Scattering from Colloid-Polymer Conjugates with Excluded Volume Effect

DOE PAGES

Li, Xin; Sanchez-Diaz, Luis E.; Smith, Gregory Scott; ...

2015-01-13

This work presents scattering functions of conjugates consisting of a colloid particle and a self-avoiding polymer chain as a model for protein-polymer conjugates and nanoparticle-polymer conjugates in solution. The model is directly derived from the two-point correlation function with the inclusion of excluded volume effects. The dependence of the calculated scattering function on the geometric shape of the colloid and polymer stiffness is investigated. The model is able to describe the experimental scattering signature of the solutions of suspending hard particle-polymer conjugates and provide additional conformational information. This model explicitly elucidates the link between the global conformation of a conjugatemore » and the microstructure of its constituent components.« less

Geometric Error Analysis in Applied Calculus Problem Solving

ERIC Educational Resources Information Center

Usman, Ahmed Ibrahim

2017-01-01

The paper investigates geometric errors students made as they tried to use their basic geometric knowledge in the solution of the Applied Calculus Optimization Problem (ACOP). Inaccuracies related to the drawing of geometric diagrams (visualization skills) and those associated with the application of basic differentiation concepts into ACOP…

Geometric Approaches to Quadratic Equations from Other Times and Places.

ERIC Educational Resources Information Center

Allaire, Patricia R.; Bradley, Robert E.

2001-01-01

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

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

Novel solutions to low-frequency problems with geometrically designed beam-waveguide systems

NASA Technical Reports Server (NTRS)

Imbriale, W. A.; Esquivel, M. S.; Manshadi, F.

1995-01-01

The poor low-frequency performance of geometrically designed beam-waveguide (BWG) antennas is shown to be caused by the diffraction phase centers being far from the geometrical optics mirror focus, resulting in substantial spillover and defocusing loss. Two novel solutions are proposed: (1) reposition the mirrors to focus low frequencies and redesign the high frequencies to utilize the new mirror positions, and (2) redesign the input feed system to provide an optimum solution for the low frequency. A novel use of the conjugate phase-matching technique is utilized to design the optimum low-frequency feed system, and the new feed system has been implemented in the JPL research and development BWG as part of a dual S-/X-band (2.3 GHz/8.45 GHz) feed system. The new S-band feed system is shown to perform significantly better than the original geometrically designed system.

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.

Investigating the relation between the geometric properties of river basins and the filtering parameters for regional land hydrology applications using GRACE models

NASA Astrophysics Data System (ADS)

Piretzidis, Dimitrios; Sideris, Michael G.

2016-04-01

This study investigates the possibilities of local hydrology signal extraction using GRACE data and conventional filtering techniques. The impact of the basin shape has also been studied in order to derive empirical rules for tuning the GRACE filter parameters. GRACE CSR Release 05 monthly solutions were used from April 2002 to August 2015 (161 monthly solutions in total). SLR data were also used to replace the GRACE C2,0 coefficient, and a de-correlation filter with optimal parameters for CSR Release 05 data was applied to attenuate the correlation errors of monthly mass differences. For basins located at higher latitudes, the effect of Glacial Isostatic Adjustment (GIA) was taken into account using the ICE-6G model. The study focuses on three geometric properties, i.e., the area, the convexity and the width in the longitudinal direction, of 100 basins with global distribution. Two experiments have been performed. The first one deals with the determination of the Gaussian smoothing radius that minimizes the gaussianity of GRACE equivalent water height (EWH) over the selected basins. The EWH kurtosis was selected as a metric of gaussianity. The second experiment focuses on the derivation of the Gaussian smoothing radius that minimizes the RMS difference between GRACE data and a hydrology model. The GLDAS 1.0 Noah hydrology model was chosen, which shows good agreement with GRACE data according to previous studies. Early results show that there is an apparent relation between the geometric attributes of the basins examined and the Gaussian radius derived from the two experiments. The kurtosis analysis experiment tends to underestimate the optimal Gaussian radius, which is close to 200-300 km in many cases. Empirical rules for the selection of the Gaussian radius have been also developed for sub-regional scale basins.

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.

SIFT optimization and automation for matching images from multiple temporal sources

NASA Astrophysics Data System (ADS)

Castillo-Carrión, Sebastián; Guerrero-Ginel, José-Emilio

2017-05-01

Scale Invariant Feature Transformation (SIFT) was applied to extract tie-points from multiple source images. Although SIFT is reported to perform reliably under widely different radiometric and geometric conditions, using the default input parameters resulted in too few points being found. We found that the best solution was to focus on large features as these are more robust and not prone to scene changes over time, which constitutes a first approach to the automation of processes using mapping applications such as geometric correction, creation of orthophotos and 3D models generation. The optimization of five key SIFT parameters is proposed as a way of increasing the number of correct matches; the performance of SIFT is explored in different images and parameter values, finding optimization values which are corroborated using different validation imagery. The results show that the optimization model improves the performance of SIFT in correlating multitemporal images captured from different sources.

Unified nonlinear analysis for nonhomogeneous anisotropic beams with closed cross sections

NASA Technical Reports Server (NTRS)

Atilgan, Ali R.; Hodges, Dewey H.

1991-01-01

A unified methodology for geometrically nonlinear analysis of nonhomogeneous, anisotropic beams is presented. A 2D cross-sectional analysis and a nonlinear 1D global deformation analysis are derived from the common framework of a 3D, geometrically nonlinear theory of elasticity. The only restrictions are that the strain and local rotation are small compared to unity and that warping displacements are small relative to the cross-sectional dimensions. It is concluded that the warping solutions can be affected by large deformation and that this could alter the incremental stiffnes of the section. It is shown that sectional constants derived from the published, linear analysis can be used in the present nonlinear, 1D analysis governing the global deformation of the beam, which is based on intrinsic equations for nonlinear beam behavior. Excellent correlation is obtained with published experimental results for both isotropic and anisotropic beams undergoing large deflections.

Three dimensional magnetic solutions in massive gravity with (non)linear field

NASA Astrophysics Data System (ADS)

Hendi, S. H.; Eslam Panah, B.; Panahiyan, S.; Momennia, M.

2017-12-01

The Noble Prize in physics 2016 motivates one to study different aspects of topological properties and topological defects as their related objects. Considering the significant role of the topological defects (especially magnetic strings) in cosmology, here, we will investigate three dimensional horizonless magnetic solutions in the presence of two generalizations: massive gravity and nonlinear electromagnetic field. The effects of these two generalizations on properties of the solutions and their geometrical structure are investigated. The differences between de Sitter and anti de Sitter solutions are highlighted and conditions regarding the existence of phase transition in geometrical structure of the solutions are studied.

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 \

Geometric scaling behavior of the scattering amplitude for DIS with nuclei

NASA Astrophysics Data System (ADS)

Kormilitzin, Andrey; Levin, Eugene; Tapia, Sebastian

2011-12-01

The main question, that we answer in this paper, is whether the initial condition can influence on the geometric scaling behavior of the amplitude for DIS at high energy. We re-write the non-linear Balitsky-Kovchegov equation in the form which is useful for treating the interaction with nuclei. Using the simplified BFKL kernel, we find the analytical solution to this equation with the initial condition given by the McLerran-Venugopalan formula. This solution does not show the geometric scaling behavior of the amplitude deeply in the saturation region. On the other hand, the BFKL Pomeron calculus with the initial condition at x=1/mR given by the solution to Balitsky-Kovchegov equation, leads to the geometric scaling behavior. The McLerran-Venugopalan formula is the natural initial condition for the Color Glass Condensate (CGC) approach. Therefore, our result gives a possibility to check experimentally which approach: CGC or BFKL Pomeron calculus, is more satisfactory.

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

PubMed

Fu, Zhongtao; Yang, Wenyu; Yang, Zhen

2013-08-01

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

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.

New Geometric-distortion Solution for STIS FUV-MAMA

NASA Astrophysics Data System (ADS)

Sohn, S. Tony

2018-04-01

We derived a new geometric distortion solution for the STIS FUV-MAMA detector. To do this, positions of stars in 89 FUV-MAMA observations of NGC 6681 were compared to an astrometric standard catalog created using WFC3/UVIS imaging data to derive a fourth-order polynomial solution that transforms raw (x, y) positions to geometrically- corrected (x, y) positions. When compared to astrometric catalog positions, the FUV- MAMA position measurements based on the IDCTAB showed residuals with an RMS of ∼ 30 mas in each coordinate. Using the new IDCTAB, the RMS is reduced to ∼ 4 mas, or 0.16 FUV-MAMA pixels, in each coordinate. The updated IDCTAB is now being used in the HST STIS pipeline to process all STIS FUV-MAMA images.

Molecular origins of osmotic second virial coefficients of proteins.

PubMed Central

Neal, B L; Asthagiri, D; Lenhoff, A M

1998-01-01

The thermodynamic properties of protein solutions are determined by the molecular interactions involving both solvent and solute molecules. A quantitative understanding of the relationship would facilitate more systematic procedures for manipulating the properties in a process environment. In this work the molecular basis for the osmotic second virial coefficient, B22, is studied; osmotic effects are critical in membrane transport, and the value of B22 has also been shown to correlate with protein crystallization behavior. The calculations here account for steric, electrostatic, and short-range interactions, with the structural and functional anisotropy of the protein molecules explicitly accounted for. The orientational dependence of the protein interactions is seen to have a pronounced effect on the calculations; in particular, the relatively few protein-protein configurations in which the apposing surfaces display geometric complementarity contribute disproportionately strongly to B22. The importance of electrostatic interactions is also amplified in these high-complementarity configurations. The significance of molecular recognition in determining B22 can explain the correlation with crystallization behavior, and it suggests that alteration of local molecular geometry can help in manipulating protein solution behavior. The results also have implications for the role of protein interactions in biological self-organization. PMID:9788942

Spectral statistics of random geometric graphs

NASA Astrophysics Data System (ADS)

Dettmann, C. P.; Georgiou, O.; Knight, G.

2017-04-01

We use random matrix theory to study the spectrum of random geometric graphs, a fundamental model of spatial networks. Considering ensembles of random geometric graphs we look at short-range correlations in the level spacings of the spectrum via the nearest-neighbour and next-nearest-neighbour spacing distribution and long-range correlations via the spectral rigidity Δ3 statistic. These correlations in the level spacings give information about localisation of eigenvectors, level of community structure and the level of randomness within the networks. We find a parameter-dependent transition between Poisson and Gaussian orthogonal ensemble statistics. That is the spectral statistics of spatial random geometric graphs fits the universality of random matrix theory found in other models such as Erdős-Rényi, Barabási-Albert and Watts-Strogatz random graphs.

GGOS and the EOP - the key role of SLR for a stable estimation of highly accurate Earth orientation parameters

NASA Astrophysics Data System (ADS)

Bloßfeld, Mathis; Panzetta, Francesca; Müller, Horst; Gerstl, Michael

2016-04-01

The GGOS vision is to integrate geometric and gravimetric observation techniques to estimate consistent geodetic-geophysical parameters. In order to reach this goal, the common estimation of station coordinates, Stokes coefficients and Earth Orientation Parameters (EOP) is necessary. Satellite Laser Ranging (SLR) provides the ability to study correlations between the different parameter groups since the observed satellite orbit dynamics are sensitive to the above mentioned geodetic parameters. To decrease the correlations, SLR observations to multiple satellites have to be combined. In this paper, we compare the estimated EOP of (i) single satellite SLR solutions and (ii) multi-satellite SLR solutions. Therefore, we jointly estimate station coordinates, EOP, Stokes coefficients and orbit parameters using different satellite constellations. A special focus in this investigation is put on the de-correlation of different geodetic parameter groups due to the combination of SLR observations. Besides SLR observations to spherical satellites (commonly used), we discuss the impact of SLR observations to non-spherical satellites such as, e.g., the JASON-2 satellite. The goal of this study is to discuss the existing parameter interactions and to present a strategy how to obtain reliable estimates of station coordinates, EOP, orbit parameter and Stokes coefficients in one common adjustment. Thereby, the benefits of a multi-satellite SLR solution are evaluated.

Holographic duals of 3d S-fold CFTs

NASA Astrophysics Data System (ADS)

Assel, Benjamin; Tomasiello, Alessandro

2018-06-01

We construct non-geometric AdS4 solutions of IIB string theory where the fields in overlapping patches are glued by elements of the S-duality group. We obtain them by suitable quotients of compact and non-compact geometric solutions. The quotient procedure suggests CFT duals as quiver theories with links involving the so-called T [U( N)] theory. We test the validity of the non-geometric solutions (and of our proposed holographic duality) by computing the three-sphere partition function Z of the CFTs. A first class of solutions is obtained by an S-duality quotient of Janus-type non-compact solutions and is dual to 3d N=4 SCFTs; for these we manage to compute Z of the dual CFT at finite N, and it agrees perfectly with the supergravity result in the large N limit. A second class has five-branes, it is obtained by a Möbius-like S-quotient of ordinary compact solutions and is dual to 3d N=3 SCFTs. For these, Z agrees with the supergravity result if one chooses the limit carefully so that the effect of the fivebranes does not backreact on the entire geometry. Other limits suggest the existence of IIA duals.

Perceptual similarity and the neural correlates of geometrical illusions in human brain structure.

PubMed

Axelrod, Vadim; Schwarzkopf, D Samuel; Gilaie-Dotan, Sharon; Rees, Geraint

2017-01-09

Geometrical visual illusions are an intriguing phenomenon, in which subjective perception consistently misjudges the objective, physical properties of the visual stimulus. Prominent theoretical proposals have been advanced attempting to find common mechanisms across illusions. But empirically testing the similarity between illusions has been notoriously difficult because illusions have very different visual appearances. Here we overcome this difficulty by capitalizing on the variability of the illusory magnitude across participants. Fifty-nine healthy volunteers participated in the study that included measurement of individual illusion magnitude and structural MRI scanning. We tested the Muller-Lyer, Ebbinghaus, Ponzo, and vertical-horizontal geometrical illusions as well as a non-geometrical, contrast illusion. We found some degree of similarity in behavioral judgments of all tested geometrical illusions, but not between geometrical illusions and non-geometrical, contrast illusion. The highest similarity was found between Ebbinghaus and Muller-Lyer geometrical illusions. Furthermore, the magnitude of all geometrical illusions, and particularly the Ebbinghaus and Muller-Lyer illusions, correlated with local gray matter density in the parahippocampal cortex, but not in other brain areas. Our findings suggest that visuospatial integration and scene construction processes might partly mediate individual differences in geometric illusory perception. Overall, these findings contribute to a better understanding of the mechanisms behind geometrical illusions.

Small-on-large geometric anelasticity

PubMed Central

2016-01-01

In this paper, we are concerned with finding exact solutions for the stress fields of nonlinear solids with non-symmetric distributions of defects (or more generally finite eigenstrains) that are small perturbations of symmetric distributions of defects with known exact solutions. In the language of geometric mechanics, this corresponds to finding a deformation that is a result of a perturbation of the metric of the Riemannian material manifold. We present a general framework that can be used for a systematic analysis of this class of anelasticity problems. This geometric formulation can be thought of as a material analogue of the classical small-on-large theory in nonlinear elasticity. We use the present small-on-large anelasticity theory to find exact solutions for the stress fields of some non-symmetric distributions of screw dislocations in incompressible isotropic solids. PMID:27956887

Calculation of skin-stiffener interface stresses in stiffened composite panels

NASA Technical Reports Server (NTRS)

Cohen, David; Hyer, Michael W.

1987-01-01

A method for computing the skin-stiffener interface stresses in stiffened composite panels is developed. Both geometrically linear and nonlinear analyses are considered. Particular attention is given to the flange termination region where stresses are expected to exhibit unbounded characteristics. The method is based on a finite-element analysis and an elasticity solution. The finite-element analysis is standard, while the elasticity solution is based on an eigenvalue expansion of the stress functions. The eigenvalue expansion is assumed to be valid in the local flange termination region and is coupled with the finite-element analysis using collocation of stresses on the local region boundaries. Accuracy and convergence of the local elasticity solution are assessed using a geometrically linear analysis. Using this analysis procedure, the influence of geometric nonlinearities and stiffener parameters on the skin-stiffener interface stresses is evaluated.

Geometric calculus-based postulates for the derivation and extension of the Maxwell equations

NASA Astrophysics Data System (ADS)

McClellan, Gene E.

2012-09-01

Clifford analysis, particularly application of the geometric algebra of three-dimensional physical space and its associated geometric calculus, enables a compact formulation of Maxwell's electromagnetic (EM) equations from a set of physically relevant and mathematically pleasing postulates. This formulation results in a natural extension of the Maxwell equations yielding wave solutions in addition to the usual EM waves. These additional solutions do not contradict experiment and have three properties in common with the apparent properties of dark energy. These three properties are that the wave solutions 1) propagate at the speed of light, 2) do not interact with ordinary electric charges or currents, and 3) possess retrograde momentum. By retrograde momentum, we mean that the momentum carried by such a wave is directed oppositely to the direction of energy transport. A "gas" of such waves generates negative pressure.

Impact of nonlinear effective interactions on group field theory quantum gravity condensates

NASA Astrophysics Data System (ADS)

Pithis, Andreas G. A.; Sakellariadou, Mairi; Tomov, Petar

2016-09-01

We present the numerical analysis of effectively interacting group field theory models in the context of the group field theory quantum gravity condensate analog of the Gross-Pitaevskii equation for real Bose-Einstein condensates including combinatorially local interaction terms. Thus, we go beyond the usually considered construction for free models. More precisely, considering such interactions in a weak regime, we find solutions for which the expectation value of the number operator N is finite, as in the free case. When tuning the interaction to the strongly nonlinear regime, however, we obtain solutions for which N grows and eventually blows up, which is reminiscent of what one observes for real Bose-Einstein condensates, where a strong interaction regime can only be realized at high density. This behavior suggests the breakdown of the Bogoliubov ansatz for quantum gravity condensates and the need for non-Fock representations to describe the system when the condensate constituents are strongly correlated. Furthermore, we study the expectation values of certain geometric operators imported from loop quantum gravity in the free and interacting cases. In particular, computing solutions around the nontrivial minima of the interaction potentials, one finds, already in the weakly interacting case, a nonvanishing condensate population for which the spectra are dominated by the lowest nontrivial configuration of the quantum geometry. This result indicates that the condensate may indeed consist of many smallest building blocks giving rise to an effectively continuous geometry, thus suggesting the interpretation of the condensate phase to correspond to a geometric phase.

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.

Wafer-scale single-crystal perovskite patterned thin films based on geometrically-confined lateral crystal growth

PubMed Central

Lee, Lynn; Baek, Jangmi; Park, Kyung Sun; Lee, Yong-EunKoo; Shrestha, Nabeen K.; Sung, Myung M.

2017-01-01

We report a facile roll-printing method, geometrically confined lateral crystal growth, for the fabrication of large-scale, single-crystal CH3NH3PbI3 perovskite thin films. Geometrically confined lateral crystal growth is based on transfer of a perovskite ink solution via a patterned rolling mould to a heated substrate, where the solution crystallizes instantly with the immediate evaporation of the solvent. The striking feature of this method is that the instant crystallization of the feeding solution under geometrical confinement leads to the unidirectional lateral growth of single-crystal perovskites. Here, we fabricated single-crystal perovskites in the form of a patterned thin film (3 × 3 inch) with a high carrier mobility of 45.64 cm2 V−1 s−1. We also used these single-crystal perovskite thin films to construct solar cells with a lateral configuration. Their active-area power conversion efficiency shows a highest value of 4.83%, which exceeds the literature efficiency values of lateral perovskite solar cells. PMID:28691697

Homogenization Theory for the Prediction of Obstructed Solute Diffusivity in Macromolecular Solutions.

PubMed

Donovan, Preston; Chehreghanianzabi, Yasaman; Rathinam, Muruhan; Zustiak, Silviya Petrova

2016-01-01

The study of diffusion in macromolecular solutions is important in many biomedical applications such as separations, drug delivery, and cell encapsulation, and key for many biological processes such as protein assembly and interstitial transport. Not surprisingly, multiple models for the a-priori prediction of diffusion in macromolecular environments have been proposed. However, most models include parameters that are not readily measurable, are specific to the polymer-solute-solvent system, or are fitted and do not have a physical meaning. Here, for the first time, we develop a homogenization theory framework for the prediction of effective solute diffusivity in macromolecular environments based on physical parameters that are easily measurable and not specific to the macromolecule-solute-solvent system. Homogenization theory is useful for situations where knowledge of fine-scale parameters is used to predict bulk system behavior. As a first approximation, we focus on a model where the solute is subjected to obstructed diffusion via stationary spherical obstacles. We find that the homogenization theory results agree well with computationally more expensive Monte Carlo simulations. Moreover, the homogenization theory agrees with effective diffusivities of a solute in dilute and semi-dilute polymer solutions measured using fluorescence correlation spectroscopy. Lastly, we provide a mathematical formula for the effective diffusivity in terms of a non-dimensional and easily measurable geometric system parameter.

High frequency scattering from a thin lossless dielectric slab. M.S. Thesis

NASA Technical Reports Server (NTRS)

Burgener, K. W.

1979-01-01

A solution for scattering from a thin dielectric slab is developed based on geometrical optics and the geometrical theory of diffraction with the intention of developing a model for a windshield of a small private aircraft for incorporation in an aircraft antenna code. Results of the theory are compared with experimental measurements and moment method calculations showing good agreement. Application of the solution is also addressed.

Combined geometric and algebraic solutions for removal of bSSFP banding artifacts with performance comparisons.

PubMed

Hoff, Michael N; Andre, Jalal B; Xiang, Qing-San

2017-02-01

Balanced steady state free precession (bSSFP) imaging suffers from off-resonance artifacts such as signal modulation and banding. Solutions for removal of bSSFP off-resonance dependence are described and compared, and an optimal solution is proposed. An Algebraic Solution (AS) that complements a previously described Geometric Solution (GS) is derived from four phase-cycled bSSFP datasets. A composite Geometric-Algebraic Solution (GAS) is formed from a noise-variance-weighted average of the AS and GS images. Two simulations test the solutions over a range of parameters, and phantom and in vivo experiments are implemented. Image quality and performance of the GS, AS, and GAS are compared with the complex sum and a numerical parameter estimation algorithm. The parameter estimation algorithm, GS, AS, and GAS remove most banding and signal modulation in bSSFP imaging. The variable performance of the GS and AS on noisy data justifies generation of the GAS, which consistently provides the highest performance. The GAS is a robust technique for bSSFP signal demodulation that balances the regional efficacy of the GS and AS to remove banding, a feat not possible with prevalent techniques. Magn Reson Med 77:644-654, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.

Evaluation of solution procedures for material and/or geometrically nonlinear structural analysis by the direct stiffness method.

NASA Technical Reports Server (NTRS)

Stricklin, J. A.; Haisler, W. E.; Von Riesemann, W. A.

1972-01-01

This paper presents an assessment of the solution procedures available for the analysis of inelastic and/or large deflection structural behavior. A literature survey is given which summarized the contribution of other researchers in the analysis of structural problems exhibiting material nonlinearities and combined geometric-material nonlinearities. Attention is focused at evaluating the available computation and solution techniques. Each of the solution techniques is developed from a common equation of equilibrium in terms of pseudo forces. The solution procedures are applied to circular plates and shells of revolution in an attempt to compare and evaluate each with respect to computational accuracy, economy, and efficiency. Based on the numerical studies, observations and comments are made with regard to the accuracy and economy of each solution technique.

Application of geometric approximation to the CPMG experiment: Two- and three-site exchange.

PubMed

Chao, Fa-An; Byrd, R Andrew

2017-04-01

The Carr-Purcell-Meiboom-Gill (CPMG) experiment is one of the most classical and well-known relaxation dispersion experiments in NMR spectroscopy, and it has been successfully applied to characterize biologically relevant conformational dynamics in many cases. Although the data analysis of the CPMG experiment for the 2-site exchange model can be facilitated by analytical solutions, the data analysis in a more complex exchange model generally requires computationally-intensive numerical analysis. Recently, a powerful computational strategy, geometric approximation, has been proposed to provide approximate numerical solutions for the adiabatic relaxation dispersion experiments where analytical solutions are neither available nor feasible. Here, we demonstrate the general potential of geometric approximation by providing a data analysis solution of the CPMG experiment for both the traditional 2-site model and a linear 3-site exchange model. The approximate numerical solution deviates less than 0.5% from the numerical solution on average, and the new approach is computationally 60,000-fold more efficient than the numerical approach. Moreover, we find that accurate dynamic parameters can be determined in most cases, and, for a range of experimental conditions, the relaxation can be assumed to follow mono-exponential decay. The method is general and applicable to any CPMG RD experiment (e.g. N, C', C α , H α , etc.) The approach forms a foundation of building solution surfaces to analyze the CPMG experiment for different models of 3-site exchange. Thus, the geometric approximation is a general strategy to analyze relaxation dispersion data in any system (biological or chemical) if the appropriate library can be built in a physically meaningful domain. Published by Elsevier Inc.

A unified construction for the algebro-geometric quasiperiodic solutions of the Lotka-Volterra and relativistic Lotka-Volterra hierarchy

NASA Astrophysics Data System (ADS)

Zhao, Peng; Fan, Engui

2015-04-01

In this paper, a new type of integrable differential-difference hierarchy, namely, the generalized relativistic Lotka-Volterra (GRLV) hierarchy, is introduced. This hierarchy is closely related to Lotka-Volterra lattice and relativistic Lotka-Volterra lattice, which allows us to provide a unified and effective way to obtain some exact solutions for both the Lotka-Volterra hierarchy and the relativistic Lotka-Volterra hierarchy. In particular, we shall construct algebro-geometric quasiperiodic solutions for the LV hierarchy and the RLV hierarchy in a unified manner on the basis of the finite gap integration theory.

Magnetic solutions in Einstein-massive gravity with linear and nonlinear fields

NASA Astrophysics Data System (ADS)

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

2018-06-01

The solutions of U(1) gauge-gravity coupling is one of the interesting models for analyzing the semi-classical nature of spacetime. In this regard, different well-known singular and nonsingular solutions have been taken into account. The paper at hand investigates the geometrical properties of the magnetic solutions by considering Maxwell and power Maxwell invariant (PMI) nonlinear electromagnetic fields in the context of massive gravity. These solutions are free of curvature singularity, but have a conic one which leads to presence of deficit/surplus angle. The emphasize is on modifications that these generalizations impose on deficit angle which determine the total geometrical structure of the solutions, hence, physical/gravitational properties. It will be shown that depending on the background spacetime [being anti de Sitter (AdS) or de Sitter (dS)], these generalizations present different effects and modify the total structure of the solutions differently.

Iso-geometric analysis for neutron diffusion problems

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

Hall, S. K.; Eaton, M. D.; Williams, M. M. R.

Iso-geometric analysis can be viewed as a generalisation of the finite element method. It permits the exact representation of a wider range of geometries including conic sections. This is possible due to the use of concepts employed in computer-aided design. The underlying mathematical representations from computer-aided design are used to capture both the geometry and approximate the solution. In this paper the neutron diffusion equation is solved using iso-geometric analysis. The practical advantages are highlighted by looking at the problem of a circular fuel pin in a square moderator. For this problem the finite element method requires the geometry tomore » be approximated. This leads to errors in the shape and size of the interface between the fuel and the moderator. In contrast to this iso-geometric analysis allows the interface to be represented exactly. It is found that, due to a cancellation of errors, the finite element method converges more quickly than iso-geometric analysis for this problem. A fuel pin in a vacuum was then considered as this problem is highly sensitive to the leakage across the interface. In this case iso-geometric analysis greatly outperforms the finite element method. Due to the improvement in the representation of the geometry iso-geometric analysis can outperform traditional finite element methods. It is proposed that the use of iso-geometric analysis on neutron transport problems will allow deterministic solutions to be obtained for exact geometries. Something that is only currently possible with Monte Carlo techniques. (authors)« less

Analysis and correction of Landsat 4 and 5 Thematic Mapper Sensor Data

NASA Technical Reports Server (NTRS)

Bernstein, R.; Hanson, W. A.

1985-01-01

Procedures for the correction and registration and registration of Landsat TM image data are examined. The registration of Landsat-4 TM images of San Francisco to Landsat-5 TM images of the San Francisco using the interactive geometric correction program and the cross-correlation technique is described. The geometric correction program and cross-correlation results are presented. The corrections of the TM data to a map reference and to a cartographic database are discussed; geometric and cartographic analyses are applied to the registration results.

Inflationary solutions in the brane world and their geometrical interpretation

NASA Astrophysics Data System (ADS)

Khoury, Justin; Steinhardt, Paul J.; Waldram, Daniel

2001-05-01

We consider the cosmology of a pair of domain walls bounding a five-dimensional bulk space-time with a negative cosmological constant, in which the distance between the branes is not fixed in time. Although there are strong arguments to suggest that this distance should be stabilized in the present epoch, no such constraints exist for the early universe and thus non-static solutions might provide relevant inflationary scenarios. We find the general solution for the standard ansatz where the bulk is foliated by planar-symmetric hypersurfaces. We show that in all cases the bulk geometry is that of anti-de Sitter (AdS5) space. We then present a geometrical interpretation for the solutions as embeddings of two de Sitter (dS4) surfaces in AdS5, which provide a simple interpretation of the physical properties of the solutions. A notable feature explained in the analysis is that two-way communication between branes expanding away from one another is possible for a finite amount of time, after which communication can proceed in one direction only. The geometrical picture also shows that our class of solutions (and related solutions in the literature) is not completely general, contrary to some claims. We then derive the most general solution for two walls in AdS5. This includes novel cosmologies where the brane tensions are not constrained to have opposite signs. The construction naturally generalizes to arbitrary FRW cosmologies on the branes.

Development of solution techniques for nonlinear structural analysis

NASA Technical Reports Server (NTRS)

Vos, R. G.; Andrews, J. S.

1974-01-01

Nonlinear structural solution methods in the current research literature are classified according to order of the solution scheme, and it is shown that the analytical tools for these methods are uniformly derivable by perturbation techniques. A new perturbation formulation is developed for treating an arbitrary nonlinear material, in terms of a finite-difference generated stress-strain expansion. Nonlinear geometric effects are included in an explicit manner by appropriate definition of an applicable strain tensor. A new finite-element pilot computer program PANES (Program for Analysis of Nonlinear Equilibrium and Stability) is presented for treatment of problems involving material and geometric nonlinearities, as well as certain forms on nonconservative loading.

Homogenization Theory for the Prediction of Obstructed Solute Diffusivity in Macromolecular Solutions

PubMed Central

Donovan, Preston; Chehreghanianzabi, Yasaman; Rathinam, Muruhan; Zustiak, Silviya Petrova

2016-01-01

The study of diffusion in macromolecular solutions is important in many biomedical applications such as separations, drug delivery, and cell encapsulation, and key for many biological processes such as protein assembly and interstitial transport. Not surprisingly, multiple models for the a-priori prediction of diffusion in macromolecular environments have been proposed. However, most models include parameters that are not readily measurable, are specific to the polymer-solute-solvent system, or are fitted and do not have a physical meaning. Here, for the first time, we develop a homogenization theory framework for the prediction of effective solute diffusivity in macromolecular environments based on physical parameters that are easily measurable and not specific to the macromolecule-solute-solvent system. Homogenization theory is useful for situations where knowledge of fine-scale parameters is used to predict bulk system behavior. As a first approximation, we focus on a model where the solute is subjected to obstructed diffusion via stationary spherical obstacles. We find that the homogenization theory results agree well with computationally more expensive Monte Carlo simulations. Moreover, the homogenization theory agrees with effective diffusivities of a solute in dilute and semi-dilute polymer solutions measured using fluorescence correlation spectroscopy. Lastly, we provide a mathematical formula for the effective diffusivity in terms of a non-dimensional and easily measurable geometric system parameter. PMID:26731550

Gaussian geometric discord in terms of Hellinger distance

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

Suciu, Serban, E-mail: serban.suciu@theory.nipne.ro; Isar, Aurelian

2015-12-07

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

Analysis and testing of axial compression in imperfect slender truss struts

NASA Technical Reports Server (NTRS)

Lake, Mark S.; Georgiadis, Nicholas

1990-01-01

The axial compression of imperfect slender struts for large space structures is addressed. The load-shortening behavior of struts with initially imperfect shapes and eccentric compressive end loading is analyzed using linear beam-column theory and results are compared with geometrically nonlinear solutions to determine the applicability of linear analysis. A set of developmental aluminum clad graphite/epoxy struts sized for application to the Space Station Freedom truss are measured to determine their initial imperfection magnitude, load eccentricity, and cross sectional area and moment of inertia. Load-shortening curves are determined from axial compression tests of these specimens and are correlated with theoretical curves generated using linear analysis.

An Improved 360 Degree and Order Model of Venus Topography

NASA Technical Reports Server (NTRS)

Rappaport, Nicole J.; Konopliv, Alex S.; Kucinskas, Algis B.; Ford, Peter G.

1999-01-01

We present an improved 360 degree and order spherical harmonic solution for Venus' topography. The new model uses the most recent set of Venus altimetry data with spacecraft positions derived from a recent high resolution gravity model. Geometric analysis indicates that the offset between the center of mass and center of figure of Venus is about 10 times smaller than that for the Earth, the Moon, or Mars. Statistical analyses confirm that the RMS topography follows a power law over the central part of the spectrum. Compared to the previous topography model, the new model is more highly correlated with Venus' harmonic gravity field.

Graph cuts with invariant object-interaction priors: application to intervertebral disc segmentation.

PubMed

Ben Ayed, Ismail; Punithakumar, Kumaradevan; Garvin, Gregory; Romano, Walter; Li, Shuo

2011-01-01

This study investigates novel object-interaction priors for graph cut image segmentation with application to intervertebral disc delineation in magnetic resonance (MR) lumbar spine images. The algorithm optimizes an original cost function which constrains the solution with learned prior knowledge about the geometric interactions between different objects in the image. Based on a global measure of similarity between distributions, the proposed priors are intrinsically invariant with respect to translation and rotation. We further introduce a scale variable from which we derive an original fixed-point equation (FPE), thereby achieving scale-invariance with only few fast computations. The proposed priors relax the need of costly pose estimation (or registration) procedures and large training sets (we used a single subject for training), and can tolerate shape deformations, unlike template-based priors. Our formulation leads to an NP-hard problem which does not afford a form directly amenable to graph cut optimization. We proceeded to a relaxation of the problem via an auxiliary function, thereby obtaining a nearly real-time solution with few graph cuts. Quantitative evaluations over 60 intervertebral discs acquired from 10 subjects demonstrated that the proposed algorithm yields a high correlation with independent manual segmentations by an expert. We further demonstrate experimentally the invariance of the proposed geometric attributes. This supports the fact that a single subject is sufficient for training our algorithm, and confirms the relevance of the proposed priors to disc segmentation.

On the Geometrical Optics Approach in the Theory of Freely-Localized Microwave Gas Breakdown

NASA Astrophysics Data System (ADS)

Shapiro, Michael; Schaub, Samuel; Hummelt, Jason; Temkin, Richard; Semenov, Vladimir

2015-11-01

Large filamentary arrays of high pressure gas microwave breakdown have been experimentally studied at MIT using a 110 GHz, 1.5 MW pulsed gyrotron. The experiments have been modeled by other groups using numerical codes. The plasma density distribution in the filaments can be as well analytically calculated using the geometrical optics approach neglecting plasma diffusion. The field outside the filament is a solution of an inverse electromagnetic problem. The solutions are found for the cylindrical and spherical filaments and for the multi-layered planar filaments with a finite plasma density at the boundaries. We present new results of this theory showing a variety of filaments with complex shapes. The solutions for plasma density distribution are found with a zero plasma density at the boundary of the filament. Therefore, to solve the inverse problem within the geometrical optics approximation, it can be assumed that there is no reflection from the filament. The results of this research are useful for modeling future MIT experiments.

Thermodynamics of water structural reorganization due to geometric confinement

NASA Astrophysics Data System (ADS)

Stroberg, Wylie; Lichter, Seth

2015-03-01

Models of aqueous solvation have successfully quantified the behavior of water near convex bodies. However, many important processes occurring in aqueous solution involve interactions between solutes and surfaces with complicated non-convex geometries. Examples include the folding of proteins, hydrophobic association of solutes, ligand-receptor binding, and water confined within nanotubes and pores. For these geometries, models for solvation of convex bodies fail to account for the added interactions associated with structural confinement. Due to water's propensity to form networks of hydrogen bonds, small alterations to the confining geometry can induce large structural rearrangement within the water. We perform systematic Monte Carlo simulations of water confined to cylindrical cavities of varying aspect ratio to investigate how small geometric changes to the confining geometry may cause large changes to the structure and thermodynamic state of water. Using the Wang-Landau algorithm, we obtain free energies, enthalpies, entropies, and heat capacities across a broad range of temperatures, and show how these quantities are influenced by the structural rearrangement of water molecules due to geometric perturbations.

An E-plane analysis of aperture-matched horn antennas using the moment method and the uniform geometrical theory of diffraction

NASA Technical Reports Server (NTRS)

Heedy, D. J.; Burnside, W. D.

1984-01-01

The moment method and the uniform geometrical theory of diffraction are utilized to obtain two separate solutions for the E-plane field pattern of an aperture-matched horn antenna. This particular horn antenna consists of a standard pyramidal horn with the following modifications: a rolled edge section attached to the aperture edges and a curved throat section. The resulting geometry provides significantly better performance in terms of the pattern, impedance, and frequency characteristics than normally obtainable. The moment method is used to calculate the E-plane pattern and BSWR of the antenna. However, at higher frequencies, large amounts of computation time are required. The uniform geometrical theory of diffraction provides a quick and efficient high frequency solution for the E-plane field pattern. In fact, the uniform geometrical theory of diffraction may be used to initially design the antenna; then, the moment method may be applied to fine tune the design. This procedure has been successfully applied to a compact range feed design.

Interface Technology for Geometrically Nonlinear Analysis of Multiple Connected Subdomains

NASA Technical Reports Server (NTRS)

Ransom, Jonathan B.

1997-01-01

Interface technology for geometrically nonlinear analysis is presented and demonstrated. This technology is based on an interface element which makes use of a hybrid variational formulation to provide for compatibility between independently modeled connected subdomains. The interface element developed herein extends previous work to include geometric nonlinearity and to use standard linear and nonlinear solution procedures. Several benchmark nonlinear applications of the interface technology are presented and aspects of the implementation are discussed.

Geometrical analysis of the LiCN vibrational dynamics: a stability geometrical indicator.

PubMed

Vergel, A; Benito, R M; Losada, J C; Borondo, F

2014-02-01

The vibrational dynamics of the LiNC/LiCN molecular system is examined making use of the Riemannian geometry. Stability and chaoticity are analyzed, in this context, by means of the Jacobi-Levi-Civita equations, derived from the Jacobi metric, and its solutions. A dynamical indicator, called stability geometrical indicator, is introduced in order to ascertain the dynamical characteristics of stability and chaos in the molecule under study.

Surface matching for correlation of virtual models: Theory and application

NASA Technical Reports Server (NTRS)

Caracciolo, Roberto; Fanton, Francesco; Gasparetto, Alessandro

1994-01-01

Virtual reality can enable a robot user to off line generate and test in a virtual environment a sequence of operations to be executed by the robot in an assembly cell. Virtual models of objects are to be correlated to the real entities they represent by means of a suitable transformation. A solution to the correlation problem, which is basically a problem of 3-dimensional adjusting, has been found exploiting the surface matching theory. An iterative algorithm has been developed, which matches the geometric surface representing the shape of the virtual model of an object, with a set of points measured on the surface in the real world. A peculiar feature of the algorithm is to work also if there is no one-to-one correspondence between the measured points and those representing the surface model. Furthermore the problem of avoiding convergence to local minima is solved, by defining a starting point of states ensuring convergence to the global minimum. The developed algorithm has been tested by simulation. Finally, this paper proposes a specific application, i.e., correlating a robot cell, equipped for biomedical use with its virtual representation.

Models for determining the geometrical properties of halo coronal mass ejections

NASA Astrophysics Data System (ADS)

Zhao, X.; Liu, Y.

2005-12-01

To this day, the prediction of space weather effects near the Earth suffer from a fundamental problem: the necessary condition for determining whether or not and when a part of the huge interplanetary counterpart (ICME) of frontside halo coronal mass ejections (CMEs) is able to hit the Earth and generate goemagnetic storms, i.e., the real angular width, the propagation direction and speed of the CMEs, cannot be measured directly because of the unfavorable geometry. To inverse these geometrical and kinematical properties we have recently developed a few geometrical models, such as the cone model, the ice cream cone model, and the spherical cone model. The inversing solution of the cone model for the 12 may 1997 halo CME has been used as an input to the ENLIL model (a 3D MHD solar wind code) and successfully predicted the ICME near the Earth (Zhao, Plukett & Liu, 2002; Odstrcil, Riley & Zhao, 2004). After briefly describing the geometrical models this presentation will discuss: 1. What kind of halo CMEs can be inversed? 2. How to select the geometrical models given a specific halo CME? 3. Whether or not the inversing solution is unique?

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

NASA Technical Reports Server (NTRS)

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

1994-01-01

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

A NASTRAN primer for the analysis of rotating flexible blades

NASA Technical Reports Server (NTRS)

Lawrence, Charles; Aiello, Robert A.; Ernst, Michael A.; Mcgee, Oliver G.

1987-01-01

This primer provides documentation for using MSC NASTRAN in analyzing rotating flexible blades. The analysis of these blades includes geometrically nonlinear (large displacement) analysis under centrifugal loading, and frequency and mode shape (normal modes) determination. The geometrically nonlinear analysis using NASTRAN Solution sequence 64 is discussed along with the determination of frequencies and mode shapes using Solution Sequence 63. A sample problem with the complete NASTRAN input data is included. Items unique to rotating blade analyses, such as setting angle and centrifugal softening effects are emphasized.

Region-Based Prediction for Image Compression in the Cloud.

PubMed

Begaint, Jean; Thoreau, Dominique; Guillotel, Philippe; Guillemot, Christine

2018-04-01

Thanks to the increasing number of images stored in the cloud, external image similarities can be leveraged to efficiently compress images by exploiting inter-images correlations. In this paper, we propose a novel image prediction scheme for cloud storage. Unlike current state-of-the-art methods, we use a semi-local approach to exploit inter-image correlation. The reference image is first segmented into multiple planar regions determined from matched local features and super-pixels. The geometric and photometric disparities between the matched regions of the reference image and the current image are then compensated. Finally, multiple references are generated from the estimated compensation models and organized in a pseudo-sequence to differentially encode the input image using classical video coding tools. Experimental results demonstrate that the proposed approach yields significant rate-distortion performance improvements compared with the current image inter-coding solutions such as high efficiency video coding.

Improving OCD time to solution using Signal Response Metrology

NASA Astrophysics Data System (ADS)

Fang, Fang; Zhang, Xiaoxiao; Vaid, Alok; Pandev, Stilian; Sanko, Dimitry; Ramanathan, Vidya; Venkataraman, Kartik; Haupt, Ronny

2016-03-01

In recent technology nodes, advanced process and novel integration scheme have challenged the precision limits of conventional metrology; with critical dimensions (CD) of device reduce to sub-nanometer region. Optical metrology has proved its capability to precisely detect intricate details on the complex structures, however, conventional RCWA-based (rigorous coupled wave analysis) scatterometry has the limitations of long time-to-results and lack of flexibility to adapt to wide process variations. Signal Response Metrology (SRM) is a new metrology technique targeted to alleviate the consumption of engineering and computation resources by eliminating geometric/dispersion modeling and spectral simulation from the workflow. This is achieved by directly correlating the spectra acquired from a set of wafers with known process variations encoded. In SPIE 2015, we presented the results of SRM application in lithography metrology and control [1], accomplished the mission of setting up a new measurement recipe of focus/dose monitoring in hours. This work will demonstrate our recent field exploration of SRM implementation in 20nm technology and beyond, including focus metrology for scanner control; post etch geometric profile measurement, and actual device profile metrology.

Geometric Models for Collaborative Search and Filtering

ERIC Educational Resources Information Center

Bitton, Ephrat

2011-01-01

This dissertation explores the use of geometric and graphical models for a variety of information search and filtering applications. These models serve to provide an intuitive understanding of the problem domains and as well as computational efficiencies to our solution approaches. We begin by considering a search and rescue scenario where both…

Tackling Misconceptions in Geometrical Optics

ERIC Educational Resources Information Center

Ceuppens, S.; Deprez, J.; Dehaene, W.; De Cock, M.

2018-01-01

To improve the teaching and learning materials for a curriculum it is important to incorporate the findings from educational research. In light of this, we present creative exercises and experiments to elicit, confront and resolve misconceptions in geometrical optics. Since ray diagrams can be both the cause and the solution for many…

Numerical and experimental investigation of the bending response of thin-walled composite cylinders

NASA Technical Reports Server (NTRS)

Fuchs, J. P.; Hyer, M. W.; Starnes, J. H., Jr.

1993-01-01

A numerical and experimental investigation of the bending behavior of six eight-ply graphite-epoxy circular cylinders is presented. Bending is induced by applying a known end-rotation to each end of the cylinders, analogous to a beam in bending. The cylinders have a nominal radius of 6 inches, a length-to-radius ratio of 2 and 5, and a radius-to-thickness ratio of approximately 160. A (+/- 45/0/90)S quasi-isotropic layup and two orthotropic layups, (+/- 45/0 sub 2)S and (+/- 45/90 sub 2)S, are studied. A geometrically nonlinear special-purpose analysis, based on Donnell's nonlinear shell equations, is developed to study the prebuckling responses and gain insight into the effects of non-ideal boundary conditions and initial geometric imperfections. A geometrically nonlinear finite element analysis is utilized to compare with the prebuckling solutions of the special-purpose analysis and to study the buckling and post buckling responses of both geometrically perfect and imperfect cylinders. The imperfect cylinder geometries are represented by an analytical approximation of the measured shape imperfections. Extensive experimental data are obtained from quasi-static tests of the cylinders using a test fixture specifically designed for the present investigation. A description of the test fixture is included. The experimental data are compared to predictions for both perfect and imperfect cylinder geometries. Prebuckling results are presented in the form of displacement and strain profiles. Buckling end-rotations, moments, and strains are reported, and predicted mode shapes are presented. Observed and predicted moment vs. end-rotation relations, deflection patterns, and strain profiles are illustrated for the post buckling responses. It is found that a geometrically nonlinear boundary layer behavior characterizes the prebuckling responses. The boundary layer behavior is sensitive to laminate orthotropy, cylinder geometry, initial geometric imperfections, applied end-rotation, and non-ideal boundary conditions. Buckling end-rotations, strains, and moments are influenced by laminate orthotropy and initial geometric imperfections. Measured buckling results correlate well with predictions for the geometrically imperfect specimens. The postbuckling analyses predict equilibrium paths with a number of scallop-shaped branches that correspond to unique deflection patterns. The observed postbuckling deflection patterns and measured strain profiles show striking similarities to the predictions in some cases. Ultimate failure of the cylinders is attributed to an interlaminar shear failure mode along the nodal lines of the postbuckling deflection patterns.

Geometric measure of pairwise quantum discord for superpositions of multipartite generalized coherent states

NASA Astrophysics Data System (ADS)

Daoud, M.; Ahl Laamara, R.

2012-07-01

We give the explicit expressions of the pairwise quantum correlations present in superpositions of multipartite coherent states. A special attention is devoted to the evaluation of the geometric quantum discord. The dynamics of quantum correlations under a dephasing channel is analyzed. A comparison of geometric measure of quantum discord with that of concurrence shows that quantum discord in multipartite coherent states is more resilient to dissipative environments than is quantum entanglement. To illustrate our results, we consider some special superpositions of Weyl-Heisenberg, SU(2) and SU(1,1) coherent states which interpolate between Werner and Greenberger-Horne-Zeilinger states.

Transformations of asymptotically AdS hyperbolic initial data and associated geometric inequalities

NASA Astrophysics Data System (ADS)

Cha, Ye Sle; Khuri, Marcus

2018-01-01

We construct transformations which take asymptotically AdS hyperbolic initial data into asymptotically flat initial data, and which preserve relevant physical quantities. This is used to derive geometric inequalities in the asymptotically AdS hyperbolic setting from counterparts in the asymptotically flat realm, whenever a geometrically motivated system of elliptic equations admits a solution. The inequalities treated here relate mass, angular momentum, charge, and horizon area. Furthermore, new mass-angular momentum inequalities in this setting are conjectured and discussed.

Backscattering from a Gaussian distributed, perfectly conducting, rough surface

NASA Technical Reports Server (NTRS)

Brown, G. S.

1977-01-01

The problem of scattering by random surfaces possessing many scales of roughness is analyzed. The approach is applicable to bistatic scattering from dielectric surfaces, however, this specific analysis is restricted to backscattering from a perfectly conducting surface in order to more clearly illustrate the method. The surface is assumed to be Gaussian distributed so that the surface height can be split into large and small scale components, relative to the electromagnetic wavelength. A first order perturbation approach is employed wherein the scattering solution for the large scale structure is perturbed by the small scale diffraction effects. The scattering from the large scale structure is treated via geometrical optics techniques. The effect of the large scale surface structure is shown to be equivalent to a convolution in k-space of the height spectrum with the following: the shadowing function, a polarization and surface slope dependent function, and a Gaussian factor resulting from the unperturbed geometrical optics solution. This solution provides a continuous transition between the near normal incidence geometrical optics and wide angle Bragg scattering results.

Near-optimal strategies for sub-decimeter satellite tracking with GPS

NASA Technical Reports Server (NTRS)

Yunck, Thomas P.; Wu, Sien-Chong; Wu, Jiun-Tsong

1986-01-01

Decimeter tracking of low Earth orbiters using differential Global Positioning System (GPS) techniques is discussed. A precisely known global network of GPS ground receivers and a receiver aboard the user satellite are needed, and all techniques simultaneously estimate the user and GPS satellite orbits. Strategies include a purely geometric, a fully dynamic, and a hybrid strategy. The last combines dynamic GPS solutions with a geometric user solution. Two powerful extensions of the hybrid strategy show the most promise. The first uses an optimized synthesis of dynamics and geometry in the user solution, while the second uses a gravity adjustment method to exploit data from repeat ground tracks. These techniques promise to deliver subdecimeter accuracy down to the lowest satellite altitudes.

Monte Carlo simulation of portal dosimetry on a rectilinear voxel geometry: a variable gantry angle solution.

PubMed

Chin, P W; Spezi, E; Lewis, D G

2003-08-21

A software solution has been developed to carry out Monte Carlo simulations of portal dosimetry using the BEAMnrc/DOSXYZnrc code at oblique gantry angles. The solution is based on an integrated phantom, whereby the effect of incident beam obliquity was included using geometric transformations. Geometric transformations are accurate within +/- 1 mm and +/- 1 degrees with respect to exact values calculated using trigonometry. An application in portal image prediction of an inhomogeneous phantom demonstrated good agreement with measured data, where the root-mean-square of the difference was under 2% within the field. Thus, we achieved a dose model framework capable of handling arbitrary gantry angles, voxel-by-voxel phantom description and realistic particle transport throughout the geometry.

Geometric Series: A New Solution to the Dog Problem

ERIC Educational Resources Information Center

Dion, Peter; Ho, Anthony

2013-01-01

This article describes what is often referred to as the dog, beetle, mice, ant, or turtle problem. Solutions to this problem exist, some being variations of each other, which involve mathematics of a wide range of complexity. Herein, the authors describe the intuitive solution and the calculus solution and then offer a completely new solution…

Initial singularity and pure geometric field theories

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Initial Ship Design Using a Pearson Correlation Coefficient and Artificial Intelligence Techniques

NASA Astrophysics Data System (ADS)

Moon, Byung Young; Kim, Soo Young; Kang, Gyung Ju

In this paper we analyzed correlation between geometrical character and resistance, and effective horse power by using Pearson correlation coefficient which is one of the data mining methods. Also we made input data to ship's geometrical character which has strong correlation with output data. We calculated effective horse power and resistance by using Neuro-Fuzzy system. To verify the calculation, 9 of 11 container ships' data were improved as data of Neuro-Fuzzy system and the others were improved as verification data. After analyzing rate of error between existing data and calculation data, we concluded that calculation data have sound agreement with existing data.

Evolutionary Optimization of a Geometrically Refined Truss

NASA Technical Reports Server (NTRS)

Hull, P. V.; Tinker, M. L.; Dozier, G. V.

2007-01-01

Structural optimization is a field of research that has experienced noteworthy growth for many years. Researchers in this area have developed optimization tools to successfully design and model structures, typically minimizing mass while maintaining certain deflection and stress constraints. Numerous optimization studies have been performed to minimize mass, deflection, and stress on a benchmark cantilever truss problem. Predominantly traditional optimization theory is applied to this problem. The cross-sectional area of each member is optimized to minimize the aforementioned objectives. This Technical Publication (TP) presents a structural optimization technique that has been previously applied to compliant mechanism design. This technique demonstrates a method that combines topology optimization, geometric refinement, finite element analysis, and two forms of evolutionary computation: genetic algorithms and differential evolution to successfully optimize a benchmark structural optimization problem. A nontraditional solution to the benchmark problem is presented in this TP, specifically a geometrically refined topological solution. The design process begins with an alternate control mesh formulation, multilevel geometric smoothing operation, and an elastostatic structural analysis. The design process is wrapped in an evolutionary computing optimization toolset.

