating the diffeomorphism has components given by the β functions of the theory. It is argued that this simple picture requires modification whenever any one of the points at which the amplitude is evaluated becomes close to any other. This modification necessitates the introduction of a connection on the space of couplings and new terms appear in the renormalization group equation involving covariant derivatives of the β function and the curvature associated with the connection. It is shown how the connection is related to the operator product expansion coefficients, but there remains an arbitrariness in its definition.

MM Algorithms for Geometric and Signomial Programming

PubMed Central

Lange, Kenneth; Zhou, Hua

2013-01-01

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. PMID:24634545

MM Algorithms for Geometric and Signomial Programming.

PubMed

Lange, Kenneth; Zhou, Hua

2014-02-01

This paper derives new algorithms for signomial programming, a generalization of geometric programming. The algorithms are based on a generic principle for optimization called the MM algorithm. In this setting, one can apply the geometric-arithmetic mean inequality and a supporting hyperplane inequality to create a surrogate function with parameters separated. Thus, unconstrained signomial programming reduces to a sequence of one-dimensional minimization problems. Simple examples demonstrate that the MM algorithm derived can converge to a boundary point or to one point of a continuum of minimum points. Conditions under which the minimum point is unique or occurs in the interior of parameter space are proved for geometric programming. Convergence to an interior point occurs at a linear rate. Finally, the MM framework easily accommodates equality and inequality constraints of signomial type. For the most important special case, constrained quadratic programming, the MM algorithm involves very simple updates.

The Substantivalist View of Spacetime Proposed by Minkowski and Its Educational Implications.

ERIC Educational Resources Information Center

Levrini, Olivia

2002-01-01

Explains that the geometrical interpretation of general relativity provides the formalism with intuitive imagery and an interpretation often presupposes a substantival space. Special relativity can also be interpreted substantivally, which is the key to laying out an internally coherent substantivalist line running from Newtonian mechanics to…

Beyond the Golden Ratio: A Calculator-Based Investigation.

ERIC Educational Resources Information Center

Glidden, Peter L.

2001-01-01

Describes computation of a continued radical to approximate the golden ratio and presents two well-known geometric interpretations of it. Uses guided-discovery to investigate different repeated radicals to see what values they approximate, the golden-rectangle interpretation of these continued radicals, and the golden-section interpretation. (KHR)

A geometric approach to failure detection and identification in linear systems

NASA Technical Reports Server (NTRS)

Massoumnia, M. A.

1986-01-01

Using concepts of (C,A)-invariant and unobservability (complementary observability) subspaces, a geometric formulation of the failure detection and identification filter problem is stated. Using these geometric concepts, it is shown that it is possible to design a causal linear time-invariant processor that can be used to detect and uniquely identify a component failure in a linear time-invariant system, assuming: (1) The components can fail simultaneously, and (2) The components can fail only one at a time. In addition, a geometric formulation of Beard's failure detection filter problem is stated. This new formulation completely clarifies of output separability and mutual detectability introduced by Beard and also exploits the dual relationship between a restricted version of the failure detection and identification problem and the control decoupling problem. Moreover, the frequency domain interpretation of the results is used to relate the concepts of failure sensitive observers with the generalized parity relations introduced by Chow. This interpretation unifies the various failure detection and identification concepts and design procedures.

Geometric figure–ground cues override standard depth from accretion-deletion

PubMed Central

Tanrıkulu, Ömer Dağlar; Froyen, Vicky; Feldman, Jacob; Singh, Manish

2016-01-01

Accretion-deletion is widely considered a decisive cue to surface depth ordering, with the accreting or deleting surface interpreted as behind an adjoining surface. However, Froyen, Feldman, and Singh (2013) have shown that when accretion-deletion occurs on both sides of a contour, accreting-deleting regions can also be perceived as in front and as self-occluding due to rotation in three dimensions. In this study we ask whether geometric figure–ground cues can override the traditional “depth from accretion-deletion” interpretation even when accretion-deletion takes place only on one side of a contour. We used two tasks: a relative-depth task (front/back), and a motion-classification task (translation/rotation). We conducted two experiments, in which texture in only one set of alternating regions was moving; the other set was static. Contrary to the traditional interpretation of accretion-deletion, the moving convex and symmetric regions were perceived as figural and rotating in three dimensions in roughly half of the trials. In the second experiment, giving different motion directions to the moving regions (thereby weakening motion-based grouping) further weakened the traditional accretion-deletion interpretation. Our results show that the standard “depth from accretion-deletion” interpretation is overridden by static geometric cues to figure–ground. Overall, the results demonstrate a rich interaction between accretion-deletion, figure–ground, and structure from motion that is not captured by existing models of depth from motion. PMID:26982528

Cardiac risk index as a simple geometric indicator to select patients for the heart-sparing radiotherapy of left-sided breast cancer.

PubMed

Sung, KiHoon; Choi, Young Eun; Lee, Kyu Chan

2017-06-01

This is a dosimetric study to identify a simple geometric indicator to discriminate patients who meet the selection criterion for heart-sparing radiotherapy (RT). The authors proposed a cardiac risk index (CRI), directly measurable from the CT images at the time of scanning. Treatment plans were regenerated using the CT data of 312 consecutive patients with left-sided breast cancer. Dosimetric analysis was performed to estimate the risk of cardiac mortality using cardiac dosimetric parameters, such as the relative heart volumes receiving ≥25 Gy (heart V 25 ). For each CT data set, in-field heart depth (HD) and in-field heart width (HW) were measured to generate the geometric parameters, including maximum HW (HW max ) and maximum HD (HD max ). Seven geometric parameters were evaluated as candidates for CRI. Receiver operating characteristic (ROC) curve analyses were used to examine the overall discriminatory power of the geometric parameters to select high-risk patients (heart V 25  ≥ 10%). Seventy-one high-risk (22.8%) and 241 low-risk patients (77.2%) were identified by dosimetric analysis. The geometric and dosimetric parameters were significantly higher in the high-risk group. Heart V 25 showed the strong positive correlations with all geometric parameters examined (r > 0.8, p < 0.001). The product of HD max and HW max (CRI) revealed the largest area under the curve (AUC) value (0.969) and maintained 100% sensitivity and 88% specificity at the optimal cut-off value of 14.58 cm 2 . Cardiac risk index proposed as a simple geometric indicator to select high-risk patients provides useful guidance for clinicians considering optimal implementation of heart-sparing RT. © 2016 The Royal Australian and New Zealand College of Radiologists.

Steering Bell-diagonal states

PubMed Central

Quan, Quan; Zhu, Huangjun; Liu, Si-Yuan; Fei, Shao-Ming; Fan, Heng; Yang, Wen-Li

2016-01-01

We investigate the steerability of two-qubit Bell-diagonal states under projective measurements by the steering party. In the simplest nontrivial scenario of two projective measurements, we solve this problem completely by virtue of the connection between the steering problem and the joint-measurement problem. A necessary and sufficient criterion is derived together with a simple geometrical interpretation. Our study shows that a Bell-diagonal state is steerable by two projective measurements iff it violates the Clauser-Horne-Shimony-Holt (CHSH) inequality, in sharp contrast with the strict hierarchy expected between steering and Bell nonlocality. We also introduce a steering measure and clarify its connections with concurrence and the volume of the steering ellipsoid. In particular, we determine the maximal concurrence and ellipsoid volume of Bell-diagonal states that are not steerable by two projective measurements. Finally, we explore the steerability of Bell-diagonal states under three projective measurements. A simple sufficient criterion is derived, which can detect the steerability of many states that are not steerable by two projective measurements. Our study offers valuable insight on steering of Bell-diagonal states as well as the connections between entanglement, steering, and Bell nonlocality. PMID:26911250

Geometric interpretations for resonances of plasmonic nanoparticles

NASA Astrophysics Data System (ADS)

Liu, Wei; Oulton, Rupert F.; Kivshar, Yuri S.

2015-07-01

The field of plasmonics can be roughly categorized into two branches: surface plasmon polaritons (SPPs) propagating in waveguides and localized surface plasmons (LSPs) supported by scattering particles. Investigations along these two directions usually employ different approaches, resulting in more or less a dogma that the two branches progress almost independently of each other, with few interactions. Here in this work we interpret LSPs from a Bohr model based geometric perspective relying on SPPs, thus establishing a connection between these two sub-fields. Besides the clear explanations of conventional scattering features of plasmonic nanoparticles, based on this geometric model we further demonstrate other anomalous scattering features (higher order modes supported at lower frequencies, and blueshift of the resonance with increasing particle sizes) and multiple electric resonances of the same order supported at different frequencies, which have been revealed to originate from backward SPP modes and multiple dispersion bands supported in the corresponding plasmonic waveguides, respectively. Inspired by this geometric model, it is also shown that, through solely geometric tuning, the absorption of each LSP resonance can be maximized to reach the single channel absorption limit, provided that the scattering and absorption rates are tuned to be equal.

3-D model-based Bayesian classification

DOE Office of Scientific and Technical Information (OSTI.GOV)

Soenneland, L.; Tenneboe, P.; Gehrmann, T.

1994-12-31

The challenging task of the interpreter is to integrate different pieces of information and combine them into an earth model. The sophistication level of this earth model might vary from the simplest geometrical description to the most complex set of reservoir parameters related to the geometrical description. Obviously the sophistication level also depend on the completeness of the available information. The authors describe the interpreter`s task as a mapping between the observation space and the model space. The information available to the interpreter exists in observation space and the task is to infer a model in model-space. It is well-knownmore » that this inversion problem is non-unique. Therefore any attempt to find a solution depend son constraints being added in some manner. The solution will obviously depend on which constraints are introduced and it would be desirable to allow the interpreter to modify the constraints in a problem-dependent manner. They will present a probabilistic framework that gives the interpreter the tools to integrate the different types of information and produce constrained solutions. The constraints can be adapted to the problem at hand.« less

Geometry and Formal Linguistics.

ERIC Educational Resources Information Center

Huff, George A.

This paper presents a method of encoding geometric line-drawings in a way which allows sets of such drawings to be interpreted as formal languages. A characterization of certain geometric predicates in terms of their properties as languages is obtained, and techniques usually associated with generative grammars and formal automata are then applied…

Geometric Representations for Discrete Fourier Transforms

NASA Technical Reports Server (NTRS)

Cambell, C. W.

1986-01-01

Simple geometric representations show symmetry and periodicity of discrete Fourier transforms (DFT's). Help in visualizing requirements for storing and manipulating transform value in computations. Representations useful in any number of dimensions, but particularly in one-, two-, and three-dimensional cases often encountered in practice.

Oceanic ridges and transform faults: Their intersection angles and resistance to plate motion

USGS Publications Warehouse

Lachenbruch, A.H.; Thompson, G.A.

1972-01-01

The persistent near-orthogonal pattern formed by oceanic ridges and transform faults defies explanation in terms of rigid plates because it probably depends on the energy associated with deformation. For passive spreading, it is likely that the ridges and transforms adjust to a configuration offering minimum resistance to plate separation. This leads to a simple geometric model which yields conditions for the occurrence of transform faults and an aid to interpretation of structural patterns in the sea floor. Under reasonable assumptions, it is much more difficult for diverging plates to spread a kilometer of ridge than to slip a kilometer of transform fault, and the patterns observed at spreading centers might extend to lithospheric depths. Under these conditions, the resisting force at spreading centers could play a significant role in the dynamics of plate-tectonic systems. ?? 1972.

Salt-induced aggregation and fusion of dioctadecyldimethylammonium chloride and sodium dihexadecylphosphate vesicles.

PubMed Central

Carmona-Ribeiro, A M; Chaimovich, H

1986-01-01

Small dioctadecyldimethylammonium chloride (DODAC) vesicles prepared by sonication fuse upon addition of NaCl as detected by several methods (electron microscopy, trapped volume determinations, temperature-dependent phase transition curves, and osmometer behavior. In contrast, small sodium dihexadecyl phosphate (DHP) vesicles mainly aggregate upon NaCl addition as shown by electron microscopy and the lack of osmometer behavior. Scatter-derived absorbance changes of small and large DODAC or DHP vesicles as a function of time after salt addition were obtained for a range of NaCl or amphiphile concentration. These changes were interpreted in accordance with a phenomenological model based upon fundamental light-scattering laws and simple geometrical considerations. Short-range hydration repulsion between DODAC (or DHP) vesicles is possibly the main energy barrier for the fusion process. Images FIGURE 2 FIGURE 9 PMID:3779002

A sophisticated cad tool for the creation of complex models for electromagnetic interaction analysis

NASA Astrophysics Data System (ADS)

Dion, Marc; Kashyap, Satish; Louie, Aloisius

1991-06-01

This report describes the essential features of the MS-DOS version of DIDEC-DREO, an interactive program for creating wire grid, surface patch, and cell models of complex structures for electromagnetic interaction analysis. It uses the device-independent graphics library DIGRAF and the graphics kernel system HALO, and can be executed on systems with various graphics devices. Complicated structures can be created by direct alphanumeric keyboard entry, digitization of blueprints, conversion form existing geometric structure files, and merging of simple geometric shapes. A completed DIDEC geometric file may then be converted to the format required for input to a variety of time domain and frequency domain electromagnetic interaction codes. This report gives a detailed description of the program DIDEC-DREO, its installation, and its theoretical background. Each available interactive command is described. The associated program HEDRON which generates simple geometric shapes, and other programs that extract the current amplitude data from electromagnetic interaction code outputs, are also discussed.

A Practical Guide to Experimental Geometrical Optics

NASA Astrophysics Data System (ADS)

Garbovskiy, Yuriy A.; Glushchenko, Anatoliy V.

2017-12-01

Preface; 1. Markets of optical materials, components, accessories, light sources and detectors; 2. Introduction to optical experiments: light producing, light managing, light detection and measuring; 3. Light detectors based on semiconductors: photoresistors, photodiodes in a photo-galvanic regime. Principles of operation and measurements; 4. Linear light detectors based on photodiodes; 5. Basic laws of geometrical optics: experimental verification; 6. Converging and diverging thin lenses; 7. Thick lenses; 8. Lens systems; 9. Simple optical instruments I: the eye and the magnifier, eyepieces and telescopes; 10. Simple optical instruments II: light illuminators and microscope; 11. Spherical mirrors; 12. Introduction to optical aberrations; 13. Elements of optical radiometry; 14. Cylindrical lenses and vials; 15. Methods of geometrical optics to measure refractive index; 16. Dispersion of light and prism spectroscope; 17. Elements of computer aided optical design; Index.

Simple geometric algorithms to aid in clearance management for robotic mechanisms

NASA Technical Reports Server (NTRS)

Copeland, E. L.; Ray, L. D.; Peticolas, J. D.

1981-01-01

Global geometric shapes such as lines, planes, circles, spheres, cylinders, and the associated computational algorithms which provide relatively inexpensive estimates of minimum spatial clearance for safe operations were selected. The Space Shuttle, remote manipulator system, and the Power Extension Package are used as an example. Robotic mechanisms operate in quarters limited by external structures and the problem of clearance is often of considerable interest. Safe clearance management is simple and suited to real time calculation, whereas contact prediction requires more precision, sophistication, and computational overhead.

Two-Year-Old Children Interpret Abstract, Purely Geometric Maps

ERIC Educational Resources Information Center

Winkler-Rhoades, Nathan; Carey, Susan C.; Spelke, Elizabeth S.

2013-01-01

In two experiments, 2.5-year-old children spontaneously used geometric information from 2D maps to locate objects in a 3D surface layout, without instruction or feedback. Children related maps to their corresponding layouts even though the maps differed from the layouts in size, mobility, orientation, dimensionality, and perspective, and even when…

Algebraic, geometric, and stochastic aspects of genetic operators

NASA Technical Reports Server (NTRS)

Foo, N. Y.; Bosworth, J. L.

1972-01-01

Genetic algorithms for function optimization employ genetic operators patterned after those observed in search strategies employed in natural adaptation. Two of these operators, crossover and inversion, are interpreted in terms of their algebraic and geometric properties. Stochastic models of the operators are developed which are employed in Monte Carlo simulations of their behavior.

La columna, el circulo y sus variantes en la poesia primera de Pedro Salinas (The Vertical Line, the Circle, and other Geometric Varieties in the Early Poetry of Pedro Salinas)

ERIC Educational Resources Information Center

De Armas, Jose R.

1970-01-01

Interprets Salinas' use of geometric figures for depicting concepts of time and infinity, and for portraying idealism and realism (the vertical line is idealism, perfection; the circle stands for reality and imperfection). (DS)

The geometric nature of weights in real complex networks

NASA Astrophysics Data System (ADS)

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

2017-01-01

The topology of many real complex networks has been conjectured to be embedded in hidden metric spaces, where distances between nodes encode their likelihood of being connected. Besides of providing a natural geometrical interpretation of their complex topologies, this hypothesis yields the recipe for sustainable Internet's routing protocols, sheds light on the hierarchical organization of biochemical pathways in cells, and allows for a rich characterization of the evolution of international trade. Here we present empirical evidence that this geometric interpretation also applies to the weighted organization of real complex networks. We introduce a very general and versatile model and use it to quantify the level of coupling between their topology, their weights and an underlying metric space. Our model accurately reproduces both their topology and their weights, and our results suggest that the formation of connections and the assignment of their magnitude are ruled by different processes.

Geometric Theory of Moving Grid Wavefront Sensor

DTIC Science & Technology

1977-06-30

Identify by block numbot) Adaptive Optics WaVefront Sensor Geometric Optics Analysis Moving Ronchi Grid "ABSTRACT (Continue an revere sdde If nooessaY...ad Identify by block nucber)A geometric optics analysis is made for a wavefront sensor that uses a moving Ronchi grid. It is shown that by simple data... optical systems being considered or being developed -3 for imaging an object through a turbulent atmosphere. Some of these use a wavefront sensor to

Improving Written Communication Through Perspective-taking

PubMed Central

Traxler, Matthew J.; Gernsbacher, Morton Ann

2014-01-01

To convey their ideas successfully, writers must envision how readers will interpret their texts. In our previous research (Traxler & Gernsbacher, 1992), we discovered that writers who received feedback from their readers successfully revised descriptions of geometric figures, whereas writers who did not receive feedback did not. We also discovered that writers who received feedback from their readers on one set of descriptions wrote better descriptions of a new set of geometric figures. We concluded that feedback—even a minimal form of feedback—helps writers learn to envision how readers will interpret their texts. In the present research, we investigated another way that writers can learn to envision how readers will interpret their texts. Our treatment placed writers “in their readers’ shoes”. In three experiments, half the writers performed a task that their readers would subsequently perform, and the other half of the writers performed a control task. In our first and second experiments, the writers who gained their readers’ perspective by performing their readers’ task successfully revised their descriptions of geometric figures, whereas writers who performed the control task did not. In our third experiment, we discovered that writers who performed their readers’ task did not improve their descriptions merely because they were exposed to examples of other writers’ descriptions. We concluded that gaining their readers’ perspective helps writers communicate more clearly because perspective-taking helps writers form a mental representation of how readers interpret their texts. PMID:25404785

Geometric Determinants of Human Spatial Memory

ERIC Educational Resources Information Center

Hartley, Tom; Trinkler, Iris; Burgess, Neil

2004-01-01

Geometric alterations to the boundaries of a virtual environment were used to investigate the representations underlying human spatial memory. Subjects encountered a cue object in a simple rectangular enclosure, with distant landmarks for orientation. After a brief delay, during which they were removed from the arena, subjects were returned to it…

Description and interpretation of the bracts epidermis of Gramineae (Poaceae) with rotated image with maximum average power spectrum (RIMAPS) technique.

PubMed

Favret, Eduardo A; Fuentes, Néstor O; Molina, Ana M; Setten, Lorena M

2008-10-01

During the last few years, RIMAPS technique has been used to characterize the micro-relief of metallic surfaces and recently also applied to biological surfaces. RIMAPS is an image analysis technique which uses the rotation of an image and calculates its average power spectrum. Here, it is presented as a tool for describing the morphology of the trichodium net found in some grasses, which is developed on the epidermal cells of the lemma. Three different species of grasses (herbarium samples) are analyzed: Podagrostis aequivalvis (Trin.) Scribn. & Merr., Bromidium hygrometricum (Nees) Nees & Meyen and Bromidium ramboi (Parodi) Rúgolo. Simple schemes representing the real microstructure of the lemma are proposed and studied. RIMAPS spectra of both the schemes and the real microstructures are compared. These results allow inferring how similar the proposed geometrical schemes are to the real microstructures. Each geometrical pattern could be used as a reference for classifying other species. Finally, this kind of analysis is used to determine the morphology of the trichodium net of Agrostis breviculmis Hitchc. As the dried sample had shrunk and the microstructure was not clear, two kinds of morphology are proposed for the trichodium net of Agrostis L., one elliptical and the other rectilinear, the former being the most suitable.

Portable design rules for bulk CMOS

NASA Technical Reports Server (NTRS)

Griswold, T. W.

1982-01-01

It is pointed out that for the past several years, one school of IC designers has used a simplified set of nMOS geometric design rules (GDR) which is 'portable', in that it can be used by many different nMOS manufacturers. The present investigation is concerned with a preliminary set of design rules for bulk CMOS which has been verified for simple test structures. The GDR are defined in terms of Caltech Intermediate Form (CIF), which is a geometry-description language that defines simple geometrical objects in layers. The layers are abstractions of physical mask layers. The design rules do not presume the existence of any particular design methodology. Attention is given to p-well and n-well CMOS processes, bulk CMOS and CMOS-SOS, CMOS geometric rules, and a description of the advantages of CMOS technology.

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

PubMed

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

2013-11-04

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

PSO (Particle Swarm Optimization) for Interpretation of Magnetic Anomalies Caused by Simple Geometrical Structures

NASA Astrophysics Data System (ADS)

Essa, Khalid S.; Elhussein, Mahmoud

2018-04-01

A new efficient approach to estimate parameters that controlled the source dimensions from magnetic anomaly profile data in light of PSO algorithm (particle swarm optimization) has been presented. The PSO algorithm has been connected in interpreting the magnetic anomaly profiles data onto a new formula for isolated sources embedded in the subsurface. The model parameters deciphered here are the depth of the body, the amplitude coefficient, the angle of effective magnetization, the shape factor and the horizontal coordinates of the source. The model parameters evaluated by the present technique, generally the depth of the covered structures were observed to be in astounding concurrence with the real parameters. The root mean square (RMS) error is considered as a criterion in estimating the misfit between the observed and computed anomalies. Inversion of noise-free synthetic data, noisy synthetic data which contains different levels of random noise (5, 10, 15 and 20%) as well as multiple structures and in additional two real-field data from USA and Egypt exhibits the viability of the approach. Thus, the final results of the different parameters are matched with those given in the published literature and from geologic results.

Geometry of the Adiabatic Theorem

ERIC Educational Resources Information Center

Lobo, Augusto Cesar; Ribeiro, Rafael Antunes; Ribeiro, Clyffe de Assis; Dieguez, Pedro Ruas

2012-01-01

We present a simple and pedagogical derivation of the quantum adiabatic theorem for two-level systems (a single qubit) based on geometrical structures of quantum mechanics developed by Anandan and Aharonov, among others. We have chosen to use only the minimum geometric structure needed for the understanding of the adiabatic theorem for this case.…

A simple HPLC method for the comprehensive analysis of cis/trans (Z/E) geometrical isomers of carotenoids for nutritional studies

USDA-ARS?s Scientific Manuscript database

Geometrical isomers of carotenoids behave differently in aspects like stability towards oxidants, bioavailability, vitamin A activity and specificity for enzymes. The availability of HPLC methods for their detailed profiling is therefore advisable to expand our knowledge on their metabolism and biol...

Student's Concept of Infinity in the Context of a Simple Geometrical Construct

ERIC Educational Resources Information Center

Jirotkova, Darina; Littler, Graham

2003-01-01

The research described in this paper was undertaken to determine student-teachers' understanding of infinity in a geometrical context. The methods of analysis of students' responses is presented and these were found to be universally applicable. The findings show that school mathematics does not generally develop the students' ideas of infinity…

Model interpretation of type III radio burst characteristics. I - Spatial aspects

NASA Technical Reports Server (NTRS)

Reiner, M. J.; Stone, R. G.

1988-01-01

The ways that the finite size of the source region and directivity of the emitted radiation modify the observed characteristics of type III radio bursts as they propagate through the interplanetary medium are investigated. A simple model that simulates the radio source region is developed to provide insight into the spatial behavior of the parameters that characterize radio bursts. The model is used to demonstrate that observed radio azimuths are systematically displaced from the geometric centroid of the exciter electron beam in such a way as to cause trajectories of the radio bursts to track back to the observer at low frequencies, rather than to follow expected Archimedean spiral-like paths. The source region model is used to investigate the spatial behavior of the peak intensities of radio bursts, and it is found that the model can qualitatively account for both the frequency dependence and the east-west asymmetry of the observed peak flux densities.

String Theory: exact solutions, marginal deformations and hyperbolic spaces

NASA Astrophysics Data System (ADS)

Orlando, Domenico

2006-10-01

This thesis is almost entirely devoted to studying string theory backgrounds characterized by simple geometrical and integrability properties. The archetype of this type of system is given by Wess-Zumino-Witten models, describing string propagation in a group manifold or, equivalently, a class of conformal field theories with current algebras. We study the moduli space of such models by using truly marginal deformations. Particular emphasis is placed on asymmetric deformations that, together with the CFT description, enjoy a very nice spacetime interpretation in terms of the underlying Lie algebra. Then we take a slight detour so to deal with off-shell systems. Using a renormalization-group approach we describe the relaxation towards the symmetrical equilibrium situation. In he final chapter we consider backgrounds with Ramond-Ramond field and in particular we analyze direct products of constant-curvature spaces and find solutions with hyperbolic spaces.

Taming the nonlinearity of the Einstein equation.

PubMed

Harte, Abraham I

2014-12-31

Many of the technical complications associated with the general theory of relativity ultimately stem from the nonlinearity of Einstein's equation. It is shown here that an appropriate choice of dynamical variables may be used to eliminate all such nonlinearities beyond a particular order: Both Landau-Lifshitz and tetrad formulations of Einstein's equation are obtained that involve only finite products of the unknowns and their derivatives. Considerable additional simplifications arise in physically interesting cases where metrics become approximately Kerr or, e.g., plane waves, suggesting that the variables described here can be used to efficiently reformulate perturbation theory in a variety of contexts. In all cases, these variables are shown to have simple geometrical interpretations that directly relate the local causal structure associated with the metric of interest to the causal structure associated with a prescribed background. A new method to search for exact solutions is outlined as well.

A simple solar radiation index for wildlife habitat studies

USGS Publications Warehouse

Keating, Kim A.; Gogan, Peter J.; Vore, John N.; Irby, Lynn R.

2007-01-01

Solar radiation is a potentially important covariate in many wildlife habitat studies, but it is typically addressed only indirectly, using problematic surrogates like aspect or hillshade. We devised a simple solar radiation index (SRI) that combines readily available information about aspect, slope, and latitude. Our SRI is proportional to the amount of extraterrestrial solar radiation theoretically striking an arbitrarily oriented surface during the hour surrounding solar noon on the equinox. Because it derives from first geometric principles and is linearly distributed, SRI offers clear advantages over aspect-based surrogates. The SRI also is superior to hillshade, which we found to be sometimes imprecise and ill-behaved. To illustrate application of our SRI, we assessed niche separation among 3 ungulate species along a single environmental axis, solar radiation, on the northern Yellowstone winter range. We detected no difference between the niches occupied by bighorn sheep (Ovis canadensis) and elk (Cervus elaphus; P = 0.104), but found that mule deer (Odocoileus hemionus) tended to use areas receiving more solar radiation than either of the other species (P < 0.001). Overall, our SRI provides a useful metric that can reduce noise, improve interpretability, and increase parsimony in wildlife habitat models containing a solar radiation component.

A new geometric invariant on initial data for the Einstein equations.

PubMed

Dain, Sergio

2004-12-03

For a given asymptotically flat initial data set for Einstein equations a new geometric invariant is constructed. This invariant measures the departure of the data set from the stationary regime; it vanishes if and only if the data are stationary. In vacuum, it can be interpreted as a measure of the total amount of radiation contained in the data.

Three dimensional inversion of magnetic survey data collected over kimberlite pipes in presence of remanent magnetization

NASA Astrophysics Data System (ADS)

Zhao, Pengzhi

Magnetic method is a common geophysical technique used to explore kimberlites. The analysis and interpretation of measured magnetic data provides the information of magnetic and geometric properties of potential kimberlite pipes. A crucial parameter of kimberlite magnetic interpretation is the remanent magnetization that dominates the classification of kimberlite. However, the measured magnetic data is the total field affected by the remanent magnetization and the susceptibility. The presence of remanent magnetization can pose severe challenges to the quantitative interpretation of magnetic data by skewing or laterally shifting magnetic anomalies relative to the subsurface source (Haney and Li, 2002). Therefore, identification of remanence effects and determination of remanent magnetization are important in magnetic data interpretation. This project presents a new method to determine the magnetic and geometric properties of kimberlite pipes in the presence of strong remanent magnetization. This method consists of two steps. The first step is to estimate the total magnetization and geometric properties of magnetic anomaly. The second step is to separate the remanent magnetization from the total magnetization. In the first step, a joint parametric inversion of total-field magnetic data and its analytic signal (derived from the survey data by Fourier transform method) is used. The algorithm of the joint inversion is based on the Gauss-Newton method and it is more stable and more accurate than the separate inversion method. It has been tested with synthetic data and applied to interpret the field data from the Lac de Gras, North-West Territories of Canada. The results of the synthetic examples and the field data applications show that joint inversion can recovers the total magnetization and geometric properties of magnetic anomaly with a good data fit and stable convergence. In the second step, the remanent magnetization is separated from the total magnetization by using a determined susceptibility. The susceptibility value is estimated by using the frequency domain electromagnetic data. The inversion method is achieved by a code, named “EM1DFM”, developed by University of British Columbia was designed to construct one of four types of 1D model, using any type of geophysical frequency domain loop-loop data with one of four variations of the inversion algorithm. The results show that the susceptibility of magnetic body is recovered, even if the depth and thickness are not well estimated. This two-step process provides a new way to determine magnetic and geometric properties of kimberlite pipes in the presence of strong remanent magnetization. The joint inversion of the total-field magnetic data and its analytic signal obtains the total magnetization and geometric properties. The frequency domain EM method provides the susceptibility. As a result, the remanent magnetization can be separated from the total magnetization accurately.

How Preservice Teachers Interpret and Respond to Student Geometric Errors

ERIC Educational Resources Information Center

Son, Ji-Won; Sinclair, Nathalie

2010-01-01

Recognizing and responding to students' thinking is essential in teaching mathematics, especially when students provide incorrect solutions. This study examined, through a teaching scenario task, elementary preservice teachers' interpretations of and responses to a student's work on a task involving reflective symmetry. Findings revealed that a…

Solving da Vinci stereopsis with depth-edge-selective V2 cells

PubMed Central

Assee, Andrew; Qian, Ning

2007-01-01

We propose a new model for da Vinci stereopsis based on a coarse-to-fine disparity-energy computation in V1 and disparity-boundary-selective units in V2. Unlike previous work, our model contains only binocular cells, relies on distributed representations of disparity, and has a simple V1-to-V2 feedforward structure. We demonstrate with random dot stereograms that the V2 stage of our model is able to determine the location and the eye-of-origin of monocularly occluded regions and improve disparity map computation. We also examine a few related issues. First, we argue that since monocular regions are binocularly defined, they cannot generally be detected by monocular cells. Second, we show that our coarse-to-fine V1 model for conventional stereopsis explains double matching in Panum’s limiting case. This provides computational support to the notion that the perceived depth of a monocular bar next to a binocular rectangle may not be da Vinci stereopsis per se (Gillam et al., 2003). Third, we demonstrate that some stimuli previously deemed invalid have simple, valid geometric interpretations. Our work suggests that studies of da Vinci stereopsis should focus on stimuli more general than the bar-and-rectangle type and that disparity-boundary-selective V2 cells may provide a simple physiological mechanism for da Vinci stereopsis. PMID:17698163

An information geometric approach to least squares minimization

NASA Astrophysics Data System (ADS)

Transtrum, Mark; Machta, Benjamin; Sethna, James

2009-03-01

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

Historical Buildings Models and Their Handling via 3d Survey: from Points Clouds to User-Oriented Hbim

NASA Astrophysics Data System (ADS)

Chiabrando, F.; Sammartano, G.; Spanò, A.

2016-06-01

This paper retraces some research activities and application of 3D survey techniques and Building Information Modelling (BIM) in the environment of Cultural Heritage. It describes the diffusion of as-built BIM approach in the last years in Heritage Assets management, the so-called Built Heritage Information Modelling/Management (BHIMM or HBIM), that is nowadays an important and sustainable perspective in documentation and administration of historic buildings and structures. The work focuses the documentation derived from 3D survey techniques that can be understood like a significant and unavoidable knowledge base for the BIM conception and modelling, in the perspective of a coherent and complete management and valorisation of CH. It deepens potentialities, offered by 3D integrated survey techniques, to acquire productively and quite easilymany 3D information, not only geometrical but also radiometric attributes, helping the recognition, interpretation and characterization of state of conservation and degradation of architectural elements. From these data, they provide more and more high descriptive models corresponding to the geometrical complexity of buildings or aggregates in the well-known 5D (3D + time and cost dimensions). Points clouds derived from 3D survey acquisition (aerial and terrestrial photogrammetry, LiDAR and their integration) are reality-based models that can be use in a semi-automatic way to manage, interpret, and moderately simplify geometrical shapes of historical buildings that are examples, as is well known, of non-regular and complex geometry, instead of modern constructions with simple and regular ones. In the paper, some of these issues are addressed and analyzed through some experiences regarding the creation and the managing of HBIMprojects on historical heritage at different scales, using different platforms and various workflow. The paper focuses on LiDAR data handling with the aim to manage and extract geometrical information; on development and optimization of semi-automatic process of segmentation, recognition and modelling of historical shapes of complex structures; on communication of historical heritage by virtual and augmented reality (VR/AR) in a 3D reconstruction of buildings aggregates from a LiDAR and UAV survey. The HBIM model have been implemented and optimized to be managed and browse by mobile devices for not only touristic or informative scopes, but also to ensure that HBIM platforms will become more easy and valuable tools helping all professionals of AEC involved in the documentation and valorisation process, that nowadays more and more distinguish CH policies.

The SPICE concept - An approach to providing geometric and other ancillary information needed for interpretation of data returned from space science instruments

NASA Technical Reports Server (NTRS)

Acton, Charles H., Jr.

1990-01-01

The Navigation Ancillary Information Facility (NAIF), acting under the direction of NASA's Office of Space Science and Applications, and with substantial participation of the planetary science community, is designing and implementing an ancillary data system - called SPICE - to assist scientists in planning and interpreting scientific observations taken from spaceborne instruments. The principal objective of the implemented SPICE system is that it will hold the essential geometric and related ancillary information needed to recover the full value of science instrument data, and that it will facilitate correlations of individual instrument datasets with data obtained from other instruments on the same or other spacecraft.

A gravitational energy–momentum and the thermodynamic description of gravity

NASA Astrophysics Data System (ADS)

Acquaviva, G.; Kofroň, D.; Scholtz, M.

2018-05-01

A proposal for the gravitational energy–momentum tensor, known in the literature as the square root of Bel–Robinson tensor (SQBR), is analyzed in detail. Being constructed exclusively from the Weyl part of the Riemann tensor, such tensor encapsulates the geometric properties of free gravitational fields in terms of optical scalars of null congruences: making use of the general decomposition of any energy–momentum tensor, we explore the thermodynamic interpretation of such geometric quantities. While the matter energy–momentum is identically conserved due to Einstein’s field equations, the SQBR is not necessarily conserved and dissipative terms could arise in its vacuum continuity equation. We discuss the possible physical interpretations of such mathematical properties.

3D tracking of laparoscopic instruments using statistical and geometric modeling.

PubMed

Wolf, Rémi; Duchateau, Josselin; Cinquin, Philippe; Voros, Sandrine

2011-01-01

During a laparoscopic surgery, the endoscope can be manipulated by an assistant or a robot. Several teams have worked on the tracking of surgical instruments, based on methods ranging from the development of specific devices to image processing methods. We propose to exploit the instruments' insertion points, which are fixed on the patients abdominal cavity, as a geometric constraint for the localization of the instruments. A simple geometric model of a laparoscopic instrument is described, as well as a parametrization that exploits a spherical geometric grid, which offers attracting homogeneity and isotropy properties. The general architecture of our proposed approach is based on the probabilistic Condensation algorithm.

Lagrangian geometrical optics of nonadiabatic vector waves and spin particles

DOE PAGES

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

2015-07-29

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

Make the First Move: How Infants Learn about Self-Propelled Objects

ERIC Educational Resources Information Center

Rakison, David H.

2006-01-01

In 3 experiments, the author investigated 16- to 20-month-old infants' attention to dynamic and static parts in learning about self-propelled objects. In Experiment 1, infants were habituated to simple noncausal events in which a geometric figure with a single moving part started to move without physical contact from an identical geometric figure…

A Comparison of the Electromagnetic and Acoustic Doppler Effects Using Geometrical Diagrams

ERIC Educational Resources Information Center

Bokor, Nandor

2009-01-01

Students often find the difference in the electromagnetic and the acoustic Doppler formulae somewhat puzzling. As is shown below, geometrical diagrams and the concept of "event"--a point in spacetime having coordinates (x,y,z,t)--can be a useful and simple way to explain the physical background behind the fundamental differences between the two…

Geometric mean IELT and premature ejaculation: appropriate statistics to avoid overestimation of treatment efficacy.

PubMed

Waldinger, Marcel D; Zwinderman, Aeilko H; Olivier, Berend; Schweitzer, Dave H

2008-02-01

The intravaginal ejaculation latency time (IELT) behaves in a skewed manner and needs the appropriate statistics for correct interpretation of treatment results. To explain the rightful use of geometrical mean IELT values and the fold increase of the geometric mean IELT because of the positively skewed IELT distribution. Linking theoretical arguments to the outcome of several selective serotonin reuptake inhibitor and modern antidepressant study results. Geometric mean IELT and fold increase of geometrical mean IELT. Log-transforming each separate IELT measurement of each individual man is the basis for the calculation of the geometric mean IELT. A drug-induced positively skewed IELT distribution necessitates the calculation of the geometric mean IELTs at baseline and during drug treatment. In a positively skewed IELT distribution, the use of the "arithmetic" mean IELT risks an overestimation of the drug-induced ejaculation delay as the mean IELT is always higher than the geometric mean IELT. Strong ejaculation-delaying drugs give rise to a strong positively skewed IELT distribution, whereas weak ejaculation-delaying drugs give rise to (much) less skewed IELT distributions. Ejaculation delay is expressed in fold increase of the geometric mean IELT. Drug-induced ejaculatory performance discloses a positively skewed IELT distribution, requiring the use of the geometric mean IELT and the fold increase of the geometric mean IELT.

A Simple Geometrical Model for Calculation of the Effective Emissivity in Blackbody Cylindrical Cavities

NASA Astrophysics Data System (ADS)

De Lucas, Javier

2015-03-01

A simple geometrical model for calculating the effective emissivity in blackbody cylindrical cavities has been developed. The back ray tracing technique and the Monte Carlo method have been employed, making use of a suitable set of coordinates and auxiliary planes. In these planes, the trajectories of individual photons in the successive reflections between the cavity points are followed in detail. The theoretical model is implemented by using simple numerical tools, programmed in Microsoft Visual Basic for Application and Excel. The algorithm is applied to isothermal and non-isothermal diffuse cylindrical cavities with a lid; however, the basic geometrical structure can be generalized to a cylindro-conical shape and specular reflection. Additionally, the numerical algorithm and the program source code can be used, with minor changes, for determining the distribution of the cavity points, where photon absorption takes place. This distribution could be applied to the study of the influence of thermal gradients on the effective emissivity profiles, for example. Validation is performed by analyzing the convergence of the Monte Carlo method as a function of the number of trials and by comparison with published results of different authors.

Decomposing the electromagnetic response of magnetic dipoles to determine the geometric parameters of a dipole conductor

NASA Astrophysics Data System (ADS)

Desmarais, Jacques K.; Smith, Richard S.

2016-03-01

A novel automatic data interpretation algorithm is presented for modelling airborne electromagnetic (AEM) data acquired over resistive environments, using a single-component (vertical) transmitter, where the position and orientation of a dipole conductor is allowed to vary in three dimensions. The algorithm assumes that the magnetic fields produced from compact vortex currents are expressed as a linear combinations of the fields arising from dipoles in the subsurface oriented parallel to the [1, 0, 0], [0, 1, 0], and [0, 0, 1], unit vectors. In this manner, AEM responses can be represented as 12 terms. The relative size of each term in the decomposition can be used to determine geometrical information about the orientation of the subsurface conductivity structure. The geometrical parameters of the dipole (location, depth, dip, strike) are estimated using a combination of a look-up table and a matrix inverted in a least-squares sense. Tests on 703 synthetic models show that the algorithm is capable of extracting most of the correct geometrical parameters of a dipole conductor when three-component receiver data is included in the interpretation procedure. The algorithm is unstable when the target is perfectly horizontal, as the strike is undefined. Ambiguities may occur in predicting the orientation of the dipole conductor if y-component data is excluded from the analysis. Application of our approach to an anomaly on line 15 of the Reid Mahaffy test site yields geometrical parameters in reasonable agreement with previous authors. However, our algorithm provides additional information on the strike and offset from the traverse line of the conductor. Disparities in the values of predicted dip and depth are within the range of numerical precision. The index of fit was better when strike and offset were included in the interpretation procedure. Tests on the data from line 15701 of the Chibougamau MEGATEM survey shows that the algorithm is applicable to situations where three-component AEM data is available.

Geometric morphometrics and virtual anthropology: advances in human evolutionary studies.

PubMed

Rein, Thomas R; Harvati, Katerina

2014-01-01

Geometric morphometric methods have been increasingly used in paleoanthropology in the last two decades, lending greater power to the analysis and interpretation of the human fossil record. More recently the advent of the wide use of computed tomography and surface scanning, implemented in combination with geometric morphometrics (GM), characterizes a new approach, termed Virtual Anthropology (VA). These methodological advances have led to a number of developments in human evolutionary studies. We present some recent examples of GM and VA related research in human evolution with an emphasis on work conducted at the University of Tübingen and other German research institutions.

Performance of friction dampersin geometric mistuned bladed disk assembly subjected to random excitations

NASA Astrophysics Data System (ADS)

Cha, Douksoon

2018-07-01

In this study, the performance of friction dampers of a geometric mistuned bladed disk assembly is examined under random excitations. The results are represented by non-dimensional variables. It is shown that the performance of the blade-to-blade damper can deteriorate when the correlated narrow band excitations have a dominant frequency near the 1st natural frequency of the bladed disk assembly. Based on a simple model of a geometric mistuned bladed disk assembly, the analytical technique shows an efficient way to design friction dampers.

The Argumentative Introduction in Oral Interpretation.

ERIC Educational Resources Information Center

Mills, Daniel; Gaer, David C.

A study examined introductions used in competitive oral interpretation events. A total of 97 introductions (from four oral interpretation events at a nationally recognized Midwestern intercollegiate forensic tournament) were analyzed using four categories: Descriptive, Simple Theme, Descriptive and Simple Theme, and Argumentative Theme. Results…

Geometric aspects in digital analysis of Multi-Spectral Scanner (MSS) data

NASA Technical Reports Server (NTRS)

Mikhail, E. M.; Baker, J. R.

1973-01-01

Present automated systems of interpretation which apply pattern recognition techniques on MSS data do not fully consider the geometry of the acquisition system. In an effort to improve the usefulness of the MSS data when digitally treated, geometric aspects are analyzed and discussed. Attempts to correct for scanner instabilities in position and orientation by affine and polynomial transformations, as well as by modified collinearity equations are described. Methods of accounting for panoramic and relief effects are also discussed. It is anticipated that reliable area as well as position determinations can be accomplished during the process of automatic interpretation. A concept for a unified approach to the treatment of remote sensing data, both metric and nonmetric is presented.

Geometric correction of satellite data using curvilinear features and virtual control points

NASA Technical Reports Server (NTRS)

Algazi, V. R.; Ford, G. E.; Meyer, D. I.

1979-01-01

A simple, yet effective procedure for the geometric correction of partial Landsat scenes is described. The procedure is based on the acquisition of actual and virtual control points from the line printer output of enhanced curvilinear features. The accuracy of this method compares favorably with that of the conventional approach in which an interactive image display system is employed.

Modern Geometric Algebra: A (Very Incomplete!) Survey

ERIC Educational Resources Information Center

Suzuki, Jeff

2009-01-01

Geometric algebra is based on two simple ideas. First, the area of a rectangle is equal to the product of the lengths of its sides. Second, if a figure is broken apart into several pieces, the sum of the areas of the pieces equals the area of the original figure. Remarkably, these two ideas provide an elegant way to introduce, connect, and…

Geometric interpretation of vertex operator algebras.

PubMed Central

Huang, Y Z

1991-01-01

In this paper, Vafa's approach to the formulation of conformal field theories is combined with the formal calculus developed in Frenkel, Lepowsky, and Meurman's work on the vertex operator construction of the Monster to give a geometric definition of vertex operator algebras. The main result announced is the equivalence between this definition and the algebraic one in the sense that the categories determined by these definitions are isomorphic. PMID:11607240

Variables separation of the spectral BRDF for better understanding color variation in special effect pigment coatings.

PubMed

Ferrero, Alejandro; Rabal, Ana María; Campos, Joaquín; Pons, Alicia; Hernanz, María Luisa

2012-06-01

A type of representation of the spectral bidirectional reflectance distribution function (BRDF) is proposed that distinctly separates the spectral variable (wavelength) from the geometrical variables (spherical coordinates of the irradiation and viewing directions). Principal components analysis (PCA) is used in order to decompose the spectral BRDF in decorrelated spectral components, and the weight that they have at every geometrical configuration of irradiation/viewing is established. This method was applied to the spectral BRDF measurement of a special effect pigment sample, and four principal components with relevant variance were identified. These four components are enough to reproduce the great diversity of spectral reflectances observed at different geometrical configurations. Since this representation is able to separate spectral and geometrical variables, it facilitates the interpretation of the color variation of special effect pigments coatings versus the geometrical configuration of irradiation/viewing.

Tour of a Simple Trigonometry Problem

ERIC Educational Resources Information Center

Poon, Kin-Keung

2012-01-01

This article focuses on a simple trigonometric problem that generates a strange phenomenon when different methods are applied to tackling it. A series of problem-solving activities are discussed, so that students can be alerted that the precision of diagrams is important when solving geometric problems. In addition, the problem-solving plan was…

Supercomputer use in orthopaedic biomechanics research: focus on functional adaptation of bone.

PubMed

Hart, R T; Thongpreda, N; Van Buskirk, W C

1988-01-01

The authors describe two biomechanical analyses carried out using numerical methods. One is an analysis of the stress and strain in a human mandible, and the other analysis involves modeling the adaptive response of a sheep bone to mechanical loading. The computing environment required for the two types of analyses is discussed. It is shown that a simple stress analysis of a geometrically complex mandible can be accomplished using a minicomputer. However, more sophisticated analyses of the same model with dynamic loading or nonlinear materials would require supercomputer capabilities. A supercomputer is also required for modeling the adaptive response of living bone, even when simple geometric and material models are use.

Analysis of Salmonella enterica Serovar Typhimurium Variable-Number Tandem-Repeat Data for Public Health Investigation Based on Measured Mutation Rates and Whole-Genome Sequence Comparisons

PubMed Central

Dimovski, Karolina; Cao, Hanwei; Wijburg, Odilia L. C.; Strugnell, Richard A.; Mantena, Radha K.; Whipp, Margaret; Hogg, Geoff

2014-01-01

Variable-number tandem repeats (VNTRs) mutate rapidly and can be useful markers for genotyping. While multilocus VNTR analysis (MLVA) is increasingly used in the detection and investigation of food-borne outbreaks caused by Salmonella enterica serovar Typhimurium (S. Typhimurium) and other bacterial pathogens, MLVA data analysis usually relies on simple clustering approaches that may lead to incorrect interpretations. Here, we estimated the rates of copy number change at each of the five loci commonly used for S. Typhimurium MLVA, during in vitro and in vivo passage. We found that loci STTR5, STTR6, and STTR10 changed during passage but STTR3 and STTR9 did not. Relative rates of change were consistent across in vitro and in vivo growth and could be accurately estimated from diversity measures of natural variation observed during large outbreaks. Using a set of 203 isolates from a series of linked outbreaks and whole-genome sequencing of 12 representative isolates, we assessed the accuracy and utility of several alternative methods for analyzing and interpreting S. Typhimurium MLVA data. We show that eBURST analysis was accurate and informative. For construction of MLVA-based trees, a novel distance metric, based on the geometric model of VNTR evolution coupled with locus-specific weights, performed better than the commonly used simple or categorical distance metrics. The data suggest that, for the purpose of identifying potential transmission clusters for further investigation, isolates whose profiles differ at one of the rapidly changing STTR5, STTR6, and STTR10 loci should be collapsed into the same cluster. PMID:24957617

Where Will the Triangle Look for It? Attributing False Beliefs to a Geometric Shape at 17 Months

ERIC Educational Resources Information Center

Surian, Luca; Geraci, Alessandra

2012-01-01

Prior research on implicit mind-reading skills has focussed on how infants anticipate other persons' actions. This study investigated whether 11- and 17-month-olds spontaneously attribute false beliefs (FB) even to a simple animated geometric shape. Infants were shown a triangle chasing a disk through a tunnel. Using an eye-tracker, we found that…

Density estimation using the trapping web design: A geometric analysis

USGS Publications Warehouse

Link, W.A.; Barker, R.J.

1994-01-01

Population densities for small mammal and arthropod populations can be estimated using capture frequencies for a web of traps. A conceptually simple geometric analysis that avoid the need to estimate a point on a density function is proposed. This analysis incorporates data from the outermost rings of traps, explaining large capture frequencies in these rings rather than truncating them from the analysis.

Legendre submanifolds in contact manifolds as attractors and geometric nonequilibrium thermodynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Goto, Shin-itiro, E-mail: sgoto@ims.ac.jp

It has been proposed that equilibrium thermodynamics is described on Legendre submanifolds in contact geometry. It is shown in this paper that Legendre submanifolds embedded in a contact manifold can be expressed as attractors in phase space for a certain class of contact Hamiltonian vector fields. By giving a physical interpretation that points outside the Legendre submanifold can represent nonequilibrium states of thermodynamic variables, in addition to that points of a given Legendre submanifold can represent equilibrium states of the variables, this class of contact Hamiltonian vector fields is physically interpreted as a class of relaxation processes, in which thermodynamicmore » variables achieve an equilibrium state from a nonequilibrium state through a time evolution, a typical nonequilibrium phenomenon. Geometric properties of such vector fields on contact manifolds are characterized after introducing a metric tensor field on a contact manifold. It is also shown that a contact manifold and a strictly convex function induce a lower dimensional dually flat space used in information geometry where a geometrization of equilibrium statistical mechanics is constructed. Legendre duality on contact manifolds is explicitly stated throughout.« less

Evaluation of SLAR and thematic mapper MSS data for forest cover mapping using computer-aided analysis techniques

NASA Technical Reports Server (NTRS)

Hoffer, R. M. (Principal Investigator)

1981-01-01

Training and test data sets for CAM1S from NS-001 MSS data for two dates (geometrically adjusted to 30 meter resolution) were used to evaluate wavelength band. Two sets of tapes containing digitized HH and HV polarization data were obtained. Because the SAR data on the 9 track tapes contained no meaningful data, the 7 track tapes were copied onto 9 track tapes at LARS. The LARSYS programs were modified and a program was written to reformat the digitized SAR data into a LARSYS format. The radar imagery is being qualitatively interpreted. Results are to be used to identify possible cover types, to produce a classification map to aid in the numerical evaluation classification of radar data, and to develop an interpretation key for radar imagery. The four spatial resolution data sets were analyzed. A program was developed to reduce the spatial distortions resulting from variable viewing distance, and geometrically adjusted data sets were generated. A flowchart of steps taken to geometrically adjust a data set from the NS-001 scanner is presented.

Geometric derivations of minimal sets of sufficient multiview constraints

USGS Publications Warehouse

Thomas, Orrin H.; Oshel, Edward R.

2012-01-01

Geometric interpretations of four of the most common determinant formulations of multiview constraints are given, showing that they all enforce the same geometry and that all of the forms commonly in use in the machine vision community are a subset of a more general form. Generalising the work of Yi Ma yields a new general 2 x 2 determinant trilinear and 3 x 3 determinant quadlinear. Geometric descriptions of degenerate multiview constraints are given, showing that it is necessary, but insufficient, that the determinant equals zero. Understanding the degeneracies leads naturally into proofs for minimum sufficient sets of bilinear, trilinear and quadlinear constraints for arbitrary numbers of conjugate observations.

A Simple Mathematical Model for Standard Model of Elementary Particles and Extension Thereof

NASA Astrophysics Data System (ADS)

Sinha, Ashok

2016-03-01

An algebraically (and geometrically) simple model representing the masses of the elementary particles in terms of the interaction (strong, weak, electromagnetic) constants is developed, including the Higgs bosons. The predicted Higgs boson mass is identical to that discovered by LHC experimental programs; while possibility of additional Higgs bosons (and their masses) is indicated. The model can be analyzed to explain and resolve many puzzles of particle physics and cosmology including the neutrino masses and mixing; origin of the proton mass and the mass-difference between the proton and the neutron; the big bang and cosmological Inflation; the Hubble expansion; etc. A novel interpretation of the model in terms of quaternion and rotation in the six-dimensional space of the elementary particle interaction-space - or, equivalently, in six-dimensional spacetime - is presented. Interrelations among particle masses are derived theoretically. A new approach for defining the interaction parameters leading to an elegant and symmetrical diagram is delineated. Generalization of the model to include supersymmetry is illustrated without recourse to complex mathematical formulation and free from any ambiguity. This Abstract represents some results of the Author's Independent Theoretical Research in Particle Physics, with possible connection to the Superstring Theory. However, only very elementary mathematics and physics is used in my presentation.

Light scattering by randomly oriented cubes and parallelepipeds. [for interpretation of observed data from planetary atmospheres

NASA Technical Reports Server (NTRS)

Liou, K. N.; Cai, Q.; Pollack, J. B.; Cuzzi, J. N.

1983-01-01

In this paper, the geometric ray tracing theory for the scattering of light by hexagonal cylinders to cubes and parallelepipeds has been modified. Effects of the real and imaginary parts of the refractive index and aspect ratio of the particle on the scattering phase function and the degree of linear polarization are investigated. Causes of the physical features in the scattering polarization patterns are identified in terms of the scattering contribution due to geometric reflections and refractions. The single-scattering phase function and polarization data presented in this paper should be of some use for the interpretation of observed scattering and polarization data from planetary atmospheres and for the physical understanding of the transfer of radiation in an atmosphere containing nonspherical particles.

Modeling late rectal toxicities based on a parameterized representation of the 3D dose distribution

NASA Astrophysics Data System (ADS)

Buettner, Florian; Gulliford, Sarah L.; Webb, Steve; Partridge, Mike

2011-04-01

Many models exist for predicting toxicities based on dose-volume histograms (DVHs) or dose-surface histograms (DSHs). This approach has several drawbacks as firstly the reduction of the dose distribution to a histogram results in the loss of spatial information and secondly the bins of the histograms are highly correlated with each other. Furthermore, some of the complex nonlinear models proposed in the past lack a direct physical interpretation and the ability to predict probabilities rather than binary outcomes. We propose a parameterized representation of the 3D distribution of the dose to the rectal wall which explicitly includes geometrical information in the form of the eccentricity of the dose distribution as well as its lateral and longitudinal extent. We use a nonlinear kernel-based probabilistic model to predict late rectal toxicity based on the parameterized dose distribution and assessed its predictive power using data from the MRC RT01 trial (ISCTRN 47772397). The endpoints under consideration were rectal bleeding, loose stools, and a global toxicity score. We extract simple rules identifying 3D dose patterns related to a specifically low risk of complication. Normal tissue complication probability (NTCP) models based on parameterized representations of geometrical and volumetric measures resulted in areas under the curve (AUCs) of 0.66, 0.63 and 0.67 for predicting rectal bleeding, loose stools and global toxicity, respectively. In comparison, NTCP models based on standard DVHs performed worse and resulted in AUCs of 0.59 for all three endpoints. In conclusion, we have presented low-dimensional, interpretable and nonlinear NTCP models based on the parameterized representation of the dose to the rectal wall. These models had a higher predictive power than models based on standard DVHs and their low dimensionality allowed for the identification of 3D dose patterns related to a low risk of complication.

Three-dimensional interpretation of TEM soundings

NASA Astrophysics Data System (ADS)

Barsukov, P. O.; Fainberg, E. B.

2013-07-01

We describe the approach to the interpretation of electromagnetic (EM) sounding data which iteratively adjusts the three-dimensional (3D) model of the environment by local one-dimensional (1D) transformations and inversions and reconstructs the geometrical skeleton of the model. The final 3D inversion is carried out with the minimal number of the sought parameters. At each step of the interpretation, the model of the medium is corrected according to the geological information. The practical examples of the suggested method are presented.

Breakdown of Spatial Parallel Coding in Children's Drawing

ERIC Educational Resources Information Center

De Bruyn, Bart; Davis, Alyson

2005-01-01

When drawing real scenes or copying simple geometric figures young children are highly sensitive to parallel cues and use them effectively. However, this sensitivity can break down in surprisingly simple tasks such as copying a single line where robust directional errors occur despite the presence of parallel cues. Before we can conclude that this…

The Thin Border between Light and Shadow

ERIC Educational Resources Information Center

Guglielmino, M.; Gratton, L. M.; Oss, S.

2010-01-01

We propose a simple, direct estimate of the Sun's diameter based on penumbra observation and measurement in a two-level approach, the first for middle-school pupils and making use of simple geometrical arguments, the second more appropriate to high-school students and based on a slightly more sophisticated approach. (Contains 5 figures.)

Geometric Constraints and the Anatomical Interpretation of Twisted Plant Organ Phenotypes

PubMed Central

Weizbauer, Renate; Peters, Winfried S.; Schulz, Burkhard

2011-01-01

The study of plant mutants with twisting growth in axial organs, which normally grow straight in the wild-type, is expected to improve our understanding of the interplay among microtubules, cellulose biosynthesis, cell wall structure, and organ biomechanics that control organ growth and morphogenesis. However, geometric constraints based on symplastic growth and the consequences of these geometric constraints concerning interpretations of twisted-organ phenotypes are currently underestimated. Symplastic growth, a fundamental concept in plant developmental biology, is characterized by coordinated growth of adjacent cells based on their connectivity through cell walls. This growth behavior implies that in twisting axial organs, all cell files rotate in phase around the organ axis, as has been illustrated for the Arabidopsis spr1 and twd1 mutants in this work. Evaluating the geometry of such organs, we demonstrate that a radial gradient in cell elongation and changes in cellular growth anisotropy must occur in twisting organs out of geometric necessity alone. In-phase rotation of the different cell layers results in a decrease of length and angle toward organ axis from the outer cell layers inward. Additionally, the circumference of each cell layer increases in twisting organs, which requires compensation through radial expansion or an adjustment of cell number. Therefore, differential cell elongation and growth anisotropy cannot serve as arguments for or against specific hypotheses regarding the molecular cause of twisting growth. We suggest instead, that based on mathematical modeling, geometric constraints in twisting organs are indispensable for the explanation of the causal connection of molecular and biomechanical processes in twisting as well as normal organs. PMID:22645544

Influence of stochastic geometric imperfections on the load-carrying behaviour of thin-walled structures using constrained random fields

NASA Astrophysics Data System (ADS)

Lauterbach, S.; Fina, M.; Wagner, W.

2018-04-01

Since structural engineering requires highly developed and optimized structures, the thickness dependency is one of the most controversially debated topics. This paper deals with stability analysis of lightweight thin structures combined with arbitrary geometrical imperfections. Generally known design guidelines only consider imperfections for simple shapes and loading, whereas for complex structures the lower-bound design philosophy still holds. Herein, uncertainties are considered with an empirical knockdown factor representing a lower bound of existing measurements. To fully understand and predict expected bearable loads, numerical investigations are essential, including geometrical imperfections. These are implemented into a stand-alone program code with a stochastic approach to compute random fields as geometric imperfections that are applied to nodes of the finite element mesh of selected structural examples. The stochastic approach uses the Karhunen-Loève expansion for the random field discretization. For this approach, the so-called correlation length l_c controls the random field in a powerful way. This parameter has a major influence on the buckling shape, and also on the stability load. First, the impact of the correlation length is studied for simple structures. Second, since most structures for engineering devices are more complex and combined structures, these are intensively discussed with the focus on constrained random fields for e.g. flange-web-intersections. Specific constraints for those random fields are pointed out with regard to the finite element model. Further, geometrical imperfections vanish where the structure is supported.

Geometric U-folds in four dimensions

NASA Astrophysics Data System (ADS)

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 \

Spin-to-Orbital Angular Momentum Mapping of Polychromatic Light

NASA Astrophysics Data System (ADS)

Rafayelyan, Mushegh; Brasselet, Etienne

2018-05-01

Reflective geometric phase flat optics made from chiral anisotropic media recently unveiled a promising route towards polychromatic beam shaping. However, these broadband benefits are strongly mitigated by the fact that flipping the incident helicity does not ensure geometric phase reversal. Here we overcome this fundamental limitation by a simple and robust add-on whose advantages are emphasized in the context of spin-to-orbital angular momentum mapping.

Fullerenes and disk-fullerenes

NASA Astrophysics Data System (ADS)

Deza, M.; Dutour Sikirić, M.; Shtogrin, M. I.

2013-08-01

A geometric fullerene, or simply a fullerene, is the surface of a simple closed convex 3-dimensional polyhedron with only 5- and 6-gonal faces. Fullerenes are geometric models for chemical fullerenes, which form an important class of organic molecules. These molecules have been studied intensively in chemistry, physics, crystallography, and so on, and their study has led to the appearance of a vast literature on fullerenes in mathematical chemistry and combinatorial and applied geometry. In particular, several generalizations of the notion of a fullerene have been given, aiming at various applications. Here a new generalization of this notion is proposed: an n-disk-fullerene. It is obtained from the surface of a closed convex 3-dimensional polyhedron which has one n-gonal face and all other faces 5- and 6-gonal, by removing the n-gonal face. Only 5- and 6-disk-fullerenes correspond to geometric fullerenes. The notion of a geometric fullerene is therefore generalized from spheres to compact simply connected two-dimensional manifolds with boundary. A two-dimensional surface is said to be unshrinkable if it does not contain belts, that is, simple cycles consisting of 6-gons each of which has two neighbours adjacent at a pair of opposite edges. Shrinkability of fullerenes and n-disk-fullerenes is investigated. Bibliography: 87 titles.

Application of geometry based hysteresis modelling in compensation of hysteresis of piezo bender actuator

NASA Astrophysics Data System (ADS)

Milecki, Andrzej; Pelic, Marcin

2016-10-01

This paper presents results of studies of an application of a new method of piezo bender actuators modelling. A special hysteresis simulation model was developed and is presented. The model is based on a geometrical deformation of main hysteresis loop. The piezoelectric effect is described and the history of the hysteresis modelling is briefly reviewed. Firstly, a simple model for main loop modelling is proposed. Then, a geometrical description of the non-saturated hysteresis is presented and its modelling method is introduced. The modelling makes use of the function describing the geometrical shape of the two hysteresis main curves, which can be defined theoretically or obtained by measurement. These main curves are stored in the memory and transformed geometrically in order to obtain the minor curves. Such model was prepared in the Matlab-Simulink software, but can be easily implemented using any programming language and applied in an on-line controller. In comparison to the other known simulation methods, the one presented in the paper is easy to understand, and uses simple arithmetical equations, allowing to quickly obtain the inversed model of hysteresis. The inversed model was further used for compensation of a non-saturated hysteresis of the piezo bender actuator and results have also been presented in the paper.

Functional programming interpreter. M. S. thesis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Robison, A.D.

1987-03-01

Functional Programming (FP) sup BAC87 is an alternative to conventional imperative programming languages. This thesis describes an FP interpreter implementation. Superficially, FP appears to be a simple, but very inefficient language. Its simplicity, however, allows it to be interpreted quickly. Much of the inefficiency can be removed by simple interpreter techniques. This thesis describes the Illinois Functional Programming (IFP) interpreter, an interactive functional programming implementation which runs under both MS-DOS and UNIX. The IFP interpreter allows functions to be created, executed, and debugged in an environment very similar to UNIX. IFP's speed is competitive with other interpreted languages such asmore » BASIC.« less

A SIX-DIMENSIONAL RIEMANNIAN MANIFOLD, ITS APPLICATIONS TO MESO- ELECTRODYNAMICS, AND A SYSTEMATIZATION OF STRONGLY INTERACTING PARTICLES

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rayski, J.

1959-01-01

A conception of a six-dimensional world enables a geometrical interpretation of the electric charge, charge c onjugation, gauge transformations, and of the electromagnetic field. The same conception explains satisfactorily the isospin, its cornection with the electric charge, and the ps- scalar character of nuclear forces. Several qualitative and some quantitative properties of strongly interacting particles (strangeness, rest masses, etc.) find an intuitive explanation within this geometrical framework. (auth)

A Geometrical Approach to Bell's Theorem

NASA Technical Reports Server (NTRS)

Rubincam, David Parry

2000-01-01

Bell's theorem can be proved through simple geometrical reasoning, without the need for the Psi function, probability distributions, or calculus. The proof is based on N. David Mermin's explication of the Einstein-Podolsky-Rosen-Bohm experiment, which involves Stern-Gerlach detectors which flash red or green lights when detecting spin-up or spin-down. The statistics of local hidden variable theories for this experiment can be arranged in colored strips from which simple inequalities can be deduced. These inequalities lead to a demonstration of Bell's theorem. Moreover, all local hidden variable theories can be graphed in such a way as to enclose their statistics in a pyramid, with the quantum-mechanical result lying a finite distance beneath the base of the pyramid.

[Three dimensional mathematical model of tooth for finite element analysis].

PubMed

Puskar, Tatjana; Vasiljević, Darko; Marković, Dubravka; Jevremović, Danimir; Pantelić, Dejan; Savić-Sević, Svetlana; Murić, Branka

2010-01-01

The mathematical model of the abutment tooth is the starting point of the finite element analysis of stress and deformation of dental structures. The simplest and easiest way is to form a model according to the literature data of dimensions and morphological characteristics of teeth. Our method is based on forming 3D models using standard geometrical forms (objects) in programmes for solid modeling. Forming the mathematical model of abutment of the second upper premolar for finite element analysis of stress and deformation of dental structures. The abutment tooth has a form of a complex geometric object. It is suitable for modeling in programs for solid modeling SolidWorks. After analysing the literature data about the morphological characteristics of teeth, we started the modeling dividing the tooth (complex geometric body) into simple geometric bodies (cylinder, cone, pyramid,...). Connecting simple geometric bodies together or substricting bodies from the basic body, we formed complex geometric body, tooth. The model is then transferred into Abaqus, a computational programme for finite element analysis. Transferring the data was done by standard file format for transferring 3D models ACIS SAT. Using the programme for solid modeling SolidWorks, we developed three models of abutment of the second maxillary premolar: the model of the intact abutment, the model of the endodontically treated tooth with two remaining cavity walls and the model of the endodontically treated tooth with two remaining walls and inserted post. Mathematical models of the abutment made according to the literature data are very similar with the real abutment and the simplifications are minimal. These models enable calculations of stress and deformation of the dental structures. The finite element analysis provides useful information in understanding biomechanical problems and gives guidance for clinical research.

Generalized sub-Schawlow-Townes laser linewidths via material dispersion

NASA Astrophysics Data System (ADS)

Pillay, Jason Cornelius; Natsume, Yuki; Stone, A. Douglas; Chong, Y. D.

2014-03-01

A recent S-matrix-based theory of the quantum-limited linewidth, which is applicable to general lasers, including spatially nonuniform laser cavities operating above threshold, is analyzed in various limits. For broadband gain, a simple interpretation of the Petermann and bad-cavity factors is presented in terms of geometric relations between the zeros and poles of the S matrix. When there is substantial dispersion, on the frequency scale of the cavity lifetime, the theory yields a generalization of the bad-cavity factor, which was previously derived for spatially uniform one-dimensional lasers. This effect can lead to sub-Schawlow-Townes linewidths in lasers with very narrow gain widths. We derive a formula for the linewidth in terms of the lasing mode functions, which has accuracy comparable to the previous formula involving the residue of the lasing pole. These results for the quantum-limited linewidth are valid even in the regime of strong line pulling and spatial hole burning, where the linewidth cannot be factorized into independent Petermann and bad-cavity factors.

Extinction by a Homogeneous Spherical Particle in an Absorbing Medium

NASA Technical Reports Server (NTRS)

Mishchenko, Michael I.; Videen, Gorden; Yang, Ping

2017-01-01

We use a recent computer implementation of the first principles theory of electromagnetic scattering to compute far-field extinction by a spherical particle embedded in an absorbing unbounded host. Our results show that the suppressing effect of increasing absorption inside the host medium on the ripple structure of the extinction efficiency factor as a function of the size parameter is similar to the well-known effect of increasing absorption inside a particle embedded in a nonabsorbing host. However, the accompanying effects on the interference structure of the extinction efficiency curves are diametrically opposite. As a result, sufficiently large absorption inside the host medium can cause negative particulate extinction. We offer a simple physical explanation of the phenomenon of negative extinction consistent with the interpretation of the interference structure as being the result of interference of the field transmitted by the particle and the diffracted field due to an incomplete wave front resulting from the blockage of the incident plane wave by the particle's geometrical projection.

First-principles variational formulation of polarization effects in geometrical optics

DOE PAGES

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

2015-10-02

The propagation of electromagnetic waves in isotropic dielectric media with local dispersion is studied under the assumption of small but nonvanishing λ/l, where λ is the wavelength and l is the characteristic inhomogeneity scale. It is commonly known that, due to nonzero λ/l, such waves can experience polarization-driven bending of ray trajectories and polarization dynamics that can be interpreted as the precession of the wave "spin". The present work reports how Lagrangians describing these effects can be deduced, rather than guessed, within a strictly classical theory. In addition to the commonly known ray Lagrangian that features the Berry connection, amore » simple alternative Lagrangian is proposed that naturally has a canonical form. The presented theory captures not only the eigenray dynamics but also the dynamics of continuous-wave fields and rays with mixed polarization, or "entangled" waves. In conclusion, the calculation assumes stationary lossless media with isotropic local dispersion, but generalizations to other media are straightforward.« less

An information-theoretic approach for the evaluation of surrogate endpoints based on causal inference.

PubMed

Alonso, Ariel; Van der Elst, Wim; Molenberghs, Geert; Buyse, Marc; Burzykowski, Tomasz

2016-09-01

In this work a new metric of surrogacy, the so-called individual causal association (ICA), is introduced using information-theoretic concepts and a causal inference model for a binary surrogate and true endpoint. The ICA has a simple and appealing interpretation in terms of uncertainty reduction and, in some scenarios, it seems to provide a more coherent assessment of the validity of a surrogate than existing measures. The identifiability issues are tackled using a two-step procedure. In the first step, the region of the parametric space of the distribution of the potential outcomes, compatible with the data at hand, is geometrically characterized. Further, in a second step, a Monte Carlo approach is proposed to study the behavior of the ICA on the previous region. The method is illustrated using data from the Collaborative Initial Glaucoma Treatment Study. A newly developed and user-friendly R package Surrogate is provided to carry out the evaluation exercise. © 2016, The International Biometric Society.

Statistical measures of Planck scale signal correlations in interferometers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hogan, Craig J.; Kwon, Ohkyung

2015-06-22

A model-independent statistical framework is presented to interpret data from systems where the mean time derivative of positional cross correlation between world lines, a measure of spreading in a quantum geometrical wave function, is measured with a precision smaller than the Planck time. The framework provides a general way to constrain possible departures from perfect independence of classical world lines, associated with Planck scale bounds on positional information. A parametrized candidate set of possible correlation functions is shown to be consistent with the known causal structure of the classical geometry measured by an apparatus, and the holographic scaling of informationmore » suggested by gravity. Frequency-domain power spectra are derived that can be compared with interferometer data. As a result, simple projections of sensitivity for specific experimental set-ups suggests that measurements will directly yield constraints on a universal time derivative of the correlation function, and thereby confirm or rule out a class of Planck scale departures from classical geometry.« less

STM images of carbon-nanotube quantum dots: Seeing a Wigner molecule of correlated electrons

NASA Astrophysics Data System (ADS)

Secchi, Andrea; Rontani, Massimo

2011-03-01

The paradigm of few-electron complexes in quantum dots (QDs) relies on the idea that the lowest quantized levels are filled according to Pauli's exclusion principle. If Coulomb repulsion is sufficiently strong to overcome the kinetic energy cost of localization, a different scenario is predicted: a ``Wigner'' molecule (WM) forms, made of electrons frozen in space according to a geometrical pattern. Despite considerable experimental effort, evidence of the WM in semiconductor QDs has been elusive so far. Here we demonstrate theoretically that WMs occur in gate-defined QDs embedded in typical semiconducting carbon nanotubes (CNTs). The unambiguous signatures of the WM state must be searched in the scanning tunneling microscopy (STM) images of the electrons. Through exact diagonalisation (ED) calculations, we unveil the inherent features of the electron molecular states. We show that, like nuclei in a usual molecule, electrons have localized wave functions and hence negligible exchange interactions. ED results for single and double QDs provide a simple interpretation for transport experiments in ultraclean CNTs.

Binocular disparities, motion parallax, and geometric perspective in Patrick Hughes's 'reverspectives': theoretical analysis and empirical findings.

PubMed

Rogers, Brian; Gyani, Alex

2010-01-01

Abstract. Patrick Hughes's 'reverspective' artworks provide a novel way of investigating the effectiveness of different sources of 3-D information for the human visual system. Our empirical findings show that the converging lines of simple linear perspective can be as effective as the rich array of 3-D cues present in natural scenes in determining what we see, even when these cues are in conflict with binocular disparities. Theoretical considerations reveal that, once the information provided by motion parallax transformations is correctly understood, there is no need to invoke higher-level processes or an interpretation based on familiarity or past experience in order to explain either the 'reversed' depth or the apparent, concomitant rotation of a reverspective artwork as the observer moves from side to side. What we see in reverspectives is the most likely real-world scenario (distal stimulus) that could have created the perspective and parallax transformations (proximal stimulus) that stimulate our visual systems.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rautman, Christopher Arthur; Lord, Anna Snider

Downhole sonar surveys from the four active U.S. Strategic Petroleum Reserve sites have been modeled and used to generate a four-volume sonar atlas, showing the three-dimensional geometry of each cavern. This volume 3 focuses on the Bryan Mound SPR site, located in southeastern Texas. Volumes 1, 2, and 4, respectively, present images for the Bayou Choctaw SPR site, Louisiana, the Big Hill SPR site, Texas, and the West Hackberry SPR site, Louisiana. The atlas uses a consistent presentation format throughout. The basic geometric measurements provided by the down-cavern surveys have also been used to generate a number of geometric attributes,more » the values of which have been mapped onto the geometric form of each cavern using a color-shading scheme. The intent of the various geometrical attributes is to highlight deviations of the cavern shape from the idealized cylindrical form of a carefully leached underground storage cavern in salt. The atlas format does not allow interpretation of such geometric deviations and anomalies. However, significant geometric anomalies, not directly related to the leaching history of the cavern, may provide insight into the internal structure of the relevant salt dome.« less

Influence of part orientation on the geometric accuracy in robot-based incremental sheet metal forming

NASA Astrophysics Data System (ADS)

Störkle, Denis Daniel; Seim, Patrick; Thyssen, Lars; Kuhlenkötter, Bernd

2016-10-01

This article describes new developments in an incremental, robot-based sheet metal forming process (`Roboforming') for the production of sheet metal components for small lot sizes and prototypes. The dieless kinematic-based generation of the shape is implemented by means of two industrial robots, which are interconnected to a cooperating robot system. Compared to other incremental sheet metal forming (ISF) machines, this system offers high geometrical form flexibility without the need of any part-dependent tools. The industrial application of ISF is still limited by certain constraints, e.g. the low geometrical accuracy. Responding to these constraints, the authors present the influence of the part orientation and the forming sequence on the geometric accuracy. Their influence is illustrated with the help of various experimental results shown and interpreted within this article.

Universal freezing of quantum correlations within the geometric approach

PubMed Central

Cianciaruso, Marco; Bromley, Thomas R.; Roga, Wojciech; Lo Franco, Rosario; Adesso, Gerardo

2015-01-01

Quantum correlations in a composite system can be measured by resorting to a geometric approach, according to which the distance from the state of the system to a suitable set of classically correlated states is considered. Here we show that all distance functions, which respect natural assumptions of invariance under transposition, convexity, and contractivity under quantum channels, give rise to geometric quantifiers of quantum correlations which exhibit the peculiar freezing phenomenon, i.e., remain constant during the evolution of a paradigmatic class of states of two qubits each independently interacting with a non-dissipative decohering environment. Our results demonstrate from first principles that freezing of geometric quantum correlations is independent of the adopted distance and therefore universal. This finding paves the way to a deeper physical interpretation and future practical exploitation of the phenomenon for noisy quantum technologies. PMID:26053239

A special form of SPD covariance matrix for interpretation and visualization of data manipulated with Riemannian geometry

NASA Astrophysics Data System (ADS)

Congedo, Marco; Barachant, Alexandre

2015-01-01

Currently the Riemannian geometry of symmetric positive definite (SPD) matrices is gaining momentum as a powerful tool in a wide range of engineering applications such as image, radar and biomedical data signal processing. If the data is not natively represented in the form of SPD matrices, typically we may summarize them in such form by estimating covariance matrices of the data. However once we manipulate such covariance matrices on the Riemannian manifold we lose the representation in the original data space. For instance, we can evaluate the geometric mean of a set of covariance matrices, but not the geometric mean of the data generating the covariance matrices, the space of interest in which the geometric mean can be interpreted. As a consequence, Riemannian information geometry is often perceived by non-experts as a "black-box" tool and this perception prevents a wider adoption in the scientific community. Hereby we show that we can overcome this limitation by constructing a special form of SPD matrix embedding both the covariance structure of the data and the data itself. Incidentally, whenever the original data can be represented in the form of a generic data matrix (not even square), this special SPD matrix enables an exhaustive and unique description of the data up to second-order statistics. This is achieved embedding the covariance structure of both the rows and columns of the data matrix, allowing naturally a wide range of possible applications and bringing us over and above just an interpretability issue. We demonstrate the method by manipulating satellite images (pansharpening) and event-related potentials (ERPs) of an electroencephalography brain-computer interface (BCI) study. The first example illustrates the effect of moving along geodesics in the original data space and the second provides a novel estimation of ERP average (geometric mean), showing that, in contrast to the usual arithmetic mean, this estimation is robust to outliers. In conclusion, we are able to show that the Riemannian concepts of distance, geometric mean, moving along a geodesic, etc. can be readily transposed into a generic data space, whatever this data space represents.

Scattering forms and the positive geometry of kinematics, color and the worldsheet

NASA Astrophysics Data System (ADS)

Arkani-Hamed, Nima; Bai, Yuntao; He, Song; Yan, Gongwang

2018-05-01

The search for a theory of the S-Matrix over the past five decades has revealed surprising geometric structures underlying scattering amplitudes ranging from the string worldsheet to the amplituhedron, but these are all geometries in auxiliary spaces as opposed to the kinematical space where amplitudes actually live. Motivated by recent advances providing a reformulation of the amplituhedron and planar N = 4 SYM amplitudes directly in kinematic space, we propose a novel geometric understanding of amplitudes in more general theories. The key idea is to think of amplitudes not as functions, but rather as differential forms on kinematic space. We explore the resulting picture for a wide range of massless theories in general spacetime dimensions. For the bi-adjoint ϕ 3 scalar theory, we establish a direct connection between its "scattering form" and a classic polytope — the associahedron — known to mathematicians since the 1960's. We find an associahedron living naturally in kinematic space, and the tree level amplitude is simply the "canonical form" associated with this "positive geometry". Fundamental physical properties such as locality and unitarity, as well as novel "soft" limits, are fully determined by the combinatorial geometry of this polytope. Furthermore, the moduli space for the open string worldsheet has also long been recognized as an associahedron. We show that the scattering equations act as a diffeomorphism between the interior of this old "worldsheet associahedron" and the new "kinematic associahedron", providing a geometric interpretation and simple conceptual derivation of the bi-adjoint CHY formula. We also find "scattering forms" on kinematic space for Yang-Mills theory and the Non-linear Sigma Model, which are dual to the fully color-dressed amplitudes despite having no explicit color factors. This is possible due to a remarkable fact—"Color is Kinematics"— whereby kinematic wedge products in the scattering forms satisfy the same Jacobi relations as color factors. Finally, all our scattering forms are well-defined on the projectivized kinematic space, a property which can be seen to provide a geometric origin for color-kinematics duality.

What Does f[subscript xx]f[subscript yy] - f[superscript 2][subscript xy] Greater than 0 "Really" Mean?

ERIC Educational Resources Information Center

McCartin, Brian J.

2008-01-01

This note presents geometric and physical interpretations of the sufficient condition for a critical point to be a strict relative extremum: f[subscript xx]f[subscript yy] - f[superscript 2][subscript xy] greater than 0. The role of the double derivative f[subscript xy] in this inequality will be highlighted in these interpretations. (Contains 14…

A new method for reporting and interpreting textural composition of spawning gravel.

Treesearch

Fredrick B. Lotspeich; Fred H. Everest

1981-01-01

A new method has been developed for collecting, sorting, and interpreting gravel quality. Samples are collected with a tri-tube freeze-core device and dry-sorted by using sieves based on the Wentworth scale. An index to the quality of gravel is obtained by dividing geometric mean particle size by the sorting coefficient (a measure of the distribution of grain sizes) of...

Goldfish (Carassius auratus) matching geometric and featural cues: a reinterpretation of some of the data of Vargas, López, Salas, and Thinus-Blanc (2004).

PubMed

Cheng, Ken

2005-11-01

Vargas, López, Salas, and Thinus-Blanc showed that goldfish (Carassius auratus) can use both geometric and featural cues in relocating a target corner in a rectangular enclosure. When featural cues (arrangement of striped walls) were put in conflict with geometric cues, results differed according to target location during training. Vargas, López, et al. explained the results of their cue conflict in terms of 2 different strategies: mapping and cue guidance. I provide an alternative, more parsimonious interpretation in which the same strategy of attempting to match as many cues as possible applies to both cases. ((c) 2005 APA, all rights reserved).

A dynamical systems approach to actin-based motility in Listeria monocytogenes

NASA Astrophysics Data System (ADS)

Hotton, S.

2010-11-01

A simple kinematic model for the trajectories of Listeria monocytogenes is generalized to a dynamical system rich enough to exhibit the resonant Hopf bifurcation structure of excitable media and simple enough to be studied geometrically. It is shown how L. monocytogenes trajectories and meandering spiral waves are organized by the same type of attracting set.

Medical image reconstruction algorithm based on the geometric information between sensor detector and ROI

NASA Astrophysics Data System (ADS)

Ham, Woonchul; Song, Chulgyu; Lee, Kangsan; Roh, Seungkuk

2016-05-01

In this paper, we propose a new image reconstruction algorithm considering the geometric information of acoustic sources and senor detector and review the two-step reconstruction algorithm which was previously proposed based on the geometrical information of ROI(region of interest) considering the finite size of acoustic sensor element. In a new image reconstruction algorithm, not only mathematical analysis is very simple but also its software implementation is very easy because we don't need to use the FFT. We verify the effectiveness of the proposed reconstruction algorithm by showing the simulation results by using Matlab k-wave toolkit.

Geometrization of quantum physics

NASA Astrophysics Data System (ADS)

Ol'Khov, O. A.

2009-12-01

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

On uniformly valid high-frequency far-field asymptotic solutions of the Helmholtz equation

NASA Technical Reports Server (NTRS)

Mcaninch, G. L.

1986-01-01

An asymptotic, large wave number approximation for the Helmholtz equation is derived. The theory is an extension of the geometric acoustic theory, and provides corrections to that theory in the form of multiplicative functions which satisfy parabolic equations. A simple example is used both to illustrate failure of the geometric theory for large propagation distances, and to show the improvement obtained by use of the new theory.

Hodograph analysis in aircraft trajectory optimization

NASA Technical Reports Server (NTRS)

Cliff, Eugene M.; Seywald, Hans; Bless, Robert R.

1993-01-01

An account is given of key geometrical concepts involved in the use of a hodograph as an optimal control theory resource which furnishes a framework for geometrical interpretation of the minimum principle. Attention is given to the effects of different convexity properties on the hodograph, which bear on the existence of solutions and such types of controls as chattering controls, 'bang-bang' control, and/or singular control. Illustrative aircraft trajectory optimization problems are examined in view of this use of the hodograph.

Semi Automated Land Cover Layer Updating Process Utilizing Spectral Analysis and GIS Data Fusion

NASA Astrophysics Data System (ADS)

Cohen, L.; Keinan, E.; Yaniv, M.; Tal, Y.; Felus, A.; Regev, R.

2018-04-01

Technological improvements made in recent years of mass data gathering and analyzing, influenced the traditional methods of updating and forming of the national topographic database. It has brought a significant increase in the number of use cases and detailed geo information demands. Processes which its purpose is to alternate traditional data collection methods developed in many National Mapping and Cadaster Agencies. There has been significant progress in semi-automated methodologies aiming to facilitate updating of a topographic national geodatabase. Implementation of those is expected to allow a considerable reduction of updating costs and operation times. Our previous activity has focused on building automatic extraction (Keinan, Zilberstein et al, 2015). Before semiautomatic updating method, it was common that interpreter identification has to be as detailed as possible to hold most reliable database eventually. When using semi-automatic updating methodologies, the ability to insert human insights based knowledge is limited. Therefore, our motivations were to reduce the created gap by allowing end-users to add their data inputs to the basic geometric database. In this article, we will present a simple Land cover database updating method which combines insights extracted from the analyzed image, and a given spatial data of vector layers. The main stages of the advanced practice are multispectral image segmentation and supervised classification together with given vector data geometric fusion while maintaining the principle of low shape editorial work to be done. All coding was done utilizing open source software components.

Genotypic Complexity of Fisher’s Geometric Model

PubMed Central

Hwang, Sungmin; Park, Su-Chan; Krug, Joachim

2017-01-01

Fisher’s geometric model was originally introduced to argue that complex adaptations must occur in small steps because of pleiotropic constraints. When supplemented with the assumption of additivity of mutational effects on phenotypic traits, it provides a simple mechanism for the emergence of genotypic epistasis from the nonlinear mapping of phenotypes to fitness. Of particular interest is the occurrence of reciprocal sign epistasis, which is a necessary condition for multipeaked genotypic fitness landscapes. Here we compute the probability that a pair of randomly chosen mutations interacts sign epistatically, which is found to decrease with increasing phenotypic dimension n, and varies nonmonotonically with the distance from the phenotypic optimum. We then derive expressions for the mean number of fitness maxima in genotypic landscapes comprised of all combinations of L random mutations. This number increases exponentially with L, and the corresponding growth rate is used as a measure of the complexity of the landscape. The dependence of the complexity on the model parameters is found to be surprisingly rich, and three distinct phases characterized by different landscape structures are identified. Our analysis shows that the phenotypic dimension, which is often referred to as phenotypic complexity, does not generally correlate with the complexity of fitness landscapes and that even organisms with a single phenotypic trait can have complex landscapes. Our results further inform the interpretation of experiments where the parameters of Fisher’s model have been inferred from data, and help to elucidate which features of empirical fitness landscapes can be described by this model. PMID:28450460

Core geometry in perspective

PubMed Central

Dillon, Moira R.; Spelke, Elizabeth S.

2015-01-01

Research on animals, infants, children, and adults provides evidence that distinct cognitive systems underlie navigation and object recognition. Here we examine whether and how these systems interact when children interpret 2D edge-based perspectival line drawings of scenes and objects. Such drawings serve as symbols early in development, and they preserve scene and object geometry from canonical points of view. Young children show limits when using geometry both in non-symbolic tasks and in symbolic map tasks that present 3D contexts from unusual, unfamiliar points of view. When presented with the familiar viewpoints in perspectival line drawings, however, do children engage more integrated geometric representations? In three experiments, children successfully interpreted line drawings with respect to their depicted scene or object. Nevertheless, children recruited distinct processes when navigating based on the information in these drawings, and these processes depended on the context in which the drawings were presented. These results suggest that children are flexible but limited in using geometric information to form integrated representations of scenes and objects, even when interpreting spatial symbols that are highly familiar and faithful renditions of the visual world. PMID:25441089

Individual differences in using geometric and featural cues to maintain spatial orientation: cue quantity and cue ambiguity are more important than cue type.

PubMed

Kelly, Jonathan W; McNamara, Timothy P; Bodenheimer, Bobby; Carr, Thomas H; Rieser, John J

2009-02-01

Two experiments explored the role of environmental cues in maintaining spatial orientation (sense of self-location and direction) during locomotion. Of particular interest was the importance of geometric cues (provided by environmental surfaces) and featural cues (nongeometric properties provided by striped walls) in maintaining spatial orientation. Participants performed a spatial updating task within virtual environments containing geometric or featural cues that were ambiguous or unambiguous indicators of self-location and direction. Cue type (geometric or featural) did not affect performance, but the number and ambiguity of environmental cues did. Gender differences, interpreted as a proxy for individual differences in spatial ability and/or experience, highlight the interaction between cue quantity and ambiguity. When environmental cues were ambiguous, men stayed oriented with either one or two cues, whereas women stayed oriented only with two. When environmental cues were unambiguous, women stayed oriented with one cue.

Coiling of elastic rods from a geometric perspective

NASA Astrophysics Data System (ADS)

Jawed, Mohammad; Brun, Pierre-Thomas; Reis, Pedro

2015-03-01

We present results from a systematic numerical investigation of the pattern formation of coiling obtained when a slender elastic rod is deployed onto a moving substrate; a system known as the elastic sewing machine (ESM). The Discrete Elastic Rods method is employed to explore the parameter space, construct phase diagrams, identify their phase boundaries and characterize the morphology of the patterns. The nontrivial geometric nonlinearities are described in terms of the gravito-bending length and the deployment height. Our results are interpreted using a reduced geometric model for the evolution of the position of the contact point with the belt and the curvature of the rod in its neighborhood. This geometric model reproduces all of the coiling patterns of the ESM, which allows us to establish a universal link between our elastic problem and the analogous patterns obtained when depositing a viscous thread onto a moving surface; a well-known system referred to as the fluid mechanical sewing machine.

Virtual Images: Going Through the Looking Glass

NASA Astrophysics Data System (ADS)

Mota, Ana Rita; dos Santos, João Lopes

2017-01-01

Virtual images are often introduced through a "geometric" perspective, with little conceptual or qualitative illustrations, hindering a deeper understanding of this physical concept. In this paper, we present two rather simple observations that force a critical reflection on the optical nature of a virtual image. This approach is supported by the reflect-view, a useful device in geometrical optics classes because it allows a visual confrontation between virtual images and real objects that seemingly occupy the same region of space.

A Non-Abelian Geometric Phase for Spin Systems

NASA Astrophysics Data System (ADS)

H M, Bharath; Boguslawski, Matthew; Barrios, Maryrose; Chapman, Michael

Berry's geometric phase has been used to characterize topological phase transitions. Recent works have addressed the question of whether generalizations of Berry's phase to mixed states can be used to characterize topological phase transitions. Berry's phase is essentially the geometric information stored in the overall phase of a quantum system. Here, we show that geometric information is also stored in the higher order spin moments of a quantum spin system. In particular, we show that when the spin vector of a quantum spin system with a spin 1 or higher is transported along a closed path inside the Bloch ball, the tensor of second moments picks up a geometric phase in the form of an SO(3) operator. Geometrically interpreting this phase is tantamount to defining a steradian angle for closed paths inside the Bloch ball. Typically the steradian angle is defined by projecting the path onto the surface of the Bloch ball. However, paths that pass through the center cannot be projected onto the surface. We show that the steradian angles of all paths, including those that pass through the center can be defined by projecting them onto a real projective plane, instead of a sphere. This steradian angle is equal to the geometric phase picked up by a spin system.

Sonar atlas of caverns comprising the U.S. Strategic Petroleum Reserve. Volume 4, West Hackberry site, Louisiana.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rautman, Christopher Arthur; Lord, Anna Snider

2007-09-01

Downhole sonar surveys from the four active U.S. Strategic Petroleum Reserve sites have been modeled and used to generate a four-volume sonar atlas, showing the three-dimensional geometry of each cavern. This volume 4 focuses on the West Hackberry SPR site, located in southwestern Louisiana. Volumes 1, 2, and 3, respectively, present images for the Bayou Choctaw SPR site, Louisiana, the Big Hill SPR site, Texas, and the Bryan Mound SPR site, Texas. The atlas uses a consistent presentation format throughout. The basic geometric measurements provided by the down-cavern surveys have also been used to generate a number of geometric attributes,more » the values of which have been mapped onto the geometric form of each cavern using a color-shading scheme. The intent of the various geometrical attributes is to highlight deviations of the cavern shape from the idealized cylindrical form of a carefully leached underground storage cavern in salt. The atlas format does not allow interpretation of such geometric deviations and anomalies. However, significant geometric anomalies, not directly related to the leaching history of the cavern, may provide insight into the internal structure of the relevant salt dome.« less

Sonar atlas of caverns comprising the U.S. Strategic Petroleum Reserve. Volume 2, Big Hill Site, Texas.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rautman, Christopher Arthur; Lord, Anna Snider

2007-08-01

Downhole sonar surveys from the four active U.S. Strategic Petroleum Reserve sites have been modeled and used to generate a four-volume sonar atlas, showing the three-dimensional geometry of each cavern. This volume 2 focuses on the Big Hill SPR site, located in southeastern Texas. Volumes 1, 3, and 4, respectively, present images for the Bayou Choctaw SPR site, Louisiana, the Bryan Mound SPR site, Texas, and the West Hackberry SPR site, Louisiana. The atlas uses a consistent presentation format throughout. The basic geometric measurements provided by the down-cavern surveys have also been used to generate a number of geometric attributes,more » the values of which have been mapped onto the geometric form of each cavern using a color-shading scheme. The intent of the various geometrical attributes is to highlight deviations of the cavern shape from the idealized cylindrical form of a carefully leached underground storage cavern in salt. The atlas format does not allow interpretation of such geometric deviations and anomalies. However, significant geometric anomalies, not directly related to the leaching history of the cavern, may provide insight into the internal structure of the relevant salt dome.« less

Sonar atlas of caverns comprising the U.S. Strategic Petroleum Reserve. Volume 1, Bayou Choctaw site, Louisiana.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rautman, Christopher Arthur; Lord, Anna Snider

2007-10-01

Downhole sonar surveys from the four active U.S. Strategic Petroleum Reserve sites have been modeled and used to generate a four-volume sonar atlas, showing the three-dimensional geometry of each cavern. This volume 1 focuses on the Bayou Choctaw SPR site, located in southern Louisiana. Volumes 2, 3, and 4, respectively, present images for the Big Hill SPR site, Texas, the Bryan Mound SPR site, Texas, and the West Hackberry SPR site, Louisiana. The atlas uses a consistent presentation format throughout. The basic geometric measurements provided by the down-cavern surveys have also been used to generate a number of geometric attributes,more » the values of which have been mapped onto the geometric form of each cavern using a color-shading scheme. The intent of the various geometrical attributes is to highlight deviations of the cavern shape from the idealized cylindrical form of a carefully leached underground storage cavern in salt. The atlas format does not allow interpretation of such geometric deviations and anomalies. However, significant geometric anomalies, not directly related to the leaching history of the cavern, may provide insight into the internal structure of the relevant salt dome.« less

Chord length distributions interpretation using a polydispersed population: Modeling and experiments

NASA Astrophysics Data System (ADS)

Cameirao, A.; Le Ba, H.; Darbouret, M.; Herri, J.-M.; Peytavy, J.-L.; Glénat, P.