U(1)-invariant membranes: The geometric formulation, Abel, and pendulum differential equations

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

Zheltukhin, A. A.; Fysikum, AlbaNova, Stockholm University, 106 91 Stockholm; NORDITA, Roslagstullsbacken 23, 106 91 Stockholm

The geometric approach to study the dynamics of U(1)-invariant membranes is developed. The approach reveals an important role of the Abel nonlinear differential equation of the first type with variable coefficients depending on time and one of the membrane extendedness parameters. The general solution of the Abel equation is constructed. Exact solutions of the whole system of membrane equations in the D=5 Minkowski space-time are found and classified. It is shown that if the radial component of the membrane world vector is only time dependent, then the dynamics is described by the pendulum equation.

Polarimetry as a tool for the study of solutions of chiral solutes.

PubMed

Orlova, Anna V; Andrade, Renato R; da Silva, Clarissa O; Zinin, Alexander I; Kononov, Leonid O

2014-01-13

Optical rotation of aqueous solutions of D-levoglucosan was studied experimentally in the 0.03-4.0 mol L(-1) concentration range and a nonlinear concentration dependence of specific optical rotation (SR) was revealed. Discontinuities observed in the concentration plot of SR (at 0.1, 0.3, 0.5, 1.0, and 2.0 mol L(-1)) are well correlated with those found by static and dynamic light scattering and identify concentration ranges in which different solution domains (supramers) may exist. The average SR experimental value for a D-levoglucosan aqueous solution ([α]D(28) -58.5±8.7 deg dm(-1) cm(-3) g(-1)) was found to be in good agreement with values obtained by theoretical calculation (TD-DFT/GIAO) of SR for 15 different conformers revealed by conformational sampling at the PCM/B3LYP/6-311++G(2d,2p)//B3LYP/6-31+G(d,p) level, which were shown to be strongly affected by the solvation microenvironment (0, 1, 2, and 3 explicit solvent molecules considered) due to local geometrical changes induced in the solute molecule. This exceptionally high sensitivity of SR makes polarimetry a unique method capable of sensing changes in the structure of supramers detected in this study. Copyright © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Electrostatics in protein–protein docking

PubMed Central

Heifetz, Alexander; Katchalski-Katzir, Ephraim; Eisenstein, Miriam

2002-01-01

A novel geometric-electrostatic docking algorithm is presented, which tests and quantifies the electrostatic complementarity of the molecular surfaces together with the shape complementarity. We represent each molecule to be docked as a grid of complex numbers, storing information regarding the shape of the molecule in the real part and information regarding the electrostatic character of the molecule in the imaginary part. The electrostatic descriptors are derived from the electrostatic potential of the molecule. Thus, the electrostatic character of the molecule is represented as patches of positive, neutral, or negative values. The potential for each molecule is calculated only once and stored as potential spheres adequate for exhaustive rotation/translation scans. The geometric-electrostatic docking algorithm is applied to 17 systems, starting form the structures of the unbound molecules. The results—in terms of the complementarity scores of the nearly correct solutions, their ranking in the lists of sorted solutions, and their statistical uniqueness—are compared with those of geometric docking, showing that the inclusion of electrostatic complementarity in docking is very important, in particular in docking of unbound structures. Based on our results, we formulate several "good electrostatic docking rules": The geometric-electrostatic docking procedure is more successful than geometric docking when the potential patches are large and when the potential extends away from the molecular surface and protrudes into the solvent. In contrast, geometric docking is recommended when the electrostatic potential around the molecules to be docked appears homogenous, that is, with a similar sign all around the molecule. PMID:11847280

Geometric Mixing, Peristalsis, and the Geometric Phase of the Stomach.

PubMed

Arrieta, Jorge; Cartwright, Julyan H E; Gouillart, Emmanuelle; Piro, Nicolas; Piro, Oreste; Tuval, Idan

2015-01-01

Mixing fluid in a container at low Reynolds number--in an inertialess environment--is not a trivial task. Reciprocating motions merely lead to cycles of mixing and unmixing, so continuous rotation, as used in many technological applications, would appear to be necessary. However, there is another solution: movement of the walls in a cyclical fashion to introduce a geometric phase. We show using journal-bearing flow as a model that such geometric mixing is a general tool for using deformable boundaries that return to the same position to mix fluid at low Reynolds number. We then simulate a biological example: we show that mixing in the stomach functions because of the "belly phase," peristaltic movement of the walls in a cyclical fashion introduces a geometric phase that avoids unmixing.

Geometric Mixing, Peristalsis, and the Geometric Phase of the Stomach

PubMed Central

Arrieta, Jorge; Cartwright, Julyan H. E.; Gouillart, Emmanuelle; Piro, Nicolas; Piro, Oreste; Tuval, Idan

2015-01-01

Mixing fluid in a container at low Reynolds number— in an inertialess environment—is not a trivial task. Reciprocating motions merely lead to cycles of mixing and unmixing, so continuous rotation, as used in many technological applications, would appear to be necessary. However, there is another solution: movement of the walls in a cyclical fashion to introduce a geometric phase. We show using journal-bearing flow as a model that such geometric mixing is a general tool for using deformable boundaries that return to the same position to mix fluid at low Reynolds number. We then simulate a biological example: we show that mixing in the stomach functions because of the “belly phase,” peristaltic movement of the walls in a cyclical fashion introduces a geometric phase that avoids unmixing. PMID:26154384

Manifold Matching: Joint Optimization of Fidelity and Commensurability

DTIC Science & Technology

2011-11-12

identified separately in p◦m, will be geometrically incommensurate (see Figure 7). Thus the null distribution of the test statistic will be inflated...into the objective function obviates the geometric incommensurability phenomenon. Thus we can es- tablish that, for a range of Dirichlet product model...from the geometric incommensu- rability phenomenon. Then q p implies that cca suffers from the spurious correlation phe- nomenon with high probability

Distribution of geometric quantum discord in photon-added coherent states

NASA Astrophysics Data System (ADS)

Daoud, M.; Kaydi, W.; El Hadfi, H.

2015-12-01

In this paper, we examine the influence of photon excitation on the monogamy property of quantum discord in tripartite coherent states of Greenberger-Horne-Zeilinger (GHZ) type. The Hilbert-Schmidt norm is used as quantifier of pairwise quantum correlations. The geometric quantum discord in all bipartite subsystems are explicitly given. We show that the geometric discord is monogamous for any photon excitation order.

A Novel Multi-Scale Domain Overlapping CFD/STH Coupling Methodology for Multi-Dimensional Flows Relevant to Nuclear Applications

NASA Astrophysics Data System (ADS)

Grunloh, Timothy P.

The objective of this dissertation is to develop a 3-D domain-overlapping coupling method that leverages the superior flow field resolution of the Computational Fluid Dynamics (CFD) code STAR-CCM+ and the fast execution of the System Thermal Hydraulic (STH) code TRACE to efficiently and accurately model thermal hydraulic transport properties in nuclear power plants under complex conditions of regulatory and economic importance. The primary contribution is the novel Stabilized Inertial Domain Overlapping (SIDO) coupling method, which allows for on-the-fly correction of TRACE solutions for local pressures and velocity profiles inside multi-dimensional regions based on the results of the CFD simulation. The method is found to outperform the more frequently-used domain decomposition coupling methods. An STH code such as TRACE is designed to simulate large, diverse component networks, requiring simplifications to the fluid flow equations for reasonable execution times. Empirical correlations are therefore required for many sub-grid processes. The coarse grids used by TRACE diminish sensitivity to small scale geometric details such as Reactor Pressure Vessel (RPV) internals. A CFD code such as STAR-CCM+ uses much finer computational meshes that are sensitive to the geometric details of reactor internals. In turbulent flows, it is infeasible to fully resolve the flow solution, but the correlations used to model turbulence are at a low level. The CFD code can therefore resolve smaller scale flow processes. The development of a 3-D coupling method was carried out with the intention of improving predictive capabilities of transport properties in the downcomer and lower plenum regions of an RPV in reactor safety calculations. These regions are responsible for the multi-dimensional mixing effects that determine the distribution at the core inlet of quantities with reactivity implications, such as fluid temperature and dissolved neutron absorber concentration.

T -folds from Yang-Baxter deformations

NASA Astrophysics Data System (ADS)

Fernández-Melgarejo, José J.; Sakamoto, Jun-ichi; Sakatani, Yuho; Yoshida, Kentaroh

2017-12-01

Yang-Baxter (YB) deformations of type IIB string theory have been well studied from the viewpoint of classical integrability. Most of the works, however, are focused upon the local structure of the deformed geometries and the global structure still remains unclear. In this work, we reveal a non-geometric aspect of YB-deformed backgrounds as T -fold by explicitly showing the associated O( D, D; ℤ) T -duality monodromy. In particular, the appearance of an extra vector field in the generalized supergravity equations (GSE) leads to the non-geometric Q-flux. In addition, we study a particular solution of GSE that is obtained by a non-Abelian T-duality but cannot be expressed as a homogeneous YB deformation, and show that it can also be regarded as a T -fold. This result indicates that solutions of GSE should be non-geometric quite in general beyond the YB deformation.

Correlation, Cost Risk, and Geometry

NASA Technical Reports Server (NTRS)

Dean, Edwin B.

1992-01-01

The geometric viewpoint identifies the choice of a correlation matrix for the simulation of cost risk with the pairwise choice of data vectors corresponding to the parameters used to obtain cost risk. The correlation coefficient is the cosine of the angle between the data vectors after translation to an origin at the mean and normalization for magnitude. Thus correlation is equivalent to expressing the data in terms of a non orthogonal basis. To understand the many resulting phenomena requires the use of the tensor concept of raising the index to transform the measured and observed covariant components into contravariant components before vector addition can be applied. The geometric viewpoint also demonstrates that correlation and covariance are geometric properties, as opposed to purely statistical properties, of the variates. Thus, variates from different distributions may be correlated, as desired, after selection from independent distributions. By determining the principal components of the correlation matrix, variates with the desired mean, magnitude, and correlation can be generated through linear transforms which include the eigenvalues and the eigenvectors of the correlation matrix. The conversion of the data to a non orthogonal basis uses a compound linear transformation which distorts or stretches the data space. Hence, the correlated data does not have the same properties as the uncorrelated data used to generate it. This phenomena is responsible for seemingly strange observations such as the fact that the marginal distributions of the correlated data can be quite different from the distributions used to generate the data. The joint effect of statistical distributions and correlation remains a fertile area for further research. In terms of application to cost estimating, the geometric approach demonstrates that the estimator must have data and must understand that data in order to properly choose the correlation matrix appropriate for a given estimate. There is a general feeling by employers and managers that the field of cost requires little technical or mathematical background. Contrary to that opinion, this paper demonstrates that a background in mathematics equivalent to that needed for typical engineering and scientific disciplines at the masters or doctorate level is appropriate within the field of cost risk.

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.

Workshop rationale

NASA Technical Reports Server (NTRS)

Billingsley, F. C.

1982-01-01

The problems involved in processing remotely sensed data are defined within the contex of the total information system structure. The correlation of various data sets through georeferencing and cataloging is emphasized along with geometric rectification. The sources and types of possible geometric errors are outlined.

Characteristics of Problem Posing of Grade 9 Students on Geometric Tasks

ERIC Educational Resources Information Center

Chua, Puay Huat; Wong, Khoon Yoong

2012-01-01

This is an exploratory study into the individual problem-posing characteristics of 480 Grade 9 Singapore students who were novice problem posers working on two geometric tasks. The students were asked to pose a problem for their friends to solve. Analyses of solvable posed problems were based on the problem type, problem information, solution type…

The Geometrical Optics PSF with Third Order Aberrations

NASA Astrophysics Data System (ADS)

Díaz-Uribe, Rufino; Campos-García, Manuel

2008-04-01

In this paper the calculation of the GPSF from the Geometrical Optics Irradiance Law (GOIL) is recalled, including some details not found in other references. Also it is explored an alternative solution based on the Irradiance Transport Equation (ITE). Some simulations of images of an extended object produced by an image forming instrument affected by spherical aberration are shown.

Basic research and data analysis for the National Geodetic Satellite Program

NASA Technical Reports Server (NTRS)

1972-01-01

Investigations of triangulation nets and scaling are reported. Adjustment of the BC-4 worldwide geometric satellite triangulation net is described, along with procedures for correcting type II data and the contents of magnetic tapes containing data from the Pageos network. Computational steps for the further reduction of partially reduced satellite image plate coordinates are outlined. The problem of improving existing triangulation systems by means of satellite super-control points was studied. The SAO-69 geometric solution was scaled with C-band radar data, resulting in SAO and C-band adjustment compatible with one another in the Western Hemisphere. The North America solution NA-6, obtained from GEOS 1 data, was readjusted with new heights as constraints on all 30 optical stations and is referred to as the NA-8 solution.

Determination of Nonlinear Stiffness Coefficients for Finite Element Models with Application to the Random Vibration Problem

NASA Technical Reports Server (NTRS)

Muravyov, Alexander A.

1999-01-01

In this paper, a method for obtaining nonlinear stiffness coefficients in modal coordinates for geometrically nonlinear finite-element models is developed. The method requires application of a finite-element program with a geometrically non- linear static capability. The MSC/NASTRAN code is employed for this purpose. The equations of motion of a MDOF system are formulated in modal coordinates. A set of linear eigenvectors is used to approximate the solution of the nonlinear problem. The random vibration problem of the MDOF nonlinear system is then considered. The solutions obtained by application of two different versions of a stochastic linearization technique are compared with linear and exact (analytical) solutions in terms of root-mean-square (RMS) displacements and strains for a beam structure.

Scattering from a cylindrical reflector: modified theory of physical optics solution.

PubMed

Yalçin, Ugur

2007-02-01

The problem of scattering from a perfectly conducting cylindrical reflector is examined with the method of the modified theory of physical optics. In this technique the physical optics currents are modified by using a variable unit vector on the scatterer's surface. These current components are obtained for the reflector, which is fed by an offset electric line source. The scattering integral is expressed by using these currents and evaluated asymptotically with the stationary phase method. The results are compared numerically by using physical optics theory, geometrical optics diffraction theory, and the exact solution of the Helmholtz equation. It is found that the modified theory of physical optics scattering field equations agrees with the geometrical optics diffraction theory and the exact solution of the Helmholtz equation.

Geometric phase of mixed states for three-level open systems

NASA Astrophysics Data System (ADS)

Jiang, Yanyan; Ji, Y. H.; Xu, Hualan; Hu, Li-Yun; Wang, Z. S.; Chen, Z. Q.; Guo, L. P.

2010-12-01

Geometric phase of mixed state for three-level open system is defined by establishing in connecting density matrix with nonunit vector ray in a three-dimensional complex Hilbert space. Because the geometric phase depends only on the smooth curve on this space, it is formulated entirely in terms of geometric structures. Under the limiting of pure state, our approach is in agreement with the Berry phase, Pantcharatnam phase, and Aharonov and Anandan phase. We find that, furthermore, the Berry phase of mixed state correlated to population inversions of three-level open system.

Analytical pricing of geometric Asian power options on an underlying driven by a mixed fractional Brownian motion

NASA Astrophysics Data System (ADS)

Zhang, Wei-Guo; Li, Zhe; Liu, Yong-Jun

2018-01-01

In this paper, we study the pricing problem of the continuously monitored fixed and floating strike geometric Asian power options in a mixed fractional Brownian motion environment. First, we derive both closed-form solutions and mixed fractional partial differential equations for fixed and floating strike geometric Asian power options based on delta-hedging strategy and partial differential equation method. Second, we present the lower and upper bounds of the prices of fixed and floating strike geometric Asian power options under the assumption that both risk-free interest rate and volatility are interval numbers. Finally, numerical studies are performed to illustrate the performance of our proposed pricing model.

SAR Polarimetry

NASA Technical Reports Server (NTRS)

vanZyl, Jakob J.

2012-01-01

Radar Scattering includes: Surface Characteristics, Geometric Properties, Dielectric Properties, Rough Surface Scattering, Geometrical Optics and Small Perturbation Method Solutions, Integral Equation Method, Magellan Image of Pancake Domes on Venus, Dickinson Impact Crater on Venus (Magellan), Lakes on Titan (Cassini Radar, Longitudinal Dunes on Titan (Cassini Radar), Rough Surface Scattering: Effect of Dielectric Constant, Vegetation Scattering, Effect of Soil Moisture. Polarimetric Radar includes: Principles of Polarimetry: Field Descriptions, Wave Polarizations: Geometrical Representations, Definition of Ellipse Orientation Angles, Scatter as Polarization Transformer, Scattering Matrix, Coordinate Systems, Scattering Matrix, Covariance Matrix, Pauli Basis and Coherency Matrix, Polarization Synthesis, Polarimeter Implementation.

Optimisation of Fabric Reinforced Polymer Composites Using a Variant of Genetic Algorithm

NASA Astrophysics Data System (ADS)

Axinte, Andrei; Taranu, Nicolae; Bejan, Liliana; Hudisteanu, Iuliana

2017-12-01

Fabric reinforced polymeric composites are high performance materials with a rather complex fabric geometry. Therefore, modelling this type of material is a cumbersome task, especially when an efficient use is targeted. One of the most important issue of its design process is the optimisation of the individual laminae and of the laminated structure as a whole. In order to do that, a parametric model of the material has been defined, emphasising the many geometric variables needed to be correlated in the complex process of optimisation. The input parameters involved in this work, include: widths or heights of the tows and the laminate stacking sequence, which are discrete variables, while the gaps between adjacent tows and the height of the neat matrix are continuous variables. This work is one of the first attempts of using a Genetic Algorithm ( GA) to optimise the geometrical parameters of satin reinforced multi-layer composites. Given the mixed type of the input parameters involved, an original software called SOMGA (Satin Optimisation with a Modified Genetic Algorithm) has been conceived and utilised in this work. The main goal is to find the best possible solution to the problem of designing a composite material which is able to withstand to a given set of external, in-plane, loads. The optimisation process has been performed using a fitness function which can analyse and compare mechanical behaviour of different fabric reinforced composites, the results being correlated with the ultimate strains, which demonstrate the efficiency of the composite structure.

Comparison of two different Radiostereometric analysis (RSA) systems with markerless elementary geometrical shape modeling for the measurement of stem migration.

PubMed

Li, Ye; Röhrl, Stephan M; Bøe, B; Nordsletten, Lars

2014-09-01

Radiostereometric analysis (RSA) is the gold standard of measurement for in vivo 3D implants migration. The aim of this study was to evaluate the in vivo precision of 2 RSA marker-based systems compared with that of marker-free, elementary geometrical shape modeling RSA. Stem migration was measured in 50 patients recruited from an on-going Randomized Controlled Trial. We performed marker-based analysis with the Um RSA and RSAcore systems and compared these results with those of the elementary geometrical shape RSA. The precision for subsidence was 0.118 mm for Um RSA, 0.141 mm for RSAcore, and 0.136 mm for elementary geometrical shape RSA. The precision for retroversion was 1.3° for elementary geometrical shape RSA, approximately 2-fold greater than that for the other methods. The intraclass correlation coefficient between the marker-based systems and elementary geometrical shape RSA was approximately 0.5 for retroversion. All 3 methods yielded ICCs for subsidence and varus-valgus rotation above 0.9. We found an excellent correlation between marker-based RSA and elementary geometrical shape RSA for subsidence and varus-valgus rotation, independent of the system used. The precisions for out-of-plane migration were inferior for elementary geometrical shape RSA. Therefore, as a mechanism of failure, retroversion may be more difficult to detect early. This is to our knowledge the first study to compare different RSA systems with or without markers on the implant. Marker-based RSA has high precision in all planes, independent of the system used. Elementary geometrical shape RSA is inferior in out-of-plane migration. Copyright © 2014 Elsevier Ltd. All rights reserved.

Image processing via VLSI: A concept paper

NASA Technical Reports Server (NTRS)

Nathan, R.

1982-01-01

Implementing specific image processing algorithms via very large scale integrated systems offers a potent solution to the problem of handling high data rates. Two algorithms stand out as being particularly critical -- geometric map transformation and filtering or correlation. These two functions form the basis for data calibration, registration and mosaicking. VLSI presents itself as an inexpensive ancillary function to be added to almost any general purpose computer and if the geometry and filter algorithms are implemented in VLSI, the processing rate bottleneck would be significantly relieved. A set of image processing functions that limit present systems to deal with future throughput needs, translates these functions to algorithms, implements via VLSI technology and interfaces the hardware to a general purpose digital computer is developed.

Lie symmetry analysis and reduction for exact solution of (2+1)-dimensional Bogoyavlensky-Konopelchenko equation by geometric approach

NASA Astrophysics Data System (ADS)

Ray, S. Saha

2018-04-01

In this paper, the symmetry analysis and similarity reduction of the (2+1)-dimensional Bogoyavlensky-Konopelchenko (B-K) equation are investigated by means of the geometric approach of an invariance group, which is equivalent to the classical Lie symmetry method. Using the extended Harrison and Estabrook’s differential forms approach, the infinitesimal generators for (2+1)-dimensional B-K equation are obtained. Firstly, the vector field associated with the Lie group of transformation is derived. Then the symmetry reduction and the corresponding explicit exact solution of (2+1)-dimensional B-K equation is obtained.

Geometric actions for three-dimensional gravity

NASA Astrophysics Data System (ADS)

Barnich, G.; González, H. A.; Salgado-Rebolledo, P.

2018-01-01

The solution space of three-dimensional asymptotically anti-de Sitter or flat Einstein gravity is given by the coadjoint representation of two copies of the Virasoro group in the former and the centrally extended BMS3 group in the latter case. Dynamical actions that control these solution spaces are usually constructed by starting from the Chern–Simons formulation and imposing all boundary conditions. In this note, an alternative route is followed. We study in detail how to derive these actions from a group-theoretical viewpoint by constructing geometric actions for each of the coadjoint orbits, including the appropriate Hamiltonians. We briefly sketch relevant generalizations and potential applications beyond three-dimensional gravity.

Interpretation of solution scattering data from lipid nanodiscs

DOE PAGES

Graziano, Vito; Miller, Lisa; Yang, Lin

2018-02-01

The structural information contained in solution scattering data from empty lipid nanodiscs is examined in the context of a multi-component geometric model. X-ray scattering data were collected on nanodiscs of different compositions at scattering vector magnitudes up to 2.0 Å −1 . Through the calculation of the partial form factor for each of the nanodisc components before the isotropic average, structural parameters in the model were correlated to the features observed in the X-ray scattering data and to the corresponding distance distribution function. It is shown that, in general, the features at ∼0.3–0.6 Å −1 in the scattering data correlate to themore » bilayer structure. The data also support the argument that the elliptical shape of nanodiscs found in model fitting is physical, rather than an artefact due to the nanodisc size distribution. The lipid chain packing peak at ∼1.5 Å −1 is visible in the data and reflects the lipid bilayer phase transition. The shape change in the distance distribution function across the phase transition suggests that the nanodiscs are more circular in the fluid phase. The implication of these findings for model fitting of empty and protein-loaded nanodiscs is discussed.« less

Some Geometric Inequalities Relating to an Interior Point in Triangle

ERIC Educational Resources Information Center

Wu, Yu-Dong; Zhang, Zhi-Hua; Liang, Chun-Lei

2010-01-01

In this short note, by using one of Li and Liu's theorems [K.-H. Li, "The solution of CIQ. 39," "Commun. Stud. Inequal." 11(1) (2004), p. 162 (in Chinese)], "s-R-r" method, Cauchy's inequality and the theory of convex function, we solve some geometric inequalities conjectures relating to an interior point in triangle. (Contains 1 figure.)

Finsler-Geometric Continuum Mechanics

DTIC Science & Technology

2016-05-01

gravitation and astrophysical applications. Physical Review D. 1977;16:1643–1663. 50. Ozakin A, Yavari A. A geometric theory of thermal stresses...to physical problems of tensile fracture, shear localization, and cavitation in solid bodies. The pseudo-Finsler approach is demonstrated to be more...Weyl-type transformation of the fundamental tensor, analytical and numerical solutions of representative example problems offer new physical insight

Power Series Solution to the Pendulum Equation

ERIC Educational Resources Information Center

Benacka, Jan

2009-01-01

This note gives a power series solution to the pendulum equation that enables to investigate the system in an analytical way only, i.e. to avoid numeric methods. A method of determining the number of the terms for getting a required relative error is presented that uses bigger and lesser geometric series. The solution is suitable for modelling the…

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.

Fictitious spin-12 operators and correlations in quadrupole nuclear spin system

NASA Astrophysics Data System (ADS)

Furman, G. B.; Goren, S. D.; Meerovich, V. M.; Sokolovsky, V. L.

The Hamiltonian and the spin operators for a spin 3/2 are represented in the basis formed by the Kronecker productions of the 2×2 Pauli matrices. This reformulation allows us to represent a spin 3/2 as a system of two coupled fictitious spins 1/2. Correlations between these fictitious spins are studied using well-developed methods. We investigate the temperature and field dependences of correlations, such as mutual information, classical correlations, entanglement, and geometric and quantum discords in the fictitious spin-1/2 system describing a nuclear spin 3/2 which is placed in magnetic and inhomogeneous electric fields. It is shown that the correlations between the fictitious spins demonstrate properties which differ from those of real two-spin systems. In contrast to real systems all the correlations between the fictitious spins do not vanish with increasing external magnetic field; at a high magnetic field the correlations tend to their limiting values. Classical correlations, quantum and geometric discords reveal a pronounced asymmetry relative to the measurements on subsystems (fictitious spins) even in a uniform magnetic field and at symmetrical EFG, η=0. The correlations depend also on the distribution of external charges, on the parameter of symmetry η. At η≠0 quantum and geometric discords have finite values in a zero magnetic field. The proposed approach may be useful in analysis of properties of particles with larger angular momentum, can provide the way to discover new physical phenomenon of quantum correlations, and can be a useful tool for similar definitions of other physical quantities of complex systems.

Long-range correlations, geometrical structure, and transport properties of macromolecular solutions. The equivalence of configurational statistics and geometrodynamics of large molecules.

PubMed

Mezzasalma, Stefano A

2007-12-04

A special theory of Brownian relativity was previously proposed to describe the universal picture arising in ideal polymer solutions. In brief, it redefines a Gaussian macromolecule in a 4-dimensional diffusive spacetime, establishing a (weak) Lorentz-Poincaré invariance between liquid and polymer Einstein's laws for Brownian movement. Here, aimed at inquiring into the effect of correlations, we deepen the extension of the special theory to a general formulation. The previous statistical equivalence, for dynamic trajectories of liquid molecules and static configurations of macromolecules, and rather obvious in uncorrelated systems, is enlarged by a more general principle of equivalence, for configurational statistics and geometrodynamics. Accordingly, the three geodesic motion, continuity, and field equations could be rewritten, and a number of scaling behaviors were recovered in a spacetime endowed with general static isotropic metric (i.e., for equilibrium polymer solutions). We also dealt with universality in the volume fraction and, unexpectedly, found that a hyperscaling relation of the form, (average size) x (diffusivity) x (viscosity)1/2 ~f(N0, phi0) is fulfilled in several regimes, both in the chain monomer number (N) and polymer volume fraction (phi). Entangled macromolecular dynamics was treated as a geodesic light deflection, entaglements acting in close analogy to the field generated by a spherically symmetric mass source, where length fluctuations of the chain primitive path behave as azimuth fluctuations of its shape. Finally, the general transformation rule for translational and diffusive frames gives a coordinate gauge invariance, suggesting a widened Lorentz-Poincaré symmetry for Brownian statistics. We expect this approach to find effective applications to solutions of arbitrarily large molecules displaying a variety of structures, where the effect of geometry is more explicit and significant in itself (e.g., surfactants, lipids, proteins).

Complex Networks/Foundations of Information Systems

DTIC Science & Technology

2013-03-06

the benefit of feedback or dynamic correlations in coding and protocol. Using Renyi correlation analysis and entropy to model this wider class of...dynamic heterogeneous conditions. Lizhong Zheng, MIT Renyi Channel Correlation Analysis (connected to geometric curvature) Network Channel

Analysis of thin plates with holes by using exact geometrical representation within XFEM.

PubMed

Perumal, Logah; Tso, C P; Leng, Lim Thong

2016-05-01

This paper presents analysis of thin plates with holes within the context of XFEM. New integration techniques are developed for exact geometrical representation of the holes. Numerical and exact integration techniques are presented, with some limitations for the exact integration technique. Simulation results show that the proposed techniques help to reduce the solution error, due to the exact geometrical representation of the holes and utilization of appropriate quadrature rules. Discussion on minimum order of integration order needed to achieve good accuracy and convergence for the techniques presented in this work is also included.

Determination of formal redox potentials in aqueous solution of copper(II) complexes with ligands having nitrogen and oxygen donor atoms and comparison with their EPR and UV-Vis spectral features.

PubMed

Tabbì, Giovanni; Giuffrida, Alessandro; Bonomo, Raffaele P

2013-11-01

Formal redox potentials in aqueous solution were determined for copper(II) complexes with ligands having oxygen and nitrogen as donor atoms. All the chosen copper(II) complexes have well-known stereochemistries (pseudo-octahedral, square planar, square-based pyramidal, trigonal bipyramidal or tetrahedral) as witnessed by their reported spectroscopic, EPR and UV-visible (UV-Vis) features, so that a rough correlation between the measured redox potential and the typical geometrical arrangement of the copper(II) complex could be established. Negative values have been obtained for copper(II) complexes in tetragonally elongated pseudo-octahedral geometries, when measured against Ag/AgCl reference electrode. Copper(II) complexes in tetrahedral environments (or flattened tetrahedral geometries) show positive redox potential values. There is a region, always in the field of negative redox potentials which groups the copper(II) complexes exhibiting square-based pyramidal arrangements. Therefore, it is suggested that a measurement of the formal redox potential could be of great help, when some ambiguities might appear in the interpretation of spectroscopic (EPR and UV-Vis) data. Unfortunately, when the comparison is made between copper(II) complexes in square-based pyramidal geometries and those in square planar environments (or a pseudo-octahedral) a little perturbed by an equatorial tetrahedral distortion, their redox potentials could fall in the same intermediate region. In this case spectroscopic data have to be handled with great care in order to have an answer about a copper complex geometrical characteristics. © 2013.

Record statistics of financial time series and geometric random walks

NASA Astrophysics Data System (ADS)

Sabir, Behlool; Santhanam, M. S.

2014-09-01

The study of record statistics of correlated series in physics, such as random walks, is gaining momentum, and several analytical results have been obtained in the past few years. In this work, we study the record statistics of correlated empirical data for which random walk models have relevance. We obtain results for the records statistics of select stock market data and the geometric random walk, primarily through simulations. We show that the distribution of the age of records is a power law with the exponent α lying in the range 1.5≤α≤1.8. Further, the longest record ages follow the Fréchet distribution of extreme value theory. The records statistics of geometric random walk series is in good agreement with that obtained from empirical stock data.

Markov chain Monte Carlo techniques and spatial-temporal modelling for medical EIT.

PubMed

West, Robert M; Aykroyd, Robert G; Meng, Sha; Williams, Richard A

2004-02-01

Many imaging problems such as imaging with electrical impedance tomography (EIT) can be shown to be inverse problems: that is either there is no unique solution or the solution does not depend continuously on the data. As a consequence solution of inverse problems based on measured data alone is unstable, particularly if the mapping between the solution distribution and the measurements is also nonlinear as in EIT. To deliver a practical stable solution, it is necessary to make considerable use of prior information or regularization techniques. The role of a Bayesian approach is therefore of fundamental importance, especially when coupled with Markov chain Monte Carlo (MCMC) sampling to provide information about solution behaviour. Spatial smoothing is a commonly used approach to regularization. In the human thorax EIT example considered here nonlinearity increases the difficulty of imaging, using only boundary data, leading to reconstructions which are often rather too smooth. In particular, in medical imaging the resistivity distribution usually contains substantial jumps at the boundaries of different anatomical regions. With spatial smoothing these boundaries can be masked by blurring. This paper focuses on the medical application of EIT to monitor lung and cardiac function and uses explicit geometric information regarding anatomical structure and incorporates temporal correlation. Some simple properties are assumed known, or at least reliably estimated from separate studies, whereas others are estimated from the voltage measurements. This structural formulation will also allow direct estimation of clinically important quantities, such as ejection fraction and residual capacity, along with assessment of precision.

A geometric viewpoint on generalized hydrodynamics

NASA Astrophysics Data System (ADS)

Doyon, Benjamin; Spohn, Herbert; Yoshimura, Takato

2018-01-01

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

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

Geometrical ambiguity of pair statistics. II. Heterogeneous media

NASA Astrophysics Data System (ADS)

Jiao, Yang; Stillinger, Frank H.; Torquato, Salvatore

2010-07-01

In the first part of this series of two papers [Y. Jiao, F. H. Stillinger, and S. Torquato, Phys. Rev. E 81, 011105 (2010)10.1103/PhysRevE.81.011105], we considered the geometrical ambiguity of pair statistics associated with point configurations. Here we focus on the analogous problem for heterogeneous media (materials). Heterogeneous media are ubiquitous in a host of contexts, including composites and granular media, biological tissues, ecological patterns, and astrophysical structures. The complex structures of heterogeneous media are usually characterized via statistical descriptors, such as the n -point correlation function Sn . An intricate inverse problem of practical importance is to what extent a medium can be reconstructed from the two-point correlation function S2 of a target medium. Recently, general claims of the uniqueness of reconstructions using S2 have been made based on numerical studies, which implies that S2 suffices to uniquely determine the structure of a medium within certain numerical accuracy. In this paper, we provide a systematic approach to characterize the geometrical ambiguity of S2 for both continuous two-phase heterogeneous media and their digitized representations in a mathematically precise way. In particular, we derive the exact conditions for the case where two distinct media possess identical S2 , i.e., they form a degenerate pair. The degeneracy conditions are given in terms of integral and algebraic equations for continuous media and their digitized representations, respectively. By examining these equations and constructing their rigorous solutions for specific examples, we conclusively show that in general S2 is indeed not sufficient information to uniquely determine the structure of the medium, which is consistent with the results of our recent study on heterogeneous-media reconstruction [Y. Jiao, F. H. Stillinger, and S. Torquato, Proc. Natl. Acad. Sci. U.S.A. 106, 17634 (2009)10.1073/pnas.0905919106]. The analytical examples include complex patterns composed of building blocks bearing the letter “T” and the word “WATER” as well as degenerate stacking variants of the densest sphere packing in three dimensions (Barlow films). Several numerical examples of degeneracy (e.g., reconstructions of polycrystal microstructures, laser-speckle patterns and sphere packings) are also given, which are virtually exact solutions of the degeneracy equations. The uniqueness issue of multiphase media reconstructions and additional structural information required to characterize heterogeneous media are discussed, including two-point quantities that contain topological connectedness information about the phases.

Model of the vertical structure of the optical parameters of the Neptune atmosphere.

NASA Astrophysics Data System (ADS)

Morozhenko, A. V.

Analyzes the wavelength dependence of the geometric albedo of Neptune's disk and estimates some parameters of the planet's atmosphere by the method based on the determination of deviations of the vertical structure of the cloud layer from the homogeneity condition. The ratio between the methane and gas scale heights is found to be about 0.4. For the upper atmosphere, components of methane, aerosol, the mean geometric radius of particles, the turbulent mixing coefficient are determined. Two solutions were found for deeper atmospheric layers. The first one suggests a rather dense cloud; in the second solution the lower cloud layer is an extension of the upper aerosol layer.

A Geometrical Framework for Covariance Matrices of Continuous and Categorical Variables

ERIC Educational Resources Information Center

Vernizzi, Graziano; Nakai, Miki

2015-01-01

It is well known that a categorical random variable can be represented geometrically by a simplex. Accordingly, several measures of association between categorical variables have been proposed and discussed in the literature. Moreover, the standard definitions of covariance and correlation coefficient for continuous random variables have been…

A theoretical study of radar return and radiometric emission from the sea

NASA Technical Reports Server (NTRS)

Peake, W. H.

1972-01-01

The applicability of the various electromagnetic models of scattering from the ocean are reviewed. These models include the small perturbation method, the geometric optics solution, the composite model, and the exact integral equation solution. The restrictions on the electromagnetic models are discussed.

Computational mechanics analysis tools for parallel-vector supercomputers

NASA Technical Reports Server (NTRS)

Storaasli, O. O.; Nguyen, D. T.; Baddourah, M. A.; Qin, J.

1993-01-01

Computational algorithms for structural analysis on parallel-vector supercomputers are reviewed. These parallel algorithms, developed by the authors, are for the assembly of structural equations, 'out-of-core' strategies for linear equation solution, massively distributed-memory equation solution, unsymmetric equation solution, general eigen-solution, geometrically nonlinear finite element analysis, design sensitivity analysis for structural dynamics, optimization algorithm and domain decomposition. The source code for many of these algorithms is available from NASA Langley.

Research issues of geometry-based visual languages and some solutions

NASA Astrophysics Data System (ADS)

Green, Thorn G.

This dissertation addresses the problem of how to design visual language systems that are based upon Geometric Algebra, and provide a visual coupling of algebraic expressions and geometric depictions. This coupling of algebraic expressions and geometric depictions provides a new means for expressing both mathematical and geometric relationships present in mathematics, physics, and Computer-Aided Geometric Design (CAGD). Another significant feature of such a system is that the result of changing a parameter (by dragging the mouse) can be seen immediately in the depiction(s) of all expressions that use that parameter. This greatly aides the cognition of the relationships between variables. Systems for representing such a coupling of algebra and geometry have characteristics of both visual language systems, and systems for scientific visualization. Instead of using a parsing or dataflow paradigm for the visual language representation, the systems instead represent equations as manipulatible constrained diagrams for their visualization. This requires that the design of such a system have (but is not limited to) a means for parsing equations entered by the user, a scheme for producing a visual representation of these equations; techniques for maintaining the coupling between the expressions entered and the diagrams displayed; algorithms for maintaining the consistency of the diagrams; and, indexing capabilities that are efficient enough to allow diagrams to be created, and manipulated in a short enough period of time. The author proposes solutions for how such a design can be realized.

A numerical solution of Duffing's equations including the prediction of jump phenomena

NASA Technical Reports Server (NTRS)

Moyer, E. T., Jr.; Ghasghai-Abdi, E.

1987-01-01

Numerical methodology for the solution of Duffing's differential equation is presented. Algorithms for the prediction of multiple equilibrium solutions and jump phenomena are developed. In addition, a filtering algorithm for producing steady state solutions is presented. The problem of a rigidly clamped circular plate subjected to cosinusoidal pressure loading is solved using the developed algorithms (the plate is assumed to be in the geometrically nonlinear range). The results accurately predict regions of solution multiplicity and jump phenomena.

Identifying presence of correlated errors in GRACE monthly harmonic coefficients using machine learning algorithms

NASA Astrophysics Data System (ADS)

Piretzidis, Dimitrios; Sra, Gurveer; Karantaidis, George; Sideris, Michael G.

2017-04-01

A new method for identifying correlated errors in Gravity Recovery and Climate Experiment (GRACE) monthly harmonic coefficients has been developed and tested. Correlated errors are present in the differences between monthly GRACE solutions, and can be suppressed using a de-correlation filter. In principle, the de-correlation filter should be implemented only on coefficient series with correlated errors to avoid losing useful geophysical information. In previous studies, two main methods of implementing the de-correlation filter have been utilized. In the first one, the de-correlation filter is implemented starting from a specific minimum order until the maximum order of the monthly solution examined. In the second one, the de-correlation filter is implemented only on specific coefficient series, the selection of which is based on statistical testing. The method proposed in the present study exploits the capabilities of supervised machine learning algorithms such as neural networks and support vector machines (SVMs). The pattern of correlated errors can be described by several numerical and geometric features of the harmonic coefficient series. The features of extreme cases of both correlated and uncorrelated coefficients are extracted and used for the training of the machine learning algorithms. The trained machine learning algorithms are later used to identify correlated errors and provide the probability of a coefficient series to be correlated. Regarding SVMs algorithms, an extensive study is performed with various kernel functions in order to find the optimal training model for prediction. The selection of the optimal training model is based on the classification accuracy of the trained SVM algorithm on the same samples used for training. Results show excellent performance of all algorithms with a classification accuracy of 97% - 100% on a pre-selected set of training samples, both in the validation stage of the training procedure and in the subsequent use of the trained algorithms to classify independent coefficients. This accuracy is also confirmed by the external validation of the trained algorithms using the hydrology model GLDAS NOAH. The proposed method meet the requirement of identifying and de-correlating only coefficients with correlated errors. Also, there is no need of applying statistical testing or other techniques that require prior de-correlation of the harmonic coefficients.

Effect of the nozzle tip’s geometrical shape on electrospray deposition of organic thin films

NASA Astrophysics Data System (ADS)

Ueda, Hiroyuki; Takeuchi, Keita; Kikuchi, Akihiko

2017-04-01

Electrospray deposition (ESD) is a favorable wet fabrication technique for organic thin films. We investigated the effects of the nozzle tip’s geometrical shape on the spraying properties of an organic solution used for ESD. Five types of cylindrical metal nozzles with zero (flat end) to four protrusions at the tips were prepared for depositing a solution of a small-molecule compound, tris(8-hydroxyquinolinato)aluminum (Alq3) solution. We confirmed that the diameter of the deposited droplets and their size dispersion decreased with an increase in the number of protrusions. The area occupation ratio of small droplets with a diameter smaller than 2 µm increased from 21 to 83% as the number of protrusions was increased from zero to four. The surface roughness root mean square of 60-nm-thick Alq3 films substantially improved from 32.5 to 6.8 nm with increasing number of protrusions.

A solution to the surface intersection problem. [Boolean functions in geometric modeling

NASA Technical Reports Server (NTRS)

Timer, H. G.

1977-01-01

An application-independent geometric model within a data base framework should support the use of Boolean operators which allow the user to construct a complex model by appropriately combining a series of simple models. The use of these operators leads to the concept of implicitly and explicitly defined surfaces. With an explicitly defined model, the surface area may be computed by simply summing the surface areas of the bounding surfaces. For an implicitly defined model, the surface area computation must deal with active and inactive regions. Because the surface intersection problem involves four unknowns and its solution is a space curve, the parametric coordinates of each surface must be determined as a function of the arc length. Various subproblems involved in the general intersection problem are discussed, and the mathematical basis for their solution is presented along with a program written in FORTRAN IV for implementation on the IBM 370 TSO system.

Experimental verification of steerability via geometric Bell-like inequalities

NASA Astrophysics Data System (ADS)

Li, Jian; Wang, Cen-Yang; Liu, Tong-Jun; Wang, Qin

2018-03-01

Quantum steering is one form of quantum correlations interpolating between entanglement and Bell nonlocality, which in some cases can be detected by various steering inequalities. Recently, a remarkable and useful steerability criterion via geometric Bell-like inequalities was established [M. Zukowski, A. Dutta, and Z. Yin, Phys. Rev. A 91, 032107 (2015), 10.1103/PhysRevA.91.032107]. We report an experimental investigation of this steering criterion and verify the geometric Bell-like steering inequality experimentally by using of the Werner states. The results demonstrate that the geometric Bell-like steering inequality is a convenient tool to detect quantum steering both theoretically and practically.

An Analysis LANDSAT-4 Thematic Mapper Geometric Properties

NASA Technical Reports Server (NTRS)

Walker, R. E.; Zobrist, A. L.; Bryant, N. A.; Gokhman, B.; Friedman, S. Z.; Logan, T. L.

1984-01-01

LANDSAT Thematic Mapper P-data of Washington, D. C., Harrisburg, PA, and Salton Sea, CA are analyzed to determine magnitudes and causes of error in the geometric conformity of the data to known Earth surface geometry. Several tests of data geometry are performed. Intraband and interband correlation and registration are investigated, exclusive of map based ground truth. The magnitudes and statistical trends of pixel offsets between a single band's mirror scans (due to processing procedures) are computed, and the inter-band integrity of registration is analyzed. A line to line correlation analysis is included.

Optical rectification using geometrical field enhancement in gold nano-arrays

NASA Astrophysics Data System (ADS)

Piltan, S.; Sievenpiper, D.

2017-11-01

Conversion of photons to electrical energy has a wide variety of applications including imaging, solar energy harvesting, and IR detection. A rectenna device consists of an antenna in addition to a rectifying element to absorb the incident radiation within a certain frequency range. We designed, fabricated, and measured an optical rectifier taking advantage of asymmetrical field enhancement for forward and reverse currents due to geometrical constraints. The gold nano-structures as well as the geometrical parameters offer enhanced light-matter interaction at 382 THz. Using the Taylor expansion of the time-dependent current as a function of the external bias and oscillating optical excitation, we obtained responsivities close to quantum limit of operation. This geometrical approach can offer an efficient, broadband, and scalable solution for energy conversion and detection in the future.

Unstructured mesh methods for CFD

NASA Technical Reports Server (NTRS)

Peraire, J.; Morgan, K.; Peiro, J.

1990-01-01

Mesh generation methods for Computational Fluid Dynamics (CFD) are outlined. Geometric modeling is discussed. An advancing front method is described. Flow past a two engine Falcon aeroplane is studied. An algorithm and associated data structure called the alternating digital tree, which efficiently solves the geometric searching problem is described. The computation of an initial approximation to the steady state solution of a given poblem is described. Mesh generation for transient flows is described.

Sudden change of geometric quantum discord in finite temperature reservoirs

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

Hu, Ming-Liang, E-mail: mingliang0301@163.com; Sun, Jian

2015-03-15

We investigate sudden change (SC) behaviors of the distance-based measures of geometric quantum discords (GQDs) for two non-interacting qubits subject to the two-sided and the one-sided thermal reservoirs. We found that the GQDs defined by different distances exhibit different SCs, and thus the SCs are the combined result of the chosen discord measure and the property of a state. We also found that the thermal reservoir may generate states having different orderings related to different GQDs. These inherent differences of the GQDs reveal that they are incompatible in characterizing quantum correlations both quantitatively and qualitatively. - Highlights: • Comparable studymore » of different distance-based geometric quantum discords. • Evolution of the geometric quantum discords in finite temperature reservoirs. • Different geometric quantum discords exhibit distinct sudden changes. • Nonunique states ordering imposed by different geometric quantum discords.« less

Morphometric approach to thermodynamic quantities of solvation of complex molecules: Extension to multicomponent solvent

NASA Astrophysics Data System (ADS)

Kodama, Ryota; Roth, Roland; Harano, Yuichi; Kinoshita, Masahiro

2011-07-01

The morphometric approach (MA) is a powerful tool for calculating a solvation free energy (SFE) and related quantities of solvation thermodynamics of complex molecules. Here, we extend it to a solvent consisting of m components. In the integral equation theories, the SFE is expressed as the sum of m terms each of which comprises solute-component j correlation functions (j = 1, …, m). The MA is applied to each term in a formally separate manner: The term is expressed as a linear combination of the four geometric measures, excluded volume, solvent-accessible surface area, and integrated mean and Gaussian curvatures of the accessible surface, which are calculated for component j. The total number of the geometric measures or the coefficients in the linear combinations is 4m. The coefficients are determined in simple geometries, i.e., for spherical solutes with various diameters in the same multicomponent solvent. The SFE of the spherical solutes are calculated using the radial-symmetric integral equation theory. The extended version of the MA is illustrated for a protein modeled as a set of fused hard spheres immersed in a binary mixture of hard spheres. Several mixtures of different molecular-diameter ratios and compositions and 30 structures of the protein with a variety of radii of gyration are considered for the illustration purpose. The SFE calculated by the MA is compared with that by the direct application of the three-dimensional integral equation theory (3D-IET) to the protein. The deviations of the MA values from the 3D-IET values are less than 1.5%. The computation time required is over four orders of magnitude shorter than that in the 3D-IET. The MA thus developed is expected to be best suited to analyses concerning the effects of cosolvents such as urea on the structural stability of a protein.

A locus problem solved by using a mechanism with three dyads and two leading elements

NASA Astrophysics Data System (ADS)

Popescu, I.; Sass, L.; Romanescu, A. E.

2016-11-01

In Geometry there are many types of loci, solved by means of classic geometrical considerations and yielding lines and arcs of circles or conics. Yet more complicated locus can be solved by means of the Theory of Mechanisms. Our research starts from a locus and provides a solution based on the Theory of Mechanisms, finding the equivalent mechanism. The structural and cinematic analysis of the mechanism is made, determining the trajectory of a point representing the locus which presents interest. The mechanism has three dyads and two leading elements, for which the movements were correlated by means of a coefficient q. For various values of q different loci were obtained, similar for close values of q but different for significantly different values of q.

Molecular modeling of the process of reversible dissolution of the collagen protein under the action of tissue-clearing agents

NASA Astrophysics Data System (ADS)

Dvoretsky, K. N.; Berezin, K. V.; Chernavina, M. L.; Likhter, A. M.; Shagautdinova, I. T.; Antonova, E. M.; Rybakov, A. V.; Grechukhina, O. N.; Tuchin, V. V.

2018-04-01

The interaction of glycerol immersion agent with collagen mimetic peptide ((GPH)9)3 and a fragment of the microfibril 5((GPH)12)3 was studied by the classical molecular dynamics method using the GROMACS software. The change in geometric parameters of collagen α-chains at various concentrations of an aqueous solution of glycerol is analyzed. It is shown that these changes nonlinearly depend on the concentration and are limited to a certain level, which correlates with the experimental data on optical clearing efficiency of human skin. A hypothesis on the cause of the decreased efficiency of optical skin clearing at high immersion agent concentrations is put forward. The molecular mechanism of immersion optical clearing of biological tissues is discussed.

MIB Galerkin method for elliptic interface problems.

PubMed

Xia, Kelin; Zhan, Meng; Wei, Guo-Wei

2014-12-15

Material interfaces are omnipresent in the real-world structures and devices. Mathematical modeling of material interfaces often leads to elliptic partial differential equations (PDEs) with discontinuous coefficients and singular sources, which are commonly called elliptic interface problems. The development of high-order numerical schemes for elliptic interface problems has become a well defined field in applied and computational mathematics and attracted much attention in the past decades. Despite of significant advances, challenges remain in the construction of high-order schemes for nonsmooth interfaces, i.e., interfaces with geometric singularities, such as tips, cusps and sharp edges. The challenge of geometric singularities is amplified when they are associated with low solution regularities, e.g., tip-geometry effects in many fields. The present work introduces a matched interface and boundary (MIB) Galerkin method for solving two-dimensional (2D) elliptic PDEs with complex interfaces, geometric singularities and low solution regularities. The Cartesian grid based triangular elements are employed to avoid the time consuming mesh generation procedure. Consequently, the interface cuts through elements. To ensure the continuity of classic basis functions across the interface, two sets of overlapping elements, called MIB elements, are defined near the interface. As a result, differentiation can be computed near the interface as if there is no interface. Interpolation functions are constructed on MIB element spaces to smoothly extend function values across the interface. A set of lowest order interface jump conditions is enforced on the interface, which in turn, determines the interpolation functions. The performance of the proposed MIB Galerkin finite element method is validated by numerical experiments with a wide range of interface geometries, geometric singularities, low regularity solutions and grid resolutions. Extensive numerical studies confirm the designed second order convergence of the MIB Galerkin method in the L ∞ and L 2 errors. Some of the best results are obtained in the present work when the interface is C 1 or Lipschitz continuous and the solution is C 2 continuous.

New closed analytical solutions for geometrically thick fluid tori around black holes. Numerical evolution and the onset of the magneto-rotational instability

NASA Astrophysics Data System (ADS)

Witzany, V.; Jefremov, P.

2018-06-01

Context. When a black hole is accreting well below the Eddington rate, a geometrically thick, radiatively inefficient state of the accretion disk is established. There is a limited number of closed-form physical solutions for geometrically thick (nonselfgravitating) toroidal equilibria of perfect fluids orbiting a spinning black hole, and these are predominantly used as initial conditions for simulations of accretion in the aforementioned mode. However, different initial configurations might lead to different results and thus observational predictions drawn from such simulations. Aims: We aim to expand the known equilibria by a number of closed multiparametric solutions with various possibilities of rotation curves and geometric shapes. Then, we ask whether choosing these as initial conditions influences the onset of accretion and the asymptotic state of the disk. Methods: We have investigated a set of examples from the derived solutions in detail; we analytically estimate the growth of the magneto-rotational instability (MRI) from their rotation curves and evolve the analytically obtained tori using the 2D magneto-hydrodynamical code HARM. Properties of the evolutions are then studied through the mass, energy, and angular-momentum accretion rates. Results: The rotation curve has a decisive role in the numerical onset of accretion in accordance with our analytical MRI estimates: in the first few orbital periods, the average accretion rate is linearly proportional to the initial MRI rate in the toroids. The final state obtained from any initial condition within the studied class after an evolution of ten or more orbital periods is mostly qualitatively identical and the quantitative properties vary within a single order of magnitude. The average values of the energy of the accreted fluid have an irregular dependency on initial data, and in some cases fluid with energies many times its rest mass is systematically accreted.

Correlation Between Geometric Similarity of Ice Shapes and the Resulting Aerodynamic Performance Degradation: A Preliminary Investigation Using WIND

NASA Technical Reports Server (NTRS)

Wright, William B.; Chung, James

1999-01-01

Aerodynamic performance calculations were performed using WIND on ten experimental ice shapes and the corresponding ten ice shapes predicted by LEWICE 2.0. The resulting data for lift coefficient and drag coefficient are presented. The difference in aerodynamic results between the experimental ice shapes and the LEWICE ice shapes were compared to the quantitative difference in ice shape geometry presented in an earlier report. Correlations were generated to determine the geometric features which have the most effect on performance degradation. Results show that maximum lift and stall angle can be correlated to the upper horn angle and the leading edge minimum thickness. Drag coefficient can be correlated to the upper horn angle and the frequency-weighted average of the Fourier coefficients. Pitching moment correlated with the upper horn angle and to a much lesser extent to the upper and lower horn thicknesses.