2012-03-01

Chord length distributions were measured during the crystallization of gas hydrates in a flow loop. The conditions on the flow loop were similar with the conditions in the marine pipelines. The flow loop was filled with water in oil emulsion and pressurized with methane (7 MPa) at low temperature (277 K). During crystallization water droplets crystallize and agglomerate. The CLD measures were interpreted in a preceding work [Le Ba et al., 2010] [1] by constructing random aggregates with known geometrical proprieties from a monodispersed population of droplets and calculating their CLD. Comparing calculated CLD with CLD from the experiment, the geometrical parameters: number of primary particles and fractal dimension of experimental aggregates are identified. However some differences remained between the experiment and the calculated CLD. In the present work the droplets population was considered polydispersed improving the comparison between the model and the experiment.

Corrections to the geometrical interpretation of bosonization

NASA Astrophysics Data System (ADS)

Steiner, Manfred; Marston, Brad

2012-02-01

Bosonization is a powerful approach for understanding certain strongly-correlated fermion systems, especially in one spatial dimension but also in higher dimensionsootnotetextA.Houghton, H.-J. Kwon and J. B. Marston, Adv. in Phys. 49, 141 (2000).. The method may be interpreted geometrically in terms of deformations of the Fermi surface, and the quantum operator that effects the deformations may be expressed in terms of a bilinear combination of fermion creation and annihilation operators. Alternatively the deformation operator has an approximate representation in terms of coherent states of bosonic fieldsootnotetextA. H. Castro Neto and E. Fradkin, Phys. Rev. B 49, 10877 (1994).. Calculation of the inner product of deformed Fermi surfaces within the two representations reveals corrections to the bosonic picture both in one and higher spatial dimensions. We discuss the implications of the corrections for efforts to improve the usefulness of multidimensional bosonization.

Study of geometric phase using classical coupled oscillators

NASA Astrophysics Data System (ADS)

Bhattacharjee, Sharba; Dey, Biprateep; Mohapatra, Ashok K.

2018-05-01

We illustrate the geometric phase associated with the cyclic dynamics of a classical system of coupled oscillators. We use an analogy between a classical coupled oscillator and a two-state quantum mechanical system to represent the evolution of the oscillator on an equivalent Hilbert space, which may be represented as a trajectory on the surface of a sphere. The cyclic evolution of the system leads to a change in phase, which consists of a dynamic phase along with an additional phase shift dependent on the geometry of the evolution. A simple experiment suitable for advanced undergraduate students is designed to study the geometric phase incurred during cyclic evolution of a coupled oscillator.

[Feature extraction for breast cancer data based on geometric algebra theory and feature selection using differential evolution].

PubMed

Li, Jing; Hong, Wenxue

2014-12-01

The feature extraction and feature selection are the important issues in pattern recognition. Based on the geometric algebra representation of vector, a new feature extraction method using blade coefficient of geometric algebra was proposed in this study. At the same time, an improved differential evolution (DE) feature selection method was proposed to solve the elevated high dimension issue. The simple linear discriminant analysis was used as the classifier. The result of the 10-fold cross-validation (10 CV) classification of public breast cancer biomedical dataset was more than 96% and proved superior to that of the original features and traditional feature extraction method.

Computer Classification of Triangles and Quadrilaterals--A Challenging Application

ERIC Educational Resources Information Center

Dennis, J. Richard

1978-01-01

Two computer exercises involving the classification of geometric figures are given. The mathematics required is relatively simple but comes from several areas--synthetic geometry, analytic geometry, and linear algebra. (MN)

Solving quantum optimal control problems using Clebsch variables and Lin constraints

NASA Astrophysics Data System (ADS)

Delgado-Téllez, M.; Ibort, A.; Rodríguez de la Peña, T.

2018-01-01

Clebsch variables (and Lin constraints) are applied to the study of a class of optimal control problems for affine-controlled quantum systems. The optimal control problem will be modelled with controls defined on an auxiliary space where the dynamical group of the system acts freely. The reciprocity between both theories: the classical theory defined by the objective functional and the quantum system, is established by using a suitable version of Lagrange’s multipliers theorem and a geometrical interpretation of the constraints of the system as defining a subspace of horizontal curves in an associated bundle. It is shown how the solutions of the variational problem defined by the objective functional determine solutions of the quantum problem. Then a new way of obtaining explicit solutions for a family of optimal control problems for affine-controlled quantum systems (finite or infinite dimensional) is obtained. One of its main advantages, is the the use of Clebsch variables allows to compute such solutions from solutions of invariant problems that can often be computed explicitly. This procedure can be presented as an algorithm that can be applied to a large class of systems. Finally, some simple examples, spin control, a simple quantum Hamiltonian with an ‘Elroy beanie’ type classical model and a controlled one-dimensional quantum harmonic oscillator, illustrating the main features of the theory, will be discussed.

Determination of Geometric and Kinematical Parameters of Coronal Mass Ejections Using STEREO Data

NASA Astrophysics Data System (ADS)

Fainshtein, V. G.; Tsivileva, D. M.; Kashapova, L. K.

2010-03-01

We present a new, relatively simple and fast method to determine true geometric and kinematical CME parameters from simultaneous STEREO A, B observations of CMEs. These parameters are the three-dimensional direction of CME propagation, velocity and acceleration of CME front, CME angular sizes and front position depending on time. The method is based on the assumption that CME shape may be described by a modification of so-called ice-cream cone models. The method has been tested for several CMEs.

Why style matters - uncertainty and structural interpretation in thrust belts.

NASA Astrophysics Data System (ADS)

Butler, Rob; Bond, Clare; Watkins, Hannah

2016-04-01

Structural complexity together with challenging seismic imaging make for significant uncertainty in developing geometric interpretations of fold and thrust belts. Here we examine these issues and develop more realistic approaches to building interpretations. At all scales, the best tests of the internal consistency of individual interpretations come from structural restoration (section balancing), provided allowance is made for heterogeneity in stratigraphy and strain. However, many existing balancing approaches give misleading perceptions of interpretational risk - both on the scale of individual fold-thrust (trap) structures and in regional cross-sections. At the trap-scale, idealised models are widely cited - fault-bend-fold, fault-propagation folding and trishear. These make entirely arbitrary choices for fault localisation and layer-by-layer deformation: precise relationships between faults and fold geometry are generally invalidated by real-world conditions of stratigraphic variation and distributed strain. Furthermore, subsurface predictions made using these idealisations for hydrocarbon exploration commonly fail the test of drilling. Rarely acknowledged, the geometric reliability of seismic images depends on the assigned seismic velocity model, which in turn relies on geological interpretation. Thus iterative approaches are required between geology and geophysics. The portfolio of commonly cited outcrop analogues is strongly biased to examples that simply conform to idealised models - apparently abnormal structures are rarely described - or even photographed! Insight can come from gravity-driven deep-water fold-belts where part of the spectrum of fold-thrust complexity is resolved through seismic imaging. This imagery shows deformation complexity in fold forelimbs and backlimbs. However, the applicability of these, weakly lithified systems to well-lithified successions (e.g. carbonates) of many foreland thrust belts remains conjectural. Examples of lithified systems will be drawn from the foothills of the Colombian Andes and the Papuan fold-belt. These show major forelimb structures with segmented steep-limbs containing substantial oil-columns, suggesting forelimb complexity in lithified sections maybe more common than predicted by idealised models. As with individual fold-thrust structures, regional cross-sections are commonly open to multiple interpretations. To date the over-reliance on comparative approaches with a narrow range of published studies (e.g. Canadian cordilleran foothills) has biased global interpretations of thrust systems. Perhaps the most significant issues relate to establishing a depth to detachment - specifically the involvement of basement at depth - especially the role of pre-existing (rift-originated) faults and their inversion. Not only do these choices impact on the local interpretation, the inferred shortening values, obtained by comparing restored section-lengths, can be radically different. Further issues arise for emergent, syn-depositional thrust systems where sedimentation prohibits flat-on-flat thrusting in favour of continuously ramping thrust trajectories. Inappropriate adoption of geometries gathered from buried (duplex) systems can create geometric interpretations that are tectono-stratigraphically invalid. This presentation illustrates these topics using a variety of thrust systems with the aim of promoting discussion on developing better interpretative strategies than those adopted hitherto.

Type II superstring field theory: geometric approach and operadic description

NASA Astrophysics Data System (ADS)

Jurčo, Branislav; Münster, Korbinian

2013-04-01

We outline the construction of type II superstring field theory leading to a geometric and algebraic BV master equation, analogous to Zwiebach's construction for the bosonic string. The construction uses the small Hilbert space. Elementary vertices of the non-polynomial action are described with the help of a properly formulated minimal area problem. They give rise to an infinite tower of superstring field products defining a {N} = 1 generalization of a loop homotopy Lie algebra, the genus zero part generalizing a homotopy Lie algebra. Finally, we give an operadic interpretation of the construction.

Recognition of Simple 3D Geometrical Objects under Partial Occlusion

NASA Astrophysics Data System (ADS)

Barchunova, Alexandra; Sommer, Gerald

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

Simple and Reliable Determination of Intravoxel Incoherent Motion Parameters for the Differential Diagnosis of Head and Neck Tumors

PubMed Central

Sasaki, Miho; Sumi, Misa; Eida, Sato; Katayama, Ikuo; Hotokezaka, Yuka; Nakamura, Takashi

2014-01-01

Intravoxel incoherent motion (IVIM) imaging can characterize diffusion and perfusion of normal and diseased tissues, and IVIM parameters are authentically determined by using cumbersome least-squares method. We evaluated a simple technique for the determination of IVIM parameters using geometric analysis of the multiexponential signal decay curve as an alternative to the least-squares method for the diagnosis of head and neck tumors. Pure diffusion coefficients (D), microvascular volume fraction (f), perfusion-related incoherent microcirculation (D*), and perfusion parameter that is heavily weighted towards extravascular space (P) were determined geometrically (Geo D, Geo f, and Geo P) or by least-squares method (Fit D, Fit f, and Fit D*) in normal structures and 105 head and neck tumors. The IVIM parameters were compared for their levels and diagnostic abilities between the 2 techniques. The IVIM parameters were not able to determine in 14 tumors with the least-squares method alone and in 4 tumors with the geometric and least-squares methods. The geometric IVIM values were significantly different (p<0.001) from Fit values (+2±4% and −7±24% for D and f values, respectively). Geo D and Fit D differentiated between lymphomas and SCCs with similar efficacy (78% and 80% accuracy, respectively). Stepwise approaches using combinations of Geo D and Geo P, Geo D and Geo f, or Fit D and Fit D* differentiated between pleomorphic adenomas, Warthin tumors, and malignant salivary gland tumors with the same efficacy (91% accuracy = 21/23). However, a stepwise differentiation using Fit D and Fit f was less effective (83% accuracy = 19/23). Considering cumbersome procedures with the least squares method compared with the geometric method, we concluded that the geometric determination of IVIM parameters can be an alternative to least-squares method in the diagnosis of head and neck tumors. PMID:25402436

New fast least-squares algorithm for estimating the best-fitting parameters due to simple geometric-structures from gravity anomalies.

PubMed

Essa, Khalid S

2014-01-01

A new fast least-squares method is developed to estimate the shape factor (q-parameter) of a buried structure using normalized residual anomalies obtained from gravity data. The problem of shape factor estimation is transformed into a problem of finding a solution of a non-linear equation of the form f(q) = 0 by defining the anomaly value at the origin and at different points on the profile (N-value). Procedures are also formulated to estimate the depth (z-parameter) and the amplitude coefficient (A-parameter) of the buried structure. The method is simple and rapid for estimating parameters that produced gravity anomalies. This technique is used for a class of geometrically simple anomalous bodies, including the semi-infinite vertical cylinder, the infinitely long horizontal cylinder, and the sphere. The technique is tested and verified on theoretical models with and without random errors. It is also successfully applied to real data sets from Senegal and India, and the inverted-parameters are in good agreement with the known actual values.

Effects of Geometric Variations on Lift Augmentation of Simple-plenum-chamber Ground-effect Models

NASA Technical Reports Server (NTRS)

Davenport, Edwin E.

1961-01-01

Considerable interest has been shown during recent years in ground-effect vehicles. Of the various types proposed, the simple-plenum-chamber vehicle has indicated promise because, although the lift augmentation obtainable appears to be less than that of an annular jet, it may be somewhat less complicated structurally. The present investigation was undertaken to study the effects of some geometric variations upon lift augmentation of a simple plenum chamber within ground proximity. The variables included the ratio inlet area to exit area, plenum-chamber depth, and entrance configuration. An optimum plenum-chamber depth appeared to be between 3 and 10 percent of the plenum-chamber diameter with a ratio of inlet diameter to plenum-chamber diameter of 0.15 for the range of plenum-chamber depths investigated. The most important effect of multiple inlets was the elimination of negative lift augmentation, which was experienced with single sharp-edged inlets, at intermediate heights. Installation of a flared inlet and a turning-vane assembly improved lift augmentation of a single-inlet configuration at intermediate heights.

New fast least-squares algorithm for estimating the best-fitting parameters due to simple geometric-structures from gravity anomalies

PubMed Central

Essa, Khalid S.

2013-01-01

A new fast least-squares method is developed to estimate the shape factor (q-parameter) of a buried structure using normalized residual anomalies obtained from gravity data. The problem of shape factor estimation is transformed into a problem of finding a solution of a non-linear equation of the form f(q) = 0 by defining the anomaly value at the origin and at different points on the profile (N-value). Procedures are also formulated to estimate the depth (z-parameter) and the amplitude coefficient (A-parameter) of the buried structure. The method is simple and rapid for estimating parameters that produced gravity anomalies. This technique is used for a class of geometrically simple anomalous bodies, including the semi-infinite vertical cylinder, the infinitely long horizontal cylinder, and the sphere. The technique is tested and verified on theoretical models with and without random errors. It is also successfully applied to real data sets from Senegal and India, and the inverted-parameters are in good agreement with the known actual values. PMID:25685472

Interpretation of styles of simple stations in Korea

NASA Astrophysics Data System (ADS)

Hwang, Minhye; Shin, Yekyeong

2018-06-01

The purpose of this paper is to apply stylistic interpretation through the exterior of simple stations in Korea. Simple Station is a kind of railway stations. It was installed when there were not a lot of passengers and it was not necessary to operate the station at a high cost. It has minimal functions such as a waiting room, an office, an operating room, and toilets and was built between the 1910s and the 1960s. The form of the building is as simple as the name of "Simple Station". That is why the reading its style is easy and obvious. But it is also difficult to interpret because of the lack of stylistic evidences. Nevertheless, in the relationship between the station and the station tree, the concept of the Picturesque and Palladian Style are found. But it is still hard to distinguish whether the whole building style is Western or Japanese. Simple Station is one of the things that Japan has built as Western Culture in Korea during the Japanese colonial era, so it is natural that its style of form is complex.

Waves and rays in plano-concave laser cavities: I. Geometric modes in the paraxial approximation

NASA Astrophysics Data System (ADS)

Barré, N.; Romanelli, M.; Lebental, M.; Brunel, M.

2017-05-01

Eigenmodes of laser cavities are studied theoretically and experimentally in two companion papers, with the aim of making connections between undulatory and geometric properties of light. In this first paper, we focus on macroscopic open-cavity lasers with localized gain. The model is based on the wave equation in the paraxial approximation; experiments are conducted with a simple diode-pumped Nd:YAG laser with a variable cavity length. After recalling fundamentals of laser beam optics, we consider plano-concave cavities with on-axis or off-axis pumping, with emphasis put on degenerate cavity lengths, where modes of different order resonate at the same frequency, and combine to form surprising transverse beam profiles. Degeneracy leads to the oscillation of so-called geometric modes whose properties can be understood, to a certain extent, also within a ray optics picture. We first provide a heuristic description of these modes, based on geometric reasoning, and then show more rigorously how to derive them analytically by building wave superpositions, within the framework of paraxial wave optics. The numerical methods, based on the Fox-Li approach, are described in detail. The experimental setup, including the imaging system, is also detailed and relatively simple to reproduce. The aim is to facilitate implementation of both the numerics and of the experiments, and to show that one can have access not only to the common higher-order modes but also to more exotic patterns.

Estimating Model Probabilities using Thermodynamic Markov Chain Monte Carlo Methods

NASA Astrophysics Data System (ADS)

Ye, M.; Liu, P.; Beerli, P.; Lu, D.; Hill, M. C.

2014-12-01

Markov chain Monte Carlo (MCMC) methods are widely used to evaluate model probability for quantifying model uncertainty. In a general procedure, MCMC simulations are first conducted for each individual model, and MCMC parameter samples are then used to approximate marginal likelihood of the model by calculating the geometric mean of the joint likelihood of the model and its parameters. It has been found the method of evaluating geometric mean suffers from the numerical problem of low convergence rate. A simple test case shows that even millions of MCMC samples are insufficient to yield accurate estimation of the marginal likelihood. To resolve this problem, a thermodynamic method is used to have multiple MCMC runs with different values of a heating coefficient between zero and one. When the heating coefficient is zero, the MCMC run is equivalent to a random walk MC in the prior parameter space; when the heating coefficient is one, the MCMC run is the conventional one. For a simple case with analytical form of the marginal likelihood, the thermodynamic method yields more accurate estimate than the method of using geometric mean. This is also demonstrated for a case of groundwater modeling with consideration of four alternative models postulated based on different conceptualization of a confining layer. This groundwater example shows that model probabilities estimated using the thermodynamic method are more reasonable than those obtained using the geometric method. The thermodynamic method is general, and can be used for a wide range of environmental problem for model uncertainty quantification.

The effect of somatic cell count data adjustment and interpretation, as outlined in European Union legislation, on herd eligibility to supply raw milk for processing of dairy products.

PubMed

More, S J; Clegg, T A; Lynch, P J; O'Grady, L

2013-06-01

Somatic cell count (SCC) limits are a key component of national and international regulation for milk quality. As yet, very limited work has been published on SCC regulatory standards, including on the effect of different approaches to SCC data adjustment and interpretation. This study examines the effect of SCC data adjustment and interpretation, as outlined in current European Union (EU) legislation, on herd eligibility to supply raw milk for processing of dairy products for human consumption, using Irish data for illustration. The study used Irish milk-recording data as a proxy for bulk tank SCC (BTSCC) data, to calculate an unadjusted monthly SCC value for each herd during each month of participation. Subsequently, 4 data adjustments were applied, as outlined in EU and national legislation: seasonal adjustment; 3-mo rolling geometric average, without accounting for a break in the supply; 3-mo rolling geometric average, after accounting for a break in the supply; and seasonal adjustment and 3-mo rolling geometric average combined, after accounting for a break in the supply. Analyses were conducted to examine the effect, during the period from 2004 to 2010, of data adjustment on the percentage of herds with herd SCC >400,000 cells/mL. In all, 4 interpretation scenarios, incorporating different data adjustment combinations, were used to estimate herd eligibility (compliant, under warning, or suspended, as defined by legislation) to supply raw milk for processing. The 4 methods of data adjustment each led to a sizable reduction (6.7, 5.0, 5.3, and 11.1 percentage points, respectively, compared with the unadjusted data) in the percentage of herds exceeding a herd SCC of 400,000 cells/mL. Herd eligibility varied by interpretation scenarios, in particular those incorporating seasonal adjustment. The study provides new perspectives on the effect of data adjustment on herd SCC and of interpretation scenarios on herd eligibility. The results provide an illustrative, rather than definitive, picture of this effect, as national authorities use BTSCC data when determining herd eligibility, whereas this study was conducted using milk-recording data as a proxy. Some aspects of the primary EU legislation are unclear, which may lead to differences in interpretation and application. The potential impact of data adjustment and milk purchaser pricing on farm-level mastitis control in Ireland is considered. Copyright © 2013 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

Geometrical approach to neural net control of movements and posture

NASA Technical Reports Server (NTRS)

Pellionisz, A. J.; Ramos, C. F.

1993-01-01

In one approach to modeling brain function, sensorimotor integration is described as geometrical mapping among coordinates of non-orthogonal frames that are intrinsic to the system; in such a case sensors represent (covariant) afferents and motor effectors represent (contravariant) motor efferents. The neuronal networks that perform such a function are viewed as general tensor transformations among different expressions and metric tensors determining the geometry of neural functional spaces. Although the non-orthogonality of a coordinate system does not impose a specific geometry on the space, this "Tensor Network Theory of brain function" allows for the possibility that the geometry is non-Euclidean. It is suggested that investigation of the non-Euclidean nature of the geometry is the key to understanding brain function and to interpreting neuronal network function. This paper outlines three contemporary applications of such a theoretical modeling approach. The first is the analysis and interpretation of multi-electrode recordings. The internal geometries of neural networks controlling external behavior of the skeletomuscle system is experimentally determinable using such multi-unit recordings. The second application of this geometrical approach to brain theory is modeling the control of posture and movement. A preliminary simulation study has been conducted with the aim of understanding the control of balance in a standing human. The model appears to unify postural control strategies that have previously been considered to be independent of each other. Third, this paper emphasizes the importance of the geometrical approach for the design and fabrication of neurocomputers that could be used in functional neuromuscular stimulation (FNS) for replacing lost motor control.

Detection of Chorus Elements and other Wave Signatures Using Geometric Computational Techniques in the Van Allen radiation belts

NASA Astrophysics Data System (ADS)

Sengupta, A.; Kletzing, C.; Howk, R.; Kurth, W. S.

2017-12-01

An important goal of the Van Allen Probes mission is to understand wave particle interactions that can energize relativistic electron in the Earth's Van Allen radiation belts. The EMFISIS instrumentation suite provides measurements of wave electric and magnetic fields of wave features such as chorus that participate in these interactions. Geometric signal processing discovers structural relationships, e.g. connectivity across ridge-like features in chorus elements to reveal properties such as dominant angles of the element (frequency sweep rate) and integrated power along the a given chorus element. These techniques disambiguate these wave features against background hiss-like chorus. This enables autonomous discovery of chorus elements across the large volumes of EMFISIS data. At the scale of individual or overlapping chorus elements, topological pattern recognition techniques enable interpretation of chorus microstructure by discovering connectivity and other geometric features within the wave signature of a single chorus element or between overlapping chorus elements. Thus chorus wave features can be quantified and studied at multiple scales of spectral geometry using geometric signal processing techniques. We present recently developed computational techniques that exploit spectral geometry of chorus elements and whistlers to enable large-scale automated discovery, detection and statistical analysis of these events over EMFISIS data. Specifically, we present different case studies across a diverse portfolio of chorus elements and discuss the performance of our algorithms regarding precision of detection as well as interpretation of chorus microstructure. We also provide large-scale statistical analysis on the distribution of dominant sweep rates and other properties of the detected chorus elements.

Imbalanced target prediction with pattern discovery on clinical data repositories.

PubMed

Chan, Tak-Ming; Li, Yuxi; Chiau, Choo-Chiap; Zhu, Jane; Jiang, Jie; Huo, Yong

2017-04-20

Clinical data repositories (CDR) have great potential to improve outcome prediction and risk modeling. However, most clinical studies require careful study design, dedicated data collection efforts, and sophisticated modeling techniques before a hypothesis can be tested. We aim to bridge this gap, so that clinical domain users can perform first-hand prediction on existing repository data without complicated handling, and obtain insightful patterns of imbalanced targets for a formal study before it is conducted. We specifically target for interpretability for domain users where the model can be conveniently explained and applied in clinical practice. We propose an interpretable pattern model which is noise (missing) tolerant for practice data. To address the challenge of imbalanced targets of interest in clinical research, e.g., deaths less than a few percent, the geometric mean of sensitivity and specificity (G-mean) optimization criterion is employed, with which a simple but effective heuristic algorithm is developed. We compared pattern discovery to clinically interpretable methods on two retrospective clinical datasets. They contain 14.9% deaths in 1 year in the thoracic dataset and 9.1% deaths in the cardiac dataset, respectively. In spite of the imbalance challenge shown on other methods, pattern discovery consistently shows competitive cross-validated prediction performance. Compared to logistic regression, Naïve Bayes, and decision tree, pattern discovery achieves statistically significant (p-values < 0.01, Wilcoxon signed rank test) favorable averaged testing G-means and F1-scores (harmonic mean of precision and sensitivity). Without requiring sophisticated technical processing of data and tweaking, the prediction performance of pattern discovery is consistently comparable to the best achievable performance. Pattern discovery has demonstrated to be robust and valuable for target prediction on existing clinical data repositories with imbalance and noise. The prediction results and interpretable patterns can provide insights in an agile and inexpensive way for the potential formal studies.

Hydraulic head estimation at unobserved locations: Approximating the distribution of the absolute error based on geologic interpretations

NASA Astrophysics Data System (ADS)

Langousis, Andreas; Kaleris, Vassilios; Xeygeni, Vagia; Magkou, Foteini

2017-04-01

Assessing the availability of groundwater reserves at a regional level, requires accurate and robust hydraulic head estimation at multiple locations of an aquifer. To that extent, one needs groundwater observation networks that can provide sufficient information to estimate the hydraulic head at unobserved locations. The density of such networks is largely influenced by the spatial distribution of the hydraulic conductivity in the aquifer, and it is usually determined through trial-and-error, by solving the groundwater flow based on a properly selected set of alternative but physically plausible geologic structures. In this work, we use: 1) dimensional analysis, and b) a pulse-based stochastic model for simulation of synthetic aquifer structures, to calculate the distribution of the absolute error in hydraulic head estimation as a function of the standardized distance from the nearest measuring locations. The resulting distributions are proved to encompass all possible small-scale structural dependencies, exhibiting characteristics (bounds, multi-modal features etc.) that can be explained using simple geometric arguments. The obtained results are promising, pointing towards the direction of establishing design criteria based on large-scale geologic maps.

A Geometric View of Complex Trigonometric Functions

ERIC Educational Resources Information Center

Hammack, Richard

2007-01-01

Given that the sine and cosine functions of a real variable can be interpreted as the coordinates of points on the unit circle, the author of this article asks whether there is something similar for complex variables, and shows that indeed there is.

On Ruch's Principle of Decreasing Mixing Distance in classical statistical physics

NASA Astrophysics Data System (ADS)

Busch, Paul; Quadt, Ralf

1990-10-01

Ruch's Principle of Decreasing Mixing Distance is reviewed as a statistical physical principle and its basic suport and geometric interpretation, the Ruch-Schranner-Seligman theorem, is generalized to be applicable to a large representative class of classical statistical systems.

A Simple Geometric Model for the Marcus Theory of Proton Transfer

ERIC Educational Resources Information Center

McLennan, Duncan J.

1976-01-01

Uses the intersecting parabola model to derive an equation that relates the observed free energy of activation for a slow proton transfer to the overall thermodynamic free energy change in the reaction. (MLH)

A Simple Method to Determine the Refractive Index of Glass.

ERIC Educational Resources Information Center

Mak, Se-yuen

1988-01-01

Describes an experiment for determining the refractive index. Discusses the experiment procedure and mathematical expression for calculating the index. Provides two geometrical diagrams and a graph for determining the index with a typical data. (YP)

Modelling acceptance of sunlight in high and low photovoltaic concentration

NASA Astrophysics Data System (ADS)

Leutz, Ralf

2014-09-01

A simple model incorporating linear radiation characteristics, along with the optical trains and geometrical concentration ratios of solar concentrators is presented with performance examples for optical trains of HCPV, LCPV and benchmark flat-plate PV.

FUNDAMENTALS OF THRESHOLD LOGIC.

DTIC Science & Technology

These notes on threshold logic are intended as intermediary material between a completely geometric, heuristic presentation and the more formal...source material available in the literature. Basic definitions and simple properties of threshold function are developed, followed by a complete treatment

Geometry and Reynolds-Number Scaling on an Iced Business-Jet Wing

NASA Technical Reports Server (NTRS)

Lee, Sam; Ratvasky, Thomas P.; Thacker, Michael; Barnhart, Billy P.

2005-01-01

A study was conducted to develop a method to scale the effect of ice accretion on a full-scale business jet wing model to a 1/12-scale model at greatly reduced Reynolds number. Full-scale, 5/12-scale, and 1/12-scale models of identical airfoil section were used in this study. Three types of ice accretion were studied: 22.5-minute ice protection system failure shape, 2-minute initial ice roughness, and a runback shape that forms downstream of a thermal anti-ice system. The results showed that the 22.5-minute failure shape could be scaled from full-scale to 1/12-scale through simple geometric scaling. The 2-minute roughness shape could be scaled by choosing an appropriate grit size. The runback ice shape exhibited greater Reynolds number effects and could not be scaled by simple geometric scaling of the ice shape.

Interaction Between Air Propellers and Airplane Structures

NASA Technical Reports Server (NTRS)

Durand, W F

1927-01-01

The purpose of this investigation was the determination of the character and amount of interaction between air propellers as usually mounted on airplanes and the adjacent parts of the airplane structure - or, more specifically, those parts of the airplane structure within the wash of the propeller, and capable of producing any significant effect on propeller performance. In report no. 177 such interaction between air propellers and certain simple geometrical forms was made the subject of investigation and report. The present investigation aims to carry this general study one stage further by substituting actual airplane structures for the simple geometrical forms. From the point of view of the present investigation, the airplane structures, viewed as an obstruction in the wake of the propeller, must also be viewed as a necessary part of the airplane and not as an appendage which might be installed or removed at will. (author)

Interpreting DNAPL saturations in a laboratory-scale injection using one- and two-dimensional modeling of GPR Data

USGS Publications Warehouse

Johnson, R.H.; Poeter, E.P.

2005-01-01

Ground-penetrating radar (GPR) is used to track a dense non-aqueous phase liquid (DNAPL) injection in a laboratory sand tank. Before modeling, the GPR data provide a qualitative image of DNAPL saturation and movement. One-dimensional (1D) GPR modeling provides a quantitative interpretation of DNAPL volume within a given thickness during and after the injection. DNAPL saturation in sublayers of a specified thickness could not be quantified because calibration of the 1D GPR model is nonunique when both permittivity and depth of multiple layers are unknown. One-dimensional GPR modeling of the sand tank indicates geometric interferences in a small portion of the tank. These influences are removed from the interpretation using an alternate matching target. Two-dimensional (2D) GPR modeling provides a qualitative interpretation of the DNAPL distribution through pattern matching and tests for possible 2D influences that are not accounted for in the 1D GPR modeling. Accurate quantitative interpretation of DNAPL volumes using GPR modeling requires (1) identification of a suitable target that produces a strong reflection and is not subject to any geometric interference; (2) knowledge of the exact depth of that target; and (3) use of two-way radar-wave travel times through the medium to the target to determine the permittivity of the intervening material, which eliminates reliance on signal amplitude. With geologic conditions that are suitable for GPR surveys (i.e., shallow depths, low electrical conductivities, and a known reflective target), the procedures in this laboratory study can be adapted to a field site to delineate shallow DNAPL source zones.

Uncovering Oscillations, Complexity, and Chaos in Chemical Kinetics Using Mathematica

NASA Astrophysics Data System (ADS)

Ferreira, M. M. C.; Ferreira, W. C., Jr.; Lino, A. C. S.; Porto, M. E. G.

1999-06-01

Unlike reactions with no peculiar temporal behavior, in oscillatory reactions concentrations can rise and fall spontaneously in a cyclic or disorganized fashion. In this article, the software Mathematica is used for a theoretical study of kinetic mechanisms of oscillating and chaotic reactions. A first simple example is introduced through a three-step reaction, called the Lotka model, which exhibits a temporal behavior characterized by damped oscillations. The phase plane method of dynamic systems theory is introduced for a geometric interpretation of the reaction kinetics without solving the differential rate equations. The equations are later numerically solved using the built-in routine NDSolve and the results are plotted. The next example, still with a very simple mechanism, is the Lotka-Volterra model reaction, which oscillates indefinitely. The kinetic process and rate equations are also represented by a three-step reaction mechanism. The most important difference between this and the former reaction is that the undamped oscillation has two autocatalytic steps instead of one. The periods of oscillations are obtained by using the discrete Fourier transform (DFT)-a well-known tool in spectroscopy, although not so common in this context. In the last section, it is shown how a simple model of biochemical interactions can be useful to understand the complex behavior of important biological systems. The model consists of two allosteric enzymes coupled in series and activated by its own products. This reaction scheme is important for explaining many metabolic mechanisms, such as the glycolytic oscillations in muscles, yeast glycolysis, and the periodic synthesis of cyclic AMP. A few of many possible dynamic behaviors are exemplified through a prototype glycolytic enzymatic reaction proposed by Decroly and Goldbeter. By simply modifying the initial concentrations, limit cycles, chaos, and birhythmicity are computationally obtained and visualized.

An Interpreted Language and System for the Visualization of Unstructured Meshes

NASA Technical Reports Server (NTRS)

Moran, Patrick J.; Gerald-Yamasaki, Michael (Technical Monitor)

1998-01-01

We present an interpreted language and system supporting the visualization of unstructured meshes and the manipulation of shapes defined in terms of mesh subsets. The language features primitives inspired by geometric modeling, mathematical morphology and algebraic topology. The adaptation of the topology ideas to an interpreted environment, along with support for programming constructs such, as user function definition, provide a flexible system for analyzing a mesh and for calculating with shapes defined in terms of the mesh. We present results demonstrating some of the capabilities of the language, based on an implementation called the Shape Calculator, for tetrahedral meshes in R^3.

Soft Tissue Structure Modelling for Use in Orthopaedic Applications and Musculoskeletal Biomechanics

NASA Astrophysics Data System (ADS)

Audenaert, E. A.; Mahieu, P.; van Hoof, T.; Pattyn, C.

2009-12-01

We present our methodology for the three-dimensional anatomical and geometrical description of soft tissues, relevant for orthopaedic surgical applications and musculoskeletal biomechanics. The technique involves the segmentation and geometrical description of muscles and neurovascular structures from high-resolution computer tomography scanning for the reconstruction of generic anatomical models. These models can be used for quantitative interpretation of anatomical and biomechanical aspects of different soft tissue structures. This approach should allow the use of these data in other application fields, such as musculoskeletal modelling, simulations for radiation therapy, and databases for use in minimally invasive, navigated and robotic surgery.

Aspects of Geodesical Motion with Fisher-Rao Metric: Classical and Quantum

NASA Astrophysics Data System (ADS)

Ciaglia, Florio M.; Cosmo, Fabio Di; Felice, Domenico; Mancini, Stefano; Marmo, Giuseppe; Pérez-Pardo, Juan M.

The purpose of this paper is to exploit the geometric structure of quantum mechanics and of statistical manifolds to study the qualitative effect that the quantum properties have in the statistical description of a system. We show that the end points of geodesics in the classical setting coincide with the probability distributions that minimise Shannon’s entropy, i.e. with distributions of zero dispersion. In the quantum setting this happens only for particular initial conditions, which in turn correspond to classical submanifolds. This result can be interpreted as a geometric manifestation of the uncertainty principle.

Delineation of soil temperature regimes from HCMM data

NASA Technical Reports Server (NTRS)

Day, R. L.; Petersen, G. W. (Principal Investigator)

1981-01-01

Supplementary data including photographs as well as topographic, geologic, and soil maps were obtained and evaluated for ground truth purposes and control point selection. A study area (approximately 450 by 450 pixels) was subset from LANDSAT scene No. 2477-17142. Geometric corrections and scaling were performed. Initial enhancement techniques were initiated to aid control point selection and soils interpretation. The SUBSET program was modified to read HCMM tapes and HCMM data were reformated so that they are compatible with the ORSER system. Initial NMAP products of geometrically corrected and scaled raw data tapes (unregistered) of the study were produced.

Duncan F. Gregory, William Walton and the development of British algebra: 'algebraical geometry', 'geometrical algebra', abstraction.

PubMed

Verburgt, Lukas M

2016-01-01

This paper provides a detailed account of the period of the complex history of British algebra and geometry between the publication of George Peacock's Treatise on Algebra in 1830 and William Rowan Hamilton's paper on quaternions of 1843. During these years, Duncan Farquharson Gregory and William Walton published several contributions on 'algebraical geometry' and 'geometrical algebra' in the Cambridge Mathematical Journal. These contributions enabled them not only to generalize Peacock's symbolical algebra on the basis of geometrical considerations, but also to initiate the attempts to question the status of Euclidean space as the arbiter of valid geometrical interpretations. At the same time, Gregory and Walton were bound by the limits of symbolical algebra that they themselves made explicit; their work was not and could not be the 'abstract algebra' and 'abstract geometry' of figures such as Hamilton and Cayley. The central argument of the paper is that an understanding of the contributions to 'algebraical geometry' and 'geometrical algebra' of the second generation of 'scientific' symbolical algebraists is essential for a satisfactory explanation of the radical transition from symbolical to abstract algebra that took place in British mathematics in the 1830s-1840s.

The Projectile Inside the Loop

ERIC Educational Resources Information Center

Varieschi, Gabriele U.

2006-01-01

The loop-the-loop demonstration can be easily adapted to study the kinematics of projectile motion, when the moving body falls inside the apparatus. Video capturing software can be used to reveal peculiar geometrical effects of this simple but educational experiment.

Implementing the "Curriculum and Evaluation Standards."

ERIC Educational Resources Information Center

Pacyga, Robert

1994-01-01

Describes two activities to analyze unit-cell structures from a geometric viewpoint and invite students to apply their mathematical understanding to scientific phenomena. Students form models of the simple cube, a building block of crystalline structures, and a methane molecule. (MDH)

Three-Point Functions in c≤1 Liouville Theory and Conformal Loop Ensembles.

PubMed

Ikhlef, Yacine; Jacobsen, Jesper Lykke; Saleur, Hubert

2016-04-01

The possibility of extending the Liouville conformal field theory from values of the central charge c≥25 to c≤1 has been debated for many years in condensed matter physics as well as in string theory. It was only recently proven that such an extension-involving a real spectrum of critical exponents as well as an analytic continuation of the Dorn-Otto-Zamolodchikov-Zamolodchikov formula for three-point couplings-does give rise to a consistent theory. We show in this Letter that this theory can be interpreted in terms of microscopic loop models. We introduce in particular a family of geometrical operators, and, using an efficient algorithm to compute three-point functions from the lattice, we show that their operator algebra corresponds exactly to that of vertex operators V_{α[over ^]} in c≤1 Liouville theory. We interpret geometrically the limit α[over ^]→0 of V_{α[over ^]} and explain why it is not the identity operator (despite having conformal weight Δ=0).

Semantic Segmentation of Building Elements Using Point Cloud Hashing

NASA Astrophysics Data System (ADS)

Chizhova, M.; Gurianov, A.; Hess, M.; Luhmann, T.; Brunn, A.; Stilla, U.

2018-05-01

For the interpretation of point clouds, the semantic definition of extracted segments from point clouds or images is a common problem. Usually, the semantic of geometrical pre-segmented point cloud elements are determined using probabilistic networks and scene databases. The proposed semantic segmentation method is based on the psychological human interpretation of geometric objects, especially on fundamental rules of primary comprehension. Starting from these rules the buildings could be quite well and simply classified by a human operator (e.g. architect) into different building types and structural elements (dome, nave, transept etc.), including particular building parts which are visually detected. The key part of the procedure is a novel method based on hashing where point cloud projections are transformed into binary pixel representations. A segmentation approach released on the example of classical Orthodox churches is suitable for other buildings and objects characterized through a particular typology in its construction (e.g. industrial objects in standardized enviroments with strict component design allowing clear semantic modelling).

Chaos in matrix models and black hole evaporation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Berkowitz, Evan; Hanada, Masanori; Maltz, Jonathan

Is the evaporation of a black hole described by a unitary theory? In order to shed light on this question—especially aspects of this question such as a black hole’s negative specific heat—we consider the real-time dynamics of a solitonic object in matrix quantum mechanics, which can be interpreted as a black hole (black zero-brane) via holography. We point out that the chaotic nature of the system combined with the flat directions of its potential naturally leads to the emission of D0-branes from the black brane, which is suppressed in the large N limit. Simple arguments show that the black zero-brane,more » like the Schwarzschild black hole, has negative specific heat, in the sense that the temperature goes up when it evaporates by emitting D0-branes. While the largest Lyapunov exponent grows during the evaporation, the Kolmogorov-Sinai entropy decreases. These are consequences of the generic properties of matrix models and gauge theory. Based on these results, we give a possible geometric interpretation of the eigenvalue distribution of matrices in terms of gravity. Applying the same argument in the M-theory parameter region, we provide a scenario to derive the Hawking radiation of massless particles from the Schwarzschild black hole. In conclusion, we suggest that by adding a fraction of the quantum effects to the classical theory, we can obtain a matrix model whose classical time evolution mimics the entire life of the black brane, from its formation to the evaporation.« less

Chaos in matrix models and black hole evaporation

DOE PAGES

Berkowitz, Evan; Hanada, Masanori; Maltz, Jonathan

2016-12-19

Is the evaporation of a black hole described by a unitary theory? In order to shed light on this question—especially aspects of this question such as a black hole’s negative specific heat—we consider the real-time dynamics of a solitonic object in matrix quantum mechanics, which can be interpreted as a black hole (black zero-brane) via holography. We point out that the chaotic nature of the system combined with the flat directions of its potential naturally leads to the emission of D0-branes from the black brane, which is suppressed in the large N limit. Simple arguments show that the black zero-brane,more » like the Schwarzschild black hole, has negative specific heat, in the sense that the temperature goes up when it evaporates by emitting D0-branes. While the largest Lyapunov exponent grows during the evaporation, the Kolmogorov-Sinai entropy decreases. These are consequences of the generic properties of matrix models and gauge theory. Based on these results, we give a possible geometric interpretation of the eigenvalue distribution of matrices in terms of gravity. Applying the same argument in the M-theory parameter region, we provide a scenario to derive the Hawking radiation of massless particles from the Schwarzschild black hole. In conclusion, we suggest that by adding a fraction of the quantum effects to the classical theory, we can obtain a matrix model whose classical time evolution mimics the entire life of the black brane, from its formation to the evaporation.« less

Length measurement and spatial orientation reconstruction of single nanowires.

PubMed

Prestopino, Giuseppe; Orsini, Andrea; Falconi, Christian; Bietti, Sergio; Verona-Rinati, Gianluca; Caselli, Federica; Bisegna, Paolo

2018-06-27

The accurate determination of the geometrical features of quasi one-dimensional nanostructures is mandatory for reducing errors and improving repeatability in the estimation of a number of geometry-dependent properties in nanotechnology. In this paper a method for the reconstruction of length and spatial orientation of single nanowires is presented. Those quantities are calculated from a sequence of scanning electron microscope images taken at different tilt angles using a simple 3D geometric model. The proposed method is evaluated on a collection of scanning electron microscope images of single GaAs nanowires. It is validated through the reconstruction of known geometric features of a standard reference calibration pattern. An overall uncertainty of about 1% in the estimated length of the nanowires is achieved. © 2018 IOP Publishing Ltd.

U-folds as K3 fibrations

NASA Astrophysics Data System (ADS)

Braun, Andreas P.; Fucito, Francesco; Morales, Jose Francisco

2013-10-01

We study four-dimensional flux vacua describing intrinsic non- perturbative systems of 3 and 7 branes in type IIB string theory. The solutions are described as compactifications of a G(ravity) theory on a Calabi Yau threefold which consists of a fibration of an auxiliary K3 surface over an S 2 base. In the spirit of F-theory, the complex structure of the K3 surface varying over the base codifies the details of the fluxes, the dilaton and the warp factors in type IIB string theory. We discuss in detail some simple examples of geometric and non-geometric solutions where the precise flux/geometry dictionary can be explicitly worked out. In particular, we describe non-geometric T-fold solutions exhibiting non-trivial T-duality monodromies exchanging 3- and 7-branes.

Far-side geometrical enhancement in surface-enhanced Raman scattering with Ag plasmonic films

NASA Astrophysics Data System (ADS)

Perera, M. Nilusha M. N.; Gibbs, W. E. Keith; Juodkazis, Saulius; Stoddart, Paul R.

2018-01-01

Surface-enhanced Raman scattering (SERS) is a surface sensitive technique where the large increase in scattering has primarily been attributed to electromagnetic and chemical enhancements. While smaller geometrical enhancements due to thin film interference and cavity resonances have also been reported, an additional enhancement in the SERS signal, referred to as the `far-side geometrical enhancement', occurs when the SERS substrate is excited through an underlying transparent dielectric substrate. Here the far-side geometrically-enhanced SERS signal has been explored experimentally in more detail. Thermally evaporated Ag plasmonic films functionalised with thiophenol were used to study the dependence of the geometrically-enhanced SERS signal on the excitation wavelength, supporting substrate material and excitation angle of incidence. The results were interpreted using a `geometrical enhancement factor' (GEF), defined as the ratio of far-side to near-side SERS signal intensity. The experimental results confirmed that the highest GEFs of 3.2-3.5× are seen closer to the localized surface plasmon resonance peak of the Ag metallic nanostructures. Interestingly, the GEF for Ag plasmonic films deposited on glass and sapphire were the same within the measurement errors, whereas increasing angle of incidence showed a decrease in the GEF. Given this improved understanding of the far-side geometrical SERS enhancement, the potential for further signal amplification and optimisation for practical sensing applications can now be considered, especially for SERS detection modes at the farend of optical fibre probes and through process windows.

Phase transition solutions in geometrically constrained magnetic domain wall models

NASA Astrophysics Data System (ADS)

Chen, Shouxin; Yang, Yisong

2010-02-01

Recent work on magnetic phase transition in nanoscale systems indicates that new physical phenomena, in particular, the Bloch wall width narrowing, arise as a consequence of geometrical confinement of magnetization and leads to the introduction of geometrically constrained domain wall models. In this paper, we present a systematic mathematical analysis on the existence of the solutions of the basic governing equations in such domain wall models. We show that, when the cross section of the geometric constriction is a simple step function, the solutions may be obtained by minimizing the domain wall energy over the constriction and solving the Bogomol'nyi equation outside the constriction. When the cross section and potential density are both even, we establish the existence of an odd domain wall solution realizing the phase transition process between two adjacent domain phases. When the cross section satisfies a certain integrability condition, we prove that a domain wall solution always exists which links two arbitrarily designated domain phases.

On a common circle: natural scenes and Gestalt rules.

PubMed

Sigman, M; Cecchi, G A; Gilbert, C D; Magnasco, M O

2001-02-13

To understand how the human visual system analyzes images, it is essential to know the structure of the visual environment. In particular, natural images display consistent statistical properties that distinguish them from random luminance distributions. We have studied the geometric regularities of oriented elements (edges or line segments) present in an ensemble of visual scenes, asking how much information the presence of a segment in a particular location of the visual scene carries about the presence of a second segment at different relative positions and orientations. We observed strong long-range correlations in the distribution of oriented segments that extend over the whole visual field. We further show that a very simple geometric rule, cocircularity, predicts the arrangement of segments in natural scenes, and that different geometrical arrangements show relevant differences in their scaling properties. Our results show similarities to geometric features of previous physiological and psychophysical studies. We discuss the implications of these findings for theories of early vision.