Geometrical Optics of Dense Aerosols

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

Hay, Michael J.; Valeo, Ernest J.; Fisch, Nathaniel J.

2013-04-24

Assembling a free-standing, sharp-edged slab of homogeneous material that is much denser than gas, but much more rare ed than a solid, is an outstanding technological challenge. The solution may lie in focusing a dense aerosol to assume this geometry. However, whereas the geometrical optics of dilute aerosols is a well-developed fi eld, the dense aerosol limit is mostly unexplored. Yet controlling the geometrical optics of dense aerosols is necessary in preparing such a material slab. Focusing dense aerosols is shown here to be possible, but the nite particle density reduces the eff ective Stokes number of the flow, amore » critical result for controlled focusing. __________________________________________________« less

Geometrical optics of dense aerosols: forming dense plasma slabs.

PubMed

Hay, Michael J; Valeo, Ernest J; Fisch, Nathaniel J

2013-11-01

Assembling a freestanding, sharp-edged slab of homogeneous material that is much denser than gas, but much more rarefied than a solid, is an outstanding technological challenge. The solution may lie in focusing a dense aerosol to assume this geometry. However, whereas the geometrical optics of dilute aerosols is a well-developed field, the dense aerosol limit is mostly unexplored. Yet controlling the geometrical optics of dense aerosols is necessary in preparing such a material slab. Focusing dense aerosols is shown here to be possible, but the finite particle density reduces the effective Stokes number of the flow, a critical result for controlled focusing.

Geometric pumping in autophoretic channels.

PubMed

Michelin, Sébastien; Montenegro-Johnson, Thomas D; De Canio, Gabriele; Lobato-Dauzier, Nicolas; Lauga, Eric

2015-08-07

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

Geometric Integration of Weakly Dissipative Systems

NASA Astrophysics Data System (ADS)

Modin, K.; Führer, C.; Soöderlind, G.

2009-09-01

Some problems in mechanics, e.g. in bearing simulation, contain subsystems that are conservative as well as weakly dissipative subsystems. Our experience is that geometric integration methods are often superior for such systems, as long as the dissipation is weak. Here we develop adaptive methods for dissipative perturbations of Hamiltonian systems. The methods are "geometric" in the sense that the form of the dissipative perturbation is preserved. The methods are linearly explicit, i.e., they require the solution of a linear subsystem. We sketch an analysis in terms of backward error analysis and numerical comparisons with a conventional RK method of the same order is given.

A New Stochastic Equivalent Linearization Implementation for Prediction of Geometrically Nonlinear Vibrations

NASA Technical Reports Server (NTRS)

Muravyov, Alexander A.; Turner, Travis L.; Robinson, Jay H.; Rizzi, Stephen A.

1999-01-01

In this paper, the problem of random vibration of geometrically nonlinear MDOF structures is considered. The solutions obtained by application of two different versions of a stochastic linearization method are compared with exact (F-P-K) solutions. The formulation of a relatively new version of the stochastic linearization method (energy-based version) is generalized to the MDOF system case. Also, a new method for determination of nonlinear sti ness coefficients for MDOF structures is demonstrated. This method in combination with the equivalent linearization technique is implemented in a new computer program. Results in terms of root-mean-square (RMS) displacements obtained by using the new program and an existing in-house code are compared for two examples of beam-like structures.

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.

Indentation of a free-falling lance penetrometer into a poroelastic seabed

NASA Astrophysics Data System (ADS)

Elsworth, Derek; Lee, Dae Sung

2005-02-01

A solution is developed for the build-up, steady and post-arrest dissipative pore fluid pressure fields that develop around a blunt penetrometer that self-embeds from freefall into the seabed. Arrest from freefall considers deceleration under undrained conditions in a purely cohesive soil, with constant shear strength with depth. The resulting decelerating velocity field is controlled by soil strength, geometric bearing capacity factors, and inertial components. At low impact velocities the embedment process is controlled by soil strength, and at high velocities by inertia. With the deceleration defined, a solution is evaluated for a point normal dislocation penetrating in a poroelastic medium with a prescribed decelerating velocity. Dynamic steady pressures, PD, develop relative to the penetrating tip geometry with their distribution conditioned by the non-dimensional penetration rate, UD, incorporating impacting penetration rate, consolidation coefficient and penetrometer radius, and the non-dimensional strength, ND, additionally incorporating undrained shear strength of the sediment. Pore pressures develop to a steady peak magnitude at the penetrometer tip, and drop as PD=1/xD with distance xD behind the tip and along the shaft. Peak induced pressure magnitudes may be correlated with sediment permeabilities, post-arrest dissipation rates may be correlated with consolidation coefficients, and depths of penetration may be correlated with shear strengths. Together, these records enable strength and transport parameters to be recovered from lance penetrometer data. Penetrometer data recorded off La Palma in the Canary Islands (J. Volcanol. Geotherm. Res. 2000; 101:253) are used to recover permeabilities and consolidation coefficients from peak pressure and dissipation response, respectively. Copyright

Long-Range Rapidity Correlations in Heavy-Light Ion Collisions

NASA Astrophysics Data System (ADS)

Kovchegov, Yuri; Wertepny, Douglas

2013-04-01

We study two-particle long-range rapidity correlations arising in the early stages of heavy ion collisions in the saturation/Color Glass Condensate framework, assuming for simplicity that one colliding nucleus is much larger than the other. We calculate the two-gluon production cross section while including all-order saturation effects in the heavy nucleus with the lowest-order rescattering in the lighter nucleus. We find four types of correlations in the two-gluon production cross section: (i) geometric correlations, (ii) HBT correlations, (iii) back-to-back correlations, and (iv) near-side azimuthal correlations which are long-range in rapidity. The geometric correlations (i) are due to the fact that nucleons are correlated by simply being confined within the same nucleus and may lead to long-range rapidity correlations for the produced particles without strong azimuthal angle dependence. Somewhat surprisingly, long-range rapidity correlations (iii) and (iv) have exactly the same amplitudes along with azimuthal and rapidity shapes: one centered around δφ=π with the other one centered around δφ=0 (here δφ is the azimuthal angle between the two produced gluons). This prediction is in agreement with the recent ALICE p+Pb data.

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.

Computational mechanics analysis tools for parallel-vector supercomputers

NASA Technical Reports Server (NTRS)

Storaasli, Olaf O.; Nguyen, Duc T.; Baddourah, Majdi; Qin, Jiangning

1993-01-01

Computational algorithms for structural analysis on parallel-vector supercomputers are reviewed. These parallel algorithms, developed by the authors, are for the assembly of structural equations, 'out-of-core' strategies for linear equation solution, massively distributed-memory equation solution, unsymmetric equation solution, general eigensolution, geometrically nonlinear finite element analysis, design sensitivity analysis for structural dynamics, optimization search analysis and domain decomposition. The source code for many of these algorithms is available.

Euclid, Fibonacci, Sketchpad.

ERIC Educational Resources Information Center

Litchfield, Daniel C.; Goldenheim, David A.

1997-01-01

Describes the solution to a geometric problem by two ninth-grade mathematicians using The Geometer's Sketchpad computer software program. The problem was to divide any line segment into a regular partition of any number of parts, a variation on a problem by Euclid. The solution yielded two constructions, one a GLaD construction and the other using…

The Role of Multiple Solution Tasks in Developing Knowledge and Creativity in Geometry

ERIC Educational Resources Information Center

Levav-Waynberg, Anat; Leikin, Roza

2012-01-01

This paper describes changes in students' geometrical knowledge and their creativity associated with implementation of Multiple Solution Tasks (MSTs) in school geometry courses. Three hundred and three students from 14 geometry classes participated in the study, of whom 229 students from 11 classes learned in an experimental environment that…

Analysis and measurement of electromagnetic scattering by pyramidal and wedge absorbers

NASA Technical Reports Server (NTRS)

Dewitt, B. T.; Burnside, Walter D.

1986-01-01

By modifying the reflection coefficients in the Uniform Geometrical Theory of Diffraction a solution that approximates the scattering from a dielectric wedge is found. This solution agrees closely with the exact solution of Rawlins which is only valid for a few minor cases. This modification is then applied to the corner diffraction coefficient and combined with an equivalent current and geometrical optics solutions to model scattering from pyramid and wedge absorbers. Measured results from 12 inch pyramid absorbers from 2 to 18 GHz are compared to calculations assuming the returns add incoherently and assuming the returns add coherently. The measured results tend to be between the two curves. Measured results from the 8 inch wedge absorber are also compared to calculations with the return being dominated by the wedge diffraction. The procedures for measuring and specifying absorber performance are discussed and calibration equations are derived to calculate a reflection coefficient or a reflectivity using a reference sphere. Shaping changes to the present absorber designs are introduced to improve performance based on both high and low frequency analysis. Some prototypes were built and tested.

Numerical Algorithm for Delta of Asian Option

PubMed Central

Zhang, Boxiang; Yu, Yang; Wang, Weiguo

2015-01-01

We study the numerical solution of the Greeks of Asian options. In particular, we derive a close form solution of Δ of Asian geometric option and use this analytical form as a control to numerically calculate Δ of Asian arithmetic option, which is known to have no explicit close form solution. We implement our proposed numerical method and compare the standard error with other classical variance reduction methods. Our method provides an efficient solution to the hedging strategy with Asian options. PMID:26266271

Anisotropic solutions by gravitational decoupling

NASA Astrophysics Data System (ADS)

Ovalle, J.; Casadio, R.; da Rocha, R.; Sotomayor, A.

2018-02-01

We investigate the extension of isotropic interior solutions for static self-gravitating systems to include the effects of anisotropic spherically symmetric gravitational sources by means of the gravitational decoupling realised via the minimal geometric deformation approach. In particular, the matching conditions at the surface of the star with the outer Schwarzschild space-time are studied in great detail, and we describe how to generate, from a single physically acceptable isotropic solution, new families of anisotropic solutions whose physical acceptability is also inherited from their isotropic parent.

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.

Effects of geometrical frustration on ferromagnetism in the Hubbard model on the generalised Shastry-Sutherland lattice

NASA Astrophysics Data System (ADS)

Farkašovský, Pavol

2018-05-01

The small-cluster exact-diagonalization calculations and the projector quantum Monte Carlo method are used to examine the competing effects of geometrical frustration and interaction on ferromagnetism in the Hubbard model on the generalised Shastry-Sutherland lattice. It is shown that the geometrical frustration stabilizes the ferromagnetic state at high electron concentrations ( n ≳ 7/4), where strong correlations between ferromagnetism and the shape of the noninteracting density of states are observed. In particular, it is found that ferromagnetism is stabilized for these values of frustration parameters, which lead to the single-peaked noninterating density of states at the band edge. Once, two or more peaks appear in the noninteracting density of states at the band edge the ferromagnetic state is suppressed. This opens a new route towards the understanding of ferromagnetism in strongly correlated systems.

Mathematical Model Formulation And Validation Of Water And Solute Transport In Whole Hamster Pancreatic Islets

PubMed Central

Benson, Charles T.; Critser, John K.

2014-01-01

Optimization of cryopreservation protocols for cells and tissues requires accurate models of heat and mass transport. Model selection often depends on the configuration of the tissue. Here, a mathematical and conceptual model of water and solute transport for whole hamster pancreatic islets has been developed and experimentally validated incorporating fundamental biophysical data from previous studies on individual hamster islet cells while retaining whole-islet structural information. It describes coupled transport of water and solutes through the islet by three methods: intracellularly, intercellularly, and in combination. In particular we use domain decomposition techniques to couple a transmembrane flux model with an interstitial mass transfer model. The only significant undetermined variable is the cellular surface area which is in contact with the intercellularly transported solutes, Ais. The model was validated and Ais determined using a 3 × 3 factorial experimental design blocked for experimental day. Whole islet physical experiments were compared with model predictions at three temperatures, three perfusing solutions, and three islet size groups. A mean of 4.4 islets were compared at each of the 27 experimental conditions and found to correlate with a coefficient of determination of 0.87 ± 0.06 (mean ± S.D.). Only the treatment variable of perfusing solution was found to be significant (p < 0.05). We have devised a model that retains much of the intrinsic geometric configuration of the system, and thus fewer laboratory experiments are needed to determine model parameters and thus to develop new optimized cryopreservation protocols. Additionally, extensions to ovarian follicles and other concentric tissue structures may be made. PMID:24950195

CORRELATION OF FLORIDA SOIL-GAS PERMEABILITIES WITH GRAIN SIZE, MOISTURE, AND POROSITY

EPA Science Inventory

The report describes a new correlation or predicting gas permeabilities of undisturbed or recompacted soils from their average grain diameter (d), moisture saturation factor (m), and porosity (p). he correlation exhibits a geometric standard deviation (GSD) of only 1.27 between m...

Structure of dimethylphenyl betaine hydrochloride studied by X-ray diffraction, DFT calculation, NMR and FTIR spectra

NASA Astrophysics Data System (ADS)

Szafran, M.; Katrusiak, A.; Dega-Szafran, Z.; Kowalczyk, I.

2013-01-01

The structure of dimethylphenyl betaine hydrochloride (1) has been studied by X-ray diffraction, DFT calculations, NMR and FTIR spectra. The crystals are monoclinic, space group P21/c. In the crystal, the Cl- anion is connected with protonated betaine through the O-H⋯Cl- hydrogen bond of 2.943(2) Å. The structures in the gas phase (2) and water solution (3) have been optimized by the B3LYP/6-311++G(d,p) approach and the geometrical results have been compared with the X-ray data of 1. The FTIR spectrum of the solid compound is consistent with the X-ray results. The probable assignments of the anharmonic experimental vibrational frequencies of the investigated chloride (1) based on the calculated harmonic frequencies in water solution (3) are proposed. The correlations between the experimental 1H and 13C NMR chemical shifts (δexp) of 1 in D2O and the magnetic isotropic shielding constants (σcalc) calculated by the GIAO/B3LYP/6-311G++(d,p) approach, using the screening solvation model (COSMO), δexp = a + b σcalc, for optimized molecule 3 in water solution are linear and correctly reproduce the experimental chemical shifts.

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.

Interfaces and hydrophobic interactions in receptor-ligand systems: A level-set variational implicit solvent approach.

PubMed

Cheng, Li-Tien; Wang, Zhongming; Setny, Piotr; Dzubiella, Joachim; Li, Bo; McCammon, J Andrew

2009-10-14

A model nanometer-sized hydrophobic receptor-ligand system in aqueous solution is studied by the recently developed level-set variational implicit solvent model (VISM). This approach is compared to all-atom computer simulations. The simulations reveal complex hydration effects within the (concave) receptor pocket, sensitive to the distance of the (convex) approaching ligand. The ligand induces and controls an intermittent switching between dry and wet states of the hosting pocket, which determines the range and magnitude of the pocket-ligand attraction. In the level-set VISM, a geometric free-energy functional of all possible solute-solvent interfaces coupled to the local dispersion potential is minimized numerically. This approach captures the distinct metastable states that correspond to topologically different solute-solvent interfaces, and thereby reproduces the bimodal hydration behavior observed in the all-atom simulation. Geometrical singularities formed during the interface relaxation are found to contribute significantly to the energy barrier between different metastable states. While the hydration phenomena can thus be explained by capillary effects, the explicit inclusion of dispersion and curvature corrections seems to be essential for a quantitative description of hydrophobically confined systems on nanoscales. This study may shed more light onto the tight connection between geometric and energetic aspects of biomolecular hydration and may represent a valuable step toward the proper interpretation of experimental receptor-ligand binding rates.

Nonlocal symmetries and Bäcklund transformations for the self-dual Yang-Mills system

NASA Astrophysics Data System (ADS)

Papachristou, C. J.; Harrison, B. Kent

1988-01-01

The observation is made that generalized evolutionary isovectors of the self-dual Yang-Mills equation, obtained by ``verticalization'' of the geometrical isovectors derived in a previous paper [J. Math. Phys. 28, 1261 (1987)], generate Bäcklund transformations for the self-dual system. In particular, new Bäcklund transformations are obtained by ``verticalizing'' the generators of point transformations on the solution manifold. A geometric ansatz for the derivation of such (generally nonlocal) symmetries is proposed.

Toric Networks, Geometric R-Matrices and Generalized Discrete Toda Lattices

NASA Astrophysics Data System (ADS)

Inoue, Rei; Lam, Thomas; Pylyavskyy, Pavlo

2016-11-01

We use the combinatorics of toric networks and the double affine geometric R-matrix to define a three-parameter family of generalizations of the discrete Toda lattice. We construct the integrals of motion and a spectral map for this system. The family of commuting time evolutions arising from the action of the R-matrix is explicitly linearized on the Jacobian of the spectral curve. The solution to the initial value problem is constructed using Riemann theta functions.

Treatment of geometric singularities in implicit solvent models

NASA Astrophysics Data System (ADS)

Yu, Sining; Geng, Weihua; Wei, G. W.

2007-06-01

Geometric singularities, such as cusps and self-intersecting surfaces, are major obstacles to the accuracy, convergence, and stability of the numerical solution of the Poisson-Boltzmann (PB) equation. In earlier work, an interface technique based PB solver was developed using the matched interface and boundary (MIB) method, which explicitly enforces the flux jump condition at the solvent-solute interfaces and leads to highly accurate biomolecular electrostatics in continuum electric environments. However, such a PB solver, denoted as MIBPB-I, cannot maintain the designed second order convergence whenever there are geometric singularities, such as cusps and self-intersecting surfaces. Moreover, the matrix of the MIBPB-I is not optimally symmetrical, resulting in the convergence difficulty. The present work presents a new interface method based PB solver, denoted as MIBPB-II, to address the aforementioned problems. The present MIBPB-II solver is systematical and robust in treating geometric singularities and delivers second order convergence for arbitrarily complex molecular surfaces of proteins. A new procedure is introduced to make the MIBPB-II matrix optimally symmetrical and diagonally dominant. The MIBPB-II solver is extensively validated by the molecular surfaces of few-atom systems and a set of 24 proteins. Converged electrostatic potentials and solvation free energies are obtained at a coarse grid spacing of 0.5Å and are considerably more accurate than those obtained by the PBEQ and the APBS at finer grid spacings.

Using Differentials to Differentiate Trigonometric and Exponential Functions

ERIC Educational Resources Information Center

Dray, Tevian

2013-01-01

Starting from geometric definitions, we show how differentials can be used to differentiate trigonometric and exponential functions without limits, numerical estimates, solutions of differential equations, or integration.

Geometric phase in entangled systems: A single-neutron interferometer experiment

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

Sponar, S.; Klepp, J.; Loidl, R.

2010-04-15

The influence of the geometric phase on a Bell measurement, as proposed by Bertlmann et al. [Phys. Rev. A 69, 032112 (2004)] and expressed by the Clauser-Horne-Shimony-Holt (CHSH) inequality, has been observed for a spin-path-entangled neutron state in an interferometric setup. It is experimentally demonstrated that the effect of geometric phase can be balanced by a change in Bell angles. The geometric phase is acquired during a time-dependent interaction with a radiofrequency field. Two schemes, polar and azimuthal adjustment of the Bell angles, are realized and analyzed in detail. The former scheme yields a sinusoidal oscillation of the correlation functionmore » S, dependent on the geometric phase, such that it varies in the range between 2 and 2{radical}(2) and therefore always exceeds the boundary value 2 between quantum mechanic and noncontextual theories. The latter scheme results in a constant, maximal violation of the Bell-like CHSH inequality, where S remains 2{radical}(2) for all settings of the geometric phase.« less

Analytic Expression of Geometric Discord in Arbitrary Mixture of any Two Bi-qubit Product Pure States

NASA Astrophysics Data System (ADS)

Xie, Chuan-Mei; Liu, Yi-Min; Xing, Hang; Zhang, Zhan-Jun

2015-04-01

Quantum correlations in a family of states comprising any mixture of a pair of arbitrary bi-qubit product pure states are studied by employing geometric discord [Phys. Rev. Lett. 105 (2010) 190502] as the quantifier. First, the inherent symmetry in the family of states about local unitary transformations is revealed. Then, the analytic expression of geometric discords in the states is worked out. Some concrete discussions and analyses on the captured geometric discords are made so that their distinct features are exposed. It is found that, the more averagely the two bi-qubit product states are mixed, the bigger geometric discord the mixed state owns. Moreover, the monotonic relationships of geometric discord with different parameters are revealed. Supported by the National Natural Science Foundation of China (NNSFC) under Grant Nos. 11375011 and 11372122, the Natural Science Foundation of Anhui Province under Grant No. 1408085MA12, and the 211 Project of Anhui University

Cobalt adatoms on graphene: Effects of anisotropies on the correlated electronic structure

NASA Astrophysics Data System (ADS)

Mozara, R.; Valentyuk, M.; Krivenko, I.; Şaşıoǧlu, E.; Kolorenč, J.; Lichtenstein, A. I.

2018-02-01

Impurities on surfaces experience a geometric symmetry breaking induced not only by the on-site crystal-field splitting and the orbital-dependent hybridization, but also by different screening of the Coulomb interaction in different directions. We present a many-body study of the Anderson impurity model representing a Co adatom on graphene, taking into account all anisotropies of the effective Coulomb interaction, which we obtained by the constrained random-phase approximation. The most pronounced differences are naturally displayed by the many-body self-energy projected onto the single-particle states. For the solution of the Anderson impurity model and analytical continuation of the Matsubara data, we employed new implementations of the continuous-time hybridization expansion quantum Monte Carlo and the stochastic optimization method, and we verified the results in parallel with the exact diagonalization method.

An accurate nonlinear finite element analysis and test correlation of a stiffened composite wing panel

NASA Astrophysics Data System (ADS)

Davis, D. D., Jr.; Krishnamurthy, T.; Stroud, W. J.; McCleary, S. L.

1991-05-01

State-of-the-art nonlinear finite element analysis techniques are evaluated by applying them to a realistic aircraft structural component. A wing panel from the V-22 tiltrotor aircraft is chosen because it is a typical modern aircraft structural component for which there is experimental data for comparison of results. From blueprints and drawings, a very detailed finite element model containing 2284 9-node Assumed Natural-Coordinate Strain elements was generated. A novel solution strategy which accounts for geometric nonlinearity through the use of corotating element reference frames and nonlinear strain-displacement relations is used to analyze this detailed model. Results from linear analyses using the same finite element model are presented in order to illustrate the advantages and costs of the nonlinear analysis as compared with the more traditional linear analysis.

An accurate nonlinear finite element analysis and test correlation of a stiffened composite wing panel

NASA Technical Reports Server (NTRS)

Davis, D. D., Jr.; Krishnamurthy, T.; Stroud, W. J.; Mccleary, S. L.

1991-01-01

State-of-the-art nonlinear finite element analysis techniques are evaluated by applying them to a realistic aircraft structural component. A wing panel from the V-22 tiltrotor aircraft is chosen because it is a typical modern aircraft structural component for which there is experimental data for comparison of results. From blueprints and drawings, a very detailed finite element model containing 2284 9-node Assumed Natural-Coordinate Strain elements was generated. A novel solution strategy which accounts for geometric nonlinearity through the use of corotating element reference frames and nonlinear strain-displacement relations is used to analyze this detailed model. Results from linear analyses using the same finite element model are presented in order to illustrate the advantages and costs of the nonlinear analysis as compared with the more traditional linear analysis.

Graphical Solution of the Monic Quadratic Equation with Complex Coefficients

ERIC Educational Resources Information Center

Laine, A. D.

2015-01-01

There are many geometrical approaches to the solution of the quadratic equation with real coefficients. In this article it is shown that the monic quadratic equation with complex coefficients can also be solved graphically, by the intersection of two hyperbolas; one hyperbola being derived from the real part of the quadratic equation and one from…

Analysis of Formation Flying in Eccentric Orbits Using Linearized Equations of Relative Motion

NASA Technical Reports Server (NTRS)

Lane, Christopher; Axelrad, Penina

2004-01-01

Geometrical methods for formation flying design based on the analytical solution to Hill's equations have been previously developed and used to specify desired relative motions in near circular orbits. By generating relationships between the vehicles that are intuitive, these approaches offer valuable insight into the relative motion and allow for the rapid design of satellite configurations to achieve mission specific requirements, such as vehicle separation at perigee or apogee, minimum separation, or a specific geometrical shape. Furthermore, the results obtained using geometrical approaches can be used to better constrain numerical optimization methods; allowing those methods to converge to optimal satellite configurations faster. This paper presents a set of geometrical relationships for formations in eccentric orbits, where Hill.s equations are not valid, and shows how these relationships can be used to investigate formation designs and how they evolve with time.

Overset meshing coupled with hybridizable discontinuous Galerkin finite elements

DOE PAGES

Kauffman, Justin A.; Sheldon, Jason P.; Miller, Scott T.

2017-03-01

We introduce the use of hybridizable discontinuous Galerkin (HDG) finite element methods on overlapping (overset) meshes. Overset mesh methods are advantageous for solving problems on complex geometrical domains. We also combine geometric flexibility of overset methods with the advantages of HDG methods: arbitrarily high-order accuracy, reduced size of the global discrete problem, and the ability to solve elliptic, parabolic, and/or hyperbolic problems with a unified form of discretization. This approach to developing the ‘overset HDG’ method is to couple the global solution from one mesh to the local solution on the overset mesh. We present numerical examples for steady convection–diffusionmore » and static elasticity problems. The examples demonstrate optimal order convergence in all primal fields for an arbitrary amount of overlap of the underlying meshes.« less

Application of the trigonal curve to the Blaszak-Marciniak lattice hierarchy

NASA Astrophysics Data System (ADS)

Geng, Xianguo; Zeng, Xin

2017-01-01

We develop a method for constructing algebro-geometric solutions of the Blaszak-Marciniak ( BM) lattice hierarchy based on the theory of trigonal curves. We first derive the BM lattice hierarchy associated with a discrete (3×3)- matrix spectral problem using Lenard recurrence relations. Using the characteristic polynomial of the Lax matrix for the BM lattice hierarchy, we introduce a trigonal curve with two infinite points, which we use to establish the associated Dubrovin-type equations. We then study the asymptotic properties of the algebraic function carrying the data of the divisor and the Baker-Akhiezer function near the two infinite points on the trigonal curve. We finally obtain algebro-geometric solutions of the entire BM lattice hierarchy in terms of the Riemann theta function.

Algebro-geometric approach for a centrally extended Uq[sl(2|2)] R-matrix

NASA Astrophysics Data System (ADS)

Martins, M. J.

2017-04-01

In this paper we investigate the algebraic geometric nature of a solution of the Yang-Baxter equation based on the quantum deformation of the centrally extended sl (2 | 2) superalgebra proposed by Beisert and Koroteev [1]. We derive an alternative representation for the R-matrix in which the matrix elements are given in terms of rational functions depending on weights sited on a degree six surface. For generic gauge the weights geometry are governed by a genus one ruled surface while for a symmetric gauge choice the weights lie instead on a genus five curve. We have written down the polynomial identities satisfied by the R-matrix entries needed to uncover the corresponding geometric properties. For arbitrary gauge the R-matrix geometry is argued to be birational to the direct product CP1 ×CP1 × A where A is an Abelian surface. For the symmetric gauge we present evidences that the geometric content is that of a surface of general type lying on the so-called Severi line with irregularity two and geometric genus nine. We discuss potential geometric degenerations when the two free couplings are restricted to certain one-dimensional subspaces.

Multiscale geometric modeling of macromolecules II: Lagrangian representation

PubMed Central

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

2013-01-01

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

Heat transfer and flow friction correlations for perforated plate matrix heat exchangers

NASA Astrophysics Data System (ADS)

Ratna Raju, L.; Kumar, S. Sunil; Chowdhury, K.; Nandi, T. K.

2017-02-01

Perforated plate matrix heat exchangers (MHE) are constructed of high conductivity perforated plates stacked alternately with low conductivity spacers. They are being increasingly used in many cryogenic applications including Claude cycle or Reversed Brayton cycle cryo-refrigerators and liquefiers. Design of high NTU (number of (heat) transfer unit) cryogenic MHEs requires accurate heat transfer coefficient and flow friction factor. Thermo-hydraulic behaviour of perforated plates strongly depends on the geometrical parameters. Existing correlations, however, are mostly expressed as functions of Reynolds number only. This causes, for a given configuration, significant variations in coefficients from one correlation to the other. In this paper we present heat transfer and flow friction correlations as functions of all geometrical and other controlling variables. A FluentTM based numerical model has been developed for heat transfer and pressure drop studies over a stack of alternately arranged perforated plates and spacers. The model is validated with the data from literature. Generalized correlations are obtained through regression analysis over a large number of computed data.

LROC Stereo Observations

NASA Astrophysics Data System (ADS)

Beyer, Ross A.; Archinal, B.; Li, R.; Mattson, S.; Moratto, Z.; McEwen, A.; Oberst, J.; Robinson, M.

2009-09-01

The Lunar Reconnaissance Orbiter Camera (LROC) will obtain two types of multiple overlapping coverage to derive terrain models of the lunar surface. LROC has two Narrow Angle Cameras (NACs), working jointly to provide a wider (in the cross-track direction) field of view, as well as a Wide Angle Camera (WAC). LRO's orbit precesses, and the same target can be viewed at different solar azimuth and incidence angles providing the opportunity to acquire `photometric stereo' in addition to traditional `geometric stereo' data. Geometric stereo refers to images acquired by LROC with two observations at different times. They must have different emission angles to provide a stereo convergence angle such that the resultant images have enough parallax for a reasonable stereo solution. The lighting at the target must not be radically different. If shadows move substantially between observations, it is very difficult to correlate the images. The majority of NAC geometric stereo will be acquired with one nadir and one off-pointed image (20 degree roll). Alternatively, pairs can be obtained with two spacecraft rolls (one to the left and one to the right) providing a stereo convergence angle up to 40 degrees. Overlapping WAC images from adjacent orbits can be used to generate topography of near-global coverage at kilometer-scale effective spatial resolution. Photometric stereo refers to multiple-look observations of the same target under different lighting conditions. LROC will acquire at least three (ideally five) observations of a target. These observations should have near identical emission angles, but with varying solar azimuth and incidence angles. These types of images can be processed via various methods to derive single pixel resolution topography and surface albedo. The LROC team will produce some topographic models, but stereo data collection is focused on acquiring the highest quality data so that such models can be generated later.

FT-IR, FT-Raman, UV spectra and DFT calculations on monomeric and dimeric structure of 2-amino-5-bromobenzoic acid.

PubMed

Karabacak, Mehmet; Cinar, Mehmet

2012-02-01

In this work, the molecular conformation, vibrational and electronic transition analysis of 2-amino-5-bromobenzoic acid (2A5BrBA) were presented for the ground state using experimental techniques (FT-IR, FT-Raman and UV) and density functional theory (DFT) employing B3LYP exchange correlation with the 6-311++G(d,p) basis set. FT-IR and FT-Raman spectra were recorded in the regions of 400-4000 cm(-1) and 50-4000 cm(-1), respectively. There are four conformers, C1, C2, C3 and C4 for this molecule. The geometrical parameters, energies and wavenumbers have been obtained for all four conformers. The computational results diagnose the most stable conformer of 2A5BrBA as the C1 form. The complete assignments of fundamental vibrations were performed on the basis of the total energy distribution (TED) of the vibrational modes, calculated with scaled quantum mechanics (SQM) method. Raman activities calculated by DFT method have been converted to the corresponding Raman intensities using Raman scattering theory. The UV spectra of investigated compound were recorded in the region of 200-400 nm for ethanol and water solutions. The electronic properties were evaluated with help of time-dependent DFT (TD-DFT) theoretically and results were compared with experimental observations. The thermodynamic properties of the studied compound at different temperatures were calculated, revealing the correlations between standard heat capacity, standard entropy, standard enthalpy changes and temperatures. The observed and the calculated geometric parameters, vibrational wavenumbers and electronic transitions were compared with observed data and found to be in good agreement. Copyright © 2011 Elsevier B.V. All rights reserved.

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.

Probabilistically Perfect Cloning of Two Pure States: Geometric Approach.

PubMed

Yerokhin, V; Shehu, A; Feldman, E; Bagan, E; Bergou, J A

2016-05-20

We solve the long-standing problem of making n perfect clones from m copies of one of two known pure states with minimum failure probability in the general case where the known states have arbitrary a priori probabilities. The solution emerges from a geometric formulation of the problem. This formulation reveals that cloning converges to state discrimination followed by state preparation as the number of clones goes to infinity. The convergence exhibits a phenomenon analogous to a second-order symmetry-breaking phase transition.

Geometrical optimization of sensors for eddy currents nondestructive testing and evaluation

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

Thollon, F.; Burais, N.

1995-05-01

Design of Non Destructive Testing (NDT) and Non Destructive Evaluation (NDE) sensors is possible by solving Maxwell`s relations with FEM or BIM. But the large number of geometrical and electrical parameters of sensor and tested material implies many results that don`t give necessarily a well adapted sensor. The authors have used a genetic algorithm for automatic optimization. After having tested this algorithm with analytical solution of Maxwell`s relations for cladding thickness measurement, the method has been implemented in finite element package.

Geometrical E-beam proximity correction for raster scan systems

NASA Astrophysics Data System (ADS)

Belic, Nikola; Eisenmann, Hans; Hartmann, Hans; Waas, Thomas

1999-04-01

High pattern fidelity is a basic requirement for the generation of masks containing sub micro structures and for direct writing. Increasing needs mainly emerging from OPC at mask level and x-ray lithography require a correction of the e-beam proximity effect. The most part of e-beam writers are raster scan system. This paper describes a new method for geometrical pattern correction in order to provide a correction solution for e-beam system that are not able to apply variable doses.

Volumetric error modeling, identification and compensation based on screw theory for a large multi-axis propeller-measuring machine

NASA Astrophysics Data System (ADS)

Zhong, Xuemin; Liu, Hongqi; Mao, Xinyong; Li, Bin; He, Songping; Peng, Fangyu

2018-05-01

Large multi-axis propeller-measuring machines have two types of geometric error, position-independent geometric errors (PIGEs) and position-dependent geometric errors (PDGEs), which both have significant effects on the volumetric error of the measuring tool relative to the worktable. This paper focuses on modeling, identifying and compensating for the volumetric error of the measuring machine. A volumetric error model in the base coordinate system is established based on screw theory considering all the geometric errors. In order to fully identify all the geometric error parameters, a new method for systematic measurement and identification is proposed. All the PIGEs of adjacent axes and the six PDGEs of the linear axes are identified with a laser tracker using the proposed model. Finally, a volumetric error compensation strategy is presented and an inverse kinematic solution for compensation is proposed. The final measuring and compensation experiments have further verified the efficiency and effectiveness of the measuring and identification method, indicating that the method can be used in volumetric error compensation for large machine tools.

TWO-PHASE FORMATION IN SOLUTIONS OF TOBACCO MOSAIC VIRUS AND THE PROBLEM OF LONG-RANGE FORCES

PubMed Central

Oster, Gerald

1950-01-01

In a nearly salt-free medium, a dilute tobacco mosaic virus solution of rod-shaped virus particles of uniform length forms two phases; the bottom optically anisotropic phase has a greater virus concentration than has the top optically isotropic phase. For a sample containing particles of various lengths, the bottom phase contains longer particles than does the top and the concentrations top and bottom are nearly equal. The longer the particles the less the minimum concentration necessary for two-phase formation. Increasing the salt concentration increases the minimum concentration. The formation of two phases is explained in terms of geometrical considerations without recourse to the concept of long-range attractive forces. The minimum concentration for two-phase formation is that concentration at which correlation in orientation between the rod-shaped particles begins to take place. This concentration is determined by the thermodynamically effective size and shape of the particles as obtained from the concentration dependence of the osmotic pressure of the solutions measured by light scattering. The effective volume of the particles is introduced into the theory of Onsager for correlation of orientation of uniform size rods and good agreement with experiment is obtained. The theory is extended to a mixture of non-uniform size rods and to the case in which the salt concentration is varied, and agreement with experiment is obtained. The thermodynamically effective volume of the particles and its dependence on salt concentration are explained in terms of the shape of the particles and the electrostatic repulsion between them. Current theories of the hydration of proteins and of long-range forces are critically discussed. The bottom layer of freshly purified tobacco mosaic virus samples shows Bragg diffraction of visible light. The diffraction data indicate that the virus particles in solution form three-dimensional crystals approximately the size of crystalline inclusion bodies found in the cells of plants suffering from the disease. PMID:15422102

Various Solution Methods, Accompanied by Dynamic Investigation, for the Same Problem as a Means for Enriching the Mathematical Toolbox

ERIC Educational Resources Information Center

Oxman, Victor; Stupel, Moshe

2018-01-01

A geometrical task is presented with multiple solutions using different methods, in order to show the connection between various branches of mathematics and to highlight the importance of providing the students with an extensive 'mathematical toolbox'. Investigation of the property that appears in the task was carried out using a computerized tool.

Various solution methods, accompanied by dynamic investigation, for the same problem as a means for enriching the mathematical toolbox

NASA Astrophysics Data System (ADS)

Oxman, Victor; Stupel, Moshe

2018-04-01

A geometrical task is presented with multiple solutions using different methods, in order to show the connection between various branches of mathematics and to highlight the importance of providing the students with an extensive 'mathematical toolbox'. Investigation of the property that appears in the task was carried out using a computerized tool.

Helmholtz dark solitons.

PubMed

Chamorro-Posada, P; McDonald, G S

2003-05-15

A general dark-soliton solution of the Helmholtz equation (with defocusing Kerr nonlinearity) that has on- and off-axis, gray and black, paraxial and Helmholtz solitons as particular solutions, is reported. Modifications to soliton transverse velocity, width, phase period, and existence conditions are derived and explained in geometrical terms. Simulations verify analytical predictions and also demonstrate spontaneous formation of Helmholtz solitons and transparency of their interactions.

Deformation analysis of the unified lunar control networks

NASA Astrophysics Data System (ADS)

Iz, H. Bâki; Chen, Yong Qi; King, Bruce Anthony; Ding, Xiaoli; Wu, Chen

2009-12-01

This study compares the latest Unified Lunar Control Network, ULCN 2005, solution with the earlier ULCN 1994 solution at global and local scales. At the global scale, the relative rotation, translation, and deformation (normal strains and shears) parameters between the two networks are estimated as a whole using their colocated station Cartesian coordinate differences. At the local scale, the network station coordinate differences are examined in local topocentric coordinate systems whose origins are located at the geometric center of quadrangles and tetrahedrons. This study identified that the omission of the topography in the old ULCN solutions shifted the geometric center of the lunar figure up to 5 km in the lunar equatorial plane and induced a few hundred-meter level global rotations of the ULCN 1994 reference frame with respect to ULCN 2005. The displacements between the old and new control networks are less than ± 2 km on the average at the local scale, which behave like translations, caused by the omission of lunar topography in the earlier solution. The contribution of local rigid body rotations and dilatational and compressional components to the local displacements are approximately ± 100 m for a quadrangle/tetrahedron of an average side length of 10 km.

Interference effects in phased beam tracing using exact half-space solutions.

PubMed

Boucher, Matthew A; Pluymers, Bert; Desmet, Wim

2016-12-01

Geometrical acoustics provides a correct solution to the wave equation for rectangular rooms with rigid boundaries and is an accurate approximation at high frequencies with nearly hard walls. When interference effects are important, phased geometrical acoustics is employed in order to account for phase shifts due to propagation and reflection. Error increases, however, with more absorption, complex impedance values, grazing incidence, smaller volumes and lower frequencies. Replacing the plane wave reflection coefficient with a spherical one reduces the error but results in slower convergence. Frequency-dependent stopping criteria are then applied to avoid calculating higher order reflections for frequencies that have already converged. Exact half-space solutions are used to derive two additional spherical wave reflection coefficients: (i) the Sommerfeld integral, consisting of a plane wave decomposition of a point source and (ii) a line of image sources located at complex coordinates. Phased beam tracing using exact half-space solutions agrees well with the finite element method for rectangular rooms with absorbing boundaries, at low frequencies and for rooms with different aspect ratios. Results are accurate even for long source-to-receiver distances. Finally, the crossover frequency between the plane and spherical wave reflection coefficients is discussed.

A new approach for handling longitudinal count data with zero-inflation and overdispersion: poisson geometric process model.

PubMed

Wan, Wai-Yin; Chan, Jennifer S K

2009-08-01

For time series of count data, correlated measurements, clustering as well as excessive zeros occur simultaneously in biomedical applications. Ignoring such effects might contribute to misleading treatment outcomes. A generalized mixture Poisson geometric process (GMPGP) model and a zero-altered mixture Poisson geometric process (ZMPGP) model are developed from the geometric process model, which was originally developed for modelling positive continuous data and was extended to handle count data. These models are motivated by evaluating the trend development of new tumour counts for bladder cancer patients as well as by identifying useful covariates which affect the count level. The models are implemented using Bayesian method with Markov chain Monte Carlo (MCMC) algorithms and are assessed using deviance information criterion (DIC).

Mathematical model formulation and validation of water and solute transport in whole hamster pancreatic islets.

PubMed

Benson, James D; Benson, Charles T; Critser, John K

2014-08-01

Optimization of cryopreservation protocols for cells and tissues requires accurate models of heat and mass transport. Model selection often depends on the configuration of the tissue. Here, a mathematical and conceptual model of water and solute transport for whole hamster pancreatic islets has been developed and experimentally validated incorporating fundamental biophysical data from previous studies on individual hamster islet cells while retaining whole-islet structural information. It describes coupled transport of water and solutes through the islet by three methods: intracellularly, intercellularly, and in combination. In particular we use domain decomposition techniques to couple a transmembrane flux model with an interstitial mass transfer model. The only significant undetermined variable is the cellular surface area which is in contact with the intercellularly transported solutes, Ais. The model was validated and Ais determined using a 3×3 factorial experimental design blocked for experimental day. Whole islet physical experiments were compared with model predictions at three temperatures, three perfusing solutions, and three islet size groups. A mean of 4.4 islets were compared at each of the 27 experimental conditions and found to correlate with a coefficient of determination of 0.87±0.06 (mean ± SD). Only the treatment variable of perfusing solution was found to be significant (p<0.05). We have devised a model that retains much of the intrinsic geometric configuration of the system, and thus fewer laboratory experiments are needed to determine model parameters and thus to develop new optimized cryopreservation protocols. Additionally, extensions to ovarian follicles and other concentric tissue structures may be made. Copyright © 2014 Elsevier Inc. All rights reserved.

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.

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.

Geometric dimension model of virtual astronaut body for ergonomic analysis of man-machine space system

NASA Astrophysics Data System (ADS)

Qianxiang, Zhou

2012-07-01

It is very important to clarify the geometric characteristic of human body segment and constitute analysis model for ergonomic design and the application of ergonomic virtual human. The typical anthropometric data of 1122 Chinese men aged 20-35 years were collected using three-dimensional laser scanner for human body. According to the correlation between different parameters, curve fitting were made between seven trunk parameters and ten body parameters with the SPSS 16.0 software. It can be concluded that hip circumference and shoulder breadth are the most important parameters in the models and the two parameters have high correlation with the others parameters of human body. By comparison with the conventional regressive curves, the present regression equation with the seven trunk parameters is more accurate to forecast the geometric dimensions of head, neck, height and the four limbs with high precision. Therefore, it is greatly valuable for ergonomic design and analysis of man-machine system.This result will be very useful to astronaut body model analysis and application.

Revealing the correlation between real-space structure and chiral magnetic order at the atomic scale

NASA Astrophysics Data System (ADS)

Hauptmann, Nadine; Dupé, Melanie; Hung, Tzu-Chao; Lemmens, Alexander K.; Wegner, Daniel; Dupé, Bertrand; Khajetoorians, Alexander A.

2018-03-01

We image simultaneously the geometric, the electronic, and the magnetic structures of a buckled iron bilayer film that exhibits chiral magnetic order. We achieve this by combining spin-polarized scanning tunneling microscopy and magnetic exchange force microscopy (SPEX) to independently characterize the geometric as well as the electronic and magnetic structures of nonflat surfaces. This new SPEX imaging technique reveals the geometric height corrugation of the reconstruction lines resulting from strong strain relaxation in the bilayer, enabling the decomposition of the real-space from the electronic structure at the atomic level and the correlation with the resultant spin-spiral ground state. By additionally utilizing adatom manipulation, we reveal the chiral magnetic ground state of portions of the unit cell that were not previously imaged with spin-polarized scanning tunneling microscopy alone. Using density functional theory, we investigate the structural and electronic properties of the reconstructed bilayer and identify the favorable stoichiometry regime in agreement with our experimental result.

Precise orbit determination for NASA's earth observing system using GPS (Global Positioning System)

NASA Technical Reports Server (NTRS)

Williams, B. G.

1988-01-01

An application of a precision orbit determination technique for NASA's Earth Observing System (EOS) using the Global Positioning System (GPS) is described. This technique allows the geometric information from measurements of GPS carrier phase and P-code pseudo-range to be exploited while minimizing requirements for precision dynamical modeling. The method combines geometric and dynamic information to determine the spacecraft trajectory; the weight on the dynamic information is controlled by adjusting fictitious spacecraft accelerations in three dimensions which are treated as first order exponentially time correlated stochastic processes. By varying the time correlation and uncertainty of the stochastic accelerations, the technique can range from purely geometric to purely dynamic. Performance estimates for this technique as applied to the orbit geometry planned for the EOS platforms indicate that decimeter accuracies for EOS orbit position may be obtainable. The sensitivity of the predicted orbit uncertainties to model errors for station locations, nongravitational platform accelerations, and Earth gravity is also presented.

Boundary integral solutions for faults in flowing rock

NASA Astrophysics Data System (ADS)

Wei, Wei

We develop new boundary-integral solutions for faulting in viscous rock and implement solutions numerically with a boundary-element computer program, called Faux_Pas. In the solutions, large permanent rock deformations near faults are treated with velocity discontinuities within linear, incompressible, creeping, viscous flows. The faults may have zero strength or a finite strength that can be a constant or varying with deformation. Large deformations are achieved by integrating step by step with the fourth-order Runge-Kutta method. With this method, the boundaries and passive markers are updated dynamically. Faux_Pas has been applied to straight and curved elementary faults, and to listric and dish compound faults, composed of two or more elementary faults, such as listric faults and dish faults, all subjected to simple shear, shortening and lengthening. It reproduces the essential geometric elements seen in seismic profiles of fault-related folds associated with listric thrust faults in the Bighorn Basin of Wyoming, with dish faults in the Appalachians in Pennsylvania, Parry Islands of Canada and San Fernando Valley, California, and with listric normal faults in the Gulf of Mexico. Faux_Pas also predicts that some of these fault-related structures will include fascinating minor folds, especially in the footwall of the fault, that have been recognized earlier but have not been known to be related to the faulting. Some of these minor folds are potential structural traps. Faux_Pas is superior in several respects to current geometric techniques of balancing profiles, such as the "fault-bend fold" construction. With Faux_Pas, both the hanging wall and footwall are deformable, the faults are mechanical features, the cross sections are automatically balanced and, most important, the solutions are based on the first principles of mechanics. With the geometric techniques, folds are drawn only in the hanging wall, the faults are simply lines, the cross sections are arbitrarily balanced and, most important, the drawings are based on unsubstantiated rules of thumb. Faux_Pas provides the first rational tool for the study of fault-related folds.

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

Analysis of Dynamic Geometric Configuration of the Aortic Channel from the Perspective of Tornado-Like Flow Organization of Blood Flow.

PubMed

Zhorzholiani, Sh T; Mironov, A A; Talygin, E A; Tsyganokov, Yu M; Agafonov, A M; Kiknadze, G I; Gorodkov, A Yu; Bokeriya, L A

2018-03-01

Analysis of the data of morphometry of aortic casts, aortography at different pressures, and multispiral computer tomography of the aorta with contrast and normal pulse pressure showed that geometric configuration of the flow channel of the aorta during the whole cardiac cycle corresponded to the conditions of self-organization of tornado-like quasipotential flow described by exact solutions of the Navier-Stokes equation and continuity of viscous fluid typical for this type of fluid flows. Increasing pressure in the aorta leads to a decrease in the degree of approximation of the channel geometry to the ratio of exact solution and increases the risk of distortions in the structure of the flow. A mechanism of evolution of tornado-like flow in the aorta was proposed.

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.

On the geometrization of quantum mechanics

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

Tavernelli, Ivano, E-mail: ita@zurich.ibm.com

Nonrelativistic quantum mechanics is commonly formulated in terms of wavefunctions (probability amplitudes) obeying the static and the time-dependent Schrödinger equations (SE). Despite the success of this representation of the quantum world a wave–particle duality concept is required to reconcile the theory with observations (experimental measurements). A first solution to this dichotomy was introduced in the de Broglie–Bohm theory according to which a pilot-wave (solution of the SE) is guiding the evolution of particle trajectories. Here, I propose a geometrization of quantum mechanics that describes the time evolution of particles as geodesic lines in a curved space, whose curvature is inducedmore » by the quantum potential. This formulation allows therefore the incorporation of all quantum effects into the geometry of space–time, as it is the case for gravitation in the general relativity.« less

Mesoporous-silica films, fibers, and powders by evaporation

DOEpatents

Bruinsma, Paul J.; Baskaran, Suresh; Bontha, Jagannadha R.; Liu, Jun

2008-05-06

This invention pertains to surfactant-templated nanometer-scale porosity of a silica precursor solution and forming a mesoporous material by first forming the silica precursor solution into a preform having a high surface area to volume ratio, then rapid drying or evaporating a solvent from the silica precursor solution. The mesoporous material may be in any geometric form, but is preferably in the form of a film, fiber, powder or combinations thereof. The rapid drying or evaporation of solvent from the solution is accomplished by layer thinning, for example spin casting, liquid drawing, and liquid spraying respectively. Production of a film is by layer thinning, wherein a layer of the silica precursor solution is formed on a surface followed by removal of an amount of the silica precursor solution and leaving a geometrically thinner layer of the silica precursor solution from which the solvent quickly escapes via evaporation. Layer thinning may be by any method including but not limited to squeegeeing and/or spin casting. In powder formation by spray drying, the same conditions of fast drying exists as in spin-casting (as well as in fiber spinning) because of the high surface-area to volume ratio of the product. When a powder is produced by liquid spraying, the particles or micro-bubbles within the powder are hollow spheres with walls composed of mesoporous silica. Mesoporous fiber formation starts with a similar silica precursor solution but with an added pre-polymer making a pituitous mixture that is drawn into a thin strand from which solvent is evaporated leaving the mesoporous fiber(s).

Mesoporous-silica films, fibers, and powders by evaporation

DOEpatents

Bruinsma, Paul J.; Baskaran, Suresh; Bontha, Jagannadha R.; Liu, Jun

1999-01-01

This invention pertains to surfactant-templated nanometer-scale porosity of a silica precursor solution and forming a mesoporous material by first forming the silica precursor solution into a preform having a high surface area to volume ratio, then rapid drying or evaporating a solvent from the silica precursor solution. The mesoporous material may be in any geometric form, but is preferably in the form of a film, fiber, powder or combinations thereof. The rapid drying or evaporation of solvent from the solution is accomplished by layer thinning, for example spin casting, liquid drawing, and liquid spraying respectively. Production of a film is by layer thinning, wherein a layer of the silica precursor solution is formed on a surface followed by removal of an amount of the silica precursor solution and leaving a geometrically thinner layer of the silica precursor solution from which the solvent quickly escapes via evaporation. Layer thinning may be by any method including but not limited to squeegeeing and/or spin casting. In powder formation by spray drying, the same conditions of fast drying exists as in spin-casting (as well as in fiber spinning) because of the high surface-area to volume ratio of the product. When a powder is produced by liquid spraying, the particles or micro-bubbles within the powder are hollow spheres with walls composed of mesoporous silica. Mesoporous fiber formation starts with a similar silica precursor solution but with an added pre-polymer making a pituitous mixture that is drawn into a thin strand from which solvent is evaporated leaving the mesoporous fiber(s).

Mesoporous-silica films, fibers, and powders by evaporation

DOEpatents

Bruinsma, P.J.; Baskaran, S.; Bontha, J.R.; Liu, J.

1999-07-13

This invention pertains to surfactant-templated nanometer-scale porosity of a silica precursor solution and forming a mesoporous material by first forming the silica precursor solution into a preform having a high surface area to volume ratio, then rapid drying or evaporating a solvent from the silica precursor solution. The mesoporous material may be in any geometric form, but is preferably in the form of a film, fiber, powder or combinations thereof. The rapid drying or evaporation of solvent from the solution is accomplished by layer thinning, for example spin casting, liquid drawing, and liquid spraying respectively. Production of a film is by layer thinning, wherein a layer of the silica precursor solution is formed on a surface followed by removal of an amount of the silica precursor solution and leaving a geometrically thinner layer of the silica precursor solution from which the solvent quickly escapes via evaporation. Layer thinning may be by any method including but not limited to squeegeeing and/or spin casting. In powder formation by spray drying, the same conditions of fast drying exists as in spin-casting (as well as in fiber spinning) because of the high surface-area to volume ratio of the product. When a powder is produced by liquid spraying, the particles or micro-bubbles within the powder are hollow spheres with walls composed of mesoporous silica. Mesoporous fiber formation starts with a similar silica precursor solution but with an added pre-polymer making a pituitous mixture that is drawn into a thin strand from which solvent is evaporated leaving the mesoporous fiber(s). 24 figs.

Nano-scaling law: geometric foundation of thiolated gold nanomolecules.

PubMed

Dass, Amala

2012-04-07

Thiolated gold nanomolecules show a power correlation between the number of gold atoms and the thiolate ligands with a 2/3 scaling similar to Platonic and Archimedean solids. Nanomolecule stability is influenced by a universal geometric factor that is foundational to its stability through the Euclidean surface rule, in addition to the electronic shell closing factor and staple motif requirements. This journal is © The Royal Society of Chemistry 2012

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.

Circumventing Imprecise Geometric Information and Development of a Unified Modeling Technique for Various Flow Regimes in Capillary Tubes

NASA Astrophysics Data System (ADS)

Abbasi, Bahman

2012-11-01

Owing to their manufacturability and reliability, capillary tubes are the most common expansion devices in household refrigerators. Therefore, investigating flow properties in the capillary tubes is of immense appeal in the said business. The models to predict pressure drop in two-phase internal flows invariably rely upon highly precise geometric information. The manner in which capillary tubes are manufactured makes them highly susceptible to geometric imprecisions, which renders geometry-based models unreliable to the point of obsoleteness. Aware of the issue, manufacturers categorize capillary tubes based on Nitrogen flow rate through them. This categorization method presents an opportunity to substitute geometric details with Nitrogen flow data as the basis for customized models. The simulation tools developed by implementation of this technique have the singular advantage of being applicable across flow regimes. Thus the error-prone process of identifying compatible correlations is eliminated. Equally importantly, compressibility and chocking effects can be incorporated in the same model. The outcome is a standalone correlation that provides accurate predictions, regardless of any particular fluid or flow regime. Thereby, exploratory investigations for capillary tube design and optimization are greatly simplified. Bahman Abbasi, Ph.D., is Lead Advanced Systems Engineer at General Electric Appliances in Louisville, KY. He conducts research projects across disciplines in the household refrigeration industry.

Drag and stability characteristics of a variety of reefed and unreefed parachute configurations at Mach 1.80 with an empirical correlation for supersonic Mach numbers

NASA Technical Reports Server (NTRS)

Couch, L. M.

1975-01-01

An investigation was conducted at Mach 1.80 in the Langley 4-foot supersonic pressure tunnel to determine the effects of variation in reefing ratio and geometric porosity on the drag and stability characteristics of four basic canopy types deployed in the wake of a cone-cylinder forebody. The basic designs included cross, hemisflo, disk-gap-band, and extended-skirt canopies; however, modular cross and standard flat canopies and a ballute were also investigated. An empirical correlation was determined which provides a fair estimation of the drag coefficients in transonic and supersonic flow for parachutes of specified geometric porosity and reefing ratio.

Method to predict external store carriage characteristics at transonic speeds

NASA Technical Reports Server (NTRS)

Rosen, Bruce S.

1988-01-01

Development of a computational method for prediction of external store carriage characteristics at transonic speeds is described. The geometric flexibility required for treatment of pylon-mounted stores is achieved by computing finite difference solutions on a five-level embedded grid arrangement. A completely automated grid generation procedure facilitates applications. Store modeling capability consists of bodies of revolution with multiple fore and aft fins. A body-conforming grid improves the accuracy of the computed store body flow field. A nonlinear relaxation scheme developed specifically for modified transonic small disturbance flow equations enhances the method's numerical stability and accuracy. As a result, treatment of lower aspect ratio, more highly swept and tapered wings is possible. A limited supersonic freestream capability is also provided. Pressure, load distribution, and force/moment correlations show good agreement with experimental data for several test cases. A detailed computer program description for the Transonic Store Carriage Loads Prediction (TSCLP) Code is included.

Position of the station Borowiec in the Doppler observation campaign WEDOC 80

NASA Astrophysics Data System (ADS)

Pachelski, W.

The position of the Doppler antenna located at the Borowiec Observatory, Poland, is analyzed based on data gathered during the WEDOC 80 study and an earlier study in 1977. Among other findings, it is determined that biases of the reference system origin can be partially eliminated by transforming absolute coordinates of two or more stations into station-to-station vector components, and by determining the vector length while the system scale remains affected by broadcast ephemerides. The standard deviations of absolute coordinates are shown to represent only the internal accuracy of the solution, and are found to depend on the geometrical configuration between the station position and the satellite passes. It is shown that significant correlations between station coordinates in translocation or multilocation are due to the poor conditioning of design matrices with respect to the origin and orientation of the reference system.

A Question of Interest

ERIC Educational Resources Information Center

Holley, Ann D.

1978-01-01

Formulas are developed which answer installment-buying questions without the use of amortization, sinking funds, or annuity tables. Applications for geometric progressions, proof by induction, solution of exponential equations, and the notion of recursive functions are displayed. (MN)

Freeway geometric design for active traffic management in Europe

DOT National Transportation Integrated Search

2011-03-01

Continued growth in travel on congested urban freeway corridors exceeds the ability of agencies to provide sufficient solutions and alternatives based on traditional roadway expansion and improvement projects. Several countries are implementing manag...

Study of solution procedures for nonlinear structural equations

NASA Technical Reports Server (NTRS)

Young, C. T., II; Jones, R. F., Jr.

1980-01-01

A method for the redution of the cost of solution of large nonlinear structural equations was developed. Verification was made using the MARC-STRUC structure finite element program with test cases involving single and multiple degrees of freedom for static geometric nonlinearities. The method developed was designed to exist within the envelope of accuracy and convergence characteristic of the particular finite element methodology used.

Are we living near the center of a local void?

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

Cusin, Giulia; Pitrou, Cyril; Uzan, Jean-Philippe, E-mail: giulia.cusin@unige.ch, E-mail: pitrou@iap.fr, E-mail: uzan@iap.fr

The properties of the cosmic microwave background (CMB) temperature and polarisation anisotropies measured by a static, off-centered observer located in a local spherically symmetric void, are described. In particular in this paper we compute, together with the standard 2-point angular correlation functions, the off-diagonal correlators, which are no more vanishing by symmetry. While the energy shift induced by the off-centered position of the observer can be suppressed by a proper choice of the observer velocity, a lensing-like effect on the CMB emission point remains. This latter effect is genuinely geometrical (e.g. non-degenerate with a boost) and reflects in the structuremore » of the off-diagonal correlators. At lowest order in this effect, the temperature and polarisation correlation matrices have non-vanishing diagonal elements, as usual, and all the off-diagonal terms are excited. This particular signature of a local void model allows one, in principle, to disentangle geometrical effects from local kinematical ones in CMB observations.« less

A computational framework to characterize and compare the geometry of coronary networks.

PubMed

Bulant, C A; Blanco, P J; Lima, T P; Assunção, A N; Liberato, G; Parga, J R; Ávila, L F R; Pereira, A C; Feijóo, R A; Lemos, P A

2017-03-01

This work presents a computational framework to perform a systematic and comprehensive assessment of the morphometry of coronary arteries from in vivo medical images. The methodology embraces image segmentation, arterial vessel representation, characterization and comparison, data storage, and finally analysis. Validation is performed using a sample of 48 patients. Data mining of morphometric information of several coronary arteries is presented. Results agree to medical reports in terms of basic geometric and anatomical variables. Concerning geometric descriptors, inter-artery and intra-artery correlations are studied. Data reported here can be useful for the construction and setup of blood flow models of the coronary circulation. Finally, as an application example, similarity criterion to assess vasculature likelihood based on geometric features is presented and used to test geometric similarity among sibling patients. Results indicate that likelihood, measured through geometric descriptors, is stronger between siblings compared with non-relative patients. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

The Scaling Group of the 1-D Invisicid Euler Equations

NASA Astrophysics Data System (ADS)

Schmidt, Emma; Ramsey, Scott; Boyd, Zachary; Baty, Roy

2017-11-01

The one dimensional (1-D) compressible Euler equations in non-ideal media support scale invariant solutions under a variety of initial conditions. Famous scale invariant solutions include the Noh, Sedov, Guderley, and collapsing cavity hydrodynamic test problems. We unify many classical scale invariant solutions under a single scaling group analysis. The scaling symmetry group generator provides a framework for determining all scale invariant solutions emitted by the 1-D Euler equations for arbitrary geometry, initial conditions, and equation of state. We approach the Euler equations from a geometric standpoint, and conduct scaling analyses for a broad class of materials.

Rapid Prototyping Technology for Manufacturing GTE Turbine Blades

NASA Astrophysics Data System (ADS)

Balyakin, A. V.; Dobryshkina, E. M.; Vdovin, R. A.; Alekseev, V. P.

2018-03-01

The conventional approach to manufacturing turbine blades by investment casting is expensive and time-consuming, as it takes a lot of time to make geometrically precise and complex wax patterns. Turbine blade manufacturing in pilot production can be sped up by accelerating the casting process while keeping the geometric precision of the final product. This paper compares the rapid prototyping method (casting the wax pattern composition into elastic silicone molds) to the conventional technology. Analysis of the size precision of blade casts shows that silicon-mold casting features sufficient geometric precision. Thus, this method for making wax patterns can be a cost-efficient solution for small-batch or pilot production of turbine blades for gas-turbine units (GTU) and gas-turbine engines (GTE). The paper demonstrates how additive technology and thermographic analysis can speed up the cooling of wax patterns in silicone molds. This is possible at an optimal temperature and solidification time, which make the process more cost-efficient while keeping the geometric quality of the final product.

Geometrically Nonlinear Shell Analysis of Wrinkled Thin-Film Membranes with Stress Concentrations

NASA Technical Reports Server (NTRS)

Tessler, Alexander; Sleight, David W.

2006-01-01

Geometrically nonlinear shell finite element analysis has recently been applied to solar-sail membrane problems in order to model the out-of-plane deformations due to structural wrinkling. Whereas certain problems lend themselves to achieving converged nonlinear solutions that compare favorably with experimental observations, solutions to tensioned membranes exhibiting high stress concentrations have been difficult to obtain even with the best nonlinear finite element codes and advanced shell element technology. In this paper, two numerical studies are presented that pave the way to improving the modeling of this class of nonlinear problems. The studies address the issues of mesh refinement and stress-concentration alleviation, and the effects of these modeling strategies on the ability to attain converged nonlinear deformations due to wrinkling. The numerical studies demonstrate that excessive mesh refinement in the regions of stress concentration may be disadvantageous to achieving wrinkled equilibrium states, causing the nonlinear solution to lock in the membrane response mode, while totally discarding the very low-energy bending response that is necessary to cause wrinkling deformation patterns.

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

Geometric versus numerical optimal control of a dissipative spin-(1/2) particle

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

Lapert, M.; Sugny, D.; Zhang, Y.

2010-12-15

We analyze the saturation of a nuclear magnetic resonance (NMR) signal using optimal magnetic fields. We consider both the problems of minimizing the duration of the control and its energy for a fixed duration. We solve the optimal control problems by using geometric methods and a purely numerical approach, the grape algorithm, the two methods being based on the application of the Pontryagin maximum principle. A very good agreement is obtained between the two results. The optimal solutions for the energy-minimization problem are finally implemented experimentally with available NMR techniques.

Frictionless contact of aircraft tires

NASA Technical Reports Server (NTRS)

Kim, Kyun O.; Tanner, John A.; Noor, Ahmed K.

1989-01-01

A computational procedure for the solution of frictionless contact problems of spacecraft tires was developed using a two-dimensional laminated anisotropic shell theory incorporating the effects of variations in material and geometric parameters, transverse shear deformation, and geometric nonlinearities to model the nose-gear tire of a space shuttle. Numerical results are presented for the case when the nose-gear tire is subjected to inflation pressure and pressed against a rigid pavement. The results are compared with experimental results obtained at NASA Langley, demonstrating a high accuracy of the model and the effectiveness of the computational procedure.

A Divergence Median-based Geometric Detector with A Weighted Averaging Filter

NASA Astrophysics Data System (ADS)

Hua, Xiaoqiang; Cheng, Yongqiang; Li, Yubo; Wang, Hongqiang; Qin, Yuliang

2018-01-01

To overcome the performance degradation of the classical fast Fourier transform (FFT)-based constant false alarm rate detector with the limited sample data, a divergence median-based geometric detector on the Riemannian manifold of Heimitian positive definite matrices is proposed in this paper. In particular, an autocorrelation matrix is used to model the correlation of sample data. This method of the modeling can avoid the poor Doppler resolution as well as the energy spread of the Doppler filter banks result from the FFT. Moreover, a weighted averaging filter, conceived from the philosophy of the bilateral filtering in image denoising, is proposed and combined within the geometric detection framework. As the weighted averaging filter acts as the clutter suppression, the performance of the geometric detector is improved. Numerical experiments are given to validate the effectiveness of our proposed method.

Quantitative investigation of red blood cell three-dimensional geometric and chemical changes in the storage lesion using digital holographic microscopy.

PubMed

Jaferzadeh, Keyvan; Moon, Inkyu

2015-11-01

Quantitative phase information obtained by digital holographic microscopy (DHM) can provide new insight into the functions and morphology of single red blood cells (RBCs). Since the functionality of a RBC is related to its three-dimensional (3-D) shape, quantitative 3-D geometric changes induced by storage time can help hematologists realize its optimal functionality period. We quantitatively investigate RBC 3-D geometric changes in the storage lesion using DHM. Our experimental results show that the substantial geometric transformation of the biconcave-shaped RBCs to the spherocyte occurs due to RBC storage lesion. This transformation leads to progressive loss of cell surface area, surface-to-volume ratio, and functionality of RBCs. Furthermore, our quantitative analysis shows that there are significant correlations between chemical and morphological properties of RBCs.

Distribution of Circles on a Circle and Correlation Between Vortex Rings of Superfluids

NASA Astrophysics Data System (ADS)

Onur Fen, Mehmet; Erkoç, Šakír

2007-05-01

Superfluids are characterized by absence of viscosity. When superfluids are rotated, differently from normal fluids, they form more than one vortex in the containers where they are placed. The number of vortices change as the rotation velocity changes, but this change is not linear. M.W. Zwierlein et al. observed the vortices in experiments, observing up to a number of 80. Experiments also showed that the vortex distributions cannot include large spaces. By using experimental data, we noticed that when we think of vortices as vortex rings, their centers are at the same geometric location and these geometric locations are concentric circles. We generalized the distribution of these geometric places and formulized it. Our formula includes the magic circle numbers. When the number of vortices reach these magic numbers, the number of geometric locations increase by 1.

A geometrical optics polarimetric bidirectional reflectance distribution function for dielectric and metallic surfaces.

PubMed

Hyde, M W; Schmidt, J D; Havrilla, M J

2009-11-23

A polarimetric bidirectional reflectance distribution function (pBRDF), based on geometrical optics, is presented. The pBRDF incorporates a visibility (shadowing/masking) function and a Lambertian (diffuse) component which distinguishes it from other geometrical optics pBRDFs in literature. It is shown that these additions keep the pBRDF bounded (and thus a more realistic physical model) as the angle of incidence or observation approaches grazing and better able to model the behavior of light scattered from rough, reflective surfaces. In this paper, the theoretical development of the pBRDF is shown and discussed. Simulation results of a rough, perfect reflecting surface obtained using an exact, electromagnetic solution and experimental Mueller matrix results of two, rough metallic samples are presented to validate the pBRDF.

Formation flying for electric sails in displaced orbits. Part I: Geometrical analysis

NASA Astrophysics Data System (ADS)

Wang, Wei; Mengali, Giovanni; Quarta, Alessandro A.; Yuan, Jianping

2017-09-01

We present a geometrical methodology for analyzing the formation flying of electric solar wind sail based spacecraft that operate in heliocentric, elliptic, displaced orbits. The spacecraft orbit is maintained by adjusting its propulsive acceleration modulus, whose value is estimated using a thrust model that takes into account a variation of the propulsive performance with the sail attitude. The properties of the relative motion of the spacecraft are studied in detail and a geometrical solution is obtained in terms of relative displaced orbital elements, assumed to be small quantities. In particular, for the small eccentricity case (i.e. for a near-circular displaced orbit), the bounds characterized by the extreme values of relative distances are analytically calculated, thus providing an useful mathematical tool for preliminary design of the spacecraft formation structure.

Avionic Air Data Sensors Fault Detection and Isolation by means of Singular Perturbation and Geometric Approach

PubMed Central

2017-01-01

Singular Perturbations represent an advantageous theory to deal with systems characterized by a two-time scale separation, such as the longitudinal dynamics of aircraft which are called phugoid and short period. In this work, the combination of the NonLinear Geometric Approach and the Singular Perturbations leads to an innovative Fault Detection and Isolation system dedicated to the isolation of faults affecting the air data system of a general aviation aircraft. The isolation capabilities, obtained by means of the approach proposed in this work, allow for the solution of a fault isolation problem otherwise not solvable by means of standard geometric techniques. Extensive Monte-Carlo simulations, exploiting a high fidelity aircraft simulator, show the effectiveness of the proposed Fault Detection and Isolation system. PMID:28946673

Optimal Information Extraction of Laser Scanning Dataset by Scale-Adaptive Reduction

NASA Astrophysics Data System (ADS)

Zang, Y.; Yang, B.

2018-04-01

3D laser technology is widely used to collocate the surface information of object. For various applications, we need to extract a good perceptual quality point cloud from the scanned points. To solve the problem, most of existing methods extract important points based on a fixed scale. However, geometric features of 3D object come from various geometric scales. We propose a multi-scale construction method based on radial basis function. For each scale, important points are extracted from the point cloud based on their importance. We apply a perception metric Just-Noticeable-Difference to measure degradation of each geometric scale. Finally, scale-adaptive optimal information extraction is realized. Experiments are undertaken to evaluate the effective of the proposed method, suggesting a reliable solution for optimal information extraction of object.

Interferometric constraints on quantum geometrical shear noise correlations

DOE PAGES

Chou, Aaron; Glass, Henry; Richard Gustafson, H.; ...

2017-07-20

Final measurements and analysis are reported from the first-generation Holometer, the first instrument capable of measuring correlated variations in space-time position at strain noise power spectral densities smaller than a Planck time. The apparatus consists of two co-located, but independent and isolated, 40 m power-recycled Michelson interferometers, whose outputs are cross-correlated to 25 MHz. The data are sensitive to correlations of differential position across the apparatus over a broad band of frequencies up to and exceeding the inverse light crossing time, 7.6 MHz. By measuring with Planck precision the correlation of position variations at spacelike separations, the Holometer searches formore » faint, irreducible correlated position noise backgrounds predicted by some models of quantum space-time geometry. The first-generation optical layout is sensitive to quantum geometrical noise correlations with shear symmetry---those that can be interpreted as a fundamental noncommutativity of space-time position in orthogonal directions. General experimental constraints are placed on parameters of a set of models of spatial shear noise correlations, with a sensitivity that exceeds the Planck-scale holographic information bound on position states by a large factor. This result significantly extends the upper limits placed on models of directional noncommutativity by currently operating gravitational wave observatories.« less

Interferometric constraints on quantum geometrical shear noise correlations

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

Chou, Aaron; Glass, Henry; Richard Gustafson, H.

Final measurements and analysis are reported from the first-generation Holometer, the first instrument capable of measuring correlated variations in space-time position at strain noise power spectral densities smaller than a Planck time. The apparatus consists of two co-located, but independent and isolated, 40 m power-recycled Michelson interferometers, whose outputs are cross-correlated to 25 MHz. The data are sensitive to correlations of differential position across the apparatus over a broad band of frequencies up to and exceeding the inverse light crossing time, 7.6 MHz. By measuring with Planck precision the correlation of position variations at spacelike separations, the Holometer searches formore » faint, irreducible correlated position noise backgrounds predicted by some models of quantum space-time geometry. The first-generation optical layout is sensitive to quantum geometrical noise correlations with shear symmetry---those that can be interpreted as a fundamental noncommutativity of space-time position in orthogonal directions. General experimental constraints are placed on parameters of a set of models of spatial shear noise correlations, with a sensitivity that exceeds the Planck-scale holographic information bound on position states by a large factor. This result significantly extends the upper limits placed on models of directional noncommutativity by currently operating gravitational wave observatories.« less

Model-assisted template extraction SRAF application to contact holes patterns in high-end flash memory device fabrication

NASA Astrophysics Data System (ADS)

Seoud, Ahmed; Kim, Juhwan; Ma, Yuansheng; Jayaram, Srividya; Hong, Le; Chae, Gyu-Yeol; Lee, Jeong-Woo; Park, Dae-Jin; Yune, Hyoung-Soon; Oh, Se-Young; Park, Chan-Ha

2018-03-01

Sub-resolution assist feature (SRAF) insertion techniques have been effectively used for a long time now to increase process latitude in the lithography patterning process. Rule-based SRAF and model-based SRAF are complementary solutions, and each has its own benefits, depending on the objectives of applications and the criticality of the impact on manufacturing yield, efficiency, and productivity. Rule-based SRAF provides superior geometric output consistency and faster runtime performance, but the associated recipe development time can be of concern. Model-based SRAF provides better coverage for more complicated pattern structures in terms of shapes and sizes, with considerably less time required for recipe development, although consistency and performance may be impacted. In this paper, we introduce a new model-assisted template extraction (MATE) SRAF solution, which employs decision tree learning in a model-based solution to provide the benefits of both rule-based and model-based SRAF insertion approaches. The MATE solution is designed to automate the creation of rules/templates for SRAF insertion, and is based on the SRAF placement predicted by model-based solutions. The MATE SRAF recipe provides optimum lithographic quality in relation to various manufacturing aspects in a very short time, compared to traditional methods of rule optimization. Experiments were done using memory device pattern layouts to compare the MATE solution to existing model-based SRAF and pixelated SRAF approaches, based on lithographic process window quality, runtime performance, and geometric output consistency.

Geometric and dosimetric evaluations of atlas-based segmentation methods of MR images in the head and neck region.

PubMed

Kieselmann, Jennifer Petra; Kamerling, Cornelis Philippus; Burgos, Ninon; Menten, Martin J; Fuller, Clifton David; Nill, Simeon; Cardoso, M Jorge; Oelfke, Uwe

2018-06-08

Owing to its excellent soft-tissue contrast, magnetic resonance (MR) imaging has found an increased application in radiation therapy (RT). Harnessing these properties for treatment planning, automated segmentation methods can alleviate the manual workload burden to the clinical workflow. We investigated atlas-based segmentation methods of organs at risk (OARs) in the head and neck (H&N) region: one approach selecting the most similar atlas from a library of segmented images and two multi-atlas approaches. The latter were based on weighted majority voting and an iterative atlas-fusion approach called STEPS. We built the atlas library from pre-treatment T1-weighted MR images of 12 patients with manual contours of the parotids, spinal cord and mandible, delineated by a clinician. Following a leave-one-out cross-validation strategy, we measured geometric accuracy calculating Dice similarity coefficients (DSC), standard and 95% Hausdorff distances (HD and HD95), as well as the mean surface distance (MSD), whereby the manual contours served as the gold standard. To benchmark the algorithm, we determined the inter-expert variability (IEV) between three experts. To investigate the dosimetric effect of segmentation inaccuracies, we implemented an auto-planning strategy within the treatment planning system Monaco (Elekta AB, Stockholm, Sweden). For each set of auto-segmented volumes of interest (VOIs), we generated a plan for a 9-beam step and shoot intensity modulated RT treatment, designed according to our institution's clinical H\\&N protocol. Superimposing the dose distributions on the gold standard VOIs, we calculated dose differences to OARs caused by contouring differences between auto-segmented and gold standard VOIs. We investigated the correlation between geometric and dosimetric differences. The mean DSC was larger than 0.8 and the mean MSD smaller than 2mm for the multi-atlas approaches, resulting in a geometric accuracy comparable to previously published results and within the range of the IEV. While dosimetric differences could be as large as 23% of the clinical goal, treatment plans fulfilled all imposed clinical goals for the gold standard OARs. Correlations between geometric and dosimetric measures were low with R²<0.5. The geometric accuracy and ability to achieve clinically acceptable treatment plans indicate the suitability of using atlas-based contours for RT treatment planning purposes. The low correlations between geometric and dosimetric measures indicate that geometric measures alone are not sufficient to predict the dosimetric impact of segmentation inaccuracies on treatment planning for the data utilised in this study. Creative Commons Attribution license.

Relative tracking control of constellation satellites considering inter-satellite link

NASA Astrophysics Data System (ADS)

Fakoor, M.; Amozegary, F.; Bakhtiari, M.; Daneshjou, K.

2017-11-01

In this article, two main issues related to the large-scale relative motion of satellites in the constellation are investigated to establish the Inter Satellite Link (ISL) which means the dynamic and control problems. In the section related to dynamic problems, a detailed and effective analytical solution is initially provided for the problem of satellite relative motion considering perturbations. The direct geometric method utilizing spherical coordinates is employed to achieve this solution. The evaluation of simulation shows that the solution obtained from the geometric method calculates the relative motion of the satellite with high accuracy. Thus, the proposed analytical solution will be applicable and effective. In the section related to control problems, the relative tracking control system between two satellites will be designed in order to establish a communication link between the satellites utilizing analytical solution for relative motion of satellites with respect to the reference trajectory. Sliding mode control approach is employed to develop the relative tracking control system for body to body and payload to payload tracking control. Efficiency of sliding mode control approach is compared with PID and LQR controllers. Two types of payload to payload tracking control considering with and without payload degree of freedom are designed and suitable one for practical ISL applications is introduced. Also, Fuzzy controller is utilized to eliminate the control input in the sliding mode controller.

The Effects of Molecular Properties on Ready Biodegradation of Aromatic Compounds in the OECD 301B CO2 Evolution Test.

PubMed

He, Mei; Mei, Cheng-Fang; Sun, Guo-Ping; Li, Hai-Bei; Liu, Lei; Xu, Mei-Ying

2016-07-01

Ready biodegradation is the primary biodegradability of a compound, which is used for discriminating whether a compound could be rapidly and readily biodegraded in the natural ecosystems in a short period and has been applied extensively in the environmental risk assessment of many chemicals. In this study, the effects of 24 molecular properties (including 2 physicochemical parameters, 10 geometrical parameters, 6 topological parameters, and 6 electronic parameters) on the ready biodegradation of 24 kinds of synthetic aromatic compounds were investigated using the OECD 301B CO2 Evolution test. The relationship between molecular properties and ready biodegradation of these aromatic compounds varied with molecular properties. A significant inverse correlation was found for the topological parameter TD, five geometrical parameters (Rad, CAA, CMA, CSEV, and N c), and the physicochemical parameter K ow, and a positive correlation for two topological parameters TC and TVC, whereas no significant correlation was observed for any of the electronic parameters. Based on the correlations between molecular properties and ready biodegradation of these aromatic compounds, the importance of molecular properties was demonstrated as follows: geometrical properties > topological properties > physicochemical properties > electronic properties. Our study first demonstrated the effects of molecular properties on ready biodegradation by a number of experiment data under the same experimental conditions, which should be taken into account to better guide the ready biodegradation tests and understand the mechanisms of the ready biodegradation of aromatic compounds.

A generalized method for determining radiation patterns of aperture antennas and its application to reflector antennas. M.S. Thesis

NASA Technical Reports Server (NTRS)

Paknys, J. R.

1982-01-01

The reflector antenna may be thought of as an aperture antenna. The classical solution for the radiation pattern of such an antenna is found by the aperture integration (AI) method. Success with this method depends on how accurately the aperture currents are known beforehand. In the past, geometrical optics (GO) has been employed to find the aperture currents. This approximation is suitable for calculating the main beam and possibly the first few sidelobes. A better approximation is to use aperture currents calculated from the geometrical theory of diffraction (GTD). Integration of the GTD currents over and extended aperture yields more accurate results for the radiation pattern. This approach is useful when conventional AI and GTD solutions have no common region of validity. This problem arises in reflector antennas. Two dimensional models of parabolic reflectors are studied; however, the techniques discussed can be applied to any aperture antenna.

Geometrical optics approach in liquid crystal films with three-dimensional director variations.

PubMed

Panasyuk, G; Kelly, J; Gartland, E C; Allender, D W

2003-04-01

A formal geometrical optics approach (GOA) to the optics of nematic liquid crystals whose optic axis (director) varies in more than one dimension is described. The GOA is applied to the propagation of light through liquid crystal films whose director varies in three spatial dimensions. As an example, the GOA is applied to the calculation of light transmittance for the case of a liquid crystal cell which exhibits the homeotropic to multidomainlike transition (HMD cell). Properties of the GOA solution are explored, and comparison with the Jones calculus solution is also made. For variations on a smaller scale, where the Jones calculus breaks down, the GOA provides a fast, accurate method for calculating light transmittance. The results of light transmittance calculations for the HMD cell based on the director patterns provided by two methods, direct computer calculation and a previously developed simplified model, are in good agreement.

Decay of solutions of the wave equation with arbitrary localized nonlinear damping

NASA Astrophysics Data System (ADS)

Bellassoued, Mourad

We study the problem of decay rate for the solutions of the initial-boundary value problem to the wave equation, governed by localized nonlinear dissipation and without any assumption on the dynamics (i.e., the control geometric condition is not satisfied). We treat separately the autonomous and the non-autonomous cases. Providing regular initial data, without any assumption on an observation subdomain, we prove that the energy decays at last, as fast as the logarithm of time. Our result is a generalization of Lebeau (in: A. Boutet de Monvel, V. Marchenko (Eds.), Algebraic and Geometric Methods in Mathematical Physics, Kluwer Academic Publishers, Dordrecht, the Netherlands, 1996, pp. 73) result in the autonomous case and Nakao (Adv. Math. Sci. Appl. 7 (1) (1997) 317) work in the non-autonomous case. In order to prove that result we use a new method based on the Fourier-Bross-Iaglintzer (FBI) transform.

Geometric phases in electric dipole searches with trapped spin-1/2 particles in general fields and measurement cells of arbitrary shape with smooth or rough walls

NASA Astrophysics Data System (ADS)

Golub, R.; Kaufman, C.; Müller, G.; Steyerl, A.

2015-12-01

The important role of geometric phases in searches for a permanent electric dipole moment of the neutron, using Ramsey separated oscillatory field nuclear magnetic resonance, was first noted by Commins [Am. J. Phys. 59, 1077 (1991), 10.1119/1.16616] and investigated in detail by Pendlebury et al. [Phys. Rev. A 70, 032102 (2004), 10.1103/PhysRevA.70.032102]. Their analysis was based on the Bloch equations. In subsequent work using the spin-density matrix, Lamoreaux and Golub [Phys. Rev. A 71, 032104 (2005), 10.1103/PhysRevA.71.032104] showed the relation between the frequency shifts and the correlation functions of the fields seen by trapped particles in general fields (Redfield theory). More recently, we presented a solution of the Schrödinger equation for spin-1 /2 particles in circular cylindrical traps with smooth walls and exposed to arbitrary fields [A. Steyerl et al., Phys. Rev. A 89, 052129 (2014), 10.1103/PhysRevA.89.052129]. Here, we extend this work to show how the Redfield theory follows directly from the Schrödinger equation solution. This serves to highlight the conditions of validity of the Redfield theory, a subject of considerable discussion in the literature [e.g., M. P. Nicholas et al., Prog. Nucl. Magn. Reson. Spectrosc. 57, 111 (2010), 10.1016/j.pnmrs.2010.04.003]. Our results can be applied where the Redfield result no longer holds, such as observation times on the order of or shorter than the correlation time and nonstochastic systems, and thus we can illustrate the transient spin dynamics, i.e., the gradual development of the shift with increasing time subsequent to the start of the free precession. We consider systems with rough, diffuse reflecting walls, cylindrical trap geometry with arbitrary cross section, and field perturbations that do not, in the frame of the moving particles, average to zero in time. We show by direct, detailed, calculation the agreement of the results from the Schrödinger equation with the Redfield theory for the cases of a rectangular cell with specular walls and of a circular cell with diffuse reflecting walls.

A coordinate free description of magnetohydrostatic equilibria

NASA Technical Reports Server (NTRS)

Martens, P. C. H.

1986-01-01

The question what geometrical restrictions are imposed on static magnetic fields by the magnetohydrostatic (MHS) equation is addressed. The general mathematical problem is therefore to determine the solutions of the MHS equations in the corona subject to an arbitrary normal component of the magnetic field at the boundary and arbitrary connectivity. What constraints the MHS equations impose on the geometry of the solutions, expressed in metric tensors, will be determined.

On relativistic generalization of Perelman's W-entropy and thermodynamic description of gravitational fields and cosmology

NASA Astrophysics Data System (ADS)

Ruchin, Vyacheslav; Vacaru, Olivia; Vacaru, Sergiu I.

2017-03-01

Using double 2+2 and 3+1 nonholonomic fibrations on Lorentz manifolds, we extend the concept of W-entropy for gravitational fields in general relativity (GR). Such F- and W-functionals were introduced in the Ricci flow theory of three dimensional (3-d) Riemannian metrics by Perelman (the entropy formula for the Ricci flow and its geometric applications. arXiv:math.DG/0211159). Non-relativistic 3-d Ricci flows are characterized by associated statistical thermodynamical values determined by W-entropy. Generalizations for geometric flows of 4-d pseudo-Riemannian metrics are considered for models with local thermodynamical equilibrium and separation of dissipative and non-dissipative processes in relativistic hydrodynamics. The approach is elaborated in the framework of classical field theories (relativistic continuum and hydrodynamic models) without an underlying kinetic description, which will be elaborated in other work. The 3+1 splitting allows us to provide a general relativistic definition of gravitational entropy in the Lyapunov-Perelman sense. It increases monotonically as structure forms in the Universe. We can formulate a thermodynamic description of exact solutions in GR depending, in general, on all spacetime coordinates. A corresponding 2+2 splitting with nonholonomic deformation of linear connection and frame structures is necessary for generating in very general form various classes of exact solutions of the Einstein and general relativistic geometric flow equations. Finally, we speculate on physical macrostates and microstate interpretations of the W-entropy in GR, geometric flow theories and possible connections to string theory (a second unsolved problem also contained in Perelman's work) in Polyakov's approach.

Rotational elasticity

NASA Astrophysics Data System (ADS)

Vassiliev, Dmitri

2017-04-01

We consider an infinite three-dimensional elastic continuum whose material points experience no displacements, only rotations. This framework is a special case of the Cosserat theory of elasticity. Rotations of material points are described mathematically by attaching to each geometric point an orthonormal basis that gives a field of orthonormal bases called the coframe. As the dynamical variables (unknowns) of our theory, we choose the coframe and a density. We write down the general dynamic variational functional for our rotational theory of elasticity, assuming our material to be physically linear but the kinematic model geometrically nonlinear. Allowing geometric nonlinearity is natural when dealing with rotations because rotations in dimension three are inherently nonlinear (rotations about different axes do not commute) and because there is no reason to exclude from our study large rotations such as full turns. The main result of the talk is an explicit construction of a class of time-dependent solutions that we call plane wave solutions; these are travelling waves of rotations. The existence of such explicit closed-form solutions is a non-trivial fact given that our system of Euler-Lagrange equations is highly nonlinear. We also consider a special case of our rotational theory of elasticity which in the stationary setting (harmonic time dependence and arbitrary dependence on spatial coordinates) turns out to be equivalent to a pair of massless Dirac equations. The talk is based on the paper [1]. [1] C.G.Boehmer, R.J.Downes and D.Vassiliev, Rotational elasticity, Quarterly Journal of Mechanics and Applied Mathematics, 2011, vol. 64, p. 415-439. The paper is a heavily revised version of preprint https://arxiv.org/abs/1008.3833

Effects of geometrical structure on spatial distribution of thermal energy in two-dimensional triangular lattices

NASA Astrophysics Data System (ADS)

Liu, Yong-Yang; Xu, Yu-Liang; Liu, Zhong-Qiang; Li, Jing; Wang, Chun-Yang; Kong, Xiang-Mu

2018-07-01

Employing the correlation matrix technique, the spatial distribution of thermal energy in two-dimensional triangular lattices in equilibrium, interacting with linear springs, is studied. It is found that the spatial distribution of thermal energy varies with the included angle of the springs. In addition, the average thermal energy of the longer springs is lower. Springs with different included angle and length will lead to an inhomogeneous spatial distribution of thermal energy. This suggests that the spatial distribution of thermal energy is affected by the geometrical structure of the system: the more asymmetric the geometrical structure of the system is, the more inhomogeneous is the spatial distribution of thermal energy.

A Study of Convergence of the PMARC Matrices Applicable to WICS Calculations

NASA Technical Reports Server (NTRS)

Ghosh, Amitabha

1997-01-01

This report discusses some analytical procedures to enhance the real time solutions of PMARC matrices applicable to the Wall Interference Correction Scheme (WICS) currently being implemented at the 12 foot Pressure Tunnel. WICS calculations involve solving large linear systems in a reasonably speedy manner necessitating exploring further improvement in solution time. This paper therefore presents some of the associated theory of the solution of linear systems. Then it discusses a geometrical interpretation of the residual correction schemes. Finally some results of the current investigation are presented.

A Study of Convergence of the PMARC Matrices Applicable to WICS Calculations

NASA Technical Reports Server (NTRS)

Ghosh, Amitabha

1997-01-01

This report discusses some analytical procedures to enhance the real time solutions of PMARC matrices applicable to the Wall Interference Correction Scheme (WICS) currently being implemented at the 12 foot Pressure Tunell. WICS calculations involve solving large linear systems in a reasonably speedy manner necessitating exploring further improvement in solution time. This paper therefore presents some of the associated theory of the solution of linear systems. Then it discusses a geometrical interpretation of the residual correction schemes. Finally, some results of the current investigation are presented.

On exact correlation functions of chiral ring operators in 2 d N=(2, 2) SCFTs via localization

NASA Astrophysics Data System (ADS)

Chen, Jin

2018-03-01

We study the extremal correlation functions of (twisted) chiral ring operators via superlocalization in N=(2, 2) superconformal field theories (SCFTs) with central charge c ≥ 3, especially for SCFTs with Calabi-Yau geometric phases. We extend the method in arXiv: 1602.05971 with mild modifications, so that it is applicable to disentangle operators mixing on S 2 in nilpotent (twisted) chiral rings of 2 d SCFTs. With the extended algorithm and technique of localization, we compute exactly the extremal correlators in 2 d N=(2, 2) (twisted) chiral rings as non-holomorphic functions of marginal parameters of the theories. Especially in the context of Calabi-Yau geometries, we give an explicit geometric interpretation to our algorithm as the Griffiths transversality with projection on the Hodge bundle over Calabi-Yau complex moduli. We also apply the method to compute extremal correlators in Kähler moduli, or say twisted chiral rings, of several interesting Calabi-Yau manifolds. In the case of complete intersections in toric varieties, we provide an alternative formalism for extremal correlators via localization onto Higgs branch. In addition, as a spinoff we find that, from the extremal correlators of the top element in twisted chiral rings, one can extract chiral correlators in A-twisted topological theories.

Static holes in the geometrically frustrated bow-tie ladder

NASA Astrophysics Data System (ADS)

Martins, George B.; Brenig, Wolfram

2008-10-01

We investigate the doping of a geometrically frustrated spin ladder with static holes by a complementary approach using exact diagonalization and quantum dimers. Results for thermodynamic properties, the singlet density of states, the hole-binding energy and the spin correlations will be presented. For the undoped systems the ground state is non-degenerate, with translationally invariant nearest-neighbor spin correlations. For the doped case, we find that static holes polarize their vicinity through a localization of singlets, reducing the frustration. This polarization induces short range repulsive forces between two holes and an oscillatory behavior of the long range two-hole energy. For most quantities investigated, we find very good agreement between the quantum dimer approach and the results from exact diagonalization.

Tracer-Test Planning Using the Efficient Hydrologic Tracer-Test Design (Ehtd) Program (2005)

EPA Science Inventory

Hydrological tracer testing is the most reliable diagnostic technique available for establishing flow trajectories and hydrologic connections and for determining basic hydraulic and geometric parameters necessary for establishing operative solute-transport processes. Tracer-test ...

Tracer-Test Planning Using the Efficient Hydrologic Tracer-Test Design (Ehtd) Program (2003)

EPA Science Inventory

Hydrological tracer testing is the most reliable diagnostic technique available for establishing flow trajectories and hydrologic connections and for determining basic hydraulic and geometric parameters necessary for establishing operative solute-transport processes. Tracer-test ...

Robot Geometry and the High School Curriculum.

ERIC Educational Resources Information Center

Meyer, Walter

1988-01-01

Description of the field of robotics and its possible use in high school computational geometry classes emphasizes motion planning exercises and computer graphics displays. Eleven geometrical problems based on robotics are presented along with the correct solutions and explanations. (LRW)

Immortal homogeneous Ricci flows

NASA Astrophysics Data System (ADS)

Böhm, Christoph; Lafuente, Ramiro A.

2018-05-01

We show that for an immortal homogeneous Ricci flow solution any sequence of parabolic blow-downs subconverges to a homogeneous expanding Ricci soliton. This is established by constructing a new Lyapunov function based on curvature estimates which come from real geometric invariant theory.

Nonlinear Local Bending Response and Bulging Factors for Longitudinal and Circumferential Cracks in Pressurized Cylindrical Shells

NASA Technical Reports Server (NTRS)

Young, Richard D.; Rose, Cheryl A.; Starnes, James H., Jr.

2000-01-01

Results of a geometrically nonlinear finite element parametric study to determine curvature correction factors or bulging factors that account for increased stresses due to curvature for longitudinal and circumferential cracks in unstiffened pressurized cylindrical shells are presented. Geometric parameters varied in the study include the shell radius, the shell wall thickness, and the crack length. The major results are presented in the form of contour plots of the bulging factor as a function of two nondimensional parameters: the shell curvature parameter, lambda, which is a function of the shell geometry, Poisson's ratio, and the crack length; and a loading parameter, eta, which is a function of the shell geometry, material properties, and the applied internal pressure. These plots identify the ranges of the shell curvature and loading parameters for which the effects of geometric nonlinearity are significant. Simple empirical expressions for the bulging factor are then derived from the numerical results and shown to predict accurately the nonlinear response of shells with longitudinal and circumferential cracks. The numerical results are also compared with analytical solutions based on linear shallow shell theory for thin shells, and with some other semi-empirical solutions from the literature, and limitations on the use of these other expressions are suggested.

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.

Three-dimensional inverse problem of geometrical optics: a mathematical comparison between Fermat's principle and the eikonal equation.

PubMed

Borghero, Francesco; Demontis, Francesco

2016-09-01

In the framework of geometrical optics, we consider the following inverse problem: given a two-parameter family of curves (congruence) (i.e., f(x,y,z)=c₁,g(x,y,z)=c₂), construct the refractive-index distribution function n=n(x,y,z) of a 3D continuous transparent inhomogeneous isotropic medium, allowing for the creation of the given congruence as a family of monochromatic light rays. We solve this problem by following two different procedures: 1. By applying Fermat's principle, we establish a system of two first-order linear nonhomogeneous PDEs in the unique unknown function n=n(x,y,z) relating the assigned congruence of rays with all possible refractive-index profiles compatible with this family. Moreover, we furnish analytical proof that the family of rays must be a normal congruence. 2. By applying the eikonal equation, we establish a second system of two first-order linear homogeneous PDEs whose solutions give the equation S(x,y,z)=const. of the geometric wavefronts and, consequently, all pertinent refractive-index distribution functions n=n(x,y,z). Finally, we make a comparison between the two procedures described above, discussing appropriate examples having exact solutions.

Numerical analysis of the turbulent fluid flow through valves. Geometrical aspects influence at different positions

NASA Astrophysics Data System (ADS)

Rigola, J.; Aljure, D.; Lehmkuhl, O.; Pérez-Segarra, C. D.; Oliva, A.

2015-08-01

The aim of this paper is to carry out a group of numerical experiments over the fluid flow through a valve reed, using the CFD&HT code TermoFluids, an unstructured and parallel object-oriented CFD code for accurate and reliable solving of industrial flows. Turbulent flow and its solution is a very complex problem due to there is a non-lineal interaction between viscous and inertial effects further complicated by their rotational nature, together with the three-dimensionality inherent in these types of flow and the non-steady state solutions. In this work, different meshes, geometrical conditions and LES turbulence models (WALE, VMS, QR and SIGMA) are tested and results compared. On the other hand, the fluid flow boundary conditions are obtained by means of the numerical simulation model of hermetic reciprocating compressors tool, NEST-compressor code. The numerical results presented are based on a specific geometry, where the valve gap opening percentage is 11% of hole diameter and Reynolds numbers given by the one-dimensional model is 4.22 × 105, with density meshes of approximately 8 million CVs. Geometrical aspects related with the orifice's shape and its influence on fluid flow behaviour and pressure drop are analysed in detail, furthermore, flow results for different valve openings are also studied.

Journal: Efficient Hydrologic Tracer-Test Design for Tracer ...

EPA Pesticide Factsheets

Hydrological tracer testing is the most reliable diagnostic technique available for the determination of basic hydraulic and geometric parameters necessary for establishing operative solute-transport processes. Tracer-test design can be difficult because of a lack of prior knowledge of the basic hydraulic and geometric parameters desired and the appropriate tracer mass to release. A new efficient hydrologic tracer-test design (EHTD) methodology has been developed to facilitate the design of tracer tests by root determination of the one-dimensional advection-dispersion equation (ADE) using a preset average tracer concentration which provides a theoretical basis for an estimate of necessary tracer mass. The method uses basic measured field parameters (e.g., discharge, distance, cross-sectional area) that are combined in functional relatipnships that descrive solute-transport processes related to flow velocity and time of travel. These initial estimates for time of travel and velocity are then applied to a hypothetical continuous stirred tank reactor (CSTR) as an analog for the hydrological-flow system to develop initial estimates for tracer concentration, tracer mass, and axial dispersion. Application of the predicted tracer mass with the hydraulic and geometric parameters in the ADE allows for an approximation of initial sample-collection time and subsequent sample-collection frequency where a maximum of 65 samples were determined to be necessary for descri

Tracer-Test Planning Using the Efficient Hydrologic Tracer ...

EPA Pesticide Factsheets

Hydrological tracer testing is the most reliable diagnostic technique available for establishing flow trajectories and hydrologic connections and for determining basic hydraulic and geometric parameters necessary for establishing operative solute-transport processes. Tracer-test design can be difficult because of a lack of prior knowledge of the basic hydraulic and geometric parameters desired and the appropriate tracer mass to release. A new efficient hydrologic tracer-test design (EHTD) methodology has been developed that combines basic measured field parameters (e.g., discharge, distance, cross-sectional area) in functional relationships that describe solute-transport processes related to flow velocity and time of travel. The new method applies these initial estimates for time of travel and velocity to a hypothetical continuously stirred tank reactor as an analog for the hydrologic flow system to develop initial estimates for tracer concentration and axial dispersion, based on a preset average tracer concentration. Root determination of the one-dimensional advection-dispersion equation (ADE) using the preset average tracer concentration then provides a theoretical basis for an estimate of necessary tracer mass.Application of the predicted tracer mass with the hydraulic and geometric parameters in the ADE allows for an approximation of initial sample-collection time and subsequent sample-collection frequency where a maximum of 65 samples were determined to be

EFFICIENT HYDROLOGICAL TRACER-TEST DESIGN (EHTD ...

EPA Pesticide Factsheets

Hydrological tracer testing is the most reliable diagnostic technique available for establishing flow trajectories and hydrologic connections and for determining basic hydraulic and geometric parameters necessary for establishing operative solute-transport processes. Tracer-test design can be difficult because of a lack of prior knowledge of the basic hydraulic and geometric parameters desired and the appropriate tracer mass to release. A new efficient hydrologic tracer-test design (EHTD) methodology has been developed that combines basic measured field parameters (e.g., discharge, distance, cross-sectional area) in functional relationships that describe solute-transport processes related to flow velocity and time of travel. The new method applies these initial estimates for time of travel and velocity to a hypothetical continuously stirred tank reactor as an analog for the hydrologic flow system to develop initial estimates for tracer concentration and axial dispersion, based on a preset average tracer concentration. Root determination of the one-dimensional advection-dispersion equation (ADE) using the preset average tracer concentration then provides a theoretical basis for an estimate of necessary tracer mass.Application of the predicted tracer mass with the hydraulic and geometric parameters in the ADE allows for an approximation of initial sample-collection time and subsequent sample-collection frequency where a maximum of 65 samples were determined to

Impact of Ice Morphology on Design Space of Pharmaceutical Freeze-Drying.

PubMed

Goshima, Hiroshika; Do, Gabsoo; Nakagawa, Kyuya

2016-06-01

It has been known that the sublimation kinetics of a freeze-drying product is affected by its internal ice crystal microstructures. This article demonstrates the impact of the ice morphologies of a frozen formulation in a vial on the design space for the primary drying of a pharmaceutical freeze-drying process. Cross-sectional images of frozen sucrose-bovine serum albumin aqueous solutions were optically observed and digital pictures were acquired. Binary images were obtained from the optical data to extract the geometrical parameters (i.e., ice crystal size and tortuosity) that relate to the mass-transfer resistance of water vapor during the primary drying step. A mathematical model was used to simulate the primary drying kinetics and provided the design space for the process. The simulation results predicted that the geometrical parameters of frozen solutions significantly affect the design space, with large and less tortuous ice morphologies resulting in wide design spaces and vice versa. The optimal applicable drying conditions are influenced by the ice morphologies. Therefore, owing to the spatial distributions of the geometrical parameters of a product, the boundary curves of the design space are variable and could be tuned by controlling the ice morphologies. Copyright © 2016 American Pharmacists Association®. Published by Elsevier Inc. All rights reserved.

Techniques for Updating Pedestrian Network Data Including Facilities and Obstructions Information for Transportation of Vulnerable People

PubMed Central

Park, Seula; Bang, Yoonsik; Yu, Kiyun

2015-01-01

Demand for a Pedestrian Navigation Service (PNS) is on the rise. To provide a PNS for the transportation of vulnerable people, more detailed information of pedestrian facilities and obstructions should be included in Pedestrian Network Data (PND) used for PNS. Such data can be constructed efficiently by collecting GPS trajectories and integrating them with the existing PND. However, these two kinds of data have geometric differences and topological inconsistencies that need to be addressed. In this paper, we provide a methodology for integrating pedestrian facilities and obstructions information with an existing PND. At first we extracted the significant points from user-collected GPS trajectory by identifying the geometric difference index and attributes of each point. Then the extracted points were used to make an initial solution of the matching between the trajectory and the PND. Two geometrical algorithms were proposed and applied to reduce two kinds of errors in the matching: on dual lines and on intersections. Using the final solution for the matching, we reconstructed the node/link structure of PND including the facilities and obstructions information. Finally, performance was assessed with a test site and 79.2% of the collected data were correctly integrated with the PND. PMID:26404307

Dynamic analysis of space-related linear and non-linear structures

NASA Technical Reports Server (NTRS)

Bosela, Paul A.; Shaker, Francis J.; Fertis, Demeter G.

1990-01-01

In order to be cost effective, space structures must be extremely light weight, and subsequently, very flexible structures. The power system for Space Station Freedom is such a structure. Each array consists of a deployable truss mast and a split blanket of photo-voltaic solar collectors. The solar arrays are deployed in orbit, and the blanket is stretched into position as the mast is extended. Geometric stiffness due to the preload make this an interesting non-linear problem. The space station will be subjected to various dynamic loads, during shuttle docking, solar tracking, attitude adjustment, etc. Accurate prediction of the natural frequencies and mode shapes of the space station components, including the solar arrays, is critical for determining the structural adequacy of the components, and for designing a dynamic control system. The process used in developing and verifying the finite element dynamic model of the photo-voltaic arrays is documented. Various problems were identified, such as grounding effects due to geometric stiffness, large displacement effects, and pseudo-stiffness (grounding) due to lack of required rigid body modes. Analysis techniques, such as development of rigorous solutions using continuum mechanics, finite element solution sequence altering, equivalent systems using a curvature basis, Craig-Bampton superelement approach, and modal ordering schemes were utilized. The grounding problems associated with the geometric stiffness are emphasized.

Dynamic analysis of space-related linear and non-linear structures

NASA Technical Reports Server (NTRS)

Bosela, Paul A.; Shaker, Francis J.; Fertis, Demeter G.

1990-01-01

In order to be cost effective, space structures must be extremely light weight, and subsequently, very flexible structures. The power system for Space Station Freedom is such a structure. Each array consists of a deployable truss mast and a split blanket of photovoltaic solar collectors. The solar arrays are deployed in orbit, and the blanket is stretched into position as the mast is extended. Geometric stiffness due to the preload make this an interesting non-linear problem. The space station will be subjected to various dynamic loads, during shuttle docking, solar tracking, attitude adjustment, etc. Accurate prediction of the natural frequencies and mode shapes of the space station components, including the solar arrays, is critical for determining the structural adequacy of the components, and for designing a dynamic controls system. The process used in developing and verifying the finite element dynamic model of the photo-voltaic arrays is documented. Various problems were identified, such as grounding effects due to geometric stiffness, large displacement effects, and pseudo-stiffness (grounding) due to lack of required rigid body modes. Analysis techniques, such as development of rigorous solutions using continuum mechanics, finite element solution sequence altering, equivalent systems using a curvature basis, Craig-Bampton superelement approach, and modal ordering schemes were utilized. The grounding problems associated with the geometric stiffness are emphasized.