Modeling ultrasound propagation through material of increasing geometrical complexity.

PubMed

Odabaee, Maryam; Odabaee, Mostafa; Pelekanos, Matthew; Leinenga, Gerhard; Götz, Jürgen

2018-06-01

Ultrasound is increasingly being recognized as a neuromodulatory and therapeutic tool, inducing a broad range of bio-effects in the tissue of experimental animals and humans. To achieve these effects in a predictable manner in the human brain, the thick cancellous skull presents a problem, causing attenuation. In order to overcome this challenge, as a first step, the acoustic properties of a set of simple bone-modeling resin samples that displayed an increasing geometrical complexity (increasing step sizes) were analyzed. Using two Non-Destructive Testing (NDT) transducers, we found that Wiener deconvolution predicted the Ultrasound Acoustic Response (UAR) and attenuation caused by the samples. However, whereas the UAR of samples with step sizes larger than the wavelength could be accurately estimated, the prediction was not accurate when the sample had a smaller step size. Furthermore, a Finite Element Analysis (FEA) performed in ANSYS determined that the scattering and refraction of sound waves was significantly higher in complex samples with smaller step sizes compared to simple samples with a larger step size. Together, this reveals an interaction of frequency and geometrical complexity in predicting the UAR and attenuation. These findings could in future be applied to poro-visco-elastic materials that better model the human skull. Copyright © 2018 The Authors. Published by Elsevier B.V. All rights reserved.

Linking indices for biodiversity monitoring to extinction risk theory.

PubMed

McCarthy, Michael A; Moore, Alana L; Krauss, Jochen; Morgan, John W; Clements, Christopher F

2014-12-01

Biodiversity indices often combine data from different species when used in monitoring programs. Heuristic properties can suggest preferred indices, but we lack objective ways to discriminate between indices with similar heuristics. Biodiversity indices can be evaluated by determining how well they reflect management objectives that a monitoring program aims to support. For example, the Convention on Biological Diversity requires reporting about extinction rates, so simple indices that reflect extinction risk would be valuable. We developed 3 biodiversity indices that are based on simple models of population viability that relate extinction risk to abundance. We based the first index on the geometric mean abundance of species and the second on a more general power mean. In a third index, we integrated the geometric mean abundance and trend. These indices require the same data as previous indices, but they also relate directly to extinction risk. Field data for butterflies and woodland plants and experimental studies of protozoan communities show that the indices correlate with local extinction rates. Applying the index based on the geometric mean to global data on changes in avian abundance suggested that the average extinction probability of birds has increased approximately 1% from 1970 to 2009. © 2014 The Authors. Conservation Biology published by Wiley Periodicals, Inc., on behalf of the Society for Conservation Biology.

Geometrical effect, optimal design and controlled fabrication of bio-inspired micro/nanotextures for superhydrophobic surfaces

NASA Astrophysics Data System (ADS)

Ma, F. M.; Li, W.; Liu, A. H.; Yu, Z. L.; Ruan, M.; Feng, W.; Chen, H. X.; Chen, Y.

2017-09-01

Superhydrophobic surfaces with high water contact angles and low contact angle hysteresis or sliding angles have received tremendous attention for both academic research and industrial applications in recent years. In general, such surfaces possess rough microtextures, particularly, show micro/nano hierarchical structures like lotus leaves. Now it has been recognized that to achieve the artificial superhydrophobic surfaces, the simple and effective strategy is to mimic such hierarchical structures. However, fabrications of such structures for these artificial surfaces involve generally expensive and complex processes. On the other hand, the relationships between structural parameters of various surface topography and wetting properties have not been fully understood yet. In order to provide guidance for the simple fabrication and particularly, to promote practical applications of superhydrophobic surfaces, the geometrical designs of optimal microtextures or patterns have been proposed. In this work, the recent developments on geometrical effect, optimal design and controlled fabrication of various superhydrophobic structures, such as unitary, anisotropic, dual-scale hierarchical, and some other surface geometries, are reviewed. The effects of surface topography and structural parameters on wetting states (composite and noncomposite) and wetting properties (contact angle, contact angle hysteresis and sliding angle) as well as adhesive forces are discussed in detail. Finally, the research prospects in this field are briefly addressed.

Full-Field Stress Determination Around Circular Discontinuity in a Tensile-Loaded Plate using x-displacements Only

NASA Astrophysics Data System (ADS)

Baek, Tae Hyun; Chung, Tae Jin; Panganiban, Henry

The significant effects of stress raisers demand well-defined evaluation techniques to accurately determine the stress along the geometric boundary. A simple and accurate method for the determination of stress concentration around circular geometric discontinuity in a tensile-loaded plate is illustrated. The method is based on the least-squares technique, mapping functions, and a complex power series representation (Laurent series) of the stress functions for the calculation of tangential stress around the hole. Traction-free conditions were satisfied at the geometric discontinuity using conformal mapping and analytic continuation. In this study, we use only a relatively small amount of x-component displacement data of points away from the discontinuity of concern with their respective coordinates. Having this information we can easily obtain full-field stresses at the edge of the geometric discontinuity. Excellent results were obtained when the number of terms of the power series expansions, m=1. The maximum stress concentration calculation results using the present method and FEM using ANSYS agree well by less than one per cent difference. Experimental advantage of the method underscores the use of relatively small amount of data which are conveniently determined being away from the edge. Moreover, the small amount of measured input data needed affords the approach suitable for applications such as the multi-parameter concept used to obtain stress intensity factors from measured data. The use of laser speckle interferometry and moiré interferometry are also potential future related fields since the optical system for one-directional measurement is much simple.

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Making Connections by Using Molecular Models in Geometry.

ERIC Educational Resources Information Center

Pacyga, Robert

1995-01-01

Describes two activities to analyze unit-cell structures from a geometric viewpoint and invites students to apply their mathematical understanding to scientific phenomena. Students form models of the simple cube, a building block of crystalline structures, and a methane molecule. (MKR)

In-group modulation of perceptual matching.

PubMed

Moradi, Zargol; Sui, Jie; Hewstone, Miles; Humphreys, Glyn W

2015-10-01

We report a novel effect of in-group bias on a task requiring simple perceptual matching of stimuli. Football fans were instructed to associate the badges of their favorite football team (in-group), a rival team (out-group), and neutral teams with simple geometric shapes. Responses to matching in-group stimuli were more efficient, and discriminability was enhanced, as compared to out-group stimuli (rival and neutral)-a result that occurred even when participants responded only to the (equally familiar) geometric shapes. Across individuals, the in-group bias on shape matching was correlated with measures of group satisfaction, and similar results were found when football fans performed the task, in the context of both the football ground and a laboratory setting. We also observed effects of in-group bias on the response criteria in some but not all of the experiments. In control studies, the advantage for in-group stimuli was not found in an independent sample of participants who were not football fans. This indicates that there was not an intrinsic advantage for the stimuli that were "in-group" for football fans. Also, performance did not differ for familiar versus unfamiliar stimuli without in-group associations. These findings indicate that group identification can affect simple shape matching.

General N=2 supersymmetric quantum mechanical model: Supervariable approach to its off-shell nilpotent symmetries

DOE Office of Scientific and Technical Information (OSTI.GOV)

Krishna, S., E-mail: skrishna.bhu@gmail.com; Shukla, A., E-mail: ashukla038@gmail.com; Malik, R.P., E-mail: rpmalik1995@gmail.com

2014-12-15

Using the supersymmetric (SUSY) invariant restrictions on the (anti-)chiral supervariables, we derive the off-shell nilpotent symmetries of the general one (0+1)-dimensional N=2 SUSY quantum mechanical (QM) model which is considered on a (1, 2)-dimensional supermanifold (parametrized by a bosonic variable t and a pair of Grassmannian variables θ and θ-bar with θ{sup 2}=(θ-bar){sup 2}=0,θ(θ-bar)+(θ-bar)θ=0). We provide the geometrical meanings to the two SUSY transformations of our present theory which are valid for any arbitrary type of superpotential. We express the conserved charges and Lagrangian of the theory in terms of the supervariables (that are obtained after the application of SUSYmore » invariant restrictions) and provide the geometrical interpretation for the nilpotency property and SUSY invariance of the Lagrangian for the general N=2 SUSY quantum theory. We also comment on the mathematical interpretation of the above symmetry transformations. - Highlights: • A novel method has been proposed for the derivation of N=2 SUSY transformations. • General N=2 SUSY quantum mechanical (QM) model with a general superpotential, is considered. • The above SUSY QM model is generalized onto a (1, 2)-dimensional supermanifold. • SUSY invariant restrictions are imposed on the (anti-)chiral supervariables. • Geometrical meaning of the nilpotency property is provided.« less

Comment on "Geochemistry of the Early Miocene volcanic succession of Northland, New Zealand, and implications for the evolution of subduction in the Southwest Pacific" by M.A. Booden, I.E.M. Smith, P.M. Black and J.L. Mauk

NASA Astrophysics Data System (ADS)

Schellart, W. P.

2012-01-01

In a recent paper Booden et al. (2011) present new geochemical and petrological data of Early Miocene volcanics from the Northland region (Northland volcanic belt) in New Zealand, and interpret these data to support a particular regional tectonic model. This tectonic model involves Early Miocene westward subduction of Cretaceous Pacific oceanic lithosphere below the Northland volcanic belt and the authors interpret the volcanic belt as a continental magmatic arc. Although the new data are not in disagreement with such a tectonic model, they provide more support for an alternative interpretation that involves a northeast-dipping subduction zone. Furthermore, geometric and plate kinematic data show that the west-dipping subduction model is unviable, geological and geophysical data contradict the model, while geodynamic arguments indicate that the model is implausible. Here it will be shown that a subduction model, involving a northeast-dipping southwestward retreating slab (made of the Late Cretaceous-Paleocene South Loyalty backarc basin lithosphere) that subsequently detaches, is in agreement with the local geology, geophysics and geochemistry, is geometrically, kinematically and geodynamically viable, and fits within the regional Southwest Pacific tectonic framework.

Planar incompressible Navier-Stokes and Euler equations: A geometric formulation

NASA Astrophysics Data System (ADS)

Dimitriou, Ioannis

2017-11-01

In this paper, a novel geometric approach for studying steady, two-dimensional, incompressible flows has been thoroughly developed. The continuity and momentum equations were expressed in the flow's intrinsic coordinate system in order to "accommodate" the geometric parameters characterizing it, namely, the local curvatures of the streamlines and their orthogonal trajectories. As a result, a new description of the governing equations was obtained, in which the concerned variables are the velocity magnitude v and a new quantity which was named geometric vorticity, Γ. The latter is defined by the curl of the global curvature vector KG and can be interpreted as the geometric signature of the known vorticity Ω. This approach leads to a new formulation of the Navier-Stokes and Euler equations, the so-called "velocity-curvature" formulation. In this framework, an expression for the flow velocity as a function of geometric parameters only was developed. This reveals that the physical information of a steady incompressible flow is imprinted in its geometry. It is this insight that makes the aforementioned formulation not only conceptually different to the existing classical descriptions, traditionally employed in both analytical and numerical applications, but also attractive, due to the advantages that it could provide at a theoretical and an experimental level. Finally, the derived results are briefly discussed, while emphasizing the implications that the identified geometry-physics interface might have in the future for planar flow analysis.

Simple views on critical binary liquid mixtures in porous glass

NASA Astrophysics Data System (ADS)

Tremblay, L.; Socol, S. M.; Lacelle, S.

2000-01-01

A simple scenario, different from previous attempts, is proposed to resolve the problem of the slow phase separation dynamics of binary liquid mixtures confined in porous Vycor glass. We demonstrate that simply mutual diffusion, renormalized by critical composition fluctuations and geometrical hindrance of the porous glass, accounts for the slow phase separation kinetics. Capillary invasion studies of porous Vycor glass by the critical isobutyric acid-water mixture, close to the consolute solution temperature, corroborate our analysis.

Large Scale Synthesis of Colloidal Si Nanocrystals and their Helium Plasma Processing into Spin-On, Carbon-Free Nanocrystalline Si Films.

PubMed

Mohapatra, Pratyasha; Mendivelso-Perez, Deyny; Bobbitt, Jonathan M; Shaw, Santosh; Yuan, Bin; Tian, Xinchun; Smith, Emily A; Cademartiri, Ludovico

2018-05-30

This paper describes a simple approach to the large scale synthesis of colloidal Si nanocrystals and their processing by He plasma into spin-on carbon-free nanocrystalline Si films. We further show that the RIE etching rate in these films is 1.87 times faster than for single crystalline Si, consistent with a simple geometric argument that accounts for the nanoscale roughness caused by the nanoparticle shape.

Cross-scale morphology

USGS Publications Warehouse

Allen, Craig R.; Holling, Crawford S.; Garmestani, Ahjond S.; El-Shaarawi, Abdel H.; Piegorsch, Walter W.

2013-01-01

The scaling of physical, biological, ecological and social phenomena is a major focus of efforts to develop simple representations of complex systems. Much of the attention has been on discovering universal scaling laws that emerge from simple physical and geometric processes. However, there are regular patterns of departures both from those scaling laws and from continuous distributions of attributes of systems. Those departures often demonstrate the development of self-organized interactions between living systems and physical processes over narrower ranges of scale.

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

PubMed

Liu, Yichao; Sun, Fei; He, Sailing

2018-01-11

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

Short-Range-Order for fcc-based Binary Alloys Revisited from Microscopic Geometry

NASA Astrophysics Data System (ADS)

Yuge, Koretaka

2018-04-01

Short-range order (SRO) in disordered alloys is typically interpreted as competition between chemical effect of negative (or positive) energy gain by mixing constituent elements and geometric effects comes from difference in effective atomic radius. Although we have a number of theoretical approaches to quantitatively estimate SRO at given temperatures, it is still unclear to systematically understand trends in SRO for binary alloys in terms of geometric character, e.g., effective atomic radius for constituents. Since chemical effect plays significant role on SRO, it has been believed that purely geometric character cannot capture the SRO trends. Despite these considerations, based on the density functional theory (DFT) calculations on fcc-based 28 equiatomic binary alloys, we find that while conventional Goldschmidt or DFT-based atomic radius for constituents have no significant correlation with SRO, atomic radius for specially selected structure, constructed purely from information about underlying lattice, can successfully capture the magnitude of SRO. These facts strongly indicate that purely geometric information of the system plays central role to determine characteristic disordered structure.

Computational theory of line drawing interpretation

NASA Technical Reports Server (NTRS)

Witkin, A. P.

1981-01-01

The recovery of the three dimensional structure of visible surfaces depicted in an image by emphasizing the role of geometric cues present in line drawings, was studied. Three key components are line classification, line interpretation, and surface interpolation. A model for three dimensional line interpretation and surface orientation was refined and a theory for the recovery of surface shape from surface marking geometry was developed. A new approach to the classification of edges was developed and implemented signatures were deduced for each of several edge types, expressed in terms of correlational properties of the image intensities in the vicinity of the edge. A computer program was developed that evaluates image edges as compared with these prototype signatures.

Interpreting Bivariate Regression Coefficients: Going beyond the Average

ERIC Educational Resources Information Center

Halcoussis, Dennis; Phillips, G. Michael

2010-01-01

Statistics, econometrics, investment analysis, and data analysis classes often review the calculation of several types of averages, including the arithmetic mean, geometric mean, harmonic mean, and various weighted averages. This note shows how each of these can be computed using a basic regression framework. By recognizing when a regression model…

New model performance index for engineering design of control systems

NASA Technical Reports Server (NTRS)

1970-01-01

Performance index includes a model representing linear control-system design specifications. Based on a geometric criterion for approximation of the model by the actual system, the index can be interpreted directly in terms of the desired system response model without actually having the model's time response.

Intelligent Tutoring and the Development of Argumentative Competence

ERIC Educational Resources Information Center

Paneque, Juan J.; Cobo, Pedro; Fortuny, Josep M.

2017-01-01

This ethnographical study aims to interpret how an intelligent tutorial system, geogebraTUTOR, mediates to the student's argumentative processes. Data consisted of four geometrical problems proposed to a group of four students aged 16-17. Qualitative analysis of two selected cases led to the identification of the development of argumentative…

Development and presentation of a roadway and roadside design course : final report, December 2009.

DOT National Transportation Integrated Search

2009-12-01

The overall goal of this course is to provide training in the elements of geometric highway : design. Specific course objectives are: : To review the geometry of horizontal and vertical alignment including simple circular : curves, compound curve...

The Lenz Vector and Orbital Analog Computers

ERIC Educational Resources Information Center

Harter, W. G.

1976-01-01

Describes a single geometrical diagram based on the Lenz vector which shows the qualitative and quantitative features of all three types of Coulomb orbits. Explains the use of a simple analog computer with an overhead projector to demonstrate many of these effects. (Author/CP)

Geometric entropy and edge modes of the electromagnetic field

NASA Astrophysics Data System (ADS)

Donnelly, William; Wall, Aron C.

2016-11-01

We calculate the vacuum entanglement entropy of Maxwell theory in a class of curved spacetimes by Kaluza-Klein reduction of the theory onto a two-dimensional base manifold. Using two-dimensional duality, we express the geometric entropy of the electromagnetic field as the entropy of a tower of scalar fields, constant electric and magnetic fluxes, and a contact term, whose leading-order divergence was discovered by Kabat. The complete contact term takes the form of one negative scalar degree of freedom confined to the entangling surface. We show that the geometric entropy agrees with a statistical definition of entanglement entropy that includes edge modes: classical solutions determined by their boundary values on the entangling surface. This resolves a long-standing puzzle about the statistical interpretation of the contact term in the entanglement entropy. We discuss the implications of this negative term for black hole thermodynamics and the renormalization of Newton's constant.

Geometric decomposition of the conformation tensor in viscoelastic turbulence

NASA Astrophysics Data System (ADS)

Hameduddin, Ismail; Meneveau, Charles; Zaki, Tamer A.; Gayme, Dennice F.

2018-05-01

This work introduces a mathematical approach to analysing the polymer dynamics in turbulent viscoelastic flows that uses a new geometric decomposition of the conformation tensor, along with associated scalar measures of the polymer fluctuations. The approach circumvents an inherent difficulty in traditional Reynolds decompositions of the conformation tensor: the fluctuating tensor fields are not positive-definite and so do not retain the physical meaning of the tensor. The geometric decomposition of the conformation tensor yields both mean and fluctuating tensor fields that are positive-definite. The fluctuating tensor in the present decomposition has a clear physical interpretation as a polymer deformation relative to the mean configuration. Scalar measures of this fluctuating conformation tensor are developed based on the non-Euclidean geometry of the set of positive-definite tensors. Drag-reduced viscoelastic turbulent channel flow is then used an example case study. The conformation tensor field, obtained using direct numerical simulations, is analysed using the proposed framework.

Archimedes meets Einstein: a millennial geometric bridge

NASA Astrophysics Data System (ADS)

Prado, Xabier; Area, Iván; Paredes, Angel; Domínguez Castiñeiras, José Manuel; Edelstein, José D.; Mira, Jorge

2018-07-01

This contribution explores some analogies between special relativity and geometrical tools developed by the ancient Greeks. The kinematics of one-dimensional elastic collisions is solved with simple ruler-and-compass constructions on conic sections. Then, a thought-provoking relation involving Lorentz transformations, Archimedes’ law of the lever and Einstein’s formula for the relativistic mass is put forward. The familiarity with classical geometry is useful in developing intuitions on deep concepts of modern physics and can be profitable for high school or basic undergraduate teaching. Moreover, it is fascinating to establish a bridge connecting beautiful ideas separated by two millennia.

Violation of geometrical scaling in pp collisions at NA61/SHINE

NASA Astrophysics Data System (ADS)

Praszalowicz, Michal

2013-04-01

We analyze geometrical scaling (GS) of negative pion multiplicity pT distributions at NA61/SHINE energies. We show that even though NA61/SHINE energies are low, one may expect to find GS in the particle spectra. We argue that qualitative behavior of ratios of multiplicities at different energies is in agreement with a simple picture of GS which is violated for pT smaller than some nonperturbative scale Λ and when larger Bjorken x of one of the scattering patrons crosses xmax⁡ above which a gluonic cloud becomes dilute and quark degrees of freedom become important.

Experimentally validated modification to Cook-Torrance BRDF model for improved accuracy

NASA Astrophysics Data System (ADS)

Butler, Samuel D.; Ethridge, James A.; Nauyoks, Stephen E.; Marciniak, Michael A.

2017-09-01

The BRDF describes optical scatter off realistic surfaces. The microfacet BRDF model assumes geometric optics but is computationally simple compared to wave optics models. In this work, MERL BRDF data is fitted to the original Cook-Torrance microfacet model, and a modified Cook-Torrance model using the polarization factor in place of the mathematically problematic cross section conversion and geometric attenuation terms. The results provide experimental evidence that this modified Cook-Torrance model leads to improved fits, particularly for large incident and scattered angles. These results are expected to lead to more accurate BRDF modeling for remote sensing.

Test of a geometric model for the modification stage of simple impact crater development

NASA Technical Reports Server (NTRS)

Grieve, R. A. F.; Coderre, J. M.; Rupert, J.; Garvin, J. B.

1989-01-01

This paper presents a geometric model describing the geometry of the transient cavity of an impact crater and the subsequent collapse of its walls to form a crater filled by an interior breccia lens. The model is tested by comparing the volume of slump material calculated from known dimensional parameters with the volume of the breccia lens estimated on the basis of observational data. Results obtained from the model were found to be consistent with observational data, particularly in view of the highly sensitive nature of the model to input parameters.

Digital image processing for information extraction.

NASA Technical Reports Server (NTRS)

Billingsley, F. C.

1973-01-01

The modern digital computer has made practical image processing techniques for handling nonlinear operations in both the geometrical and the intensity domains, various types of nonuniform noise cleanup, and the numerical analysis of pictures. An initial requirement is that a number of anomalies caused by the camera (e.g., geometric distortion, MTF roll-off, vignetting, and nonuniform intensity response) must be taken into account or removed to avoid their interference with the information extraction process. Examples illustrating these operations are discussed along with computer techniques used to emphasize details, perform analyses, classify materials by multivariate analysis, detect temporal differences, and aid in human interpretation of photos.

Nonplanar on-shell diagrams and leading singularities of scattering amplitudes

NASA Astrophysics Data System (ADS)

Chen, Baoyi; Chen, Gang; Cheung, Yeuk-Kwan E.; Li, Yunxuan; Xie, Ruofei; Xin, Yuan

2017-02-01

Bipartite on-shell diagrams are the latest tool in constructing scattering amplitudes. In this paper we prove that a Britto-Cachazo-Feng-Witten (BCFW) decomposable on-shell diagram process a rational top form if and only if the algebraic ideal comprised the geometrical constraints are shifted linearly during successive BCFW integrations. With a proper geometric interpretation of the constraints in the Grassmannian manifold, the rational top form integration contours can thus be obtained, and understood, in a straightforward way. All rational top form integrands of arbitrary higher loops leading singularities can therefore be derived recursively, as long as the corresponding on-shell diagram is BCFW decomposable.

Variational analysis of the coupling between a geometrically exact Cosserat rod and an elastic continuum

NASA Astrophysics Data System (ADS)

Sander, Oliver; Schiela, Anton

2014-12-01

We formulate the static mechanical coupling of a geometrically exact Cosserat rod to a nonlinearly elastic continuum. In this setting, appropriate coupling conditions have to connect a one-dimensional model with director variables to a three-dimensional model without directors. Two alternative coupling conditions are proposed, which correspond to two different configuration trace spaces. For both, we show existence of solutions of the coupled problems, using the direct method of the calculus of variations. From the first-order optimality conditions, we also derive the corresponding conditions for the dual variables. These are then interpreted in mechanical terms.

The Local Geometry of Multiattribute Tradeoff Preferences

PubMed Central

McGeachie, Michael; Doyle, Jon

2011-01-01

Existing representations for multiattribute ceteris paribus preference statements have provided useful treatments and clear semantics for qualitative comparisons, but have not provided similarly clear representations or semantics for comparisons involving quantitative tradeoffs. We use directional derivatives and other concepts from elementary differential geometry to interpret conditional multiattribute ceteris paribus preference comparisons that state bounds on quantitative tradeoff ratios. This semantics extends the familiar economic notion of marginal rate of substitution to multiple continuous or discrete attributes. The same geometric concepts also provide means for interpreting statements about the relative importance of different attributes. PMID:21528018

Fitness in time-dependent environments includes a geometric phase contribution

PubMed Central

Tănase-Nicola, Sorin; Nemenman, Ilya

2012-01-01

Phenotypic evolution implies sequential rise in frequency of new genomic sequences. The speed of the rise depends, in part, on the relative fitness (selection coefficient) of the mutant versus the ancestor. Using a simple population dynamics model, we show that the relative fitness in dynamical environments is not equal to the geometric average of the fitness over individual environments. Instead, it includes a term that explicitly depends on the sequence of the environments. For slowly varying environments, this term depends only on the oriented area enclosed by the trajectory taken by the system in the environment state space. It is closely related to the well-studied geometric phases in classical and quantum physical systems. We discuss possible biological implications of these observations, focusing on evolution of novel metabolic or stress-resistant functions. PMID:22112653

Genetic Algorithms and Local Search

NASA Technical Reports Server (NTRS)

Whitley, Darrell

1996-01-01

The first part of this presentation is a tutorial level introduction to the principles of genetic search and models of simple genetic algorithms. The second half covers the combination of genetic algorithms with local search methods to produce hybrid genetic algorithms. Hybrid algorithms can be modeled within the existing theoretical framework developed for simple genetic algorithms. An application of a hybrid to geometric model matching is given. The hybrid algorithm yields results that improve on the current state-of-the-art for this problem.

Tour of a simple trigonometry problem

NASA Astrophysics Data System (ADS)

Poon, Kin-Keung

2012-06-01

This article focuses on a simple trigonometric problem that generates a strange phenomenon when different methods are applied to tackling it. A series of problem-solving activities are discussed, so that students can be alerted that the precision of diagrams is important when solving geometric problems. In addition, the problem-solving plan was implemented in a high school and the results indicated that students are relatively weak in problem-solving abilities but they understand and appreciate the thinking process in different stages and steps of the activities.

Stress Measurement by Geometrical Optics

NASA Technical Reports Server (NTRS)

Robinson, R. S.; Rossnagel, S. M.

1986-01-01

Fast, simple technique measures stresses in thin films. Sample disk bowed by stress into approximately spherical shape. Reflected image of disk magnified by amount related to curvature and, therefore, stress. Method requires sample substrate, such as cheap microscope cover slide, two mirrors, laser light beam, and screen.

Sharing Teaching Ideas.

ERIC Educational Resources Information Center

Mathematics Teacher, 1981

1981-01-01

The following ideas are presented: plans for constructing a calculator bin rack that provides a place for a school to store and charge calculators; a lesson in geometry based on a news article about salt containers; and a very simple approach to the concept of infinite geometric series. (MP)

Evaluating Constraints on Heavy-Ion SEE Susceptibility Imposed by Proton SEE Testing and Other Mixed Environments

NASA Technical Reports Server (NTRS)

Ladbury, R. L.; Lauenstein, J.-M.

2016-01-01

We develop metrics for assessing the effectiveness of proton SEE data for bounding heavy-ion SEE susceptibility. The metrics range from simple geometric criteria requiring no knowledge of the test articles to bounds of SEE rates.

Conductivity noise in transmembrane ion channels due to ion concentration fluctuations via diffusion.

PubMed

Mak, D O; Webb, W W

1997-03-01

A Green's function approach is developed from first principles to evaluate the power spectral density of conductance fluctuations caused by ion concentration fluctuations via diffusion in an electrolyte system. This is applied to simple geometric models of transmembrane ion channels to obtain an estimate of the magnitude of ion concentration fluctuation noise in the channel current. Pure polypeptide alamethicin forms stable ion channels with multiple conductance states in artificial phospholipid bilayers isolated onto tips of micropipettes with gigaohm seals. In the single-channel current recorded by voltage-clamp techniques, excess noise was found after the background instrumental noise and the intrinsic Johnson and shot noises were removed. The noise que to ion concentration fluctuations via diffusion was isolated by the dependence of the excess current noise on buffer ion concentration. The magnitude of the concentration fluctuation noise derived from experimental data lies within limits estimated using our simple geometric channel models. Variation of the noise magnitude for alamethicin channels in various conductance states agrees with theoretical prediction.

German Children's Use of Word Order and Case Marking to Interpret Simple and Complex Sentences: Testing Differences between Constructions and Lexical Items

ERIC Educational Resources Information Center

Brandt, Silke; Lieven, Elena; Tomasello, Michael

2016-01-01

Children and adults follow cues such as case marking and word order in their assignment of semantic roles in simple transitives (e.g., "the dog chased the cat"). It has been suggested that the same cues are used for the interpretation of complex sentences, such as transitive relative clauses (RCs) (e.g., "that's the dog that chased…

Influence of education level on design-induced N170 and P300 components of event related potentials in the human brain.

PubMed

Begum, Tahamina; Reza, Faruque; Ahmed, Izmer; Abdullah, Jafri Malin

2014-03-01

Simple geometric and organic shapes and their arrangement are being used in different neuropsychology tests for the assessment of cognitive function, special memory and also for the therapy purpose in different patient groups. Until now there is no electrophysiological evidence of cognitive function determination for simple geometric, organic shapes and their arrangement. Then the main objective of this study is to know the cortical processing and amplitude, latency of visual induced N170 and P300 event related potential components on different geometric, organic shapes and their arrangement and different educational influence on it, which is worthwhile to know for the early and better treatment for those patient groups. While education influenced on cognitive function by using auditory oddball task, little is known about the influence of education on cognitive function induced by visual attention task in case of the choice of geometric, organic shapes and their arrangements. Using a 128-electrode sensor net, we studied the responses of the choice of the different geometric and organic shapes randomly in experiment 1 and their arrangements in experiment 2 in the high, medium and low education groups. In both experiments, subjects push the button "1" or "2" if like or dislike, respectively. Total 45 healthy subjects (15 in each group) were recruited. ERPs were measured from 11 electrode sites and analyzed to see the evoked N170/N240 and P300 ERP components. There were no differences between like and dislike in amplitudes even in latencies in every stimulus in both experiments. We fixed geometric shapes and organic shapes stimuli only, not like and dislike. Upon the stimulus types, N170 ERP component was found instead of N240, in occipito-temporal (T5, T6, O1 and O2) locations where the amplitude is the highest at O2 location and P300 was distributed in the central (Cz and Pz) locations in both experiments in all groups. In experiment 1, significant low amplitude and non-significant larger latency of the N170 component are found out at O1 location for both stimuli in low education group comparing medium education groups, but in experiment 2, there is no significant difference between stimuli among groups in amplitude and latency. In both experiments, P300 component was found in Cz and Pz locations though the amplitudes are higher at Cz than Pz areas. In experiment 1, medium education group evoked significantly (geometric shape stimuli, P = 0.05; organic shape stimuli, P = 0.02) higher amplitude of P300 component comparing low education group at Cz location. Whereas, there is no significant difference of amplitudes among groups across stimuli in Cz and Pz locations in experiment 2. Latencies have no significant differences in both experiments among groups also, but longer latency are found in low education group at Cz location comparing medium education group, though not significant. We conclude that simple geometric shapes, organic shapes and their arrangements evoked visual N170 component at temporo-occipital areas with right lateralization and P300 ERP component at centro-parietal areas. Significant low amplitude of N170 and P300 ERP components and longer latencies during different shape stimuli in low education group prove that, low education significantly influence on visual cognitive functions in low education group.

Simplified versus geometrically accurate models of forefoot anatomy to predict plantar pressures: A finite element study.

PubMed

Telfer, Scott; Erdemir, Ahmet; Woodburn, James; Cavanagh, Peter R

2016-01-25

Integration of patient-specific biomechanical measurements into the design of therapeutic footwear has been shown to improve clinical outcomes in patients with diabetic foot disease. The addition of numerical simulations intended to optimise intervention design may help to build on these advances, however at present the time and labour required to generate and run personalised models of foot anatomy restrict their routine clinical utility. In this study we developed second-generation personalised simple finite element (FE) models of the forefoot with varying geometric fidelities. Plantar pressure predictions from barefoot, shod, and shod with insole simulations using simplified models were compared to those obtained from CT-based FE models incorporating more detailed representations of bone and tissue geometry. A simplified model including representations of metatarsals based on simple geometric shapes, embedded within a contoured soft tissue block with outer geometry acquired from a 3D surface scan was found to provide pressure predictions closest to the more complex model, with mean differences of 13.3kPa (SD 13.4), 12.52kPa (SD 11.9) and 9.6kPa (SD 9.3) for barefoot, shod, and insole conditions respectively. The simplified model design could be produced in <1h compared to >3h in the case of the more detailed model, and solved on average 24% faster. FE models of the forefoot based on simplified geometric representations of the metatarsal bones and soft tissue surface geometry from 3D surface scans may potentially provide a simulation approach with improved clinical utility, however further validity testing around a range of therapeutic footwear types is required. Copyright © 2015 Elsevier Ltd. All rights reserved.

Influence of muscle-tendon complex geometrical parameters on modeling passive stretch behavior with the Discrete Element Method.

PubMed

Roux, A; Laporte, S; Lecompte, J; Gras, L-L; Iordanoff, I

2016-01-25

The muscle-tendon complex (MTC) is a multi-scale, anisotropic, non-homogeneous structure. It is composed of fascicles, gathered together in a conjunctive aponeurosis. Fibers are oriented into the MTC with a pennation angle. Many MTC models use the Finite Element Method (FEM) to simulate the behavior of the MTC as a hyper-viscoelastic material. The Discrete Element Method (DEM) could be adapted to model fibrous materials, such as the MTC. DEM could capture the complex behavior of a material with a simple discretization scheme and help in understanding the influence of the orientation of fibers on the MTC׳s behavior. The aims of this study were to model the MTC in DEM at the macroscopic scale and to obtain the force/displacement curve during a non-destructive passive tensile test. Another aim was to highlight the influence of the geometrical parameters of the MTC on the global mechanical behavior. A geometrical construction of the MTC was done using discrete element linked by springs. Young׳s modulus values of the MTC׳s components were retrieved from the literature to model the microscopic stiffness of each spring. Alignment and re-orientation of all of the muscle׳s fibers with the tensile axis were observed numerically. The hyper-elastic behavior of the MTC was pointed out. The structure׳s effects, added to the geometrical parameters, highlight the MTC׳s mechanical behavior. It is also highlighted by the heterogeneity of the strain of the MTC׳s components. DEM seems to be a promising method to model the hyper-elastic macroscopic behavior of the MTC with simple elastic microscopic elements. Copyright © 2015 Elsevier Ltd. All rights reserved.

Capability of geometric features to classify ships in SAR imagery

NASA Astrophysics Data System (ADS)

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.

On the validity of the arithmetic-geometric mean method to locate the optimal solution in a supply chain system

NASA Astrophysics Data System (ADS)

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.

Teaching and Assessing Polygons Using Technology

ERIC Educational Resources Information Center

Soucie, Tanja; Radovic, Nikol; Svedrec, Renata; Kokic, Ivana

2011-01-01

Studying geometry is an integral component of learning mathematics because it allows students to analyse and interpret the world they live in as well as equip them with tools they can apply in other areas of mathematics. Therefore, students need to develop an understanding of geometric concepts as well as gaining adequate geometry related skills.…

Determination of the Conservation Time of Periodicals for Optimal Shelf Maintenance of a Library.

ERIC Educational Resources Information Center

Miyamoto, Sadaaki; Nakayama, Kazuhiko

1981-01-01

Presents a method based on a constrained optimization technique that determines the time of removal of scientific periodicals from the shelf of a library. A geometrical interpretation of the theoretical result is given, and a numerical example illustrates how the technique is applicable to real bibliographic data. (FM)

Vapor-Liquid Equilibria Using the Gibbs Energy and the Common Tangent Plane Criterion

ERIC Educational Resources Information Center

Olaya, Maria del Mar; Reyes-Labarta, Juan A.; Serrano, Maria Dolores; Marcilla, Antonio

2010-01-01

Phase thermodynamics is often perceived as a difficult subject with which many students never become fully comfortable. The Gibbsian geometrical framework can help students to gain a better understanding of phase equilibria. An exercise to interpret the vapor-liquid equilibrium of a binary azeotropic mixture, using the equilibrium condition based…

Orthogonal Projection in Teaching Regression and Financial Mathematics

ERIC Educational Resources Information Center

Kachapova, Farida; Kachapov, Ilias

2010-01-01

Two improvements in teaching linear regression are suggested. The first is to include the population regression model at the beginning of the topic. The second is to use a geometric approach: to interpret the regression estimate as an orthogonal projection and the estimation error as the distance (which is minimized by the projection). Linear…

Unpacking Rouché's Theorem

ERIC Educational Resources Information Center

Howell, Russell W.; Schrohe, Elmar

2017-01-01

Rouché's Theorem is a standard topic in undergraduate complex analysis. It is usually covered near the end of the course with applications relating to pure mathematics only (e.g., using it to produce an alternate proof of the Fundamental Theorem of Algebra). The "winding number" provides a geometric interpretation relating to the…

Infinite-mode squeezed coherent states and non-equilibrium statistical mechanics (phase-space-picture approach)

NASA Technical Reports Server (NTRS)

Yeh, Leehwa

1993-01-01

The phase-space-picture approach to quantum non-equilibrium statistical mechanics via the characteristic function of infinite-mode squeezed coherent states is introduced. We use quantum Brownian motion as an example to show how this approach provides an interesting geometrical interpretation of quantum non-equilibrium phenomena.

Comparing Latent Structures of the Grade of Membership, Rasch, and Latent Class Models

ERIC Educational Resources Information Center

Erosheva, Elena A.

2005-01-01

This paper focuses on model interpretation issues and employs a geometric approach to compare the potential value of using the Grade of Membership (GoM) model in representing population heterogeneity. We consider population heterogeneity manifolds generated by letting subject specific parameters vary over their natural range, while keeping other…

Numerical Integration with GeoGebra in High School

ERIC Educational Resources Information Center

Herceg, Dorde; Herceg, Dragoslav

2010-01-01

The concept of definite integral is almost always introduced as the Riemann integral, which is defined in terms of the Riemann sum, and its geometric interpretation. This definition is hard to understand for high school students. With the aid of mathematical software for visualisation and computation of approximate integrals, the notion of…

The Hyperbolic Sine Cardinal and the Catenary

ERIC Educational Resources Information Center

Sanchez-Reyes, Javier

2012-01-01

The hyperbolic function sinh(x)/x receives scant attention in the literature. We show that it admits a clear geometric interpretation as the ratio between length and chord of a symmetric catenary segment. The inverse, together with the use of dimensionless parameters, furnishes a compact, explicit construction of a general catenary segment of…

Virtual Images: Going through the Looking Glass

ERIC Educational Resources Information Center

Mota, Ana Rita; Lopes dos Santos, João

2017-01-01

Virtual images are often introduced through a "geometric" perspective, with little conceptual or qualitative illustrations, hindering a deeper understanding of this physical concept. In this paper, we present two rather simple observations that force a critical reflection on the optical nature of a virtual image. This approach is…

Athabascan Beading.

ERIC Educational Resources Information Center

Pitka, Lilly; And Others

For many years flowers and leaves formed the bulk of Alaskan Athabascan beadwork designs. Early Athabascan beadwork consisted primarily of simple geometric patterns, but after the advent of the French in Canada, elaborate floral designs popular in 18th and 19th century France were translated into Woodland Indian beadwork. In traditional procedure…

Crash-Energy Absorbing Composite Structure and Method of Fabrication

NASA Technical Reports Server (NTRS)

Kellas, Sotiris (Inventor); Carden, Huey D. (Inventor)

1996-01-01

A stand-alone, crash-energy absorbing structure and fabrication method are provided. A plurality of adjoining rigid cells are each constructed of resin-cured fiber reinforcement and are arranged in a geometric configuration. The fiber reinforcement can be in the form of a fabric or braided fibers wrapped about a core that is either left in place or removed from the ultimate cured structure. The geometric configuration of cells is held together with more fiber reinforcement (in the form of fabric or braided fibers) in order to integrate the cells in the geometric configuration. The additional fiber reinforcement is resin-cured to the cells. Curing of the cells and ultimate structure can occur in a single step. In applications where post-crash integrity is necessary, ductile fibers can be used to integrate the cells in the geometric configuration. The novelty of the present invention is that simple fabrication techniques are used to create structures that can be formed in a variety of net stable shapes without additional reinforcement and can withstand combined loading while crushing in a desired direction.

Geometrically nonlinear transient vibrations of actively damped anti-symmetric angle ply laminated composite shallow shell using active fibre composite (AFC) actuators

NASA Astrophysics Data System (ADS)

Ashok, M. H.; Shivakumar, J.; Nandurkar, Santosh; Khadakbhavi, Vishwanath; Pujari, Sanjay

2018-02-01

In present work, the thin laminated composite shallow shell as smart structure with AFC material’s ACLD treatment is analyzed for geometrically nonlinear transient vibrations. The AFC material is used to make the constraining layer of the ACLD treatment. Golla-Hughes-McTavish (GHM) is used to model the constrained viscoelastic layer of the ACLD treatment in time domain. Along with a simple first-order shear deformation theory the Von Kármán type non-linear strain displacement relations are used for deriving this electromechanical coupled problem. A 3-dimensional finite element model of smart composite panels integrated with the ACLD treated patches has been modelled to reveal the performance of ACLD treated patches on improving the damping properties of slender anti-symmetric angle-ply laminated shallow shell, in controlling the transient vibrations which are geometrically nonlinear. The mathematical results explain that the ACLD treated patches considerably enhance the damping properties of anti-symmetric angle-ply panels undergoing geometrically nonlinear transient vibrations.

Real-world spatial regularities affect visual working memory for objects.

PubMed

Kaiser, Daniel; Stein, Timo; Peelen, Marius V

2015-12-01

Traditional memory research has focused on measuring and modeling the capacity of visual working memory for simple stimuli such as geometric shapes or colored disks. Although these studies have provided important insights, it is unclear how their findings apply to memory for more naturalistic stimuli. An important aspect of real-world scenes is that they contain a high degree of regularity: For instance, lamps appear above tables, not below them. In the present study, we tested whether such real-world spatial regularities affect working memory capacity for individual objects. Using a delayed change-detection task with concurrent verbal suppression, we found enhanced visual working memory performance for objects positioned according to real-world regularities, as compared to irregularly positioned objects. This effect was specific to upright stimuli, indicating that it did not reflect low-level grouping, because low-level grouping would be expected to equally affect memory for upright and inverted displays. These results suggest that objects can be held in visual working memory more efficiently when they are positioned according to frequently experienced real-world regularities. We interpret this effect as the grouping of single objects into larger representational units.

Accuracy of 1D microvascular flow models in the limit of low Reynolds numbers.

PubMed

Pindera, Maciej Z; Ding, Hui; Athavale, Mahesh M; Chen, Zhijian

2009-05-01

We describe results of numerical simulations of steady flows in tubes with branch bifurcations using fully 3D and reduced 1D geometries. The intent is to delineate the range of validity of reduced models used for simulations of flows in microcapillary networks, as a function of the flow Reynolds number Re. Results from model problems indicate that for Re less than 1 and possibly as high as 10, vasculatures may be represented by strictly 1D Poiseuille flow geometries with flow variation in the axial dimensions only. In that range flow rate predictions in the different branches generated by 1D and 3D models differ by a constant factor, independent of Re. When the cross-sectional areas of the branches are constant these differences are generally small and appear to stem from an uncertainty of how the individual branch lengths are defined. This uncertainty can be accounted for by a simple geometrical correction. For non-constant cross-sections the differences can be much more significant. If additional corrections for the presence of branch junctions and flow area variations are not taken into account in 1D models of complex vasculatures, the resultant flow predictions should be interpreted with caution.

“Do-it-yourself in vitro vasculature that recapitulates in vivo geometries for investigating endothelial-blood cell interactions”

PubMed Central

Mannino, Robert G.; Myers, David R.; Ahn, Byungwook; Wang, Yichen; Margo Rollins; Gole, Hope; Lin, Angela S.; Guldberg, Robert E.; Giddens, Don P.; Timmins, Lucas H.; Lam, Wilbur A.

2015-01-01

Investigating biophysical cellular interactions in the circulation currently requires choosing between in vivo models, which are difficult to interpret due in part to the hemodynamic and geometric complexities of the vasculature; or in vitro systems, which suffer from non-physiologic assumptions and/or require specialized microfabrication facilities and expertise. To bridge that gap, we developed an in vitro “do-it-yourself” perfusable vasculature model that recapitulates in vivo geometries, such as aneurysms, stenoses, and bifurcations, and supports endothelial cell culture. These inexpensive, disposable devices can be created rapidly (<2 hours) with high precision and repeatability, using standard off-the-shelf laboratory supplies. Using these “endothelialized” systems, we demonstrate that spatial variation in vascular cell adhesion molecule (VCAM-1) expression correlates with the wall shear stress patterns of vascular geometries. We further observe that the presence of endothelial cells in stenoses reduces platelet adhesion but increases sickle cell disease (SCD) red blood cell (RBC) adhesion in bifurcations. Overall, our method enables researchers from all disciplines to study cellular interactions in physiologically relevant, yet simple-to-make, in vitro vasculature models. PMID:26202603

Narayanaswamy's 1971 aging theory and material time

NASA Astrophysics Data System (ADS)

Dyre, Jeppe C.

2015-09-01

The Bochkov-Kuzovlev nonlinear fluctuation-dissipation theorem is used to derive Narayanaswamy's phenomenological theory of physical aging, in which this highly nonlinear phenomenon is described by a linear material-time convolution integral. A characteristic property of the Narayanaswamy aging description is material-time translational invariance, which is here taken as the basic assumption of the derivation. It is shown that only one possible definition of the material time obeys this invariance, namely, the square of the distance travelled from a configuration of the system far back in time. The paper concludes with suggestions for computer simulations that test for consequences of material-time translational invariance. One of these is the "unique-triangles property" according to which any three points on the system's path form a triangle such that two side lengths determine the third; this is equivalent to the well-known triangular relation for time-autocorrelation functions of aging spin glasses [L. F. Cugliandolo and J. Kurchan, J. Phys. A: Math. Gen. 27, 5749 (1994)]. The unique-triangles property implies a simple geometric interpretation of out-of-equilibrium time-autocorrelation functions, which extends to aging a previously proposed framework for such functions in equilibrium [J. C. Dyre, e-print arXiv:cond-mat/9712222 (1997)].

Quaternary fluvial terraces of the Tiber Valley: geochronologic and geometric constraints on the back-arc magmatism-related uplift in central Italy.

PubMed

Marra, Fabrizio; Florindo, Fabio; Petronio, Carmelo

2017-05-31

Through a geomorphological study relying on statistically assessed classes of hilltop elevations, we reconstruct a suite of paleo-surfaces along the Tiber River Valley north of Rome that we identify as fluvial terraces formed by interplay between global sea-level fluctuations and regional upift. Using biostratigraphic constraints provided by marine through continental deposits of Santernian age, we recognize the oldest terrace in this area, corresponding to an early coastal plain of late Santernian-Emilian age. By assuming the simple chronological principle of a staircase geometry we correlate the sea-level highstands of MIS 21 through MIS 5 with the lowest eight paleo-surfaces. By plotting against time the cumulated terrace elevations and the average elevation of the Santernian coastline in the investigated area, we detect rates of uplift during the last 1.8 Ma. Two major pulses of uplift are recognized 0.86 through 0.5 Ma, and 0.25 Ma through the Present, which are interpreted as driven by the subduction process and uprising of metasomatized magma bodies on the Tyrrhenian Sea Margin of central Italy, superimposied on a smaller isostatic component of uplift.

Interaction without intent: the shape of the social world in Huntington’s disease

PubMed Central

Rickards, Hugh E.