On the nullspace of TLS multi-station adjustment

NASA Astrophysics Data System (ADS)

Sterle, Oskar; Kogoj, Dušan; Stopar, Bojan; Kregar, Klemen

2018-07-01

In the article we present an analytic aspect of TLS multi-station least-squares adjustment with the main focus on the datum problem. The datum problem is, compared to previously published researches, theoretically analyzed and solved, where the solution is based on nullspace derivation of the mathematical model. The importance of datum problem solution is seen in a complete description of TLS multi-station adjustment solutions from a set of all minimally constrained least-squares solutions. On a basis of known nullspace, estimable parameters are described and the geometric interpretation of all minimally constrained least squares solutions is presented. At the end a simulated example is used to analyze the results of TLS multi-station minimally constrained and inner constrained least-squares adjustment solutions.

Eshelby's problem of a spherical inclusion eccentrically embedded in a finite spherical body

PubMed Central

He, Q.-C.

2017-01-01

Resorting to the superposition principle, the solution of Eshelby's problem of a spherical inclusion located eccentrically inside a finite spherical domain is obtained in two steps: (i) the solution to the problem of a spherical inclusion in an infinite space; (ii) the solution to the auxiliary problem of the corresponding finite spherical domain subjected to appropriate boundary conditions. Moreover, a set of functions called the sectional and harmonic deviators are proposed and developed to work out the auxiliary solution in a series form, including the displacement and Eshelby tensor fields. The analytical solutions are explicitly obtained and illustrated when the geometric and physical parameters and the boundary condition are specified. PMID:28293141

Approximate Joint Diagonalization and Geometric Mean of Symmetric Positive Definite Matrices

PubMed Central

Congedo, Marco; Afsari, Bijan; Barachant, Alexandre; Moakher, Maher

2015-01-01

We explore the connection between two problems that have arisen independently in the signal processing and related fields: the estimation of the geometric mean of a set of symmetric positive definite (SPD) matrices and their approximate joint diagonalization (AJD). Today there is a considerable interest in estimating the geometric mean of a SPD matrix set in the manifold of SPD matrices endowed with the Fisher information metric. The resulting mean has several important invariance properties and has proven very useful in diverse engineering applications such as biomedical and image data processing. While for two SPD matrices the mean has an algebraic closed form solution, for a set of more than two SPD matrices it can only be estimated by iterative algorithms. However, none of the existing iterative algorithms feature at the same time fast convergence, low computational complexity per iteration and guarantee of convergence. For this reason, recently other definitions of geometric mean based on symmetric divergence measures, such as the Bhattacharyya divergence, have been considered. The resulting means, although possibly useful in practice, do not satisfy all desirable invariance properties. In this paper we consider geometric means of covariance matrices estimated on high-dimensional time-series, assuming that the data is generated according to an instantaneous mixing model, which is very common in signal processing. We show that in these circumstances we can approximate the Fisher information geometric mean by employing an efficient AJD algorithm. Our approximation is in general much closer to the Fisher information geometric mean as compared to its competitors and verifies many invariance properties. Furthermore, convergence is guaranteed, the computational complexity is low and the convergence rate is quadratic. The accuracy of this new geometric mean approximation is demonstrated by means of simulations. PMID:25919667

Regular black holes in f(T) Gravity through a nonlinear electrodynamics source

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

Junior, Ednaldo L.B.; Rodrigues, Manuel E.; Houndjo, Mahouton J.S., E-mail: ednaldobarrosjr@gmail.com, E-mail: esialg@gmail.com, E-mail: sthoundjo@yahoo.fr

2015-10-01

We seek to obtain a new class of exact solutions of regular black holes in f(T) Gravity with non-linear electrodynamics material content, with spherical symmetry in 4D. The equations of motion provide the regaining of various solutions of General Relativity, as a particular case where the function f(T)=T. We developed a powerful method for finding exact solutions, where we get the first new class of regular black holes solutions in the f(T) Theory, where all the geometrics scalars disappear at the origin of the radial coordinate and are finite everywhere, as well as a new class of singular black holes.

Solute transport by flow yields geometric shocks in shape evolution

NASA Astrophysics Data System (ADS)

Huang, Jinzi (Mac); Davies Wykes, Megan; Hajjar, George; Ristroph, Leif; Shelley, Michael

2017-11-01

Geological processes such as erosion and dissolution of surfaces often lead to striking shapes with strikingly sharp features. We present observations of such features forming in dissolution under gravity. In our experiment, a dissolving body with initially smooth surface evolves into an increasingly sharp needle shape. A mathematical model of its shape dynamics, derived from a boundary layer theory, predicts that a geometric shock forms at the tip of dissolved body, with the tip curvature becoming infinite in finite time. We further discuss the model's application to similar processes, such as flow driven erosion which can yield corners.

Gravitational instantons, self-duality, and geometric flows

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

Bourliot, F.; Estes, J.; Petropoulos, P. M.

2010-05-15

We discuss four-dimensional 'spatially homogeneous' gravitational instantons. These are self-dual solutions of Euclidean vacuum Einstein equations. They are endowed with a product structure RxM{sub 3} leading to a foliation into three-dimensional subspaces evolving in Euclidean time. For a large class of homogeneous subspaces, the dynamics coincides with a geometric flow on the three-dimensional slice, driven by the Ricci tensor plus an so(3) gauge connection. The flowing metric is related to the vielbein of the subspace, while the gauge field is inherited from the anti-self-dual component of the four-dimensional Levi-Civita connection.

Refraction at a curved dielectric interface - Geometrical optics solution

NASA Technical Reports Server (NTRS)

Lee, S.-W.; Sheshadri, M. S.; Mittra, R.; Jamnejad, V.

1982-01-01

The transmission of a spherical or plane wave through an arbitrarily curved dielectric interface is solved by the geometrical optics theory. The transmitted field is proportional to the product of the conventional Fresnel's transmission coefficient and a divergence factor (DF), which describes the cross-sectional variation (convergence or divergence) of a ray pencil as the latter propagates in the transmitted region. The factor DF depends on the incident wavefront, the curvatures of the interface, and the relative indices of the two media. Explicit matrix formulas for calculating DF are given, and its physical significance is illustrated via examples.

Geometrical optics and optimal transport.

PubMed

Rubinstein, Jacob; Wolansky, Gershon

2017-10-01

The Fermat principle is generalized to a system of rays. It is shown that all the ray mappings that are compatible with two given intensities of a monochromatic wave, measured at two planes, are stationary points of a canonical functional, which is the weighted average of the actions of all the rays. It is further shown that there exist at least two stationary points for this functional, implying that in the geometrical optics regime the phase from intensity problem has inherently more than one solution. The caustic structures of all the possible ray mappings are analyzed. A number of simulations illustrate the theoretical considerations.

A numerical study of electromagnetic scattering from ocean like surfaces

NASA Technical Reports Server (NTRS)

Lentz, R. R.

1972-01-01

The integral equations describing electromagnetic scattering from one dimensional conducting surfaces are formulated and numerical results are presented. The results are compared with those obtained using approximate methods such as physical optics, geometrical optics, and perturbation theory. The integral equation solutions show that the surface radius of curvature must be greater than 2.5 wavelengths for either the physical optics or geometric optics to give satisfactory results. It has also been shown that perturbation theory agrees with the exact fields as long as the root mean square surface roughness is less than one-tenth of a wavelength.

Nonadiabatic fluctuation in the measured geometric phase

NASA Astrophysics Data System (ADS)

Ai, Qing; Huo, Wenyi; Long, Gui Lu; Sun, C. P.

2009-08-01

We study how the nonadiabatic effect causes the observable fluctuation in the “geometric phase” for a two-level system, which is defined as the experimentally measurable quantity in the adiabatic limit. From the Rabi exact solution to this model, we give a reasonable explanation to the experimental discovery of phase fluctuation in the superconducting circuit system [P. J. Leek, J. M. Fink, A. Blais, R. Bianchetti, M. Göppl, J. M. Gambetta, D. I. Schuster, L. Frunzio, R. J. Schoelkopf, and A. Wallraf, Science 318, 1889 (2007)], which seemed to be regarded as the conventional experimental error.

Topological defects in two-dimensional liquid crystals confined by a box

NASA Astrophysics Data System (ADS)

Yao, Xiaomei; Zhang, Hui; Chen, Jeff Z. Y.

2018-05-01

When a spatially uniform system that displays a liquid-crystal ordering on a two-dimensional surface is confined inside a rectangular box, the liquid crystal direction field develops inhomogeneous textures accompanied by topological defects because of the geometric frustrations. We show that the rich variety of nematic textures and defect patterns found in recent experimental and theoretical studies can be classified by the solutions of the rather fundamental, extended Onsager model. This is critically examined based on the determined free energies of different defect states, as functions of a few relevant, dimensionless geometric parameters.

Contribution of Apollo lunar photography to the establishment of selenodetic control

NASA Technical Reports Server (NTRS)

Dermanis, A.

1975-01-01

Among the various types of available data relevant to the establishment of geometric control on the moon, the only one covering significant portions of the lunar surface (20%) with sufficient information content, is lunar photography, taken at the proximity of the moon from lunar orbiters. The idea of free geodetic networks is introduced as a tool for the statistical comparison of the geometric aspects of the various data used. Methods were developed for the updating of the statistics of observations and the a priori parameter estimates to obtain statistically consistent solutions by means of the optimum relative weighting concept.

Geometric Analyses of Rotational Faults.

ERIC Educational Resources Information Center

Schwert, Donald Peters; Peck, Wesley David

1986-01-01

Describes the use of analysis of rotational faults in undergraduate structural geology laboratories to provide students with applications of both orthographic and stereographic techniques. A demonstration problem is described, and an orthographic/stereographic solution and a reproducible black model demonstration pattern are provided. (TW)

On Dynamics of Spinning Structures

NASA Technical Reports Server (NTRS)

Gupta, K. K.; Ibrahim, A.

2012-01-01

This paper provides details of developments pertaining to vibration analysis of gyroscopic systems, that involves a finite element structural discretization followed by the solution of the resulting matrix eigenvalue problem by a progressive, accelerated simultaneous iteration technique. Thus Coriolis, centrifugal and geometrical stiffness matrices are derived for shell and line elements, followed by the eigensolution details as well as solution of representative problems that demonstrates the efficacy of the currently developed numerical procedures and tools.

Further Evidence for Increasing Pressure and a Non-spherical Shape in Triton's Atmosphere

NASA Astrophysics Data System (ADS)

Person, M. J.; Elliot, J. L.; McDonald, S. W.; Buie, M. W.; Dunham, E. W.; Millis, R. L.; Nye, R. A.; Olkin, C. B.; Wasserman, L. H.; Young, L. A.; Hubbard, W. B.; Hill, R.; Reitsema, H. J.; Pasachoff, J. M.; Babcock, B. A.; McConnochie, T. M.; Stone, R. C.

2000-10-01

An occultation by Triton of a star denoted as Tr176 by McDonald & Elliot (AJ 109, 1352), was observed on 1997 July 18 from various locations in Australia and North America. After an extensive prediction effort, two complete chords of the occultation were recorded by our PCCD portable data systems. These chords were combined with three others recorded by another group (Sicardy et al., BAAS 30, 1107) to provide an overall geometric solution for Triton's atmosphere at the occultation pressure. A simple circular fit to these five chords yielded a half-light radius of 1439 +/- 10 km, however least squares fitting revealed a significant deviation from the simple circular projection of a spherical atmosphere. The best fitting ellipse (a first order deviation from the circular solution) yielded a mean radius of 1440 +/- 6 km and an ellipticity of 0.040 +/- 0.003. To further characterize the non-spherical solutions to the geometric fits, methods were developed to analyze the data assuming both circular and elliptical profiles. Circular and elliptically focused light curve models corresponding to the best fitting circular and elliptical geometric solutions were fit to the data. Using these light curve fits, the mean pressure at the 1400 km radius (48 km altitude) derived from all the data was 2.23 +/- 0.28 microbar for the circular model and 2.45 +/- 0.32 microbar for the elliptical model. These pressures agree with those for the Tr180 occultation (which occurred a few months later), so these results are consistent with the conclusions of Elliot et al. (Icarus 143, 425) that Triton's surface pressure has increased from 14.0 microbar at the time of the Voyager encounter to 19.0 microbar in 1997. The mean equivalent-isothermal temperature at 1400 km was 43.6 +/- 3.7 K for the circular model and 42.0 +/- 3.6 K for the elliptical model. Within their calculated errors, the equivalent-isothermal temperatures were the same for all Triton latitudes probed.

Optical Implementation Of The Synthetic Discrimination Function

NASA Astrophysics Data System (ADS)

Butler, Steve; Riggins, James

1985-01-01

Computer-generated holograms of geometrical shape and synthetic discriminant function (SDF) matched filters are modeled and produced. The models include ideal correlations and Allebach-Keegan binary holograms. A distinction between Phase-Only-Information and Phase-Only-Material Filters is demonstrated. Signal-to-noise and efficiency measurements were made on the resultant correlation planes.

One-norm geometric quantum discord and critical point estimation in the XY spin chain

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

Cheng, Chang-Cheng; Wang, Yao; Guo, Jin-Liang, E-mail: guojinliang80@163.com

2016-11-15

In contrast with entanglement and quantum discord (QD), we investigate the thermal quantum correlation in terms of Schatten one-norm geometric quantum discord (GQD) in the XY spin chain, and analyze their capabilities in detecting the critical point of quantum phase transition. We show that the one-norm GQD can reveal more properties about quantum correlation between two spins, especially for the long-range quantum correlation at finite temperature. Under the influences of site distance, anisotropy and temperature, one-norm GQD and its first derivative make it possible to detect the critical point efficiently for a general XY spin chain. - Highlights: • Comparingmore » with entanglement and QD, one-norm GQD is more robust versus the temperature. • One-norm GQD is more efficient in characterization of long-range quantum correlation between two distant qubits. • One-norm GQD performs well in highlighting the critical point of QPT at zero or low finite temperature. • One-norm GQD has a number of advantages over QD in detecting the critical point of the spin chain.« less

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.

Common aero vehicle autonomous reentry trajectory optimization satisfying waypoint and no-fly zone constraints

NASA Astrophysics Data System (ADS)

Jorris, Timothy R.

2007-12-01

To support the Air Force's Global Reach concept, a Common Aero Vehicle is being designed to support the Global Strike mission. "Waypoints" are specified for reconnaissance or multiple payload deployments and "no-fly zones" are specified for geopolitical restrictions or threat avoidance. Due to time critical targets and multiple scenario analysis, an autonomous solution is preferred over a time-intensive, manually iterative one. Thus, a real-time or near real-time autonomous trajectory optimization technique is presented to minimize the flight time, satisfy terminal and intermediate constraints, and remain within the specified vehicle heating and control limitations. This research uses the Hypersonic Cruise Vehicle (HCV) as a simplified two-dimensional platform to compare multiple solution techniques. The solution techniques include a unique geometric approach developed herein, a derived analytical dynamic optimization technique, and a rapidly emerging collocation numerical approach. This up-and-coming numerical technique is a direct solution method involving discretization then dualization, with pseudospectral methods and nonlinear programming used to converge to the optimal solution. This numerical approach is applied to the Common Aero Vehicle (CAV) as the test platform for the full three-dimensional reentry trajectory optimization problem. The culmination of this research is the verification of the optimality of this proposed numerical technique, as shown for both the two-dimensional and three-dimensional models. Additionally, user implementation strategies are presented to improve accuracy and enhance solution convergence. Thus, the contributions of this research are the geometric approach, the user implementation strategies, and the determination and verification of a numerical solution technique for the optimal reentry trajectory problem that minimizes time to target while satisfying vehicle dynamics and control limitation, and heating, waypoint, and no-fly zone constraints.

Nonlinear flap-lag-extensional vibrations of rotating, pretwisted, preconed beams including Coriolis effects

NASA Technical Reports Server (NTRS)

Subrahmanyam, K. B.; Kaza, K. R. V.

1985-01-01

The effects of pretwist, precone, setting angle, Coriolis forces and second degree geometric nonlinearities on the natural frequencies, steady state deflections and mode shapes of rotating, torsionally rigid, cantilevered beams were studied. The governing coupled equations of flap lag extensional motion are derived including the effects of large precone and retaining geometric nonlinearities up to second degree. The Galerkin method, with nonrotating normal modes, is used for the solution of both steady state nonlinear equations and linear perturbation equations. Parametric indicating the individual and collective effects of pretwist, precone, Coriolis forces and second degree geometric nonlinearities on the steady state deflection, natural frequencies and mode shapes of rotating blades are presented. It is indicated that the second degree geometric nonlinear terms, which vanish for zero precone, can produce frequency changes of engineering significance. Further confirmation of the validity of including those generated by MSC NASTRAN. It is indicated that the linear and nonlinear Coriolis effects must be included in analyzing thick blades. The Coriolis effects are significant on the first flatwise and the first edgewise modes.

Geometric factor and influence of sensors in the establishment of a resistivity-moisture relation in soil samples

NASA Astrophysics Data System (ADS)

López-Sánchez, M.; Mansilla-Plaza, L.; Sánchez-de-laOrden, M.

2017-10-01

Prior to field scale research, soil samples are analysed on a laboratory scale for electrical resistivity calibrations. Currently, there are a variety of field instruments to estimate the water content in soils using different physical phenomena. These instruments can be used to develop moisture-resistivity relationships on the same soil samples. This assures that measurements are performed on the same material and under the same conditions (e.g., humidity and temperature). A geometric factor is applied to the location of electrodes, in order to calculate the apparent electrical resistivity of the laboratory test cells. This geometric factor can be determined in three different ways: by means of the use of an analytical approximation, laboratory trials (experimental approximation), or by the analysis of a numerical model. The first case, the analytical approximation, is not appropriate for complex cells or arrays. And both, the experimental and numerical approximation can lead to inaccurate results. Therefore, we propose a novel approach to obtain a compromise solution between both techniques, providing a more precise determination of the geometrical factor.

n-D shape/texture optimal synthetic description and modeling by GEOGINE

NASA Astrophysics Data System (ADS)

Fiorini, Rodolfo A.; Dacquino, Gianfranco F.

2004-12-01

GEOGINE(GEOmetrical enGINE), a state-of-the-art OMG (Ontological Model Generator) based on n-D Tensor Invariants for multidimensional shape/texture optimal synthetic description and learning, is presented. Usually elementary geometric shape robust characterization, subjected to geometric transformation, on a rigorous mathematical level is a key problem in many computer applications in different interest areas. The past four decades have seen solutions almost based on the use of n-Dimensional Moment and Fourier descriptor invariants. The present paper introduces a new approach for automatic model generation based on n -Dimensional Tensor Invariants as formal dictionary. An ontological model is the kernel used for specifying ontologies so that how close an ontology can be from the real world depends on the possibilities offered by the ontological model. By this approach even chromatic information content can be easily and reliably decoupled from target geometric information and computed into robus colour shape parameter attributes. Main GEOGINEoperational advantages over previous approaches are: 1) Automated Model Generation, 2) Invariant Minimal Complete Set for computational efficiency, 3) Arbitrary Model Precision for robust object description.

Solution and solid-state effects on NMR chemical shifts in sesquiterpene lactones: NMR, X-ray, and theoretical methods.

PubMed

Dračínský, Martin; Buděšínský, Miloš; Warżajtis, Beata; Rychlewska, Urszula

2012-01-12

Selected guaianolide type sesquiterpene lactones were studied combining solution and solid-state NMR spectroscopy with theoretical calculations of the chemical shifts in both environments and with the X-ray data. The experimental (1)H and (13)C chemical shifts in solution were successfully reproduced by theoretical calculations (with the GIAO method and DFT B3LYP 6-31++G**) after geometry optimization (DFT B3LYP 6-31 G**) in vacuum. The GIPAW method was used for calculations of solid-state (13)C chemical shifts. The studied cases involved two polymorphs of helenalin, two pseudopolymorphs of 6α-hydroxydihydro-aromaticin and two cases of multiple asymmetric units in crystals: one in which the symmetry-independent molecules were connected by a series of hydrogen bonds (geigerinin) and the other in which the symmetry-independent molecules, deprived of any specific intermolecular interactions, differed in the conformation of the side chain (badkhysin). Geometrically different molecules present in the crystal lattices could be easily distinguished in the solid-state NMR spectra. Moreover, the experimental differences in the (13)C chemical shifts corresponding to nuclei in different polymorphs or in geometrically different molecules were nicely reproduced with the GIPAW calculations.

Gamma-Ray Light Curves from Pulsar Magnetospheres with Finite Conductivity

NASA Technical Reports Server (NTRS)

Harding, A. K.; Kalapotharakos, C.; Kazanas, D.; Contopoulos, I.

2012-01-01

The Fermi Large Area Telescope has provided an unprecedented database for pulsar emission studies that includes gamma-ray light curves for over 100 pulsars. Modeling these light curves can reveal and constrain the geometry of the particle accelerator, as well as the pulsar magnetic field structure. We have constructed 3D magnetosphere models with finite conductivity, that bridge the extreme vacuum and force-free solutions used in previous light curves modeling. We are investigating the shapes of pulsar gamma-ray light curves using these dissipative solutions with two different approaches: (l) assuming geometric emission patterns of the slot gap and outer gap, and (2) using the parallel electric field provided by the resistive models to compute the trajectories and . emission of the radiating particles. The light curves using geometric emission patterns show a systematic increase in gamma-ray peak phase with increasing conductivity, introducing a new diagnostic of these solutions. The light curves using the model electric fields are very sensitive to the conductivity but do not resemble the observed Fermi light curves, suggesting that some screening of the parallel electric field, by pair cascades not included in the models, is necessary

Hilbert-Schmidt Measure of Pairwise Quantum Discord for Three-Qubit X States

NASA Astrophysics Data System (ADS)

Daoud, M.; Laamara, R. Ahl; Seddik, S.

2015-10-01

The Hilbert-Schmidt distance between a mixed three-qubit state and its closest state is used to quantify the amount of pairwise quantum correlations in a tripartite system. Analytical expressions of geometric quantum discord are derived. A particular attention is devoted to two special classes of three-qubit X states. They include three-qubit states of W, GHZ and Bell type. We also discuss the monogamy property of geometric quantum discord in some mixed three-qubit systems.

Eliminating sun glare disturbance at signalized intersections by a vehicle to infrastructure wireless communication : final report.

DOT National Transportation Integrated Search

2016-05-01

Due to sun glare disturbances, drivers may encounter fatal threats on roadways, particularly at signalized intersections. Many studies have attempted to develop applicable solutions, such as avoiding sun positions, road geometric redirections, and we...

A spatial length scale analysis of turbulent temperature and velocity fluctuations within and above an orchard canopy

USGS Publications Warehouse

Wang, Y.S.; Miller, D.R.; Anderson, D.E.; Cionco, R.M.; Lin, J.D.

1992-01-01

Turbulent flow within and above an almond orchard was measured with three-dimensional wind sensors and fine-wire thermocouple sensors arranged in a horizontal array. The data showed organized turbulent structures as indicated by coherent asymmetric ramp patterns in the time series traces across the sensor array. Space-time correlation analysis indicated that velocity and temperature fluctuations were significantly correlated over a transverse distance more than 4m. Integral length scales of velocity and temperature fluctuations were substantially greater in unstable conditions than those in stable conditions. The coherence spectral analysis indicated that Davenport's geometric similarity hypothesis was satisfied in the lower frequency region. From the geometric similarity hypothesis, the spatial extents of large ramp structures were also estimated with the coherence functions.

Eye movements in patients with schizophrenia: visual stimuli, semantic content and psychiatric symptoms.

PubMed

Ishizuka, K; Kashiwakura, M; Oiji, A

1998-05-01

In order to explore a possible association between psychiatric symptoms and eye movements, 32 patients with schizophrenia were examined using an eye mark recorder in combination with the Positive and Negative Syndrome Scale, and were compared with 32 controls. Four types of figures were presented to the subjects: geometrical figures, drawings, story drawings, and sentences. Mean eye fixation time was significantly longer and mean eye scanning length was significantly shorter for the patients than for controls, not only in response to the geometric figures, but also in response to the story drawings. Eye fixation time and scanning velocity were positively correlated with degrees of thought disturbance. The number of eye fixations, eye fixation time and scanning velocity were negatively correlated with degree of depressive tendency.

Revisiting the two formulations of Bianchi identities and their implications on moduli stabilization

NASA Astrophysics Data System (ADS)

Shukla, Pramod

2016-08-01

In the context of non-geometric type II orientifold compactifications, there have been two formulations for representing the various NS-NS Bianchi-identities. In the first formulation, the standard three-form flux ( H 3), the geometric flux ( ω) and the non-geometric fluxes ( Q and R) are expressed by using the real six-dimensional indices (e.g. {H}_{ijk}, {ω_{ij}}^k, {Q_i}{_{jk}} and R ijk ), and this formulation has been heavily utilized for simplifying the scalar potentials in toroidal-orientifolds. On the other hand, relevant for the studies beyond toroidal backgrounds, a second formulation is utilized in which all flux components are written in terms of various involutively even/odd (2 , 1)- and (1 , 1)-cohomologies of the complex threefold. In the lights of recent model building interests and some observations made in [1, 2], in this article, we revisit two most commonly studied toroidal examples in detail to illustrate that the present forms of these two formulations are not completely equivalent. To demonstrate the same, we translate all the identities of the first formulation into cohomology ingredients, and after a tedious reshuffling of the subsequent constraints, interestingly we find that all the identities of the second formulation are embedded into the first formulation which has some additional constraints. In addition, we look for the possible solutions of these Bianchi identities in a detailed analysis, and we find that some solutions can reduce the size of scalar potential very significantly, and in some cases are too strong to break the no-scale structure completely. Finally, we also comment on the influence of imposing some of the solutions of Bianchi identities in studying moduli stabilization.

Aeroelastic coupling of geometrically nonlinear structures and linear unsteady aerodynamics: Two formulations

NASA Astrophysics Data System (ADS)

Demasi, L.; Livne, E.

2009-07-01

Two different time domain formulations of integrating commonly used frequency-domain unsteady aerodynamic models based on a modal approach with full order finite element models for structures with geometric nonlinearities are presented. Both approaches are tailored to flight vehicle configurations where geometric stiffness effects are important but where deformations are moderate, flow is attached, and linear unsteady aerodynamic modeling is adequate, such as low aspect ratio wings or joined-wing and strut-braced wings at small to moderate angles of attack. Results obtained using the two approaches are compared using both planar and non-planar wing configurations. Sub-critical and post-flutter speeds are considered. It is demonstrated that the two methods lead to the same steady solution for the sub-critical case after the transients subside. It is also shown that the two methods predict the amplitude and frequency of limit cycle oscillation (when present) with the same accuracy.

Black hole acoustics in the minimal geometric deformation of a de Laval nozzle

NASA Astrophysics Data System (ADS)

da Rocha, Roldão

2017-05-01

The correspondence between sound waves, in a de Laval propelling nozzle, and quasinormal modes emitted by brane-world black holes deformed by a 5D bulk Weyl fluid are here explored and scrutinized. The analysis of sound waves patterns in a de Laval nozzle in the laboratory, reciprocally, is here shown to provide relevant data about the 5D bulk Weyl fluid and its on-brane projection, comprised by the minimal geometrically deformed compact stellar distribution on the brane. Acoustic perturbations of the gas fluid flow in the de Laval nozzle are proved to coincide with the quasinormal modes of black holes solutions deformed by the 5D Weyl fluid, in the geometric deformation procedure. Hence, in a phenomenological Eötvös-Friedmann fluid brane-world model, the realistic shape of a de Laval nozzle is derived and its consequences studied.

Geometrical pose and structural estimation from a single image for automatic inspection of filter components

NASA Astrophysics Data System (ADS)

Liu, Yonghuai; Rodrigues, Marcos A.

2000-03-01

This paper describes research on the application of machine vision techniques to a real time automatic inspection task of air filter components in a manufacturing line. A novel calibration algorithm is proposed based on a special camera setup where defective items would show a large calibration error. The algorithm makes full use of rigid constraints derived from the analysis of geometrical properties of reflected correspondence vectors which have been synthesized into a single coordinate frame and provides a closed form solution to the estimation of all parameters. For a comparative study of performance, we also developed another algorithm based on this special camera setup using epipolar geometry. A number of experiments using synthetic data have shown that the proposed algorithm is generally more accurate and robust than the epipolar geometry based algorithm and that the geometric properties of reflected correspondence vectors provide effective constraints to the calibration of rigid body transformations.

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.

Absolute and geometric parameters of contact binary BO Arietis

NASA Astrophysics Data System (ADS)

Gürol, B.; Gürsoytrak, S. H.; Bradstreet, D. H.

2015-08-01

We present the results of our investigation on the geometrical and physical parameters of the W UMa type binary system BO Ari from analyzed CCD (BVRI) light curves and radial velocity data. The photometric data were obtained in 2009 and 2010 at Ankara University Observatory (AUO) and the spectroscopic observations were made in 2007 and 2010 at TUBITAK National Observatory (TUG). These light and radial velocity observations were analyzed simultaneously by using the Wilson-Devinney (2013 revision) code to obtain absolute and geometrical parameters. The system was determined to be an A-type W UMa system. Combining our photometric solution with the spectroscopic data we derived masses and radii of the eclipsing system to be M1 = 0.995M⊙,M2 = 0.189M⊙,R1 = 1.090R⊙ and R2 = 0.515R⊙ . Finally, we discuss the evolutionary status of the system.

Absolute and geometric parameters of contact binary V1918 Cyg

NASA Astrophysics Data System (ADS)

Gürol, B.

2016-08-01

We present the results of our investigation on the geometrical and physical parameters of the W UMa type binary system V1918 Cyg from analyzed CCD (BVR) light curves and radial velocity data. We used the photometric data published by Yang et al. (2013) and spectroscopic data obtained in 2012 at TUBITAK National Observatory (TUG). The light and radial velocity observations were analyzed simultaneously by using the Wilson-Devinney (2015 revision) code to obtain absolute and geometrical parameters of the system. It is confirmed that the system is an A-type W UMa as indicated by Yang et al. (2013). Combining our spectroscopic data with the photometric solution we derived masses and radii of the eclipsing system as M1 = 1.302M⊙ , M2 = 0.362M⊙ , R1 = 1.362R⊙ and R2 = 0.762R⊙ . Finally, we discuss the evolutionary status of the system.

A critical examination of stresses in an elastic single lap joint

NASA Technical Reports Server (NTRS)

Cooper, P. A.; Sawyer, J. W.

1979-01-01

The results of an approximate nonlinear finite-element analysis of a single lap joint are presented and compared with the results of a linear finite-element analysis, and the geometric nonlinear effects caused by the load-path eccentricity on the adhesive stress distributions are determined. The results from finite-element, Goland-Reissner, and photoelastic analyses show that for a single lap joint the effect of the geometric nonlinear behavior of the joint has a sizable effect on the stresses in the adhesive. The Goland-Reissner analysis is sufficiently accurate in the prediction of stresses along the midsurface of the adhesive bond to be used for qualitative evaluation of the influence of geometric or material parametric variations. Detailed stress distributions in both the adherend and adhesive obtained from the finite-element analysis are presented to provide a basis for comparison with other solution techniques.

Quantization of geometric phase with integer and fractional topological characterization in a quantum Ising chain with long-range interaction.

PubMed

Sarkar, Sujit

2018-04-12

An attempt is made to study and understand the behavior of quantization of geometric phase of a quantum Ising chain with long range interaction. We show the existence of integer and fractional topological characterization for this model Hamiltonian with different quantization condition and also the different quantized value of geometric phase. The quantum critical lines behave differently from the perspective of topological characterization. The results of duality and its relation to the topological quantization is presented here. The symmetry study for this model Hamiltonian is also presented. Our results indicate that the Zak phase is not the proper physical parameter to describe the topological characterization of system with long range interaction. We also present quite a few exact solutions with physical explanation. Finally we present the relation between duality, symmetry and topological characterization. Our work provides a new perspective on topological quantization.

Bistatic scattering from a cone frustum

NASA Technical Reports Server (NTRS)

Ebihara, W.; Marhefka, R. J.

1986-01-01

The bistatic scattering from a perfectly conducting cone frustum is investigated using the Geometrical Theory of Diffraction (GTD). The first-order GTD edge-diffraction solution has been extended by correcting for its failure in the specular region off the curved surface and in the rim-caustic regions of the endcaps. The corrections are accomplished by the use of transition functions which are developed and introduced into the diffraction coefficients. Theoretical results are verified in the principal plane by comparison with the moment method solution and experimental measurements. The resulting solution for the scattered fields is accurate, easy to apply, and fast to compute.

A uniform GTD analysis of the EM diffraction by a thin dielectric/ferrite half-plane and related configurations

NASA Technical Reports Server (NTRS)

Rojas, Roberto G.

1985-01-01

A uniform geometrical theory of diffraction (UTD) solution is developed for the problem of the diffraction by a thin dielectric/ferrite half plane when it is excited by a plane, cylindrical, or surface wave field. Both transverse electric and transverse magnetic cases are considered. The solution of this problem is synthesized from the solutions to the related problems of EM diffraction by configurations involving perfectly conducting electric and magnetic walls covered by a dielectric/ferrite half-plane of one half the thickness of the original half-plane.

Analytical solutions with Generalized Impedance Boundary Conditions (GIBC)

NASA Technical Reports Server (NTRS)

Syed, H. H.; Volakis, John L.

1991-01-01

Rigorous uniform geometrical theory of diffraction (UTD) diffraction coefficients are presented for a coated convex cylinder simulated with generalized impedance boundary conditions. In particular, ray solutions are obtained which remain valid in the transition region and reduce uniformly to those in the deep lit and shadow regions. These involve new transition functions in place of the usual Fock-type integrals, characteristics to the impedance cylinder. A uniform asymptotic solution is also presented for observations in the close vicinity of the cylinder. The diffraction coefficients for the convex cylinder are obtained via a generalization of the corresponding ones for the circular cylinder.

Elementary functions in thermodynamic Bethe ansatz

NASA Astrophysics Data System (ADS)

Suzuki, J.

2015-05-01

Some years ago, Fendley found an explicit solution to the thermodynamic Bethe ansatz (TBA) equation for an N=2 supersymmetric theory in 2D with a specific F-term. Motivated by this, we seek explicit solutions for other super-potential cases utilizing the idea from the ODE/IM correspondence. We find that the TBA equations, corresponding to a wider class of super-potentials, admit solutions in terms of elementary functions such as modified Bessel functions and confluent hyper-geometric series. Based on talks given at ‘Infinite Analysis 2014’ (Tokyo, 2014) and at ‘Integrable lattice models and quantum field theories’ (Bad Honnef, 2014).

Analytical characterization of engineered ZnO nanoparticles relevant for hazard assessment

NASA Astrophysics Data System (ADS)

Bragaru, Adina; Kusko, Mihaela; Vasile, Eugeniu; Simion, Monica; Danila, Mihai; Ignat, Teodora; Mihalache, Iuliana; Pascu, Razvan; Craciunoiu, Florea

2013-01-01

The optoelectronic properties of zinc oxide nanoparticles (ZnO-NPs) have determined development of novel applications in catalysis, paints, wave filters, UV detectors, transparent conductive films, solar cells, or sunscreens. While the immediate advantages of using nano-ZnO in glass panel coatings and filter screens for lamps, as protecting products against bleaching, have been demonstrated, the potential environmental effect of the engineered NPs and the associated products was not fully estimated; this issue being of utmost importance, as these materials will be supplied to the market in quantities of tons per year, equating to thousands of square meters. In this study, ZnO-NPs with commercial name Zincox™ have been subjected to a comprehensive characterization, relevant for hazard assessment, using complementary physico-chemical methods. Therefore, the morphological investigations have been corroborated with XRD pattern analyses and UV-Vis absorption related properties resulting an excellent correlation between the geometrical sizes revealed by microscopy (8.0-9.0 nm), and, respectively, the crystallite size (8.2-9.5 nm) and optical size (7.8 nm) calculated from the last two techniques' data. Furthermore, the hydrodynamic diameter of ZnO-NPs and stability of aqueous dispersions with different concentration of nanoparticles have been analyzed as function of significant solution parameters, like concentration, pH and solution ionic strength. The results suggest that solution chemistry exerts a strong influence on ZnO dissolution stability, the complete set of analyses providing useful information toward better control of dosage during biotoxicological tests.

A geometric multigrid preconditioning strategy for DPG system matrices

DOE PAGES

Roberts, Nathan V.; Chan, Jesse

2017-08-23

Here, the discontinuous Petrov–Galerkin (DPG) methodology of Demkowicz and Gopalakrishnan (2010, 2011) guarantees the optimality of the solution in an energy norm, and provides several features facilitating adaptive schemes. A key question that has not yet been answered in general – though there are some results for Poisson, e.g.– is how best to precondition the DPG system matrix, so that iterative solvers may be used to allow solution of large-scale problems.

The extended tracking network and indications of baseline precision and accuracy in the North Andes

NASA Technical Reports Server (NTRS)

Freymueller, Jeffrey T.; Kellogg, James N.

1990-01-01

The CASA Uno Global Positioning System (GPS) experiment (January-February 1988) included an extended tracking network which covered three continents in addition to the network of scientific interest in Central and South America. The repeatability of long baselines (400-1000 km) in South America is improved by up to a factor of two in the horizontal vector baseline components by using tracking stations in the Pacific and Europe to supplement stations in North America. In every case but one, the differences between the mean solutions obtained using different tracking networks was equal to or smaller than day-to-day rms repeatabilities for the same baselines. The mean solutions obtained by using tracking stations in North America and the Pacific agreed at the 2-3 millimeter level with those using tracking stations in North America and Europe. The agreement of the extended tracking network solutions suggests that a broad distribution of tracking stations provides better geometric constraints on the satellite orbits and that solutions are not sensitive to changes in tracking network configuration when an extended network is use. A comparison of the results from the North Andes and a baseline in North America suggests that the use of a geometrically strong extended tracking network is most important when the network of interest is far from North America.

Memprot: a program to model the detergent corona around a membrane protein based on SEC–SAXS data

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

Pérez, Javier, E-mail: javier.perez@synchrotron-soleil.fr; Koutsioubas, Alexandros; Synchrotron SOLEIL, L’Orme des Merisiers, BP 48, Saint-Aubin, 91192 Gif-sur-Yvette

Systematic SAXS simulations have been analysed over a wide range of parameters in order to better understand the detergent corona around a membrane protein. The application of small-angle X-ray scattering (SAXS) to structural investigations of transmembrane proteins in detergent solution has been hampered by two main inherent hurdles. On the one hand, the formation of a detergent corona around the hydrophobic region of the protein strongly modifies the scattering curve of the protein. On the other hand, free micelles of detergent without a precisely known concentration coexist with the protein–detergent complex in solution, therefore adding an uncontrolled signal. To gainmore » robust structural information on such systems from SAXS data, in previous work, advantage was taken of the online combination of size-exclusion chromatography (SEC) and SAXS, and the detergent corona around aquaporin-0, a membrane protein of known structure, could be modelled. A precise geometrical model of the corona, shaped as an elliptical torus, was determined. Here, in order to better understand the correlations between the corona model parameters and to discuss the uniqueness of the model, this work was revisited by analyzing systematic SAXS simulations over a wide range of parameters of the torus.« less

Terrain shape index: quantifying effect of minor landforms on tree height

Treesearch

W. Henry McNab

1989-01-01

In the southern Appalachians, the distribution and growth of trees are highly correlated with local topography, but the relationships have been ditficult to describe quantitatively. A quantitative expression of the geometric shape of the land surface (terrain shape index) is described and correlated with oventory tree heights and site quality. Application of the index...

Calculating excess volumes of binary solutions with allowance for structural differences between mixed components

NASA Astrophysics Data System (ADS)

Balankina, E. S.

2016-06-01

Analytical dependences of a volume's properties on the differences between the geometric structures of initial monosystems are obtained for binary systems simulated by a grain medium. The effect of microstructural parameter k (the ratio of volumes of molecules of mixed components) on the concentration behavior of the relative excess molar volume of different types of real binary solutions is analyzed. It is established that the contribution due to differences between the volumes of molecules and coefficients of the packing density of mixed components is ~80-100% for mutual solutions of n-alkanes and ~55-80% of the experimental value of the relative excess molar volume for water solutions of n-alcohols.

On Teaching Thermodynamics

ERIC Educational Resources Information Center

Debbasch, F.

2011-01-01

The logical structure of classical thermodynamics is presented in a modern, geometrical manner. The first and second law receive clear, operatively oriented statements and the Gibbs free energy extremum principle is fully discussed. Applications relevant to chemistry, such as phase transitions, dilute solutions theory and, in particular, the law…

Diffraction of a Gaussian beam in a three-dimensional smoothly inhomogeneous medium: an eikonal-based complex geometrical-optics approach.

PubMed

Berczynski, Pawel; Bliokh, Konstantin Yu; Kravtsov, Yuri A; Stateczny, Andrzej

2006-06-01

We present an ab initio account of the paraxial complex geometrical optics (CGO) in application to scalar Gaussian beam propagation and diffraction in a 3D smoothly inhomogeneous medium. The paraxial CGO deals with quadratic expansion of the complex eikonal and reduces the wave problem to the solution of ordinary differential equations of the Riccati type. This substantially simplifies the description of Gaussian beam diffraction as compared with full-wave or parabolic (quasi-optics) equations. For a Gaussian beam propagating in a homogeneous medium or along the symmetry axis in a lenslike medium, the CGO equations possess analytical solutions; otherwise, they can be readily solved numerically. As a nontrivial example we consider Gaussian beam propagation and diffraction along a helical ray in an axially symmetric waveguide medium. It is shown that the major axis of the beam's elliptical cross section grows unboundedly; it is oriented predominantly in the azimuthal (binormal) direction and does not obey the parallel-transport law.

Time scale of random sequential adsorption.

PubMed

Erban, Radek; Chapman, S Jonathan

2007-04-01

A simple multiscale approach to the diffusion-driven adsorption from a solution to a solid surface is presented. The model combines two important features of the adsorption process: (i) The kinetics of the chemical reaction between adsorbing molecules and the surface and (ii) geometrical constraints on the surface made by molecules which are already adsorbed. The process (i) is modeled in a diffusion-driven context, i.e., the conditional probability of adsorbing a molecule provided that the molecule hits the surface is related to the macroscopic surface reaction rate. The geometrical constraint (ii) is modeled using random sequential adsorption (RSA), which is the sequential addition of molecules at random positions on a surface; one attempt to attach a molecule is made per one RSA simulation time step. By coupling RSA with the diffusion of molecules in the solution above the surface the RSA simulation time step is related to the real physical time. The method is illustrated on a model of chemisorption of reactive polymers to a virus surface.

A hybrid model of laser energy deposition for multi-dimensional simulations of plasmas and metals

NASA Astrophysics Data System (ADS)

Basko, Mikhail M.; Tsygvintsev, Ilia P.

2017-05-01

The hybrid model of laser energy deposition is a combination of the geometrical-optics ray-tracing method with the one-dimensional (1D) solution of the Helmholtz wave equation in regions where the geometrical optics becomes inapplicable. We propose an improved version of this model, where a new physically consistent criterion for transition to the 1D wave optics is derived, and a special rescaling procedure of the wave-optics deposition profile is introduced. The model is intended for applications in large-scale two- and three-dimensional hydrodynamic codes. Comparison with exact 1D solutions demonstrates that it can fairly accurately reproduce the absorption fraction in both the s- and p-polarizations on arbitrarily steep density gradients, provided that a sufficiently accurate algorithm for gradient evaluation is used. The accuracy of the model becomes questionable for long laser pulses simulated on too fine grids, where the hydrodynamic self-focusing instability strongly manifests itself.

Impact of adhesive surface and volume of luting resin on fracture resistance of root filled teeth.

PubMed

Krastl, G; Gugger, J; Deyhle, H; Zitzmann, N U; Weiger, R; Müller, B

2011-05-01

To investigate the correlation between geometric parameters of severely compromised root filled (RCT) pre-molar teeth with irregular root canals and their fracture resistance. The null hypothesis tested was that the fracture resistance of root filled teeth is not influenced by: (i) the adhesive surface of the post-space preparation (A(PS) ), (ii) the coronal tooth surface (A(A) ), (iii) the amount of resin cement (V(C) ) and (iv) the Young's modulus of the specimens. A total of 48 noncarious human pre-molar teeth with irregular root canals were decoronated, root filled and adhesively restored with post-retained direct composite crowns. After thermomechanical loading (1,200,000×, 5-50° C), static load was applied until failure. The geometric parameters of the tooth were evaluated by microcomputed tomography (μCT) using impressions taken after post-space preparation. Linear regression analyses were performed to correlate the geometric parameters of the specimens with their fracture resistance. The amount of resin cement (V(C) ) comprised up to 88% of the entire post-space (mean 67%) and had no impact on the maximal load (P = 0.88). The latter was significantly influenced by post-space preparation (P = 0.003). Amongst the geometric parameters tested, the surface area in the root canal had the greatest impact on fracture resistance of root filled pre-molars restored with posts and composite crowns, whilst the fit of the post was less important. © 2011 International Endodontic Journal.

Geometric evolution of complex networks with degree correlations

NASA Astrophysics Data System (ADS)

Murphy, Charles; Allard, Antoine; Laurence, Edward; St-Onge, Guillaume; Dubé, Louis J.

2018-03-01

We present a general class of geometric network growth mechanisms by homogeneous attachment in which the links created at a given time t are distributed homogeneously between a new node and the existing nodes selected uniformly. This is achieved by creating links between nodes uniformly distributed in a homogeneous metric space according to a Fermi-Dirac connection probability with inverse temperature β and general time-dependent chemical potential μ (t ) . The chemical potential limits the spatial extent of newly created links. Using a hidden variable framework, we obtain an analytical expression for the degree sequence and show that μ (t ) can be fixed to yield any given degree distributions, including a scale-free degree distribution. Additionally, we find that depending on the order in which nodes appear in the network—its history—the degree-degree correlations can be tuned to be assortative or disassortative. The effect of the geometry on the structure is investigated through the average clustering coefficient 〈c 〉 . In the thermodynamic limit, we identify a phase transition between a random regime where 〈c 〉→0 when β <βc and a geometric regime where 〈c 〉>0 when β >βc .

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.

The Data Transfer Kit: A geometric rendezvous-based tool for multiphysics data transfer

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

Slattery, S. R.; Wilson, P. P. H.; Pawlowski, R. P.

2013-07-01

The Data Transfer Kit (DTK) is a software library designed to provide parallel data transfer services for arbitrary physics components based on the concept of geometric rendezvous. The rendezvous algorithm provides a means to geometrically correlate two geometric domains that may be arbitrarily decomposed in a parallel simulation. By repartitioning both domains such that they have the same geometric domain on each parallel process, efficient and load balanced search operations and data transfer can be performed at a desirable algorithmic time complexity with low communication overhead relative to other types of mapping algorithms. With the increased development efforts in multiphysicsmore » simulation and other multiple mesh and geometry problems, generating parallel topology maps for transferring fields and other data between geometric domains is a common operation. The algorithms used to generate parallel topology maps based on the concept of geometric rendezvous as implemented in DTK are described with an example using a conjugate heat transfer calculation and thermal coupling with a neutronics code. In addition, we provide the results of initial scaling studies performed on the Jaguar Cray XK6 system at Oak Ridge National Laboratory for a worse-case-scenario problem in terms of algorithmic complexity that shows good scaling on 0(1 x 104) cores for topology map generation and excellent scaling on 0(1 x 105) cores for the data transfer operation with meshes of O(1 x 109) elements. (authors)« less

Joint pricing and production management: a geometric programming approach with consideration of cubic production cost function

NASA Astrophysics Data System (ADS)

Sadjadi, Seyed Jafar; Hamidi Hesarsorkh, Aghil; Mohammadi, Mehdi; Bonyadi Naeini, Ali

2015-06-01

Coordination and harmony between different departments of a company can be an important factor in achieving competitive advantage if the company corrects alignment between strategies of different departments. This paper presents an integrated decision model based on recent advances of geometric programming technique. The demand of a product considers as a power function of factors such as product's price, marketing expenditures, and consumer service expenditures. Furthermore, production cost considers as a cubic power function of outputs. The model will be solved by recent advances in convex optimization tools. Finally, the solution procedure is illustrated by numerical example.

Geometrical-optics solution to light scattering by droxtal ice crystals.

PubMed

Zhang, Zhibo; Yang, Ping; Kattawar, George W; Tsay, Si-Chee; Baum, Bryan A; Hu, Yongxiang; Heymsfield, Andrew J; Reichardt, Jens

2004-04-20

We investigate the phase matrices of droxtals at wavelengths of 0.66 and 11 microm by using an improved geometrical-optics method. An efficient method is developed to specify the incident rays and the corresponding impinging points on the particle surface necessary to initialize the ray-tracing computations. At the 0.66-microm wavelength, the optical properties of droxtals are different from those of hexagonal ice crystals. At the 11-microm wavelength, the phase functions for droxtals are essentially featureless because of strong absorption within the particles, except for ripple structures that are caused by the phase interference of the diffracted wave.

Asymmetric design for Compound Elliptical Concentrators (CEC) and its geometric flux implications

NASA Astrophysics Data System (ADS)

Jiang, Lun; Winston, Roland

2015-08-01

The asymmetric compound elliptical concentrator (CEC) has been a less discussed subject in the nonimaging optics society. The conventional way of understanding an ideal concentrator is based on maximizing the concentration ratio based on a uniformed acceptance angle. Although such an angle does not exist in the case of CEC, the thermodynamic laws still hold and we can produce concentrators with the maximum concentration ratio allowed by them. Here we restate the problem and use the string method to solve this general problem. Built on the solution, we can discover groups of such ideal concentrators using geometric flux field, or flowline method.

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.

Reconstructed imaging of acoustic cloak using time-lapse reversal method

NASA Astrophysics Data System (ADS)

Zhou, Chen; Cheng, Ying; Xu, Jian-yi; Li, Bo; Liu, Xiao-jun

2014-08-01

We proposed and investigated a solution to the inverse acoustic cloak problem, an anti-stealth technology to make cloaks visible, using the time-lapse reversal (TLR) method. The TLR method reconstructs the image of an unknown acoustic cloak by utilizing scattered acoustic waves. Compared to previous anti-stealth methods, the TLR method can determine not only the existence of a cloak but also its exact geometric information like definite shape, size, and position. Here, we present the process for TLR reconstruction based on time reversal invariance. This technology may have potential applications in detecting various types of cloaks with different geometric parameters.

Diffusion equations and the time evolution of foreign exchange rates

NASA Astrophysics Data System (ADS)

Figueiredo, Annibal; de Castro, Marcio T.; da Fonseca, Regina C. B.; Gleria, Iram

2013-10-01

We investigate which type of diffusion equation is most appropriate to describe the time evolution of foreign exchange rates. We modify the geometric diffusion model assuming a non-exponential time evolution and the stochastic term is the sum of a Wiener noise and a jump process. We find the resulting diffusion equation to obey the Kramers-Moyal equation. Analytical solutions are obtained using the characteristic function formalism and compared with empirical data. The analysis focus on the first four central moments considering the returns of foreign exchange rate. It is shown that the proposed model offers a good improvement over the classical geometric diffusion model.

Exposure to ultrafine particles and PM 2.5 in four Sydney transport modes

NASA Astrophysics Data System (ADS)

Knibbs, Luke D.; de Dear, Richard J.

2010-08-01

Concentrations of ultrafine (<0.1 μm) particles (UFPs) and PM 2.5 (<2.5 μm) were measured whilst commuting along a similar route by train, bus, ferry and automobile in Sydney, Australia. One trip on each transport mode was undertaken during both morning and evening peak hours throughout a working week, for a total of 40 trips. Analyses comprised one-way ANOVA to compare overall (i.e. all trips combined) geometric mean concentrations of both particle fractions measured across transport modes, and assessment of both the correlation between wind speed and individual trip means of UFPs and PM 2.5, and the correlation between the two particle fractions. Overall geometric mean concentrations of UFPs and PM 2.5 ranged from 2.8 (train) to 8.4 (bus) × 10 4 particles cm -3 and 22.6 (automobile) to 29.6 (bus) μg m -3, respectively, and a statistically significant difference ( p < 0.001) between modes was found for both particle fractions. Individual trip geometric mean concentrations were between 9.7 × 10 3 (train) and 2.2 × 10 5 (bus) particles cm -3 and 9.5 (train) to 78.7 (train) μg m -3. Estimated commuter exposures were variable, and the highest return trip mean PM 2.5 exposure occurred in the ferry mode, whilst the highest UFP exposure occurred during bus trips. The correlation between fractions was generally poor, and in keeping with the duality of particle mass and number emissions in vehicle-dominated urban areas. Wind speed was negatively correlated with, and a generally poor determinant of, UFP and PM 2.5 concentrations, suggesting a more significant role for other factors in determining commuter exposure.

Analysis of shell-type structures subjected to time-dependent mechanical and thermal loading

NASA Technical Reports Server (NTRS)

Simitses, G. J.; Riff, R.

1987-01-01

A general mathematical model and solution methodologies for analyzing structural response of thin, metallic shell-type structures under large transient, cyclic, or static thermomechanical loads are developed. Among the system responses, which are associated with these load conditions, are thermal buckling, creep buckling and ratcheting. Thus, geometric as well as material type nonlinearities (of high order) can be anticipated and must be considered in the development of the mathematical model. Furthermore, this must also be accommodated in the solution procedures.

Analysis of shell-type structures subjected to time-dependent mechanical and thermal loading

NASA Technical Reports Server (NTRS)

Simitses, G. J.; Carlson, R. L.; Riff, R.

1987-01-01

A general mathematical model and solution methodologies are being developed for analyzing structural response of thin, metallic shell-type structures under large transient, cyclic, or static thermomechanical loads. Among the system responses, which were associated with these load conditions, were thermal buckling, creep buckling, and ratcheting. Thus, geometric as well as material-type nonlinearities (of high order) can be anticipated and must be considered in the development of the mathematical model. Furthermore, this must also be accommodated in the solution process.

Causal Structure around Spinning 5-DIMENSIONAL Cosmic Strings

NASA Astrophysics Data System (ADS)

Slagter, Reinoud Jan

2008-09-01

We present a numerical solution of a stationary 5-dimensional spinning cosmic string in the Einstein-Yang-Mills (EYM) model, where the extra bulk coordinate ψ is periodic. It turns out that when gψψ approaches zero, i.e., a closed time-like curve (CTC) would appear, the solution becomes singular. We also investigated the geometrical structure of the static 5D cosmic string. Two opposite moving 5D strings could, in contrast with the 4D case, fulfil the Gott condition for CTC formation.

Non-isothermal elastoviscoplastic snap-through and creep buckling of shallow arches

NASA Technical Reports Server (NTRS)

Simitses, G. J.; Riff, R.

1987-01-01

The problem of buckling of shallow arches under transient thermomechanical loads is investigated. The analysis is based on nonlinear geometric and constitutive relations, and is expressed in a rate form. The material constitutive equations are capable of reproducing all non-isothermal, elasto-viscoplastic characteristics. The solution scheme is capable of predicting response which includes pre and postbuckling with creep and plastic effects. The solution procedure is demonstrated through several examples which include both creep and snap-through behavior.

Exact Cosmological Models with Yang–Mills Fields on Lyra Manifold

NASA Astrophysics Data System (ADS)

Shchigolev, V. K.; Bezbatko, D. N.

2018-04-01

The present study deals with the Friedmann-Robertson-Walker cosmological models with Yang-Mills (YM) fields in Lyra geometry. The energy-momentum tensor of the YM fields for our models is obtained with the help of an exact solution to the YM equations with minimal coupling to gravity. Two specific exact solutions of the model are obtained regarding the effective equation of state and the exponential law of expansion. The physical and geometric behavior of the model is also discussed.

Regularity of Solutions of the Nonlinear Sigma Model with Gravitino

NASA Astrophysics Data System (ADS)

Jost, Jürgen; Keßler, Enno; Tolksdorf, Jürgen; Wu, Ruijun; Zhu, Miaomiao

2018-02-01

We propose a geometric setup to study analytic aspects of a variant of the super symmetric two-dimensional nonlinear sigma model. This functional extends the functional of Dirac-harmonic maps by gravitino fields. The system of Euler-Lagrange equations of the two-dimensional nonlinear sigma model with gravitino is calculated explicitly. The gravitino terms pose additional analytic difficulties to show smoothness of its weak solutions which are overcome using Rivière's regularity theory and Riesz potential theory.

An efficient solution procedure for the thermoelastic analysis of truss space structures

NASA Technical Reports Server (NTRS)

Givoli, D.; Rand, O.

1992-01-01

A solution procedure is proposed for the thermal and thermoelastic analysis of truss space structures in periodic motion. In this method, the spatial domain is first descretized using a consistent finite element formulation. Then the resulting semi-discrete equations in time are solved analytically by using Fourier decomposition. Geometrical symmetry is taken advantage of completely. An algorithm is presented for the calculation of heat flux distribution. The method is demonstrated via a numerical example of a cylindrically shaped space structure.

A Model for Axial Magnetic Bearings Including Eddy Currents

NASA Technical Reports Server (NTRS)

Kucera, Ladislav; Ahrens, Markus

1996-01-01

This paper presents an analytical method of modelling eddy currents inside axial bearings. The problem is solved by dividing an axial bearing into elementary geometric forms, solving the Maxwell equations for these simplified geometries, defining boundary conditions and combining the geometries. The final result is an analytical solution for the flux, from which the impedance and the force of an axial bearing can be derived. Several impedance measurements have shown that the analytical solution can fit the measured data with a precision of approximately 5%.

Density functional theory and phytochemical study of Pistagremic acid

NASA Astrophysics Data System (ADS)

Ullah, Habib; Rauf, Abdur; Ullah, Zakir; Fazl-i-Sattar; Anwar, Muhammad; Shah, Anwar-ul-Haq Ali; Uddin, Ghias; Ayub, Khurshid

2014-01-01

We report here for the first time a comparative theoretical and experimental study of Pistagremic acid (P.A). We have developed a theoretical model for obtaining the electronic and spectroscopic properties of P.A. The simulated data showed nice correlation with the experimental data. The geometric and electronic properties were simulated at B3LYP/6-31 G (d, p) level of density functional theory (DFT). The optimized geometric parameters of P.A were found consistent with those from X-ray crystal structure. Differences of about 0.01 and 0.15 Å in bond length and 0.19-1.30° degree in the angles, respectively; were observed between the experimental and theoretical data. The theoretical vibrational bands of P.A were found to correlate with the experimental IR spectrum after a common scaling factor of 0.963. The experimental and predicted UV-Vis spectra (at B3LYP/6-31+G (d, p)) have 36 nm differences. This difference from experimental results is because of the condensed phase nature of P.A. Electronic properties such as Ionization Potential (I.P), Electron Affinities (E.A), co-efficient of highest occupied molecular orbital (HOMO), co-efficient of lowest unoccupied molecular orbital (LUMO) of P.A were estimated for the first time however, no correlation can be made with experiment. Inter-molecular interaction and its effect on vibrational (IR), electronic and geometric parameters were simulated by using Formic acid as model for hydrogen bonding in P.A.

Geometry and scaling laws of excursion and iso-sets of enstrophy and dissipation in isotropic turbulence

NASA Astrophysics Data System (ADS)

Elsas, José Hugo; Szalay, Alexander S.; Meneveau, Charles

2018-04-01

Motivated by interest in the geometry of high intensity events of turbulent flows, we examine the spatial correlation functions of sets where turbulent events are particularly intense. These sets are defined using indicator functions on excursion and iso-value sets. Their geometric scaling properties are analysed by examining possible power-law decay of their radial correlation function. We apply the analysis to enstrophy, dissipation and velocity gradient invariants Q and R and their joint spatial distributions, using data from a direct numerical simulation of isotropic turbulence at Reλ ≈ 430. While no fractal scaling is found in the inertial range using box-counting in the finite Reynolds number flow considered here, power-law scaling in the inertial range is found in the radial correlation functions. Thus, a geometric characterisation in terms of these sets' correlation dimension is possible. Strong dependence on the enstrophy and dissipation threshold is found, consistent with multifractal behaviour. Nevertheless, the lack of scaling of the box-counting analysis precludes direct quantitative comparisons with earlier work based on multifractal formalism. Surprising trends, such as a lower correlation dimension for strong dissipation events compared to strong enstrophy events, are observed and interpreted in terms of spatial coherence of vortices in the flow.

Complementarity between tripartite quantum correlation and bipartite Bell-inequality violation in three-qubit states

NASA Astrophysics Data System (ADS)

Pandya, Palash; Misra, Avijit; Chakrabarty, Indranil

2016-11-01

We find a single parameter family of genuinely entangled three-qubit pure states, called the maximally Bell-inequality violating states (MBV), which exhibit maximum Bell-inequality violation by the reduced bipartite system for a fixed amount of genuine tripartite entanglement quantified by the so-called tangle measure. This in turn implies that there holds a complementary relation between the Bell-inequality violation by the reduced bipartite systems and the tangle present in the three-qubit states, not necessarily pure. The MBV states also exhibit maximum Bell-inequality violation by the reduced bipartite systems of the three-qubit pure states with a fixed amount of genuine tripartite correlation quantified by the generalized geometric measure, a genuine entanglement measure of multiparty pure states, and the discord monogamy score, a multipartite quantum correlation measure from information-theoretic paradigm. The aforementioned complementary relation has also been established for three-qubit pure states for the generalized geometric measure and the discord monogamy score, respectively. The complementarity between the Bell-inequality violation by the reduced bipartite systems and the genuine tripartite correlation suggests that the Bell-inequality violation in the reduced two-qubit system comes at the cost of the total tripartite correlation present in the entire system.

Riemannian geometry of thermodynamics and systems with repulsive power-law interactions.

PubMed

Ruppeiner, George

2005-07-01

A Riemannian geometric theory of thermodynamics based on the postulate that the curvature scalar R is proportional to the inverse free energy density is used to investigate three-dimensional fluid systems of identical classical point particles interacting with each other via a power-law potential energy gamma r(-alpha) . Such systems are useful in modeling melting transitions. The limit alpha-->infinity corresponds to the hard sphere gas. A thermodynamic limit exists only for short-range (alpha>3) and repulsive (gamma>0) interactions. The geometric theory solutions for given alpha>3 , gamma>0 , and any constant temperature T have the following properties: (1) the thermodynamics follows from a single function b (rho T(-3/alpha) ) , where rho is the density; (2) all solutions are equivalent up to a single scaling constant for rho T(-3/alpha) , related to gamma via the virial theorem; (3) at low density, solutions correspond to the ideal gas; (4) at high density there are solutions with pressure and energy depending on density as expected from solid state physics, though not with a Dulong-Petit heat capacity limit; (5) for 33.7913 a phase transition is required to go between these regimes; (7) for any alpha>3 we may include a first-order phase transition, which is expected from computer simulations; and (8) if alpha-->infinity, the density approaches a finite value as the pressure increases to infinity, with the pressure diverging logarithmically in the density difference.

Orientation-independent measures of ground motion

USGS Publications Warehouse

Boore, D.M.; Watson-Lamprey, Jennie; Abrahamson, N.A.

2006-01-01

The geometric mean of the response spectra for two orthogonal horizontal components of motion, commonly used as the response variable in predictions of strong ground motion, depends on the orientation of the sensors as installed in the field. This means that the measure of ground-motion intensity could differ for the same actual ground motion. This dependence on sensor orientation is most pronounced for strongly correlated motion (the extreme example being linearly polarized motion), such as often occurs at periods of 1 sec or longer. We propose two new measures of the geometric mean, GMRotDpp, and GMRotIpp, that are independent of the sensor orientations. Both are based on a set of geometric means computed from the as-recorded orthogonal horizontal motions rotated through all possible non-redundant rotation angles. GMRotDpp is determined as the ppth percentile of the set of geometric means for a given oscillator period. For example, GMRotDOO, GMRotD50, and GMRotD100 correspond to the minimum, median, and maximum values, respectively. The rotations that lead to GMRotDpp depend on period, whereas a single-period-independent rotation is used for GMRotIpp, the angle being chosen to minimize the spread of the rotation-dependent geometric mean (normalized by GMRotDpp) over the usable range of oscillator periods. GMRotI50 is the ground-motion intensity measure being used in the development of new ground-motion prediction equations by the Pacific Earthquake Engineering Center Next Generation Attenuation project. Comparisons with as-recorded geometric means for a large dataset show that the new measures are systematically larger than the geometric-mean response spectra using the as-recorded values of ground acceleration, but only by a small amount (less than 3%). The theoretical advantage of the new measures is that they remove sensor orientation as a contributor to aleatory uncertainty. Whether the reduction is of practical significance awaits detailed studies of large datasets. A preliminary analysis contained in a companion article by Beyer and Bommer finds that the reduction is small-to-nonexistent for equations based on a wide range of magnitudes and distances. The results of Beyer and Bommer do suggest, however, that there is an increasing reduction as period increases. Whether the reduction increases with other subdivisions of the dataset for which strongly correlated motions might be expected (e.g., pulselike motions close to faults) awaits further analysis.

Magnetic Fluctuations in the Hubbard Model on Kagome-based Frustrated Lattices

NASA Astrophysics Data System (ADS)

Udagawa, Masafumi; Motome, Yukitoshi

2008-03-01

We report our results on the interplay between electron correlation and magnetic fluctuations in the geometrically-frustrated Kagome and hyper-Kagome Hubbard models at half filling. These models have two different geometrical units important in the low-energy physics: the frustrated triangle and the non-frustrated loop with even-number sites. In order to treat both of them on equal footing, we apply cluster dynamical mean-field theory to large-size clusters up to 12 sites. By calculating the spin susceptibility χ(q, φ), we have found in the Kagome system that an anomalous one-dimensional magnetic correlation previously found near the Mott transition [1] is observed even in the non-interacting case at high temperature, and its temperature range gradually suppressed by increasing electron correlation. This behavior is ascribed to the nesting property at the van-Hove singularity preserved under electron correlation. We will also present the results for hyper-Kagome system in relation to the recent experiments on Na4Ir3O8 [2]. [1] T. Ohashi et al., Phys. Rev. Lett. 97, 066401 (2006)[2] Y. Okamoto et al., Phys. Rev. Lett. 99, 137207 (2007)

Classification of Mls Point Clouds in Urban Scenes Using Detrended Geometric Features from Supervoxel-Based Local Contexts

NASA Astrophysics Data System (ADS)

Sun, Z.; Xu, Y.; Hoegner, L.; Stilla, U.

2018-05-01

In this work, we propose a classification method designed for the labeling of MLS point clouds, with detrended geometric features extracted from the points of the supervoxel-based local context. To achieve the analysis of complex 3D urban scenes, acquired points of the scene should be tagged with individual labels of different classes. Thus, assigning a unique label to the points of an object that belong to the same category plays an essential role in the entire 3D scene analysis workflow. Although plenty of studies in this field have been reported, this work is still a challenging task. Specifically, in this work: 1) A novel geometric feature extraction method, detrending the redundant and in-salient information in the local context, is proposed, which is proved to be effective for extracting local geometric features from the 3D scene. 2) Instead of using individual point as basic element, the supervoxel-based local context is designed to encapsulate geometric characteristics of points, providing a flexible and robust solution for feature extraction. 3) Experiments using complex urban scene with manually labeled ground truth are conducted, and the performance of proposed method with respect to different methods is analyzed. With the testing dataset, we have obtained a result of 0.92 for overall accuracy for assigning eight semantic classes.

Geometrically Nonlinear Static Analysis of 3D Trusses Using the Arc-Length Method

NASA Technical Reports Server (NTRS)

Hrinda, Glenn A.

2006-01-01

Rigorous analysis of geometrically nonlinear structures demands creating mathematical models that accurately include loading and support conditions and, more importantly, model the stiffness and response of the structure. Nonlinear geometric structures often contain critical points with snap-through behavior during the response to large loads. Studying the post buckling behavior during a portion of a structure's unstable load history may be necessary. Primary structures made from ductile materials will stretch enough prior to failure for loads to redistribute producing sudden and often catastrophic collapses that are difficult to predict. The responses and redistribution of the internal loads during collapses and possible sharp snap-back of structures have frequently caused numerical difficulties in analysis procedures. The presence of critical stability points and unstable equilibrium paths are major difficulties that numerical solutions must pass to fully capture the nonlinear response. Some hurdles still exist in finding nonlinear responses of structures under large geometric changes. Predicting snap-through and snap-back of certain structures has been difficult and time consuming. Also difficult is finding how much load a structure may still carry safely. Highly geometrically nonlinear responses of structures exhibiting complex snap-back behavior are presented and analyzed with a finite element approach. The arc-length method will be reviewed and shown to predict the proper response and follow the nonlinear equilibrium path through limit points.

An image adaptive, wavelet-based watermarking of digital images

NASA Astrophysics Data System (ADS)

Agreste, Santa; Andaloro, Guido; Prestipino, Daniela; Puccio, Luigia

2007-12-01

In digital management, multimedia content and data can easily be used in an illegal way--being copied, modified and distributed again. Copyright protection, intellectual and material rights protection for authors, owners, buyers, distributors and the authenticity of content are crucial factors in solving an urgent and real problem. In such scenario digital watermark techniques are emerging as a valid solution. In this paper, we describe an algorithm--called WM2.0--for an invisible watermark: private, strong, wavelet-based and developed for digital images protection and authenticity. Using discrete wavelet transform (DWT) is motivated by good time-frequency features and well-matching with human visual system directives. These two combined elements are important in building an invisible and robust watermark. WM2.0 works on a dual scheme: watermark embedding and watermark detection. The watermark is embedded into high frequency DWT components of a specific sub-image and it is calculated in correlation with the image features and statistic properties. Watermark detection applies a re-synchronization between the original and watermarked image. The correlation between the watermarked DWT coefficients and the watermark signal is calculated according to the Neyman-Pearson statistic criterion. Experimentation on a large set of different images has shown to be resistant against geometric, filtering and StirMark attacks with a low rate of false alarm.

Background-Error Correlation Model Based on the Implicit Solution of a Diffusion Equation

DTIC Science & Technology

2010-01-01

1 Background- Error Correlation Model Based on the Implicit Solution of a Diffusion Equation Matthew J. Carrier* and Hans Ngodock...4. TITLE AND SUBTITLE Background- Error Correlation Model Based on the Implicit Solution of a Diffusion Equation 5a. CONTRACT NUMBER 5b. GRANT...2001), which sought to model error correlations based on the explicit solution of a generalized diffusion equation. The implicit solution is

Optimization of the blade trailing edge geometric parameters for a small scale ORC turbine

NASA Astrophysics Data System (ADS)

Zhang, L.; Zhuge, W. L.; Peng, J.; Liu, S. J.; Zhang, Y. J.

2013-12-01

In general, the method proposed by Whitfield and Baines is adopted for the turbine preliminary design. In this design procedure for the turbine blade trailing edge geometry, two assumptions (ideal gas and zero discharge swirl) and two experience values (WR and γ) are used to get the three blade trailing edge geometric parameters: relative exit flow angle β6, the exit tip radius R6t and hub radius R6h for the purpose of maximizing the rotor total-to-static isentropic efficiency. The method above is established based on the experience and results of testing using air as working fluid, so it does not provide a mathematical optimal solution to instruct the optimization of geometry parameters and consider the real gas effects of the organic, working fluid which must be taken into consideration for the ORC turbine design procedure. In this paper, a new preliminary design and optimization method is established for the purpose of reducing the exit kinetic energy loss to improve the turbine efficiency ηts, and the blade trailing edge geometric parameters for a small scale ORC turbine with working fluid R123 are optimized based on this method. The mathematical optimal solution to minimize the exit kinetic energy is deduced, which can be used to design and optimize the exit shroud/hub radius and exit blade angle. And then, the influence of blade trailing edge geometric parameters on turbine efficiency ηts are analysed and the optimal working ranges of these parameters for the equations are recommended in consideration of working fluid R123. This method is used to modify an existing ORC turbine exit kinetic energy loss from 11.7% to 7%, which indicates the effectiveness of the method. However, the internal passage loss increases from 7.9% to 9.4%, so the only way to consider the influence of geometric parameters on internal passage loss is to give the empirical ranges of these parameters, such as the recommended ranges that the value of γ is at 0.3 to 0.4, and the value of τ is at 0.5 to 0.6.

Do Dogs Know the Trammel of Archimedes?

ERIC Educational Resources Information Center

Schwartz, Mark

2011-01-01

The refraction problem, well-known in calculus and physics, continues to reveal new insights. This paper presents a geometric solution in which the trammel of Archimedes plays the prominent role. When properly configured, the trammel generates an ellipse and its family of normal lines. One normal line in particular intersects the boundary…

Exploring Geometric Sequences

ERIC Educational Resources Information Center

Reiser, Elana

2016-01-01

In this brief article Elana Reiser describes her favorite lesson that combines popular culture with mathematics in a way that motivates student thinking and participation. Exploring open-ended problems, students may feel uneasy at first, but working in small groups often leads them to experiment with a variety of solutions. Reiser explains that…

Journal: Efficient Hydrologic Tracer-Test Design for Tracer-Mass Estimation and Sample Collection Frequency, 1 Method Development

EPA Science Inventory

Hydrological tracer testing is the most reliable diagnostic technique available for the determination of basic hydraulic and geometric parameters necessary for establishing operative solute-transport processes. Tracer-test design can be difficult because of a lack of prior knowl...

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…

Comparing Three Methods of Geometrical Approach in Visualizing Differential Equations

ERIC Educational Resources Information Center

KarimiFardinpour, Younes; Gooya, Zahra

2018-01-01

This paper concerns "planes-coordination" and "long-term-prediction" difficulties. These are specifically the case when students attempt to visualize solution curves of autonomous differential equations for predicting the long-term behavior of various initial conditions. To address these issues, a study was conducted in which…

Guards, Galleries, Fortresses, and the Octoplex

ERIC Educational Resources Information Center

Michael, T. S.

2011-01-01

The art gallery problem asks for the maximum number of stationary guards required to protect the interior of a polygonal art gallery with "n" walls. This article explores solutions to this problem and several of its variants. In addition, some unsolved problems involving the guarding of geometric objects are presented.

A Geometric Solution of a Cournot Ogilopoly with Nonidentical Firms.

ERIC Educational Resources Information Center

Sarkar, Jyotirmoy; Gupta, Barnali; Pal, Debashis

1998-01-01

Maintains that a proper understanding of the Augustin Cournot model of imperfect competition and strategic interactions among firms in various contexts is essential for economics education. Although most models rely on complicated algebra, this one requires nothing more than high school level geometry. Includes a graphical analysis. (MJP)

Solution of electromagnetic scattering and radiation problems using a spectral domain approach - A review

NASA Technical Reports Server (NTRS)

Mittra, R.; Ko, W. L.; Rahmat-Samii, Y.

1979-01-01

This paper presents a brief review of some recent developments on the use of the spectral-domain approach for deriving high-frequency solutions to electromagnetics scattering and radiation problems. The spectral approach is not only useful for interpreting the well-known Keller formulas based on the geometrical theory of diffraction (GTD), it can also be employed for verifying the accuracy of GTD and other asymptotic solutions and systematically improving the results when such improvements are needed. The problem of plane wave diffraction by a finite screen or a strip is presented as an example of the application of the spectral-domain approach.

Analytical study of fractional equations describing anomalous diffusion of energetic particles

NASA Astrophysics Data System (ADS)

Tawfik, A. M.; Fichtner, H.; Schlickeiser, R.; Elhanbaly, A.

2017-06-01

To present the main influence of anomalous diffusion on the energetic particle propagation, the fractional derivative model of transport is developed by deriving the fractional modified Telegraph and Rayleigh equations. Analytical solutions of the fractional modified Telegraph and the fractional Rayleigh equations, which are defined in terms of Caputo fractional derivatives, are obtained by using the Laplace transform and the Mittag-Leffler function method. The solutions of these fractional equations are given in terms of special functions like Fox’s H, Mittag-Leffler, Hermite and Hyper-geometric functions. The predicted travelling pulse solutions are discussed in each case for different values of fractional order.

Metrics on the relative spacecraft motion invariant manifold.

PubMed

Gurfil, P; Kholshevnikov, Konstantin V

2005-12-01

This paper establishes a methodology for obtaining the general solution to the spacecraft relative motion problem by utilizing Cartesian configuration space in conjunction with classical orbital elements. The geometry of the relative motion configuration space is analyzed, and the relative motion invariant manifold is determined. Most importantly, the geometric structure of the relative motion problem is used to derive useful metrics for quantification of the minimum, maximum, and mean distance between spacecraft for commensurable and non-commensurable mean motions. A number of analytic solutions, as well as useful examples, are provided, illustrating the calculated bounds. A few particular cases are given that yield simple solutions.

Satellite triangulation in Europe from WEST and ISAGEX data. [computer programs

NASA Technical Reports Server (NTRS)

Leick, A.; Arur, M.

1975-01-01

Observational data that was acquired during the West European Satellite Triangulation (WEST) program and the International Satellite Geodesy Experiment (ISAGEX) campaign was obtained for the purpose of performing a geometric solution to improve the present values of coordinates of the European stations in the OSU WN14 solutions, adding some new stations and assessing the quality of the WN14 solution with the help of the additional data available. The status of the data as received, the preprocessing required and the preliminary tests carried out for the initial screening of the data are described. The adjustment computations carried out and the results of the adjustments are discussed.

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

Levay, Peter; Nagy, Szilvia; Pipek, Janos

An elementary formula for the von Neumann and Renyi entropies describing quantum correlations in two-fermionic systems having four single-particle states is presented. An interesting geometric structure of fermionic entanglement is revealed. A connection with the generalized Pauli principle is established.

Toward Higher-Order Mass Detection: Influence of an Adsorbate's Rotational Inertia and Eccentricity on the Resonant Response of a Bernoulli-Euler Cantilever Beam.

PubMed

Heinrich, Stephen M; Dufour, Isabelle

2015-11-19

In this paper a new theoretical model is derived, the results of which permit a detailed examination of how the resonant characteristics of a cantilever are influenced by a particle (adsorbate) attached at an arbitrary position along the beam's length. Unlike most previous work, the particle need not be small in mass or dimension relative to the beam, and the adsorbate's geometric characteristics are incorporated into the model via its rotational inertia and eccentricity relative to the beam axis. For the special case in which the adsorbate's (translational) mass is indeed small, an analytical solution is obtained for the particle-induced resonant frequency shift of an arbitrary flexural mode, including the effects of rotational inertia and eccentricity. This solution is shown to possess the exact first-order behavior in the normalized particle mass and represents a generalization of analytical solutions derived by others in earlier studies. The results suggest the potential for "higher-order" nanobeam-based mass detection methods by which the multi-mode frequency response reflects not only the adsorbate's mass but also important geometric data related to its size, shape, or orientation (i.e., the mass distribution), thus resulting in more highly discriminatory techniques for discrete-mass sensing.

Toward Higher-Order Mass Detection: Influence of an Adsorbate’s Rotational Inertia and Eccentricity on the Resonant Response of a Bernoulli-Euler Cantilever Beam

PubMed Central

Heinrich, Stephen M.; Dufour, Isabelle

2015-01-01

In this paper a new theoretical model is derived, the results of which permit a detailed examination of how the resonant characteristics of a cantilever are influenced by a particle (adsorbate) attached at an arbitrary position along the beam’s length. Unlike most previous work, the particle need not be small in mass or dimension relative to the beam, and the adsorbate’s geometric characteristics are incorporated into the model via its rotational inertia and eccentricity relative to the beam axis. For the special case in which the adsorbate’s (translational) mass is indeed small, an analytical solution is obtained for the particle-induced resonant frequency shift of an arbitrary flexural mode, including the effects of rotational inertia and eccentricity. This solution is shown to possess the exact first-order behavior in the normalized particle mass and represents a generalization of analytical solutions derived by others in earlier studies. The results suggest the potential for “higher-order” nanobeam-based mass detection methods by which the multi-mode frequency response reflects not only the adsorbate’s mass but also important geometric data related to its size, shape, or orientation (i.e., the mass distribution), thus resulting in more highly discriminatory techniques for discrete-mass sensing. PMID:26610493

Analytic Approximations to the Free Boundary and Multi-dimensional Problems in Financial Derivatives Pricing

NASA Astrophysics Data System (ADS)

Lau, Chun Sing

This thesis studies two types of problems in financial derivatives pricing. The first type is the free boundary problem, which can be formulated as a partial differential equation (PDE) subject to a set of free boundary condition. Although the functional form of the free boundary condition is given explicitly, the location of the free boundary is unknown and can only be determined implicitly by imposing continuity conditions on the solution. Two specific problems are studied in details, namely the valuation of fixed-rate mortgages and CEV American options. The second type is the multi-dimensional problem, which involves multiple correlated stochastic variables and their governing PDE. One typical problem we focus on is the valuation of basket-spread options, whose underlying asset prices are driven by correlated geometric Brownian motions (GBMs). Analytic approximate solutions are derived for each of these three problems. For each of the two free boundary problems, we propose a parametric moving boundary to approximate the unknown free boundary, so that the original problem transforms into a moving boundary problem which can be solved analytically. The governing parameter of the moving boundary is determined by imposing the first derivative continuity condition on the solution. The analytic form of the solution allows the price and the hedging parameters to be computed very efficiently. When compared against the benchmark finite-difference method, the computational time is significantly reduced without compromising the accuracy. The multi-stage scheme further allows the approximate results to systematically converge to the benchmark results as one recasts the moving boundary into a piecewise smooth continuous function. For the multi-dimensional problem, we generalize the Kirk (1995) approximate two-asset spread option formula to the case of multi-asset basket-spread option. Since the final formula is in closed form, all the hedging parameters can also be derived in closed form. Numerical examples demonstrate that the pricing and hedging errors are in general less than 1% relative to the benchmark prices obtained by numerical integration or Monte Carlo simulation. By exploiting an explicit relationship between the option price and the underlying probability distribution, we further derive an approximate distribution function for the general basket-spread variable. It can be used to approximate the transition probability distribution of any linear combination of correlated GBMs. Finally, an implicit perturbation is applied to reduce the pricing errors by factors of up to 100. When compared against the existing methods, the basket-spread option formula coupled with the implicit perturbation turns out to be one of the most robust and accurate approximation methods.

On the Solutions of Two-Extended Principal Conformal Toda Theory

NASA Astrophysics Data System (ADS)

Chao, L.; Hou, B. Y.

1994-02-01

The solutions of the two-extended principal conformal Toda theory (2-EPCT theory, also called bosonic superconformal Toda theory) are constructed in two different ways: (1) Leznov-Saveliev algebraic analysis and (2) the associated chiral embedding surface. The first approach gives rise to the general solution in terms of appropriate matrix elements in different fundamental representations of the underlying Lie algebra, whilst the second one leads to a special solution in the form of Wronski determinants and their co-minors, and it gives an explicit geometrical interpretation of the WZNW → 2-EPCT reduction. The key points of both approaches are the chiral vectors derived recently by the authors, which constitute a closed exchange algebra of the theory.

Geometric parameter analysis to predetermine optimal radiosurgery technique for the treatment of arteriovenous malformation

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

Mestrovic, Ante; Clark, Brenda G.; Department of Medical Physics, British Columbia Cancer Agency, Vancouver, British Columbia

2005-11-01

Purpose: To develop a method of predicting the values of dose distribution parameters of different radiosurgery techniques for treatment of arteriovenous malformation (AVM) based on internal geometric parameters. Methods and Materials: For each of 18 previously treated AVM patients, four treatment plans were created: circular collimator arcs, dynamic conformal arcs, fixed conformal fields, and intensity-modulated radiosurgery. An algorithm was developed to characterize the target and critical structure shape complexity and the position of the critical structures with respect to the target. Multiple regression was employed to establish the correlation between the internal geometric parameters and the dose distribution for differentmore » treatment techniques. The results from the model were applied to predict the dosimetric outcomes of different radiosurgery techniques and select the optimal radiosurgery technique for a number of AVM patients. Results: Several internal geometric parameters showing statistically significant correlation (p < 0.05) with the treatment planning results for each technique were identified. The target volume and the average minimum distance between the target and the critical structures were the most effective predictors for normal tissue dose distribution. The structure overlap volume with the target and the mean distance between the target and the critical structure were the most effective predictors for critical structure dose distribution. The predicted values of dose distribution parameters of different radiosurgery techniques were in close agreement with the original data. Conclusions: A statistical model has been described that successfully predicts the values of dose distribution parameters of different radiosurgery techniques and may be used to predetermine the optimal technique on a patient-to-patient basis.« less

Computing multiple periodic solutions of nonlinear vibration problems using the harmonic balance method and Groebner bases

NASA Astrophysics Data System (ADS)

Grolet, Aurelien; Thouverez, Fabrice

2015-02-01

This paper is devoted to the study of vibration of mechanical systems with geometric nonlinearities. The harmonic balance method is used to derive systems of polynomial equations whose solutions give the frequency component of the possible steady states. Groebner basis methods are used for computing all solutions of polynomial systems. This approach allows to reduce the complete system to an unique polynomial equation in one variable driving all solutions of the problem. In addition, in order to decrease the number of variables, we propose to first work on the undamped system, and recover solution of the damped system using a continuation on the damping parameter. The search for multiple solutions is illustrated on a simple system, where the influence of the retained number of harmonic is studied. Finally, the procedure is applied on a simple cyclic system and we give a representation of the multiple states versus frequency.

Simultaneous observation solutions for NASA-MOTS and SPEOPT station positions on the North American datum

NASA Technical Reports Server (NTRS)

Reece, J. S.; Marsh, J.

1973-01-01

Simultaneous observations of the GEOS-I and II flashing lamps by the NASA MOTS and SPEOPT cameras on the North American Datum (NAD) were analyzed using geometrical techniques to provide an adjustment of the station coordinates. Two separate adjustments were obtained. An optical data only solution was computed in which the solution scale was provided by the Rosman-Mojave distance obtained from a dynamic station solution. In a second adjustment, scaling was provided by processing simultaneous laser ranging data from Greenbelt and Wallops Island in a combined optical-laser solution. Comparisons of these results with previous GSFC dynamical solutions indicate an rms agreement on the order of 4 meters or better in each coordinate. Comparison with a detailed gravimetric geoid of North America yields agreement of 3 meters or better for mainland U.S. stations and 7 and 3 meters, respectively, for Bermuda and Puerto Rico.

Metal Sorbing Vesicles: Light Scattering Characterization and Metal Sorbtion Behavior.

NASA Astrophysics Data System (ADS)

van Zanten, John Hollis

1992-01-01

The research described herein consisted of two parts: light scattering characterization of vesicles and kinetic investigations of metal sorbing vesicles. Static light scattering techniques can be used to determine the geometric size, shape and apparent molecular weight of phosphatidylcholine vesicles in aqueous suspension. A Rayleigh-Gans-Debye (RGD) approximation analysis of multiangle scattered light intensity data yields the size and degree of polydispersity of the vesicles in solution, while the Zimm plot technique provides the radius of gyration and apparent weight-average molecular weight. Together the RGD approximation and Zimm plots can be used to confirm the geometric shape of vesicles and can give a good estimate of the vesicle wall thickness in some cases. Vesicles varying from 40 to 115 nm in diameter have been characterized effectively. The static light scattering measurements indicate that, as expected, phosphatidylcholine vesicles in this size range scatter light as isotropic hollow spheres. Additionally, static and dynamic light scattering measurements have been made and compared with one another. The values for geometric radii determined by static light scattering typically agree with those estimated by dynamic light scattering to within a few percent. Interestingly however, dynamic measurements suggest that there is a significant degree of polydispersity present in the vesicle dispersions, while static measurements indicate near size monodisperse dispersions. Metal sorbing vesicles which harbor ionophores, such as antibiotic A23187 and synthetic carriers, in their bilayer membranes have been produced. These vesicles also encapsulate the chelating compound, nitrilotriacetate, to provide the driving force for metal ion uptake. Very dilute dispersions (on the order of 0.03% w/v) of these metal sorbing vesicles were capable of removing Cd ^{2+} and Pb^{2+ } from dilute aqueous solution (5 ppm and less) and concentrating these metal ions several hundred to more than a thousand fold in the vesicle interior in a few minutes time. Synthetic ionophores were found to preferentially transport Pb^{2+} over Cd^{2+}, thus suggesting that engineered vesicle dispersions can be used as selective separations media. The effect of ionophore concentration, solution pH, solution ionic strength, initial metal ion concentration and vesicle concentration have been investigated.

Physical optics-based diffraction coefficient for a wedge with different face impedances.

PubMed

Umul, Yusuf Ziya

2018-03-20

A new diffraction field expression is introduced with the aid of the modified theory of physical optics for a wedge with different face impedances. First, the scattered geometrical optics fields are determined when both faces of the wedge are illuminated by the incident wave. The geometrical optics waves are then expressed in terms of the sum of two different fields that occur for different impedance wedges. The diffracted fields are determined for the two cases separately, and the total diffracted field is obtained as a sum of these waves. Lastly, the uniform field expressions are obtained, and the resultant fields are numerically compared with the solution of Maliuzhinets.

Information geometry and its application to theoretical statistics and diffusion tensor magnetic resonance imaging

NASA Astrophysics Data System (ADS)

Wisniewski, Nicholas Andrew

This dissertation is divided into two parts. First we present an exact solution to a generalization of the Behrens-Fisher problem by embedding the problem in the Riemannian manifold of Normal distributions. From this we construct a geometric hypothesis testing scheme. Secondly we investigate the most commonly used geometric methods employed in tensor field interpolation for DT-MRI analysis and cardiac computer modeling. We computationally investigate a class of physiologically motivated orthogonal tensor invariants, both at the full tensor field scale and at the scale of a single interpolation by doing a decimation/interpolation experiment. We show that Riemannian-based methods give the best results in preserving desirable physiological features.

Reflectance of micron-sized dust particles retrieved with the Umov law

NASA Astrophysics Data System (ADS)

Zubko, Evgenij; Videen, Gorden; Zubko, Nataliya; Shkuratov, Yuriy

2017-03-01

The maximum positive polarization Pmax that initially unpolarized light acquires when scattered from a particulate surface inversely correlates with its geometric albedo A. In the literature, this phenomenon is known as the Umov law. We investigate the Umov law in application to single-scattering submicron and micron-sized agglomerated debris particles, model particles that have highly irregular morphology. We find that if the complex refractive index m is constrained to Re(m)=1.4-1.7 and Im(m)=0-0.15, model particles of a given size distribution have a linear inverse correlation between log(Pmax) and log(A). This correlation resembles what is measured in particulate surfaces, suggesting a similar mechanism governing the Umov law in both systems. We parameterize the dependence of log(A) on log(Pmax) of single-scattering particles and analyze the airborne polarimetric measurements of atmospheric aerosols reported by Dolgos & Martins in [1]. We conclude that Pmax ≈ 50% measured by Dolgos & Martins corresponds to very dark aerosols having geometric albedo A=0.019 ± 0.005.

An introduction to the interim digital SAR processor and the characteristics of the associated Seasat SAR imagery

NASA Technical Reports Server (NTRS)

Wu, C.; Barkan, B.; Huneycutt, B.; Leang, C.; Pang, S.

1981-01-01

Basic engineering data regarding the Interim Digital SAR Processor (IDP) and the digitally correlated Seasat synthetic aperature radar (SAR) imagery are presented. The correlation function and IDP hardware/software configuration are described, and a preliminary performance assessment presented. The geometric and radiometric characteristics, with special emphasis on those peculiar to the IDP produced imagery, are described.

Encounter Models for the Littoral Regions of the National Airspace System

DTIC Science & Technology

2010-09-15

Jeff Richardson, Steven Schimmelpfennig, Richard Whitlock, Lt. Han Saydam, Lt. Tanuxay Keooudom, James Evans, TSgt. Christopher Cosper, Lt. Luke Marron...24 17 Correlated geometric feature comparison. 25 A- l Aircraft vertical rate in uncorrelated encounters. 31 A-2 Uncorrelated continuous feature...in correlated encounters. 35 B- l Approach angle (/3) and bearing (x) definition. 39 C- l Horizontal plane encounter initialization. 42 C-2

The effect of impeller type on silica sol formation in laboratory scale agitated tank

NASA Astrophysics Data System (ADS)

Nurtono, Tantular; Suprana, Yayang Ade; Latif, Abdul; Dewa, Restu Mulya; Machmudah, Siti; Widiyastuti, Winardi, Sugeng

2016-02-01

The multiphase polymerization reaction of the silica sol formation produced from silicic acid and potassium hydroxide solutions in laboratory scale agitated tank was studied. The reactor is equipped with four segmental baffle and top entering impeller. The inside diameter of reactor is 9 cm, the baffle width is 0.9 cm, and the impeller position is 3 cm from tank bottom. The diameter of standard six blades Rushton and three blades marine propeller impellers are 5 cm. The silicic acid solution was made from 0.2 volume fraction of water glass (sodium silicate) solution in which the sodium ion was exchanged by hydrogen ion from cation resin. The reactor initially filled with 286 ml silicic acid solution was operated in semi batch mode and the temperature was kept constant in 60 °C. The 3 ml/minute of 1 M potassium hydroxide solution was added into stirred tank and the solution was stirred. The impeller rotational speed was varied from 100 until 700 rpm. This titration was stopped if the solution in stirred tank had reached the pH of 10-The morphology of the silica particles in the silica sol product was analyzed by Scanning Electron Microscope (SEM). The size of silica particles in silica sol was measured based on the SEM image. The silica particle obtained in this research was amorphous particle and the shape was roughly cylinder. The flow field generated by different impeller gave significant effect on particle size and shape. The smallest geometric mean of length and diameter of particle (4.92 µm and 2.42 µm, respectively) was generated in reactor with marine propeller at 600 rpm. The reactor with Rushton impeller produced particle which the geometric mean of length and diameter of particle was 4.85 µm and 2.36 µm, respectively, at 150 rpm.

The effect of impeller type on silica sol formation in laboratory scale agitated tank

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

Nurtono, Tantular; Suprana, Yayang Ade; Latif, Abdul

2016-02-08

The multiphase polymerization reaction of the silica sol formation produced from silicic acid and potassium hydroxide solutions in laboratory scale agitated tank was studied. The reactor is equipped with four segmental baffle and top entering impeller. The inside diameter of reactor is 9 cm, the baffle width is 0.9 cm, and the impeller position is 3 cm from tank bottom. The diameter of standard six blades Rushton and three blades marine propeller impellers are 5 cm. The silicic acid solution was made from 0.2 volume fraction of water glass (sodium silicate) solution in which the sodium ion was exchanged by hydrogen ion from cationmore » resin. The reactor initially filled with 286 ml silicic acid solution was operated in semi batch mode and the temperature was kept constant in 60 °C. The 3 ml/minute of 1 M potassium hydroxide solution was added into stirred tank and the solution was stirred. The impeller rotational speed was varied from 100 until 700 rpm. This titration was stopped if the solution in stirred tank had reached the pH of 10-The morphology of the silica particles in the silica sol product was analyzed by Scanning Electron Microscope (SEM). The size of silica particles in silica sol was measured based on the SEM image. The silica particle obtained in this research was amorphous particle and the shape was roughly cylinder. The flow field generated by different impeller gave significant effect on particle size and shape. The smallest geometric mean of length and diameter of particle (4.92 µm and 2.42 µm, respectively) was generated in reactor with marine propeller at 600 rpm. The reactor with Rushton impeller produced particle which the geometric mean of length and diameter of particle was 4.85 µm and 2.36 µm, respectively, at 150 rpm.« less

Improving the Accuracy of Direct Geo-referencing of Smartphone-Based Mobile Mapping Systems Using Relative Orientation and Scene Geometric Constraints.

PubMed

Alsubaie, Naif M; Youssef, Ahmed A; El-Sheimy, Naser

2017-09-30

This paper introduces a new method which facilitate the use of smartphones as a handheld low-cost mobile mapping system (MMS). Smartphones are becoming more sophisticated and smarter and are quickly closing the gap between computers and portable tablet devices. The current generation of smartphones are equipped with low-cost GPS receivers, high-resolution digital cameras, and micro-electro mechanical systems (MEMS)-based navigation sensors (e.g., accelerometers, gyroscopes, magnetic compasses, and barometers). These sensors are in fact the essential components for a MMS. However, smartphone navigation sensors suffer from the poor accuracy of global navigation satellite System (GNSS), accumulated drift, and high signal noise. These issues affect the accuracy of the initial Exterior Orientation Parameters (EOPs) that are inputted into the bundle adjustment algorithm, which then produces inaccurate 3D mapping solutions. This paper proposes new methodologies for increasing the accuracy of direct geo-referencing of smartphones using relative orientation and smartphone motion sensor measurements as well as integrating geometric scene constraints into free network bundle adjustment. The new methodologies incorporate fusing the relative orientations of the captured images and their corresponding motion sensor measurements to improve the initial EOPs. Then, the geometric features (e.g., horizontal and vertical linear lines) visible in each image are extracted and used as constraints in the bundle adjustment procedure which correct the relative position and orientation of the 3D mapping solution.

Improving the Accuracy of Direct Geo-referencing of Smartphone-Based Mobile Mapping Systems Using Relative Orientation and Scene Geometric Constraints

PubMed Central

Alsubaie, Naif M.; Youssef, Ahmed A.; El-Sheimy, Naser

2017-01-01

This paper introduces a new method which facilitate the use of smartphones as a handheld low-cost mobile mapping system (MMS). Smartphones are becoming more sophisticated and smarter and are quickly closing the gap between computers and portable tablet devices. The current generation of smartphones are equipped with low-cost GPS receivers, high-resolution digital cameras, and micro-electro mechanical systems (MEMS)-based navigation sensors (e.g., accelerometers, gyroscopes, magnetic compasses, and barometers). These sensors are in fact the essential components for a MMS. However, smartphone navigation sensors suffer from the poor accuracy of global navigation satellite System (GNSS), accumulated drift, and high signal noise. These issues affect the accuracy of the initial Exterior Orientation Parameters (EOPs) that are inputted into the bundle adjustment algorithm, which then produces inaccurate 3D mapping solutions. This paper proposes new methodologies for increasing the accuracy of direct geo-referencing of smartphones using relative orientation and smartphone motion sensor measurements as well as integrating geometric scene constraints into free network bundle adjustment. The new methodologies incorporate fusing the relative orientations of the captured images and their corresponding motion sensor measurements to improve the initial EOPs. Then, the geometric features (e.g., horizontal and vertical linear lines) visible in each image are extracted and used as constraints in the bundle adjustment procedure which correct the relative position and orientation of the 3D mapping solution. PMID:28973958

Causal structures in Gauss-Bonnet gravity

NASA Astrophysics Data System (ADS)

Izumi, Keisuke

2014-08-01

We analyze causal structures in Gauss-Bonnet gravity. It is known that Gauss-Bonnet gravity potentially has superluminal propagation of gravitons due to its noncanonical kinetic terms. In a theory with superluminal modes, an analysis of causality based on null curves makes no sense, and thus, we need to analyze them in a different way. In this paper, using the method of the characteristics, we analyze the causal structure in Gauss-Bonnet gravity. We have the result that, on a Killing horizon, gravitons can propagate in the null direction tangent to the Killing horizon. Therefore, a Killing horizon can be a causal edge as in the case of general relativity; i.e. a Killing horizon is the "event horizon" in the sense of causality. We also analyze causal structures on nonstationary solutions with (D-2)-dimensional maximal symmetry, including spherically symmetric and flat spaces. If the geometrical null energy condition, RABNANB≥0 for any null vector NA, is satisfied, the radial velocity of gravitons must be less than or equal to that of light. However, if the geometrical null energy condition is violated, gravitons can propagate faster than light. Hence, on an evaporating black hole where the geometrical null energy condition is expected not to hold, classical gravitons can escape from the "black hole" defined with null curves. That is, the causal structures become nontrivial. It may be one of the possible solutions for the information loss paradox of evaporating black holes.

A Non-Cut Cell Immersed Boundary Method for Use in Icing Simulations

NASA Technical Reports Server (NTRS)

Sarofeen, Christian M.; Noack, Ralph W.; Kreeger, Richard E.

2013-01-01

This paper describes a computational fluid dynamic method used for modelling changes in aircraft geometry due to icing. While an aircraft undergoes icing, the accumulated ice results in a geometric alteration of the aerodynamic surfaces. In computational simulations for icing, it is necessary that the corresponding geometric change is taken into consideration. The method used, herein, for the representation of the geometric change due to icing is a non-cut cell Immersed Boundary Method (IBM). Computational cells that are in a body fitted grid of a clean aerodynamic geometry that are inside a predicted ice formation are identified. An IBM is then used to change these cells from being active computational cells to having properties of viscous solid bodies. This method has been implemented in the NASA developed node centered, finite volume computational fluid dynamics code, FUN3D. The presented capability is tested for two-dimensional airfoils including a clean airfoil, an iced airfoil, and an airfoil in harmonic pitching motion about its quarter chord. For these simulations velocity contours, pressure distributions, coefficients of lift, coefficients of drag, and coefficients of pitching moment about the airfoil's quarter chord are computed and used for comparison against experimental results, a higher order panel method code with viscous effects, XFOIL, and the results from FUN3D's original solution process. The results of the IBM simulations show that the accuracy of the IBM compares satisfactorily with the experimental results, XFOIL results, and the results from FUN3D's original solution process.

Analytic calculations of hyper-Raman spectra from density functional theory hyperpolarizability gradients

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

Ringholm, Magnus; Ruud, Kenneth; Bast, Radovan

We present the first analytic calculations of the geometrical gradients of the first hyperpolarizability tensors at the density-functional theory (DFT) level. We use the analytically calculated hyperpolarizability gradients to explore the importance of electron correlation effects, as described by DFT, on hyper-Raman spectra. In particular, we calculate the hyper-Raman spectra of the all-trans and 11-cis isomers of retinal at the Hartree-Fock (HF) and density-functional levels of theory, also allowing us to explore the sensitivity of the hyper-Raman spectra on the geometrical characteristics of these structurally related molecules. We show that the HF results, using B3LYP-calculated vibrational frequencies and force fields,more » reproduce the experimental data for all-trans-retinal well, and that electron correlation effects are of minor importance for the hyper-Raman intensities.« less

Diversity of Chemical Bonding and Oxidation States in MS 4 Molecules of Group 8 Elements

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

Huang, Wei; Jiang, Ning; Schwarz, W. H. Eugen

The geometric and electronic ground-state structures of six MS 4 molecules (M = group-8 metals Fe, Ru, Os, Hs, Sm, and Pu) have been studied by using quantum-chemical density-functional and correlated wave-function approaches. The MS 4 species are compared to analogous MO 4 species recently investi-gated (Inorg. Chem. 2016, 55: 4616). Metal oxidation state (MOS) of high value VIII appears in low- spin singlet Td geometric species (Os,Hs)S 4 and (Ru,Os,Hs)O 4, whereas low MOS=II appears in high- spin septet D 2d species Fe(S 2) 2 and (slightly excited) metastable Fe(O 2) 2. The ground states of all other moleculesmore » have intermediate MOS values, containing S 2-, S 2 2-, S2 1- (and resp. O 2--, O 1-, O 2 2-, O 2 1-) ligands, bonded by ionic, covalent and correlative contributions.« less

Structure and Function in Homodimeric Enzymes: Simulations of Cooperative and Independent Functional Motions.

PubMed

Wells, Stephen A; van der Kamp, Marc W; McGeagh, John D; Mulholland, Adrian J

2015-01-01

Large-scale conformational change is a common feature in the catalytic cycles of enzymes. Many enzymes function as homodimers with active sites that contain elements from both chains. Symmetric and anti-symmetric cooperative motions in homodimers can potentially lead to correlated active site opening and/or closure, likely to be important for ligand binding and release. Here, we examine such motions in two different domain-swapped homodimeric enzymes: the DcpS scavenger decapping enzyme and citrate synthase. We use and compare two types of all-atom simulations: conventional molecular dynamics simulations to identify physically meaningful conformational ensembles, and rapid geometric simulations of flexible motion, biased along normal mode directions, to identify relevant motions encoded in the protein structure. The results indicate that the opening/closure motions are intrinsic features of both unliganded enzymes. In DcpS, conformational change is dominated by an anti-symmetric cooperative motion, causing one active site to close as the other opens; however a symmetric motion is also significant. In CS, we identify that both symmetric (suggested by crystallography) and asymmetric motions are features of the protein structure, and as a result the behaviour in solution is largely non-cooperative. The agreement between two modelling approaches using very different levels of theory indicates that the behaviours are indeed intrinsic to the protein structures. Geometric simulations correctly identify and explore large amplitudes of motion, while molecular dynamics simulations indicate the ranges of motion that are energetically feasible. Together, the simulation approaches are able to reveal unexpected functionally relevant motions, and highlight differences between enzymes.

Structure and Function in Homodimeric Enzymes: Simulations of Cooperative and Independent Functional Motions

PubMed Central

McGeagh, John D.; Mulholland, Adrian J.

2015-01-01

Large-scale conformational change is a common feature in the catalytic cycles of enzymes. Many enzymes function as homodimers with active sites that contain elements from both chains. Symmetric and anti-symmetric cooperative motions in homodimers can potentially lead to correlated active site opening and/or closure, likely to be important for ligand binding and release. Here, we examine such motions in two different domain-swapped homodimeric enzymes: the DcpS scavenger decapping enzyme and citrate synthase. We use and compare two types of all-atom simulations: conventional molecular dynamics simulations to identify physically meaningful conformational ensembles, and rapid geometric simulations of flexible motion, biased along normal mode directions, to identify relevant motions encoded in the protein structure. The results indicate that the opening/closure motions are intrinsic features of both unliganded enzymes. In DcpS, conformational change is dominated by an anti-symmetric cooperative motion, causing one active site to close as the other opens; however a symmetric motion is also significant. In CS, we identify that both symmetric (suggested by crystallography) and asymmetric motions are features of the protein structure, and as a result the behaviour in solution is largely non-cooperative. The agreement between two modelling approaches using very different levels of theory indicates that the behaviours are indeed intrinsic to the protein structures. Geometric simulations correctly identify and explore large amplitudes of motion, while molecular dynamics simulations indicate the ranges of motion that are energetically feasible. Together, the simulation approaches are able to reveal unexpected functionally relevant motions, and highlight differences between enzymes. PMID:26241964

A Novel Paradigm for Computer-Aided Design: TRIZ-Based Hybridization of Topologically Optimized Density Distributions

NASA Astrophysics Data System (ADS)

Cardillo, A.; Cascini, G.; Frillici, F. S.; Rotini, F.

In a recent project the authors have proposed the adoption of Optimization Systems [1] as a bridging element between Computer-Aided Innovation (CAI) and PLM to identify geometrical contradictions [2], a particular case of the TRIZ physical contradiction [3]. A further development of the research [4] has revealed that the solutions obtained from several topological optimizations can be considered as elementary customized modeling features for a specific design task. The topology overcoming the arising geometrical contradiction can be obtained through a manipulation of the density distributions constituting the conflicting pair. Already two strategies of density combination have been identified as capable to solve geometrical contradictions and several others are under extended testing. The paper illustrates the most recent results of the ongoing research mainly related to the extension of the algorithms from 2D to 3D design spaces. The whole approach is clarified by means of two detailed examples, where the proposed technique is compared with classical multi-goal optimization.