2015-01-01

Huntington’s disease (HD) is an inherited neurodegenerative condition. Patients with this movement disorder can exhibit deficits on tasks involving Theory of Mind (ToM): the ability to understand mental states such as beliefs and emotions. We investigated mental state inference in HD in response to ambiguous animations involving geometric shapes, while exploring the impact of symptoms within cognitive, emotional and motor domains. Forty patients with HD and twenty healthy controls described the events in videos showing random movements of two triangles (i.e. floating), simple interactions (e.g. following) and more complex interactions prompting the inference of mental states (e.g. one triangle encouraging the other). Relationships were explored between animation interpretation and measures of executive functioning, alexithymia and motor symptoms. Individuals with HD exhibited alexithymia and a reduced tendency to spontaneously attribute intentions to interacting triangles on the animations task. Attribution of intentions on the animations task correlated with motor symptoms and burden of pathology. Importantly, patients without motor symptoms showed similar ToM deficits despite intact executive functions. Subtle changes in ToM that are unrelated to executive dysfunction could therefore feature in basal ganglia disorders prior to motor onset. PMID:25680992

Edge effects and geometric constraints: a landscape-level empirical test.

PubMed

Ribeiro, Suzy E; Prevedello, Jayme A; Delciellos, Ana Cláudia; Vieira, Marcus Vinícius

2016-01-01

Edge effects are pervasive in landscapes yet their causal mechanisms are still poorly understood. Traditionally, edge effects have been attributed to differences in habitat quality along the edge-interior gradient of habitat patches, under the assumption that no edge effects would occur if habitat quality was uniform. This assumption was questioned recently after the recognition that geometric constraints tend to reduce population abundances near the edges of habitat patches, the so-called geometric edge effect (GEE). Here, we present the first empirical, landscape-level evaluation of the importance of the GEE in shaping abundance patterns in fragmented landscapes. Using a data set on the distribution of small mammals across 18 forest fragments, we assessed whether the incorporation of the GEE into the analysis changes the interpretation of edge effects and the degree to which predictions based on the GEE match observed responses. Quantitative predictions were generated for each fragment using simulations that took into account home range, density and matrix use for each species. The incorporation of the GEE into the analysis changed substantially the interpretation of overall observed edge responses at the landscape scale. Observed abundances alone would lead to the conclusion that the small mammals as a group have no consistent preference for forest edges or interiors and that the black-eared opossum Didelphis aurita (a numerically dominant species in the community) has on average a preference for forest interiors. In contrast, incorporation of the GEE suggested that the small mammal community as a whole has a preference for forest edges, whereas D. aurita has no preference for forest edges or interiors. Unexplained variance in edge responses was reduced by the incorporation of GEE, but remained large, varying greatly on a fragment-by-fragment basis. This study demonstrates how to model and incorporate the GEE in analyses of edge effects and that this incorporation is necessary to properly interpret edge effects in landscapes. It also suggests that geometric constraints alone are unlikely to explain the variability in edge responses of a same species among different areas, highlighting the need to incorporate other ecological factors into explanatory models of edge effects. © 2015 The Authors. Journal of Animal Ecology © 2015 British Ecological Society.

Plasmon Geometric Phase and Plasmon Hall Shift

NASA Astrophysics Data System (ADS)

Shi, Li-kun; Song, Justin C. W.

2018-04-01

The collective plasmonic modes of a metal comprise a simple pattern of oscillating charge density that yields enhanced light-matter interaction. Here we unveil that beneath this familiar facade plasmons possess a hidden internal structure that fundamentally alters its dynamics. In particular, we find that metals with nonzero Hall conductivity host plasmons with an intricate current density configuration that sharply departs from that of ordinary zero Hall conductivity metals. This nontrivial internal structure dramatically enriches the dynamics of plasmon propagation, enabling plasmon wave packets to acquire geometric phases as they scatter. At boundaries, these phases accumulate allowing plasmon waves that reflect off to experience a nonreciprocal parallel shift. This plasmon Hall shift, tunable by Hall conductivity as well as plasmon wavelength, displaces the incident and reflected plasmon trajectories and can be readily probed by near-field photonics techniques. Anomalous plasmon geometric phases dramatically enrich the nanophotonics toolbox, and yield radical new means for directing plasmonic beams.

A geometric modeler based on a dual-geometry representation polyhedra and rational b-splines

NASA Technical Reports Server (NTRS)

Klosterman, A. L.

1984-01-01

For speed and data base reasons, solid geometric modeling of large complex practical systems is usually approximated by a polyhedra representation. Precise parametric surface and implicit algebraic modelers are available but it is not yet practical to model the same level of system complexity with these precise modelers. In response to this contrast the GEOMOD geometric modeling system was built so that a polyhedra abstraction of the geometry would be available for interactive modeling without losing the precise definition of the geometry. Part of the reason that polyhedra modelers are effective is that all bounded surfaces can be represented in a single canonical format (i.e., sets of planar polygons). This permits a very simple and compact data structure. Nonuniform rational B-splines are currently the best representation to describe a very large class of geometry precisely with one canonical format. The specific capabilities of the modeler are described.

Geometric mechanics of periodic pleated origami.

PubMed

Wei, Z Y; Guo, Z V; Dudte, L; Liang, H Y; Mahadevan, L

2013-05-24

Origami structures are mechanical metamaterials with properties that arise almost exclusively from the geometry of the constituent folds and the constraint of piecewise isometric deformations. Here we characterize the geometry and planar and nonplanar effective elastic response of a simple periodically folded Miura-ori structure, which is composed of identical unit cells of mountain and valley folds with four-coordinated ridges, defined completely by two angles and two lengths. We show that the in-plane and out-of-plane Poisson's ratios are equal in magnitude, but opposite in sign, independent of material properties. Furthermore, we show that effective bending stiffness of the unit cell is singular, allowing us to characterize the two-dimensional deformation of a plate in terms of a one-dimensional theory. Finally, we solve the inverse design problem of determining the geometric parameters for the optimal geometric and mechanical response of these extreme structures.

On the relationship between topological and geometric defects.

PubMed

Griffin, Sinéad M; Spaldin, Nicola A

2017-08-31

The study of topology in solids is undergoing a renaissance following renewed interest in the properties of ferroic domain walls as well as recent discoveries regarding skyrmionic lattices. Each of these systems possess a property that is 'protected' in a symmetry sense, and is defined rigorously using a branch of mathematics known as topology. In this article we review the formal definition of topological defects as they are classified in terms of homotopy theory, and discuss the precise symmetry-breaking conditions that lead to their formation. We distinguish topological defects from defects that arise from the details of the stacking or structure of the material but are not protected by symmetry, and we propose the term 'geometric defects' to describe the latter. We provide simple material examples of both topological and geometric defect types, and discuss the implications of the classification on the resulting material properties.

Optical and biometric relationships of the isolated pig crystalline lens.

PubMed

Vilupuru, A S; Glasser, A

2001-07-01

To investigate the interrelationships between optical and biometric properties of the porcine crystalline lens, to compare these findings with similar relationships found for the human lens and to attempt to fit this data to a geometric model of the optical and biometric properties of the pig lens. Weight, focal length, spherical aberration, surface curvatures, thickness and diameters of 20 isolated pig lenses were measured and equivalent refractive index was calculated. These parameters were compared and used to geometrically model the pig lens. Linear relationships were identified between many of the lens biometric and optical properties. The existence of these relationships allowed a simple geometrical model of the pig lens to be calculated which offers predictions of the optical properties. The linear relationships found and the agreement observed between measured and modeled results suggest that the pig lens confirms to a predictable, preset developmental pattern and that the optical and biometric properties are predictably interrelated.

MX Siting Investigation. Gravity Survey - Southern Snake Valley (Ferguson Desert), Utah.

DTIC Science & Technology

1980-03-28

Topographic Center (DMAHTC), head- quartered in Cheyenne, Wyoming. DMAHTC reduces the data to Simple Bouguer Anomaly (see Section A1.4, Appendix Al.0...Valley, Utah . . . . . ......... . . . . . 3 3 Complete Bouguer Anomaly Contours 4 Interpreted Gravity Profile SE-3,4 5 Interpreted Gravity Profile SE...observations and reduced them to Simple Bouguer Anomalies (SBA) for each station as described in Appendix Al.0. Up to three levels of terrain corrections were

Quasi-probabilities in conditioned quantum measurement and a geometric/statistical interpretation of Aharonov's weak value

NASA Astrophysics Data System (ADS)

Lee, Jaeha; Tsutsui, Izumi

2017-05-01

We show that the joint behavior of an arbitrary pair of (generally noncommuting) quantum observables can be described by quasi-probabilities, which are an extended version of the standard probabilities used for describing the outcome of measurement for a single observable. The physical situations that require these quasi-probabilities arise when one considers quantum measurement of an observable conditioned by some other variable, with the notable example being the weak measurement employed to obtain Aharonov's weak value. Specifically, we present a general prescription for the construction of quasi-joint probability (QJP) distributions associated with a given combination of observables. These QJP distributions are introduced in two complementary approaches: one from a bottom-up, strictly operational construction realized by examining the mathematical framework of the conditioned measurement scheme, and the other from a top-down viewpoint realized by applying the results of the spectral theorem for normal operators and their Fourier transforms. It is then revealed that, for a pair of simultaneously measurable observables, the QJP distribution reduces to the unique standard joint probability distribution of the pair, whereas for a noncommuting pair there exists an inherent indefiniteness in the choice of such QJP distributions, admitting a multitude of candidates that may equally be used for describing the joint behavior of the pair. In the course of our argument, we find that the QJP distributions furnish the space of operators in the underlying Hilbert space with their characteristic geometric structures such that the orthogonal projections and inner products of observables can be given statistical interpretations as, respectively, “conditionings” and “correlations”. The weak value Aw for an observable A is then given a geometric/statistical interpretation as either the orthogonal projection of A onto the subspace generated by another observable B, or equivalently, as the conditioning of A given B with respect to the QJP distribution under consideration.

Lie group model neuromorphic geometric engine for real-time terrain reconstruction from stereoscopic aerial photos

NASA Astrophysics Data System (ADS)

Tsao, Thomas R.; Tsao, Doris

1997-04-01

In the 1980's, neurobiologist suggested a simple mechanism in primate visual cortex for maintaining a stable and invariant representation of a moving object. The receptive field of visual neurons has real-time transforms in response to motion, to maintain a stable representation. When the visual stimulus is changed due to motion, the geometric transform of the stimulus triggers a dual transform of the receptive field. This dual transform in the receptive fields compensates geometric variation in the stimulus. This process can be modelled using a Lie group method. The massive array of affine parameter sensing circuits will function as a smart sensor tightly coupled to the passive imaging sensor (retina). Neural geometric engine is a neuromorphic computing device simulating our Lie group model of spatial perception of primate's primal visual cortex. We have developed the computer simulation and experimented on realistic and synthetic image data, and performed a preliminary research of using analog VLSI technology for implementation of the neural geometric engine. We have benchmark tested on DMA's terrain data with their result and have built an analog integrated circuit to verify the computational structure of the engine. When fully implemented on ANALOG VLSI chip, we will be able to accurately reconstruct a 3D terrain surface in real-time from stereoscopic imagery.

Geometrical tile design for complex neighborhoods.

PubMed

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.

Analytical and numerical modeling of an axisymmetrical electrostatic transducer with interior geometrical discontinuity.

PubMed

Honzík, Petr; Podkovskiy, Alexey; Durand, Stéphane; Joly, Nicolas; Bruneau, Michel

2013-11-01

The main purpose of the paper is to contribute at presenting an analytical and a numerical modeling which would be relevant for interpreting the couplings between a circular membrane, a peripheral cavity having the same external radius as the membrane, and a thin air gap (with a geometrical discontinuity between them), and then to characterize small scale electrostatic receivers and to propose procedures that could be suitable for fitting adjustable parameters to achieve optimal behavior in terms of sensitivity and bandwidth expected. Therefore, comparison between these theoretical methods and characterization of several shapes is dealt with, which show that the models would be appropriate to address the design of such transducers.

The elastic theory of shells using geometric algebra

PubMed Central

Lasenby, J.; Agarwal, A.

2017-01-01

We present a novel derivation of the elastic theory of shells. We use the language of geometric algebra, which allows us to express the fundamental laws in component-free form, thus aiding physical interpretation. It also provides the tools to express equations in an arbitrary coordinate system, which enhances their usefulness. The role of moments and angular velocity, and the apparent use by previous authors of an unphysical angular velocity, has been clarified through the use of a bivector representation. In the linearized theory, clarification of previous coordinate conventions which have been the cause of confusion is provided, and the introduction of prior strain into the linearized theory of shells is made possible. PMID:28405404

The elastic theory of shells using geometric algebra.

PubMed

Gregory, A L; Lasenby, J; Agarwal, A

2017-03-01

We present a novel derivation of the elastic theory of shells. We use the language of geometric algebra, which allows us to express the fundamental laws in component-free form, thus aiding physical interpretation. It also provides the tools to express equations in an arbitrary coordinate system, which enhances their usefulness. The role of moments and angular velocity, and the apparent use by previous authors of an unphysical angular velocity, has been clarified through the use of a bivector representation. In the linearized theory, clarification of previous coordinate conventions which have been the cause of confusion is provided, and the introduction of prior strain into the linearized theory of shells is made possible.

Adiabatic transport of qubits around a black hole

NASA Astrophysics Data System (ADS)

Viennot, David; Moro, Olivia

2017-03-01

We consider localized qubits evolving around a black hole following a quantum adiabatic dynamics. We develop a geometric structure (based on fibre bundles) permitting to describe the quantum states of a qubit and the spacetime geometry in a single framework. The quantum decoherence induced by the black hole on the qubit is analysed in this framework (the role of the dynamical and geometric phases in this decoherence is treated), especially for the quantum teleportation protocol when one qubit falls to the event horizon. A simple formula to compute the fidelity of the teleportation is derived. The case of a Schwarzschild black hole is analysed.

Adiabatic dynamics of one-dimensional classical Hamiltonian dissipative systems

NASA Astrophysics Data System (ADS)

Pritula, G. M.; Petrenko, E. V.; Usatenko, O. V.

2018-02-01

A linearized plane pendulum with the slowly varying mass and length of string and the suspension point moving at a slowly varying speed is presented as an example of a simple 1D mechanical system described by the generalized harmonic oscillator equation, which is a basic model in discussion of the adiabatic dynamics and geometric phase. The expression for the pendulum geometric phase is obtained by three different methods. The pendulum is shown to be canonically equivalent to the damped harmonic oscillator. This supports the mathematical conclusion, not widely accepted in physical community, of no difference between the dissipative and Hamiltonian 1D systems.

Expression-invariant representations of faces.

PubMed

Bronstein, Alexander M; Bronstein, Michael M; Kimmel, Ron

2007-01-01

Addressed here is the problem of constructing and analyzing expression-invariant representations of human faces. We demonstrate and justify experimentally a simple geometric model that allows to describe facial expressions as isometric deformations of the facial surface. The main step in the construction of expression-invariant representation of a face involves embedding of the facial intrinsic geometric structure into some low-dimensional space. We study the influence of the embedding space geometry and dimensionality choice on the representation accuracy and argue that compared to its Euclidean counterpart, spherical embedding leads to notably smaller metric distortions. We experimentally support our claim showing that a smaller embedding error leads to better recognition.

Geometrical optics model of Mie resonances

PubMed

Roll; Schweiger

2000-07-01

The geometrical optics model of Mie resonances is presented. The ray path geometry is given and the resonance condition is discussed with special emphasis on the phase shift that the rays undergo at the surface of the dielectric sphere. On the basis of this model, approximate expressions for the positions of first-order resonances are given. Formulas for the cavity mode spacing are rederived in a simple manner. It is shown that the resonance linewidth can be calculated regarding the cavity losses. Formulas for the mode density of Mie resonances are given that account for the different width of resonances and thus may be adapted to specific experimental situations.

Geometrically derived difference formulae for the numerical integration of trajectory problems

NASA Technical Reports Server (NTRS)

Mcleod, R. J. Y.; Sanz-Serna, J. M.

1981-01-01

The term 'trajectory problem' is taken to include problems that can arise, for instance, in connection with contour plotting, or in the application of continuation methods, or during phase-plane analysis. Geometrical techniques are used to construct difference methods for these problems to produce in turn explicit and implicit circularly exact formulae. Based on these formulae, a predictor-corrector method is derived which, when compared with a closely related standard method, shows improved performance. It is found that this latter method produces spurious limit cycles, and this behavior is partly analyzed. Finally, a simple variable-step algorithm is constructed and tested.

Index of Refraction without Geometry

ERIC Educational Resources Information Center

Farkas, N.; Henriksen, P. N.; Ramsier, R. D.

2006-01-01

This article presents several activities that permit students to determine the index of refraction of transparent solids and liquids using simple equipment without the need for geometrical relationships, special lighting or optical instruments. Graphical analysis of the measured data is shown to be a useful method for determining the index of…

Optics Demonstrations Using Cylindrical Lenses

ERIC Educational Resources Information Center

Ivanov, Dragia; Nikolov, Stefan

2015-01-01

In this paper we consider the main properties of cylindrical lenses and propose several demonstrational experiments that can be performed with them. Specifically we use simple glasses full of water to demonstrate some basic geometrical optics principles and phenomena. We also present some less standard experiments that can be performed with such…

Using Antenna Arrays to Motivate the Study of Sinusoids

ERIC Educational Resources Information Center

Becker, J. P.

2010-01-01

Educational activities involving antenna arrays to motivate the study of sinusoids are described. Specifically, using fundamental concepts related to phase and simple geometric arguments, students are asked to predict the location of interference nulls in the radiation pattern of two-element phased array antennas. The location of the radiation…

Connecting Dynamic Representations of Simple Mathematical Objects with the Construction and Exploration of Conic Sections

ERIC Educational Resources Information Center

Santos-Trigo, Manuel; Espinosa-Perez, Hugo; Reyes-Rodriguez, Aaron

2008-01-01

Different technological artefacts may offer distinct opportunities for students to develop resources and strategies to formulate, comprehend and solve mathematical problems. In particular, the use of dynamic software becomes relevant to assemble geometric configurations that may help students reconstruct and examine mathematical relationships. In…

Interference Phenomenon with Mobile Displays

ERIC Educational Resources Information Center

Trantham, Kenneth

2015-01-01

A simple experiment is presented in which the spacing and geometric pattern of pixels in mobile displays is measured. The technique is based on optical constructive interference. While the experiment is another opportunity to demonstrate wave interference from a grating-like structure, this can also be used to demonstrate concepts of solid state…

Recognition-by-Components: A Theory of Human Image Understanding.

ERIC Educational Resources Information Center

Biederman, Irving

1987-01-01

The theory proposed (recognition-by-components) hypothesizes the perceptual recognition of objects to be a process in which the image of the input is segmented at regions of deep concavity into an arrangement of simple geometric components. Experiments on the perception of briefly presented pictures support the theory. (Author/LMO)

Recognizing simple polyhedron from a perspective drawing

NASA Astrophysics Data System (ADS)

Zhang, Guimei; Chu, Jun; Miao, Jun

2009-10-01

Existed methods can't be used for recognizing simple polyhedron. In this paper, three problems are researched. First, a method for recognizing triangle and quadrilateral is introduced based on geometry and angle constraint. Then Attribute Relation Graph (ARG) is employed to describe simple polyhedron and line drawing. Last, a new method is presented to recognize simple polyhedron from a line drawing. The method filters the candidate database before matching line drawing and model, thus the recognition efficiency is improved greatly. We introduced the geometrical characteristics and topological characteristics to describe each node of ARG, so the algorithm can not only recognize polyhedrons with different shape but also distinguish between polyhedrons with the same shape but with different sizes and proportions. Computer simulations demonstrate the effectiveness of the method preliminarily.

Geometric phase effects in the ultracold D + HD $$ \\rightarrow $$ D + HD and D + HD $$\\leftrightarrow $$ H + D 2 reactions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kendrick, Brian Kent; Hazra, Jisha; Balakrishnan, Naduvaluth

The results of accurate quantum reactive scattering calculations for the D + HD(v = 4, j = 0)more » $$\\to $$ D + HD($$v^{\\prime} $$, $$j^{\\prime} $$), D + HD(v = 4, j = 0) $$\\to $$ H + D2($$v^{\\prime} $$, $$j^{\\prime} $$) and H + D2(v = 4, j = 0) $$\\to $$ D + HD($$v^{\\prime} $$, $$j^{\\prime} $$) reactions are presented for collision energies between $$1\\,\\mu {\\rm{K}}$$ and $$100\\,{\\rm{K}}$$. The ab initio BKMP2 PES for the ground electronic state of H3 is used and all values of total angular momentum between $J=0-4$ are included. The general vector potential approach is used to include the geometric phase. The rotationally resolved, vibrationally resolved, and total reaction rate coefficients are reported as a function of collision energy. Rotationally resolved differential cross sections are also reported as a function of collision energy and scattering angle. Large geometric phase effects appear in the ultracold reaction rate coefficients which result in a significant enhancement or suppression of the rate coefficient (up to 3 orders of magnitude) relative to calculations which ignore the geometric phase. The results are interpreted using a new quantum interference mechanism which is unique to ultracold collisions. Significant effects of the geometric phase also appear in the rotationally resolved differential cross sections which lead to a very different oscillatory structure in both energy and scattering angle. Several shape resonances occur in the 1–$$10\\,{\\rm{K}}$$ energy range and the geometric phase is shown to significantly alter the predicted resonance spectrum. The geometric phase effects and ultracold rate coefficients depend sensitively on the nuclear spin. Furthermore, experimentalists may be able to control the reaction by the selection of a particular nuclear spin state.« less

Geometric phase effects in the ultracold D + HD $$ \\rightarrow $$ D + HD and D + HD $$\\leftrightarrow $$ H + D 2 reactions

DOE PAGES

Kendrick, Brian Kent; Hazra, Jisha; Balakrishnan, Naduvaluth

2016-12-15

The results of accurate quantum reactive scattering calculations for the D + HD(v = 4, j = 0)more » $$\\to $$ D + HD($$v^{\\prime} $$, $$j^{\\prime} $$), D + HD(v = 4, j = 0) $$\\to $$ H + D2($$v^{\\prime} $$, $$j^{\\prime} $$) and H + D2(v = 4, j = 0) $$\\to $$ D + HD($$v^{\\prime} $$, $$j^{\\prime} $$) reactions are presented for collision energies between $$1\\,\\mu {\\rm{K}}$$ and $$100\\,{\\rm{K}}$$. The ab initio BKMP2 PES for the ground electronic state of H3 is used and all values of total angular momentum between $J=0-4$ are included. The general vector potential approach is used to include the geometric phase. The rotationally resolved, vibrationally resolved, and total reaction rate coefficients are reported as a function of collision energy. Rotationally resolved differential cross sections are also reported as a function of collision energy and scattering angle. Large geometric phase effects appear in the ultracold reaction rate coefficients which result in a significant enhancement or suppression of the rate coefficient (up to 3 orders of magnitude) relative to calculations which ignore the geometric phase. The results are interpreted using a new quantum interference mechanism which is unique to ultracold collisions. Significant effects of the geometric phase also appear in the rotationally resolved differential cross sections which lead to a very different oscillatory structure in both energy and scattering angle. Several shape resonances occur in the 1–$$10\\,{\\rm{K}}$$ energy range and the geometric phase is shown to significantly alter the predicted resonance spectrum. The geometric phase effects and ultracold rate coefficients depend sensitively on the nuclear spin. Furthermore, experimentalists may be able to control the reaction by the selection of a particular nuclear spin state.« less

Monitoring land degradation in southern Tunisia: A test of LANDSAT imagery and digital data

NASA Technical Reports Server (NTRS)

Hellden, U.; Stern, M.

1980-01-01

The possible use of LANDSAT imagery and digital data for monitoring desertification indicators in Tunisia was studied. Field data were sampled in Tunisia for estimation of mapping accuracy in maps generated through interpretation of LANDSAT false color composites and processing of LANDSAT computer compatible tapes respectively. Temporal change studies were carried out through geometric registration of computer classified windows from 1972 to classified data from 1979. Indications on land degradation were noted in some areas. No important differences, concerning results, between the interpretation approach and the computer processing approach were found.

Tracking Small Artists

NASA Astrophysics Data System (ADS)

Russell, James C.; Klette, Reinhard; Chen, Chia-Yen

Tracks of small animals are important in environmental surveillance, where pattern recognition algorithms allow species identification of the individuals creating tracks. These individuals can also be seen as artists, presented in their natural environments with a canvas upon which they can make prints. We present tracks of small mammals and reptiles which have been collected for identification purposes, and re-interpret them from an esthetic point of view. We re-classify these tracks not by their geometric qualities as pattern recognition algorithms would, but through interpreting the 'artist', their brush strokes and intensity. We describe the algorithms used to enhance and present the work of the 'artists'.

An Automatic Method for Geometric Segmentation of Masonry Arch Bridges for Structural Engineering Purposes

NASA Astrophysics Data System (ADS)

Riveiro, B.; DeJong, M.; Conde, B.

2016-06-01

Despite the tremendous advantages of the laser scanning technology for the geometric characterization of built constructions, there are important limitations preventing more widespread implementation in the structural engineering domain. Even though the technology provides extensive and accurate information to perform structural assessment and health monitoring, many people are resistant to the technology due to the processing times involved. Thus, new methods that can automatically process LiDAR data and subsequently provide an automatic and organized interpretation are required. This paper presents a new method for fully automated point cloud segmentation of masonry arch bridges. The method efficiently creates segmented, spatially related and organized point clouds, which each contain the relevant geometric data for a particular component (pier, arch, spandrel wall, etc.) of the structure. The segmentation procedure comprises a heuristic approach for the separation of different vertical walls, and later image processing tools adapted to voxel structures allows the efficient segmentation of the main structural elements of the bridge. The proposed methodology provides the essential processed data required for structural assessment of masonry arch bridges based on geometric anomalies. The method is validated using a representative sample of masonry arch bridges in Spain.

The impact of robustness of deformable image registration on contour propagation and dose accumulation for head and neck adaptive radiotherapy.

PubMed

Zhang, Lian; Wang, Zhi; Shi, Chengyu; Long, Tengfei; Xu, X George

2018-05-30

Deformable image registration (DIR) is the key process for contour propagation and dose accumulation in adaptive radiation therapy (ART). However, currently, ART suffers from a lack of understanding of "robustness" of the process involving the image contour based on DIR and subsequent dose variations caused by algorithm itself and the presetting parameters. The purpose of this research is to evaluate the DIR caused variations for contour propagation and dose accumulation during ART using the RayStation treatment planning system. Ten head and neck cancer patients were selected for retrospective studies. Contours were performed by a single radiation oncologist and new treatment plans were generated on the weekly CT scans for all patients. For each DIR process, four deformation vector fields (DVFs) were generated to propagate contours and accumulate weekly dose by the following algorithms: (a) ANACONDA with simple presetting parameters, (b) ANACONDA with detailed presetting parameters, (c) MORFEUS with simple presetting parameters, and (d) MORFEUS with detailed presetting parameters. The geometric evaluation considered DICE coefficient and Hausdorff distance. The dosimetric evaluation included D 95 , D max , D mean , D min , and Homogeneity Index. For geometric evaluation, the DICE coefficient variations of the GTV were found to be 0.78 ± 0.11, 0.96 ± 0.02, 0.64 ± 0.15, and 0.91 ± 0.03 for simple ANACONDA, detailed ANACONDA, simple MORFEUS, and detailed MORFEUS, respectively. For dosimetric evaluation, the corresponding Homogeneity Index variations were found to be 0.137 ± 0.115, 0.006 ± 0.032, 0.197 ± 0.096, and 0.006 ± 0.033, respectively. The coherent geometric and dosimetric variations also consisted in large organs and small organs. Overall, the results demonstrated that the contour propagation and dose accumulation in clinical ART were influenced by the DIR algorithm, and to a greater extent by the presetting parameters. A quality assurance procedure should be established for the proper use of a commercial DIR for adaptive radiation therapy. © 2018 The Authors. Journal of Applied Clinical Medical Physics published by Wiley Periodicals, Inc. on behalf of American Association of Physicists in Medicine.

Renormalization group flows and continual Lie algebras

NASA Astrophysics Data System (ADS)

Bakas, Ioannis

2003-08-01

We study the renormalization group flows of two-dimensional metrics in sigma models using the one-loop beta functions, and demonstrate that they provide a continual analogue of the Toda field equations in conformally flat coordinates. In this algebraic setting, the logarithm of the world-sheet length scale, t, is interpreted as Dynkin parameter on the root system of a novel continual Lie algebra, denoted by Script G(d/dt;1), with anti-symmetric Cartan kernel K(t,t') = delta'(t-t'); as such, it coincides with the Cartan matrix of the superalgebra sl(N|N+1) in the large-N limit. The resulting Toda field equation is a non-linear generalization of the heat equation, which is integrable in target space and shares the same dissipative properties in time, t. We provide the general solution of the renormalization group flows in terms of free fields, via Bäcklund transformations, and present some simple examples that illustrate the validity of their formal power series expansion in terms of algebraic data. We study in detail the sausage model that arises as geometric deformation of the O(3) sigma model, and give a new interpretation to its ultra-violet limit by gluing together two copies of Witten's two-dimensional black hole in the asymptotic region. We also provide some new solutions that describe the renormalization group flow of negatively curved spaces in different patches, which look like a cane in the infra-red region. Finally, we revisit the transition of a flat cone C/Zn to the plane, as another special solution, and note that tachyon condensation in closed string theory exhibits a hidden relation to the infinite dimensional algebra Script G(d/dt;1) in the regime of gravity. Its exponential growth holds the key for the construction of conserved currents and their systematic interpretation in string theory, but they still remain unknown.

Koszul information geometry and Souriau Lie group thermodynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barbaresco, Frédéric, E-mail: frederic.barbaresco@thalesgroup.com

The François Massieu 1869 idea to derive some mechanical and thermal properties of physical systems from 'Characteristic Functions', was developed by Gibbs and Duhem in thermodynamics with the concept of potentials, and introduced by Poincaré in probability. This paper deals with generalization of this Characteristic Function concept by Jean-Louis Koszul in Mathematics and by Jean-Marie Souriau in Statistical Physics. The Koszul-Vinberg Characteristic Function (KVCF) on convex cones will be presented as cornerstone of 'Information Geometry' theory, defining Koszul Entropy as Legendre transform of minus the logarithm of KVCF, and Fisher Information Metrics as hessian of these dual functions, invariant bymore » their automorphisms. In parallel, Souriau has extended the Characteristic Function in Statistical Physics looking for other kinds of invariances through co-adjoint action of a group on its momentum space, defining physical observables like energy, heat and momentum as pure geometrical objects. In covariant Souriau model, Gibbs equilibriums states are indexed by a geometric parameter, the Geometric (Planck) Temperature, with values in the Lie algebra of the dynamical Galileo/Poincaré groups, interpreted as a space-time vector, giving to the metric tensor a null Lie derivative. Fisher Information metric appears as the opposite of the derivative of Mean 'Moment map' by geometric temperature, equivalent to a Geometric Capacity or Specific Heat. These elements has been developed by author in [10][11].« less

Littelmann path model for geometric crystals, Whittaker functions on Lie groups and Brownian motion

NASA Astrophysics Data System (ADS)

Chhaibi, Reda

2013-02-01

Generally speaking, this thesis focuses on the interplay between the representations of Lie groups and probability theory. It subdivides into essentially three parts. In a first rather algebraic part, we construct a path model for geometric crystals in the sense of Berenstein and Kazhdan, for complex semi-simple Lie groups. We will mainly describe the algebraic structure, its natural morphisms and parameterizations. The theory of total positivity will play a particularly important role. Then, we anticipate on the probabilistic part by exhibiting a canonical measure on geometric crystals. It uses as ingredients the superpotential for the flag manifold and a measure invariant under the crystal actions. The image measure under the weight map plays the role of Duistermaat-Heckman measure. Its Laplace transform defines Whittaker functions, providing an interesting formula for all Lie groups. Then it appears clearly that Whittaker functions are to geometric crystals, what characters are to combinatorial crystals. The Littlewood-Richardson rule is also exposed. Finally we present the probabilistic approach that allows to find the canonical measure. It is based on the fundamental idea that the Wiener measure will induce the adequate measure on the algebraic structures through the path model. In the last chapter, we show how our geometric model degenerates to the continuous classical Littelmann path model and thus recover known results. For example, the canonical measure on a geometric crystal of highest weight degenerates into a uniform measure on a polytope, and recovers the parameterizations of continuous crystals.

The Role of a Dynamic Software Program for Geometry in the Strategies High School Mathematics Students Employ

ERIC Educational Resources Information Center

Hollebrands, Karen F.

2007-01-01

This study investigated the ways in which the technological tool, The Geometer's Sketchpad, mediated the understandings that high school Honors Geometry students developed about geometric transformations by focusing on their uses of technological affordances and the ways in which they interpreted technological results in terms of figure and…

Zig-Zagging in Geometrical Reasoning in Technological Collaborative Environments: A Mathematical Working Space-Framed Study Concerning Cognition and Affect

ERIC Educational Resources Information Center

Gómez-Chacón, Inés Ma.; Romero Albaladejo, Isabel Ma.; del Mar García López, Ma.

2016-01-01

This study highlights the importance of cognition-affect interaction pathways in the construction of mathematical knowledge. Scientific output demands further research on the conceptual structure underlying such interaction aimed at coping with the high complexity of its interpretation. The paper discusses the effectiveness of using a dynamic…

Closed Paths of Light Trapped in a Closed Fermat Curve

ERIC Educational Resources Information Center

Dana-Picard, Thierry; Naiman, Aaron

2002-01-01

Geometric constructions have previously been shown that can be interpreted as rays of light trapped either in polygons or in conics, by successive reflections. The same question, trapping light in closed Fermat curves, is addressed here. Numerical methods are used to study the behaviour of the reflection points of a triangle when the degree of the…

Mathematics Teachers' Visualization of Complex Number Multiplication and the Roots of Unity in a Dynamic Geometry Environment

ERIC Educational Resources Information Center

Caglayan, Gunhan

2016-01-01

This qualitative research, drawing on the theoretical frameworks by Even (1990, 1993) and Sfard (2007), investigated five high school mathematics teachers' geometric interpretations of complex number multiplication along with the roots of unity. The main finding was that mathematics teachers constructed the modulus, the argument, and the conjugate…

Residuals and the Residual-Based Statistic for Testing Goodness of Fit of Structural Equation Models

ERIC Educational Resources Information Center

Foldnes, Njal; Foss, Tron; Olsson, Ulf Henning

2012-01-01

The residuals obtained from fitting a structural equation model are crucial ingredients in obtaining chi-square goodness-of-fit statistics for the model. The authors present a didactic discussion of the residuals, obtaining a geometrical interpretation by recognizing the residuals as the result of oblique projections. This sheds light on the…

Graphical Representation of Complex Solutions of the Quadratic Equation in the "xy" Plane

ERIC Educational Resources Information Center

McDonald, Todd

2006-01-01

This paper presents a visual representation of complex solutions of quadratic equations in the xy plane. Rather than moving to the complex plane, students are able to experience a geometric interpretation of the solutions in the xy plane. I am also working on these types of representations with higher order polynomials with some success.

German Children’s Use of Word Order and Case Marking to Interpret Simple and Complex Sentences: Testing Differences Between Constructions and Lexical Items

PubMed Central

Brandt, Silke; Lieven, Elena; Tomasello, Michael

2016-01-01

ABSTRACT Children and adults follow cues such as case marking and word order in their assignment of semantic roles in simple transitives (e.g., the dog chased the cat). It has been suggested that the same cues are used for the interpretation of complex sentences, such as transitive relative clauses (RCs) (e.g., that’s the dog that chased the cat) (Bates, Devescovi, & D’Amico, 1999). We used a pointing paradigm to test German-speaking 3-, 4-, and 6-year-old children’s sensitivity to case marking and word order in their interpretation of simple transitives and transitive RCs. In Experiment 1, case marking was ambiguous. The only cue available was word order. In Experiment 2, case was marked on lexical NPs or demonstrative pronouns. In Experiment 3, case was marked on lexical NPs or personal pronouns. Whereas the younger children mainly followed word order, the older children were more likely to base their interpretations on the more reliable case-marking cue. In most cases, children from both age groups were more likely to use these cues in their interpretation of simple transitives than in their interpretation of transitive RCs. Finally, children paid more attention to nominative case when it was marked on first-person personal pronouns than when it was marked on third-person lexical NPs or demonstrative pronouns, such as der Löwe ‘the-NOM lion’ or der ‘he-NOM.’ They were able to successfully integrate this case-marking cue in their sentence processing even when it appeared late in the sentence. We discuss four potential reasons for these differences across development, constructions, and lexical items. (1) Older children are relatively more sensitive to cue reliability. (2) Word order is more reliable in simple transitives than in transitive RCs. (3) The processing of case marking might initially be item-specific. (4) The processing of case marking might depend on its saliency and position in the sentence. PMID:27019652

An analytic-geometric model of the effect of spherically distributed injection errors for Galileo and Ulysses spacecraft - The multi-stage problem

NASA Technical Reports Server (NTRS)

Longuski, James M.; Mcronald, Angus D.

1988-01-01

In previous work the problem of injecting the Galileo and Ulysses spacecraft from low earth orbit into their respective interplanetary trajectories has been discussed for the single stage (Centaur) vehicle. The central issue, in the event of spherically distributed injection errors, is what happens to the vehicle? The difficulties addressed in this paper involve the multi-stage problem since both Galileo and Ulysses will be utilizing the two-stage IUS system. Ulysses will also include a third stage: the PAM-S. The solution is expressed in terms of probabilities for total percentage of escape, orbit decay and reentry trajectories. Analytic solutions are found for Hill's Equations of Relative Motion (more recently called Clohessy-Wiltshire Equations) for multi-stage injections. These solutions are interpreted geometrically on the injection sphere. The analytic-geometric models compare well with numerical solutions, provide insight into the behavior of trajectories mapped on the injection sphere and simplify the numerical two-dimensional search for trajectory families.

The pentagon relation and incidence geometry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Doliwa, Adam, E-mail: doliwa@matman.uwm.edu.pl; Sergeev, Sergey M., E-mail: Sergey.Sergeev@canberra.edu.au

2014-06-01

We define a map S:D²×D²→D²×D², where D is an arbitrary division ring (skew field), associated with the Veblen configuration, and we show that such a map provides solutions to the functional dynamical pentagon equation. We explain that fact in elementary geometric terms using the symmetry of the Veblen and Desargues configurations. We introduce also another map of a geometric origin with the pentagon property. We show equivalence of these maps with recently introduced Desargues maps which provide geometric interpretation to a non-commutative version of Hirota's discrete Kadomtsev–Petviashvili equation. Finally, we demonstrate that in an appropriate gauge the (commutative version ofmore » the) maps preserves a natural Poisson structure—the quasiclassical limit of the Weyl commutation relations. The corresponding quantum reduction is then studied. In particular, we discuss uniqueness of the Weyl relations for the ultra-local reduction of the map. We give then the corresponding solution of the quantum pentagon equation in terms of the non-compact quantum dilogarithm function.« less

On the unification of nuclear-structure theory: A response to Bortignon and Broglia

NASA Astrophysics Data System (ADS)

Cook, Norman D.

2016-09-01

Nuclear-structure theory is unusual among the diverse fields of quantum physics. Although it provides a coherent description of all known isotopes on the basis of a quantum-mechanical understanding of nucleon states, nevertheless, in the absence of a fundamental theory of the nuclear force acting between nucleons, the prediction of all ground-state and excited-state nuclear binding energies is inherently semi-empirical. I suggest that progress can be made by returning to the foundational work of Eugene Wigner from 1937, where the mathematical symmetries of nucleon states were first defined. Those symmetries were later successfully exploited in the development of the independent-particle model ( IPM ˜ shell model , but the geometrical implications noted by Wigner were neglected. Here I review how the quantum-mechanical, but remarkably easy-to-understand geometrical interpretation of the IPM provides constraints on the parametrization of the nuclear force. The proposed "geometrical IPM" indicates a way forward toward the unification of nuclear-structure theory that Bortignon and Broglia have called for.

Percolation and cooperation with mobile agents: geometric and strategy clusters.

PubMed

Vainstein, Mendeli H; Brito, Carolina; Arenzon, Jeferson J

2014-08-01

We study the conditions for persistent cooperation in an off-lattice model of mobile agents playing the Prisoner's Dilemma game with pure, unconditional strategies. Each agent has an exclusion radius r(P), which accounts for the population viscosity, and an interaction radius r(int), which defines the instantaneous contact network for the game dynamics. We show that, differently from the r(P)=0 case, the model with finite-sized agents presents a coexistence phase with both cooperators and defectors, besides the two absorbing phases, in which either cooperators or defectors dominate. We provide, in addition, a geometric interpretation of the transitions between phases. In analogy with lattice models, the geometric percolation of the contact network (i.e., irrespective of the strategy) enhances cooperation. More importantly, we show that the percolation of defectors is an essential condition for their survival. Differently from compact clusters of cooperators, isolated groups of defectors will eventually become extinct if not percolating, independently of their size.

Geometric model of pseudo-distance measurement in satellite location systems

NASA Astrophysics Data System (ADS)

Panchuk, K. L.; Lyashkov, A. A.; Lyubchinov, E. V.

2018-04-01

The existing mathematical model of pseudo-distance measurement in satellite location systems does not provide a precise solution of the problem, but rather an approximate one. The existence of such inaccuracy, as well as bias in measurement of distance from satellite to receiver, results in inaccuracy level of several meters. Thereupon, relevance of refinement of the current mathematical model becomes obvious. The solution of the system of quadratic equations used in the current mathematical model is based on linearization. The objective of the paper is refinement of current mathematical model and derivation of analytical solution of the system of equations on its basis. In order to attain the objective, geometric analysis is performed; geometric interpretation of the equations is given. As a result, an equivalent system of equations, which allows analytical solution, is derived. An example of analytical solution implementation is presented. Application of analytical solution algorithm to the problem of pseudo-distance measurement in satellite location systems allows to improve the accuracy such measurements.

Discovering biclusters in gene expression data based on high-dimensional linear geometries

PubMed Central

Gan, Xiangchao; Liew, Alan Wee-Chung; Yan, Hong

2008-01-01

Background In DNA microarray experiments, discovering groups of genes that share similar transcriptional characteristics is instrumental in functional annotation, tissue classification and motif identification. However, in many situations a subset of genes only exhibits consistent pattern over a subset of conditions. Conventional clustering algorithms that deal with the entire row or column in an expression matrix would therefore fail to detect these useful patterns in the data. Recently, biclustering has been proposed to detect a subset of genes exhibiting consistent pattern over a subset of conditions. However, most existing biclustering algorithms are based on searching for sub-matrices within a data matrix by optimizing certain heuristically defined merit functions. Moreover, most of these algorithms can only detect a restricted set of bicluster patterns. Results In this paper, we present a novel geometric perspective for the biclustering problem. The biclustering process is interpreted as the detection of linear geometries in a high dimensional data space. Such a new perspective views biclusters with different patterns as hyperplanes in a high dimensional space, and allows us to handle different types of linear patterns simultaneously by matching a specific set of linear geometries. This geometric viewpoint also inspires us to propose a generic bicluster pattern, i.e. the linear coherent model that unifies the seemingly incompatible additive and multiplicative bicluster models. As a particular realization of our framework, we have implemented a Hough transform-based hyperplane detection algorithm. The experimental results on human lymphoma gene expression dataset show that our algorithm can find biologically significant subsets of genes. Conclusion We have proposed a novel geometric interpretation of the biclustering problem. We have shown that many common types of bicluster are just different spatial arrangements of hyperplanes in a high dimensional data space. An implementation of the geometric framework using the Fast Hough transform for hyperplane detection can be used to discover biologically significant subsets of genes under subsets of conditions for microarray data analysis. PMID:18433477

A Simple Derivation of Kepler's Laws without Solving Differential Equations

ERIC Educational Resources Information Center

Provost, J.-P.; Bracco, C.

2009-01-01

Proceeding like Newton with a discrete time approach of motion and a geometrical representation of velocity and acceleration, we obtain Kepler's laws without solving differential equations. The difficult part of Newton's work, when it calls for non-trivial properties of ellipses, is avoided by the introduction of polar coordinates. Then a simple…

Finding Quality Geometry Apps: Not as Simple as a[superscript 2] + b[superscript 2] = c[superscript 2

ERIC Educational Resources Information Center

Larkin, Kevin

2016-01-01

Trying to find quality apps for use in mathematics classes can be time consuming and bewildering. This article outlines a process for evaluating apps and provides teachers with access to comprehensive qualitative evaluations of 53 geometrical apps based on pedagogical, mathematical and cognitive fidelities.

Geometry of Cournot-Nash Equilibrium with Application to Commons and Anticommons

ERIC Educational Resources Information Center

D'Agata, Antonio

2010-01-01

The author develops a simple geometric analysis of Cournot-Nash equilibrium in the price-quantity space by exploiting the economic content of the first-order condition. The approach makes it clear that strategic interdependency in oligopoly originates from externalities among producers. This explains why cartels are unstable and casts oligopoly…

Perceptual Effects of Social Salience: Evidence from Self-Prioritization Effects on Perceptual Matching

ERIC Educational Resources Information Center

Sui, Jie; He, Xun; Humphreys, Glyn W.

2012-01-01

We present novel evidence showing that new self-relevant visual associations can affect performance in simple shape recognition tasks. Participants associated labels for themselves, other people, or neutral terms with geometric shapes and then immediately judged whether subsequent label-shape pairings were matched. Across 4 experiments there was a…

Geometrical Simplification of the Dipole-Dipole Interaction Formula

ERIC Educational Resources Information Center

Kocbach, Ladislav; Lubbad, Suhail

2010-01-01

Many students meet dipole-dipole potential energy quite early on when they are taught electrostatics or magnetostatics and it is also a very popular formula, featured in encyclopedias. We show that by a simple rewriting of the formula it becomes apparent that, for example, by reorienting the two dipoles, their attraction can become exactly twice…

Elementary Visual Hallucinations and Their Relationships to Neural Pattern-Forming Mechanisms

ERIC Educational Resources Information Center

Billock, Vincent A.; Tsou, Brian H.

2012-01-01

An extraordinary variety of experimental (e.g., flicker, magnetic fields) and clinical (epilepsy, migraine) conditions give rise to a surprisingly common set of elementary hallucinations, including spots, geometric patterns, and jagged lines, some of which also have color, depth, motion, and texture. Many of these simple hallucinations fall into a…

A Brief History of Partitions of Numbers, Partition Functions and Their Modern Applications

ERIC Educational Resources Information Center

Debnath, Lokenath

2016-01-01

This paper is written to commemorate the centennial anniversary of the Mathematical Association of America. It deals with a short history of different kinds of natural numbers including triangular, square, pentagonal, hexagonal and "k"-gonal numbers, and their simple properties and their geometrical representations. Included are Euclid's…

Analogy and Dynamic Geometry System Used to Introduce Three-Dimensional Geometry

ERIC Educational Resources Information Center

Mammana, M. F.; Micale, B.; Pennisi, M.

2012-01-01

We present a sequence of classroom activities on Euclidean geometry, both plane and space geometry, used to make three dimensional geometry more catchy and simple. The activity consists of a guided research activity that leads the students to discover unexpected properties of two apparently distant geometrical entities, quadrilaterals and…

Site-to-Source Finite Fault Distance Probability Distribution in Probabilistic Seismic Hazard and the Relationship Between Minimum Distances

NASA Astrophysics Data System (ADS)

Ortega, R.; Gutierrez, E.; Carciumaru, D. D.; Huesca-Perez, E.