Parameterizations for ensemble Kalman inversion

NASA Astrophysics Data System (ADS)

Chada, Neil K.; Iglesias, Marco A.; Roininen, Lassi; Stuart, Andrew M.

2018-05-01

The use of ensemble methods to solve inverse problems is attractive because it is a derivative-free methodology which is also well-adapted to parallelization. In its basic iterative form the method produces an ensemble of solutions which lie in the linear span of the initial ensemble. Choice of the parameterization of the unknown field is thus a key component of the success of the method. We demonstrate how both geometric ideas and hierarchical ideas can be used to design effective parameterizations for a number of applied inverse problems arising in electrical impedance tomography, groundwater flow and source inversion. In particular we show how geometric ideas, including the level set method, can be used to reconstruct piecewise continuous fields, and we show how hierarchical methods can be used to learn key parameters in continuous fields, such as length-scales, resulting in improved reconstructions. Geometric and hierarchical ideas are combined in the level set method to find piecewise constant reconstructions with interfaces of unknown topology.

Impulse propagation in the nocturnal boundary layer: analysis of the geometric component.

PubMed

Blom, Philip; Waxler, Roger

2012-05-01

On clear dry nights over flat land, a temperature inversion and stable nocturnal wind jet lead to an acoustic duct in the lowest few hundred meters of the atmosphere. An impulsive signal propagating in such a duct is received at long ranges from the source as an extended wave train consisting of a series of weakly dispersed distinct arrivals followed by a strongly dispersed low-frequency tail. The leading distinct arrivals have been previously shown to be well modeled by geometric acoustics. In this paper, the geometric acoustics approximation for the leading arrivals is investigated. Using the solutions of the eikonal and transport equations, travel times, amplitudes, and caustic structures of the distinct arrivals have been determined. The time delay between and relative amplitudes of the direct-refracted and single ground reflection arrivals have been investigated as parameters for an inversion scheme. A two parameter quadratic approximation to the effective sound speed profile has been fit and found to be in strong agreement with meteorological measurements from the time of propagation.

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.

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.

Polarization ellipse and Stokes parameters in geometric algebra.

PubMed

Santos, Adler G; Sugon, Quirino M; McNamara, Daniel J

2012-01-01

In this paper, we use geometric algebra to describe the polarization ellipse and Stokes parameters. We show that a solution to Maxwell's equation is a product of a complex basis vector in Jackson and a linear combination of plane wave functions. We convert both the amplitudes and the wave function arguments from complex scalars to complex vectors. This conversion allows us to separate the electric field vector and the imaginary magnetic field vector, because exponentials of imaginary scalars convert vectors to imaginary vectors and vice versa, while exponentials of imaginary vectors only rotate the vector or imaginary vector they are multiplied to. We convert this expression for polarized light into two other representations: the Cartesian representation and the rotated ellipse representation. We compute the conversion relations among the representation parameters and their corresponding Stokes parameters. And finally, we propose a set of geometric relations between the electric and magnetic fields that satisfy an equation similar to the Poincaré sphere equation.

Situating the Debate on "Geometrical Algebra" within the Framework of Premodern Algebra.

PubMed

Sialaros, Michalis; Christianidis, Jean

2016-06-01

Argument The aim of this paper is to employ the newly contextualized historiographical category of "premodern algebra" in order to revisit the arguably most controversial topic of the last decades in the field of Greek mathematics, namely the debate on "geometrical algebra." Within this framework, we shift focus from the discrepancy among the views expressed in the debate to some of the historiographical assumptions and methodological approaches that the opposing sides shared. Moreover, by using a series of propositions related to Elem. II.5 as a case study, we discuss Euclid's geometrical proofs, the so-called "semi-algebraic" alternative demonstrations attributed to Heron of Alexandria, as well as the solutions given by Diophantus, al-Sulamī, and al-Khwārizmī to the corresponding numerical problem. This comparative analysis offers a new reading of Heron's practice, highlights the significance of contextualizing "premodern algebra," and indicates that the origins of algebraic reasoning should be sought in the problem-solving practice, rather than in the theorem-proving tradition.

Uav-Based Automatic Tree Growth Measurement for Biomass Estimation

NASA Astrophysics Data System (ADS)

Karpina, M.; Jarząbek-Rychard, M.; Tymków, P.; Borkowski, A.

2016-06-01

Manual in-situ measurements of geometric tree parameters for the biomass volume estimation are time-consuming and economically non-effective. Photogrammetric techniques can be deployed in order to automate the measurement procedure. The purpose of the presented work is an automatic tree growth estimation based on Unmanned Aircraft Vehicle (UAV) imagery. The experiment was conducted in an agriculture test field with scots pine canopies. The data was collected using a Leica Aibotix X6V2 platform equipped with a Nikon D800 camera. Reference geometric parameters of selected sample plants were measured manually each week. In situ measurements were correlated with the UAV data acquisition. The correlation aimed at the investigation of optimal conditions for a flight and parameter settings for image acquisition. The collected images are processed in a state of the art tool resulting in a generation of dense 3D point clouds. The algorithm is developed in order to estimate geometric tree parameters from 3D points. Stem positions and tree tops are identified automatically in a cross section, followed by the calculation of tree heights. The automatically derived height values are compared to the reference measurements performed manually. The comparison allows for the evaluation of automatic growth estimation process. The accuracy achieved using UAV photogrammetry for tree heights estimation is about 5cm.

Molecular Static Third-Order Polarizabilities of Carbon-Cage Fullerene and Their Correlation with Three Geometric Properties: Symmetry, Aromaticity, and Size

NASA Technical Reports Server (NTRS)

Moore, C. E.; Cardelino, B. H.; Frazier, D. O.; Niles, J.; Wang, X.-Q.

1998-01-01

The static third-order polarizabilities (gamma) of C60, C70, five isomers of C78 and two isomers of C84 were analyzed in terms of three properties, from a geometric point of view: symmetry, aromaticity and size. The polarizability values were based on the finite field approximation using a semiempirical Hamiltonian (AM1) and applied to molecular structures obtained from density functional theory calculations. Symmetry was characterized by the molecular group order. The selection of 6-member rings as aromatic was determined from an analysis of bond lengths. Maximum interatomic distance and surface area were the parameters considered with respect to size. Based on triple linear regression analysis, it was found that the static linear polarizability (alpha) and gamma in these molecules respond differently to geometrical properties: alpha depends almost exclusively on surface area while gamma is affected by a combination of number of aromatic rings, length and group order, in decreasing importance. In the case of alpha, valence electron contributions provide the same information as all-electron estimates. For gamma, the best correlation coefficients are obtained when all-electron estimates are used and when the dependent parameter is ln(gamma) instead of gamma.

Effect of Mach number, valve angle and length to diameter ratio on thermal performance in flow of air through Ranque Hilsch vortex tube

NASA Astrophysics Data System (ADS)

Devade, Kiran D.; Pise, Ashok T.

2017-01-01

Ranque Hilsch vortex tube is a device that can produce cold and hot air streams simultaneously from pressurized air. Performance of vortex tube is influenced by a number of geometrical and operational parameters. In this study parametric analysis of vortex tube is carried out. Air is used as the working fluid and geometrical parameters like length to diameter ratio (15, 16, 17, 18), exit valve angles (30°-90°), orifice diameters (5, 6 and 7 mm), 2 entry nozzles and tube divergence angle 4° is used for experimentation. Operational parameters like pressure (200-600 kPa), cold mass fraction (0-1) is varied and effect of Mach number at the inlet of the tube is investigated. The vortex tube is tested at sub sonic (0 < Ma < 1), sonic (Ma = 1) and supersonic (1 < Ma < 2) Mach number, and its effect on thermal performance is analysed. As a result it is observed that, higher COP and low cold end temperature is obtained at subsonic Ma. As CMF increases, COP rises and cold and temperature drops. Optimum performance of the tube is observed for CMF up to 0.5. Experimental correlations are proposed for optimum COP. Parametric correlation is developed for geometrical and operational parameters.

Geometric isomerism in pentacoordinate Cu2+ complexes: equilibrium, kinetic, and density functional theory studies reveal the existence of equilibrium between square pyramidal and trigonal bipyramidal forms for a tren-derived ligand.

PubMed

Algarra, Andrés G; Basallote, Manuel G; Castillo, Carmen E; Clares, M Paz; Ferrer, Armando; García-España, Enrique; Llinares, José M; Máñez, M Angeles; Soriano, Conxa

2009-02-02

A ligand (L1) (bis(aminoethyl)[2-(4-quinolylmethyl)aminoethyl]amine) containing a 4-quinolylmethyl group attached to one of the terminal amino groups of tris(2-aminoethyl)amine (tren) has been prepared, and its protonation constants and stability constants for the formation of Cu(2+) complexes have been determined. Kinetic studies on the formation of Cu(2+) complexes in slightly acidic solutions and on the acid-promoted complex decomposition strongly suggest that the Cu(2+)-L1 complex exists in solution as a mixture of two species, one of them showing a trigonal bipyramidal (tbp) coordination environment with an absorption maximum at 890 nm in the electronic spectrum, and the other one being square pyramidal (sp) with a maximum at 660 nm. In acidic solution only a species with tbp geometry is formed, whereas in neutral and basic solutions a mixture of species with tbp and sp geometries is formed. The results of density functional theory (DFT) calculations indicate that these results can be rationalized by invoking the existence of an equilibrium of hydrolysis of the Cu-N bond with the amino group supporting the quinoline ring so that CuL1(2+) would be actually a mixture of tbp [CuL1(H(2)O)](2+) and sp [CuL1(H(2)O)(2)](2+). As there are many Cu(2+)-polyamine complexes with electronic spectra that show two overlapping bands at wavelengths close to those observed for the Cu(2+)-L1 complex, the existence of this kind of equilibrium between species with two different geometries can be quite common in the chemistry of these compounds. A correlation found between the position of the absorption maximum and the tau parameter measuring the distortion from the idealized tbp and sp geometries can be used to estimate the actual geometry in solution of this kind of complex.

Correcting spacecraft jitter in HiRISE images

USGS Publications Warehouse

Sutton, S. S.; Boyd, A.K.; Kirk, Randolph L.; Cook, Debbie; Backer, Jean; Fennema, A.; Heyd, R.; McEwen, A.S.; Mirchandani, S.D.; Wu, B.; Di, K.; Oberst, J.; Karachevtseva, I.

2017-01-01

Mechanical oscillations or vibrations on spacecraft, also called pointing jitter, cause geometric distortions and/or smear in high resolution digital images acquired from orbit. Geometric distortion is especially a problem with pushbroom type sensors, such as the High Resolution Imaging Science Experiment (HiRISE) instrument on board the Mars Reconnaissance Orbiter (MRO). Geometric distortions occur at a range of frequencies that may not be obvious in the image products, but can cause problems with stereo image correlation in the production of digital elevation models, and in measuring surface changes over time in orthorectified images. The HiRISE focal plane comprises a staggered array of fourteen charge-coupled devices (CCDs) with pixel IFOV of 1 microradian. The high spatial resolution of HiRISE makes it both sensitive to, and an excellent recorder of jitter. We present an algorithm using Fourier analysis to resolve the jitter function for a HiRISE image that is then used to update instrument pointing information to remove geometric distortions from the image. Implementation of the jitter analysis and image correction is performed on selected HiRISE images. Resulting corrected images and updated pointing information are made available to the public. Results show marked reduction of geometric distortions. This work has applications to similar cameras operating now, and to the design of future instruments (such as the Europa Imaging System).

Influence of third-degree geometric nonlinearities on the vibration and stability of pretwisted, preconed, rotating blades

NASA Technical Reports Server (NTRS)

Subrahmanyam, K. B.; Kaza, K. R. V.

1986-01-01

The governing coupled flapwise bending, edgewise bending, and torsional equations are derived including third-degree geometric nonlinear elastic terms by making use of the geometric nonlinear theory of elasticity in which the elongations and shears are negligible compared to unity. These equations are specialized for blades of doubly symmetric cross section with linear variation of pretwist over the blade length. The nonlinear steady state equations and the linearized perturbation equations are solved by using the Galerkin method, and by utilizing the nonrotating normal modes for the shape functions. Parametric results obtained for various cases of rotating blades from the present theoretical formulation are compared to those produced from the finite element code MSC/NASTRAN, and also to those produced from an in-house experimental test rig. It is shown that the spurious instabilities, observed for thin, rotating blades when second degree geometric nonlinearities are used, can be eliminated by including the third-degree elastic nonlinear terms. Furthermore, inclusion of third degree terms improves the correlation between the theory and experiment.

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.

Geometric Evaluation of the Effect of Prosthetic Rehabilitation on Facial Asymmetry in Patients with Unilateral Maxillectomy.

PubMed

Aswehlee, Amel M; Hattori, Mariko; Elbashti, Mahmoud E; Sumita, Yuka I; Taniguchi, Hisashi

This study aimed (1) to geometrically evaluate areas of facial asymmetry in patients with two different types of maxillectomy defect compared to a control group, (2) to geometrically evaluate the effect of an obturator prosthesis on facial asymmetry, and (3) to investigate the correlation between three-dimensional (3D) deviation values and number of missing teeth. Facial data from 13 normal control participants and 26 participants with two types of maxillectomy defect (groups 1 and 2) were acquired with a noncontact 3D digitizer. Facial asymmetry was evaluated by superimposing a facial scan onto its mirror scan using 3D evaluation software. Facial scans with and without obturator prostheses were also superimposed to evaluate the obturator effect. The correlation between 3D deviation values and number of missing teeth was also evaluated. Statistical analyses were performed. Facial asymmetry was significantly different between the control group and each maxillectomy defect group (group 1: P < .0001 and P = .020 without and with obturator, respectively; group 2: P < .0001 for both conditions). There were no significant differences in asymmetry between groups 1 and 2 either without or with obturator (P = .457 and P = .980, respectively). There was a significant difference in the obturator effect between groups 1 and 2 (P = .038). 3D deviation values were positively correlated with number of missing teeth in group 1 (r = 0.594, P = .032), but not in group 2. A noncontact 3D digitizer and 3D deviation assessment were effective for analyzing facial data of maxillectomy patients. Obturators were effective for improving facial deformities in these patients.

Evaluation of holonomic quantum computation: adiabatic versus nonadiabatic.

PubMed

Cen, LiXiang; Li, XinQi; Yan, YiJing; Zheng, HouZhi; Wang, ShunJin

2003-04-11

Based on the analytical solution to the time-dependent Schrödinger equations, we evaluate the holonomic quantum computation beyond the adiabatic limit. Besides providing rigorous confirmation of the geometrical prediction of holonomies, the present dynamical resolution offers also a practical means to study the nonadiabaticity induced effects for the universal qubit operations.

Numerical Solutions of the Complete Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Robinson, David F.; Hassan, H. A.

1997-01-01

This report details the development of a new two-equation turbulence closure model based on the exact turbulent kinetic energy k and the variance of vorticity, zeta. The model, which is applicable to three dimensional flowfields, employs one set of model constants and does not use damping or wall functions, or geometric factors.

Tilted Kantowski-Sachs cosmological model in Brans-Dicke theory of gravitation

NASA Astrophysics Data System (ADS)

Pawar, D. D.; Shahare, S. P.; Dagwal, V. J.

2018-02-01

Tilted Kantowski-Sachs cosmological model in Brans-Dicke theory for perfect fluid has been investigated. The general solution of field equations in Brans-Dicke theory for the combined scalar and tensor field are obtained by using power law relation. Also, some physical and geometrical parameters are obtained and discussed.

Nonstandard Methods in Lie Theory

ERIC Educational Resources Information Center

Goldbring, Isaac Martin

2009-01-01

In this thesis, we apply model theory to Lie theory and geometric group theory. These applications of model theory come via nonstandard analysis. In Lie theory, we use nonstandard methods to prove two results. First, we give a positive solution to the local form of Hilbert's Fifth Problem, which asks whether every locally euclidean local…

Generation of unstructured grids and Euler solutions for complex geometries

NASA Technical Reports Server (NTRS)

Loehner, Rainald; Parikh, Paresh; Salas, Manuel D.

1989-01-01

Algorithms are described for the generation and adaptation of unstructured grids in two and three dimensions, as well as Euler solvers for unstructured grids. The main purpose is to demonstrate how unstructured grids may be employed advantageously for the economic simulation of both geometrically as well as physically complex flow fields.

Hamilton-Jacobi theory in multisymplectic classical field theories

NASA Astrophysics Data System (ADS)

de León, Manuel; Prieto-Martínez, Pedro Daniel; Román-Roy, Narciso; Vilariño, Silvia

2017-09-01

The geometric framework for the Hamilton-Jacobi theory developed in the studies of Cariñena et al. [Int. J. Geom. Methods Mod. Phys. 3(7), 1417-1458 (2006)], Cariñena et al. [Int. J. Geom. Methods Mod. Phys. 13(2), 1650017 (2015)], and de León et al. [Variations, Geometry and Physics (Nova Science Publishers, New York, 2009)] is extended for multisymplectic first-order classical field theories. The Hamilton-Jacobi problem is stated for the Lagrangian and the Hamiltonian formalisms of these theories as a particular case of a more general problem, and the classical Hamilton-Jacobi equation for field theories is recovered from this geometrical setting. Particular and complete solutions to these problems are defined and characterized in several equivalent ways in both formalisms, and the equivalence between them is proved. The use of distributions in jet bundles that represent the solutions to the field equations is the fundamental tool in this formulation. Some examples are analyzed and, in particular, the Hamilton-Jacobi equation for non-autonomous mechanical systems is obtained as a special case of our results.

Engineering controls for furniture strippers to meet the OSHA methylene chloride PEL.

PubMed

Estill, Cheryl Fairfield; Watkins, Daniel S; Shulman, Stanley A; Kurimo, Robert W; Kovein, Ronald J

2002-01-01

This case study demonstrates how methylene chloride exposures during furniture stripping can be reduced to below the Occupational Safety and Health Administration (OSHA) permissible exposure limit (PEL) of 25 ppm (as an 8-hour time-weighted average). Five surveys were conducted at one facility; the first four resulted in employee exposure geometric means from 39 to 332 ppm. For the fifth survey local exhaust ventilation was used at the stripping tank and the rinsing area, which together exhausted 138 m3/min (4860 ft3/min). Additional controls included providing adequate make-up air, adding paraffin wax to the stripping solution, raising the level of the stripping solution in the tank, and discussing good work practices with the employee. The employees' methylene chloride exposures during the fifth survey resulted in a geometric mean of 5.6 ppm with a 95% upper confidence limit of 8.3 ppm, which was found to be significantly lower than the OSHA PEL and the OSHA action level of 12.5 ppm. The cost of the ventilation system was $8900.

Valuing options in shot noise market

NASA Astrophysics Data System (ADS)

Laskin, Nick

2018-07-01

A new exactly solvable option pricing model has been introduced and elaborated. It is assumed that a stock price follows a Geometric shot noise process. An arbitrage-free integro-differential option pricing equation has been obtained and solved. The new Greeks have been analytically calculated. It has been shown that in diffusion approximation the developed option pricing model incorporates the well-known Black-Scholes equation and its solution. The stochastic dynamic origin of the Black-Scholes volatility has been uncovered. To model the observed market stock price patterns consisting of high frequency small magnitude and low frequency large magnitude jumps, the superposition of two Geometric shot noises has been implemented. A new generalized option pricing equation has been obtained and its exact solution was found. Merton's jump-diffusion formula for option price was recovered in diffusion approximation. Despite the non-Gaussian nature of probability distributions involved, the new option pricing model has the same degree of analytical tractability as the Black-Scholes model and the Merton jump-diffusion model. This attractive feature allows one to derive exact formulas to value options and option related instruments in the market with jump-like price patterns.

On global solutions of the random Hamilton-Jacobi equations and the KPZ problem

NASA Astrophysics Data System (ADS)

Bakhtin, Yuri; Khanin, Konstantin

2018-04-01

In this paper, we discuss possible qualitative approaches to the problem of KPZ universality. Throughout the paper, our point of view is based on the geometrical and dynamical properties of minimisers and shocks forming interlacing tree-like structures. We believe that the KPZ universality can be explained in terms of statistics of these structures evolving in time. The paper is focussed on the setting of the random Hamilton-Jacobi equations. We formulate several conjectures concerning global solutions and discuss how their properties are connected to the KPZ scalings in dimension 1  +  1. In the case of general viscous Hamilton-Jacobi equations with non-quadratic Hamiltonians, we define generalised directed polymers. We expect that their behaviour is similar to the behaviour of classical directed polymers, and present arguments in favour of this conjecture. We also define a new renormalisation transformation defined in purely geometrical terms and discuss conjectural properties of the corresponding fixed points. Most of our conjectures are widely open, and supported by only partial rigorous results for particular models.

Buckling delamination of the circular sandwich plate with piezoelectric face and elastic core layers under rotationally symmetric external pressure

NASA Astrophysics Data System (ADS)

Akbarov, Surkay D.; Cafarova, Fazile I.; Yahnioglu, Nazmiye

2017-02-01

The axisymmetric buckling delamination of the piezoelectric circular sandwich plate with piezoelectric face and elastic (metal) core layers around the interface penny-shaped cracks is investigated. The case is considered where short-circuit conditions with respect to the electrical potential on the upper and lower and also lateral surfaces of face layers are satisfied. It is assumed that the edge surfaces of the cracks have an infinitesimal rotationally symmetric initial imperfection and the development of this imperfection with rotationally symmetric compressive forces acting on the lateral surface of the plate is studied by employing the exact geometrically non-linear field equations and relations of electro-elasticity for piezoelectric materials. Solution to the considered nonlinear problem is reduced to solution of the series boundary value problems derived by applying the linearization procedure with respect to small imperfection of the sought values. Numerical results reveal the effect of piezoelectricity as well as geometrical and material parameters on the critical values are determined numerically by employing finite element method (FEM).

Class of regular bouncing cosmologies

NASA Astrophysics Data System (ADS)

Vasilić, Milovan

2017-06-01

In this paper, I construct a class of everywhere regular geometric sigma models that possess bouncing solutions. Precisely, I show that every bouncing metric can be made a solution of such a model. My previous attempt to do so by employing one scalar field has failed due to the appearance of harmful singularities near the bounce. In this work, I use four scalar fields to construct a class of geometric sigma models which are free of singularities. The models within the class are parametrized by their background geometries. I prove that, whatever background is chosen, the dynamics of its small perturbations is classically stable on the whole time axis. Contrary to what one expects from the structure of the initial Lagrangian, the physics of background fluctuations is found to carry two tensor, two vector, and two scalar degrees of freedom. The graviton mass, which naturally appears in these models, is shown to be several orders of magnitude smaller than its experimental bound. I provide three simple examples to demonstrate how this is done in practice. In particular, I show that graviton mass can be made arbitrarily small.

Coded aperture ptychography: uniqueness and reconstruction

NASA Astrophysics Data System (ADS)

Chen, Pengwen; Fannjiang, Albert

2018-02-01

Uniqueness of solution is proved for any ptychographic scheme with a random mask under a minimum overlap condition and local geometric convergence analysis is given for the alternating projection (AP) and Douglas-Rachford (DR) algorithms. DR is shown to possess a unique fixed point in the object domain and for AP a simple criterion for distinguishing the true solution among possibly many fixed points is given. A minimalist scheme, where the adjacent masks overlap 50% of the area and each pixel of the object is illuminated by exactly four illuminations, is conveniently parametrized by the number q of shifted masks in each direction. The lower bound 1  -  C/q 2 is proved for the geometric convergence rate of the minimalist scheme, predicting a poor performance with large q which is confirmed by numerical experiments. The twin-image ambiguity is shown to arise for certain Fresnel masks and degrade the performance of reconstruction. Extensive numerical experiments are performed to explore the general features of a well-performing mask, the optimal value of q and the robustness with respect to measurement noise.

Analysis of shell-type structures subjected to time-dependent mechanical and thermal loading

NASA Technical Reports Server (NTRS)

Simitses, G. J.; Riff, R.

1988-01-01

This research is performed to develop a general mathematical model and solution methodologies for analyzing structural response of thin, metallic shell-type structures under large transient, cyclic or static thermomechanical loads. Among the system responses, which are associated with these load conditions, are thermal buckling, creep buckling, and ratcheting. Thus, geometric as well as material-type nonlinearities (of high order) can be anticipated and must be considered in the development of the mathematical model. Furthermore, this must also be accommodated in the solution procedures.

Analysis of shell-type structures subjected to time-dependent mechanical and thermal loading

NASA Technical Reports Server (NTRS)

Simitses, George J.

1990-01-01

The development of a general mathematical model and solution methodologies for analyzing structural response of thin, metallic shell-like structures under dynamic and/or static thermomechanical loads is examined. In the mathematical model, geometric as well as material-type of nonlinearities are considered. Traditional as well as novel approaches are reported and detailed applications are presented in the appendices. The emphasis for the mathematical model, the related solution schemes, and the applications, is on thermal viscoelastic and viscoplastic phenomena, which can predict creep and ratchetting.

Analysis of shell-type structures subjected to time-dependent mechanical and thermal loading

NASA Technical Reports Server (NTRS)

Simitses, G. J.

1991-01-01

This report deals with the development of a general mathematical model and solution methodology for analyzing the structural response of thin, metallic shell-like structures under dynamic and/or static thermomechanical loads. In the mathematical model, geometric as well as the material-type of nonlinearities are considered. Traditional as well as novel approaches are reported and detailed applications are presented in the appendices. The emphasis for the mathematical model, the related solution schemes, and the applications, is on thermal viscoelastic and viscoplastic phenomena, which can predict creep and ratchetting.

Extreme value problems without calculus: a good link with geometry and elementary maths

NASA Astrophysics Data System (ADS)

Ganci, Salvatore

2016-11-01

Some classical examples of problem solving, where an extreme value condition is required, are here considered and/or revisited. The search for non-calculus solutions appears pedagogically useful and intriguing as shown through a rich literature. A teacher, who teaches both maths and physics, (as happens in Italian High schools) can find in these kinds of problems a mind stimulating exercise compared with the standard solution obtained by the differential calculus. A good link between the geometric and analytical explanations is so established.

Analysis of shell-type structures subjected to time-dependent mechanical and thermal loading

NASA Technical Reports Server (NTRS)

Simitses, G. J.

1989-01-01

The objective is to develop a general mathematical model and solution methodologies for analyzing structural response of thin, metallic shell-type structures under large transient, cyclic, or static thermomechanical loads. Among the system responses, which are associated with these load conditions, are thermal buckling, creep buckling, and racheting. Thus, geometric as well as material-type nonlinearities (of high order) can be anticipated and must be considered in the development of the mathematical model. Furthermore, this must also be accommodated in the solution procedures.

Analysis of shell-type structures subjected to time-dependent mechanical and thermal loading

NASA Technical Reports Server (NTRS)

Simitses, G. J.; Riff, R.

1988-01-01

The objective of this research is to develop a general mathematical model and solution methodologies for analyzing structural response of thin, metallic shell-type structures under large transient, cyclic or static thermomechanical loads. Among the system responses, which are associated with these load conditions, are thermal buckling, creep buckling and racheting. Thus, geometric as well as material-type nonlinearities (of high order) can be anticipated and must be considered in the development of the mathematical model. Furthermore, this must also be accommodated in the solution procedures.

Finite-dimensional linear approximations of solutions to general irregular nonlinear operator equations and equations with quadratic operators

NASA Astrophysics Data System (ADS)

Kokurin, M. Yu.

2010-11-01

A general scheme for improving approximate solutions to irregular nonlinear operator equations in Hilbert spaces is proposed and analyzed in the presence of errors. A modification of this scheme designed for equations with quadratic operators is also examined. The technique of universal linear approximations of irregular equations is combined with the projection onto finite-dimensional subspaces of a special form. It is shown that, for finite-dimensional quadratic problems, the proposed scheme provides information about the global geometric properties of the intersections of quadrics.

Analytical solutions to the problem of transient heat transfer in living tissue.

NASA Technical Reports Server (NTRS)

Shitzer, A.; Chato, J. C.

1971-01-01

An analytical model of transient heat transfer in living biological tissue is considered. The model includes storage, generation, conduction, and convective transport of heat in the tissue. Solutions for rectangular and cylindrical coordinates are presented and discussed. Transient times for reaching the ?locally fully developed' temperature profile were found to be of the order of 5 to 25 min. These transients are dominated by a geometrical parameters and, to a lesser extent, by a parameter representing the ratio of heat supplied by blood flow to heat conducted in the tissue.

Fedosov differentials and Catalan numbers

NASA Astrophysics Data System (ADS)

Löffler, Johannes

2010-06-01

The aim of the paper is to establish a non-recursive formula for the general solution of Fedosov's 'quadratic' fixed-point equation (Fedosov 1994 J. Diff. Geom. 40 213-38). Fedosov's geometrical fixed-point equation for a differential is rewritten in a form similar to the functional equation for the generating function of Catalan numbers. This allows us to guess the solution. An adapted example for Kaehler manifolds of constant sectional curvature is considered in detail. Also for every connection on a manifold a familiar classical differential will be introduced. Dedicated to the memory of Nikolai Neumaier.

Investigation of LANDSAT D Thematic Mapper geometric performance: Line to line and band to band registration. [Toulouse, France and Mississippi, U.S.A.

NASA Technical Reports Server (NTRS)

Begni, G.; BOISSIN; Desachy, M. J.; PERBOS

1984-01-01

The geometric accuray of LANDSAT TM raw data of Toulouse (France) raw data of Mississippi, and preprocessed data of Mississippi was examined using a CDC computer. Analog images were restituted on the VIZIR SEP device. The methods used for line to line and band to band registration are based on automatic correlation techniques and are widely used in automated image to image registration at CNES. Causes of intraband and interband misregistration are identified and statistics are given for both line to line and band to band misregistration.

Characterizing nonclassical correlations via local quantum Fisher information

NASA Astrophysics Data System (ADS)

Kim, Sunho; Li, Longsuo; Kumar, Asutosh; Wu, Junde

2018-03-01

We define two ways of quantifying the quantum correlations based on quantum Fisher information (QFI) in order to study the quantum correlations as a resource in quantum metrology. By investigating the hierarchy of measurement-induced Fisher information introduced in Lu et al. [X. M. Lu, S. Luo, and C. H. Oh, Phys. Rev. A 86, 022342 (2012), 10.1103/PhysRevA.86.022342], we show that the presence of quantum correlation can be confirmed by the difference of the Fisher information induced by the measurements of two hierarchies. In particular, the quantitative quantum correlations based on QFI coincide with the geometric discord for pure quantum states.

3D displacement field measurement with correlation based on the micro-geometrical surface texture

NASA Astrophysics Data System (ADS)

Bubaker-Isheil, Halima; Serri, Jérôme; Fontaine, Jean-François

2011-07-01

Image correlation methods are widely used in experimental mechanics to obtain displacement field measurements. Currently, these methods are applied using digital images of the initial and deformed surfaces sprayed with black or white paint. Speckle patterns are then captured and the correlation is performed with a high degree of accuracy to an order of 0.01 pixels. In 3D, however, stereo-correlation leads to a lower degree of accuracy. Correlation techniques are based on the search for a sub-image (or pattern) displacement field. The work presented in this paper introduces a new correlation-based approach for 3D displacement field measurement that uses an additional 3D laser scanner and a CMM (Coordinate Measurement Machine). Unlike most existing methods that require the presence of markers on the observed object (such as black speckle, grids or random patterns), this approach relies solely on micro-geometrical surface textures such as waviness, roughness and aperiodic random defects. The latter are assumed to remain sufficiently small thus providing an adequate estimate of the particle displacement. The proposed approach can be used in a wide range of applications such as sheet metal forming with large strains. The method proceeds by first obtaining cloud points using the 3D laser scanner mounted on a CMM. These points are used to create 2D maps that are then correlated. In this respect, various criteria have been investigated for creating maps consisting of patterns, which facilitate the correlation procedure. Once the maps are created, the correlation between both configurations (initial and moved) is carried out using traditional methods developed for field measurements. Measurement validation was conducted using experiments in 2D and 3D with good results for rigid displacements in 2D, 3D and 2D rotations.

Simulation of synthetic discriminant function optical implementation

NASA Astrophysics Data System (ADS)

Riggins, J.; Butler, S.

1984-12-01

The optical implementation of geometrical shape and synthetic discriminant function matched filters is computer modeled. The filter implementation utilizes the Allebach-Keegan computer-generated hologram algorithm. Signal-to-noise and efficiency measurements were made on the resultant correlation planes.

Angular correlations of photons from solution diffraction at a free-electron laser encode molecular structure

DOE PAGES

Mendez, Derek; Watkins, Herschel; Qiao, Shenglan; ...

2016-09-26

During X-ray exposure of a molecular solution, photons scattered from the same molecule are correlated. If molecular motion is insignificant during exposure, then differences in momentum transfer between correlated photons are direct measurements of the molecular structure. In conventional small- and wide-angle solution scattering, photon correlations are ignored. This report presents advances in a new biomolecular structural analysis technique, correlated X-ray scattering (CXS), which uses angular intensity correlations to recover hidden structural details from molecules in solution. Due to its intense rapid pulses, an X-ray free electron laser (XFEL) is an excellent tool for CXS experiments. A protocol is outlinedmore » for analysis of a CXS data set comprising a total of half a million X-ray exposures of solutions of small gold nanoparticles recorded at the Spring-8 Ångström Compact XFEL facility (SACLA). From the scattered intensities and their correlations, two populations of nanoparticle domains within the solution are distinguished: small twinned, and large probably non-twinned domains. Finally, it is shown analytically how, in a solution measurement, twinning information is only accessible via intensity correlations, demonstrating how CXS reveals atomic-level information from a disordered solution of like molecules.« less

Modelisation geometrique par NURBS pour le design aerodynamique des ailes d'avion

NASA Astrophysics Data System (ADS)

Bentamy, Anas

The constant evolution of the computer science gives rise to many research areas especially in computer aided design. This study is part, of the advancement of the numerical methods in engineering computer aided design, specifically in aerospace science. The geometric modeling based on NURBS has been applied successfully to generate a parametric wing surface for aerodynamic design while satisfying manufacturing constraints. The goal of providing a smooth geometry described with few parameters has been achieved. In that case, a wing design including ruled surfaces at the leading edge slat and at the flap, and, curved central surfaces with intrinsic geometric property coming from conic curves, necessitates 130 control points and 15 geometric design variables. The 3D character of the wing need to be analyzed by techniques of investigation of surfaces in order to judge conveniently the visual aspect and detect any sign inversion in both directions of parametrization u and nu. Color mapping of the Gaussian curvature appears to be a very effective tools in visualization. The automation of the construction has been attained using an heuristic optimization algorithm, simulated annealing. The relative high speed of convergence to the solutions confirms its practical interest in engineering problems nowadays. The robustness of the geometric model has been tested successfully with an academic inverse design problem. The results obtained allow to foresee multiple possible applications from an extension to a complete geometric description of an airplane to the interaction with others disciplines belonging to a preliminary aeronautical design process.

Quantum correlations for bipartite continuous-variable systems

NASA Astrophysics Data System (ADS)

Ma, Ruifen; Hou, Jinchuan; Qi, Xiaofei; Wang, Yangyang

2018-04-01

Two quantum correlations Q and Q_P for (m+n)-mode continuous-variable systems are introduced in terms of average distance between the reduced states under the local Gaussian positive operator-valued measurements, and analytical formulas of these quantum correlations for bipartite Gaussian states are provided. It is shown that the product states do not contain these quantum correlations, and conversely, all (m+n)-mode Gaussian states with zero quantum correlations are product states. Generally, Q≥ Q_{P}, but for the symmetric two-mode squeezed thermal states, these quantum correlations are the same and a computable formula is given. In addition, Q is compared with Gaussian geometric discord for symmetric squeezed thermal states.

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

Prescribing the mixed scalar curvature of a foliated Riemann-Cartan manifold

NASA Astrophysics Data System (ADS)

Rovenski, Vladimir Y.; Zelenko, Leonid

2018-03-01

The mixed scalar curvature is the simplest curvature invariant of a foliated Riemannian manifold. We explore the problem of prescribing the leafwise constant mixed scalar curvature of a foliated Riemann-Cartan manifold by conformal change of the structure in tangent and normal to the leaves directions. Under certain geometrical assumptions and in two special cases: along a compact leaf and for a closed fibered manifold, we reduce the problem to solution of a nonlinear leafwise elliptic equation for the conformal factor. We are looking for its solutions that are stable stationary solutions of the associated parabolic equation. Our main tool is using of majorizing and minorizing nonlinear heat equations with constant coefficients and application of comparison theorems for solutions of Cauchy's problem for parabolic equations.

Apparent relationship between solar-sector boundaries and 300-mb vorticity: Possible explanation in terms of upward propagation of planetary-scale waves

NASA Technical Reports Server (NTRS)

Deland, R. J.

1974-01-01

The selection process for sector structure boundary crossings used in vorticity correlation studies is examined and the possible influence of ascending planetary scale waves is assessed. It is proposed that some of the observed correlations between geomagnetic and meteorological variations may be due to meteorological effects on the geometric variables, rather than due to common solar origin.

Rational solutions of CYBE for simple compact real Lie algebras

NASA Astrophysics Data System (ADS)

Pop, Iulia; Stolin, Alexander

2007-04-01

In [A.A. Stolin, On rational solutions of Yang-Baxter equation for sl(n), Math. Scand. 69 (1991) 57-80; A.A. Stolin, On rational solutions of Yang-Baxter equation. Maximal orders in loop algebra, Comm. Math. Phys. 141 (1991) 533-548; A. Stolin, A geometrical approach to rational solutions of the classical Yang-Baxter equation. Part I, in: Walter de Gruyter & Co. (Ed.), Symposia Gaussiana, Conf. Alg., Berlin, New York, 1995, pp. 347-357] a theory of rational solutions of the classical Yang-Baxter equation for a simple complex Lie algebra g was presented. We discuss this theory for simple compact real Lie algebras g. We prove that up to gauge equivalence all rational solutions have the form X(u,v)={Ω}/{u-v}+t1∧t2+⋯+t∧t2n, where Ω denotes the quadratic Casimir element of g and {ti} are linearly independent elements in a maximal torus t of g. The quantization of these solutions is also emphasized.

The two NUT-like solutions of Ernst equation

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

Wu Yabo; Dong Peng; Deng Xuemei

By applying Ehlers transformation to Schwarzschild and Kerr solutions of Ernst equation and choosing the suitable coordinate transformations, the two NUT-like solutions, i.e., the so called NUT-Taub-like and the Kerr-NUT-like solutions are obtained which not only can, respectively, reduce to Schwarzschild and Kerr solutions when the parameter l{sup '}=0, but also can also reduce to the NUT-Taub metric and Kerr-NUT metric, respectively, when l{sup '} satisfies the some approximation. Meanwhile it is shown that in the NUT-Taub and Kerr-NUT solutions the range of value for the parameter l interpreted as the gravomagnetic monopole cannot be arbitrary and should be confinedmore » by mass of the source to vertical bar l vertical bar<

Quasirandom geometric networks from low-discrepancy sequences

NASA Astrophysics Data System (ADS)

Estrada, Ernesto

2017-08-01

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

Geometric stability of topological lattice phases

PubMed Central

Jackson, T. S.; Möller, Gunnar; Roy, Rahul

2015-01-01

The fractional quantum Hall (FQH) effect illustrates the range of novel phenomena which can arise in a topologically ordered state in the presence of strong interactions. The possibility of realizing FQH-like phases in models with strong lattice effects has attracted intense interest as a more experimentally accessible venue for FQH phenomena which calls for more theoretical attention. Here we investigate the physical relevance of previously derived geometric conditions which quantify deviations from the Landau level physics of the FQHE. We conduct extensive numerical many-body simulations on several lattice models, obtaining new theoretical results in the process, and find remarkable correlation between these conditions and the many-body gap. These results indicate which physical factors are most relevant for the stability of FQH-like phases, a paradigm we refer to as the geometric stability hypothesis, and provide easily implementable guidelines for obtaining robust FQH-like phases in numerical or real-world experiments. PMID:26530311

Smart mug to measure hand's geometrical mechanical impedance.

PubMed

Hondori, Hossein Mousavi; Tech, Ang Wei

2011-01-01

A novel device, which looks like a mug, has been proposed for measuring the impedance of human hand. The device is designed to have convenient size and light weight similar to an ordinary coffee mug. It contains a 2-axis inertia sensor to monitor vibration and a small motor to carry an eccentric mass (m=100 gr, r=2 cm, rpm=600). The centrifugal force due to the rotating mass applies a dynamic force to the hand that holds the mug. Correlation of the acceleration signals with the perturbing force gives the geometrical mechanical impedance. Experimental results on a healthy subject shows that impedance is posture dependant while it changes with the direction of the applied perturbing force. For nine postures the geometrical impedance is obtained all of which have elliptical shapes. The method can be used for assessment of spasticity and monitoring stability in patients with stroke or similar problems.

Geometrical Description of fractional quantum Hall quasiparticles

NASA Astrophysics Data System (ADS)

Park, Yeje; Yang, Bo; Haldane, F. D. M.

2012-02-01

We examine a description of fractional quantum Hall quasiparticles and quasiholes suggested by a recent geometrical approach (F. D. M. Haldane, Phys. Rev. Lett. 108, 116801 (2011)) to FQH systems, where the local excess electric charge density in the incompressible state is given by a topologically-quantized ``guiding-center spin'' times the Gaussian curvature of a ``guiding-center metric tensor'' that characterizes the local shape of the correlation hole around electrons in the fluid. We use a phenomenological energy function with two ingredients: the shear distortion energy of area-preserving distortions of the fluid, and a local (short-range) approximation to the Coulomb energy of the fluctuation of charge density associated with the Gaussian curvature. Quasiparticles and quasiholes of the 1/3 Laughlin state are modeled as ``punctures'' in the incompressible fluid which then relax by geometric distortion which generates Gaussian curvature, giving rise to the charge-density profile around the topological excitation.

Modified geometrical optics of a smoothly inhomogeneous isotropic medium: the anisotropy, Berry phase, and the optical Magnus effect.

PubMed

Bliokh, K Yu; Bliokh, Yu P

2004-08-01

We present a modification of the geometrical optics method, which allows one to properly separate the complex amplitude and the phase of the wave solution. Appling this modification to a smoothly inhomogeneous isotropic medium, we show that in the first geometrical optics approximation the medium is weakly anisotropic. The refractive index, being dependent on the direction of the wave vector, contains the correction, which is proportional to the Berry geometric phase. Two independent eigenmodes of right-hand and left-hand circular polarizations exist in the medium. Their group velocities and phase velocities differ. The difference in the group velocities results in the shift of the rays of different polarizations (the optical Magnus effect). The difference in the phase velocities causes an increase of the Berry phase along with the interference of two modes leading to the familiar Rytov law about the rotation of the polarization plane of a wave. The theory developed suggests that both the optical Magnus effect and the Berry phase are accompanying nonlocal topological effects. In this paper the Hamilton ray equations giving a unified description for both of these phenomena have been derived and also a novel splitting effect for a ray of noncircular polarization has been predicted. Specific examples are also discussed.

[Determination of ventricular volumes by a non-geometric method using gamma-cineangiography].

PubMed

Faivre, R; Cardot, J C; Baud, M; Verdenet, J; Berthout, P; Bidet, A C; Bassand, J P; Maurat, J P

1985-08-01

The authors suggest a new way of determining ventricular volume by a non-geometric method using gamma-cineangiography. The results obtained by this method were compared with those obtained by a geometric methods and contrast ventriculography in 94 patients. The new non-geometric method supposes that the radioactive tracer is evenly distributed in the cardiovascular system so that blood radioactivity levels can be measured. The ventricular volume is then equal to the ratio of radioactivity in the LV zone to that of 1 ml of blood. Comparison of the radionuclide and angiographic data in the first 60 patients showed systematic values--despite a satisfactory statistical correlation (r = 0.87, y = 0.30 X + 6.3). This underestimation is due to the phenomenon of attenuation related to the depth of the heart in the thoracic cage and to autoabsorption at source, the degree of which depends on the ventricular volume. An empirical method of calculation allows correction for these factors by taking into account absorption in the tissues by relating to body surface area and autoabsorption at source by correcting for the surface of isotopic ventricular projection expressed in pixels. Using the data of this empirical method, the correction formula for radionuclide ventricular volume is obtained by a multiple linear regression: corrected radionuclide volume = K X measured radionuclide volume (Formula: see text). This formula was applied in the following 34 patients. The correlation between the uncorrected and corrected radionuclide volumes and the angiographic volumes was improved (r = 0.65 vs r = 0.94) and the values were more accurate (y = 0.18 X + 26 vs y = 0.96 X + 1.5).(ABSTRACT TRUNCATED AT 250 WORDS)

Rostro-dorsal and rostro-lateral skull morphologic variability in three age-groups of the Egyptian mongoose (Herpestes ichneumon) (Linnaeus, 1758): implications of certain orbital parameters - angular geometric approach.

PubMed

Samuel, M O; Wanmi, N; Usende, L

2016-01-01

This study evaluated 30 skulls of the grey mongoose divided into three age-groups (6 pups, 10 juveniles and 14 adults) for skull shape variability determination. Specific geometric shapes were drawn from defined points. Angular geometric measurements of shapes derived from rostro-dorsal and rostro-lateral parts of the skull included; orbital angles (with and without the mandible), comprising of viscero-cranium, skull and orbital index that was calculated to evaluate the correlations, if any, with angles measured. It was observed that orbital height and width became higher with age; there was stronger correlation in this regard between pups and juveniles compared with juveniles and adults. There is a reduction (narrowing) in BrEcEc, BrEcN, EcPEc, EcEnN and NwNNw angles with concomitant enlargement of BrEcP, BrEcN, EcNEc, EnNEn, EcNNw and EnNP with age. The decline in the skull index shows a decrease in rate of skull width growth relative to rostro-facial length and demonstrates non-proportionality to zygoma bowing. Significantly varied orbital parameters include the inter-canthii distance and implications of certain significant variables observed in some geometric orbital measurements of the tropical mongoose (Herpestes ichneumon). The survey hypothesizes the observations follow typical carnivoran phylogenic affinity, differentiates this species from similar herpestid versions and is an estimation of functional morphology with respect to bite size. It is further suggested to contribute to visual acuity in timing of bite delivery as well an adaptation in prey summarisation. This study will serve as baseline information in herpestid cranial investigations. Such facial features are useful in population studies, species identification, eco-migrant species surveillance and species ontogenic evolution.

The Camassa-Holm equation as an incompressible Euler equation: A geometric point of view

NASA Astrophysics Data System (ADS)

Gallouët, Thomas; Vialard, François-Xavier

2018-04-01

The group of diffeomorphisms of a compact manifold endowed with the L2 metric acting on the space of probability densities gives a unifying framework for the incompressible Euler equation and the theory of optimal mass transport. Recently, several authors have extended optimal transport to the space of positive Radon measures where the Wasserstein-Fisher-Rao distance is a natural extension of the classical L2-Wasserstein distance. In this paper, we show a similar relation between this unbalanced optimal transport problem and the Hdiv right-invariant metric on the group of diffeomorphisms, which corresponds to the Camassa-Holm (CH) equation in one dimension. Geometrically, we present an isometric embedding of the group of diffeomorphisms endowed with this right-invariant metric in the automorphisms group of the fiber bundle of half densities endowed with an L2 type of cone metric. This leads to a new formulation of the (generalized) CH equation as a geodesic equation on an isotropy subgroup of this automorphisms group; On S1, solutions to the standard CH thus give radially 1-homogeneous solutions of the incompressible Euler equation on R2 which preserves a radial density that has a singularity at 0. An other application consists in proving that smooth solutions of the Euler-Arnold equation for the Hdiv right-invariant metric are length minimizing geodesics for sufficiently short times.

Single molecule dynamics at a mechanically controllable break junction in solution at room temperature.

PubMed

Konishi, Tatsuya; Kiguchi, Manabu; Takase, Mai; Nagasawa, Fumika; Nabika, Hideki; Ikeda, Katsuyoshi; Uosaki, Kohei; Ueno, Kosei; Misawa, Hiroaki; Murakoshi, Kei

2013-01-23

The in situ observation of geometrical and electronic structural dynamics of a single molecule junction is critically important in order to further progress in molecular electronics. Observations of single molecular junctions are difficult, however, because of sensitivity limits. Here, we report surface-enhanced Raman scattering (SERS) of a single 4,4'-bipyridine molecule under conditions of in situ current flow in a nanogap, by using nano-fabricated, mechanically controllable break junction (MCBJ) electrodes. When adsorbed at room temperature on metal nanoelectrodes in solution to form a single molecule junction, statistical analysis showed that nontotally symmetric b(1) and b(2) modes of 4,4'-bipyridine were strongly enhanced relative to observations of the same modes in solid or aqueous solutions. Significant changes in SERS intensity, energy (wavenumber), and selectivity of Raman vibrational bands that are coincident with current fluctuations provide information on distinct states of electronic and geometrical structure of the single molecule junction, even under large thermal fluctuations occurring at room temperature. We observed the dynamics of 4,4'-bipyridine motion between vertical and tilting configurations in the Au nanogap via b(1) and b(2) mode switching. A slight increase in the tilting angle of the molecule was also observed by noting the increase in the energies of Raman modes and the decrease in conductance of the molecular junction.

Hydrogen Epoch of Reinozation Array (HERA) Calibrated FFT Correlator Simulation

NASA Astrophysics Data System (ADS)

Salazar, Jeffrey David; Parsons, Aaron

2018-01-01

The Hydrogen Epoch of Reionization Array (HERA) project is an astronomical radio interferometer array with a redundant baseline configuration. Interferometer arrays are being used widely in radio astronomy because they have a variety of advantages over single antenna systems. For example, they produce images (visibilities) closely matching that of a large antenna (such as the Arecibo observatory), while both the hardware and maintenance costs are significantly lower. However, this method has some complications; one being the computational cost of correlating data from all of the antennas. A correlator is an electronic device that cross-correlates the data between the individual antennas; these are what radio astronomers call visibilities. HERA, being in its early stages, utilizes a traditional correlator system. The correlator cost scales as N2, where N is the number of antennas in the array. The purpose of a redundant baseline configuration array setup is for the use of a more efficient Fast Fourier Transform (FFT) correlator. FFT correlators scale as Nlog2N. The data acquired from this sort of setup, however, inherits geometric delay and uncalibrated antenna gains. This particular project simulates the process of calibrating signals from astronomical sources. Each signal “received” by an antenna in the simulation is given random antenna gain and geometric delay. The “linsolve” Python module was used to solve for the unknown variables in the simulation (complex gains and delays), which then gave a value for the true visibilities. This first version of the simulation only mimics a one dimensional redundant telescope array detecting a small amount of sources located in the volume above the antenna plane. Future versions, using GPUs, will handle a two dimensional redundant array of telescopes detecting a large amount of sources in the volume above the array.

Analysis of high-aspect-ratio jet-flap wings of arbitrary geometry

NASA Technical Reports Server (NTRS)

Lissaman, P. B. S.

1973-01-01

An analytical technique to compute the performance of an arbitrary jet-flapped wing is developed. The solution technique is based on the method of Maskell and Spence in which the well-known lifting-line approach is coupled with an auxiliary equation providing the extra function needed in jet-flap theory. The present method is generalized to handle straight, uncambered wings of arbitrary planform, twist, and blowing (including unsymmetrical cases). An analytical procedure is developed for continuous variations in the above geometric data with special functions to exactly treat discontinuities in any of the geometric and blowing data. A rational theory for the effect of finite wing thickness is introduced as well as simplified concepts of effective aspect ratio for rapid estimation of performance.

Geometrical-Based Navigation System Performance Assessment in the Space Service Volume Using a Multiglobal Navigation Satellite System Methodology

NASA Technical Reports Server (NTRS)

Welch, Bryan W.

2016-01-01

NASA is participating in the International Committee on Global Navigation Satellite Systems (GNSS) (ICG)'s efforts towards demonstrating the benefits to the space user in the Space Service Volume (SSV) when a multi-GNSS solution space approach is utilized. The ICG Working Group: Enhancement of GNSS Performance, New Services and Capabilities has started a three phase analysis initiative as an outcome of recommendations at the ICG-10 meeting, in preparation for the ICG-11 meeting. The first phase of that increasing complexity and fidelity analysis initiative is based on a pure geometrically-derived access technique. The first phase of analysis has been completed, and the results are documented in this paper.

Cooperating knowledge-based systems

NASA Technical Reports Server (NTRS)

Feigenbaum, Edward A.; Buchanan, Bruce G.

1988-01-01

This final report covers work performed under Contract NCC2-220 between NASA Ames Research Center and the Knowledge Systems Laboratory, Stanford University. The period of research was from March 1, 1987 to February 29, 1988. Topics covered were as follows: (1) concurrent architectures for knowledge-based systems; (2) methods for the solution of geometric constraint satisfaction problems, and (3) reasoning under uncertainty. The research in concurrent architectures was co-funded by DARPA, as part of that agency's Strategic Computing Program. The research has been in progress since 1985, under DARPA and NASA sponsorship. The research in geometric constraint satisfaction has been done in the context of a particular application, that of determining the 3-D structure of complex protein molecules, using the constraints inferred from NMR measurements.

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.

Time domain simulation of the response of geometrically nonlinear panels subjected to random loading

NASA Technical Reports Server (NTRS)

Moyer, E. Thomas, Jr.

1988-01-01

The response of composite panels subjected to random pressure loads large enough to cause geometrically nonlinear responses is studied. A time domain simulation is employed to solve the equations of motion. An adaptive time stepping algorithm is employed to minimize intermittent transients. A modified algorithm for the prediction of response spectral density is presented which predicts smooth spectral peaks for discrete time histories. Results are presented for a number of input pressure levels and damping coefficients. Response distributions are calculated and compared with the analytical solution of the Fokker-Planck equations. RMS response is reported as a function of input pressure level and damping coefficient. Spectral densities are calculated for a number of examples.

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.

Detection of circuit-board components with an adaptive multiclass correlation filter

NASA Astrophysics Data System (ADS)

Diaz-Ramirez, Victor H.; Kober, Vitaly

2008-08-01

A new method for reliable detection of circuit-board components is proposed. The method is based on an adaptive multiclass composite correlation filter. The filter is designed with the help of an iterative algorithm using complex synthetic discriminant functions. The impulse response of the filter contains information needed to localize and classify geometrically distorted circuit-board components belonging to different classes. Computer simulation results obtained with the proposed method are provided and compared with those of known multiclass correlation based techniques in terms of performance criteria for recognition and classification of objects.

Rational engineering correlations of diffusional and inertial particle deposition behavior in non-isothermal forced convection environments

NASA Technical Reports Server (NTRS)

Rosner, D. E.; Gokoglu, S. A.; Israel, R.

1982-01-01

A multiparameter correlation approach to the study of particle deposition rates in engineering applications is discussed with reference to two specific examples, one dealing with thermophoretically augmented small particle convective diffusion and the other involving larger particle inertial impaction. The validity of the correlations proposed here is demonstrated through rigorous computations including all relevant phenomena and interactions. Such representations are shown to minimize apparent differences between various geometric, flow, and physicochemical parameters, allowing many apparently different physicochemical situations to be described in a unified way.

Optimizing highly noncoplanar VMAT trajectories: the NoVo method.

PubMed

Langhans, Marco; Unkelbach, Jan; Bortfeld, Thomas; Craft, David

2018-01-16

We introduce a new method called NoVo (Noncoplanar VMAT Optimization) to produce volumetric modulated arc therapy (VMAT) treatment plans with noncoplanar trajectories. While the use of noncoplanar beam arrangements for intensity modulated radiation therapy (IMRT), and in particular high fraction stereotactic radiosurgery (SRS), is common, noncoplanar beam trajectories for VMAT are less common as the availability of treatment machines handling these is limited. For both IMRT and VMAT, the beam angle selection problem is highly nonconvex in nature, which is why automated beam angle selection procedures have not entered mainstream clinical usage. NoVo determines a noncoplanar VMAT solution (i.e. the simultaneous trajectories of the gantry and the couch) by first computing a [Formula: see text] solution (beams from every possible direction, suitably discretized) and then eliminating beams by examing fluence contributions. Also all beam angles are scored via geometrical considerations only to find out the usefulness of the whole beam space in a very short time. A custom path finding algorithm is applied to find an optimized, continuous trajectory through the most promising beam angles using the calculated score of the beam space. Finally, using this trajectory a VMAT plan is optimized. For three clinical cases, a lung, brain, and liver case, we compare NoVo to the ideal [Formula: see text] solution, nine beam noncoplanar IMRT, coplanar VMAT, and a recently published noncoplanar VMAT algorithm. NoVo comes closest to the [Formula: see text] solution considering the lung case (brain and liver case: second), as well as improving the solution time by using geometrical considerations, followed by a time effective iterative process reducing the [Formula: see text] solution. Compared to a recently published noncoplanar VMAT algorithm, using NoVo the computation time is reduced by a factor of 2-3 (depending on the case). Compared to coplanar VMAT, NoVo reduces the objective function value by 24%, 49% and 6% for the lung, brain and liver cases, respectively.

Optimizing highly noncoplanar VMAT trajectories: the NoVo method

NASA Astrophysics Data System (ADS)

Langhans, Marco; Unkelbach, Jan; Bortfeld, Thomas; Craft, David

2018-01-01

We introduce a new method called NoVo (Noncoplanar VMAT Optimization) to produce volumetric modulated arc therapy (VMAT) treatment plans with noncoplanar trajectories. While the use of noncoplanar beam arrangements for intensity modulated radiation therapy (IMRT), and in particular high fraction stereotactic radiosurgery (SRS), is common, noncoplanar beam trajectories for VMAT are less common as the availability of treatment machines handling these is limited. For both IMRT and VMAT, the beam angle selection problem is highly nonconvex in nature, which is why automated beam angle selection procedures have not entered mainstream clinical usage. NoVo determines a noncoplanar VMAT solution (i.e. the simultaneous trajectories of the gantry and the couch) by first computing a 4π solution (beams from every possible direction, suitably discretized) and then eliminating beams by examing fluence contributions. Also all beam angles are scored via geometrical considerations only to find out the usefulness of the whole beam space in a very short time. A custom path finding algorithm is applied to find an optimized, continuous trajectory through the most promising beam angles using the calculated score of the beam space. Finally, using this trajectory a VMAT plan is optimized. For three clinical cases, a lung, brain, and liver case, we compare NoVo to the ideal 4π solution, nine beam noncoplanar IMRT, coplanar VMAT, and a recently published noncoplanar VMAT algorithm. NoVo comes closest to the 4π solution considering the lung case (brain and liver case: second), as well as improving the solution time by using geometrical considerations, followed by a time effective iterative process reducing the 4π solution. Compared to a recently published noncoplanar VMAT algorithm, using NoVo the computation time is reduced by a factor of 2-3 (depending on the case). Compared to coplanar VMAT, NoVo reduces the objective function value by 24%, 49% and 6% for the lung, brain and liver cases, respectively.

Analysis of 3D OCT images for diagnosis of skin tumors

NASA Astrophysics Data System (ADS)

Raupov, Dmitry S.; Myakinin, Oleg O.; Bratchenko, Ivan A.; Zakharov, Valery P.; Khramov, Alexander G.

2018-04-01

Skin cancer is one of the fastest growing type of cancer. It represents the most commonly diagnosed malignancy, surpassing lung, breast, colorectal and prostate cancer. So, diagnostics for different types of skin cancer on early stages is a very high challenge for medicine industry. New optical imaging techniques have been developed in order to improve diagnostics precision. Optical coherence tomography (OCT) is based on low-coherence interferometry to detect the intensity of backscattered infrared light from biological tissues by measuring the optical path length. OCT provides the advantage of real-time, in vivo, low-cost imaging of suspicious lesions without having to proceed directly to a tissue biopsy. The post-processing techniques can be used for improving the precision of diagnostics and providing solutions to overcome limitations for OCT. Image processing can include noise filtration and evaluation of textural, geometric, morphological, spectral, statistic and other features. The main idea of this investigation is using information received from multiple analyze on 2D- and 3D-OCT images for skin tumors differentiating. At first, we tested the computer algorithm on OCT data hypercubes and separated B- and C-scans. Combination of 2D and 3D data give us an opportunity to receive common information about tumor (geometric and morphological characteristics) and use more powerful algorithms for features evaluation (fractal and textural) on these separated scans. These groups of features provide closer connection to classical wide-used ABCDE criteria (Asymmetry, Border irregularity, Color, Diameter, Evolution). We used a set of features consisting of fractal dimension, Haralick's, Gabor's, Tamura's, Markov random fields, geometric features and many others. We could note about good results on the test sets in differentiation between BCC and Nevus, MM and Healthy Skin. We received dividing MM from Healthy Skin with sensitivity more 90% and specificity more 92% (168 B-scans from 8 species) by using three Haralick's features like Contrast, Correlation and Energy. The results are very promising to be tested for new cases and new bigger sets of OCT images.

Diophantine Equations as a Context for Technology-Enhanced Training in Conjecturing and Proving

ERIC Educational Resources Information Center

Abramovich, Sergei; Sugden, Stephen J.

2008-01-01

Solving indeterminate algebraic equations in integers is a classic topic in the mathematics curricula across grades. At the undergraduate level, the study of solutions of non-linear equations of this kind can be motivated by the use of technology. This article shows how the unity of geometric contextualization and spreadsheet-based amplification…

The Shape of a Sausage: A Challenging Problem in the Calculus of Variations

ERIC Educational Resources Information Center

Deakin, Michael A. B.

2010-01-01

Many familiar household objects (such as sausages) involve the maximization of a volume under geometric constraints. A flexible but inextensible membrane bounds a volume which is to be filled to capacity. In the case of the sausage, a full analytic solution is here provided. Other related but more difficult problems seem to demand approximate…

Moisture Content and Migration Dynamics in Unsaturated Porous Media

NASA Technical Reports Server (NTRS)

Homsy, G. M.

1993-01-01

Fundamental studies of fluid mechanics and transport in partially saturated soils are presented. Solution of transient diffusion problems in support of the development of probes for the in-situ measurement of moisture content is given. Numerical and analytical methods are used to study the fundamental problem of meniscus and saturation front propagation in geometric models of porous media.

Kinoform optics applied to X-ray photon correlation spectroscopy.

PubMed

Sandy, A R; Narayanan, S; Sprung, M; Su, J-D; Evans-Lutterodt, K; Isakovic, A F; Stein, A

2010-05-01

Moderate-demagnification higher-order silicon kinoform focusing lenses have been fabricated to facilitate small-angle X-ray photon correlation spectroscopy (XPCS) experiments. The geometric properties of such lenses, their focusing performance and their applicability for XPCS measurements are described. It is concluded that one-dimensional vertical X-ray focusing via silicon kinoform lenses significantly increases the usable coherent flux from third-generation storage-ring light sources for small-angle XPCS experiments.

Geometrical calibration of an AOTF hyper-spectral imaging system

NASA Astrophysics Data System (ADS)

Špiclin, Žiga; Katrašnik, Jaka; Bürmen, Miran; Pernuš, Franjo; Likar, Boštjan

2010-02-01

Optical aberrations present an important problem in optical measurements. Geometrical calibration of an imaging system is therefore of the utmost importance for achieving accurate optical measurements. In hyper-spectral imaging systems, the problem of optical aberrations is even more pronounced because optical aberrations are wavelength dependent. Geometrical calibration must therefore be performed over the entire spectral range of the hyper-spectral imaging system, which is usually far greater than that of the visible light spectrum. This problem is especially adverse in AOTF (Acousto- Optic Tunable Filter) hyper-spectral imaging systems, as the diffraction of light in AOTF filters is dependent on both wavelength and angle of incidence. Geometrical calibration of hyper-spectral imaging system was performed by stable caliber of known dimensions, which was imaged at different wavelengths over the entire spectral range. The acquired images were then automatically registered to the caliber model by both parametric and nonparametric transformation based on B-splines and by minimizing normalized correlation coefficient. The calibration method was tested on an AOTF hyper-spectral imaging system in the near infrared spectral range. The results indicated substantial wavelength dependent optical aberration that is especially pronounced in the spectral range closer to the infrared part of the spectrum. The calibration method was able to accurately characterize the aberrations and produce transformations for efficient sub-pixel geometrical calibration over the entire spectral range, finally yielding better spatial resolution of hyperspectral imaging system.

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

Ranganathan, V; Kumar, P; Bzdusek, K

Purpose: We propose a novel data-driven method to predict the achievability of clinical objectives upfront before invoking the IMRT optimization. Methods: A new metric called “Geometric Complexity (GC)” is used to estimate the achievability of clinical objectives. Here, GC is the measure of the number of “unmodulated” beamlets or rays that intersect the Region-of-interest (ROI) and the target volume. We first compute the geometric complexity ratio (GCratio) between the GC of a ROI (say, parotid) in a reference plan and the GC of the same ROI in a given plan. The GCratio of a ROI indicates the relative geometric complexitymore » of the ROI as compared to the same ROI in the reference plan. Hence GCratio can be used to predict if a defined clinical objective associated with the ROI can be met by the optimizer for a given case. Basically a higher GCratio indicates a lesser likelihood for the optimizer to achieve the clinical objective defined for a given ROI. Similarly, a lower GCratio indicates a higher likelihood for the optimizer to achieve the clinical objective defined for the given ROI. We have evaluated the proposed method on four Head and Neck cases using Pinnacle3 (version 9.10.0) Treatment Planning System (TPS). Results: Out of the total of 28 clinical objectives from four head and neck cases included in the study, 25 were in agreement with the prediction, which implies an agreement of about 85% between predicted and obtained results. The Pearson correlation test shows a positive correlation between predicted and obtained results (Correlation = 0.82, r2 = 0.64, p < 0.005). Conclusion: The study demonstrates the feasibility of the proposed method in head and neck cases for predicting the achievability of clinical objectives with reasonable accuracy.« less

Transfer factors of natural radionuclides and (137)Cs from soil to plants used in traditional medicine in central Serbia.

PubMed

Djelic, Gorica; Krstic, Dragana; Stajic, Jelena M; Milenkovic, Biljana; Topuzovic, Marina; Nikezic, Dragoslav; Vucic, Dusica; Zeremski, Tijana; Stankovic, Milan; Kostic, Dragana

2016-07-01

Transfer factors of natural radionuclides and (137)Cs from soil to plants used in traditional medicine were determined. The transfer factors (TF) were calculated as Bq kg(-1) of dry plant per Bq kg(-1) of dry soil. Mass activity concentrations of (226)Ra, (232)Th, (40)K and (137)Cs in soil and plant samples were measured with high purity germanium detector (HPGe). The concentrations of As, Co, Cr, Cu, Mn, Ni, Pb and Zn were determined, as well as the cation exchange capacity (CEC) and the content of exchangeable cations (Ca, Mg, K, Na). Wide ranges of values were obtained for all the metals, especially for Cr and Ni. The Absalom model was used for determination of the amount of (137)Cs transferred from soil to plant based on soil characteristics such as pH, exchangeable potassium, humus and clay contents. The estimated transfer factors were in the range from 0.011 to 0.307 with an arithmetic mean of 0.071, median of 0.050, geometric mean of 0.053 and geometric standard deviation (GSD) of 2.08. This value agreed well with that calculated from the measurements of 0.069, geometric mean 0.040 and GSD 3.19. Correlations between radionuclides, metals, physicochemical properties and transfer factors were determined by Spearman correlation coefficient. There was a strong positive correlation between (137)Cs transfer factor and the ratio of transfer factor for K and (137)Cs. Principal Component Analysis (PCA) was performed in order to identify some pattern of data. Copyright © 2016. Published by Elsevier Ltd.

Leg edema quantification for heart failure patients via 3D imaging.

PubMed

Hayn, Dieter; Fruhwald, Friedrich; Riedel, Arthur; Falgenhauer, Markus; Schreier, Günter

2013-08-14

Heart failure is a common cardiac disease in elderly patients. After discharge, approximately 50% of all patients are readmitted to a hospital within six months. Recent studies show that home monitoring of heart failure patients can reduce the number of readmissions. Still, a large number of false positive alarms as well as underdiagnoses in other cases require more accurate alarm generation algorithms. New low-cost sensors for leg edema detection could be the missing link to help home monitoring to its breakthrough. We evaluated a 3D camera-based measurement setup in order to geometrically detect and quantify leg edemas. 3D images of legs were taken and geometric parameters were extracted semi-automatically from the images. Intra-subject variability for five healthy subjects was evaluated. Thereafter, correlation of 3D parameters with body weight and leg circumference was assessed during a clinical study at the Medical University of Graz. Strong correlation was found in between both reference values and instep height, while correlation in between curvature of the lower leg and references was very low. We conclude that 3D imaging might be a useful and cost-effective extension of home monitoring for heart failure patients, though further (prospective) studies are needed.

Strong Unitary and Overlap Uncertainty Relations: Theory and Experiment

NASA Astrophysics Data System (ADS)

Bong, Kok-Wei; Tischler, Nora; Patel, Raj B.; Wollmann, Sabine; Pryde, Geoff J.; Hall, Michael J. W.

2018-06-01

We derive and experimentally investigate a strong uncertainty relation valid for any n unitary operators, which implies the standard uncertainty relation and others as special cases, and which can be written in terms of geometric phases. It is saturated by every pure state of any n -dimensional quantum system, generates a tight overlap uncertainty relation for the transition probabilities of any n +1 pure states, and gives an upper bound for the out-of-time-order correlation function. We test these uncertainty relations experimentally for photonic polarization qubits, including the minimum uncertainty states of the overlap uncertainty relation, via interferometric measurements of generalized geometric phases.

Heat exchanger selection and design analyses for metal hydride heat pump systems

DOE PAGES

Mazzucco, Andrea; Voskuilen, Tyler G.; Waters, Essene L.; ...

2016-01-01

This paper presents a design analysis for the development of highly efficient heat exchangers within stationary metal hydride heat pumps. The design constraints and selected performance criteria are applied to three representative heat exchangers. The proposed thermal model can be applied to select the most efficient heat exchanger design and provides outcomes generally valid in a pre-design stage. Heat transfer effectiveness is the principal performance parameter guiding the selection analysis, the results of which appear to be mildly (up to 13%) affected by the specific Nusselt correlation used. The thermo-physical properties of the heat transfer medium and geometrical parameters aremore » varied in the sensitivity analysis, suggesting that the length of independent tubes is the physical parameter that influences the performance of the heat exchangers the most. The practical operative regions for each heat exchanger are identified by finding the conditions over which the heat removal from the solid bed enables a complete and continuous hydriding reaction. The most efficient solution is a design example that achieves the target effectiveness of 95%.« less

Certainty grids for mobile robots

NASA Technical Reports Server (NTRS)

Moravec, H. P.

1987-01-01

A numerical representation of uncertain and incomplete sensor knowledge called Certainty Grids has been used successfully in several mobile robot control programs, and has proven itself to be a powerful and efficient unifying solution for sensor fusion, motion planning, landmark identification, and many other central problems. Researchers propose to build a software framework running on processors onboard the new Uranus mobile robot that will maintain a probabilistic, geometric map of the robot's surroundings as it moves. The certainty grid representation will allow this map to be incrementally updated in a uniform way from various sources including sonar, stereo vision, proximity and contact sensors. The approach can correctly model the fuzziness of each reading, while at the same time combining multiple measurements to produce sharper map features, and it can deal correctly with uncertainties in the robot's motion. The map will be used by planning programs to choose clear paths, identify locations (by correlating maps), identify well-known and insufficiently sensed terrain, and perhaps identify objects by shape. The certainty grid representation can be extended in the same dimension and used to detect and track moving objects.

Spectroscopic investigations using density functional theory on 2-methoxy- 4(phenyliminomethyl)phenol: A non linear optical material

NASA Astrophysics Data System (ADS)

Hijas, K. M.; Madan Kumar, S.; Byrappa, K.; Geethakrishnan, T.; Jeyaram, S.; Nagalakshmi, R.

2018-03-01

Single crystals of 2-methoxy-4(phenyliminomethyl)phenol were grown from ethanol by slow evaporation solution growth technique. Single crystal X-ray diffraction experiment reveals the crystallization in orthorhombic system having non-centrosymmetric space group C2221. Geometrical optimization by density functional theory method was carried out using Gaussian program and compared with experimental results. Detailed experimental and theoretical vibrational analyses were carried out and the results were correlated to find close agreement. Thermal analyses show the material is thermally stable with a melting point of 159 °C. Natural bond orbital analysis was carried out to explain charge transfer interactions through hydrogen bonding. Relatively smaller HOMO-LUMO band gap favors the non linear optical activity of the molecule. Natural population analysis and molecular electrostatic potential calculations visualize the charge distribution in an isolated molecule. Calculated first-order molecular hyperpolarizability and preliminary second harmonic generation test carried out using Kurtz-Perry technique establish 2-methoxy-4(phenyliminomethyl)phenol crystal as a good non linear optical material. Z-scan proposes the material for reverse saturable absorption.

Soil temperature investigations using satellite acquired thermal-infrared data in semi-arid regions. Thesis. Final Report; [Utah

NASA Technical Reports Server (NTRS)

Day, R. L.; Petersen, G. W.

1983-01-01

Thermal-infrared data from the Heat Capacity Mapping Mission satellite were used to map the spatial distribution of diurnal surface temperatures and to estimate mean annual soil temperatures (MAST) and annual surface temperature amplitudes (AMP) in semi-arid east central Utah. Diurnal data with minimal snow and cloud cover were selected for five dates throughout a yearly period and geometrically co-registered. Rubber-sheet stretching was aided by the WARP program which allowed preview of image transformations. Daytime maximum and nighttime minimum temperatures were averaged to generation average daily temperature (ADT) data set for each of the five dates. Five ADT values for each pixel were used to fit a sine curve describing the theoretical annual surface temperature response as defined by a solution of a one-dimensinal heat flow equation. Linearization of the equation produced estimates of MAST and AMP plus associated confidence statistics. MAST values were grouped into classes and displayed on a color video screen. Diurnal surface temperatures and MAST were primarily correlated with elevation.

Coupled bending-torsion steady-state response of pretwisted, nonuniform rotating beams using a transfer-matrix method

NASA Technical Reports Server (NTRS)

Gray, Carl E., Jr.

1988-01-01

Using the Newtonian method, the equations of motion are developed for the coupled bending-torsion steady-state response of beams rotating at constant angular velocity in a fixed plane. The resulting equations are valid to first order strain-displacement relationships for a long beam with all other nonlinear terms retained. In addition, the equations are valid for beams with the mass centroidal axis offset (eccentric) from the elastic axis, nonuniform mass and section properties, and variable twist. The solution of these coupled, nonlinear, nonhomogeneous, differential equations is obtained by modifying a Hunter linear second-order transfer-matrix solution procedure to solve the nonlinear differential equations and programming the solution for a desk-top personal computer. The modified transfer-matrix method was verified by comparing the solution for a rotating beam with a geometric, nonlinear, finite-element computer code solution; and for a simple rotating beam problem, the modified method demonstrated a significant advantage over the finite-element solution in accuracy, ease of solution, and actual computer processing time required to effect a solution.

Causal properties of nonlinear gravitational waves in modified gravity

NASA Astrophysics Data System (ADS)

Suvorov, Arthur George; Melatos, Andrew

2017-09-01

Some exact, nonlinear, vacuum gravitational wave solutions are derived for certain polynomial f (R ) gravities. We show that the boundaries of the gravitational domain of dependence, associated with events in polynomial f (R ) gravity, are not null as they are in general relativity. The implication is that electromagnetic and gravitational causality separate into distinct notions in modified gravity, which may have observable astrophysical consequences. The linear theory predicts that tachyonic instabilities occur, when the quadratic coefficient a2 of the Taylor expansion of f (R ) is negative, while the exact, nonlinear, cylindrical wave solutions presented here can be superluminal for all values of a2. Anisotropic solutions are found, whose wave fronts trace out time- or spacelike hypersurfaces with complicated geometric properties. We show that the solutions exist in f (R ) theories that are consistent with Solar System and pulsar timing experiments.

Cosmic acceleration from M theory on twisted spaces

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

Neupane, Ishwaree P.; Wiltshire, David L.

2005-10-15

In a recent paper [I. P. Neupane and D. L. Wiltshire, Phys. Lett. B 619, 201 (2005).] we have found a new class of accelerating cosmologies arising from a time-dependent compactification of classical supergravity on product spaces that include one or more geometric twists along with nontrivial curved internal spaces. With such effects, a scalar potential can have a local minimum with positive vacuum energy. The existence of such a minimum generically predicts a period of accelerated expansion in the four-dimensional Einstein conformal frame. Here we extend our knowledge of these cosmological solutions by presenting new examples and discuss themore » properties of the solutions in a more general setting. We also relate the known (asymptotic) solutions for multiscalar fields with exponential potentials to the accelerating solutions arising from simple (or twisted) product spaces for internal manifolds.« less

Segmentation and texture analysis of structural biomarkers using neighborhood-clustering-based level set in MRI of the schizophrenic brain.

PubMed

Latha, Manohar; Kavitha, Ganesan

2018-02-03

Schizophrenia (SZ) is a psychiatric disorder that especially affects individuals during their adolescence. There is a need to study the subanatomical regions of SZ brain on magnetic resonance images (MRI) based on morphometry. In this work, an attempt was made to analyze alterations in structure and texture patterns in images of the SZ brain using the level-set method and Laws texture features. T1-weighted MRI of the brain from Center of Biomedical Research Excellence (COBRE) database were considered for analysis. Segmentation was carried out using the level-set method. Geometrical and Laws texture features were extracted from the segmented brain stem, corpus callosum, cerebellum, and ventricle regions to analyze pattern changes in SZ. The level-set method segmented multiple brain regions, with higher similarity and correlation values compared with an optimized method. The geometric features obtained from regions of the corpus callosum and ventricle showed significant variation (p < 0.00001) between normal and SZ brain. Laws texture feature identified a heterogeneous appearance in the brain stem, corpus callosum and ventricular regions, and features from the brain stem were correlated with Positive and Negative Syndrome Scale (PANSS) score (p < 0.005). A framework of geometric and Laws texture features obtained from brain subregions can be used as a supplement for diagnosis of psychiatric disorders.

Elasticity solutions for a class of composite laminate problems with stress singularities

NASA Technical Reports Server (NTRS)

Wang, S. S.

1983-01-01

A study on the fundamental mechanics of fiber-reinforced composite laminates with stress singularities is presented. Based on the theory of anisotropic elasticity and Lekhnitskii's complex-variable stress potentials, a system of coupled governing partial differential equations are established. An eigenfunction expansion method is introduced to determine the orders of stress singularities in composite laminates with various geometric configurations and material systems. Complete elasticity solutions are obtained for this class of singular composite laminate mechanics problems. Homogeneous solutions in eigenfunction series and particular solutions in polynomials are presented for several cases of interest. Three examples are given to illustrate the method of approach and the basic nature of the singular laminate elasticity solutions. The first problem is the well-known laminate free-edge stress problem, which has a rather weak stress singularity. The second problem is the important composite delamination problem, which has a strong crack-tip stress singularity. The third problem is the commonly encountered bonded composite joints, which has a complex solution structure with moderate orders of stress singularities.

On the Flow of a Compressible Fluid by the Hodograph Method. II - Fundamental Set of Particular Flow Solutions of the Chaplygin Differential Equation

NASA Technical Reports Server (NTRS)

Garrick, I. E.; Kaplan, Carl

1944-01-01

The differential equation of Chaplygin's jet problem is utilized to give a systematic development of particular solutions of the hodograph flow equations, which extends the treatment of Chaplygin into the supersonic range and completes the set of particular solutions. The particular solutions serve to place on a reasonable basis the use of velocity correction formulas for the comparison of incompressible and compressible flows. It is shown that the geometric-mean type of velocity correction formula introduced in part I has significance as an over-all type of approximation in the subsonic range. A brief review of general conditions limiting the potential flow of an adiabatic compressible fluid is given and application is made to the particular solutions, yielding conditions for the existence of singular loci in the supersonic range. The combining of particular solutions in accordance with prescribed boundary flow conditions is not treated in the present paper.

Ring correlations in random networks.

PubMed

Sadjadi, Mahdi; Thorpe, M F

2016-12-01

We examine the correlations between rings in random network glasses in two dimensions as a function of their separation. Initially, we use the topological separation (measured by the number of intervening rings), but this leads to pseudo-long-range correlations due to a lack of topological charge neutrality in the shells surrounding a central ring. This effect is associated with the noncircular nature of the shells. It is, therefore, necessary to use the geometrical distance between ring centers. Hence we find a generalization of the Aboav-Weaire law out to larger distances, with the correlations between rings decaying away when two rings are more than about three rings apart.

Fungible Correlation Matrices: A Method for Generating Nonsingular, Singular, and Improper Correlation Matrices for Monte Carlo Research.

PubMed

Waller, Niels G

2016-01-01

For a fixed set of standardized regression coefficients and a fixed coefficient of determination (R-squared), an infinite number of predictor correlation matrices will satisfy the implied quadratic form. I call such matrices fungible correlation matrices. In this article, I describe an algorithm for generating positive definite (PD), positive semidefinite (PSD), or indefinite (ID) fungible correlation matrices that have a random or fixed smallest eigenvalue. The underlying equations of this algorithm are reviewed from both algebraic and geometric perspectives. Two simulation studies illustrate that fungible correlation matrices can be profitably used in Monte Carlo research. The first study uses PD fungible correlation matrices to compare penalized regression algorithms. The second study uses ID fungible correlation matrices to compare matrix-smoothing algorithms. R code for generating fungible correlation matrices is presented in the supplemental materials.

Effect of stenosis eccentricity on the functionality of coronary bifurcation lesions-a numerical study.

PubMed

Pagiatakis, Catherine; Tardif, Jean-Claude; L'Allier, Philippe L; Mongrain, Rosaire

2017-12-01

Interventional cardiologists still rely heavily on angiography for the evaluation of coronary lesion severity, despite its poor correlation with the presence of ischemia. In order to improve the accuracy of the current diagnostic procedures, an understanding of the relative influence of geometric characteristics on the induction of ischemia is required. This idea is especially important for coronary bifurcation lesions (CBLs), whose treatment is complex and is associated with high rates of peri- and post-procedural clinical events. Overall, it is unclear which geometric and morphological parameters of CBLs influence the onset of ischemia. More specifically, the effect of stenosis eccentricity is unknown. Computational fluid dynamic simulations, under a geometric multiscale framework, were executed for seven CBL configurations within the left main coronary artery bifurcation. Both concentric and eccentric stenosis profiles of mild to severe constriction were considered. By using a geometric multiscale framework, the fractional flow reserve, which is the gold-standard clinical diagnostic index, could be calculated and was compared between the eccentric and concentric profiles for each case. The results suggested that for configurations where the supplying vessel is stenosed, eccentricity could have a notable effect on and therefore be an important factor that influences configuration functionality.

Real-time geometry-aware augmented reality in minimally invasive surgery.

PubMed

Chen, Long; Tang, Wen; John, Nigel W

2017-10-01

The potential of augmented reality (AR) technology to assist minimally invasive surgery (MIS) lies in its computational performance and accuracy in dealing with challenging MIS scenes. Even with the latest hardware and software technologies, achieving both real-time and accurate augmented information overlay in MIS is still a formidable task. In this Letter, the authors present a novel real-time AR framework for MIS that achieves interactive geometric aware AR in endoscopic surgery with stereo views. The authors' framework tracks the movement of the endoscopic camera and simultaneously reconstructs a dense geometric mesh of the MIS scene. The movement of the camera is predicted by minimising the re-projection error to achieve a fast tracking performance, while the three-dimensional mesh is incrementally built by a dense zero mean normalised cross-correlation stereo-matching method to improve the accuracy of the surface reconstruction. The proposed system does not require any prior template or pre-operative scan and can infer the geometric information intra-operatively in real time. With the geometric information available, the proposed AR framework is able to interactively add annotations, localisation of tumours and vessels, and measurement labelling with greater precision and accuracy compared with the state-of-the-art approaches.

Multiscale unfolding of real networks by geometric renormalization

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

Hierarchically partitioned nonlinear equation solvers

NASA Technical Reports Server (NTRS)

Padovan, Joseph

1987-01-01

By partitioning solution space into a number of subspaces, a new multiply constrained partitioned Newton-Raphson nonlinear equation solver is developed. Specifically, for a given iteration, each of the various separate partitions are individually and simultaneously controlled. Due to the generality of the scheme, a hierarchy of partition levels can be employed. For finite-element-type applications, this includes the possibility of degree-of-freedom, nodal, elemental, geometric substructural, material and kinematically nonlinear group controls. It is noted that such partitioning can be continuously updated, depending on solution conditioning. In this context, convergence is ascertained at the individual partition level.

General Series Solutions for Stresses and Displacements in an Inner-fixed Ring

NASA Astrophysics Data System (ADS)

Jiao, Yongshu; Liu, Shuo; Qi, Dexuan

2018-03-01

The general series solution approach is provided to get the stress and displacement fields in the inner-fixed ring. After choosing an Airy stress function in series form, stresses are expressed by infinite coefficients. Displacements are obtained by integrating the geometric equations. For an inner-fixed ring, the arbitrary loads acting on outer edge are extended into two sets of Fourier series. The zero displacement boundary conditions on inner surface are utilized. Then the stress (and displacement) coefficients are expressed by loading coefficients. A numerical example shows the validity of this approach.

Binary Mixture of Perfect Fluid and Dark Energy in Modified Theory of Gravity

NASA Astrophysics Data System (ADS)

Shaikh, A. Y.

2016-07-01

A self consistent system of Plane Symmetric gravitational field and a binary mixture of perfect fluid and dark energy in a modified theory of gravity are considered. The gravitational field plays crucial role in the formation of soliton-like solutions, i.e., solutions with limited total energy, spin, and charge. The perfect fluid is taken to be the one obeying the usual equation of state, i.e., p = γρ with γ∈ [0, 1] whereas, the dark energy is considered to be either the quintessence like equation of state or Chaplygin gas. The exact solutions to the corresponding field equations are obtained for power-law and exponential volumetric expansion. The geometrical and physical parameters for both the models are studied.

Benchmark solution of the dynamic response of a spherical shell at finite strain

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

Versino, Daniele; Brock, Jerry S.

2016-09-28

Our paper describes the development of high fidelity solutions for the study of homogeneous (elastic and inelastic) spherical shells subject to dynamic loading and undergoing finite deformations. The goal of the activity is to provide high accuracy results that can be used as benchmark solutions for the verification of computational physics codes. Furthermore, the equilibrium equations for the geometrically non-linear problem are solved through mode expansion of the displacement field and the boundary conditions are enforced in a strong form. Time integration is performed through high-order implicit Runge–Kutta schemes. Finally, we evaluate accuracy and convergence of the proposed method bymore » means of numerical examples with finite deformations and material non-linearities and inelasticity.« less

A triangular thin shell finite element: Nonlinear analysis. [structural analysis

NASA Technical Reports Server (NTRS)

Thomas, G. R.; Gallagher, R. H.

1975-01-01

Aspects of the formulation of a triangular thin shell finite element which pertain to geometrically nonlinear (small strain, finite displacement) behavior are described. The procedure for solution of the resulting nonlinear algebraic equations combines a one-step incremental (tangent stiffness) approach with one iteration in the Newton-Raphson mode. A method is presented which permits a rational estimation of step size in this procedure. Limit points are calculated by means of a superposition scheme coupled to the incremental side of the solution procedure while bifurcation points are calculated through a process of interpolation of the determinants of the tangent-stiffness matrix. Numerical results are obtained for a flat plate and two curved shell problems and are compared with alternative solutions.

An analytic cosmology solution of Poincaré gauge gravity

NASA Astrophysics Data System (ADS)

Lu, Jianbo; Chee, Guoying

2016-06-01

A cosmology of Poincaré gauge theory is developed. An analytic solution is obtained. The calculation results agree with observation data and can be compared with the ΛCDM model. The cosmological constant puzzle is the coincidence and fine tuning problem are solved naturally at the same time. The cosmological constant turns out to be the intrinsic torsion and curvature of the vacuum universe, and is derived from the theory naturally rather than added artificially. The dark energy originates from geometry, includes the cosmological constant but differs from it. The analytic expression of the state equations of the dark energy and the density parameters of the matter and the geometric dark energy are derived. The full equations of linear cosmological perturbations and the solutions are obtained.

Modeling methanol transfer in the mesoporous catalyst for the methanol-to-olefins reaction by the time-fractional diffusion equation

NASA Astrophysics Data System (ADS)

Zhokh, Alexey A.; Strizhak, Peter E.

2018-04-01

The solutions of the time-fractional diffusion equation for the short and long times are obtained via an application of the asymptotic Green's functions. The derived solutions are applied to analysis of the methanol mass transfer through H-ZSM-5/alumina catalyst grain. It is demonstrated that the methanol transport in the catalysts pores may be described by the obtained solutions in a fairly good manner. The measured fractional exponent is equal to 1.20 ± 0.02 and reveals the super-diffusive regime of the methanol mass transfer. The presence of the anomalous transport may be caused by geometrical restrictions and the adsorption process on the internal surface of the catalyst grain's pores.

Geometric correction method for 3d in-line X-ray phase contrast image reconstruction

PubMed Central

2014-01-01

Background Mechanical system with imperfect or misalignment of X-ray phase contrast imaging (XPCI) components causes projection data misplaced, and thus result in the reconstructed slice images of computed tomography (CT) blurred or with edge artifacts. So the features of biological microstructures to be investigated are destroyed unexpectedly, and the spatial resolution of XPCI image is decreased. It makes data correction an essential pre-processing step for CT reconstruction of XPCI. Methods To remove unexpected blurs and edge artifacts, a mathematics model for in-line XPCI is built by considering primary geometric parameters which include a rotation angle and a shift variant in this paper. Optimal geometric parameters are achieved by finding the solution of a maximization problem. And an iterative approach is employed to solve the maximization problem by using a two-step scheme which includes performing a composite geometric transformation and then following a linear regression process. After applying the geometric transformation with optimal parameters to projection data, standard filtered back-projection algorithm is used to reconstruct CT slice images. Results Numerical experiments were carried out on both synthetic and real in-line XPCI datasets. Experimental results demonstrate that the proposed method improves CT image quality by removing both blurring and edge artifacts at the same time compared to existing correction methods. Conclusions The method proposed in this paper provides an effective projection data correction scheme and significantly improves the image quality by removing both blurring and edge artifacts at the same time for in-line XPCI. It is easy to implement and can also be extended to other XPCI techniques. PMID:25069768

Evaluation of Spatial Uncertainties In Modeling of Cadastral Systems

NASA Astrophysics Data System (ADS)

Fathi, Morteza; Teymurian, Farideh

2013-04-01

Cadastre plays an essential role in sustainable development especially in developing countries like Iran. A well-developed Cadastre results in transparency of estates tax system, transparency of data of estate, reduction of action before the courts and effective management of estates and natural sources and environment. Multipurpose Cadastre through gathering of other related data has a vital role in civil, economic and social programs and projects. Iran is being performed Cadastre for many years but success in this program is subject to correct geometric and descriptive data of estates. Since there are various sources of data with different accuracy and precision in Iran, some difficulties and uncertainties are existed in modeling of geometric part of Cadastre such as inconsistency between data in deeds and Cadastral map which cause some troubles in execution of cadastre and result in losing national and natural source, rights of nation. Now there is no uniform and effective technical method for resolving such conflicts. This article describes various aspects of such conflicts in geometric part of cadastre and suggests a solution through some modeling tools of GIS.

A practical application of the geometrical theory on fibered manifolds to an autonomous bicycle motion in mechanical system with nonholonomic constraints

NASA Astrophysics Data System (ADS)

Haddout, Soufiane

2018-01-01

The equations of motion of a bicycle are highly nonlinear and rolling of wheels without slipping can only be expressed by nonholonomic constraint equations. A geometrical theory of general nonholonomic constrained systems on fibered manifolds and their jet prolongations, based on so-called Chetaev-type constraint forces, was proposed and developed in the last decade by O. Krupková (Rossi) in 1990's. Her approach is suitable for study of all kinds of mechanical systems-without restricting to Lagrangian, time-independent, or regular ones, and is applicable to arbitrary constraints (holonomic, semiholonomic, linear, nonlinear or general nonholonomic). The goal of this paper is to apply Krupková's geometric theory of nonholonomic mechanical systems to study a concrete problem in nonlinear nonholonomic dynamics, i.e., autonomous bicycle. The dynamical model is preserved in simulations in its original nonlinear form without any simplifying. The results of numerical solutions of constrained equations of motion, derived within the theory, are in good agreement with measurements and thus they open the possibility of direct application of the theory to practical situations.

A combined dynamic analysis method for geometrically nonlinear vibration isolators with elastic rings

NASA Astrophysics Data System (ADS)

Hu, Zhan; Zheng, Gangtie

2016-08-01

A combined analysis method is developed in the present paper for studying the dynamic properties of a type of geometrically nonlinear vibration isolator, which is composed of push-pull configuration rings. This method combines the geometrically nonlinear theory of curved beams and the Harmonic Balance Method to overcome the difficulty in calculating the vibration and vibration transmissibility under large deformations of the ring structure. Using the proposed method, nonlinear dynamic behaviors of this isolator, such as the lock situation due to the coulomb damping and the usual jump resulting from the nonlinear stiffness, can be investigated. Numerical solutions based on the primary harmonic balance are first verified by direct integration results. Then, the whole procedure of this combined analysis method is demonstrated and validated by slowly sinusoidal sweeping experiments with different amplitudes of the base excitation. Both numerical and experimental results indicate that this type of isolator behaves as a hardening spring with increasing amplitude of the base excitation, which makes it suitable for isolating both steady-state vibrations and transient shocks.

On Flexible Tubes Conveying Fluid: Geometric Nonlinear Theory, Stability and Dynamics

NASA Astrophysics Data System (ADS)

Gay-Balmaz, François; Putkaradze, Vakhtang

2015-08-01

We derive a fully three-dimensional, geometrically exact theory for flexible tubes conveying fluid. The theory also incorporates the change of the cross section available to the fluid motion during the dynamics. Our approach is based on the symmetry-reduced, exact geometric description for elastic rods, coupled with the fluid transport and subject to the volume conservation constraint for the fluid. We first derive the equations of motion directly, by using an Euler-Poincaré variational principle. We then justify this derivation with a more general theory elucidating the interesting mathematical concepts appearing in this problem, such as partial left (elastic) and right (fluid) invariance of the system, with the added holonomic constraint (volume). We analyze the fully nonlinear behavior of the model when the axis of the tube remains straight. We then proceed to the linear stability analysis and show that our theory introduces important corrections to previously derived results, both in the consistency at all wavelength and in the effects arising from the dynamical change of the cross section. Finally, we derive and analyze several analytical, fully nonlinear solutions of traveling wave type in two dimensions.

Static Holes in Geometrically Frustrated Bow Tie Ladder

NASA Astrophysics Data System (ADS)

Martins, George; Brenig, Wolfram

2007-03-01

Doping of the geometrically frustrated bow-tie spin ladder with static holes is investigated by a complementary approach using exact diagonalization and hard-core quantum dimers. Results for the thermodynamics in the undoped case, the singlet density of states, the hole-binding energy, and the spin correlations will be presented. We find that the static holes polarize their vicinity by a localization of singlets in order to reduce the frustration. As a consequence the singlet polarization cloud induces short range repulsive forces between the holes with oscillatory longer range behavior. For those systems we have studied, most results for the quantum dimer approach are found to be qualitatively if not quantitatively in agreement with exact diagonalization. The ground state of the undoped system is non-degenerate with translationally invariant nearest-neighbor spin correlations up to a few unit cells, which is consistent with a spin liquid state or a valence bond crystal with very large unit cell. C. Waldtmann, A. Kreutzmann, U. Schollwock, K. Maisinger, and H.-U. Everts, Phys. Rev. B 62, 9472 (2000).

Density-functional theory applied to d- and f-electron systems

NASA Astrophysics Data System (ADS)

Wu, Xueyuan

Density functional theory (DFT) has been applied to study the electronic and geometric structures of prototype d- and f-electron systems. For the d-electron system, all electron DFT with gradient corrections to the exchange and correlation functionals has been used to investigate the properties of small neutral and cationic vanadium clusters. Results are in good agreement with available experimental and other theoretical data. For the f-electron system, a hybrid DFT, namely, B3LYP (Becke's 3-parameter hybrid functional using the correlation functional of Lee, Yang and Parr) with relativistic effective core potentials and cluster models has been applied to investigate the nature of chemical bonding of both the bulk and the surfaces of plutonium monoxide and dioxide. Using periodic models, the electronic and geometric structures of PuO2 and its (110) surface, as well as water adsorption on this surface have also been investigated using DFT in both local density approximation (LDA) and generalized gradient approximation (GGA) formalisms.

Comparative Geostatistical Analysis of Flowmeter and Direct-Push Hydraulic Conductivity Profiles at the MADE Site

NASA Astrophysics Data System (ADS)

Bohling, G.; Liu, G.; Knobbe, S. J.; Reboulet, E. C.; Hyndman, D. W.; Dietrich, P.; Butler, J. J.

2010-12-01

Spatial variations in hydraulic conductivity (K) are a critical control on subsurface solute transport. Characterization of such variations at the resolution (cm to dm) required for transport investigations, however, has proven to be a formidable challenge. A new generation of direct-push (DP) tools has now been developed for the characterization of vertical K variations at this resolution. These tools, which can be run in high- (0.015-m) and low- (0.4 m) resolution modes, were recently applied to the extensively studied and highly heterogeneous MADE site. Results from a geostatistical analysis of 64 DP K profiles compare favorably with the flowmeter K data that have served as the primary basis for previous MADE studies. The global statistics of the low-resolution DP and flowmeter K data are in excellent agreement. The correlation structures for the high-resolution DP data show excellent agreement with those computed from the flowmeter data. However, the geometric mean DP K value for high-resolution profiling is roughly one order of magnitude lower than the geometric mean flowmeter K value, possibly as a result of the biases inherent in each approach compounded with differences in the areal distribution of flowmeter and DP profile locations. A DP profile through the MADE aquifer to a depth of 12 m can be completed as rapidly as 1.5-2 hours, a small fraction of the time required to obtain a single flowmeter profile when well drilling, installation, and development are considered. The results of this study demonstrate that DP profiling is a practically feasible approach for characterization of spatial variations in K at the resolution required for transport investigations in highly heterogeneous systems.

Prediction of Hip Failure Load: In Vitro Study of 80 Femurs Using Three Imaging Methods and Finite Element Models-The European Fracture Study (EFFECT).

PubMed

Pottecher, Pierre; Engelke, Klaus; Duchemin, Laure; Museyko, Oleg; Moser, Thomas; Mitton, David; Vicaut, Eric; Adams, Judith; Skalli, Wafa; Laredo, Jean Denis; Bousson, Valérie

2016-09-01

Purpose To evaluate the performance of three imaging methods (radiography, dual-energy x-ray absorptiometry [DXA], and quantitative computed tomography [CT]) and that of a numerical analysis with finite element modeling (FEM) in the prediction of failure load of the proximal femur and to identify the best densitometric or geometric predictors of hip failure load. Materials and Methods Institutional review board approval was obtained. A total of 40 pairs of excised cadaver femurs (mean patient age at time of death, 82 years ± 12 [standard deviation]) were examined with (a) radiography to measure geometric parameters (lengths, angles, and cortical thicknesses), (b) DXA (reference standard) to determine areal bone mineral densities (BMDs), and (c) quantitative CT with dedicated three-dimensional analysis software to determine volumetric BMDs and geometric parameters (neck axis length, cortical thicknesses, volumes, and moments of inertia), and (d) quantitative CT-based FEM to calculate a numerical value of failure load. The 80 femurs were fractured via mechanical testing, with random assignment of one femur from each pair to the single-limb stance configuration (hereafter, stance configuration) and assignment of the paired femur to the sideways fall configuration (hereafter, side configuration). Descriptive statistics, univariate correlations, and stepwise regression models were obtained for each imaging method and for FEM to enable us to predict failure load in both configurations. Results Statistics reported are for stance and side configurations, respectively. For radiography, the strongest correlation with mechanical failure load was obtained by using a geometric parameter combined with a cortical thickness (r(2) = 0.66, P < .001; r(2) = 0.65, P < .001). For DXA, the strongest correlation with mechanical failure load was obtained by using total BMD (r(2) = 0.73, P < .001) and trochanteric BMD (r(2) = 0.80, P < .001). For quantitative CT, in both configurations, the best model combined volumetric BMD and a moment of inertia (r(2) = 0.78, P < .001; r(2) = 0.85, P < .001). FEM explained 87% (P < .001) and 83% (P < .001) of bone strength, respectively. By combining (a) radiography and DXA and (b) quantitative CT and DXA, correlations with mechanical failure load increased to 0.82 (P < .001) and 0.84 (P < .001), respectively, for radiography and DXA and to 0.80 (P < .001) and 0.86 (P < .001) , respectively, for quantitative CT and DXA. Conclusion Quantitative CT-based FEM was the best method with which to predict the experimental failure load; however, combining quantitative CT and DXA yielded a performance as good as that attained with FEM. The quantitative CT DXA combination may be easier to use in fracture prediction, provided standardized software is developed. These findings also highlight the major influence on femoral failure load, particularly in the trochanteric region, of a densitometric parameter combined with a geometric parameter. (©) RSNA, 2016 Online supplemental material is available for this article.

A 2.5-dimensional viscous, resistive, advective magnetized accretion-outflow coupling in black hole systems: a higher order polynomial approximation

NASA Astrophysics Data System (ADS)

Ghosh, Shubhrangshu

2017-09-01

The correlated and coupled dynamics of accretion and outflow around black holes (BHs) are essentially governed by the fundamental laws of conservation as outflow extracts matter, momentum and energy from the accretion region. Here we analyze a robust form of 2.5-dimensional viscous, resistive, advective magnetized accretion-outflow coupling in BH systems. We solve the complete set of coupled MHD conservation equations self-consistently, through invoking a generalized polynomial expansion in two dimensions. We perform a critical analysis of the accretion-outflow region and provide a complete quasi-analytical family of solutions for advective flows. We obtain the physically plausible outflow solutions at high turbulent viscosity parameter α (≳ 0.3), and at a reduced scale-height, as magnetic stresses compress or squeeze the flow region. We found that the value of the large-scale poloidal magnetic field B P is enhanced with the increase of the geometrical thickness of the accretion flow. On the other hand, differential magnetic torque (-{r}2{\\bar{B}}\\varphi {\\bar{B}}z) increases with the increase in \\dot{M}. {\\bar{B}}{{P}}, -{r}2{\\bar{B}}\\varphi {\\bar{B}}z as well as the plasma beta β P get strongly augmented with the increase in the value of α, enhancing the transport of vertical flux outwards. Our solutions indicate that magnetocentrifugal acceleration plausibly plays a dominant role in effusing out plasma from the radial accretion flow in a moderately advective paradigm which is more centrifugally dominated. However in a strongly advective paradigm it is likely that the thermal pressure gradient would play a more contributory role in the vertical transport of plasma.

Dispersions of geometric TiO2 nanomaterials and their toxicity to RPMI 2650 nasal epithelial cells

NASA Astrophysics Data System (ADS)

Tilly, Trevor B.; Kerr, Lei L.; Braydich-Stolle, Laura K.; Schlager, John J.; Hussain, Saber M.

2014-11-01

Titanium dioxide (TiO2) based nanofilaments—nanotube, nanowire, nanorod—have gained interest for industrial, electrical, and as of recent, medical applications due to their superior performance over TiO2 nanoparticles. Safety assessment of these nanomaterials is critical to protect workers, patients, and bystanders as these technologies become widely implemented. Additionally, TiO2 based nanofilaments can easily be inhaled by humans and their high aspect ratio, much like asbestos fibers, may make them toxic in the respiratory system. The tendency of TiO2 nanofilaments to aggregate makes evaluating their nanotoxicity difficult and the results controversial, because incomplete dispersion results in larger particle sizes that are no longer in the nano dimensional size range. TiO2 nanofilaments are aggregated and difficult to disperse homogeneously in solution by conventional methods, such as sonication and vortexing. In this study, a microfluidic device was utilized to produce stable, homogeneous dosing solutions necessary for in vitro toxicity evaluation by eliminating any toxicity caused by aggregated TiO2 nanomaterials. The toxicity results could then be directly correlated to the TiO2 nanostructure itself. The toxicity of four TiO2 nanogeometries—nanotube, nanowire, nanorod, and nanoparticle—were assessed in RPMI 2650 human nasal epithelial cells at representative day, week, and month in vitro exposure dosages of 10, 50, 100 μg/ml, respectively. All TiO2 based nanomaterials dispersed by the microfluidic method were nontoxic to RPMI 2650 cells at the concentrations tested, whereas higher concentrations of 100 μg/ml of nanowires and nanotubes dispersed by sonication reduced viability up to 27 %, indicating that in vitro toxicity results may be controlled by the dispersion of dosing solutions.

A review of crop canopy reflectance models

NASA Technical Reports Server (NTRS)

Goel, N. S. (Principal Investigator)

1982-01-01

Various models for calculating crop canopy reflectance, in the visible and infrared wavelengths, from the optical and geometrical properties of a canopy and its constituents are reviewed. The radiative transfer equation is discussed as well as both analytical and numerical crop reflectance models which are manifestations of the solution of this equation. Recommendations are made for further work in modeling of canopy reflectance.

Dirichlet to Neumann operator for Abelian Yang-Mills gauge fields

NASA Astrophysics Data System (ADS)

Díaz-Marín, Homero G.

We consider the Dirichlet to Neumann operator for Abelian Yang-Mills boundary conditions. The aim is constructing a complex structure for the symplectic space of boundary conditions of Euler-Lagrange solutions modulo gauge for space-time manifolds with smooth boundary. Thus we prepare a suitable scenario for geometric quantization within the reduced symplectic space of boundary conditions of Abelian gauge fields.

Geometrical Solutions of Quadratic Equations.

ERIC Educational Resources Information Center

Grewal, A. S.; Godloza, L.

1999-01-01

Demonstrates that the equation of a circle (x-h)2 + (y-k)2 = r2 with center (h; k) and radius r reduces to a quadratic equation x2-2xh + (h2 + k2 -r2) = O at the intersection with the x-axis. Illustrates how to determine the center of a circle as well as a point on a circle. (Author/ASK)

Geometric Approach to Orbital Formation Mission Design

DTIC Science & Technology

2004-03-01

limitations, several individuals have used their resources to im- prove upon the Clohessy and Wiltshire model. First order oblateness affects are added to... Clohessy and Wiltshire solutions by Schaub and Alfriend [21] who de- scribe the relative orbit using Delaunay [7] orbital elements. Further perturbation...a methodology using a sliding mode framework. Irvin [11] investigated minimal fuel reconfiguration techniques using the Clohessy and Wiltshire