2017-12-01

We present a method to compute the conditional and no-conditional probability density function (PDF) of the finite fault distance distribution (FFDD). Two cases are described: lines and areas. The case of lines has a simple analytical solution while, in the case of areas, the geometrical probability of a fault based on the strike, dip, and fault segment vertices is obtained using the projection of spheres in a piecewise rectangular surface. The cumulative distribution is computed by measuring the projection of a sphere of radius r in an effective area using an algorithm that estimates the area of a circle within a rectangle. In addition, we introduce the finite fault distance metrics. This distance is the distance where the maximum stress release occurs within the fault plane and generates a peak ground motion. Later, we can apply the appropriate ground motion prediction equations (GMPE) for PSHA. The conditional probability of distance given magnitude is also presented using different scaling laws. A simple model of constant distribution of the centroid at the geometrical mean is discussed, in this model hazard is reduced at the edges because the effective size is reduced. Nowadays there is a trend of using extended source distances in PSHA, however it is not possible to separate the fault geometry from the GMPE. With this new approach, it is possible to add fault rupture models separating geometrical and propagation effects.

Unified Generic Geometric-Decompositions for Consensus or Flocking Systems of Cooperative Agents and Fast Recalculations of Decomposed Subsystems Under Topology-Adjustments.

PubMed

Li, Wei

2016-06-01

This paper considers a unified geometric projection approach for: 1) decomposing a general system of cooperative agents coupled via Laplacian matrices or stochastic matrices and 2) deriving a centroid-subsystem and many shape-subsystems, where each shape-subsystem has the distinct properties (e.g., preservation of formation and stability of the original system, sufficiently simple structures and explicit formation evolution of agents, and decoupling from the centroid-subsystem) which will facilitate subsequent analyses. Particularly, this paper provides an additional merit of the approach: considering adjustments of coupling topologies of agents which frequently occur in system design (e.g., to add or remove an edge, to move an edge to a new place, and to change the weight of an edge), the corresponding new shape-subsystems can be derived by a few simple computations merely from the old shape-subsystems and without referring to the original system, which will provide further convenience for analysis and flexibility of choice. Finally, such fast recalculations of new subsystems under topology adjustments are provided with examples.

An Accurate Non-Cooperative Method for Measuring Textureless Spherical Target Based on Calibrated Lasers.

PubMed

Wang, Fei; Dong, Hang; Chen, Yanan; Zheng, Nanning

2016-12-09

Strong demands for accurate non-cooperative target measurement have been arising recently for the tasks of assembling and capturing. Spherical objects are one of the most common targets in these applications. However, the performance of the traditional vision-based reconstruction method was limited for practical use when handling poorly-textured targets. In this paper, we propose a novel multi-sensor fusion system for measuring and reconstructing textureless non-cooperative spherical targets. Our system consists of four simple lasers and a visual camera. This paper presents a complete framework of estimating the geometric parameters of textureless spherical targets: (1) an approach to calibrate the extrinsic parameters between a camera and simple lasers; and (2) a method to reconstruct the 3D position of the laser spots on the target surface and achieve the refined results via an optimized scheme. The experiment results show that our proposed calibration method can obtain a fine calibration result, which is comparable to the state-of-the-art LRF-based methods, and our calibrated system can estimate the geometric parameters with high accuracy in real time.

RNICO: a new simple geometric index for assessing the impact of urban development pattern on peak flows in urban catchments

NASA Astrophysics Data System (ADS)

Kasaee Roodsari, B.; Chandler, D. G.

2016-12-01

Urban sprawl is widespread across the world and the associated hydrologic impacts are increasing in peri-urban catchments due to increased area of impervious. There is a strong agreement on the positive correlation between the fractional impervious area and peak flows in urban catchments. Nevertheless, the effect of land development pattern on peak flows is not well investigated. In this study, a new simple geometric index, Relative Nearness of Imperviousness to the Catchment Outlet (RNICO), is defined to correlate imperviousness distribution of peri-urban catchments to runoff peak flows. Results of applying RNICO to 20 sub-catchments in New York State showed a strong positive correlation (R2>0.97) between RNICO and runoff peak flows for small peri-urban catchments (A< 42 km2) indicating higher flood risk of downstream urbanization. For large catchments (A> 42 km2), no correlation was indicated between RNICO and peak flows. We highlight the necessity of a greater discharge monitoring network at small peri-urban catchments to support local urban flood forecast.

An Accurate Non-Cooperative Method for Measuring Textureless Spherical Target Based on Calibrated Lasers

PubMed Central

Wang, Fei; Dong, Hang; Chen, Yanan; Zheng, Nanning

2016-01-01

Strong demands for accurate non-cooperative target measurement have been arising recently for the tasks of assembling and capturing. Spherical objects are one of the most common targets in these applications. However, the performance of the traditional vision-based reconstruction method was limited for practical use when handling poorly-textured targets. In this paper, we propose a novel multi-sensor fusion system for measuring and reconstructing textureless non-cooperative spherical targets. Our system consists of four simple lasers and a visual camera. This paper presents a complete framework of estimating the geometric parameters of textureless spherical targets: (1) an approach to calibrate the extrinsic parameters between a camera and simple lasers; and (2) a method to reconstruct the 3D position of the laser spots on the target surface and achieve the refined results via an optimized scheme. The experiment results show that our proposed calibration method can obtain a fine calibration result, which is comparable to the state-of-the-art LRF-based methods, and our calibrated system can estimate the geometric parameters with high accuracy in real time. PMID:27941705

Geometries in Soft Matter From Geometric Frustration, Liquid Droplets to Electrostatics in Solution

NASA Astrophysics Data System (ADS)

Yao, Zhenwei

This thesis explores geometric aspects of soft matter systems. The topics covered fall into three categories: (i) geometric frustrations, including the interplay of geometry and topological defects in two dimensional systems, and the frustration of a planar sheet attached to a curved surface; (ii) geometries of liquid droplets, including the curvature driven instabilities of toroidal liquid droplets and the self-propulsion of droplets on a spatially varying surface topography; (iii) the study of the electric double layer structure around charged spherical interfaces by a geometric method. In (i), we study the crystalline order on capillary bridges with varying Gaussian curvature. Energy requires the appearance of topological defects on the surface, which are natural spots for biological activity and chemical functionalization. We further study how liquid crystalline order deforms flexible structured vesicles. In particular we find faceted tetrahedral vesicle as the ground state, which may lead to the design of supra-molecular structures with tetrahedral symmetry and new classes of nano-carriers. Furthermore, by a simple paper model we explore the geometric frustration on a planar sheet when brought to a negative curvature surface in a designed elasto-capillary system. In (ii), motivated by the idea of realizing crystalline order on a stable toroidal droplet and a beautiful experiment on toroidal droplets, we study the Rayleigh instability and the shrinking instability of thin and fat toroidal droplets, where the toroidal geometry plays an essential role. In (iii), by a geometric mapping we construct an approximate analytic spherical solution to the nonlinear Poisson-Boltzmann equation, and identify the applicability regime of the solution. The derived geometric solution enables further analytical study of spherical electrostatic systems such as colloidal suspensions.

A Closed Parameterization of DNA–Damage by Charged Particles, as a Function of Energy — A Geometrical Approach

PubMed Central

Van den Heuvel, Frank

2014-01-01

Purpose To present a closed formalism calculating charged particle radiation damage induced in DNA. The formalism is valid for all types of charged particles and due to its closed nature is suited to provide fast conversion of dose to DNA-damage. Methods The induction of double strand breaks in DNA–strings residing in irradiated cells is quantified using a single particle model. This leads to a proposal to use the cumulative Cauchy distribution to express the mix of high and low LET type damage probability generated by a single particle. A microscopic phenomenological Monte Carlo code is used to fit the parameters of the model as a function of kinetic energy related to the damage to a DNA molecule embedded in a cell. The model is applied for four particles: electrons, protons, alpha–particles, and carbon ions. A geometric interpretation of this observation using the impact ionization mean free path as a quantifier, allows extension of the model to very low energies. Results The mathematical expression describes the model adequately using a chi–square test (). This applies to all particle types with an almost perfect fit for protons, while the other particles seem to result in some discrepancies at very low energies. The implementation calculating a strict version of the RBE based on complex damage alone is corroborated by experimental data from the measured RBE. The geometric interpretation generates a unique dimensionless parameter for each type of charged particle. In addition, it predicts a distribution of DNA damage which is different from the current models. PMID:25340636

The methods of optical physics as a mean of the objects’ molecular structure identification (on the base of the research of dophamine and adrenaline molecules)

NASA Astrophysics Data System (ADS)

Elkin, M. D.; Alykova, O. M.; Smirnov, V. V.; Stefanova, G. P.

2017-01-01

Structural and dynamic models of dopamine and adrenaline are proposed on the basis of ab initio quantum calculations of the geometric and electronic structure. The parameters of the adiabatic potential are determined, a vibrational states interpretation of the test compound is proposed in this work. The analysis of the molecules conformational structure of the substance is made. A method for calculating the shifts of vibrational excitation frequencies in 1,2,4-threesubstituted of benzole is presented. It is based on second order perturbation theory. A choice of method and basis for calculation of a fundamental vibrations frequencies and intensities of the bands in the IR and Raman spectra is justified. The technique for evaluation of anharmonicity with cubic and quartic force constants is described. The paper presents the results of numerical experiments, geometric parameters of molecules, such as the valence bond lengths and angles between them. We obtain the frequency of the vibrational states and values of their integrated intensities. The interpretation of vibration of conformers is given. The results are in good agreement with experimental values. Proposed frequency can be used to identify the compounds of the vibrational spectra of molecules. The calculation was performed quantum density functional method DFT/B3LYP. It is shown that this method can be used to modeling the geometrical parameters molecular and electronic structure of various substituted of benzole. It allows us to construct the structural-dynamic models of this class of compounds by numerical calculations.

Magnetic Interaction in the Geometrically Frustrated Triangular LatticeAntiferromagnet CuFeO2

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ye, Feng; Fernandez-Baca, Jaime A; Fishman, Randy Scott

2007-01-01

The spin wave excitations of the geometrically frustrated triangular lattice antiferromagnet (TLA) CuFeO2 have been measured using high resolution inelastic neutron scattering. Antiferromagnetic interactions up to third nearest neighbors in the ab plane (J1, J2, J3, with J2=J1 0:44 and J3=J1 0:57), as well as out-of-plane coupling (Jz, with Jz=J1 0:29) are required to describe the spin wave dispersion relations, indicating a three dimensional character of the magnetic interactions. Two energy deeps in the spin wave dispersion occur at the incommensurate wavevectors associated with multiferroic phase, and can be interpreted as dynamic precursors to the magnetoelectric behavior in this system.

T-duality simplifies bulk-boundary correspondence: the noncommutative case

NASA Astrophysics Data System (ADS)

Hannabuss, Keith C.; Mathai, Varghese; Thiang, Guo Chuan

2018-05-01

We state and prove a general result establishing that T-duality, or the Connes-Thom isomorphism, simplifies the bulk-boundary correspondence, given by a boundary map in K-theory, in the sense of converting it to a simple geometric restriction map. This settles in the affirmative several earlier conjectures of the authors and provides a clear geometric picture of the correspondence. In particular, our result holds in arbitrary spatial dimension, in both the real and complex cases, and also in the presence of disorder, magnetic fields, and H-flux. These special cases are relevant both to string theory and to the study of the quantum Hall effect and topological insulators with defects in condensed matter physics.

Tracking and imaging humans on heterogeneous infrared sensor arrays for law enforcement applications

NASA Astrophysics Data System (ADS)

Feller, Steven D.; Zheng, Y.; Cull, Evan; Brady, David J.

2002-08-01

We present a plan for the integration of geometric constraints in the source, sensor and analysis levels of sensor networks. The goal of geometric analysis is to reduce the dimensionality and complexity of distributed sensor data analysis so as to achieve real-time recognition and response to significant events. Application scenarios include biometric tracking of individuals, counting and analysis of individuals in groups of humans and distributed sentient environments. We are particularly interested in using this approach to provide networks of low cost point detectors, such as infrared motion detectors, with complex imaging capabilities. By extending the capabilities of simple sensors, we expect to reduce the cost of perimeter and site security applications.

T-duality, non-geometry and Lie algebroids in heterotic double field theory

NASA Astrophysics Data System (ADS)

Blumenhagen, Ralph; Sun, Rui

2015-02-01

A number of issues in heterotic double field theory are studied. This includes the analysis of the T-dual configurations of a flat constant gauge flux background, which turn out to be non-geometric. Performing a field redefinition to a non-geometric frame, these T-duals take a very simple form reminiscent of the constant Q- and R-flux backgrounds. In addition, it is shown how the analysis of arXiv:1304.2784 generalizes to heterotic generalized geometry. For every field redefinition specified by an O( D, D + n) transformation, the structure of the resulting supergravity action is governed by the differential geometry of a corresponding Lie algebroid.

Geometrical families of mechanically stable granular packings

NASA Astrophysics Data System (ADS)

Gao, Guo-Jie; Blawzdziewicz, Jerzy; O'Hern, Corey S.

2009-12-01

We enumerate and classify nearly all of the possible mechanically stable (MS) packings of bidipserse mixtures of frictionless disks in small sheared systems. We find that MS packings form continuous geometrical families, where each family is defined by its particular network of particle contacts. We also monitor the dynamics of MS packings along geometrical families by applying quasistatic simple shear strain at zero pressure. For small numbers of particles (N<16) , we find that the dynamics is deterministic and highly contracting. That is, if the system is initialized in a MS packing at a given shear strain, it will quickly lock into a periodic orbit at subsequent shear strain, and therefore sample only a very small fraction of the possible MS packings in steady state. In studies with N>16 , we observe an increase in the period and random splittings of the trajectories caused by bifurcations in configuration space. We argue that the ratio of the splitting and contraction rates in large systems will determine the distribution of MS-packing geometrical families visited in steady state. This work is part of our long-term research program to develop a master-equation formalism to describe macroscopic slowly driven granular systems in terms of collections of small subsystems.

Interactive graphic editing tools in bioluminescent imaging simulation

NASA Astrophysics Data System (ADS)

Li, Hui; Tian, Jie; Luo, Jie; Wang, Ge; Cong, Wenxiang

2005-04-01

It is a challenging task to accurately describe complicated biological tissues and bioluminescent sources in bioluminescent imaging simulation. Several graphic editing tools have been developed to efficiently model each part of the bioluminescent simulation environment and to interactively correct or improve the initial models of anatomical structures or bioluminescent sources. There are two major types of graphic editing tools: non-interactive tools and interactive tools. Geometric building blocks (i.e. regular geometric graphics and superquadrics) are applied as non-interactive tools. To a certain extent, complicated anatomical structures and bioluminescent sources can be approximately modeled by combining a sufficient large number of geometric building blocks with Boolean operators. However, those models are too simple to describe the local features and fine changes in 2D/3D irregular contours. Therefore, interactive graphic editing tools have been developed to facilitate the local modifications of any initial surface model. With initial models composed of geometric building blocks, interactive spline mode is applied to conveniently perform dragging and compressing operations on 2D/3D local surface of biological tissues and bioluminescent sources inside the region/volume of interest. Several applications of the interactive graphic editing tools will be presented in this article.

Geometrical Tile Design for Complex Neighborhoods

PubMed Central

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 × 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 × (2k + 1) rectangle. PMID:19956398

Dosimetry in x-ray-based breast imaging

PubMed Central

Dance, David R; Sechopoulos, Ioannis

2016-01-01

The estimation of the mean glandular dose to the breast (MGD) for x-ray based imaging modalities forms an essential part of quality control and is needed for risk estimation and for system design and optimisation. This review considers the development of methods for estimating the MGD for mammography, digital breast tomosynthesis (DBT) and dedicated breast CT (DBCT). Almost all of the methodology used employs Monte Carlo calculated conversion factors to relate the measurable quantity, generally the incident air kerma, to the MGD. After a review of the size and composition of the female breast, the various mathematical models used are discussed, with particular emphasis on models for mammography. These range from simple geometrical shapes, to the more recent complex models based on patient DBCT examinations. The possibility of patient-specific dose estimates is considered as well as special diagnostic views and the effect of breast implants. Calculations using the complex models show that the MGD for mammography is overestimated by about 30% when the simple models are used. The design and uses of breast-simulating test phantoms for measuring incident air kerma are outlined and comparisons made between patient and phantom-based dose estimates. The most widely used national and international dosimetry protocols for mammography are based on different simple geometrical models of the breast, and harmonisation of these protocols using more complex breast models is desirable. PMID:27617767

Dosimetry in x-ray-based breast imaging

NASA Astrophysics Data System (ADS)

Dance, David R.; Sechopoulos, Ioannis

2016-10-01

The estimation of the mean glandular dose to the breast (MGD) for x-ray based imaging modalities forms an essential part of quality control and is needed for risk estimation and for system design and optimisation. This review considers the development of methods for estimating the MGD for mammography, digital breast tomosynthesis (DBT) and dedicated breast CT (DBCT). Almost all of the methodology used employs Monte Carlo calculated conversion factors to relate the measurable quantity, generally the incident air kerma, to the MGD. After a review of the size and composition of the female breast, the various mathematical models used are discussed, with particular emphasis on models for mammography. These range from simple geometrical shapes, to the more recent complex models based on patient DBCT examinations. The possibility of patient-specific dose estimates is considered as well as special diagnostic views and the effect of breast implants. Calculations using the complex models show that the MGD for mammography is overestimated by about 30% when the simple models are used. The design and uses of breast-simulating test phantoms for measuring incident air kerma are outlined and comparisons made between patient and phantom-based dose estimates. The most widely used national and international dosimetry protocols for mammography are based on different simple geometrical models of the breast, and harmonisation of these protocols using more complex breast models is desirable.

When the Classroom Floor Becomes the Complex Plane: Addition and Multiplication as Ways of Bodily Navigation

ERIC Educational Resources Information Center

Nemirovsky, Ricardo; Rasmussen, Chris; Sweeney, George; Wawro, Megan

2012-01-01

In this article we contribute a perspective on mathematical embodied cognition consistent with a phenomenological understanding of perception and body motion. It is based on the analysis of 4 selected episodes in 1 session of an undergraduate mathematics class. The theme of this particular class session was the geometric interpretation of the…

The Preparation and Characterization of the Geometric Isomers of a Coordination Complex: cis- and trans-bis Glycinato Copper (II) Monohydrates.

ERIC Educational Resources Information Center

O'Brien, Paul

1982-01-01

Preparation of cis and trans isomers of the kinetically labile bis glycinato copper (II) has a number of advantages including its facility, economy, ready theoretical interpretation, and biological relevance. Background information, laboratory procedures, results/discussion are provided for this experiment which can be completed in a single,…

Leaf light reflectance, transmittance, absorptance, and optical and geometrical parameters for eleven plant genera with different leaf mesophyll arrangements.

NASA Technical Reports Server (NTRS)

Gausman, H. W.; Allen, W. A.; Wiegand, C. L.; Escobar, D. E.; Rodriguez, R. R.

1971-01-01

Review of research on radiation interactions within plant canopies and communities and interactions of various leaf structures (mesophyll arrangements) with electromagnetic radiation involved in the interpretation of data sensed from air or spacecraft. The hypothesis underlying the research reported is that leaf mesophyll arrangements influence spectral energy measurements of leaves.

Strong dependence of rain-induced lidar depolarization on the illumination angle: experimental evidence and geometrical-optics interpretation.

PubMed

Roy, G; Bissonnette, L R

2001-09-20

Backscatter and depolarization lidar measurements from clouds and precipitation are reported as functions of the elevation angle of the pointing lidar direction. We recorded the data by scanning the lidar beam (Nd:YAG) at a constant angular speed of ~3.5 degrees /s while operating at a repetition rate of 10 Hz. We show that in rain there is an evident and at times spectacular dependence on the elevation angle. That dependence appears to be sensitive to raindrop size. We have developed a three-dimensional polarization-dependent ray-tracing algorithm to calculate the backscatter and the depolarization ratio by large nonspherical droplets. We have applied it to raindrop shapes derived from existing static and dynamic (oscillating) models. We show that many of the observed complex backscatter and depolarization features can be interpreted to a good extent by geometrical optics. These results suggest that there is a definite need for more extensive calculations of the scattering phase matrix elements for large deformed raindrops as functions of the direction of illumination. Obvious applications are retrieval of information on the liquid-solid phase of precipitation and on the size and the vibration state of raindrops.

Geometric adjustments to account for eye eccentricity in processing horizontal and vertical eye and head movement data

NASA Technical Reports Server (NTRS)

Huebner, W. P.; Paloski, W. H.; Reschke, M. F.; Bloomberg, J. J.

1995-01-01

Neglecting the eccentric position of the eyes in the head can lead to erroneous interpretation of ocular motor data, particularly for near targets. We discuss the geometric effects that eye eccentricity has on the processing of target-directed eye and head movement data, and we highlight two approaches to processing and interpreting such data. The first approach involves determining the true position of the target with respect to the location of the eyes in space for evaluating the efficacy of gaze, and it allows calculation of retinal error directly from measured eye, head, and target data. The second approach effectively eliminates eye eccentricity effects by adjusting measured eye movement data to yield equivalent responses relative to a specified reference location (such as the center of head rotation). This latter technique can be used to standardize measured eye movement signals, enabling waveforms collected under different experimental conditions to be directly compared, both with the measured target signals and with each other. Mathematical relationships describing these approaches are presented for horizontal and vertical rotations, for both tangential and circumferential display screens, and efforts are made to describe the sensitivity of parameter variations on the calculated results.

Discretization independence implies non-locality in 4D discrete quantum gravity

NASA Astrophysics Data System (ADS)

Dittrich, Bianca; Kamiński, Wojciech; Steinhaus, Sebastian

2014-12-01

The 4D Regge action is invariant under 5-1 and 4-2 Pachner moves, which define a subset of (local) changes of the triangulation. Given this fact, one might hope to find a local path integral measure that makes the quantum theory invariant under these moves and hence makes the theory partially triangulation invariant. We show that such a local invariant path integral measure does not exist for the 4D linearized Regge theory. To this end we uncover an interesting geometric interpretation for the Hessian of the 4D Regge action. This geometric interpretation will allow us to prove that the determinant of the Hessian of the 4D Regge action does not factorize over four-simplices or subsimplices. It furthermore allows us to determine configurations where this Hessian vanishes, which only appears to be the case in degenerate backgrounds or if one allows for different orientations of the simplices. We suggest a non-local measure factor that absorbs the non-local part of the determinant of the Hessian under 5-1 moves as well as a local measure factor that is preserved for very special configurations.

Statistical geometric affinity in human brain electric activity

NASA Astrophysics Data System (ADS)

Chornet-Lurbe, A.; Oteo, J. A.; Ros, J.

2007-05-01

The representation of the human electroencephalogram (EEG) records by neurophysiologists demands standardized time-amplitude scales for their correct conventional interpretation. In a suite of graphical experiments involving scaling affine transformations we have been able to convert electroencephalogram samples corresponding to any particular sleep phase and relaxed wakefulness into each other. We propound a statistical explanation for that finding in terms of data collapse. As a sequel, we determine characteristic time and amplitude scales and outline a possible physical interpretation. An analysis for characteristic times based on lacunarity is also carried out as well as a study of the synchrony between left and right EEG channels.

Constraints on interpretations structural trap in 4 dimensions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kelsch, K.D.; Kowalik, W.S.; Kluth, C.F.

1995-04-01

Interpretation of the geometry of the structural hydrocarbon trap continues to be one of the fundamental risks in exploration for, and production of, hydrocarbons. New geometric and computer tools are being developed to improve those interpretations by allowing the incremental restoration of structures in three dimensions. This adds powerful constraints on the structural interpretation because it requires that the interpretation be rational and consistent not only for the structure in the line of one cross section at the present time, but also for all moments during its development in 3 dimensions. It is possible to gather information, such as juxtapositionmore » of different reservoir units through time to evaluate the development of seals or leaks with respect to trap formation and to maturation and migration of hydrocarbons. In addition, software is available to produce interactive 3D images of the data that allow the interpreter to see the 4D restoration as it proceeds, but also to change the viewing orientation. This allows the interpreter to {open_quotes}move{close_quotes} through the restoration and examine areas critical for the interpretation as the restoration proceeds while viewing in 3D. While some of these tools are still under development, we have applied them successfully to model and real data sets.« less

Conifer ovulate cones accumulate pollen principally by simple impaction.

PubMed

Cresswell, James E; Henning, Kevin; Pennel, Christophe; Lahoubi, Mohamed; Patrick, Michael A; Young, Phillipe G; Tabor, Gavin R

2007-11-13

In many pine species (Family Pinaceae), ovulate cones structurally resemble a turbine, which has been widely interpreted as an adaptation for improving pollination by producing complex aerodynamic effects. We tested the turbine interpretation by quantifying patterns of pollen accumulation on ovulate cones in a wind tunnel and by using simulation models based on computational fluid dynamics. We used computer-aided design and computed tomography to create computational fluid dynamics model cones. We studied three species: Pinus radiata, Pinus sylvestris, and Cedrus libani. Irrespective of the approach or species studied, we found no evidence that turbine-like aerodynamics made a significant contribution to pollen accumulation, which instead occurred primarily by simple impaction. Consequently, we suggest alternative adaptive interpretations for the structure of ovulate cones.

Conifer ovulate cones accumulate pollen principally by simple impaction

PubMed Central

Cresswell, James E.; Henning, Kevin; Pennel, Christophe; Lahoubi, Mohamed; Patrick, Michael A.; Young, Phillipe G.; Tabor, Gavin R.

2007-01-01

In many pine species (Family Pinaceae), ovulate cones structurally resemble a turbine, which has been widely interpreted as an adaptation for improving pollination by producing complex aerodynamic effects. We tested the turbine interpretation by quantifying patterns of pollen accumulation on ovulate cones in a wind tunnel and by using simulation models based on computational fluid dynamics. We used computer-aided design and computed tomography to create computational fluid dynamics model cones. We studied three species: Pinus radiata, Pinus sylvestris, and Cedrus libani. Irrespective of the approach or species studied, we found no evidence that turbine-like aerodynamics made a significant contribution to pollen accumulation, which instead occurred primarily by simple impaction. Consequently, we suggest alternative adaptive interpretations for the structure of ovulate cones. PMID:17986613

Demystifying the memory effect: A geometrical approach to understanding speckle correlations

NASA Astrophysics Data System (ADS)

Prunty, Aaron C.; Snieder, Roel K.

2017-05-01

The memory effect has seen a surge of research into its fundamental properties and applications since its discovery by Feng et al. [Phys. Rev. Lett. 61, 834 (1988)]. While the wave trajectories for which the memory effect holds are hidden implicitly in the diffusion probability function [Phys. Rev. B 40, 737 (1989)], the physical intuition of why these trajectories satisfy the memory effect has often been masked by the derivation of the memory correlation function itself. In this paper, we explicitly derive the specific trajectories through a random medium for which the memory effect holds. Our approach shows that the memory effect follows from a simple conservation argument, which imposes geometrical constraints on the random trajectories that contribute to the memory effect. We illustrate the time-domain effects of these geometrical constraints with numerical simulations of pulse transmission through a random medium. The results of our derivation and numerical simulations are consistent with established theory and experimentation.

Effect of geometrical constraint condition on the formation of nanoscale twins in the Ni-based metallic glass composite

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, M H; Kim, B S; Kim, D H

2014-04-25

We investigated the effect of geometrically constrained stress-strain conditions on the formation of nanotwins in alpha-brass phase reinforced Ni59Zr20Ti16Si2Sn3 metallic glass (MG) matrix deformed under macroscopic uniaxial compression. The specific geometrically constrained conditions in the samples lead to a deviation from a simple uniaxial state to a multi-axial stress state, for which nanocrystallization in the MG matrix together with nanoscale twinning of the brass reinforcement is observed in localized regions during plastic flow. The nanocrystals in the MG matrix and the appearance of the twinned structure in the reinforcements indicate that the strain energy is highly confined and the localmore » stress reaches a very high level upon yielding. Both the effective distribution of reinforcements on the strain enhancement of composite and the effects of the complicated stress states on the development of nanotwins in the second-phase brass particles are discussed.« less

Control of morphology and formation of highly geometrically confined magnetic skyrmions

PubMed Central

Jin, Chiming; Li, Zi-An; Kovács, András; Caron, Jan; Zheng, Fengshan; Rybakov, Filipp N.; Kiselev, Nikolai S.; Du, Haifeng; Blügel, Stefan; Tian, Mingliang; Zhang, Yuheng; Farle, Michael; Dunin-Borkowski, Rafal E

2017-01-01

The ability to controllably manipulate magnetic skyrmions, small magnetic whirls with particle-like properties, in nanostructured elements is a prerequisite for incorporating them into spintronic devices. Here, we use state-of-the-art electron holographic imaging to directly visualize the morphology and nucleation of magnetic skyrmions in a wedge-shaped FeGe nanostripe that has a width in the range of 45–150 nm. We find that geometrically-confined skyrmions are able to adopt a wide range of sizes and ellipticities in a nanostripe that are absent in both thin films and bulk materials and can be created from a helical magnetic state with a distorted edge twist in a simple and efficient manner. We perform a theoretical analysis based on a three-dimensional general model of isotropic chiral magnets to confirm our experimental results. The flexibility and ease of formation of geometrically confined magnetic skyrmions may help to optimize the design of skyrmion-based memory devices. PMID:28580935

Critical space-time networks and geometric phase transitions from frustrated edge antiferromagnetism

NASA Astrophysics Data System (ADS)

Trugenberger, Carlo A.

2015-12-01

Recently I proposed a simple dynamical network model for discrete space-time that self-organizes as a graph with Hausdorff dimension dH=4 . The model has a geometric quantum phase transition with disorder parameter (dH-ds) , where ds is the spectral dimension of the dynamical graph. Self-organization in this network model is based on a competition between a ferromagnetic Ising model for vertices and an antiferromagnetic Ising model for edges. In this paper I solve a toy version of this model defined on a bipartite graph in the mean-field approximation. I show that the geometric phase transition corresponds exactly to the antiferromagnetic transition for edges, the dimensional disorder parameter of the former being mapped to the staggered magnetization order parameter of the latter. The model has a critical point with long-range correlations between edges, where a continuum random geometry can be defined, exactly as in Kazakov's famed 2D random lattice Ising model but now in any number of dimensions.

Physical objects as vehicles of cultural transmission: maintaining harmony and uniqueness through colored geometric patterns.

PubMed

Ishii, Keiko; Miyamoto, Yuri; Rule, Nicholas O; Toriyama, Rie

2014-02-01

We examined how cultural values of harmony and uniqueness are represented and maintained through physical media (i.e., colorings of geometric patterns) and how individuals play an active role in selecting and maintaining such cultural values. We found that colorings produced by European American adults and children were judged as more unique, whereas colorings produced by Japanese adults and children were judged as more harmonious, reflecting cultural differences in values. Harmony undergirded Japanese participants' preferences for colorings, whereas uniqueness undergirded European American participants' preferences for colorings. These cultural differences led participants to prefer own-culture colorings over other-culture colorings. Moreover, bicultural participants' preferences acculturated according to their identification with their host culture. Furthermore, child rearers in Japan and Canada gave feedback about the children's colorings that were consistent with their culture's values. These findings suggest that simple geometric patterns can embody cultural values that are socialized and reinforced from an early age.

Development of multi-component explosive lenses for arbitrary phase velocity generation

NASA Astrophysics Data System (ADS)

Loiseau, Jason; Huneault, Justin; Petel, Oren; Goroshin, Sam; Frost, David; Higgins, Andrew; Zhang, Fan

2013-06-01

The combination of explosives with different detonation velocities and lens-like geometric shaping is a well-established technique for producing structured detonation waves. This technique can be extended to produce nearly arbitrary detonation phase velocities for the purposes of sequentially imploding pressurized tubes or driving Mach disks through high-density metalized explosives. The current study presents the experimental development of accelerating, multi-component lenses designed using simple geometric optics and idealized front curvature. The fast explosive component is either Composition C4 (VOD = 8 km/s) or Primasheet 1000 (VOD = 7 km/s), while the slow component varies from heavily amine-diluted nitromethane (amine mass fraction exceeding 20%) to packed metal and glass particle beds wetted with amine-sensitized nitromethane. The applicability of the geometric optic analog to such highly heterogeneous explosives is also investigated. The multi-layered lens technique is further developed as a means of generating a directed mass and momentum flux of metal particles via Mach-disk formation and jetting in circular and oval planar lenses.

Generation and assessment of turntable SAR data for the support of ATR development

NASA Astrophysics Data System (ADS)

Cohen, Marvin N.; Showman, Gregory A.; Sangston, K. James; Sylvester, Vincent B.; Gostin, Lamar; Scheer, C. Ruby

1998-10-01

Inverse synthetic aperture radar (ISAR) imaging on a turntable-tower test range permits convenient generation of high resolution two-dimensional images of radar targets under controlled conditions for testing SAR image processing and for supporting automatic target recognition (ATR) algorithm development. However, turntable ISAR images are often obtained under near-field geometries and hence may suffer geometric distortions not present in airborne SAR images. In this paper, turntable data collected at Georgia Tech's Electromagnetic Test Facility are used to begin to assess the utility of two- dimensional ISAR imaging algorithms in forming images to support ATR development. The imaging algorithms considered include a simple 2D discrete Fourier transform (DFT), a 2-D DFT with geometric correction based on image domain resampling, and a computationally-intensive geometric matched filter solution. Images formed with the various algorithms are used to develop ATR templates, which are then compared with an eye toward utilization in an ATR algorithm.

A multiblock multigrid three-dimensional Euler equation solver

NASA Technical Reports Server (NTRS)

Cannizzaro, Frank E.; Elmiligui, Alaa; Melson, N. Duane; Vonlavante, E.

1990-01-01

Current aerodynamic designs are often quite complex (geometrically). Flexible computational tools are needed for the analysis of a wide range of configurations with both internal and external flows. In the past, geometrically dissimilar configurations required different analysis codes with different grid topologies in each. The duplicity of codes can be avoided with the use of a general multiblock formulation which can handle any grid topology. Rather than hard wiring the grid topology into the program, it is instead dictated by input to the program. In this work, the compressible Euler equations, written in a body-fitted finite-volume formulation, are solved using a pseudo-time-marching approach. Two upwind methods (van Leer's flux-vector-splitting and Roe's flux-differencing) were investigated. Two types of explicit solvers (a two-step predictor-corrector and a modified multistage Runge-Kutta) were used with multigrid acceleration to enhance convergence. A multiblock strategy is used to allow greater geometric flexibility. A report on simple explicit upwind schemes for solving compressible flows is included.

Analysis of a piezoelectric bimorph plate with a central-attached mass as an energy harvester.

PubMed

Jiang, Shunong; Hu, Yuantai

2007-07-01

This article analyzes the performance of a piezoelectric energy harvester in the flexural mode for scavenging ambient vibration energy. The energy harvester consists of a piezoelectric bimorph plate with a central-attached mass. The linear piezoelectricity theory is applied to evaluate the performance dependence upon the physical and geometrical parameters of the model bimorph plate. The analytical solution for the flexural motion of the piezoelectric bimorph plate energy harvester shows that the output power density increases initially, reaches a maximum, then decreases monotonically with the increasing load impedance, which is normalized by a parameter that is a simple combination of the physical and geometrical parameters of the scavenging structure, the bimorph plate, and the frequency of the ambient vibration, underscoring the importance for the load circuit to have the impedance desirable by the scavenging structure. The numerical results illustrate the considerably enhanced performances by adjusting the physical and geometrical parameters of the scavenging structure.

Self-Assembly of Mesoscale Isomers: The Role of Pathways and Degrees of Freedom

PubMed Central

Pandey, Shivendra; Johnson, Daniel; Kaplan, Ryan; Klobusicky, Joseph; Menon, Govind; Gracias, David H.

2014-01-01

The spontaneous self-organization of conformational isomers from identical precursors is of fundamental importance in chemistry. Since the precursors are identical, it is the multi-unit interactions, characteristics of the intermediates, and assembly pathways that determine the final conformation. Here, we use geometric path sampling and a mesoscale experimental model to investigate the self-assembly of a model polyhedral system, an octahedron, that forms two isomers. We compute the set of all possible assembly pathways and analyze the degrees of freedom or rigidity of intermediates. Consequently, by manipulating the degrees of freedom of a precursor, we were able to experimentally enrich the formation of one isomer over the other. Our results suggest a new approach to direct pathways in both natural and synthetic self-assembly using simple geometric criteria. We also compare the process of folding and unfolding in this model with a geometric model for cyclohexane, a well-known molecule with chair and boat conformations. PMID:25299051

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

NASA Astrophysics Data System (ADS)

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

2003-12-01

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

How effective are geometric morphometric techniques for assessing functional shape variation? An example from the great ape temporomandibular joint.

PubMed

Terhune, Claire E

2013-08-01

Functional shape analyses have long relied on the use of shape ratios to test biomechanical hypotheses. This method is powerful because of the ease with which results are interpreted, but these techniques fall short in quantifying complex morphologies that may not have a strong biomechanical foundation but may still be functionally informative. In contrast, geometric morphometric methods are continually being adopted for quantifying complex shapes, but they tend to prove inadequate in functional analyses because they have little foundation in an explicit biomechanical framework. The goal of this study was to evaluate the intersection of these two methods using the great ape temporomandibular joint as a case study. Three-dimensional coordinates of glenoid fossa and mandibular condyle shape were collected using a Microscribe digitizer. Linear distances extracted from these landmarks were analyzed using a series of one-way ANOVAs; further, the landmark configurations were analyzed using geometric morphometric techniques. Results suggest that the two methods are broadly similar, although the geometric morphometric data allow for the identification of shape differences among taxa that were not immediately apparent in the univariate analyses. Furthermore, this study suggests several new approaches for translating these shape data into a biomechanical context by adjusting the data using a biomechanically relevant variable. Copyright © 2013 Wiley Periodicals, Inc.

Luminous flux and illumination

NASA Astrophysics Data System (ADS)

Schröer, H.

2001-06-01

Themes of this book are luminous flux and illumination. The book begins with definitions of the notions luminous flux and solid angle. Then the luminous flux through simple geometrical areas as circle, ball, triangles and n-gons is treated. Chapter 7 deals with luminous flux through general surfaces. A comparison between photometric and radiation dimensions follow. The next chapter contains the luminous flux through simple areas in medium (gas). At last illumination and temperature are presented. The content is interesting for opticians, light technicians and all physicists and natural scientists, who have to do with radiation. There is an english and a german edition.

Multivariate geometry as an approach to algal community analysis

USGS Publications Warehouse

Allen, T.F.H.; Skagen, S.

1973-01-01

Multivariate analyses are put in the context of more usual approaches to phycological investigations. The intuitive common-sense involved in methods of ordination, classification and discrimination are emphasised by simple geometric accounts which avoid jargon and matrix algebra. Warnings are given that artifacts result from technique abuses by the naive or over-enthusiastic. An analysis of a simple periphyton data set is presented as an example of the approach. Suggestions are made as to situations in phycological investigations, where the techniques could be appropriate. The discipline is reprimanded for its neglect of the multivariate approach.

Analysis of specular resonance in dielectric bispheres using rigorous and geometrical-optics theories.

PubMed

Miyazaki, Hideki T; Miyazaki, Hiroshi; Miyano, Kenjiro

2003-09-01

We have recently identified the resonant scattering from dielectric bispheres in the specular direction, which has long been known as the specular resonance, to be a type of rainbow (a caustic) and a general phenomenon for bispheres. We discuss the details of the specular resonance on the basis of systematic calculations. In addition to the rigorous theory, which precisely describes the scattering even in the resonance regime, the ray-tracing method, which gives the scattering in the geometrical-optics limit, is used. Specular resonance is explicitly defined as strong scattering in the direction of the specular reflection from the symmetrical axis of the bisphere whose intensity exceeds that of the scattering from noninteracting bispheres. Then the range of parameters for computing a particular specular resonance is specified. This resonance becomes prominent in a wide range of refractive indices (from 1.2 to 2.2) in a wide range of size parameters (from five to infinity) and for an arbitrarily polarized light incident within an angle of 40 degrees to the symmetrical axis. This particular scattering can stay evident even when the spheres are not in contact or the sizes of the spheres are different. Thus specular resonance is a common and robust phenomenon in dielectric bispheres. Furthermore, we demonstrate that various characteristic features in the scattering from bispheres can be explained successfully by using intuitive and simple representations. Most of the significant scatterings other than the specular resonance are also understandable as caustics in geometrical-optics theory. The specular resonance becomes striking at the smallest size parameter among these caustics because its optical trajectory is composed of only the refractions at the surfaces and has an exceptionally large intensity. However, some characteristics are not accounted for by geometrical optics. In particular, the oscillatory behaviors of their scattering intensity are well described by simple two-wave interference models.

Sampling design for spatially distributed hydrogeologic and environmental processes

USGS Publications Warehouse

Christakos, G.; Olea, R.A.

1992-01-01

A methodology for the design of sampling networks over space is proposed. The methodology is based on spatial random field representations of nonhomogeneous natural processes, and on optimal spatial estimation techniques. One of the most important results of random field theory for physical sciences is its rationalization of correlations in spatial variability of natural processes. This correlation is extremely important both for interpreting spatially distributed observations and for predictive performance. The extent of site sampling and the types of data to be collected will depend on the relationship of subsurface variability to predictive uncertainty. While hypothesis formulation and initial identification of spatial variability characteristics are based on scientific understanding (such as knowledge of the physics of the underlying phenomena, geological interpretations, intuition and experience), the support offered by field data is statistically modelled. This model is not limited by the geometric nature of sampling and covers a wide range in subsurface uncertainties. A factorization scheme of the sampling error variance is derived, which possesses certain atttactive properties allowing significant savings in computations. By means of this scheme, a practical sampling design procedure providing suitable indices of the sampling error variance is established. These indices can be used by way of multiobjective decision criteria to obtain the best sampling strategy. Neither the actual implementation of the in-situ sampling nor the solution of the large spatial estimation systems of equations are necessary. The required values of the accuracy parameters involved in the network design are derived using reference charts (readily available for various combinations of data configurations and spatial variability parameters) and certain simple yet accurate analytical formulas. Insight is gained by applying the proposed sampling procedure to realistic examples related to sampling problems in two dimensions. ?? 1992.

Estimating volume, biomass, and potential emissions of hand-piled fuels

Treesearch

Clinton S. Wright; Cameron S. Balog; Jeffrey W. Kelly

2009-01-01

Dimensions, volume, and biomass were measured for 121 hand-constructed piles composed primarily of coniferous (n = 63) and shrub/hardwood (n = 58) material at sites in Washington and California. Equations using pile dimensions, shape, and type allow users to accurately estimate the biomass of hand piles. Equations for estimating true pile volume from simple geometric...

Young Children's Spontaneous Use of Geometry in Maps

ERIC Educational Resources Information Center

Shusterman, Anna; Lee, Sang Ah; Spelke, Elizabeth S.

2008-01-01

Two experiments tested whether 4-year-old children extract and use geometric information in simple maps without task instruction or feedback. Children saw maps depicting an arrangement of three containers and were asked to place an object into a container designated on the map. In Experiment 1, one of the three locations on the map and the array…

Pre-Modeling Ensures Accurate Solid Models

ERIC Educational Resources Information Center

Gow, George

2010-01-01

Successful solid modeling requires a well-organized design tree. The design tree is a list of all the object's features and the sequential order in which they are modeled. The solid-modeling process is faster and less prone to modeling errors when the design tree is a simple and geometrically logical definition of the modeled object. Few high…

A comparison of analytic and bayesian approaches for characterizing thermal hysteresis in cattle using algebraic and geometric distances

USDA-ARS?s Scientific Manuscript database

A high ambient temperature poses a serious threat to cattle. Above a certain threshold, an animal’s body temperature (Tb) appears to be driven by the hot cyclic air temperature (Ta) and hysteresis occurs. Elliptical hysteresis describes the output of a process in response to a simple harmonic input,...

Refractive Index of a Transparent Liquid Measured with a Concave Mirror

ERIC Educational Resources Information Center

Joshi, Amitabh; Serna, Juan D.

2012-01-01

Measuring the refractive index "n" of a substance or medium is part of every introductory physics course. Various approaches to determine this index have been developed over the years based on the different ways light reflects and transmits in the medium. In this paper, the authors would like to present a simple geometrical derivation of the…

Recognition of 3-D Scene with Partially Occluded Objects

NASA Astrophysics Data System (ADS)

Lu, Siwei; Wong, Andrew K. C...

1987-03-01

This paper presents a robot vision system which is capable of recognizing objects in a 3-D scene and interpreting their spatial relation even though some objects in the scene may be partially occluded by other objects. An algorithm is developed to transform the geometric information from the range data into an attributed hypergraph representation (AHR). A hypergraph monomorphism algorithm is then used to compare the AHR of objects in the scene with a set of complete AHR's of prototypes. The capability of identifying connected components and interpreting various types of edges in the 3-D scene enables us to distinguish objects which are partially blocking each other in the scene. Using structural information stored in the primitive area graph, a heuristic hypergraph monomorphism algorithm provides an effective way for recognizing, locating, and interpreting partially occluded objects in the range image.

Acquisition and analysis of angle-beam wavefield data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dawson, Alexander J.; Michaels, Jennifer E.; Levine, Ross M.

2014-02-18

Angle-beam ultrasonic testing is a common practical technique used for nondestructive evaluation to detect, locate, and characterize a variety of material defects and damage. Greater understanding of the both the incident wavefield produced by an angle-beam transducer and the subsequent scattering from a variety of defects and geometrical features is anticipated to increase the reliability of data interpretation. The focus of this paper is on acquiring and analyzing propagating waves from angle-beam transducers in simple, defect-free plates as a first step in the development of methods for flaw characterization. Unlike guided waves, which excite the plate throughout its thickness, angle-beammore » bulk waves bounce back and forth between the plate surfaces, resulting in the well-known multiple “skips” or “V-paths.” The experimental setup consists of a laser vibrometer mounted on an XYZ scanning stage, which is programmed to move point-to-point on a rectilinear grid to acquire waveform data. Although laser vibrometry is now routinely used to record guided waves for which the frequency content is below 1 MHz, it is more challenging to acquire higher frequency bulk waves in the 1–10 MHz range. Signals are recorded on the surface of an aluminum plate that were generated from a 5 MHz, 65° refracted angle, shear wave transducer-wedge combination. Data are analyzed directly in the x-t domain, via a slant stack Radon transform in the τ-p (offset time-slowness) domain, and via a 2-D Fourier transform in the ω-k domain, thereby enabling identification of specific arrivals and modes. Results compare well to those expected from a simple ray tracing analysis except for the unexpected presence of a strong Rayleigh wave.« less

The Relativistic Geometry and Dynamics of Electrons

NASA Astrophysics Data System (ADS)

Atiyah, M. F.; Malkoun, J.

2018-02-01

Atiyah and Sutcliffe (Proc R Soc Lond Ser A 458:1089-1115, 2002) made a number of conjectures about configurations of N distinct points in hyperbolic 3-space, arising from ideas of Berry and Robbins (Proc R Soc Lond Ser A 453:1771-1790, 1997). In this paper we prove all these conjectures, purely geometrically, but we also provide a physical interpretation in terms of Electrons.

THRESHOLD LOGIC.

DTIC Science & Technology

synthesis procedures; a ’best’ method is definitely established. (2) ’Symmetry Types for Threshold Logic’ is a tutorial expositon including a careful...development of the Goto-Takahasi self-dual type ideas. (3) ’Best Threshold Gate Decisions’ reports a comparison, on the 2470 7-argument threshold ...interpretation is shown best. (4) ’ Threshold Gate Networks’ reviews the previously discussed 2-algorithm in geometric terms, describes our FORTRAN

Narayanaswamy’s 1971 aging theory and material time

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dyre, Jeppe C., E-mail: dyre@ruc.dk

2015-09-21

The Bochkov-Kuzovlev nonlinear fluctuation-dissipation theorem is used to derive Narayanaswamy’s phenomenological theory of physical aging, in which this highly nonlinear phenomenon is described by a linear material-time convolution integral. A characteristic property of the Narayanaswamy aging description is material-time translational invariance, which is here taken as the basic assumption of the derivation. It is shown that only one possible definition of the material time obeys this invariance, namely, the square of the distance travelled from a configuration of the system far back in time. The paper concludes with suggestions for computer simulations that test for consequences of material-time translational invariance.more » One of these is the “unique-triangles property” according to which any three points on the system’s path form a triangle such that two side lengths determine the third; this is equivalent to the well-known triangular relation for time-autocorrelation functions of aging spin glasses [L. F. Cugliandolo and J. Kurchan, J. Phys. A: Math. Gen. 27, 5749 (1994)]. The unique-triangles property implies a simple geometric interpretation of out-of-equilibrium time-autocorrelation functions, which extends to aging a previously proposed framework for such functions in equilibrium [J. C. Dyre, e-print arXiv:cond-mat/9712222 (1997)].« less

Anisotropic Scattering Shadow Compensation Method for Remote Sensing Image with Consideration of Terrain

NASA Astrophysics Data System (ADS)

Wang, Qiongjie; Yan, Li

2016-06-01

With the rapid development of sensor networks and earth observation technology, a large quantity of high resolution remote sensing data is available. However, the influence of shadow has become increasingly greater due to the higher resolution shows more complex and detailed land cover, especially under the shadow. Shadow areas usually have lower intensity and fuzzy boundary, which make the images hard to interpret automatically. In this paper, a simple and effective shadow (including soft shadow) detection and compensation method is proposed based on normal data, Digital Elevation Model (DEM) and sun position. First, we use high accuracy DEM and sun position to rebuild the geometric relationship between surface and sun at the time the image shoot and get the hard shadow boundary and sky view factor (SVF) of each pixel. Anisotropic scattering assumption is accepted to determine the soft shadow factor mainly affected by diffuse radiation. Finally, an easy radiation transmission model is used to compensate the shadow area. Compared with the spectral detection method, our detection method has strict theoretical basis, reliable compensation result and minor affected by the image quality. The compensation strategy can effectively improve the radiation intensity of shadow area, reduce the information loss brought by shadow and improve the robustness and efficiency of the classification algorithms.

An experimental study of noise in mid-infrared quantum cascade lasers of different designs

NASA Astrophysics Data System (ADS)

Schilt, Stéphane; Tombez, Lionel; Tardy, Camille; Bismuto, Alfredo; Blaser, Stéphane; Maulini, Richard; Terazzi, Romain; Rochat, Michel; Südmeyer, Thomas

2015-04-01

We present an experimental study of noise in mid-infrared quantum cascade lasers (QCLs) of different designs. By quantifying the high degree of correlation occurring between fluctuations of the optical frequency and voltage between the QCL terminals, we show that electrical noise is a powerful and simple mean to study noise in QCLs. Based on this outcome, we investigated the electrical noise in a large set of 22 QCLs emitting in the range of 7.6-8 μm and consisting of both ridge-waveguide and buried-heterostructure (BH) lasers with different geometrical designs and operation parameters. From a statistical data processing based on an analysis of variance, we assessed that ridge-waveguide lasers have a lower noise than BH lasers. Our physical interpretation is that additional current leakages or spare injection channels occur at the interface between the active region and the lateral insulator in the BH geometry, which induces some extra noise. In addition, Schottky-type contacts occurring at the interface between the n-doped regions and the lateral insulator, i.e., iron-doped InP, are also believed to be a potential source of additional noise in some BH lasers, as observed from the slight reduction in the integrated voltage noise observed at the laser threshold in several BH-QCLs.

Anticrossproducts and cross divisions.

PubMed

de Leva, Paolo

2008-01-01

This paper defines, in the context of conventional vector algebra, the concept of anticrossproduct and a family of simple operations called cross or vector divisions. It is impossible to solve for a or b the equation axb=c, where a and b are three-dimensional space vectors, and axb is their cross product. However, the problem becomes solvable if some "knowledge about the unknown" (a or b) is available, consisting of one of its components, or the angle it forms with the other operand of the cross product. Independently of the selected reference frame orientation, the known component of a may be parallel to b, or vice versa. The cross divisions provide a compact and insightful symbolic representation of a family of algorithms specifically designed to solve problems of such kind. A generalized algorithm was also defined, incorporating the rules for selecting the appropriate kind of cross division, based on the type of input data. Four examples of practical application were provided, including the computation of the point of application of a force and the angular velocity of a rigid body. The definition and geometrical interpretation of the cross divisions stemmed from the concept of anticrossproduct. The "anticrossproducts of axb" were defined as the infinitely many vectors x(i) such that x(i)xb=axb.

A Model-Based Approach for Microvasculature Structure Distortion Correction in Two-Photon Fluorescence Microscopy Images

PubMed Central

Dao, Lam; Glancy, Brian; Lucotte, Bertrand; Chang, Lin-Ching; Balaban, Robert S; Hsu, Li-Yueh

2015-01-01

SUMMARY This paper investigates a post-processing approach to correct spatial distortion in two-photon fluorescence microscopy images for vascular network reconstruction. It is aimed at in vivo imaging of large field-of-view, deep-tissue studies of vascular structures. Based on simple geometric modeling of the object-of-interest, a distortion function is directly estimated from the image volume by deconvolution analysis. Such distortion function is then applied to sub volumes of the image stack to adaptively adjust for spatially varying distortion and reduce the image blurring through blind deconvolution. The proposed technique was first evaluated in phantom imaging of fluorescent microspheres that are comparable in size to the underlying capillary vascular structures. The effectiveness of restoring three-dimensional spherical geometry of the microspheres using the estimated distortion function was compared with empirically measured point-spread function. Next, the proposed approach was applied to in vivo vascular imaging of mouse skeletal muscle to reduce the image distortion of the capillary structures. We show that the proposed method effectively improve the image quality and reduce spatially varying distortion that occurs in large field-of-view deep-tissue vascular dataset. The proposed method will help in qualitative interpretation and quantitative analysis of vascular structures from fluorescence microscopy images. PMID:26224257

The role of the fusiform face area in social cognition: implications for the pathobiology of autism.

PubMed Central

Schultz, Robert T; Grelotti, David J; Klin, Ami; Kleinman, Jamie; Van der Gaag, Christiaan; Marois, René; Skudlarski, Pawel

2003-01-01

A region in the lateral aspect of the fusiform gyrus (FG) is more engaged by human faces than any other category of image. It has come to be known as the 'fusiform face area' (FFA). The origin and extent of this specialization is currently a topic of great interest and debate. This is of special relevance to autism, because recent studies have shown that the FFA is hypoactive to faces in this disorder. In two linked functional magnetic resonance imaging (fMRI) studies of healthy young adults, we show here that the FFA is engaged by a social attribution task (SAT) involving perception of human-like interactions among three simple geometric shapes. The amygdala, temporal pole, medial prefrontal cortex, inferolateral frontal cortex and superior temporal sulci were also significantly engaged. Activation of the FFA to a task without faces challenges the received view that the FFA is restricted in its activities to the perception of faces. We speculate that abstract semantic information associated with faces is encoded in the FG region and retrieved for social computations. From this perspective, the literature on hypoactivation of the FFA in autism may be interpreted as a reflection of a core social cognitive mechanism underlying the disorder. PMID:12639338

Evolution of sparsity and modularity in a model of protein allostery

NASA Astrophysics Data System (ADS)

Hemery, Mathieu; Rivoire, Olivier

2015-04-01

The sequence of a protein is not only constrained by its physical and biochemical properties under current selection, but also by features of its past evolutionary history. Understanding the extent and the form that these evolutionary constraints may take is important to interpret the information in protein sequences. To study this problem, we introduce a simple but physical model of protein evolution where selection targets allostery, the functional coupling of distal sites on protein surfaces. This model shows how the geometrical organization of couplings between amino acids within a protein structure can depend crucially on its evolutionary history. In particular, two scenarios are found to generate a spatial concentration of functional constraints: high mutation rates and fluctuating selective pressures. This second scenario offers a plausible explanation for the high tolerance of natural proteins to mutations and for the spatial organization of their least tolerant amino acids, as revealed by sequence analysis and mutagenesis experiments. It also implies a faculty to adapt to new selective pressures that is consistent with observations. The model illustrates how several independent functional modules may emerge within the same protein structure, depending on the nature of past environmental fluctuations. Our model thus relates the evolutionary history of proteins to the geometry of their functional constraints, with implications for decoding and engineering protein sequences.

Essential core of the Hawking–Ellis types

NASA Astrophysics Data System (ADS)

Martín-Moruno, Prado; Visser, Matt

2018-06-01

The Hawking–Ellis (Segre–Plebański) classification of possible stress–energy tensors is an essential tool in analyzing the implications of the Einstein field equations in a more-or-less model-independent manner. In the current article the basic idea is to simplify the Hawking–Ellis type I, II, III, and IV classification by isolating the ‘essential core’ of the type II, type III, and type IV stress–energy tensors; this being done by subtracting (special cases of) type I to simplify the (Lorentz invariant) eigenvalue structure as much as possible without disturbing the eigenvector structure. We will denote these ‘simplified cores’ type II0, type III0, and type IV0. These ‘simplified cores’ have very nice and simple algebraic properties. Furthermore, types I and II0 have very simple classical interpretations, while type IV0 is known to arise semi-classically (in renormalized expectation values of standard stress–energy tensors). In contrast type III0 stands out in that it has neither a simple classical interpretation, nor even a simple semi-classical interpretation. We will also consider the robustness of this classification considering the stability of the different Hawking–Ellis types under perturbations. We argue that types II and III are definitively unstable, whereas types I and IV are stable.

Coriolis effect in optics: unified geometric phase and spin-Hall effect.

PubMed

Bliokh, Konstantin Y; Gorodetski, Yuri; Kleiner, Vladimir; Hasman, Erez

2008-07-18

We examine the spin-orbit coupling effects that appear when a wave carrying intrinsic angular momentum interacts with a medium. The Berry phase is shown to be a manifestation of the Coriolis effect in a noninertial reference frame attached to the wave. In the most general case, when both the direction of propagation and the state of the wave are varied, the phase is given by a simple expression that unifies the spin redirection Berry phase and the Pancharatnam-Berry phase. The theory is supported by the experiment demonstrating the spin-orbit coupling of electromagnetic waves via a surface plasmon nanostructure. The measurements verify the unified geometric phase, demonstrated by the observed polarization-dependent shift (spin-Hall effect) of the waves.

Bias effects on the electronic spectrum of a molecular bridge

DOE Office of Scientific and Technical Information (OSTI.GOV)

Phillips, Heidi; Prociuk, Alexander; Dunietz, Barry D

2011-01-01

In this paper the effect of bias and geometric symmetry breaking on the electronic spectrum of a model molecular system is studied. Geometric symmetry breaking can either enhance the dissipative effect of the bias, where spectral peaks are disabled, or enable new excitations that are absent under zero bias conditions. The spectralanalysis is performed on a simple model system by solving for the electronic response to an instantaneously impulsive perturbation in the dipole approximation. The dynamical response is extracted from the electronic equations of motion as expressed by the Keldysh formalism. This expression provides for the accurate treatment of themore » electronic structure of a bulk-coupled system at the chosen model Hamiltonian electronic structure level.« less

Geometric representation of spin correlations and applications to ultracold systems

NASA Astrophysics Data System (ADS)

Mukherjee, Rick; Mirasola, Anthony E.; Hollingsworth, Jacob; White, Ian G.; Hazzard, Kaden R. A.

2018-04-01

We provide a one-to-one map between the spin correlations and certain three-dimensional shapes, analogous to the map between single spins and Bloch vectors, and demonstrate its utility. Much as one can reason geometrically about dynamics using a Bloch vector—e.g., a magnetic field causes it to precess and dissipation causes it to shrink—one can reason similarly about the shapes we use to visualize correlations. This visualization demonstrates its usefulness by unveiling the hidden structure in the correlations. For example, seemingly complex correlation dynamics can be described as simple motions of the shapes. We demonstrate the simplicity of the dynamics, which is obscured in conventional analyses, by analyzing several physical systems of relevance to cold atoms.

Emergence of Soft Communities from Geometric Preferential Attachment

PubMed Central

Zuev, Konstantin; Boguñá, Marián; Bianconi, Ginestra; Krioukov, Dmitri

2015-01-01

All real networks are different, but many have some structural properties in common. There seems to be no consensus on what the most common properties are, but scale-free degree distributions, strong clustering, and community structure are frequently mentioned without question. Surprisingly, there exists no simple generative mechanism explaining all the three properties at once in growing networks. Here we show how latent network geometry coupled with preferential attachment of nodes to this geometry fills this gap. We call this mechanism geometric preferential attachment (GPA), and validate it against the Internet. GPA gives rise to soft communities that provide a different perspective on the community structure in networks. The connections between GPA and cosmological models, including inflation, are also discussed. PMID:25923110

High-fidelity meshes from tissue samples for diffusion MRI simulations.

PubMed

Panagiotaki, Eleftheria; Hall, Matt G; Zhang, Hui; Siow, Bernard; Lythgoe, Mark F; Alexander, Daniel C

2010-01-01

This paper presents a method for constructing detailed geometric models of tissue microstructure for synthesizing realistic diffusion MRI data. We construct three-dimensional mesh models from confocal microscopy image stacks using the marching cubes algorithm. Random-walk simulations within the resulting meshes provide synthetic diffusion MRI measurements. Experiments optimise simulation parameters and complexity of the meshes to achieve accuracy and reproducibility while minimizing computation time. Finally we assess the quality of the synthesized data from the mesh models by comparison with scanner data as well as synthetic data from simple geometric models and simplified meshes that vary only in two dimensions. The results support the extra complexity of the three-dimensional mesh compared to simpler models although sensitivity to the mesh resolution is quite robust.

Geometrically distributed one-dimensional photonic crystals for light-reflection in all angles.

PubMed

Alagappan, G; Wu, P

2009-07-06

We demonstrate that a series of one-dimensional photonic crystals made of any dielectric materials, with the periods are distributed in a geometrical progression of a common ratio, r < rc (theta,P), where rc is a structural parameter that depends on the angle of incidence, theta, and polarization, P, is capable of blocking light of any spectral range. If an omni-directional reflection is desired for all polarizations and for all incident angles smaller than thetao, then r < rc (theta(o),p), where p is the polarization with the electric field parallel to the plane of incidence. We present simple and formula like expressions for rc, width of the bandgap, and minimum number of photonic crystals to achieve a perfect light reflection.

Integral geometry and holography

DOE PAGES

Czech, Bartlomiej; Lamprou, Lampros; McCandlish, Samuel; ...

2015-10-27

We present a mathematical framework which underlies the connection between information theory and the bulk spacetime in the AdS 3/CFT 2 correspondence. A key concept is kinematic space: an auxiliary Lorentzian geometry whose metric is defined in terms of conditional mutual informations and which organizes the entanglement pattern of a CFT state. When the field theory has a holographic dual obeying the Ryu-Takayanagi proposal, kinematic space has a direct geometric meaning: it is the space of bulk geodesics studied in integral geometry. Lengths of bulk curves are computed by kinematic volumes, giving a precise entropic interpretation of the length ofmore » any bulk curve. We explain how basic geometric concepts -- points, distances and angles -- are reflected in kinematic space, allowing one to reconstruct a large class of spatial bulk geometries from boundary entanglement entropies. In this way, kinematic space translates between information theoretic and geometric descriptions of a CFT state. As an example, we discuss in detail the static slice of AdS 3 whose kinematic space is two-dimensional de Sitter space.« less

Perspective Imagery in Synthetic Scenes used to Control and Guide Aircraft during Landing and Taxi: Some Issues and Concerns

NASA Technical Reports Server (NTRS)

Johnson, Walter W.; Kaiser, Mary K.

2003-01-01

Perspective synthetic displays that supplement, or supplant, the optical windows traditionally used for guidance and control of aircraft are accompanied by potentially significant human factors problems related to the optical geometric conformality of the display. Such geometric conformality is broken when optical features are not in the location they would be if directly viewed through a window. This often occurs when the scene is relayed or generated from a location different from the pilot s eyepoint. However, assuming no large visual/vestibular effects, a pilot cad often learn to use such a display very effectively. Important problems may arise, however, when display accuracy or consistency is compromised, and this can usually be related to geometrical discrepancies between how the synthetic visual scene behaves and how the visual scene through a window behaves. In addition to these issues, this paper examines the potentially critical problem of the disorientation that can arise when both a synthetic display and a real window are present in a flight deck, and no consistent visual interpretation is available.

Strings on complex multiplication tori and rational conformal field theory with matrix level

NASA Astrophysics Data System (ADS)

Nassar, Ali

Conformal invariance in two dimensions is a powerful symmetry. Two-dimensional quantum field theories which enjoy conformal invariance, i.e., conformal field theories (CFTs) are of great interest in both physics and mathematics. CFTs describe the dynamics of the world sheet in string theory where conformal symmetry arises as a remnant of reparametrization invariance of the world-sheet coordinates. In statistical mechanics, CFTs describe the critical points of second order phase transitions. On the mathematics side, conformal symmetry gives rise to infinite dimensional chiral algebras like the Virasoro algebra or extensions thereof. This gave rise to the study of vertex operator algebras (VOAs) which is an interesting branch of mathematics. Rational conformal theories are a simple class of CFTs characterized by a finite number of representations of an underlying chiral algebra. The chiral algebra leads to a set of Ward identities which gives a complete non-perturbative solution of the RCFT. Identifying the chiral algebra of an RCFT is a very important step in solving it. Particularly interesting RCFTs are the ones which arise from the compactification of string theory as sigma-models on a target manifold M. At generic values of the geometric moduli of M, the corresponding CFT is not rational. Rationality can arise at particular values of the moduli of M. At these special values of the moduli, the chiral algebra is extended. This interplay between the geometric picture and the algebraic description encoded in the chiral algebra makes CFTs/RCFTs a perfect link between physics and mathematics. It is always useful to find a geometric interpretation of a chiral algebra in terms of a sigma-model on some target manifold M. Then the next step is to figure out the conditions on the geometric moduli of M which gives a RCFT. In this thesis, we limit ourselves to the simplest class of string compactifications, i.e., strings on tori. As Gukov and Vafa proved, rationality selects the complex-multiplication tori. On the other hand, the study of the matrix-level affine algebra Um,K is motivated by conformal field theory and the fractional quantum Hall effect. Gannon completed the classification of U m,K modular-invariant partition functions. Here we connect the algebra U2,K to strings on 2-tori describable by rational conformal field theories. We point out that the rational conformal field theories describing strings on complex-multiplication tori have characters and partition functions identical to those of the matrix-level algebra Um,K. This connection makes obvious that the rational theories are dense in the moduli space of strings on Tm, and may prove useful in other ways.

Analysis of structural correlations in a model binary 3D liquid through the eigenvalues and eigenvectors of the atomic stress tensors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Levashov, V. A.

2016-03-07

It is possible to associate with every atom or molecule in a liquid its own atomic stress tensor. These atomic stress tensors can be used to describe liquids’ structures and to investigate the connection between structural and dynamic properties. In particular, atomic stresses allow to address atomic scale correlations relevant to the Green-Kubo expression for viscosity. Previously correlations between the atomic stresses of different atoms were studied using the Cartesian representation of the stress tensors or the representation based on spherical harmonics. In this paper we address structural correlations in a 3D model binary liquid using the eigenvalues and eigenvectorsmore » of the atomic stress tensors. This approach allows to interpret correlations relevant to the Green-Kubo expression for viscosity in a simple geometric way. On decrease of temperature the changes in the relevant stress correlation function between different atoms are significantly more pronounced than the changes in the pair density function. We demonstrate that this behaviour originates from the orientational correlations between the eigenvectors of the atomic stress tensors. We also found correlations between the eigenvalues of the same atomic stress tensor. For the studied system, with purely repulsive interactions between the particles, the eigenvalues of every atomic stress tensor are positive and they can be ordered: λ{sub 1} ≥ λ{sub 2} ≥ λ{sub 3} ≥ 0. We found that, for the particles of a given type, the probability distributions of the ratios (λ{sub 2}/λ{sub 1}) and (λ{sub 3}/λ{sub 2}) are essentially identical to each other in the liquids state. We also found that λ{sub 2} tends to be equal to the geometric average of λ{sub 1} and λ{sub 3}. In our view, correlations between the eigenvalues may represent “the Poisson ratio effect” at the atomic scale.« less

Analysis of structural correlations in a model binary 3D liquid through the eigenvalues and eigenvectors of the atomic stress tensors.

PubMed

Levashov, V A

2016-03-07

It is possible to associate with every atom or molecule in a liquid its own atomic stress tensor. These atomic stress tensors can be used to describe liquids' structures and to investigate the connection between structural and dynamic properties. In particular, atomic stresses allow to address atomic scale correlations relevant to the Green-Kubo expression for viscosity. Previously correlations between the atomic stresses of different atoms were studied using the Cartesian representation of the stress tensors or the representation based on spherical harmonics. In this paper we address structural correlations in a 3D model binary liquid using the eigenvalues and eigenvectors of the atomic stress tensors. This approach allows to interpret correlations relevant to the Green-Kubo expression for viscosity in a simple geometric way. On decrease of temperature the changes in the relevant stress correlation function between different atoms are significantly more pronounced than the changes in the pair density function. We demonstrate that this behaviour originates from the orientational correlations between the eigenvectors of the atomic stress tensors. We also found correlations between the eigenvalues of the same atomic stress tensor. For the studied system, with purely repulsive interactions between the particles, the eigenvalues of every atomic stress tensor are positive and they can be ordered: λ1 ≥ λ2 ≥ λ3 ≥ 0. We found that, for the particles of a given type, the probability distributions of the ratios (λ2/λ1) and (λ3/λ2) are essentially identical to each other in the liquids state. We also found that λ2 tends to be equal to the geometric average of λ1 and λ3. In our view, correlations between the eigenvalues may represent "the Poisson ratio effect" at the atomic scale.

Fernandina caldera collapse morphology in geometric and dynamic comparison to sandbox models, subsidence sinks over nuclear-explosion cavities, and some other calderas

NASA Astrophysics Data System (ADS)

Howard, K. A.

2009-12-01

The 1968 collapse structure of Fernandina caldera (1.5 km3 collapsed) and also the smaller Darwin Bay caldera in Galápagos each closely resembles morphologically the structural zoning of features found in depressions collapsed into nuclear-explosion cavities (“sinks” of Houser, 1969) and in coherent sandbox-collapse models. Coherent collapses characterized by faulting, folding, and organized structure contrast with spalled pit craters (and lab experiments with collapsed powder) where disorganized piles of floor rubble result from tensile failure of the roof. Subsidence in coherent mode, whether in weak sand in the lab, stronger desert alluvium for nuclear-test sinks, or in hard rock for calderas, exhibits consistent morphologic zones. Characteristically in the sandbox and the nuclear-test analogs these include a first-formed central plug that drops along annular reverse faults. This plug and a surrounding inward-tilted or monoclinal ring (hanging wall of the reverse fault) contract as the structure expands outward by normal faulting, wherein peripheral rings of distending material widen the upper part of the structure along inward-dipping normal faults and compress inner zones and help keep them intact. In Fernandina, a region between the monocline and the outer zone of normal faulting is interpreted, by comparison to the analogs, to overlie the deflation margin of an underlying magma chamber. The same zoning pattern is recognized in structures ranging from sandbox subsidence features centimeters across, to Alae lave lake and nuclear-test sinks tens to hundreds of meters across, to Fenandina’s 2x4 km-wide collapse, to Martian calderas tens of kilometers across. Simple dimensional analysis using the height of cliffs as a proxie for material strength implies that the geometric analogs are good dynamic analogs, and validates that the pattern of both reverse and normal faulting that has been reported consistently from sandbox modeling applies widely to calderas.

Effect of Solar Wind Drag on the Determination of the Properties of Coronal Mass Ejections from Heliospheric Images

NASA Astrophysics Data System (ADS)

Lugaz, N.; Kintner, P.

2013-07-01

The Fixed-Φ (FΦ) and Harmonic Mean (HM) fitting methods are two methods to determine the "average" direction and velocity of coronal mass ejections (CMEs) from time-elongation tracks produced by Heliospheric Imagers (HIs), such as the HIs onboard the STEREO spacecraft. Both methods assume a constant velocity in their descriptions of the time-elongation profiles of CMEs, which are used to fit the observed time-elongation data. Here, we analyze the effect of aerodynamic drag on CMEs propagating through interplanetary space, and how this drag affects the result of the FΦ and HM fitting methods. A simple drag model is used to analytically construct time-elongation profiles which are then fitted with the two methods. It is found that higher angles and velocities give rise to greater error in both methods, reaching errors in the direction of propagation of up to 15∘ and 30∘ for the FΦ and HM fitting methods, respectively. This is due to the physical accelerations of the CMEs being interpreted as geometrical accelerations by the fitting methods. Because of the geometrical definition of the HM fitting method, it is more affected by the acceleration than the FΦ fitting method. Overall, we find that both techniques overestimate the initial (and final) velocity and direction for fast CMEs propagating beyond 90∘ from the Sun-spacecraft line, meaning that arrival times at 1 AU would be predicted early (by up to 12 hours). We also find that the direction and arrival time of a wide and decelerating CME can be better reproduced by the FΦ due to the cancelation of two errors: neglecting the CME width and neglecting the CME deceleration. Overall, the inaccuracies of the two fitting methods are expected to play an important role in the prediction of CME hit and arrival times as we head towards solar maximum and the STEREO spacecraft further move behind the Sun.

Preschool-aged children have difficulty constructing and interpreting simple utterances composed of graphic symbols.

PubMed

Sutton, Ann; Trudeau, Natacha; Morford, Jill; Rios, Monica; Poirier, Marie-Andrée

2010-01-01

Children who require augmentative and alternative communication (AAC) systems while they are in the process of acquiring language face unique challenges because they use graphic symbols for communication. In contrast to the situation of typically developing children, they use different modalities for comprehension (auditory) and expression (visual). This study explored the ability of three- and four-year-old children without disabilities to perform tasks involving sequences of graphic symbols. Thirty participants were asked to transpose spoken simple sentences into graphic symbols by selecting individual symbols corresponding to the spoken words, and to interpret graphic symbol utterances by selecting one of four photographs corresponding to a sequence of three graphic symbols. The results showed that these were not simple tasks for the participants, and few of them performed in the expected manner - only one in transposition, and only one-third of participants in interpretation. Individual response strategies in some cases lead to contrasting response patterns. Children at this age level have not yet developed the skills required to deal with graphic symbols even though they have mastered the corresponding spoken language structures.

An experimental investigation of wall-interference effects for parachutes in closed wind tunnels

DOE Office of Scientific and Technical Information (OSTI.GOV)

Macha, J.M.; Buffington, R.J.

1989-09-01

A set of 6-ft-diameter ribbon parachutes (geometric porosities of 7%, 15%, and 30%) was tested in various subsonic wind tunnels covering a range of geometric blockages from 2% to 35%. Drag, base pressure, and inflated geometry were measured under full-open, steady-flow conditions. The result drag areas and pressure coefficients were correlated with the bluff-body blockage parameter (i.e., drag area divided by tunnel cross-sectional area) according to the blockage theory of Maskell. The data show that the Maskell theory provides a simple, accurate correction for the effective increase in dynamic pressure caused by wall constraint for both single parachutes and clusters.more » For single parachutes, the empirically derived blockage factor K{sub M} has the value of 1.85, independent of canopy porosity. Derived values of K{sub M} for two- and three-parachute clusters are 1.35 and 1.59, respectively. Based on the photometric data, there was no deformation of the inflated shape of the single parachutes up to a geometric blockage of 22%. In the case of the three-parachute cluster, decreases in both the inflated diameter and the spacing among member parachutes were observed at a geometric blockage of 35%. 11 refs., 9 figs., 3 tabs.« less

Buckling Analysis of a Honeycomb-Core Composite Cylinder with Initial Geometric Imperfections

NASA Technical Reports Server (NTRS)

Cha, Gene; Schultz, Marc R.

2013-01-01

Thin-walled cylindrical shell structures often have buckling as the critical failure mode, and the buckling of such structures can be very sensitive to small geometric imperfections. The buckling analyses of an 8-ft-diameter, 10-ft-long honeycomb-core composite cylinder loaded in pure axial compression is discussed in this document. Two loading configurations are considered configuration 1 uses simple end conditions, and configuration 2 includes additional structure that may more closely approximate experimental loading conditions. Linear eigenvalue buckling analyses and nonlinear analyses with and without initial geometric imperfections were performed on both configurations. The initial imperfections were introduced in the shell by applying a radial load at the midlength of the cylinder to form a single inward dimple. The critical bifurcation buckling loads are predicted to be 924,190 lb and 924,020 lb for configurations 1 and 2, respectively. Nonlinear critical buckling loads of 918,750 lb and 954,900 lb were predicted for geometrically perfect configurations 1 and 2, respectively. Lower-bound critical buckling loads for configurations 1 and 2 with radial perturbations were found to be 33% and 36% lower, respectively, than the unperturbed critical loads. The inclusion of the load introduction cylinders in configuration 2 increased the maximum bending-boundary-layer rotation up to 11%.

Complexity and approximability for a problem of intersecting of proximity graphs with minimum number of equal disks

NASA Astrophysics Data System (ADS)

Kobylkin, Konstantin

2016-10-01

Computational complexity and approximability are studied for the problem of intersecting of a set of straight line segments with the smallest cardinality set of disks of fixed radii r > 0 where the set of segments forms straight line embedding of possibly non-planar geometric graph. This problem arises in physical network security analysis for telecommunication, wireless and road networks represented by specific geometric graphs defined by Euclidean distances between their vertices (proximity graphs). It can be formulated in a form of known Hitting Set problem over a set of Euclidean r-neighbourhoods of segments. Being of interest computational complexity and approximability of Hitting Set over so structured sets of geometric objects did not get much focus in the literature. Strong NP-hardness of the problem is reported over special classes of proximity graphs namely of Delaunay triangulations, some of their connected subgraphs, half-θ6 graphs and non-planar unit disk graphs as well as APX-hardness is given for non-planar geometric graphs at different scales of r with respect to the longest graph edge length. Simple constant factor approximation algorithm is presented for the case where r is at the same scale as the longest edge length.

Automated detection of qualitative spatio-temporal features in electrocardiac activation maps.

PubMed

Ironi, Liliana; Tentoni, Stefania

2007-02-01

This paper describes a piece of work aiming at the realization of a tool for the automated interpretation of electrocardiac maps. Such maps can capture a number of electrical conduction pathologies, such as arrhytmia, that can be missed by the analysis of traditional electrocardiograms. But, their introduction into the clinical practice is still far away as their interpretation requires skills that belongs to very few experts. Then, an automated interpretation tool would bridge the gap between the established research outcome and clinical practice with a consequent great impact on health care. Qualitative spatial reasoning can play a crucial role in the identification of spatio-temporal patterns and salient features that characterize the heart electrical activity. We adopted the spatial aggregation (SA) conceptual framework and an interplay of numerical and qualitative information to extract features from epicardial maps, and to make them available for reasoning tasks. Our focus is on epicardial activation isochrone maps as they are a synthetic representation of spatio-temporal aspects of the propagation of the electrical excitation. We provide a computational SA-based methodology to extract, from 3D epicardial data gathered over time, (1) the excitation wavefront structure, and (2) the salient features that characterize wavefront propagation and visually correspond to specific geometric objects. The proposed methodology provides a robust and efficient way to identify salient pieces of information in activation time maps. The hierarchical structure of the abstracted geometric objects, crucial in capturing the prominent information, facilitates the definition of general rules necessary to infer the correlation between pathophysiological patterns and wavefront structure and propagation.

Virtual Ray Tracing as a Conceptual Tool for Image Formation in Mirrors and Lenses

ERIC Educational Resources Information Center

Heikkinen, Lasse; Savinainen, Antti; Saarelainen, Markku

2016-01-01

The ray tracing method is widely used in teaching geometrical optics at the upper secondary and university levels. However, using simple and straightforward examples may lead to a situation in which students use the model of ray tracing too narrowly. Previous studies show that students seem to use the ray tracing method too concretely instead of…

A Laboratory Activity on the Eddy Current Brake

ERIC Educational Resources Information Center

Molina-Bolivar, J. A.; Abella-Palacios, A. J.

2012-01-01

The aim of this paper is to introduce a simple and low-cost experimental setup that can be used to study the eddy current brake, which considers the motion of a sliding magnet on an inclined conducting plane in terms of basic physical principles. We present a set of quantitative experiments performed to study the influence of the geometrical and…

Viviani Polytopes and Fermat Points

ERIC Educational Resources Information Center

Zhou, Li

2012-01-01

Given a set of oriented hyperplanes P = {p1, . . . , pk} in R[superscript n], define v : R[superscript n] [right arrow] R by v(X) = the sum of the signed distances from X to p[subscript 1], . . . , p[subscript k], for any point X [is a member of] R[superscript n]. We give a simple geometric characterization of P for which v is constant, leading to…

Development of the local magnification method for quantitative evaluation of endoscope geometric distortion

NASA Astrophysics Data System (ADS)

Wang, Quanzeng; Cheng, Wei-Chung; Suresh, Nitin; Hua, Hong

2016-05-01

With improved diagnostic capabilities and complex optical designs, endoscopic technologies are advancing. As one of the several important optical performance characteristics, geometric distortion can negatively affect size estimation and feature identification related diagnosis. Therefore, a quantitative and simple distortion evaluation method is imperative for both the endoscopic industry and the medical device regulatory agent. However, no such method is available yet. While the image correction techniques are rather mature, they heavily depend on computational power to process multidimensional image data based on complex mathematical model, i.e., difficult to understand. Some commonly used distortion evaluation methods, such as the picture height distortion (DPH) or radial distortion (DRAD), are either too simple to accurately describe the distortion or subject to the error of deriving a reference image. We developed the basic local magnification (ML) method to evaluate endoscope distortion. Based on the method, we also developed ways to calculate DPH and DRAD. The method overcomes the aforementioned limitations, has clear physical meaning in the whole field of view, and can facilitate lesion size estimation during diagnosis. Most importantly, the method can facilitate endoscopic technology to market and potentially be adopted in an international endoscope standard.

Simple Spreadsheet Models For Interpretation Of Fractured Media Tracer Tests

EPA Science Inventory

An analysis of a gas-phase partitioning tracer test conducted through fractured media is discussed within this paper. The analysis employed matching eight simple mathematical models to the experimental data to determine transport parameters. All of the models tested; two porous...

Building simple multiscale visualizations of outcrop geology using virtual reality modeling language (VRML)

NASA Astrophysics Data System (ADS)

Thurmond, John B.; Drzewiecki, Peter A.; Xu, Xueming

2005-08-01

Geological data collected from outcrop are inherently three-dimensional (3D) and span a variety of scales, from the megascopic to the microscopic. This presents challenges in both interpreting and communicating observations. The Virtual Reality Modeling Language provides an easy way for geoscientists to construct complex visualizations that can be viewed with free software. Field data in tabular form can be used to generate hierarchical multi-scale visualizations of outcrops, which can convey the complex relationships between a variety of data types simultaneously. An example from carbonate mud-mounds in southeastern New Mexico illustrates the embedding of three orders of magnitude of observation into a single visualization, for the purpose of interpreting depositional facies relationships in three dimensions. This type of raw data visualization can be built without software tools, yet is incredibly useful for interpreting and communicating data. Even simple visualizations can aid in the interpretation of complex 3D relationships that are frequently encountered in the geosciences.

Utilizing LANDSAT imagery to monitor land-use change - A case study in Ohio

NASA Technical Reports Server (NTRS)

Gordon, S. I.

1980-01-01

A study, performed in Ohio, of the nature and extent of interpretation errors in the application of Landsat imagery to land-use planning and modeling is reported. Potential errors associated with the misalignment of pixels after geometric correction and with misclassification of land cover or land use due to spectral similarities were identified on interpreted computer-compatible tapes of a portion of Franklin County for two adjacent days of 1975 and one day of 1973, and the extents of these errors were quantified by comparison with a ground-checked set of aerial-photograph interpretations. The open-space and agricultural categories are found to be the most consistently classified, while the more urban areas were classified correctly only from about 43 to 8% of the time. It is thus recommended that the direct application of Landsat data to land-use planning must await improvements in classification techniques and accuracy.

Real-time Human Activity Recognition

NASA Astrophysics Data System (ADS)

Albukhary, N.; Mustafah, Y. M.

2017-11-01

The traditional Closed-circuit Television (CCTV) system requires human to monitor the CCTV for 24/7 which is inefficient and costly. Therefore, there’s a need for a system which can recognize human activity effectively in real-time. This paper concentrates on recognizing simple activity such as walking, running, sitting, standing and landing by using image processing techniques. Firstly, object detection is done by using background subtraction to detect moving object. Then, object tracking and object classification are constructed so that different person can be differentiated by using feature detection. Geometrical attributes of tracked object, which are centroid and aspect ratio of identified tracked are manipulated so that simple activity can be detected.

A (historical) remark on the Darwin-Schiaparelli evolution theory.

PubMed

Freguglia, Paolo

2016-01-01

The aim of this paper is a free interpretation and reconstruction of a part of Giovanni Virginio Schiaparelli's essay (1898) where the author presents some ideas about a correspondence between living organisms and geometrical curves. From our analysis we derive a new approach to the ago-antagonist conception of the Darwinian evolution theory which is a continuation of [2]. Copyright: © 2016 by Fabrizio Serra editore, Pisa · Roma.

Observation of shadowing of neutrino- and antineutrino-nucleus interactions and comparison with PCAC predictions

NASA Astrophysics Data System (ADS)

Allport, P. P.; Erriquez, O.; Guy, J.; Venus, W.; Aderholz, M.; Berggren, M.; Bullock, F. W.; Calicchio, M.; Coghen, T.; Cooper-Sarkar, A. M.; Jones, G. T.; Marage, P.; Mobayyen, M.; Morrison, D. R. O.; Neveu, M.; Parker, M. A.; Radojicic, D.; Sansum, R. A.; Saitta, B.; Schmitz, N.; Simopoulou, E.; O'neale, S.; Van Apeldoorn, G.; Varvell, K.; Vayaki, A.; Wachsmuth, H.; Wittek, W.; BEBC WA59 Collaboration

1989-12-01

Comparing the kinematical distributions of events obtained on neon and deuterium targets in similar experimental conditions reveals a reduction of the neutrino and antineutrino charged current cross section per nucleon in neon at low Q2. The effect, interpreted as due to geometric shadowing of the weak propagator in interactions of neutrinos and antineutrinos with nuclei, agrees well with predictions derived from PCAC.

A Study of Computer-Aided Geometric Optical Design.

DTIC Science & Technology

1982-10-01

short programs on tape. A computer account number and Cyber computer manuals were obtained. A familiarity with the use and maintenance of computer files...in the interpretation of the information. Ray fans, spot diagrams, wavefront variance, Strehl ratio, vignetting .- diagrams Pnd optical transfer...other surface begins to cut off these rays (20:113). This is characterized by a loss of intensity at the outside of the image. A known manual

Instabilities of Shallow Dynamic Thermocapillary Liquid Layers

NASA Technical Reports Server (NTRS)

Schwabe, D.; Moeller, U.; Schneider, J.; Scharmann, A.

1992-01-01

In the experiments reported here, correlation measurements with three fixed thermocouples and direct optical observations of the dynamically deformed liquid-gas interface were used to study the spatiotemporal structure of stable and unstable thermocapillary flows. The frequency, wavelength, phase speed, angle of propagation, and stability limits are reported for two geometrically different configurations of thermocapillary flow in side-heated thin liquid layers. A theoretical interpretation of the results is presented.

Applications of Subleading-Color Amplitudes in N = 4 SYM Theory

DOE PAGES

Naculich, Stephen G.; Nastase, Horatiu; Schnitzer, Howard J.

2011-01-01

A numore » mber of features and applications of subleading-color amplitudes of N = 4 SYM theory are reviewed. Particular attention is given to the IR divergences of the subleading-color amplitudes, the relationships of N = 4 SYM theory to N = 8 supergravity, and to geometric interpretations of one-loop subleading-color and N k MHV amplitudes of N = 4 SYM theory.« less

Crystallography of decahedral and icosahedral particles. I - Geometry of twinning

NASA Technical Reports Server (NTRS)

Yang, C. Y.

1979-01-01

The crystal structure of the tetrahedral twins in multiply-twinned particles with decahedral and icosahedral point group symmetries has been examined and correlated with the face-centered cubic structure. Details on the crystal structure as well as the geometrical relationships among twins in each particle are presented. These crystallographic facts serve as a basis for the interpretation of small particle images obtained with advanced methods of transmission electron microscopy.

Unified framework for information integration based on information geometry

PubMed Central

Oizumi, Masafumi; Amari, Shun-ichi

2016-01-01

Assessment of causal influences is a ubiquitous and important subject across diverse research fields. Drawn from consciousness studies, integrated information is a measure that defines integration as the degree of causal influences among elements. Whereas pairwise causal influences between elements can be quantified with existing methods, quantifying multiple influences among many elements poses two major mathematical difficulties. First, overestimation occurs due to interdependence among influences if each influence is separately quantified in a part-based manner and then simply summed over. Second, it is difficult to isolate causal influences while avoiding noncausal confounding influences. To resolve these difficulties, we propose a theoretical framework based on information geometry for the quantification of multiple causal influences with a holistic approach. We derive a measure of integrated information, which is geometrically interpreted as the divergence between the actual probability distribution of a system and an approximated probability distribution where causal influences among elements are statistically disconnected. This framework provides intuitive geometric interpretations harmonizing various information theoretic measures in a unified manner, including mutual information, transfer entropy, stochastic interaction, and integrated information, each of which is characterized by how causal influences are disconnected. In addition to the mathematical assessment of consciousness, our framework should help to analyze causal relationships in complex systems in a complete and hierarchical manner. PMID:27930289

Influence of optimized leading-edge deflection and geometric anhedral on the low-speed aerodynamic characteristics of a low-aspect-ratio highly swept arrow-wing configuration. [langley 7 by 10 foot tunnel

NASA Technical Reports Server (NTRS)

Coe, P. L., Jr.; Huffman, J. K.

1979-01-01

An investigation conducted in the Langley 7 by 10 foot tunnel to determine the influence of an optimized leading-edge deflection on the low speed aerodynamic performance of a configuration with a low aspect ratio, highly swept wing. The sensitivity of the lateral stability derivative to geometric anhedral was also studied. The optimized leading edge deflection was developed by aligning the leading edge with the incoming flow along the entire span. Owing to spanwise variation of unwash, the resulting optimized leading edge was a smooth, continuously warped surface for which the deflection varied from 16 deg at the side of body to 50 deg at the wing tip. For the particular configuration studied, levels of leading-edge suction on the order of 90 percent were achieved. The results of tests conducted to determine the sensitivity of the lateral stability derivative to geometric anhedral indicate values which are in reasonable agreement with estimates provided by simple vortex-lattice theories.

Multi-target-qubit unconventional geometric phase gate in a multi-cavity system

NASA Astrophysics Data System (ADS)

Liu, Tong; Cao, Xiao-Zhi; Su, Qi-Ping; Xiong, Shao-Jie; Yang, Chui-Ping

2016-02-01

Cavity-based large scale quantum information processing (QIP) may involve multiple cavities and require performing various quantum logic operations on qubits distributed in different cavities. Geometric-phase-based quantum computing has drawn much attention recently, which offers advantages against inaccuracies and local fluctuations. In addition, multiqubit gates are particularly appealing and play important roles in QIP. We here present a simple and efficient scheme for realizing a multi-target-qubit unconventional geometric phase gate in a multi-cavity system. This multiqubit phase gate has a common control qubit but different target qubits distributed in different cavities, which can be achieved using a single-step operation. The gate operation time is independent of the number of qubits and only two levels for each qubit are needed. This multiqubit gate is generic, e.g., by performing single-qubit operations, it can be converted into two types of significant multi-target-qubit phase gates useful in QIP. The proposal is quite general, which can be used to accomplish the same task for a general type of qubits such as atoms, NV centers, quantum dots, and superconducting qubits.

Simple and practical approach for computing the ray Hessian matrix in geometrical optics.

PubMed

Lin, Psang Dain

2018-02-01

A method is proposed for simplifying the computation of the ray Hessian matrix in geometrical optics by replacing the angular variables in the system variable vector with their equivalent cosine and sine functions. The variable vector of a boundary surface is similarly defined in such a way as to exclude any angular variables. It is shown that the proposed formulations reduce the computation time of the Hessian matrix by around 10 times compared to the previous method reported by the current group in Advanced Geometrical Optics (2016). Notably, the method proposed in this study involves only polynomial differentiation, i.e., trigonometric function calls are not required. As a consequence, the computation complexity is significantly reduced. Five illustrative examples are given. The first three examples show that the proposed method is applicable to the determination of the Hessian matrix for any pose matrix, irrespective of the order in which the rotation and translation motions are specified. The last two examples demonstrate the use of the proposed Hessian matrix in determining the axial and lateral chromatic aberrations of a typical optical system.

Geometric frustration and compatibility conditions for two-dimensional director fields.

PubMed

Niv, Idan; Efrati, Efi

2018-01-17

Bent core (or banana shaped) liquid-crystal-forming-molecules locally favor an ordered state of zero splay and constant bend. Such a state, however, cannot be realized in the plane and the resulting liquid-crystalline phase is frustrated and must exhibit some compromise of these two mutually contradicting local intrinsic tendencies. This constitutes one of the most well-studied examples in which the intrinsic geometry of the constituents of a material gives rise to a geometrically frustrated assembly. Such geometric frustration is not only natural and ubiquitous but also leads to a striking variety of morphologies of ground states and exotic response properties. In this work we establish the necessary and sufficient conditions for two scalar functions, s and b to describe the splay and bend of a director field in the plane. We generalize these compatibility conditions for geometries with non-vanishing constant Gaussian curvature, and provide a reconstruction formula for the director field depending only on the splay and bend fields and their derivatives. Finally, we discuss optimal compromises for simple incompatible cases where the locally preferred values of the splay and bend cannot be simultaneously achieved.

A study on axial and torsional resonant mode matching for a mechanical system with complex nonlinear geometries

NASA Astrophysics Data System (ADS)

Watson, Brett; Yeo, Leslie; Friend, James

2010-06-01

Making use of mechanical resonance has many benefits for the design of microscale devices. A key to successfully incorporating this phenomenon in the design of a device is to understand how the resonant frequencies of interest are affected by changes to the geometric parameters of the design. For simple geometric shapes, this is quite easy, but for complex nonlinear designs, it becomes significantly more complex. In this paper, two novel modeling techniques are demonstrated to extract the axial and torsional resonant frequencies of a complex nonlinear geometry. The first decomposes the complex geometry into easy to model components, while the second uses scaling techniques combined with the finite element method. Both models overcome problems associated with using current analytical methods as design tools, and enable a full investigation of how changes in the geometric parameters affect the resonant frequencies of interest. The benefit of such models is then demonstrated through their use in the design of a prototype piezoelectric ultrasonic resonant micromotor which has improved performance characteristics over previous prototypes.

Algebraic reasoning for the enhancement of data-driven building reconstructions

NASA Astrophysics Data System (ADS)

Meidow, Jochen; Hammer, Horst

2016-04-01

Data-driven approaches for the reconstruction of buildings feature the flexibility needed to capture objects of arbitrary shape. To recognize man-made structures, geometric relations such as orthogonality or parallelism have to be detected. These constraints are typically formulated as sets of multivariate polynomials. For the enforcement of the constraints within an adjustment process, a set of independent and consistent geometric constraints has to be determined. Gröbner bases are an ideal tool to identify such sets exactly. A complete workflow for geometric reasoning is presented to obtain boundary representations of solids based on given point clouds. The constraints are formulated in homogeneous coordinates, which results in simple polynomials suitable for the successful derivation of Gröbner bases for algebraic reasoning. Strategies for the reduction of the algebraical complexity are presented. To enforce the constraints, an adjustment model is introduced, which is able to cope with homogeneous coordinates along with their singular covariance matrices. The feasibility and the potential of the approach are demonstrated by the analysis of a real data set.

Semi-automated contour recognition using DICOMautomaton

NASA Astrophysics Data System (ADS)

Clark, H.; Wu, J.; Moiseenko, V.; Lee, R.; Gill, B.; Duzenli, C.; Thomas, S.

2014-03-01

Purpose: A system has been developed which recognizes and classifies Digital Imaging and Communication in Medicine contour data with minimal human intervention. It allows researchers to overcome obstacles which tax analysis and mining systems, including inconsistent naming conventions and differences in data age or resolution. Methods: Lexicographic and geometric analysis is used for recognition. Well-known lexicographic methods implemented include Levenshtein-Damerau, bag-of-characters, Double Metaphone, Soundex, and (word and character)-N-grams. Geometrical implementations include 3D Fourier Descriptors, probability spheres, boolean overlap, simple feature comparison (e.g. eccentricity, volume) and rule-based techniques. Both analyses implement custom, domain-specific modules (e.g. emphasis differentiating left/right organ variants). Contour labels from 60 head and neck patients are used for cross-validation. Results: Mixed-lexicographical methods show an effective improvement in more than 10% of recognition attempts compared with a pure Levenshtein-Damerau approach when withholding 70% of the lexicon. Domain-specific and geometrical techniques further boost performance. Conclusions: DICOMautomaton allows users to recognize contours semi-automatically. As usage increases and the lexicon is filled with additional structures, performance improves, increasing the overall utility of the system.

Multi-target-qubit unconventional geometric phase gate in a multi-cavity system.

PubMed

Liu, Tong; Cao, Xiao-Zhi; Su, Qi-Ping; Xiong, Shao-Jie; Yang, Chui-Ping

2016-02-22

Cavity-based large scale quantum information processing (QIP) may involve multiple cavities and require performing various quantum logic operations on qubits distributed in different cavities. Geometric-phase-based quantum computing has drawn much attention recently, which offers advantages against inaccuracies and local fluctuations. In addition, multiqubit gates are particularly appealing and play important roles in QIP. We here present a simple and efficient scheme for realizing a multi-target-qubit unconventional geometric phase gate in a multi-cavity system. This multiqubit phase gate has a common control qubit but different target qubits distributed in different cavities, which can be achieved using a single-step operation. The gate operation time is independent of the number of qubits and only two levels for each qubit are needed. This multiqubit gate is generic, e.g., by performing single-qubit operations, it can be converted into two types of significant multi-target-qubit phase gates useful in QIP. The proposal is quite general, which can be used to accomplish the same task for a general type of qubits such as atoms, NV centers, quantum dots, and superconducting qubits.

Inexact trajectory planning and inverse problems in the Hamilton–Pontryagin framework

PubMed Central

Burnett, Christopher L.; Holm, Darryl D.; Meier, David M.

2013-01-01

We study a trajectory-planning problem whose solution path evolves by means of a Lie group action and passes near a designated set of target positions at particular times. This is a higher-order variational problem in optimal control, motivated by potential applications in computational anatomy and quantum control. Reduction by symmetry in such problems naturally summons methods from Lie group theory and Riemannian geometry. A geometrically illuminating form of the Euler–Lagrange equations is obtained from a higher-order Hamilton–Pontryagin variational formulation. In this context, the previously known node equations are recovered with a new interpretation as Legendre–Ostrogradsky momenta possessing certain conservation properties. Three example applications are discussed as well as a numerical integration scheme that follows naturally from the Hamilton–Pontryagin principle and preserves the geometric properties of the continuous-time solution. PMID:24353467

Aerial gamma ray and magnetic survey: Nebraska/Texas Project, the Tyler, Texarkana, and Waco quadrangles of Texas, Oklahoma, Arkansas, and Louisiana. Final report

DOE Office of Scientific and Technical Information (OSTI.GOV)

Not Available

During the months of September and October, 1979, EG and G geoMetrics collected 8866 line miles of high sensitivity airborne radiometric and magnetic data. Data were gathered primarily within the state of Texas, in three 1 x 2 degree NTMS quadrangles. This project is part of the Department of Energy's National Uranium Resource Evaluation Program. All radiometric and magnetic data were fully corrected and interpreted by geoMetrics and are presented as four Volumes (one Volume I and three Volume II's). The quadrangles are dominated by Cretaceous and Tertiary marine sediments. The cretaceous rocks are largely shallow marine sediments of biogenicmore » origin, whereas the Tertiary sequence represents transgressing shelf and slope deposits. No uranium deposits are known in this area (Schnabel, 1955).« less

Quantum Hurwitz numbers and Macdonald polynomials

NASA Astrophysics Data System (ADS)

Harnad, J.

2016-11-01

Parametric families in the center Z(C[Sn]) of the group algebra of the symmetric group are obtained by identifying the indeterminates in the generating function for Macdonald polynomials as commuting Jucys-Murphy elements. Their eigenvalues provide coefficients in the double Schur function expansion of 2D Toda τ-functions of hypergeometric type. Expressing these in the basis of products of power sum symmetric functions, the coefficients may be interpreted geometrically as parametric families of quantum Hurwitz numbers, enumerating weighted branched coverings of the Riemann sphere. Combinatorially, they give quantum weighted sums over paths in the Cayley graph of Sn generated by transpositions. Dual pairs of bases for the algebra of symmetric functions with respect to the scalar product in which the Macdonald polynomials are orthogonal provide both the geometrical and combinatorial significance of these quantum weighted enumerative invariants.

Motorizing fibres with geometric zero-energy modes

NASA Astrophysics Data System (ADS)

Baumann, Arthur; Sánchez-Ferrer, Antoni; Jacomine, Leandro; Martinoty, Philippe; Le Houerou, Vincent; Ziebert, Falko; Kulić, Igor M.

2018-06-01

Responsive materials1-3 have been used to generate structures with built-in complex geometries4-6, linear actuators7-9 and microswimmers10-12. These results suggest that complex, fully functional machines composed solely from shape-changing materials might be possible13. Nonetheless, to accomplish rotary motion in these materials still relies on the classical wheel and axle motifs. Here we explore geometric zero-energy modes to elicit rotary motion in elastic materials in the absence of a rigid wheel travelling around an axle. We show that prestrained polymer fibres closed into rings exhibit self-actuation and continuous motion when placed between two heat baths due to elastic deformations that arise from rotational-symmetry breaking around the rod's axis. Our findings illustrate a simple but robust model to create active motion in mechanically prestrained objects.

High-frequency CAD-based scattering model: SERMAT

NASA Astrophysics Data System (ADS)

Goupil, D.; Boutillier, M.

1991-09-01

Specifications for an industrial radar cross section (RCS) calculation code are given: it must be able to exchange data with many computer aided design (CAD) systems, it must be fast, and it must have powerful graphic tools. Classical physical optics (PO) and equivalent currents (EC) techniques have proven their efficiency on simple objects for a long time. Difficult geometric problems occur when objects with very complex shapes have to be computed. Only a specific geometric code can solve these problems. We have established that, once these problems have been solved: (1) PO and EC give good results on complex objects of large size compared to wavelength; and (2) the implementation of these objects in a software package (SERMAT) allows fast and sufficiently precise domain RCS calculations to meet industry requirements in the domain of stealth.

Generation of three-dimensional delaunay meshes from weakly structured and inconsistent data

NASA Astrophysics Data System (ADS)

Garanzha, V. A.; Kudryavtseva, L. N.

2012-03-01

A method is proposed for the generation of three-dimensional tetrahedral meshes from incomplete, weakly structured, and inconsistent data describing a geometric model. The method is based on the construction of a piecewise smooth scalar function defining the body so that its boundary is the zero isosurface of the function. Such implicit description of three-dimensional domains can be defined analytically or can be constructed from a cloud of points, a set of cross sections, or a "soup" of individual vertices, edges, and faces. By applying Boolean operations over domains, simple primitives can be combined with reconstruction results to produce complex geometric models without resorting to specialized software. Sharp edges and conical vertices on the domain boundary are reproduced automatically without using special algorithms. Refs. 42. Figs. 25.

DFX via the Internet

NASA Astrophysics Data System (ADS)

Wagner, Rick; Castanotto, Giuseppe; Goldberg, Kenneth A.

1995-11-01

The Internet offers tremendous potential for rapid development of mechanical products to meet global competition. In the past several years, a number of geometric algorithms have been developed to evaluate manufacturing properties such as feedability, fixturability, assemblability, etc. This class of algorithms is sometimes termed `DFX: Design for X'. One problem is that most of these algorithms are tailored to a particular CAD system and format and so have not been widely tested by industry. the World Wide Web may offer a solution: its simple interface language may become a de facto standard for the exchange of geometric data. In this preliminary paper we describe one model for remote analysis of CAD models that we believe holds promise for use in industry (e.g. during the design cycle) and in research (e.g. to encourage verification of results).

The use of photostimulable phosphor systems for periodic quality assurance in radiotherapy.

PubMed

Conte, L; Bianchi, C; Cassani, E; Monciardini, M; Mordacchini, C; Novario, R; Strocchi, S; Stucchi, P; Tanzi, F

2008-03-01

The fusion of radiological and optical images can be achieved through charging a photostimulable phosphor plate (PSP) with an exposure to a field of X- or gamma-rays, followed by exposure to an optical image which discharges the plate in relation to the amount of incident light. According to this PSP characteristic, we developed a simple method for periodic quality assurance (QA) of light/radiation field coincidence, distance indicator, field size indicators, crosshair centering, coincidence of radiation and mechanical isocenter for linear accelerators. The geometrical accuracy of radiological units can be subjected to the same QA method. Further, the source position accuracy for an HDR remote afterloader can be checked by taking an autoradiography of the radioactive source and simultaneously an optical image of a reference geometrical system.

Applied statistics in ecology: common pitfalls and simple solutions

Treesearch

E. Ashley Steel; Maureen C. Kennedy; Patrick G. Cunningham; John S. Stanovick

2013-01-01

The most common statistical pitfalls in ecological research are those associated with data exploration, the logic of sampling and design, and the interpretation of statistical results. Although one can find published errors in calculations, the majority of statistical pitfalls result from incorrect logic or interpretation despite correct numerical calculations. There...

Interpreting the spectral behavior of MWC 314

NASA Astrophysics Data System (ADS)

Frasca, A.; Miroshnichenko, A. S.; Rossi, C.; Friedjung, M.; Marilli, E.; Muratorio, G.; Busà, I.

2016-01-01

Context. MWC 314 is one of the most luminous stars in the Milky Way. Its fundamental parameters are similar to those of luminous blue variables (LBVs), although no large photometric variations have been recorded. Moreover, it shows no evidence of either a dust shell or a relevant spectral variability. Aims: The main purpose of this work is to clarify the origin of the radial velocity and line profile variations exhibited by absorption and emission lines. Methods: We analyzed the radial velocity (RV) variations displayed by the absorption lines from the star's atmosphere using high-resolution optical spectra and fitting the RV curve with an eccentric orbit model. We also studied the RV and profile variations of some permitted and forbidden emission lines of metallic ions with a simple geometric model. The behavior of the Balmer and He I lines has also been investigated. Results: Fourier analysis applied to the RV of the absorption lines clearly shows a 60-day periodicity. A dense coverage of the RV curve allowed us to derive accurate orbital parameters. The RV of the Fe II emission lines varies in the same way, but with a smaller amplitude. Additionally, the intensity ratio of the blue/red peaks of these emission lines correlates with the RV variations. The first three members of the Balmer series as well as [N II] lines display a nearly constant RV and no profile variations in phase with the orbital motion instead. The He I λ5876 Å line shows a strongly variable profile with broad and blue-shifted absorption components that reach velocities of ≤-1000 km s-1 in some specific orbital phases. Conclusions: Our data and analysis provide strong evidence that the object is a binary system composed of a supergiant B[e] star and an undetected companion. The emission lines with a non-variable RV could originate in a circumbinary region. For the Fe II emission lines, we propose a simple geometrical two-component model where a compact source of Fe II emission, moving around the center of mass, is affected by a static extra absorption that originates from a larger area. Finally, the blue-shifted absorption in the He I λ5876 Å line could be the result of density enhancements in the primary star wind that is flowing towards the companion, and which is best observed when projected over the disk of the primary star. Based on observations made at the 0.91 m of Catania Observatory, the OHP telescopes and the 1.83 m telescope of the Asiago Observatory.

Nonlinear transient analysis via energy minimization

NASA Technical Reports Server (NTRS)

Kamat, M. P.; Knight, N. F., Jr.

1978-01-01

The formulation basis for nonlinear transient analysis of finite element models of structures using energy minimization is provided. Geometric and material nonlinearities are included. The development is restricted to simple one and two dimensional finite elements which are regarded as being the basic elements for modeling full aircraft-like structures under crash conditions. The results indicate the effectiveness of the technique as a viable tool for this purpose.

Occurrence of hydrodynamic cavitation.

PubMed

Nosov, V R; Gómez-Mancilla, J C; Meda-Campaña, J A

2011-01-01

In this paper, the conditions under which cavitation (or liquid film rupture) can or cannot occur in thin layers of moving liquid are derived for three typical cases. At the same time, expressions depending on geometrical and movement parameters, where cavitation might start, are given. The results are obtained using simple engineering terms, which can be used in cases whether it is necessary to avoid cavitation or to induce it.

Permutation parity machines for neural cryptography.

PubMed

Reyes, Oscar Mauricio; Zimmermann, Karl-Heinz

2010-06-01

Recently, synchronization was proved for permutation parity machines, multilayer feed-forward neural networks proposed as a binary variant of the tree parity machines. This ability was already used in the case of tree parity machines to introduce a key-exchange protocol. In this paper, a protocol based on permutation parity machines is proposed and its performance against common attacks (simple, geometric, majority and genetic) is studied.

The Development of Mental State Attributions in Women with X-Monosomy, and the Role of Monoamine Oxidase B in the Sociocognitive Phenotype

ERIC Educational Resources Information Center

Lawrence, K.; Jones, A.; Oreland, L.; Spektor, D.; Mandy, W.; Campbell, R.; Skuse, D.

2007-01-01

We hypothesized that women with Turner syndrome (45,X) with a single X-chromosome inherited from their mother may show mentalizing deficits compared to women of normal karyotype with two X-chromosomes (46,X). Simple geometrical animation events (two triangles moving with apparent intention in relation to each other) which usually elicit…

Permutation parity machines for neural cryptography

DOE Office of Scientific and Technical Information (OSTI.GOV)

Reyes, Oscar Mauricio; Escuela de Ingenieria Electrica, Electronica y Telecomunicaciones, Universidad Industrial de Santander, Bucaramanga; Zimmermann, Karl-Heinz

2010-06-15

Recently, synchronization was proved for permutation parity machines, multilayer feed-forward neural networks proposed as a binary variant of the tree parity machines. This ability was already used in the case of tree parity machines to introduce a key-exchange protocol. In this paper, a protocol based on permutation parity machines is proposed and its performance against common attacks (simple, geometric, majority and genetic) is studied.

LMSS drive simulator for multipath propagation

NASA Technical Reports Server (NTRS)

Vishakantaiah, Praveen; Vogel, Wolfhard J.

1989-01-01

A three-dimensional drive simulator for the prediction of Land Mobile Satellite Service (LMSS) multipath propagation was developed. It is based on simple physical and geometrical rules and can be used to evaluate effects of scatterer numbers and positions, receiving antenna pattern, and satellite frequency and position. It is shown that scatterers close to the receiver have the most effect and that directive antennas suppress multipath interference.

Understanding the complexity of the Lévy-walk nature of human mobility with a multi-scale cost∕benefit model.

PubMed

Scafetta, Nicola

2011-12-01

Probability distributions of human displacements have been fit with exponentially truncated Lévy flights or fat tailed Pareto inverse power law probability distributions. Thus, people usually stay within a given location (for example, the city of residence), but with a non-vanishing frequency they visit nearby or far locations too. Herein, we show that an important empirical distribution of human displacements (range: from 1 to 1000 km) can be well fit by three consecutive Pareto distributions with simple integer exponents equal to 1, 2, and (>) 3. These three exponents correspond to three displacement range zones of about 1 km ≲Δr≲10 km, 10 km ≲Δr≲300 km, and 300 km ≲Δr≲1000 km, respectively. These three zones can be geographically and physically well determined as displacements within a city, visits to nearby cities that may occur within just one-day trips, and visit to far locations that may require multi-days trips. The incremental integer values of the three exponents can be easily explained with a three-scale mobility cost∕benefit model for human displacements based on simple geometrical constrains. Essentially, people would divide the space into three major regions (close, medium, and far distances) and would assume that the travel benefits are randomly∕uniformly distributed mostly only within specific urban-like areas. The three displacement distribution zones appear to be characterized by an integer (1, 2, or >3) inverse power exponent because of the specific number (1, 2, or >3) of cost mechanisms (each of which is proportional to the displacement length). The distributions in the first two zones would be associated to Pareto distributions with exponent β = 1 and β = 2 because of simple geometrical statistical considerations due to the a priori assumption that most benefits are searched in the urban area of the city of residence or in the urban area of specific nearby cities. We also show, by using independent records of human mobility, that the proposed model predicts the statistical properties of human mobility below 1 km ranges, where people just walk. In the latter case, the threshold between zone 1 and zone 2 may be around 100-200 m and, perhaps, may have been evolutionary determined by the natural human high resolution visual range, which characterizes an area of interest where the benefits are assumed to be randomly and uniformly distributed. This rich and suggestive interpretation of human mobility may characterize other complex random walk phenomena that may also be described by a N-piece fit Pareto distributions with increasing integer exponents. This study also suggests that distribution functions used to fit experimental probability distributions must be carefully chosen for not improperly obscuring the physics underlying a phenomenon.

High-Performance Liquid Chromatography in the Undergraduate Chemical Engineering Laboratory

ERIC Educational Resources Information Center

Frey, Douglas D.; Guo, Hui; Karnik, Nikhila

2013-01-01

This article describes the assembly of a simple, low-cost, high-performance liquid chromatography (HPLC) system and its use in the undergraduate chemical engineering laboratory course to perform simple experiments. By interpreting the results from these experiments students are able to gain significant experience in the general method of…

Simple Techniques for Microclimate Measurement.

ERIC Educational Resources Information Center

Unwin, D. M.

1978-01-01

Describes simple ways of measuring the very local climate near the ground, and explains what these measurements mean. Equipment included a solar radiometer, a dew point instrument, and a thermocouple psychrometer. Examples are given of field measurements taken with some of the equipment and the results and their interpretation are discussed.…

DOE Office of Scientific and Technical Information (OSTI.GOV)

Leger, M.; Morvan, J.M.; Thibaut, M.

Restoration of a geologic structure at earlier times is a good means to criticize, and next to improve, its interpretation. Restoration softwares already exist in 2D, but a lot of work remains to be done in 3D. The authors focus on the interbedding slip phenomenon, with bed-length and volume conservation. They unfold a (geometrical) foliation by optimizing following least-squares criteria: horizontalness, bed-length and volume conservation, under equality constraints related to the position of the ``binding`` or ``pin-surface``

Symmetries and conservation laws of a nonlinear sigma model with gravitino

NASA Astrophysics Data System (ADS)

Jost, Jürgen; Keßler, Enno; Tolksdorf, Jürgen; Wu, Ruijun; Zhu, Miaomiao

2018-06-01

We study the symmetries and invariances of a version of the action functional of the nonlinear sigma model with gravitino, as considered in Jost et al. (2017). The action is invariant under rescaled conformal transformations, super Weyl transformations, and diffeomorphisms. In particular cases the functional possesses a degenerate supersymmetry. The corresponding conservation laws lead to a geometric interpretation of the energy-momentum tensor and supercurrent as holomorphic sections of appropriate bundles.

Design of integration-ready metasurface-based infrared absorbers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ogando, Karim, E-mail: karim@cab.cnea.gov.ar; Pastoriza, Hernán

2015-07-28

We introduce an integration ready design of metamaterial infrared absorber, highly compatible with many kinds of fabrication processes. We present the results of an exhaustive experimental characterization, including an analysis of the effects of single meta-atom geometrical parameters and collective arrangement. We confront the results with the theoretical interpretations proposed in the literature. Based on the results, we develop a set of practical design rules for metamaterial absorbers in the infrared region.

Saturated Fats and Cardiovascular Disease: Interpretations Not as Simple as They Once Were.

PubMed

Bier, Dennis M

2016-09-09

Historically, the so-called "lipid hypothesis" has focused on the detrimental role of saturated fats per se in enhancing the risks of cardiovascular disease. Recently, a body of new information and systematic analyses of available data have questioned simple interpretation of the relationship of dietary saturated fats and of individual saturated fatty acids to CVD risk. Thus, current assessments of risks due to dietary fat consumption that emphasize the confounding nature of the dietary macronutrients substituted for dietary saturated fats and give broader recognition to the effect of patterns of food intake as a whole are the most productive approach to an overall healthy diet.

Fate of the Hoop Conjecture in Quantum Gravity.

PubMed

Anzà, Fabio; Chirco, Goffredo

2017-12-08

We consider a closed region R of 3D quantum space described via SU(2) spin networks. Using the concentration of measure phenomenon we prove that, whenever the ratio between the boundary ∂R and the bulk edges of the graph overcomes a finite threshold, the state of the boundary is always thermal, with an entropy proportional to its area. The emergence of a thermal state of the boundary can be traced back to a large amount of entanglement between boundary and bulk degrees of freedom. Using the dual geometric interpretation provided by loop quantum gravity, we interpret such phenomenon as a pregeometric analogue of Thorne's "hoop conjecture," at the core of the formation of a horizon in general relativity.

Mechanical trapping of particles in granular media

NASA Astrophysics Data System (ADS)

Kerimov, Abdulla; Mavko, Gary; Mukerji, Tapan; Al Ibrahim, Mustafa A.

2018-02-01

Mechanical trapping of fine particles in the pores of granular materials is an essential mechanism in a wide variety of natural and industrial filtration processes. The progress of invading particles is primarily limited by the network of pore throats and connected pathways encountered by the particles during their motion through the porous medium. Trapping of invading particles is limited to a depth defined by the size, shape, and distribution of the invading particles with respect to the size, shape, and distribution of the host porous matrix. Therefore, the trapping process, in principle, can be used to obtain information about geometrical properties, such as pore throat and particle size, of the underlying host matrix. A numerical framework is developed to simulate the mechanical trapping of fine particles in porous granular media with prescribed host particle size, shape, and distribution. The trapping of invading particles is systematically modeled in host packings with different host particle distributions: monodisperse, bidisperse, and polydisperse distributions of host particle sizes. Our simulation results show quantitatively and qualitatively to what extent trapping behavior is different in the generated monodisperse, bidisperse, and polydisperse packings of spherical particles. Depending on host particle size and distribution, the information about extreme estimates of minimal pore throat sizes of the connected pathways in the underlying host matrix can be inferred from trapping features, such as the fraction of trapped particles as a function of invading particle size. The presence of connected pathways with minimum and maximum of minimal pore throat diameters can be directly obtained from trapping features. This limited information about the extreme estimates of pore throat sizes of the connected pathways in the host granular media inferred from our numerical simulations is consistent with simple geometrical estimates of extreme value of pore and throat sizes of the densest structural arrangements of spherical particles and geometrical Delaunay tessellation analysis of the pore space of host granular media. Our results suggest simple relations between the host particle size and trapping features. These relationships can be potentially used to describe both the dynamics of the mechanical trapping process and the geometrical properties of the host granular media.

Mechanical trapping of particles in granular media.

PubMed

Kerimov, Abdulla; Mavko, Gary; Mukerji, Tapan; Al Ibrahim, Mustafa A

2018-02-01

Mechanical trapping of fine particles in the pores of granular materials is an essential mechanism in a wide variety of natural and industrial filtration processes. The progress of invading particles is primarily limited by the network of pore throats and connected pathways encountered by the particles during their motion through the porous medium. Trapping of invading particles is limited to a depth defined by the size, shape, and distribution of the invading particles with respect to the size, shape, and distribution of the host porous matrix. Therefore, the trapping process, in principle, can be used to obtain information about geometrical properties, such as pore throat and particle size, of the underlying host matrix. A numerical framework is developed to simulate the mechanical trapping of fine particles in porous granular media with prescribed host particle size, shape, and distribution. The trapping of invading particles is systematically modeled in host packings with different host particle distributions: monodisperse, bidisperse, and polydisperse distributions of host particle sizes. Our simulation results show quantitatively and qualitatively to what extent trapping behavior is different in the generated monodisperse, bidisperse, and polydisperse packings of spherical particles. Depending on host particle size and distribution, the information about extreme estimates of minimal pore throat sizes of the connected pathways in the underlying host matrix can be inferred from trapping features, such as the fraction of trapped particles as a function of invading particle size. The presence of connected pathways with minimum and maximum of minimal pore throat diameters can be directly obtained from trapping features. This limited information about the extreme estimates of pore throat sizes of the connected pathways in the host granular media inferred from our numerical simulations is consistent with simple geometrical estimates of extreme value of pore and throat sizes of the densest structural arrangements of spherical particles and geometrical Delaunay tessellation analysis of the pore space of host granular media. Our results suggest simple relations between the host particle size and trapping features. These relationships can be potentially used to describe both the dynamics of the mechanical trapping process and the geometrical properties of the host granular media.

Global Geometric Properties of Martian Impact Craters: A Preliminary Assessment Using Mars Orbiter Laser Altimeter (MOLA)

NASA Technical Reports Server (NTRS)

Garvin, J. B.; Sakimoto, S. E. H.; Schnetzler, C.; Frawley, J. J.

1999-01-01

Impact craters on Mars have been used to provide fundamental insights into the properties of the martian crust, the role of volatiles, the relative age of the surface, and on the physics of impact cratering in the Solar System. Before the three-dimensional information provided by the Mars Orbiter Laser Altimeter (MOLA) instrument which is currently operating in Mars orbit aboard the Mars Global Surveyor (MGS), impact features were characterized morphologically using orbital images from Mariner 9 and Viking. Fresh-appearing craters were identified and measurements of their geometric properties were derived from various image-based methods. MOLA measurements can now provide a global sample of topographic cross-sections of martian impact features as small as approx. 2 km in diameter, to basin-scale features. We have previously examined MOLA cross-sections of Northern Hemisphere and North Polar Region impact features, but were unable to consider the global characteristics of these ubiquitous landforms. Here we present our preliminary assessment of the geometric properties of a globally-distributed sample of martian impact craters, most of which were sampled during the initial stages of the MGS mapping mission (i.e., the first 600 orbits). Our aim is to develop a framework for reconsidering theories concerning impact cratering in the martian environment. This first global analysis is focused upon topographically-fresh impact craters, defined here on the basis of MOLA topographic profiles that cross the central cavities of craters that can be observed in Viking-based MDIM global image mosaics. We have considered crater depths, rim heights, ejecta topologies, cross-sectional "shapes", and simple physical models for ejecta emplacement. To date (May, 1999), we have measured the geometric properties of over 1300 impact craters in the 2 to 350 km diameter size interval. A large fraction of these measured craters were sampled with cavity-center cross-sections during the first two months of MGS mapping. Many of these craters are included in Nadine Barlow's Catalogue of Martian Impact Craters, although we have treated simple craters smaller than about 7 km in greater detail than all previous investigations. Additional information is contained in the original extended abstract.

Geometrical meaning of winding number and its characterization of topological phases in one-dimensional chiral non-Hermitian systems

NASA Astrophysics Data System (ADS)

Yin, Chuanhao; Jiang, Hui; Li, Linhu; Lü, Rong; Chen, Shu

2018-05-01

We unveil the geometrical meaning of winding number and utilize it to characterize the topological phases in one-dimensional chiral non-Hermitian systems. While chiral symmetry ensures the winding number of Hermitian systems are integers, it can take half integers for non-Hermitian systems. We give a geometrical interpretation of the half integers by demonstrating that the winding number ν of a non-Hermitian system is equal to half of the summation of two winding numbers ν1 and ν2 associated with two exceptional points, respectively. The winding numbers ν1 and ν2 represent the times of the real part of the Hamiltonian in momentum space encircling the exceptional points and can only take integers. We further find that the difference of ν1 and ν2 is related to the second winding number or energy vorticity. By applying our scheme to a non-Hermitian Su-Schrieffer-Heeger model and an extended version of it, we show that the topologically different phases can be well characterized by winding numbers. Furthermore, we demonstrate that the existence of left and right zero-mode edge states is closely related to the winding number ν1 and ν2.

A shape-based segmentation method for mobile laser scanning point clouds

NASA Astrophysics Data System (ADS)

Yang, Bisheng; Dong, Zhen

2013-07-01

Segmentation of mobile laser point clouds of urban scenes into objects is an important step for post-processing (e.g., interpretation) of point clouds. Point clouds of urban scenes contain numerous objects with significant size variability, complex and incomplete structures, and holes or variable point densities, raising great challenges for the segmentation of mobile laser point clouds. This paper addresses these challenges by proposing a shape-based segmentation method. The proposed method first calculates the optimal neighborhood size of each point to derive the geometric features associated with it, and then classifies the point clouds according to geometric features using support vector machines (SVMs). Second, a set of rules are defined to segment the classified point clouds, and a similarity criterion for segments is proposed to overcome over-segmentation. Finally, the segmentation output is merged based on topological connectivity into a meaningful geometrical abstraction. The proposed method has been tested on point clouds of two urban scenes obtained by different mobile laser scanners. The results show that the proposed method segments large-scale mobile laser point clouds with good accuracy and computationally effective time cost, and that it segments pole-like objects particularly well.

Global regularizing flows with topology preservation for active contours and polygons.

PubMed

Sundaramoorthi, Ganesh; Yezzi, Anthony

2007-03-01

Active contour and active polygon models have been used widely for image segmentation. In some applications, the topology of the object(s) to be detected from an image is known a priori, despite a complex unknown geometry, and it is important that the active contour or polygon maintain the desired topology. In this work, we construct a novel geometric flow that can be added to image-based evolutions of active contours and polygons in order to preserve the topology of the initial contour or polygon. We emphasize that, unlike other methods for topology preservation, the proposed geometric flow continually adjusts the geometry of the original evolution in a gradual and graceful manner so as to prevent a topology change long before the curve or polygon becomes close to topology change. The flow also serves as a global regularity term for the evolving contour, and has smoothness properties similar to curvature flow. These properties of gradually adjusting the original flow and global regularization prevent geometrical inaccuracies common with simple discrete topology preservation schemes. The proposed topology preserving geometric flow is the gradient flow arising from an energy that is based on electrostatic principles. The evolution of a single point on the contour depends on all other points of the contour, which is different from traditional curve evolutions in the computer vision literature.

Annual forest inventory estimates based on the moving average

Treesearch

Francis A. Roesch; James R. Steinman; Michael T. Thompson

2002-01-01

Three interpretations of the simple moving average estimator, as applied to the USDA Forest Service's annual forest inventory design, are presented. A corresponding approach to composite estimation over arbitrarily defined land areas and time intervals is given for each interpretation, under the assumption that the investigator is armed with only the spatial/...

Building a Smart Portal for Astronomy

NASA Astrophysics Data System (ADS)

Derriere, S.; Boch, T.

2011-07-01

The development of a portal for accessing astronomical resources is not an easy task. The ever-increasing complexity of the data products can result in very complex user interfaces, requiring a lot of effort and learning from the user in order to perform searches. This is often a design choice, where the user must explicitly set many constraints, while the portal search logic remains simple. We investigated a different approach, where the query interface is kept as simple as possible (ideally, a simple text field, like for Google search), and the search logic is made much more complex to interpret the query in a relevant manner. We will present the implications of this approach in terms of interpretation and categorization of the query parameters (related to astronomical vocabularies), translation (mapping) of these concepts into the portal components metadata, identification of query schemes and use cases matching the input parameters, and delivery of query results to the user.

Robot geometry calibration

NASA Technical Reports Server (NTRS)

Hayati, Samad; Tso, Kam; Roston, Gerald

1988-01-01

Autonomous robot task execution requires that the end effector of the robot be positioned accurately relative to a reference world-coordinate frame. The authors present a complete formulation to identify the actual robot geometric parameters. The method applies to any serial link manipulator with arbitrary order and combination of revolute and prismatic joints. A method is also presented to solve the inverse kinematic of the actual robot model which usually is not a so-called simple robot. Experimental results performed by utilizing a PUMA 560 with simple measurement hardware are presented. As a result of this calibration a precision move command is designed and integrated into a robot language, RCCL, and used in the NASA Telerobot Testbed.

How to use 3D shadows for simple microscopy and vibrometry

NASA Astrophysics Data System (ADS)

Parikesit, Gea O. F.; Kusumaningtyas, Indraswari

2017-07-01

In 2014, we reported that shadows can be displayed in 3D using a stereoscopic setup. We now report that the 3D shadows can also be used to perform simple measurements, which are suitable for physics education in schools and colleges. Two different types of measurements are demonstrated, i.e. microscopy and vibrometry. Both types of measurements take advantage of the geometrical optics of the 3D shadows, where the 3D position of an object can be estimated using the coordinates of the colored light sources and the coordinates of the colored shadow images. We also include several student activities that can raise the students’ curiosity and capability.

Optimal ancilla-free Pauli+V circuits for axial rotations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Blass, Andreas; Bocharov, Alex; Gurevich, Yuri

We address the problem of optimal representation of single-qubit rotations in a certain unitary basis consisting of the so-called V gates and Pauli matrices. The V matrices were proposed by Lubotsky, Philips, and Sarnak [Commun. Pure Appl. Math. 40, 401–420 (1987)] as a purely geometric construct in 1987 and recently found applications in quantum computation. They allow for exceptionally simple quantum circuit synthesis algorithms based on quaternionic factorization. We adapt the deterministic-search technique initially proposed by Ross and Selinger to synthesize approximating Pauli+V circuits of optimal depth for single-qubit axial rotations. Our synthesis procedure based on simple SL{sub 2}(ℤ) geometrymore » is almost elementary.« less

Visualization of atomic-scale phenomena in superconductors: application to FeSe

DOE Office of Scientific and Technical Information (OSTI.GOV)

Choubey, Peayush; Berlijn, Tom; Kreisel, Andreas

Here we propose a simple method of calculating inhomogeneous, atomic-scale phenomena in superconductors which makes use of the wave function information traditionally discarded in the construction of tight-binding models used in the Bogoliubov-de Gennes equations. The method uses symmetry- based first principles Wannier functions to visualize the effects of superconducting pairing on the distribution of electronic states over atoms within a crystal unit cell. Local symmetries lower than the global lattice symmetry can thus be exhibited as well, rendering theoretical comparisons with scanning tunneling spectroscopy data much more useful. As a simple example, we discuss the geometric dimer states observedmore » near defects in superconducting FeSe.« less

Visualization of atomic-scale phenomena in superconductors: application to FeSe

DOE PAGES

Choubey, Peayush; Berlijn, Tom; Kreisel, Andreas; ...

2014-10-31

Here we propose a simple method of calculating inhomogeneous, atomic-scale phenomena in superconductors which makes use of the wave function information traditionally discarded in the construction of tight-binding models used in the Bogoliubov-de Gennes equations. The method uses symmetry- based first principles Wannier functions to visualize the effects of superconducting pairing on the distribution of electronic states over atoms within a crystal unit cell. Local symmetries lower than the global lattice symmetry can thus be exhibited as well, rendering theoretical comparisons with scanning tunneling spectroscopy data much more useful. As a simple example, we discuss the geometric dimer states observedmore » near defects in superconducting FeSe.« less

The envelope of ballistic trajectories and elliptic orbits

NASA Astrophysics Data System (ADS)

Butikov, Eugene I.

2015-11-01

Simple geometric derivations are given for the shape of the "safety domain" boundary for the family of Keplerian orbits of equal energy in a central gravitational field and for projectile trajectories in a uniform field. Examples of practical uses of the envelope of the family of orbits are discussed and illustrated by computer simulations. This material is appropriate for physics teachers and undergraduate students studying classical mechanics and orbital motions.

Investigations and Tests in the Towing Basin at Guidonia

NASA Technical Reports Server (NTRS)

Cremona, C

1939-01-01

The experimental methods at the Guidonia towing basin are discussed including specifications. Some of the components examined are the bridge towing carriage, side towing carriage, catapult installation, and dynamometer systems. Tests were performed on hulls and floats, as well as motor boats and torpedo shaped bodies. Theoretical investigations were also performed to determine pressure distributions on geometrically simple bodies, propagation of small wave motions, and planing and submerged surfaces.

Geometry of proteins: hydrogen bonding, sterics, and marginally compact tubes.

PubMed

Banavar, Jayanth R; Cieplak, Marek; Flammini, Alessandro; Hoang, Trinh X; Kamien, Randall D; Lezon, Timothy; Marenduzzo, Davide; Maritan, Amos; Seno, Flavio; Snir, Yehuda; Trovato, Antonio

2006-03-01

The functionality of proteins is governed by their structure in the native state. Protein structures are made up of emergent building blocks of helices and almost planar sheets. A simple coarse-grained geometrical model of a flexible tube barely subject to compaction provides a unified framework for understanding the common character of globular proteins. We argue that a recent critique of the tube idea is not well founded.

Geometry of proteins: Hydrogen bonding, sterics, and marginally compact tubes

NASA Astrophysics Data System (ADS)

Banavar, Jayanth R.; Cieplak, Marek; Flammini, Alessandro; Hoang, Trinh X.; Kamien, Randall D.; Lezon, Timothy; Marenduzzo, Davide; Maritan, Amos; Seno, Flavio; Snir, Yehuda; Trovato, Antonio

2006-03-01

The functionality of proteins is governed by their structure in the native state. Protein structures are made up of emergent building blocks of helices and almost planar sheets. A simple coarse-grained geometrical model of a flexible tube barely subject to compaction provides a unified framework for understanding the common character of globular proteins. We argue that a recent critique of the tube idea is not well founded.

Serum Dioxin and Memory Among Veterans of Operation Ranch Hand

DTIC Science & Technology

2007-09-01

logical memory and visual reproductions subtests. In 1987, the WMS-R was published, expanding on the original WMS and creating a more thorough and...the Verbal Paired Associates subtest, the Logical Memory subtest (immediate and delayed recall), and the Visual Reproduction subtest (immediate and...Visual Reproduction subtest, designed to assess visual memory, the veteran was asked to draw from memory four simple geometric designs that were each

Vehicle Concept Model Abstractions for Integrated Geometric, Inertial, Rigid Body, Powertrain, and FE Analysis

DTIC Science & Technology

2011-01-01

refinement of the vehicle body structure through quantitative assessment of stiffness and modal parameter changes resulting from modifications to the beam...differential placed on the axle , adjustment of the torque output to the opposite wheel may be required to obtain the correct solution. Thus...represented by simple inertial components with appropriate model connectivity instead to determine the free modal response of powertrain type

The Cross Product of Two Vectors Is Not Just Another Vector--A Major Misconception Being Perpetuated in Calculus and Vector Analysis Textbooks.

ERIC Educational Resources Information Center

Elk, Seymour B.

1997-01-01

Suggests that the cross product of two vectors can be more easily and accurately explained by starting from the perspective of dyadics because then the concept of vector multiplication has a simple geometrical picture that encompasses both the dot and cross products in any number of dimensions in terms of orthogonal unit vector components. (AIM)

Validating and improving a zero-dimensional stack voltage model of the Vanadium Redox Flow Battery

NASA Astrophysics Data System (ADS)

König, S.; Suriyah, M. R.; Leibfried, T.

2018-02-01

Simple, computationally efficient battery models can contribute significantly to the development of flow batteries. However, validation studies for these models on an industrial-scale stack level are rarely published. We first extensively present a simple stack voltage model for the Vanadium Redox Flow Battery. For modeling the concentration overpotential, we derive mass transfer coefficients from experimental results presented in the 1990s. The calculated mass transfer coefficient of the positive half-cell is 63% larger than of the negative half-cell, which is not considered in models published to date. Further, we advance the concentration overpotential model by introducing an apparent electrochemically active electrode surface which differs from the geometric electrode area. We use the apparent surface as fitting parameter for adapting the model to experimental results of a flow battery manufacturer. For adapting the model, we propose a method for determining the agreement between model and reality quantitatively. To protect the manufacturer's intellectual property, we introduce a normalization method for presenting the results. For the studied stack, the apparent electrochemically active surface of the electrode is 41% larger than its geometrical area. Hence, the current density in the diffusion layer is 29% smaller than previously reported for a zero-dimensional model.

Comparison of geometrical shock dynamics and kinematic models for shock-wave propagation

NASA Astrophysics Data System (ADS)

Ridoux, J.; Lardjane, N.; Monasse, L.; Coulouvrat, F.

2018-03-01

Geometrical shock dynamics (GSD) is a simplified model for nonlinear shock-wave propagation, based on the decomposition of the shock front into elementary ray tubes. Assuming small changes in the ray tube area, and neglecting the effect of the post-shock flow, a simple relation linking the local curvature and velocity of the front, known as the A{-}M rule, is obtained. More recently, a new simplified model, referred to as the kinematic model, was proposed. This model is obtained by combining the three-dimensional Euler equations and the Rankine-Hugoniot relations at the front, which leads to an equation for the normal variation of the shock Mach number at the wave front. In the same way as GSD, the kinematic model is closed by neglecting the post-shock flow effects. Although each model's approach is different, we prove their structural equivalence: the kinematic model can be rewritten under the form of GSD with a specific A{-}M relation. Both models are then compared through a wide variety of examples including experimental data or Eulerian simulation results when available. Attention is drawn to the simple cases of compression ramps and diffraction over convex corners. The analysis is completed by the more complex cases of the diffraction over a cylinder, a sphere, a mound, and a trough.

Geometrical model for martensitic phase transitions: Understanding criticality and weak universality during microstructure growth.

PubMed

Torrents, Genís; Illa, Xavier; Vives, Eduard; Planes, Antoni

2017-01-01

A simple model for the growth of elongated domains (needle-like) during a martensitic phase transition is presented. The model is purely geometric and the only interactions are due to the sequentiality of the kinetic problem and to the excluded volume, since domains cannot retransform back to the original phase. Despite this very simple interaction, numerical simulations show that the final observed microstructure can be described as being a consequence of dipolar-like interactions. The model is analytically solved in 2D for the case in which two symmetry related domains can grow in the horizontal and vertical directions. It is remarkable that the solution is analytic both for a finite system of size L×L and in the thermodynamic limit L→∞, where the elongated domains become lines. Results prove the existence of criticality, i.e., that the domain sizes observed in the final microstructure show a power-law distribution characterized by a critical exponent. The exponent, nevertheless, depends on the relative probabilities of the different equivalent variants. The results provide a plausible explanation of the weak universality of the critical exponents measured during martensitic transformations in metallic alloys. Experimental exponents show a monotonous dependence with the number of equivalent variants that grow during the transition.

Using growth and arrest of Richtmyer-Meshkov instabilities and Lagrangian simulations to study high-rate material strength

NASA Astrophysics Data System (ADS)

Prime, M. B.; Vaughan, D. E.; Preston, D. L.; Buttler, W. T.; Chen, S. R.; Oró, D. M.; Pack, C.

2014-05-01

Experiments applying a supported shock through mating surfaces (Atwood number = 1) with geometrical perturbations have been proposed for studying strength at strain rates up to 107/s using Richtmyer-Meshkov (RM) instabilities. Buttler et al. recently reported experimental results for RM instability growth in copper but with an unsupported shock applied by high explosives and the geometrical perturbations on the opposite free surface (Atwood number = -1). This novel configuration allowed detailed experimental observation of the instability growth and arrest. We present results and interpretation from numerical simulations of the Buttler RM instability experiments. Highly-resolved, two-dimensional simulations were performed using a Lagrangian hydrocode and the Preston-Tonks-Wallace (PTW) strength model. The model predictions show good agreement with the data. The numerical simulations are used to examine various assumptions previously made in an analytical model and to estimate the sensitivity of such experiments to material strength.

A new interpretation of the bee fossil Melitta willardi Cockerell (Hymenoptera, Melittidae) based on geometric morphometrics of the wing.

PubMed

Dewulf, Alexandre; De Meulemeester, Thibaut; Dehon, Manuel; Engel, Michael S; Michez, Denis

2014-01-01

Although bees are one of the major lineages of pollinators and are today quite diverse, few well-preserved fossils are available from which to establish the tempo of their diversification/extinction since the Early Cretaceous. Here we present a reassessment of the taxonomic affinities of Melitta willardiCockerell 1909, preserved as a compression fossil from the Florissant shales of Colorado, USA. Based on geometric morphometric wing shape analyses M. willardi cannot be confidently assigned to the genus Melitta Kirby (Anthophila, Melittidae). Instead, the species exhibits phenotypic affinity with the subfamily Andreninae (Anthophila, Andrenidae), but does not appear to belong to any of the known genera therein. Accordingly, we describe a new genus, Andrenopteryx gen. n., based on wing shape as well as additional morphological features and to accommodate M. willardi. The new combination Andrenopteryx willardi (Cockerell) is established.

Single particle momentum and angular distributions in hadron-hadron collisions at ultrahigh energies

NASA Technical Reports Server (NTRS)

Chou, T. T.; Chen, N. Y.

1985-01-01

The forward-backward charged multiplicity distribution (P n sub F, n sub B) of events in the 540 GeV antiproton-proton collider has been extensively studied by the UA5 Collaboration. It was pointed out that the distribution with respect to n = n sub F + n sub B satisfies approximate KNO scaling and that with respect to Z = n sub F - n sub B is binomial. The geometrical model of hadron-hadron collision interprets the large multiplicity fluctuation as due to the widely different nature of collisions at different impact parameters b. For a single impact parameter b, the collision in the geometrical model should exhibit stochastic behavior. This separation of the stochastic and nonstochastic (KNO) aspects of multiparticle production processes gives conceptually a lucid and attractive picture of such collisions, leading to the concept of partition temperature T sub p and the single particle momentum spectrum to be discussed in detail.

Beyond Discrete Vacuum Spacetimes

NASA Astrophysics Data System (ADS)

McDonald, Jonathan; Miller, Warner

2008-04-01

In applications to pre-geometric models of quantum gravity, one expects matter to play an important role in the geometry of the spacetime. Such models often posit that the matter fields play a crucial role in the determination of the spacetime geometry. However, it is not well understood at a fundamental level how one couples matter into the Regge geometry. In order to better understand the nature of such theories that rely on Regge Calculus, we must first gain a better understanding of the role of matter in a lattice spacetime. We investigate consistent methods of incorporating matter into spacetime, and particularly focus on the role of spinors in Regge Calculus. Since spinors are fundamental to fermionic fields, this investigation is crucial in understanding fermionic coupling to discrete spacetime. Our focus is primarily on the geometric interpretation of the fields on the lattice geometry with a goal on understanding the dynamic coupling between the fields and the geometry.

A method for the geometric and densitometric standardization of intraoral radiographs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Duckworth, J.E.; Judy, P.F.; Goodson, J.M.

1983-07-01

The interpretation of dental radiographs for the diagnosis of periodontal disease conditions poses several difficulties. These include the inability to adequately reproduce the projection geometry and optical density of the exposures. In order to improve the ability to extract accurate quantitative information from a radiographic survey of periodontal status, a method was developed which provided for consistent reproduction of both geometric and densitometric exposure parameters. This technique employed vertical bitewing projections in holders customized to individual segments of the dentition. A copper stepwedge was designed to provide densitometric standardization, and wire markers were included to permit measurement of angular variation.more » In a series of 53 paired radiographs, measurement of alveolar crest heights was found to be reproducible within approximately 0.1 mm. This method provided a full mouth radiographic survey using seven films, each complete with internal standards suitable for computer-based image processing.« less